QANTITATE ANNI TROPICI, EIVSQVE COR.

RECTIONE, QVO HACTENVS RES, publica Chriftiana vfa eft, cum noua anni ciuilis forma,quæ à vero tropico naturali,quàm minimum femperdiE crepet.

^Authors Tahirn yirOiT). ,gt;4iierto Leo^ Wno aigt; KltraieHo,/. f^, DoSore amp;nbsp;'Xiaf^emaricamp;t

tOLONIÀE AGRIPPINAÉ Apud GodefridumKempenfem.

Anno.M. D. LXXVHL

SANCTISSP MO PATRI ACDOMf-NO, D-. GREGORIO EIVS

NOMINIS XIII. PONTIFICI

MAXIMO.

ALBERTYS LEONL NVS HVMILIME SECOM MENDANS S. O. P.

Ogiranti mi/n /^j[gt;enumero de reéus /}uman^ 5 amp;nbsp;/frajènti mü dtßaru, em/^ue mjJèrys ^ magnoJolet Cjf^Joiatio ^ tuc^dita tïS.P,intuert,et gergedere mü-dan/eyniuerßtatispulchntudnem, /nea^ue

fcientiarum zir rerum yentarém, amp;nbsp;admir anda 2)ei ogera.JdtMaurem admiraidtus tntel-ieSfu f^umano, mhddiuim^ ig/a anima yiderh Cuim ytsßimma^^ excedentta,diuina èonira-tió radijs lUußrara, conßrmata^ no modo Hci « tnedijsinarumn^yndi^ue drcumßnatiama • laßgerare ^ rerum j^ natural jum cogninoneta ßreipereßd amp;nbsp;mund um tranßendere,Jülgt;lA ^ß^^/^ß^iffffiCtileßefijM regiones mtfißif^

Î tl STOL A

foßit. Quæ eu artentiiis magna cum ammi yâ iuptare mecR cofidero^in meneê/erè yemr^aii-fo^^ iueundßtmü eß rejgt;etere tir recoreian eh-wnum il/ü P/atone. Inter euiuspr^clar^imè ßripea,mi/)t yeimaximèJgt;lacet,amp;ingenij/a-^ eukate^amma^^ dignitatem exjirimere ytde-tunJ-Jomine contcmßationisgratta natu eße. 7)iUinißima^roßeGfo,no^iß^ß/mßianis^erJie tuo cogitada amp;nbsp;yertßima setentia, fimodo eii contc^iatione i adtjifd/oti^entdßue Deig/o-riaeommunemi^ ytititatem,^uamad Jiroj/ria re/ata^ßdet Ctindianapr^eeJita amp;nbsp;do£irina coßeffamur. T^orro mew,ration^, amp;nbsp;intede-{ Ü* in ^omineßui/imitatisßdefaeiuttgrauißt moru saffißimorü^j óominu turn di^iaßngtd-1ießigieter:tüßa£ia/'orti/sime. Jda, ^ ide J^la to in 'rimieoßcji/nioß/i^ia a/ßrmat.2dun^ua mai^ lonü iumano generi Deorü munere datu eße,aut datü iri.f^ei,auod Cicero coßrmatmu-^uamßtiif Zaudari digne /loße/Mo/oj^t^ami cut ^uijOareat, omne temguf atattsßne mo!e-‘ ßia/ioßit degere.TdèHs id re^it interjgt;retari it cet,de anima,^ute diuina inßiratione, amp;gra-tia,adrationem,''virtutem, t^r contemjilatione nbsp;nbsp;nbsp;'

^m aßen dit amp;fieruenit. adna^arc/mcßidoß nbsp;nbsp;j

inter acerhßma tor ment a, crüdataß^ '^i^ensicum amp;Jgt;dt} cor/ufßium contunderé-mr,

DEMCATORIA.'

tur.Quieto i^yè ïn/ra^o^Jem/er amnio. Titn t^e}tun(/e,in^uir,iyina\arc/gt;i yajculum. Se/Z Jf/ura^ne m noßrafiäe et cianora,7*rojgt;/gt;eta rüiEreniitarumj’Martyrutnjahorum^ju/intt ßitumße ammifortitudine e^em^la.Èsi^^iii^ éttf ommluf h^uie/o conßat ma^nam eße ani^ tna t^tuinttarê.Ee conß^uenterf^uoi^ PAihß Jgt;hi aurea jEaßentetiä:2\[iMfgt;rietioßus eße te foreßgmßcare yoluerntJ'^Magnu eße mgenij ßuüü.Eoß^ mérita no reßtlßolo nomtne cen^ * sedos eße ibomines;^^ carntsi/Zeceirts irretiti^ ß*^/% ^o^if^^iotits in yoZuJitatem amp;corjgt;ora~ Zta aZ^ijaentes./nteZZeSum,Tantum O/erato. rem,yeZottoß(mJgt;atiuntur:yeZtmfelt;Zitumßtt-ßinere maZunt;^otius, ^uam ex eo ZiZerato à muZtitudine,amp;ßenßui{m cZgt;ao,ßuSZum eüJgt; ereifere,^uem/roßert yZerrimum, omnium^u» maximum. tanto^ßmfer matore,amp;iZtuinia-rem,quanto ma^tf amp;nbsp;ZtZgt;eriiis,ßcum eße.coZZi-fereßiZicet in ynum y tret, raiZioß^j omnes aeZ centrum reuocareß^ in ynitatem recifereßt wna^ inßirationi coßormem fr^ßarefoteß. Jßtomagtf turf eßt naZts CZrifiianis,^ ^uiita gratia, ionitas amp;nbsp;mißericertZia 2)et cognitie • ßünt,amp;taZetum exfonere maneZatum e/ZJ au^ eeßare aZt^uo moiZo,aut non etreumßieere eZ^ ffgentißime, aut non omne conßZium, Za^eni\^ « 3 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;lt;«»fer-

ÏPISTOLA çonferre,ail hnore i/iuina majejlatti,amp;C/jri- nbsp;nbsp;nbsp;Tlt;

fiiana fnonarcé/iaytilirarem. £i P/nloJôpht ^ui^/em j a^ßrußt ^Æ^ue munelij/enerrantes, t^ recoi/ita natura arcana,anima^ ionaßru tantes,yniuerß^uk^ritueiinem,Deo ßc Jgt;roctt rante,a^eruerunt,noiß^. têeatram o/ittmariî ßeienaarum non minus neeeßarium ^uàm iueü ^urn ^ro^oßerüt. Sie £titca ae/animu, 'Pèy-ßca at^cor/tu inuenta et tradita/ünt. Sic in itt cem/rodijt ^ßronomia,cuius'inter alias ma~ ^nu^ amp;nbsp;neeeßanus e/i yßis ,Jùmma^ue y till-ias,'Vt non iniuria Ptolemäus Ægy/tius, Di t^its ^l/honßus Pltßaniarum T^x.'l^licolaus Co/ernicus,aeleam tnßauranelam,amp;aßolue-dam,certes tem/orum interuaUts /rotlullt di-tiinitus,yideantur.Hac etenim yna,omnium maxime,mentes àßnßlus amp;nbsp;terrents/ertur-iationthus alßrahitßr/umße eleuat, in cS-tem/lationem,admtrationem,amorem, ^ inue ' Jiigationem diuinarum amp;ßintuahum rerugt; Si yerà etiam dicamus elementa/uheße aßrli ai ijßue/bueri,tem/erari,amp;mijcert^conßa-ti oratne, amp;/er/etua yanetate: modßtrnmis Plnloßb/lns t^r Theblogts/lacune yideo,mul ^ißue rattonilus, et argumetis dißutari/oß ^/cio./Jahehmusex ea mtraiilem tUam, (^ nbsp;nbsp;*

/i^/yrnmam ^hyßearumrerum iff infinites

dedicatoria;

^aäus ^/i/^inSam ^iuerßtarem.Hae tkni^ue] ß^naitem^ora,(lies,amp;annas, eer ta rationa no lis eißinguiti^artitioneni^ue temj/or^ e/ocet, fiuius ojgt;e Zulitts (ß/ar annum ciuilem ati So^ its cur^m meliorem^ forma ret/egit : ^ua et. iamnum T^ßui/tea Cirifiana'vtttur^hcet ea aß/an anno naturaliplurimum aierrare,ß^ ^uentium tem^orum olfruationes t/ocuerint^ ytfuo Zoco tZemonfrasmus, /n ^uofinè no ma fame /gt;tc mtrari nopoßum: exfZuriZmoßriße euZi iZoZZi/^tmif ^ßroZogiSy^ut annum corrige ret aZiam^/ormam excogitaret,inuentum ÿ^ ß neminem. Quauis amp;nbsp;tropicif'oZarts anni ^ua titas,a(Zamußim à Cofiermcoßt exjgt;Zicata, (^ÿquot; ßmmi PSeifces ,reZZißime CZgt;ri/ZianareZigio nifro/^icientesßmfer annis^ißnt, ytfßZi e-9nen(Zarentur,ne iZiutiuf,oi nimiam intercaZa-ttönern annus yuZgartsa foZari cZißrejgt;ans:fe-gt;

' ßum nataZZs Domini à Iruma yersus afatent ßnßm transßerret.ne^ueßeßum Paß^atts Z^u ic oZuiamJiroiZire continuéf erger et. C(etera~ ^ueforro omnia aiZcorreZZiorem fatum retZu-cerentur. T. ^uo^ue J. P.S. Zgt;Zs ^roximis an nZs iZZueZfeiZuZo agitantemgrauiorum occupa-’ * tionum interne tu in aZiuiZ tetn/gt;us iZißuZiß au-tZiui,Ex ^uo ^uicZem tempore, cogitaui mea^ ^unntZo^ue operam,^uaZem ^uaZem CZ^rif^nf

EPISTOLA

S^i^ultica in ea re nauare^Tuiefj SanSitatO: . iujii^imo eieftslerio,quantum in me eßet,Jaei/~ facere.^oätarnen meumJfrofoßt:um,t:um ma tora /iutita:tum temperum mtßeriateltutiui ex traxerunt. See^cum anno Sepeuageßmo ßxro, Louany agerem.indeßte (ß/oniam ,gt;igripjgt;i-na cogitarem/ugiensßmjgt;er rurias, ^uî^. in-ßechxi^amp; ^e/^ora^a ’Belgia mißemme aü^uot annti tailara eß, mußt mets non minus, inimi. cas^auamforrunts tiamnoßis.J^ecum egerunt ea ae re iiomtnuf Comehus l^alertus, Domi-nu^ Ptertus Smenga: J-Jic IJeèraica;/iie,La tma lingua,clo^i^imißro/eßireSj in imitatie mia Louanienß, yin de Clgt;rißtana reßuhlica ßentientes re^è:meriti^j optime. Qui Chrt/lia-m or its Ironorem, tu Tua Sanllitatis auélori-tatem, amp;nbsp;yoluntatemproponentes,enixè à me coten(lerunt,yt ^nnif ormam conßantem, amp;nbsp;cü Solls cur/it ^uam proximè congruentem, c5 tnentarer,yt ijdem menßesßjdem dies, eunde in ^odiaco locum /imper reßerrent. Turn yul-garls anni dultani yitium,totamß^,yua de tro^ /ici anni diuerßtate eßßdoHrinam lucide ex-

• /licarem,omnilußßie notamßacerem. Quiluf yerißime reßgt;onderem:alios e^ permultos ^ßrologia dollißimos,mc^ multo exercita ^f.^ref’ià quilles iliaßßeranda etpetenda eßent.

. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;DEDICATORîA. ■ nbsp;nbsp;,

tafnen recejgt;i mef'al^urü,^uo(iamp;jiulUc^e yri-fitari Tuæ^ SaniUfar^ auêforirari no ykrô^ ^ ^uam^rimufe o^erre, rur/ißimum ducerê. ProJ/ofltum yero meum^cœpra^-j iami/uiiu ^ie-Itierartoßo^lißtmorum /jominum, tnei^^ ama~ ti^tmorumjù^ù amp;nbsp;ai^/^ort^none confirmare-tur./nea yero re:a/iudex aüo me eleeinuit elite tiùs. 2^am elum frétera amp;nbsp;2\leoeertcoru a/lro-nomica olgt;ßruata reuoluo.CoJgt;ernici^uidê cal-culufn,longe aliorum omniu/ù^Jtutatione^rte- . cellere^owniumi^ eße yerißimum inuem^atfa. men maxime^araaoxa,ea^j iy/ioelteß nitence: ^ua licetingentoßßima,eloilißima^^, in rerum naturaJùlfi/iere,ne^ aelmitti^oßit, multos^^ ret injoletia eleterreat.Qws entm nonßu^eat^ temegloium tot mottéuf circumagi^7^e^ tarnen tile ytr non omntlus laiielilgt;.eßexenelief,et celelraneluf eß.dtgnißtmuf, cuius memortam excitant omnes anni conséquentes. Ei nam^ motuum ceeleßium re/lttutio amp;nbsp;emendatio ac-cejgt;ta ferenda eß . Eorrà ex altera/gt;ate tabulas motuum cœlellium yttioßßimas oßendi. E tem theortcas^quas Georgius Eeuriachita o-lim qd Eto lemtsi doSlrtnam nouas eßecit,pla- • pè exoleuiße.Siquide nunc aliter/è hahet nomenonßles: aliter motus ^quinochorum^^ ^arumiaugiumiac in tilts yidere eß. EUrne et^^

• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;« 5 nbsp;nbsp;nbsp;nbsp;nbsp;M»^

EPISTOLA

îamTltteMotnenon ^uàma/ijùr^^a^fai/df^ft^ con^ruenti /^^ot^gt;eßi tucantur : iamjgt;rii/ein nottßimum eß. Com/gt;lexuf ita^^ totam ^/fro^ tiomiami^uod rei^ulüc« Qrtßiatiteytiiißi-tnumjne^'^'^^oiptKois non^ maximeneceßariu t/uxi;Cojgt;ernici Jo^rifi^tn,ad Soiü moèi/itare fam^ß^uetes lyj)otigt;eßs,reuocauiSierra ta tnen eum motum aedii^ui amp;nbsp;te^uinolihorumitt /feiiaCteß^artefiro^reßuißti^ßaceret ; neca naturte rationieuf eßet aiienu^. nouaj^ ^/aw tieoricasCyt yocant} caleßium motuum, aei faiulas/rutenicasfomnium ^uas munätts ia-/gt;et exa^lißimasJa eie£?iß,yiro Eraßno ßeyn Ao/e/o ex CoJ/emici tJo^^rina e^t^eßas eßea.ßa ^ogcjiratereaaej ^^ronomiaaeJieci, Omnia^ 6eec cum comentatione eJe yera anm ciuiittre-ßitutwne coniungenJa ^ exißimaui.Ee om-nUuSilute^Jir^rtim Sanliitati/unJameta tir rationes tottus reijiaterent.Eorro meü lac tie correÜione anni o/ußeuium T.S.Jirimo ^uo~ ^ue temporeJgt;raßns oßerre conßttueram,noit fan^ua eiignüßtis:ßd ^uodaTua San^itate

, tiujmodi argumenti iiirum ex/ietiturn./iiieo^i • non ingratumßore audiueram. Cu/erem^/or

J^i/iuiiiica: (ßrißiana,quanta inmeeßeti g^deße.Eerum moram im^reßioni iiuiu^ ii^^^ y^u^^ufißiurima negotia, 'Meuß^ e^ßeßüs

, ÜEDICATORIA. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«

â Colonia,K^/atis /Huturm^.Eoautetn 'vt re^ Ji/,intelkxi Ti S. tam in hc ej/è : yt annum e^ mentiet ,j)ulgt;lice^ue rntjlts literis ^ae/)emati cos^uo/^^adea rem exliortari, Quotlutma^ gnam animo meo 'volujgt;ratem,aelmtrationem^ aililuxit:7^m/ciücet toties a^itatam,^ ince /tam,nuncjgt;oeißimuin èac mumli/èneSa, ael exttum/gt;erelu^u iri,/ta^emfeat maximam,, fore,yt Tua Salfitatts aufgt;icijs,ecclefa Ciri fiiana, tot ia annts miferrimè lacer at a ai omni urnfuUuum amp;nbsp;tem^ejlatu in/idtu, ael traduit iitatemJgt;erueniens,jùum nitore, amp;nbsp;elecorë ex 2)eimiJèricortlia,ali^uanelo récif iat.Etat ^^ a~ nimorum, amp;nbsp;yoluntatum, ad ynitatem fdet conuerfo, amp;nbsp;immutatio.Q«afrofter miin iic frimuconuenitigratulari Clgt;ri/liants omnih^ eof^ hor tari,y t mecum yna, Deurn omnifoten temfuffliciter oret. Ti Tuam SanSlitate 4ua dtutifimè conferuas incolumem, eius conjtlia,^ fèmferad fhri/liani orhii ytilitatëfrouehere dignetur.Princifes aüt omnes ohfccrentur,yc huic rei tam fansite,ta ytili,tam^j/àlutari,fa tieant,omnem^ curam,eliligentiam et ofe,aclhi heat. Porto hune meu labor em, S.P. omnem^gt; in hac re of er a, me^ if firnferuudeehtif.on^ ^uafofum hnmilitate T.S.ofero.Colonite griffmaanno 1^7i.menje’Maw, ** *

A4gt;lt;%t

AD NOBILISS. CLA»

RISSIMVMQVE VIRVM

D. ALBERTVM LEONINVM VltraieHen. V.I C. ó'Mathema-ticum ceteberr.

nïifios ffitlyyecs i'ft ÄciißccvitiSi zT^Xo viz nóMotxi p.oi mfl ffoü TToftibv l^èÏTo Kóyov.

lAouavs y^MMS ^««r*®» iti’^n^ov ÏovTA,

T^sSe tre ni nx^vs Ti^^^s IttOLVOf^ófMUop :

KwvS’dJlès xavravSoi ZTc^MV Kedfoio SzSovIof

T^v T^TTMo^^ainv T9^ ÄüXacßavloj i^wv, « l'èl}^a. Tt Tti'^A ffiStv ^vyy^dppx^A y’i^zet n^Sf o» Sou $éovsu Kaytiut luZi/jU^ à'rfof taels’

ÇVFFRIDVS PETRYS LEO Vardienfis Frifius, V. LProfcffor.

Colonise an. Dn. 1577.

1 DE VERA dVANTI* TATE ANNI TROPICI, ET RATIONE CORRIGENDl AN,

N V M dv ILEMi

SVm Deusomnipotens, mundi fabricarn côditurus.incompræ-hcnfibili fua prouidcntia, tcpus ex infinito defini jllct. Pofuit et-tiarn aftra,que vt agentia media rationefque ideales, mirabili illud diuerfitate partirentur.Suocalorefcilicet,curfuq;perpe-tuo,pulcherrimam rerum varietatem, elemc-taremquc vniuerfitatem conferuarent: turn hominibus figna,tempora,dies, amp;annos,(vt eft apud MoyfenJcertafque fcilicet, tempcrij partes, fine diftinftiones rebus humanis ne-ceftarias fuppcditarent * Et ab initio quidem fimplicifsima Ephimeride vfi funt morta-les. Et expoftea memoriae humanæ imbecilli-tate, temporumque varietate fcnticntes, amp;nbsp;edofti, nimis excrefcentem dierum multi-tudinem in minores numéros, contrahen-dam,plurefque in partes efle diftribuendam, animum aduertere, cceleftefquc motus dili-gentiùs obferuare cceperunt « Itaquc cùm' amp;nbsp;aliæ res plurimæ hortarentur, ipfaque Maieftas baud dubie in opens fui conwit flationem,amp; admirationem impel!^ct^ /a-, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;perctj

bt VERÀ QUANTITATE |)cretque. In ccelum, oculis animoque cotl-uerfi ;inuenerunt,ftellas eas,quas fixas ob mó tus tarditatem dicimus, vno eodemq; omnes: feptem veró Planetas, proprio quemque dictum naturalium numero, fuas in calo perio-dos contra motum firmamenti complentes,o-mnemnaturçdiuerfitaté, ipfumq;adeo tépus efficcre.

Quod Plato oftendens ;peruagationes, in-quit, aftroru, idipfumfunt,quod ritèdicitur tempus multitudine infinitaamp; varietatemira bili prçditç.Eft enim intelledu facile, q, perfc óus numerus temporis, perfeâum tüc demu compleat annum, cum oólo ambitus perfeâis fuis eurfibus^d idem fe caput retulennt, Porto ex iam diétis motibus,quos annos vocaue-te,alij quidem ali am magnitudinis amp;nbsp;initij ra-tioncm ineuntes, plerique tarnen omnes fere, VelLunç,vel Solis periodicoscurfus, vt maxi Ineinfignes.accommodatifsimofque fupputa dis temporibus amp;nbsp;return mcmoriçconferuan dç,amplexi lunt. Quorum hic 565. diebus, amp;nbsp;fcx Boris circiter,totum cœli ambitum,amp; duo decimobliqui inter duos mundi polos zodia-ci figna,perluftrans,accefTu amp;nbsp;receffu fuo, qua tuor præcipuas, maxiraafque temporis amp;: na-•turæ vicifsitudines,vcr,a;Qatem, autumrum, hyeméabfolueret.I1la decies amp;nbsp;bis, intcrea ^iikm adfequés, varijs diüerfórum cœli loco-rtiHjlyderuaiqueudijs nabuU/Ctiam didis quatuor

ÉT COkRÊCt. Ai^NL t ( fJUatuorannipartibuSjinultifariamadduccret j qualitatem.

; Græci autem,amp; Hebraei, Annum lunarem

^ adfumentes,quem duodecim menfibus luna# I ‘ ribus finiebant,intercalatione,poft, Solaris pö 1 riodi exceflum fupplentes,con(ècuti funt. Vt , nouilunia in ipfum cuiufque menfis initiumj | perpétua inciderét.Aequinolt;ftiaporró,folfti* tiaque,intra certos dies fuiquodquemenfis, 'vltröcitroque vagarétur. Acgyptij vero, qul annos duodecim menfibus tncenorum die-rum terminabant, amp;nbsp;dies quinque ad finem adijcientesjiueintercalantes, profex deinde horis ex Integra periodo Solarireliquis,quar-toquoqueanno, primumdiem menfis Thot (à quo ipfis initium erat anni)in prscedentem proximè,transfcrentes. Habuerunt numeri in plures partes gquales diuifibilis, commodita* tem,fupputandis aftrorum motibusneccfla-riam. At primus dies Thot,fingulis quadrien-nijs,iq.. horarum fpatio procurrens, amp;nbsp;antici-pans, ducebat anni principium, per omnes o-mnium menfiü dies A verno enim çquinodiô recedens ad hyemem, ac inde per autumnum amp;nbsp;çftatépergens, rurfum iungebatur çquino-Öio vernali : peraâo anno magno toü -xuvimÜ

i Continente annos Aegyptios 1461.vel quater, , 3^5. amp;nbsp;vnum,colligendum ex quaterpi. die- |k bus,amp;fex horis,quibus fingulis 365. annisr *

1 procedebat. ' ' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;* '

Tan-

DE VERA QVANTITATE

Tandem lulius Csfar inftituit annos luliit nos, cum Solis curfu propius congruentes, .qui finguli continerent dies 3(^5. ex (ex autem iioris,quibus Solis reditus ad idem aequino-étiû maior effcputabatur,vn’ accrefcerct dies quarto cuique anno, qui inde vocatus eft in-tercalarisfiuebisfextilis. Initium verö anni, vt effet more Romano ab ipfa media node, quæ primam lanuarijlucem antecedit.

Huius autem anni luliani forma, qua Chri ftiana Ecclefia libentifsimè amplexa,etiamnü retinet,( relato tarnen annorum ealculo amp;nbsp;fe-riead eämediam nodemdecembris vltimäj quaeChrifti natiuitatem proximè fecuta eft^ quem Cæfaràfuoimperio fuerat aufpicatus) cgregiafancamp;pulchra Lunares annos excel-lit.quod in ijs bngulis,nee Integra folis Perio-dus.ldeoq;nec4.illam requêtes tempeftates; quibus vita regitur ,comparaturcjue redifsi-mè,contineantur. Aegyptios autem, quód ob intercalationem illam diei,§quinodia amp;nbsp;folfti tiaminimè vaga,ijfdemferè adhæreantdieb. Itaque hyems,xftas, ver, autumnus, eofdcnl menfes,eofdemque femper retineantdies, vel nifi longo temporis fpatio commutent. Cuius caufam nunc aperiemus.Nam et huius luliani • nbsp;nbsp;quantitas, eiufq; intercalatio, etii alijsomnib.

mukùmantecellit,tarnen vitiopenitusnonca J;et.fiquidem præter veram tropici anni quan*

» titatem hue reditupi folis ad idem vel çquinOi

ST CORRECT. ANNI, 9 SiuVelfolftitium/qiiiftmper minus, qu^m fex luxas,vltradies j^iS^.continet^quadrantes diei inregros colligens.æquinoélia amp;nbsp;folftitia, in pricedences dies fen lim abire cogatannu-que ciuilem à naturali tropico diuellat.Fucrit enim,exempli gratia,folftitium hyemale, vel pun6tumCapricorni,quoSol longifsimeano bisSeprcntrionalibusdigrefru5,reuerti inten« dit. Fnerit,inquam,vnaqueanni ciuilis printi pium,primolanuarij,meridie. Ponatur etiam-, iingulis tropicisannis ad fex illas horas,deefle quartampartem vnius.Igitur quarto póft anno, idemfolftitiumfeparatum ab anni noftri introitu,meridiem lanuarij vna hora antcuer tet.amp; limiliter quarto deinde anno,duabus hd ris. Itaque perpetüó nimiam noftram inter-'calationemfugiens, versus autumnales amp;nbsp;æ-ftiuosmeniès perget, adeoqucin lanuarium tandem ipfum ver,deinde æftatem, amp;nbsp;autum-num fuccedere continget, dummodo ne diC foluaturmundi compago.Ex quo apparet lu lianum hunc,quo vtimur, annum,minime Solls moturn obferuare,minimc eftefolarem: quipimo nihil aliud præftare,quàm certutn numfcfum,qui eadem opera poterit efte mille dierum.Quotautem,quantafqueincommö ditates adfcrat,h#; anni ciuilisà vero tropico feparatio,notilsimum arbitror. Et,vt alia o-i mittam, nemo fanèvel.memoriam natiuitatts fuse fmgulisannisredè celebrauer,it,vcWiem' de.

DE VERA QVANTITATE defignaritxitra aftronomiæcognitioncm, Sc fupputandi laboré. enimuero h quis natus fit prima 1 anuarij in ipfo squinodio autumnali, ftultifsimu fuerit eius natale ex huius anni ra-tione,prima lanuarij iam in bruma exiftenté, afferere. Succuret leüori fortafsis hoc loco: minoré elle luliançintercalationiserroré,quâ vt de tanta mcnfium commutatione, in haC mundi fenefta timendum fit.Scio quidem, ne-que alia de caufà adduxi, quam vt fine alijsar-gumentisbreuiterdemonftrem.Periodum fö larc veros annos conftitucre,tcpus noftramq; vitam metiri.Neq; magis eiïc natalem dié, can dem prima lanuarij.fi brumanifi vno die,quä £ dies nonaginta indedifcefferit. Attamé hoC ipfum quod ta parui fit, ia à Chriffi natiuitatc iz. fcrèdierum peperiterrorê.Sed,neego in ré fatisnotalongiorfim.Fatcnturomnes. Nafi-quis roget, vel ipfum luliü Cæfaré, eiufq; Ma-thematicos,refpóderétopinor:Sevoluiirc annos folari periodo definire,amp; putare idfecófc lt;utos efre,vel proximè omnino.Chriftiahi et-jam,exiftimare amp;nbsp;credere annos fuos effé fola* res. Oés autem,vno ore, non dierum cógerié, fed earn dicent fequærere cómoditatem, qua * nbsp;nbsp;annus folarispræftat. Vtomnib.etiamaftrono

mica ignorantib.anniuerftria temporu momé-^aJjfdé Temper adhærctia dieb.nota effent. Il-•Jtwnq; affeétuü fimilitudiné , corporis amp;nbsp;têpo-ïis dfl^ofitioné, qua Sol ad punöü Natiuitatis

, 'éT' . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;quot;nbsp;re-

ÊT CORRECT. ÀNNI. t« hediés afferre folet,opperiri amp;nbsp;præfcire liceret» Reâifsimèfentiût.Atlongètamé aliter feres habet.Ncq; enim ia dies méfiü ijdem funt ^ qui fuerût.Non primus lanuarij dies.idé, qui fuit téporeChri(h.Sedquitun£fuk lamiarij duo. decimus,eü nunc priraû fecimus.Sempcrq; ló-gius hoe malü ferpet. Quandoquidé annus tro picus minor femper èft, fuitq; Co, quo nos vti-mur. epomniu doâifsimorû Mathematicorü öbferuatióes teftatur. Verütaméluliani Aftro nomi nó excufatióe fölü,fed laudedignifsimi, relèftis ceterisannorü,qantcain vfuerantin-cómoditatib.,pximiijs, q vlli alijmotü Solis, annumq; naturale imltati.eum fólü errorc re-liquerüt.qué tollere nó potcrat.Nacum tropicus annus, quod inTheoriamotuûcœleftiûo-ftendimus,t!uâtitate mutetur.Cuius diueffita-iis reftirutionéipli pcedétiu temporü obferua-tiónib. hand fatis inftrucli,fcire nópoffcnt.In-lienirétaütaniiitropiciquantitatêjamp; tue effe 565. d’.erü,5.horarü,amp; 5j'.minutorü,amp; qüadrin gentis annis,perpetuöcreuiiïe. PutarUnt non infulsc earn ad lex horas, aut etiam vlteriiis progreffuram, annuraq; ideó Julianum mul-tisfeculisinfenübiliter à natural! difcrepatu-ium.Quódea $.minuta bueduodecima vnius , hors pars,qua folarem excedebat,per motum annitandem, fpatio 400. circiter annorum^^ complerentur Neq; veró pofsétcito.vIrraTi-* baue aliquam magnipendendam,amp; me mil* - “ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ß 2 lequù

bEVERA QVANTITATE

le quidéannis4.dicrii differentia efficere. At» que iplis ita venia mcritô dada eft.Nobis autc Chriftianis,qui annu« quanti tatis anomaliam cognitam ptnitus habemus, ex dodifsimoru, virorum: Timocharis, Hipparchi i Menelai, PtolemaeijAlbategnij.Arzahelis, D. Alphon-fi Hifpaniarum Kegis, IoannisRegiomótani, Nicolai Copernici, aliorumqueplurimorum obferuationibus. Turpifsimum lit, neque vl-lo modo excufabile, verfari ofcitantes amp;nbsp;negli gentes.eo in erroi c diutius. Qui tanto blij Dei beneficioobllrifti: quoin hanc, ipfe, veniens iniferiarum amp;nbsp;lachrymarum vallem,nospec-cato,moitf diabolo, mancipatos, vindicauit, Dcoquc patri fuoreconciliauit,vt vita ac pace frueremuræterna. Omnimeritocura.omni animi contentione, omnib. viribus nitide hac redtberemus, Noftriq; Redemptoris verum natalem diem,Gngulis annis gratifsima memo ria,maximaquecum veneratione,amp; fpirituali Ixtitia excipere amp;nbsp;colere.Fuitautemfnon line myfterio, opinor, ^ inip(aßruma,quem noSs huius vitioü anni formam fequentcs, ad ver paulatim transferimus. Eóq; tandem redibit res.vtfeftum Pafchatis, fempercum æquino-, Ûio verno afcendenSjCoincidat, magno Chri-ftianæ religionis ludibrio, cum fefto natiuita-^is.Quod 11 autem tune, ipfe pudor amp;nbsp;necefsi-•tlTv^ebit, velpotius extorquebitcorreótio-nera. Cur earn non repræfentamus eonfeftim?

Egiffe

ETCORRECT. ANNE ii Ïgiffequidem olim in Concilie NicanoPa* tres,de reéta Pafchatis célébra tione,proditum eftmemoriæ.Diuque póft,Romanos Pontifices ea de re peritos AftronomijcófuluilTe Do nee quidam Dionyfius Abbas, ædito faftoru libro,ac ratione inueniendi annorum nouilu* nia, videreturin perpetuum Pafchatis veras amp;nbsp;iuftaecelebration! pi ofpexjfle. Cùm tamé vix vnifeculo eius dodrina fufficcret.exquoet-iam alius quidam error irrepfir. Qtiibusde caufisnonaginta ferè ab hincannisjoannem ifigncm Mathematicum, cuocatum,Romam ve-niflelegimus,vtfaftos emendaret, certamque. quandam amp;nbsp;conftantem anni rationem inirct. At illum mors præuenit, res infeda kucufque manfit.Voluiitaque,quantum in meeft,Chri ftianæ Reip.hanc nauarc operam, anniq; for-nia,quoadeiusfieripoffet, proq; mei ingenij tenuitate,condere, qux à Solis periodo amp;nbsp;anno natural! quamminimùm lèmper difcre-paret. Simulquerationes,omniacjue adhanc rem perti nentia,omnibus hominibus nota fa-cere , doläifq; Viris vel probanda vel corrigera etiam proponere.

Demonftratum efi in Theoria noftra, du-plicem effe Zodiacum.Stellatum amp;nbsp;Apparen- ’ tem ; ex quibus Copernicus duos item annota reélifsimè alTumit. Syde/eum, vnum j Sol,?d idem in ftellata fphxra pundturn ra. ß 5 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;diens

DE VERA QVANTITATE ^iens diebus 565.horis 6,miri.9.fec. 59. daudif, Alterum tiopicum.,cuius quantitas inçqualis ad pnonem comparata^dignofeitur, nimirum veraçquinoétiorû annua precefsio ( quç pro-, pterçquihoôtiorumanomalianiinçqualiscft) femper ablata, oftendit quantutropjeusquiC que à fyderei quantitate deficiat. ttenim maxima vnius anni equinodiorum equatione.

queeft“' ^——-ablata,cx çquali prgcefsio-

ne equinodij annua :. reftant-areü Sol çqualiter percurrit, minutis horç 14. tertijs 58.quih.maximus tropicus,minor elt fy dcrco,exiftensdierum565.hor.5.mi.55.fec.38. Tr^opkF ^^’■^’ “• Atlimili a;quatloneaddita,fït arcu$ anniquaquen^ Sol percurrit minutis horx titajque' SI «■ ' . .

cx caiifla alt;5 icc. 42.circiter.quibus minimus tropicus dl prçccfsio data fydera quantitate, Habens dies, 565. Hor^ 1115çqui. j,min.42.1ec.5 ■ .Nequeannustropicus,('quan noa cfle jyj^ ^^ obferuatis colligere licet ) vel propiùs Minima accedere,vel longiusdifcederc ab anni fyderei nopici quantitate poteft.Suntporró amp;nbsp;aliæ caufæ di-quantas uerlitatis tropicorum annorum. Namamp;pro-excadé

ET CORRECT. ANNI, la tusinæqualitas, ipfos annosfydereosimmu-îanj.

Mutationc demû eccêtricitatis Solis anni fy-derei.tropiciq; diucrfam accipiunt quantitate.

' Quæ omnia in Theoria motuum cœleftiû traditafunt.

Atque vt has quatuor caufas obferuarede-bet,qui veram cuiufq-, tropici anni quantitate, ad amufsim amp;nbsp;curiosè fcire defideratzlta in no ftro propofito, tres poftremæ non funt necef-fariae,propter fummam motus apogij amp;nbsp;eccen tricitatis tarditatem^

Sufficitaut folam æquinodiorum præcefsio nem animaduertiffe,cuius anomalia, quç poft Chrifti Domini natiuitatem, annis Aegyptijs i65ydiebus na. horis ^.fuum cópleuerit in cir-culo anomalari circuitumjingulos fui circuli, quadrantesabfoluit, f vt in Theoria odendi-tur}annis Aegypt.42C).diebus9i.hor. 6.quar ta videlicet periodic! temporis parte.Quod té-poris fpatium,fi excelTu fydereorum totidem annorum fuppleatur,habebitampliusdiesno. horas 4.mi.52.fec.i5.tert.45.quibus.f.annify-derei 429. amp;nbsp;quarta vnius,fuperant totidé A e-gyptios.Interea aüt.f.annis Aegypt.429.dieb. 9i.hor. 6. Aequinoótiü æqualiter procefsit in , ecliptica.cótrafignorumordiné^’ '”’ *’--Mlt;t tusautem diuerfitatis,finito primo quadraji-fe, pçrcurritin contrariam partem

‘ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;71. 2i.5O. nbsp;nbsp;nbsp;,

ß 4 fcmi- •

DE VERA QVANTITATE femîdiametrum fcilicet parui circulijhifque fubtradis exçquali precefsione , remanent FJ^-î^’^ quem cclipticç areum, Sol çqua^

. diebus,hot. m,

liter percurrit. ————quç 11 ,demantur çx®±J12L-2n: reliqui fiunt ?i:_Jl25iJ?i?L.-110. nbsp;nbsp;4. nbsp;nbsp;nbsp;31. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;* nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;JOS. 7. nbsp;nbsp;nbsp;nbsp;31. quos veri tropici anni, fuperaddunt 419. Ae-t gyptiisannis,amp; quartçparti vnius. At noftra intercalatio annique luliani fuperaddunt dies 10 7. boras 7 mtn.jo.vndeapparetnoftramin-tercalationem annislulianis 429. amp;nbsp;quarta Vr tiius,eocjiie primo anomaliç quadrante, exce-dereiuftam tropicorum annorum quantitatéf ^:J*“*^- Quç çqualiter diftributa, often, dunt lineulisannis ~ quot;'■^‘ temerè interca-o. à. 48. lata. Seflo auté toto eo primi quadrantis tempore in quatuor partes, licebit primo eentena-rio hor. min.

, 5^^. 5* 54-

Secundo 3^5- 5. 5z«

Tertio 36$. j. jo, Quarto 3 6 5. 5. 49. veramtropicianniquantitatem cenfere, eitra ^liquem raagnipendendum errorem.

Ad tempusautem peratlifecundi quadran lis, quod erit ab initio annorum Chrifti, çgy-ji^ijs annis 2o8i.diebus 213. horis9. Anomalia «mftîçritfemidianjetrumincandera cum ç-

ET CORRECT. ANNE i» «JUaliprçccfsione partem. plis itaq; lundis fit fumma®.^-^^ ^ quem arcum Sol percurrit, diebus 7.horis’^.mln.44.quibus fubtraélis ex exceffu fydereorum Annorum rémanent dies102.h0t.21.min.48.fec.18.tcr.45;. quos cq fccundo anomalif quadrante, tropici anni fu-pepaddût429. Aegypt amp;nbsp;quarts vnius. Vnde noftram intercalàtionem eo tempore erroré.

Di. hor

---^panturam efleliquet.

Primç autem eius temporis quartç annos ce fere licebit, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;

i65. 5- 4^-Secundç. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;365. nbsp;5.

Tertiç nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;565. 5.

Vltimç. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;365. 5.

Tertij deinde quadrantis tempore,quod c-rit complctû poft Chriftum,ann.'2în. di.304. hor.i5.cundcm.E:—!ïï_ J1_ errorem noftra intercalatio inducet:eademq; erit tropicorum quantitas,fcilicçtprimæ**'• *’^’'^• 365- 5- 43'

Secundç nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;3 6 $. nbsp;1.

Tertiç nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;3$S. 5.

Vltimç nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;365. 5. 48.

Deinde ad finem vltimi quadrantis to- • tamque anomaliam completam , quod crit poft Chriftum,annis Aegypt.2941 di.jç.^yr.'^ ß 5, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;• lit

*■ er VERA QVANTITATE M.Intercalatio noftra, vt in primo quadrants' excedet ------candemq; tropicorum quan titatem, fentiemus ,fcilicet pies. hor. min

Sec. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;j. jo.

Ter. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;5, nbsp;nbsp;52.

^* . 54-

Etcolledisomnibus, habemus fab initio motus anomaliæ incipiendo) dies ii. boras iiî. min.24.quibuscommunisnoder annus ana-turaliaberrat,fingulisännis Aegyptijs 1717. Vitioitaque noftræintercalationis clarifsimè demondrato, hac ratione potifsimum amp;nbsp;ap-tifsimè in poderum occurri pode exidimo. Si centelimo quinquagedmo cuiqueanno, vnus adimatur dies. Ita enim femper minimo annus vulgaris à vero Tropico differctzfçpiùs ad amudim,vel omnino proximè cum co coq ueniet.

Nam à principio motus anomaliç primis 45O.annis tres eximentes dies,vix 4.horaruni differentiam relinquemus inter naturale amp;nbsp;vulgare anni principium.Finitis deinde fequé-tibus 450 . annis. vno folo die amp;nbsp;paucis horis • difsidebunt. Tertio autem quadrante comple-• tisexinde fcilicet4$o. rurfum annis,ad duos ^ies amp;nbsp;aliquot boras error procedet,nec vltrà. J’oliennamqueminuetur, rurfumqueadeon-functiOnemambo principia fpeâabunt/cpe-

IT CORRECT. ANNI 14 {ettj;-amp; confeguptar ftatos fuos dies foil’s con-ueriio Sicqueperpetuoprincipiumanni cun-dem foljs locum habebitvel omnino proxi-

Vtautem,quodrcftat,amp; eum errorem,qui aCHRlS'TO nato irrepfit,tollamus,reuo-candusprimiimeftannusadeumftatum,quo fuit tempore eo quo Chriftus Dominus natus eft:quod vt quamprimum fiat,venerandaeius memoria vrget,fiet autem,fi alicuiusanni,ve-lutj huius Septuagefimi feptimi, vel 78.Dece-bre, 20. diebus finiamus, vt calêdç lanuarij lint 2i.quas feftum Natiuitatis conluetodieruin-teruallo prçcedet. V el fi ad ipfum brumç pun-0um Natiuitatem Domini referre placetjj. dies cruntauferendi.Deinde porro anno Domini lyp.Primum adimere diem,amp; Decem-brem jo.clauderediebus ,fueritoptimu, quo cius ademptionis numeratione,ab Anno Domini i6o0.aufpijantes,ternis perpetuôlubi» Içisnotabilem amp;nbsp;inlignem reddamus. Itaque Natiuitas Chrifti Domini nofiri femper fecun dum gradum Capricorni vel proximèjamp; hye-mem,Pafcha femper vernale tempus cum A-prili,nobisadferent.Placuitautemab eo anni ftatu, qui fuit temporeC^hrifti ^ne minimuni quidem reccdere,ne receptum haftenus mo-, rem amp;nbsp;fedorum inEcdelia ordinem intertur-bantes,rem totam confufiorem amp;nbsp;difh^liol^ rtdderemus.Prgterquam quód ca onviia mj^ fteriq

’ DFVERÀ QVANTITATE .f fterio minimè carere üt credibile. Sed vt 8i ï^i? tercalatione eadem, cæterifqueomnibus ma-t/t‘*^éïL nétibus.folummodoir.dies vniaiinoadem-^H'Ü. ptosjingulifque deinde 150. vnurd adimendu ' nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;effe, meminiffe^neceflumeffet. Alioquin cer-

teamp;aliæpoffentexcogitarianni forms ,pul-chrumque fuerit inchoaffe annum,abipfofol ftitioHyberno, feftoque Natiuitatis.quoet-iam confequeremur, vt æquinoâium vernii in primummenlis diem femper, vclproximè. FeftumquePafchatisin eundem femper men-femincideret. Neque minùsoptabileeffet,vt interluniaprimum qusqueme«iis diemob-, tineant Sed his,alijfq; omnibus,eum quem di’ ximus ffatum,multis nominibus antecel-lerc,meritcqu e prsferendum effe exiftimamus.

FINIS,

TÇA corp l s A G o G E

AD ASTRONOMIAM, GEOMETR lAM, ET HOROLOGIOGRA.

P H 1 A M.

tyiuthore T^ohli yiro,7)i igt;4ilerto Ltt~ wno ai ^kraieSfo,/, K. 2)offer9

amp; 'Mariematico^

COLONIAÈ AGRIEPINAE Apud Godefridum Kempenfem.

Amio.M. D. LXXVlil.

DEFINITIONES ET

THEOREMATA GEO.

METRICA.

SN G V L O s rcâiiineos cóftituit redarum linearum concurfus. reftum quidem, perpendicula-ris:coq; minorem due acutum, pronior, anguftiorqjimaiorera fiueobtufumjatior.

• i.I taque angulusobtufus continet reft urn amp;nbsp;acutum,reftus acutum.

• 3. nbsp;nbsp;nbsp;Et refta linca fuper reftam confiftens, facit duosréftos,aut duobus reftis squales.

• 4. nbsp;nbsp;nbsp;Parallels funt ad inuicem ills reft æ lines, quæjn inbnitum licet prodüftæ,nunquâ con currunt,angulumüeefficiunt.

• 5. Parallelograma fpatia quadrilatera,quæ pa. raUelislineis funt contlula.eorumque partira

» funt reftangula,partira non.

• 6. nbsp;nbsp;nbsp;Circuli paralleli ad inuicem, quorum plana fi direftèproduc5tur,nunqua fecarefe mu tuoinuenientur.

• 7 nbsp;nbsp;nbsp;Quadratum eftquodex quatuor reftis li-neis squalibus conftruftü quatuor reftosan-gülos habet.

• 8. nbsp;nbsp;nbsp;ömnesin circulo femidiametri, à eehtro fc^icet ad circumferétiam duftæ hint inter fc* aequales,omniumq; reftarum in circul^nea*

ISAGOGE.

^m,cn: diameter maxima,fecatque circuluià bifariam.

j). Segmcntumcirculi,fubarcu fiueperiphe-ria,eique (bbtenfa reâalineafquæ arcu m eum à toto circulo abfeindens, Babs fegmenti dieu tur}continetur.

ïo.Triangulum redilineum,auttria inæqua-lia habet latera,quod fcalenum:aut tria æqua-lia,quod æquilaterum: aüt duo tantum æqua-Îia,quodlfofelesliue çquicrurium. Kurlum-que redangulum, quod reâum angulum ha-bet:amblygonium,quüdobturum:oxygoni-um,quod acutum habet angulnm,dicitur. n.Si duo triangula habcant duo latera duobus lateribus vtl'unque vtriqueæqualia, amp;nbsp;angulum angulo æqualem,qui fub duobus illis,la-teribus æqualibus continetur,habebunt etiam bafin bah çqualem,acreliquos angulosreli-quis angulis çquales,vtrunque vtriq;,fub qui-bus æqualia latera fubtenduntur, eritq; trian-gulum trianguFo omnino çquale.

Item, fi duo triangula habcant tria latera fingula fingulis çqualia,habebunt etiam angu los çqualia latera refpicientes çquales.

{iuitniutuaeoiumapplicationead oculum paten-tia lettore demonßratiotie non e^ent.

la.Sicetiam in quibusduoanguli, vterque v-trique funt çquales,amp; vnuni latus vni lateri ç-quiltjbuequodçquahbusadiacet angulis,feu quo vnr çqualium anguloruin fubtenditur^

AD ASTRONOMIAM, lî ömnia fuùt æqualia.

15. Si duæ reétæ lines fe mutuô fecuerint, an-galas ad interfeftiônemfe mutuo refpiciétes, fiuc oppofitos,faciunt squales.

Vf hic Aamp;S.C amp;nbsp;D. finit atjualesper j. pramifiH» 14 Omnes in trîarigulo anguli fimul fumptî funt duobus redis squales. Vnoque trianguli latere produdo,angulus externus duobus internis oppofitis eft çqualis.

^æ itapatebunt.fimt in hacfigura, tria trianguli nquilateraamp; aquiangula,amp; anguli A,C.D./unt duob. reâü aqualaper s.pramijfum,^ C.c^ M. Item A.amp; O./ùntaquales per fecundam partem n. huius, ergo to-tue angulus M.C.A. externus, aqualù efioamp; M.an~ gulis internis. Ex fequenti etiam theoremate angulos al ternos M amp;nbsp;C.aqualesefiè liquet.

1$. In duas parallelas restas lineas incidens/e-da linea fàcit duos internosangulos çquales» duobus redis,amp; angulum externum çqualem interno oppofito amp;nbsp;ad eafdem partes,Ôc.'Wgu* los altcrnatira inter fe squales.

y Nam

i^am niß duo au^uh fnterni,ßtlicet N amp;nbsp;D.eßent squales duobus reaü^non eßim tllji linea paraUeU/ed tx alterutraparte concurrètes^efficerent ntatigulum, tertio^an^uloduosi'eaotßipplerent,ex r^fJunta^al o quinftperpendiculari ducio ex alterulro annula obtußo, ad alteram liueamclaudamustrian^nlum: exempli^ra tia^ex Dad;. patebit idemper 14.nam S.s.G.angu-lus reclus aqualis annuls N. amp;nbsp;annula 3. D iç, item annulus ;. V.G. réélus efi,patet^ ad oculum: Er^o lotus annulus D. cum angulo, N. duobus réélis a-qualis eß. Et quia annulus D. cum annula G.E. L. ex i.buius duos reblos efficit, quemadmodum cgt; cum angulo N.ergofequitur^angulum G.E.L. aqualemeß fi an^ulo N-óquot; eadem ratione vel per i}.butus,an^uli, ^^ ér O.M 1^ D alternatim squales. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;\

• Jé. Ifbfcelium triangulorum adbafin confié • ftentes anguli funt inter fe equales.

X nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Adhuiiu

À b AS T KO NOMI AM. nbsp;nbsp;nbsp;nbsp;it

, Afi huius demoßrationem demittenda eß line a reflag ^t, hie N.O.q reliquH annuls et baßn diuidat bifariä, ^•ßyt eß)perpendicularitad baßn effe cocedalur,fgt;a tetprepißtum adminiculo/4.huius, na P.amp; E. angu tirelti,lt;^ C.amp; A.squales. Sin odiose negetur,ergo cü ^■et E.ßntinaquales^alter obtufiis,alteracitP,et C.et A.aquales^erüt Bamp; D. inaqaales centraal, hui w.

^7‘ Triangula Ifolceles vel equilaterfi eóftrui tur,ppedicularis excitatur,angulus 8i reda li-nea bifaria fecitur.ratioe 8. huius,adminiculö duorücirculorü çqualiûjVtpatct ex hac figura.

• 18. nbsp;nbsp;nbsp;In omni triangulo maius latus maiore ari-gulumrubtendit,amp; viceverfa.

onenditurreducendo ad trian^^ulum aquicrurium ex tnaiori fciUcetan^ulo admaim lätus duäareäalineaj f‘^^P^ fecundampartem ra-huius.

• 19. nbsp;nbsp;nbsp;Parallelogrammahabent angulös.amp; late ta qü® ex aduerfofurtt inter fe æqualia,’bifa-riamq; per diaraetrum fecantur.

f * Tr».

Trebaripotefi exi2,huiusadmmtcu[o vllima par-’ ao. Et ex huiuspræcedentis ratione pendet triangula fupereadem Hue çquali ba(î,amp; in c-ifdem parallelis cóftituta.efTe inter feçqualia. EtparaUelogrammum effe duplumtriangu-lo,cumquo amp;nbsp;eandembafin habueritjamp; in ijfdem fucritparallelis. Item triangula quord eadë fuerit altitudo, ita fe habere inter fe vt ba fes,fimiliterque parallelogramma.

lt; 21. intriangulisreócangulis,quadratü,quod à latere reâumangulum fubtendentè defcri-bitur, squale eft ijs duobus quadratis^qujeX reliquis trianguli latehbus conftctuntur.

Nam in triangula re^angulo A.B.C. demijfa pérquot;

• ftnikcularii B. E.oftendttparaUelegrammum A.F- £• aqualeejfe quadrat» D, Bgt; A-ßquidetnduetrta/g“^^

AD ASTRONOMIAM. 19 D A.Ciamp; A.F.B.propteraqualitatem binoram late-rum, amp;nbsp;an^uU A, qui in vtroque confiât, vno reilt» amp;nbsp;communi B. A. C./ùnt inter fe aqualia per 11. hu-ius:Triangulum autem D. A. C.efi dtmidtum D.B.A. amp;nbsp;A, B,B.dimidiumy A- ^~ E.perpracedentem ^fimili-ter duitis Iweüex AadL,c^exB ad M. mantfeßum euadet, E. C. M. aquiualeré, B.C.E.ficqüepatet propofitum.

21. In circulo angulus ad centrum duplex eft anguli adperipherîam,cùm fuerit eadem peri pheria bafis angulorum.

Probatur perficundampartem 14, huim adminku-lo deeimifixti.

25, Aequiangulorum triangulorum propor-tionalia funt latera, quscircum æqualesangu Ios,amp; homologa funt latera quæ çqualib. an-gulisfubtenduntur.

Vt lalerit ad lattis in vno irian^ulo eadem eH propor tio^quafimilis laterit adfimile latus in alt er o irian^ulo tquian^ulo,

24. Si quatuor redj lineç proportionales fue rint, quodfub extremis comprghenditur re- • öangulum quadrilaterum, çquale efl ^:i quod fubmedijs comprçhenditur reâangul»,. ƒ ^^odinnunlerii^)ocmodopatetgt;vi a ad S.fie 6.

7 3 sid-f.

ISAGOCV

»d 4. nam ouater duodeeïm valent fêxies oélo, amp;nbsp;mal-, tiplkatü S.cumó.produétojjdiuifoper n.exit quarts tas numerus proportwnalu 4,

i^. Si tres redæ lineç proportionales fucrint, qtiodlub'extrcmis Gomprehenditur reSan-' gulû,æqualeeftei ,tjuod à media defcribitur' quadrato.vt^. 6.4. nam quater nouem,valét fexiesfex.

t^dßnuum re^orum e^oSfrinam/erritjenria.

tborda eft reéla linea fubtendens aliquem infemicirculoarcum.Diameterautemtotum femicirculum fubtendit amp;nbsp;claudit.

Sinus reâus,cft dimidiura chords, nam H-nea reda ex centro circuli, dufta orthogonaÜ. ter ad chordam,diuidit earn, eiufq; circumfe-rentiam bifariam,in duos fcilicet arcus, duof-que finus rcétos squales.

Circulus continens more aftronomico ^éo. I graduSjdiuiditui'perduas diametrosfecantes fc orthogonaliterjn 4.quadrantesdic,vt 4 ad centrum anguli redi continentes quilibet cit-cumferentiam po.graduum, fimul efficiant 56o.gradus Cue partes. Nam anguli ad centrum fe habent inter fe, vt arcus,quos reâis • fuis lineis abfcindunt,eodemcjuc partium nu-merocenfentur.

Itaq; anguli amp;nbsp;circumferentis mutuapræ-•ftant inter fe cognitionem.

* Et quia reâi ad curuum non eft certa pro^ • portio^confeóta eft linuum reétorum tabula, • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;qtiï

AD ASTRONOMIAM. a® tjuæ adaptans,quantû fieri potuit, finus redos arcubus,amp; angulisad centrum,in partib.qua-lium fèmidiameter fubtendens quadrantein circuli, didaque finus totus, aflumpta eft 6000000.alterum ex altero notum reddit, ex arcubus fcilicet finus,amp; vice uerfa.eamque præterea præftat commoditatcm.vt aliç quan titates ad earn proportionem relata: inueftiga-ri prompte amp;nbsp;fciri pofsint.

Si verb triangulum reailineum infcriptum fucritcirculojtücduorcdiangulicomprehé-duntjóo.graduSjdatifqueanguIorum quanti tatibus,dantur etiam circumferen tiæ, co mo-do.quo 360. gradus funt duobus redis æqua-les:namamp; in hoccafuangulorum amp;arcuum,^ eadem oft proportio. Deinde autcm ex tabula finuum innotefcunt latera trian^uli, in parti., bus illicaftumptis, amp;nbsp;confçquctcr in quibuC uis alijs menfuris per regulam proportionum. Notandum vero in hoe cafu, dimidiatis arcubus horum latciumjaquam chordarum qua-titates elTc fumendas.

Quodfi velproportiones fairem angulo-rum trianguli inter ie fucrint notæ,innotefcét etiam quantitates per diélam proportionum regulam.- exempli gratia, fit vous angulus 10. alter 7. tertius 3.3ggreg.atis illis tribus , hunt ao.vtautem ap.adquemuis angulum in ijlde partibus,fic 180. vel 360. numerus duorum* tedoium ad eundem angulum ingradibus,*

7 4 nume.

IS A G o GE

numcroq; Aftronomis vûtato. Itaque multi-plicato feci^do per tertiumjamp; deinde eo pro-duóto diuiloper primum, exitquarta quantitas quæfita, iuxta modü regulse proportionu.

Cognitis etiam duobus angulis tertius igno-rari nequit,nimirum fubtrahendo duorù qua, titates ex numero duorum redorum.

Sicirculoinfcriptum fittriangulum,cuius ballslitdiametercirculi, angulusbafin refpi-ciens erit redus amp;nbsp;vice verfa.

In circulo anguli qui in eodem funt fegme tOjquorum fcilicet balis, eft refta fegmenti li-nea,funt inter fe æqualcs.

Itacß triangulorum redilineorum quantita tes amp;nbsp;proportiones angulorum amp;nbsp;laterum, al-teru ex altero fcire licet p 21. huius,adminicu-lo tabula linuû.varijs modis^potifsimus tarne eft vt quofuis triangulos oblatos efficiamus redangulos:Memores,trcs angulos planos eft fe duobus redis æquales ; qui continent iuxta tabulam lînuum gradus 180.Item fimilium ar cuum amp;nbsp;finuum eâdem effe inter fe proportip nem: Sieproportio quæ in tabula finuum eft inpartib diametri illicalTumptis.omniualio-rum in ali js quibufuis partibus proportionem * manifeflat.Præterea vt fuper vno trianguli an ^ulo,tanquam centro, circulum dçferibamus iuxta quantitatem vnius lateris, vcl vt ipfum ^ianguJum circulo circumferibamus, prout • rei amp;nbsp;opens varietas exiger.

De

AD ASTRONOMIAM. *1

' 2)e trian^uhó/jgt;^aric0fiue conueXK..

Triangulum fp^æricumjVt hic intelligt-muSjdefcribitur ex tribus maximorura circu-lorum circumferentijs,quorum idem eft centrum. Angulorum autem fphæricorum quantitas intclligitur fecundu circunferentia Circuli maximi,qui in pûfto anguli tahquâ polo de-fcribitur, quamq; circumierentia quadrantes çirculqrum angulum conftituentium interci-piunt,nam qualis eft hçc circumferentia ad to turn circulumjöo.graduum.fic angulus ille fe habet ad quatuor reftos, ad centrum fphærx.

7'^gu/te ^uatiam ai/jf^/gt;iericorum rrian^u~ lorum co^nirionem.

Ïn triagulo fphçrico redagulo.fi latus oppo fitum apgulo nó redodato,notü fit, ipfius fi-nus multiplicatus pcrfinütoiü amp;nbsp;deinde per finum dati anguli non reéti,diuifus', producit Cnumlaterisredum angulum fubtendentis.

Sin latus datum redo opponatur angulo,e-iusfinusper finum anguli dati multiplicatus, aediuifusper finum totum, producit finum lateris dato angulo non redo,oppofiti.

Quod fi autem latus datum,fit inter angulum redum,amp; nó redum datum, ipfius finus perfinü cóplemétianguli dati multiplicatus, • amp;nbsp;diuifus per finütotum,producit finücopie, niëti anguli tertij ignoti, eoq; cóplemeilto lüb^ tl ado ex ^0. reftat quatitas anguli mcogniti.

7 5 E1

ISAGOGE /,

Et hæc fufficiunt açlqueuis triangula fphar« rica.cum liceat ea reducere femper ad reßan-S^l^’

^e quantitate/ttfierßcierumifara/klogrant-morum, triangti/orum,^ianorum, cir-cuh amp;^^lt;era.

Areaquadrati habetur ex multipficationc vnius lateris in fe. Parallelogrammi reßangu-li aream notam facit multiplicatio vnius maio rum laterum,in vnumminorum laterum.

In triangulo reßangulo,medietas quadran, guli ex duobus latcribus reßum anguium có* prehendentibus,eftareatrianguli,vt hfuerint vtrumque8. area eritja.

In oxygonio fi fucrit equilaterus.dußo V-no latere in fe, amp;nbsp;produßo multiplicato per 13 quodqueindeprouenit diuidendo per jo^ in quotiente habebitur area. VeHicetdußa perpendiculari ipfum partiri in duo triangu-r la reßanguia, quæcompofitaconftituuntpa rallelogrammum reßangulum : vnde multU plicando pcrpcndicularem cum dimidio v-niuslateris habetur area.Sin æquicrurius fuc-ritdimidiumlateris inæqualis multiphcandu critin fe.Itemcpalterumæqualiumin fe.amp; ab • hoefeeiido produßo fi fubtrahaturillu dprf-• cedens, radix quadrata refidui dabit perpen • diculji ein, quxduéla in dimidium lateris in-^quahs oflendit aream . b^m perpendicu.' laris

AD ASTRONOMIAM. « laris efficit duo triangula relt;?tangula,quoruin coniunâione fit Parallelogrammum redan-gulum. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;.j

Circuliproportioaddiametrum,coinmu-niter fumitur, vt 22. ad 7.

Area circuli habetur multiplicando medie-. tatem circumferentiæ in medietaté diametri.

Quadruplum autem ares maximi in fphæ-, ra circuli,eft tota area vel üiperficies conuexa fphæræ. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;1-

Solidum vero corpus totum fphxræ inno-r tefcit,fi produdum ex multiplicationc diame tri in fe,inultiplicatum fueritper vndecim,in-dequepfoueniens diuifiira per 21. Nam quo; tiens'häbebit çrafsitudinem fphxræ in men, fura cubica , vt fi ab initio fuerit affumpta figura pedalis , fumma erit pedum cubito-rum.

Cubi vero redanguli quadrati totum corpus innotefcit multiplicationccubica fcilicct Vniuslatcris in feprimo,ac rurfum in produ-Öum,vt6.in6.amp; in jó-fittotacrafsitudo 216. Si vero non fit quadratus,fed altera parte lon-giorcubus, tune longitudinera ducemusin areamlatitudinis.vtfitlatus, latitudinis quin-que,ergo area 25.in quam duftum latus longitudinis, quod fit i2,often-

dit totam crafsitudi- nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«

nemjoo.

ISAGOGE

7)e moJo Jimetieni/i aititudines amp;nbsp;flatta, ' Communior eft per fcalam altimetra, qua ed quadratum additum quadranti Geometri co. qui fi circumfcriptus etiam fuerit triangu-loaquicrurioj poterit,meaquidein fententia, adquafuisdimenGones, plagarum raundi amp;nbsp;locorum inter fe diftindiones, horolographi-ca,amp; obferuationes etiam Phænomenon,fuE-, ficere.dummodo ex Solis fplendorc, linca me ridiana haberi pofsit,aut etiam quouis tempore (5adfitacusferreusMagneteimbutus,buc index Magnetinus, pyxide eius idiotropiana amp;nbsp;declinationem habente ( quam compafluni yocantjconclufus.aut quadrantis bafi eodem modo infcrtus.figura aût inûrumenti talis eft

AD ASTRONOMIAM. ïj

• A. C.B.quadrans Hue quanta pars circuli di Uifa in 90.partes æquales.

N.C R.O. quadratum, cuius duo latera có currentia in 4j.gradu quadratis funt in ii.par* tes squales diuifa.

C.O.eft régula mobilis cum pinnacidijs cd troadhsrens.

• C. B. ba li s qu ad ran tis.

Quandiu autem res,cuiu$ quantitas qusri-tu r,confpicitu r per latu s quadrati O.N. altitu-do rei orthogonaliter creds, fuperat fpatium plani inter oculummcnforisamp; rem eleuatant fecundum proportionem 12. ad numerum per quem regulatunctranlit. Idquepropterlimi-litudinem triagulorum çquiangulorum,quo-rum latera funt proportionalia,vtL.]Vl. rese-leuata,C.M. radius vifiuus buchypothenu' fa.C.L.fpacium plani.amp; huictriangulosqui-angulum eft N.C.LErgo vt NC ii.taliü partium,ad N I.in ijfdem partibus,ficML. adC L.in alia quauis menfura,amp; vice veria vt LN. ad N C. lic C L.ad L M. Ergo cognitis tribus quantitatibus,quarta per regulam proportid-numinnotefcit.

In concurfu autem duorum quadrati late-rum,cónfpeda rei altitudo,squalis eft Ipatid, lt;]uia tune funt duo triangula squicruria. •

Perlatusautem KO.b radiusttanfeat,v{ C.P.Spatium plani fuperat altitudinem rei feft cudum proportionem didam, eadem femper

ISA GOG E ratîone ex fimilitudine trianguloru percipied da.Exempli gratia, fi hypothenufa tr3featpèr humerum4. amp;fpatium plani (it 20. pedes, critaltitudo6o.pcdes.Nam vt^. adti. lie20. ad 60.

Notandu,pi autem,âltitudiniinuent3B Temper addenda clTe ftaturam menfutatis ab ocu-load terram. Et vt balls quadrantis.lltparal-lela,fineæquididetpiano Horizontis,quod, perpendieulodemilToper foramina A, N. facile eft.

Quod fi autem aceeffu impedito, interuaL lummetirinequeamus,dupliciin linea refla ftatione, erit agendum . Exempli gratia, in prima ftatione radius per latus fuperius quadrat! tranfit, in punâo numeri 4. re-troccdo redirurTurnque videofummitatem reipernumcrum 6.eiuTdem lateris,amp; mino-rilubtrado exmaiori,remanent2. vt autem 12.ad 2.fic altitudo rciad fpatium plani, inter . duasftationes,quodfit2o.pedes, ergoaltitu-doerit 120. pedes præterftaturam didam. Si verb perinferiuslatustranfeat radius,fitque fpatium plani fcilicet maius altitudine,diuidc-mus 12. per numerum prims ftationis, itc per • numerum lecunds, mitioremq; quotientem • fubtrahemus3maiori,amp; cfi refiduo fiuediffe-^rcntia,diuifofpatio plani interduas ftationes •habebimus in quotiente altitudinem rei, • cui tarnen addenda eft ftatura menfurantist ire-• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;...

ÀD AStRÖl^ÖMlAM. ’♦ Frequens autem vfus amp;nbsp;exercitatio docebit Geometram fumere numéros,in quibus o-peratio line fradionc numeri procedit, aliafq} commoditates amp;nbsp;compendia.

Pofluntetiam dimenliones fieri foliusbacu-iiincertas partes squales diuifi adminiculo pertriangula eciam fimilia.

Vtfit D F. turris,BC.bacillus,amp; in A.öcuIuS ïmenfurantis,itaque vtC A. fpatium inter ocu lum amp;nbsp;baculü,fic A F. fpatium inter oculfi amp;nbsp;turrisimumfeadem menfura metiendü,qua ifeb3culus,)fe habet ad altitudinem turris D» F.Quodfi verofpatiii A.F.fciri non pofsit tune fic procedendum crit.

ocu*

ISAGOGE

oculus,præterea triangulus A.B. C. in cam rë faftus ex ære cum pinnacidijs,aequicrurius,lä-tera Habens diuifa in eafdem fiüe fimilescum baculo partes,qui fuperponendus erit baculö, vtimumturris videatur per A.C. foramina'» aut noftro inftrumento premiflb,res fi militer cxpediri poteft. Sunt hic itaque rurfum triari-gula fimilia, A.B C. C.N.M. amp;nbsp;M. C. O. ex quibusömniainnotefcunt.nam vt A.B, fehà betad B C. fic R M,vel CO. bacillus fe habet ad C R,cui æquale eft M O. amp;nbsp;confequenter totum N.M.fpatium ignorari non poteft.

Curandum veroeft, vttriangulus reöèfil perponatur baculo,fintquefcilicet A.B. amp;nbsp;I. K.M.parallelæ.Item R.B. amp;JV1 N. vtq;men-fura fit in omnibus eiufdem generis,amp; forami na inftrumenti angufta,fitque imum rei eleua tæ in eodem plano amp;nbsp;fuperficie cum loco men furantis.

Fit etiam dimenfio adminiculo fpeculi pla-ni,ad quod in ten-a iacés, tandiu accedenduin vel recedendum ab co erit cum baculo in cerras partes diuifo,vtpræcisè per fummitatem baculi eredi, videatur in fpeculo fummitas rêi feleuatæ.fiunt enim duo triangula çquiangula, ideoque fimilia, quorum prima'duo latera fi-• milia,funt radij vifualesconcurrétesin medio fpeculi,fecundaduo, funtfpatiumplani inter • baculum amp;nbsp;medium fpeculi, amp;nbsp;inter rem elè-teatam amp;nbsp;medium lpeculj,tertiaduo^untma-gnu

AD ASTRONOMIÀM if Ijnitudo baculi,amp; altitudo rci eleuatæ.

Dr ratione ymlrarum, amp;nbsp;tnodii men~ Jurani^tjgt;er ymèras. .

Sit hie circulas meridianus in quo finus al-titudinis fupremç partis corporis Solaris G T. nam T E.fit planum horizontis,amp; Solis fupre ma pars in G Sinus complementi altitudinis Solis G F.ResereclaB.A. eiufque vmbrare-da B C,Res æquidiftans plano Horizontis ,fit E A. reddens vmbram verfam £ D.in re ere* óaorthogonaliter ad fuperficiem Horizontis,velutimuro,qui fitE P. ergoex triangulis hic limilibus videtur, quód vt finus altitudinis Solis G TJe habet ad finum complementi G F.aequalemfcilicet T A.fic altitudo rei c-redæ A B.ad vmbram reftam B C.amp; vt finus complcmétialtitudinis, ad finum altitudinis, ’ fic A E.res muro infixa, ad E D. vmbram fu-* am verfam.

Hinc

ISAGOGÊ

Hincctiam,vice ver(a,altitudo Solis inrto* tefcit:nam quadrata altitudinis reiamp;vrnbras reftae iunda, faciünt quadratum A G. amp;nbsp;radi-cis extraßione venit quantitas A C. vtque ilia fe habet ad A B.altitudinem reijic fin us torus A G. ad finum altitudinis GT. quodcla-riùs liquet defcripto circulo in puncto C. tan-quamcentroiuxta longitudinem C. A. nam A B.amp; GT.eruntfimiliumarruum.Hinc latitude regionis,amp; locus Solis in zodiaco fcirl pofTunt, ratioautem elï habenda, quód,quia extremitascorporis Solis vmbram facit, omnium return vmbræ reftæ,amp; verfæ, fempet fintminores illis, quas radius ex centro Solis éfficeret:ideoquèei,qui extabulis fimul o-perari volet, necelTariam effe cognitionem apparentis Solis diametri.Cuius quantitas vél exTheorianoftrafumipoteft, vel hoc modo inueRigari»

Sit fquot; -reSa A B.vmbra rcâa,E.Solis fupe-fiorc

ÀD ASTRONOM! AM. 25 tiore parte proueniens in C. ergo angulüs A. C.B.metituraltitudtnemfupremæ Solis partis, rurfum eodem tépore Rylus infixus F E. iaciatvmbram ex infima Solis parte in B. er-çoex quantitate anguli E.F.B.qui æqualis eft angulo B.innctefcit altitudo infimæ paitis. Et ex harum differentia,quantitas diâa, amp;nbsp;ve ra cenrri altitudo.

Cùm altitudo Soliseft45.grad. tuncres e-reâavmbræfuæeftæqualis, quiafinus com-plementicui fimilis eft vmbra, cftxqualis fi-nuialtitudinis. Vbiveró maioreft Solisaltitudo, tune res ad vmbram fuam fe habet, vt duodecim adpunâa Scalæ:Sin minor,tunc itafe habet vmbra ad rei altitudinem.

Ante meridiem autem continue decrefcit finuscomplementi, amp;nbsp;vmbra hmiliter fit mi* nor altitudine.poft meridiem crefcitdiélus fi-nus, fimulque vmbra magis ac magis excedit altitudinem rei.

Quod autem circa æquinoélia, vmbræ meridians fingulis diebus apparentem ha-beant differentiam,circa folftitia minime, fit propter declinationis diuerfitatem.

Lunafquia terrs proximiorjfacit in eadem fupra horizontem,eleuatione maiorera vrn-* bram,quàm Sol. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«

Omnes autem res eodem temporecunf S 2 vra-

ISAGOGE

vmbris fuis fe habent iimiliter, itaq; quod ad has dimenfiones attinet, licet fimpliciter rent aliquam eiufque vmbram metiri, amp;nbsp;adhanc proportionem,cum tertia quantitate, fiue vm bra,alterius rei quantitate quartam,ipfius fciU cetreiquæfitam,elicei-é.

2)f inuenfione iine^ meriiüanä.

Poteft fierimagnetini indicis adminiculo, vel per quadratem. Vel fi duâo circulo in pla no Horix-ontali, elue æquidiftante fuperficie ilylusinfixus fit eius centro orthogonaliter, cuius vmbræ cxtremitas obferuetur ante amp;nbsp;poft meridiem in circumferentia iftius circulij duóta per medium ita notati arcus,perque een trum circuli,linearefta.eritquælita meridia-na. Nam propter fimiles complemétorum fi-nus in æqualibus arcubus ante amp;nbsp;poft mendie vrabra deficit.

De /yorolo^iorum Solarium con/èlftone.

AD ASTRONOMIAM. 27

Ducatur ex centro quadrantis linea refia 'A.D.quærepræfentetæquinoftialem circulü, iuxta latitudincm regionis C. Ü. 50 gr. à verti ce fcilicet numerando, quæ aequalis eft eleua-tioni polijdtque B. R. A. bafis quadrantis, C. P.A.latus quadrantis perpendiculare , per lil neamautem A. D. ducatur alia orthogonali-ter, vtP.T. R.

Ex hac itaq; figura licet conftruerejVel horizontale horologiumnn quo horçnotantur, ftylufque infigitur,ad planum horizontis, cive a^quidiftantem fupcrficiem,vel murale, line verticale,cùm ftylusin muro,aliaverupcr-ficicperpendiculariter ad planum horizontis creéta,vmbram iaciendo noras dénotât.

NamT A.fempereft femidiametcr æqua-loris.R A.Horizontalis,P A.muralishorolo gij femidiameter.

Conftrucndi autem modus talis eft, vt lu Vclis Horizontale,due feraicirculum C A.iu-

. s Y «*

ISAGOGE

ytaquantitatem femidiametri æquatorîs, K-neaque C. A. protracta, vfque ad quantitatei» femidiametri horit,ontalis,defcribc femicir-culum D A.tota igiturlinea D. C. continebit -quantitatcm femidiametri æquatoris amp;nbsp;hori-z-ontalis, duoque illi femicirculi contingent fc: per côtaâum autem eorum duöalinea re-ét:a,longa fatis, deinde diuide femicirculum æ-quatoris C A.in ii.partes Hue arcus squales, amp;lineisreâis pereas diuiliones excentroC.’ duöis ad lineam contingentem, iungéds func reftçexcétroD.in vtramq; partem, vbicunq; enim hs circumferentiam fdi femicirculi Icili-cetD A.tranfibunt,illichoras denotabit ftyli vmbra,iuxta ordinem in figura adlcriptum. Stylusautem in centro D. eleuandus erit exa-dèfuper lineam meridianam fiue hors duo-decims A D.iuxta quantitatem anguli P. A* T.inprscedenti figura, cui angulo squalls eftangulusT.K. A. Curandum veró,nefty-lus in aliqüam partem à linea meridiana decli-net. Itaquehors videbunturordineprstcri-pto,nam in linea 6.D.(5.erunt fexts matutina amp;nbsp;vefpertina, amp;nbsp;ficconfequenter vfquead ho ram duodecimam meridianam , ab vtraq; autem hora fexta, noétem versùs,eodem ordinc • éadem interuallaobtinebunt, produótisfcili-•cetlineis horarijs percentrum ad alteram cir-•culimediecatem, eritque idem fpatium inter ” » nbsp;nbsp;d.^j.item^ö.^ 7. matutinas,quod inter 6.amp;$.

. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;item

*

AD ASTRONOMIAM, nbsp;nbsp;nbsp;nbsp;tg

item Ö.amp; 7. vefpertinas.Et hæc omnia ita pre-parari,acdeindecirciniopein quamuis tranC fern fuperficiem poffunt, quæ tarnen sequidi« flare debet plano Horiz,ontis,amp; ftylus lepræ-, fentans axem æquatoris exaâc feptentrio-pem versus tendere, lic,vtlinea hors duodc* cimæ lit dirçâè inter Meridiem amp;nbsp;Scpten-trionem.

Nondifsimilisautemeft ratio,in conftru-Ôione verticalis horologij.nifi quod femicir-cuius fcribituriuxta quantitatem femidiame-tri verticalis, ftylufque erigitur iuxta quantitatem anguli R. A.T.præcedentisflguræ,vel eiæqualis,T. P. A.Præterea horæ contrario ac in præcedenti modo, notandæ funt, vt hic fcilicet fit prima, vbi illic vndecima. Curade-niq; adhibenda eft, vt huius ereétæ fuperficiei, vnum latus Meridiem, alterum Septentriona exadè amp;direâè afpiciat:quamobrem ctiam in eo, nifi u.horae çquales habentur, reliquas verb horas ftylus tranfiens fuperficiem , in latere eius Septcntrionali denotabit, tradu-cendas circini ope, fignandafqueeodem,quo diximusmodo.

Reliquaverohorologiorum genera minus peceffaria, pro fua,quifque,induftria amp;nbsp;lólertiainuenire poterit.latiorem- * queTheoriam exSebaftiano ^

Munfteropetere. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;•

S 4 De

I s A G o G E

DeJü^^utanila yr Hum, aliorum^ue iocorUM inferß eiißantia in miüariliff ex co^ni ta eorum longifudine amp;Hti tuainc^,

Paralleli,fphæræ circuli hie funt inter çqua torem amp;nbsp;vtrumquepolum, æquidiftantes x-quatori.

JVlericliani autem,qui tranfeunt per polos mundi fecantes æquatorem, omnefque paral-lelos bifariam, amp;nbsp;ex his cuius quifque loci ver ticem fimul pertranlit, eius eft loci meri-dianus.

Latitude locorum, diciturdiftantia verti-cisab æquatorein meridiano,versus auftrum vel feptcntrionem,amp;diftantialocorum in la-titudine eft fecundum earn diueriitatem.

Lógitudo locorü fupputatur in æquatore amp;nbsp;ab inlulis Canarijs f vbi Occidentis quæda me taftatuitur) Oriétem versùsper noftrum He inifphærium vfq; ad eafd em Infulas cótinua-ta per inferius Hemifphærium numcratio, jöo.gradus complet, quorum fingulis refpon dere 15 miliaria Germanica communia, com-• munior affe rit Aftronomorum amp;nbsp;Geogra-ephorum fententia.

^ Singulaautem ea miliaria continental, fta-^ia, vel4000.pailiis, quinque lingulos pedum,

AD ASTRONOMIAM. a^ ^um,pes autem 4. palmos, palmus 4. digitos habet.

Diftantia locorum in longitudine,eft arcus aequatoris, vel eius paral!eli inrerceptus inter corum locorum meridianos.

Si loca fub eodem meridiano fita, latitudi-ne tantùm differunt,tunc fubtrada minori la-titudine ex maiorijrebduum refolutum in mi liariaquæfitammanifeftatdiftantiam.

At li fub eodem parallelo fita, longitudinc fola differunt,tunc mukiplicato finu, femifsis differentiæ longitudinis,in finum complemé-ti latitudinisjd eft, in finum eius arcus, quo quadrans circuli completur, amp;nbsp;produdo diui fo per finum totum, quotiens oftendit finum medij arcus diftantiæ,eoq; duplato amp;nbsp;reduâo vt antea,habetur di ftantia.

Attamen fciendum hic eft, quöd ciim meridian! longitudinem metientesjimilia qui-dem aequatoris amp;nbsp;parallelorum fegmentaab-lcindant,fednon æqualia, maximum fcilicer, fpatium eodem graduum numero in aequato-re fiue maximo circulo includant, minus veró in parallelis, quandoquidem illi contraâio-res femper versùs polos fiunt, necelfe eft vbi fituslocorum eft in parallc!o terreftri,con-uertere gradus iftius parallel!in gradus aequa* torisfiuemaximi circuli adquem omnislor^ gitudo relata eft,quoitincris quantitas obfe*. uatisconfejatiensinueniatur.

Î 5

Sit in hoc circulo merilt;liaoo,P.Q. çquatOP, N.O. horizon, C K. circulus verticalis, A. amp;nbsp;M.poli çquatons.C D.parallelus eiusloci,C. A.complementum latitudinis eiufq; finus A. B. line etiam G Dfemidiameter eius paralleli, vndeapparet hnum complementi latitudinis femper effe/emidiametru m para Ueli, eius lo-ci,quia funt Gnus redi eiufdem arcus.Ex quo confequenttr per regulam proportionum in-notefcit,quod grad us conti neat circumfercn-tiaparalleli,quales çquator habet,560.tali mo do:Semidiameterçquatoris, hue Gnus totus dat quadrantes 90. graduum , quot eorunde graduû quadrates, dabit femidiameter paralic li,cuius tanquam Gnus complementi latitudinis quatitas ex tabula GnuumGameda eft. SiC.

• Qiiod G loca longitudine amp;nbsp;latitudine ^différant, primiim quidem conuertenda erit •differentia longitudinis vtriufque paralleli, in gradus çquatoris, vt habeantur fegmenta duo.

AD ASTRONOMIAM. 3« duo,di£Fercntix longitudinis, pro cuiufuis pa-ralleli ratione, amp;minori fegmento dempto, èmaiori^relidui liue exceffus medietas adijcié da eft minori fegmento, cuius ita adaudi qua-dratum , amp;nbsp;quadratum differentiæ latitudi-nis, æquiualent quadrato diftantiæ locorum. Vnde ex illis duobus lundis radix quadrata eft arcus diftantiæ in eradibus maximi cir-culi.

Logißiee u/ißronomica.

Logifticen Gue fupputadi rationem Aftro, nomicara apponere.nequidhi« deeffet, ope-ræpretiumduxi. Sciendum autemeft Aftro-nomos cdmpendio amp;nbsp;breuitati feruientes, ex gradibus,fiuealijsquibufuis partibus amp;nbsp;men-iuris,quas Integra vocant,ab vna parte, continua diuifione fexagenaria, tfficere fcrupula, liue minuta,prima,fecunda,tertia, quarta, amp;nbsp;fic confequenter : ab altera autem parte, continua multiplicatione fexagenaria, plura integra in fcxagenas fimijjter primas, fecun-das,amp; estera, concludere Guç contrahere.. Sic vtvnum integrum valeat 60 . minuta prima, eaque fingula rurfum 60. minuta fe-cunda,amp; licconfequenter, 60. vero intégrât fiue gradus vel duo figna coeli communia contineat vna fexagena prima, fiue If-gnum Phyftcum. Quarum 60. rurfum fub-fun^

I s A G o Q E

funt vni fexagens fecund$,talefquc ^o. dein-ccps vna includitfexagena tertia, fieque in infinitum abvtraqueparte procedi poteft,tali ordine , amp;nbsp;fuperiores numeri refoluuntur multiplicatione in inferiores, vel inferiores di uifione fexagenaria contrahuntur in fuperiores.

fexageoæ. gradus. minuta.

———--

4. 3. 2. I. O. 1. 2.3.4. J. integrum.

DeJ^ecitiuf quatuor t^irirAme tic^ ^Aßrofiomka, t

Et additio hiequidem nihil diferepatà vul-gari,nequeinfubtraétione allquid dtfficulta-tishabebit, qui meminerit iamdiöae fexage-narias progrefsionis, quód vnico exemplopa-tebit

Exhoenumerofi 4. 49.5 0.^1.4'272 4^ fubtrahantur, ^. ^^.^. 21.247^ ®“*^- o- 53.44.10.18.47-

In multiplicatione yero hæ regulae feruiét aninus excrcitato.

Primùm quod in numeris ciufde fpeciei,fci-Ûcec

AD ASTRONOMIAM. nbsp;nbsp;nbsp;nbsp;j»

licet ab alterutro integri latere eodem, inter femultiplicandis, notæ numerorum iundae oftendunt denominationem numeri produ-di, in eadem fpecie.vtminuta prima, in minu ta prima. Hunt minuta fccunda, ßc fexagenæ primæ,in fexagenas fecundas,producuntfexa genas tertias»

Jpfaautem Integra multiplicantia nihil de denominatione amp;nbsp;fpecie multiplicandi in pro dudo mutant, vbi autem numeri multiplican di funtdiuerfx fpeciei, vt fexagenæ in ß:ru-pula, tune denominatio produdi tantum ex-crefcet à nota minoris numeri, amp;nbsp;versùs integrum afcendens promouebitur,quantum nota numeri maioris fuperat integrum: vtduæ fexagenæ primæ in duo fcrupula fecunda efficient 4. fcrupula prima . Nam fi quatuor fcrupula fecunda multiplicaueris per 60. gradus, produceturtantus numerus fe-cundorum , vt ex eo fexagenaria diuifionc prodeant 4. fcrupula prima, quod idem ef-feciffet vna fexagena prima æquiualens 60. gradibus.

In diuifioncautem,quatuor funt diuerfita tes,autenim numerusmaiorisnotæ,ideft, re-motiorisab integrodiuidendus eftpernume-rumeiufdemvel minoris notæ in eadem ta-e men fpecie:amp; tune nota diuiforis fubtrada ex^ nota diuidcndi,refiduum ofienditdenomina^ tionemineadem femper fpecie, vt fi quarta minu-

ISAGÓGE ' * rhinütadiuidasin fecunda minuta,quótierisï. rit fccundorum. Aut eiufdem quidem fpeciei^ fed minor nota diuidenda eft per maiorem.Et hicdenominatio produdi tanto integrum, in alterolatere fiue fpecie excedet, quanto nota diuiföris,maior eft nota diuidendi. vt ft fecunda diuidantur per quarta, quótiens erit fecundorum, fcrupulorum quidem, ftdiui-fto fuit in fexagenis,at fexagenarum, ft in fera pulis. Quod ex refolutione numeri facilè patet:exempli gratia, diuidantur 60. minuta I perduofecunda,prodeûr3o.fexagenæprim£, 60.autem minuta faciunt 3600. fecunda qu« diuifaperduofecunda,pariunt 1800, intégra» quibusrurfum diuifis per 60. exeût vt antea^ 3o.fex3genæ primæ.

Tertioautem, vbi diuifor amp;nbsp;diuidendus funt diuerfæ fpeciei, denomirtatio produâi tantùm recedit à nota diuidendi fub eadem fpecie,quantum nota diuiforis abeft ab inte-gro, vt fi très fexagenæ primæ diuidantur in tria fcrupulaprima,prouenietvna fexagena fecûda. amp;nbsp;fi quatuor fcrupula primadiuidasp duas fexagenas primas, prouenient duo fcrupula fecunda.

* Q^od fi autem numerus diuidendus, qul-• uis maiorisdenominationis, minortameneft % diuifore,refoluenduseritin proximè minô-* res,donec maior euadat.

.. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Ex-

V

ÀD ASTRONOMIAM.

£xetnjgt;lum t/iuißon^»

• #• ni. 2.

• 4. 20. 40 arcus Zocîiaci diuidendus per 29. 30. motumLunæhorarium. Reduâ:iitaque4. gradusad minuta,Hunt Coniunâè 26o.niinuta,inquibus,diuidendoj video quotieshabcantur 29. minuta Jamp; pro. ducuntur 8.intégra, per quæ multiplicato toto diuiforeproucnient^^-qujBfubduâa eic diuidendo,relinquunt ”•.■, *• iam rurfum , quii 24 minuta diuidi non poflunt per 29. re-foluoiilain fecunda, additilq;4o. fiuntiimul 1480. fecunda,quaediuifa per 29.relinquerent quidem 51.minuta,fed quia quotiens hic mul-tiplicatusin totum diuiforem pareretnume-rum,qüi à fuperiori fubtrahi non poffet, capie mus folùm $0.cuius multiplicati in totum diuiforem fumma fubtraâa ex —~ reftant Ib lùmquinq;fecunda, quærurfum refolutain numerum qui diuidi 29 pofsit, amp;nbsp;diuifamul-tiplicat3,fubtrafta,efficientquotientemio.fe-cundorum,amp; rcftabunt5.tertia , amp;nbsp;fie vlte-riùs.fi curiosè magis, quàrn vtiliterprogre-dilibet.

Iraq; Luna perçurritarcumzodiaci propo-lt; fitum bons 8 minutis hors 50.amp; lotfeeundis.

iduri*

ISAGOGE

Pluribus autem modis hæc res fuccedit,fa-cilime autem omnium, refolutisab initio amp;nbsp;reduftis omnibus numeris ad vnum,eumqu6 extremum numerum, vt incxemplopropo-fitoadfecunda.Et hæc omnia pendent ex régula proportionum: vt fi diceretur,Luna per curritarcumzodiaci -— vna hora: quan-i». 30.

turn temporis dabit in percurfionearcus.

4- 20.40.

Vnitasautem integrorum, neq;multipli. cat,neq;diuidit.

Porro in reliquis omnibus, præter diftas denominationumdiuerritates,nihil hæcà vul gari difcrepat diuifio.

Z)f ret/u^iotie numeri non ^uaJrati ailnume* rum, ex /^Korat^ixJ/of/ir exrra/n ^uàm minimam reiin^uensfra-ifionem,

Invulgari fit exemplum: 6. aureifunt radix quadrata4o aureorum jreflantqueq., aurei , itaque refoluendi erunt aurei in minores nummos , idque non fimpliciter, fed quadrate,vt 16 affes val eat aureus, ergo multi ^ plicatis 1(5.in fe,amp; cum produâo,fi multiplier « turq-o.radixquadrata erunt loi affes.

• In aftronomica numerus nó quadratusper fexagenanamultiplicationéquadradusefi, vt 1(58;

Àb ASTRONOMIÀM. nbsp;nbsp;nbsp;nbsp;nbsp;îï

^6^8.fecundorum,radix quadrata eft xa.lcrupu laprimaamp;57.fecunda,fed reliqua manent 24* fecunda. Ducenda igitur funt amp;nbsp;rcfoluenda, multiplicatione,omn!aillafecundain quarta, cùm tertia non lintnumerus qiladratüs,amp; radix erit -77Jecunda,reftantq;fola loyi.qùar-ta,quôd fi minorem etiam numerifraóHonem veliraus,refoluendus erit numerus abînitip in fexta,amp; radix erit tertiorum : denominatio e-nim radicis cft medietas denominatipnis nu-toeri ex quoextrahitur.quandoquidem radix duda in fe panat quadratum.Ideoq; ap-paret tertia,quintareliquafq;

imparis numeri denomi- u. à nationes non cfle -, numéros quà-dratos»

i)eift-

AD ASTRONOMIAM. j|

Dt inuentione Jecünationis /gt;artium ecliptica,

Inuenitur declinatio per finum reâum diHantiæpunâi Hue partis eclipticæ propofi-tæl proximo æquinoâiali punâ:o,amp; finum «nguli interfeöionis æquatoris amp;nbsp;eclipticæ. Nam.vt finus totus fe habet ad finum an-guli dicti, fic finusj diftantiæ ad finum declinationis quæfitæ.

Tabula JeertnatiottK ^ua communiftr ytunfur arrißces^

4

AD ASTRONOMIAM.' M

7)e ^cenßone re^apartium ecliptica

Afcenfio rcéta,Eft arcus squatoris intcrce-ptus inter duos circulos magnos,quorû vnuj per polos mundi amp;nbsp;pundum æquinodij ver-ni(aquonumeratio afcenfionü redarumin-cipitversus çonfequentia fignorum)tranfit; alter per partem eclipncæ propofitam. Vel fimpliciter: Eft arcus æquatoris coafcédens in fphæra reâa,ab Arietein çonfequentia figno-mm numcratus.

Inueniturautem afcenfio reda per finum ’ complementidiftantiae à proximo pundoæ- ‘ quinoétiali,amp;per finum complementi decli-nationis partis propofitæiWam, vt eorum ma }or febabetad finum totum, fic minor, ad fi, imm eius circumferentiæ, cuius comply.

mentum eftafcenfio redaquç. fita, rcfpedu pundi x-quinodialis proximo

AD ASTRONOMIAM. iy

Ex hac autem tabula licet aliarum omnium partium afcenfionem reólam inuenire. Sciendum etenim çft,affenfionesreöas quatuor e« clipticæ quadrantum effe squales, refpeöu punäi æquinoâialis,à quo initium fumunt,amp; cuiufque fcilicet quadrantis ab a:quinoftiali punâo incipiens afcenfiorefla, finiretureo-dem modo m 9o.fcilicet ab Ariete amp;nbsp;Libra v-trinqueadCancri amp;nbsp;Capricorni, principium. Sedeùmnumeratio ab Ariete Temper conti-nuetur, necefle eft vbi punÖum ecliptics,cuius afcenlio reâa quæritur^diftat vitra qua-drantem ab Ariete, calculum inire etiam à Libra,tanquam punâosquinoótiali,amp; (icin-uentum ex hac tabula numerum refpondente numéro diftantiç fubtrahere » 90. refiduum-queadderead9o.vtCancri primus gradusfe-iufdem diftantiæ à Libra,cuius 29.gradus Geminorum ab Ariete ) habet afcenlionem reää

Iecundus9z.i2 Quod fi autem ecliptics pundum fuperat femicirculum,ab A riete,calculus eodem modo abfo]uitur,fed inuento nu nicro addendifuntgradus 180.

De am^htui/tne ortiua^arüum eciijfriae.

Circumferentiahorizontisinterasquatorem amp;nbsp;punäum propohtum ita inuenitur:vt linus t 5 redus

ISAGOGE

reclus elcuationis æquatoris fupra horix,oigt; tem, ad finum totum, fic finus dedinationit ad fmuamplitudinis ortiuæ eiufdem pundci-

De (ii^erentia a/cenßonali partium ec lexica amp;nbsp;quantitate c/terum artiß. ciaiium.

Eft ea æquatoris portio, qua totus arcus a-fcendens ineo tempore,quo punäum ecliptû Cæpropofitum ab oriente ad meridiem venir,, maior vel minor eft quadrante, Sc habetur ex finibus complementorum declinationis Sc am plitudinis ortiuæ,eiufdem pundi. Nam vt eo rummaiorfe habet ad finum totum, fic minor ad finum cius circûferentiæquæfubtraélaex pu. relinquit differentiam afcenfionalem, amp;nbsp;hæcadiedaquadranti, indeclinatione borea, vel fubtrada in auftrali, oftenditdimidium, circumferentisæquatoris, qua totusilledies conftat, eoq;diuifo perij. prodeunthorææ-quales,dimidijdiei. Seorfum etiam,quantum temporis æqualis competat differentiæ afcen-fionali notum facit régula proportionum ,cû fingulis fex horis æqualibus, 90. æquatoris gradus abortu,ad meridiem, ventant Ja ijs au k tem regionibus vbi eleuatio poli,maxims dc-’ clinationisSoliscomplementum excedit,ma-► ximi diei quantitatem oftendit,Tempus,quo Solpartem ecliptics fçmper fupra Horizonte ap.

AD ASTRONOMIAM. jj apparenteni,pé( agrat.Qtis ecUpticæ pan com modifsirnè inuemtur fi eleuationiæquatoris tanquam dcclin^tioni, conuçnientcm ecliptics arcumex tabuladedinationisfumamus, c-ius enim complementi duplum,gradus fiue portionemzodiacifernpcr eminentem often-dit numerandam ab arcu ex tabula declination nisitainüentó. Porro dimidia dici quantitas continet boras à meridie vfque ad occafum Solis,eadem verb fubtrafta ex duodecim Boris remanet hora ortus Solis à media node. Subtradis etiam diei hpris ex 24. quantita-tem noétis innotefcere apertum eft. Hors Dehoris autem insquales bue temporales amp;nbsp;Plane- Planetatarum , fern per funt 12. in die,in has reduci tun»' poffupt squales horæ,çonueifæ primùm in gi adusfiue tempora,quod fit multiplicando per ij.Sr prominutis 4. vnius hors capiendo vnym gradum.eoq; toto aggiqgato diuilo per ^n.prodit quahtitas hors temporalis.

De ajeenßofte dh^ua partium echfidca^.

Arcus squatoris coafeendens in obliqua fphæra habetur adminiculo differentiæ afcen-fionalis,auferfndæabafcen(ione reda pundi^y^* propofiri fi ülnd déclinât in feptentrionem, adijciends autem eidem fi declinatio fit auftrilt; na. Conuerfo ^utem modoeademaddita vet ablata prodit delcenfio obliqua. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;t

• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Lon- f

ISAGOGB

Lotigîtudo oK^uot inß^niorut»ßel/arum fi* xarum ai ^rietK/gt;rimafieiiaiamp;la^ titui/o fil gcà/ftica»

jM

Ï

MOTVVM COELE-STIVM, REFERENS DO.

CTRINAM ET CALCVLVM CO-pcrriici,admobiïitatem Solis’, eamquc fequentes Hypothefes,cumnoua demotuipfius terrae fen. tentia amp;nbsp;hypó.

theü.

ITEM DE VERAQJANTITATE iinni trepici,eiu}^ correiHone,quo baclenm ReJpubluit Chrißiana v/a eft. cum noua antà ciuilûforma, qua à ver o tropico natur ah quam mnimu mfimper dif-crepet.

QVIBVS ETIAM ACCES, utifagogcadAftronomiam,Geo- , metriam, amp;nbsp;Horolo. giographiam.

%^ur^ore T^oiili yiro,?). ,gt;merro.Lfa^ ninoaè f^kraieHo,/. K. f)o£fori , , amp;^ar/;emaaco.

COLONIAE AGRIPPINAE*/ -r

ApudGodcfridumKempenfexil,' nbsp;nbsp;nbsp;/

Aiuw.M^ p. LXiVU^ ------' nbsp;nbsp;'

AD ALBERTVM LEO-'

NINVM I.V. DOCTOREM,

GENERE, DOCTRINA ET VIR-TVTE NOBILE M.

ANDRE AE PAPII

GANDENSIS.

DOHa, Cojfernici/ dederunt qui firipta, laborefi Vel ndtffe,al^'sgloria iujlafuit.

/^in,multütievi/aqutdeni:pars,cunéla nouantem, Mir art potiüs quant valuer efequi.

Keef as eß aliter, Quü enim ingredient thus audaxe Pralata obfiurum luee apertret her .•

Pedderet aut cala motiu ; w congrua return Naturafiant magna reperta viri ;

Te prater ? Nee vero etiarn ( cede improbe liuor')

Te prater,tanto par apert vUus erat, Alterte,interpresfatt quad fi/dera voluunt:

At que idem earth vtiice S oer at h is.

Non te ego nunc igitur ( quan quam bac quoq^ maxh ma) laudem. Aut lußa penitus templafitbifie Dea .• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;'

Sermonum voces autperdidiciffe duorum-, Dum Gallos lufiras,Italiam^grauem. ’Nobihum hts,equtdem,/üperaßt tgnobile vutguss , Attala humanit altt'us,illa locant.

Coloniae Vbiorum.

M. D. LXXYII.

SEkENISSP

MO PRINCIPI AC DOMING, D, NICOLAO TONTIG, DV CI V ENETIARVM Toti^ue Venctæ Reipublicxpotentifsi-mae, Albertus Leoninus foclicita. tem perpetuam;amp; S. O. P.

^gnaßm^er/ni^ in Kumanoge nere ojgt;inio}iu,Jèntenriarü amp;nbsp;tUi^i cij i/iuer/it^rem J. 5°. quot;^agnatn ifem;^otlorum y^i^ e^e/re^uen tiam amp;im^uitateni: noei^imum, atleo^ue ni^il mirum ei 'viderifiore/i:^^ (Itßm

ßionem ingenij, amp;nbsp;circunßßts i^ß cor^or^ te^ ntèrasß)ß(unl^ue turlas,amp; natura cor/rorea yarietatem^rauam^ue indinationem, rede txjgt;en(/ês, /udicium inßtpremo intededwgra^ duponendum,amp;a certaratione,iancautem ai exadißtma cognitione de/endere conßdera~ uerit.'hJe^ue aut de re nonj^emtus J/erce^t^t yere amp;nbsp;ex certa ratione tudtcart : aut eoru^K ^ua mintmè intediguntur rationemßiri ' ß.Hinc ida^uidem dodorum yirorum di^^

ITISTOLA'

inproutrlij fere confuetueiinent yenerutft:7^f Jftitor y/tra crefidam. 2)e arte non tutrice t niß arti/ex. Cni^ue inßta arte creäenelum eß.Sci-entta maiorem non óalet inimicum^^uàt^ igno rantem. /Jemine imJierjto méUeß imußittf» i^i/erunt emm/'^ientes iUi yiri, ^rtes eße rotum ^uj/Jam ex/i/nriiw memirtt amp;Jim fheiJuf comjpofitum,non aj yno ne^ue y no eo~ t/em^uefeJ à ^luni/tt amp;nbsp;/onpo tembare/erfe ßum, aJcuittf eegnitjonemßne mu/to /aiore, 9xercitatione,y/u,/ierd/gt;ient/iß/ertia,iu(/icij inatur2tate,ye/ e/tuino anima contemp/atiua ^ ajßraßa acurntne/eruenin no/^ofit./iim ^uaiame/iximut tnul/um eße ßne tognitione /ue/icium. ^Ju/tißariam natura cont/ittonemj J^Jagnum^/à/e fu/icio im/e/imentumeßei-’ ^ßm inc/inationem motum^ natura^cuiM /» i/u,nonraro,ingenia areïloßnß» in tranß-uerßm agi,amp; in t/ßsßnßum amp;yitiorum te^ Ke/ratj/roua/ui, continuât. 2Ju//am Jeni^ in-Ifit/ta potior em caufarn, ^uam ß/am ignoranti eim:2/u//am y er à matertam eße a^tioremj^ua erum excel/entiam, cum/gt;ercißien/i /ßßcu/-te coniun/Zam. Sunt autem, yt ajgt;jgt;aret,amp; mmonio P^i/o/ôfgt;/où/acet,^uinÇj a/return ^gnitionemmagißriautes^ amp;tan^uamgra-'lts ininte/Zeßif, Ssn/ui emm yel extenori.

NVNCVPATORTA.

^P^tnferwriirei^rimiim o^jeSaiCxintle a^^^t^ ma^inationem i/ucitur,ex ^ua najatur o^tnio^ yux rurjurn i/t/cur/u yarto examinât a, tra-e^itur menti, ea^ue/u/remam üü manumim-fonens,propria tntcikSiisfacuitatei^ei e/iui-na iUummatione etymon rei amp;nbsp;enar^iam,j!ienè fopnojcit,amp; e^iJudicat.J-its metsijs/anè amp;grit eittgt;uf,ad return /ut^iciaprocei^ere,amp;à corjgt;o-ralts natur te motiéueJe aJJèrere, ammumjue iSr memoria ceÜulamjlurimarum optimarum -^ue return co^nitione tnjiruere i/eèet,^ui re^è amp;nbsp;ex certa ratione jronunciaturu^ erit. Qua feßime conueniunt,cum muit à maxima Z^omi -num Jatte,ouilus nihileßjrochutus, t^uàm te mere ad tuatcandum Jroßlire natura^ue e^x af feuillus induigere. Quafrofter turn ni^defia tam yenißum Jofit e^, ^uod non altcui kkv-fov yideatur.Tdddtam omnièut numerts aiß lutum amp;nbsp;elalgt;oratum,^uodnonßcurrat ca/u-mnias.Solent/èrè ^uifüos laloresinjul/licum. emittere cujiunt,ma^norum yirorum amp;nbsp;T'rin. ajumJatroamoftéi cauerefiasj iucuiratio-nes commendare amp;nbsp;gratiores ettam reddere,^^^^ JtaJ^ amp;nbsp;e^o ciim mea de corre^itone annidui-^r id commentationt Tèeoriam motuum caießi^ ^• ^ ^S^^^^ “^^ *^^^°^omiam, Geometriam^ J amp;nbsp;ddoroio^raj/dam adiun^ere in rem firißi- d

f*J 3 ani *

. nbsp;nbsp;. EPISTOLA

^ni or i^ ej^ ducerem, Qe/ti cireumj^iefri ^ui rumautoritate in j^ro/u^ant^K maieuoiorutn iniurijs amp;nbsp;oètreifarioniéttf 'Vti,mea^^:ri/ra ^ramunire (ir acce^tiora e/ficereJtoj^èm.^e^ tarnen iac Joia aut/gt;rtecijgt;ua,/èel akiormthi cauJa/uie,S.7^,'ygt;( f^, J*. £. eoti^ Keneta ^i-jpul’.^otentißimte/gt;iec %lat/gt;emaaca injcriiie-i re ^e^care^: Ciarißima S.D£X.e/e tuo inge~ aio amp;'^trttitïluf/ama.J/i/a^^ £eneti norntnis ^lateßas^omnes me^j cum/^rimM in/ui ae^mira tionem ra^te,/er/gt;eruo^ reuerentia amp;nbsp;amaril nexit oi/inSos tenet.E^uie/em auü non/ù^i^ dat Eeneforum in reltt!^erenats,yedonjilio^ rum/ruâèfiam, yelammorum mot/erattonem, /iiietn,con/lanfiam/'ortifutiinemiConcorJiamt amp;nbsp;ynieatem. Qua tnter omnes yna 7Q;//uE £meta tot tam annd/iatum/uum ßorentißi-mum tenens ,/ummte amp;nbsp;incom/arad/d excel-ientia;,J)rißi^ue/ecult, amp;nbsp;Tamana grauitatff 'Virtutts^ exem/lü re/ert. S/ellata^ clomi amp;nbsp;militia yirtute, amp;gulgt;ernan^tßientia,Gmne moralem//rHe/o/dam com/lellttur, omnes^Ut ^\^/dlo/ci//;os /u/ierat^/am ycro Tuam,S.I^.X quot;yiirtuiê/'ortunaianimi/j hona^^utslàtlf dtgnè ‘ ^tlflrare et enumerarefaleat^Su/ßcif/anè hqc . \, f/nü: ££lSlE^'0rume^é2)£C£'^\c^.ea^/i{nJ-\ ma laus ç/l,à^uelati/lïmfs lauelatü,amp;Serenißi

DKDICATORIA.

fnorum ej^ Pnncijgt;em.7\li/n/aurem ejlyirtu^ ^e,amp; ammijpuic/mtui/tne./cn^uam rai^io ^i-Mntcjgt;uic6rïtHi/tnt4 in i/^um ymuerjum rra/~ /^yi!P}amai!/iitf.Cui}ii/'ama,ytßos }Jgt;ßu^ iani ^afff,a7/icirattra^ir^ amp;^ieuincir mirahürer, ^^^ yero ^ux tn 6oc ülro conanentur à T^i-/ui, /^enecee i/:gmrare aliéna «^ exißima. unael^nam,^ro amjilißimi imperij lange lafe^ /raienßeminenaafferrinet:jgt;erßgt;elh!,^uie île ^nm correUwnelüntirarwniènf,Summa Pan fßci,(ir commum Chrißiam arils yriltratia-peramùrte/iare. Kethßimum ettamfareßero ßuiliaßs Aßranamiteßjfam motuum ceeleßiutn Pleana ex Co/gt;ernici reßieueione ralullsJiru-tenteis conucnieeem,ßguri^,^uamßerijiotuiCi maxime illußratam halere, /ucundißtmum 'Veroomniliis^caliultluiusexcelletiamcagno^ fere^Ù- cum inreriari Pliloß/ilta,Pyrlagara amp;nbsp;fiter aßrfrurte myflertf camp ar are. Prii mum nan^j Quatlexfacrießripeura amp;plila. fophite intime penetraltluspraferri pafir^ Rundum circafepfimi millenarijprincipiumt eneeriturum. f Si y lia maelà lamini nan de die^ ttutlorafèddeykimo/àleem annarum mille-À nario comeHura rehUaefi} yidelieur idem a- 1 ßendere, fellarum ßxarum progreßiis,^ue et^ temper e ad proprium amp;primum ^uadracum fifgt;t^a yff^fßfffätfirH^i^m fotinsjplilafà-

* nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;thaà

; nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Ï 1*1 STOL A

f^ice fignißcare ^o^ùnt.^uater ettam time iff tari/ißtma moru/uiße ü^uet,inßaiit^ ^uareu tneäia^rx/iaci ai /e^uatoreoib^wtas.'Mart ^^0^ j ßcun(iumjgt;/}}/oßojgt;hs iußieia minißerf tue tertiu,regimin^ moe/erälitar /jaienas.Si-tm/iter ^e^uino^iorü anomaliajolti^uitatii l^oe^iaci zir eccentricitat^ Soh^imaxima muret tîo,cuèü e/uoe/enarij,numéro annorü coßiruie, ^uepiato^ernicioßüm rcgni^iimgertjsj 'VrUè, tgt;mnilusi^ßiariliif,muratione^ ae^erre a/ßr-mat. Quorum conteglatio nogarua Zialetßta~ üirate.Ne^ mtnuSiDrßero ae/eQalir,^uori in imne hlellü ira neeeßaria ^Uts^ eSgeßaßnr,ye Juo marte ^uihler ^ßronomiaadire,rotius^ mati'e/eosgußu^ercijiereex eo/loßir. Preere^ tea aut^lat/jematica harmoma ae/eo^^ igß* cif culijym^oltcü c/jaraifere,cui znßtaymraris na tura tegerie^yirrute amp;nbsp;conßenßm animoru,ga ct^ßgf^ißtar,maxime conuemre amp;nbsp;tieieri ße^-netoruPrudentie amp;nbsp;eScore/tee /ue/tco. Quagro-^ter ^uot^mi/n lamdue/üßuir in yon^ amp;ßaeer^ ya/e/e ograut,nunc meos ^oße laborer ammu^ ynà ßrogenßßimu amp;nbsp;Jee/jtißtmum f^. J. e^eeit^ ►co amp;nbsp;àumiürer commeneio,yt^ K S.ßßei/ere uua^ aue/^orttaee c5jgt;le£lt t^gnetur rogo/Deui ^gr.'^lax.KS.^ua e/iurißime coßruet amp;2^rti J/uit^fneratUearur/iergeruo.

Coloniae Agrippinx nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;gt;

Ai^.ij/S.mCöUMaiO,

DE MOTV

PRAECESSIONIS Æ-

QyiNOCTIORVM AEQVA

Ll MEDIO,ET APPARENT! DIVER. fo^eorumj^ quantitate amp;nbsp;cur^ù/erio-i^ico:/tem de motu oi/iquitattsßue decltnatioms equator t^ ^^odtaco.

j^NlTIO fciendum eft edi-Majpticam inter duos Zodiaci polos TŒamp; inipfo 2odiâco media, diui-^Jamene,vt omnes communiter more aftfonomico circuli,in 3 6 o.gradus, fiue partes æquales,quarum quolibet deinde fubdiuiditur in 60 minuta bue fcrupulaprima, eaq; fingularurfum infecuda totidem, fimilique perpetua diuifione fexa-genaria ad tertia,quarta, minutifsimasque par ticulas peruenirtPrçterea eas partes omnes di-ftributas effeinn. arcus, buefpatia circuliæ-qualia,quaEtricenis diftinäagradibus vocan-tur bgna:du6tique à polis zodiaci per hçc ecli-pticæpunda femicirculi.totam fphxram par-tiuntur in u.prædifta x.odiaci bgna: vt omnes ^ hoc modo ftellæ, omnia in fphæra loca cert«^ bgno,graduiamp;minutofubiiciantur. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;,

Horum autem bgnoru initium duobus mot A dis accipitur, vel abipbus aftri arietis primai

A ftella /

THEOM A

yojjjj» ftellafixa, vtfingulafpatiafingula ferc Cort-fieUatus. tineantftellata figna, vtfuntcerta congerie, inquofi- numéro, amp;qualitateftellarum confpicua,vel gnorum ab interfedione vernali,vtprimum arietis pu-®5lt;*®/quot;- âum fitipfumsquînoftium vernum.

prima a- Atque hunc fignorum ordinem numera-ïietisftcl tionemq; Copernicus apparentem zodiacum, la fixa, ilium vocatftellatum.

2odia- Motus autem præcefsionis æquinoétioru eft,quo primum arietis apparentis pundum fi-ueæquinoâium vernum (quodreliqua appa-rentiszodiaci figna eodem femper interuallo fequuntur)àprima arietisftellafixa recedere folique obuiam procedere inuenitur,idq; inæ-qualiter.

Motusobliquitatiseft, quoangulus inter-

tatisfiue feâionis cclipticæ amp;nbsp;æquatoris,diuerfam for. dedina. titur quantitatem, ipfaq; confequenterz,odia-tjonij. æquatore obüquitas fiuedcclinatio vel augetur vel minuitur.

£xquibus fequituranni tropici quantitatem inueniri inæqualem, Hellas autem fixas videri fccundum fuccefsionem fignorum in

auténunc propiùs accedere,nunc longiùsab o remoueri; pro maiori fcilicet vel minori iusdiftantiaà z-odiaco, in quo eandem iplæ itudinem femper obtinent.

Quorum omnium caufamveteresMatbe-X'matici in diuerfos zodiacos, nonâ oûauamq; cœlo-

Mot WM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;a

èœlorum fphæram referre, neutiquam tarnen feopumattigifle vilifunt, adeoq;nequc ipfiim Ptolomçum,neque D. Alphonfum Hi-fpaniarum Regem,aftronomiæ inftauratores huic parti fatisfeciffe.pofteriorum temporuirt obferuata manifeftarunt.

Tandem vero Copernicus- fufficiente ob-feruationum copiainftruôlus.fûmma diligentia omnibus omnium ætatû motibus inter fe collatisamp; examinatis, inucnit, omnem præ-cefsionis æquinodtiorum apparentem diuerfi-tatem fiue inæqualitatem 1717. annis Aegy-ptijscompleri. Ipfamque obliquitatem duplo eius temporis Ipatio femel reftitui.

Quorum ratio per binas polorum mundi librationes cômodifsimè elucidatur,anumptis tjuodneceffum fuit polis mûdi medijs amp;nbsp;ima-ginarijs ad quorum locum motumq; as-qualem amp;nbsp;medium, omnis inæquali-tas reuocatacomparataquecer-tisterminis,ratione, amp;nbsp;cal-culo,po{ret com-pra:hendi.

A z SCHE.

SIt itaquc p. o. q. ecliptica cuius polus n,

D polus æquatoris médius,fuper quo defcriptus æquinoâialis médius fccet z-odia-cum in o. vtilla interfedio fitaries medius amp;nbsp;ionfequenter p. capricorniq. cancri puncta

\ lum zodiaci.ad punctum cancri,vtfit fcilicet

. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;colurus

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;j

Colurus folftitiorum mediorum,in quo,dedi-ftantia polorum z.odiaciamp; æquatoris (quam fequiturmutuaillorum circulorum declina-tio amp;nbsp;interfedio) ftatuendum eft.Sit itaque n. d.media diftantia medium efficiens anguli in-i terfedionis amp;nbsp;declinationis quantitatem.

A.n.maxima b. n. minima polorum diftan-tia.Diuifa autem tota diftantiarum differentia fine areu a. b. in quatuor partes squales fuper polo d.tanquam centro fiant circuli,a.b. tranP ienspermaximam minimamque diftantiam, amp;f.e.duasprædifl:arum partium compleâês, ineiusque circumferétia capto centro f.fuper eo defcribatur squalis ipfi circulus g. h. tranfi-ensperd. polum medium.

Addatur prsterea circulus intortusa.l.d. m.b.r. d.fia.Et ad eum modum conftitutis o-mnibus intelligendum eft, d.polum medium totamqueadeo lineamp.q. moueri circa polum zodiaci squaliter inpraecedentia, contra fignorumfcilicetordinem:vndeçquatorispo-lus médius defcribeteo motu circum polum Zodiaci circulumd.4.5.

Et confequenter interfedio squinodij me dij o.feretur squaliter in præcedentes fignife-ri partes,ftellsquc fixs in contrarium ab g-^r quinodij pundo abire videbuntur plané, vtÄ in eo videre liceatnonæ veterum MathematikV corumfphæræmotum.

Hgc autem gqualis æquinodiorum prg_ ' ƒ• A j cefsio ;

THEOR lA

tcfsiofingulis annis Aegyptijs cóficitin CcH-Oiianti- ptica®—^^-^^’vt totaperiodus fitann.Aegy-aUvo”* ptiÓKÜ a58i6. quorü finguli cótinent dies ^ßf vj,“ nbsp;nbsp;nbsp;nbsp;nbsp;Proindeïpolis medijs ven amp;nbsp;apparentes mOdi poli in tranfuerfum aâidiuerlitatéprç-çefsionisamp;iobliquitatis inducunt.quodcircu-lariter fieri per motum compofitum ex dua-busin diuerfas partes librationibus, hoc modo ofienditur.

Sit h. extremitas axisterræ, fiue verusæ-quatoris polus,eiusque motus in fuo circulo à fummitateg. fupercentrof. femperduplus ad piotumiplius f. incirtuloc e.vel(quodidem eft) ad motum totius lineæd.f.g. fuper centro d.in circulo a.b exempli gratia:fuerlnt g amp;nbsp;h. Imiul in a.indeautem d'^cedcnsf.confccitar-cum,c.f. evi duplus eft g.h. per 19. tertij amp;nbsp;jz. JextiEuclidis.

Vnde fequiturhoc motuipfum h.polum, femper maneredurfumq;aG deorsii reperein linea a.b cuietia lineag.h.femper eritortho-gonalis.

Item obliquitatem mutari,nam polo vero exiftente in a. defcriptus fuper eo æquinoétia-M lis,tranfibitquidem pero feélionem mediam, jtled angulum interfeélioms maximum,maxi-^^mamqueefficiet dechnationem: in e.autem Z Jjiediam, in d.minimam.

-‘. Et ciim globus terrs ea axis fui librationc \ fiinulrooueatur, ciusque medium inter duos . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;?olo^

MOTVVM COELEST. 4 polos, fiueipfe xquinodialis terreftrisfeui fémperfe accommodât cceleftis, vtpofteadi-cemus)propius ad eclipticam inclinet, vel lon-giùsabcafcauertat,fit vtftellæ fixæ refpeâu æquatoris mutari latitudine inueniantur,citiC. fîme quidem amp;nbsp;maxime circa mediam obli-quitatem,vbi velocifsima declinationis eft mu tatio,tardifsimè auté circa extrema, id eft,maximam minimarnque declinationum, nimi-rum,quia xqualibus circuli a.b.arcubus(quos squali tempore d.f.g. linea percurrit) maxi-mi refpondentfinus fiuc partes ex linea circa medium, minims in extremis, quod h. litera fans manifeftum reddit.

Atque hicmotus obliquitatis dicituretia . .

A. r , -r ■ r I- nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Anoma anomaha limplex cohciens Imgulis annisin Uj circuloa.b.LJIiJlL-totumque complens cir- P''’' quot;* O.».I7.1 . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;* nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;r nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tabuli» cuitum annis Aegyptijs ^4^4. quibus h.polus pruteni-aba.maximadiftantia(vndemotushuius ini- cii.amp;Co tiumftatuitur}adb. rurfumque ad a. pci ue- P«®“®‘ niens omnem declinationis diuerfitatemper-agit amp;nbsp;reftituit.

Diameter autem circuli a.b. fine differentia intermaximam minimaq; obliquitatem inue-nitur minutorum2 4. vt maxima declinatio

fit.

media minima

quales circulus magnus tranfiens per polos , . A 4 zodiaci ƒ

T H E o R I A

xodiaci Sc squatorispundaquefolftitialiaha.« bet^6o. gradus.

Diuérfitas deinde æquinoâiorum praeceC fionis hac ratione contingit : nam polus verus tranfiturusexa. verfusb. pcrillam redamli-neam,quod modödiximuSjrefleäitur aliali-bratione extra illam,duciturque in circulo in-tortoexa. verfusl. extremum inconfequen-tia fignorum limitem à medio,amp; interea linea abipïb dufta orthogonalis ad lineam a.b. con tinuèdemóftrat,quantum prior libratiohuic fecundæpermixtafiuemotusobliquitatisde-fcendendo conficiat ipatip

Proinde fuper polo vero in 1. defcriptus æ-quinoöialisefficiet feétionem int. angulum autem talem ac fi ipfe polus efTet in c,

Indeautemrurfum polus verus abeadem femper libratione per intortum circulum duót us versus præcedentia bue contra fignorum ordinem excipitur à concurrentibusfi-mul vtrifq;motibusind. quod fitvbif.g.qua drantemabfoluit, atqueibi omnimodo çqui-noétialis apparens vnitur çqualiimaginario, qui exinde rurfum feparatur amp;nbsp;h.mobile cum Imeaorthogonalitendit adminimam diftan-tiamb.amp; polus ipfedenuó eademrationere-ïBeftiturversùsm. extremum in præcedentia ^.medio limitem vbi defcriptus æquinoétia-^tranfibitperx coq; Ipaciox.o.prçcedit ve-Eaamp;apparensfedio mediamamp;exm* rcuer-tens,

MOTVVM COELEST. , , S Unspolusvnitur h. mobiliin b. minimumq; efficitobliquitatis angulum in feâione media o.quo tempore hçc refleftio fiuelibratio tota peregit equinoétiorum anomalia,fuamq; periodum quandoquidem in vtramq; parte, extremum à medio terminum attigerit. Obli-quitatis autem motus dimidiam duntaxat, vn-dc amp;nbsp;hçc fimplex amp;nbsp;illa duplex anomalia vo-catur.Porró eodemfemper modo amp;h. mobile furfum reuertitur,amp; polus repetit extremum in confequentia limitem in r. fimiliterq; extremum in præcedentia in f, poftque in a, fuum complet rurfus circuitum codé temporis fpatio bis reftituens æquinoâiorum ano-maliam duplicem,femel fimplicem.

Semidiameter autem huius reflexionisin Vtramuisfcilicetpartem,vt c. l.velr.e.Itemc. f.vele.m.inuenitur minutorum aS.vttotafit 56. proximè cui arcus zodiaci x.o.t. relpondcs oftenditur per fphericorum triangulorum do ótrinam^i— Sciendum autem bic eft præfup ponireflexionem fieri in linea 9.8. coluroæ-quinodiorum mediorumtranfeunte per po* lum amp;çquinoétiamedia, apparentemq;çqui* nodialemeum incidereadangulosreétos.ne- lt;nbsp;queetcnim libratio poli extra illum, aliquanj^^ fenfibilemdifÏerentiam parit propter paruita-% temdiftantiæ,quemadmodû nee reflexioc:1^ V tra colurum folftitiorura in quantitate deelt? nationis. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;f \

A s EX hin

- nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;THEORIA

Exhisitaq; liquet cùmpolus in colurofol' flitiorum fimiilq; in coluro squinodtiorum mediorum loco mutetur, id eft.moucatur in longitudinem (imul amp;nbsp;obliquitatcm xodiaci, etiamfedionem æquinodiorum vnaq;decli-nationis quantitatem mutarijllumquepolo-rum motum compofitum defcribcre circula Intortum quern diximus, amp;nbsp;confequenter fe-äionem apparentem velocifsimè moucri circa mediam,exindefenlim tardius, amp;nbsp;in extremis tardifsimè, quia fcilicet refledio poIi à me diofenlim curuiorem lineam percurrit, propter librationem declinationis, vnde æquali tempore minus ac minus femper apparensæ-quinoéliumà mediopromouetur.

Liquet etiam non itodiacum,quod vetcres mathematici exiftimarût.fedequatoré mutari.

Præterea fciendum eft, Copernicum huic terras motui fecudum Nychthimenon fiue re* uolutionem diurnam anneâere,quam nos fir mamentotribuentes,folumq;çquinoftioruni præccfsionis amp;nbsp;obliquitatis motum tardifsi-roum in terrç globum referentes præCupponi-mus, quodneceffum eft polos reuolutioniJ firmamenti,fiue digitos motricis virtutis fc-jqui polos terræ apparentes, vbicunq; hi ima-V^inatione vtrinq;produâi cœlum fteHatum ' contingunt, illic etiam vt videantur polifir-*ƒ 3^amenti fiuepunéla fuperquæ totaceeleftis ;»*^ (phases lingulis 14. horis circumuertitur, fie • ’ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Ytelt;

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«

Vieadrculuminccelo intortum ßmilemque terrae conuerfioni defcribant,amp; confeqiienter aequinoétialis coeleftis femper refpondeat ter-« rcftri.quæomnianaturaliter fieri pofTunt et-' iamqüecirculariter: vt fi ftatuamus terrain in paruocirculo æquakm præcefsionem, reli-qua vero omnia fuper proprio centro perfice-re Item centrum cii culiintorti coeleftis ferri circulariter fuper eodem axe parui circuli, qué diximus.alijfque modis à naturae præce-ptis amp;nbsp;rationibus minimè alieni s, quos hic referte haud neceffarium duxi. Quid enim fi-mus ingeniofi in re, quam certo cognofcere nemomortalium poteft, velquorfumdctu-cnda aequalitate amp;nbsp;cyclopaedia motuum cœ-leftium,laboremus curiofiùs?neque enim Dei omnipotentiam Ariftotelicis argumentis cir-cumfcribere fas eft, nee return diuinarum per feétionem amp;nbsp;excellentiam humana rationc 4 nbsp;nbsp;nbsp;amp;nbsp;iudicio metiri, fed diuina mente intueri dc-

cet: fufficit enim quod omnes Aftronomicae Hypothefes potifsimum fpeftant,vtcerta nu merandi ratione motus coclcftes fupputarc li-ceat.

Ego porto fimpliciter ftatuo, quod ita fe habere omninócredibileeft.globumterraBi * in medio mundi fe conuertere lùpcr proprio C centro, amp;nbsp;tanquamaxe Zodiaci, inclination^ , vero vel cardinum adminiculo fieri amp;nbsp;polOT aequatoris terreftris tendentes inpraecedentia ' lignorqna •

T H E OR I A

fîgnorum defcribere circumaxemzodiacicip culum contortum, polosque reuolutionisfir* mamenti obferuare motum polorum terriB, £imilesq;circulos efficere circum polos zodia d, quavnica trtrçcouerfione diuerfitatéob-liquitatis amp;nbsp;prçcefsionis çquinoâiorû iam di-étam fentiamus,nam quod aliqua difcrepan-tia in velocitate amp;nbsp;tarditate motus obliquita-tis(fi çquahtatem tueamur} videri pofsit,facile excufat multifq« rationibus paruitas diffe-rentiæ declinationis fummaque motus tar-ditas.

JSfO r^^ m T’ o THE SIS i^E^ ^race/sto a^uinoSfïorfim ina^uaii^ amp;nbsp;om^uL tadó ^^odiaci a^ a^uatore diuerßtas de-mot^iratur per motum terra.

NA m i. eft polus zodiaci circum quem po-lus terræ amp;nbsp;æquatoris verus a. per con* ' ^^ uerfionem terræ defcribit circulum contor-

tum

MOTWM. COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i

tüab.l.f.h.o. qöomotupuda xquinoöialia ferunturin præcedentes figniferi partes,fci-licetcontra luccefsionem lignorum, amp;nbsp;obli-quitas etiarn mutatur,cliuerlïmodè, nam aba. vfque ad medium in m. praecefsio æquinoftio rumfcnfimaugetur.Inderurfum fenfim mi-nuitur vfquead b. acrurfum velociiisprocc-dit vfqueadmedium,vbi velocifsimè vtantea procedit, poftquein 1. fummam rurfumcqn-fequiturtarditatem, quemadmodum inb.amp; a. amp;nbsp;fc perpetuo. Interea auté obliquitas mü-tatur,nam maxima polorum zodiaci amp;nbsp;sequa-toris diftantiaf.c.cft.2^ 52.minimai. c.23.28. differentia c. fminutorum 24.

Polus autem fpatia illa fingula,fcilicet,ab a. ad 1.amp; deinde ad f percurritannis Aegyptijs 3434.quibus omnis obliquitas femel reftitui-tur, à maxima enim adminimam, amp;nbsp;rurfum admaximamtranlit, æquinoâiorum autem praecefsio fiue procelfus bis binas intercadi-uerfitates,fcilicet velócitatis amp;nbsp;tarditatis per» ncit:promouetur autem interea—■-—,: Fuit autem polus tempore conditi mundi in o.ten-dens verfus a, amp;nbsp;b. nunc autem eft circa n.pun óum autem aequinoöiale hoemotu totüzo-diacum circuit annis Aegyptijs 25816. fuumq; * . circuitum finit polus in eadé obliquitatis quä f titatcin o.fed decrefcente quæ ab initio crèfc^ bat. Hicautemcirculus aequaliter inlèredic inftar ferU context!,vel fpince corons 30. an- , salit •

i . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;THEORlA. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;.

gulisobtufis æqualibusnotabilisjfpatîo atinö rum Agyptiorû$i5io. num.multismyfterijs^ hauddubièapud Pythagoricos admirabili.

Prædida autemomniavt in plano reftè delineari nequeunt : Ita in fphæra folida circi-niopefacilliraè confpiciuntur. Plura veröde bis qui volet confulat libellum noftrum^qué jn gratiam amp;nbsp;honorem doâifsimi viri D.Pie-|. riiSmengaj'^feiroris Hebrçi in Academia 1 Louanienfi,noftri amici editum inferipfimus Commentarium in doétrinam præcefsionis xquinoétiorum amp;nbsp;obliquitatis zodiaci,ln quo omnia ad hanc materiampertinentia, adeoq; minima quæq; Mathematicè perfecuti fumus»

Porrô emendatam hiftoriamobferuatio-num^quibus hæcdoârina fundata eft,appone rc operæpretium duxi,eftquetalis.

/-ii/loria oljèruarionum-

Timochares Alexandrinus à morte Aie-xandrimagni,ideft,à primo die Thoth primi menfis Aegyptiorû pofl: Alexandriinteritum annis Aegyptijscompletis nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;jo.

Inuenit fplcam virginis elongatam à folftitialî

•• ^ . Item ftellamè tribus in fronte fcorpijlucenti-

* K bus maxime Boreamprimamq; in ordinefor-

* mationis iftius figni ab autumnali æquino-

,' 4 -fcc__Ü

Idêrurfum Timochares 12. annis Aegy-

,. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;MÖTWM COOLEST. nbsp;nbsp;nbsp;nbsp;nbsp;«

ptijspôftinuenitfpicâprçdiâani abæftiuo fol fiilio diftare,----■ JLÜ

Obiter aüt hic addendû putauiquod adob-feruationes Timocharis attinct,prioré illam de fpicafaâS eiîep. die martij fecundû Romanos. 5,aûttybi fecundû Aegyptios,fcilicet vl_ traannoscópletosdiebusi24.amp; 8.horis poft Alexandri mortêjprçdiâæ verôfcorpij ftcllae locü obleruatû fuifle id.Phaophi Aegyptioru, ii.autê decemb. fecundû Rom.amp; à morte A-lexand.diebus 4$.horis i$. vitra ann. côpletos. Hipparchus anno ab Alexand.morte i96.poft Timocharis priorê ann. Acgyptijs ilt;56.reperit bahlifci leonis lógitudinc à folftitio fftiuo-Ul*

Menelaus Geometra Romanus annisAe-gyptijsàmorte Alexand 421. amp;nbsp;diebus 1^4. fcilicet 15.mechir Aegyptioru, 10. lanuarijfe-cundum Romanos pon: Hipparchum annis Aegyptijs 226. viditfpicam diftare àpunéto aeftiui folftitij---

Ptolomçus annis 4()i.diebus 2i9.poft morte Alexandri,poftMenelaûauté annis 40. die-bus 55.offenditbaf)Iifcum leonis à folftitio æ-ftiuo----^—Ü . 1

Prçdidam korpij ftellam ab autumnaliæ- r

quinoftio— quot;---------

fpica virginis à cancri folftitio

THEOMA

^lahometuî Aratcfisüue Albatcgniusà morte Alcxandri annis Aegyptijs uoj.cópletis cir citer,poft Ptolomçum annis completis 741 ob fcruauitlongitudinem ftellæ fcorpij abautu-

niaequinoöio--„llJïk

7- 50-

Bafiliciafolftitio nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;44.0. Copernicus anno Domini 152$. poft Alexan-dri mortem 18490. Aegyptio,poft Albategnij autem obferuationem annis Aegyptijs completis 645. deprçhendit ïpicamJprincipioli-

brae--^L^’ proximè

17. it. ‘

Similiter cóftatdeobliquitate,naPtolomguï earn inuenit--—--

U 51.10,

Albategnius nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;25 jy.

Poft quem annis 190. Arzahel 23.34.

Propbatius annis 230. poft 23.32. proximè Copernicus nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;25.28.24 circiter. Cùmitaque à Timochare ad hodiernum vfquetempus annis 1870. hjedodrina cófta-reinueniatur.vcrifimileeft amp;nbsp;æqualem mo-turn verèalTumptum, vereque squinodioru præcefsionis fupputationi in omne tempus eP fèprofpeélum.

' • DE ^10D0 ET \^T70N^ Z^/’/'^i^^^^i oiti^uitatem amp;nbsp;te^uinoSfïorum ^ /rteeeßtonem ex taiuii^ /frurenic0.

AD calculum obliquitatis pertinet fcire maximam proftaph«refin fjue «quatio-• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nem

MOTVVM COELEST. » hem inter mediam obliquitatcm amp;nbsp;minimam vel maximam,fcilicet areüm töluri folftitialij d.a. veld.b.effeminutorum iz.eaque totacir cumferentiéportione a.b. vti licere,tanquam linea reda citra fenlibilcni errorem propter paruitatem.

Itaque in tabulis diuifa, fecundum doârû hamfinuum l eélorumtota vtrinq; æquatioi netanquam femidiametro incirculo a b. per motum anomaliç fimplicisfqui à maximçdi-ftantiælimite,fcilicer aba. incipitjlcitur quantum æquatio bue differentia à medio vel ere-feat,vel decrefcat, quautumq; mediçobliqui-tati in fuperiori femieireulo addendum, amp;nbsp;irt ^nferiori auferendum lit.

Adprscefsionis squinoétioiüm fupputâ-liönemintclligcndam lit in hóecireulod.l.nl.

L.a.m.portioèelipticr,a. fedio mrdijæ-. ’ quinoat ij, amp;nbsp;huius cireuli ce itrum,quod per motum poli medj æqualitcr femper dueirur cumtotoeoeirculo in prgcedentia lignorbm^ fcilicet verfus mi

B L.e«- J

THEORlA

L.extremusin confequentia fignorum Cd ftionis limes.

M inpræcedétiaextremus.

D.a.c. defcendens à polo z,odiaci fecanfqi drculum bifariam.

tota afit La. m.oftefa eft ante ergoeius medietas——■■■^' ^'eft maxima

“ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;71. li^O.

Vtrinquesquatio inter medium amp;appa-gt; rensasquinodium, quaetiam vti licet tanqua linea reâa. Ponatur itaque,motum duplicis anomaliaecircumcurrerehunccirculum arqua liter,amp; incipereà punétod.amp;fecundumeuui motumapparensæquinoétiû difeedere à medio in vtranquepartem, rurfumq; accedere, Ita vtreélaàloco motus demiffalineaortho-gonaliterad diametrum circuli femper often-datfeétionemapparentem, amp;nbsp;arcus eclipticæ inter mediam amp;nbsp;apparentem feótionemipfa fcilicet prçcefsionisæquirtoâiorum aquatio tio præ fitfinus redus circumferentiç huius circuli, cefsionir anomalaris à medio vlque ad locum motusï iquino. exempli gratia a.n, æquatio, quam dat motus ,ftioium d.p.en etiarn eiufdem arcus linus redus.Itaq; ** ^ huiuscirculidiametro diuifa fecundum do-• ,|ótrinam linuum redorumfquod apparenslê.» dioinfuoamediadifcelTu eiufmodi ferère-_ , gfilam vel proximè feruare inueniaturjcon-^ ihtutæfuntin tabulisïquationes.

' • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Proindo

MOtWM COELEST. r«

Ï’roindein d. apparentis squinoótijleéiid vnitaeft, æquali liuemediecùm pollis verus edina. p^cedentis xquinoâiorum fchema-tis, ex.d. verö procedentemotu anomalie in-cipit æquatio crefcere, donee motus cord'eâo quadrante,fit in l.lîmul cü veriæquinoâij fe-Ôione,amp; polusetiam in Linde fenlim minui-turæquatio,donee eófedo femieireuloinc. amEgfeéliones rurfüm (int vnitçin a.polufqj fit in d. amp;eodeni modo fit maxima aequatiö in m.poloetiamexiftentein ni. denuoq;tota euanefeitin a. vbi motus hiepcrado eircuitu eft rurfiim in d. ipleque polus in b. vel a.

Supputatisigitur ex tabulismotu præceP fionisxquali amp;nbsp;motu anomalis fimpliciSjde-inde ea anomalia duplicata, habetur locus poli in circulointorto,amp; motus anomaliç in cir-culoxquinoéliorum d.l. m. cum quocapituv prodaphçrefis fine æquatio pixcefsionis æ-quinoóliorum,qux vtante lêmicirculum du-plicis anomaliç aufertur æquali præcefsioni, (quæ tamdiu maior eft vera) ita poft Icmicir-culü contraria ratione additur,vt verus amp;nbsp;ap-parens motus amp;nbsp;locus prxeefsiohis æquino-dij à prima ftella arietis habeatur.

Lx quibus omnibus iam notandum eft,toto huius motus fuperiori femiclrculo fcilicet ab m. per ipfum d. ad 1.amp; in prxcedenti iqui-w hodiorumlchemate quadiupolus verasten dit ab Cad L yelabm.adr. quod idem eft, ap-

‘ Ba parenteqgt;

T H E O R I À

parcntcm feftionem ferri contra motum mègt; clium,vnde cùm femper ipli aliquid demat, inucnitur præcefsiô tardiùs procedere, tai diC Cmèautem circa medium, vbi apparcns motus æquali tépore maximas medio motüi partes adimit,exinde fenfjm minores, adeoq; circa l.amp;m.cû apparcns nihil,aut vix fênlibili-ter promoueatur, fitvt æquinoétiorum præ-cefsioaliqu3diu æqualem amp;nbsp;mediam quanti-tatem obtinere inueniatur. In inferiori vtro femicirculoab 1. ad in.amp; in prçcedenti çquino éliorum figura etiam ab 1. ad m. vel ab r. ad fi tendentibus vtrifquc motib.in eandem parte præcefsiô velocior fentitur, amp;nbsp;vclocifsima quidem circa medium vbi apparens motus æ-quali maximas partes fuperaddit.

£x quibus lequitur d. in hoc poftremo cir culoamp;in pramifla æquinoôtioium figuraa. vel b efle fummç tarditacis çquinodtiorü prç-ceßionislimitemjexinde lenlim crefcere çqui nodiorum motum, amp;nbsp;in I. çqualem confequi quantitatem, deinde fummâ velocitatcm in c. cui refpondetin prçmifla figura d. tamq-,fum mam velocitatcm rurlum definercin æ.^ualfi tatem in ra. quç denuà tranfit in fummam tar- , ditatemind.

Preienti autem hoc temporc motus anoma Jiçiimplicis inuenitur in lecundociiculiano-malaris quadranteg.b prope b. minimaqu« obliquitas hoc noRro feculo futura ell amp;nbsp;fum 1 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ma sequi-

MOTVVM COELEST. inasquinoótiorum prieel ionistarditas.

£x quibus omnibus liquet annitropici qui tkatem eandem ferè nunc eire,qui amp;nbsp;tuit tem poreTimocharis,Hipparchi amp;nbsp;Ptolomii.

T/^eoria motm Sa/i^.

Cum fummiaediuinifsimi illi Philofophi primicœleftium return inueftigatores mira-bilem diucrlltatem amp;: iniqualitatem planeta-rum pei uagationibus inelle depi ihendilient: Illudin pi iinis negotij libi mcumbeie exi-ftimar t,vtin eorum txplicationecircularem motumjanquam perfeétifsimum conuenien-tifsimumque.perfeétilsimis cotporibus vbiq; conferuadoipfam iniqualitaem àcœlefti per-feélione omninó alienilsimam legregarent, certifque rationibus amp;nbsp;limitibus, quoadtius fieri pofletjConcluderent.Itaque quotquot vn quamadtradendam poflt ris Phenomenódo-ótrinamanimum adieceiunt.omni indullria omnique animi intentione quammaximèac-commodatasei rei Hypothefes excogitate amp;nbsp;exCeometriç incxpugnabilibus argumentis depromere ftuduerunt.

Etprimiim quidem in Sole lïmplicifsiml, alioquin inter omnes planetas motus cum liquidé tarnen pateret eum ecliptiççfemicircu-losadamufsim int r Ie squales msqualiter , percurrere boreü rcilicettardiiis.auftriini ve * rovelotius: Seniel preterea in anno ad lum-

B j mum

T H K O M A mufnaliquodfaftigiumà mundo longrfsimè afeendere, idqueipfuracontingere infepten-trionalix-odiacifemicirculo femel, ecôtrà, v* biadpundum oppolitumin auftraUmedietî^ te veniret, fieri terræpropinquifsimum ex di-uerfaapparétis corporis Solaris diametri ma-gnitudine exploratum haberent. Statuendum elfe euidétifsimè fenferunt, ferri Solem in circula terrae eccentrico, fuper cuius centro ipfe motus per fe conftanter æqualis, ad mundi tarnen centrum comparatusinçqualis,acçquali tempore inaequales zodiaci arcus pertranfire viderctur, maximos quidem circa perigion, - punâum fcilicetcirculiecccntricipropinquif” tû au”» frnumterrç.minimosautécirca apogion fine Solis. ’ augem,punâ:um fcilicet circuli Solaris à terra Aux So. rcmotifsimumiquæ duopunâanota redditli b* nea vel diameter mundi per centra terrç amp;nbsp;ec centrici produâ:a,quam lineam apogij vel au*, gisappelkrelicet.

Proinde diftinguentes inuicem hos motus, ilium quidem çqualem medium, ad quem re-uocareturalterinçqualis amp;nbsp;diucrfus,quem ap parentem motum dixêre.

^ Sciendum autem eft, lupputationem roo-tuû Planetarum inlongitudinem, initiumfu

•1 mereàprimaftellaarictisfixa.

, Prætcrea,quôdlocus Solis médius in zodia-._ nbsp;* co demonftretur per lineam ex ccntro mundi

’•» nbsp;nbsp;nbsp;paraUelam ci, quæ ex centro, eccentrici ad cor-

‘ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;po“?.

pens Solaris centrum du eta illudcircûferrcin fuo circula vidctur.

Médius etiara motus Planète eft arcus zo-dipci abariete ftellato vfque ad earn linea mun d(,fecundumfuccefsionem fignorum.

Apparentera autem locum oftendit linea ex centro mundi, per corporis Solaris centra ad zodiacum protraâa, motufque Solisappa-rens eft ab ariete ad eum locum.

AtquePlanetaexiftente in apogçovelpc-rigæo eccentrici,duo illi prxdiéti motus,vnu$ funt, coincidentibus tune lineis ex centro mü-di,amp; eccentrici in eundem zodiaci locum,aliàs verofemper différentes pro quantitate arcus Angu-Zodiaci,quern angulus ad centrum terrç inter lu^æqu* duas mundi lineas, medijfcilicet in zodiaco amp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;p

apparentis loci Solis defignatrices compra;hen dit,cui angulo squalls etia eft ille angulus que eccentricitasfideft, diftantia centri eccentrici Angul» in linea augis à centro mundCefHeit ad centruefeentrL corporis Solaris inter lineas müdi amp;nbsp;eccentri- f‘t3tis Cicompræhenfura. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;f“™’*«»

Atquearcus xodiaci praedidtus fine differentia inter æqualem medium amp;nbsp;appai entern ^jqyj. inotum,dicitur çquatioorbis, incipiens abaotioorbi» pogiofenfimaugeri, doncclol veniatadlon-in ^|^j^ gitudines medias, quas hie intelligemus pro duobus pundtis circuli eccentrici,qua: linea ex nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;*

centromundiperipfamlinea augis orthogo^, Sahter, vtrinqueprodudta dénotât. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;• •

B 4 Wic f •

T H E o, R I A

lUic autcm exiOente fole^ac in zodiaco quit ^em apparente meuio inter apogion amp;peri-gion loco, maximus æquationis angulusma-^imann confequentcr æquationem facit, qu« ex eoloco rurfum decrcicit,donccin perigæo, vnitislineis nulla proidùs fiat,inde in alterofc inicircuload longirudinem vfq;mediam dc-ftuöcrefcens.pollea minuituramp; inaugeom-ninô euancfcit.

At dubitabit hic aliquis fortaffe, cur mediu pîanetç motum terniinctlinea ex centromû-di,amp; non potiùs ex centro ecrentrici,quæcir, CumducitSplem æqualiter. Præterea quo patio angulus eccentricitatii fitæqualisangulo squationis. Ad quç feiendum ell,quodcùm Sol fuper proprio cetroæqualesin fuocircu-loarcus çquali tempore pertranfeat,neque id pofsitlimul fuper alio centropræftai e.lineam confequenterex centro eccentric! delignare æqualcm motum in eccentrico,fed in zodiaco limul non pof t: inquocùmneccf elit eum feire.opus fuit linea ex centro mundi paralic* la.quætantumfemperin z-odiaco peragratæ-qualiter,quantum linea eccentric! in eces ntri-ço, turn squales femper angulos ad centrum quæq;iuum,cu linea augisconflituentes,pro-pterarquidiflantiam, æqualesetiam (iuelimi-lescirculoi um arcuscompraehendant. In has /lutéduaspaiallelas incidenslinea mundi per corpus folareprqtraöa facit angulos squales, eumfcili-

MOTWM COELIST. q çum fcilicet,qui ad centrum mundi comprae. hendit equationem, ei qui centrum corporis folaris à linca eccentrici, amp;nbsp;linea mundi conti-nttur,refpondens eccentricitati Gue tertio i-llius trianguli laten. V ndè apparet çquationes inter medium amp;nbsp;appaiétemmotumSolislern per fe habere,iuxta quantitatem anguli eccen-tricitatis,vtdiximus.

Schema /raiii^oruni.

B.o c.ecliptica,Guezodiacus defcriptusfu pcrcentro mundi a.

E.f.t.circulus cccentricus folis, in plano e* clipticæ,cuiusctntrumd in eoq;apogion hue aux e pengion f

B.c linea augisdemonftransinzodiacolö-cum apogij b.pei igij c,

B $ O. arietis.

rH BO RI A

O.arletis ftellati principiumàquo cakulul incipit,amp; motus verfùsconfequentiafignorû.

T.locus i n eccentrico, vbi tunc eft SoI,cum linea medij motus a. o, fempçr æquidiftansli-neçd.t.cftin ariete:amp; hçduælincçfemperpa-ralleJg xqualitcr fcrûtur,vnainzodiaco,altera in eccentrico fingulis diebus----- o nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;o.! 9 8.11.

qual iü totus circulas habet gradus j 6 o. fem-perq; tantum diftat corpus Solis in eccentrico à principio motus t.quantum linea medij motus in zodiaco à principio arictis, ftc vtt. fit tan quarries eccentrici.

t.1. amp;nbsp;f.q. arcus squales, quos Sol squali tempore percurrit,quibus refpondcnt b.r.c.i. arcus zodiaci inæquales.

P. f. longitudines mediæ.

D. p.locus Solis in longitudinc media.

A m. locus medij motus tune in z-odiaco.

A.n.linea apparcntiç,demonftran.s locum 8( motum apparentem à principio arictis.

N.m.çquatio inter jqualc mediü amp;nbsp;apparenté motum hic maxima,quia continetur maxima æquationisangulo n a.mlt;cui equalis eft d.p a. angulus oppofituseccentricitat.dgt;a. tertio latere ifliustrianguli d.p.a.

Ex hisautem liquet, qu5diuSolabaugeeC' centrici non confecit ftmicirculum,anguluin squalitatise.d.p.maiorem effe anguloappa-(entigb a p.pro quantitateanguli æquationis

MOTWM COEIEJT. nbsp;nbsp;nbsp;nbsp;nbsp;lt;4

fiuc eCcentricitatis d. p a. mediumque motii ciïemaiorem, Huediftantioremà luoprind-pioquaapparens:contrailum autem euenirc poft femicirculum, quapropter in priori xqua tio fubtrabitur çquali motui, in pafteriori fc-micirculo additur, ad habendum verum amp;nbsp;ap parentem locum.

Patet etiam Solé ideo diutius hçrcre in me-dietate zodiaci, vbi eft eius apogion, quia ma-iorem illic circuli fui portionem percurrit quâ in altera.

Prxterea notandum eft, Solcm circaaugern apparere tardifsimum, circa eius oppohtum velocifsimumjntermedijscjue locis medium: nam cum æqualesmagnitudines, fecund um opticam rationem,quô rcmotiores.eö videan tur minores, amp;nbsp;fub minori angulo,ideó appa-rcns motus circa apogium çqualitemporeæ-qualibusque eccentrici arcubus minimoszo-! diaciarcus exhibet Inde veröfenfim maiores, donecin longitudine media equalis medij mo tus quanti tatem omnino adfequatur. Inde autem fpeöantibus medio amp;nbsp;apparent! motibus rurfus ad coniunâioncm,angulus aquarionis contrahi,ipfeapparens motus maiores fubin-de zodiaci arcus çquali tempore percurrcndo, nbsp;nbsp;*

ipfam medij motus quantitatem fupcraro « pergitvfque adperigium, vbifumma veloci tas,quæ deinde in mediam amp;nbsp;circa apogium in fummam Urdit^tem tranfit. ' nbsp;nbsp;nbsp;nbsp;nbsp;,,,• ’

THFOMA

Exquibus manifeftum cuadit çqualc medium motum, amp;apparenteniinapogioamp; pe-^•igio, vnitosloco maxime tarnen quantitate interfedikrepare.côtràin lógitudinibus me-dijs maximo locorum interuallo d’Hunttos# quantitate nihil aut jnfenfibilittr differre.

Item tota æquatione difti ibuta inæqualia circuli fpaiia,ab apogio ad longitudinem me-diam,ac deinde ad perigion maximas eius par ticulasjiuedifferentias obting re, circa auge amp;nbsp;oppoiitum, quibus d fferentijs apparenna arquai itate minorell,ab apogio quidem ad ló-gitudinesmédias, rcliqua autem circulipor-tionemaior.

De motu ajgt;o^isi Soi^,

Aux fiueapogion folare, quodPtolomço fixum videbatur, polka pleriqut Mathematu ci ahj aliter ferricompereruntjandem Copernicus lummus ai tikxcollatis interfeomnib. pmnium temporum obferuationibus,deprae-henditapogium non folùm per motum pras-çefsionis acquinoCtioru poftponi, vtetiam o-

mnia Ikllata ligna led prçterea proprio quo-que motu in lignoium conlequcntia abire, çumquemotiidiuerlimodè nunc augeri,nunc minui,aliquando etiam in prçcedentia hgno-fum omnino conuerfum,certos tarnen amp;nbsp;prf-^nitos limites non excedere.

' Pqdpolitio autem,que fit per æquinoâio-•• run»

MOTWM COELEST. i^ ïum motum nihil hic facit ad noftrum caku-lum,qui nimirum incipit ab 3rietefixo,fedcl proprius motus locum eius transférât in ftella tozod aco,qua tranOationem lequiturmuta-tio æquationis lingulorum locorum,Item lori gitudinum mediarum quadrante femperzo-diaci à vero apogio diftantium,maxime is nobis conhderandus tft.

Huicautem proprioaugis motui annexant inuenitCopemicusmutationem eccentricita-tis Soli5,nó minus Icitu neceffariarn ad cogni-tionem veri loei Soils,quâdoquidem eiusdi-uertitatem diueifa neceflario (equaturanguli æquationis quanti tas, mutato etenim triangu-11 vnolatere, mutaturamp; angulus eioppolitus.

Porró leparato rurfum medio æquali apo-gximotu abapparenti diuerlo , vtcrq; vnacü cccentrotetis diuer(itate eiufmodi pulchef-fima Hypotheb demonftratur.

Veclaratid

•4

Declaratiofchematis.

L. m. o, circulas zodiacus, cuius amp;nbsp;mundi centrum d.c.minima diftantia centri circuli ec céntrici Solisd.b maxima eccentrotes.

B.c.igitur differentia inter maximam mini mamque eccentricitatemjn cuius medio a.cc-trurn eft eccentric! medij, amp;nbsp;imaginarij p.q.r. amp;nbsp;per hoc centrum a. linea ex centro mundi tranfiensdenotabit femperapogion medium fiueæquale, quod hic eft in o.

B.c.paruus circulus fuper centro mediae ec-centricitatis a. tranfiens per maximam mini-taamque à centro mundi diftantiam.

Intelligendum iameft, totam hanclineant, d. a.o. cum æquali apogio amp;nbsp;eccentrico medici JJgt;aruoquecirculo duci æqualiter fuper centro • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;mundi

Contrà vero centrum veri apparentis amp;nbsp;mo bilis eccentrici f.n.t. moueriin circumferctia paruiirtiuscirculij primumin præcedentiaeo modo,vt cum fuerit in b.tunc maxima etiam appareat eccentricitas,ap ogiumque medium, amp;apparens (inteodem zodiaci loco,cum linea mundi per vtriufejue eccentrici medij amp;nbsp;apparentis centra tranleat.

Atexhoclocoincipiunt fegregari, amp;nbsp;medium quidem apogium in confequentia tendit vt diólum eft,b.autem centrum apparentis in fuocircello incipit defcédere vcrfiisg.inprjx cedcnti3,amp; per locum ipfius b.duüa Imea mu-di ofteridit augem veram amp;nbsp;apparentem,ab-d'-iélamefTeinprçcedentia fignorum, diucr-famque ab atquaü partem, fimulque decreuiC. fe eccentroteta : proindc vbi b. venerit vfque adIocum,vbi lineaaugis apparentisexcentro fcilicttmundi edufta , contingitcircclli peri-pheriam. non fccat quod bic fit ing.tunepræ-difra linea oftendit eccentricitatis apparentis c]uantitatcm d.g. amp;nbsp;locum apparentisapogæi in m.amp;. o.m. arcum cclipticç,maximam æqua-tionem inter squale amp;nbsp;apparens apogium-^' circiter. Inde pergéte b. versùs c.minuitur rur fumsquatio,tiamd.m. incipit regredi versus o.incoofequentiafecandoparuura tirculum ioau

THEORIA l^onecij.conftituto inc. minimaapparcatec-centotes d.ciunftifquerurfum apogijs medio amp;nbsp;apparéti nulla lit æquatio.Indeb.tendit ver sùs h. amp;nbsp;linea mundi fecante circulum.crcfcit tccentricitas,itemque æquatio,donee in punkto contadus fiat maxima vt antea,fed in con-fequentia,ac deinde minuitur donee perafta eapcriodoin maxima rurfum ecc-ntricitate iungantur eodem amboapogia loco;

Atque huius motus in paruociiculopenö dusabibluitur eodem temporis fpatio,quo amp;nbsp;motusanomaliæ obliquitatisjiuedeclinatio-niszodiaci ab æquatore, annis fcilicet Aegy-ptijs 5434. feque hi duo motus ad inUicem ha-bentæqualiter vt maxima exidente interlè-^ionis eclipticç amp;nbsp;xquatoris angulo maxima^ quedechnatione maxima etiam fiteccentrici-tas æqualiter deinde ambo ad minimam rur-fumquead maximamt ndunt.

Diameter autem huius parui circuit ftatui-tur partium 9510. qualium lemidiametcrec-tentricifolisefiioooooo.amp; minimaeccentrö tes earundem ^irpo.

Porro ex præferipta 'figura liquet quod cd -angulus h.a.i ïequalisa.i d anguloæquationis, compræhendatarcumk i.eccentrici h quadrate vfqucad longitudinem med'5,femperpun-étumlongitudin s mediæ in cceehtrieo folis diftareà quadrante pro quantitate angulix-tjuationis, vnde quanto maior ent eccèntiici tas/antd

MOTVVM COELEST. t^ hntopropiùs verfus perigion eccentrici,erit longitudo media, femperque ipfaeccentrotes oritæqualisfinuireâoarcus eccentrici àqua-drante, vfque adlongitudinem mediam.

Item,quanto eccentricitas ßtmaior, tanto etiamangulum æquationis effe maioré.Ideoq; in maximaeccentricitate, maximas continge-reæquationes, in minima minimas.

Item centro exiftente in fuperiori circelli parte motum apogæi folaris effe tardum,in in-ieriori vero apparere velocem.

Præterea obiter hóe fciendum eft.quód cü hac nofira aetate b. centrum progreflum inue-niatur vltra g. prope c. minimam etiam nobis iamiaminftare eccentricitatem.

Item,per motum apogæi diuerfum eiufque hypothefin non inferri aliquam notabilem inæqualitatcm, autdiuerlitatem motui Solis in eccentrico.

Z)(? moiloJü^purant^i yerum locum Sollf.

Primum requiritur motusSolis fimplex, quieftabarietefixo. amp;annua anomalia Solis y^°^ fimplex,quæeftmotusSolis médius, abapo- jg, gæo medio. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;liïfim-'

Deinde per anomaliam obliquitatis inuen- plcx. tacentri æquatione,diflrerétia fcilicet, inter ve. * rum amp;nbsp;medium apogij locum,eaque vel addi- anoma-ta vel fubtrafta, prodit anomalia coæquata,’^®’quot;^^^ quæ eft arcus xodiaci à vera auge,A fque ad lo- jjj ‘ nbsp;nbsp;' turn raedij motus, cuifimilis fempereft arcus anäta.

C tccentri-J

tHÉORiA

Èccentrici, abipfius veroapogio vfq; ad corpus folare.propter angu!oriimad centra pari-t3tem,proindepercoæquatam anomaliam ac-cipituræquatio orbisequalem amp;nbsp;apparentem motumSolis interiacens. Cùm vero equatio-nes orbis (üpputatç fint in tabulis ad minimam cccentricitatem,addituscft fmgulis orbislocis exceflus, quoeæ, quæ contingunt in maxima eccentricltate excedunt,ad intermedias autem eccentricitates inuenta funt fcrupula proportional ia.diuifafcilicetipfa differentia inter ma Ximum minimumque æquationis angulum, in Óo.partes, Si ad earn rationé cóHituta fcrupula, prçdifta fuppeditat anomaüa obliquira tis fecundu quantitate fcilicet,exceffus cuiufq^ ccccntricitatis anguli fuper minimum , amp;nbsp;vt 60, fcrupula in maxima ecccntricitate totum cxceflum (ingulis locisaddunt, bc interme-dijs partem proportionale per regulampro-' portionum liuetrium vt vocanteliciendam, hoc modo6o.dant totum exceffum, quantum dabunt 50. amp;c.

Notandum porro eff, anomaliam annuam Solis fimplicem in tabulis fub fe continere mo turn apogij medium pro eius tnim quantitate * minor conftituta eft medio motu Solis, vtiri motuannuo‘’----2- amp;fimiliter indiurno

Maximaçquatio orbis in minima eccentri-

. citateinueniturs-----

ia maxi'»*

MOTVVM COELESt. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;j^

Ïh maxima nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;2.23.2,,

Vt fit differentia nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;'’•3^-45*

Typm o/letji/ens caicuütm Soh^,

Locus medij apogij Aequalis motus Sölis compolitus Aequatip centri Aequatioorbis Per exceflum abfoluta

Ç. O. arcus quera centrum apparentis^ccen/

THEORlA

trici confecit, qui hîc defcriptus fuper centré o.eftc.b.nl.

T. centrum paruicirculi.

L.Iocus apogij medij.

P.locus veii apogaeiin z,odiaco,c.in ccccntri-. co.m.e medius motusSolis in zodiaco, B. locus Solis in ecccntrico, cuius linea ferri-per parallela eft ad earn, quae medium locum in zodiacooftendit.

N.b.arcus squalls motusSolis ineccentried limilis arcui m.e. in ecliptica.

L.e.anomaliaannuaSolis fimplcXi L.p.squatio centri.

Ex quibus apparet quod per anomalia ob-* liquitatis habetur æquatio centri,amp; fcrupula proportionalia.

Praeterea.qiiod fubtrafto motu anomalias annus fimplicis ex motu longitudinisrema-neat diftantia medij apogsi à prima ftella arie-tis,ex qua ft fubtrahatur æquatio 1. p. reliqua fiet diftantia apparentisapogæi abcadem fteU la:contrarioautem modo cadem æquatio ad-dita vel fubtrada anomaliæ ftmplici annus cam coæquat.

M.d.verusamp; apparens motus amp;nbsp;locusSö-lisin ecliptica, quem demonftratlincaf.b.d. D.f.e.angulus æquationis.

D.e.squatio orbis, amp;nbsp;arcus ecliptics auferen-,. dus e.x squali motu, vt verus amp;nbsp;apparens mo-*• tusab ariete fixo maneat,cui tandem adieda * nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;prscefsio-

MOTVVM COELEST, ly praecefsione æquinodiorû prodit verus motus Solis, abçquinodio verno ad illud tempus.

2)e P/^anomeno Lunte.

LunæPhænomenon quatuorinlongitudi-nemotibusquatuorq;conft3tcirculis, habet enim duos epicyclos, quorum primi Sc maio-ris centrum defcribit, motufuo fuper centra mundi circulum Lunarem,terre homocentrû fedobliquumad eclipticç planum propter ex curium Lunæ in latitudinem : de quopoftea. A tque hic motus centri primi epicycli procedit, fecundû Riccefsionem fignorû, æqualiter à loco Solis medio fingulis diebus

° li 11.16.41.19. quibus fi addatur diurnus Solis motus me-dius erunt, “777^ quos lingulis diebus centrii primi epicycli in x.odiaco peragrat,vocaturq; motus longitudinisà Sole æqualis excedens anni Aegyptij , fpatio motum Solis me*

vitra duodecim intégras reuolutiones, in hui’ autemprimi peripheria cft centrum fecundi epicycli, cuius circumfercntiæinfixiimcftcor pus Lunare. Atq; hi duo epicycli funt in codé cum circulo obliquo plano. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;,

Porto centrum fecundi, fertur in circumfe-yçntia primi,fuperq; eius centro æqualitcr fin-C 3 gulis

T H E o RI A

^Hs diebus .

incipicnsà fumma abfideprimi epicyclifquä lt;^enotatlinca müdiper centrum primi dufta) contra fuccefsionem fignorum, versùsprçce-dentia,vocaturq; anomalia LunariSjperficiens, luum circulum -7^,—üTiyT«: amp;nbsp;anm v-nius Aegyptijfpatio vitra tredccim intégras

reuolutioncs percurrens ~7~77 quibus dif-fert à motu Solis annuo.Poftrcmó corpus Lunare mouetur fupercentrofecundi epicyclià fumma eius ablidc (qua linea ex centro primi

per centrum fecundi duâa defignat) æquali* terversùsconfequentiafignorum, atquehic ■ motus duplus, femper exiftens ad motum lon gitudinis,vocatur duplex longitudo,eumque feruat ordinem amp;nbsp;regulam, vt in omnibus có-iunâionibus amp;nbsp;oppofitionibus Solis amp;nbsp;Liinae medijs:id efl,quando linea mundi,quæ centra primi circumducit,eft velin loco SoJis medio, velcidireétè oppofita, tune corpus Lunaefit inpuóto fecundi epicycli centro primi epicy* cliproximo, vbicunq;tunc inueniaturipfura fecundi centrum.In quadraturis vero medijs. vbilcilicctprædiâa linea, vel motuslongitu-dinisdiftiterit quadrante à loco Solis medio, in vtramuis partem, tune Luna femper eft in punfto fui epicycli remoti fsimo à centroprimi,in fumma fcilicet abiide, eiusrcfpeâu.

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;19

Conftituto itaque centro primi epicycli, in medio loco Solis,ac centro fccundi in abiide fumma primi,Lunaque tune exidenteinop-pofitoaugis fuiepicycli, vt didum eft.Om-nes prædidi motus, hoc modo incipiunt feen-dum raticinem prædidam, centri quidem pri-mi epicycli cum linea mundi,in confequentia, centri autem fecundi in praecedentia,corporis Lunaris. hic etiam primo in præcedentia,cùm fit in inferior! femicirculo.

Ex quibus iam notandum eft,motum lon-gitudinis æqualem ditbus 27. amp;nbsp;8. horis circi-tertotum zodiacum perluftrarc, ad Solis verb medium locum reuerti diebus zp. horis 12.ferupulisprirnisvniushoræ 44. fee. 5. tert.12 proximo,quibus finguhs fit coniundio media amp;nbsp;dimidio fpatio, oppofitio,Quadratu ræ'autem medio ad amufsim tempore inter có iundionem amp;nbsp;oppofitionem.

Tempus verb.quomotuslongitudinis amp;nbsp;a- Temput nomaliæfimuireuertuntur,id elf, vt centrum “^^'æ fecundi in ipfa fyzygia media fit in apogio pri- ^^Jj^ mi,eftdierum 126037. amp;vnius circiterhorx 5coppo_ vel anni Aegyptij ^45. dies82.8«: vna hora. fitionii

Notandum præterea efi, motum longitu- Solls. dinisLuna: du^liciter variari, ac insqualem •K apparere,primum propter motum anomaliæ qui in fuperiori circuli portione motui medio demit, in inferior! addit, fecundo per moturu çorporis Lunaris, qui motum anomaliæ in in- • •

C 4 feriori ƒ

THEORIA

inferior! circuli parte intendit, in fupcriori retardât,amp; propterea duplici etiam opuseffeae-quatione:quæ omnia ad oculum ita patent.

Schema moruum Luna,

B.f.circulusLunaris obliquus adecliptica fuper centro mundi a.

P.i.n. epicyclus primus ciufdemcumcir-culo obliquo plani, vti amp;nbsp;c.d.i. epicyclus fe-çundus.

L.apogion epicycli primi,n.perigion.

B.autem hiceftin medio loco Solis,ideoq» Lunaind.

L.ecntrumhïcetiamin auge.

Ex hoc autem loco b. mouetur à loco Solis, medio ver^ùs confequentia, eftquemotuslon gitudinis xqualij.

L.cen-.• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;- nbsp;nbsp;nbsp;nbsp;3*

MOTVVM ÇOELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ji

L. centrum versùs t.in præcedentia,eftque anomaliaLunaris.

Corpus Lunæ ex d versus i.eftque duplex longitudo, cuius motus angulus adcentrum fecundi, femperadangulum,qui adcentrum mundi compræhendit arcum longitudinis.cii differunt dupluseft. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i

£xquibus omnibus notandum venit, ma-ximam^minimamque Lunç altitudinem,amp; re motionem à terra, quæ effe polsit,conti ngere inLunadiuidua,veIquadraturis medijsmam tune exiftente Luna femper remotifsima à cé-tro primi,quadocunque accident, vt centrum fecundi (imul fit in apogio primi,erit maxima Luns altitudo, tota fcilicet diametro ep cydi fecundi,maior qua ea.quæeodemlocoinr ■-ua plenaùe Luna contingit, contraque eadc i diametro minor,quado centrum fecundi f -ritinperigæoprimi.

De ratione cakuh motus Lunx.

Supputato extabulis motu longituJiu à Soleamp; motu anomaliæ æqualis.- deinde j. r a equa-duplicatam longitudinem accipitur æquatio tiofccui^ fecundi epicycli, quae cftarcus epicycli primi, di epi«^ interceptusà duabus lineis excentro primi, '^^’•^ quarum vna du6ta ad centrum fecubdi demo-ftrat motum æqualis anomaliæ,ab abiîde fum nbsp;nbsp;nbsp;*

ma primi,altera verb, ad ipfum centrum corporis Lunarisoftenditipbusdiftantiarn ab ca- . •

C 5 dem”

THEOMA

dem abfide amp;nbsp;coæquatam anomaliam. Hxc autem æquatiofen(îmcrefcit, donee Lunare corpus confeâis 78.circiter gradibus ab initio fui motus fuerit in punfto contaélusnd cft,v-■ bi linea ex centre primi ad corpus Lunæ.con-tingit, epicycli fecundicircüferentiam,non fe^ c^t, vbi maxima proftaphærefis inter æqualé

apparentem anomaus motum

quæ ex eo loco minuitur, donnée Luna confe-ôofemicirculofuerit in augefui epicycli,re-fpeducentri primi, vbinullacftæquatio,e\-iftentibus nimirum corpore Lunari amp;nbsp;centro fccûdi,in eadem primi epicycli Iinca,inde rur-fum incipiensæquatio eadem rationefe habet vlquead peraâum duplicis longitudiniscir-lt;uitum,vbi denuô nulla eft: atq; hæc æquatio additur anomalie æquali ante femicirculum duplicis longitudinis, quia tâdiu diftantia corporis Lunarisàsûmaabfideprimi, maior eft, contraria rationcpoft femicirculum aufertur, vthabeaturcoæquata anomalia, diftantiafei-licet corporis Lunæ à fumma abfide,cum qua deinde inueftigatur proftaphærefis primi epi-‘ nbsp;nbsp;nbsp;nbsp;nbsp;cycli,quæ eft arcus zodiaci, intcrceptusadua-

^« buslincis, àcentro mund.i exeuntibus, quaru vnatranfitpercentrum primi epicycli, altéra

• • nbsp;nbsp;nbsp;per corpus Lunæ, vtea vel addita vel fubtra- ' ^famotuilongitudinisæquali, habeatur vera

• • nbsp;nbsp;nbsp;. Lunæ diftantia, motufque apparens à medio « • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;/ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;loco,

MOT WM COELES’T. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i*

locoSolis. Hæcautem prædiâaerefeens fem-pervel decrefcens, in pundhis contaâus maxima, in peraóto autem co^quatg anomalig cir lt;:ulo,vel femicirculo nulla eft.

Cùm autem harum çquationumquantita$ per omnia epicyeli primi loea variet, pro difta tiamaiore vel minore corporis Lunæà centra primi, namquePlaneta exiftéte in minima diftantia,in pppolito fcilicetaugis^ui epicycli, fi defcribatur circulas fupercentro primiper centrum corporis Lunaris erit epicyclus primus omnium minimus, amp;nbsp;eófequenter angu-kis aquation is ad centrum mundi eritangu-ftior,amp; lines mundi libi inuicem propinquio-j es, minimam in zodiaco æquationem com-prshendent, contra vbi Planeta fuerit in auge lui circuli, defcribetur epicyclus primusomnium maximus, maximaque! vbiq;erit çqua-tio. Intermedijs diftantijs, medij etiamerunt epicycli primi, medisquesquationes.

Intabulisigitur conllitutis æquationibus adminimum çpicyclum primum additus eft excc{Ius,quo eç quæ contingunt in circulo de-lcripto,fecundum maximam LunsdiftantiS, excedunt prçdiâas in minima diftantiacon- * tingçntes. Vtque etiam intermedijs quantita- «k tibusprouifum effet,excogitata funtfcrupula proportionaliaadexcelfum maximisquatio- • nis angulifuper minimum in6o. partesdiui-f^m,amp;fecundum earn rationem duplex Ion- . *

S‘tudo,r •

THIO RIA

Çitudo, cuius motus incipit l minima diflantia minimoque angulo, fuppeditat fcrupula præ-diâa,quç in auge maxima icilicet diftantia 60. totum addunt lingulis cpicycli primi locis cx-cefTum: Intermedijs autem locis minora partem proportionalem. '

Exceffum verö, ipfamquc çquationem ac-cipere neceffum fuit, per cosquatam anoma-liam,quaenimirùm locum in epicyclo primo notum facit, pro cuius diftantia à fummaab-üde çquationes crefcunt vel decrefcunt, vt di-Öum eft.

Ita autem abfoluta primi cpicycli æquatio ne ablata ante fcmicirculum, addita autem æ-quali longitudinis motui poft lemicirculum coaequateanomaliç, habetur longitudo à me-4iolocoSolis vera.

lj/:ti calculi mo/lum re/erens.

Motus

^lotuf.in ^oc/cremate/ùnt. hicdius fiue çqualis longitudinis à Sole 5. g. m. 1. 31 4.

J. Ï5. 12.

4-4^4?-iÏ« O9?‘-59.

4-5Î-Ï1-5^» 0.5.17.42.

ï-44 •Ï9-4‘

THEORIÀ

C.mötus longitudinis æqualis à medio Îôc3 ^Solis in confequentia.

D.t.m.arcus cpicycli primi, quem percurriÉ inomalia æqualis à fumma abfide d.

R.p.o.arcus quem percurrit corpus Lunare.

C.n. linea dufta ex centro primi,ad circum-ferentiam per corpus Lunç.quod èft in o.

M.n.æquatio fecundi epicycli, auferenda a-nomaliçæquali vt maneatd.t.n.anomaliacO. æquata,que minor eft quàm d,t m.

O.h.g. epicyclus primus, hicdefcriptusfu-per eodem centro c. iuxta diftantiam Lunæ, à centro primi fcilicet c.o.

A.l.arcus zodiaci,amp; æquatio primi epicycli; interæqualem amp;verum Lunæ àmediolocd Solis motum, intercepta à duabus lineis,ex cê-tro mundi b a,b 1. quæ hic propter minorera cpicyclum primum, quem Corpus Planète hic defcribit,angufiiorem arigulum compræhen-dunt, quam fi in eadem centri m.diftantia ab abfide fumma primi, maiorem circulum Pla-heta longiùs à centroprimi diftans deferipfiC fet. Attamen ampliorem cótinentes angulum, ‘ quàm fi Planetain minimadiflätia minimum tffecilletcirculü, exceflusadditione abfolutä hicredduntæquationem. Proinde hæc primi

• • nbsp;nbsp;nbsp;epicycli æquatio addenda eft çquali mo*

_. tui,vt liquet. Itaque verusmo-

• • nbsp;nbsp;nbsp;. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tuslongitudini à medio

• • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;loco Solis eft c.d,l.

MOTVVM GOEIE Î^T. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;#4

J)e ^uantuate/rimi ^^ecuneit ejgt;jcyc/i.

Diameter epicycli fecundi,eft partium 47351 qualium quæ ex centro terræ ad circulum Lu narem,vel centrum primi eft nbsp;nbsp;nbsp;nbsp;nbsp;loooooi

Et femidiameter primi epicycli,ex ipfius fci licet centro vfquead centrum fecundi eftea-rundem nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;10 974. proximè.

Qux hoe modo per doftrinam linuum re-dorum inuétafunt,defcripto minimocpicy-clo primo,l'ecundü minimam diftantiam,quæ in nouilunio velpieniluniocontingit,vtdilt;Su eftjit anomalix motus co loei in epicyclo primo, vt linea mundi tranliens per corpus Plane tetangat,epicyclum prirnum non fecet, fiihile fiat in quadraturis, maximoque epicyclo primo, (iequé vtrobiq; treslineæ, vnafcilicet ex centro mundi ad centrum primi, altera ex eo-dem centro ad corpus Lunarein pundo conta ótus.tertia ex centroprimi ad Lunam, pun-dumq; contadus conftituunt triangulum,re-danguluminamangulusad pundum conta-dus,femper eft rcdus.Ideoque in illis triangu lislinea ex centromundi ad centröprimifub. tendens redumangülum eftfinustotus, le-midiameter autem epicycli,finus redus arcus fine anguliæquationisquéfubtendit.Inuenta itaq; per obferuationes maxima in pudo cóta-dus minimaediftantiæ æquatio ^~^ notam fecitquatitatem femidiametri minimi epicycli

THEORIÀ

til ex tabula finuum,partium 8(?o8. qualiuin finustotuseftiooooo.rurfuminpunÖocon-taótus maxima diftantiæ eadéæquatio obfcr-uata ^.-’-^datfinum reólum,ipfamquefemi-diametri maximi epicydi quantitatem,earun-dem partium 13341.Ergo fubtraäo minori ex maiorij reliqua fit diameter epicydi fecundi, eiusque dimidio addito minoris epicydi femi diametro prodit femidiameter epicydi primi, tranfeuntis per centrum fecundi.

De quarto motu Luh/e,^ui eß ca-^ieii Draconif.

Circuius Lunæ, vt antea diximus, eft obli-quusadedipticamj'ecantenimfemutuóbifa-riam,quarum fedionum loca in ecliptica nota reddit diameter ex centromundi vtrinque produda träliehs etiam percirculum Lunaré, fuper qua diametro,tanquam axe,vna circuit Lunaris medietas ab ecliptica versùs fepten-trionem,alteraversùs meridiem déclinât,inua riabili perpetuó amp;nbsp;fixa dedinationis quanti täte,quç in punótis maximç diftantiæ eft 5 -gra-.duum,quales circulas magnusper polos edi-pticæ,amp; prædidaduo pundatranfiens, habt. 360. Atquehç duæfeôciones,l)ue nodi diame-traliter oppoliti vócantur caput amp;caudà Dra Conis,caput quidé ea fedio,àqua Luna intras feptentnonalem fuicirculi, partem tendit ad boreura limitem, pundum fcilicet circuli maxims

MOTwM COELlST. xr kimæ ab ecliptica ad S eptentrioné dccUnatio-nis,diftans à capite po-gradibus, vel quadran-te circuli,amp; ad eum vfq; limitera ctefcens Lune ab ecliptica latitude borea, fit quinque gra-duum.vt diximus,diciturqueLunaafcenden« feptentrionalis,ex eo verb, maxiraç diftantiæ loco defcendens,incipit repetere eclipticam,amp; peraäo circuli quadrante à boreo limite, rur-fum in altera feâione,quç cauda dicitur,eft in plano eclipticæ, nullam Habens latitudinem, inde defcendcns in medietatem fui circuli,au-ftralem acquirit in limite auftrino 90. gradib, àcaudadiftante,eandem maximam latitudinem 5 graduum aufiralem,amp; ab eo loco afcen dit Luna ad fedionem capitis,vbi in plano rur fum eclipticæ côflituta,omni latitudine caret.

Porrô circa has duas fediones, fiunt cclip-fesSolis amp;nbsp;Lunæ, vbi fcilicet Vel in oppofitio-ne luminarium, Luna interuetu terræ lumine Solispriuatur,velipfaincóiundioneinterpo-fitu fui opaci corporis, Solare lumen obtegit. In alijs autem zodiaci locis Luna propter latitudinem à Solis itinere ; neque radijs Solaribus obftaculo eft, amp;nbsp;ipfa luce lucens Solis ipfi-us radios,amp; lumen plenèpcrceptum homini-busminiftrat.Sed de eclipfibuspluradicentuf fub finem huius libri.

Porrô caput amp;nbsp;cauda, duoq-, limites eadcm femper quantitate inter fe diftantes, non ma-tiét ijfdem zodiaci locis, fcd virtute cuiufdam

THEORIA

fupenons orbis mouentur fupcr centro murt^ di,versùs prscedentia fignorum,fingulis die-bus, tJ!L2‘_±_l: completq;ille motus lui o. 3. nbsp;nbsp;10. 46,3,. r '

Periodum,annis Aegypt.18. diebus 223 horis d.min.j.fecundis vnius horæ 36.

Pe rationeJuJ^putaneii motum (^a/)itió dracon^i

Motus latitudinis mcdius fiue squalis, ineï pitin tabulisprutcnicis à boreo limite incon-lequentia, eftq; elongatio medij motus Lunæ iïue cetri epycidi primi,abipfolimite boreo, comprehendens tarnen fub 1e motum ipfum borei limitis in contrariam partem : pro tanto enim raaiorconftitutuseftmotu longitudinis medio.

Motus autem veruslatitudinis.efl: ipfius Lu naris corporis diftantia à boreo limite, quani æquatio primi epicycli abfoluta , addita vel fubtrada medio motui,notam facit. Vnde liquet fubtraßo motu latitudinis,fiue elonga-tione medij motus à limite boreo ex diftantia ipfius medij motus ab arietc, neceflario rema-1 nere diftantiam borci limitis ab eadem ftella, * amp;nbsp;confequenter innotefcere loca nodorum amp;nbsp;limitis, veramque Lunælatitudinem,quæ fup-putaturincirculo magno perpolos ecliptics, amp;nbsp;verum Lunæ locum tranfeunte.

• , nbsp;nbsp;nbsp;“ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;^j^urÀ

1 ^

MOTWM COELEST, tlt;

J'i^ura cakulum eiuf^ t^eonam referent^

AEqualis iongitudo Lunae à prima ftella

S. g. m. 1. 3 4.

S. II. 5«- J- «S- gt;*•

Aequalismotuslatitudinis à 4.59.50. 27.4. n. boreo limite,

Diftantia borci limitis à prima ftella A-rietis, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;0.12 27,58.15.7.

B .o.c.t. circulas Lunaris,cuius vna medietas o.b.t.intelligatur extra planum eclipticçde clinare versus feptentrionem,altera o c.t. versus auftrum inüariabili dcclinatione.

O verÔamp; t-punda effe in plano ecliptic®, cö diameter mundi m.a.n. illic tranfeatpercircu lum lunarem, demonfträs circulorum fedio-ócracopmuncni.

THÏORIA ’

N.locuS capitis in ecliptica, quod tali nota Q fcribitur,aliafque dicitur nodus cuehens, Ara bibus genz-ahar.

M.punctum oppofitum,locus caudæ,quç tali nota Î5 dcpingttuf,aliàs diéta nodus deuehésé B.boreusIimeSjC.auftralis.

P.m.q.motüs médius à prima ftella Arietis.

B.C.r.motus æqualis latitudinis.

De mot» tnum /û^ertorum,

Tresfuperiores,Saturnus fcilicet, lupiter, amp;nbsp;Mars,habent quilibet epicyclifm, qui defer tur in circula terræ eccentrico obliquo ad edi pticam,proptermotum alium in latitudinem,. dequopoflea.Proindeduplicitendunthi pla retæ in longitudinem motu : nam amp;nbsp;centrum epicycli ducitur in eccentrico versùs confe-quentialîgnorum,non tarnen fuperproprio eiuseccentrici centro æqualiter,fed fuperalio lt;juodam pundo in liheaapogij tantum diftan te à centro prçdifti deferentis eccentrici, quan turn hoc à centro mûdi, amp;nbsp;adcirculû fuper eo pundo defcriptü,ei uidé cuius amp;nbsp;ipfe deferens quantitatisamp; plani,æqualem, regularemque feruare curfum inueniuntur: vnde ille eccétri cusæquansdicitur. '

Atquepredidus motusdicitur longitudû nis æqualis,bue mediusjnitium fumens ab A-rietefixo,eumq; demonfiratin zodiaco linea ex centro mundi,çquidiftans lincç, quç ex eeß

• tro çquanus,ad çentrum epicycli ducitur.

M o T V V M C OE t E Î T. »? f Prgtcrea ipfe Planeta mouetur in epicyclo versùsconfequentia ab auge eins media ( quä iinea ex centro çquantis, per centrum epicy-clitranfiensoftendit(çqualiter, tantum qi fem, per,quatum folis motus medius fuperat quo-uis tempore motum lôngitudinis,planetç mediumjin his etenim planens duo prædidi motus iunftiçquiualent numero,motui Solis me dio,eiufquelocum notumreddunt, queraad-modum vice vcrfa,eorum altero fubtraélo ex medio folis motu, remanet numerus motus al terius,fcilicet vel lógitudinis à prima ftella A-netis,velplanete in fuoepicycloabaugcmc-i dia qui motus commutationis medius fiueg’ qualisdicitur.

Ex quibus notandum eft motum ccntrifiuj per proprio centro defcrentis, amp;nbsp;planetç fu-per proprio epicycli centro, irregulärem cHe, eorumquc çqualitatcm pendereab çqualibus ad centrum çquantis angulis, manentetarnen femper epicycli centro m eccentrico deferen-te,amp;cpnfequepter motum centri in inferiors deferentis medietate apparcre Yelociorem, in fuperiori tardiorem cum æqualibus, æquan-tis circuli arcubus maiores xodiaçi, circa perigion minores, circa apogion refpondcant. Contrà,motum planetæ in epicyclo velocio-rem effe in fuperiori deferentis parte, tardio-tem in inferior!, Idque propter mobilitatcm jmgis mediæ,quam linea ex centro deferentis .

^ 3 Peç '

^T HJE o R l A

per centrum epicycli ad eius circumferentiam duda.fixaq; manens,manifeftam facit,cùm ni-mirurn ad eius locum fixum aux media nunc accedendomunc recedédo diuerfimodè fe ha-beat,qucadmodum amp;nbsp;aux epicycli vera, qua per lineam ex centro mundi denotatur. Vnde cùm planetaæqualitcr femper ab auge media prt)cedat;jinaius fpatium confeceritin fuo circule adiutus accelfu fui principij, fcilicet augis mediç,minus,cùm per eius receifum in contra-riam partem fimulvelutirapiatur, . t

Notandum prætere3,in omnibus coniun-öionibus Solis amp;nbsp;planetçmcdijs,ipfum plane-ta effe in auge epicycli media.In oppofitionib. ■vero medijs in oppofito augis mediæ,quâdoq dë duo planetç motus çquiualeat motui Solis.

Sc/^ema t/gt;eorilt;e trium/upertorMtn.

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;t#

P. h.i. todiacus, eiufque amp;nbsp;mundi centrum a« B.centrum deferentis d.f. e.

C.centrum æquantisp.l.t. D.b.q lineaapogij.

N.m.longitudincs mediae,quas oftcditdiamcJ ter deferentis orthogonalis ad lineam augis.

B.r.demonftrans locum in epicyclofixum, ad quê c. s.aux media amp;nbsp;a. o. aux vera diucrfimo dcfehabent,amp; in longitudinib. mcdijslógifsi* mèæqualiter ab co remotç funt,vnde illic maxima inter æqualem amp;nbsp;apparentem locum.cft differentia flue æquatio,atque hæ très lines v-niunturinlineaapogij.vtvidereclf. r , D.centrû Eîc in loco Solis medio, vnde amp;nbsp;Planera in auge media,quæ hic etia eft vcra, à quo ambo mouenturin çonfequentia fignorum. T.k.p.l. arcus çquantis æqualibus ad centrum æquantis angulis comprehend, quibus relpon dent in zodiaco ,q.i.circa perigi on maior, amp;nbsp;x. z. circa apogion minor, aux media tota fiipe-riori deferentis medietate, motùcorporis Planets fequitur,ideoqueintenditcontrà in infe-riorifemicirculo.

2)e a^ogijs trïufn/u/gt;eriorum»

Apogia horum Planetarum folo fixaruftcl-larum motu[ferriVeteribus crédita, Copernicus proprio motu in confequétia tendere in-uenit,atq; lise predida funt, quç hi très Planets communia inter fe feruat, fub diuerfa tamé motuum quantitate,

D 4

Nam Saturni longitudinis motus cft fing« lis Aegyptijs annis-------------ÏrS-^L: fingulifquediebus nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;0.2.0.17. totaque eius periodus confiât annis Aegyptijs, 2^.diebusi74.horis5 amp;2i.min.ho^.

Eiusautem apogion.quod hoc anno 76.CÓ pleto,efi?^-p^-fagittarij ftellatæ fphæræ, mouetur fingulis annis fecundum fuccefsio* nem fienorura.--g. quot;}• ^- ?• 4.

® nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;o. o. 36.40.41.

Motus longitud.diurnus------?:_^jJL±_*

- nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;4 S9-7-54-Annuus nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;30.19.41. tota periodus perficitur annis vndecim, dieb. 517.horis14.min.5j.

A pogion ipfius, quod co dem tempore fuit ^*4?7?' '^*’’8*“*’ fiellatæ,mouetur fingulis an-

Mart if.

Annuus. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;5.11.16.18.28.40.

totum ambito pcrcurritfpatio vnius anni Ac-gyptij,dierumq;521.hor.23. min.51.proxime. A pogion,ejj predido téporç fuit Iconis g:7’: ftellati,mouetur fingulis annis-—_5ù-i_L_±: 0. Z8.44-37.

ßee^L

MOTWM COELEST. 1gt;

Decakulotrium^upertorunt,

Duplici hic calculus vtitur æquanone,qu3 rum prior difta eccentri, verumlongitudinis centri epicyclimotumabæquali,amp; confequé ter mediam eiufdem centri dillantiam, à loco apogij in zodiaco, amp;nbsp;apparentem veramq; di-■ftantiam,itemæqualem commutationis mo-tuin,à vero amp;nbsp;apparétidifcemit Secundaquæ dicitur æquatio orbis,médiat inter verum een tri epic y cli,amp; verum ipßus Itellæin z.odiaco locum.

Subtraâo itaque motu amp;nbsp;loco apogij à pri ma ftella arictis,ex motu longitudinis, rema-net anomalia eccentri,id eft^diftantia centri e-picycli ab auge eccentri in confequentia, quaï anteomniaeft neceflaria,cum fecundumdi-uerlîtatemdiftantiç,çquationes varient,vt ante oftenfum eft.

Proinde per hanc venamur çquationem eCT centri,arcum fcilicet todiaci comprehenfuni inter duas lineas c centro mundi ad z.odiacum protra(ftas,quarum vna lineæ æquantis æqui-diftans demonftrat locum equalem:altera per centrum epicycli tranfiens, verum eins centri locum oftcndit, amp;. hæc æquatio, vt nulla eft in auge eccentrici vel eius oppolito, concurren-tibus tune æquali amp;nbsp;apparent! motibus, lie in longitudinibus medijs maxima,addeda vel au ferenda,vt ex præcedentibus intelligi poteft.

Bodem que modo amp;nbsp;ratione additur vel au

5 fer-

THEORÏAux

fertur anomaliæ eccentri, vt habcatur ver» diftantia ab apogio, quae eft anpmalia coae-quata. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;P

Sedcótrariofempcr modoéadem æquatio vel additur vel aufertur motui bue anomaliæ commutationis, eftque tune arcus epicycli, duas interiacens lineas, quarum vna à centro aequantis per centrum epicycli duftamediam augem,àqua motus cómutationis æqualis ini-tium fumit, altera ^ centro terræ per epicycli centrum, veram eius augem,verumq; amp;nbsp;appa-rens motus initium debgnat.

Quod autem hæc æquatio in z.odiaco,amp;in epicyclo eiufdem fit rationis, fitpropter æqua les angulos ad centra,quibus fimiles arcus infi Hunt: vnde arcus æquationis in epicyelo fe habet ad totum epicyclum, quemadmodura arcus zodiaci ad totum zodiacum,cuius in præce dentibus etiam mentio fada fuit.

Proinde per coæquatam hoc modo commutationis anomaliam accepta æquatione or-bis, (quot;quæ eft arcus zodiaci comprehenfus inter duas lineas è centromundi,quarum vna tranfit per centrum epicycli, altera per ipfura planetæ corpus, ) prodit verus amp;nbsp;apparens Pla netæ locus à prima ftella Arietis.

Porrö,cü hæ æquationesorbis pro maiori propinquitate vel diftantia centri epicyclià cé tro mundi differant,amp; cùm epicycli motus tar ,dè procédât, ftella autem in epicyclo fæpius com-

MOT WM COELEST. 30 Commutetur , fupputatæ primùm funtprædi-Ôææquationcs omnibus in circumferentiae-picycli locis contingentes, cùm centrum epi-cyclieftinapogioeccentri, vbifunt omnium minimæ, propter maximam à mundo remo* tionem : præterea adiundus eft exceftus, quo maximæ contingentes,cùm centrum eft in perigio'propinquifsimum mundo exceduntJn-termedijs autera à mundo diftantijs profpe-étum eft,diuifo toto exceflu maximæ æquatio nis fuper rinpimam in 6o.partes, amp;nbsp;ad cam ra-tionem conftimta fcrupula pj;oportionalia,ac-cipiunturperanomaliam eccentri, quæ,vt in perigiodo.totum exceffum fuperadduntjic intermedijslocisminora, partem proportionalem,vtæquatioorbiseuadat abfoluta. Vbi autem coæquata apomalia commutationis vel nihileft , vel femicirculus, exiftente fcilicet, PJancta, in apogio vclpecigiq veto epicycli, tunccoincidentibuslineismundiip vnum locum, nulla eft hæç orbis æquatio, nullufque confequenter exceffus, fed verus locus epicycli, eft idem amp;nbsp;Planetæ , intermedijs autem locis crefcit , amp;nbsp;decrcfcit, quæ amp;nbsp;reli-qua omnia ex præcedentibus nota latis ar-bitror.

Schéma moilum/ùjipueantii motum Saturni iümot^irans.

Motus

THEORI A

3^

Motus Solis médius in fecundo gradu virlt; ginis,vtluprl

Aequalis motus cómutationis ^—^•- ”• *: ^' *'

* nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;II. J- 26. J«.S7.

Aequalis motus longitudinisàprima Hella a-rietis. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;3.20.1517.10 yó» loc’apogçià prima ftella Ar. 4.0.43.45». 40 anomalia eccentri nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;y. 19 29.27.30,

anomalia eccentri coæquata y.23 32. yo.30.

aequalismotuslongit.coxq. 3.24.16.40.10.

anomalia commut.adçquata y. 8. o. 3. 38. verus motus Iongitudini5,amp; locus fteHæ,à pri ma ftella arietis. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;3.i9.yi 39.40.

C.r.b.zodiacus.

A. centrum mundi,n. aequantis,g. centrum d®* fercntiSjl.p.q.

A.b.locusSoJis medius.

. A.c motus longitudinisSaturni xqualis-R.lo»

MOTVVM COELEST. p R.locusapogæi.

R.b.c.anomalia eccentri.

O.m.t anomalia commutationis æqualis,amp; Planetæ locus int.

C.e. æquatio eccentri addenda motui longitu dinis amp;nbsp;anomaliæ eccentri çquali, vt habcatur verus motus longitudinis,centri a e,amp; anoma lia eccentri coæquata,vcra fcilicet diftantia cc tri ab auge r. b.e.

Huic autetn arcui fimilis o.m. propter equ» les anguloso Z m.amp;ca e. auferendae|contrario, vt patct, motuicommutationis, quo amp;nbsp;is habeatur verus amp;nbsp;coæquatus m.s.t.

D.e.a:quatïoorbis,aufcrenda vero ccntri motui,vt maneat verus amp;nbsp;apparés Planetæ locus a d.abariçtefixa,cui dcmum adijcienda cftpræcefsio Aequinoftiorum.

Demoruyenerif.

Venus eofdem quos amp;nbsp;très fup6riorc$ hâ-bctorbes,eccentricum fcilicet deferctemob-liquum ad eclipticam,amp; epicyclum : item cir-culum æquantem, cuius centrum eodem modo diftatàcentro deferentis,ad eumq;fe habet motus epicycli amp;nbsp;planetæ, quemadmodii in tribus fuperioribus, à quibus tarnen in alijs quibufdam Venus differt.Nam aux eius eccé-trici Temper fixa manet in i8.gradu,2i.mi.tau-n ftellati, præterea motus Veneris æqualis in löngitudinem jideft , centri epicycli medius motus ab ariete,Temper idem eil fecundum ló

THEORIA

gitudinem qui Sc Solis motus medius, vndé lèmper media eft corum coniunétio, babitoq; vnius motu, fiue loco medio,habetur amp;nbsp;locus alterius,magis.n.alligataSoli Venus, non habet nifi expatiationes,(îueelongationesàloco Solis medio in vtramquc pattern, pro quantitate fui epicycli. Motus veto commutationis liuePlanetç in epicyclo,eft,quo excurrens mo tum Solis medium fuperat, incipiés ab auge e-picycli media versùs confequentia fignorum.

.111;—3l_± totumque perfi-Î6. 59- l*.

cienscircuitum,diebus583. horisn.min.io.

Centrum autem epicycli eodem cumSolis medio motu,fpatio, totû zodiacum percurrit, vtdidumeft.

Ex quibus notandum,Venerem in auge e-picycli diredamjn eius oppofito rétrograda, latere combuftam fub radijs Solis,inde excurrentem amp;nbsp;expatiantem circa Solern, ab auge quidem vfque ad perigion,Hefperi nomen ac-cipcre,qu5diu radijs folaribus liberata, vefpe-ri poft occafum Solis fupra Horizontem vide-tur:à perigio autem ad apogion, Luciferi nomen,quamdiu Solis exortum matutinum prç cedit confpicua.

Sciendum præterea maximam elongationé àvero lococcntri epicycli, fiue æquationé or-bis,contingere ytrinq-, in pundis epicycli, vbi ’ . linea mundi duöa per corpus Planetæ, contin

^MOTWM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;}t

gk.epicyclum non fecat,atq; hæc minima omnium cumepicycli centrum cftin apogsoec-centri,eft ^—^’ Maxima,cum idem centrum cftin perigioeccentri.^^^^^' Maximaautem eccentrifquatioeft, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;g- m. x.

Admonere autem bic operæpretium du-xi,has V eneris Proftaphçrefeis non conuenire ad amufsim mobilitati Softs, eique hypotheft, quam præmifimus,nam aftoquin manentibus ijfdem orbis æquationibus,dilFerentia æquali-tatisamp; apparentiænon eritnift partis vnius,amp; 4o.minutorum,ipfaque eccentricitas deferen* tis 5o.minutorû,quaftû femidiameter deferé-tis eft 60.vel manente cadem çquationis eccen tri amp;nbsp;eccétricitatis quatitate, neceflariomaxi-I ma orbis aequatio in perigæoeritcirciter ^-^-^ I Cçteraporrôomniaadmotusamp; calculuper tinentia,cùm communia habeat cum tribus lu perioribusjnde petenda pretereo.

Obiter verb hic aftronomiæCandidatûad-monédum efteputaui,q) amp;nbsp;ad Mercurij theo-riam pertinet,a£:quationes orbis differre abe-longationibus à loco Softs medio, ills etenim funtdiftantiæPlanetçà vero lococentri epicy cli squato per additionem vel fubtraélionem çquationis eccentri,vnde femper pro quantita te iftius çquationis fiue djfterentiç inter äqualem

T H Ä O II I A

lem amp;nbsp;apparétem motû, aut minores aut maid res funt ipfis elógationibus, imaginandç enim funtin his duobus Plafietis treslineç parallelçi (vtiamfacilioris demonftrationis gratia lati-tudinem negligamus)quarum vna eft ex cétro æquantis Planetæ, altera ex centro excentrici Solis,tertia ex centro mundi, quæ motfi amp;nbsp;locum vtriufqueæqualem inzodiaco refert,quç très propter apogiorum amp;nbsp;eccentricitatis di-uerbtatem, nunquamfimulomnesad amuC firn in eundem locum concurrunt.

Præterea lincam apparentem, qua: corpora Solis,amp; horum Plahetarumconiungit, in Ve-nere non femper,in Mercurio nunquam tran-fire percentrum epicycli.

Item,centrum epicycli Veneris, amp;nbsp;corpus folarc tunc folùm ineadem verimotus linea inueniri,quado çquatio orbis in Sole,amp; æqua ti eccentri in Vcnereaequalesfunt,fimulq; vcl adduntur vcl auferuntur.

Porro vthoru Planetarum itenlq;triu fupc-rioruaffumpti motus amp;nbsp;Phçnomena congrue tiùs per motum terræ expediuntur, ita lî qs o-tio amp;nbsp;ingenij felicitate afflues,meritoq; labo-ris premia amp;nbsp;frudu prouocatus,diligétifsijnè motus obreruare,aliamq; quandâ circulorü ra tionéin Venere,Mercurio,amp; Martepfertim excogitare amp;nbsp;inuenire(fp fieri poireputo)ftu-duerit,fecerit is ré omnib.doétis viris optatif funa,amp; in Aftronomia apprimè neccHariam.’

Scha-

kOTWM COELEJf. nbsp;nbsp;nbsp;nbsp;nbsp;y

Schema caku/i f^eneri^.

Î centrum mundi,edeferentis df C.æquantis centrum.

I m.motus longkudinis Solis Sc Veneris*_____ $• g. m. 2. 3.

. i. 3».i6.4|.^5j

Ï* m.anomalia eccentri.-

N m.xquatioeccentri.

I n.mctüslóngitüdinis coæquatus amp;nbsp;verus cê-tri locus. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;5. g. m.^^

A.banomalia commutationis xqualiSjamp; locus planets in b.

O.ai b. ànomalia commutationis coaequatà—

E KL :

THEORIA

Nl.æquatio orbis,amp; locus verus ipfiüs PfaritLi

• s . g. m. z. j.

J- 14- }• Sgt;. 4».

De moeu ‘^lercurij.

Mercurius mouetur in latitudinem, amp;nbsp;Ion* gitudinemgt;feddeillo motuinlatitudiné poil* ca dicemus:motus autcm lógitudinis fit in cir-culo eccentrico, at maiori varietate quàm eu-iufuis præcedentium, quod ad oculum meliùs cxplicabitur.

Schma t6eoria^ ^fercury continens.

Sit igitur i.h.g.zodiacus, in cuius medio ce-trumterræ a.

H.r.o.g. linea apogi),atquehæcquæ veteribus

• amp; nbsp;nbsp;nbsp;Ptolemæofixa videbatur, mouetur fuper

• • ^cntromundijproprioraotufcilicetinftenata Y ’ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;fph«^

^ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;,|

Ipbçra Gngulisannis locum apogæi fecundum füceefsionem fignöri'iträsfcrcns, ■^‘ —'■■^' ^' ^'

o nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;’ o. o. S7-So. j».

apogion autem ad annosChrifti completos, ï576.fuit ~^,^’ fcorpij ftellati.

Porro inlinèaapogij fit diftantiaa. b. amp;nbsp;faper b.centro defcribatur eccétricus m.fi. qui æquans vocabitur.

Sit etiam diftantiabc.dupla priori, in eiufej; Îfiedio Riper d.fiatparuuscirculus tranfies per c.b.Rintque ergo ibi tria æquàlia fpatia a b.amp; b d amp;nbsp;d c.

Super c.autem centrodefcriptus circulas r. o. eft eccentricus deferens epicyclum fibiin-fixum.

Intelligatur iam eccentricitatem Mercuri) vâriari,ac b.quidem ede minirnam,c.màximâ, omnefq; eius ih longitudinem motiis hóe modo proctdere.

Centrum epicycli fertur in orbe fuo de-ferente fecundum (üccefsionem fignorum,fcd irregularitcrfupcrpropriocentro c.æqualitcr veró fuper centro aequantis b. eiufq; medium motum fiuelöcum in xodiaco oftendit linea mundi parallela ei,quæ ex centro æquantis ad téntrum epicycli ducitur.

Atque hic motus longitudinis centrl medius, initium fumens à prima Relia a-rictisjfemper «qualiscR medio motui Solis, £ z fis*

THEORIÀ

fîcvt vnamundi lineavtriufq; locum mediü in zodiaco demonftret, quemadmodura in Venere.

Præterea ipfe plarieta in cpicyclo fecundum fucccfsioncm fignorum mouetur çqualiter ab auge epicycli media, fquam linea ex ccntro æ-quantis dénotât ) fingulisdiebus ?' ”''^'.’1 fua complensreuolutionem, diebusiij. hor. 17. min ji.proximè, clique hic motus commuta-tionis æqualis.quo Mercurius expatians à loco Solis vtrinquediuagatur, circa apogiUmenim epicycli ibliconiunôtus, deinde ex dus radijs emergens, vefpcri poft occafum Solis le confpi ciendum præbet, donee maximam elongatio-nem vefpertinam confecutus, poft retrogre-diens,amp; radijs exceptus Solis,circa perigion ei rurfum coniungitur,ac inde excurrenSjfur^ö-req; Solis fen firn exutus, manc eius aduenturn prænunciat, maximamcj;maturinam diftantia attingens, rurfum reucrtitur,adconiündionc properans.

Porto Iciendum præterea eft, ecccntricum deferentem elfe mobilem , eiufque centrum c duci in paruo circulo,fuper eius ccntro d. à fu-periori parte,fcilicetà loco maximx cccentri-citatis versus præcedentia,eiufque motus pe-riodum eodem temporis fpatio cum anoma-liaccccntriliue motulongitudinis centri epi-jcycli medio ab auge mediajÇqualiter comple.

ri.Vn-

MOTVVM COELEST.

pi. Vndeanguli iflorum duorum motuü fem-per funt æquales,arcufque (imilcs, eaque regu la hiccentrimotus procedit, vtcùmcentrum epicycli eft in ipfa linea apogij in r, tuneipfum quoq;deferentis centrum c. eft in maximadi-ftantia à centro mundi,amp; in ipfa eadem apogij linea, inde autem difcedente epicyclo versiis confequentia fuper centro aequan tis çqualiter, ipfum quoque centrum apparentis eccentrici tantundem temper tendit in contrariam partem,eoq; transfert orbem fuum amp;nbsp;augem ve-ram,auulfam à linea mediæ augis excentrici ç-quantis,

Jix quitus confequenter patct ipfam veram eccentricitatem fenlim minorem Hcri,item cé-trum epicycli, cùm femper manens in mobili fuo deferente,tendat ad ipfuspeiigion, etiam fenfim propinquius ad mudum accedere, quâ-uis iplius augis defcenlio longius à müdo femper detrudat ipfum perigion.Confeélis autem quatuor (ignis ab apogio æquantis, ipfe epicy-clus propinquifsimus mundo cxiftit, quo tem pore centrum mobile percurfis etiam iio.afu pcrioricircelli partegradibus in præcedentia, eft in punflo vbi linea ex centro mundi contin gitparuum circulum, amp;nbsp;ex centro defcrentis

trum æquantis, ipfumque apogion verum,eft in maxima à loco medij remotione, fcilicct^o. grad.in zodiaco,pro quantitate nimirum angu, •,lt;

É 3 li ad* )

Vadcentrumundi,quem fubtenditfemidiame ter circclli in iUo triangulo reétagulo, vnde ex; data iftius maximæ remotionis quâtitate,inno tefcit quantitas circelli,vel contrà femidiame-tri data magnitudo,maximatn augis verçelô-gationem notant reddit, per doétrinam trian-gulorum pianorum.

Ex prædido aût contaétus loco,tcndente cé-tromobiliversùs minima à mundo diftantiâ, incipitapogion verum recurreread augemæJ quantis,amp; centrum cpicycli lôgiùs rurium rein oucri à mundo,cum perigçon deferentis,cui. iampropinquum cft, propter appropinquatio nem centri mobilis ad centrum mundi, magis femperinde remouetur, donee centrum mobile peraâofçmicirculoefficiat minimam ec-centricitatem in b,vnitifque deferente amp;nbsp;equa te,apogium verum lit iundum medio in m.h. centrumq;epicyeli confeâofemicirculoin n. perigæo deferentis amp;nbsp;æquantis.IIlinc autem ce trum mobile, amp;nbsp;centrum epicycli ad diuerfas in fuo quodque circulo pergentia partes,com-mutatis locis, amp;nbsp;feparatisçquanteamp; deferéte, çafdemexhibentvicinitatisdiuerGtatcs,fic vt lt;ùm centrum epicycli fueritduorum fignoi u Ipatio vltra perigxon proueftum, vel S fignis kilicet ab initio motus : tunc rurfum in maxima ad centrum mundi fit accefsione,quae inde i;urfumminuitur vfqueadaugem, vbi maxi.

. ma eft remouo.

Ex qui-

MOTVVM COELEST. K

Ex quibus iam notandurn eft centrum epf-cycli in vnareuolutionc bis fieri humillimum terraequeproximum.femelautemaltifsimuni co zodiac i loco, vbi eft aux æquantis, à quo loco anomalia eccentri æqualis initium fumit.

Praeterea quod fi defcripti$ eccétricis fuper omnibus centri mobilis locis circumducatur lines per omnia cetri epicycli loea, oui forma ça fitrelatura.

De/uppurarione motuum %^lercurtj.

Calculus Nlercurij fitomnino vtin tribus fuperioribus,nifi quód motum medium com-munem habeat cumSole, differtetiam à Vene re quod propter apogæi mobilitatem,locus e-iusprimùm inueniendus eft,per quem habea-turannomalia eccentri,cum eaqueæquatioec

vel auferenda,vti in precedentibus.

Præterea per coæquatam commutationis a-nomaliam accipiuntur xquationes orbis, qu® fupputatæ ad omnia epicycli loca, cum centra epicycli eft in maxima à mundo rcmot!o.ne(v-bifunt omnium minimxfcilicet in punéliscó taduSÏl.ïll^)Adiunélumhabentcxceftumc5 tingentium in minima diftantia, ad cuius ex-celtus diuifi in 60. partes, proportionem, eófti-tutafcrupula proportionalia,crcfcunt vfque ad dilbntiam quatuor fignorum abapogiOjV

E 4 biöü

TH E O II I A

t3i(lt;o.minimam epicycli à mundo elongatioc nem indicantiajotum exceffum fùperaddunt, maximamq; often dunt æquationem orbis in punétis contaâus, 5—Ex coautcmloco • nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;’ 15- Jl- 3S-fcrupulorum multitudo propter contraâio-nem anguli æquationis minuitur aliquantùm, vfque ad perigæon,ac inde rurfum creftés /patio duorü ftgnorû fit maxima, fcilicet 60. qu. deinceps decrefcunt, amp;inapog;o nulla funt Schéma cakuh motuum %lercurij.

Tn .

X.c.a.linea apogij æquâtis,fiuemedij,cuius I0-fus in t.ab arietis prima ftella diftas

? nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;A cto.

MOTWM COEIEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;?T

A centrum mundi,c.æquantis,amp; h z.eccentric eus çquans.R.Iocus longit. centri æqualisjîuç motus Sohs medq. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;^i^ssi.

T. e.r.anomalia eccentri.

X.c d.motus centri mobilis,æqualis, annoma-hæ eccentri.

S b.deferenseccentricusdefcriptus fupercenlt; tro d.

L.r.æquatio eccentri,cui fimilis eftjn epicyclo o.n.

A.l,locus longitud. coxquatus amp;nbsp;verus -- —s

1.34-43 4S-49SJ N.o.m.motus commutât. æqualisamp; locus PU nets in m.

O. m. anomalia commutationis casquata.—-5. g. m i. 3. 4.

1 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;4- 31. S3. 1*. 4SI. SI, (

i.squatio orbis. .

Ah verus Planere loc’.à prima ftella arietis____ S g- m. H 3. 4. ?. 14.50. 37.49.53.

T)e ^uandtare amp;nbsp;J/roJiortione orlittm, i^iametrorum, amp;nbsp;eccentnarari^ ^um^ue P/aiierarum.

Saturni.

Didantia centri deferentis epicyclum ?i c^ tro mundijtaliàm partium eft 5^81, qualium qua: ex centra terrs adapogion deferentis eft nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;loooqo.

^i nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;a

THEORlA

Et ea qux ex centre mundi ad perigion 89239»

Ergotota diameter ab apogio ad perigçon nbsp;nbsp;.

189239«.

Eiufquedimidiä, femidiameter fcilicet defe-rentis nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;94lt;ïi9.proximc.

Semidiaraeterepicycliearundé 10308. Sed qualium femidiameter deferentis eft, looooo» taliü eccentricitas deferétis nbsp;nbsp;nbsp;^6^9 proximè. amp;nbsp;totidem diflantia centri çquantis fypra centrum deferentis, , nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;» louis. ^ centre mundi adaugem deferétis 10000o# A centre mundi ad periggon 91314. proximè«

Ergo totadiameter. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;191314.

Etdimidia. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;95^57-

Et femidiameter epicycli nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;*833$.

Et eccentricitas nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;434^*

Sed qualium femidiameter eccentrici defcren tiseft, nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;100000. talium eccentricitas deferentis, 4Ï3lt;^* amp;nbsp;totidem centrum iquantis fupra centrum deferentisin eadem diametro.

Martis.

A centre mûdi ad apogion deferentis 100000

Ad perigion , nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;82Ö44.

Et femidiameter deferentis

Semidiameter epicycH nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;60041.

Eccentricitas deferentis

»

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;jj

Sed qualium femidiameter deferentis eft lOOOOO.' talium eccentricitas nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;958$ circiter.

Totidemqueaequantis centrum füpra centrü deferentis.

Veneris.

A centro mundi ad augé deferentis 10000a.' Adperigium nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;96818.

Etdimidia nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;98414.

Et femidiameter epicycK nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;70805.

Eteccentricitas nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;1586.

Sed qualium femidiameter deferentis eft

10000. talium eccentricitas nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i6i5proximè

Ettotidcm ccccntricitasæquantisà deferente, Mercurij

A centro mundi ad augem deferentis infum-madiftantia nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;100000.

A centro mundi ad perigium circuli æquan-tis nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;81608»

Ergo tota illa linea Hue diameter 181608, Etdimidiafcilicet à deferentis auge maxims altitudinis,vlque ad centrum parui circuli, 91304-

His ablatis ex lo'cooo. remanet diftan. tia centri parui circuli à centro mundi 8696.

Huiufquedimidiapars eft eccentricitas squa tis à centro mundi. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;4548'-

ci-uft^

THEORIA

éiufquetriplo fubtrafto ex icoooo, remanet femidiameterdeferentis nbsp;nbsp;nbsp;nbsp;StJpjö. femidiameter epicycli. nbsp;nbsp;nbsp;nbsp;nbsp;3265 8. proximè. fed qualium femidiameter deferentis——» eft nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;100000.

talium diftantia centri çquantis à centro mun-di nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;50oo.circiter.

Notandum autem hic eft,eccentricitatem louis, V eneris,amp; Martis,fenfibiliter decreuif? fe à Ptolemæo ad Copernicum.

2)e/gt;aJ?ioniltff, yt yoeanr, P/anerarum, amp;^rimutn i/e i^edinatione amp;nbsp;iat:ituäinz_^.

Declinatio ftellæ, propriè dicitur diHantig eiusabæquinoétiali, fupputatain circulo magno tranfeunte per polos mundi, amp;nbsp;locutn ilellje,

Latitudo autem eft diftantia ab ecliptica in circulo magno per locum ftellæamp; polos edi-pticæ duâ:o,compræhenfa inter duas ex cétro eclipticçjiue mundi lineas, quarum vna refta in plano eclipticæ perfedionem communem circuli magni cum ecliptica, altera per corpus ftçHæ ad çirculum magnum ducitur.

Quemadmodum longitudo aftri, vt hoe 0-• nbsp;nbsp;nbsp;nbsp;biter hic adijciam,cft diftantia ab A riete in có-

fequentia lignorum, compræhenlà inter duos fçmicirculos magnos,quorum vnus à polis zo Z . diaciperpudumarietis, alter per eoldem polos

MOTVVM COELESf. 3» }ós amp;nbsp;locum ftellæ tranfit, fupputatain gradi-busedipticae, maximi nimirum circuli inter duoszodiacipolos,etfi ftellafæpènon inipfa ecliptica,fed in eius parallelis verfetur.

PorroSolfemper fub ecliptica, in eiufquc plano exiftens declinationem quidem, at nullam admittitlatitudinem.

DeLunæetiam vniformiin vtramquepar-tcmlatitudine diâumiupràeft, reftatautem vt amp;nbsp;reliquorum quinque euagationis ab ecliptica moaûamp; rationé paucis perftringamus* De iatitutiine mum^upemorum.

Éccentricihorum Planetarum orbes obli-qui,vtdiximu5 ecliptica; planum fecant,quæ quidem circulorum mutua fedio fit fuper cé-tro amp;nbsp;diametro mundi,diüidens zodiacum bL fariam.itacjue fe habet j vt ca pars eccentrici in qüaeft aux,declinetab ecliptica versùs Septen trionem,altera versus auftrum, inuariabili amp;nbsp;fixa declinationis quantitate: punävm autem maximædeclinationis, in Martequidem fiti-pfj aux, vel omnino proximè,in loue verb di-ftet ab auge viginti gradibusinconfequentia fignorum,in Saturno fitante augem in præce-dentiajo.gradibus, atque hæcadaugium loca ita fe habent perpetuo, vnde per proprium a-pogiorummotum,prædilt;Sa maxime declina-lionis punda amp;nbsp;nodi fqui amp;nbsp;caput caudaq; vt in Lunavocantur)traducunturfecundumfuc cefsionem fignorum in ftellata iphjera,quem-admoj.

THEORIA idmodum motu præcefsionis æquinoâiorâ poftponuntur in apparcnti zodiaco,quod no-turn eft.

Adprididamautem eccentrici declinatio nem ita fe accommodât epicyclus eiufque diameter tranfiens per augem veram,ciufqueop-pofitum,vt cum cetrum epicycli eft in nodisj tota epicycli fnperficies plana lit in piano ecliptics,amp; aux vera,eiufq; oppolitum direde irt fuperficicdefercntiseccentrici;Indeautem re-cedentecentro,prsdicha diameter incipit feca replahumliuefupcrficiem defercntis,amp; aux vera continué magis acmagisabeodeclinarc versus eClipticam,amp; oppolitu augisconfequc-ter versus ea à luperficie defercntis parte muri di,vel feptentrionalcm fcilicet vel auftralem, ad qua inclinata eft portio deferentis,in qua c-picycl i centrum tune vcrlatur, donee ad limi-tern deferentisboreum vel auftrinu,ipfum epi cycli centrum veniat,quo zodiaci loco diftate à nodis vtrinq;9o.gradibus zodiaci fecunduni longitudinem,maximainuenituraugis ciufq; oppoliti in contrarias partes à deferente declinatio , quæ deinde decrefcitad nodum altern^ manente intereadiarnetro epicycli f quæ per centrum epicycli amp;nbsp;diametrum augis veræ or thogonaliter ducitur^femper parallela ad planum ecliptics.

Liquet igitur hanc lógitudinem epicycli me diarumjdiametrumfemperfecareplanûdcfe;

MOTWM COELEST. 4« rentis.præterquam in limitibus maximæ eccs trici declinationis.vbi punâa piani defereotis longitudinibus epicycli medijs contermina,æ-qualiteredam ab ecliptica dUiant. Contra aut diametrum augis vers femperfecare fuper freiem deferentis,practerquam in nodis.

Prxterea centra epicycli exiftente extra no dos,augem veram femper efTcinterfuperficiê ecliptics, amp;. deferentis,eiufque oppofitum ex-« travtramque.

Item centra defcrentis amp;nbsp;squantis eße extra planum ecliptics,ipfumque Planets orbem fc étum effe in portiones insquales,ecliptica vc-ró vt diétumeft in partes squales, vndenodo-rum amp;nbsp;Iimitum in xodiaco loca quadrantc ma neant ab inuicem perpetuodiUinda.

Notandum deniq; eft indinationem epicycli earn effictre in eadem eccentri dcclinatione, la titudinum quantitatis diffcrentiam,vt amp;nbsp;peri-gss excédant eas qus circa augem epicycli cö tingunt. PrSterea amp;nbsp;auftrales propter maiorc ad centrum mundi propinquitatem maiores lint in inferior! epicycli medietatefeptétriona libus;contrà autem in fuperiori portioncàbo-realibus fuperentur.

Habitudinem autem diametri mediarum longitudinum ad ecliptics planum, faccre v-triufque lateris epicycli latitudines squales,Sc in nodis nullas.

£t latitudines aliquorum locorum hoc modo

THEORIA

fnodo inftrumenris obferuate’, declinationeni defei-entis,amp; epicycli notamfecerunt, ad qua deinde reliquorum omnium locorum latitu-dines perdoélrinam planorumtriang.amp; admi niculodiftantiaruma mundo diametriq; epi-cycli notç quantitatis conftitutçfunr.

Prçterea obiter hic adijciehdüm effe duxi Ïineas augis verç amp;nbsp;mediç , earumque oppofi-torum indicatrices, cum tranfeuntes per centrum epicycli, femper tarnen maneatin fuper-ficiecccentrici,fieri ad inclinationem epicycli - plicatilesvtitadicam,eundemquefemperfer-uare in epicyclo locum, que omnia h oc mö^ do ad oculum exponi poffunt.

figura iatituiiinM trium/ù/erioruni^

MOT WM cost EST. nbsp;nbsp;nbsp;nbsp;nbsp;41

Kl.centrum mundi amp;nbsp;ecfipticæ. d. b.c.

D. o. p. circulas magnus in quo fupputan-turlatitudines.

M, d.feâio communis»

L. n. r. s. epicycli in diuerfa à mundo di-ftantia,eiufdem quantitatis amp;nbsp;in eadem èccen trici declinatione.quam linea m. p. per centra tranHens^manifedam facit.

(

7)ecakulobeifu(lifH4trium/ii^e^ : riorunii,

Supputata eft in tabulis latitudo, omnibus epicycli circumferentiç locis contingens,cùm centrum epicycli eft in purufto deferentis maxim« declinationis, vbi 6ó. fcrupula propor-tionaliatotam accipiuntlatitudinem portam,alijs locis pauciora,partem ipfius proportionalem!

’ nbsp;nbsp;nbsp;nbsp;’ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;/ ‘Ma.

MOTVVM COElESt.

4*

De latirudine rentre amp;nbsp;’Mercury,

Obferuatum eft hos duos Planetastriplu ci ratione in latitudinem ab eclyptica difcede-re, quarum prima eft deuiatio eccentrici: fupcrficies namque defcrentis fecans ccliptu cam fuper centro mundi bifariam,itafe habet, vtcùm epicydi centrum diftatab auge aquantis in vtramuis partem nonaginta Zo-diaci gradibus, vbi caput amp;nbsp;cauda hums deuia-tionis funt, tune ipla lit in plano ecliptica, ex ijs autem locis procedente epicyclo, incipit pradida eccentrici fuperficics lecarc planuni ecliptica amp;nbsp;cum ipfo epicyclo deuiare ab eo, in Venere femper versus aquiloncm,ih Mercurio versus meridiem, donee centrum epicydi veniat ad augem aquantis,vel eius oppofitum, vbi maxima eft deuiatio , qua deinde decrefcit vfquead nodum. Huic autem deferentis agitation! fe accommodât re-flexioquadam epicydi,nam diameter lon-gitudinum mediarumepicydi,qua fecatfeï-licetdiamctrum augis, verç orthogonaliter, reflectitur vnaquecum eo latera fiuemedie-lates epicydi fuper diametro augis verg epi-cycli tanquam axe,tali régula, vt cùm centrum epicydi eft in nodo capitis, tune nulla fgt;t reflcxio,ab eo autem loco medietas epi-

THEORIA

tycli finiftra vel orientalis, qux fcilicet eft ab auge epicycli vera versus confequentia fignorum, incipit refleéli fuper prædido a-xe, in Venerc à fuperficie deferentis ad Se-ptcntrionem, in Mercurio ad auftrum, alte-raque medietas in oppofitam confcquenter partem vfque ad augem æquantis,vbi maxima fit rcflexio,quæ deinccps minuitur,amp;in nodo altero nulla eft ; rurfumque ab hoc caudæ nodo incipit,fed in contrarias partes, prçdidæ fcilicet medietatis finiftræ,in Vénéré versùs meriÜicmJn Mercurio versùsaqui-loncm vfque ad oppofitum augis æquantis vbi maxima, quæ fimiliter decrefcit vfq;ad nodum, atq; hoc modo laterum epicycli latù tudines perpetuo alternat hæc reflexio»

Tertia ratio continet inclinationem plani epicycli ad planû deferentis: cû etenim centrû epicycli eft in auge æquantis,tune diameter tranfiens peraugem veram eiufq;oppofitum eftdireâè coniunâa piano deferentis,ab eo verô loco aux verainclinari incipit,in Venere verfusfeptentrionemjn Mercurio ad meri-' diem,amp; oppofitum augis veræin contrariam ^ partem,doneccentrumepicycli veniatadno-, dum caudç vbi maxima eft augis verç à piano • deferentisdeclinatio,deindeaût prçdiâa diameter fenfim reuertens in oppofito augis ç-gt; quantis rurfum vnitur deferentisfuperficici, _amp; ex eo loco difcedente epicyclo,aux vera de-nud

MOTWM COELEST, 4, nuoincipit dcclinare,fed in Venere ad merk diem,in Mercurio ad aquilonem, v fque ad no dum capitis, vbi maxime inclinata deinceps ad luperficiem deferentis redit,vt antea,omnis( j in auge çquantis euanefcit declinatio. Quorum omnium varietates fubieda tabella com-plcditur»

Deuiatio maxima,

V eneris borea, Mercurij auftrina.

Maxima reflexio. Siniftræ medietatis. in Venere ad meridiem : In Mercurio ad boream.

Nullainclinatio.

^4ullainclinatio.

^ 3

r nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;THEOMA

^e moJo/u/gt;jgt;utandt ladtuiitnts (Quorum

~ ; inferiorum^

Calculus hicpatet ex præcedentibus ; nam Colledis fingulis latitudinibus, ( quæ fcilicet , vel rationedeuiationis,reflexionis,amp; déclina tionis contingunt quouis Planets in epicyclo loco)fecundum inuentam fcrupulorum pro-portionalium multitudinem,ijsque omnibus vel aggregatiSjfi eiufdem fuerint qualitatis, vel minore ex maiori fubtraâa’, fi diuerfs, fummareliquaquantitatem amp;nbsp;qualitatem la-titudin is ab ecliptica oftendit.

Se^a^ionièuf ^ua Planetif ratione eccen-trici amp;nbsp;e/icycü contingunt.

Planets in fuperiori epicycli parte dicun-turdiredi, quandiu fcilicet linea verimotus ad corpus Planets excentro’mundi protra-éta,fecundum fuccefsionem fignorum procédons,additipfi apparent! centri epicycli mo-tui,verum corporis Planets motum : qui eft Veruj différends due partes ipfius totius squatio-corporis ^is orbis refpondentes fingulis,epicycli arcu-nanÂæ bus:amp;cùmlinea prsdifta æqualibustempo-ribus squalique nimirùm in epicyclo curfu, maximas eiulmodi partes circa apogion epicycli abfcindat atque addat, fit vt motus cen-

• tfi maxime illic intendatur,Planetaq; videa-’ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tur / nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;’ \

MOTWM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;4^

tur vclocifsimus ratione epicycli, rui corporis Planets apparenti v€locitati,fi accedat ma ^ xima velocitas apparentis motus centri epicy di,qus fit ratione eccentricitatis, tune eo loei Planetaduab. decaufisfummam merito ob- ' tinet velocitatem.

Atquehædifferentiæ squationis ab auge epicycli fenfirn decrefcentes propter circuli conuexitatem,Planets etiam apparentem mo turn minorem reddunt donee Planeta totius fuselongationis fpatium emcnfus, veniat in circumferentia epicycli ad punöum conta-dus fipiftrum fiueorientale,(vbi vcri motus linea trafiens per corpus Planets ad Zodiacö, contingit fcilicet epicycli peripheriS non fe-cat) quo loco ipfe Planeta fuocurfu nihil aut infenfibiliter motum centri in^odiaco pro-mouet. Inde autem prsdida linea fecarerur-fus epicyclum,recurreread centrum epicycli, relegereq;percurfa z-odiaci loca, maioresque fubindesquationis partes motui centri apparenti adimendo ipfum retardate vi detur, donee differentia squationis abla tiua,fiue appa-rens Planets motus,amp; veruscentri motus, eodem temporis fpatioinueniantur squales: . tune enim his duobus motibus contral ijs, fi-biqueinuicemobnitentibus,çompéfatis,cùm • alter alterum tollat,Planeta eodem z,odiaci lo coaliquantulummanereideoq; ftarefiuecó-fiffere videtur:8e arcus epicycli ab auge vera*

F 5 3d

THIOMA

ad hoé vfque pundum, dicitur ftationis prL mæ. ExeoautemlocoPlanetæ apparens motus fuperarc motum centri incipit, amp;confe-quenter Planetaretrogredi, amp;nbsp;in pricedentia bgnorum tendere fentitur,tantü femper.qua-tum fubtraéliomotuscentri reliquü facit, amp;nbsp;plurimum quidem circa perigium epicycli,v-bi maximasæquationisdifferentias in contra-riam pattern perträfit, à pcrigio autem motu« Planetæ apparens fenfim minuitur, Planetaq; denuó in occidentali epicycli parte ftare com-peritur,atq; arcus ab auge vcra perftationem primam ad hoe vfque pun(Sum,dicitur ftatio-nis fecunds. Ab hoe autem loco fuperare mo-

(undum fucceff.fignorum apparenter moue-fi incipit, quäuis ipfa veri motuslineaetiam-num in præcedentia feratur vfq; ad pun(^tum contaétus fecundum, (iue occidentale, vbi am bo motus in eandem confentientes partem,ve locitatem deinceps adaugere pergunt.

Hæc autemduocontaétuspundta æquali-ter quidem,at non femper,neq; in omnibus e-picycliseodem interiiallo, à perigæo verodi-ftant,nam amp;nbsp;niaior cpicyclorum amplitudo, amp;nbsp;minor acentro mundi diftantia, maiorem ipfisadperigje^m praedidtum, propinquitaté çfficiunt, augenfesnimirum angulum aequa-tionis ad centrum mundi,vnde conlcquenter «jiigulus ad cetrura epicycli comprehédens ar-cum

MOTW'M COSIEST. 4# cum fiuediftantiam à pundo contadus ad pe-rigaeum verum contrahitur,tantoq;anguftior ncccirario, ipfeque arcus minor redditur ^ vt (quadoquidem angulus ad pundum cótadus femper eft redus per 17. tertij EuclidisJ iftius triangulifquodduælincæ mundi cum femi-diametro cpicycli conftituuntjtres anguli.ma néant duobus réélis æquales.quod neceffum eft.Vndecognitoxquationisangulo.diftâtia pundorum contadus à perigeo veto latere non poteft.

Loca veroftationum,tertiainruper de cau-fa,diuerfa fcilicet motuû inter feproportione, variantur, vnde foli etiam Mercurio peculiare eft vtcontrà,quàm in reliquis Planetis,propin quifsima lint opofito augis verse epicycli,cùm centrum cpicycli eft in maximaamundodi-ftantia,remotioraverôcùmin perigio eccen-triullicetcnimPlanctatardius,hic autem ve* locius raotum centri adçquat,quandoquidem propter eccentricitatis,epicycli,fuic]; in epicy-do curfus magnitudinem^additio exceftus ma iorem proportionaliter conciliât iplius apparent! motui velocitatem, quàm _motul centra çquationis eccentri additio.

Porro cognita ftationeprima, innotefcit amp;nbsp;fecunda, cùm ambo ilia punda equaliter à perigæo vero epicycli eiufque oppofito di-ftent, arcusque epicycli interea comprehen-fus,fuperior quidé diredionis, alter inferior, dick

THEOIIÏA » dicitur rétrogradationis, quorum quanti tas variât fecundum prædiâas très caufas.

Lunaautemetß epicyclum habeat,retro* gradation! tarnen vel ftationi obnoxia nó eft, nunqenim motus epicycli fecüdi,motum pri-miexæquare, nedum fuperare, fed intendere amp;nbsp;retardate folùmpoteft. Vndediuerfimodè vel velox vel tarda videtur.

Planetæ auâi numero dicuntur, quando aequatiofuperadditur medio motui.

Auftiqj curfu,cùm linea veri motus citius quàmlineamedij motus,aut fecundum fuc. ceff.fignorum incedit,aliàs minuti.

Omnesautem velocitatis amp;nbsp;tarditatis eo-rum diuerfitates amp;nbsp;gradusex praecedentibus patent.

AuóH lumine dicuntur,Inferiores, quan-diu recedunt à Sole vfque ad maxima: elonga* tionislimitem ; Superiores quandiu fol ab i-pfis, fcilicct vfque ad oppofitionem, cxinde minuti.

Orientales matutini,ciim ante folem oriun tur,occidentales amp;nbsp;vefpertinicùm occidunt poft folem.

Orientes ortu matutino vel vefpertino cu itajmanèvel vefperiiconfpicuielTe, occiden-^çs cum ita occultariincipiunt.

MOT WM COEtEST. _ ^y Ditem/rore-primi ^^/eé^us yeh/'/aritionu

LunteJgt;oß coniunßionem.

Tribusdecaufis Luna àconiunâione fb-lis citius vel tardiusmortalibusapparere inci-pit.Nam fi coniunâiocontingatin medietate ecliptics ,quæeftà fine lagittarij,per arietem vfque ad finem geminorum, velociüs liberata folis præfentiafeptentrionalibus populispro-dibitcófpicua,quam fi in altera, quandoquidé ipfius parallelus fiue circulus motu firmamen ti diurno defcriptus borealior cxiftens paraile lo folari, etiam interuallum temporis inter oc cafum folis amp;nbsp;luns, ipfamque folis abfentiam adauget: plures etenim funt gradus in paraile-lo luns ab Horizonte ad lunam,quàra in zodia co à foie adlunam.

Ländern qjrationem Habens fecundacaula eft lunælatitudo.

Tertia deniquevelocitas motus veri luns vel tarditas.

Lt his omnibus concurrétibus vel citißi-me, amp;nbsp;vnius diei ferè fpatio,vêtus amp;nbsp;noua,vel tardifsimè,amp; quarto die côlpicietur, alioquin fecundum rationem caufarum fecundo vel tertio die.

Defaraliaxi/tue diuerßeate ßß^e^us.

Cùm vera aftrorum in firmamento loca terminentur per lineam ex centro mundi e-duâanijfitplerunquc in ijs quidem Planetis .

ad

’' ŸKÏÔMA

id quorum altitudinem orbiumq; quantki* tem,femidiameterglobiterrsex centro fcilu eet ad eius fuperficiem, fen (ibilem, habet pro-« portionem, vt, præfertim amp;nbsp;maximein Lunà citima nimirum terræ, minus autem in Mercu rio V enere amp;nbsp;Sole,minimumque in Marte.fit Inquam vt locus vifus fineapparens quem dc-monftrat linea ex oculo afpicientis protraâa, différât à loco vero,quæ differentia vocatur parallaxis,amp; eft arcus circuli magni per pun-dum verticale,fine x.enith amp;nbsp;verum locum aftri tranfeuntis,interceptus inter verum amp;nbsp;apparentem locum.per illas duas prsdidaslü neas.atquehæedifferentiatanto maior quanto aftrum propinquius eft Honwrithtanto-que minor quanto propinquiusinuenitur ver tici,adeo vt coincidentibus tandem illis dua-bus lineis,fjt omnino nulla.

Præterca minoraftri àmundodiftantiama-iorem vbiq-, differétiam efiicit, vt diócum eft, vnde parallaxes lunç excedût parallaxes foils.

Prædida autem refpeäus refpedu verticis parallaxis efticit duplicem afpeótus diuerfita-tem refpedu eclipticæ locumejue Planetg in longitudine amp;nbsp;latitudine alterat.

Diuerfitasaiit'afpeétus in longitudine, eft arcüsipftuseclipticçinterceptusinterduos fe-•micirculos magnos, quorum vnus à polis ecli pticçperlocum ftelleverum,alter ab ijfdeni

. polis per locum vifum tranßt.

Diucr-

MOTVVM COÊlEST. 4«

t)iuerfjtas in latitudine eft arcus circuli ma gni per polos eclipticæ Si locum äftri verum tranfeuntis,comprchenfus inter duos circuloj cclipticçparallelos, quorum vnus per locum verum veramque fcilicet latitudinem, alter per locum vifum ducitur.

Nobisautemfeptentrionalibusiunçlatitu-do auftralior femper,idcoquc citraeclipticam minor.vltra autem, maior videtur quàm reue rà fit.

Ex quibus iam notandum eft veram lumi-narium coniunâ;ionem,quç fit per lineas veri motus.differreàvifibili,quam lineçîvifusin eundem locum fecundum longitudinem co-euntes efficiunt.

Et fi coniundio vera fiat inter gradum e-diptieç orientera,eiufque nonagefimum ab afcendente,tunc vifibilis earn prçcefierit, inter eundem autem nonagefimum amp;nbsp;occidentem, veram vifibilis fequitur.

In ipfo autem nonagefimo gradu, cum fem per fit in circulo per polos zodiaci amp;nbsp;zenith tranfeunte, nulla contingit in longitudinem parallaxis, coincidentibus nimirùm tunc li-neis ex centro,mundi, eiufque fuperficie, du-Ûis.

(THEORIÀ

• •. in priori Gt Horizon n. o. t. oriens n.occu dens t.

j O.centrum globi terrât.

• • K. m. n. referai primo circulum verticals,' pro 1

MOTWM COELEJT. nbsp;nbsp;nbsp;nbsp;4j

proz-odiaco vtm.fitnon punétum vertical« lèd medium ecliptics inter orientem amp;nbsp;occi-dentemjiuegradus 90. eclipticsaboriente.

D.n. vifibilis o.k. vera coniunlt;S:io,reliqua patent per fe.

In altera figura,r. a, c.f, portio z.odiaci eft»

L.a.b. circulusaltitudinisa verticedefcen-dens.

A.locus Planets verus,b. vifuï fiue appa-rens.

A.bparallaxis verticis.

A.c.longitudinis.

B.c latitudinis, qus tanto femper magis au geturquantómaior eft regionis latitudo fiue poli elcuatio.

Liquet autem has tres conftituere triangu lüredangulum,cuius hypothenufa fiue latus reâo angulo oppofitum,fit parallaxis verti-cis:eodemq; pon o modo fe habere vbi vcrus locus eft extra eclipticam.

De ^nantteaee ahiruJmum So/i4 amp;nbsp;Lums.

Qitalium femidiameterterrs,ex cius fcili-cetcentroadfuperficiem eftpars vna, talium diftantia Solis in apogso à centro terrs eft hocfsculo nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;1179,

C £(,

TH EORlA

rdiuiduæ Çmaxima ab code centre» \ ealtitudoóS.cum trientc. EtLunsA (^minima. nbsp;nbsp;nbsp;52.17 min. /nouævelj maxima* nbsp;nbsp;nbsp;65.30.min. ^plenx Lminima. nbsp;nbsp;nbsp;55. 8.min.

Se ratione ca/cuü/gt;araUaxeon So/14 amp;nbsp;Lunte, in arcu/o aicteui/im^ rej^eifu yer-tict4 contingentium.

Ad barum parallaxium inueftigationem habetur in tabulisprutenicis fub finem,canon generalisparalIax.Solis amp;nbsp;Lunat.in cir.altitud. Eiufq; v(us traditur præcepto52 Ratio autem itafe habet.

AcquaIcs in circulo altitudinis ab vtraq; ver* ticis partediftâtiæ.f versus orientale in primo quadrate,vel occidétalé horizótem in vitimo quadrate,squales dant parallaxes, q idcirco, (cótinuata diftatiaiü numerationep orienté, nealio numi roróordincopus eilet; duplica-tis accipiuntur diliantijs.Et in Lunaquidé:pri • mum,fecund' limitis.contingctes fcilicet cum in noua plenanc Luna,centrum epicycli fecun di eft in apogso primi.his autem in prsceden-ti columnula additus eft defeótus,vel differen tiaprimi amp;nbsp;fecundilimitis, qua minores funt ills quseodem centri loco eademq; diftantiai contingunt in quadraturis fiue Luna diuidua, propter maiorem tune eiusà terra altitudiné.

Atq; vtintermedijs etiam inter fyzygias amp;

• nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;qua-

MÓTWM COELÉST. ,• VJtiaciraturas, altitudinum varietatibus, quas duplex longitudo eodemcentri epicycli in ai* pogio primi loco^efficit, prouifum effet, con-ftituta^funt fcrupula proportionalia niinoHs epicycli, quæ,vbi duplex longitudoconfecit femicirculum,(exiftentefcilicetPlaneta in auge fecundi ; 60. totam differcntiam fubtrahch-uam effe ex inuenta apogaea parallaxi ollen-dunnaliàspauciora,partem proportionalem: vt fit parallaxis apogga^conueniens tali Plane-tçinepicyclo fecundo fitui,cvimcentrurfi eft in apogio primi,emendata.

Similiter fi centrü fecundi fuerit in perig^o primi,accipiuntur parallaxes tertijlimitis,con-ftitute ad nouam plenamue Lunam, ac emen-dantur,fi necefie fit, iuxta fcrupula proportionalia minoris epicycli, per difterentiam tertij amp;nbsp;quartilimitis,qua fcilicet contingentes in iquadraturis propter minoréaltitudincm exec duntprçcedentcs,vtfichabeatur véraac emen data parallaxisperigçà

Vbi autem manentibus reliqüis,centrum e-picycli fecundi fuerit intermedijs,inter apo-gion amp;nbsp;perigion epicycli primi,locis, tune per lubtraéiionem accepta düarUm prçdiétarum differentia, ciufq; parte proportionàli congruent! ferupulis proportionalibus maioris epicy cli,percoçquatamanomaliam inueniédis, aa-dita^pogçç emendatç prodit vera parallaxis «ddàtam difiantiam fitumq; Planet^/

C 2. ParaV

rApogaea maxima' ParallaxisLunaeingra I di.amp; fcrupulis circuli J in fphæra magni, 360.«^ graduum, quod amp;nbsp;de | fequentibus intelligen

dum eft. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;tPerigsea maxima

MOTWM COÏLÈST. j» ' Parallaxis auté Solisfimpliciteraccipltur per duplicatas diftantias inueniturq; ad hori-zontem maximaqua indifferenter m o-mnibusSolisabaugcdiftantijs vti licet,citra errorem.

Ad fupputationem deinde parallaxeólon gitudinis amp;nbsp;latitudinis danturcanones trian-guliorthogonij,inquibus,ad diuerfas regio-num latitudines, fupputata eftproportio late-rum prædiâi trium parallaxeon trianguli in partibus,qualium hypothenufa fiue parallaxis verticisadfumitur 6o-. Itaquedefumptis excanonelateribus longitudinis amp;nbsp;latitudinis, fcitur per regulam proportionum quantum illiscompetat ex partibus veræ inuenta: verticis parallaxeosivtexempli gratia,öc'.lia-bent4o.quantumcompetet 50 amp;lic dercli« quis. Sciendum autemadparallaxesverticis in Luna contingentes conftitutum efle inta-bulis,Canonemfpecia!em Solis amp;nbsp;Lunæ no-uaeincirculoaltitudinis.exquo,minori labo-re amp;nbsp;compcdiolms fumi poffuntper diftantia à vertice amp;nbsp;motum anomalie,

quot;De ecli/gt;ß Lunte amp;nbsp;So/^.

Initio feien dum eft Lunam à terra, terram à Sole fuperari magnitudine.Ideoqucconfe-quenter vmbram terra: fquæ mortalibus no-lt;ftemefficlt referre coni rotundam amp;nbsp;acumi-natamformam,per cuius medium linea ex*

. G 3 cen-

T E o RIA

ccntro Solis pcrq; mundi centrum amp;nbsp;in plano' ipfiuscirculi lokris veisùs oppofitum Soli in eclipticalocüdireftè extéditur, adeoq;ipfura eclipticç planum, per centrum mundi, totum conü fecat medium,ipfeq; coni vertex circum lertur fub ecliptica centro corporis folaris Temper oppofitusdiametraliter.

liane autem vmbram.vt maxima Solis à mundo diftantia,longifsimam,ita minima,bre tiilsimam ftridifsimamq; reddit, quandoqui-dem extremi corporis folaris radij ttrrç orbe inferior! hic loco contingentes,citius etiam co num prçfecent,anguftioribusq; terminis indu dant. Proindè,vbi Luna plena fine oppolita Soli propc nodos prçdiâam vmbram euitare non poteft,tunc ipfa per fe opaca luceq; luccns Solis,ncccirariö,velaliqualui parte obfcura-tur,fitq; eclipfis partialis: vel tota, fitq; ecliplis totalis:amp; vel cum mor3(eaquetantó maiore, quanto diameter vmbrç eius loci,quem Luna pertraniit, magis cxcedit quantitatem diame-tri Lunç,} vel line mora : vbi exiftentibus his diametris, çqualis magnitudinis, Luna ftatim altera fui parte emergens, ne minimum qui* dem temporis,toto fuo corpore in ymbra mo ratur.

In ipGs autem nodis,capite fcificet vel cau* da Draconis,Luna Temper totalem eclipfim lubit.

, Semper etiam eclipfes Lunç funt vniuerfa-

M o T V V M C OE L E S T, ,» les,omnibus fcilicet hominibus,quibusipfum corpus Lunç confpicuum cft videntur principe , finis, amp;nbsp;magnitudinis ratione, çqualiter, quia Luna verè,vt diétum cft,luce non fua pri uatur.

Alijs autem locis zodiaciJatitudinis benefi «io libcra,nihil mali patitur,nullamq; luminis iaâuram facit.

Futurçautemlunariseclipfis eft indicium, fi fub ipfam veram prope nodos oppofitio-nem, vera Lunç latitudo, minor inueniatur, quam aggregatum ex femidiametro apparen-ti corporis lunaris amp;nbsp;femidiametro vmbrç, v-bi Luna tranfit.Sin fuerint inter fe çqu31ia,f o-num corpus Lunecontinget,non ingredietun corumq; ratio eft manifefta enam veraJatitu-do Lunç cft centri iplius corporis ab ecliptica diftantia, fi itaque cxplanocclipticefinquo medium eft coni,vt diximus^femidiameter vmbrç eduâa, iungatur femidiametro Lunç, totaq; illalinea plùs inueniatur fubtenderein circulo latitudinis magno,quam diftantia centri, fcquitur neceftarià globum Luneimmer-fumefte vmbrçcirculo,aliàsvero velomnino eum euadere aut foliim attingcre.

Aliudprïtercafignum Ptolemxustradit:fi fub ipfam fcilicet mediam oppoutionem inter equalem Lune locum amp;nbsp;alterutrum nodort'i, interiedum fuerit fpatium minus grad. i$.cij

G 4 ».min*

THEORIA

12. min. tuncprimùm pofsibilc effe vmbram tangiàLuna.

Præfenti autem mundi œtate fi locus me-diæ oppofitionis inueniatur diftareà nodogr, 14. min.24 certumfit,non futuram effe edi-piin,intra illos autem terminos fieri poffe.

Admagnitudinem denique obfcurationis Lunæ amp;nbsp;durationem prænofcendam,requiri-, tur prater veram eius Jantudinem^cognitio turn Lunæ apparentisdiametri, (quot;quam minor à terra altitudo femper maiorem reddit ) turn, vmbræ diametri eiusloci, quo Luna tranfit, quam etiaroin cadem Lunæ diftantia , Solis maior vel minor altitudo variât.

Atque prædidaruradiamçtrorum quantitates itafehabent.

Çdiuiduæ,ig. ^j. apogxæj

Inou® vel ^plenæ, 50. 0., fdiuidue, 5 7.34. perigseæJ

fnouævel • [plen«, 55.38. - nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;m.

Diameter vmbræ2 çLunæapogææ, 76. 36. :lt;ùm Soi fuerit in^ranfituss^hocfseculo nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;^

apog«o 5 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;. a’«”g®®,i nbsp;nbsp;nbsp;P5’-3i*

THBORIA

Variatio diametri vmbrae maxima eft’mio. ï. fec,fo.quibus minor eft vmbraträfitus cum Sol eft in perigio,quàm cumin auge.

Licet autem in omnibus Solis à mundo di-ftantijs citra notabilem valde errorem tali pro portione venari vmbraetranfitus quaritatem, vt fciliceteius diameter fe habcat ad Lunae ap-parentem diametrum,quemadmodum 13. ad 5.

Diameter autem Lung amp;nbsp;Solis diuiditur ab Aftronomisin 12. partes aequales,quas digito» 1 fiuepundavocant.

Minuta incidentig funt,quibus in partial!, vel totali fine mora, centrum corporis Lu- ' ng fuperat motum Solis ab initio defcdus ad medium eius, fed ab initio defeäus ad totalem obfcu ration era , in totali cum mo- ; ra.

Minuta morg dimidig funt etiam todiaci _| minuta,quibuscentrumLung fuperat motum Solis ab initio totius obfcurationis vfqucad j medium totiuseclipfistempus,quod quidem à veri plenilunij fiue oppofitionis tempore nondiffertfenfibiliter. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;*

Hisautemferupulis diuifis per fuperatio-nem Lung à Sole horariam, prodit tempus quoLunaeapeurrit, amp;nbsp;ex hoc totius deliquij tempos innotefeit. Etenim in partiali, fiue to^ tab fine mora,lólum incidentig tempos duplL '

J

MOT WM COEIEST, j* lt;atum totam ccIipGsdurationem odendit fads exaâè.

Intotaliautem cum mora, temporis inci-lt;îentiçamp; temporis morç dimidiç iunâorum fumma dupl icata,eandem totius eclipfis quan titatem recidit.

Minuta autcmegreflus fine replctionis inJ teUiguntur vel à medio totius ddiquij, vel ab initio eroerfionis Lunç ad finem ecliplis, quç çommuniter vt equalia fcrupulis incidentig fumuntur,etf) parua fit differentia propter ci-tam motus lunaris variationem.

Plures qu^m n. digiti ecliptici fignificant moram,tot fcilicet duodecimis, ipfum tranfi-tumLunæ in vmbra,maiorem effe corporis lunaris diametro.

Adrationem folarium eclipfium, quæ in coniunâionibus fiuenouilunijs prope vel in podis contingentibus fiunt: Sciendum eft, lu-nam opaci folidi amp;nbsp;adiaphani corporis fui in-terpolitu, aliquam aliquando folaris luminis pattern auertere,aliquado etiam,quia terrç eft maxime vicin3,totum Solem licetmulto ma-iorem obtegere, veruntamen line vlla,mora, propter motus fui velocitatem folisq; jnagni-tudinem,neq; etiam vniuerfaliter cmfdem hemifphærij terreni incolis Sol ecliplatur, propter afpedus diuerfitatem,euro Sol lumçq iuum femper retineat.

•' [THEORIA

* Futurs folaris edipfis certifsimum eftargU mentum,fi fub apparentcm fynodon,vifa Lu-n5e*la(itudo,minór eflfumma femidiametro-furh apparenttum,Solis amp;nbsp;Lunæ:cùiii enim v-ttaqne bt diflantfa centri Lunæ à plano eclipti cæ,debent faltem squales effe, vt corpus Lung ft'ôW'împediatgîobum Solis.

* Ptollemçus alram infuperdijudicandi régit Ïam traditjcilicet fi ad mediam fyzygiam no-uilunijinonis gqualis latitudinis LunçFucrit mator partibus ë^ min 19.amp; minor part. 101. min.2i.aut maior ij8.3S.amp; minor 290.41.tunc poffe fieri echplîn,de qua extra illos terminos timendumnon fit.

' Ad magnitudinemautem durationemque obfcuravonis,prçterparallaxium, vifçlatitu-0inis,Lune4; diametri, notitiam,etiam iplius Solis diametri eogrtitio necefiaria cil. Hoc autem Qculo diameter Solis apparens eft g x.

’ inapogço 0.31.3 8 inperigeo 0.35.34.

Interjnediorum autem locorum diametri accipiuntur per motum Solis hora ' ium ,qui fc habet^d apparentem diametrum,vt5.ad66. proportionalis ferè fug difiantie.

Minuta irteidentiç in edi pli folari, funt mû nura zodiaci, qnçLuna fecundum apparenti-am, ab initio defeétus vfque ad eius medium . pe*-

MOTVVM COEIEST. nbsp;nbsp;nbsp;nbsp;nbsp;it

vifum,fiue apparentem motum Lunc àSoIe horarium,exitteirfpusprincipij vfque ad medium ecliplis,amp; huictempori gquale vulgo ftatuitur,tempus egreffus, à medio fcilicet vC quead finem deliquij quamuis aliqua difleren tia pofsit efle propter parallaxes.DupIi-eâto igitur predido tempore habetur tota du.

ratio. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;’

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;;(

De ratione ma^nitui^m^ Solt^,Luna,amp; Terr^iaelinuicemi

Ratio diamefriSoIis ad diamctrum terras fe habet vtpartcs 5.min,27.circiter,ad partent vnam,vcl,vti44z}..ad 265. vnde per cubicam multiplicationem manifeftum euadit folidum corpus Solis maius elle globo terrx 162. minui oftaua parte vnius.

Ratiodiametriterrç ad diametrüm Lunç eft vt 7 ad 2. vnde terra Lunam fiiperat45.minus oéaua parte vnius,id eft Lune.

Sol autem Lunam excedit 7000. minui 6 2 .

Maxima Vcrticis vmbrç|à mundi centro di ftantiajcilicet ipfe axis vmbrç vellinea in medio coni à centro mundi vfque adverticem, cum Sol fuerit in auge,eft talium 265.qualiurà femidiameterterrç eft pars vna.

De ^J^e^îtl/tf.

Non fine ratione pythagorica, quinq; po-tifsimùm in firmaméto afpeâus,recepto5 effc apud Aftrologos,verifimile eft.Quorum primus, coniuného, ('talicharaéteredéfignari lolita éj )cft,cùm locum eundem vnius eundé4; alterius in diuerfa altitudine vna demonftrat redla linea ex centro terre eduda.

4(. Sextilis vel Hexagonus,loca,(5o.circuli magni gradibus diftantia, continet, vt in ecliptica, Ariesgeminosdextro,ilium hifiniftro , fextilialjaiciunt. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;Q Qua-

■T THEORl A

O Quadratus vel tetragonus 90. gradibus, loca diftinguit,in quo afpedu funt Aries amp;nbsp;Cancer.

A Trigonus no.graduum habetintcruallu, quo diftant inter fe A ries amp;nbsp;Leo.

Oppol!tionein,eadem mundi diameter per centrum terre vtrinq; produôa, indicat.

Omnes autem afpeftus vocantur partiles funtq; fortifsimi,quorum quç cos dénotât recta linea ne minimum quidem minutumjn a-liquam partem aberret:aliàs,platici,affluentcs Sedeßuentes.

Radij liniftri cum firmamentoferuntur, i-deoq; validiorescenfcntur. Dextri autem fe-cundum fuccefsionem hgnorum fe extenden-tes, motu firmamenti qua li auferuntur, id-eoq;debiliorcs.

Referunturautem omnes afpeäus, ftelh-rum quidem amp;nbsp;Planetarum,ad eclipticam po-tilsimüm,locorum cœlfad çquinoftialem,

Epochteßue rae^ices motuum cosleßtum amp;nbsp;comufiSltofium Eiauftarum.

Apponere hic operçpretium duxi,epochas, adqiiasfubfcquentiumtemporuin motus reien iamp;fupputaripolsint,quod ex hoeparuo libello,(iiiealijstabulis facile elf cuiuis vel pau kdufn faitem io alironomica logiftice vcr-fato.

Ad tépus itaq; quo hic author in luce editus eft

MOTVVM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;jy

èft quod fuit anno domini i545.i2.Septembris manè inter prima amp;nbsp;fecundam. Suntq; cóplcti Anni. Menfes. Dies. Hor®. Minuta.

1542. nbsp;nbsp;nbsp;nbsp;8. nbsp;nbsp;nbsp;nbsp;ii. i. 28.

ad meridianum clarifsim® vrbis Vltraiedi, motus coeleftesinueni, vt fequuntur.

^e^uino3tj quot;verni, Aequalis motus præceff. æquinodio. __S. g. m. 2. nbsp;nbsp;nbsp;nbsp;4.

0. 27.4. 2. 57.0. ’Anomaliafimplex. 2. 48.3 0.42.5 2.2 0. Vera præcefsio æquinoâij à prima ftella A-rictis. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;0. 27.31.54.18.0.

Aequalisfimplex. nbsp;nbsp;2. 32.16.43.49.53.

Anomaliaannuafjrnp.i. 20.2 8.26.42.0.. Verus amp;nbsp;apparens locus ab æquinoélio ver-

no. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;2. 57.59.8. 16.53.

Media fine squalls longltudo à Sole.

2. 3941.21.29.25. Anomaliaæqualis. 4. 41.43.15.38.32. ^Vera diüantia à vero squinoftio vernali.

5- 44’47’4i‘3i»ï8.

Veradiftantia ab æquinoôio vernali fecun-dumlucceiï.fignorum.5. 9. 59.22.33.7.. ‘ '^ ” nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;H Acqua-

tÖEORlA

• s. nbsp;nbsp;nbsp;g. m. L ;.\4;

Aequalislongit. 5. 20. 15. 17. 10.-156.

• • Acqualisanoma.cóm.5.12. 3. 2^. jg. 57. Locus apogsi à prima ftella Arietis.

4. o. 45.49.40.0.

Veruslocus abæquinoétio vernali.

■ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;5‘ 47-i3-53‘58.56.

Acqualislongit. 5. 13.15.14.47.15..

Aequalis mot’cómut. 5. 19.1. 29.2. 34.

Locus apogæi à prima ftella Arietis. ^- ?8-3,4-“4-lt;5. 40.

V era diftantia à vero «quinoâlo 3- 3i-n-4gt;5 ’19-

Aequalislongit. i. 50.9. 56.52.52.

Anomalia commut. æqualis. o. 42^6. 46.57. 1.

Locus apogij à prima ftella Arietis.

2. 0. 5. 5. 11.0.

Veruslocusab«quinodio vernali. 2 4 34.24.3. 10.5».

. Aequalis motus. vtfolis* Anomal.cômut.çqual. f. 55455* Locus apogij à prima ftella Arietis. o. 48.21.

Vera diftantia ab squinoâio vernali.

3’ 4i*?i-3i-7‘J?-Locui

MOTVVii GOEtEST. nbsp;nbsp;nbsp;nbsp;nbsp;j|

?

tocus apogijàprima ftdla Arietis.

5« ji.z3.5. 29.0. Verus locus ab æquinodio vernäh.

i. 42.22.32.7. 53;

Si cui iam libeàtfupputare ex hoc libello loca Planetarum, hoc modo procedendum e-fitSit animus Icire verum locum Veneris ad horam duodecimam primi diei menfis Se-ptembris, Anni 1577. in meridiano Vitrage-dinoïS.' lunt à tempore natahtio prgmifso dies. hoiac. mm. , i . nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;i-

te. nr“b quot;'Slt;' reijciatur33,365.dies ô.horçÿ minuta 39.fecunda, fquibusfingulis Sol totum abfoluens circulum, eundem lèm-per repetit in Rellatafphcralocum^'remancnt: dies h'r. mi. t.-c.

jj^^;; 7^ ——^ cum quibus multiplicando çqualem lolis motumdiurnum vel horarium conficimus^^—^^ funtlèxagenç graduü fiue figna phyfica,5.gra.48.m.38.quç fi addan turradici premiflç,proucniût reieéto integrO circulo,~——locus amp;nbsp;motus folis çqualis à prima ftella Arietis,fcilicet in 21 gradu Leonis ftellati. Ideoque anomalia eccentri Veneris 7-^7—7^ amp;nbsp;centrum epicych circa longitu-dinem media exiftiqvnde çquatione eccentri

THKOB-t A

—Tubtrafla remanet verus ccntri epicycU =‘- O- s. g. m. locus

lam anomalia commutationis eodem tno-Ho reieâis 21. integris circulis rcmanetcoæ-lt;juata-—-—amp; quia maxima xquatio orbts In longitudinibus medijs ecccntri eft gr. 4^. proxime,amp; punftacontaftus à veroperigaeO etiam 4f.gr.amp;aliquot min.Iiquetorbis xqua-tione hic effc gr.45 amp;nbsp;aliquot min.ldcoqbelo cut Venerismatutinx direâæ,eft:in 7.gradu canCriftellatijamp;adieifta vera xquinodi] prx-cefsionefimiliterinuenienda.prodit vcrus e-ius motus ab æquinoâio verno,

Et codem modo in omnibus, fecando »-quationes pfoportionaliteramp; cum indicio, licet motus m longitudinem amp;nbsp;latitudmcm in-ucnirefatis exaôte,nogt;aütem aliquandoquod fperamus.amatorcs huiusartis non paruo la-bore amp;nbsp;difficultate!euaturi,facilem, amp;com-pendiofumpl3nèlupputand-,etlamq;dirigen-difvt vocant modum edcmus, li modo amp;nbsp;vi-tam DeuSjOtijq; paru m concédant reliquaftu-dia,nuncautem quædam ex tabulis PruteniciS defumpta hic apponere in rem ftudioforum cffeduximus.

Parsfemidiametri circuli æquinoétiorum Hue æquatio præcefsionis xquinoâiorum amp;nbsp;■ finus

In Sole.

vcIJ5ij.Ceft«qaatioA. 46. 0.

i^j.rcentn z^.,6.

fnLuna,

5S'** nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;^ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;rg'*- ^- ^»

45* C gt;? ’ j.^fecundie- Jic.i 1.45.

** cilongitudinc ’gt;78. ^veKig^.^picydi 'gt;12.2^.57.

AooA nbsp;/26o.\ nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;ƒ11.33.56.

C^jo-J VSO-/ nbsp;nbsp;nbsp;nbsp;nbsp;M. 15UO.

Maxima autem epicycli primi æquatio in pundo contadus: Maxims diiUntis efl^'“™^'adcoæquatamanomaliamgra-duum^ig.

MOTWM COEIEST. nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;«»

Porrö meminiffe debet düigens logifta ha-bendam ede rationem diuerfitatis meridiano-rum:nâ fexêpli gratia) qui motus nodro meri diano Vltraleétino ad horam duodecimam congruent,erunt illis,qui duobus gradib.lunt orientaliores,oétominutis horæ ante meridiem, fingulis enim horis æqualibus, i5.a;quato-risgradus,amp; bngulis4.horæ minutis vnus æ-quatoris gradus afcedit^ quaproptcr tabulam longitudinis fubiunximus,vt ex ea tempore «quato,motus cum epochispofitisreâècon-tinuaripofsint.

Tabulam verb æquationis diemm natura-lium bic minus neceffariam, prætermiG, fatisi cxiftimans,admonuinedies naturales çquales, quibus motus squales metimur , continere prstertotum squatoris circuitum,portinnen lam refpondétem ei zodiaci particuls, quam .Solinterea ab æquinoftio medio squaliter percurrit.Veri autem dies naturales, Solis in^ tereaverum motûà vero æquinoâio eiq;re-fpondentéæquatoris arcû,fingulis firmaméti . çôuerlionibus fuperaddunt: vnde dies çqualis femper continet,æquatoris gradus 360.mi.59. fèc.amp;verus aût,cûfol f^eritinlôgitudinib.me diis,folûcû co côueniés:aliàs minor vel maior eft,’ob motus Solis varietatc,amp; quôd zodiaci, fegmentis æqualibusnô refpôdeât æqualia æ-quatorisfegméta in firmamenti conuerfione. Vndecuicuriofiùsextabulisfupputaredatuî,

THÏORIA

temporis çquatio minimè negligenda eft ob motus lunæ velocitatem.

ComunSfionef Planerarum médité,

ConiunâioSaturniamp; louis media, fit fin-' gulis annis Aegyptijs i9.diebu$3ii.horis ij Sf aliquot horçminutis.

Èrit autem media eorum coniundio, id eft lines medij motus in eundem z-odiaci locun^ conuenient,anno Domini nofiri 1585. i^.men-fis Oâobris inter n.amp;iz.merid.

' JVlars medio motu coniungitur cum loue fingulis fgyptijs annis x.diebus8lt;ï’. horisio. inin.a5.fcc.43,eritq; media eorum coniunétio anno Domini 1577. ^7’ i^cnüs Septembris, maneà media noße horis 6. min.i4.proximè.

Saturnum Mars media longitudine adfc-quitur fingulis Çgyptijs annis a.dieb.j hor.18. min.aj.Vt anno 15 7 8. 9.Maij,hor.3.min.4O» poft meridiem,in Capricorno.

Sol media longitudme Saturnum adfequi-turdiebus 378.hora i. min. 46.vtJ9.Dccem-bris,i8.min. horæ poft meridiem, Anno 1577. fecundum calculum Romanum.

Sol, Venus, Merçurius, medio motuiun-guntur Marti fingulis fgyptijs annis z. diebus * 49.hor.z2.minut zz,*Vtannoi$77.z3.Augufti maneà media no(fte.hor.4.min ic^inVirgine, Ijdem tres adfequuntur louem, anno çgy-

* ptijcgt;,diebus33.horis2i. min.u, ytanno 1577,

gt; nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;5 Sclt;

kOTWM COELEST. nbsp;nbsp;nbsp;nbsp;nbsp;4,

^.Septcmbris,i7,minutishoraepoftmcridienX in Virgine.

Luna foli medio motu cOniungitur fingu-Ïis diebus 29. hor. 12. min. 44, fec.3.ter.i2.mc-dioquetemporeopponitur Eritautemnoui-lunium hue coniunöio Solis amp;nbsp;Lunç media, anno ij77.i2.Scptembris, maneàmedianoûe horis8.min.ii.lt;èc.^4.

Quçomniaad meridianum Vltraieótinum funt relata.

Apparentes verb amp;nbsp;veras coniundiones prefcirelicebitadminiculo motuum diurno-rumapparcntium nam minore vnius Planetj fubtraóto ex maiorialtcriusamp;cumreGduodi uifadiftantia,quotiensdiem verç coniundio-nis habebit:re(iduum deinde fi quod fueritex diftantia refolutuin horas, multiplicatii.f per 24.itaq;rurfusdiuifum pereundédiuiforé/u-peraddetquoticnti horas,amp; limiliter minuta.

Prima Hella Arietisfuit coniunda cum ç-quinoöio verno, ante Chriftum annis egy- ' I nbsp;nbsp;prijs 39 7.amp;diebus ic/.Eadem in mundiexor

dio fuit in 8. gr. Aquarij apparentis, tempore

! diluuij in primo g.pifcium.

Obliquitasfiuedeclinatio çquatoris tem-porecóditimundi, paru fuperabat media quan titaté,erat.n. eins motus in 24.gra. vltimi qua-drâtis circüli anomalaris:tcmpore diluuij fuie t parum infra mediam quantitatem eiufq; motus in i7.circiter,gradufecundi quadrantis.

~ nbsp;nbsp;nbsp;nbsp;’ Ta.

THEOM A

Talula lougiruiiiK^ aliquot locorum amp;nbsp;latitutitnii.

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