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Removing DESpecs directory which deserted to git
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:GWS4WXH4.xml</dcterms:identifier> <dcterms:creator identifier="GND:100044069">Biancani, Giuseppe</dcterms:creator> <dcterms:title xml:lang="la">Sphaera mvndi, sev cosmographia demonstratiua, ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia</dcterms:title> <dcterms:alternative xml:lang="la">Sphaera mundi, seu cosmographia demonstrativa, ac facile methodo tradita : in qua totius Mundi fabrica, una cum novis, Tychonis, Kepleri, Galilaei, aliorumque ; Astronomorum adinuentis continentur ; Accessere I. Brevis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Novum instrumentum ad Horologia</dcterms:alternative> <dcterms:date xsi:type="dcterms:W3CDTF">1635</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language> <dcterms:rights>CC-BY-SA</dcterms:rights> <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> <parameters>despecs = 1.1.2</parameters> <log>pagination goes wrong starting from 0093.jpg (should be 73 rather than 71) pagination goes wrong again on 0102.jpg (again two numbers duplicated) conflict resolved on 0105.jpg pagination is wrong on 0141.jpg (should be 119 rather than 117) 5750: changed &lt;12&gt;_In Menſibus Anni Bißextilis._ to &lt;h&gt;_In Menſibus Anni Bißextilis._&lt;/h&gt; Same: 5803, 7987, 8046, 8080</log> </metadata> <text xml:lang="la" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/> <pb file="0002" n="2"/> <pb file="0003" n="3"/> <pb file="0004" n="4"/> <pb file="0005" n="5"/> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head1" xml:space="preserve">SPHÆRA MVNDI, <lb/>SEV <lb/>COSMOGRAPHIA</head> <head xml:id="echoid-head2" xml:space="preserve">Demonſtratiua, ac facili Methodo tradita:</head> <head xml:id="echoid-head3" xml:space="preserve">In qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilæi, alio-<lb/>rumq́; Aſtronomorum adinu ntis continetur.</head> <head xml:id="echoid-head4" xml:space="preserve">ACCESSERE</head> <p style="it"> <s xml:id="echoid-s1" xml:space="preserve">I. </s> <s xml:id="echoid-s2" xml:space="preserve">Breuis introductio ad Geographiam.</s> <s xml:id="echoid-s3" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4" xml:space="preserve">II. </s> <s xml:id="echoid-s5" xml:space="preserve">Apparatus ad Mathematicarum studium.</s> <s xml:id="echoid-s6" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7" xml:space="preserve">III. </s> <s xml:id="echoid-s8" xml:space="preserve">Echometria, idest Geometrica tractatio de Echo.</s> <s xml:id="echoid-s9" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10" xml:space="preserve">IV. </s> <s xml:id="echoid-s11" xml:space="preserve">Nouum inſtrumentum ad Horologia deſcribenda. </s> <s xml:id="echoid-s12" xml:space="preserve">opus poſtbumum.</s> <s xml:id="echoid-s13" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div3" type="section" level="1" n="3"> <head xml:id="echoid-head5" xml:space="preserve">AVTHORE IOSEPHO BLANCANO BONON. E´ SOC. IESV, <lb/>Mathematicarum in Gymnaſio Parmenſi profeſſore. <lb/>Ad Illuſtriſſimum, ac Nobiliſſimum <lb/>PETRVM FRANCISCVM MALASPINAM <lb/>AEDIFICIORVM MARCHIONEM.</head> <figure> <image file="0005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0005-01"/> </figure> <p> <s xml:id="echoid-s14" xml:space="preserve">MVTINÆ, Ex Typographia Iuliani Caſſiani 1635.</s> <s xml:id="echoid-s15" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16" xml:space="preserve">SVPERIORVM PERMISSV.</s> <s xml:id="echoid-s17" xml:space="preserve"/> </p> <pb file="0006" n="6"/> <pb file="0007" n="7"/> <figure> <image file="0007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0007-01"/> </figure> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head6" xml:space="preserve">ILLVSTRISS. AC NOBILISSIMO <lb/>PETRO FRANCISCO MALASPINÆ <lb/>AEDIFICIORVM MARCHIONI. <lb/>IOSEPH BLANCANVS, S. P. D.</head> <p> <s xml:id="echoid-s18" xml:space="preserve">CAeleſtem Sphæram Atlas Mauritaniæ Rex humeris ſuſtinuiſ-<lb/>ſe creditus eſt, quòd primus Solis, Lunæ, Aſtrorumq; </s> <s xml:id="echoid-s19" xml:space="preserve">om-<lb/>nium curſus ſolertia animique vigore compræhenderit, pri-<lb/>muſquede Sphæra ab ſe inuenta inter homines diſſeruerit:</s> <s xml:id="echoid-s20" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s21" xml:space="preserve">-- -- vbi Cælifer Atlas <lb/>Axem humero torquet stellis ardentibus aptum.</s> <s xml:id="echoid-s22" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s23" xml:space="preserve">Quorſum hæc Illuſtriſs. </s> <s xml:id="echoid-s24" xml:space="preserve">atque Atauis Marchionibus edite <lb/>Marchio? </s> <s xml:id="echoid-s25" xml:space="preserve">En noua ad te venit Mundi Sphæra, quæ in lu-<lb/>cem proditura, ac noui pariter Atlantis indiga, te ſuum ſibi ſupplex cooptat At-<lb/>lantem; </s> <s xml:id="echoid-s26" xml:space="preserve">demiſſe videlicet humanitatem tuam deprecatur, vt ſuſtinere, ac fauore <lb/>tuo amplecti, tuerique non dedigneris. </s> <s xml:id="echoid-s27" xml:space="preserve">Enimuero quemadmodum noſtra hæc <lb/>Sphæra, Mundi Sphæram, ac Fabricam repræſentat, & </s> <s xml:id="echoid-s28" xml:space="preserve">exprimit; </s> <s xml:id="echoid-s29" xml:space="preserve">ita tu quoque <lb/>& </s> <s xml:id="echoid-s30" xml:space="preserve">quidem aptius Atlantem illum regia nobilitate, ſummaque eruditione effingis <lb/>atque imitaris, vt propterea nouæ Sphæræ nouus Atlas futuris ſis quam aptiſſi-<lb/>mus. </s> <s xml:id="echoid-s31" xml:space="preserve">Etenim fuerit ille regia ſanguinis nobilitate præditus, tu fortè hac ex par-<lb/>te ei minimè concedis. </s> <s xml:id="echoid-s32" xml:space="preserve">Quis enim vel leuiter hiſtorica eruditione tinctus eſt, qui <lb/>ignoret Malaſpinarum genus, quanta quamque antica inter Italicas omnes fami-<lb/>lias nobilitate pręfulgeat? </s> <s xml:id="echoid-s33" xml:space="preserve">conſtat enim eam ab Ilduino Longobardo Med@olanenſi <lb/>Duce antiquo, ac perpetuo ſtemmate deriuari, atque iam inde ab 800. </s> <s xml:id="echoid-s34" xml:space="preserve">& </s> <s xml:id="echoid-s35" xml:space="preserve">amplius <lb/>annis, in Etruria primum, poſtea in Gallia Ciſalpinam etiam, latè dominatam eſ-<lb/>ſe, atque etiamnum dominari. </s> <s xml:id="echoid-s36" xml:space="preserve">Cum enim Lucæ, & </s> <s xml:id="echoid-s37" xml:space="preserve">Lucenſis prouinciæ Marchio <lb/>Sigifridus Malaſpina in Lombardiam migraſſet. </s> <s xml:id="echoid-s38" xml:space="preserve">Parmamq; </s> <s xml:id="echoid-s39" xml:space="preserve">ab Saracenorum in-<lb/>curſionibus liberaſſet, Parmæ Comes eligitur Atho Sigiberti filius Parmenſi do-<lb/>minio Regenſe ctiam adiunxit, Canuſſiumque Arcem munitiſſimam condidit. <lb/></s> <s xml:id="echoid-s40" xml:space="preserve">Tedaldus Athonis filius, Comes vti pater extitit, ſed præterea Ferrariæ ac Man-<lb/>tuæ Marchio inſtituitur. </s> <s xml:id="echoid-s41" xml:space="preserve">Huius frater Sigibertus fit Marchio Ateſtis, vnde clariſ- <pb file="0008" n="8"/> ſima Eſtenſium familia propagata eſt. </s> <s xml:id="echoid-s42" xml:space="preserve">Bonifacius Tedaldi filius Canuſſij Comes, <lb/>Mantuæ, Ferrariæ, Parmæ Marchio, ac Tuſciæ Dux potentiſs. </s> <s xml:id="echoid-s43" xml:space="preserve">inter primum Ita-<lb/>liæ Principes connumeratus eſt. </s> <s xml:id="echoid-s44" xml:space="preserve">Hic ex Beatrice Corradi Imperatoris filia vxore, <lb/>Mathildem illam pietate æquè, ac militari gloria inſignem procreauit, quæ magnæ <lb/>Italiæ Comitiſſa, appellata eſt; </s> <s xml:id="echoid-s45" xml:space="preserve">quæque Chriſtianæ Reipublicæ contra eius hoſtes <lb/>immaniſſimos inuicta ſæpius propugnatrix extitit. </s> <s xml:id="echoid-s46" xml:space="preserve">Hanc vero magnam Mathil-<lb/>dem ex Malaſpinarum ſtirpe exortam eſſe, præter cætera teſtantur adhuc antiquæ <lb/>eius imagines, quæ ſpinam Malaſpinarum inſignè manu dextera geſtant. </s> <s xml:id="echoid-s47" xml:space="preserve">Porrò <lb/>ex his manifeſtum eſt Malaſpinarum ſanguinem Dominiorum, ac Principatuum <lb/>fertilem, tum Eſtenſes Principes, tum Canuſſianos Comites propagaſſe, ſed etiam-<lb/>num quot Illuſtriſs. </s> <s xml:id="echoid-s48" xml:space="preserve">Malaſpinarum Marchiones toti Italiæ honori, a@q; </s> <s xml:id="echoid-s49" xml:space="preserve">ornamen-<lb/>to ſunt? </s> <s xml:id="echoid-s50" xml:space="preserve">quàm latè adhuc in Lucenſi Prouincia dominatus exercent? </s> <s xml:id="echoid-s51" xml:space="preserve">Inter quos, <lb/>ſicuti animo, ac virtutibus celſior, ita etiam Ditionem, tuam cæteris altiorem ſor-<lb/>titus es, quippe ſumma Apẽnini iuga ſub tua poteſtate habes ac tenes. </s> <s xml:id="echoid-s52" xml:space="preserve">quain re per-<lb/>belle accidit, vt ditio tua Atlanticæ ditioni ſit adſimilis; </s> <s xml:id="echoid-s53" xml:space="preserve">ille enim in editiſſimus <lb/>Mauritaniæ montibus imperabat, qui ab eo poſtea Atlantes denominati ſunt; </s> <s xml:id="echoid-s54" xml:space="preserve">tu <lb/>pariter in editiſſimis Italiæ iugis dominium obtines, vt veluti Arcis Italiæ Præfe-<lb/>ctus cælitus deſtinatus fueris. </s> <s xml:id="echoid-s55" xml:space="preserve">Quin etiam ſicuti ille ſyderalis ſcientiæ callentiſſi-<lb/>mus erat, tu quoque non ſolum Aſtronomicis, verum etiam cæteris omnibus diſci-<lb/>plinis egregiè ab ineunte ætate imbutus, totum æuum ad hanc vſq; </s> <s xml:id="echoid-s56" xml:space="preserve">viridem ſene-<lb/>ctam, Philoſophiæ beneficio fęliciter tranſegiſti. </s> <s xml:id="echoid-s57" xml:space="preserve">Verùm de tua, tam in belli, quam <lb/>pacis artibus præſtantia, alias in dedicatione noſtri Operis de locis Mathematicis <lb/>apud Ariſtotelem, quamuis breuius, quam par erat, nonnulla innuimus. </s> <s xml:id="echoid-s58" xml:space="preserve">Vt igitur <lb/>Atlantem omnino referre videaris nihil aliud deeſſe videtur, niſi vt mundi Sphæ-<lb/>ram tuis humeris, tuo videlicet patrocinio, noſtrum hoc de mundi Sphæra opus ſu-<lb/>ftinere, ne graueris; </s> <s xml:id="echoid-s59" xml:space="preserve">quod à te dimiſsè, atq; </s> <s xml:id="echoid-s60" xml:space="preserve">enixè deprecor. </s> <s xml:id="echoid-s61" xml:space="preserve">quod ſi pro humanitate <lb/>tua non denegaueris, hoc noſtra hæc Sphæra tanto nixa, ac ſuffulta Atlante, cæleſti <lb/>fiet ipſi Sphęrę non immeritò fortaſſe ęmulabitur. </s> <s xml:id="echoid-s62" xml:space="preserve">Incolumen, ac tibi fælicem, Deo <lb/>Opt. </s> <s xml:id="echoid-s63" xml:space="preserve">Max. </s> <s xml:id="echoid-s64" xml:space="preserve">longæuitatem tueatur. </s> <s xml:id="echoid-s65" xml:space="preserve">Vale. </s> <s xml:id="echoid-s66" xml:space="preserve">Parmæ Idibus Februarij M. </s> <s xml:id="echoid-s67" xml:space="preserve">DC. </s> <s xml:id="echoid-s68" xml:space="preserve">XVII.</s> <s xml:id="echoid-s69" xml:space="preserve"/> </p> <pb file="0009" n="9"/> </div> <div xml:id="echoid-div5" type="section" level="1" n="5"> <head xml:id="echoid-head7" xml:space="preserve">PRÆFATIO.</head> <p style="it"> <s xml:id="echoid-s70" xml:space="preserve">PRopoſitum mihi est Tractatum de Sphæra conſcribere, quẽ aptius forte Coſmographiam <lb/>dixerim: </s> <s xml:id="echoid-s71" xml:space="preserve">in ea enim non ſolum illos decem or dinarios circulos, vt moris est explicabo: <lb/></s> <s xml:id="echoid-s72" xml:space="preserve">verum etiam de omnibus Mundi partibus, Elementis videlicet, Cælis atq: </s> <s xml:id="echoid-s73" xml:space="preserve">Syderibus, <lb/>ea omnia, & </s> <s xml:id="echoid-s74" xml:space="preserve">quidem abstruſiora, ſcituque iucundiora, ac dignior a pertractabo quæ ſo-<lb/>lent à peritioris Aſtronomis in penitiori Aſtronomia, multaingenij ſubtilitate demon-<lb/>ſtrari. </s> <s xml:id="echoid-s75" xml:space="preserve">ea ſunt partium hanc Mundi Fabricam componentium, or do, magnitudines, com-<lb/>menſurationes, figuræ, motus, illuminationes; </s> <s xml:id="echoid-s76" xml:space="preserve">ex quibus Mundanæ huius Architesturæ conſtructio, quæ <lb/>nihil præſt antior in hac rerum vniuerſitate ſciri poteſt, mir abiliter elucet: </s> <s xml:id="echoid-s77" xml:space="preserve">Quæ quidem omnia non ſolũ <lb/>nuda in medium proferam, verum quantumuis abſtruſa, Mathematicis demonſtrationihus, & </s> <s xml:id="echoid-s78" xml:space="preserve">verò fa-<lb/>cillimis comprobabo; </s> <s xml:id="echoid-s79" xml:space="preserve">in quibus demonstrãdis conſulto abſtincbo ab illis impeditis rationibus, quibus pla-<lb/>norum out ſphæricorum triangulorum doctrina, atq; </s> <s xml:id="echoid-s80" xml:space="preserve">adeò ſinuum tangẽtium, ſecantium, tædioſis intri-<lb/>catiſq; </s> <s xml:id="echoid-s81" xml:space="preserve">calculationibus, neceſſariaest. </s> <s xml:id="echoid-s82" xml:space="preserve">verum vtar methodo adeo facili, & </s> <s xml:id="echoid-s83" xml:space="preserve">clara, vt allatæ à nobis argu-<lb/>mentationes à quibuſuis, penè etiã ageometretis, intelligi queant. </s> <s xml:id="echoid-s84" xml:space="preserve">Ea propter vereor @e mihi Astronomiæ <lb/>peritiores iure ſuccenſeant, quòd eorum abdita, atq; </s> <s xml:id="echoid-s85" xml:space="preserve">admir anda quæque quodammodo prosiituerim, ac <lb/>in vulgus duxerim propalanda. </s> <s xml:id="echoid-s86" xml:space="preserve">Ad hanc porrò ſcriptionem iucundam hiſce rationibus adductus ſum.</s> <s xml:id="echoid-s87" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s88" xml:space="preserve">Prima fuit rerum Aſtronomicarum noua atq; </s> <s xml:id="echoid-s89" xml:space="preserve">admir anda inuenta: </s> <s xml:id="echoid-s90" xml:space="preserve">hoc enim eruditißimo Ae<unsure/>uo com-<lb/>plures ſyderum cultores, atq; </s> <s xml:id="echoid-s91" xml:space="preserve">obſeruatores ſolertiſsimi extiterunt, quorum diligenti opera, magna ſy-<lb/>der ali huic ſcientiæ acceſsio facta est. </s> <s xml:id="echoid-s92" xml:space="preserve">præterea mirabili illud Teleſcopij recens Opticorum inuentum, <lb/>plurima mortalibus, anteactis omnibus ſæculis ignota, cælitus commonstrauit. </s> <s xml:id="echoid-s93" xml:space="preserve">vnde eiuſdem etiam ſcien <lb/>tiæ magnum factum est incrementum. </s> <s xml:id="echoid-s94" xml:space="preserve">Ea propter viſum est tandem præſentibus, ac conſultiſsimis <lb/>Aſtronomis (quos in hac re Authores ſequor) nouam quoq; </s> <s xml:id="echoid-s95" xml:space="preserve">Sphæram isthæc omnia complectentem cudi <lb/>oportere. </s> <s xml:id="echoid-s96" xml:space="preserve">inter quos præcipuus, atq; </s> <s xml:id="echoid-s97" xml:space="preserve">inſtar omniũ ſufficiat hoc loco P. </s> <s xml:id="echoid-s98" xml:space="preserve">Clauius, qn<unsure/>i in vltima ſuæ Spharæ <lb/>editione to. </s> <s xml:id="echoid-s99" xml:space="preserve">3. </s> <s xml:id="echoid-s100" xml:space="preserve">ſuorum operum. </s> <s xml:id="echoid-s101" xml:space="preserve">pag. </s> <s xml:id="echoid-s102" xml:space="preserve">75. </s> <s xml:id="echoid-s103" xml:space="preserve">moriturientẽ imit atus olorem, ſic cecinit: </s> <s xml:id="echoid-s104" xml:space="preserve">@olo tamen hoc loco, le-<lb/>ctorem latere, instrumentũ quoddam in Belgio nuper eſſe repertũ, quo cernuntur plurimæ Stellæ in Fir-<lb/>mamento, quæ ſine eo, nullo modo videri poſſunt; </s> <s xml:id="echoid-s105" xml:space="preserve">Luna quoq; </s> <s xml:id="echoid-s106" xml:space="preserve">quando est ſemiplena mirũ in modum fra-<lb/>cta, & </s> <s xml:id="echoid-s107" xml:space="preserve">a ſper a apparet: </s> <s xml:id="echoid-s108" xml:space="preserve">præterea eodem instrumento, Venerem recipere lumen à Sole instar Lunæ fit ma-<lb/>nifestum, nã quaſi alter a Lunula corniculata nunc magis, nunc minus cernitur, Saturnus quoq; </s> <s xml:id="echoid-s109" xml:space="preserve">habet <lb/>duas Stellas ſe minores, ſibiq; </s> <s xml:id="echoid-s110" xml:space="preserve">coniũctas. </s> <s xml:id="echoid-s111" xml:space="preserve">Iupiter habet quatuer Stellas erraticas: </s> <s xml:id="echoid-s112" xml:space="preserve">vt diligenter, & </s> <s xml:id="echoid-s113" xml:space="preserve">accu-<lb/>ratè Galilæus in Nuntio ſydereo, & </s> <s xml:id="echoid-s114" xml:space="preserve">alibi literis mandauit, quæ cum ita ſint, videãt Astronomi quo pacto <lb/>orbescælestes conſtituendi ſint, vt hæc phænomena ſaluari poſsint. </s> <s xml:id="echoid-s115" xml:space="preserve">Hactenus P. </s> <s xml:id="echoid-s116" xml:space="preserve">Clauius: </s> <s xml:id="echoid-s117" xml:space="preserve">quibus veterẽ <lb/>Aſtronomiam tot nouitatibus auctã noua indigere reſt aur atione indicat: </s> <s xml:id="echoid-s118" xml:space="preserve">quapropter nouã quoq; </s> <s xml:id="echoid-s119" xml:space="preserve">Sphæ-<lb/>ram neceſſario conſcribendam eſſe coram multis ſæpius edixit, quæ cuncta hæc noua<unsure/> compræhenderet, ne <lb/>Astronomiæ Tyrones, ac cæteros eius candidatos huc illuc ad varios libellos diſtrahi oporteret.</s> <s xml:id="echoid-s120" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s121" xml:space="preserve">Secunda mihi cauſa fuit Auditorum meorum neceſsitas, ij enim ſingulis annis mecum conquereban-<lb/>tur nullam extare Sphæram, quæ certa, claræ<unsure/>, ac demonſtratiua methodo ſyderalis ſcientiæ Iſagogem <lb/>traderet. </s> <s xml:id="echoid-s122" xml:space="preserve">vt igitur eorum commodo conſulerem prouinciam hanc non detrectaui.</s> <s xml:id="echoid-s123" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s124" xml:space="preserve">Tertia tandem, vt plurium alioquin Doctorum virorum iuſto deſiderio, ac precibus morem gererẽ, qu@ <lb/>præſtantiſsimè ſyderum doctrinæ percupidi, obſcuritate tamen Astronomicorum librorum abſterriti, <lb/>plurimo labore irrito, votis ſuis adeo iuſtis defraudabantur. </s> <s xml:id="echoid-s125" xml:space="preserve">Hiſcè igitur præcipuè de cauſis, tractatio-<lb/>nem hanc amplexus ſum, qua faciles, perſpicuæq; </s> <s xml:id="echoid-s126" xml:space="preserve">adeò demonſtrationes exhibentur, vt inde Lectores <lb/>ſcientificè res Aſtronomicas omnium pulcherrimas, ac iucundiſsimas, magna del@ctatione haurire poſ-<lb/>ſint, atq; </s> <s xml:id="echoid-s127" xml:space="preserve">præstantiſsimam hanc philoſophiam adipiſci.</s> <s xml:id="echoid-s128" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s129" xml:space="preserve">Cæterum prolegomena illa, quæ de inuentoribus deque Astronomiæ partibus præmitti ſolent: </s> <s xml:id="echoid-s130" xml:space="preserve">partim <lb/>ex noſtra clarorum Mathematicorum Chronologia, quam vna cum locis Ariſtotelis Mathematicis edidi-<lb/>mus; </s> <s xml:id="echoid-s131" xml:space="preserve">partim ex Apparatu ad Mathematicas addiſcendas, quẽ huic operi ſubnectemus, ſuppleri poterunt. <lb/></s> <s xml:id="echoid-s132" xml:space="preserve">Quæ vero de ipſius præſtantia iucunàitate, atq; </s> <s xml:id="echoid-s133" xml:space="preserve">vtilitate, pręponi in more est, cùm apud omnes, authores <lb/>omnibus ſint ob@<unsure/>ia, viſum eſt ſuperuacaneum ea nũc iterum repetere; </s> <s xml:id="echoid-s134" xml:space="preserve">hoc tamen vnico Plato@e ex ſepti-<lb/>mo de Repub. </s> <s xml:id="echoid-s135" xml:space="preserve">loco contentierimus. </s> <s xml:id="echoid-s136" xml:space="preserve">Oculus, nimirum, animæ, qui ab alijs ſtudijs obcæcatur, defodi-<lb/>@urq́; </s> <s xml:id="echoid-s137" xml:space="preserve">à Mathematicis ſolis recreatur, ac reuiuiſcit. </s> <s xml:id="echoid-s138" xml:space="preserve">quapropter huc conſonat illud C. </s> <s xml:id="echoid-s139" xml:space="preserve">Manlij carmen;</s> <s xml:id="echoid-s140" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s141" xml:space="preserve">Ornarires ipſa negat, contenta doceri.</s> <s xml:id="echoid-s142" xml:space="preserve"/> </p> <pb file="0010" n="10"/> </div> <div xml:id="echoid-div6" type="section" level="1" n="6"> <head xml:id="echoid-head8" xml:space="preserve">TOTIVS OPERIS PARTITIO.</head> <note style="it" position="right" xml:space="preserve"> <lb/>APPARATVS AD SPHÆRAM. <lb/>1 # Circulum Datum in gr. 360. diuidere. <lb/>2 # Angulorum quantitatem metiri. <lb/>3 # Omne triangulum habere tres angulos æquales <lb/># duobus rectis. <lb/>4 # Triangula æquiangula habere latera proportio-<lb/># nalia. <lb/>5 # Datis duobus angulis trianguli, alterum trian-<lb/># gulum illi proportionale constituere. <lb/>6 # Cognitis duobus angulis, & vno latere, reliquo-<lb/># rum laterum trianguli quantitatem inuenire. <lb/>7 # Sphæram Armillarem construere. <lb/>8 # Quadrantem, & quadratum Astronomicum con-<lb/># struere. <lb/># PRIMVS LIBER <lb/># De Circulis Sphæræ. <lb/>Cap. 1 # Suppoſitiones explicantur. <lb/>2 # De circulis Sphæræ generatim. <lb/>3 # De Horizonte. <lb/>4 # De Meridiano. <lb/>5 # De Aequatore, ſeu Aequinoctiali. <lb/>6 # De Zodiaco. <lb/>7 # De duobus Coluris. <lb/>8 # De duobus Tropicis. <lb/>9 # De duobus circulis Polaribus. <lb/>10 # De circulo ſecundi motus. <lb/>11 # De alijs circulis, qui in Sphæra materiali non po-<lb/># nuntur. <lb/>12 # De Zonis, & climatibus. <lb/># LIBER SECVNDVS <lb/># De toto Mundo in vniuerſum. <lb/>Cap. 1 # De loco <lb/>2 # De motu <lb/>3 # De figura # Mundi. <lb/>4 # De magnitudine <lb/>5 # De lumine, & vmbra <lb/># LIBER TERTIVS <lb/># De parte Elementari. <lb/>Cap. 1 # De loco <lb/>2 # De figura # Elementorum. <lb/>3 # De motu. <lb/>3 # De magnitudine <lb/># LIBER QVARTVS <lb/># De Terra. <lb/>Cap. 1 # De loco <lb/>2 # De motu <lb/>3 # De illuminatione, & vmbra <lb/>4 # De ſigura, & mutatione rotunditatis # Terræ. <lb/>5 # De maguitudine <lb/>6 # De altitudine montium <lb/>7 # De arenæ numero <lb/># LIBER QVINTVS <lb/># De Aqua, ſeu de Mari. <lb/>Cap. 1 # Deloco. <lb/>2 # De motu, & refluxu <lb/>3 # De figura # Aquæ, mariſue. <lb/>4 # De quantitate <lb/># LIBER SEXTVS <lb/># De Aere. <lb/>Cap. 1 # De loco. <lb/>2 # De motu <lb/>3 # De figura # Aeris. <lb/>4 # De illuminatione <lb/>5 # De quantitate <lb/># LIBER SEPTIMVS <lb/># De Aethere ſeu putato Igne. <lb/>Cap. 1 # De loco <lb/>2 # De figura <lb/>3 # De motu. # Aetberis ſeu Ignis. <lb/>4 # De illuminatione <lb/>5 # De quantitate <lb/>6 # Appendix problematum ex dict@s ſoluendorum. <lb/># LIBER OCTAVVS. <lb/># De Cœlo vniuerſim. <lb/>Cap. 1 # De loco <lb/>2 # De figura <lb/>3 # De motibus # Cœlorum. <lb/>4 # De numero, & magnitudine <lb/># LIBER NONVS <lb/># De Luna. <lb/>Cap. 1 # De loco <lb/>2 # De motibus <lb/>3 # De illuminatione <lb/>4 # De maculis <lb/>5 # De Eclipſibus # Lunæ. <lb/>6 # De vmbra <lb/>7 # De figura <lb/>8 # De magnitudine <lb/>9 # De altitudine lunarium montium. <lb/>10 # De Lunæ temporibus. <lb/>11 # De calculo, & Tabulis Aſtronomicis. <lb/>12 # Explicatio ſex Tabularum Aſtronomicarum <lb/># eorumq; vſu. <lb/>13 # De numeris Aſtronomicis. <lb/>14 # De vſu tabularũ, & calculo Lunæ, ac motuũ ipſius <lb/># LIBER DECIMVS <lb/># De Sole. <lb/>Cap. 1 # De loco, & distantia <lb/>2 # De figura <lb/>3 # De magnitudine # Solis. <lb/>4 # De motibus <pb file="0011" n="11"/> 5 # De Aequinoctij tempore obſeruando. <lb/>6 # De Anni quantitate. <lb/>7 # De medijs Solis motibus. <lb/>8 # De Anomalia motus Solis. <lb/>9 # De Apogæo, & Eccentricitate inuenienda. <lb/>10 # De Solis temporibus. <lb/>11 # De Annis Biſſextilibus. <lb/>12 # De illuminatione Solis. <lb/>13 # De quantitate dierum naturalium. <lb/>14 # De quantitate dierum artificialium. <lb/>15 # De quantitate crepuſculorum. <lb/>16 # De Horis. <lb/>17 # De illuminatione rotunda Solis. <lb/>18 # De calculo motuum Solis, & vſu Tabularum eius <lb/>20 # De maculis Solis. <lb/># LIBER VNDECIMVS <lb/># De Mercurio. <lb/>Cap.1 # De loco <lb/>2 # De motibus <lb/>3 # De figura # Me curij. <lb/>4 # De illuminatione, & vmbra <lb/>5 # De magnitudine <lb/>6 # De calculo motuum <lb/># LIBER DVODECIMVS <lb/># De Venere. <lb/>Cap.1 # De loco <lb/>2 # De illuminatione, & vmbra <lb/>3 # De figura # V eneris. <lb/>4 # De motibus <lb/>5 # De magnitudine <lb/>6 # De calculo motuum <lb/># LIBER DECIMVSTERTIVS <lb/># De Marte. <lb/>Cap.1 # De loco <lb/>2 # De motu <lb/>3 # De figura # Martis. <lb/>4 # De illuminatione, & vmbra <lb/>5 # De magnitudine <lb/>6 # De calo<unsure/>ulo motu@m <lb/># LIBER DECIMVSQVARTVS <lb/># De Ioue. <lb/>Cap.1 # De loco <lb/>2 # De motibus <lb/>3 # De illuminatione, & vmbra <lb/>4 # De figura # Iouis. <lb/>5 # De magnitudine <lb/>6 # De calo<unsure/>ulo motuum <lb/>7 # De qua@uor comitibus <lb/># LIBER DECIMVSQVINTVS <lb/># De Saturno. <lb/>Cap.1 # De loco <lb/>2 # De illuminatione, & vmbra <lb/>3 # De figura <lb/>4 # De magnitudine # Saturni. <lb/>5 # De motu <lb/>6 # De calc@lo motuum <lb/>7 # De comitibus <lb/># LIBER DECIMVSSEXTVS <lb/># De Cometis. <lb/>Cap.1 # De figura, & magnita<unsure/>dine apparenti <lb/>2 # De motu, & cauda <lb/>3 # De parallaxi # Cometarũ <lb/>4 # De loco <lb/>5 # De vera magnitudine, & materia <lb/>6 # Detrabe, & Cometa anni 1618. <lb/># LIBER DECIMVSSEPTIMVS <lb/># De Firmamento, & Stellis fixis. <lb/>Cap.1 # De loco firmamenti, & partitione constellationũ. <lb/>2 # De numero Stellarum. <lb/>3 # De locis Stellarum in firmamento. <lb/>4 # De Polyonimia Stellarum, & Aſteriſmorum. <lb/># Catalogus Stellarum. <lb/>5 # De Sphæræ Arateæ, & Globi Aſtronomici con-<lb/># ſtructione. <lb/>6 # De Stellis in Cœlo dignoſo<unsure/>endis. <lb/>7 # De motibus fixarum, & præceſſione Aequino-<lb/># ctiorum. <lb/>8 # De calculo motus prædicti. <lb/>9 # De motu trepidationis. <lb/>10 # De ortu, & occaſu ſyderum. <lb/>11 # De Aliter de ortu, & occaſu ſyderum. <lb/>12 # De lumine affixarum. <lb/>13 # De figura affixarum. <lb/>14 # De magnitudine affixarum. <lb/># LIBER DECIMVSOCTAVVS <lb/># Denouis Stellis. <lb/>Cap.1 # De apparitione Stellarum nouarum. <lb/>2 # De Stella in Caſſiopea anni 1571. <lb/>3 # De Stella in Cygno anni 1600. <lb/>4 # De Stella in Serpentario anni 1601. <lb/>5 # De generatione, & materia nouarum Stellarum. <lb/>6 # De firmamento. <lb/>7 # De noua Sphæra, & primo mobili. <lb/># EPILOGVS PER TABELLAS. <lb/>Tab.1 # Diſtantiæ Sphærarum, & ſyderum. <lb/>2 # Proportiones ſemidiametri terræ ad ſemidiame-<lb/># tros ſyderum. <lb/>3 # Magnitudines Sphærarum, & ſyderum comparatæ <lb/># cum terra. <lb/>4 # Proportio diam. Solis ad diam. terræ, & ſyderum. <lb/>5 # Eorundem maxima diſtantia à Sole. <lb/>6 # Eorundem vmbra maxima. <lb/>7 # Eorundem motus medij. <lb/>Appendix de Horologijs auxilio Sphæræ materialis. <lb/># INDEX OPVSCVLORVM. <lb/>Introductio ad Geographiam. <lb/>Appar atus ad Mathematicas addiſcendas. <lb/>Echometria ſeu de natura Echus, Geom@trica tra<unsure/>ctatio. <lb/>Conſtructio Inſtrumenti ad Hor<unsure/>ologia ſolaria deſcribenda. <lb/># opus poſthumum. <lb/></note> <pb file="0012" n="12"/> </div> <div xml:id="echoid-div7" type="section" level="1" n="7"> <head xml:id="echoid-head9" xml:space="preserve">INDEX RERVM NOTABILIVM <lb/>IN SPHÆRAM.</head> <note style="it" position="right" xml:space="preserve"> <lb/>A <lb/>AEdificiorum antiquorum fundamenta. <lb/># pag. # 41 <lb/>Aequatoris offitia, & ſitus. # 16 <lb/>Aequi@octiorum tempus. # 15 <lb/>Momentũ obſeruare. 103. Sectio apud <lb/># quas Stellas initio mundi. # 178 <lb/>Aeris locus, & motus. 54. Figura illuminatio, quan-<lb/># titas. # 55 <lb/>Aetheris locus. 56. Figura, motus, illuminatio, quan-<lb/># titas. # 57 <lb/>Altitudo poli, & latitudo regionis. 29. Eam inuenire. <lb/># pag. # 15 <lb/>Altitudo Solis ſupra Horizontem. # 16 <lb/>Altitudines ex vmbra metiri. # 32 <lb/>Altitudo Stellarum ſupra Horizontem. # 11 <lb/>Analemma quid, & vſus eius. # 212, 213 <lb/>Angulorum menſuratio. # 2 <lb/>Annus Lunaris quotuplex. # 77 <lb/>Annus Solaris, Tropicus, & Sydereus. # 104 <lb/>Annus Biſſextilis 108. Anni varia principia 108. Me-<lb/># tonis annus. # 77 <lb/>Anomalia Lunæ 92. Solis. # 105 <lb/>Antipodes, & c. # 192 <lb/>Apogæum Lunæ 92. Solis. # 105 <lb/>Aquæ locus 48. Motus figura 49. 51. Quantitas. # 53 <lb/>Arenæ numerus. # 47 <lb/>Aſcenſio, & deſcenſio ſyderum. Vide ortum, & occaſum. <lb/>Aſcenſio recta, & obliqua. # 19 <lb/>Aſpectus planetarum. # 72 <lb/>Atmoſphæra quid. # 55 <lb/>Aureus numerus. # 77. 95 <lb/>Azimuta quid. # 26 <lb/>Axis quid. # 7 <lb/>B <lb/>BIbliotheca ſelecta librorum Mathematicorum. # 207 <lb/>Biſſextus. # 108 <lb/>C <lb/>CAlculus Astronomicus in communi. # 78 <lb/>Calendarij correctio. # 108 <lb/>Callipica period@s. # 77 <lb/>Chorograpbia. # 201 <lb/>Circuli in gradu<unsure/>s diuiſio. # 1 <lb/>Circuli capacitas mira. # 29 <lb/>Circulorum differentia. # 8 <lb/>Circuli ſecundi motus. # 25 <lb/>Centrum molis, & grauitatis. <lb/>Climata. # 194 <lb/>Cœlum quotuplex, cuius ſubstantiæ. # 63. 64 <lb/>Coluri quid. # 23 <lb/>Comet æ. # 155. ad 162 <lb/>Contrarietas motuum in planetis. # 26 <lb/>Conuerſio graduum, & c. in horas. # 18 <lb/>Crepuſcula, & eorum quantitas. # 111. 116 <lb/>D <lb/>DFclinatio quid 19. Eam reperire. # 21 <lb/>Declinatio Eclipticæ pro varijs ſæculis. # 24 <lb/>Diameter apparens planetarum 70. Vera. # 187 <lb/>Dies naturalis, & artificialis, & eorum quantitas. # 109 <lb/>Directionis linea. # 10. 59 <lb/>E <lb/>ECcentricitas Solis. # 106 <lb/>Echo, eiuſq; cauſæ. # 219 <lb/>Ecclipſes Lunæ ad quid vtiles 36. Quomodo fiant. # 72 <lb/># Earum prædictio. # 98 <lb/>Ecclipſis Solis prædictionem attentare 130. Earum cauſæ <lb/># 122. Ecclipſium Solis obſeruatio. # 123 <lb/>Ecclipſis miraculoſa in Paſſione Domini. # 123 <lb/>Elementorum proportiones. # 58 <lb/>Epactæ inuentio. # 95 <lb/>F <lb/>FIrmamenti distantia, & c. # 178 <lb/>G <lb/>GAlaxia quid, & eius ſitus in Cœlo. # 164 <lb/>Globus Geographicus. # 197 <lb/>Gradus quot ſcrupula contineat. # 89 <lb/>Gradus vnus in terra quot milliaria continent. & # 44 <lb/>H <lb/>HOrarum in horas conuerſio, & ſpecies variæ. # 123 <lb/>Horizontis officia, ſitus, & c. # 9 <lb/>Horologiornm deſcriptio per Sphæram. # 189 <lb/>Horologiorum deſcrib. inſtrum. # 229 <lb/>I <lb/>INtroductio ad Geographiam. # 193 <lb/>Iſoperim etræ figuræ quæ. # 29 <lb/>Iouis diſtantia. Figura. Motus. Calculus. Comites. <lb/># pag. # 156. ad 551 <lb/>L <lb/>LAbinæ terrarum. # 41 <lb/>Latitudo geographica. # 19. 195 <lb/>Latitudo ortiua, & occidua quid, & quanta. # 10 <lb/>Latitudo ſyderum 20. Lnnæ. # 88. & 94 <lb/>Libellæ vſus. # 10 <lb/>Lineæ æquinoctialis inuentio 16. & meridianæ. # 12 <lb/>Linea medij, & verimotus Lunæ 71. Solis. # 105 <lb/>Locorum Tabula. # 196 <lb/>Longitudo ſyderum quid. # 20 <lb/>Longitudo locorum. # 195 <lb/>Lucis propagatio quomodo fiat. # 31 <lb/>Lunæ locus 65. Motus 68. Illuminatio 71. Maculæ # 71. <lb/># Vmbra 73. Ecclipſes 72. & 98. Figura 73. Magni-<lb/># tudo 74. Montes lunares. # 77 <lb/>Lunæ tempore 77. Tabulæ motuum eius 79. Anomaliæ <lb/># inuentio 92. Nodi inuentio. # 94 <pb file="0013" n="13"/> Latitudinem inuenire 94. Aetatem, & nouilunia in-<lb/># uenire. # 95 <lb/>Luna quot horis @otu luceat. # 97 <lb/>M <lb/>MAculœ Lunæ 71. Solis. # 130 <lb/>Magnitudines ſyderum. # 187 <lb/>Maris fluxus, & refluxus 49. Figura 51. Quantitas # 53 <lb/>Martis diſtantia. Motus. Calculus. # 143 <lb/>Mathematicarum diuiſio. # 205 <lb/>Mediatio Cœli quid. # 19 <lb/>Menſuræ geometricæ. # 43 <lb/>Mercurij locus. Figura, motus, calculus, & c. vſq; ad # 137 <lb/>Meridiani circuli officium 11. Meridianæ inuentio. # 12 <lb/>Montium altitudinem metiri. # 46 <lb/>Montes Lunares. # 77 <lb/>Montium decrementa vnde. # 41 <lb/>Motus medij ſyderum. # 188 <lb/>Motus Sphæralis planetarum. # 63. 70 <lb/>Mundi interitus 42. Nec æternus fuit. Ibid. Figura. # 29 <lb/>N <lb/>NOna Sphæra. # 186 <lb/>Nouilunij inuentio. # 95 <lb/>Numerorum Aſtronomicorum vſus. # 89 <lb/>O <lb/>ORtus, & occaſum ſyderum. # 179 <lb/>P <lb/>PArallaxis quid 66. Lunæ. Ibid. Cometarum. # 157 <lb/>Pedis Romani menſura. # 43 <lb/>Perigæum, vide Apogæum. <lb/>Polialtitudinem inuenire. # 15 <lb/>Polares circuli quid. # 25 <lb/>Planetarum velocitas. # 66 <lb/>Planetæ statio. Directio. Retrogradatio. # 134 <lb/>Primum mobile. # 186 <lb/>Q <lb/>QVadrans, & quadratum Aſtronomicum. # 6 <lb/>S <lb/>SAturni figura. Distantia, motus, comites. # 152 <lb/># ad 155. <lb/>Scintillatio ſyderum. # 181 <lb/>Semidiameter Sphærarum, & ſyderum. # 186. 187 <lb/>Solis distantia àterra 99. Figura 101. Magnitudo ibid. <lb/># Motus 103. Eorum inuestigatio 105. Apogæũ 106. <lb/>Solis tempora 107. Illuminatio 109. 121. Ortus 121. <lb/># Ecclipſes 122. Tabulæ motus eius 125. Ecclipſium, <lb/># prædictio 131. Solis maculæ. # 131 <lb/>Solſtitium quid. # 24 <lb/>Sphæræ Armillaris conſtructio 5. Arateæ. # 174 <lb/>Sphæræ capacitas. # 30 <lb/>Sphæra recta, obliqua, paralella. # 8, & 198 <lb/>Sphærarum proportio ex diametro. # 46 <lb/>Spiralis motus. # 63. 70 <lb/>Stellæ fixæ. Partitio 163. Locus in firmamento # 164. <lb/># Polionymia 165. Catalogus 166. Obſeruatio earum, <lb/># in Cęlo 175. Motus earum 176. Velocitas. # 178 <lb/>Stellæ nouæ 183. Earum generatio. # 185 <lb/>Syſtema Tychonicum 27. Copernicum, & Philolai. # 33 <lb/>T <lb/>TErræ locus 36. Motus 37. Vmbra 38. 188. Figura <lb/># 39. Mutatio rotunditas ex alluuionibus 40. Ma-<lb/># gnitudo. # 43 <lb/>Trabs meteorologica. # 161 <lb/>Trepidationis motus. # 178 <lb/>Triangulorum proprietates 2. & 3. Menſura laterum # 4 <lb/>Z <lb/>ZOnæ. # 25. & 193 <lb/></note> <pb file="0014" n="14"/> <p> <s xml:id="echoid-s143" xml:space="preserve">EGo Marcus Garzonius, Prouincialis Prouinciæ Venetæ Soc. </s> <s xml:id="echoid-s144" xml:space="preserve">Ieſu, ex authori-<lb/>tate Admodum R. </s> <s xml:id="echoid-s145" xml:space="preserve">P. </s> <s xml:id="echoid-s146" xml:space="preserve">N. </s> <s xml:id="echoid-s147" xml:space="preserve">Præpoſiti Generalis Mutij Vitelleſchi, facultatem <lb/>concedo P. </s> <s xml:id="echoid-s148" xml:space="preserve">loſepho Blancano, eiuſdem Societati Sacerdoti, typis mandandi opus <lb/>quod Sphæra Mundi inſcribitur, vna cum Introductione ad Geographiam, Ap-<lb/>paratu ad Mathematicum ſtudium, & </s> <s xml:id="echoid-s149" xml:space="preserve">Echometria: </s> <s xml:id="echoid-s150" xml:space="preserve">omnia à deputatis PP. </s> <s xml:id="echoid-s151" xml:space="preserve">eiuſ-<lb/>dem Societatis recognita, & </s> <s xml:id="echoid-s152" xml:space="preserve">approbata. </s> <s xml:id="echoid-s153" xml:space="preserve">Bononiæ 20. </s> <s xml:id="echoid-s154" xml:space="preserve">Nouembris 1619.</s> <s xml:id="echoid-s155" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s156" xml:space="preserve">Marcus Garzonius.</s> <s xml:id="echoid-s157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s158" xml:space="preserve">LIbrum hunc inſcriptum Sphæra Mundi, &</s> <s xml:id="echoid-s159" xml:space="preserve">c. </s> <s xml:id="echoid-s160" xml:space="preserve">conſcriptum vero à P. </s> <s xml:id="echoid-s161" xml:space="preserve">Ioſepho <lb/>Blancano Societati Ieſu, diligentius vidi, atque animaduerti ego infraſcri-<lb/>ptus, & </s> <s xml:id="echoid-s162" xml:space="preserve">quia in ipſo nihil non conſonum bonis moribus, Sac. </s> <s xml:id="echoid-s163" xml:space="preserve">Canonibus, & </s> <s xml:id="echoid-s164" xml:space="preserve">Ro-<lb/>mano indici depræhendi; </s> <s xml:id="echoid-s165" xml:space="preserve">quin eundem maxima eruditione repertum reperi, ideo <lb/>illum eundem typis mandari poſſe exiſtimaui.</s> <s xml:id="echoid-s166" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s167" xml:space="preserve">Imprimatur igitur, Ego Fr. </s> <s xml:id="echoid-s168" xml:space="preserve">Hieronymus Onuphrius Romanus, Theologus <lb/>Collegiatus, Lector publicus, ac Sanctiſſimæ Inquiſitionis Conſultor, pro Reue-<lb/>rendiſs. </s> <s xml:id="echoid-s169" xml:space="preserve">P. </s> <s xml:id="echoid-s170" xml:space="preserve">M. </s> <s xml:id="echoid-s171" xml:space="preserve">Paulo de Garrexio, Inquiſitore Bonon.</s> <s xml:id="echoid-s172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s173" xml:space="preserve">EGo D. </s> <s xml:id="echoid-s174" xml:space="preserve">Homobonus de Bonis, Cler. </s> <s xml:id="echoid-s175" xml:space="preserve">reg. </s> <s xml:id="echoid-s176" xml:space="preserve">S. </s> <s xml:id="echoid-s177" xml:space="preserve">Pauli, & </s> <s xml:id="echoid-s178" xml:space="preserve">in Metropoſitana Eccleſia <lb/>Bonon. </s> <s xml:id="echoid-s179" xml:space="preserve">Pœnitentiarius, vidi opus M. </s> <s xml:id="echoid-s180" xml:space="preserve">Reu. </s> <s xml:id="echoid-s181" xml:space="preserve">P. </s> <s xml:id="echoid-s182" xml:space="preserve">Ioſephi Blancani ex Societate <lb/>Ieſu, quod Sphæra Mundi, &</s> <s xml:id="echoid-s183" xml:space="preserve">c. </s> <s xml:id="echoid-s184" xml:space="preserve">inſcribitur, & </s> <s xml:id="echoid-s185" xml:space="preserve">quia illud nil continere animad-<lb/>uerti, quod chriſtianæ fidei dogmatibus, & </s> <s xml:id="echoid-s186" xml:space="preserve">vel bonis moribus aduerſetur, quin <lb/>potius naturalis Philoſophiæ ſtudioſis multum commodum allaturum, in lucem <lb/>edi poſſe cenſui, &</s> <s xml:id="echoid-s187" xml:space="preserve">c.</s> <s xml:id="echoid-s188" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s189" xml:space="preserve">D. </s> <s xml:id="echoid-s190" xml:space="preserve">Homobonus P. </s> <s xml:id="echoid-s191" xml:space="preserve">pro Illuſtriſſimo, & </s> <s xml:id="echoid-s192" xml:space="preserve">Reuerendiſs. </s> <s xml:id="echoid-s193" xml:space="preserve">Card. </s> <s xml:id="echoid-s194" xml:space="preserve">Archiepiſc. </s> <s xml:id="echoid-s195" xml:space="preserve">Bonon.</s> <s xml:id="echoid-s196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s197" xml:space="preserve">Iterum Imprimatur</s> </p> <p> <s xml:id="echoid-s198" xml:space="preserve">Fr. </s> <s xml:id="echoid-s199" xml:space="preserve">Iacobus de Lauda Inquiſitor Mutinæ.</s> <s xml:id="echoid-s200" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s201" xml:space="preserve">V. </s> <s xml:id="echoid-s202" xml:space="preserve">Scipio Sacratus pro Sereniſſimo Duce.</s> <s xml:id="echoid-s203" xml:space="preserve"/> </p> <pb file="0015" n="15"/> <p> <s xml:id="echoid-s204" xml:space="preserve">A B. </s> <s xml:id="echoid-s205" xml:space="preserve">axis Mundi, & </s> <s xml:id="echoid-s206" xml:space="preserve">dia-<lb/>metrum colurorum.</s> <s xml:id="echoid-s207" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s208" xml:space="preserve">A. </s> <s xml:id="echoid-s209" xml:space="preserve">Polus arcticus.</s> <s xml:id="echoid-s210" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s211" xml:space="preserve">B. </s> <s xml:id="echoid-s212" xml:space="preserve">polus antarcticus.</s> <s xml:id="echoid-s213" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s214" xml:space="preserve">E F. </s> <s xml:id="echoid-s215" xml:space="preserve">Poli Zodiaci.</s> <s xml:id="echoid-s216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s217" xml:space="preserve">P Q Circulus ſecundi <lb/>Mobilis.</s> <s xml:id="echoid-s218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s219" xml:space="preserve">E O, N F. </s> <s xml:id="echoid-s220" xml:space="preserve">Diametri cir-<lb/>culorum polarium.</s> <s xml:id="echoid-s221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s222" xml:space="preserve">A C D B. </s> <s xml:id="echoid-s223" xml:space="preserve">Colurus ſol-<lb/>ſtitiorum; </s> <s xml:id="echoid-s224" xml:space="preserve">qui etiam <lb/>referre poteſt Meri-<lb/>dianum: </s> <s xml:id="echoid-s225" xml:space="preserve">Meridianus <lb/> <anchor type="figure" xlink:label="fig-0015-01a" xlink:href="fig-0015-01"/> tamen eſt maior Co-<lb/>luro, cum eum intra <lb/>ſe contineat.</s> <s xml:id="echoid-s226" xml:space="preserve"/> </p> <div xml:id="echoid-div7" type="float" level="2" n="1"> <figure xlink:label="fig-0015-01" xlink:href="fig-0015-01a"> <image file="0015-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0015-01"/> </figure> </div> <p> <s xml:id="echoid-s227" xml:space="preserve">I K L M. </s> <s xml:id="echoid-s228" xml:space="preserve">Diametri tro-<lb/>picorum.</s> <s xml:id="echoid-s229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s230" xml:space="preserve">D C. </s> <s xml:id="echoid-s231" xml:space="preserve">Diameter aequa-<lb/>toris.</s> <s xml:id="echoid-s232" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s233" xml:space="preserve">L K. </s> <s xml:id="echoid-s234" xml:space="preserve">Eclyptica dimidia, <lb/>& </s> <s xml:id="echoid-s235" xml:space="preserve">Zodiaci dimidium.</s> <s xml:id="echoid-s236" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s237" xml:space="preserve">G H. </s> <s xml:id="echoid-s238" xml:space="preserve">Diameter Hori-<lb/>zontis.</s> <s xml:id="echoid-s239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s240" xml:space="preserve">G L N H. </s> <s xml:id="echoid-s241" xml:space="preserve">Alueus Sphæ-<lb/>ra continens.</s> <s xml:id="echoid-s242" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div9" type="section" level="1" n="8"> <head xml:id="echoid-head10" xml:space="preserve">EPIGRAMMA. <lb/>IN SPHÆRAM P. BLANCANI.</head> <p style="it"> <s xml:id="echoid-s243" xml:space="preserve">ARchimedæas timuiſſe est creditus artes, <lb/>Clauſa videns fragili Iuppiter astra globo.</s> <s xml:id="echoid-s244" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s245" xml:space="preserve">Illa tamen perijt, quia vitrea, & </s> <s xml:id="echoid-s246" xml:space="preserve">vnica, & </s> <s xml:id="echoid-s247" xml:space="preserve">ipſi <lb/>Sphæra Syracuſio contumulata ſeni.</s> <s xml:id="echoid-s248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s249" xml:space="preserve">Hæc non ex vitro, non vna, aut clauſa ſepulchro eſt <lb/>Sphæra, ſed Auctori viuit vbique ſuo.</s> <s xml:id="echoid-s250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s251" xml:space="preserve">Fac iumulo incluſam, nostro Archimede ſepulto, <lb/>Ipſa quoque in tenebris astra ſepulta forent.</s> <s xml:id="echoid-s252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s253" xml:space="preserve">In cinere hoc ſcrutanda forent tùm ſydera, & </s> <s xml:id="echoid-s254" xml:space="preserve">vrnam <lb/>Quæ cælum tegeret, non vio<unsure/>lare nefas.</s> <s xml:id="echoid-s255" xml:space="preserve"/> </p> <pb file="0016" n="16"/> <pb o="1" file="0017" n="17"/> </div> <div xml:id="echoid-div10" type="section" level="1" n="9"> <head xml:id="echoid-head11" xml:space="preserve">APPARATVS <lb/>AD SPHÆRAM.</head> <p> <s xml:id="echoid-s256" xml:space="preserve">QVoniam vt rectè Plato in Epin. </s> <s xml:id="echoid-s257" xml:space="preserve">dixit Geometria, & </s> <s xml:id="echoid-s258" xml:space="preserve">Arithmetica, veluti duabus ali@ <lb/>Aſtronomia indiget, quibus ad Aſtra, atq́; </s> <s xml:id="echoid-s259" xml:space="preserve">adeò per vniuerſum Mundum euolare <lb/>poſſit, ideo</s> </p> <p> <s xml:id="echoid-s260" xml:space="preserve">Primo ſuppono auditorem, aut lectorem huius Sphæræ ex Geometria ſaltem Defi-<lb/>nitiones, reliquaque principia Geometriæ, quæ primo Euclidis libro pręmittun-<lb/>tur, percepiſſe. </s> <s xml:id="echoid-s261" xml:space="preserve">porrò quo pluribus Geometricis rebus fuerit inſtructus, eò melius, <lb/>ac facilius, quæ dicenda ſunt, arripiet: </s> <s xml:id="echoid-s262" xml:space="preserve">vnde in Academijs noſtræ Societatis, & </s> <s xml:id="echoid-s263" xml:space="preserve"><lb/>quidem optima Methodo, ſolent Noſtri ſaltem primum Euclidis Elementum, <lb/>auditoribus noſtris prælegere, antequam ad Sphæræ explicationẽ aggrediantur. <lb/></s> <s xml:id="echoid-s264" xml:space="preserve">Secundo ex Arithmetica opus cſt, ſaltem numerorum Numerationem callere, nec-<lb/>non leuiter ſaltem intellexiſle, quid Additio, quid Subtractio, quid Multiplicatio, quid Diuiſio, quid Au-<lb/>rea regula, ſeu trium, quid radix quadrata. </s> <s xml:id="echoid-s265" xml:space="preserve">Demum Fractorum numerorum Numerationem, ſeu valorem <lb/>cognoſcere. </s> <s xml:id="echoid-s266" xml:space="preserve">Quapropter operæ pretium eſſet ante huius Sphæræ prælectiones ex Arithmetica practica <lb/>P.</s> <s xml:id="echoid-s267" xml:space="preserve">Clauij, quæ breuis, & </s> <s xml:id="echoid-s268" xml:space="preserve">clara eſt, iſta aliquatenus prælibaſſe.</s> <s xml:id="echoid-s269" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s270" xml:space="preserve">Ad hæc, vt ea, quæ dicturi ſumus, ea perſpicuitate demonſtrare poſſimus, quæ ab omnibus, vel Mathema-<lb/>tico puluere vix tinctis in telligi queant, opus ea eſt, quæ ſequuntur præmittere.</s> <s xml:id="echoid-s271" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div11" type="section" level="1" n="10"> <head xml:id="echoid-head12" style="it" xml:space="preserve">Circulum datum iu partes, ſeu gradus 360. diuidere. # Præpoſ. 1.</head> <p> <s xml:id="echoid-s272" xml:space="preserve">SIT datus circulus B C D E. </s> <s xml:id="echoid-s273" xml:space="preserve">cuius centrum A. </s> <s xml:id="echoid-s274" xml:space="preserve">eum ſic in gradus 360. </s> <s xml:id="echoid-s275" xml:space="preserve">diuides. </s> <s xml:id="echoid-s276" xml:space="preserve">Primo per centrum A. </s> <s xml:id="echoid-s277" xml:space="preserve">du-<lb/>catur duæ diametri B D. </s> <s xml:id="echoid-s278" xml:space="preserve">& </s> <s xml:id="echoid-s279" xml:space="preserve">E C. </s> <s xml:id="echoid-s280" xml:space="preserve">quæ ſe mutuo ad angulos rectos ſecent: </s> <s xml:id="echoid-s281" xml:space="preserve">ſic enim circulus erit in quatuor <lb/>partes æquales diuiſus, quæ quadrantes appellantur, quorum quilibet gr. </s> <s xml:id="echoid-s282" xml:space="preserve">90. </s> <s xml:id="echoid-s283" xml:space="preserve">cõtinebit. </s> <s xml:id="echoid-s284" xml:space="preserve">Quod autem æquales <lb/> <anchor type="figure" xlink:label="fig-0017-01a" xlink:href="fig-0017-01"/> ſint, patet ex ſcholio 27. </s> <s xml:id="echoid-s285" xml:space="preserve">Propoſ. </s> <s xml:id="echoid-s286" xml:space="preserve">3. </s> <s xml:id="echoid-s287" xml:space="preserve">Euclidis, quod etiã circino exacte <lb/>acuminato experiri potes. </s> <s xml:id="echoid-s288" xml:space="preserve">Enimuero perſpicuitatis cauſa vtemur <lb/>huiuſmodi probationibus ab experientia deſumptis, quæ quamu@s <lb/>Geometricam illam præciſionẽ non aſſe quantur, nihilominus eui-<lb/>dentiam ac certitudinẽ nullo negotio inducunt. </s> <s xml:id="echoid-s289" xml:space="preserve">Etenim in rebus <lb/>Geometricis, & </s> <s xml:id="echoid-s290" xml:space="preserve">Arithmetricis ſiue in Magnitudin bus & </s> <s xml:id="echoid-s291" xml:space="preserve">Nume-<lb/>ris, experientiæ demonſtrationibus æquiualent. </s> <s xml:id="echoid-s292" xml:space="preserve">Non omnino à <lb/>Geometricis tamen rationibus abſtinebimus, ſed in gratiam eorũ, <lb/>qui Geometrica callent, citabimus vbique, cũ è re noſtra fuerit, eas <lb/>Geometrarũ demonſtrationes, ex quibus res propoſica comproba-<lb/>tur, vti in præſentia fecimus.</s> <s xml:id="echoid-s293" xml:space="preserve"/> </p> <div xml:id="echoid-div11" type="float" level="2" n="1"> <figure xlink:label="fig-0017-01" xlink:href="fig-0017-01a"> <image file="0017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0017-01"/> </figure> </div> <p> <s xml:id="echoid-s294" xml:space="preserve">Circinum poſtea exacte acuminatũ dilata ad interuallum ſemi-<lb/>diametri A B. </s> <s xml:id="echoid-s295" xml:space="preserve">quo interuallo ſeruato pone alterum circini pedem <lb/>n B. </s> <s xml:id="echoid-s296" xml:space="preserve">altero verò nota hinc inde duo puncta F G. </s> <s xml:id="echoid-s297" xml:space="preserve">eodem modo po-<lb/>ſito altero pede in C. </s> <s xml:id="echoid-s298" xml:space="preserve">alia duo pũcta hinc, & </s> <s xml:id="echoid-s299" xml:space="preserve">inde notabis H I. </s> <s xml:id="echoid-s300" xml:space="preserve">idem <lb/>fac ex puncto D. </s> <s xml:id="echoid-s301" xml:space="preserve">ſignando duo puncta N K. </s> <s xml:id="echoid-s302" xml:space="preserve">& </s> <s xml:id="echoid-s303" xml:space="preserve">tandem alia duo ex <lb/>E. </s> <s xml:id="echoid-s304" xml:space="preserve">vtrinque, quæ ſint L M. </s> <s xml:id="echoid-s305" xml:space="preserve">hoc modo erit totus circulus in 12. </s> <s xml:id="echoid-s306" xml:space="preserve">par-<lb/>tes æquales diuiſus, vt experientia conſtat. </s> <s xml:id="echoid-s307" xml:space="preserve">ratio vero eſt, quia in-<lb/>teruallũ ſemidiametri ſexies ſuam periferiam percurrit, ex quarti Euclidis Elem. </s> <s xml:id="echoid-s308" xml:space="preserve">quare arcus B F. </s> <s xml:id="echoid-s309" xml:space="preserve">contine-<lb/>bit gr. </s> <s xml:id="echoid-s310" xml:space="preserve">60. </s> <s xml:id="echoid-s311" xml:space="preserve">quia arcus B F. </s> <s xml:id="echoid-s312" xml:space="preserve">eſt ſexta circuli pars, & </s> <s xml:id="echoid-s313" xml:space="preserve">in toto circulo, continentur gr. </s> <s xml:id="echoid-s314" xml:space="preserve">360. </s> <s xml:id="echoid-s315" xml:space="preserve">quorum pars ſexta, pa-<lb/>riter eſt gr. </s> <s xml:id="echoid-s316" xml:space="preserve">60. </s> <s xml:id="echoid-s317" xml:space="preserve">totidem etiam continebit ar us C I. </s> <s xml:id="echoid-s318" xml:space="preserve">quare tres arcus B I. </s> <s xml:id="echoid-s319" xml:space="preserve">I F. </s> <s xml:id="echoid-s320" xml:space="preserve">F C. </s> <s xml:id="echoid-s321" xml:space="preserve">ſinguli continebunt gr. </s> <s xml:id="echoid-s322" xml:space="preserve">30. <lb/></s> <s xml:id="echoid-s323" xml:space="preserve">cum enim arcus B F. </s> <s xml:id="echoid-s324" xml:space="preserve">complectatur gr. </s> <s xml:id="echoid-s325" xml:space="preserve">60. </s> <s xml:id="echoid-s326" xml:space="preserve">reliquus arcus F C. </s> <s xml:id="echoid-s327" xml:space="preserve">reliquos 30. </s> <s xml:id="echoid-s328" xml:space="preserve">continebit, qui ſuperſunt vſq; </s> <s xml:id="echoid-s329" xml:space="preserve">ad <lb/>quadrantis B C. </s> <s xml:id="echoid-s330" xml:space="preserve">complementum, hoc eſt, vſque ad 90. </s> <s xml:id="echoid-s331" xml:space="preserve">eadem ratione arcus B I. </s> <s xml:id="echoid-s332" xml:space="preserve">comprehendet gr. </s> <s xml:id="echoid-s333" xml:space="preserve">30. </s> <s xml:id="echoid-s334" xml:space="preserve">& </s> <s xml:id="echoid-s335" xml:space="preserve">con <lb/>ſequenter reliquus arcus I C. </s> <s xml:id="echoid-s336" xml:space="preserve">reis quos 30. </s> <s xml:id="echoid-s337" xml:space="preserve">gradus habebit: </s> <s xml:id="echoid-s338" xml:space="preserve">totus igitur circulus erit in 12. </s> <s xml:id="echoid-s339" xml:space="preserve">æquas partes diui-<lb/>ſus, quarum ſingulæ tricenos gradus continebunt. </s> <s xml:id="echoid-s340" xml:space="preserve">Rurſus vnamquamq; </s> <s xml:id="echoid-s341" xml:space="preserve">earum diuide bifariam, ſeu in duas-<lb/>parte, æquas, vt vide factum in quadrante B C. </s> <s xml:id="echoid-s342" xml:space="preserve">in punctis n. </s> <s xml:id="echoid-s343" xml:space="preserve">o. </s> <s xml:id="echoid-s344" xml:space="preserve">p. </s> <s xml:id="echoid-s345" xml:space="preserve">ſicque tota periferia erit ſecta in 24. </s> <s xml:id="echoid-s346" xml:space="preserve">partes <lb/>quarum ſingulæ gr. </s> <s xml:id="echoid-s347" xml:space="preserve">15. </s> <s xml:id="echoid-s348" xml:space="preserve">comprehendent. </s> <s xml:id="echoid-s349" xml:space="preserve">Rurſus harum quælibet in partes 3. </s> <s xml:id="echoid-s350" xml:space="preserve">æquas ſubdiuidue, vt in parte <lb/>B. </s> <s xml:id="echoid-s351" xml:space="preserve">factum in cernis, quare quælibet earum quinis gradibus conſtabit: </s> <s xml:id="echoid-s352" xml:space="preserve">tandem eas ſingulas in 5. </s> <s xml:id="echoid-s353" xml:space="preserve">partes æquat <lb/>exactè partire, eritque vnaquęque earum gradus vnus, hacq; </s> <s xml:id="echoid-s354" xml:space="preserve">ratione tota circũferentia, diuiſa erit in gr. </s> <s xml:id="echoid-s355" xml:space="preserve">360. </s> <s xml:id="echoid-s356" xml:space="preserve"><lb/>quod erat faciendum. </s> <s xml:id="echoid-s357" xml:space="preserve">Nos tamen ob paruitatẽ figuræ nequiuimus ſubdiuidere tres partesarcus B n. </s> <s xml:id="echoid-s358" xml:space="preserve">in ſuos <lb/>5. </s> <s xml:id="echoid-s359" xml:space="preserve">gradus. </s> <s xml:id="echoid-s360" xml:space="preserve">Si verò adhuc exactius operari velis, id aſſequeris per latus Pentangoni in dato circulo delcriben-<lb/>di, hac ratione, ſit ſemidiameter E. </s> <s xml:id="echoid-s361" xml:space="preserve">A. </s> <s xml:id="echoid-s362" xml:space="preserve">diuiſa bifariam in puncto T. </s> <s xml:id="echoid-s363" xml:space="preserve">poſtea altero circini crure in T. </s> <s xml:id="echoid-s364" xml:space="preserve">poſito, al- <pb o="2" file="0018" n="18" rhead="Apparatus ad Sphœram."/> terum extende ad punctum B. </s> <s xml:id="echoid-s365" xml:space="preserve">atque hac apertura, nota punctum q, in ſemidiametro A C. </s> <s xml:id="echoid-s366" xml:space="preserve">in quo, ſito eodẽ <lb/>crure, alterum dilata vſq; </s> <s xml:id="echoid-s367" xml:space="preserve">ad B. </s> <s xml:id="echoid-s368" xml:space="preserve">atque hoc interuallo, manente eodem crure in B. </s> <s xml:id="echoid-s369" xml:space="preserve">altero imprime in circuli <lb/>peripheria punctum r, erit enim arcus B r, quinta pars totius circuli, ſeu graduum 72. </s> <s xml:id="echoid-s370" xml:space="preserve">cum autem B p, ſit gr. <lb/></s> <s xml:id="echoid-s371" xml:space="preserve">75. </s> <s xml:id="echoid-s372" xml:space="preserve">eritarcus r p, gr. </s> <s xml:id="echoid-s373" xml:space="preserve">3. </s> <s xml:id="echoid-s374" xml:space="preserve">eo igitur accuratè diuiſo in 5. </s> <s xml:id="echoid-s375" xml:space="preserve">partes æquales, totidem gradus ac proinde gradũ etiam <lb/>vnum obtinebis, &</s> <s xml:id="echoid-s376" xml:space="preserve">c. </s> <s xml:id="echoid-s377" xml:space="preserve">huius praxis demõſtratio eſt apud Ptolem. </s> <s xml:id="echoid-s378" xml:space="preserve">lib. </s> <s xml:id="echoid-s379" xml:space="preserve">1. </s> <s xml:id="echoid-s380" xml:space="preserve">Magnæ conſtr. </s> <s xml:id="echoid-s381" xml:space="preserve">quã refert etiam P. </s> <s xml:id="echoid-s382" xml:space="preserve">Cla-<lb/>uius ad 16. </s> <s xml:id="echoid-s383" xml:space="preserve">quarti Elem. </s> <s xml:id="echoid-s384" xml:space="preserve">Schol. </s> <s xml:id="echoid-s385" xml:space="preserve">2.</s> <s xml:id="echoid-s386" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s387" xml:space="preserve">Porrò quoniam Aſtronomi vnum gradum diuidunt in 60. </s> <s xml:id="echoid-s388" xml:space="preserve">particulas, quas alij Minuta, alij Prima, appel-<lb/>lant: </s> <s xml:id="echoid-s389" xml:space="preserve">propterea ſi circulus datus ſit adeo magnus, vt vlteriori partitioni ſufficiat, valde è re noſtra erit, ſin-<lb/>gulos gradus in 60. </s> <s xml:id="echoid-s390" xml:space="preserve">huiuſmudi prima ſeu minuta diſſecuiſſe; </s> <s xml:id="echoid-s391" xml:space="preserve">aut ſaltem in 5. </s> <s xml:id="echoid-s392" xml:space="preserve">partes æquas, quarum ſingu-<lb/>læ 12. </s> <s xml:id="echoid-s393" xml:space="preserve">minuta contineant. </s> <s xml:id="echoid-s394" xml:space="preserve">ſtatuunt præterea Aſtronomi, vnum primum continere 60. </s> <s xml:id="echoid-s395" xml:space="preserve">particulas, quas ſe-<lb/>cunda appellant, pariter vnum ſecundum continere 60. </s> <s xml:id="echoid-s396" xml:space="preserve">Tertia, &</s> <s xml:id="echoid-s397" xml:space="preserve">c. </s> <s xml:id="echoid-s398" xml:space="preserve">ſcribunt autem breuitatis cauſa, hu-<lb/>iuſmodi particulas hoc compendio, v. </s> <s xml:id="echoid-s399" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s400" xml:space="preserve"> <anchor type="note" xlink:label="note-0018-01a" xlink:href="note-0018-01"/> ideſt gr. </s> <s xml:id="echoid-s401" xml:space="preserve">3. </s> <s xml:id="echoid-s402" xml:space="preserve">Prima 4. </s> <s xml:id="echoid-s403" xml:space="preserve">ſecunda 7. </s> <s xml:id="echoid-s404" xml:space="preserve">& </s> <s xml:id="echoid-s405" xml:space="preserve">tertia 15. </s> <s xml:id="echoid-s406" xml:space="preserve">&</s> <s xml:id="echoid-s407" xml:space="preserve">c. </s> <s xml:id="echoid-s408" xml:space="preserve">pro numero enim apicum |. </s> <s xml:id="echoid-s409" xml:space="preserve">||. </s> <s xml:id="echoid-s410" xml:space="preserve">|||. </s> <s xml:id="echoid-s411" xml:space="preserve">ſuperpoſitionem de-<lb/>nominantur Prima, Secunda, Tertia, &</s> <s xml:id="echoid-s412" xml:space="preserve">c.</s> <s xml:id="echoid-s413" xml:space="preserve"/> </p> <div xml:id="echoid-div12" type="float" level="2" n="2"> <note position="right" xlink:label="note-0018-01" xlink:href="note-0018-01a" xml:space="preserve"> <lb/>G. # |. # ||. # |||. <lb/>3. # 4. # 7. # 15. <lb/></note> </div> <p> <s xml:id="echoid-s414" xml:space="preserve">Hocloco illud quoq; </s> <s xml:id="echoid-s415" xml:space="preserve">non ignorandum: </s> <s xml:id="echoid-s416" xml:space="preserve">ſi plures circuli ex eodem centro ſint deſcripti, ſeu ſint concen-<lb/>trici, atq; </s> <s xml:id="echoid-s417" xml:space="preserve">ex centro duę rectæ lineæ vſque ad vltimum circulum producantur, erunt arcus omnium circu-<lb/>lorum concentricorum inter cas intercepti ſimiles inuicem. </s> <s xml:id="echoid-s418" xml:space="preserve">ideſt tot gradus erunt in arcu minoris circuli, <lb/>quot in arcu maioris, vt in præcedenti figuræ duæ rectæ A C. </s> <s xml:id="echoid-s419" xml:space="preserve">A F. </s> <s xml:id="echoid-s420" xml:space="preserve">comprehendunt duos arcus F C. </s> <s xml:id="echoid-s421" xml:space="preserve">R S. <lb/></s> <s xml:id="echoid-s422" xml:space="preserve">totq; </s> <s xml:id="echoid-s423" xml:space="preserve">gradus ſunt in vno atq; </s> <s xml:id="echoid-s424" xml:space="preserve">in altero: </s> <s xml:id="echoid-s425" xml:space="preserve">in minori quidem minores, in maiori vero maiores pro ratione cir-<lb/>culorum; </s> <s xml:id="echoid-s426" xml:space="preserve">quod ex ſe manifeſtum videtur, & </s> <s xml:id="echoid-s427" xml:space="preserve">experientia comprobari poteſt, & </s> <s xml:id="echoid-s428" xml:space="preserve">P. </s> <s xml:id="echoid-s429" xml:space="preserve">Clauius in ſcholio pro-<lb/>poſ. </s> <s xml:id="echoid-s430" xml:space="preserve">33. </s> <s xml:id="echoid-s431" xml:space="preserve">ſexti Elem. </s> <s xml:id="echoid-s432" xml:space="preserve">illud Geometricè demonſtrauit. </s> <s xml:id="echoid-s433" xml:space="preserve">Gradus dicti ſunt a gradiendo, quod præcipuè inſer-<lb/>uiant in cognoſcendis ſolis ac reliquorum Planetarum gradibus.</s> <s xml:id="echoid-s434" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div14" type="section" level="1" n="11"> <head xml:id="echoid-head13" style="it" xml:space="preserve">Qua ratione Angulorum quantitates menſurentur. # Propoſ. 2.</head> <p> <s xml:id="echoid-s435" xml:space="preserve">GEometræ tantum dicunt eſſe quemlibet angulum, quantus arcus, qui ex ſummitate anguli tãquam cen-<lb/>tro deſcribitur, quique inter duas lineas angulum illum facientes intercipitur, eique ſubtenditur, vt in <lb/>ſuperiori figura angulus B A F. </s> <s xml:id="echoid-s436" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s437" xml:space="preserve">60. </s> <s xml:id="echoid-s438" xml:space="preserve">quia arcus B F. </s> <s xml:id="echoid-s439" xml:space="preserve">illi ſubtenſus, deſcriptuſque ex A. </s> <s xml:id="echoid-s440" xml:space="preserve">extremitate <lb/>eiuſdem anguli B A F. </s> <s xml:id="echoid-s441" xml:space="preserve">eſt pariter gr. </s> <s xml:id="echoid-s442" xml:space="preserve">60. </s> <s xml:id="echoid-s443" xml:space="preserve">ſimiliter angulus F A C. </s> <s xml:id="echoid-s444" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s445" xml:space="preserve">30. </s> <s xml:id="echoid-s446" xml:space="preserve">quia arcus F C. </s> <s xml:id="echoid-s447" xml:space="preserve">illi ſubtenſus eſt <lb/>gr. </s> <s xml:id="echoid-s448" xml:space="preserve">30. </s> <s xml:id="echoid-s449" xml:space="preserve">angulus vero B A C. </s> <s xml:id="echoid-s450" xml:space="preserve">qui rectus eſt co@tinet quantitatem gr. </s> <s xml:id="echoid-s451" xml:space="preserve">90. </s> <s xml:id="echoid-s452" xml:space="preserve">quia arcus B C. </s> <s xml:id="echoid-s453" xml:space="preserve">gr. </s> <s xml:id="echoid-s454" xml:space="preserve">pariter 90. </s> <s xml:id="echoid-s455" xml:space="preserve">conti-<lb/>net; </s> <s xml:id="echoid-s456" xml:space="preserve">vnde omnes recti anguli ſunt gr. </s> <s xml:id="echoid-s457" xml:space="preserve">90. </s> <s xml:id="echoid-s458" xml:space="preserve">ratio, huius eſt quia v@ex vltima ſexti Elem. </s> <s xml:id="echoid-s459" xml:space="preserve">Patet, arcus habent <lb/>eandem inter ſe proportionem, quam habent anguli quos ſubrendunt, v. </s> <s xml:id="echoid-s460" xml:space="preserve">g. </s> <s xml:id="echoid-s461" xml:space="preserve">ita eſt arcus B F. </s> <s xml:id="echoid-s462" xml:space="preserve">ad F C. </s> <s xml:id="echoid-s463" xml:space="preserve">vti eſt <lb/>angulus B A F. </s> <s xml:id="echoid-s464" xml:space="preserve">ad angulum F A C. </s> <s xml:id="echoid-s465" xml:space="preserve">quod etiam facilè patere poteſt; </s> <s xml:id="echoid-s466" xml:space="preserve">ſi conſideremus arcum illum, qui angu-<lb/>lo opponitur, augeri, & </s> <s xml:id="echoid-s467" xml:space="preserve">minui ad diuaricationem, ac conſtrictionem linearum; </s> <s xml:id="echoid-s468" xml:space="preserve">ac proinde tantum eſſe, <lb/>quantus eſt angulus illi inſiſtens.</s> <s xml:id="echoid-s469" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s470" xml:space="preserve">Debetautem angulus, quando per tres litera@ eſt nominandus, ita nominari vt litera illa, quæ eſt ad an-<lb/>guli apicem medio loco proferatur, v. </s> <s xml:id="echoid-s471" xml:space="preserve">g. </s> <s xml:id="echoid-s472" xml:space="preserve">angulus, qui ad A. </s> <s xml:id="echoid-s473" xml:space="preserve">efficitur à duabus lineis B A. </s> <s xml:id="echoid-s474" xml:space="preserve">F A. </s> <s xml:id="echoid-s475" xml:space="preserve">nominandus <lb/>eſt angulus B A F. </s> <s xml:id="echoid-s476" xml:space="preserve">aut F A B. </s> <s xml:id="echoid-s477" xml:space="preserve">non autem B F A. </s> <s xml:id="echoid-s478" xml:space="preserve">aut F B A.</s> <s xml:id="echoid-s479" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div15" type="section" level="1" n="12"> <head xml:id="echoid-head14" style="it" xml:space="preserve">Omne triangulum habere tres angulos continentes gr. 180. hoc est, aquales eſſe <lb/>duobus rectis angulis. # Propoſ 3.</head> <p> <s xml:id="echoid-s480" xml:space="preserve">EVclides hoc Geometricè docet ad 32. </s> <s xml:id="echoid-s481" xml:space="preserve">primi, quæ vel Geometrię Tyronibus notiſſima eſt. </s> <s xml:id="echoid-s482" xml:space="preserve">quod ſi lecto@ <lb/>adeo Geometria leuiter imbutus ſi@, vt eam nondum perceperit liceat nobis in gratiam eius, huius pro-<lb/>poſitionis tale experimentum afferre. </s> <s xml:id="echoid-s483" xml:space="preserve">Sit trianguum quodcũque A B C. </s> <s xml:id="echoid-s484" xml:space="preserve">Dico tres ipſius angulos A B C. <lb/></s> <s xml:id="echoid-s485" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0018-01a" xlink:href="fig-0018-01"/> ſimul ſumptos eſſe æquales duobus rectis angulis, ſeu continere gradus 180 <lb/>ex prima enim propoſitione ſuperiori manifeſtum eſt duos angulos rectos <lb/>continere gr. </s> <s xml:id="echoid-s486" xml:space="preserve">180. </s> <s xml:id="echoid-s487" xml:space="preserve">Facto ig@tur cẽtro in A. </s> <s xml:id="echoid-s488" xml:space="preserve">deſcribitur arcus D E. </s> <s xml:id="echoid-s489" xml:space="preserve">qui per pri-<lb/>mam pro poſitionem huius apparatus, expendatur. </s> <s xml:id="echoid-s490" xml:space="preserve">quot gradus continat per <lb/>diuiſionem circuli vel ſemicirculi, vel quadrant@s, cu@us pars ſit ipſe arcus. <lb/></s> <s xml:id="echoid-s491" xml:space="preserve">idem faciendum erit, circa reliquos angulos B C. </s> <s xml:id="echoid-s492" xml:space="preserve">vt eorũ gradus inueſtigen-<lb/>tur: </s> <s xml:id="echoid-s493" xml:space="preserve">Inuentis igitur gradibus ſingulorũ angulorum, ij ſimul addantur, ſum-<lb/>mainque ſemper efficient gr. </s> <s xml:id="echoid-s494" xml:space="preserve">180. </s> <s xml:id="echoid-s495" xml:space="preserve">quæ eſt quanti as d@orũ rectoium: </s> <s xml:id="echoid-s496" xml:space="preserve">Et hoc <lb/>erat probandum. </s> <s xml:id="echoid-s497" xml:space="preserve">idem experiri poteris hoc modo, nam ſi componantur ſi-<lb/>mul tres arcus tribus angulis ſubtenſi, ſemicirculum conflabunt. </s> <s xml:id="echoid-s498" xml:space="preserve">Aliter ſic <lb/>idem experieris: </s> <s xml:id="echoid-s499" xml:space="preserve">ſacto diligenter triangulo ex charta; </s> <s xml:id="echoid-s500" xml:space="preserve">ipſius angulos reſcin-<lb/>de, eoſque ad centrum A. </s> <s xml:id="echoid-s501" xml:space="preserve">circuli figuræ Propoſ. </s> <s xml:id="echoid-s502" xml:space="preserve">1. </s> <s xml:id="echoid-s503" xml:space="preserve">alterum apud alterum <lb/>applica, ita vt mucrones angulorum ſimul conuen@ant ad A. </s> <s xml:id="echoid-s504" xml:space="preserve">lateraque eo-<lb/>rum ſe mutuo contingant: </s> <s xml:id="echoid-s505" xml:space="preserve">ſtatim enim videbis eos occupare ſpatium, cui in <lb/>periferia ſubtenduntur gr. </s> <s xml:id="echoid-s506" xml:space="preserve">180. </s> <s xml:id="echoid-s507" xml:space="preserve">ſiue ſemicirculus; </s> <s xml:id="echoid-s508" xml:space="preserve">& </s> <s xml:id="echoid-s509" xml:space="preserve">latera extrema efficient <lb/>lineam rectam, quæ cum diametro congruet.</s> <s xml:id="echoid-s510" xml:space="preserve"/> </p> <div xml:id="echoid-div15" type="float" level="2" n="1"> <figure xlink:label="fig-0018-01" xlink:href="fig-0018-01a"> <image file="0018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0018-01"/> </figure> </div> <pb o="3" file="0019" n="19" rhead="Pars prima."/> </div> <div xml:id="echoid-div17" type="section" level="1" n="13"> <head xml:id="echoid-head15" style="it" xml:space="preserve">Triangula æquiangula habere latera proportionalia. # Propoſ. 4.</head> <p> <s xml:id="echoid-s511" xml:space="preserve">SInt duo triangula A B C. </s> <s xml:id="echoid-s512" xml:space="preserve">D E F. </s> <s xml:id="echoid-s513" xml:space="preserve">æquiangula, ideſt angulus A. </s> <s xml:id="echoid-s514" xml:space="preserve">ſit æqualis angulo D. </s> <s xml:id="echoid-s515" xml:space="preserve">angulus B. </s> <s xml:id="echoid-s516" xml:space="preserve">angu-<lb/>lo E. </s> <s xml:id="echoid-s517" xml:space="preserve">angulus C. </s> <s xml:id="echoid-s518" xml:space="preserve">angulo F. </s> <s xml:id="echoid-s519" xml:space="preserve">dicentur hæc duo triangula ſimilia, eruntque latera vnius proportiona@ia la-<lb/>lateribus alterius, quæ ſunt circa æquales angulos, quæq; </s> <s xml:id="echoid-s520" xml:space="preserve">æqualibus angulis ſubtenduntur, v.</s> <s xml:id="echoid-s521" xml:space="preserve">g. </s> <s xml:id="echoid-s522" xml:space="preserve">qu@a anguli <lb/>A D. </s> <s xml:id="echoid-s523" xml:space="preserve">ſunt ęquales, erunt latera conſtituentia angulum A. </s> <s xml:id="echoid-s524" xml:space="preserve">analoga lateribus cõſtituentibus angulum D. </s> <s xml:id="echoid-s525" xml:space="preserve">ſi a-<lb/>men ordinatim ſumantur prout opponuutur angulis æqualibus, quare erit vt A B. </s> <s xml:id="echoid-s526" xml:space="preserve">ad A C. </s> <s xml:id="echoid-s527" xml:space="preserve">ita D E. </s> <s xml:id="echoid-s528" xml:space="preserve">ad D F. <lb/></s> <s xml:id="echoid-s529" xml:space="preserve">ſunt enim priora duo circa angulum A. </s> <s xml:id="echoid-s530" xml:space="preserve">qui eſt æqualis angulo D. </s> <s xml:id="echoid-s531" xml:space="preserve">circa quem ſunt reliqua duo, & </s> <s xml:id="echoid-s532" xml:space="preserve">priora duo <lb/>opponuntur angulis C. </s> <s xml:id="echoid-s533" xml:space="preserve">& </s> <s xml:id="echoid-s534" xml:space="preserve">B. </s> <s xml:id="echoid-s535" xml:space="preserve">qui ſunt æquales angulis duobus F E. </s> <s xml:id="echoid-s536" xml:space="preserve">quibus eodem ordine reſpondent rel. </s> <s xml:id="echoid-s537" xml:space="preserve">qua <lb/>duo latera. </s> <s xml:id="echoid-s538" xml:space="preserve">Similiter erit vt A B. </s> <s xml:id="echoid-s539" xml:space="preserve">ad B C. </s> <s xml:id="echoid-s540" xml:space="preserve">ſic D E. </s> <s xml:id="echoid-s541" xml:space="preserve">ad E F. </s> <s xml:id="echoid-s542" xml:space="preserve">quę ſunt circa angulos pares B E. </s> <s xml:id="echoid-s543" xml:space="preserve">& </s> <s xml:id="echoid-s544" xml:space="preserve">ordinatim re-<lb/> <anchor type="figure" xlink:label="fig-0019-01a" xlink:href="fig-0019-01"/> ſpondent angulis paribus C F. </s> <s xml:id="echoid-s545" xml:space="preserve">atque A. </s> <s xml:id="echoid-s546" xml:space="preserve">& </s> <s xml:id="echoid-s547" xml:space="preserve">D. </s> <s xml:id="echoid-s548" xml:space="preserve">tandem <lb/>erit vt B C. </s> <s xml:id="echoid-s549" xml:space="preserve">ad C A. </s> <s xml:id="echoid-s550" xml:space="preserve">ita E F. </s> <s xml:id="echoid-s551" xml:space="preserve">ad F D. </s> <s xml:id="echoid-s552" xml:space="preserve">quę angulos C F. <lb/></s> <s xml:id="echoid-s553" xml:space="preserve">pares circunſiſtunt, paribuſque angulis ordinatim <lb/>ſubtenduntur. </s> <s xml:id="echoid-s554" xml:space="preserve">Hanc propoſitionem probat Geome-<lb/>tricè Euclides ad 4. </s> <s xml:id="echoid-s555" xml:space="preserve">ſexti. </s> <s xml:id="echoid-s556" xml:space="preserve">Tyro autem practicè idem <lb/>experiri poterit circino perfectè a cuminato: </s> <s xml:id="echoid-s557" xml:space="preserve">ſi enim <lb/>inuenerit latus A B. </s> <s xml:id="echoid-s558" xml:space="preserve">æqualilateri A C. </s> <s xml:id="echoid-s559" xml:space="preserve">inuenit etiam <lb/>D E. </s> <s xml:id="echoid-s560" xml:space="preserve">par lateri D F. </s> <s xml:id="echoid-s561" xml:space="preserve">Quod ſi idem A B. </s> <s xml:id="echoid-s562" xml:space="preserve">ſit duplum <lb/>lateris A C. </s> <s xml:id="echoid-s563" xml:space="preserve">pariter latus D E. </s> <s xml:id="echoid-s564" xml:space="preserve">duplũ erit lateris D F. </s> <s xml:id="echoid-s565" xml:space="preserve"><lb/>Et ſi A B. </s> <s xml:id="echoid-s566" xml:space="preserve">nouies, decieſuè contineatur in A C. </s> <s xml:id="echoid-s567" xml:space="preserve">toties <lb/>etiã D E. </s> <s xml:id="echoid-s568" xml:space="preserve">continebitur in D F. </s> <s xml:id="echoid-s569" xml:space="preserve">& </s> <s xml:id="echoid-s570" xml:space="preserve">ſic de alijs propor-<lb/>tionibus: </s> <s xml:id="echoid-s571" xml:space="preserve">vt tripla, dupla, &</s> <s xml:id="echoid-s572" xml:space="preserve">c. </s> <s xml:id="echoid-s573" xml:space="preserve">Similiter reperiet eaſ-<lb/>dẽ habere analogias reliqua latera A B. </s> <s xml:id="echoid-s574" xml:space="preserve">ad B C. </s> <s xml:id="echoid-s575" xml:space="preserve">quas <lb/>D E. </s> <s xml:id="echoid-s576" xml:space="preserve">ad E F. </s> <s xml:id="echoid-s577" xml:space="preserve">necnon B C. </s> <s xml:id="echoid-s578" xml:space="preserve">ad C A. </s> <s xml:id="echoid-s579" xml:space="preserve">quas E F. </s> <s xml:id="echoid-s580" xml:space="preserve">ad F D. </s> <s xml:id="echoid-s581" xml:space="preserve"><lb/>atque in varijs triangulorum æquiangulorum formis, ſemper vera comperiet.</s> <s xml:id="echoid-s582" xml:space="preserve"/> </p> <div xml:id="echoid-div17" type="float" level="2" n="1"> <figure xlink:label="fig-0019-01" xlink:href="fig-0019-01a"> <image file="0019-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0019-01"/> </figure> </div> </div> <div xml:id="echoid-div19" type="section" level="1" n="14"> <head xml:id="echoid-head16" style="it" xml:space="preserve">Datis duobus angulis vnius trianguli, alterum triangulum constituere, quod illi ſit ſimile, <lb/>quod habe at latera analoga lateribus illius. # Propoſ. 5.</head> <p> <s xml:id="echoid-s583" xml:space="preserve">AD problema iſtud conficiendum excogitauimus huiuſmodi fi-<lb/> <anchor type="figure" xlink:label="fig-0019-02a" xlink:href="fig-0019-02"/> guram ſeu inſtrumentum. </s> <s xml:id="echoid-s584" xml:space="preserve">In plana quapiam ſuperficie ſatis <lb/>magna, ducatur linea A B. </s> <s xml:id="echoid-s585" xml:space="preserve">quantumuis longa; </s> <s xml:id="echoid-s586" xml:space="preserve">in qua facto ini-<lb/>tio ab A. </s> <s xml:id="echoid-s587" xml:space="preserve">ſumantur ope circini particulæ decem æquales, & </s> <s xml:id="echoid-s588" xml:space="preserve">con-<lb/>tinuæ, ſicque habebitur pars vna huius lineæ conſtans 10. </s> <s xml:id="echoid-s589" xml:space="preserve">æquis <lb/>particulis. </s> <s xml:id="echoid-s590" xml:space="preserve">hæc eadem ſumatur decies continenter, ita vt tota A C. <lb/></s> <s xml:id="echoid-s591" xml:space="preserve">contineat 100. </s> <s xml:id="echoid-s592" xml:space="preserve">particulas; </s> <s xml:id="echoid-s593" xml:space="preserve">numerique ſingulis ſui adſcribantur, vti <lb/>vides in figura. </s> <s xml:id="echoid-s594" xml:space="preserve">Poſtea centro C. </s> <s xml:id="echoid-s595" xml:space="preserve">& </s> <s xml:id="echoid-s596" xml:space="preserve">interuallo C E. </s> <s xml:id="echoid-s597" xml:space="preserve">deſcribatur ſe-<lb/>micirculus B D E. </s> <s xml:id="echoid-s598" xml:space="preserve">ac centro interuallo A E. </s> <s xml:id="echoid-s599" xml:space="preserve">ducatur quadrans E F. </s> <s xml:id="echoid-s600" xml:space="preserve"><lb/>Facto deinde initio ab E. </s> <s xml:id="echoid-s601" xml:space="preserve">diuidatur per primam Propoſ. </s> <s xml:id="echoid-s602" xml:space="preserve">huius, ſemi-<lb/>circulus in 180. </s> <s xml:id="echoid-s603" xml:space="preserve">gradus: </s> <s xml:id="echoid-s604" xml:space="preserve">Quadrans vero in 90. </s> <s xml:id="echoid-s605" xml:space="preserve">& </s> <s xml:id="echoid-s606" xml:space="preserve">quiliber eorum gra-<lb/>dus ru@ſum ſecetur ſaltem in 5. </s> <s xml:id="echoid-s607" xml:space="preserve">particulas, quarũ ſingulæ contineant <lb/>minuta 12. </s> <s xml:id="echoid-s608" xml:space="preserve">numerique gr. </s> <s xml:id="echoid-s609" xml:space="preserve">ſuis locis apponantur: </s> <s xml:id="echoid-s610" xml:space="preserve">licet nos pręſenti fi-<lb/>guræ, quæ parua eſt, confuſionis vitandæ cauſa, tãtummodo gradus, <lb/>eoſq; </s> <s xml:id="echoid-s611" xml:space="preserve">tantum per quindenos annotauerimus. </s> <s xml:id="echoid-s612" xml:space="preserve">ſit iam aliquod Trian-<lb/>gulum vbicumque illud fuerit, cuius tamen duos angulos notos ha-<lb/>beamus, vnus, v.</s> <s xml:id="echoid-s613" xml:space="preserve">g. </s> <s xml:id="echoid-s614" xml:space="preserve">ſit rectus, ideſt gr. </s> <s xml:id="echoid-s615" xml:space="preserve">90. </s> <s xml:id="echoid-s616" xml:space="preserve">alter vero acutus gr. </s> <s xml:id="echoid-s617" xml:space="preserve">v.</s> <s xml:id="echoid-s618" xml:space="preserve">g. </s> <s xml:id="echoid-s619" xml:space="preserve">15. </s> <s xml:id="echoid-s620" xml:space="preserve"><lb/>erit reliquus neceſſario gr. </s> <s xml:id="echoid-s621" xml:space="preserve">75. </s> <s xml:id="echoid-s622" xml:space="preserve">cum omnes tres anguli cuiuſuis trian-<lb/>guli contineant, per tertiam Propoſ. </s> <s xml:id="echoid-s623" xml:space="preserve">huius gr. </s> <s xml:id="echoid-s624" xml:space="preserve">180. </s> <s xml:id="echoid-s625" xml:space="preserve">huiuſmodi trian-<lb/>gulo ſic conſtitues triangulumſimile inexpoſito inſtrumento. </s> <s xml:id="echoid-s626" xml:space="preserve">Ex <lb/>centro C. </s> <s xml:id="echoid-s627" xml:space="preserve">ſemicirculi duc lineam C D. </s> <s xml:id="echoid-s628" xml:space="preserve">ad gr. </s> <s xml:id="echoid-s629" xml:space="preserve">90. </s> <s xml:id="echoid-s630" xml:space="preserve">quæ faciet angulos <lb/>rectos cum diametro ad C. </s> <s xml:id="echoid-s631" xml:space="preserve">poſtea ex A centro quadrantis per gr. </s> <s xml:id="echoid-s632" xml:space="preserve">15. </s> <s xml:id="echoid-s633" xml:space="preserve"><lb/>duc lineam A G. </s> <s xml:id="echoid-s634" xml:space="preserve">occurrentẽ ipſi C D. </s> <s xml:id="echoid-s635" xml:space="preserve">in G. </s> <s xml:id="echoid-s636" xml:space="preserve">eritque triangulũ A C G. </s> <s xml:id="echoid-s637" xml:space="preserve"><lb/>conſtructum ſimile, & </s> <s xml:id="echoid-s638" xml:space="preserve">analogum illitriangulo; </s> <s xml:id="echoid-s639" xml:space="preserve">cum enim habeat <lb/>angulum ad C. </s> <s xml:id="echoid-s640" xml:space="preserve">rectum continentem ſcilicet gr. </s> <s xml:id="echoid-s641" xml:space="preserve">90. </s> <s xml:id="echoid-s642" xml:space="preserve">& </s> <s xml:id="echoid-s643" xml:space="preserve">angulum ad A. </s> <s xml:id="echoid-s644" xml:space="preserve"><lb/>gr. </s> <s xml:id="echoid-s645" xml:space="preserve">15. </s> <s xml:id="echoid-s646" xml:space="preserve">ex ſecũda Propoſitione huius, erit conſequenter reliquus an-<lb/>gulus ad G. </s> <s xml:id="echoid-s647" xml:space="preserve">gr. </s> <s xml:id="echoid-s648" xml:space="preserve">75. </s> <s xml:id="echoid-s649" xml:space="preserve">quare erit propoſito triangulo æquiangulum, & </s> <s xml:id="echoid-s650" xml:space="preserve"><lb/>ſimile, & </s> <s xml:id="echoid-s651" xml:space="preserve">proinde per quartam huius, habebit latera lateribus illius <lb/>analoga, ſeu proportionalia. </s> <s xml:id="echoid-s652" xml:space="preserve">ſit alterum triangulum ambligonium, <lb/>cuius angulus obtuſus ſit, v.</s> <s xml:id="echoid-s653" xml:space="preserve">g. </s> <s xml:id="echoid-s654" xml:space="preserve">gr. </s> <s xml:id="echoid-s655" xml:space="preserve">120. </s> <s xml:id="echoid-s656" xml:space="preserve">alter vero ſit gr. </s> <s xml:id="echoid-s657" xml:space="preserve">15. </s> <s xml:id="echoid-s658" xml:space="preserve">tertius erit <lb/>45. </s> <s xml:id="echoid-s659" xml:space="preserve">huic triangulũ ſimile in parata figura ſic efficies; </s> <s xml:id="echoid-s660" xml:space="preserve">duc lineam C H. </s> <s xml:id="echoid-s661" xml:space="preserve"><lb/>in ſemicirculo per gr. </s> <s xml:id="echoid-s662" xml:space="preserve">120. </s> <s xml:id="echoid-s663" xml:space="preserve">itidẽ lineam A H. </s> <s xml:id="echoid-s664" xml:space="preserve">in quadrante per gr. </s> <s xml:id="echoid-s665" xml:space="preserve">15. </s> <s xml:id="echoid-s666" xml:space="preserve"><lb/>occurrentem alteri in H. </s> <s xml:id="echoid-s667" xml:space="preserve">erit triangulũ A C H. </s> <s xml:id="echoid-s668" xml:space="preserve">ſimile prædicto ima- <pb o="4" file="0020" n="20" rhead="Apparatus ad Sphœram."/> ginario trigono: </s> <s xml:id="echoid-s669" xml:space="preserve">per ſecundam enim huius angulus A C H. </s> <s xml:id="echoid-s670" xml:space="preserve">eſt gr. </s> <s xml:id="echoid-s671" xml:space="preserve">120. </s> <s xml:id="echoid-s672" xml:space="preserve">angulus vero C A H. </s> <s xml:id="echoid-s673" xml:space="preserve">gr. </s> <s xml:id="echoid-s674" xml:space="preserve">15. </s> <s xml:id="echoid-s675" xml:space="preserve">ergo neceſ-<lb/>ſario reliquus angulus ad H. </s> <s xml:id="echoid-s676" xml:space="preserve">æqualis erit reliquo angulo dati trianguli, quare per quartã huius, erunt latera <lb/>huius trianguli analoga lateribus illius, eo modo, ac ordine, quem ibi diximus. </s> <s xml:id="echoid-s677" xml:space="preserve">Sit tandem datum triãgulum <lb/>Oxigoniũ, cuius duo anguli ſint cogniti, vnus quidem gr. </s> <s xml:id="echoid-s678" xml:space="preserve">30. </s> <s xml:id="echoid-s679" xml:space="preserve">alter gr. </s> <s xml:id="echoid-s680" xml:space="preserve">35. </s> <s xml:id="echoid-s681" xml:space="preserve">ducantur lineæ C I. </s> <s xml:id="echoid-s682" xml:space="preserve">quidem per gr. <lb/></s> <s xml:id="echoid-s683" xml:space="preserve">75. </s> <s xml:id="echoid-s684" xml:space="preserve">in ſemicirculo. </s> <s xml:id="echoid-s685" xml:space="preserve">A I. </s> <s xml:id="echoid-s686" xml:space="preserve">vero per 30. </s> <s xml:id="echoid-s687" xml:space="preserve">in quadrante, factumq; </s> <s xml:id="echoid-s688" xml:space="preserve">erit trigonum C A I. </s> <s xml:id="echoid-s689" xml:space="preserve">illi ſimile, atque analogum, <lb/>vt ex nuper citatis propoſit. </s> <s xml:id="echoid-s690" xml:space="preserve">patet. </s> <s xml:id="echoid-s691" xml:space="preserve">Si occurrant anguli continentes gradus, & </s> <s xml:id="echoid-s692" xml:space="preserve">minuta, ſimiliter in figura <lb/>accipienda ſunt minuta vltra gradus. </s> <s xml:id="echoid-s693" xml:space="preserve">Linea A C. </s> <s xml:id="echoid-s694" xml:space="preserve">conſtans particulis 100. </s> <s xml:id="echoid-s695" xml:space="preserve">latinis modulus appellatur; </s> <s xml:id="echoid-s696" xml:space="preserve">recen-<lb/>tioribus vero ſcala, quoniam reliquorum laterum eſt modulus, ideſt, menſura.</s> <s xml:id="echoid-s697" xml:space="preserve"/> </p> <div xml:id="echoid-div19" type="float" level="2" n="1"> <figure xlink:label="fig-0019-02" xlink:href="fig-0019-02a"> <image file="0019-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0019-02"/> </figure> </div> </div> <div xml:id="echoid-div21" type="section" level="1" n="15"> <head xml:id="echoid-head17" style="it" xml:space="preserve">Cognitis duobus angulis, & vno latere ſecundum aliquam menſuram, alicuius dati trianguli@ <lb/>reliquorum quoque laterum quantitatem inuenire. # Propoſ. 6.</head> <p> <s xml:id="echoid-s698" xml:space="preserve">ESt autem propoſitio hæc, Tyroni magni facienda, ac diligenter addiſcenda, eſt enim Aſtronomicarum <lb/>demonſtrationum baſis, ac fundamentum. </s> <s xml:id="echoid-s699" xml:space="preserve">Sit v. </s> <s xml:id="echoid-s700" xml:space="preserve">g. </s> <s xml:id="echoid-s701" xml:space="preserve">propoſitum trigonum imaginarium huiuſmodi: <lb/></s> <s xml:id="echoid-s702" xml:space="preserve">intelligatur primo linea ducta à centro terræ vſque ad Lunam: </s> <s xml:id="echoid-s703" xml:space="preserve">altera à Luna, vſq; </s> <s xml:id="echoid-s704" xml:space="preserve">ad habitatorẽ noſtri Ho-<lb/>rizontis; </s> <s xml:id="echoid-s705" xml:space="preserve">tertia ab eodem habitare, ideſt, ſuperficie terræ, quam nos incolimus ad centrum terræ deſcendat: </s> <s xml:id="echoid-s706" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0020-01a" xlink:href="fig-0020-01"/> quod triangulum OCL. <lb/></s> <s xml:id="echoid-s707" xml:space="preserve">aliquo modo cõtemplari <lb/>poteris in adiecta figura; </s> <s xml:id="echoid-s708" xml:space="preserve"><lb/>Angulus enim O C L. </s> <s xml:id="echoid-s709" xml:space="preserve">ad <lb/>centrum terræ cognitus <lb/>ſit, v. </s> <s xml:id="echoid-s710" xml:space="preserve">g. </s> <s xml:id="echoid-s711" xml:space="preserve">gr. </s> <s xml:id="echoid-s712" xml:space="preserve">45. </s> <s xml:id="echoid-s713" xml:space="preserve">alter an-<lb/>gulus, C O L. </s> <s xml:id="echoid-s714" xml:space="preserve">ad oculum <lb/>habitatoris notus, ſit gr. </s> <s xml:id="echoid-s715" xml:space="preserve"><lb/>133. </s> <s xml:id="echoid-s716" xml:space="preserve">latus præterea O C. </s> <s xml:id="echoid-s717" xml:space="preserve"><lb/>cognitũ, ſit linea ab ocu-<lb/>lo ad centrũ mundi, quæ <lb/>eſt ſemidiameter, cogni-<lb/>tain milliarijs, eſt enim <lb/>fere milliariorum 3436. </s> <s xml:id="echoid-s718" xml:space="preserve"><lb/>Iam propoſitum ſit inue <lb/>ſtigare quantitatẽ lateris <lb/>pertinentis à centro ter-<lb/>ræ ad vſq; </s> <s xml:id="echoid-s719" xml:space="preserve">Lunam, ideſt <lb/>diſtantiam Lunæ à terræ <lb/>cẽtro; </s> <s xml:id="echoid-s720" xml:space="preserve">fiat igitur per quin <lb/>tam præcedẽtem propo-<lb/>ſitionem, triangulum ſi-<lb/>mile huic imaginario, ac <lb/>magno triangulo prædi-<lb/>cto, hac tamen conditio-<lb/>ne vt angulus factus in quadrante inſtrumenti ad A. </s> <s xml:id="echoid-s721" xml:space="preserve">ſit æqualis angulo ad centrum terræ; </s> <s xml:id="echoid-s722" xml:space="preserve">angulus vero qui <lb/>fiet ad C. </s> <s xml:id="echoid-s723" xml:space="preserve">centrum ſemicirculi par ſit angulo facto in ſuperficie terrę apud habitatoris oculum. </s> <s xml:id="echoid-s724" xml:space="preserve">ſic enim latus <lb/>inſtrumenti A C. </s> <s xml:id="echoid-s725" xml:space="preserve">qui reliquorum modulus, ac menſura eſſe debet, quod cognitum ſit, reſpondebit ſemidia-<lb/>metro terræ, quę pariter nota eſt. </s> <s xml:id="echoid-s726" xml:space="preserve">Quia ergo triangulum hoc in inſtrumento factũ, eſt ſimile triangulo ma-<lb/>gno acimaginario, cuius latera quòd inacc@ſſibilia ſint, menſurare nequimus: </s> <s xml:id="echoid-s727" xml:space="preserve">habetq; </s> <s xml:id="echoid-s728" xml:space="preserve">latera circa angulum <lb/>A. </s> <s xml:id="echoid-s729" xml:space="preserve">analoga lateribus illius circa centrum terræ poſitis; </s> <s xml:id="echoid-s730" xml:space="preserve">ſi@gitur triangulum in ſtrumenti A C H. </s> <s xml:id="echoid-s731" xml:space="preserve">habuerit an-<lb/>gulos prædictos, ſeu ęquales angulis trianguli magni O C L. </s> <s xml:id="echoid-s732" xml:space="preserve">eritvt latus A C. </s> <s xml:id="echoid-s733" xml:space="preserve">ad latus v.</s> <s xml:id="echoid-s734" xml:space="preserve">g. </s> <s xml:id="echoid-s735" xml:space="preserve">A H. </s> <s xml:id="echoid-s736" xml:space="preserve">ita ſemidia-<lb/>meter terræ oc, ad diſtantiam c l, Lunæ à terra. </s> <s xml:id="echoid-s737" xml:space="preserve">quare quoties latus A C. </s> <s xml:id="echoid-s738" xml:space="preserve">quod eſt 100. </s> <s xml:id="echoid-s739" xml:space="preserve">continebitur in alte-<lb/>ro latere V G. </s> <s xml:id="echoid-s740" xml:space="preserve">A H. </s> <s xml:id="echoid-s741" xml:space="preserve">toties etiam ſemidiameter terrę continebitur in diſtantia Lunæ à terra. </s> <s xml:id="echoid-s742" xml:space="preserve">experire igitur <lb/>per circinum quoties latus A C. </s> <s xml:id="echoid-s743" xml:space="preserve">ingrediatur in latus A H. </s> <s xml:id="echoid-s744" xml:space="preserve">& </s> <s xml:id="echoid-s745" xml:space="preserve">ſi opus fuerit producere latus A H. </s> <s xml:id="echoid-s746" xml:space="preserve">extra inſtru-<lb/>mentum, appoſita al@qua plana ſuperficie, v.</s> <s xml:id="echoid-s747" xml:space="preserve">g. </s> <s xml:id="echoid-s748" xml:space="preserve">Magna tabula, id fiat. </s> <s xml:id="echoid-s749" xml:space="preserve">quoties igitur latus A C. </s> <s xml:id="echoid-s750" xml:space="preserve">ingredietur <lb/>in latus A H. </s> <s xml:id="echoid-s751" xml:space="preserve">toties ſemidiameter terræ nota neceſſario ingredietur in diſtantiam Luna à terra, hoc eſt, to-<lb/>ties in ea continebuntur milliaria 3436. </s> <s xml:id="echoid-s752" xml:space="preserve">vnde cognita atque perſpecta erit Lunaris illa altitudo, quæ latus <lb/>vnumæ quidem inacceſſum trianguli dati magni efficiebat.</s> <s xml:id="echoid-s753" xml:space="preserve"/> </p> <div xml:id="echoid-div21" type="float" level="2" n="1"> <figure xlink:label="fig-0020-01" xlink:href="fig-0020-01a"> <image file="0020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0020-01"/> </figure> </div> <p> <s xml:id="echoid-s754" xml:space="preserve">Quod ſi accidat iatus A C. </s> <s xml:id="echoid-s755" xml:space="preserve">nec ſemel, nec bis, teruè pręcisè contineri in latere A H. </s> <s xml:id="echoid-s756" xml:space="preserve">tunc per circinum ac-<lb/>cipiendum eſt ipſum A C. </s> <s xml:id="echoid-s757" xml:space="preserve">applicandumque lateri A H. </s> <s xml:id="echoid-s758" xml:space="preserve">quoties fieri poteſt, & </s> <s xml:id="echoid-s759" xml:space="preserve">poſtea pars, quæ ſupereſt de <lb/>latere A H. </s> <s xml:id="echoid-s760" xml:space="preserve">accipienda eſt circini interuallo, viciſſimq; </s> <s xml:id="echoid-s761" xml:space="preserve">applicando ipſi A C. </s> <s xml:id="echoid-s762" xml:space="preserve">incipiendo ab A. </s> <s xml:id="echoid-s763" xml:space="preserve">vt appareat <lb/>quantæ parti ipſius adęquetur, v.</s> <s xml:id="echoid-s764" xml:space="preserve">g. </s> <s xml:id="echoid-s765" xml:space="preserve">quia latus A C. </s> <s xml:id="echoid-s766" xml:space="preserve">ſemel tantum integrè continetur in latere A H. </s> <s xml:id="echoid-s767" xml:space="preserve">triangu-<lb/>li conſtructi in inſtrumento, adæquaturque parti ipſius A L. </s> <s xml:id="echoid-s768" xml:space="preserve">quæ propterea eſſe 100. </s> <s xml:id="echoid-s769" xml:space="preserve">apparet: </s> <s xml:id="echoid-s770" xml:space="preserve">vt reliquam <lb/>quoque partem L H. </s> <s xml:id="echoid-s771" xml:space="preserve">cognoſcamus, eam interuallo circini acceptam vicifſim adaptabimus lateri A C. </s> <s xml:id="echoid-s772" xml:space="preserve">inci-<lb/>pientes ab A. </s> <s xml:id="echoid-s773" xml:space="preserve">congruetque, v.</s> <s xml:id="echoid-s774" xml:space="preserve">g. </s> <s xml:id="echoid-s775" xml:space="preserve">parti eius A 30. </s> <s xml:id="echoid-s776" xml:space="preserve">quę eſt 30. </s> <s xml:id="echoid-s777" xml:space="preserve">particularum: </s> <s xml:id="echoid-s778" xml:space="preserve">quare tota A H. </s> <s xml:id="echoid-s779" xml:space="preserve">erit 130. </s> <s xml:id="echoid-s780" xml:space="preserve">partium, <lb/>qualium A C. </s> <s xml:id="echoid-s781" xml:space="preserve">eſt 100. </s> <s xml:id="echoid-s782" xml:space="preserve">proportio igitur earum nota: </s> <s xml:id="echoid-s783" xml:space="preserve">latuſque A H. </s> <s xml:id="echoid-s784" xml:space="preserve">notum, quod intendebamus.</s> <s xml:id="echoid-s785" xml:space="preserve"/> </p> <pb o="5" file="0021" n="21" rhead="Pars Prima."/> </div> <div xml:id="echoid-div23" type="section" level="1" n="16"> <head xml:id="echoid-head18" style="it" xml:space="preserve">Sphæram materialem, atque Armilarem coſtruere. Propoſ 7.</head> <p> <s xml:id="echoid-s786" xml:space="preserve">TRes Sphæras ſolent Aſtronomi ad res cæleſtes facilius declarandas conſtruere. </s> <s xml:id="echoid-s787" xml:space="preserve">Prima dicitur Sphæra <lb/>Armillaris; </s> <s xml:id="echoid-s788" xml:space="preserve">eſtque inſtrumentum quoddam ex pluribus circulis, aut armillis in Sphæræ figuram ſimul <lb/>coaptatis compoſitũ, quo totius Mundi fabrica, & </s> <s xml:id="echoid-s789" xml:space="preserve">motus percommodè explicantur: </s> <s xml:id="echoid-s790" xml:space="preserve">atq; </s> <s xml:id="echoid-s791" xml:space="preserve">eodem nos in præ-<lb/>ſenti opere vſuri ſumus, eiuſq; </s> <s xml:id="echoid-s792" xml:space="preserve">conſtructionem nunc expoſituri. </s> <s xml:id="echoid-s793" xml:space="preserve">Secunda dicitur Sphœra Aratæa, ab Arato <lb/>poeta Græco; </s> <s xml:id="echoid-s794" xml:space="preserve">qui eam elegantiſſimis verſibus explicauit: </s> <s xml:id="echoid-s795" xml:space="preserve">communiter dicitur Globus Aſtronomicus; </s> <s xml:id="echoid-s796" xml:space="preserve">in eo <lb/>enim omnes ſtellarum inerrantium conſtellationes ſuis locis, ac nominibus depinguntur, facileq; </s> <s xml:id="echoid-s797" xml:space="preserve">addiſcun-<lb/>tur, de ea nos etiam in tractatu de ſtellis, agemus. </s> <s xml:id="echoid-s798" xml:space="preserve">Tertia eſt Globus Geographicus, in quo@maris, ac terræ <lb/>ſuperficies ſuis locis, magnitudinibus, ac nominibus depinguntur. </s> <s xml:id="echoid-s799" xml:space="preserve">Vt igitur Armillarem Sphæram fabrice-<lb/> <anchor type="figure" xlink:label="fig-0021-01a" xlink:href="fig-0021-01"/> mur; </s> <s xml:id="echoid-s800" xml:space="preserve">parentur primo ex ſolida materia tres circuli omnino inter ſe ęquales: </s> <s xml:id="echoid-s801" xml:space="preserve">& </s> <s xml:id="echoid-s802" xml:space="preserve">quartus etiã tan-<lb/>to illis minor vt intra eos laxè contineatur. </s> <s xml:id="echoid-s803" xml:space="preserve">in duobus circulorũ æqualium crenæ, ſiue inciſuræ <lb/>fi ant diametraliter oppoſitæ tales, vt ij poſſint ad angulos rectos ſimul in eis mutuò coaptari, & </s> <s xml:id="echoid-s804" xml:space="preserve"><lb/>tam concaua, quam conuexa ipſorũ eſſe in eadem ſphęrica ſuperficie. </s> <s xml:id="echoid-s805" xml:space="preserve">in his inciſuris fiãt duo par <lb/>ua foramina ex diametro pariter oppoſita, quæ poli Mundi erunt. </s> <s xml:id="echoid-s806" xml:space="preserve">Poſtea eorũ alter diuidatur <lb/>per primam Propoſ. </s> <s xml:id="echoid-s807" xml:space="preserve">in gr. </s> <s xml:id="echoid-s808" xml:space="preserve">360. </s> <s xml:id="echoid-s809" xml:space="preserve">atq; </s> <s xml:id="echoid-s810" xml:space="preserve">in eodẽ fiant parua duo ex diametro foramina, quæ à polis <lb/>Mundi diſtent per gr. </s> <s xml:id="echoid-s811" xml:space="preserve">23. </s> <s xml:id="echoid-s812" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s813" xml:space="preserve">fiant itidẽ in quarto minoreq; </s> <s xml:id="echoid-s814" xml:space="preserve">circulo duo foramina ex diametro, ac <lb/>deinde duobus axiculis minor circuli maiori inſeratur, vt ipſius foramina foraminibus maioris <lb/>reſpondeant, ac duobus axiculis per foramina vtriuſq; </s> <s xml:id="echoid-s815" xml:space="preserve">traiectis, ita intra eũ appendatur, vt ſuper <lb/>axiculos illos conuolui poſſit. </s> <s xml:id="echoid-s816" xml:space="preserve">Hi duo axiculi erũt partes axis Zodiaci, foramina vero erunt poli <lb/>eiuſdẽ Zodiaci. </s> <s xml:id="echoid-s817" xml:space="preserve">quo facto duo maiores circuli mutuis ipſorũ crenis ad polos Mundi conſoliden-<lb/>tur; </s> <s xml:id="echoid-s818" xml:space="preserve">perq; </s> <s xml:id="echoid-s819" xml:space="preserve">polos Mundi, axis ferreus traijciatur, qui axis erit Mũdi. </s> <s xml:id="echoid-s820" xml:space="preserve">in eius medio paruulus glo-<lb/>bus terram referens transfixus hęreat; </s> <s xml:id="echoid-s821" xml:space="preserve">porrò hi duo circuli Coluri dicuntur; </s> <s xml:id="echoid-s822" xml:space="preserve">alter Solſtitiorũ cui <lb/>poli Zodiaci inſunt; </s> <s xml:id="echoid-s823" xml:space="preserve">alter vero Aequinoctiorum: </s> <s xml:id="echoid-s824" xml:space="preserve">Minor vero illis incluſus dici poteſt ſecũdum <lb/>mobile, aut circulus, ſecundi motus: </s> <s xml:id="echoid-s825" xml:space="preserve">cui propterea debet affigi exiguus orbiculus Solem, aut Lu-<lb/>nam referens, ac diſtans a polis Zodiaci gr. </s> <s xml:id="echoid-s826" xml:space="preserve">90. </s> <s xml:id="echoid-s827" xml:space="preserve">Deinde in vtroque Coluro a polis Mundi per <lb/>quadrãtem circuli, ſeu per gr. </s> <s xml:id="echoid-s828" xml:space="preserve">90. </s> <s xml:id="echoid-s829" xml:space="preserve">fiant aliæ inciſuræ, quæ quatuor erunt; </s> <s xml:id="echoid-s830" xml:space="preserve">ſimiliter aliæ quatuor <lb/>in reliquo, ex tribus æqualium circulorũ, æqualiter inuicem, ſeu per quadrantem diſtantes: </s> <s xml:id="echoid-s831" xml:space="preserve">qui-<lb/>bus inciſuris, mutuò duobus Coluris ita inſeratur, vt eorum concaua, conuexaq; </s> <s xml:id="echoid-s832" xml:space="preserve">in eadem ſint <lb/>ſphærica ſuperficie; </s> <s xml:id="echoid-s833" xml:space="preserve">erit hic Æquator, ſeu Æquinoctialis, diſtabitq; </s> <s xml:id="echoid-s834" xml:space="preserve">ab vtroq; </s> <s xml:id="echoid-s835" xml:space="preserve">Mũdi polo æqua-<lb/>liter. </s> <s xml:id="echoid-s836" xml:space="preserve">Poſt hæc ab Æquatore vtrinque ad polos in Coluris numerentur 23. </s> <s xml:id="echoid-s837" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s838" xml:space="preserve">gr. </s> <s xml:id="echoid-s839" xml:space="preserve">ibiq; </s> <s xml:id="echoid-s840" xml:space="preserve">inciſioni-<lb/>bus factis applicentur vtrinq; </s> <s xml:id="echoid-s841" xml:space="preserve">ab Æquatore duo circuli, quiæqua es erunt, atq; </s> <s xml:id="echoid-s842" xml:space="preserve">Æquactori@pa-<lb/>ralelli, eorumq; </s> <s xml:id="echoid-s843" xml:space="preserve">extrema ſuperficies ſuperficiem Colurorum non excedat. </s> <s xml:id="echoid-s844" xml:space="preserve">hornm diametrum <lb/>ſic habebis, circino accipe interuallum, quod eſt inter duas inciſuras eiuſdem Coluri, verſus eun <lb/>dem polum, quo habito poteris ambitum horum circulorum deſcribere; </s> <s xml:id="echoid-s845" xml:space="preserve">hi autem Tropici vo-<lb/>cabuntur. </s> <s xml:id="echoid-s846" xml:space="preserve">Rurſus ab vtroque polo, numeratis gr. </s> <s xml:id="echoid-s847" xml:space="preserve">23. </s> <s xml:id="echoid-s848" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s849" xml:space="preserve">in Coluris, ijſque inibi inciſis, affigan-<lb/>tur duo alij parui circuli eadem ratione, qui per Zodiaci polos tranſibunt: </s> <s xml:id="echoid-s850" xml:space="preserve">quique circuli pola-<lb/>res nominantur: </s> <s xml:id="echoid-s851" xml:space="preserve">eruntque paralelli Aequatori, ac Tropicis. </s> <s xml:id="echoid-s852" xml:space="preserve">Secundum hæc, paretur Armilla, <lb/>ſeu faſcia quædam pro Zodiaco eiuſdem longitudinis cũ ambitu Æquatoris, latitudinis autem <lb/>gr. </s> <s xml:id="echoid-s853" xml:space="preserve">12. </s> <s xml:id="echoid-s854" xml:space="preserve">quam bifariam ſecet recta linea ſecundum longitudinem, cui Eclyptica nomen erit: </s> <s xml:id="echoid-s855" xml:space="preserve">hæc <lb/>diuidatur in 12. </s> <s xml:id="echoid-s856" xml:space="preserve">partes æquales, per quarum diuiſiones lineæ perpendiculariter ductæ diuidant <lb/>etiam Zodiacum in 12. </s> <s xml:id="echoid-s857" xml:space="preserve">partes, quæ ſigna dicuntur.</s> <s xml:id="echoid-s858" xml:space="preserve">@Rurſus Eclypticæ prædictæ partes 12. </s> <s xml:id="echoid-s859" xml:space="preserve">ſecen-<lb/>tur ſingulæ in 30. </s> <s xml:id="echoid-s860" xml:space="preserve">gr. </s> <s xml:id="echoid-s861" xml:space="preserve">ſicque tota erit in gr. </s> <s xml:id="echoid-s862" xml:space="preserve">360. </s> <s xml:id="echoid-s863" xml:space="preserve">diuiſa. </s> <s xml:id="echoid-s864" xml:space="preserve">adſcribantur tandem ſecus eam, ex vna <lb/>parte characteres ac nomina ſignorum, ex altera vero partes duodecim menſes in ſuos dies di-<lb/>uiſi, reſpondẽtes exactè duodecim fignis ſibi debitis, vt in appoſita figura facile videre eſt. </s> <s xml:id="echoid-s865" xml:space="preserve">cùm <lb/>autem in anno communi ſint dies 365. </s> <s xml:id="echoid-s866" xml:space="preserve">vtile erit ducta linea ipſi Ecly pticæ proxima, ac paralel-<lb/>la eam in partes 365. </s> <s xml:id="echoid-s867" xml:space="preserve">æquas diuidere, quæ ſingulæ ſingulis diebus debeantur, atq; </s> <s xml:id="echoid-s868" xml:space="preserve">in menſes di-<lb/>ſtribuantur; </s> <s xml:id="echoid-s869" xml:space="preserve">debet autem 21. </s> <s xml:id="echoid-s870" xml:space="preserve">dies Ianuarij reſpondere initio Aquarij. </s> <s xml:id="echoid-s871" xml:space="preserve">20. </s> <s xml:id="echoid-s872" xml:space="preserve">Februarij initio Pi-<lb/>ſcium. </s> <s xml:id="echoid-s873" xml:space="preserve">21. </s> <s xml:id="echoid-s874" xml:space="preserve">Martij initio Arietis. </s> <s xml:id="echoid-s875" xml:space="preserve">21. </s> <s xml:id="echoid-s876" xml:space="preserve">Aprilis initio Tauri. </s> <s xml:id="echoid-s877" xml:space="preserve">22. </s> <s xml:id="echoid-s878" xml:space="preserve">Maij initio Geminorum. </s> <s xml:id="echoid-s879" xml:space="preserve">Iunij 22. <lb/></s> <s xml:id="echoid-s880" xml:space="preserve">initio Cancri. </s> <s xml:id="echoid-s881" xml:space="preserve">Iulij 23. </s> <s xml:id="echoid-s882" xml:space="preserve">initio Leonis. </s> <s xml:id="echoid-s883" xml:space="preserve">Auguſti 23. </s> <s xml:id="echoid-s884" xml:space="preserve">initio Virginis. </s> <s xml:id="echoid-s885" xml:space="preserve">Septembris 23. </s> <s xml:id="echoid-s886" xml:space="preserve">initio Libræ. </s> <s xml:id="echoid-s887" xml:space="preserve"><lb/>Octobris 24. </s> <s xml:id="echoid-s888" xml:space="preserve">initio Scorpionis. </s> <s xml:id="echoid-s889" xml:space="preserve">Nouembris 23. </s> <s xml:id="echoid-s890" xml:space="preserve">initio Sagittarij. </s> <s xml:id="echoid-s891" xml:space="preserve">22. </s> <s xml:id="echoid-s892" xml:space="preserve">Decembris initio Capricor-<lb/>ni, vt ipſa figura vtcumque demonſtrat: </s> <s xml:id="echoid-s893" xml:space="preserve">vnde ſequitur cæteros quoq; </s> <s xml:id="echoid-s894" xml:space="preserve">dies cæteris gradibus ſibi <lb/>debitis appoſitos eſſe. </s> <s xml:id="echoid-s895" xml:space="preserve">Conſtructus hoc modo Zodiacus, cæteris iam hoc pacto compingendus <lb/>eſt: </s> <s xml:id="echoid-s896" xml:space="preserve">Initium Eclypti<unsure/>cæ, ſeu Arietis coincidat cum initio Aequatoris, ideſt, cum communi ſe-<lb/>ctione Æquatoris, & </s> <s xml:id="echoid-s897" xml:space="preserve">Coluri Æquinoctiorum: </s> <s xml:id="echoid-s898" xml:space="preserve">deinde tẽdat per communem ſectionem alterius <lb/>Tropici, & </s> <s xml:id="echoid-s899" xml:space="preserve">Coluri<unsure/> ſolſtitiorum, quæ ſectio d@ſtat a polo Zodiaci per quadrantem, ſeu per gr. </s> <s xml:id="echoid-s900" xml:space="preserve">90. </s> <s xml:id="echoid-s901" xml:space="preserve"><lb/>ita vt initium Cancri fit in ipſa ſectione: </s> <s xml:id="echoid-s902" xml:space="preserve">Hinc per alteram ſectionem Æquatoris, cum Coluro <lb/>pariter Æquinoctiorum, ita vt initiũ Libræ ſit in ipſa ſectione. </s> <s xml:id="echoid-s903" xml:space="preserve">inde tranſiens per alterius Tro <lb/>pici cum Coluro pariter ſolſtitiorum ſectionem, ita vt initium Capricorni ſit in ea, ſicq; </s> <s xml:id="echoid-s904" xml:space="preserve">ſuum <lb/>complens orbem deſinat cũ Arietis initio vnde incepit. </s> <s xml:id="echoid-s905" xml:space="preserve">debet autem ipſius extima ſuperficies, <lb/>eſſe in eadem cæterorum circulorum ſphæricitate. </s> <s xml:id="echoid-s906" xml:space="preserve">in hac porro poſitione Eclyptica æquidiſta-<lb/>bit vndiq; </s> <s xml:id="echoid-s907" xml:space="preserve">ab vtroq; </s> <s xml:id="echoid-s908" xml:space="preserve">polo Zodiaci per 90. </s> <s xml:id="echoid-s909" xml:space="preserve">gradus: </s> <s xml:id="echoid-s910" xml:space="preserve">polus vero Mundi ad quẽ Cancer vergit, erit <pb o="6" file="0022" n="22" rhead="Apparatus ad Sphœram."/> polus Arcticus; </s> <s xml:id="echoid-s911" xml:space="preserve">Item vero Antarcticus: </s> <s xml:id="echoid-s912" xml:space="preserve">eritq; </s> <s xml:id="echoid-s913" xml:space="preserve">totus Zodiacus, in quatuor æquas partesà Coluris diſſectus.</s> <s xml:id="echoid-s914" xml:space="preserve"/> </p> <div xml:id="echoid-div23" type="float" level="2" n="1"> <figure xlink:label="fig-0021-01" xlink:href="fig-0021-01a"> <image file="0021-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0021-01"/> </figure> </div> <p> <s xml:id="echoid-s915" xml:space="preserve">Quoniam vero prædicti circuli omnes materialem craſſitiem habent aliquam, quam tamen habere mini-<lb/>mè deberent, cũ circulos Geometricos referant, qui lineæ ſunt ſecundum longitudinem impartibiles, ideſt <lb/>non poſſunt ſcindi per longum; </s> <s xml:id="echoid-s916" xml:space="preserve">ideo per mediũ ſingulorum ſecundum longitudinem deſcribendæ ſunt li-<lb/>neæ circulares, quæ eos ſecundum longitudinem bifariam ſecent, qui circuli in Æquatore, Tropicis, & </s> <s xml:id="echoid-s917" xml:space="preserve">Po-<lb/>laribus deſcribẽdi ſunt ex polis Mundi tanquam ex centris; </s> <s xml:id="echoid-s918" xml:space="preserve">in Coluris vero ex ſectionibus eorũ cum Æqua-<lb/>tore: </s> <s xml:id="echoid-s919" xml:space="preserve">Hæ enim peripheriæ lineares melius repræſentant cæleſtes circulos. </s> <s xml:id="echoid-s920" xml:space="preserve">poſtea Æquator diuidendus eſt <lb/>per primam huius in partes 360. </s> <s xml:id="echoid-s921" xml:space="preserve">quę tempora appellantur, numeri ſaltem ſingulis denis aſcribendi facto ini-<lb/>tio à,<unsure/> communi ſectione eius cum Eclyptica, & </s> <s xml:id="echoid-s922" xml:space="preserve">procedendo ſecundum ordinem ſignorum Zodiaci, ſicque <lb/>pars nonageſima Æquatoris erit in Coluro ſolſticiorum, diſtans à Cancro gr. </s> <s xml:id="echoid-s923" xml:space="preserve">23. </s> <s xml:id="echoid-s924" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s925" xml:space="preserve">& </s> <s xml:id="echoid-s926" xml:space="preserve">c.</s> <s xml:id="echoid-s927" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s928" xml:space="preserve">Atque hæc circulorum compago aptè dici poteſt primum mobile, hi enim circuli in primo mobili eſſe <lb/>concipiuntur.</s> <s xml:id="echoid-s929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s930" xml:space="preserve">Nunc alius circulus, qui Meridianus dicitur parandus eſt tantæ magnitudinis; </s> <s xml:id="echoid-s931" xml:space="preserve">vt concauum eius prædi-<lb/>ctum mobile complectatur, non tamen ita arctè, quin intra ipſum moueri illud queat, quare in duobus ex <lb/>diametro foraminibus in ipſo factis, axis mundi exeratur, vt circa ipſum primum mobile liberè conuerti <lb/>poſſit. </s> <s xml:id="echoid-s932" xml:space="preserve">valde autem è re eſſet, ſi vna eius Meridiani ſuperficies lateris, ita introrſum per circuitum excaue-<lb/>retur, vt eius concaua peripheria præcisè per mediam longitudinem ipſius Meridiani gyrans, etiam per <lb/>Mundi polos tranſiret. </s> <s xml:id="echoid-s933" xml:space="preserve">diuidendus autem eſt ex haci e<unsure/>adem parte in gr. </s> <s xml:id="echoid-s934" xml:space="preserve">360. </s> <s xml:id="echoid-s935" xml:space="preserve">Quorum numeri debent à polis <lb/>incipere, & </s> <s xml:id="echoid-s936" xml:space="preserve">ad Aequatorem vſque creſcere, vt in Aequatore ſit gr. </s> <s xml:id="echoid-s937" xml:space="preserve">90. </s> <s xml:id="echoid-s938" xml:space="preserve">communis vtriſq; </s> <s xml:id="echoid-s939" xml:space="preserve">numerationibus.</s> <s xml:id="echoid-s940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s941" xml:space="preserve">Reſtat vltimo loco Horizon, qui tantæ magnitudinis fabricandus eſt, vt concauum eius æquale omnino <lb/> <anchor type="figure" xlink:label="fig-0022-01a" xlink:href="fig-0022-01"/> ſit concauo Meridiani, habeatq; </s> <s xml:id="echoid-s942" xml:space="preserve">latitudinem, non ſecun-<lb/>dum concauum aut conuexum, ſed ſecundum lateralem <lb/>ſuperficiem tantum, vt in ea Mundi plagæ ventiq; </s> <s xml:id="echoid-s943" xml:space="preserve">ſcribi <lb/>poſſunt, binæque ex diametro inciſuræ excauari, quæ Me-<lb/>ridianum circulum ad angulos rectos cum Horizõte exci-<lb/>pl<unsure/>ant: </s> <s xml:id="echoid-s944" xml:space="preserve">diuidatur in gr. </s> <s xml:id="echoid-s945" xml:space="preserve">360. </s> <s xml:id="echoid-s946" xml:space="preserve">ſiue in 4. </s> <s xml:id="echoid-s947" xml:space="preserve">quadrantes, quorum <lb/>numeri à Septentrione, & </s> <s xml:id="echoid-s948" xml:space="preserve">Meridie incipiẽtes, atq; </s> <s xml:id="echoid-s949" xml:space="preserve">vtrin-<lb/>que prodeuntes, deſinant in gr. </s> <s xml:id="echoid-s950" xml:space="preserve">90. </s> <s xml:id="echoid-s951" xml:space="preserve">ad Ortum, & </s> <s xml:id="echoid-s952" xml:space="preserve">Occaſum. <lb/></s> <s xml:id="echoid-s953" xml:space="preserve">ſic abſolutus Horizon incumbet ſuæ baſi, ita vt fulciatur <lb/>brachiolis in modum aluei rotundi conformatis. </s> <s xml:id="echoid-s954" xml:space="preserve">in quem <lb/>alueum Meridianus vna cum reliqua compage per Hori-<lb/>zontis ſectiones immiſſus præcisè medius ſupra Horizon-<lb/>tem perpẽdiculariter erigatur, ac medius infra Horizon-<lb/>tem deſcendat, occurratq; </s> <s xml:id="echoid-s955" xml:space="preserve">fundo aluei, vbi aliqua ſectura <lb/>retineatur ne huc, illuc, a rectitudine deflectat. </s> <s xml:id="echoid-s956" xml:space="preserve">Neq; </s> <s xml:id="echoid-s957" xml:space="preserve">ve-<lb/>ro cum Horizonte conſolidari debet, vt per eius in-ciſio-<lb/>nes ſuſque deque reuolui poſſit: </s> <s xml:id="echoid-s958" xml:space="preserve">debet tandem Horizon <lb/>eſſe paralellus inferiori plano ſuæ baſis, ſeu plantæ ſui pe-<lb/>dis. </s> <s xml:id="echoid-s959" xml:space="preserve">vbi ex vſu erit ſi acus magnetica in aliqua loculamen-<lb/>to librata, contineatur, cuius vſus poſtea apparebit. </s> <s xml:id="echoid-s960" xml:space="preserve">Quo-<lb/>rum omnium ac totius Sphæræ Armillaris ſiguram inſpice in pagina ante apparatum immediatè poſita.</s> <s xml:id="echoid-s961" xml:space="preserve"/> </p> <div xml:id="echoid-div24" type="float" level="2" n="2"> <figure xlink:label="fig-0022-01" xlink:href="fig-0022-01a"> <image file="0022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0022-01"/> </figure> </div> </div> <div xml:id="echoid-div26" type="section" level="1" n="17"> <head xml:id="echoid-head19" style="it" xml:space="preserve">Quadrantem Astronomicum, vnà cum quadrato conſtruere. # Propoſ. 8.</head> <p> <s xml:id="echoid-s962" xml:space="preserve">VT melius res Aſtronomicas doceamus, indigemus aliquando huiuſmodi quadrante. </s> <s xml:id="echoid-s963" xml:space="preserve">ex aliqua igitur <lb/>ſolida, ac firma materia conſtruatur quadratum A B C D. </s> <s xml:id="echoid-s964" xml:space="preserve">quale figura vtcumque oſtendit, cuius ſin-<lb/> <anchor type="figure" xlink:label="fig-0022-02a" xlink:href="fig-0022-02"/> gula latera, ſint ſaltem duorum aut trium pedum, quo ve-<lb/>ro maius, eo etiam vtilius erit. </s> <s xml:id="echoid-s965" xml:space="preserve">facto deinde centro in C. <lb/></s> <s xml:id="echoid-s966" xml:space="preserve">interuallo C B. </s> <s xml:id="echoid-s967" xml:space="preserve">deſcribatur quadrans circuli B C D. </s> <s xml:id="echoid-s968" xml:space="preserve">diui-<lb/>datur que in gr. </s> <s xml:id="echoid-s969" xml:space="preserve">90. </s> <s xml:id="echoid-s970" xml:space="preserve">cum ſit quarta circuli pars: </s> <s xml:id="echoid-s971" xml:space="preserve">& </s> <s xml:id="echoid-s972" xml:space="preserve">quilibet <lb/>gradus ſaltem in particulas 5. </s> <s xml:id="echoid-s973" xml:space="preserve">ſubdiuidatur per primam <lb/>ropoſ. </s> <s xml:id="echoid-s974" xml:space="preserve">huius. </s> <s xml:id="echoid-s975" xml:space="preserve">pendeat perpendiculũ D I. </s> <s xml:id="echoid-s976" xml:space="preserve">iuxta lineam ali-<lb/>quam per medium lateris A D. </s> <s xml:id="echoid-s977" xml:space="preserve">ductam. </s> <s xml:id="echoid-s978" xml:space="preserve">adſit etiam Dio-<lb/>ptra circa centrum C. </s> <s xml:id="echoid-s979" xml:space="preserve">mobilis, cuius latus C E. </s> <s xml:id="echoid-s980" xml:space="preserve">per cen-<lb/>trum C. </s> <s xml:id="echoid-s981" xml:space="preserve">tranſeat, quod fiduciæ lineam ſolent appellare. </s> <s xml:id="echoid-s982" xml:space="preserve"><lb/>erigantur ex Dioptræ ſuperficie exteriori duo pinancidia <lb/>perpendiculariter, atque inuicem paralella: </s> <s xml:id="echoid-s983" xml:space="preserve">in quorum <lb/>medio ſint exigua duo foramina directè ſupra lineam fi-<lb/>duciæ facta, atque in eadem altitudine. </s> <s xml:id="echoid-s984" xml:space="preserve">ſint præterea in <lb/>pinnularum ſummitatibus duæ rimulæ ſibi mutuo in ea-<lb/>dem altitudine reſpõdentes. </s> <s xml:id="echoid-s985" xml:space="preserve">Deinde duo latera A B. </s> <s xml:id="echoid-s986" xml:space="preserve">B C. </s> <s xml:id="echoid-s987" xml:space="preserve"><lb/>diuidantur in partes 60. </s> <s xml:id="echoid-s988" xml:space="preserve">æquales, vti figura demonſtrat. </s> <s xml:id="echoid-s989" xml:space="preserve"><lb/>Tandem ſit etiam in angulo A. </s> <s xml:id="echoid-s990" xml:space="preserve">paratum foramen, cui cum <lb/>opus fuerit Dioptra poſſit affigi, ac circa ipſum conuolui.</s> <s xml:id="echoid-s991" xml:space="preserve"/> </p> <div xml:id="echoid-div26" type="float" level="2" n="1"> <figure xlink:label="fig-0022-02" xlink:href="fig-0022-02a"> <image file="0022-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0022-02"/> </figure> </div> </div> <div xml:id="echoid-div28" type="section" level="1" n="18"> <head xml:id="echoid-head20" xml:space="preserve">FINIS PARTIS PRIMÆ.</head> <pb o="7" file="0023" n="23"/> </div> <div xml:id="echoid-div29" type="section" level="1" n="19"> <head xml:id="echoid-head21" xml:space="preserve">SPHÆRÆ MATERIALIS. <lb/>ET MVNDANÆ <lb/>SIMVL EXPLICATIO. <lb/>LIBER PRIMVS.</head> <figure> <image file="0023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0023-01"/> </figure> </div> <div xml:id="echoid-div30" type="section" level="1" n="20"> <head xml:id="echoid-head22" style="it" xml:space="preserve">Suppoſitiones. Cap. I.</head> <p> <s xml:id="echoid-s992" xml:space="preserve">1 PRæterilla, quæ extrinſecus accepta tam ex Geometria, quam ex Arithmetica, vt <lb/>initio apparatus dictum eſt, ſupponit Aſtronomia; </s> <s xml:id="echoid-s993" xml:space="preserve">adhuc alia intrinſeca, & </s> <s xml:id="echoid-s994" xml:space="preserve">ſibi <lb/>propria principia, ac veluti fundamenta ſupponit, quæ quidem duplicis ſunt <lb/>generis, alia enim appellant Aſtronomi Phęnomena, ſeu Apparentias, eò quod <lb/>omnibus etiam vulgò appareant, ac manifeſta ſint, vti ſunt; </s> <s xml:id="echoid-s995" xml:space="preserve">Stellas, Lunam, & </s> <s xml:id="echoid-s996" xml:space="preserve"><lb/>Solem oriri, ac occidere. </s> <s xml:id="echoid-s997" xml:space="preserve">omnia ſydera moueri ab Oriente in Occidentem: </s> <s xml:id="echoid-s998" xml:space="preserve">So-<lb/>lem hyeme humilius incedere, æſtate vero altius: </s> <s xml:id="echoid-s999" xml:space="preserve">non ſemper Solem ex eodem <lb/>Horizontis loco aſcendere, & </s> <s xml:id="echoid-s1000" xml:space="preserve">alia id genus complura ſupponimus ceu cunctis <lb/>notiſſima.</s> <s xml:id="echoid-s1001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1002" xml:space="preserve">Alterum genus principiorum ex ſe habet Aſtronomia aliũde non petitorum, quæ <lb/>πηρύσεις, ideſt obſeruationes appellantur: </s> <s xml:id="echoid-s1003" xml:space="preserve">ſunt autem cognitiones quædam ab experimentis comparatæ, <lb/>quæ non omnibus, vti apparentiæ, innoteſcunt, ſed ijs tantummodo, qui diligenti opera, atq; </s> <s xml:id="echoid-s1004" xml:space="preserve">inſtrumentis <lb/>ad id artificiosè elaboratis, in ſtellarum ſcientiam nauiter incumbunt; </s> <s xml:id="echoid-s1005" xml:space="preserve">huius generis ſunt, Solis, ac Lunæ <lb/>diametros viſibiles, aliquando maiores, aliquando minores videri; </s> <s xml:id="echoid-s1006" xml:space="preserve">Solem in parte Zodiaci Boreali am-<lb/>plius octo diebus immorari, quam in Auſtriali: </s> <s xml:id="echoid-s1007" xml:space="preserve">huiuſmodi etiam ſunt, Planetas aliquando eſſe retrogrados, <lb/>aliquando ſtationarios, veloces, tardos, directos, & </s> <s xml:id="echoid-s1008" xml:space="preserve">alia.</s> <s xml:id="echoid-s1009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1010" xml:space="preserve">2 Cum de Sphæra acturi ſimus, tria de ea præmittere debemus, quorum primum eſt ipſius Etymologia. <lb/></s> <s xml:id="echoid-s1011" xml:space="preserve">Sphęra igitur, græca vox eſt, quæ latine<unsure/> redditur pila, aut globus. </s> <s xml:id="echoid-s1012" xml:space="preserve">ſecundum eſt ipſius deſinitio, quã Theo-<lb/>doſius Tripolita in ſuis ſphœricis Elementis aſſert in hunc modum: </s> <s xml:id="echoid-s1013" xml:space="preserve">Sphęra eſt corpus ſolidum, rotundum, <lb/>vnica ſuperficie contentum, in cuius medio punctum eſt, à<unsure/> quo omnes lineæ ductæ ad circunferentiam, vel <lb/>ad ambientem ſuperficiem ſunt æquales: </s> <s xml:id="echoid-s1014" xml:space="preserve">quod punctum dicitur centrum Sphœræ Diameter vero Sphęræ <lb/>eſt linea recta tranſiens per centrum eius, atque vtrinq; </s> <s xml:id="echoid-s1015" xml:space="preserve">ad vltimam ſuperficiem deſinens. </s> <s xml:id="echoid-s1016" xml:space="preserve">Axis autem eſt <lb/>vna ex diametris circa quam Sphera reuoluitur, & </s> <s xml:id="echoid-s1017" xml:space="preserve">denominaturab ἀξἐω græco, quod reuoluere ſignificat. </s> <s xml:id="echoid-s1018" xml:space="preserve"><lb/>extrema vero axis puncta poli dicuntur à πολεω, ideſt verto.</s> <s xml:id="echoid-s1019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1020" xml:space="preserve">Orbis porrò differt à<unsure/> Sphęra, quod hæc ad centrum vſque ſit ſolida, & </s> <s xml:id="echoid-s1021" xml:space="preserve">vnica exteriori ſuperficie ſit con-<lb/>tenta, quæ conuexa dicitur; </s> <s xml:id="echoid-s1022" xml:space="preserve">ille vero non eſt ſolidus, ſed intus vacuus, vnde & </s> <s xml:id="echoid-s1023" xml:space="preserve">duabus ſuperficiebus termi-<lb/>natur, extrinſeca, quæ conuexa eſt, & </s> <s xml:id="echoid-s1024" xml:space="preserve">interna, quæ concaua: </s> <s xml:id="echoid-s1025" xml:space="preserve">tales imaginamur eſſe Cælos.</s> <s xml:id="echoid-s1026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1027" xml:space="preserve">Cæterum quamuis Sphęra Armillaris non ſit ſolida, nec propriè ſit Sphęra, aut Orbis, quia tamen eius <lb/>circuli Sphęram Mundi vtcumque repræſentant, ideo Sphęra dicitur. </s> <s xml:id="echoid-s1028" xml:space="preserve">Eius definitionem initio propoſ. </s> <s xml:id="echoid-s1029" xml:space="preserve">7. <lb/></s> <s xml:id="echoid-s1030" xml:space="preserve">apparatus attullimus.</s> <s xml:id="echoid-s1031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1032" xml:space="preserve">3 Loco prænotandum eſt. </s> <s xml:id="echoid-s1033" xml:space="preserve">poſitionem, ſeu potius conſtitutionem Sphęræ triplicem eſſe, quemadmo-<lb/>dum etiam ipſius mundanæ Sphęræ vnde oritur Sphęra recta, obliqua, & </s> <s xml:id="echoid-s1034" xml:space="preserve">pararella: </s> <s xml:id="echoid-s1035" xml:space="preserve">quando enim ita con-<lb/>ſtituitur vt vterque polus ſit in horizonte dicitur Sphęra recta, quod in tali ſitu Æquator, ac circuli ei para-<lb/>lelli, tropici, ac polares recta aſcendant ſupra Horizontem, ideſt angulos rectos cum eo efficiant: </s> <s xml:id="echoid-s1036" xml:space="preserve">Quando <lb/>vero vnus polorum ſupra Horizontem citra verticem, alter vero infra Horizontem exiſtit, dicitur Sphę-<lb/>ra obliqua, quoniam Æquator ac ei paralelli circuli oblique ſiue ad angulos obliquos Horizontem ſecant: <lb/></s> <s xml:id="echoid-s1037" xml:space="preserve">Quando tandem alter polorum Zenith, ſeu verticem, alter vero Nadir, ſiue imum Cæli occupat, paralella <lb/>dici debet Sphęra, ex eo quod Æquator, atq; </s> <s xml:id="echoid-s1038" xml:space="preserve">ipſi paralelli circuli conſtituantur ad Horizontem, imo in hac <lb/>poſitione Æquator ad vnguem ipſi Horizonti congruit. </s> <s xml:id="echoid-s1039" xml:space="preserve">Verum de varijs mundanæ Sphęræ conſtitutioni-<lb/>bus, atq; </s> <s xml:id="echoid-s1040" xml:space="preserve">habitationibus, quæ ab illis oriuntur, ſeorſim in fine operis agendum erit.</s> <s xml:id="echoid-s1041" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1042" xml:space="preserve">Cauſa huius mutationis Sphęræ, eſt rotunditas (vt enim poſtea probabimus terra rotunda eſt) ex rotundi-<lb/>tate enim terræ prouenit, vt varia loca, varios habeant horizontes, quorũ aliqui tranſeant per mundi polos, <lb/>hincque oritur Sphęra recta: </s> <s xml:id="echoid-s1043" xml:space="preserve">alij polum alterum ſupra ſe eleuatum, alterumvero depreſſum quadrantenus <lb/>habeant, atq; </s> <s xml:id="echoid-s1044" xml:space="preserve">hæc eſt obliqua Sphœra; </s> <s xml:id="echoid-s1045" xml:space="preserve">vnus tandem ſolus. </s> <s xml:id="echoid-s1046" xml:space="preserve">Horizon habeat alterum polorum altiſſimum, <pb o="8" file="0024" n="24" rhead="De Circulis Shpæræ."/> <anchor type="figure" xlink:label="fig-0024-01a" xlink:href="fig-0024-01"/> id eſt vertici incumbentem, alterum vero hu-<lb/>millimum, ideſt, Cęli imum occupantem: </s> <s xml:id="echoid-s1047" xml:space="preserve">qui <lb/>ſtatus paralellam Sphęram conſtituit. </s> <s xml:id="echoid-s1048" xml:space="preserve">quę om <lb/>nia liceat perſpicuę<unsure/> in appoſito ſchemate cõ-<lb/>templari; </s> <s xml:id="echoid-s1049" xml:space="preserve">in quo tres ſint diuerſi habitatores <lb/>G H I. </s> <s xml:id="echoid-s1050" xml:space="preserve">in tribus locis in ſuperficie terræ ro-<lb/>tunda. </s> <s xml:id="echoid-s1051" xml:space="preserve">ex hac rotunditate oriuntur eorum <lb/>diuerſi Horizontes; </s> <s xml:id="echoid-s1052" xml:space="preserve">habitator enim G. </s> <s xml:id="echoid-s1053" xml:space="preserve">habet <lb/>Horizontem. </s> <s xml:id="echoid-s1054" xml:space="preserve">A D. </s> <s xml:id="echoid-s1055" xml:space="preserve">tranſeuntem per mundi <lb/>polos, vnde habet Spęram rectam habitator <lb/>ad H. </s> <s xml:id="echoid-s1056" xml:space="preserve">habebit alium Horizontem B E. </s> <s xml:id="echoid-s1057" xml:space="preserve">quia <lb/>debet quilibet habitator perpendicularis, ſuo <lb/>Horizonte inſiſtere, quando ſtat: </s> <s xml:id="echoid-s1058" xml:space="preserve">qui Hori-<lb/>zon B E. </s> <s xml:id="echoid-s1059" xml:space="preserve">infra polum D. </s> <s xml:id="echoid-s1060" xml:space="preserve">ex vna parte depri-<lb/>mitur: </s> <s xml:id="echoid-s1061" xml:space="preserve">ex altera vero ſupra polum A. </s> <s xml:id="echoid-s1062" xml:space="preserve">attolli-<lb/>tur, quæ eſt Sphæræ obliquæ conditio. </s> <s xml:id="echoid-s1063" xml:space="preserve">tan-<lb/>dem eadem de cauſa, habitator ad I. </s> <s xml:id="echoid-s1064" xml:space="preserve">horizon-<lb/>tem alium habebit C F. </s> <s xml:id="echoid-s1065" xml:space="preserve">cui pro vertice alter <lb/>vero A. </s> <s xml:id="echoid-s1066" xml:space="preserve">pro Nadir erit: </s> <s xml:id="echoid-s1067" xml:space="preserve">quam Sphæram no-<lb/>minabimus paralellam. </s> <s xml:id="echoid-s1068" xml:space="preserve">rotunditas igitur ter-<lb/>ræ varios efficit Horizontes, ac proinde va-<lb/>rias Sphęræ habitudines.</s> <s xml:id="echoid-s1069" xml:space="preserve"/> </p> <div xml:id="echoid-div30" type="float" level="2" n="1"> <figure xlink:label="fig-0024-01" xlink:href="fig-0024-01a"> <image file="0024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0024-01"/> </figure> </div> <p> <s xml:id="echoid-s1070" xml:space="preserve">4 Tandem lectorem monitum velim, ad noſtræ Sphęræ intelligentiam neceſſarium eſſe habere ob ocu-<lb/>los Armillarem Spęram materialem, qualem nos ſupra conſtruximus, vel ſaltem aliam: </s> <s xml:id="echoid-s1071" xml:space="preserve">aliter non ſine ma-<lb/>gna difficultate ſæpius illi hærendum fore denuncio.</s> <s xml:id="echoid-s1072" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div32" type="section" level="1" n="21"> <head xml:id="echoid-head23" style="it" xml:space="preserve">De Circulis Sphæræ generatim. Cap. II.</head> <p> <s xml:id="echoid-s1073" xml:space="preserve">PRimo ſciat lector, aut auditor huius doctrinæ, Circulos hoſce ex quibus materialis compingitur, Sphæ-<lb/>ra nullo modo Cęlos vllos repręſentare, ſed tantum referre Circulos aut potius circumferentias quaſdã, <lb/>quas in primo Mobili, aut ſupremo Cælo Aſtronomi optimis rationibus concipiunt eſſe deſcriptas: </s> <s xml:id="echoid-s1074" xml:space="preserve">quod <lb/>ideo monere initio volui, quia animaduerti ſæpius Aſtronomiæ Tyrones hac in re grauiter decipi.</s> <s xml:id="echoid-s1075" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1076" xml:space="preserve">2 Hiautem Circuli ſunt vndecim, Horizon, Meridianus, Zodiacus, Æquator, Colurus ſolſtitiorum, <lb/>Tropicus Cancri, Tropicus Capricornus, Circulus polaris arcticus, Circulus polaris antarcticus; </s> <s xml:id="echoid-s1077" xml:space="preserve">Et Circu-<lb/>lus ſecundi motus: </s> <s xml:id="echoid-s1078" xml:space="preserve">qui ſolusnon eſt concipiendus in ſupremo Cęlo, ſed infra ipſum in regione Planetarum.</s> <s xml:id="echoid-s1079" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1080" xml:space="preserve">3. </s> <s xml:id="echoid-s1081" xml:space="preserve">Horum ſex priores dicuntur Circuli maximi, ſeu etiam maiores; </s> <s xml:id="echoid-s1082" xml:space="preserve">reliqui vero minores dicuntur. </s> <s xml:id="echoid-s1083" xml:space="preserve">Ma-<lb/>ximiſunt qui totam Sphæram bifariam, ſeu in partes æquales diuidunt, idemq; </s> <s xml:id="echoid-s1084" xml:space="preserve">cum Sphæra centrum poſ-<lb/>ſident, ſuntque propterea reliquis maiores. </s> <s xml:id="echoid-s1085" xml:space="preserve">Minores ij ſunt, qui Sphæram inæqualia non diuidunt, aliud-<lb/>que centrum habent à centro Sphæræ, ac propterea minores ſunt prædictis: </s> <s xml:id="echoid-s1086" xml:space="preserve">quæ omnia in materiali Sphæ-<lb/>ra recognoſcere poteris.</s> <s xml:id="echoid-s1087" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1088" xml:space="preserve">4 Alij ſunt inuicem paralelli, vt Æquator, Tropici, & </s> <s xml:id="echoid-s1089" xml:space="preserve">Polares; </s> <s xml:id="echoid-s1090" xml:space="preserve">alij ſunt inuicem concurrentes vt Zo-<lb/>diacus cum Æquatore, Coluris, & </s> <s xml:id="echoid-s1091" xml:space="preserve">Tropicis.</s> <s xml:id="echoid-s1092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1093" xml:space="preserve">5 Omnes Circuli maiores ſe mutuo bifariam, ideſt, in æqua ſecant; </s> <s xml:id="echoid-s1094" xml:space="preserve">ſic vides in Sphæra materiali Hori-<lb/>zontem, ſecare bifariam Meridianum, & </s> <s xml:id="echoid-s1095" xml:space="preserve">viciſſim; </s> <s xml:id="echoid-s1096" xml:space="preserve">pariter Æquatorem bifariam ſecari ab Horizonti, & </s> <s xml:id="echoid-s1097" xml:space="preserve"><lb/>Meridiano, & </s> <s xml:id="echoid-s1098" xml:space="preserve">è contra. </s> <s xml:id="echoid-s1099" xml:space="preserve">Minores verò Circuli neq; </s> <s xml:id="echoid-s1100" xml:space="preserve">inuicem, neq; </s> <s xml:id="echoid-s1101" xml:space="preserve">maiores circulos mutuo bifariam diui-<lb/>dunt: </s> <s xml:id="echoid-s1102" xml:space="preserve">quamuis poſſint ipſi a maioribus bifariam ſecari, ſic Polares, & </s> <s xml:id="echoid-s1103" xml:space="preserve">Tropici per æqua ſecantur ab vtroque <lb/>Coluro, non tamen eos bifariam patiuntur.</s> <s xml:id="echoid-s1104" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1105" xml:space="preserve">6 Alij fixi ſunt, ac ſtabiles qui ſcilicet motu diurno neutiquam aguntur: </s> <s xml:id="echoid-s1106" xml:space="preserve">vti ſunt Horizon, & </s> <s xml:id="echoid-s1107" xml:space="preserve">Meridia-<lb/>nus: </s> <s xml:id="echoid-s1108" xml:space="preserve">alij ſunt mobiles, qui videlicet diurna conuerſione reuoluuntur, vti ſunt reliqui omnes, ex quibus pars <lb/>illa Sphęræ componitur, quam primum mobile appellandam eſſe cenſuimus, quæq; </s> <s xml:id="echoid-s1109" xml:space="preserve">intra Meridianum cir-<lb/>ca axem mundi circumuoluitur.</s> <s xml:id="echoid-s1110" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1111" xml:space="preserve">7 Alij vnici, & </s> <s xml:id="echoid-s1112" xml:space="preserve">ſingulares ſunt, vt Æquator, Zodiacus, & </s> <s xml:id="echoid-s1113" xml:space="preserve">cæteri omnes, præter Horizontem, & </s> <s xml:id="echoid-s1114" xml:space="preserve">Meri-<lb/>dianum, qui ſunt plurales. </s> <s xml:id="echoid-s1115" xml:space="preserve">ſunt enim in Mundo infiniti Horizontes, & </s> <s xml:id="echoid-s1116" xml:space="preserve">Meridia@i; </s> <s xml:id="echoid-s1117" xml:space="preserve">ſingula enim terræ lo-<lb/>ca, habent pro rium Horizontem, vt in præcedenti figura tria loca G H I. </s> <s xml:id="echoid-s1118" xml:space="preserve">tres habent diuerſos Horizon-<lb/>tes; </s> <s xml:id="echoid-s1119" xml:space="preserve">vnde quotloca, tot Horizontes. </s> <s xml:id="echoid-s1120" xml:space="preserve">ſimiliter innumeri ſunt Meridiani, quia quælibet loca, quorum alie <lb/>alijs ſunt Orientaliora, aut Occidentaliora ſub diuerſis exiſtunt Meridianis. </s> <s xml:id="echoid-s1121" xml:space="preserve">Et quamuis in Sphæra mate-<lb/>ria@@ſit vnicus tantum Horizon, ac Meridianus, ij tamen Horizontes, ac Meridianos omnes poſi biles pro <lb/>varia Sphæræ conſti@utione repræſentare poſſunt: </s> <s xml:id="echoid-s1122" xml:space="preserve">at verò eſt vnus tantum in Mundo Zodiacus, vnuſq; </s> <s xml:id="echoid-s1123" xml:space="preserve">tan <lb/>tum Æquatori, & </s> <s xml:id="echoid-s1124" xml:space="preserve">cæteri omnes vnici in Mundo ſunt.</s> <s xml:id="echoid-s1125" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1126" xml:space="preserve">8 Notandum eſt tandem, centrum, & </s> <s xml:id="echoid-s1127" xml:space="preserve">polum alicuius Circuli in Sphæra deſcripti, inuicem deferre. </s> <s xml:id="echoid-s1128" xml:space="preserve">po-<lb/>lus enim eſt punctum in ſuperficie ſphærica a quo Circuli peripheria æquidiſtat, ſeu a quo omnes lineæ du-<lb/>ctæ ad eam ſu tæquales: </s> <s xml:id="echoid-s1129" xml:space="preserve">& </s> <s xml:id="echoid-s1130" xml:space="preserve">ex quo tanquam centro Circulus deſcribi poteſt: </s> <s xml:id="echoid-s1131" xml:space="preserve">ſic polus Mundi arcticus eſt po <lb/>@us non ſolũ Æquatoris, ſed etiam Tropici Cancri; </s> <s xml:id="echoid-s1132" xml:space="preserve">& </s> <s xml:id="echoid-s1133" xml:space="preserve">Circulus polaris. </s> <s xml:id="echoid-s1134" xml:space="preserve">ſupra aliter definitus eſt polus, extre- <pb o="9" file="0025" n="25" rhead="Liber Primus."/> num ſcilicet axis. </s> <s xml:id="echoid-s1135" xml:space="preserve">centrum verò circuli in Sphæra deſcripti eſt in medio illius plani, cuius ille Circulus eſt <lb/>circumferentia, quare neceſſario eſt iutra Sphæram, non in ſuperficie vt eſt polus: </s> <s xml:id="echoid-s1136" xml:space="preserve">ſic centrum Æquatoris eſt <lb/>idem cum centro Sphæræ. </s> <s xml:id="echoid-s1137" xml:space="preserve">Hucuſque de Circulis vniuerſis egimus, nunc de ijſdem ſigillatim agendum, atq; <lb/></s> <s xml:id="echoid-s1138" xml:space="preserve">de ſingulis quatuor conſideranda, Etymologia, Deſinitio, vna cum centris, ac polis: </s> <s xml:id="echoid-s1139" xml:space="preserve">Poſitio ſeu ſitus ipſius <lb/>in Mundo. </s> <s xml:id="echoid-s1140" xml:space="preserve">Vltimo vſus eiuſdem. </s> <s xml:id="echoid-s1141" xml:space="preserve">Danda eſt autem à lectore diligenter opera, vt hæc quæ de Circulis di-<lb/>cenda ſunt, ea Circuli Sphæræ Mundi præcipuè applicet, de ijſq; </s> <s xml:id="echoid-s1142" xml:space="preserve">intelligat; </s> <s xml:id="echoid-s1143" xml:space="preserve">horum enim cauſa, & </s> <s xml:id="echoid-s1144" xml:space="preserve">in hunc <lb/>finem circuli materiales, & </s> <s xml:id="echoid-s1145" xml:space="preserve">Sphæra ex ipſis componitur, ſed iam ad Horizontem.</s> <s xml:id="echoid-s1146" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div33" type="section" level="1" n="22"> <head xml:id="echoid-head24" style="it" xml:space="preserve">DeHorizonte. Cap. III.</head> <p> <s xml:id="echoid-s1147" xml:space="preserve">HOrizon igitur ſic dicitur à verbo græco, ὁρίζομαι, quod latinè vertitur finio, & </s> <s xml:id="echoid-s1148" xml:space="preserve">termino, vnde à latinis <lb/>finitor, & </s> <s xml:id="echoid-s1149" xml:space="preserve">terminator appellatur, quòd viſum noſtrum terminet. </s> <s xml:id="echoid-s1150" xml:space="preserve">Eſt enim Horizon circulus maximus <lb/>diuidens totam mundi Sphæram in duas partes æquales, ſeu in duo hemiſphæria, quorum alterum, quod <lb/>ſupremum dicitur, totum vi detur ab hab@tatore eiuſdem Horizontis, alterum vero totum infra eundem la-<lb/>tet, ac proinde inferum dicitur, nec cerni poteſt ab eodem habitatore, quia Horizon viſionem ipſius finit, <lb/>ac terminat, ita vt nihil infra Horizontem videre poſſit. </s> <s xml:id="echoid-s1151" xml:space="preserve">vnde ſequitur centrum eius eſſe idem cum centro <lb/>Mundi: </s> <s xml:id="echoid-s1152" xml:space="preserve">& </s> <s xml:id="echoid-s1153" xml:space="preserve">polos eius coincidere, alterum quidem cum Vertice habitatoris proprij, alterum vero cum imo <lb/>cæli. </s> <s xml:id="echoid-s1154" xml:space="preserve">in præcedenti figura tres lineæ A D. </s> <s xml:id="echoid-s1155" xml:space="preserve">B E. </s> <s xml:id="echoid-s1156" xml:space="preserve">C F. </s> <s xml:id="echoid-s1157" xml:space="preserve">ſunt pro tribus diametris trium Horizõtium, quorum <lb/>proprij habitatores ſunt ad G H I. </s> <s xml:id="echoid-s1158" xml:space="preserve">cum ſuis verticibus, & </s> <s xml:id="echoid-s1159" xml:space="preserve">Imis, ſeu Zenith, & </s> <s xml:id="echoid-s1160" xml:space="preserve">Nadir; </s> <s xml:id="echoid-s1161" xml:space="preserve">quare vt Horizontem <lb/>rectè concipiamus, debemus imaginari planiciem quandam per centrum terræ, vel Mundi tranſeuntem, <lb/>& </s> <s xml:id="echoid-s1162" xml:space="preserve">ad nullam partem, ſeu ex nulla parte inclinatam, eleuatamuè, ſeu vt aiunt ad libellam conſtitutam; </s> <s xml:id="echoid-s1163" xml:space="preserve">atq; <lb/></s> <s xml:id="echoid-s1164" xml:space="preserve">tam immenſam, & </s> <s xml:id="echoid-s1165" xml:space="preserve">quoquouerſus extenſam, vt ad extrema Mundi circumquaque pertineat. </s> <s xml:id="echoid-s1166" xml:space="preserve">talem plani-<lb/>ciem refert ad oculum tranquilla maris ſuperficies, ſi inferius ad centrum terræ imaginatione deprimatur. </s> <s xml:id="echoid-s1167" xml:space="preserve"><lb/>huiuſmodi etiam eſt ex parte planum alicuius magni pauimenti, ſi imaginatione ad cælum vſque quoquo-<lb/>uerſus extendatur.</s> <s xml:id="echoid-s1168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1169" xml:space="preserve">Porro Aſtronomi diſtingunt Horizontem; </s> <s xml:id="echoid-s1170" xml:space="preserve">vnum Aſtronomicum de quo hactenus loquuti ſumus; </s> <s xml:id="echoid-s1171" xml:space="preserve">alte-<lb/>rum phyſicum, & </s> <s xml:id="echoid-s1172" xml:space="preserve">ſenſibilem, qui ab illo differt, quod non tranſeat per centrum Mundi, vel terræ, ſed ſu-<lb/>perficiei terræ ibi incumbit, vbi proprius ipſius habitator exiſtit; </s> <s xml:id="echoid-s1173" xml:space="preserve">eſt enim ſpatium illud in ſuperficie terræ, <lb/>mariſuè, quod acies oculorum circumducta, ſublatis omnibus impedimentis, conſpicere poteſt, vt in præ-<lb/>cedenti figura linea K L. </s> <s xml:id="echoid-s1174" xml:space="preserve">refert Horizontem ſenſibilem proprij habitatoris ad G M N. </s> <s xml:id="echoid-s1175" xml:space="preserve">vero eſt pro Hori-<lb/>zonte phyſico habitatoris ad H O P. </s> <s xml:id="echoid-s1176" xml:space="preserve">tandem pro finitore ſui habitatoris ad I. </s> <s xml:id="echoid-s1177" xml:space="preserve">& </s> <s xml:id="echoid-s1178" xml:space="preserve">ſic de alijs omnibus terræ <lb/>locis. </s> <s xml:id="echoid-s1179" xml:space="preserve">Eſt autem hic Horizon alteri Aſtronomico æquidiſtans, vti in figura factum eſt. </s> <s xml:id="echoid-s1180" xml:space="preserve">quod inde neceſſa-<lb/>rio prouenit, quia ſi linea recta tangit medium punctum alicuius arcus, paralella eſt alteri lineæ, quæ illum <lb/>cum inſtar cnordæ ſubtendit; </s> <s xml:id="echoid-s1181" xml:space="preserve">ſic quia linea K L. </s> <s xml:id="echoid-s1182" xml:space="preserve">tangit medium punctum G. </s> <s xml:id="echoid-s1183" xml:space="preserve">arcus R G I. </s> <s xml:id="echoid-s1184" xml:space="preserve">idcirco eſt alteri <lb/>rectæ R I. </s> <s xml:id="echoid-s1185" xml:space="preserve">illi arcui ſubtenſæ paralella, quod & </s> <s xml:id="echoid-s1186" xml:space="preserve">Clauius in ſcholio propoſ. </s> <s xml:id="echoid-s1187" xml:space="preserve">27. </s> <s xml:id="echoid-s1188" xml:space="preserve">tertij demonſtrat: </s> <s xml:id="echoid-s1189" xml:space="preserve">& </s> <s xml:id="echoid-s1190" xml:space="preserve">expe-<lb/>rientia conſtare poteſt, ſi figura accurate delineatur.</s> <s xml:id="echoid-s1191" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1192" xml:space="preserve">Ille dicitur Aſtronomicus, quia Aſtronomis vſui eſt: </s> <s xml:id="echoid-s1193" xml:space="preserve">hic vero naturalis, & </s> <s xml:id="echoid-s1194" xml:space="preserve">ſenſibilis, quòd ſenſu percipia-<lb/>tur; </s> <s xml:id="echoid-s1195" xml:space="preserve">eſt enim vti dicebamus, vel illa maris tranquilli plana ſuperficies, vel etiã alicuius planę regionis æquor, <lb/>quod oculis cernitur, quodque ſecundum ſenſus iudicium, quamuis globoſumſit, planum tamen apparet; <lb/></s> <s xml:id="echoid-s1196" xml:space="preserve">& </s> <s xml:id="echoid-s1197" xml:space="preserve">quamuis non admodum magnum ſit, videtur tamen vſque ad cælum vndique pertingere. </s> <s xml:id="echoid-s1198" xml:space="preserve">quantum au-<lb/>rem ſit ſpacium iſtud, quo in terra, vel in mari viſus maxime protenditur, hoc eſt, quam late, Horizon ſen-<lb/>ſibilis circumcirca ab oculo noſtro pateat, difficile eſt determinare, quoniam terminus vifionis vltimus tam <lb/>in mari, quam in terra, admodum incertus eſt: </s> <s xml:id="echoid-s1199" xml:space="preserve">vt propterea variæ ſint hac de re ſcriptorum ſententiæ Era-<lb/>toſthenes enim ſtatuit ſemidiametrum eius, ideſt, maximam viſus protenſionem eſſe milliariorum 44. </s> <s xml:id="echoid-s1200" xml:space="preserve">Ma-<lb/>crobius milliariorum 23. </s> <s xml:id="echoid-s1201" xml:space="preserve">Proclus milliariorum 250. </s> <s xml:id="echoid-s1202" xml:space="preserve">Albertus vero Magnus milliariorum 125. </s> <s xml:id="echoid-s1203" xml:space="preserve">Plerique <lb/>alij, quorum verior ſententia reputatur eandem produnt milliariorum 63. </s> <s xml:id="echoid-s1204" xml:space="preserve">fere. </s> <s xml:id="echoid-s1205" xml:space="preserve">Cur autem hic Horizon, <lb/>tam breui ſpacio concludatur, cauſa eſt terræ, ac maris rotunditas; </s> <s xml:id="echoid-s1206" xml:space="preserve">quoniam enim oculus in conuexo huius <lb/>rotundæ ſuperfici collocatus eſt, fit vt lineæ rectæ ab eo egredicntes, ſecundum quas v@ſus fertur, quæ lineæ <lb/>ideo viſuales à perſpectiuis dicuntur, ſint lineæ globoſam terræ ſuperficiem tangentes, quare oculus nequit <lb/>maius ſpacium intueri, quam illud, quod hæ lineæ aliquo modo attingunt, quod quidem exiguum eſt, vt <lb/>optici demonſtrant: </s> <s xml:id="echoid-s1207" xml:space="preserve">ibiq; </s> <s xml:id="echoid-s1208" xml:space="preserve">viſio deſinit vbi rotunditas terræ ab his lineis ſenſibiliter deorſum deſcendit. </s> <s xml:id="echoid-s1209" xml:space="preserve">cum <lb/>præterea viſio fiat ſecundum prædictas lineas rectas ſequitur nihil ab oculo videri poſſe, quod infra eas exi-<lb/>ſtat: </s> <s xml:id="echoid-s1210" xml:space="preserve">vnde oculus habitatoris ad G. </s> <s xml:id="echoid-s1211" xml:space="preserve">quia ponitur ibi in terræ ſuperficie, nihil videre poterit, quod ſit in fra li-<lb/>neam K G L. </s> <s xml:id="echoid-s1212" xml:space="preserve">ſed tantum ea, quæ ſupra eam exiſtent. </s> <s xml:id="echoid-s1213" xml:space="preserve">In cælo tamen videt pariter duo puncta K A. </s> <s xml:id="echoid-s1214" xml:space="preserve">& </s> <s xml:id="echoid-s1215" xml:space="preserve">L D. </s> <s xml:id="echoid-s1216" xml:space="preserve"><lb/>quia ob immenſam a nobis cæli diſtan@iam, ſpacia K A. </s> <s xml:id="echoid-s1217" xml:space="preserve">& </s> <s xml:id="echoid-s1218" xml:space="preserve">L D. </s> <s xml:id="echoid-s1219" xml:space="preserve">euadunt inſenſibilia. </s> <s xml:id="echoid-s1220" xml:space="preserve">Verum quidem eſt <lb/>quod propter vapores Horizontem obſidentes videmus aliquando Solem, ac Lunam, etiamſi nondum Ho-<lb/>rizontem Aſtronomicum attigerint, vt Aſtronomorum obſeruatio docet; </s> <s xml:id="echoid-s1221" xml:space="preserve">cuius cauſa eſt linearum v@ſualiũ <lb/>refractio. </s> <s xml:id="echoid-s1222" xml:space="preserve">ſeu obliquatio a vaporibus illi effecta, ita v@ poſſint ad Solem latitantem pertine@e: </s> <s xml:id="echoid-s1223" xml:space="preserve">ſed hac de re <lb/>opticorum eſt pertractare. </s> <s xml:id="echoid-s1224" xml:space="preserve">P@æterea h@cillud annotandum, quod ſupra innuimus, Hor zõtem hunc vtrum-<lb/>que non eſſe circulos vnicos, ſed plurales; </s> <s xml:id="echoid-s1225" xml:space="preserve">quælibet enim loca terræ habent ſuos Horizontes Aſtronomi-<lb/>cum, & </s> <s xml:id="echoid-s1226" xml:space="preserve">Phyſicum. </s> <s xml:id="echoid-s1227" xml:space="preserve">In Sphæra tamen ponitur Aſtronomicus, qui vicem gerit omnium Hor zontum in mu-<lb/>do poſſibilium, ex varia enim Sphæræ conſtitutione, poteſt ipſe omnes Horizontes poſſibiles referre: </s> <s xml:id="echoid-s1228" xml:space="preserve">vn-<lb/>de poteſt etiam effici Horizon rectus, obliquus, & </s> <s xml:id="echoid-s1229" xml:space="preserve">paralellus, ijſdem de cauſis, quibus dicitur Sphæra recta, <lb/>obliqua, & </s> <s xml:id="echoid-s1230" xml:space="preserve">paralella.</s> <s xml:id="echoid-s1231" xml:space="preserve"/> </p> <pb o="10" file="0026" n="26" rhead="De Circulis Sphæræ."/> <p> <s xml:id="echoid-s1232" xml:space="preserve">Sed vt eius in mundo ſitum, ac poſitionem rectè inueniamus, in quouis terræ loco, vti ſolemus. </s> <s xml:id="echoid-s1233" xml:space="preserve">Libella, <lb/>inſtrumento Architectis familiari, vulgo Liuello, quo ipſi pauimenta, & </s> <s xml:id="echoid-s1234" xml:space="preserve">plura alia plana in modum Hori-<lb/>zontis, ſeu Horizonti æquidiſtantia conſtituunt: </s> <s xml:id="echoid-s1235" xml:space="preserve">quæ plana dicũtur Horizontalia. </s> <s xml:id="echoid-s1236" xml:space="preserve">eſt autem horum plano-<lb/>rum ea poſitio, vt ad nullam partem ſint inclinata, aut eleuata, verum æquè proſtrata ſint; </s> <s xml:id="echoid-s1237" xml:space="preserve">qualis apparet eſ-<lb/>ſe aquæ quieſcentis ſuperficies. </s> <s xml:id="echoid-s1238" xml:space="preserve">hæc enim ad omnes partes æqualiter iacet. </s> <s xml:id="echoid-s1239" xml:space="preserve">Libella autem inſtrumentum eſt <lb/> <anchor type="figure" xlink:label="fig-0026-01a" xlink:href="fig-0026-01"/> talis conditionis, vt in eo vna linea ſit alteri perpendicularis, vt in figura <lb/>linea A D. </s> <s xml:id="echoid-s1240" xml:space="preserve">eſt perpendicularis lineæ B C. </s> <s xml:id="echoid-s1241" xml:space="preserve">eamque in D. </s> <s xml:id="echoid-s1242" xml:space="preserve">bifariam ſecet. </s> <s xml:id="echoid-s1243" xml:space="preserve">a <lb/>ſummo autem lineæ A D. </s> <s xml:id="echoid-s1244" xml:space="preserve">ideſt à puncto A. </s> <s xml:id="echoid-s1245" xml:space="preserve">deſcendat liberè perpendicu-<lb/>lum A E. </s> <s xml:id="echoid-s1246" xml:space="preserve">vſus eius talis eſt; </s> <s xml:id="echoid-s1247" xml:space="preserve">cum planum aliquod conſtituendum eſt Hori-<lb/>zontale, aut ad L@bellam, id prius per ſenſus æſtimationem iuxta Horizon <lb/>tem ſternunt; </s> <s xml:id="echoid-s1248" xml:space="preserve">ei deinde Libellam ſic ſuperponunt, vt linea B C. </s> <s xml:id="echoid-s1249" xml:space="preserve">quæ baſis <lb/>eſt inſtrumenti, plano illi tota applicetur, inſtrumẽtum vero ſic ſuper eum <lb/>erigatur, vt perpendiculum A E. </s> <s xml:id="echoid-s1250" xml:space="preserve">liberè cadens, & </s> <s xml:id="echoid-s1251" xml:space="preserve">ſuperficiem inſtrumen-<lb/>ti radens, lineæ A D. </s> <s xml:id="echoid-s1252" xml:space="preserve">ad vnguem reſpondeat quod vt melius efficiat, ex-<lb/>cauari ſolet feneſtella è regione perpendiculi E. </s> <s xml:id="echoid-s1253" xml:space="preserve">intra quam in hac opera-<lb/>tione, ipſum perpendiculum excipitur, ne inſtrumento occurrens a libera <lb/>demiſſione impediatur. </s> <s xml:id="echoid-s1254" xml:space="preserve">ſic igitur perpendiculo ſtante, erit neceſſario ba-<lb/>fis B C. </s> <s xml:id="echoid-s1255" xml:space="preserve">in ſitu Horizontis, eum enim cum perpendiculo A E. </s> <s xml:id="echoid-s1256" xml:space="preserve">faciat angu-<lb/>los hinc indè æquales, hoc eſt ſit æqualiter inclinata, quæ eſt poſitio Horizontalis, erit & </s> <s xml:id="echoid-s1257" xml:space="preserve">ipſa in ſitu Hori-<lb/>zontis fita, & </s> <s xml:id="echoid-s1258" xml:space="preserve">conſequenter planum cui adhęret ſecundum illam dimenſionem erit Horizontaie. </s> <s xml:id="echoid-s1259" xml:space="preserve">yt autem <lb/>conſtet ipſum eſſe Horizontale ſecundum omnes partes, oportet vt libella eidem plano ſuperpoſita, & </s> <s xml:id="echoid-s1260" xml:space="preserve">cir-<lb/>cumuoluta circa lineam perpendicularem, tanquam axem, ſemper perpendiculũ ſuæ lineæ, exactè reſpon-<lb/>deat, ſic enim planum illud ſecundum omnes ſui partes, ac dimenſionem ad libellam ſitum erit, & </s> <s xml:id="echoid-s1261" xml:space="preserve">conſe-<lb/>quenter Horizontale dici merebitur. </s> <s xml:id="echoid-s1262" xml:space="preserve">talis autem plani alicuius conſtitutio, cum ad multa alia ſit vtilis, tum <lb/>etiam vt rectè Horizontis concipiamus. </s> <s xml:id="echoid-s1263" xml:space="preserve">Reliquum eſt, vt nonnulla, etiam de Horizontis habitatore dica-<lb/>mus, atque in primis notandum quemlibet Horizontem propriè loquendo, vnicum habere tantum habita-<lb/>torem, cum enim vti diximus, quot ſunt loca, tot etiam Horizontes, quotque loca, tot etiam habitatores <lb/>ſint, ſequitur ſingulos habitatores proprios etiam Horizontem nanciſci. </s> <s xml:id="echoid-s1264" xml:space="preserve">Quilibet porrò habitator, cum-<lb/>ſtat, ſuo Horizonti perpendiculariter in centro eius inſiſtit, ideſt, linea ducta ſecundum hominis longitu-<lb/>dinem altitudinemuè Horizonti perpendiculariter eſt, quę linea ſi producatur vtrinque, trãſit per Zenith, <lb/>centrum Horizontis, centrum terræ, ac Nadir; </s> <s xml:id="echoid-s1265" xml:space="preserve">qualis in figura eſt linea C G F. </s> <s xml:id="echoid-s1266" xml:space="preserve">ad habitatorem G. </s> <s xml:id="echoid-s1267" xml:space="preserve">reliqua <lb/>pariter corpora, quæ in altum eriguntur, vt turres, columnæ, parietes, debent eſſe in hac linea, quæ ne ca-<lb/>dant, debet etiam per eorum grauitatis centrum eadem linea, & </s> <s xml:id="echoid-s1268" xml:space="preserve">præterea per baſim eorum tranſire; </s> <s xml:id="echoid-s1269" xml:space="preserve">aliter <lb/>erecta ſtare nequeunt, ſed concidunt & </s> <s xml:id="echoid-s1270" xml:space="preserve">proſternuntur. </s> <s xml:id="echoid-s1271" xml:space="preserve">hæc linea, Directionis linea dicitur. </s> <s xml:id="echoid-s1272" xml:space="preserve">eadem ratione <lb/>homines minime ſtare queunt, niſi hæc linea per centrum grauitatis, ac ſimul per baſim eorum, hoc eſt per <lb/>interuallum intra p@antas interiectum, quæ eſt eorum baſis, deſcendat. </s> <s xml:id="echoid-s1273" xml:space="preserve">prædicta omnia in figura, vbi ſunt <lb/>varij habitatore cum ſuis Horizontibus, ac lineis Directionis contemplari poſſumus.</s> <s xml:id="echoid-s1274" xml:space="preserve"/> </p> <div xml:id="echoid-div33" type="float" level="2" n="1"> <figure xlink:label="fig-0026-01" xlink:href="fig-0026-01a"> <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/> </figure> </div> <p> <s xml:id="echoid-s1275" xml:space="preserve">Officia autem, ſiue vſus Horizontis ſunt hi; </s> <s xml:id="echoid-s1276" xml:space="preserve">Primo totam mundi Sphæram diuidit vt dictum eſt, in duo <lb/>hemiſpæria; </s> <s xml:id="echoid-s1277" xml:space="preserve">in ſuperum ſcilicet, & </s> <s xml:id="echoid-s1278" xml:space="preserve">inferum, ſeu in cõſpicuum a ſuo habitatore, & </s> <s xml:id="echoid-s1279" xml:space="preserve">in eidem occultum.</s> <s xml:id="echoid-s1280" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1281" xml:space="preserve">2 Concurrit ad Sphæram rectam, obliquam, ac paralellam conſtituendam vti ſupra expoſuimus.</s> <s xml:id="echoid-s1282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1283" xml:space="preserve">3 Determinat Ortum, & </s> <s xml:id="echoid-s1284" xml:space="preserve">Occaſum ſyderum; </s> <s xml:id="echoid-s1285" xml:space="preserve">cum enim motu primi mobilis, ſeu motu diurno, Aſtra ab <lb/>Oriente, in Occidentem circumferantur, oriri tunc dicuntur quando ſupra Horizontem emergunt; </s> <s xml:id="echoid-s1286" xml:space="preserve">occi-<lb/>dere autem quando infra eumdem demergũtur. </s> <s xml:id="echoid-s1287" xml:space="preserve">Duo verò puncta, quæ in limbo Horizontis notantur ho-<lb/>minibus, Ortus, & </s> <s xml:id="echoid-s1288" xml:space="preserve">Occaſus, ſuntque apud ſectiones communes Horizontis, & </s> <s xml:id="echoid-s1289" xml:space="preserve">Æquatoris, dicuntur Ortus, <lb/>& </s> <s xml:id="echoid-s1290" xml:space="preserve">Occaſus veri, ſeu Æquinoctialis, eo quod ortiuarum, & </s> <s xml:id="echoid-s1291" xml:space="preserve">occiduarum latitudinem medium teneant, ſintq; <lb/></s> <s xml:id="echoid-s1292" xml:space="preserve">prope Æquatore; </s> <s xml:id="echoid-s1293" xml:space="preserve">vt mox exponam.</s> <s xml:id="echoid-s1294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1295" xml:space="preserve">4 In Horizonte ſumuntur, vel menſurantur latitudines ortiuæ, & </s> <s xml:id="echoid-s1296" xml:space="preserve">occiduæ; </s> <s xml:id="echoid-s1297" xml:space="preserve">eſt enim amplitudo, ſeu la-<lb/>titudo ortiua, occiduauè, arcus Horizontis inter punctum Ortus, & </s> <s xml:id="echoid-s1298" xml:space="preserve">Occaſus Æquinoctialis, & </s> <s xml:id="echoid-s1299" xml:space="preserve">punctum il-<lb/>lud in Horizonte, vbi ſydus oritur occidituè: </s> <s xml:id="echoid-s1300" xml:space="preserve">eſt autem amplitudo ortiua, æqualis amplitudini occiduæ, <lb/>v.</s> <s xml:id="echoid-s1301" xml:space="preserve">g. </s> <s xml:id="echoid-s1302" xml:space="preserve">latitudo ortiua Solis, quando eſt in principio Cancri, tropicumque eius percurrit, eſt in el<unsure/>euatione po-<lb/>li gr. </s> <s xml:id="echoid-s1303" xml:space="preserve">44. </s> <s xml:id="echoid-s1304" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s1305" xml:space="preserve">qualis eſt Parmæ graduum fere 37. </s> <s xml:id="echoid-s1306" xml:space="preserve">totidemque graduũ erit latitudo occidua tunc temporis: </s> <s xml:id="echoid-s1307" xml:space="preserve">vt ex <lb/>Sphęra materiali, eleuato polo Arctico gr. </s> <s xml:id="echoid-s1308" xml:space="preserve">44. </s> <s xml:id="echoid-s1309" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s1310" xml:space="preserve">ſupra Horizontem videre eſt. </s> <s xml:id="echoid-s1311" xml:space="preserve">ſi ad quodlibet tempus vis <lb/>ſcire latitud nem ortiuam, occiduamue Solis, pone gradum Eclypticæ, quem Sol tunc percurrit in Hori-<lb/>zonte, eleuato polo Sphæræ, vt conuenit tuæ habitationi; </s> <s xml:id="echoid-s1312" xml:space="preserve">nam arcus Horizontis inter Æquatorem, & </s> <s xml:id="echoid-s1313" xml:space="preserve">gra-<lb/>dum illum, erit quæſita latitudo. </s> <s xml:id="echoid-s1314" xml:space="preserve">porrò infra docebo inuenire gradum Solis, & </s> <s xml:id="echoid-s1315" xml:space="preserve">poli altitudinem.</s> <s xml:id="echoid-s1316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1317" xml:space="preserve">5 Sequitur ex prædictis de Ortu, & </s> <s xml:id="echoid-s1318" xml:space="preserve">Occaſu, Horizontem etiam determinare quantitatem diei, ac no-<lb/>ctis artificialis; </s> <s xml:id="echoid-s1319" xml:space="preserve">eſt enim dies artificialis mora Solis ſupra Horizontem, ideſt tempus ab Ortu ad Occaſum. <lb/></s> <s xml:id="echoid-s1320" xml:space="preserve">Nox autem artificialis eſt mora Solis infra Horizontem, ideſt tempus ab Occaſu ad Ortum. </s> <s xml:id="echoid-s1321" xml:space="preserve">Dicitur autem <lb/>dies artiſicialis, quod art@bus exercendis inſeruata qua ratione, nonnulii etiam appellant diem artificialem <lb/>totum illud tempus, quod ab initio crepuſculi matutini, vſque ad finem veſpertini intercipitur: </s> <s xml:id="echoid-s1322" xml:space="preserve">totum enim <lb/>illud temporis ſpacium artificibus, ac operibus aptum eſt. </s> <s xml:id="echoid-s1323" xml:space="preserve">Hinc ſequitur</s> </p> <p> <s xml:id="echoid-s1324" xml:space="preserve">6 Ipſum eſſe terminum diei, ac noctis, vt palam eſt ex dictis: </s> <s xml:id="echoid-s1325" xml:space="preserve">vnde nonnulli populi diem naturalem ab <lb/>Horizonte incipiunt, vt Itali, qui ab Occaſu Solis diem naturalem auſpicantur: </s> <s xml:id="echoid-s1326" xml:space="preserve">alij vero ab Ortu, vt olim <pb o="11" file="0027" n="27" rhead="Liber Primus."/> Babilonif: </s> <s xml:id="echoid-s1327" xml:space="preserve">eſt autem dies naturalis integra Solis conuerſio conſta@s die, ac nocte artificiali.</s> <s xml:id="echoid-s1328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1329" xml:space="preserve">7 Determinat quãtitatem duorum circulorum Æquatoris, ac Tropicis paralellorum, qui intelliguntur <lb/>deſcribi ex polis Mundi interuallo vſq; </s> <s xml:id="echoid-s1330" xml:space="preserve">ad Horizontem, ideſt qui tangant Horizontem in punctis vbi Me-<lb/>ridianus eum ſecat. </s> <s xml:id="echoid-s1331" xml:space="preserve">qui deſcribitur ex po@o conſpicuo, dicitur circulus paralellus ſemper apparentium ma-<lb/>ximus: </s> <s xml:id="echoid-s1332" xml:space="preserve">qui verò ex occulto polo circinare vſq; </s> <s xml:id="echoid-s1333" xml:space="preserve">ad Horizontis contactum intelligitur, dicitur paralellorum <lb/>ſemper occultorum maximus: </s> <s xml:id="echoid-s1334" xml:space="preserve">maximi videlicet reſpectu aliorum omnium, qui intra eos ex ijſdem polis <lb/>delineari poſſunt: </s> <s xml:id="echoid-s1335" xml:space="preserve">ac propterea ijſdem minores. </s> <s xml:id="echoid-s1336" xml:space="preserve">Hos porrò binos circulos, antiqui Sphæræ ſcriptores, vti <lb/>Proclus, appellabant circulos poiares; </s> <s xml:id="echoid-s1337" xml:space="preserve">circuli tamen noſtri polares coincidunt cum iſtis in rebus, cuius po-<lb/>lus eleuatur gr. </s> <s xml:id="echoid-s1338" xml:space="preserve">23. </s> <s xml:id="echoid-s1339" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s1340" xml:space="preserve">Nam ſi in ſphæra materiali polus tantundem eleuetur, circuli noſtri polares Horizon-<lb/>tem exactè perſtringent. </s> <s xml:id="echoid-s1341" xml:space="preserve">Omnes porrò ſtellæ quæ intra ipſos ad polos comprehenduntur ſunt Ortus, & </s> <s xml:id="echoid-s1342" xml:space="preserve"><lb/>Occaſus expertes: </s> <s xml:id="echoid-s1343" xml:space="preserve">illæ quidem, quæ circumpolares, ac conſpicuæ ſunt, perpetuæ ſunt apparicionis: </s> <s xml:id="echoid-s1344" xml:space="preserve">aliæ ve-<lb/>rò alterius depreſſi poli circũpolares, ſunt perpetuæ occultationis; </s> <s xml:id="echoid-s1345" xml:space="preserve">vt in materiali Sphæra rite conſtituta <lb/>apparere poteſt.</s> <s xml:id="echoid-s1346" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1347" xml:space="preserve">8 Horizon eſt initium à quo altitudines, & </s> <s xml:id="echoid-s1348" xml:space="preserve">depreſſiones ſtellarum ſumuntur, aut numerantur: </s> <s xml:id="echoid-s1349" xml:space="preserve">nume-<lb/>rantur enim in circulis ab horizonte incipientibus, & </s> <s xml:id="echoid-s1350" xml:space="preserve">ab eo aſcendentibus recta, ſeu perpe@diculariter, & </s> <s xml:id="echoid-s1351" xml:space="preserve"><lb/>per ſtellam propoſitam incedentibus, & </s> <s xml:id="echoid-s1352" xml:space="preserve">inde per verticem loci; </s> <s xml:id="echoid-s1353" xml:space="preserve">qui propterea circuli Verticales dicuntur. <lb/></s> <s xml:id="echoid-s1354" xml:space="preserve">tanta autem eſt altitudo alicuius Aſtri, quantus eſt Arcus circuli huius Verticalis inter horizontem, & </s> <s xml:id="echoid-s1355" xml:space="preserve">ip-<lb/>ſum aſtrum interceptus: </s> <s xml:id="echoid-s1356" xml:space="preserve">idem de depreſſione intelligendum, quæ tanta eſt quantus eſt arcus Verticalis ab <lb/>Horizonte vſq; </s> <s xml:id="echoid-s1357" xml:space="preserve">depreſſam ſtellam interiectus: </s> <s xml:id="echoid-s1358" xml:space="preserve">totq; </s> <s xml:id="echoid-s1359" xml:space="preserve">graduum eſſe dicuntur prædictæ altitudines, & </s> <s xml:id="echoid-s1360" xml:space="preserve">depreſ-<lb/>ſiones, quot gradus ſunt in prædictis arcubus. </s> <s xml:id="echoid-s1361" xml:space="preserve">ſumi autem debent hæ diſtantiæ in circulis ad horizontem <lb/>perpendicularibus, quoniam diſtantia debet ſumi ſecundum lineas breuiſſimas, quales ſunt perpendicula-<lb/>res, linea enim perpendicularis vnica eſt, ſtata, & </s> <s xml:id="echoid-s1362" xml:space="preserve">determinata, quia ab vno loco yna tantum perpendicu-<lb/>laris erigi poteſt; </s> <s xml:id="echoid-s1363" xml:space="preserve">at obliquæ lineæ infinitæ ex eodem loco duci poſſunt, & </s> <s xml:id="echoid-s1364" xml:space="preserve">ideo ſunt variæ, & </s> <s xml:id="echoid-s1365" xml:space="preserve">indetermina-<lb/>tæ quantitatis, ideo inconueniens eſt ſecundum eas, diſtantias menſurare; </s> <s xml:id="echoid-s1366" xml:space="preserve">ſequeretur enim idem punctum <lb/>ab eodem loco habere diſtantiam eandem, maiorem, & </s> <s xml:id="echoid-s1367" xml:space="preserve">minorem, quod eſt abſurdum: </s> <s xml:id="echoid-s1368" xml:space="preserve">quapropter cum vo-<lb/>lumus metiri altitudinem poli, ſeu diſtantiam eius ab horizonte, eam menſuramus in circulo Meridiano, <lb/>qui vnus eſt ex circulis verticalibus, & </s> <s xml:id="echoid-s1369" xml:space="preserve">perpendicularibus ad horizontem, vnde tanta poli altitudo ſupra <lb/>horizontem in quauis regione quantus eſt Meridiani arcus ab horizonte, vſque ad ipſum polum. </s> <s xml:id="echoid-s1370" xml:space="preserve">Eadem <lb/>omnino intelligas de depreſſionibus inſra horizontem, quæ pariter in verticalibus circulis, & </s> <s xml:id="echoid-s1371" xml:space="preserve">perpendi-<lb/>cularibus ad horizontem ſumendæ; </s> <s xml:id="echoid-s1372" xml:space="preserve">Quando igitur dicemus, Sol initium Crepuſculi eſt infra horizontem <lb/>gr. </s> <s xml:id="echoid-s1373" xml:space="preserve">18. </s> <s xml:id="echoid-s1374" xml:space="preserve">hi 18. </s> <s xml:id="echoid-s1375" xml:space="preserve">accipiendi ſunt in circulo verticali deſcendente infra horizontem recta, & </s> <s xml:id="echoid-s1376" xml:space="preserve">per Solem tranſeun <lb/>te: </s> <s xml:id="echoid-s1377" xml:space="preserve">cuius pars ab horizonte vſque ad Solem eſt arcus gr. </s> <s xml:id="echoid-s1378" xml:space="preserve">18. </s> <s xml:id="echoid-s1379" xml:space="preserve">hoc dixerim propter Aſtronomiæ Tyrones, qui <lb/>haſce diſtantias non in circulis verticalibus, & </s> <s xml:id="echoid-s1380" xml:space="preserve">rectis, ſed in Aequatore aut in Zodiaco accipiendas eſſe falsò <lb/>exiſtimant. </s> <s xml:id="echoid-s1381" xml:space="preserve">Altitudinem igitur Solis ſupra horizontem ſic per Sphæram materialem reperies. </s> <s xml:id="echoid-s1382" xml:space="preserve">Conſtitues <lb/>horizontem Sphæræ exactè ad Libellam ſeu æquidiſtantem horizonti Mundi, poſtea obuerte Meridianum <lb/>ad Solem ita vt ipſa ſit verticalis tranſiens per Solem, quod tunc erit cum vmbra partis illius illuſtratæ tota <lb/>cadet in partem eiuſdem oppoſitam, tunc ſtylo tange Meridianum in tali gradu, vt vmbra ſtyli cadat ad cen <lb/>trum Sphæræ, arcus enim Meridiani ab horizonte vſque ad ſtylum terminatus, erit altitudo quæſita.</s> <s xml:id="echoid-s1383" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1384" xml:space="preserve">9 In horizonte conſtituta ſunt quatuor puncta, quæ ipſum in quatuor quadrantes dirimunt; </s> <s xml:id="echoid-s1385" xml:space="preserve">quæque <lb/>nobis, quatuor mundi plagas, ac præcipuos ventos indicant; </s> <s xml:id="echoid-s1386" xml:space="preserve">ſunt autem Ortus, Occaſus, Septentrio, Meri-<lb/>dies, vt videre eſt in horizontis limbo, cuius figuram ad 7. </s> <s xml:id="echoid-s1387" xml:space="preserve">Propoſitionem apparatus exhibui: </s> <s xml:id="echoid-s1388" xml:space="preserve">cui præterea <lb/>addidi, quatuor alios ventos, minus principales, quorum cognitio, & </s> <s xml:id="echoid-s1389" xml:space="preserve">per ſe iucunda eſt, atq; </s> <s xml:id="echoid-s1390" xml:space="preserve">etiam ad multa <lb/>@onducit; </s> <s xml:id="echoid-s1391" xml:space="preserve">Quæomnia vt rectè horizon indicet, debet prius Aſtronomicè cõſtitui, vti ſequenti cap. </s> <s xml:id="echoid-s1392" xml:space="preserve">docebo.</s> <s xml:id="echoid-s1393" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div35" type="section" level="1" n="23"> <head xml:id="echoid-head25" style="it" xml:space="preserve">De Meridiano Circulo. Cap. IV.</head> <p> <s xml:id="echoid-s1394" xml:space="preserve"><emph style="bf">M</emph>Eridianus circulus à Meridie nomen accepit, quoniam eſt terminus, & </s> <s xml:id="echoid-s1395" xml:space="preserve">index temporis Meridiani <lb/>quamprimum enim eum Sol attigerit, meridies eſt: </s> <s xml:id="echoid-s1396" xml:space="preserve">Eſt autem circulus Maximus tranſiens per vtrũ-<lb/>que mundi polum, per Verticem, & </s> <s xml:id="echoid-s1397" xml:space="preserve">Imum cæli; </s> <s xml:id="echoid-s1398" xml:space="preserve">item per puncta duo Septentrionis, & </s> <s xml:id="echoid-s1399" xml:space="preserve">Auſtri, quæ in hori-<lb/>zonte illius loci notantur, cuius eſt Meridianus: </s> <s xml:id="echoid-s1400" xml:space="preserve">centrum eius eſt idem cum centro Mundi; </s> <s xml:id="echoid-s1401" xml:space="preserve">Poli vero ſunt <lb/>punta duo Ortus, & </s> <s xml:id="echoid-s1402" xml:space="preserve">Occaſus æquinoctialis in horizonte notata: </s> <s xml:id="echoid-s1403" xml:space="preserve">diſtant enim ab eo vndique per gr. </s> <s xml:id="echoid-s1404" xml:space="preserve">3<unsure/>0. </s> <s xml:id="echoid-s1405" xml:space="preserve">ſicuti <lb/>neceſſe eſt: </s> <s xml:id="echoid-s1406" xml:space="preserve">eſt autem de genere fixorum circulorum, quia nullo ſicuti etiam horizon cietur motu, verum <lb/>omnes alij circuli intra hos duos, vti materialis Sphæra demonſtrat, conuoluuntur. </s> <s xml:id="echoid-s1407" xml:space="preserve">Præterea eſt de gene-<lb/>re pluralium circulorum, innumeri namque in mundo ſunt Meridiani, ſicut etiam horizontes; </s> <s xml:id="echoid-s1408" xml:space="preserve">omnes ta-<lb/>men per Mundi polos, & </s> <s xml:id="echoid-s1409" xml:space="preserve">vertices tranſite debent; </s> <s xml:id="echoid-s1410" xml:space="preserve">Quemadmodum in Pepone omnes illæ diuiſiones tran-<lb/>ſeunt per eius pedem, ac florem, veluti duos ipſius polos. </s> <s xml:id="echoid-s1411" xml:space="preserve">In eo tamen Meridiani, & </s> <s xml:id="echoid-s1412" xml:space="preserve">horizontes differunt, <lb/>quod tot ſint horizontes in Mundo, quot ſunt in terra loca, at verò non tot Meridiani, quot loca: </s> <s xml:id="echoid-s1413" xml:space="preserve">innume-<lb/>enim loca, ſub eode Meridiano exiſtunt, vt facilè in materiali Sphæra cognoſcere eſt: </s> <s xml:id="echoid-s1414" xml:space="preserve">Vnicus tamen Sphæ-<lb/>ræ materialis Meridianus, omnes Meridianus Mundi ob Sphæræ conuerſionem repræſentare poteſt: </s> <s xml:id="echoid-s1415" xml:space="preserve">in ea <lb/>enim conuerſione omnia terræ loca, ſub ipſo tanquam ſub proprio ſucceſſiuè conſtituuntur. </s> <s xml:id="echoid-s1416" xml:space="preserve">tandem Meri-<lb/>dianus recta proprio horizonti inſiſtit, bifariamque ſe mutuo diuidunt. </s> <s xml:id="echoid-s1417" xml:space="preserve">Vt autem quilibet habitator pro-<lb/>prij Meridiani poſitionem, ac ſitum in mundo perfectè inueniat, atque cognoſcat, ei neceſſe eſt prius Me-<lb/>ridianam lineam inuenire. </s> <s xml:id="echoid-s1418" xml:space="preserve">quæ nihil aliud eſt, quam veluti veſtigium quoddam ipſius Meridiani in hori- <pb o="12" file="0028" n="28" rhead="Liber Primus."/> zonte ſenſibili impreſſum. </s> <s xml:id="echoid-s1419" xml:space="preserve">per hanc vero lineam, non ſolum circuli Meridiani, ſed totius mundi ſituatio-<lb/>nem in quauis habitatione facilè erit cognoſcere; </s> <s xml:id="echoid-s1420" xml:space="preserve">quæ cognitio iucunda æquè, atq; </s> <s xml:id="echoid-s1421" xml:space="preserve">ad multa vtilis eſt. </s> <s xml:id="echoid-s1422" xml:space="preserve">por-<lb/>rò cum plures huiuſce lineæ inueſtigandæ modi ſint.</s> <s xml:id="echoid-s1423" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1424" xml:space="preserve">Primo proponam rationem Aſtronomicam quæ cæteris certior, & </s> <s xml:id="echoid-s1425" xml:space="preserve">exactior eſt. </s> <s xml:id="echoid-s1426" xml:space="preserve">In plano igitur horizon-<lb/>tali, ſeu ad Libellam conſtituto, deſcribantur vt in figura ſequenti vides plures circuli, ex eodem centro E. <lb/></s> <s xml:id="echoid-s1427" xml:space="preserve">ex quo poſtea erigatur ſtylus perdendicularis; </s> <s xml:id="echoid-s1428" xml:space="preserve">quod tunc fiet, quando eius vertex F. </s> <s xml:id="echoid-s1429" xml:space="preserve">æquidiſtabit ab vna ex <lb/>illis periferijs, tunc autem æquidiſtabit, quando poſito altero circini pede in tribus locis circumferentiæ <lb/>illius, alter pes ſeruato eodem interuallo apicem ſtyli accurate tetigerit. </s> <s xml:id="echoid-s1430" xml:space="preserve">quamuis etiam auxilio Amuſſis idẽ <lb/>effici poſſit. </s> <s xml:id="echoid-s1431" xml:space="preserve">his paratis; </s> <s xml:id="echoid-s1432" xml:space="preserve">hora quapiam antemeridiana obſeruetur extremitas vmbræ donec præcisè circum-<lb/> <anchor type="figure" xlink:label="fig-0028-01a" xlink:href="fig-0028-01"/> ferentiam alienam attingat, qualis eſſet vmbra E G. </s> <s xml:id="echoid-s1433" xml:space="preserve">quæpræci-<lb/>sè exteriorem circulum pungit: </s> <s xml:id="echoid-s1434" xml:space="preserve">Rurſus pomeridiano tempore, <lb/>vmbræ apex obſeruetur, donec iterum ad eũdem circulum exa-<lb/>ctè pertineat, cuiuſmodi eſt vmbra E H. </s> <s xml:id="echoid-s1435" xml:space="preserve">quod ſi vmbra longior <lb/>fit, quam vt intra circulos recipiatur, ſl<unsure/>ylus erit decurtãdus. </s> <s xml:id="echoid-s1436" xml:space="preserve">plu-<lb/>res verò circuli deſcribuntur, vt tutior ac certior obſeruatio ſuc<unsure/>-<lb/>cedat; </s> <s xml:id="echoid-s1437" xml:space="preserve">Hiſce igitur duobus punctis diligenter in eodem circu-<lb/>lo notatis, diuidatnr arcus G H. </s> <s xml:id="echoid-s1438" xml:space="preserve">bifariam in D. </s> <s xml:id="echoid-s1439" xml:space="preserve">ducta enim linea <lb/>B E D. </s> <s xml:id="echoid-s1440" xml:space="preserve">ipſa erit meridiana linea quæſita; </s> <s xml:id="echoid-s1441" xml:space="preserve">hoc eſt, erit communis <lb/>ſectio meridiani circuli cum ſenſibili horizonte, ſupra quam <lb/>perpẽdiculariter meridianus illius loci erigitur, ac per verticem <lb/>eius tranſit. </s> <s xml:id="echoid-s1442" xml:space="preserve">Et parte vero vbi B. </s> <s xml:id="echoid-s1443" xml:space="preserve">in quolibet horizonte ad Bo-<lb/>reales mundi partes ſito, eſt pars mundi Auſtralis, & </s> <s xml:id="echoid-s1444" xml:space="preserve">pũctus me-<lb/>ridiei; </s> <s xml:id="echoid-s1445" xml:space="preserve">ex parte verò oppoſita vbi D. </s> <s xml:id="echoid-s1446" xml:space="preserve">eſt plaga Borealis, & </s> <s xml:id="echoid-s1447" xml:space="preserve">pun-<lb/>ctus Septentrionis. </s> <s xml:id="echoid-s1448" xml:space="preserve">Hac igitur ratione Aſtronomicè meridiani <lb/>circuli poſitionem reperire ſolent. </s> <s xml:id="echoid-s1449" xml:space="preserve">Cuius hæc ratio eſt; </s> <s xml:id="echoid-s1450" xml:space="preserve">quia duę <lb/>vmbræ E G. </s> <s xml:id="echoid-s1451" xml:space="preserve">E G. </s> <s xml:id="echoid-s1452" xml:space="preserve">ſunt æquales: </s> <s xml:id="echoid-s1453" xml:space="preserve">Ergo etiam Sol tempore vm-<lb/>brarum harum, erat æque altus ſupra horizontem, ergo tempo-<lb/>re matutino dum vmbra E G. </s> <s xml:id="echoid-s1454" xml:space="preserve">efficiebat, erat æque eleuatus, ac tẽpore vmbræ E H. </s> <s xml:id="echoid-s1455" xml:space="preserve">pomeridiano; </s> <s xml:id="echoid-s1456" xml:space="preserve">ſed quan-<lb/>do Sol eſt hiſce duobus momentis æquè altus, tunc etiam æquè diſtat à meridiano circulo, & </s> <s xml:id="echoid-s1457" xml:space="preserve">conſequenter <lb/>a puncto B. </s> <s xml:id="echoid-s1458" xml:space="preserve">lineæ meridianæ Auſtrali; </s> <s xml:id="echoid-s1459" xml:space="preserve">quoniã Sol æquabiliter aſcendit vſque ad merid em, & </s> <s xml:id="echoid-s1460" xml:space="preserve">poſtea æqua-<lb/>biliter tantundem deſcendit, vt in Sphæra materiali videre poteris in Tropicis, & </s> <s xml:id="echoid-s1461" xml:space="preserve">Aequatore, dum Sol aut <lb/>Tropicos, aut Aequatorem percurrit: </s> <s xml:id="echoid-s1462" xml:space="preserve">videbis enim partes horum circulorum a meridiano æquidiſtantes, <lb/>eſſe ab horizonte æquè eleuatas. </s> <s xml:id="echoid-s1463" xml:space="preserve">cum igitur Sol id temporis æquidiſtet a meridiano, neceſl<unsure/>ario etiam vm-<lb/>brarum vertices G H. </s> <s xml:id="echoid-s1464" xml:space="preserve">altitudinibus Solis è regione reſpondentes, æquè diſtabunt à puncto Boreali D. </s> <s xml:id="echoid-s1465" xml:space="preserve">lineæ <lb/>meridianæ; </s> <s xml:id="echoid-s1466" xml:space="preserve">quare diuiſo arcu G H. </s> <s xml:id="echoid-s1467" xml:space="preserve">bifariam in D. </s> <s xml:id="echoid-s1468" xml:space="preserve">punctum D. </s> <s xml:id="echoid-s1469" xml:space="preserve">æquidiſtabit ab H. </s> <s xml:id="echoid-s1470" xml:space="preserve">& </s> <s xml:id="echoid-s1471" xml:space="preserve">G. </s> <s xml:id="echoid-s1472" xml:space="preserve">Rurſus quia pun-<lb/>ctum E. </s> <s xml:id="echoid-s1473" xml:space="preserve">eſt horizontis phyſici centrum, tranſibit neceſſario per ipſum meridianus, ac proinde linea meri-<lb/>diana; </s> <s xml:id="echoid-s1474" xml:space="preserve">ducta igitur linea D E B. </s> <s xml:id="echoid-s1475" xml:space="preserve">ipſa erit meridiana quæſita in plano horizontali. </s> <s xml:id="echoid-s1476" xml:space="preserve">Ex qua meridiani poſito <lb/>rectè cognoſcetur.</s> <s xml:id="echoid-s1477" xml:space="preserve"/> </p> <div xml:id="echoid-div35" type="float" level="2" n="1"> <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a"> <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0028-01"/> </figure> </div> <p> <s xml:id="echoid-s1478" xml:space="preserve">In planis porrò non horizontalibus, ſed rectis ad horizontem, ſeu verticalibus, vti ſunt parietrs domorũ, <lb/>linea meridiana eſt linea perpendicularis ad horizontem deſcendens, quia meridianus circulus, omnes hu-<lb/>iuſmodi muros ſecat in linea, quæ eſt horizonti perpendicularis: </s> <s xml:id="echoid-s1479" xml:space="preserve">quę ſectio eſt veſtigium eius in talibus mu-<lb/>ris; </s> <s xml:id="echoid-s1480" xml:space="preserve">vt autem eam reperias, oblato parieti confige ſtylum, poſtea diligenter nota momentum illud quo vm-<lb/>bra ſtyli E F. </s> <s xml:id="echoid-s1481" xml:space="preserve">lineæ meridianæ E D. </s> <s xml:id="echoid-s1482" xml:space="preserve">in horizontali plano, ad vnguem congruet: </s> <s xml:id="echoid-s1483" xml:space="preserve">atq; </s> <s xml:id="echoid-s1484" xml:space="preserve">eodem momento no-<lb/>ta apicem vmbra ſtyli muro confixi; </s> <s xml:id="echoid-s1485" xml:space="preserve">ac deſcendentem per notam ibi factam perpendiculo, duc lineam per-<lb/>pendicularem, hæc enim erit inibi meridiana linea.</s> <s xml:id="echoid-s1486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1487" xml:space="preserve">Alium modum docet Gemma Friſius cap. </s> <s xml:id="echoid-s1488" xml:space="preserve">3. </s> <s xml:id="echoid-s1489" xml:space="preserve">de vſu globi Aſtronomici, pulcherrimum quidem, & </s> <s xml:id="echoid-s1490" xml:space="preserve">Aſtro-<lb/>nomicum (breuitatis cauſa eum prætermitto) quo eadem opera non ſolum Meridianum, ſed Aequatorem, <lb/>& </s> <s xml:id="echoid-s1491" xml:space="preserve">poli altitudinem ingeniosè, & </s> <s xml:id="echoid-s1492" xml:space="preserve">rectè inueſtigat. </s> <s xml:id="echoid-s1493" xml:space="preserve">Sed per Sphæram materialem in plano horizontali ſic <lb/>lineam Meridianam reperies. </s> <s xml:id="echoid-s1494" xml:space="preserve">obſerua duas Solis altitudines æquales, vnam antemeridianam, alteram po-<lb/>meridianam, vt ſupra cum de horizonte docuimus; </s> <s xml:id="echoid-s1495" xml:space="preserve">& </s> <s xml:id="echoid-s1496" xml:space="preserve">in vtraque nota vmbram meridiani in plano hori-<lb/>zontali propoſito cadentem, quæ erit recta: </s> <s xml:id="echoid-s1497" xml:space="preserve">illud diligenter curandum eſt, vt Sphæra in vtraque obſerua-<lb/>tione maneat in vno eodemq; </s> <s xml:id="echoid-s1498" xml:space="preserve">loco, ſed tantummodo ibidem perſiſtens gyretur. </s> <s xml:id="echoid-s1499" xml:space="preserve">Iam duæ deſigaatæ vm-<lb/>bræ, ſi producantur verſus Sphæram ſe mutuo ſecabunt; </s> <s xml:id="echoid-s1500" xml:space="preserve">In puncto igitur ſectionis facto centro, deſcribe <lb/>arcum inter vtramque vmbram, vel ad partem Borealem, vel ad Auſtralem; </s> <s xml:id="echoid-s1501" xml:space="preserve">hunc arcum bifariam ſeca, nam <lb/>per punctum diuiſion s, & </s> <s xml:id="echoid-s1502" xml:space="preserve">centram, ducta recta linea, ipſa erit meridiana.</s> <s xml:id="echoid-s1503" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1504" xml:space="preserve">Alij præterea extant modi huius iucundę inquiſitionis, qui quamuis Aſtronomici non ſint neq; </s> <s xml:id="echoid-s1505" xml:space="preserve">adeo exa-<lb/>cti, ſunt tamen digniſſimi qui ſciantur. </s> <s xml:id="echoid-s1506" xml:space="preserve">Primus ſit is qui per alicuius arboris inciſionem perſicitur; </s> <s xml:id="echoid-s1507" xml:space="preserve">uius ref<unsure/> <lb/>gratia eligatur arbor quæpiam in agri planicie longé à parietibus, vbi arbor illa vndiq; </s> <s xml:id="echoid-s1508" xml:space="preserve">a Sole liberè ſemper <lb/>ſuerit colluſtrata, & </s> <s xml:id="echoid-s1509" xml:space="preserve">calefacta; </s> <s xml:id="echoid-s1510" xml:space="preserve">eius etiam truncus ſit rectus, & </s> <s xml:id="echoid-s1511" xml:space="preserve">teres: </s> <s xml:id="echoid-s1512" xml:space="preserve">truncus igitur hic medius ſecetur, ita vt <lb/>ſectio ſit horizonti paralella, inferiorq; </s> <s xml:id="echoid-s1513" xml:space="preserve">pars trunci erecta in ſuo naturali ſtatu remaneat: </s> <s xml:id="echoid-s1514" xml:space="preserve">iam ſectio, quæ in <lb/>ſummitate eius erit, benè complanetur, & </s> <s xml:id="echoid-s1515" xml:space="preserve">ecce apparebunt tibi in eius plano plures circuli, & </s> <s xml:id="echoid-s1516" xml:space="preserve">quidem ec-<lb/>@entrici, ideſt, circa idem centrũ non conſiſtentes, ſed ex vna parte ad inuicem propinquiores, ex altera ve-<lb/>ro laxiores erunt; </s> <s xml:id="echoid-s1517" xml:space="preserve">pars igitur illa, quæ denfiores habet circulos ad Septentrionalem mundi plagam vergit;</s> <s xml:id="echoid-s1518" xml:space="preserve"> <pb o="13" file="0029" n="29" rhead="Liber Primus."/> <anchor type="figure" xlink:label="fig-0029-01a" xlink:href="fig-0029-01"/> oppoſita verò quæ rariores, ad Meridionalem. </s> <s xml:id="echoid-s1519" xml:space="preserve">Quare ſi à parte denſiore ad rario-<lb/>rẽ ducta fuerit linea, erit ipſa Meridiana, quod ego in pruni arbore expertus ſum. <lb/></s> <s xml:id="echoid-s1520" xml:space="preserve">quæ omnia in appoſita figura cernere licebit. </s> <s xml:id="echoid-s1521" xml:space="preserve">Porrò non ſolum plantarum auxi-<lb/>lio ſagax natura nos ad hanc inueſtigationem comparauit, verum etiam metallis, <lb/>ac lapidibus mirum in modum eam indidit, vt eam poſtea hominumſolertia per-<lb/>ſcrutaretur, ac reuelaret. </s> <s xml:id="echoid-s1522" xml:space="preserve">Ferrum igitur metallum adeo rude, ac durum, quam mi-<lb/>rum eſt, hanc lineam, ſeu has mundi plagas, quodammodo mortales edocere: </s> <s xml:id="echoid-s1523" xml:space="preserve">nam <lb/>ſi acum ferream ſubtiliſſimam ſuper aquæ ſuperficiem in vaſe aliquo quieſcentẽ, <lb/>ita artificiosè, ac dexterè deponamus, vt non demergatur, ſed ſupernatet, ea poſt-<lb/>quam in ſuperficie aquę lentiſſimè in gyrum ſe commouerit, tandem ita conquie-<lb/>ſcet, vt ex vna parte Boream, ex altera Auſtrum oſtendat, ſeu iuxta meridianam <lb/>lineam conquieſcet. </s> <s xml:id="echoid-s1524" xml:space="preserve">De modo ponendi acum in aquam vt innatet, infra dicemus <lb/>in Problematibus, interim media acu exiguum ſuber traiectum eam in ſummo aquæ innare faciat.</s> <s xml:id="echoid-s1525" xml:space="preserve"/> </p> <div xml:id="echoid-div36" type="float" level="2" n="2"> <figure xlink:label="fig-0029-01" xlink:href="fig-0029-01a"> <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-01"/> </figure> </div> <p> <s xml:id="echoid-s1526" xml:space="preserve">Idem præſtabit quæuis ferrea haſta, ſi ex filo ita (in loco ab omni aeris cõmotione carente) ſuſpendatur, <lb/>vt in æqu@librio pendeat, tan dem enim iuxta meridianam longitudinem requieſcet.</s> <s xml:id="echoid-s1527" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1528" xml:space="preserve">Iam verò in re tam præclara, lapides neutiquam metallis concedere natura permiſit. </s> <s xml:id="echoid-s1529" xml:space="preserve">Enimuero quam <lb/>mirabilis eſt illa Magnetis lapidis proprietas, qua ſi liberè moueri poſſit, ex vna eademque ſemper ſui parte <lb/>Boream, ex altera verò illi auerſa Meridiem aſpicit: </s> <s xml:id="echoid-s1530" xml:space="preserve">vtautem id efficiat in ſuperficie aquæ manentis pona-<lb/>tur prius tabella, quæ innatet: </s> <s xml:id="echoid-s1531" xml:space="preserve">ſuper hanc Magnes, quaſi in nauicula liberè nauigare poſſit, nam tãdem quo-<lb/>tieſcunque id fiat, ſemper ita conſiſtet, vt vnam eandemq; </s> <s xml:id="echoid-s1532" xml:space="preserve">ſui ipſius partem Boreæ, alteram verò huic auer-<lb/>ſam Auſtro obuertat.</s> <s xml:id="echoid-s1533" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1534" xml:space="preserve">Hanc porrò miram proprietatem liberaliter acubus ferreis ſolo attactu ita communicat, vt eam illæ lon-<lb/>gè perfectiorem à ſeipſis, quam a magnete oſtentent: </s> <s xml:id="echoid-s1535" xml:space="preserve">vt autem acus ferrea, quæ hanc virtutem à magnete <lb/>imbiberit, rectius meridiani poſitionẽ indicare poſſit, ita fabricari debet, vt in apice alicuius ſtyli æquilibra-<lb/> <anchor type="figure" xlink:label="fig-0029-02a" xlink:href="fig-0029-02"/> ta inſiſtens liberè circunueri poſſit: </s> <s xml:id="echoid-s1536" xml:space="preserve">quales in viatorijs Horologijs induſtrij <lb/>Germani fabricatas imponunt. </s> <s xml:id="echoid-s1537" xml:space="preserve">hoc enim modo acus hæc collocata, tandem ſe <lb/>iuxta meridiei lineam ſiſtet. </s> <s xml:id="echoid-s1538" xml:space="preserve">In quo quidem miraculo, nouum aliud non mi-<lb/>nus admirandum obſeruatum eſt: </s> <s xml:id="echoid-s1539" xml:space="preserve">nam non eodem modo, vbique terrarũ acus <lb/>huiuſmodi meridianæ lineæ alludunt; </s> <s xml:id="echoid-s1540" xml:space="preserve">ſed alicubi exactè ipſi congruunt: </s> <s xml:id="echoid-s1541" xml:space="preserve">alicu-<lb/>bi verò ab ea variè declinant: </s> <s xml:id="echoid-s1542" xml:space="preserve">In Italia, ac regionibus ei adiacentibus declinat <lb/>gr. </s> <s xml:id="echoid-s1543" xml:space="preserve">6. </s> <s xml:id="echoid-s1544" xml:space="preserve">vt appoſita figura indicat; </s> <s xml:id="echoid-s1545" xml:space="preserve">in qua linea S M. </s> <s xml:id="echoid-s1546" xml:space="preserve">eſt vera meridiana, linea ve-<lb/>rò A B. </s> <s xml:id="echoid-s1547" xml:space="preserve">eſt linea ſupr@ quam tandẽ acus magnetica conquieſcit, quæ à Septen-<lb/>trione verſus Ortum euariat gr. </s> <s xml:id="echoid-s1548" xml:space="preserve">6. </s> <s xml:id="echoid-s1549" xml:space="preserve">particula enim S A. </s> <s xml:id="echoid-s1550" xml:space="preserve">eſt gr. </s> <s xml:id="echoid-s1551" xml:space="preserve">6. </s> <s xml:id="echoid-s1552" xml:space="preserve">à<unsure/> Meridie verò <lb/>in Occaſum totidem grad@bus exorbitat, eſt enim M B. </s> <s xml:id="echoid-s1553" xml:space="preserve">gr. </s> <s xml:id="echoid-s1554" xml:space="preserve">6. </s> <s xml:id="echoid-s1555" xml:space="preserve">qua cautione ad-<lb/>hibita, per eam rectè meridianam comperiemus: </s> <s xml:id="echoid-s1556" xml:space="preserve">vt in paſſim, ac vuigò fit dum <lb/>Horologijs ſolaribus, ac Germanicis vtimur.</s> <s xml:id="echoid-s1557" xml:space="preserve"/> </p> <div xml:id="echoid-div37" type="float" level="2" n="3"> <figure xlink:label="fig-0029-02" xlink:href="fig-0029-02a"> <image file="0029-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-02"/> </figure> </div> <p> <s xml:id="echoid-s1558" xml:space="preserve">In hac porrò meridianæ lineæ inuentione per acum magneticum cauendum eſt à duobus. </s> <s xml:id="echoid-s1559" xml:space="preserve">primo à ferri, <lb/>cuiuſpiam propinquitate, v. </s> <s xml:id="echoid-s1560" xml:space="preserve">g. </s> <s xml:id="echoid-s1561" xml:space="preserve">à ferreis gratibus, aut alijs huiuſmodi, quæ in muris paſſim reperiuntur. </s> <s xml:id="echoid-s1562" xml:space="preserve">Se-<lb/>cundo à lateribus, lateres enim ſunt magnetici, idque variè, pro varia eorum coctura, quare non ſecus ac fer-<lb/>rum, magneticum acum a ſuo ſicu deturbant. </s> <s xml:id="echoid-s1563" xml:space="preserve">vnde fit vt lineæ meridianæ in planis murorum horizontali-<lb/>bus hoc modo repertæ, non parum, vt me docuit experientia, a vero earum fitu aberrent.</s> <s xml:id="echoid-s1564" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1565" xml:space="preserve">Multa autem alia ſcitu iucundiſſima, ac noua de hac re habentur apud Guilelmum Guilbertum Londi-<lb/>nenſem de Magnetica Philoſophia.</s> <s xml:id="echoid-s1566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1567" xml:space="preserve">Cum igitur arcanis tot modis in plantis, metallis, lapidibus, natura nos ad inuentũ iſtud inſtruxerit, quid <lb/>aliud ſiguificare voluit, quam maximi illud momenti eſſe, ſecumq; </s> <s xml:id="echoid-s1568" xml:space="preserve">multas afferre vtilitates, ac iucundita-<lb/>tes; </s> <s xml:id="echoid-s1569" xml:space="preserve">Quod quidem (ſi hac in re fari fas eſt) diuinitus etiam oſtenſum eſt; </s> <s xml:id="echoid-s1570" xml:space="preserve">Angeli etenim ij, qui ſacrã Æd m <lb/>lauretanam illuc vbi nunc religioſiſſime colitur, comportarunt, inibi ſic eam conſtituere, vt vna ipſius fa-<lb/>eies ad Meridiem, altera ei auerſa a Septentrionem directè, atque exactè obuertatur; </s> <s xml:id="echoid-s1571" xml:space="preserve">& </s> <s xml:id="echoid-s1572" xml:space="preserve">cõſequenter alij duo <lb/>parietes ſuper duabus meridianis lineis ſiti ſint, ac meridianis circuli<unsure/>s congruant.</s> <s xml:id="echoid-s1573" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1574" xml:space="preserve">Quod & </s> <s xml:id="echoid-s1575" xml:space="preserve">Hiſtorici narrant, & </s> <s xml:id="echoid-s1576" xml:space="preserve">ego cum inibi religionis cauſa agerem, per magneticam pyxidem diligen-<lb/>@er experiens, magna, ac religioſa, animi voluptate comperi ita ſe rem habere.</s> <s xml:id="echoid-s1577" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1578" xml:space="preserve">Templum pariter Salomonis, quod ſeptem mundi miraculis longè mirabilius extitit, & </s> <s xml:id="echoid-s1579" xml:space="preserve">quod Deum ip-<lb/>ſum Architectorum habuit, ad quatuor mundi plagas ita conſtitutum erat, vt duo ipſius latera oppoſita li-<lb/>neis meridianis incumberent; </s> <s xml:id="echoid-s1580" xml:space="preserve">hac enim ratione, vt facræ literæ loquuntur, ipſius frons, ac porta maior erat <lb/>Orientalis; </s> <s xml:id="echoid-s1581" xml:space="preserve">huic oppoſita Occidentalis; </s> <s xml:id="echoid-s1582" xml:space="preserve">reliquæ duæ facies, Septẽtrionem vna, altera Meridiem ad vnguem <lb/>aſpiciebant; </s> <s xml:id="echoid-s1583" xml:space="preserve">Atque hæc de linea hac meridiana.</s> <s xml:id="echoid-s1584" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1585" xml:space="preserve">Vſus autem meridiani hi ſunt: </s> <s xml:id="echoid-s1586" xml:space="preserve">Primo dirimit totam mundi Sphæram in duo hemiſpæriæ, Orientale <lb/>videlicet, & </s> <s xml:id="echoid-s1587" xml:space="preserve">Occidentale.</s> <s xml:id="echoid-s1588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1589" xml:space="preserve">2 Indicat ipſum meridiei inſtans, Sole enim ipſum ſupra horizontem attingẽte, meridies eſt; </s> <s xml:id="echoid-s1590" xml:space="preserve">ſimiliter <lb/>& </s> <s xml:id="echoid-s1591" xml:space="preserve">mediæ no&</s> <s xml:id="echoid-s1592" xml:space="preserve">is tempus, Sole enim Meridiani ſemicirculum inferum adeunte, media nox eſt.</s> <s xml:id="echoid-s1593" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1594" xml:space="preserve">3 Solis circulationes ſuperas, ideſt, arcum diurnum, ſiue diem artificialem bifariam dirimit, in arcum <lb/>ſemidiurnum Matutinum, & </s> <s xml:id="echoid-s1595" xml:space="preserve">ſemidiurnum Veſpertinum. </s> <s xml:id="echoid-s1596" xml:space="preserve">Similiter lationes Solis inferas, ideſt, arcus no-<lb/>cturnos in partes æquas partitur: </s> <s xml:id="echoid-s1597" xml:space="preserve">vt in Sphæra materiali videre eſt, ſi conſideres Æquatores, ac duos Tropi- <pb o="14" file="0030" n="30" rhead="De circulis Sphæræ."/> cos, qua parte ſupra horizontem exiſtunt à meridiano in æqualia ſecari: </s> <s xml:id="echoid-s1598" xml:space="preserve">& </s> <s xml:id="echoid-s1599" xml:space="preserve">ſimiliter infra horizontem. </s> <s xml:id="echoid-s1600" xml:space="preserve">ſune <lb/>autem hi tres circuli, tres Solis circulationes (vt poſtea explicabimus) ſiue tres diurnæ conuerſiones, & </s> <s xml:id="echoid-s1601" xml:space="preserve">ſi-<lb/>cuti eas meridianus diuidit, ſic etiam cæteras omnes, quas toto anno Sol ſingulis diebus peragit, & </s> <s xml:id="echoid-s1602" xml:space="preserve">quarum <lb/>circuli in Sphæra non ponuntur, idem meridianus partitur.</s> <s xml:id="echoid-s1603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1604" xml:space="preserve">A meridiano circulò initium diei naturalis ſumunt Aſtronomi; </s> <s xml:id="echoid-s1605" xml:space="preserve">cum autem dies naturalis ſit integra So-<lb/>lis circa mundum reuolutio, dies Aſtronomicus Sole meridianum occupante incipiet, atq; </s> <s xml:id="echoid-s1606" xml:space="preserve">ad eundem Sole <lb/>iterum redeunte deſinet. </s> <s xml:id="echoid-s1607" xml:space="preserve">A meridie autem potius, quam ab horizonte diem inchoare maluerunt Aſtrono-<lb/>mi, quoniam in omni regione, atq; </s> <s xml:id="echoid-s1608" xml:space="preserve">habitatione Sol ſemper eodem modo ad meridianum ſe habet, ad hori-<lb/>zontem verò varietates ſubit; </s> <s xml:id="echoid-s1609" xml:space="preserve">quare dies ad meridiem relatus vbique vniformis, ac ſtabilis eſt, ad horizon-<lb/>tem verò relatus variationibus obnoxius eſt, quæ Aſtronomis negotium faceſſunt. </s> <s xml:id="echoid-s1610" xml:space="preserve">Quapropter ſapienter <lb/>faciunt pleræque nationes, Hiſpani, Galli, Belgæ, Germani, Poloni, qui hoc diei genere communiter <lb/>vtuntur.</s> <s xml:id="echoid-s1611" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1612" xml:space="preserve">5 Metitur maxima Aſtrorum altitudines ſupra horizontem; </s> <s xml:id="echoid-s1613" xml:space="preserve">cum enim eum Aſtra attingunt, tunc ma-<lb/>ximè ab horizote attoluntur, tantaq; </s> <s xml:id="echoid-s1614" xml:space="preserve">eſt eorum meridiana altitudo, quæ eſt omnium maxima, quantus eſt <lb/>meridiani arcus ab horizonte vſq; </s> <s xml:id="echoid-s1615" xml:space="preserve">ad Aſtrum interiectus. </s> <s xml:id="echoid-s1616" xml:space="preserve">Hanc portò, tum Solis, tum Aſtrorum meridianã <lb/>eleuationem reperies, primo per quadrantem Aſtronomicum propoſ. </s> <s xml:id="echoid-s1617" xml:space="preserve">8. </s> <s xml:id="echoid-s1618" xml:space="preserve">apparatus hoc modo.</s> <s xml:id="echoid-s1619" xml:space="preserve"/> </p> <figure> <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/> </figure> <p> <s xml:id="echoid-s1620" xml:space="preserve">Illud Aſtronomicè conſtitue, ideſt, in plano quopiam ho-<lb/>rizontalis, vt latus A B. </s> <s xml:id="echoid-s1621" xml:space="preserve">Quadrantis ſit horizonti paralel-<lb/>lum, & </s> <s xml:id="echoid-s1622" xml:space="preserve">ſimul ſupra lineam mer@dianam inibi accuratè du-<lb/>ctam; </s> <s xml:id="echoid-s1623" xml:space="preserve">latus verò A D. </s> <s xml:id="echoid-s1624" xml:space="preserve">ſit perpendiculariter erectum, cu-<lb/>ius gratia perpendiculum D I. </s> <s xml:id="echoid-s1625" xml:space="preserve">debet propriè linea æqui-<lb/>diſtare, ac liberè iuxta latus A D. </s> <s xml:id="echoid-s1626" xml:space="preserve">radens deſcendere<unsure/>; </s> <s xml:id="echoid-s1627" xml:space="preserve">La-<lb/>tus autem C B. </s> <s xml:id="echoid-s1628" xml:space="preserve">meridiem verſus aſpiciat. </s> <s xml:id="echoid-s1629" xml:space="preserve">Splendente iam <lb/>in meridie Sole, Dioptra quadranti adhærens ſuſque de-<lb/>que tollatur, donec Solis radius per vtrumq; </s> <s xml:id="echoid-s1630" xml:space="preserve">pinnularum <lb/>foramen æquè illabatur: </s> <s xml:id="echoid-s1631" xml:space="preserve">in quo Dioptræ ſitu, latus ipſius <lb/>C E. </s> <s xml:id="echoid-s1632" xml:space="preserve">indicabit in quadrante gradus altitudinis meridiane, <lb/>qui eſſent, v.</s> <s xml:id="echoid-s1633" xml:space="preserve">g. </s> <s xml:id="echoid-s1634" xml:space="preserve">in arcu D E. </s> <s xml:id="echoid-s1635" xml:space="preserve">gr. </s> <s xml:id="echoid-s1636" xml:space="preserve">36. </s> <s xml:id="echoid-s1637" xml:space="preserve">tanta enim eſt eleuatio <lb/>ſupra horizontem, quantus eſt arcus quadrantis à puncto <lb/>D. </s> <s xml:id="echoid-s1638" xml:space="preserve">vſque ad Dioptram numeratus.</s> <s xml:id="echoid-s1639" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1640" xml:space="preserve">Quod ſi ſydus minus collucens obijciatur, tunc vice radij ip-<lb/>ſius, vtemur radio viſuali, ideſt, per vtrumque rimulam <lb/>in pinnularem ſumitatibus exciſam, in aſtrum collimabi-<lb/>mus, atq; </s> <s xml:id="echoid-s1641" xml:space="preserve">interim latus E C. </s> <s xml:id="echoid-s1642" xml:space="preserve">Dioptræ in quadrante me-<lb/>ridianæ gradus, ac graduum partes indigitabit.</s> <s xml:id="echoid-s1643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1644" xml:space="preserve">Alio præterea modo, & </s> <s xml:id="echoid-s1645" xml:space="preserve">quidẽ ſubtiliori idem hoc pacto obſeruabimus: </s> <s xml:id="echoid-s1646" xml:space="preserve">inuenta (vti ſuperius docuimus) <lb/>in plano quopiam horizontali, linea meridiana, erigatur ex ea ſtylus plano perpendicularis; </s> <s xml:id="echoid-s1647" xml:space="preserve">cum enim ip-<lb/>ſius vmbra lineam meridianam occupauerit, habebit Sol meridianam latitudinem; </s> <s xml:id="echoid-s1648" xml:space="preserve">notetur igitur tunc tem <lb/>poris extremum vmbræ in ipſa meridiana exiſtens. </s> <s xml:id="echoid-s1649" xml:space="preserve">atque in eodem plano a pede ſtyli ducatur linea perpen <lb/>dicularis meridianæ lineæ, ſitque ipſi ſtylo æqualis, tandem ab extremo vmbræ prænotato, ducatur linea <lb/>vſque ad extremum lineæ ſtylo æqualis: </s> <s xml:id="echoid-s1650" xml:space="preserve">v.</s> <s xml:id="echoid-s1651" xml:space="preserve">g. </s> <s xml:id="echoid-s1652" xml:space="preserve">ſit in plano meridiana A B. </s> <s xml:id="echoid-s1653" xml:space="preserve">ſtylus B C. </s> <s xml:id="echoid-s1654" xml:space="preserve">recta B E. </s> <s xml:id="echoid-s1655" xml:space="preserve">ſtylo æqua-<lb/>lis ad angulos rectos ipſi meridianæ; </s> <s xml:id="echoid-s1656" xml:space="preserve">vmbra ſtyli pertineat ad A. </s> <s xml:id="echoid-s1657" xml:space="preserve">& </s> <s xml:id="echoid-s1658" xml:space="preserve">ab A. </s> <s xml:id="echoid-s1659" xml:space="preserve">extremo vmbræ ducta ſit, A D. </s> <s xml:id="echoid-s1660" xml:space="preserve">erit <lb/>angulus D A B. </s> <s xml:id="echoid-s1661" xml:space="preserve">altitudo Solis meridiana. </s> <s xml:id="echoid-s1662" xml:space="preserve">& </s> <s xml:id="echoid-s1663" xml:space="preserve">quoniam vti propoſ. </s> <s xml:id="echoid-s1664" xml:space="preserve">2. </s> <s xml:id="echoid-s1665" xml:space="preserve">appar. </s> <s xml:id="echoid-s1666" xml:space="preserve">quantitas angulorum deſumi-<lb/>tur ex arcu illi ſubtento: </s> <s xml:id="echoid-s1667" xml:space="preserve">facto centro in A. </s> <s xml:id="echoid-s1668" xml:space="preserve">deſcribatur arcus F E. </s> <s xml:id="echoid-s1669" xml:space="preserve">atque quot gradus contineat, expendatur <lb/>per eandem propoſitionem, tot enim gradibus Solis meridiana altitudo conſtabit. </s> <s xml:id="echoid-s1670" xml:space="preserve">Ratio eſt, quia ſi cogi-<lb/>temus triangulum A B D. </s> <s xml:id="echoid-s1671" xml:space="preserve">ex plano in quo iacet aſiurgere manente latere A B. </s> <s xml:id="echoid-s1672" xml:space="preserve">fixo tanquam axe huius mo-<lb/>tus, ita vt latus D B. </s> <s xml:id="echoid-s1673" xml:space="preserve">congruat ſtylo B C. </s> <s xml:id="echoid-s1674" xml:space="preserve">tranſibit latus A D. </s> <s xml:id="echoid-s1675" xml:space="preserve">per ſtyli verticem, quia punctum D. </s> <s xml:id="echoid-s1676" xml:space="preserve">congruet <lb/>mucroni C. </s> <s xml:id="echoid-s1677" xml:space="preserve">ſtyli; </s> <s xml:id="echoid-s1678" xml:space="preserve">& </s> <s xml:id="echoid-s1679" xml:space="preserve">proinde linea A D. </s> <s xml:id="echoid-s1680" xml:space="preserve">ragio Solis per eundem verticem, & </s> <s xml:id="echoid-s1681" xml:space="preserve">in A. </s> <s xml:id="echoid-s1682" xml:space="preserve">tandentem congruet; </s> <s xml:id="echoid-s1683" xml:space="preserve">vn-<lb/>de manifeſtè Solis altitudinem ſupra horizontale planum indicabit igitur quanta eſt inclinatio lineæ A D. <lb/></s> <s xml:id="echoid-s1684" xml:space="preserve">ſiue quantus eſt angulus ad A. </s> <s xml:id="echoid-s1685" xml:space="preserve">ſiue arcus F E. </s> <s xml:id="echoid-s1686" xml:space="preserve">tanta erit meridiana altitudo Solis: </s> <s xml:id="echoid-s1687" xml:space="preserve">nam in hac trianguli ele-<lb/>uatione angulus ad A. </s> <s xml:id="echoid-s1688" xml:space="preserve">nihil eſt variatus; </s> <s xml:id="echoid-s1689" xml:space="preserve">quare etiamſi triangulum non aſſurgat, nihi@ominus angulus ad A. </s> <s xml:id="echoid-s1690" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0030-02a" xlink:href="fig-0030-02"/> ſiue arcus eius F E, quantitatem quæſitã pateſaciet. </s> <s xml:id="echoid-s1691" xml:space="preserve">poſſumus <lb/>autem expeditè prædictum arcum cognoſcere, hoc modo ac-<lb/>cipiatur circino linea A E. </s> <s xml:id="echoid-s1692" xml:space="preserve">inſtrumenti propoſ. </s> <s xml:id="echoid-s1693" xml:space="preserve">5. </s> <s xml:id="echoid-s1694" xml:space="preserve">appar. </s> <s xml:id="echoid-s1695" xml:space="preserve">& </s> <s xml:id="echoid-s1696" xml:space="preserve">ei <lb/>æqualis in latere A D. </s> <s xml:id="echoid-s1697" xml:space="preserve">huius triãguli ſumatur, quæ ſit v.</s> <s xml:id="echoid-s1698" xml:space="preserve">g. </s> <s xml:id="echoid-s1699" xml:space="preserve">A F. <lb/></s> <s xml:id="echoid-s1700" xml:space="preserve">deinde circino accipiatur arcus F E. </s> <s xml:id="echoid-s1701" xml:space="preserve">appliceturque arcui qua-<lb/>drantis inſtrumẽti, facto initio ab E. </s> <s xml:id="echoid-s1702" xml:space="preserve">ſitq; </s> <s xml:id="echoid-s1703" xml:space="preserve">v.</s> <s xml:id="echoid-s1704" xml:space="preserve">gr. </s> <s xml:id="echoid-s1705" xml:space="preserve">arcus illi æqua-<lb/>lis E K. </s> <s xml:id="echoid-s1706" xml:space="preserve">qui gr. </s> <s xml:id="echoid-s1707" xml:space="preserve">30. </s> <s xml:id="echoid-s1708" xml:space="preserve">continet: </s> <s xml:id="echoid-s1709" xml:space="preserve">altitudo igitur quæſita meridia-<lb/>na totidem gr. </s> <s xml:id="echoid-s1710" xml:space="preserve">erit: </s> <s xml:id="echoid-s1711" xml:space="preserve">ſicque in quadrante, aut etiam in ſemicir-<lb/>culo eiuſdẽ inſtrumenti, fi angulus eſſet obtuſus, ſemper abſq; </s> <s xml:id="echoid-s1712" xml:space="preserve"><lb/>nouæ diuiſionis labore, apparebit in grad. </s> <s xml:id="echoid-s1713" xml:space="preserve">& </s> <s xml:id="echoid-s1714" xml:space="preserve">minutis quanti-<lb/>tas cuiuſuis arcus, ſeu anguli. </s> <s xml:id="echoid-s1715" xml:space="preserve">Hiſce duobus prædictis modis, <lb/>ideſt, per quadrantem, & </s> <s xml:id="echoid-s1716" xml:space="preserve">per vmbram ſtyli in plano horizontali, cæteræ quoq; </s> <s xml:id="echoid-s1717" xml:space="preserve">altitudines non meridianæ <pb o="15" file="0031" n="31" rhead="Liber Primus."/> inueſtigari poſſunt, neglecta tunc meridiana linea: </s> <s xml:id="echoid-s1718" xml:space="preserve">ſed in ſecundo modo per vmbram ſtyli, ſatis eſt accipe-<lb/>re vmbram ipſam pro latere vno trianguli A B D. </s> <s xml:id="echoid-s1719" xml:space="preserve">vti quilibet ſuo marte facilè exequi pote rit. </s> <s xml:id="echoid-s1720" xml:space="preserve">alios huius <lb/>inueſtigationis modos, veluti implicatiores, de induſtria miſſos facio.</s> <s xml:id="echoid-s1721" xml:space="preserve"/> </p> <div xml:id="echoid-div38" type="float" level="2" n="4"> <figure xlink:label="fig-0030-02" xlink:href="fig-0030-02a"> <image file="0030-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-02"/> </figure> </div> <p> <s xml:id="echoid-s1722" xml:space="preserve">6 In ipſo me@idiano ſex puncta maximè notanda exiſtunt, duo mundi poli, Vertex, & </s> <s xml:id="echoid-s1723" xml:space="preserve">Imum cæli; </s> <s xml:id="echoid-s1724" xml:space="preserve">Se-<lb/>ptentrio, & </s> <s xml:id="echoid-s1725" xml:space="preserve">Meridies. </s> <s xml:id="echoid-s1726" xml:space="preserve">Quorum poſtrema, quatuor eodem modo ſe habent in omni terræ loco, vbiq; </s> <s xml:id="echoid-s1727" xml:space="preserve">enim <lb/>Septentrio, & </s> <s xml:id="echoid-s1728" xml:space="preserve">Meridies apud communes meridiani, & </s> <s xml:id="echoid-s1729" xml:space="preserve">horizontis ſectiones exiſtunt; </s> <s xml:id="echoid-s1730" xml:space="preserve">Vertex vero, & </s> <s xml:id="echoid-s1731" xml:space="preserve">Imũ, <lb/>vbiq; </s> <s xml:id="echoid-s1732" xml:space="preserve">diſtant per quadrantes, ideſt gr. </s> <s xml:id="echoid-s1733" xml:space="preserve">90. </s> <s xml:id="echoid-s1734" xml:space="preserve">ab horizonte, ille ſupra, hic infra: </s> <s xml:id="echoid-s1735" xml:space="preserve">ſiue ſunt poli horizontis. </s> <s xml:id="echoid-s1736" xml:space="preserve">At <lb/>vero duo poli variam pro locorum varietate ſortiuntur ab horizonte altitudinem, quæ altitudo, vt ſupra <lb/>innuimus, ſumenda eſt in circulo meridiano, quia tanta eſt poli altitudo, aut depreſſio, quanta eſt meridia-<lb/>ni portio ab horizonte ad vtrumuis polum.</s> <s xml:id="echoid-s1737" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1738" xml:space="preserve">Quoniam verò cognitio altitudinis poli cuiuſuis regionis, ſeu horizontis, magni eſt in rebus Aſtronomi-<lb/>cis momenti, eius hoc loco expeditiorem, ac certiorem inuentionem exponam. </s> <s xml:id="echoid-s1739" xml:space="preserve">Quadransigitur noſter, <lb/>Aſtronomicè in plano horizontali collocetur, vti ſupra dictum eſt, ideſt, ſupra lineam meridianam perpen <lb/>diculariter, ſed ita vt latus B C. </s> <s xml:id="echoid-s1740" xml:space="preserve">verſus Septentrionem ſpectet: </s> <s xml:id="echoid-s1741" xml:space="preserve">hac enim ratione erit conſtitutus in plano <lb/>circuli meridiani, ſiue meridianum referet, & </s> <s xml:id="echoid-s1742" xml:space="preserve">proinde polum conſpicuum directè aſpiciet. </s> <s xml:id="echoid-s1743" xml:space="preserve">quo parato, ini-<lb/>tio alicuius noctis longioris, & </s> <s xml:id="echoid-s1744" xml:space="preserve">ſerenæ, oculus per rimulas pinnularum Dioptræ aſpiciens ad ſtellam quam-<lb/>piam ex ſemper apparentibus collimet; </s> <s xml:id="echoid-s1745" xml:space="preserve">nam Dioptra interim ſtellæ altitudinem in arcu D E B. </s> <s xml:id="echoid-s1746" xml:space="preserve">indicabit, <lb/>quæ ſit v. </s> <s xml:id="echoid-s1747" xml:space="preserve">g. </s> <s xml:id="echoid-s1748" xml:space="preserve">D E. </s> <s xml:id="echoid-s1749" xml:space="preserve">gr. </s> <s xml:id="echoid-s1750" xml:space="preserve">36. </s> <s xml:id="echoid-s1751" xml:space="preserve">poſtea poſt horas circiter, duodecim eandem ſtellam reuiſat, eam enim iterum qua-<lb/>dranti appropinquantem inueniet: </s> <s xml:id="echoid-s1752" xml:space="preserve">in eam igitur cùm exactè è regione quadrantis fuerit, iterum collimet, <lb/>notando eius nouam altitudinem, v.</s> <s xml:id="echoid-s1753" xml:space="preserve">g. </s> <s xml:id="echoid-s1754" xml:space="preserve">D G. </s> <s xml:id="echoid-s1755" xml:space="preserve">Dioptra enim punctum G. </s> <s xml:id="echoid-s1756" xml:space="preserve">v. </s> <s xml:id="echoid-s1757" xml:space="preserve">g. </s> <s xml:id="echoid-s1758" xml:space="preserve">attinget. </s> <s xml:id="echoid-s1759" xml:space="preserve">poſt hæc, arcũ E G. <lb/></s> <s xml:id="echoid-s1760" xml:space="preserve">qui inter binas altitudines intercipitur bifariam diuidat, ſitq; </s> <s xml:id="echoid-s1761" xml:space="preserve">diuiſio in H. </s> <s xml:id="echoid-s1762" xml:space="preserve">punctum H. </s> <s xml:id="echoid-s1763" xml:space="preserve">directè polum aſpi-<lb/>ciet; </s> <s xml:id="echoid-s1764" xml:space="preserve">& </s> <s xml:id="echoid-s1765" xml:space="preserve">arcus D H. </s> <s xml:id="echoid-s1766" xml:space="preserve">erit poli quæſita ſublimitas. </s> <s xml:id="echoid-s1767" xml:space="preserve">cui æqualis neceſſario erit alterius poli depreſſio. </s> <s xml:id="echoid-s1768" xml:space="preserve">huius ra-<lb/>tio eſt, quia ſtellæ illæ ad polum, conſpicuum ſitæ, ſunt ſempiternæ apparitionis, ac proinde propè polum <lb/>diurnas conuerſiones abſoluunt; </s> <s xml:id="echoid-s1769" xml:space="preserve">quare ſingulis duodenis horis ad meridianum reuertuntur; </s> <s xml:id="echoid-s1770" xml:space="preserve">quæ igitur ini-<lb/>tio noctis meridianum ſeu quadrantem pertranſierit, eadem poſt horas 12. </s> <s xml:id="echoid-s1771" xml:space="preserve">ſemicirculum abſoluens, ad eun-<lb/>dem meridianum, ſed tamen in alia altitudine reuertetur; </s> <s xml:id="echoid-s1772" xml:space="preserve">cum autem gyri eius ſint circumpolares, erit po-<lb/>lus inter vtramque altitudinem veluti centrum, medius. </s> <s xml:id="echoid-s1773" xml:space="preserve">ſi verò contingat obſeruatam ſtellam propius ho-<lb/>rizontem deſcendere, conſultum fuerit, aliam ab horizonte remotiorem, ac polum quam proximè circun-<lb/>dantem affumere. </s> <s xml:id="echoid-s1774" xml:space="preserve">quæ enim horizontem magis appetunt, eæ ob inſidentes horizõti vapores refractionem <lb/>patiuntur, ac proinde iuſto altiores collimantibus apparent: </s> <s xml:id="echoid-s1775" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s1776" xml:space="preserve">obſeruationi fallaciam inducerent. </s> <s xml:id="echoid-s1777" xml:space="preserve"><lb/>Sed etiam ex materiali Sphæra, idem reperies ſic; </s> <s xml:id="echoid-s1778" xml:space="preserve">Habeas primum gradum Eciypticæ, quem Sol obtinet <lb/>tunc, cum hanc poli altitudinem quæris: </s> <s xml:id="echoid-s1779" xml:space="preserve">nos infra in Eclyptica, officio 9. </s> <s xml:id="echoid-s1780" xml:space="preserve">id docemus gradum hunc meri-<lb/>diano applica. </s> <s xml:id="echoid-s1781" xml:space="preserve">Iam Sphæra Aſtronomicè ſita, Sole autem meridiem efficiente, ac Sphæra illuſtrante, ita <lb/>meridianum reuolue per horizontis inciſuras, vt vmbra Zodiaci tota cadat in partem alteram ipſius Zodia-<lb/>ci exactè, ideſt, pars Zodiaci illuſtrata, alteram partem exactè adumbret; </s> <s xml:id="echoid-s1782" xml:space="preserve">in hoc enim ſitu polus Sphęræ ean-<lb/>dem ſortietur altitudinem ſupra horlzontem Sphæræ quam polus mundi habet ſupra mundi horizontem. </s> <s xml:id="echoid-s1783" xml:space="preserve"><lb/>Non eſt autem ignorandum tantam eſſe poli altitudinem, quanta eſt eiuſdem loci latitudo.</s> <s xml:id="echoid-s1784" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1785" xml:space="preserve">Poſſumus autem per Magneticam acum, eo modo accomodatam, quem docet Guilelmus Gilbertus de <lb/>Magnetica Philoſophia, hanc poli altitudinem @imari. </s> <s xml:id="echoid-s1786" xml:space="preserve">porro huius nouæ, acmirabiſis Herculei lapidis <lb/>proprietatis, primus, ac nouus obſeruator extitit Robertus Normanus, vt ipſe in ſuo attractiuo tradit: <lb/></s> <s xml:id="echoid-s1787" xml:space="preserve">quare lapis hic verè Herculeus; </s> <s xml:id="echoid-s1788" xml:space="preserve">non ſolum ad meridianam lineam, ſed etiam ad poli altitudinem, hoc eſt, <lb/>ad mundi Sphæræ conſtitutionem nos edocendum, magna erga nos naturæ munificentia, natus, atq; </s> <s xml:id="echoid-s1789" xml:space="preserve">in <lb/>Aſtronomorum auxilium comparatus videtur: </s> <s xml:id="echoid-s1790" xml:space="preserve">vt merito non ſolum Herculeus, ſed etiam lapis dici merea-<lb/>tur Aſtronomicus.</s> <s xml:id="echoid-s1791" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1792" xml:space="preserve">7 Inuenta @am linea meridiana in horizontali plano, necnon poli altitudine, ſupra illud, facile erit ma-<lb/>terialem Sphæram Aſtronomicè collocare: </s> <s xml:id="echoid-s1793" xml:space="preserve">quæ res perſæpe in hac ſphærali ſcientia vſui eſt; </s> <s xml:id="echoid-s1794" xml:space="preserve">fit autem hoc <lb/>modo. </s> <s xml:id="echoid-s1795" xml:space="preserve">Eam in plano horizontali in quo ſit meridiana deſignata, ſtatuatur, ita vt & </s> <s xml:id="echoid-s1796" xml:space="preserve">horizon ſit exactè ho-<lb/>rizontali plano æquidiſtans, ideſt, ad libeſlam ſitus, & </s> <s xml:id="echoid-s1797" xml:space="preserve">meridianus ad vnguem meridiei lineæ incumbat, & </s> <s xml:id="echoid-s1798" xml:space="preserve"><lb/>polus conſpicuus ad Septentrionem conuerſus, ſit ſupra horizontem eleuatus iuxta loci dati eleuationem. <lb/></s> <s xml:id="echoid-s1799" xml:space="preserve">In hac enim ſituatione omnes Sphæræ partes, ac circuli partibus, ac ciroulis Sphæræ mundi correſpon-<lb/>debunt; </s> <s xml:id="echoid-s1800" xml:space="preserve">Vnde totius mundi conſtitutionem in data regione cognoſces, ideſt, ex qua parte ſit Septentrio, <lb/>ex qua Meridies, vbi Oriens, Occidens, vnde venti omnes expirent. </s> <s xml:id="echoid-s1801" xml:space="preserve">Quod ſi erexeris è verticè Sphæ-<lb/>ræ bracteola. </s> <s xml:id="echoid-s1802" xml:space="preserve">vel quippiam a vento facilè mobile, id flantem tunc ventum indicabit, nomina enim vento-<lb/>rum ſcripta ſunt in horizonte; </s> <s xml:id="echoid-s1803" xml:space="preserve">is igitur ventus fl bit, à quo directè bracteola auertetur. </s> <s xml:id="echoid-s1804" xml:space="preserve">Ex eadem Sphæræ <lb/>poſitione apparebit, vbl in cælo ſit polus conſpicuus; </s> <s xml:id="echoid-s1805" xml:space="preserve">Qua etiam Æquator, ac Tropici in cælo incedant, <lb/>atque à vertice diſtent: </s> <s xml:id="echoid-s1806" xml:space="preserve">& </s> <s xml:id="echoid-s1807" xml:space="preserve">alia huiuſmodi. </s> <s xml:id="echoid-s1808" xml:space="preserve">Hæc eſt igitur Aſtronomica Sphæræ conſtitutio, quam opere-<lb/>prætium eſt rectè percipere.</s> <s xml:id="echoid-s1809" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1810" xml:space="preserve">8 Meridianus circulus Geographis plurimum vſui eſt, opera enim ipſius locorum longitudines, ac la-<lb/>titudines metiuntur. </s> <s xml:id="echoid-s1811" xml:space="preserve">Eſt autem Geographis locorum longitudo, diſtantia eorum ab vltimo terræ termi-<lb/>no occidentali terræ, inquam, priſ is cognitæ: </s> <s xml:id="echoid-s1812" xml:space="preserve">vltimæ autem terræ continentes occidentales, erantoræ <lb/>maritimæ Hiſpaniæ, & </s> <s xml:id="echoid-s1813" xml:space="preserve">Africæ occidentales, quæ Atlantico Oceano alluuntur; </s> <s xml:id="echoid-s1814" xml:space="preserve">Inſulæ vero omn@um oc-<lb/>@identali ſſimæ erant, quæ in eodem O@eano ſitæ Fortunatæ dicuntur; </s> <s xml:id="echoid-s1815" xml:space="preserve">Qua propter ſtatuerunt harum In-<lb/>ſ@larum meridianum debere eſſe primum omnium meridianorum numerando, deinceps cæteros meridia- <pb o="16" file="0032" n="32" rhead="De Circulis Sphæræ."/> nos verſus orientem procedendo. </s> <s xml:id="echoid-s1816" xml:space="preserve">Eſt igitur longitudo alicuius loci propriè loquendo, diſtantia meridia-<lb/>ni alicuius loci a meridiano Fortunatarum: </s> <s xml:id="echoid-s1817" xml:space="preserve">quæ diſtantia ſumenda eſt in Æquatore, per eum enim omnes <lb/>meridiani perpendiculariter tranſeunt, quare tanta eſt, v.</s> <s xml:id="echoid-s1818" xml:space="preserve">g. </s> <s xml:id="echoid-s1819" xml:space="preserve">longitudo Parmæ, quantus eſt arcus Aequato-<lb/>ris à meridiano Fortunatarum, vſq; </s> <s xml:id="echoid-s1820" xml:space="preserve">ad Parmæ meridianum numeratus in grad. </s> <s xml:id="echoid-s1821" xml:space="preserve">v.</s> <s xml:id="echoid-s1822" xml:space="preserve">g. </s> <s xml:id="echoid-s1823" xml:space="preserve">32. </s> <s xml:id="echoid-s1824" xml:space="preserve">cauſa verò cur Geo-<lb/>graphi hanc diſtantiam appellarint longitudinem, fuit quia portio terræ tunc temporis cognitæ, longior <lb/>erit ab Occidente ad Orientem procedendo, quam ab Auſtroad Septentrionem, quapropter eam dimen-<lb/>ſionem meritò longitudinem appellarunt; </s> <s xml:id="echoid-s1825" xml:space="preserve">quare hæc longitudo nihil aliud eſt, quam diſtantia a primo il-<lb/>lo meridiano ſecundum terræ longitudinem.</s> <s xml:id="echoid-s1826" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1827" xml:space="preserve">9 Inſeruit pariter meridianus latitudinibus locorum menſurandis, ac numerandis; </s> <s xml:id="echoid-s1828" xml:space="preserve">Eſt enim locus la-<lb/>titudo arcus meridiani eiuſdem loci ab Aequatore vſq; </s> <s xml:id="echoid-s1829" xml:space="preserve">ad datum locum numeratus: </s> <s xml:id="echoid-s1830" xml:space="preserve">quæ dimenſio dicta eſt <lb/>latitudo: </s> <s xml:id="echoid-s1831" xml:space="preserve">quoniam dimenſio terræ antiquitus cognitæ, quæ ab Auſtro in Septentrionem patebat, anguſtior <lb/>erat altera, quæ ab Occidente in Orientem prætendebatur: </s> <s xml:id="echoid-s1832" xml:space="preserve">dimenſio autem anguſtior in alijs huiuſmodi <lb/>rebus. </s> <s xml:id="echoid-s1833" xml:space="preserve">latitudo ſolet appellari: </s> <s xml:id="echoid-s1834" xml:space="preserve">quare latitudo locorum eſt diſtantia eorum ab Aequatore ſecundum terræ <lb/>latitudinem. </s> <s xml:id="echoid-s1835" xml:space="preserve">porrò olim locorum omnium cognitionem latitudo erat tantum Borealis; </s> <s xml:id="echoid-s1836" xml:space="preserve">nunc autem poſt <lb/>Noui orbis, & </s> <s xml:id="echoid-s1837" xml:space="preserve">multarum aliarum prouinciarum detectionem, plurima ſunt loca vltra Aequatorem, quo-<lb/>rum latitudines in Auſtrum excurrunt. </s> <s xml:id="echoid-s1838" xml:space="preserve">Hæc breuius explicaui, quia fuſius, ea explicare munus eſt Geogra-<lb/>phi; </s> <s xml:id="echoid-s1839" xml:space="preserve">ego id præſtabo in Geographiæ introductione, ad finem operis: </s> <s xml:id="echoid-s1840" xml:space="preserve">vbi etiam quoniam valde è re Aſtro-<lb/>nomica eſt, longitudinem, & </s> <s xml:id="echoid-s1841" xml:space="preserve">latitudinem præcipuorum locorum in promptu habere, dabo Tabellam eo-<lb/>rum longitudines, ac latitudinem continentem.</s> <s xml:id="echoid-s1842" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div40" type="section" level="1" n="24"> <head xml:id="echoid-head26" style="it" xml:space="preserve">De Aequatore, ſeu Aequinoctiali circulo. # Cap. V.</head> <p> <s xml:id="echoid-s1843" xml:space="preserve">ABſolutis duobus circulis pluralibus, ac fixis, reliqui ſunt ij, qui ſingulares, ac mobiles dicuntur, quorum <lb/>primus, ac omnium nobiliſſimus eſt Aequator, vel Aequinoctialis, ſic dictus, quod quando Sol ad eum <lb/>peruenit, æquantur dies noctibus, ideſt, dies artificialis noctibus artificialibus, ſeu Aequinoctium efficitur. <lb/></s> <s xml:id="echoid-s1844" xml:space="preserve">Eſt autem Aequator circulus maximus, quem cum Sol percurrit efficit vbique terrarum Aequinoctium. </s> <s xml:id="echoid-s1845" xml:space="preserve"><lb/>Eius centrum eſt idem cum centro mundi, eiuſque poli ſunt etiam poli mundi, ac primi mobilis, ſuper qui-<lb/>bus motus diurnus peragitur; </s> <s xml:id="echoid-s1846" xml:space="preserve">quorũ alter qui nobis eleuatur dicitur Arcticus ab Arcto, ideſt, Vrſa conſtella-<lb/>tione illi proxima: </s> <s xml:id="echoid-s1847" xml:space="preserve">alter vero quod huic opponatur propterea Antarcticus appellatur; </s> <s xml:id="echoid-s1848" xml:space="preserve">Eſt autem vnicus in <lb/>mundo Aequator. </s> <s xml:id="echoid-s1849" xml:space="preserve">eſt præterea mobilis, motu ſcilicet diurno, totus reuoluitur.</s> <s xml:id="echoid-s1850" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1851" xml:space="preserve">Eius autem in mundo poſitionem ſic rectè concipiemus: </s> <s xml:id="echoid-s1852" xml:space="preserve">Inuenta namq; </s> <s xml:id="echoid-s1853" xml:space="preserve">linea meridiana, vti ſuperiori <lb/>capite docuimus, ducatur per centrum E. </s> <s xml:id="echoid-s1854" xml:space="preserve">illius figuræ linea A C. </s> <s xml:id="echoid-s1855" xml:space="preserve">faciens angulos rectos cum meridiana, hęc <lb/>erit linea Aequinoctialis, ideſt, veſtigium Aequatoris in horizonte ſenſibili. </s> <s xml:id="echoid-s1856" xml:space="preserve">punctum A. </s> <s xml:id="echoid-s1857" xml:space="preserve">verum ortum C. <lb/></s> <s xml:id="echoid-s1858" xml:space="preserve">vero occaſum verum monſtrabunt: </s> <s xml:id="echoid-s1859" xml:space="preserve">vnde etiam apparet duas lineas Aequinoct alem, & </s> <s xml:id="echoid-s1860" xml:space="preserve">Meridianam ſecare <lb/>totum horizontem in æquales quatuor quadrantes.</s> <s xml:id="echoid-s1861" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1862" xml:space="preserve">Aliter Aequinoctialem lineam, abſque meridiana, inueniemus hoc modo; </s> <s xml:id="echoid-s1863" xml:space="preserve">tempore alterutrius Aequi-<lb/>noctij in plano quopiam horizontali, & </s> <s xml:id="echoid-s1864" xml:space="preserve">aprico, erigatur ſtylus, deinde interdiu notentur quotuis pun-<lb/>cta per quæ vmbræ apex inceſſerit, omnia enim illa puncta Aequinoctij die ſunt in linea recta, quoniam <lb/>tunc apex vmbræ incedit per lineam rectã in plano horizontali; </s> <s xml:id="echoid-s1865" xml:space="preserve">hęc igitur linea eſt, & </s> <s xml:id="echoid-s1866" xml:space="preserve">dicitur linea Aequa-<lb/>toris, per quam videlicet Aequator horizonti inſeritur; </s> <s xml:id="echoid-s1867" xml:space="preserve">huius cauſam afferre Gnomonici eſt. </s> <s xml:id="echoid-s1868" xml:space="preserve">vide igitur P. <lb/></s> <s xml:id="echoid-s1869" xml:space="preserve">Clauij Gnomoni cam lib. </s> <s xml:id="echoid-s1870" xml:space="preserve">1. </s> <s xml:id="echoid-s1871" xml:space="preserve">prop. </s> <s xml:id="echoid-s1872" xml:space="preserve">11. </s> <s xml:id="echoid-s1873" xml:space="preserve">corol. </s> <s xml:id="echoid-s1874" xml:space="preserve">2.</s> <s xml:id="echoid-s1875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1876" xml:space="preserve">Imò quolibet die ſic eam breuiter reperies; </s> <s xml:id="echoid-s1877" xml:space="preserve">nam ſi in eodem circulo, quem ſpra adhibuimus pro inuen-<lb/>tione lineæ meridianæ, notaueris tantum duo puncta G H. </s> <s xml:id="echoid-s1878" xml:space="preserve">eaque recta linea coniunxerit, erit ea Aequi-<lb/>noctialis.</s> <s xml:id="echoid-s1879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1880" xml:space="preserve">Verum non ſatis eſt Aequinoctialem lineam cognoſcere ad perfectam Aequatoris ſituationem percipien <lb/>dam, ſed præterea opus eſt cognoſcere, quomodo ſe habeat ad horizontem. </s> <s xml:id="echoid-s1881" xml:space="preserve">in Sphęra enim recta Aequator <lb/>erigitur ſupra horizontem ad angulos rectos & </s> <s xml:id="echoid-s1882" xml:space="preserve">per verticem tranſit: </s> <s xml:id="echoid-s1883" xml:space="preserve">in Sphæra verò paralella horizonti <lb/>Aequator coincidit, & </s> <s xml:id="echoid-s1884" xml:space="preserve">poli eius ſant ijdem cum poli huius, ideſt, cum Vertice, & </s> <s xml:id="echoid-s1885" xml:space="preserve">Imo: </s> <s xml:id="echoid-s1886" xml:space="preserve">in cæteris autẽ obli-<lb/>quis Sphæris Aequator facit cum horizonte angulos acutos qui varij ſunt pro varietate obliquarum Sphę-<lb/>rarum, hanc igitur Aequatoris ad horizontem habitudinem ſic indagabimus. </s> <s xml:id="echoid-s1887" xml:space="preserve">Inueniatur primo, vt ſupe-<lb/>rius dictum eſt in poli altitudo, deinde huius altitudinis accipiatur complementum vſque ad 90. </s> <s xml:id="echoid-s1888" xml:space="preserve">gr. </s> <s xml:id="echoid-s1889" xml:space="preserve">ideſt, <lb/>complementum quadrantis, nam iſtud complementum erit eleuatio, ſeu angulus Aequatoris cum horizon-<lb/> <anchor type="figure" xlink:label="fig-0032-01a" xlink:href="fig-0032-01"/> te. </s> <s xml:id="echoid-s1890" xml:space="preserve">habetur autem hoc complementum, ſi gradus altitudinis polaris deman-<lb/>tur a gr. </s> <s xml:id="echoid-s1891" xml:space="preserve">90. </s> <s xml:id="echoid-s1892" xml:space="preserve">nam reſidui gradus erunt angulus Aequatoris quæſitus, exempli <lb/>gr. </s> <s xml:id="echoid-s1893" xml:space="preserve">quia eleuatio poli Parmenſis eſt gr. </s> <s xml:id="echoid-s1894" xml:space="preserve">44. </s> <s xml:id="echoid-s1895" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s1896" xml:space="preserve">qui ſi a 90. </s> <s xml:id="echoid-s1897" xml:space="preserve">demãtur, remanet 45. </s> <s xml:id="echoid-s1898" xml:space="preserve">{1/2}. <lb/></s> <s xml:id="echoid-s1899" xml:space="preserve">qui ſunt præd@ctum complementum, & </s> <s xml:id="echoid-s1900" xml:space="preserve">proinde ſunt eleuatio Aequatoris in <lb/>hoc Parmenſi horizonte. </s> <s xml:id="echoid-s1901" xml:space="preserve">Demonſtratio huius hæc eſt, quia dictum comple-<lb/>mentum eſt vbique æquale eleuationi Aequatoris. </s> <s xml:id="echoid-s1902" xml:space="preserve">ſit in præſenti figura me-<lb/>ridianus circulus A C F. </s> <s xml:id="echoid-s1903" xml:space="preserve">horizon A E. </s> <s xml:id="echoid-s1904" xml:space="preserve">æquator G D. </s> <s xml:id="echoid-s1905" xml:space="preserve">poli mundi B F. </s> <s xml:id="echoid-s1906" xml:space="preserve">arcus <lb/>A E. </s> <s xml:id="echoid-s1907" xml:space="preserve">eſt altitudo poli ſupra horizontem, arcus vero B C. </s> <s xml:id="echoid-s1908" xml:space="preserve">eſt complementum <lb/>eius: </s> <s xml:id="echoid-s1909" xml:space="preserve">arcus D E. </s> <s xml:id="echoid-s1910" xml:space="preserve">eſt altitudo æquatoris; </s> <s xml:id="echoid-s1911" xml:space="preserve">probandum eſt, arcum B C. </s> <s xml:id="echoid-s1912" xml:space="preserve">eſſe æqua-<lb/>lem arcus D E. </s> <s xml:id="echoid-s1913" xml:space="preserve">quia igitur arcus B D. </s> <s xml:id="echoid-s1914" xml:space="preserve">eſt quadrans, ideſt, gr. </s> <s xml:id="echoid-s1915" xml:space="preserve">90. </s> <s xml:id="echoid-s1916" xml:space="preserve">tantum enim <lb/>diſtat polus a circulo maximo, qualis eſt æquator: </s> <s xml:id="echoid-s1917" xml:space="preserve">pariter arcus C E. </s> <s xml:id="echoid-s1918" xml:space="preserve">eſt qua- <pb o="17" file="0033" n="33" rhead="Liber Primus."/> crans, ideſt, gr. </s> <s xml:id="echoid-s1919" xml:space="preserve">90. </s> <s xml:id="echoid-s1920" xml:space="preserve">ob eandem rationem, quia videlicet C E. </s> <s xml:id="echoid-s1921" xml:space="preserve">eſt polus horizontis: </s> <s xml:id="echoid-s1922" xml:space="preserve">ergo C E. </s> <s xml:id="echoid-s1923" xml:space="preserve">B D. </s> <s xml:id="echoid-s1924" xml:space="preserve">ſunt æqua-<lb/>les; </s> <s xml:id="echoid-s1925" xml:space="preserve">dematur iam arcus C D. </s> <s xml:id="echoid-s1926" xml:space="preserve">qui vtrique communis eſt, ſic enim demitur æquale ab æqualibus; </s> <s xml:id="echoid-s1927" xml:space="preserve">qui igitur <lb/>remanent duo arcus B C. </s> <s xml:id="echoid-s1928" xml:space="preserve">D E. </s> <s xml:id="echoid-s1929" xml:space="preserve">erunt æquales, ſed B C. </s> <s xml:id="echoid-s1930" xml:space="preserve">eſt complementum altitudinis poli A B. </s> <s xml:id="echoid-s1931" xml:space="preserve">ad com-<lb/>plendum quadrantem A D. </s> <s xml:id="echoid-s1932" xml:space="preserve">D E. </s> <s xml:id="echoid-s1933" xml:space="preserve">verò eſt eleuatio æquatoris ſupra horizontem, ergo complementum al-<lb/>titudinis poli eſt æqualis eleuationi æquatoris, quod erat demonſtrandum. </s> <s xml:id="echoid-s1934" xml:space="preserve">Idem ad ſenſum ex materiali <lb/>Sphæra oſtendere eſt, nam eleuato altero polorum ad quamlibet altitudinem, ſtatim apparebit arcum me-<lb/>ridiani inter polum, & </s> <s xml:id="echoid-s1935" xml:space="preserve">verticem interiectum, qui altitudinis poli eſt complementum, eſſe æqualem arcui <lb/>meridiani ab horizonte, vſque ad æquatorem interceptum, qui angulo æquatoris ſubtenditur, ac proinde <lb/>eiuſdem quantitatem indicat.</s> <s xml:id="echoid-s1936" xml:space="preserve"/> </p> <div xml:id="echoid-div40" type="float" level="2" n="1"> <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a"> <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0032-01"/> </figure> </div> <p> <s xml:id="echoid-s1937" xml:space="preserve">Cæterum in Sphæra recta, vterque dictorum arcuum eſt quadrans; </s> <s xml:id="echoid-s1938" xml:space="preserve">In paral ella vero Sphæra altitudo <lb/>poli eſt in teger quadrans, quare nullum relinquitur complementum; </s> <s xml:id="echoid-s1939" xml:space="preserve">& </s> <s xml:id="echoid-s1940" xml:space="preserve">ſicuti ibi nullum eſt tale comple-<lb/>mentum, ſic etiam nulla eſt Aequatoris eleuatio, cui æquale ſit. </s> <s xml:id="echoid-s1941" xml:space="preserve">Habita igitur linea Aequinoctiali, & </s> <s xml:id="echoid-s1942" xml:space="preserve">an-<lb/>gulo Aequatoris, extra Sphæram paralellam, facilè cuique erit Aequatoris perfectam in proprio horizonte <lb/>poſitionem imaginari.</s> <s xml:id="echoid-s1943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1944" xml:space="preserve">Vſus Aequatoris hi ſnnt. </s> <s xml:id="echoid-s1945" xml:space="preserve">Primo, totam mundi Sphæram in duo dirimit hemiſphęria, Boreale videlicet, <lb/>& </s> <s xml:id="echoid-s1946" xml:space="preserve">Auſtrale: </s> <s xml:id="echoid-s1947" xml:space="preserve">vnde etiam ipſum terræ globum pariter in partem Borealem, & </s> <s xml:id="echoid-s1948" xml:space="preserve">Auſtralem partitur.</s> <s xml:id="echoid-s1949" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1950" xml:space="preserve">2 Eſt regula, & </s> <s xml:id="echoid-s1951" xml:space="preserve">menſura primi motus, ſeu motus diurni, quo ſcilicet totum cælum vna cum Sole ſpa-<lb/>cio 24. </s> <s xml:id="echoid-s1952" xml:space="preserve">horarum circa axem mundi reuoluitur, qui motus procedit ab Ortu, & </s> <s xml:id="echoid-s1953" xml:space="preserve">tendit per meridiem ad Oc-<lb/>caſum, atque inde per mediam noctem deſcendens, iterum ad Ortum reuertitur. </s> <s xml:id="echoid-s1954" xml:space="preserve">dicitur motus diurnus, <lb/>quia ex hac integra reuolutione dies naturalis perficitur. </s> <s xml:id="echoid-s1955" xml:space="preserve">Eſt autem Aequator huius motus menſura, quia <lb/>ipſe eodem motu vniformiter, ac regulariter mouetur, habet enim eoſdem polos, & </s> <s xml:id="echoid-s1956" xml:space="preserve">axem quos hic primus <lb/>motus: </s> <s xml:id="echoid-s1957" xml:space="preserve">mouetur vniformiter, ac regulariter. </s> <s xml:id="echoid-s1958" xml:space="preserve">nam temporibus æqualibet mouentur partes æquales, ideſt, <lb/>eadem ſemper velocitate, v. </s> <s xml:id="echoid-s1959" xml:space="preserve">g. </s> <s xml:id="echoid-s1960" xml:space="preserve">ſingulis horis eleuantur gr. </s> <s xml:id="echoid-s1961" xml:space="preserve">15. </s> <s xml:id="echoid-s1962" xml:space="preserve">ipſius ſupra horizontem, aut meridianum <lb/>prætereunt, vti Aſtronomicæ obſeruationes docent. </s> <s xml:id="echoid-s1963" xml:space="preserve">atque hoc eſt nobiliſſimum, ac præcipuum ipſius <lb/>munus.</s> <s xml:id="echoid-s1964" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1965" xml:space="preserve">3 Cum motus Aequatoris ſit vniformis regularis, & </s> <s xml:id="echoid-s1966" xml:space="preserve">ſemper æquè velox, merito Aſtronomi eum pro <lb/>inenſura cæterorum motuum aſſumpſerunt, ſeu ex motu ipſius tempus fabricati ſunt, eſt enim tempus, vt <lb/>aiunt Philoſophi, nihil aliud quam menſura motus. </s> <s xml:id="echoid-s1967" xml:space="preserve">hac de cauſa Aſtronomi ſæpè partes Aequatoris appel-<lb/>lant tempora, quas in Zodiaco gradus propriè dicunt; </s> <s xml:id="echoid-s1968" xml:space="preserve">ſic eleuatio gr. </s> <s xml:id="echoid-s1969" xml:space="preserve">15. </s> <s xml:id="echoid-s1970" xml:space="preserve">efficit vnam temporis horam, & </s> <s xml:id="echoid-s1971" xml:space="preserve"><lb/>integra Aequatoris reuolutio, vna cum tanta eiuſdem particula, quæ reſpondeat progreſſui diurno Solis <lb/>in Zodiaco, diem naturalem perficit. </s> <s xml:id="echoid-s1972" xml:space="preserve">eodem modo menſes, anni, & </s> <s xml:id="echoid-s1973" xml:space="preserve">reliqua tempora, quibus reliquos alio-<lb/>rum Planetarum, ſyderum, ac rerum motus, necnon durationes menſuramus, ex Aequatoris reuolutioni-<lb/>bus conſtituuntur. </s> <s xml:id="echoid-s1974" xml:space="preserve">Aduertendum vero ſingulos quindenos gradus non efficere exactè vnam horam, vti <lb/>exempli cauſa poſuimus, ſed exiguum quid amplius requiri, de quo ſuo loco, cum de diebus agetur. </s> <s xml:id="echoid-s1975" xml:space="preserve">Vt au-<lb/>tem melius percipiatur quot Aequatoris partes, quibus, & </s> <s xml:id="echoid-s1976" xml:space="preserve">quot temporibus reſpondeant, placuit ſe quen-<lb/>tem Tabellam ſubiungere.</s> <s xml:id="echoid-s1977" xml:space="preserve"/> </p> <pb o="18" file="0034" n="34" rhead="De Circulis Shpæræ."/> <note position="right" xml:space="preserve"> <lb/>######### Conuerſio Gra. min. & ſec. Aequatoris in horas, minuta, ſecunda, \\ & tertia horarum. <lb/>Æquat. \\ Gra. # H. # M. # Æquat. \\ Gra. # H. # M. # Æquat. \\ Gra. # H. # M. <lb/>1 # 0 # 4 # 31 # 2 # 4 # 70 # 4 # 40 <lb/>2 # 0 # 8 # 32 # 2 # 8 # 80 # 5 # 20 <lb/>3 # 0 # 12 # 33 # 2 # 12 # 90 # 6 # 0 <lb/>4 # 0 # 16 # 34 # 2 # 16 # 100 # 6 # 40 <lb/>5 # 0 # 20 # 35 # 2 # 20 # 110 # 7 # 20 <lb/>6 # 0 # 24 # 36 # 2 # 24 # 120 # 8 # 0 <lb/>7 # 0 # 28 # 37 # 2 # 28 # 130 # 8 # 40 <lb/>8 # 0 # 32 # 38 # 2 # 32 # 140 # 9 # 20 <lb/>9 # 0 # 36 # 39 # 2 # 36 # 150 # 10 # 0 <lb/>10 # 0 # 40 # 40 # 2 # 40 # 160 # 10 # 40 <lb/>11 # 0 # 44 # 41 # 2 # 44 # 170 # 11 # 20 <lb/>12 # 0 # 48 # 42 # 2 # 48 # 180 # 12 # 0 <lb/>13 # 0 # 52 # 43 # 2 # 52 # 190 # 12 # 40 <lb/>14 # 0 # 56 # 44 # 2 # 56 # 200 # 13 # 20 <lb/>15 # 1 # 0 # 45 # 3 # 0 # 210 # 14 # 0 <lb/>16 # 1 # 4 # 46 # 3 # 4 # 220 # 14 # 40 <lb/>17 # 1 # 8 # 47 # 3 # 8 # 230 # 15 # 20 <lb/>18 # 1 # 12 # 48 # 3 # 12 # 240 # 16 # 0 <lb/>19 # 1 # 16 # 49 # 3 # 16 # 250 # 16 # 40 <lb/>20 # 1 # 20 # 50 # 3 # 20 # 260 # 17 # 20 <lb/>21 # 1 # 24 # 51 # 3 # 24 # 270 # 18 # 0 <lb/>22 # 1 # 28 # 52 # 3 # 28 # 280 # 18 # 40 <lb/>23 # 1 # 32 # 53 # 3 # 32 # 290 # 19 # 20 <lb/>24 # 1 # 36 # 54 # 3 # 36 # 300 # 20 # 0 <lb/>25 # 1 # 40 # 55 # 3 # 40 # 310 # 20 # 40 <lb/>26 # 1 # 44 # 56 # 3 # 44 # 320 # 21 # 20 <lb/>27 # 1 # 48 # 57 # 3 # 48 # 330 # 22 # 0 <lb/>28 # 1 # 52 # 58 # 3 # 52 # 340 # 22 # 40 <lb/>29 # 1 # 56 # 59 # 3 # 56 # 350 # 23 # 20 <lb/>30 # 2 # 0 # 60 # 4 # 0 # 360 # 24 # 0 <lb/>Mi. \\ Se. \\ Æqui. # Mi. \\ Se. # Se. \\ Te. # Mi. \\ Se. \\ Æqui. # Mi. \\ Se. # Se. \\ Te. # Mi. \\ Se. \\ Æqui. # Mi. \\ Se. # Se. \\ Te. <lb/></note> </div> <div xml:id="echoid-div42" type="section" level="1" n="25"> <head xml:id="echoid-head27" style="it" xml:space="preserve">Vſus Tabellæ.</head> <p> <s xml:id="echoid-s1978" xml:space="preserve">CVm volueris gradus Æquinoctialis commutare in horas, accipe dati gradus numerũ ſub titulo Æqua-<lb/>toris, & </s> <s xml:id="echoid-s1979" xml:space="preserve">mox dextrorſum in columna proxima habebis numerum horarum, & </s> <s xml:id="echoid-s1980" xml:space="preserve">min. </s> <s xml:id="echoid-s1981" xml:space="preserve">gradibus datis re-<lb/>ſpondentium: </s> <s xml:id="echoid-s1982" xml:space="preserve">ſic vides gr. </s> <s xml:id="echoid-s1983" xml:space="preserve">27. </s> <s xml:id="echoid-s1984" xml:space="preserve">Aequatoris reſpondere hor. </s> <s xml:id="echoid-s1985" xml:space="preserve">1. </s> <s xml:id="echoid-s1986" xml:space="preserve">48 |. </s> <s xml:id="echoid-s1987" xml:space="preserve">Quod ſi datum numerum graduum in-<lb/>tegrum non reperias in Tabella, quære in ea numerum proxime minorem dato, cum ſuis horis, & </s> <s xml:id="echoid-s1988" xml:space="preserve">min. </s> <s xml:id="echoid-s1989" xml:space="preserve">de-<lb/>inde cum reliquo numeri dati, accipe hor. </s> <s xml:id="echoid-s1990" xml:space="preserve">& </s> <s xml:id="echoid-s1991" xml:space="preserve">min. </s> <s xml:id="echoid-s1992" xml:space="preserve">ei debita: </s> <s xml:id="echoid-s1993" xml:space="preserve">eaque cum prioribus coniunge, v.</s> <s xml:id="echoid-s1994" xml:space="preserve">g. </s> <s xml:id="echoid-s1995" xml:space="preserve">dantur <lb/>gr. </s> <s xml:id="echoid-s1996" xml:space="preserve">75. </s> <s xml:id="echoid-s1997" xml:space="preserve">qui numerus non reperiuntur in Tabella, accipe igitur 70. </s> <s xml:id="echoid-s1998" xml:space="preserve">proxime minorẽ, cui debentur hor. </s> <s xml:id="echoid-s1999" xml:space="preserve">4. </s> <s xml:id="echoid-s2000" xml:space="preserve">40 |. <lb/></s> <s xml:id="echoid-s2001" xml:space="preserve">deinde cum reliquo 5. </s> <s xml:id="echoid-s2002" xml:space="preserve">accipio hor. </s> <s xml:id="echoid-s2003" xml:space="preserve">0. </s> <s xml:id="echoid-s2004" xml:space="preserve">min. </s> <s xml:id="echoid-s2005" xml:space="preserve">20. </s> <s xml:id="echoid-s2006" xml:space="preserve">quæ prioribus addida faciunt hor. </s> <s xml:id="echoid-s2007" xml:space="preserve">5. </s> <s xml:id="echoid-s2008" xml:space="preserve">quæ debentur gr. </s> <s xml:id="echoid-s2009" xml:space="preserve">75. </s> <s xml:id="echoid-s2010" xml:space="preserve">por-<lb/>rò in Tractatu de Luna, docebo qua ratione hi numeri Aſtronomici addantur, ſubtrahantur, &</s> <s xml:id="echoid-s2011" xml:space="preserve">c.</s> <s xml:id="echoid-s2012" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2013" xml:space="preserve">Si verò minuta, vel ſecunda graduum in tempus conuertenda ſint, accipe datum numerum min. </s> <s xml:id="echoid-s2014" xml:space="preserve">&</s> <s xml:id="echoid-s2015" xml:space="preserve">c. </s> <s xml:id="echoid-s2016" xml:space="preserve">ſu-<lb/>pra titulos min. </s> <s xml:id="echoid-s2017" xml:space="preserve">& </s> <s xml:id="echoid-s2018" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2019" xml:space="preserve">poſito in pede Tabulæ; </s> <s xml:id="echoid-s2020" xml:space="preserve">quia eadem ſeries numerorũ quę inſeruit gradibus Aequato-<lb/>ris, inſeruit etiam minutis, & </s> <s xml:id="echoid-s2021" xml:space="preserve">ſecundis: </s> <s xml:id="echoid-s2022" xml:space="preserve">propter eaſdem proportiones: </s> <s xml:id="echoid-s2023" xml:space="preserve">& </s> <s xml:id="echoid-s2024" xml:space="preserve">ſequentes columnæ ad dexteram <lb/>dabunt minuta, ſec. </s> <s xml:id="echoid-s2025" xml:space="preserve">&</s> <s xml:id="echoid-s2026" xml:space="preserve">c. </s> <s xml:id="echoid-s2027" xml:space="preserve">horarum, prout tituli ipſarum inferiores in dicant: </s> <s xml:id="echoid-s2028" xml:space="preserve">quia hi numeri modo euadunt <lb/>min. </s> <s xml:id="echoid-s2029" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2030" xml:space="preserve">ter. </s> <s xml:id="echoid-s2031" xml:space="preserve">ſic minutis 30. </s> <s xml:id="echoid-s2032" xml:space="preserve">Aequatoris reſpondent hor. </s> <s xml:id="echoid-s2033" xml:space="preserve">2|. </s> <s xml:id="echoid-s2034" xml:space="preserve">0||. </s> <s xml:id="echoid-s2035" xml:space="preserve">& </s> <s xml:id="echoid-s2036" xml:space="preserve">32|. </s> <s xml:id="echoid-s2037" xml:space="preserve">Aequatoris reſpondent hor. </s> <s xml:id="echoid-s2038" xml:space="preserve">2|. </s> <s xml:id="echoid-s2039" xml:space="preserve">8||. <lb/></s> <s xml:id="echoid-s2040" xml:space="preserve">pariter ſecundis 30. </s> <s xml:id="echoid-s2041" xml:space="preserve">Aequatoris reſpondent hor. </s> <s xml:id="echoid-s2042" xml:space="preserve">2|. </s> <s xml:id="echoid-s2043" xml:space="preserve">0||. </s> <s xml:id="echoid-s2044" xml:space="preserve">&</s> <s xml:id="echoid-s2045" xml:space="preserve">c.</s> <s xml:id="echoid-s2046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2047" xml:space="preserve">Si autem velis horas, min. </s> <s xml:id="echoid-s2048" xml:space="preserve">ſec. </s> <s xml:id="echoid-s2049" xml:space="preserve">conuertere in gradus, minutis, ſecundis Aequatoris, vtere inuerſo ordi-<lb/>ne Tabellæ, v.</s> <s xml:id="echoid-s2050" xml:space="preserve">g. </s> <s xml:id="echoid-s2051" xml:space="preserve">vni horæ, & </s> <s xml:id="echoid-s2052" xml:space="preserve">4|. </s> <s xml:id="echoid-s2053" xml:space="preserve">acceptis ſub titulo Hor. </s> <s xml:id="echoid-s2054" xml:space="preserve">Min. </s> <s xml:id="echoid-s2055" xml:space="preserve">reſpondente in ſiniſtro latere graduum <pb o="19" file="0035" n="35" rhead="Pars Prima."/> Aequatoris grad. </s> <s xml:id="echoid-s2056" xml:space="preserve">16. </s> <s xml:id="echoid-s2057" xml:space="preserve">& </s> <s xml:id="echoid-s2058" xml:space="preserve">ſic de reliquis, quæ ſolers, & </s> <s xml:id="echoid-s2059" xml:space="preserve">induſtrius Lector facilè per ſe reperiet.</s> <s xml:id="echoid-s2060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2061" xml:space="preserve">Aliter idem ſine Tabella hac, aſſequemur per ſolam multiplicationem, & </s> <s xml:id="echoid-s2062" xml:space="preserve">diuiſionẽ multiplicentur gra-<lb/>dus, minuta, ſecunda, &</s> <s xml:id="echoid-s2063" xml:space="preserve">c. </s> <s xml:id="echoid-s2064" xml:space="preserve">per quatuor nam producti numeri dabunt partes temporis vel horæ, vna deno-<lb/>minationes minores, quam ſint partes Aequatoris multiplicatæ, ideſt productus numerus ex multiplica-<lb/>tione graduum, dabit minuta horarum; </s> <s xml:id="echoid-s2065" xml:space="preserve">& </s> <s xml:id="echoid-s2066" xml:space="preserve">ex min. </s> <s xml:id="echoid-s2067" xml:space="preserve">Aequatoris, prouenient ſecunda horarum, &</s> <s xml:id="echoid-s2068" xml:space="preserve">c. </s> <s xml:id="echoid-s2069" xml:space="preserve">v.</s> <s xml:id="echoid-s2070" xml:space="preserve">g.</s> <s xml:id="echoid-s2071" xml:space="preserve">gr.</s> <s xml:id="echoid-s2072" xml:space="preserve">9. <lb/></s> <s xml:id="echoid-s2073" xml:space="preserve">multiplicati per 4. </s> <s xml:id="echoid-s2074" xml:space="preserve">dabunt minuta horæ 36 |. </s> <s xml:id="echoid-s2075" xml:space="preserve">minuta 40. </s> <s xml:id="echoid-s2076" xml:space="preserve">Aequatoris, dabunt ſecunda 160. </s> <s xml:id="echoid-s2077" xml:space="preserve">horarum, quæ ef-<lb/>ficiunt min. </s> <s xml:id="echoid-s2078" xml:space="preserve">2|. </s> <s xml:id="echoid-s2079" xml:space="preserve">40||. </s> <s xml:id="echoid-s2080" xml:space="preserve">ſecunda 20||. </s> <s xml:id="echoid-s2081" xml:space="preserve">quadrupli ata efficient 80|||. </s> <s xml:id="echoid-s2082" xml:space="preserve">tertia horæ, ideſt 1||. </s> <s xml:id="echoid-s2083" xml:space="preserve">20|||. </s> <s xml:id="echoid-s2084" xml:space="preserve">Econtra ſi ho-<lb/>ræ, & </s> <s xml:id="echoid-s2085" xml:space="preserve">minuta, ſecunda, tertia horæ diuidantur per 4. </s> <s xml:id="echoid-s2086" xml:space="preserve">producent partes Aequatoris vna denominatione <lb/>maiores partibus horarijs, ideſt, ex tertijs hor. </s> <s xml:id="echoid-s2087" xml:space="preserve">prouenient ſecunda graduum: </s> <s xml:id="echoid-s2088" xml:space="preserve">ex ſecundis hor. </s> <s xml:id="echoid-s2089" xml:space="preserve">prouenient <lb/>min. </s> <s xml:id="echoid-s2090" xml:space="preserve">graduum: </s> <s xml:id="echoid-s2091" xml:space="preserve">ex minutis hor. </s> <s xml:id="echoid-s2092" xml:space="preserve">prodibunt gradus: </s> <s xml:id="echoid-s2093" xml:space="preserve">ex horis denique, producentur partes vnius ſexagenæ <lb/>graduum. </s> <s xml:id="echoid-s2094" xml:space="preserve">ſic, ſi hora 1. </s> <s xml:id="echoid-s2095" xml:space="preserve">20|. </s> <s xml:id="echoid-s2096" xml:space="preserve">40||. </s> <s xml:id="echoid-s2097" xml:space="preserve">diuidantur per 4. </s> <s xml:id="echoid-s2098" xml:space="preserve">producentur primus vnus quadrans, vnius ſexagenæ gra-<lb/>duum, ideſt, gr. </s> <s xml:id="echoid-s2099" xml:space="preserve">15. </s> <s xml:id="echoid-s2100" xml:space="preserve">deinde 20|. </s> <s xml:id="echoid-s2101" xml:space="preserve">diuiſa per 4. </s> <s xml:id="echoid-s2102" xml:space="preserve">efficient 5. </s> <s xml:id="echoid-s2103" xml:space="preserve">gradus: </s> <s xml:id="echoid-s2104" xml:space="preserve">40||. </s> <s xml:id="echoid-s2105" xml:space="preserve">vero dabunt, 10|. </s> <s xml:id="echoid-s2106" xml:space="preserve">hor. </s> <s xml:id="echoid-s2107" xml:space="preserve">ſic etiam horę 4. </s> <s xml:id="echoid-s2108" xml:space="preserve"><lb/>diuiſæ per 4. </s> <s xml:id="echoid-s2109" xml:space="preserve">efficient, 1. </s> <s xml:id="echoid-s2110" xml:space="preserve">ſexagenam graduum: </s> <s xml:id="echoid-s2111" xml:space="preserve">& </s> <s xml:id="echoid-s2112" xml:space="preserve">patet, quia viciſſim 60. </s> <s xml:id="echoid-s2113" xml:space="preserve">gr. </s> <s xml:id="echoid-s2114" xml:space="preserve">efficiunt horas 4.</s> <s xml:id="echoid-s2115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2116" xml:space="preserve">4 Bis in anno facit Aequinoctium: </s> <s xml:id="echoid-s2117" xml:space="preserve">quod accidit cum Sol eſt in principio Arietis, aut Libræ, vbi ſcilicet <lb/>Eclyptica Aequatorem ſecat: </s> <s xml:id="echoid-s2118" xml:space="preserve">in hiſce enim duobus punctis Sol ob diurnam conuerſionem, Aequatorem <lb/>terit. </s> <s xml:id="echoid-s2119" xml:space="preserve">quod vt rectè intelligas, conſtitue Solem Sphæræ materialis, qui circulo ſecundi motus, affixus eſt, <lb/>ſub altero horum punctorum, vti in principio Arietis; </s> <s xml:id="echoid-s2120" xml:space="preserve">eoque ibi manente, motu diurno circũuolue Sphæ-<lb/>ram: </s> <s xml:id="echoid-s2121" xml:space="preserve">atque interim obſerua viam Solis, eumque videbis Aequatoris iter obire. </s> <s xml:id="echoid-s2122" xml:space="preserve">Quoniam vero Aequator <lb/>ab horizonte bifariam ſecatur, cum vterque ſit circulus maximus, erit ſemper vnus ipſius ſemicirculus ſu-<lb/>pra horizontem, alter infrà: </s> <s xml:id="echoid-s2123" xml:space="preserve">& </s> <s xml:id="echoid-s2124" xml:space="preserve">quia Sol pariter cum Aequatore vniformiter mouetur, fit vt arcus diurnus, <lb/>ſit ſemper æqualis arcui nocturno, ideſt, dies nocti æqualis in vniuerſa terra: </s> <s xml:id="echoid-s2125" xml:space="preserve">excepta Sphæra paralelia, in <lb/>qua æquator non ſecatur ab horizonte, ſed ipſi congruit. </s> <s xml:id="echoid-s2126" xml:space="preserve">idem accidit in principio Libræ.</s> <s xml:id="echoid-s2127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2128" xml:space="preserve">5 Ab Aequatore incipiunt declinationes omnium cæli punctorum, & </s> <s xml:id="echoid-s2129" xml:space="preserve">Stellarum: </s> <s xml:id="echoid-s2130" xml:space="preserve">eſt autem declinatio, <lb/>diſtantia alicuius Stellæ ab Aequatore incipiens, & </s> <s xml:id="echoid-s2131" xml:space="preserve">verſus alterutrum polorum tendens: </s> <s xml:id="echoid-s2132" xml:space="preserve">quæ diſtantia ſu-<lb/>mitur, & </s> <s xml:id="echoid-s2133" xml:space="preserve">menſuratur in circulo maximo tranſeunte per mundi polos, & </s> <s xml:id="echoid-s2134" xml:space="preserve">Stellam propoſitam, eſtque tanta, <lb/>quantus eſt arcus prædicti circuli, inter Aequatorem, & </s> <s xml:id="echoid-s2135" xml:space="preserve">Stellas concluſus. </s> <s xml:id="echoid-s2136" xml:space="preserve">huiuſmodi verò circuli dicuntur <lb/>circuli declinationum, & </s> <s xml:id="echoid-s2137" xml:space="preserve">conincidunt cum aliquo meridiano, ad vitandam tamen confuſionem non ponun-<lb/>tur in Sphæra materiali.</s> <s xml:id="echoid-s2138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2139" xml:space="preserve">6 Sicuti Aequator in Cælo terminus eſt, à quo Aſtronomi declinationes incipiunt, ſic in terra termi-<lb/>nus eſt, à quo Geographi latitudines exordiuntur: </s> <s xml:id="echoid-s2140" xml:space="preserve">quod autem in Cælo eſt declinatio, idem omnino in ter-<lb/>ra eſt latitudo; </s> <s xml:id="echoid-s2141" xml:space="preserve">eſt enim latitudo cuiuſuis loci in terra, diſtantia eius ab Aequatore accepta, & </s> <s xml:id="echoid-s2142" xml:space="preserve">menſurata in <lb/>meridiano illius, ideſt, eſt arcus meridiani ab Aequatore vſq; </s> <s xml:id="echoid-s2143" xml:space="preserve">ad illum locum numeratus. </s> <s xml:id="echoid-s2144" xml:space="preserve">Meridiani verò <lb/>eodem modo ſe habent ad Aequatorem in terra, ſicuti circuli declinationum ad eundem Aequinoctialem <lb/>in Cælo, tranſeunt enim vtrique per polos Aequatoris.</s> <s xml:id="echoid-s2145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2146" xml:space="preserve">Porrò ſciendum eſt apud Geographos ſemper latitudinem regionis eſſe æqualem altitudine polari eiuſ-<lb/>dem, quod adhibita ſuperiori figura ſic oſtenditur. </s> <s xml:id="echoid-s2147" xml:space="preserve">in ea enim arcus A C. </s> <s xml:id="echoid-s2148" xml:space="preserve">æquatur arcui C E. </s> <s xml:id="echoid-s2149" xml:space="preserve">cùm ſint ambo <lb/>quadrantes: </s> <s xml:id="echoid-s2150" xml:space="preserve">præterea arcus B C. </s> <s xml:id="echoid-s2151" xml:space="preserve">æquatur arcui D E. </s> <s xml:id="echoid-s2152" xml:space="preserve">vti ſupra oſtenſum eſt; </s> <s xml:id="echoid-s2153" xml:space="preserve">Ergo ſi hi duo demantur a qua-<lb/>drantibus A C. </s> <s xml:id="echoid-s2154" xml:space="preserve">C E. </s> <s xml:id="echoid-s2155" xml:space="preserve">arcus qui remanent A B. </s> <s xml:id="echoid-s2156" xml:space="preserve">C D. </s> <s xml:id="echoid-s2157" xml:space="preserve">erunt æquales, quia ſi ab æqualibus æqualia demas, quæ <lb/>remanent æqualia ſunt; </s> <s xml:id="echoid-s2158" xml:space="preserve">ſed arcus A B. </s> <s xml:id="echoid-s2159" xml:space="preserve">eſt poli altitudo C D. </s> <s xml:id="echoid-s2160" xml:space="preserve">verò eſt diſtantia Verticis ab Aequatore, ſiue <lb/>loci in terra ab Aequatore terreſtri: </s> <s xml:id="echoid-s2161" xml:space="preserve">ſunt igitur æquales, quod erat demonſtrandũ. </s> <s xml:id="echoid-s2162" xml:space="preserve">Idem in materiali Sphæ-<lb/>ra contemplari poteris; </s> <s xml:id="echoid-s2163" xml:space="preserve">videbis enim ſemper altitudinem poli, eſſe æqualem latitudini prædictæ.</s> <s xml:id="echoid-s2164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2165" xml:space="preserve">7 Iuxta Aequatorem ſumunt Aſtronomi aſcenſiones, deſcenſiones, & </s> <s xml:id="echoid-s2166" xml:space="preserve">cæli mediationes, quę nihil aliud <lb/>ſunt, quam quidam arcus eiuſdem Aequatoris, quibus Aſtronomi menſurant ortum, occaſum, cælique me-<lb/>diationem alicuius arcus Eclipticæ, aut alicuius gradus, vel Stellæ: </s> <s xml:id="echoid-s2167" xml:space="preserve">vt enim dictum eſt, motus Aequatoris <lb/>ob ipſius vniformitatem, & </s> <s xml:id="echoid-s2168" xml:space="preserve">æquabilitatem cæte is lationibus menſurandis idoneus eſt. </s> <s xml:id="echoid-s2169" xml:space="preserve">Aſcenfio alicuius <lb/>arcus Eclypticæ eſt arcus Aequatoris, qui ſimul cum eo cooritur; </s> <s xml:id="echoid-s2170" xml:space="preserve">Deſcenſio verò eſt arcus Aequatoris, qui <lb/>vna cum eodem occidit; </s> <s xml:id="echoid-s2171" xml:space="preserve">Mediatio cæli eſt a rcus pariter Aequatoris qui cum eodem meridianum pertran-<lb/>ſit. </s> <s xml:id="echoid-s2172" xml:space="preserve">At vero aſcenſio alicuius puncti Eclypticæ, vel alicuius Stellæ, ſimiliter eſt arcus Aequatoris a ſectione <lb/>verna, ſeu ab Arietis initio verſus Orientem, ſeu ſecundum ſignorum ordinem, & </s> <s xml:id="echoid-s2173" xml:space="preserve">ſequelam, vſque ad hori-<lb/>zontem computatus, dum punctum illud, vel illa Stella eſt in horizonte, vel oritur. </s> <s xml:id="echoid-s2174" xml:space="preserve">idem proportionaliter <lb/>de cæli mediatione, ac deſcenſione eiuſdem puncti, vel ſtellæ intelligendum eſt. </s> <s xml:id="echoid-s2175" xml:space="preserve">Porrò aſcenſio, & </s> <s xml:id="echoid-s2176" xml:space="preserve">deſcen-<lb/>ſio duplex eſt recta, & </s> <s xml:id="echoid-s2177" xml:space="preserve">obliqua. </s> <s xml:id="echoid-s2178" xml:space="preserve">Recta eſt, quæ ſit apud horizontem rectum, ſeu in Sphæra recta: </s> <s xml:id="echoid-s2179" xml:space="preserve">obliqua, <lb/>quæ in obliquo horizonte, ſeu obliqua Sphæra. </s> <s xml:id="echoid-s2180" xml:space="preserve">Eſt autem aduertendum aſcenſiones, & </s> <s xml:id="echoid-s2181" xml:space="preserve">deſcenſiones re-<lb/>@as æquales eſſe cæli mediationibus; </s> <s xml:id="echoid-s2182" xml:space="preserve">Meridianus enim apud quem perficiuntur mediationes, eſt inſtar re-<lb/>cti horizontis, ideſt, eodem modo ſe habet ad Aequatorem, quo horizon rectus; </s> <s xml:id="echoid-s2183" xml:space="preserve">quia vterq; </s> <s xml:id="echoid-s2184" xml:space="preserve">angulos rectos <lb/>cum Aequatore efficit: </s> <s xml:id="echoid-s2185" xml:space="preserve">imo meridianus omnis coincidit cum aliquo horizonte recto. </s> <s xml:id="echoid-s2186" xml:space="preserve">Hæc vero fuſius ex-<lb/>plicare eſt alterius loci, vbi videlicet agitur de ijs rebus, quarum aſcenſiones, deſcenſiones, mediationes con-<lb/>ſiderantur, vt ſunt Eclyptica, necnon Ortus, & </s> <s xml:id="echoid-s2187" xml:space="preserve">Occaſus ſtellarum.</s> <s xml:id="echoid-s2188" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div43" type="section" level="1" n="26"> <head xml:id="echoid-head28" style="it" xml:space="preserve">De Zodiaco. # Cap. VI.</head> <p> <s xml:id="echoid-s2189" xml:space="preserve">ZOdiacus vox græca eſt: </s> <s xml:id="echoid-s2190" xml:space="preserve">ζωδιακος enim græcè dicitur à nomine ζωδιον, quod animalculum ſignificat. </s> <s xml:id="echoid-s2191" xml:space="preserve">Et <lb/>quoniã in Zodiaco collocata ſunt animalia illa Aries, Taurus, &</s> <s xml:id="echoid-s2192" xml:space="preserve">c. </s> <s xml:id="echoid-s2193" xml:space="preserve">ideo appellatus eſt a græcis ζωδιακος.</s> <s xml:id="echoid-s2194" xml:space="preserve"> <pb o="20" file="0036" n="36" rhead="De Circulis Sphæræ."/> Alatinis autem dicitur ſignifer maximè à Poetis, quod in eo animalia illa, quæ etiã ſigna dicuntur, exiſtant. <lb/></s> <s xml:id="echoid-s2195" xml:space="preserve">nominaturetiam circulus obliquus, quia vt videre eſt in Sphæra materiali, obliquus, ſeu tranſuerſus eſt ad <lb/>alios circulos inuicem paralellos, ideſt, ad Æquatorem, Tropicos, & </s> <s xml:id="echoid-s2196" xml:space="preserve">Polares.</s> <s xml:id="echoid-s2197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2198" xml:space="preserve">Eſt autem Zodiacus circulus maximus, vel potius Zona, aut Armilla quædam latitudinem habens 12. </s> <s xml:id="echoid-s2199" xml:space="preserve">gra-<lb/>duum, & </s> <s xml:id="echoid-s2200" xml:space="preserve">ſecundum nonnullos 14. </s> <s xml:id="echoid-s2201" xml:space="preserve">quem linea Eclyptica bifariam in longum ſecat, ſic dicta ab Eclypſibus, <lb/>quæ aut in ea, aut apud eam fiunt: </s> <s xml:id="echoid-s2202" xml:space="preserve">dicitur etiam à Ptolemæo circulus qui per medium ſignorum eſt. </s> <s xml:id="echoid-s2203" xml:space="preserve">eſt au-<lb/>tem Eclyptica circulus maximus cuius centrum congruit centro mundi, eiuſque poli diſtant a polis mundi <lb/>gr. </s> <s xml:id="echoid-s2204" xml:space="preserve">23. </s> <s xml:id="echoid-s2205" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2206" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s2207" xml:space="preserve">ipſa declinat ab æquatore, ſeu facit angulum cum æquatore hac tempeſtate gr. </s> <s xml:id="echoid-s2208" xml:space="preserve">pariter 23. </s> <s xml:id="echoid-s2209" xml:space="preserve">{1/2}. <lb/></s> <s xml:id="echoid-s2210" xml:space="preserve">hanc autem Eclypticæ, ac Zodiaci obliquitatem primus obſeruauit Anaximander Thaletis ſucceſ@or, anno <lb/>ferè 700. </s> <s xml:id="echoid-s2211" xml:space="preserve">ante humani generis ſalutem, vt cõſtat ex noſtra clarorum Mathematicorum Chronolog@a, quam <lb/>cum @ocis Mathematicis apud Ariſtotelem edidimus. </s> <s xml:id="echoid-s2212" xml:space="preserve">Eclyptica autem propriè eſt via, & </s> <s xml:id="echoid-s2213" xml:space="preserve">orbita Solis, quã <lb/>ipſe proprio motu centroque ſuo perpetuo terit: </s> <s xml:id="echoid-s2214" xml:space="preserve">Quapropter cum Aſtronomi inquirere volunt maximam <lb/>Eclypticæ declinationem, quæ menſuratur in Coluro ſolſtitiorum obſeruant meridianam, ſeu maximam. </s> <s xml:id="echoid-s2215" xml:space="preserve"><lb/>Solis altitudinem ſupra horizontem, circa ſolſtitium æſtiuum per quadrantem noſtrum Aſtronomicè col-<lb/>locatum, ex qua maxima altitudine detrahunt æquatoris altitudinem, quam ſupra inuenimus, & </s> <s xml:id="echoid-s2216" xml:space="preserve">remanet <lb/>maxima Eclypticæ declinatio, quam hoc tempore ponimus eſſe gr. </s> <s xml:id="echoid-s2217" xml:space="preserve">23. </s> <s xml:id="echoid-s2218" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2219" xml:space="preserve">quamuis Tychoni ſit 23. </s> <s xml:id="echoid-s2220" xml:space="preserve">31|.</s> <s xml:id="echoid-s2221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2222" xml:space="preserve">Refert autem Zodiacus viam omnium Planetarum, quam motu proprio obambulant, quo ab Occaſu in<unsure/> <lb/>Ortum ſub ipſo progrediuntur. </s> <s xml:id="echoid-s2223" xml:space="preserve">ſicuti enim ęquator eſt propter Primum motũ, ſeu diurnũ; </s> <s xml:id="echoid-s2224" xml:space="preserve">ita Zodiacus eſt <lb/>propter motum ſecundum, qui eſt proprius Planeta@um. </s> <s xml:id="echoid-s2225" xml:space="preserve">Obſeruatum eſt enim ab Aſtronomis Planetas om-<lb/>nes, Solem, Lunam, & </s> <s xml:id="echoid-s2226" xml:space="preserve">reliquos, non ſolum motu d@urno ab Ortu in Occaſum 24. </s> <s xml:id="echoid-s2227" xml:space="preserve">horis circumuerti; </s> <s xml:id="echoid-s2228" xml:space="preserve">verum <lb/>etiam ſuis proprijs motibus ſub Zodiaco ferri ab Occaſu in Ortum, non tamen directè, leu obliquè, ideſt, per <lb/>viam quandam, quæ æquatorem obliquè ſecat: </s> <s xml:id="echoid-s2229" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s2230" xml:space="preserve">ab eo deflectit, tam in Septentrionem, quam in me-<lb/>ridiem, quam viam Zodiacum appellarunt. </s> <s xml:id="echoid-s2231" xml:space="preserve">Hunc autem motum ſecundum manifeſtius videbis in Luna, <lb/>quàm in alijs, ſi enim eam obſeruaueris ad ſtellas fixas, videbis eam quotidie yeſperi reſpectu earum ad quas <lb/>relata eſt, eſſe magis Orientalem, ideſt, eas præterire verſus Orientem, ipſa vera ad Occaſum remanere.</s> <s xml:id="echoid-s2232" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2233" xml:space="preserve">Idem apparet comparata ad Solem Luna, cum præſertim noua eſt, manifeſtè enim omnes videmus eam <lb/>magis quotidie ab eo verſus Orientem recedere. </s> <s xml:id="echoid-s2234" xml:space="preserve">Neque verò putandum eſt eundem Planetam duobus h<unsure/>i-<lb/>ſce motibus eodem tempore ferri in contrarias partes, hoc enim impoſſibile eſt, ſed ſemper magis Occiden <lb/>tem verſus appropinquat, quia motus diurnus velocior eſt motu eius proprio, & </s> <s xml:id="echoid-s2235" xml:space="preserve">ideo præualet, & </s> <s xml:id="echoid-s2236" xml:space="preserve">ſuperat; <lb/></s> <s xml:id="echoid-s2237" xml:space="preserve">& </s> <s xml:id="echoid-s2238" xml:space="preserve">proinde Planetam ad Occidentem, vel inuitum quaſi rapit: </s> <s xml:id="echoid-s2239" xml:space="preserve">interim tamen minimè Planeta præpeditur, <lb/>quo minus per Zodiacum paululum verſus Orientem, progrediatur. </s> <s xml:id="echoid-s2240" xml:space="preserve">exemplo ſit formica poſita in princi-<lb/>pio Arietis, adeò tardè verſus Orientem incedens, vt vno die gradum vnum tantum abſoluat: </s> <s xml:id="echoid-s2241" xml:space="preserve">quo eodem <lb/>die, motu diurno conuertatur circa totum mundum ſimul cum Zodiaco, & </s> <s xml:id="echoid-s2242" xml:space="preserve">primo illo gradu, quem inte-<lb/>rim inambulabat: </s> <s xml:id="echoid-s2243" xml:space="preserve">certum eſt eam ſemper velocius ad partes Occidentis deferri, quamuis eodem tempore. </s> <s xml:id="echoid-s2244" xml:space="preserve"><lb/>gradum primum Arietis tardè ſcandat. </s> <s xml:id="echoid-s2245" xml:space="preserve">ſed hæc alibi fuſius explicanda ſunt. </s> <s xml:id="echoid-s2246" xml:space="preserve">Quantum autem declinent <lb/>ſingula Eclyuticæ puncta ab æquatore facilè eſt in Sphæra materiali, aut globo aliquo Aſtronomico fa-<lb/>brefacto reperire, in qua Sphæra, vel in quo globo conſtituta ſit@ prius Eclyptica ſecundum maximam. </s> <s xml:id="echoid-s2247" xml:space="preserve"><lb/>eius declinationem, per obſeruationem inuentam, quam noſtra ætatc ponimus eſſe graduum 23. </s> <s xml:id="echoid-s2248" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2249" xml:space="preserve">quæ de-<lb/>clinatio eſt angulus, quem facit cum æquatore, & </s> <s xml:id="echoid-s2250" xml:space="preserve">quem menſurat Colurus ſolſtitiorum; </s> <s xml:id="echoid-s2251" xml:space="preserve">ſi enim per ſingula <lb/>eius puncta, ducantur circuli declinationum, de quibus ſupra dictum eſt, erunt eorum arcus inter dicta pun-<lb/>cta, & </s> <s xml:id="echoid-s2252" xml:space="preserve">Æquinoctialem interpoſiti eorum declinationes ab æquatore. </s> <s xml:id="echoid-s2253" xml:space="preserve">Quam declinationem ſic reperies ex <lb/>materiali Sphæra: </s> <s xml:id="echoid-s2254" xml:space="preserve">applica quoduis Eclypticæ punctum circulo mer@diano, & </s> <s xml:id="echoid-s2255" xml:space="preserve">numera gradus meridiani in-<lb/>ter punctum illud Eclypticæ, & </s> <s xml:id="echoid-s2256" xml:space="preserve">æquatorem interceptos, ij enim erunt quęſita illius puncti declinatio; </s> <s xml:id="echoid-s2257" xml:space="preserve">quia <lb/>hac ratione meridianus fungitur officio omnium circulorum declinationum. </s> <s xml:id="echoid-s2258" xml:space="preserve">eandem declinationem ſic cir <lb/>cino accipies; </s> <s xml:id="echoid-s2259" xml:space="preserve">pone pedem alterum in puncto Eclypticæ quouis, alterum ita dilata vt lineam æquatoris cir-<lb/>cinando attingat: </s> <s xml:id="echoid-s2260" xml:space="preserve">apertura circini applicetur Eclypticæ, aut Æquatori, & </s> <s xml:id="echoid-s2261" xml:space="preserve">apparebit quot graduũ ea, decli-<lb/>natio ſit; </s> <s xml:id="echoid-s2262" xml:space="preserve">Tandem Aſtronomi vt expeditè has declinationes reperiant, condidere ſibi Tabellam ſequentem.</s> <s xml:id="echoid-s2263" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div44" type="section" level="1" n="27"> <head xml:id="echoid-head29" style="it" xml:space="preserve">Vſus, & declaratio Tabulæ ſequentis.</head> <p> <s xml:id="echoid-s2264" xml:space="preserve">TAbula continet columnas quinque, in prima ſunt gr. </s> <s xml:id="echoid-s2265" xml:space="preserve">30. </s> <s xml:id="echoid-s2266" xml:space="preserve">inſeruientes ſex ſignis ſuperioribus. </s> <s xml:id="echoid-s2267" xml:space="preserve">In ſecunda <lb/>ſunt gradus, & </s> <s xml:id="echoid-s2268" xml:space="preserve">min. </s> <s xml:id="echoid-s2269" xml:space="preserve">declinationum, quæ debentur gradibus primæ columnæ: </s> <s xml:id="echoid-s2270" xml:space="preserve">hæ autem declinationes <lb/>ſupra ſe habent duo ſigna ♈. </s> <s xml:id="echoid-s2271" xml:space="preserve">& </s> <s xml:id="echoid-s2272" xml:space="preserve">♎. </s> <s xml:id="echoid-s2273" xml:space="preserve">quia eodem modo hæc duo ſigna declinant ab Æquatore, vt in Sphæra <lb/>materiali patet. </s> <s xml:id="echoid-s2274" xml:space="preserve">habent etiam infra alia duo ſigna ♓. </s> <s xml:id="echoid-s2275" xml:space="preserve">& </s> <s xml:id="echoid-s2276" xml:space="preserve">♍. </s> <s xml:id="echoid-s2277" xml:space="preserve">quia hæc duo habenteaſdem cum ſuperioribus <lb/>declinationes, quamuis inuerſo ordine. </s> <s xml:id="echoid-s2278" xml:space="preserve">Tertia, & </s> <s xml:id="echoid-s2279" xml:space="preserve">quarta columna, ex modo dictis ſatis intelligi poſſunt. <lb/></s> <s xml:id="echoid-s2280" xml:space="preserve">Quinta columna continet gr. </s> <s xml:id="echoid-s2281" xml:space="preserve">30. </s> <s xml:id="echoid-s2282" xml:space="preserve">inferiorum ſex ſignorum, qui gradus inuerſo ordine, ſcribuntur, quia vt <lb/>dixi, ſex ſigna inferiora habent eaſdem declinationes cum ſuperioribus, ſed ordine inuerſo, vt in Sphæra <lb/>videre eſt.</s> <s xml:id="echoid-s2283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2284" xml:space="preserve">Cum igitur ſcire libuerit declinationem alicuius gradus Eclypticæ, ſi eius ſignum fuerit ſuperius, accipe <lb/>gradum oblatum in prima columna, & </s> <s xml:id="echoid-s2285" xml:space="preserve">è regione eius dextrorſum procedendo ſub ſigno eius, accipe nume-<lb/>rum graduum, & </s> <s xml:id="echoid-s2286" xml:space="preserve">minutorum, quæ declinationem quæſitam conficiunt, v. </s> <s xml:id="echoid-s2287" xml:space="preserve">g. </s> <s xml:id="echoid-s2288" xml:space="preserve">declinatio gr. </s> <s xml:id="echoid-s2289" xml:space="preserve">14. </s> <s xml:id="echoid-s2290" xml:space="preserve">♉. </s> <s xml:id="echoid-s2291" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s2292" xml:space="preserve">16. <lb/></s> <s xml:id="echoid-s2293" xml:space="preserve">min. </s> <s xml:id="echoid-s2294" xml:space="preserve">6. </s> <s xml:id="echoid-s2295" xml:space="preserve">ſi vero gradus, cuius declinationem quæris, pertineat ad vnum ex ſignis inferioribus, eum accipe in <pb o="21" file="0037" n="37" rhead="Liber Primus."/> @olumna quinta, & </s> <s xml:id="echoid-s2296" xml:space="preserve">è regione eius ſiniſtrorſum procedendo vſque ad columnam ſigni illius, accipe nume-<lb/>rum ibi ſcriptum, v. </s> <s xml:id="echoid-s2297" xml:space="preserve">g. </s> <s xml:id="echoid-s2298" xml:space="preserve">declinatio gr. </s> <s xml:id="echoid-s2299" xml:space="preserve">4. </s> <s xml:id="echoid-s2300" xml:space="preserve">♋. </s> <s xml:id="echoid-s2301" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s2302" xml:space="preserve">23. </s> <s xml:id="echoid-s2303" xml:space="preserve">28|. </s> <s xml:id="echoid-s2304" xml:space="preserve">quæ communis cſt etiam 4. </s> <s xml:id="echoid-s2305" xml:space="preserve">gradui ♑. </s> <s xml:id="echoid-s2306" xml:space="preserve">Hinc co-<lb/>gnito gradu, in quo Sol verſatur, facilè promiſio modo, Solis declinationem cognoſcemus. </s> <s xml:id="echoid-s2307" xml:space="preserve">ſi autem gra-<lb/>dibus oblatis adhæſerint aliquot minuta, debes pro minutis illius accipere declinationem tanto maiorem, <lb/>vel minorem, quantum proportio exegerit: </s> <s xml:id="echoid-s2308" xml:space="preserve">nam ſi declinationes creſcant, vt fit in 6. </s> <s xml:id="echoid-s2309" xml:space="preserve">ſignis ſuperioribus <lb/>Tabellæ, acccipitur ma@or; </s> <s xml:id="echoid-s2310" xml:space="preserve">ſi verò decreſcant, vt in 6. </s> <s xml:id="echoid-s2311" xml:space="preserve">ſignis inferioribus Tab. </s> <s xml:id="echoid-s2312" xml:space="preserve">accipitur minor.</s> <s xml:id="echoid-s2313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div45" type="section" level="1" n="28"> <head xml:id="echoid-head30" style="it" xml:space="preserve">Tabula declinationem omnium Eclypticæ graduum, <lb/>& conſequenter Solis.</head> <note position="right" xml:space="preserve"> <lb/># ♈ # ♎ # ♉ # ♏ # ♊ # ♐ <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/>0 # 0 # 0 # 11 # 31 # 20 # 13 # 30 <lb/>1 # 0 # 24 # 11 # 52 # 20 # 26 # 29 <lb/>2 # 0 # 48 # 12 # 13 # 20 # 38 # 28 <lb/>3 # 3 # 12 # 12 # 33 # 20 # 50 # 27 <lb/>4 # 3 # 36 # 12 # 54 # 21 # 1 # 26 <lb/>5 # 3 # 58 # 13 # 14 # 21 # 12 # 25 <lb/>6 # 2 # 23 # 13 # 34 # 21 # 23 # 24 <lb/>7 # 2 # 47 # 13 # 54 # 21 # 33 # 23 <lb/>8 # 3 # 11 # 14 # 14 # 21 # 43 # 22 <lb/>9 # 3 # 35 # 14 # 33 # 21 # 53 # 21 <lb/>10 # 3 # 58 # 14 # 52 # 22 # 2 # 20 <lb/>11 # 4 # 0 # 15 # 11 # 22 # 10 # 19 <lb/>12 # 4 # 46 # 15 # 29 # 22 # 19 # 18 <lb/>13 # 5 # 0 # 15 # 48 # 22 # 26 # 17 <lb/>14 # 5 # 32 # 16 # 6 # 22 # 34 # 16 <lb/>15 # 5 # 56 # 16 # 24 # 22 # 41 # 15 <lb/>16 # 6 # 10 # 16 # 41 # 22 # 47 # 14 <lb/>17 # 6 # 42 # 16 # 58 # 22 # 53 # 13 <lb/>18 # 7 # 5 # 17 # 16 # 22 # 59 # 12 <lb/>19 # 7 # 28 # 17 # 32 # 22 # 4 # 11 <lb/>20 # 7 # 51 # 17 # 48 # 23 # 9 # 10 <lb/>21 # 8 # 13 # 18 # 4 # 23 # 13 # 9 <lb/>22 # 8 # 36 # 18 # 18 # 23 # 17 # 8 <lb/>23 # 8 # 58 # 18 # 35 # 23 # 20 # 7 <lb/>24 # 9 # 21 # 18 # 50 # 23 # 23 # 6 <lb/>25 # 9 # 43 # 19 # 5 # 23 # 26 # 5 <lb/>26 # 10 # 5 # 19 # 19 # 23 # 28 # 4 <lb/>27 # 10 # 26 # 19 # 33 # 23 # 29 # 3 <lb/>28 # 10 # 48 # 19 # 47 # 23 # 31 # 2 <lb/>29 # 11 # 9 # 20 # 0 # 23 # 31 # 1 <lb/>30 # 11 # 31 # 20 # # 13 # 23 # 31 # 0 <lb/># ♓ # ♍ # ♒ # ♌ # ♑ # ♋ <lb/></note> <pb o="22" file="0038" n="38" rhead="De Circulis Sphæræ."/> <p> <s xml:id="echoid-s2314" xml:space="preserve">Diuiditur primo Zodiacus ab æquatore in duos ſemicirculos, vnum Borealem in quo ſunt ſex ſigna Bo-<lb/>realia: </s> <s xml:id="echoid-s2315" xml:space="preserve">& </s> <s xml:id="echoid-s2316" xml:space="preserve">alterum Auſtralem in quo ſunt ſex ſigna Auſtralia.</s> <s xml:id="echoid-s2317" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2318" xml:space="preserve">Diuiditur etiam à Coluris in quatuor quadrantes, quorum primus incipit à principio Arietis, eſtq; </s> <s xml:id="echoid-s2319" xml:space="preserve">qua-<lb/>drans Veris: </s> <s xml:id="echoid-s2320" xml:space="preserve">Secundus incipit cum Cancro, eſtque Æſtiuus. </s> <s xml:id="echoid-s2321" xml:space="preserve">Tertio ab initio Libræ, qui Autumnai<unsure/>is eſt: <lb/></s> <s xml:id="echoid-s2322" xml:space="preserve">Quartus a<unsure/> Caprico@no, hyemique deputatur, dicunturque initia horum quadrantum quatuor puncta Car-<lb/>dinalia.</s> <s xml:id="echoid-s2323" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2324" xml:space="preserve">Diuiditur 3. </s> <s xml:id="echoid-s2325" xml:space="preserve">in 6. </s> <s xml:id="echoid-s2326" xml:space="preserve">ſigna phyſica: </s> <s xml:id="echoid-s2327" xml:space="preserve">ſignum autem phyſicum eſt ſexta pars Zodiaci; </s> <s xml:id="echoid-s2328" xml:space="preserve">& </s> <s xml:id="echoid-s2329" xml:space="preserve">dicitur phyſicum, ſeu <lb/>naturale, quod naturaliter, ideſt, ſine vllo artificio circulus omnes diuidatur in partes, 6. </s> <s xml:id="echoid-s2330" xml:space="preserve">eadem nimirum <lb/>circini apertura, qua ipſe circulus deſcriptus fuerit.</s> <s xml:id="echoid-s2331" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2332" xml:space="preserve">Diuiditur 4. </s> <s xml:id="echoid-s2333" xml:space="preserve">in 12. </s> <s xml:id="echoid-s2334" xml:space="preserve">ſigna communia, quorum ſingula continent gr. </s> <s xml:id="echoid-s2335" xml:space="preserve">30. </s> <s xml:id="echoid-s2336" xml:space="preserve">quare ſignum vnum ex his, erit in <lb/>primo mob@@i ſuperficies quadrangula longa gr. </s> <s xml:id="echoid-s2337" xml:space="preserve">30. </s> <s xml:id="echoid-s2338" xml:space="preserve">lata ve ò 12. </s> <s xml:id="echoid-s2339" xml:space="preserve">hanc porro diuiſionem in 12. </s> <s xml:id="echoid-s2340" xml:space="preserve">ſigna, primus <lb/>excogitauit Cleoſtratus: </s> <s xml:id="echoid-s2341" xml:space="preserve">anno ante Chriſti natiuitatem fe@è 700. </s> <s xml:id="echoid-s2342" xml:space="preserve">vt patet ex noſtra c@arorum Mathemati-<lb/>corum Chronologia. </s> <s xml:id="echoid-s2343" xml:space="preserve">Ordo autem horum ſignorum eſt, vt initium ſuman@ à communi ſectione æquatoris, <lb/>Coluri Æquinoctiorum, & </s> <s xml:id="echoid-s2344" xml:space="preserve">ipſius Eclyp@icæ procedendo Orientem verſus, ita vt primum ſit Aries, ſecun-<lb/>dum Taurus, tertium Gemini, & </s> <s xml:id="echoid-s2345" xml:space="preserve">ſic deinceps: </s> <s xml:id="echoid-s2346" xml:space="preserve">qui proceſius dicitur ſucceſſio, & </s> <s xml:id="echoid-s2347" xml:space="preserve">conſequentia ſignorum; </s> <s xml:id="echoid-s2348" xml:space="preserve">cui <lb/>contrarius proceſſus dicitur præcedentia ſignorum. </s> <s xml:id="echoid-s2349" xml:space="preserve">merito autem Aſtronomi inde ſumpſerunt initium, <lb/>quia Sole illuc appetente, Ver incipit, quæ prima anni veluti iuuentus eſt, quæque plantas omnes, atque <lb/>animalia omnia quaſi rediuiua iterum reſtaurat. </s> <s xml:id="echoid-s2350" xml:space="preserve">ab hoc etiam tempore omnes ferè nationes anni exordium <lb/>ſumpſerunt; </s> <s xml:id="echoid-s2351" xml:space="preserve">atque ab eodem mundiipſius ortum, atque creationem extitiſſe, complures S S. </s> <s xml:id="echoid-s2352" xml:space="preserve">Patrum exi-<lb/>ſtimarunt.</s> <s xml:id="echoid-s2353" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2354" xml:space="preserve">Diuiditur 5. </s> <s xml:id="echoid-s2355" xml:space="preserve">à Coluro ſolſtitiorum in duos ſemicirculos, quorum alter, qui à Capricorno, vſque ad Can-<lb/>crum pertinet dicitur aſcendens, quia in noſtra Sphæra obliqua dum Planetæ eum motu proprio obambu-<lb/>lant, quotidie magis ad noſtrum verticem accedunt, magiſq; </s> <s xml:id="echoid-s2356" xml:space="preserve">ſupra horizontem elati incedunt, ſeu diurnas <lb/>reuolutiones, ſeu ſpiras quotidie vertici noſtro proximiores deſcribunt. </s> <s xml:id="echoid-s2357" xml:space="preserve">alter verò qui à<unsure/> Cancro, vſque ad <lb/>Capricornum reuertitur, ob contrarias rationes dicitur deſcendens.</s> <s xml:id="echoid-s2358" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2359" xml:space="preserve">Porrò difficile eſt ipſius in mundo poſitionem veram concipere, nullam enim certam habet ſituationem, <lb/>non enim vt nonnulli mobiles circu@@ in eodem ſemper loco gyratur, ſed ob diurnam conuerſionem perpe-<lb/>tuo locum mutat, atque tranſuerſim, ſuper alienos polos videlicet æquatoris, torquetur. </s> <s xml:id="echoid-s2360" xml:space="preserve">quem motum de-<lb/>bes diligenter in Sphæra materiali contemplari. </s> <s xml:id="echoid-s2361" xml:space="preserve">hanc tam@n ipſius ſucceſſiuam, & </s> <s xml:id="echoid-s2362" xml:space="preserve">variam ſituationem, ſic <lb/>poſſumus interdiu reperire: </s> <s xml:id="echoid-s2363" xml:space="preserve">collocetur Sphæra Aſtronomicè vt in meridiano docui, in loco tamen à<unsure/> Sole <lb/>colluſtrato: </s> <s xml:id="echoid-s2364" xml:space="preserve">poſtea ſi Sol eſt in Zodiaci ſemicirculo aſcendente, motu diurno moueatur pars illa Sphæræ, <lb/>quam ſupra primum mobile appellauimus, ita vt prædictus ſemicirculus Soli obuertatur, ac diligenter huc <lb/>illuc verſetur, donec vmbra ipſius præcisè obumbret alterum ei oppoſitum ſemicirculum; </s> <s xml:id="echoid-s2365" xml:space="preserve">ſi vero fuerit Sol <lb/>in ſemicirculo deſcendente, idem proportionaliter faciendum eſt, quo facto inuenta erit illa Zodiaci poſi-<lb/>tio inſtantanea: </s> <s xml:id="echoid-s2366" xml:space="preserve">Zodiacus enim Cæli, Zodiaco materiali exactè reſpond bit, vel hic ſuo ſitu illum repręſen-<lb/>tabit. </s> <s xml:id="echoid-s2367" xml:space="preserve">Noctu verò id difficilius eſt: </s> <s xml:id="echoid-s2368" xml:space="preserve">ſi tamen quis conſtellationem Zodiaci quampiam in Cęlo cognoſcit, ei <lb/>ita obuertat ſignum, quod illi cognomen eſt in Sphæra materiali, vt materiale ſit aliquanto occidentalius; <lb/></s> <s xml:id="echoid-s2369" xml:space="preserve">ſic enim aliquo modo Zodiacus materialis cæleſtem t@bi repræſentabit. </s> <s xml:id="echoid-s2370" xml:space="preserve">cur autem ſigna Sphæræ materialis <lb/>debeant eſſe occidentaliora cæleſtibus dicetur ſuo loco de ſtellis.</s> <s xml:id="echoid-s2371" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2372" xml:space="preserve">Zodiaci autem, & </s> <s xml:id="echoid-s2373" xml:space="preserve">Eclypticæ munia hæc ſunt. </s> <s xml:id="echoid-s2374" xml:space="preserve">Primum eſt regula, & </s> <s xml:id="echoid-s2375" xml:space="preserve">menſura motus ſecundi, ideſt, mo-<lb/>tuum Planetarum, de quo dudum diximus, in Zodiaco enim computamus motus proprios ſingulorum Pla-<lb/>netarum, & </s> <s xml:id="echoid-s2376" xml:space="preserve">Stellarum etiam fixarum, quoniam ſecundum eius longitudinem, & </s> <s xml:id="echoid-s2377" xml:space="preserve">ſecundum ſignorum con-<lb/>ſequentiam in eo progrediuntur; </s> <s xml:id="echoid-s2378" xml:space="preserve">tantum enim dicimus Planetam profeciſſe, quantũ ab initio Arietis, quod <lb/>eſt Zodiaci initium, rece@@erit ſecundum ſignorum ordinem. </s> <s xml:id="echoid-s2379" xml:space="preserve">ſicuti æquator menſurat diurnum, & </s> <s xml:id="echoid-s2380" xml:space="preserve">primum <lb/>motum, ſic Zodiacus metitur Planetarum proprium, & </s> <s xml:id="echoid-s2381" xml:space="preserve">ſecundum.</s> <s xml:id="echoid-s2382" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2383" xml:space="preserve">2 Ex prædicto officio oritur ſecundum, quo Aſtronomi longitudinem ſyderum determinant. </s> <s xml:id="echoid-s2384" xml:space="preserve">Eſt enim <lb/>longitudo ſyderis arcus Eclypticæ ab initio Arietis inchoatus, & </s> <s xml:id="echoid-s2385" xml:space="preserve">ſecundum ſignorum ſequelam computa-<lb/>tus, vſq; </s> <s xml:id="echoid-s2386" xml:space="preserve">ad circulum maximum, qui per polos Eclypticæ, & </s> <s xml:id="echoid-s2387" xml:space="preserve">propoſitam ſtellam pertranſit, v.</s> <s xml:id="echoid-s2388" xml:space="preserve">g. </s> <s xml:id="echoid-s2389" xml:space="preserve">Stellæ quæ <lb/>ſunt in Coluro ſolſtitiorum, habebunt longitudinem 90. </s> <s xml:id="echoid-s2390" xml:space="preserve">graduum, quia hic Colurus tranſit per polos Ecly-<lb/>pticæ, & </s> <s xml:id="echoid-s2391" xml:space="preserve">Stellas, Planetaſuè in ipſo ex@@ten@es, & </s> <s xml:id="echoid-s2392" xml:space="preserve">di@@at a @rincipio Zodiaci gr. </s> <s xml:id="echoid-s2393" xml:space="preserve">90. </s> <s xml:id="echoid-s2394" xml:space="preserve">dicitur autem hæc diſtan-<lb/>tia longitudo, quia ſumitur penes Zodiaci longitudinem, & </s> <s xml:id="echoid-s2395" xml:space="preserve">circuli illi max@mi, qui eam terminant, dicũtur <lb/>circuli @atitud@num, quia præcipuum eorum munus eſt exhibere ſyderum latitudines, nam</s> </p> <p> <s xml:id="echoid-s2396" xml:space="preserve">3 Eclyptica eſt terminus a quo latitudines ſyderum computantur. </s> <s xml:id="echoid-s2397" xml:space="preserve">eſt autem latitudo ſtellarum diſtan-<lb/>tia ipſarum ab Eclyptica verſus alterutrum poloru<unsure/>m ipſius, accepta in circulo latitudinis, de quo antea di-<lb/>ctum eſt. </s> <s xml:id="echoid-s2398" xml:space="preserve">vel eſt arcus circuli maximi per polos Eclypticę, & </s> <s xml:id="echoid-s2399" xml:space="preserve">ſtellam incedentis inter Eclypticam, & </s> <s xml:id="echoid-s2400" xml:space="preserve">ſtellam <lb/>interiectus. </s> <s xml:id="echoid-s2401" xml:space="preserve">dicta eſt autem latitudo, quia ſumitur ſecundum Zodiaci latitudinem, & </s> <s xml:id="echoid-s2402" xml:space="preserve">eſt duplex Borealis, & </s> <s xml:id="echoid-s2403" xml:space="preserve"><lb/>Auſtralis, nam</s> </p> <p> <s xml:id="echoid-s2404" xml:space="preserve">4 Eclyptica diuidit totum mundum in duo hemiſphæria Boreale, & </s> <s xml:id="echoid-s2405" xml:space="preserve">Auſtrale, quemadmodum etiam <lb/>æquator. </s> <s xml:id="echoid-s2406" xml:space="preserve">vnde fit vt eadem puncta,<unsure/> quæ inter Ec@ypticam, & </s> <s xml:id="echoid-s2407" xml:space="preserve">æquatorem exiſtunt, ſint reſpectu Eclypticæ <lb/>Auſtralia, reſpectu verò æquatoris Borealia, vel è contra.</s> <s xml:id="echoid-s2408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2409" xml:space="preserve">5 In Eclyptica a@@ignantur omnium ſtellarum loca, etiamſi valdè diſtent ab ea; </s> <s xml:id="echoid-s2410" xml:space="preserve">nam quæuis ſtella dici-<lb/>@ur eſſe in eo Eclypticæ gradu, per quem circulis latitud nis eiuſdem ſteliæ incedit: </s> <s xml:id="echoid-s2411" xml:space="preserve">v. </s> <s xml:id="echoid-s2412" xml:space="preserve">g. </s> <s xml:id="echoid-s2413" xml:space="preserve">ſtellæ omnes, quæ <lb/>@unt in Coluro ſolſtitiorum dicuntur eſſe in primo gradu Cancri, dummodo ſia<unsure/>t in eo Coluri ſemicirculo, <pb o="23" file="0039" n="39" rhead="Liber Primus."/> qui per initium Cancri tranſit, & </s> <s xml:id="echoid-s2414" xml:space="preserve">terminatur a polis, ſeu deſinit ad Eclypticæ polos. </s> <s xml:id="echoid-s2415" xml:space="preserve">aliæ verò, quæ ſunt in <lb/>altera medietate, erunt in prima Capricorni parte. </s> <s xml:id="echoid-s2416" xml:space="preserve">Similiter ſydera omnia dicuntur eſſe in eo Zodiaci ſi-<lb/>gno, quamuis non ſint intra ipſum, nec ſub ipſo, per quod circulus quiſpiam latitudinis tranſiens, etiam per <lb/>ſydus, illud tranſeat.</s> <s xml:id="echoid-s2417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2418" xml:space="preserve">6 Sub Eclyptica, vel ſaltem propè eam fiunt Eclypſes luminarium Lunæ, ac Solis, vnde Eclyptica de-<lb/>nominata eſt.</s> <s xml:id="echoid-s2419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2420" xml:space="preserve">7 Exhibet nobis Eclyptica puncta quatuor Cardinalia, duo videlicet Aequinoctia, vnum verum in prin <lb/>cipio Arietis, alterum Autumnale in principio Libræ: </s> <s xml:id="echoid-s2421" xml:space="preserve">& </s> <s xml:id="echoid-s2422" xml:space="preserve">duo ſolſtitia, vnum æſtiuum in principio Cancri, <lb/>alterum hyemale, vel brumale in principio Capr@corni, de quibus ſuo loco agetur.</s> <s xml:id="echoid-s2423" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2424" xml:space="preserve">8 Quoniam verò Zodiacus irregulariter oritur, occidit, & </s> <s xml:id="echoid-s2425" xml:space="preserve">cælum mediat, ideſt, non vniformiter, nec <lb/>æquabiliter vti æquator; </s> <s xml:id="echoid-s2426" xml:space="preserve">ideo Aſtronomi menſurant ortus, & </s> <s xml:id="echoid-s2427" xml:space="preserve">occaſus partium, vel arcuum Zodiaci, vel po-<lb/>tius Eclypticæ per partes, aut arcus æquatoris, quæ illis cooriuntur, occidunt, ac cælum mediant, vel quæ il-<lb/>lis coaſcendunt, aut condeſcendunt, quos æquatoris arcus propterea appellant aſcenſiones, deſcenſiones, ac <lb/>de quibus ſuo loco fuſius agemus.</s> <s xml:id="echoid-s2428" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2429" xml:space="preserve">9 Zodiacus noſter oſtendit in quo gradu Sol quotidie verſetur, ſi dies oblata quota ſit non ignoretur. <lb/></s> <s xml:id="echoid-s2430" xml:space="preserve">Nam cum in noſtro Zodiaco poſuerimus dies menſium correſpondentes gradibus ſignorum, ſi propoſitum <lb/>diem in Zodiaco reperias, è regione illius erit gradus ille, quem Sol tunc occupat.</s> <s xml:id="echoid-s2431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2432" xml:space="preserve">Anno tamen Biſſextili, quo Februarius habet dies 29. </s> <s xml:id="echoid-s2433" xml:space="preserve">pro die 29. </s> <s xml:id="echoid-s2434" xml:space="preserve">accipe primũ diem Martij, ſicque dein-<lb/>ceps vſq; </s> <s xml:id="echoid-s2435" xml:space="preserve">ad finem anni ſemper pro oblato die accipiendus eſt ſequens: </s> <s xml:id="echoid-s2436" xml:space="preserve">quia dies 29. </s> <s xml:id="echoid-s2437" xml:space="preserve">non eſt in Zodiaco de-<lb/>ſcriptus, idcirca tunc dies propoſita 29. </s> <s xml:id="echoid-s2438" xml:space="preserve">tranſit in locum primæ Martij, & </s> <s xml:id="echoid-s2439" xml:space="preserve">ſic etiam reliqui dies protrudũtur <lb/>ſupra ſequentes.</s> <s xml:id="echoid-s2440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2441" xml:space="preserve">Aliter ex materiali Sphæra: </s> <s xml:id="echoid-s2442" xml:space="preserve">ſtatuè Sphæram Aſtronomicè, deinde meridianam Solis altitudinem obſer-<lb/>ua, vti ſupra docui: </s> <s xml:id="echoid-s2443" xml:space="preserve">poſtea reuoluè primum mobile, notando quinam gradus Eclypticæ tranſeant ſub gradu <lb/>illo meridiani, qui terminus eſt ſolaris altitudinis depręhenſæ: </s> <s xml:id="echoid-s2444" xml:space="preserve">is enim erit ille gradus, quem tunc Sol occu-<lb/>pat. </s> <s xml:id="echoid-s2445" xml:space="preserve">quia verò bini gradus illac tranſibunt, illum accipies, qui pręſenti tempeſtati congruet. </s> <s xml:id="echoid-s2446" xml:space="preserve">Exactius tamen <lb/>idem aſſequeris ex calculo Solis. </s> <s xml:id="echoid-s2447" xml:space="preserve">de quo ſuo loco dicetur.</s> <s xml:id="echoid-s2448" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2449" xml:space="preserve">10 Vtuntur Aſtronomi breuitatis cauſa Characteribus ſignorum Zodiaci loco nominum, quod etiam <lb/>nos deinceps factitabimus. </s> <s xml:id="echoid-s2450" xml:space="preserve">♈, ſunt cornua Arietis. </s> <s xml:id="echoid-s2451" xml:space="preserve">♉, caput Tauri cornutum. </s> <s xml:id="echoid-s2452" xml:space="preserve">♊. </s> <s xml:id="echoid-s2453" xml:space="preserve">ſignificat coniunctos Ge-<lb/>minos: </s> <s xml:id="echoid-s2454" xml:space="preserve">deberent ſcribi ſic, I<unsure/>I<unsure/>. </s> <s xml:id="echoid-s2455" xml:space="preserve">♋, ſunt duo oculi cum cornibus Cancri: </s> <s xml:id="echoid-s2456" xml:space="preserve">♌, cauda Leonis. </s> <s xml:id="echoid-s2457" xml:space="preserve">♍, pro ariſta Vir-<lb/>ginis, ſed deberet eſſe productior. </s> <s xml:id="echoid-s2458" xml:space="preserve">♎, imago alterius lancis. </s> <s xml:id="echoid-s2459" xml:space="preserve">♏, refert ipſum Scorpionem. </s> <s xml:id="echoid-s2460" xml:space="preserve">♐, ſagittæ Sagit-<lb/>tarij imago. </s> <s xml:id="echoid-s2461" xml:space="preserve">♑. </s> <s xml:id="echoid-s2462" xml:space="preserve">Capricornum ipſum aliquo modo repræſentat. </s> <s xml:id="echoid-s2463" xml:space="preserve">♒, flumini aſſimilatur. </s> <s xml:id="echoid-s2464" xml:space="preserve">♓, Piſces ſimul alli-<lb/>gatos figurat memoriæ autem cauſa hoc diſticho ſigna 12. </s> <s xml:id="echoid-s2465" xml:space="preserve">compræhenduntur.</s> <s xml:id="echoid-s2466" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s2467" xml:space="preserve">Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo, <lb/>Libraq́<unsure/>ue, Scorpius, Arcitenens, Caper, Amphora, Piſces.</s> <s xml:id="echoid-s2468" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div46" type="section" level="1" n="29"> <head xml:id="echoid-head31" style="it" xml:space="preserve">De duobus Coluris. Cap. VII.</head> <p> <s xml:id="echoid-s2469" xml:space="preserve">QVod ad eorum etymon attinet, audiendus eſt Macrobius lib. </s> <s xml:id="echoid-s2470" xml:space="preserve">1. </s> <s xml:id="echoid-s2471" xml:space="preserve">de ſomnio Scipionis, præter hos inquit, <lb/>alij duo ſunt Coluri, quibus nomen dedit imperfecta conuerſio. </s> <s xml:id="echoid-s2472" xml:space="preserve">quæ ſic explico, Kολ{ομ}ρος græca vox eſt, <lb/>imperfectum ſignificans: </s> <s xml:id="echoid-s2473" xml:space="preserve">quia igitur in noſtra obliqua mundi Sphæra, in qua primi Aſtronomiæ <lb/>cultores, qui nomina rebus Aſtronomicis indiderunt, imperfectè hoſcè duos circulos apparere videbant, <lb/>eos ideo Coluros quaſi imperfectos denominarunt. </s> <s xml:id="echoid-s2474" xml:space="preserve">quod autem imperfectè appareant in obliqua Sphæra, <lb/>facilè in meteriali Sphæra videre eſt; </s> <s xml:id="echoid-s2475" xml:space="preserve">eleuato enim noſtro Arctico polo vtcumque, v. </s> <s xml:id="echoid-s2476" xml:space="preserve">g. </s> <s xml:id="echoid-s2477" xml:space="preserve">gradibus 23. </s> <s xml:id="echoid-s2478" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2479" xml:space="preserve">ita <lb/>ſcilicet vt vterque polarium circulorum horizontem contingat, vnus ſuperius, alter inferius, ſi poſtea mo-<lb/>tu diurno Sphæra moueatur, illico apparebit@illam Colurorum partem, quæ intra polarem circulum An-<lb/>tarcticum continetur, nunquam ſupra noſtrum horizontem eleuari; </s> <s xml:id="echoid-s2480" xml:space="preserve">idem in quauis Sphæræ obliquitate vi-<lb/>debis accidere, præterquam in Sphæra recta, vbi toti, ſucceſſiuè tamen, ſupra horizontem aſcendunt.</s> <s xml:id="echoid-s2481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2482" xml:space="preserve">Sunt autem coluri dno circuli maximi mobiles, ac ſingulares, tranſeuntes ambo per mundi polos, ibique <lb/>ſe mutuo ortogonaliter, ſeu ad angulos rectos ſecantes, tianſeuntes etiam per quatuor puncta Zodiaci Car-<lb/>dinalia: </s> <s xml:id="echoid-s2483" xml:space="preserve">vnde ille qui tranſit per puncta ſolſtitial<unsure/>ia dicitur colurus ſolſtitiorum, in quo etiam ſunt duo poli <lb/>Eclypticæ; </s> <s xml:id="echoid-s2484" xml:space="preserve">alter dicitur colurus Æquinoctiorum, quod per puncta duo Æquinoctialia incedat. </s> <s xml:id="echoid-s2485" xml:space="preserve">quid verò <lb/>ſolſtitium, quid Æquinoctium, dicetur ſuo loco.</s> <s xml:id="echoid-s2486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2487" xml:space="preserve">Inuentio autem ſituationis eorum in mundo, eodem modo, & </s> <s xml:id="echoid-s2488" xml:space="preserve">eadem opera qua, & </s> <s xml:id="echoid-s2489" xml:space="preserve">Zodiaci ineunda eſt: <lb/></s> <s xml:id="echoid-s2490" xml:space="preserve">motu, enim primi mobilis perpetuo locum, vna cum Zodiaco variant; </s> <s xml:id="echoid-s2491" xml:space="preserve">quapropter Sphæra Aſtronomicè <lb/>collocata in eadem conſtitutione, qua Zodiacum demoſtrat, etiam coluros per quatuor eius puncta Cardi-<lb/>nalia incedentes, rectè in cælo nobis repræſentare poterit; </s> <s xml:id="echoid-s2492" xml:space="preserve">ac proinde eos recte concipere poterimus.</s> <s xml:id="echoid-s2493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2494" xml:space="preserve">Colurorum officia ſunt. </s> <s xml:id="echoid-s2495" xml:space="preserve">Primum; </s> <s xml:id="echoid-s2496" xml:space="preserve">Vſus eorum materialis mihi magis videtur quam, vt aiunt formalis: </s> <s xml:id="echoid-s2497" xml:space="preserve">vi-<lb/>dentur enim in materiali Sphæra potius poni, vt cæteros circulos mobiles ſuſtineant, quam vt in cælo cir-<lb/>culos vllos repręſentent. </s> <s xml:id="echoid-s2498" xml:space="preserve">poſſumus tamen aptè dicere eos fungi officio primi mobilis, in eo enim, vt alias <lb/>diximus omnes circulos concipiendos eſſe Aſtronomi præcipiunt. </s> <s xml:id="echoid-s2499" xml:space="preserve">Cùm igitur videamus cæteros circulos <lb/>Coluris incumbere, ijſque inniti, non ſecus, ac in primo mobili, idcirco eos illud referre non eſt inconue-<lb/>niens aſſerere.</s> <s xml:id="echoid-s2500" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2501" xml:space="preserve">2 Oſtendunt illa@ quatuor puncta Zodiaci Cardinalia.</s> <s xml:id="echoid-s2502" xml:space="preserve"/> </p> <pb o="24" file="0040" n="40" rhead="De Circulis Sphæræ."/> <p> <s xml:id="echoid-s2503" xml:space="preserve">3 In coluro ſolſtitiorum deſumitur menſura, & </s> <s xml:id="echoid-s2504" xml:space="preserve">quantitas maximæ declinationis Eclypticæ, nec<unsure/>non <lb/>diſtantiæ polorum eiuſdem à polis æquatoris: </s> <s xml:id="echoid-s2505" xml:space="preserve">tanta autem eſt maxima Eclypticæ declinatio ab æquatore <lb/>quantus eſt arcus huius coluri inter æquatorem, & </s> <s xml:id="echoid-s2506" xml:space="preserve">Eclypticam interiectus, alteraque tanta eſt diſtantia po-<lb/>lorum Eclypti æ a polis mundi. </s> <s xml:id="echoid-s2507" xml:space="preserve">Hanc porrò maximam Eclypticæ declinationem variam varijs tempori-<lb/>bus Aſtronomi compererunt; </s> <s xml:id="echoid-s2508" xml:space="preserve">de qua varietate in Tropicis dicendum erit.</s> <s xml:id="echoid-s2509" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div47" type="section" level="1" n="30"> <head xml:id="echoid-head32" style="it" xml:space="preserve">De duobus Tropicis. Cap. VIII.</head> <p> <s xml:id="echoid-s2510" xml:space="preserve">A Bſoluta iam maximorum ſex circulorum tractatione de quatuor minoribus agendum eſt, ac primum <lb/>de Tropicis.</s> <s xml:id="echoid-s2511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2512" xml:space="preserve">Τροπικος græcis idem eſt, ac latinis reuerſiuus; </s> <s xml:id="echoid-s2513" xml:space="preserve">ſicigitur dicti ſunt hi duo circuli, quòd in cælo indicent <lb/>Solis reuerſiones aut reditus, vt mox dicam.</s> <s xml:id="echoid-s2514" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2515" xml:space="preserve">Sunt enim Tropici duo circuli minores, & </s> <s xml:id="echoid-s2516" xml:space="preserve">æquatori paralelli, qui in cælo nihil aliud ſunt, quam veluti <lb/>extremæ duæ Solis diurnæ circulationes, ad quas Sol motu proprio hinc inde ab æquatore excurrit, & </s> <s xml:id="echoid-s2517" xml:space="preserve">in-<lb/>de poſtea iterum ad æquatorem paulatim redire incipit, quamuis Sol non circulos, ſed ſpirales lineas de-<lb/>ſcribat, vt ſuo loco explicabitur. </s> <s xml:id="echoid-s2518" xml:space="preserve">ſunt autem veluti binæ ſolaris euagationis metæ, ac carceres, intra quos <lb/>perpetuo Sol diſcurrit. </s> <s xml:id="echoid-s2519" xml:space="preserve">hos in materiali Sphęra, referunt bini Tropici. </s> <s xml:id="echoid-s2520" xml:space="preserve">vterque autem ab æquatore tantum <lb/>diſtat, quanta eſt maxima Eclypticæ declinatio, quæ hodie in communi vſu cenſetur eſſe gr. </s> <s xml:id="echoid-s2521" xml:space="preserve">23. </s> <s xml:id="echoid-s2522" xml:space="preserve">30|. </s> <s xml:id="echoid-s2523" xml:space="preserve">Ecly-<lb/>pticam enim in eo puncto, quod maximè ab Æquatore recedit contingunt. </s> <s xml:id="echoid-s2524" xml:space="preserve">horum ille, qui ad Boream ver-<lb/>git Tropicus Cancri dicitur, quod initium Cancri attingat. </s> <s xml:id="echoid-s2525" xml:space="preserve">dicitur etiam æſtiuus, Septentr@onalis, &</s> <s xml:id="echoid-s2526" xml:space="preserve">c. </s> <s xml:id="echoid-s2527" xml:space="preserve">alter <lb/>qui in Auſtrum recedit, Capricorni tropicus, hyemalis, Auſtralis, ſimili ratione nuncupatur.</s> <s xml:id="echoid-s2528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2529" xml:space="preserve">Inuentio Tropicorum in cælo, eadem opera, qua etiam maxima Eclypticæ, aut Solis declinatio haberi <lb/>poteſt; </s> <s xml:id="echoid-s2530" xml:space="preserve">nimirum per quadrantem Aſtronomicum aſtronomicè collocatum; </s> <s xml:id="echoid-s2531" xml:space="preserve">oportet obſeruare maximam.</s> <s xml:id="echoid-s2532" xml:space="preserve"><unsure/> <lb/>Solis altitudinem meridianam ſupra horizontem per illos dies, quibus Sol propè initium ♋. </s> <s xml:id="echoid-s2533" xml:space="preserve">verſatur: </s> <s xml:id="echoid-s2534" xml:space="preserve">ea <lb/>enim dabit maximam Eclypticæ declinationem, & </s> <s xml:id="echoid-s2535" xml:space="preserve">conſequenter locum, per quem Tropicus ♋. </s> <s xml:id="echoid-s2536" xml:space="preserve">dicendus <lb/>eſt æquatori paralellus, in quadrante autem apparebit arcus maximę declinationis, is ſcilicet, qui inter gra-<lb/>dum æquatoris iam inuentum, & </s> <s xml:id="echoid-s2537" xml:space="preserve">gradum Tropici modo obſeruatum, interijcitur. </s> <s xml:id="echoid-s2538" xml:space="preserve">tantundem ab æquato-<lb/>re verſus Auſtrum recedit alter Tropicus; </s> <s xml:id="echoid-s2539" xml:space="preserve">cuius altitudo ſupra horizontem habetur, ſi tempore hyemali@ <lb/>ſolſtitij obſeruetur per quadrantem minima Solis ſupra horizontem altitudo meridiana; </s> <s xml:id="echoid-s2540" xml:space="preserve">ſed cauendum eſt <lb/>ab hallucinatione, quam refractiones vaporum horizontem obſidentium inducere poſſunt; </s> <s xml:id="echoid-s2541" xml:space="preserve">ex quibus Sol <lb/>iuſto altior ſpectatur. </s> <s xml:id="echoid-s2542" xml:space="preserve">quapropter ſatius eſt habito ♋. </s> <s xml:id="echoid-s2543" xml:space="preserve">Tropico; </s> <s xml:id="echoid-s2544" xml:space="preserve">alterum ♑. </s> <s xml:id="echoid-s2545" xml:space="preserve">ad eandem diſtantiam, ſed Au-<lb/>ſtralem collocare. </s> <s xml:id="echoid-s2546" xml:space="preserve">Solis autem, & </s> <s xml:id="echoid-s2547" xml:space="preserve">Eclypticæ maxima declinatio varia, varijs ſeculis reperta eſt.</s> <s xml:id="echoid-s2548" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Eratoſthenes, Hipparcus, Ptolemæus eam faciunt. # gr. 23. 51|. <lb/>Albategnius poſt Ptolemæus annis 750. a Chriſto 880. # gr. 23. 35|. <lb/>Arzahel ab Albnegnio an. 190. # gr. 23. 34|. <lb/>Almeon Almanſonis ab Arzaele an. 70. # gr. 23. 33|. <lb/>Profatius Iudæus poſtea an. 160. Chriſti 1300. # gr. 23. 32|. <lb/>Purbachius, & Regiomontanus an. Chriſti 1460. # gr. 23. 28|. <lb/>Vernerius & Copernicus an. Chriſti 15 14. # gr. 23. 28|. <lb/>Tycho Braze, an. Chriſti 1580. # gr. 23. 31|. <lb/></note> <p> <s xml:id="echoid-s2549" xml:space="preserve">Qua ex varietate ſequitur, etiam neceſſario Tropicos eodem modo variari. </s> <s xml:id="echoid-s2550" xml:space="preserve">cuius variationis latitudo ſit <lb/>quaſi 24|. </s> <s xml:id="echoid-s2551" xml:space="preserve">vt patet ex præmiſſis obſeruationibus.</s> <s xml:id="echoid-s2552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2553" xml:space="preserve">Tropicorum munera ſunt. </s> <s xml:id="echoid-s2554" xml:space="preserve">Primum oſtendunt extremas Solis metas, ſeu extremos duos paralellos cir-<lb/>culos, quos Sol motu diurno deſcribit, tunc quando eſt in ijs Eclypticæ punctis, quæ maximè ab æquatore <lb/>recedunt; </s> <s xml:id="echoid-s2555" xml:space="preserve">& </s> <s xml:id="echoid-s2556" xml:space="preserve">in quibus in obliqua Sphæra longiſſimos, ac breuiſſimos facit dies, ac noctes artificiales: </s> <s xml:id="echoid-s2557" xml:space="preserve">So@e <lb/>enim principium ♋. </s> <s xml:id="echoid-s2558" xml:space="preserve">obtinente, longiſſima dies nobis, ac breuiſſima nox, contingunt; </s> <s xml:id="echoid-s2559" xml:space="preserve">percurrit enim tunc <lb/>Tropicum ♋. </s> <s xml:id="echoid-s2560" xml:space="preserve">cuius arcus diurnus, in noſtra Sphęra obliquitate, longiſſimus eſt; </s> <s xml:id="echoid-s2561" xml:space="preserve">nocturnus verò breuiſſimu@ <lb/>omnium qui in tota anni periodo contingunt, contraria accidunt Sole ♑. </s> <s xml:id="echoid-s2562" xml:space="preserve">initium inuadente.</s> <s xml:id="echoid-s2563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2564" xml:space="preserve">2 So@ſtitia contingunt Sole iuxta puncta Tropica verſante. </s> <s xml:id="echoid-s2565" xml:space="preserve">dicitur autem ſo@ſt@tium, quaſi ſolis ſtatio, <lb/>quòd Sol tunc videatur ſtare, ideſt, non videtur accedere ad noſtrum Verticem, aut ab eo recedere, vel non <lb/>videtur ſupra horizontem vno die magis quam altero in meridiano eleuari, aut deprimi. </s> <s xml:id="echoid-s2566" xml:space="preserve">pariter videtur in <lb/>eodem loco horizontis oriri, & </s> <s xml:id="echoid-s2567" xml:space="preserve">occidere, ſed apparet quotidie perc<unsure/>umdem cæli gyrum recurrere; </s> <s xml:id="echoid-s2568" xml:space="preserve">re vera <lb/>tamen quotidie paru quid, quod ſenſu vix percipitur, a Tropicis recedit, aut ad eos accedit; </s> <s xml:id="echoid-s2569" xml:space="preserve">circa verò pun-<lb/>cta Aequinoctialia admodum ſenſibiliter Sol accedit, & </s> <s xml:id="echoid-s2570" xml:space="preserve">recedit à<unsure/> noſtro Vertice, ſeu ſupra horizontem ele-<lb/>uatur, aut deprimitur. </s> <s xml:id="echoid-s2571" xml:space="preserve">ex hac Solis ſtatione ſequitur etiam dies ac nocte quodammodo ſtare, ideſt nec au-<lb/>geri, nec minui: </s> <s xml:id="echoid-s2572" xml:space="preserve">non igitur ſolſtitium contingit reſpectu motus diurni, quia vid@mus ſemper Solem hoc <lb/>motu circumferri: </s> <s xml:id="echoid-s2573" xml:space="preserve">neq; </s> <s xml:id="echoid-s2574" xml:space="preserve">reſpectu motus Solis proprij, quia certum eſt eum quotidie vnum quaſi gradum in <lb/>Zodiacc<unsure/> progredi.</s> <s xml:id="echoid-s2575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2576" xml:space="preserve">Cauſa vero @olſtitiorũ eſt Eclypticæ ad Tropicos ſituatio; </s> <s xml:id="echoid-s2577" xml:space="preserve">nam vti materialis Sphæra oſtendit, ipſa Ecly-<lb/>ptica ante, & </s> <s xml:id="echoid-s2578" xml:space="preserve">poſt puncta ſolſtitialia, extenditur ſecus ipſos Tropicos, minimumque ab eis recedit, ſed illis <lb/>longo ſpatio adhæret, v. </s> <s xml:id="echoid-s2579" xml:space="preserve">g. </s> <s xml:id="echoid-s2580" xml:space="preserve">gr. </s> <s xml:id="echoid-s2581" xml:space="preserve">15. </s> <s xml:id="echoid-s2582" xml:space="preserve">Eclypticæ præcedentes, & </s> <s xml:id="echoid-s2583" xml:space="preserve">15. </s> <s xml:id="echoid-s2584" xml:space="preserve">ſequentes punctum ſolſtitij ♋. </s> <s xml:id="echoid-s2585" xml:space="preserve">ipſi Tropi-<lb/>co, val@è adhæret, quare quando Sol per eos graditur, parum @emper a Tropico recedit, ſed ſinguns diebu@ <lb/>motu diurno gyrum circumducit ipſi Tropico proximũ, aut qui inſenſib@liter ab eo diſcrepat. </s> <s xml:id="echoid-s2586" xml:space="preserve">atq; </s> <s xml:id="echoid-s2587" xml:space="preserve">hæc eſt <lb/>ſolſtitij ratio, & </s> <s xml:id="echoid-s2588" xml:space="preserve">cauſa.</s> <s xml:id="echoid-s2589" xml:space="preserve"/> </p> <pb o="25" file="0041" n="41" rhead="Liber Primus."/> <p> <s xml:id="echoid-s2590" xml:space="preserve">3 Oſtendunt quantitatem diei maximi, & </s> <s xml:id="echoid-s2591" xml:space="preserve">minimi: </s> <s xml:id="echoid-s2592" xml:space="preserve">item noctis maximæ, & </s> <s xml:id="echoid-s2593" xml:space="preserve">minimæ: </s> <s xml:id="echoid-s2594" xml:space="preserve">nam in quauis <lb/>Sphæræ conſtitutione vſque ad poli eleuationem gr. </s> <s xml:id="echoid-s2595" xml:space="preserve">66. </s> <s xml:id="echoid-s2596" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2597" xml:space="preserve">eæ Tropicorum portiones, quæ ſupra horizon <lb/>tem extant, efficiunt arcus diurnos; </s> <s xml:id="echoid-s2598" xml:space="preserve">eæ verò quę infra horizontẽ latent, efficiunt arcus nocturnos. </s> <s xml:id="echoid-s2599" xml:space="preserve">in Sphæ-<lb/>ra recta arcus diurni ſunt æquales, tum inuicem, tum cum nocturnis. </s> <s xml:id="echoid-s2600" xml:space="preserve">in Sphæri<unsure/>s obliquis ſuperior portio <lb/>Tropici vergentis ad polum eleuatum, efficit arcum diurnum maximum totius anni, porti<unsure/>o vero inferior <lb/>dat arcum nocturnum breuiſſimum: </s> <s xml:id="echoid-s2601" xml:space="preserve">è contrario portiones alterius Tropici, ſuperior exhibetarcu n<unsure/> diur-<lb/>num breuiſſimum; </s> <s xml:id="echoid-s2602" xml:space="preserve">inferior ver<unsure/>ò nocturnum longiſſimum. </s> <s xml:id="echoid-s2603" xml:space="preserve">Illud etiam notandum, arcum diurnum vnius <lb/>Tropici eſſe æqualem nocturno alterius, & </s> <s xml:id="echoid-s2604" xml:space="preserve">viciſſim.</s> <s xml:id="echoid-s2605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2606" xml:space="preserve">In Sphæra tamen cuius polus eleuatur pręcise 66. </s> <s xml:id="echoid-s2607" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2608" xml:space="preserve">vnus Tropicus totus ſupra horizontem extat, eumq; <lb/></s> <s xml:id="echoid-s2609" xml:space="preserve">in puncto tangit, vnde arcus diurnus eſt integer circulus horarum 24. </s> <s xml:id="echoid-s2610" xml:space="preserve">alter Tropicus totus latet infra hori-<lb/>zontem, eumque in puncto tangit, nocturnuſq; </s> <s xml:id="echoid-s2611" xml:space="preserve">arcus eſt integer circulus horarum 24. </s> <s xml:id="echoid-s2612" xml:space="preserve">In alijs Sphæris vbi <lb/>maior eſt eleuatio, quam gr. </s> <s xml:id="echoid-s2613" xml:space="preserve">66. </s> <s xml:id="echoid-s2614" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2615" xml:space="preserve">Tropici non amplius oſtendunt has quantitates, ſed arcus Eclypticæid <lb/>præſtat, quæ omnia Sphæra Armillaris facilè oſtendet.</s> <s xml:id="echoid-s2616" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2617" xml:space="preserve">4 Concurrunt ad Zonas conſtituendas, vti poſtea dicemus.</s> <s xml:id="echoid-s2618" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div48" type="section" level="1" n="31"> <head xml:id="echoid-head33" style="it" xml:space="preserve">De duobus Circulis Polaribus. Cap. I X.</head> <p> <s xml:id="echoid-s2619" xml:space="preserve">APolis mundi polares dicuntur, quòd propè eos atq; </s> <s xml:id="echoid-s2620" xml:space="preserve">ex eis circunſcribantur. </s> <s xml:id="echoid-s2621" xml:space="preserve">ille polaris Arcticus ab Ar-<lb/>ctico polo: </s> <s xml:id="echoid-s2622" xml:space="preserve">hic verò polaris Antarcticus ab Antarctico polo. </s> <s xml:id="echoid-s2623" xml:space="preserve">Nihil verò aliud ſunt, quam diurnæ con-<lb/>uerſiones polorum Eclypticæ circa Aequatoris polos, quæ abijſdem diſtant gr. </s> <s xml:id="echoid-s2624" xml:space="preserve">23. </s> <s xml:id="echoid-s2625" xml:space="preserve">{1/2}.</s> <s xml:id="echoid-s2626" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2627" xml:space="preserve">Porrò veteres græci, aliter polares hoſce circulos accipiebant (vti apud Proclum, & </s> <s xml:id="echoid-s2628" xml:space="preserve">Cleomedem in ſuis <lb/>Sphæris videre eſt;) </s> <s xml:id="echoid-s2629" xml:space="preserve">Circulos enim polares ſtatuebant eſſe duos circulos æquatori paralellos, vnum ad Bo-<lb/>ream, alterum ad Auſtrum, horizõtes perſtringentes, quorum poli eſſent ijdem cum polis mundi, & </s> <s xml:id="echoid-s2630" xml:space="preserve">con-<lb/>ſequenter vnus eſſet ſupra horizontem totus, alter vero infra. </s> <s xml:id="echoid-s2631" xml:space="preserve">ille autem eſt omnium paralellorum ſemper <lb/>apparentium maximus hic verò ſemper deliteſcẽtium maximus. </s> <s xml:id="echoid-s2632" xml:space="preserve">ex quibus patet, polares hoſce gręcorum <lb/>circulos in Sphęra recta nullos eſſe; </s> <s xml:id="echoid-s2633" xml:space="preserve">cum enim in ea polimundi horizonti inſint, nullum reſtat interuallum <lb/>quo deſcribantur: </s> <s xml:id="echoid-s2634" xml:space="preserve">in Sphæris verò obliquis non eſſe vbique eiuſdem quantitatis (vti ſunt latinorum pola-<lb/>res) ſed quo polus mundi elatior eſt, eo etiam maiores illos effici. </s> <s xml:id="echoid-s2635" xml:space="preserve">In Sphæra tandem paralella coincidunt <lb/>cum horizonte, & </s> <s xml:id="echoid-s2636" xml:space="preserve">æquatore. </s> <s xml:id="echoid-s2637" xml:space="preserve">quæ omnia in materiali Sphæra ad prædictas poſitiones conſtituta, facilè eſt <lb/>contemplari.</s> <s xml:id="echoid-s2638" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2639" xml:space="preserve">Polarium noſtrorum in cælo ſitum ſi in tua regione ritè velis concipere, colloca quadrantem noſtrum <lb/>aſtronomicè verſus conſpicuum polum, atq; </s> <s xml:id="echoid-s2640" xml:space="preserve">in eo nota grad. </s> <s xml:id="echoid-s2641" xml:space="preserve">altitudinis poli, poſtea tam ſupra eum, quam <lb/>infra, numera gr. </s> <s xml:id="echoid-s2642" xml:space="preserve">23. </s> <s xml:id="echoid-s2643" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s2644" xml:space="preserve">atq; </s> <s xml:id="echoid-s2645" xml:space="preserve">per vtrumque terminum applica Dioptram, nam ſi per eam ſic applicatam in-<lb/>ſpexeris in cælum, oculis tuis occurrent puncta duo in cælo, per quæ polaris circulus polo mundi circum-<lb/>ſcribendus eſt, atq; </s> <s xml:id="echoid-s2646" xml:space="preserve">concipiendus ſituationem autem polarium ſecundum græcos ſic concipies, in eodem <lb/>quadrante vt prius conſtituto, numera ab horizonte ſurſum gradus altitudinis poli duplos, ac per ſupre-<lb/>mum gradum tranſeunte Dioptra, videbis per eam cæli punctum, per quod, & </s> <s xml:id="echoid-s2647" xml:space="preserve">per contractum horizontis <lb/>cum meridiano, imaginare circulum ex polo mundi deſcriptum; </s> <s xml:id="echoid-s2648" xml:space="preserve">talem enim habet iu cælo ſitum circulus <lb/>polaris græcorum, ſeu paralellorum ſemper apparentium maximus. </s> <s xml:id="echoid-s2649" xml:space="preserve">eadem proporrionaliter concipienda <lb/>ſunt circa polum infra horizontem depreſſum.</s> <s xml:id="echoid-s2650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2651" xml:space="preserve">Vſus circulorum polarium noſtratium rarus eſt: </s> <s xml:id="echoid-s2652" xml:space="preserve">Geographis tamen inſeruit ad frigidas Zonas definien-<lb/>das. </s> <s xml:id="echoid-s2653" xml:space="preserve">apud græcos verò paralellus ſemper apparentium maximus oſtendit omnes ſtellas, quæ ortus, & </s> <s xml:id="echoid-s2654" xml:space="preserve">occa-<lb/>@@s ſunt expertes, ac proinde ſempiternæ apparitionis dicũtur. </s> <s xml:id="echoid-s2655" xml:space="preserve">alter verò occultorum maximus ſtellas om-<lb/>@@s compræhendit ortus, & </s> <s xml:id="echoid-s2656" xml:space="preserve">occaſus pariter immunes, ſed ſempiternæ occultationis.</s> <s xml:id="echoid-s2657" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div49" type="section" level="1" n="32"> <head xml:id="echoid-head34" style="it" xml:space="preserve">De Circulo ſecundi motus. Cap. X.</head> <p> <s xml:id="echoid-s2658" xml:space="preserve">DIe<unsure/>itur circulus ſecundi motus, quoniam factus eſt, vt oſtendat motum ſecundum: </s> <s xml:id="echoid-s2659" xml:space="preserve">in mundo enim, v@ <lb/>poſtea e<unsure/>xplicabimus, eſt motus primus ſiue diurnus, qui communis eſt toti mundo; </s> <s xml:id="echoid-s2660" xml:space="preserve">eſt etiam motus ſe-<lb/>cundus qui non eſt toti mũdo communis, ſed Planetarum proprius: </s> <s xml:id="echoid-s2661" xml:space="preserve">quamuis enim Zodiacus oſtẽdat viam <lb/>h<unsure/>uius motus ſecundi, non tamen Planetam vllum, qui hunc imitetur motum, exhibet: </s> <s xml:id="echoid-s2662" xml:space="preserve">at noſter hic circu-<lb/>lus planetam quendam materialem, ſub Zodiaco defert, ita vt proprium plenetarum motum rectè imitari <lb/>poſſit. </s> <s xml:id="echoid-s2663" xml:space="preserve">quapropter hic circulus non in primo mobili concipiendus eſt, vt alij, ſed infra primum mobile, & </s> <s xml:id="echoid-s2664" xml:space="preserve"><lb/>propterea eum infrà alios, qui ſunt in primo mobili collocauimus, ita vt in polis Eclypticæ ſuper ſuo dia-<lb/>metro, non ſuper mundi axem, vt alij conuertatur.</s> <s xml:id="echoid-s2665" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2666" xml:space="preserve">Vtilitas huius circuli, & </s> <s xml:id="echoid-s2667" xml:space="preserve">vſus eius magnifaciendus eſt, omnium enim difficultatum maximæ ſuccurrit: <lb/></s> <s xml:id="echoid-s2668" xml:space="preserve">manifeſtat enim qua ratione motus planetarum proprius, qui communiter primo motui contrarius dici-<lb/>tur, cum eodem concordet, ideſt, ad ſenſum oſtendit, qua ratione planeta quiſpiam moueatur, vt aiunt, mo <lb/>tibus contrarijs, motu ſcilicet primo ab ortu in occaſum, & </s> <s xml:id="echoid-s2669" xml:space="preserve">motu ſecundo, & </s> <s xml:id="echoid-s2670" xml:space="preserve">proprio ab occaſu in ortum. </s> <s xml:id="echoid-s2671" xml:space="preserve"><lb/>enimuero hanc vnam rem, difficilè admodum ab Aſtronomiæ Tyronibus percipi, l<unsure/>õga annorum experien <lb/>tia in auditoribus meis cõpertum habeo; </s> <s xml:id="echoid-s2672" xml:space="preserve">quę tamen huius circuli auxilio ſine vlla difficultate intelligitur <lb/>ſic enim oculis ſubijciuntur ea, quę prius impoſſibilia videbantur, quæq; </s> <s xml:id="echoid-s2673" xml:space="preserve">ſola cogitatione vix compræhen <lb/>@ poterant. </s> <s xml:id="echoid-s2674" xml:space="preserve">hoc autem modo agendum eſt: </s> <s xml:id="echoid-s2675" xml:space="preserve">manu altera motu diurno ab oriente, in occidentem Sphæram <pb o="26" file="0042" n="42" rhead="De Circulis Sphæræ."/> conuerte, atq; </s> <s xml:id="echoid-s2676" xml:space="preserve">eodem tempore, manu altera prędictum circulum lentè admodum ſecundũ<unsure/> ordinem ſigno-<lb/>rum impelle, ita vt materialem Solem tardè deſerat à<unsure/> primo, v.</s> <s xml:id="echoid-s2677" xml:space="preserve">g.</s> <s xml:id="echoid-s2678" xml:space="preserve">gr.</s> <s xml:id="echoid-s2679" xml:space="preserve">♈. </s> <s xml:id="echoid-s2680" xml:space="preserve">ad ſecundum: </s> <s xml:id="echoid-s2681" xml:space="preserve">qua ratione, conuer <lb/>ſione vna diurna peracta, ſol materialis gradum vnũ verſus orientem peregerit: </s> <s xml:id="echoid-s2682" xml:space="preserve">ſic enim clarè videbis qua <lb/>ratione ſol contrarijs motibus moueatur, ideſt, motu proprio, gradum vnum in Zodiaco verſus ortum, & </s> <s xml:id="echoid-s2683" xml:space="preserve"><lb/>motu diurno ad occidentem totam circulationem abſoluat: </s> <s xml:id="echoid-s2684" xml:space="preserve">& </s> <s xml:id="echoid-s2685" xml:space="preserve">qua ratione ſol verè ſemper occaſui appro-<lb/>pinquet, qua muis reſpectu Zodiaci in contrariam partem lentè retrocedat: </s> <s xml:id="echoid-s2686" xml:space="preserve">videbis etiam qua ratione hi <lb/>duo motus, in tertium coaleſcant, qui ſpiralis eſt; </s> <s xml:id="echoid-s2687" xml:space="preserve">quo vltimo ſol circa mundum perpetuo ſpiratim reuol-<lb/>uitur: </s> <s xml:id="echoid-s2688" xml:space="preserve">vt infra fuſius de Sole.</s> <s xml:id="echoid-s2689" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div50" type="section" level="1" n="33"> <head xml:id="echoid-head35" style="it" xml:space="preserve">De alijs Circulis, qui in materiali Sphæra non ponuntur. Cap. XI.</head> <p> <s xml:id="echoid-s2690" xml:space="preserve">PRæter prædictos circulos, alios complures imaginantur in cælo Aſtronomi, quos ad vitandam confu-<lb/>ſionem materiali Sphæræ minimè addendos eſſe cenſuerunt. </s> <s xml:id="echoid-s2691" xml:space="preserve">de eorum numero ſunt</s> </p> <p> <s xml:id="echoid-s2692" xml:space="preserve">1 Verticales; </s> <s xml:id="echoid-s2693" xml:space="preserve">ſic dicti, quòd per vertices omnium locorum ad ſingula horizontis puncta perpendicu-<lb/>lariter deſcendunt. </s> <s xml:id="echoid-s2694" xml:space="preserve">eorum vſus eſt in menſurandis Stellarum altitudinibus ſupra horizontem, aut depreſ-<lb/>ſionibus infra. </s> <s xml:id="echoid-s2695" xml:space="preserve">eos Arabes Azimut appellant.</s> <s xml:id="echoid-s2696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2697" xml:space="preserve">2 Circuli declinationum; </s> <s xml:id="echoid-s2698" xml:space="preserve">qui tranſeunt per polos mundi, ac perpendiculariter per ſingula æquatoris<unsure/> <lb/>puncta: </s> <s xml:id="echoid-s2699" xml:space="preserve">menfurant hi declinationes, ſeu diſtantias ſyderum ab æquatore.</s> <s xml:id="echoid-s2700" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2701" xml:space="preserve">3 Circuli latitudinum; </s> <s xml:id="echoid-s2702" xml:space="preserve">qui per Eclypticæ polos, ac per ſingulas Eclypticæ puncta perpendiculariter <lb/>incedunt: </s> <s xml:id="echoid-s2703" xml:space="preserve">his metiuntur Aſtronomi di@ãtias ſyderum ab Eclyptica, quas ideò latitudines appellant, quod <lb/>ſecundum Zodiaci latitudinem, non autem ſecundum longitudinem accipiantur.</s> <s xml:id="echoid-s2704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2705" xml:space="preserve">4 Imaginantur per ſingula cæli<unsure/> puncta innumeros æquatori paralellos; </s> <s xml:id="echoid-s2706" xml:space="preserve">præcipuè vero eos, quos ſol <lb/>diurnis conuerſionibus hinc inde ab æquatore deſcribit, qui ſunt ferè 182. </s> <s xml:id="echoid-s2707" xml:space="preserve">de quorum numero eſt ęquator <lb/>ipſe eorum medius, & </s> <s xml:id="echoid-s2708" xml:space="preserve">duo Tropici, qui omnium extremi ſunt: </s> <s xml:id="echoid-s2709" xml:space="preserve">(re vera tamen ſol non circulos, ſed ſpiras <lb/>ducit;) </s> <s xml:id="echoid-s2710" xml:space="preserve">vſus eorum eſſet oſtendere dierum, & </s> <s xml:id="echoid-s2711" xml:space="preserve">noctum inæqualitatem in Sphæris obliquis: </s> <s xml:id="echoid-s2712" xml:space="preserve">ęqualitatem ve-<lb/>ròin Sphæra recta: </s> <s xml:id="echoid-s2713" xml:space="preserve">vti ſuperius de Tropicis diximus.</s> <s xml:id="echoid-s2714" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2715" xml:space="preserve">5 Concipiunt infinitos horizonti paralellos, quos progreſſionum, & </s> <s xml:id="echoid-s2716" xml:space="preserve">altitudinum, & </s> <s xml:id="echoid-s2717" xml:space="preserve">depreſſionum.</s> <s xml:id="echoid-s2718" xml:space="preserve"><unsure/> <lb/>appellant: </s> <s xml:id="echoid-s2719" xml:space="preserve">hos Arabes Almincatarat dicunt. </s> <s xml:id="echoid-s2720" xml:space="preserve">de horum numero eſt circulus Crepuſculi, qui horizonti pa-<lb/>ralellus infra eum gr. </s> <s xml:id="echoid-s2721" xml:space="preserve">18. </s> <s xml:id="echoid-s2722" xml:space="preserve">deprimitur; </s> <s xml:id="echoid-s2723" xml:space="preserve">ad quem cum Sol peruenit, Crepuſculi initium, aut finem facit.</s> <s xml:id="echoid-s2724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2725" xml:space="preserve">6 Circuli domorum, ac poſitionum ſunt; </s> <s xml:id="echoid-s2726" xml:space="preserve">quibus multa nugantur Aſtrologi iudiciarij.</s> <s xml:id="echoid-s2727" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2728" xml:space="preserve">7 Tandem ſunt circuli Horarij, de quibus in Gnomonicis agitur. </s> <s xml:id="echoid-s2729" xml:space="preserve">hi in horologijs ſolaribus horas <lb/>nidicant.</s> <s xml:id="echoid-s2730" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2731" xml:space="preserve">Hos omnes in Aſtrolabijs, ſeu Planiſphærijs depingunt, & </s> <s xml:id="echoid-s2732" xml:space="preserve">explicant Aſtronomi.</s> <s xml:id="echoid-s2733" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div51" type="section" level="1" n="34"> <head xml:id="echoid-head36" style="it" xml:space="preserve">De quinque Zonis, & Climatibus. Cap. XII.</head> <p> <s xml:id="echoid-s2734" xml:space="preserve">EXplicatis iam Sphæræ circulis, facile eſt intelligere, quidnam ſint Zonæ, quiſuè earum vſus. </s> <s xml:id="echoid-s2735" xml:space="preserve">Zonæ <lb/>enim ſunt quinque faſciæ (ζων<unsure/>η etiam faſciat ſignificat) quæ totum cælum, ac terram circuncingunt.</s> <s xml:id="echoid-s2736" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2737" xml:space="preserve">Ea, quæ torrida appellatur inter vtrumq; </s> <s xml:id="echoid-s2738" xml:space="preserve">Tropicum contenta, mundum ambit.</s> <s xml:id="echoid-s2739" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2740" xml:space="preserve">Duæ verò temperatæ huic vtrinque aſſident, continenturque intra Tropicos, & </s> <s xml:id="echoid-s2741" xml:space="preserve">Polares circulos lati-<lb/>norum.</s> <s xml:id="echoid-s2742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2743" xml:space="preserve">Reliquæ duæ frigidæ impropriè Zonæ dicuntur, intra circulos enim latinorum Polares continentur.</s> <s xml:id="echoid-s2744" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2745" xml:space="preserve">Zonarum vſus maximè in Geographia apparet: </s> <s xml:id="echoid-s2746" xml:space="preserve">Terræ enim globus cæleſtibus Zoni<unsure/>s ſubdiuiditur, ac<unsure/> <lb/>polis pariter inſignitur: </s> <s xml:id="echoid-s2747" xml:space="preserve">à qualitatibus autem Zonarum, calore, temperie, frigore, etiam earum habitato-<lb/>res, animalia, plantæ afficiuntur. </s> <s xml:id="echoid-s2748" xml:space="preserve">quare de eis fuſius in introductione ad Geographiam.</s> <s xml:id="echoid-s2749" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2750" xml:space="preserve">Climata pariter ſunt Zonulæ quædam æquatori paralellæ, terramq; </s> <s xml:id="echoid-s2751" xml:space="preserve">ſecundum longitudinem præcin-<lb/>gentes: </s> <s xml:id="echoid-s2752" xml:space="preserve">tanta latitudine præditæ, quanta di<unsure/>es maxima inibi per ſemihoram variatur, ideſt in termino, v. </s> <s xml:id="echoid-s2753" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s2754" xml:space="preserve">Boreali dies maxima longior eſt per ſemihoram, quam in termino Auſtrali. </s> <s xml:id="echoid-s2755" xml:space="preserve">Vitruuius libro primo ſic, <lb/>Κλιμα, græca dictio, quæ ſpatium terræ habitatæ ſignificat, duobus paralellis concluſum, quo diei longi-<lb/>tudo ad dimidiam horam variatur. </s> <s xml:id="echoid-s2756" xml:space="preserve">verum res penitus Geographica eſt.</s> <s xml:id="echoid-s2757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2758" xml:space="preserve">De Galaxia, aut via lactea, nonnulli, neſcio quo iure, inter Sphæræ circulos tractant: </s> <s xml:id="echoid-s2759" xml:space="preserve">verum nullo mo-<lb/>do inter hoſce circulos connumeranda eſt, cum nihil aliud ſit, quam quidam firmamenti candor, ex debili <lb/>innumerarum ſtellarum lumine proueniens. </s> <s xml:id="echoid-s2760" xml:space="preserve">Hæc igitur in Sphæræ materialis explicationem ſufficiant.</s> <s xml:id="echoid-s2761" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div52" type="section" level="1" n="35"> <head xml:id="echoid-head37" xml:space="preserve">Finis Libri Primi.</head> <pb o="27" file="0043" n="43"/> </div> <div xml:id="echoid-div53" type="section" level="1" n="36"> <head xml:id="echoid-head38" xml:space="preserve">LIBER SECVNDVS <lb/>DE TOTO MVNDO <lb/>IN VNIVERSVM.</head> <p> <s xml:id="echoid-s2762" xml:space="preserve">QVæ præmiſſa ſunt in Sphæræ Armillaris explicationem, vt circulos quoſdam in <lb/>Cælo, ac Mundo vniuerſo probè conciperemus, ſunt reſpectu eorum, quæ ſe-<lb/>quuntur veluti principia quædam, vnde in nobiliſſimam rerum Aſtronomica-<lb/>rum, ſeu totius Mundanæ fabricę cognitionem venire valeamus.</s> <s xml:id="echoid-s2763" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2764" xml:space="preserve">Porrò Mundus, teſte Plinio, a perfecta abſolutaque elegantia denominatus eſt: </s> <s xml:id="echoid-s2765" xml:space="preserve">in <lb/>quod, & </s> <s xml:id="echoid-s2766" xml:space="preserve">græcæ vocis appellatio conſentit; </s> <s xml:id="echoid-s2767" xml:space="preserve">eum enim græci Kοσμον, hoc eſt, or-<lb/>namentum appellauerunt. </s> <s xml:id="echoid-s2768" xml:space="preserve">Mundus verò eſt corpus ſphæricum omnia conti-<lb/>nens, ſeu conſtans ex cælis, ſyderibus, elementis, ac mixtis. </s> <s xml:id="echoid-s2769" xml:space="preserve">Aſtronomica autem <lb/>conſideratio quinque potiſſimum circa hanc mundi ſtructuram inueſtigare niti-<lb/>tur: </s> <s xml:id="echoid-s2770" xml:space="preserve">videlicet, locum, motum, illuminationem, figuram, quantitatem, non ſo-<lb/>lum totius mundanæ Sphæræ, ſed etiam ſingularum eius partium:</s> <s xml:id="echoid-s2771" xml:space="preserve"><unsure/> ex quibus huius futuræ tractationis, cla-<lb/>ra methodus iam perſpicitur, quam nobis integram Ariſtoteles primo. </s> <s xml:id="echoid-s2772" xml:space="preserve">Poſt. </s> <s xml:id="echoid-s2773" xml:space="preserve">te. </s> <s xml:id="echoid-s2774" xml:space="preserve">24. </s> <s xml:id="echoid-s2775" xml:space="preserve">tradidiſſet, ſi illumi-<lb/>nationem non omiſiſiet. </s> <s xml:id="echoid-s2776" xml:space="preserve">prædicta igitur quinque in ſingulis præcipuè perſcrutabimur; </s> <s xml:id="echoid-s2777" xml:space="preserve">tum, ſi quæ alia ex <lb/> <anchor type="figure" xlink:label="fig-0043-01a" xlink:href="fig-0043-01"/> illis tanquam conſectaria deduci <lb/>debuerint, ea minimè omitten-<lb/>da curabimus. </s> <s xml:id="echoid-s2778" xml:space="preserve">huius igitur mun-<lb/>danę molis rudem hanc qualem-<lb/>cumque cõtemplare anatomen, <lb/>in appoſita figura, quam deinde <lb/>particulatim perueſtigabimus.</s> <s xml:id="echoid-s2779" xml:space="preserve"/> </p> <div xml:id="echoid-div53" type="float" level="2" n="1"> <figure xlink:label="fig-0043-01" xlink:href="fig-0043-01a"> <image file="0043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0043-01"/> </figure> </div> <p> <s xml:id="echoid-s2780" xml:space="preserve">Quæ quidẽ figura oſtenditom <lb/>nes Mũdi partes, & </s> <s xml:id="echoid-s2781" xml:space="preserve">quo ſitu, quo-<lb/>uè ordines ex ijs Mundi Fabrica <lb/>conſtruatur: </s> <s xml:id="echoid-s2782" xml:space="preserve">& </s> <s xml:id="echoid-s2783" xml:space="preserve">id quidem ſecun-<lb/>dum communem tam antiquo-<lb/>rum, quam recentiorum ſenten-<lb/>tiam, vt deinceps patebit; </s> <s xml:id="echoid-s2784" xml:space="preserve">mens <lb/>enim mea, & </s> <s xml:id="echoid-s2785" xml:space="preserve">ſcopus eſt, in hoc <lb/>opere veterum hypotheſes com-<lb/>muniter receptas primo tradere, <lb/>atq; </s> <s xml:id="echoid-s2786" xml:space="preserve">ijs inſiſtere: </s> <s xml:id="echoid-s2787" xml:space="preserve">ita tamen vt etiã <lb/>recentiorũ nouas obſeruationes, <lb/>& </s> <s xml:id="echoid-s2788" xml:space="preserve">inuenta minime negligenda. <lb/></s> <s xml:id="echoid-s2789" xml:space="preserve">cẽſuerit; </s> <s xml:id="echoid-s2790" xml:space="preserve">vt ſcilicet rerum Aſtro-<lb/>nomicarum plena cognitio tra-<lb/>datur, & </s> <s xml:id="echoid-s2791" xml:space="preserve">cuique liberum ſit de to <lb/>ta hac materia abundè philoſo-<lb/>phari.</s> <s xml:id="echoid-s2792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2793" xml:space="preserve">In hac igitur figura, globulus <lb/>niger in medio ſitus, ac litera T, <lb/>notatus, Terræ, & </s> <s xml:id="echoid-s2794" xml:space="preserve">Aquæ globu-<lb/>lum refert, cuius cẽtrum, eſt cen-<lb/>trum totius Mundi. </s> <s xml:id="echoid-s2795" xml:space="preserve">Spatiũ R S, <lb/>eirca Terram, eſt locus Aeris, & </s> <s xml:id="echoid-s2796" xml:space="preserve">Aetheris, vſq; </s> <s xml:id="echoid-s2797" xml:space="preserve">ad gyrum Lunæ. </s> <s xml:id="echoid-s2798" xml:space="preserve">P Q, eſt gyrus Lunæ circa elementarem <lb/>Sphæram; </s> <s xml:id="echoid-s2799" xml:space="preserve">N O, gyrus Solis circa Terram; </s> <s xml:id="echoid-s2800" xml:space="preserve">L M, gvrus Mercurij circa Solem; </s> <s xml:id="echoid-s2801" xml:space="preserve">I K, gyrus Veneris cir-<lb/>ea Solem; </s> <s xml:id="echoid-s2802" xml:space="preserve">G H, gyrus Martis; </s> <s xml:id="echoid-s2803" xml:space="preserve">E F, gyrus Iouis; </s> <s xml:id="echoid-s2804" xml:space="preserve">C D, gyrus Saturni: </s> <s xml:id="echoid-s2805" xml:space="preserve">omnes circa Solem; </s> <s xml:id="echoid-s2806" xml:space="preserve">A B, octaua <lb/>Sphæra Stellarum fixarum, ſeu firmamentum circa Terræ, ac Mundi centrum; </s> <s xml:id="echoid-s2807" xml:space="preserve">V X, refert Empyreum <lb/>Cælum, Beatarum mentium ſedem, totam hanc Mundi Fabricam ambiens.</s> <s xml:id="echoid-s2808" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div55" type="section" level="1" n="37"> <head xml:id="echoid-head39" style="it" xml:space="preserve">De Mundi loco. Cap. I.</head> <p> <s xml:id="echoid-s2809" xml:space="preserve">ESſe in loco impropriè Mundo conuenit: </s> <s xml:id="echoid-s2810" xml:space="preserve">ſed ipſe potius omniũ rerum in eo exiſtentium locus eſt, cum <lb/>in eo omnia collocentur. </s> <s xml:id="echoid-s2811" xml:space="preserve">ſiue enim loco pro ſuperficie alterius corporis mundum ambientis cum non- <pb o="28" file="0044" n="44" rhead="De Mundi fabrica."/> nullis philoſophis ſumas, cum naturali lumine incertum ſit huiuſmodi corpus extra mundum circumſi-<lb/>ſtere; </s> <s xml:id="echoid-s2812" xml:space="preserve">incertum pariter erit hac ratione mundum aliquo loco contineri. </s> <s xml:id="echoid-s2813" xml:space="preserve">ſi verò cum alijs, locum pro ſpa-<lb/>tio, quod loca tum occupat, determinato certis a Mundi centro, ac polis diſtantijs, acceperis; </s> <s xml:id="echoid-s2814" xml:space="preserve">manifeſtum <lb/>eſt neq; </s> <s xml:id="echoid-s2815" xml:space="preserve">hoc pacto mundum vllo loco definiri; </s> <s xml:id="echoid-s2816" xml:space="preserve">poli enim, & </s> <s xml:id="echoid-s2817" xml:space="preserve">centrũ mundi, potius alijs rebus mundis con-<lb/>tentis diſtantias ac loca determinant, quam ipſi mundo.</s> <s xml:id="echoid-s2818" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2819" xml:space="preserve">Poſſumus tamen, idque opereprætium eſt; </s> <s xml:id="echoid-s2820" xml:space="preserve">ſinguli in proprijs regionibus, aut habitationibus totius vni-<lb/>uerſi ſituationem, ac poſitionem, quæ eſt quædam locati conditio, compertam habere, ideſt, cognoſcere <lb/>in noſtra habitatione ex qua parte ſint ſingulæ quatuor mundi plagæ, ac præcipui venti; </s> <s xml:id="echoid-s2821" xml:space="preserve">quatenus polus <lb/>eleuetur; </s> <s xml:id="echoid-s2822" xml:space="preserve">Æquator, ac reliqui circuli, quam in cælo poſitionem habeant, &</s> <s xml:id="echoid-s2823" xml:space="preserve">c. </s> <s xml:id="echoid-s2824" xml:space="preserve">quod facilè obtinere eſt, ex <lb/>meridianæ lineæ inuentione<unsure/>, ac reliquorum, cum Aſtronomica Sphæræ collocatione, vti in præcedenti <lb/>de Circulis tractatu abundè docuimus.</s> <s xml:id="echoid-s2825" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div56" type="section" level="1" n="38"> <head xml:id="echoid-head40" style="it" xml:space="preserve">De totius Mundi motu. Cap. II.</head> <p> <s xml:id="echoid-s2826" xml:space="preserve">AN totus mundus progreſſiuo motu, ita promoueatur, vt locum ſubinde ſecundum ſe totum permu-<lb/>tet, nihil ſtatuo, cum talis motus indicium apud nos ſit nullum; </s> <s xml:id="echoid-s2827" xml:space="preserve">nam etiamſi hoc motu mundus pro-<lb/>pelleretur, illum tamen omnino nos latere oporteret: </s> <s xml:id="echoid-s2828" xml:space="preserve">quemadmodum enim ij, qui in magna Naui celeri-<lb/>ter acta occluſi ſunt, ita vt nihil extra ipſam videre queant, nullo modo eam impelli animaduertũt, eodem <lb/>nos pariter modo in hoc veluti ingenti mundi Nauigio concluſi, nec quidquam præter ipſum intuentes, <lb/>quamuis celerrimè progrederetur, nulla tamen ratione talem motum animaduerteremus. </s> <s xml:id="echoid-s2829" xml:space="preserve">eo igitur omiſ-<lb/>ſo de alio omnibus manifeſto diſſeramus.</s> <s xml:id="echoid-s2830" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2831" xml:space="preserve">Dico igitur totam hanc mundi machinam moueri motu volutationis, ſeu gytationis, eo ſcilicet modo, <lb/>quo Sphæra quæpiam binis i<unsure/>nnixa polis in torno poſita conuerti ſolet: </s> <s xml:id="echoid-s2832" xml:space="preserve">videm<unsure/>us enim omnes ſtellas in cæ-<lb/>lo ab ortu in occaſum, quotidiana conuerſione in orbem reuolui, non aliter, ac ſi cuidam Sphæræ, quæ <lb/>polis hærens tornaretur, affixæ eſſent: </s> <s xml:id="echoid-s2833" xml:space="preserve">paucæ enim earum ſua gyratione circulum maximum deſcribunt, <lb/>cæteræ minores circulos eoſq; </s> <s xml:id="echoid-s2834" xml:space="preserve">tanto mi<unsure/>nores, quanto magis ab illis diſtiterint; </s> <s xml:id="echoid-s2835" xml:space="preserve">ita vt quæ ab illis maximè <lb/>hinc inde recedunt, minimos circellos quaſi circa polos ſuis circuitibus oſtentent. </s> <s xml:id="echoid-s2836" xml:space="preserve">quod efficiunt non ſe-<lb/>cus, ac ſi in aliquo globo, ſuper axe ſuo, ac polis reuoluto veherentur. </s> <s xml:id="echoid-s2837" xml:space="preserve">id autem luculentiſſimè apparet in <lb/>ſtellis circumpolaribus, quæ in obliquis Sphæris, ſunt ſempiternæ apparitionis, hæ enim conſpicuos circa <lb/>noſtrum polum circulos, eo ſemper minores, quo ei viciniores circumducunt. </s> <s xml:id="echoid-s2838" xml:space="preserve">Idem præterea Aſtronomi <lb/>in Planetis obſeruarunt; </s> <s xml:id="echoid-s2839" xml:space="preserve">Planetæ enim intra duos Tropicos, aut parum extra eoſdem, diurna gyratione <lb/>per paralellos æquatori eo ſemper minores reuoluuntur, quo ab eo remotiores fuerint. </s> <s xml:id="echoid-s2840" xml:space="preserve">Ex motibus igi-<lb/>tur tam errantium, quam inerrantium ſyderũ colligimus partem mundi cęleſtem in orbem agitari. </s> <s xml:id="echoid-s2841" xml:space="preserve">Quod <lb/>verò ad Elementarem, ac ſublunarem attinet, nonnulli olim aerem eodem motu circumagi exiſtimabant, <lb/>quòd cometas in ſupremę aeris regione motu diurno ab ipſo aere in diurnũ gyrum circumuehi putabant: <lb/></s> <s xml:id="echoid-s2842" xml:space="preserve">verum enim verò, vt ſuo loco patebit, neutiquam fieri poteſt, vt cometæ, tam humili loco, tanta velocita-<lb/>te circum ferantur, tandiuq; </s> <s xml:id="echoid-s2843" xml:space="preserve">a nobis conſpiciantur. </s> <s xml:id="echoid-s2844" xml:space="preserve">eodem etiam motu mare percelli, nonnulli vt P. </s> <s xml:id="echoid-s2845" xml:space="preserve">Ioſe-<lb/>phus Acoſta, Nautarum experimentis confiſi, probare contendunt: </s> <s xml:id="echoid-s2846" xml:space="preserve">Nautæ enim Luſitanorũ quiad orien-<lb/>tis Indos, ac Sinas continenter nauigant, ac renauigant, experiuntur ſe ſemper tardius ad orientem, quam <lb/>ad occaſum nauigationes abſoluere, non ſecus, ac ſi in ortum aduerſis, in occaſum verò ſecundis fluctibus <lb/>nauigarent; </s> <s xml:id="echoid-s2847" xml:space="preserve">idque tanto manifeſtius, quanto æquatori propinquius velificauerint. </s> <s xml:id="echoid-s2848" xml:space="preserve">quod manifeſtum eſt ſi-<lb/>gnum, non ſolum mare, ſed etiam aerem diurna conuerſione, aliqua ſaltem ex parte, conuerti; </s> <s xml:id="echoid-s2849" xml:space="preserve">qua enim <lb/>ratione hoc motu a cælis afficeretur, nif<unsure/>i prius aeris regio eodem affecta eſf<unsure/>et? </s> <s xml:id="echoid-s2850" xml:space="preserve">ſic igitur tota mundi Sphæ-<lb/>ra (præter terram, quæ tamen ad totum mundum inſenſibilis eſt) motu hoc diurno ad modum Sphærę <lb/>reuoluitur; </s> <s xml:id="echoid-s2851" xml:space="preserve">quod probare volebamus.</s> <s xml:id="echoid-s2852" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2853" xml:space="preserve">Porrò<unsure/> hic motus omnium nobiliſſimus eſt tum quia totam mundi molem commoueat: </s> <s xml:id="echoid-s2854" xml:space="preserve">tum etiam quia <lb/>ſphæricus eſt, qui cæteris motibus nobilitate præſtat. </s> <s xml:id="echoid-s2855" xml:space="preserve">dicitur motus diurnus, quòd diurno ſpatio 24. </s> <s xml:id="echoid-s2856" xml:space="preserve">hora-<lb/>rum perficiatur: </s> <s xml:id="echoid-s2857" xml:space="preserve">dicitur primus, & </s> <s xml:id="echoid-s2858" xml:space="preserve">primi mobilis, quòd eum à primo, ac ſuperiori orbe in alias inferiores <lb/>mundi partes deriuari primiores putarint Aſtronomi; </s> <s xml:id="echoid-s2859" xml:space="preserve">fit enim ſuper polis, & </s> <s xml:id="echoid-s2860" xml:space="preserve">axe mundi, atq; </s> <s xml:id="echoid-s2861" xml:space="preserve">æquatoris.</s> <s xml:id="echoid-s2862" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div57" type="section" level="1" n="39"> <head xml:id="echoid-head41" style="it" xml:space="preserve">De Mundi fabrica. Cap. III.</head> <p> <s xml:id="echoid-s2863" xml:space="preserve">MVndum eſſe figura ſphærica præditum Philoſophi, atque Aſtronomi omnes ſequentibus rationibus <lb/>cenſuerunt.</s> <s xml:id="echoid-s2864" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2865" xml:space="preserve">1 Ratio prima deſumitur ex eius diurno motu, de quo modo diſſeruimus; </s> <s xml:id="echoid-s2866" xml:space="preserve">is enim manifeſtat mũdum, <lb/>ac præcipuè cœlũ moueri ſphæricè, ſeu ad modũ Sphæræ circa proprium axem, ac polos; </s> <s xml:id="echoid-s2867" xml:space="preserve">vt enim dictum <lb/>cſt, Planetæ, ac ſydera omnia; </s> <s xml:id="echoid-s2868" xml:space="preserve">imò Elementa ipſa in gyrum ab ortu in occaſum, nõ ſecus, ac in Sphæra con-<lb/>tingit, reuoluuntur; </s> <s xml:id="echoid-s2869" xml:space="preserve">quæ omnia argumento ſunt ſupremam cæli partem eſſe ſphæricam, ſeu globoſam, ac <lb/>proinde mundum figura ſphærica eſſe præditum.</s> <s xml:id="echoid-s2870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2871" xml:space="preserve">2 Sumitur a ſphæricæ figuræ, ac mundi ipſius nobilitate, ac perfectione: </s> <s xml:id="echoid-s2872" xml:space="preserve">perfectiſſimo namque, ac per-<lb/>fectiſſimo corpori, vti eſt mundus, debetur figura omnium perfectiſſima, ac nobiliſſima, quę eſt ſphæricæ: <lb/></s> <s xml:id="echoid-s2873" xml:space="preserve">exiſtimandum igitur eſt, ſapientiſſimum mundi Architectorem, Deum videlicet O. </s> <s xml:id="echoid-s2874" xml:space="preserve">M. </s> <s xml:id="echoid-s2875" xml:space="preserve">ei ſpæricam figu-<lb/>ram indidiſſe.</s> <s xml:id="echoid-s2876" xml:space="preserve"/> </p> <pb o="29" file="0045" n="45" rhead="Liber Secundus."/> <p> <s xml:id="echoid-s2877" xml:space="preserve">Quod autem ſphæra ſit omnium figurarum, tam planarum, quam ſolidarum perfectiſſima hiſce ratio-<lb/>nibus patebit, primo ſicut circulus omnibus planis figuris præcellit, ita quoq; </s> <s xml:id="echoid-s2878" xml:space="preserve">ſphæra ſolidas omnes figuras <lb/>antecellit; </s> <s xml:id="echoid-s2879" xml:space="preserve">nam ſicut circulus vnica linea, ſic ſphæra vnica ſuperficie concluditur; </s> <s xml:id="echoid-s2880" xml:space="preserve">ſicut in circulo apparet <lb/>maxima partiũ conſormitas, ac ſimilitudo, qua a medio vniformiter diſtant; </s> <s xml:id="echoid-s2881" xml:space="preserve">ita etiam omnes ſphæræ par-<lb/>tes ab ipſius medio conſimiliter recedunt, vnde etiã ipſius maxima pulchritudo exoritur: </s> <s xml:id="echoid-s2882" xml:space="preserve">præterea in neu-<lb/>tra harum figurarum principium, aut finem eſt aſſignare: </s> <s xml:id="echoid-s2883" xml:space="preserve">Inſuper, vtraque eundem ſemper in ſua reuolu-<lb/>tione locum occupat. </s> <s xml:id="echoid-s2884" xml:space="preserve">tandem vtraque eſt omnium figurarum ſibi Iſoperimetrarum maximè capax. </s> <s xml:id="echoid-s2885" xml:space="preserve">ſed ne <lb/>longior ſim, vide Proemium Mecha. </s> <s xml:id="echoid-s2886" xml:space="preserve">quæſt. </s> <s xml:id="echoid-s2887" xml:space="preserve">Ari otelis, cum noſtra explicatione in libro locorum Mathe-<lb/>maticorum Ariſtotelis, vbi de admirandis circu@s proprietatibus fuſius diſſeritur. </s> <s xml:id="echoid-s2888" xml:space="preserve">porrò ſphæram eſſe cir-<lb/>culo præſtantiorem hinc patet; </s> <s xml:id="echoid-s2889" xml:space="preserve">ille enim ſuperficies eſt duabus tantum dimenſionibus longitudine, & </s> <s xml:id="echoid-s2890" xml:space="preserve">la-<lb/>titudine prædita; </s> <s xml:id="echoid-s2891" xml:space="preserve">hæc verò eſt corpus tribus dimenſionibus conſtans, latitudine, longitudine, profundita-<lb/>te, qua propter omnium figurarum, tum planarum, tum ſolidarum ſphæra obtinet principatum.</s> <s xml:id="echoid-s2892" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2893" xml:space="preserve">Vt autem ratio illa deſumpta à capacitate Iſoperimetrarum figurarum probè percipiatur, nonnulla de <lb/>Iſoperimetris figuris in medium ſunt proferenda.</s> <s xml:id="echoid-s2894" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2895" xml:space="preserve">Iſoperimetræ igitur figuræ ſunt, quæ habent æquales ambitus, ſeu circum ferentias, ſiue ſint figuræ pla-<lb/>næ, ſiue ſolidæ, ideſt, ſuperficies, aut corpora; </s> <s xml:id="echoid-s2896" xml:space="preserve">quod, & </s> <s xml:id="echoid-s2897" xml:space="preserve">eorum nomen pulchrè indicat ισος, enim græcè, <lb/>æqualem, ſignificat: </s> <s xml:id="echoid-s2898" xml:space="preserve">@εριμετρος autem ambitum valet. </s> <s xml:id="echoid-s2899" xml:space="preserve">vbi notandum eſt per figuram, cum Geometris, in-<lb/>telligendam eſſe aeream, ſeu ſpatium tam planum, quam ſolidum terminatum aliqua peripheria, aut am-<lb/>bitu, non autem ipſum ambitum ſolum, vt Geometriæ expertes perperam ſolent exiſtimare. </s> <s xml:id="echoid-s2900" xml:space="preserve">Cum igitur <lb/>dicimus duas planas figuras, v. </s> <s xml:id="echoid-s2901" xml:space="preserve">g. </s> <s xml:id="echoid-s2902" xml:space="preserve">triangulum vnum, & </s> <s xml:id="echoid-s2903" xml:space="preserve">quadratum vnum eſſe inuicem Iſoperimetra, in-<lb/>telligimus duas ſuperficies, vnam triangularem, alteram quadratam habere æqualem ambitum, qui ambi-<lb/>tus erit linea, eas terminans. </s> <s xml:id="echoid-s2904" xml:space="preserve">cum verò dicimus duo corpora eſſe Iſoperimetra, v. </s> <s xml:id="echoid-s2905" xml:space="preserve">g. </s> <s xml:id="echoid-s2906" xml:space="preserve">cubum vnũ vni ſphæ-<lb/>ræ eſſe Iſoperimetrum, intelligimus ſpatia eorum ſolida, ſeu eorum ſoliditates habere æquales ambitus, <lb/>ideſt, terminari æqualibus ſuperficiebus, corpora enim ſuperficiebus terminantur.</s> <s xml:id="echoid-s2907" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2908" xml:space="preserve">Aduertendum præterea eſt, duas figuras planam alteram, alteram vero ſolidam, nulla ratione poſſe eſſe <lb/>mutuo Iſoperimetras, quia cum earum ambitus ſint diuerſi generis, planorum enim ſunt lineæ ambientes, <lb/>ſolidarum verò ſuperficies, nequeunt inter ipſas reperiri vllæ proportiones, vt conſtat ex definitione ter-<lb/>tia lib. </s> <s xml:id="echoid-s2909" xml:space="preserve">5. </s> <s xml:id="echoid-s2910" xml:space="preserve">Elem. </s> <s xml:id="echoid-s2911" xml:space="preserve">Euclidis; </s> <s xml:id="echoid-s2912" xml:space="preserve">quare neq; </s> <s xml:id="echoid-s2913" xml:space="preserve">proportionem æqualitatis inter eas reperire erit, ideſt, linea, & </s> <s xml:id="echoid-s2914" xml:space="preserve">ſuper-<lb/> <anchor type="figure" xlink:label="fig-0045-01a" xlink:href="fig-0045-01"/> ficies neq; </s> <s xml:id="echoid-s2915" xml:space="preserve">æquales, neq; </s> <s xml:id="echoid-s2916" xml:space="preserve">inæqua-<lb/>les inuicem eſie poſſunt. </s> <s xml:id="echoid-s2917" xml:space="preserve">his præ-<lb/>notatis probandum eſt circulum <lb/>inter omnes planas figuras Iſo-<lb/>perimetras ſphæram verò inter <lb/>ſolidas pariter Iſoperimetras eſ-<lb/>ſe capaciſſimam. </s> <s xml:id="echoid-s2918" xml:space="preserve">Exponãtur pri-<lb/>mo aliquot planæ figuræ Iſope-<lb/>rimetræ, quarum prima ſit trian-<lb/>gulum Iſoſceles, vt in figura vi-<lb/>des, cuius ſingula latera cõſtent lineolis 5. </s> <s xml:id="echoid-s2919" xml:space="preserve">æqualibus, baſis verò 6. </s> <s xml:id="echoid-s2920" xml:space="preserve">ſic enim eius perimeter, ſeu ambitus con-<lb/>tinebit huiuſmodi lineolas 16. </s> <s xml:id="echoid-s2921" xml:space="preserve">quarum modulus ſit linea F. </s> <s xml:id="echoid-s2922" xml:space="preserve">diuiſa in 16. </s> <s xml:id="echoid-s2923" xml:space="preserve">particulas æquales. </s> <s xml:id="echoid-s2924" xml:space="preserve">ſecunda figu-<lb/>ra ſit quadratum, cuius ſingula latera contineant quatuor lineolas æquales prædictis, ſic enim erit eius <lb/>perimeter 16. </s> <s xml:id="echoid-s2925" xml:space="preserve">Tertia ſic circulus, cuius perimeter, vel peripheria compræhendat etiam 16. </s> <s xml:id="echoid-s2926" xml:space="preserve">ex prædictis <lb/>lineolis. </s> <s xml:id="echoid-s2927" xml:space="preserve">Cum igitur omnium perimeter ſit 16. </s> <s xml:id="echoid-s2928" xml:space="preserve">ſecundum æquales menſuras, erunt omnes tres inuicem I<unsure/>ſo-<lb/>perimetræ. </s> <s xml:id="echoid-s2929" xml:space="preserve">conſtruximus autem circulum alijs duabus Iſoperimetrũ hac ratione: </s> <s xml:id="echoid-s2930" xml:space="preserve">conſtat enim ex demon-<lb/>ſtratis ab Archimede, quod etiam experimento patere poteſt, circumferẽtiam circuli ad ſuam diametrum <lb/>habere ferè eandem rationem quam habent 22. </s> <s xml:id="echoid-s2931" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s2932" xml:space="preserve">quare per auream Arithmeticæ regulam, reperio ita <lb/>ſe habere 22. </s> <s xml:id="echoid-s2933" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s2934" xml:space="preserve">quemadmodum 16. </s> <s xml:id="echoid-s2935" xml:space="preserve">ambitus ſcilicet quaſi circuli, ad 5. </s> <s xml:id="echoid-s2936" xml:space="preserve">& </s> <s xml:id="echoid-s2937" xml:space="preserve">vnam vndecimam, quare 5. </s> <s xml:id="echoid-s2938" xml:space="preserve">& </s> <s xml:id="echoid-s2939" xml:space="preserve"><lb/>vna vndecima ex illis lineolis, erit quæſita diameter. </s> <s xml:id="echoid-s2940" xml:space="preserve">huius diametri dimidium eſt 2. </s> <s xml:id="echoid-s2941" xml:space="preserve">& </s> <s xml:id="echoid-s2942" xml:space="preserve">ſex vndecimę, acce-<lb/>ptis igitur pro ſemidiametro 2. </s> <s xml:id="echoid-s2943" xml:space="preserve">& </s> <s xml:id="echoid-s2944" xml:space="preserve">ſex vndecimis ex prædictis lineolis. </s> <s xml:id="echoid-s2945" xml:space="preserve">earum interuallo deſcriptus eſt cir-<lb/>culus alijs duabus figuris Iſoperimeter, iam ſingularum areæ menſurandæ ſunt, vt appareat circulum eſſe <lb/>earum capaciſſimum, atq; </s> <s xml:id="echoid-s2946" xml:space="preserve">adeo maximum.</s> <s xml:id="echoid-s2947" xml:space="preserve"/> </p> <div xml:id="echoid-div57" type="float" level="2" n="1"> <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a"> <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0045-01"/> </figure> </div> <p> <s xml:id="echoid-s2948" xml:space="preserve">Quemadmodum autem Geometræ aptè lineas æqualibus lineis metiuntur, ita etiam ſuperficies, ſeu pla-<lb/>nas figuras æqualibus planis, videlicet æqualibus quadratis menſurant, quia, vel teſte Ariſtotele, menſura <lb/>debet eſſe eiuſdem generis cũ re menſurata, menſuratio trianguli ſic perficitur; </s> <s xml:id="echoid-s2949" xml:space="preserve">ducta perpendiculari A D. <lb/></s> <s xml:id="echoid-s2950" xml:space="preserve">quæ baſim bifariam ſecat, dimidium baſis, quod eſt 3. </s> <s xml:id="echoid-s2951" xml:space="preserve">ducitur in perpendiculum A D. </s> <s xml:id="echoid-s2952" xml:space="preserve">quod eſt 4. </s> <s xml:id="echoid-s2953" xml:space="preserve">vnde pro-<lb/>ducuntur 12. </s> <s xml:id="echoid-s2954" xml:space="preserve">ideſt, 12. </s> <s xml:id="echoid-s2955" xml:space="preserve">quadrata æqualia, quorum latera ſunt lineolæ æquales prædictæ, hac autem 12. </s> <s xml:id="echoid-s2956" xml:space="preserve">qua-<lb/>drata conſtituunt aream trianguli, & </s> <s xml:id="echoid-s2957" xml:space="preserve">proinde ipſius magnitudinem produnt. </s> <s xml:id="echoid-s2958" xml:space="preserve">quod manifeſtius ſit, ſi com-<lb/>pleatur rectangulum A D B E. </s> <s xml:id="echoid-s2959" xml:space="preserve">id enim erit æquale toti triangulo A B C. </s> <s xml:id="echoid-s2960" xml:space="preserve">vt figuram contemplanti patere <lb/>poteſt; </s> <s xml:id="echoid-s2961" xml:space="preserve">& </s> <s xml:id="echoid-s2962" xml:space="preserve">ex 42. </s> <s xml:id="echoid-s2963" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s2964" xml:space="preserve">Euclidis. </s> <s xml:id="echoid-s2965" xml:space="preserve">Continet autem hoc rectangulum 12. </s> <s xml:id="echoid-s2966" xml:space="preserve">parua quadrata, quæ eſt area <lb/>trianguli, vt dictum eſt. </s> <s xml:id="echoid-s2967" xml:space="preserve">Quadratum autem continet 16. </s> <s xml:id="echoid-s2968" xml:space="preserve">quadrata æqualia prædictis: </s> <s xml:id="echoid-s2969" xml:space="preserve">quare ipſius area ma-<lb/>ior eſt area trianguli; </s> <s xml:id="echoid-s2970" xml:space="preserve">quoniam quamuis illi ſit Iſoperimetrum magis tamen ad rotũditatem accedit, ideſt, <lb/>anguli ipſius magis dilatantur, ac proinde euadit capacius, ac maius. </s> <s xml:id="echoid-s2971" xml:space="preserve">Circuli menſuratio ſic abſoluitur à <lb/>Geometris; </s> <s xml:id="echoid-s2972" xml:space="preserve">ducunt ſemidiametrum in ſemicircumferentiam, & </s> <s xml:id="echoid-s2973" xml:space="preserve">quod producitur eſt circuli area, ſeu quan <pb o="30" file="0046" n="46" rhead="De Mundi Fabrica."/> titas; </s> <s xml:id="echoid-s2974" xml:space="preserve">ducta igitur ſemidiametro 2. </s> <s xml:id="echoid-s2975" xml:space="preserve">cum ſex vndecimis in 8. </s> <s xml:id="echoid-s2976" xml:space="preserve">ſemicircumferentiam, producitur 20 cum qua-<lb/>tuor vndecimis pro circuli area. </s> <s xml:id="echoid-s2977" xml:space="preserve">id clarè perſpicitur conſtructo rectangulo ex ſemidiametro, & </s> <s xml:id="echoid-s2978" xml:space="preserve">ſemicircũ-<lb/>ferentia, vti vides in figura, ſic enim ſemidiameter ducitur in circumſerentiam; </s> <s xml:id="echoid-s2979" xml:space="preserve">in eo rectangulo vides <lb/>contineri 16. </s> <s xml:id="echoid-s2980" xml:space="preserve">parua quadrata, & </s> <s xml:id="echoid-s2981" xml:space="preserve">alia 8. </s> <s xml:id="echoid-s2982" xml:space="preserve">rectangula, quadratis minora, quę tamen æqualia ſunt 4. </s> <s xml:id="echoid-s2983" xml:space="preserve">& </s> <s xml:id="echoid-s2984" xml:space="preserve">quatuor <lb/>vndecimis quadratis, quibus circulus quadratum ſuperat. </s> <s xml:id="echoid-s2985" xml:space="preserve">hæc praxis probatur à P. </s> <s xml:id="echoid-s2986" xml:space="preserve">Clauio in Geom. </s> <s xml:id="echoid-s2987" xml:space="preserve">practi-<lb/>ca lib. </s> <s xml:id="echoid-s2988" xml:space="preserve">4. </s> <s xml:id="echoid-s2989" xml:space="preserve">cap. </s> <s xml:id="echoid-s2990" xml:space="preserve">6. </s> <s xml:id="echoid-s2991" xml:space="preserve">& </s> <s xml:id="echoid-s2992" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s2993" xml:space="preserve">4. </s> <s xml:id="echoid-s2994" xml:space="preserve">lib. </s> <s xml:id="echoid-s2995" xml:space="preserve">7. </s> <s xml:id="echoid-s2996" xml:space="preserve">idem aliqua ex parte experiri poteris, ſi enim prædi ctus circulus diuidatur <lb/>in parua quadrata prædictis æqualia, apparebit eum multa plura ex ijs continere quam 16. </s> <s xml:id="echoid-s2997" xml:space="preserve">vti videre eſt in <lb/>circulo P. </s> <s xml:id="echoid-s2998" xml:space="preserve">pr<unsure/>iori æquali, vnde patet circulum eſſe trium harum figurarum Iſoperimetrarũ capaciſſimum, <lb/>idemque accidet in omnibus alijs figuris: </s> <s xml:id="echoid-s2999" xml:space="preserve">vbi obſeruandum eſt illam ſemper eſſe capaciorem, quæ ro-<lb/>tundior eſt.</s> <s xml:id="echoid-s3000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3001" xml:space="preserve">Ex demonſtratis è contrario patet, eandem ſuperficiem minori ambitu contineri, quo ambitus fuerit <lb/>rotundior. </s> <s xml:id="echoid-s3002" xml:space="preserve">Præterea manifeſtum eſt eos hallucinari poſſe, qui vrbes, aut regiones Iſoperimetr as æqua-<lb/>les eſſe exiſtimant; </s> <s xml:id="echoid-s3003" xml:space="preserve">aut eas eſſe maiores, quæ maiori ambitu ambiuntur; </s> <s xml:id="echoid-s3004" xml:space="preserve">cũ eadem area ſub minori, & </s> <s xml:id="echoid-s3005" xml:space="preserve">ma-<lb/>iori ambitu coarctari poſſit. </s> <s xml:id="echoid-s3006" xml:space="preserve">vide Pappum Alexandrinum lib. </s> <s xml:id="echoid-s3007" xml:space="preserve">5. </s> <s xml:id="echoid-s3008" xml:space="preserve">collectionum, aut Clauium lib. </s> <s xml:id="echoid-s3009" xml:space="preserve">7. </s> <s xml:id="echoid-s3010" xml:space="preserve">Geom. <lb/></s> <s xml:id="echoid-s3011" xml:space="preserve">pract. </s> <s xml:id="echoid-s3012" xml:space="preserve">ſed iam ad ſolida tranſeamus.</s> <s xml:id="echoid-s3013" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3014" xml:space="preserve">Exponantur igitur, ex. </s> <s xml:id="echoid-s3015" xml:space="preserve">gr. </s> <s xml:id="echoid-s3016" xml:space="preserve">tria ſolida Iſoperimetra, Paralellepipedum, Cubus, Sphæra. </s> <s xml:id="echoid-s3017" xml:space="preserve">quorũ ambien-<lb/>tes ſuperficies conſtent ex 24. </s> <s xml:id="echoid-s3018" xml:space="preserve">æqualibus quadratis, quorum modulus ſit quadratum M. </s> <s xml:id="echoid-s3019" xml:space="preserve">Paralellepipedum <lb/> <anchor type="figure" xlink:label="fig-0046-01a" xlink:href="fig-0046-01"/> corpus quadratum oblungum inſtar trabis, cuius oppoſita <lb/>facies ſunt paralellæ. </s> <s xml:id="echoid-s3020" xml:space="preserve">quod autem in figura exponitur am-<lb/>bitu 6. </s> <s xml:id="echoid-s3021" xml:space="preserve">faciebus, ſeu planis, quorum 4. </s> <s xml:id="echoid-s3022" xml:space="preserve">lõgiora, ſingula con-<lb/>tinent 5. </s> <s xml:id="echoid-s3023" xml:space="preserve">quadrata cum dimidio: </s> <s xml:id="echoid-s3024" xml:space="preserve">extrema verò duo vnum <lb/>tantum. </s> <s xml:id="echoid-s3025" xml:space="preserve">Cubus verò tetminatur 6. </s> <s xml:id="echoid-s3026" xml:space="preserve">quadratis ſaciebus, in <lb/>quibus ſingulis ſunt 4. </s> <s xml:id="echoid-s3027" xml:space="preserve">quadrata. </s> <s xml:id="echoid-s3028" xml:space="preserve">Sphæra autem debet, & </s> <s xml:id="echoid-s3029" xml:space="preserve"><lb/>ipſa ſphærica ſuperficie ambiri, quæ 24. </s> <s xml:id="echoid-s3030" xml:space="preserve">ex ijſdem quadra-<lb/>tis æqualis ſit. </s> <s xml:id="echoid-s3031" xml:space="preserve">conſtruitur autem ſphæra prædicto cubo Iſoperimetra hoc modo. </s> <s xml:id="echoid-s3032" xml:space="preserve">Accipitur quarta pars <lb/>ſuperficiei eam ambituræ, ideſt, parua 6. </s> <s xml:id="echoid-s3033" xml:space="preserve">quadrata ex ijs, quæ cubum ambiunt, in circulum redi guntur (vti <lb/>docet Clauius in fine lib. </s> <s xml:id="echoid-s3034" xml:space="preserve">6. </s> <s xml:id="echoid-s3035" xml:space="preserve">Elem. </s> <s xml:id="echoid-s3036" xml:space="preserve">Euclidis, aut in Geom. </s> <s xml:id="echoid-s3037" xml:space="preserve">pract. </s> <s xml:id="echoid-s3038" xml:space="preserve">lib. </s> <s xml:id="echoid-s3039" xml:space="preserve">7. </s> <s xml:id="echoid-s3040" xml:space="preserve">num. </s> <s xml:id="echoid-s3041" xml:space="preserve">4. </s> <s xml:id="echoid-s3042" xml:space="preserve">appendicis) erit enim is circu-<lb/>lus, circulus maximus futuræ ſphæræ, ac proinde diameter eius eiuſdem ſphæræ diameter erit; </s> <s xml:id="echoid-s3043" xml:space="preserve">habita igi-<lb/>tur diametro, habebitur etiam ſphæra, ſicque tria aderunt Iſoperimetra, quæ etiam Mechanicè, diligenti <lb/>tamen opera, ex aliqua ductili materia, veluti ex cera, confici poſſunt, quòd Lectoris induſtr@æ relinquo. <lb/></s> <s xml:id="echoid-s3044" xml:space="preserve">Prædicta igitur tria Iſoperimetra iam menſuranda ſunt, ideſt, earum capacitates inueſtigandæ: </s> <s xml:id="echoid-s3045" xml:space="preserve">porrò li-<lb/>neas lineis, & </s> <s xml:id="echoid-s3046" xml:space="preserve">ſuperficies quadratis ſuperficiebus menſuramus, ita etiam corpora corporibus, cub@s videli-<lb/>cet metimur, quia teſte Ariſtotele, menſura debet eſſe eiuſdem generis, cum re menſurata. </s> <s xml:id="echoid-s3047" xml:space="preserve">Primo igitur <lb/>ex lib. </s> <s xml:id="echoid-s3048" xml:space="preserve">5. </s> <s xml:id="echoid-s3049" xml:space="preserve">Geom. </s> <s xml:id="echoid-s3050" xml:space="preserve">pract. </s> <s xml:id="echoid-s3051" xml:space="preserve">Clauij, Paralellepipedum capit paruos cubos 5 {1/2}. </s> <s xml:id="echoid-s3052" xml:space="preserve">vt etiam ex ſolo figuræ aſpectu pa-<lb/>tet. </s> <s xml:id="echoid-s3053" xml:space="preserve">Cubus autem capit paruos 8. </s> <s xml:id="echoid-s3054" xml:space="preserve">cubos ex ijſdem, quare ſuperat Paralellepipedum cubis 2 {1/2}. </s> <s xml:id="echoid-s3055" xml:space="preserve">ſphæram ſic <lb/>menſurabis, per circinum diligenter, accipe diametrũ circuli maximi datæ ſphæræ, quem ſupra diximus <lb/>continere parua 6. </s> <s xml:id="echoid-s3056" xml:space="preserve">quadrata ex ibi aſſumptis; </s> <s xml:id="echoid-s3057" xml:space="preserve">eam diametrum inuenies cõtinere paulo plus quam 2. </s> <s xml:id="echoid-s3058" xml:space="preserve">& </s> <s xml:id="echoid-s3059" xml:space="preserve">duas <lb/>tertias ex lineolis, ſeu lateribus quadratorum prædictorum; </s> <s xml:id="echoid-s3060" xml:space="preserve">hanc etiam diametrum ſic reperies, quoniam <lb/>area circuli ad quadratum ſuæ diametri habet proportionem ſicuti ferè 11. </s> <s xml:id="echoid-s3061" xml:space="preserve">ad 14. </s> <s xml:id="echoid-s3062" xml:space="preserve">ex prop @. </s> <s xml:id="echoid-s3063" xml:space="preserve">2. </s> <s xml:id="echoid-s3064" xml:space="preserve">lib 4. </s> <s xml:id="echoid-s3065" xml:space="preserve">Geom-<lb/>pract. </s> <s xml:id="echoid-s3066" xml:space="preserve">Clauij, ſi per auream regulam fiat, vt 11. </s> <s xml:id="echoid-s3067" xml:space="preserve">ad 14. </s> <s xml:id="echoid-s3068" xml:space="preserve">ita 6. </s> <s xml:id="echoid-s3069" xml:space="preserve">area circuli, ad aliud, inuenies 7. </s> <s xml:id="echoid-s3070" xml:space="preserve">cum ſeptem vn-<lb/>decimis pro quadrato diametri: </s> <s xml:id="echoid-s3071" xml:space="preserve">huius quadrati radix, erit etiam circuli diameter; </s> <s xml:id="echoid-s3072" xml:space="preserve">ea autem radix ſit linea <lb/>2. </s> <s xml:id="echoid-s3073" xml:space="preserve">& </s> <s xml:id="echoid-s3074" xml:space="preserve">duo tertia, quamuis ſit vera radice minor: </s> <s xml:id="echoid-s3075" xml:space="preserve">hic igitur radix ſi multiplicetur in ſextam partem ſuperfi-<lb/>ciei ambientis ſphærã, ideſt, in 4. </s> <s xml:id="echoid-s3076" xml:space="preserve">productus numerus erit ſphæræ ſoliditas, ex propoſ. </s> <s xml:id="echoid-s3077" xml:space="preserve">7. </s> <s xml:id="echoid-s3078" xml:space="preserve">lib. </s> <s xml:id="echoid-s3079" xml:space="preserve">5. </s> <s xml:id="echoid-s3080" xml:space="preserve">Geom. </s> <s xml:id="echoid-s3081" xml:space="preserve">pract. </s> <s xml:id="echoid-s3082" xml:space="preserve"><lb/>Clauij, productus autẽ numerus ex ductu 2. </s> <s xml:id="echoid-s3083" xml:space="preserve">& </s> <s xml:id="echoid-s3084" xml:space="preserve">duobus tertijs, ſeu octo tertijs, ideſt, 10 cũ duabus tert@js, igi-<lb/>tur cubi 10. </s> <s xml:id="echoid-s3085" xml:space="preserve">cum duabus tertijs paruis ex ijſdem, qui conflant Paralellepipedũ, & </s> <s xml:id="echoid-s3086" xml:space="preserve">cubum, cõſtituuntſphæ-<lb/>ræ ſoliditatem, ſeu aream ſolidam. </s> <s xml:id="echoid-s3087" xml:space="preserve">quæ quantitas quamuis ſit vera minor ob aſlumptas proportiones, ad-<lb/>huctamen ſuperat multo alia duo corpora Iſoperimetra, eſt enim ad Paralellepipedum ferè dupla, cubum <lb/>verò ſuperat paruis cub@s 2 {1/2}. </s> <s xml:id="echoid-s3088" xml:space="preserve">ad eum enim ſe habet, vt 10. </s> <s xml:id="echoid-s3089" xml:space="preserve">cum duabus tertijs, ad 8. </s> <s xml:id="echoid-s3090" xml:space="preserve">idem accidit omnibus <lb/>alijs @olidis ſphæræ Iſoperimetris. </s> <s xml:id="echoid-s3091" xml:space="preserve">patet igitur ſphæram eſſe omnium Iſoperimetrarum capaciſſimam. </s> <s xml:id="echoid-s3092" xml:space="preserve"><lb/>quod erat probandum.</s> <s xml:id="echoid-s3093" xml:space="preserve"/> </p> <div xml:id="echoid-div58" type="float" level="2" n="2"> <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a"> <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/> </figure> </div> <p> <s xml:id="echoid-s3094" xml:space="preserve">Aliter eorum quantitates Mechanicè expendere poſſumus, ideſt, pondere examinare. </s> <s xml:id="echoid-s3095" xml:space="preserve">nam ſi paralel-<lb/>lepipedum pendit libras 5 {1/2}. </s> <s xml:id="echoid-s3096" xml:space="preserve">cubus pendet 8. </s> <s xml:id="echoid-s3097" xml:space="preserve">ſphæra, vero pluſquam 10. </s> <s xml:id="echoid-s3098" xml:space="preserve">cum duabus tertijs, debent autem <lb/>eſſe ex eadem materia, & </s> <s xml:id="echoid-s3099" xml:space="preserve">quidem in pondere homogena. </s> <s xml:id="echoid-s3100" xml:space="preserve">Hic etiam aduertendum eſt, corpus illud reli-<lb/>quis eſſe capacius, quod magis ad ſphæricitatem accedit; </s> <s xml:id="echoid-s3101" xml:space="preserve">quod eius anguli magis dilatentur. </s> <s xml:id="echoid-s3102" xml:space="preserve">Ex demon-<lb/>ſtratis etiam ſequitur, eandem materiam ſub figura ſphærica minori ſuperficie ambiri, quàm ſub quauis <lb/>alia figura: </s> <s xml:id="echoid-s3103" xml:space="preserve">quare eadem materia a ſphæricam ad cubicam translata figuram, maiori ambiente ſuperficie <lb/>indigeret. </s> <s xml:id="echoid-s3104" xml:space="preserve">Patet igitur circulum inter planas, ſphæram inter ſolidas, eſſe capaciſſimas. </s> <s xml:id="echoid-s3105" xml:space="preserve">Vide Clauium <lb/>de figuris Iſoperimetris in Geom. </s> <s xml:id="echoid-s3106" xml:space="preserve">pract.</s> <s xml:id="echoid-s3107" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3108" xml:space="preserve">3 Ratio, ſi mundus non eſſet ſphęr@cus, ſequeretur Deum, naturamuè fruſtra ſuperficiem aliquam fe-<lb/>ciſſe; </s> <s xml:id="echoid-s3109" xml:space="preserve">eadem enim mundi materia ſub alia quauis figura quam ſphęrica, ind@geret, vti ſupra annotauimus, <lb/>maiori ſuperficie ambiente: </s> <s xml:id="echoid-s3110" xml:space="preserve">quare cum poſſit exiſtere cum minori ſuperficie, ſi ſit ſphærica, cur ad aliam. <lb/></s> <s xml:id="echoid-s3111" xml:space="preserve">figuram fuiſſe redigenda, quæ la xiori ambitu indueretur.</s> <s xml:id="echoid-s3112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3113" xml:space="preserve">4 Apes, Veſpæ, Crabrones, ſuis cellulis capaciſſimam omnium figurarum replentium vacuum, attri- <pb o="31" file="0047" n="47" rhead="Liber Secundus."/> buunt; </s> <s xml:id="echoid-s3114" xml:space="preserve">quidniigitur Deus, & </s> <s xml:id="echoid-s3115" xml:space="preserve">natura in hac mira mundi architectatione, figurarum capaciſſimam coopta-<lb/>rint? </s> <s xml:id="echoid-s3116" xml:space="preserve">vide loca Ariſtotelis Mathematica cum noſtra expoſitione ad tex. </s> <s xml:id="echoid-s3117" xml:space="preserve">66. </s> <s xml:id="echoid-s3118" xml:space="preserve">tertij. </s> <s xml:id="echoid-s3119" xml:space="preserve">de cælo, vbi admiranda <lb/>hæc Apum induſtria exponitur.</s> <s xml:id="echoid-s3120" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3121" xml:space="preserve">Atq; </s> <s xml:id="echoid-s3122" xml:space="preserve">hæ ſunt rationes, quæ quidem ſatis probabiliter mundum eſſe ſphæricum perſuadent, non tamen <lb/>euidenter euincunt: </s> <s xml:id="echoid-s3123" xml:space="preserve">potuit enim D. </s> <s xml:id="echoid-s3124" xml:space="preserve">O. </s> <s xml:id="echoid-s3125" xml:space="preserve">M. </s> <s xml:id="echoid-s3126" xml:space="preserve">aliqua de cauſa nobis ignota, aliam ei attribuiſſe figuram.</s> <s xml:id="echoid-s3127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3128" xml:space="preserve">Hiſce porrò<unsure/> quæ lumine naturali dicta ſunt, addenda exiſtimaui nonnulla, ex ſacris literis, in confirma-<lb/>tionem rotunditatis Mundi. </s> <s xml:id="echoid-s3129" xml:space="preserve">ea autem ſunt, quæ noſter Pererius tom. </s> <s xml:id="echoid-s3130" xml:space="preserve">1. </s> <s xml:id="echoid-s3131" xml:space="preserve">lib. </s> <s xml:id="echoid-s3132" xml:space="preserve">2. </s> <s xml:id="echoid-s3133" xml:space="preserve">cap. </s> <s xml:id="echoid-s3134" xml:space="preserve">3. </s> <s xml:id="echoid-s3135" xml:space="preserve">in Geneſim, de hac re <lb/>ſcribit. </s> <s xml:id="echoid-s3136" xml:space="preserve">vbi cum aſſeruiſſet Philoſophiæ atq; </s> <s xml:id="echoid-s3137" xml:space="preserve">Aſtronomorum ſententiam de Mundi rotunditate, poſtea ſic <lb/>ſubdit; </s> <s xml:id="echoid-s3138" xml:space="preserve">quare non ſunt nobis audiendi Scriptores quidam Eccleſiaſtici, qui cælum eſſe rotundum non mo-<lb/>do negarunt, ſed etiam ſacris literis aduerſari exiſtimarunt: </s> <s xml:id="echoid-s3139" xml:space="preserve">Atenimuero tantum abeſt vt contraria ſen-<lb/>tentia, contraria ſit Diuinæ ſcripturæ, vt cum ea mirificè concordet. </s> <s xml:id="echoid-s3140" xml:space="preserve">Enimuero cælum eſſe rotundum, <lb/>nec vno loco, nec obſcurè indicat ſacra ſcriptura, nam in lib. </s> <s xml:id="echoid-s3141" xml:space="preserve">Eccleſiaſt. </s> <s xml:id="echoid-s3142" xml:space="preserve">Diuina Sapientia ſic loquitur; </s> <s xml:id="echoid-s3143" xml:space="preserve">Gy-<lb/>rum cæli circuiui ſola, quod textus græcus ſignificantius exprimit, dicit enim, gyrum cæli rotundaui, ſiue <lb/>conglobaui ſola. </s> <s xml:id="echoid-s3144" xml:space="preserve">& </s> <s xml:id="echoid-s3145" xml:space="preserve">apud Iob, cùm dicitur; </s> <s xml:id="echoid-s3146" xml:space="preserve">ſub quo curuantur qui portant orbem, ideſt, mundum, clarè ſi-<lb/>gnificatur mundum eſſe orbem, ſeu globum. </s> <s xml:id="echoid-s3147" xml:space="preserve">tandem verba illa in cap. </s> <s xml:id="echoid-s3148" xml:space="preserve">8. </s> <s xml:id="echoid-s3149" xml:space="preserve">Prou. </s> <s xml:id="echoid-s3150" xml:space="preserve">Gyro valiabant abyſſos, ſi-<lb/>gnificant circulo cæleſtium corporum inanitatem hanc quę intra cælos eſt, circundatam eſſe. </s> <s xml:id="echoid-s3151" xml:space="preserve">hæc ille. </s> <s xml:id="echoid-s3152" xml:space="preserve">por-<lb/>ro de cæli Empyrei figura Theologorum eſt diſputare, ac determinare non noſtrum.</s> <s xml:id="echoid-s3153" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div60" type="section" level="1" n="40"> <head xml:id="echoid-head42" style="it" xml:space="preserve">De Mundi quantitate, & Magnitudine. Cap. IIII.</head> <p> <s xml:id="echoid-s3154" xml:space="preserve">QVod ad diſcretam attinet quantitatem, ideſt, vtrum vnus, an plures ſunt mundi, nihil certi naturæ <lb/>lu mine aſſeri poſſe exiſtimo, neq; </s> <s xml:id="echoid-s3155" xml:space="preserve">noſtrum eſt id inquirere.</s> <s xml:id="echoid-s3156" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3157" xml:space="preserve">De continua verò, ideſt, de mundi magnitudine, nihil in præſentia ſtatuere poſſumus; </s> <s xml:id="echoid-s3158" xml:space="preserve">cum totius mun-<lb/>di magnitudo paulatim per partes ipſum componẽtes magna Aſtronomorum ſagacitate indagetur; </s> <s xml:id="echoid-s3159" xml:space="preserve">qua-<lb/>re ad finem vſq; </s> <s xml:id="echoid-s3160" xml:space="preserve">præſentis tractatus differendum, vbi oſtendemus totius Mundanæ Sphærægyrum con-<lb/>tinere milliariorum Aſtronomicorum 302.</s> <s xml:id="echoid-s3161" xml:space="preserve">412.</s> <s xml:id="echoid-s3162" xml:space="preserve">000. </s> <s xml:id="echoid-s3163" xml:space="preserve">& </s> <s xml:id="echoid-s3164" xml:space="preserve">ſemidiametrum Mundi conſtare ex ſemidiametris <lb/>terræ 14.</s> <s xml:id="echoid-s3165" xml:space="preserve">000. </s> <s xml:id="echoid-s3166" xml:space="preserve">quæ faciunt milliaria noſtratia 48.</s> <s xml:id="echoid-s3167" xml:space="preserve">111.</s> <s xml:id="echoid-s3168" xml:space="preserve">000.</s> <s xml:id="echoid-s3169" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div61" type="section" level="1" n="41"> <head xml:id="echoid-head43" style="it" xml:space="preserve"><emph style="bf">De mundano lumine, & vmbra. Cap. V.</emph></head> <p> <s xml:id="echoid-s3170" xml:space="preserve">QVa ratione mundus ab aliquo externo, ac non mũdano lumine colluſtretur, atq; </s> <s xml:id="echoid-s3171" xml:space="preserve">inde vmbram emit-<lb/>tat, non inquirimus, quia nullum habemus huius colluſtrationis indicium, aut fundamentum. </s> <s xml:id="echoid-s3172" xml:space="preserve">Verum <lb/>ex vſu fuerit, ob ea, quæ dicentur, nonnulla de mundana luce, & </s> <s xml:id="echoid-s3173" xml:space="preserve">vmbra, quibus interiora mundi <lb/>lumine, & </s> <s xml:id="echoid-s3174" xml:space="preserve">tenebris perfunduntur, vniuerſim ex aſtronomica optices parte prænotaſſe.</s> <s xml:id="echoid-s3175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3176" xml:space="preserve">1 Omne corpus lucidũ, ac luminoſum, vti Sol, lumen ab ſe per lineas rectas, ſeu per rectos radios quo-<lb/>quo verſum emittit: </s> <s xml:id="echoid-s3177" xml:space="preserve">imò quodlibet lucidi corporis punctum idem efficit.</s> <s xml:id="echoid-s3178" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3179" xml:space="preserve">2 Lumen iſtud, non æquèomnia obuiantia corpora perſundit, ſed aliter diaphana ſeu tranſparẽtia, vti <lb/>aerem, & </s> <s xml:id="echoid-s3180" xml:space="preserve">cælum: </s> <s xml:id="echoid-s3181" xml:space="preserve">aliter den@a, & </s> <s xml:id="echoid-s3182" xml:space="preserve">opaca, vti terram, lapides, Lunam. </s> <s xml:id="echoid-s3183" xml:space="preserve">D@aphana quidem lumen adueniens <lb/>ſuſcipiunt, ſed liberum illud tranſmittunt, nec ſiſtunt, aut reflectunt: </s> <s xml:id="echoid-s3184" xml:space="preserve">Opaca verò lumen ſe inuadens ſiſten-<lb/>do, ac detinendo, ab eodem illuminantur; </s> <s xml:id="echoid-s3185" xml:space="preserve">illudq; </s> <s xml:id="echoid-s3186" xml:space="preserve">in aduerſum reflectendo conſpicua omnibus reddũtur: <lb/></s> <s xml:id="echoid-s3187" xml:space="preserve">aer, aut criſtallus quia lumen tranſmittũt, etiamſi ab eo perſpicua, non tamen conſpicua reddu ntur. </s> <s xml:id="echoid-s3188" xml:space="preserve">paries <lb/>vel terra, quia lumeu detinent, non ab eo ſolum illuminantur, ſed etiam ab eo viſibilia efficiuntur. </s> <s xml:id="echoid-s3189" xml:space="preserve">aer, & </s> <s xml:id="echoid-s3190" xml:space="preserve"><lb/>æther, quia lucem liberam præterlabi ſinunt, ideo vmbram nullam emittunt, quoniam vmbra eſt lucis pri-<lb/>@atio, quam iſthæc diaphana nullam efficiunt. </s> <s xml:id="echoid-s3191" xml:space="preserve">Opaca verò corpora, cum lucem, ne vlterius peruadat, in-<lb/> <anchor type="figure" xlink:label="fig-0047-01a" xlink:href="fig-0047-01"/> hibeant, ideo in parte lumini auerſa, negatio-<lb/>nem luminis, quæ ipſiſſima eſt vmbra, efficiũt.</s> <s xml:id="echoid-s3192" xml:space="preserve"/> </p> <div xml:id="echoid-div61" type="float" level="2" n="1"> <figure xlink:label="fig-0047-01" xlink:href="fig-0047-01a"> <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0047-01"/> </figure> </div> <p> <s xml:id="echoid-s3193" xml:space="preserve">3. </s> <s xml:id="echoid-s3194" xml:space="preserve">Hanc lucem per lineas rectas, ſeu per re-<lb/>ctos radios, protendi ac euibrari vmbrarũ do-<lb/>cet experientia; </s> <s xml:id="echoid-s3195" xml:space="preserve">videmus enim vmbras ex om <lb/>ni parte rectis lineis terminari, quæ rectæ li-<lb/>neæ, ſeu radij debent intelligi produci à cor-<lb/>pore vmbroſo per aerem, vſq; </s> <s xml:id="echoid-s3196" xml:space="preserve">ad vmbræ finẽ: <lb/></s> <s xml:id="echoid-s3197" xml:space="preserve">quod hinc facilius percipltur. </s> <s xml:id="echoid-s3198" xml:space="preserve">quia ſi quæ opa-<lb/>ca lumini obijciantur, ea ſolum lumine priua-<lb/>ri videmus, quæ obici illi, ac lumini in dire-<lb/>ctum ſint fita. </s> <s xml:id="echoid-s3199" xml:space="preserve">hanc linearum rectitudinem, <lb/>nobis oſtendunt in ſequentibus figuris duæ <lb/>lineæ A E. </s> <s xml:id="echoid-s3200" xml:space="preserve">& </s> <s xml:id="echoid-s3201" xml:space="preserve">B F. </s> <s xml:id="echoid-s3202" xml:space="preserve">quæ vmbram luminoſæ <lb/>ſphæræ A B. </s> <s xml:id="echoid-s3203" xml:space="preserve">vndique terminant, pro quibns <lb/>intelligere etiam poſſumus duos radios re-<lb/>ctos A E. </s> <s xml:id="echoid-s3204" xml:space="preserve">B F.</s> <s xml:id="echoid-s3205" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3206" xml:space="preserve">4 Præmittendum eſt, vmbram eſſe non <lb/>ſolum illam ſuperficiem tenebroſam in ſolo, <pb o="32" file="0048" n="48" rhead="De Mundi Fabrica"/> aut pariete apparentem, ſed eſſe in aere quid ſolidum, aut corporeum non illuminatum; </s> <s xml:id="echoid-s3207" xml:space="preserve">eſt enim vmbra <lb/>in toto illo aere, directo lumine non perfuſo, qui in parte corporis illuminantis auerſa latet: </s> <s xml:id="echoid-s3208" xml:space="preserve">qui quidẽ aer <lb/>ſpatium quoddam occupat tres habens dimenſiones: </s> <s xml:id="echoid-s3209" xml:space="preserve">vmbra verò, quæ in pauimento, aut muro nigricans <lb/>ce@nitur, eſt illius vmbræ ſolidæ ſectio, vel terminus factus à pariete; </s> <s xml:id="echoid-s3210" xml:space="preserve">vt in figuris, in quarum prima ſphæ-<lb/>ra A B. </s> <s xml:id="echoid-s3211" xml:space="preserve">illuminante alteram ſphæram C D. </s> <s xml:id="echoid-s3212" xml:space="preserve">proijcitur vmbra C D. </s> <s xml:id="echoid-s3213" xml:space="preserve">F E. </s> <s xml:id="echoid-s3214" xml:space="preserve">quæ nihil aliud eſt, quam aer ille <lb/>rectis radijs ſphæræ lucidæ non perſuſus qui aer corpulẽtus eſt: </s> <s xml:id="echoid-s3215" xml:space="preserve">circulus autem obſcurus E F. </s> <s xml:id="echoid-s3216" xml:space="preserve">parieti G H. <lb/></s> <s xml:id="echoid-s3217" xml:space="preserve">adhærens, eſt terminus, ſeu ſectio illius vmbræ corporeæ, facta ab ipſo pariete.</s> <s xml:id="echoid-s3218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3219" xml:space="preserve">5 Notandum aliam eſſe lucem primariam, iliam ſcilicet quæ nullo obice recta fertur: </s> <s xml:id="echoid-s3220" xml:space="preserve">aliam ſecunda-<lb/>riam, quæ ſcilicet ex illa aliquo modo, ſed tamen valde debilior, hinc inde deriuatur: </s> <s xml:id="echoid-s3221" xml:space="preserve">ſic in vmbra non om-<lb/>mno tenebroſa, lumen aliquod videmus, quod ſ@cundarium eſt; </s> <s xml:id="echoid-s3222" xml:space="preserve">ſic etiam in conclaui directis radijs imper-<lb/>uio, lucem ſecundariam, & </s> <s xml:id="echoid-s3223" xml:space="preserve">aliquando tertiariam cernimus.</s> <s xml:id="echoid-s3224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3225" xml:space="preserve">6 Lucem, vti diximus, vlterius ſemper recta tendere, id quidem per idem medium, ſeu ei@ſdem tran-<lb/>ſparentiæ diaphanum verum eſt: </s> <s xml:id="echoid-s3226" xml:space="preserve">ſi verò ſecundum medium, ſeu diaphanum alterius denſitatis occurrat, <lb/>ibi radius refrangitur, ideſt, angulum in eo confinio facit; </s> <s xml:id="echoid-s3227" xml:space="preserve">inde tamen iterum rectus protenditur, exceptis <lb/>rad js perpendicularibus, qui ſoli non refranguntur, ſed recta tendunt. </s> <s xml:id="echoid-s3228" xml:space="preserve">ſimiliter ſi corpus opacum, quod <lb/>pl<unsure/>anè læuig. </s> <s xml:id="echoid-s3229" xml:space="preserve">tum, ac perpolitum, inſtar ſpeculi ſit, radianti lumini obijciatur, lumen illinc, reflectitur, ac <lb/>reſilit, vt in ſpeculis paſſim cernimus; </s> <s xml:id="echoid-s3230" xml:space="preserve">quod tamen reflexum lumen, per lineas rectas reuertitur. </s> <s xml:id="echoid-s3231" xml:space="preserve">hinc ori-<lb/> <anchor type="figure" xlink:label="fig-0048-01a" xlink:href="fig-0048-01"/> tur lux triplex, directa, refracta, <lb/>reflexa. </s> <s xml:id="echoid-s3232" xml:space="preserve">in præſenti figura cor-<lb/>pus lucidum A. </s> <s xml:id="echoid-s3233" xml:space="preserve">poſitum ſit, v. </s> <s xml:id="echoid-s3234" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s3235" xml:space="preserve">in ęthere aut aere puro, emittat-<lb/>que duos radios A B. </s> <s xml:id="echoid-s3236" xml:space="preserve">& </s> <s xml:id="echoid-s3237" xml:space="preserve">A D. </s> <s xml:id="echoid-s3238" xml:space="preserve">oc-<lb/>currentes denſiori corpori, v. </s> <s xml:id="echoid-s3239" xml:space="preserve">g. </s> <s xml:id="echoid-s3240" xml:space="preserve"><lb/>aeri caliginoſo, aut aquę, in con-<lb/>finio lineæ D B. </s> <s xml:id="echoid-s3241" xml:space="preserve">radius A B. </s> <s xml:id="echoid-s3242" xml:space="preserve">quia <lb/>perpendicularis eſt ad aquam, recta vſq; </s> <s xml:id="echoid-s3243" xml:space="preserve">in C. </s> <s xml:id="echoid-s3244" xml:space="preserve">tendit: </s> <s xml:id="echoid-s3245" xml:space="preserve">at verò radius A D. </s> <s xml:id="echoid-s3246" xml:space="preserve">quia obliquè aquæ accidit ideo <lb/>refrangitur in D. </s> <s xml:id="echoid-s3247" xml:space="preserve">in confinio ſcilicet; </s> <s xml:id="echoid-s3248" xml:space="preserve">poſtea tamen per D E. </s> <s xml:id="echoid-s3249" xml:space="preserve">iterum rectus progreditur. </s> <s xml:id="echoid-s3250" xml:space="preserve">In altera figura <lb/>lucidum A. </s> <s xml:id="echoid-s3251" xml:space="preserve">radium A B. </s> <s xml:id="echoid-s3252" xml:space="preserve">in ſpeculum D E. </s> <s xml:id="echoid-s3253" xml:space="preserve">immittit; </s> <s xml:id="echoid-s3254" xml:space="preserve">hic radius, quia obliquus eſt ad ſpeculum, ideo ad par-<lb/>tem alteram reflectitur: </s> <s xml:id="echoid-s3255" xml:space="preserve">fiuntq; </s> <s xml:id="echoid-s3256" xml:space="preserve">duo anguli æquales, angulus ſcilicet A B D. </s> <s xml:id="echoid-s3257" xml:space="preserve">qui angulus incidentiæ dici-<lb/>tur, & </s> <s xml:id="echoid-s3258" xml:space="preserve">angulus C B E. </s> <s xml:id="echoid-s3259" xml:space="preserve">qui reflexionis eſt. </s> <s xml:id="echoid-s3260" xml:space="preserve">quòd ſi radius A B. </s> <s xml:id="echoid-s3261" xml:space="preserve">perpẽdicularis eſſet ſpeculo, qualis eſſet A D. </s> <s xml:id="echoid-s3262" xml:space="preserve"><lb/>in ſe ipſum reflecteretur.</s> <s xml:id="echoid-s3263" xml:space="preserve"/> </p> <div xml:id="echoid-div62" type="float" level="2" n="2"> <figure xlink:label="fig-0048-01" xlink:href="fig-0048-01a"> <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-01"/> </figure> </div> <p> <s xml:id="echoid-s3264" xml:space="preserve">7 Poſita hac radiorum recta proceffione ſequuntur tres vmbrarum differentiæ, quarum exemplain <lb/>ſphæricis corporibus exhibeo. </s> <s xml:id="echoid-s3265" xml:space="preserve">Primo enim ſi lucida ſphæra, ſphæra ſibiæqualem irradiat, eius exactè hę-<lb/>miſphærium illuſtrat, vmbraque rotunda columnaris, ſeu cylindrica in infinitum proijc@tur, vt prima fi-<lb/>gura indicat. </s> <s xml:id="echoid-s3266" xml:space="preserve">Secundo, ſphæra minorem ſphæram illuminens, pluſquam hæmiſphærium illuminat, vm-<lb/>braque exurgit conica, vt in ſecunda figura. </s> <s xml:id="echoid-s3267" xml:space="preserve">quantum autem vltra hęmiſphærium illuſtret, perpulchrè do-<lb/>cet angulus vmbræ, quantus enim eſt angulus acuminis vmbræ conicę, tantus eſt exceſ@us vltra hæmiſphæ-<lb/>rium illuſtratus: </s> <s xml:id="echoid-s3268" xml:space="preserve">vt patebit cum de vmbra terræ tractabitur. </s> <s xml:id="echoid-s3269" xml:space="preserve">Tertio, ſphæra maiorem ſphæram illuſtrans <lb/>minuſquam hæmiſphærium illuſtrat: </s> <s xml:id="echoid-s3270" xml:space="preserve">vmbraque protenditur in amplum, & </s> <s xml:id="echoid-s3271" xml:space="preserve">infinitum, quæ Calathoidis <lb/>eſt, vt in tertia figura apparet: </s> <s xml:id="echoid-s3272" xml:space="preserve">quantus autem ſit ille defectus, docebit angulus G. </s> <s xml:id="echoid-s3273" xml:space="preserve">qui ex concurſu radio-<lb/>rum extremorum ad partem alteram fieret; </s> <s xml:id="echoid-s3274" xml:space="preserve">de quo alias. </s> <s xml:id="echoid-s3275" xml:space="preserve">Cum autem Sol ſit maior cæteris omnibus cor-<lb/>poribus opacis perpetuis, ſequitur omnes vmbras ſolares eſſe conicas. </s> <s xml:id="echoid-s3276" xml:space="preserve">Sed his addatur ſequens Corol-<lb/>larium.</s> <s xml:id="echoid-s3277" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3278" xml:space="preserve">8 Ex vmbra corporis erectis cognita, illius altitudinem ſic explorabis. </s> <s xml:id="echoid-s3279" xml:space="preserve">ſit altitudo C D. </s> <s xml:id="echoid-s3280" xml:space="preserve">perpendicu-<lb/>lariter erecta; </s> <s xml:id="echoid-s3281" xml:space="preserve">eam ſic metiere; </s> <s xml:id="echoid-s3282" xml:space="preserve">menſura prius vmbram eius A D. </s> <s xml:id="echoid-s3283" xml:space="preserve">quæ ſit, v. </s> <s xml:id="echoid-s3284" xml:space="preserve">g. </s> <s xml:id="echoid-s3285" xml:space="preserve">paſſuum 12. </s> <s xml:id="echoid-s3286" xml:space="preserve">deinde erecto <lb/> <anchor type="figure" xlink:label="fig-0048-02a" xlink:href="fig-0048-02"/> baculo B E. </s> <s xml:id="echoid-s3287" xml:space="preserve">ex ipſa vmbra cu ius altitudo tanta ſit; </s> <s xml:id="echoid-s3288" xml:space="preserve">vt eius vm-<lb/>bra præcisè perueniat vſque ad A. </s> <s xml:id="echoid-s3289" xml:space="preserve">ſiue cuius ſummitatis ſit in <lb/>confinio vmbræ, & </s> <s xml:id="echoid-s3290" xml:space="preserve">radij A C. </s> <s xml:id="echoid-s3291" xml:space="preserve">vmbram terminantis; </s> <s xml:id="echoid-s3292" xml:space="preserve">menſura <lb/>igitur eius vmbram A E. </s> <s xml:id="echoid-s3293" xml:space="preserve">quæ ſit v. </s> <s xml:id="echoid-s3294" xml:space="preserve">g. </s> <s xml:id="echoid-s3295" xml:space="preserve">quatuor paſſuum, bacu-<lb/>lus verò ſit 2. </s> <s xml:id="echoid-s3296" xml:space="preserve">paſſuum: </s> <s xml:id="echoid-s3297" xml:space="preserve">iam dico ita ſe habere A E. </s> <s xml:id="echoid-s3298" xml:space="preserve">ad E B. </s> <s xml:id="echoid-s3299" xml:space="preserve">ſi-<lb/>cuti, A D. </s> <s xml:id="echoid-s3300" xml:space="preserve">ad D C. </s> <s xml:id="echoid-s3301" xml:space="preserve">& </s> <s xml:id="echoid-s3302" xml:space="preserve">quia A E. </s> <s xml:id="echoid-s3303" xml:space="preserve">eſt dupla ipſius E B. </s> <s xml:id="echoid-s3304" xml:space="preserve">pariter <lb/>A D. </s> <s xml:id="echoid-s3305" xml:space="preserve">dupla erit ipſius D C. </s> <s xml:id="echoid-s3306" xml:space="preserve">& </s> <s xml:id="echoid-s3307" xml:space="preserve">quia A D. </s> <s xml:id="echoid-s3308" xml:space="preserve">eſt paſius 12. </s> <s xml:id="echoid-s3309" xml:space="preserve">erit ipſa <lb/>D C. </s> <s xml:id="echoid-s3310" xml:space="preserve">paſſus 6. </s> <s xml:id="echoid-s3311" xml:space="preserve">quæſita altitudo. </s> <s xml:id="echoid-s3312" xml:space="preserve">huius demonſtratio pendet ex <lb/>duobus triangulis æquiangulis A D C. </s> <s xml:id="echoid-s3313" xml:space="preserve">A E B. </s> <s xml:id="echoid-s3314" xml:space="preserve">quorum latera <lb/>circa æquales angulos ordinatim ſint proportionalia; </s> <s xml:id="echoid-s3315" xml:space="preserve">vt ex apparatu patet.</s> <s xml:id="echoid-s3316" xml:space="preserve"/> </p> <div xml:id="echoid-div63" type="float" level="2" n="3"> <figure xlink:label="fig-0048-02" xlink:href="fig-0048-02a"> <image file="0048-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-02"/> </figure> </div> </div> <div xml:id="echoid-div65" type="section" level="1" n="42"> <head xml:id="echoid-head44" xml:space="preserve">Finis Libri Secundi.</head> <pb o="33" file="0049" n="49"/> </div> <div xml:id="echoid-div66" type="section" level="1" n="43"> <head xml:id="echoid-head45" xml:space="preserve">LIBER TERTIVS <lb/>DEPARTIBVS MVNDI, <lb/>ET PRIMO DE PARTE ELEMENTARI.</head> <p> <s xml:id="echoid-s3317" xml:space="preserve">CVm tota Mundi fabrica, ex duabus præcipuis partibus conſtet, Elementari videlicet, atque Cęleſti, <lb/>de vtraq; </s> <s xml:id="echoid-s3318" xml:space="preserve">ſeorſim ſecundum præſcriptam methodum agendum eſt: </s> <s xml:id="echoid-s3319" xml:space="preserve">& </s> <s xml:id="echoid-s3320" xml:space="preserve">quidem primò de Elementari.</s> <s xml:id="echoid-s3321" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div67" type="section" level="1" n="44"> <head xml:id="echoid-head46" style="it" xml:space="preserve">De loco partis Elementaris. Cap. I.</head> <p> <s xml:id="echoid-s3322" xml:space="preserve">HÆc inferior mundi pars, quæ ex Elementis componitur (quæ tria ne, an quatuor ſint, Phyſiologis <lb/>diſputandum relinquimus) tota intra Lunares gyros continetur, vnde etiam ſublunaris appellatur, <lb/>videmus enim ex quouis terræ loco Lunarem globum circa terram eodem modo reuolui. </s> <s xml:id="echoid-s3323" xml:space="preserve">porròita ſita <lb/>eſt, vt circa Mundi centrum, æqualiter vndiq; </s> <s xml:id="echoid-s3324" xml:space="preserve">exurgat, vt ex ijs, quæ de ſingulis Elementis dicenda ſunt <lb/>manifeſtum erit.</s> <s xml:id="echoid-s3325" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3326" xml:space="preserve">Hæc porrò de huius ſphæræ loco dicta ſint ſecundum communiorem Aſtronomorum ſententiam, quá <lb/>nos quoque ſequimur; </s> <s xml:id="echoid-s3327" xml:space="preserve">& </s> <s xml:id="echoid-s3328" xml:space="preserve">quorum Mundi ſyſtema, vel conſtitutionem initio huius tertiæ partis exhibui-<lb/>mus. </s> <s xml:id="echoid-s3329" xml:space="preserve">Enimuerò altera Aſtronomorum tum veterum, tum recentiorem ſecta, multo aliter de mundi ſy-<lb/>ſtemate, non equidem vt reor ad veritatem, ſed ad ingenij oſtentationem, opinatur: </s> <s xml:id="echoid-s3330" xml:space="preserve">non enim Elemen-<lb/>r<unsure/>arem globum, circa mundi medium conſtituunt, ſed eius locum cum Solis loco commutant: </s> <s xml:id="echoid-s3331" xml:space="preserve">Solem nam-<lb/>que in totius vniuerſi medio ſiſtunt; </s> <s xml:id="echoid-s3332" xml:space="preserve">Elementarem verò ſphæram, & </s> <s xml:id="echoid-s3333" xml:space="preserve">quidem Lunari cælo circundatam, <lb/>ibi, vnde Solem detraxerunt, ſubſtituunt: </s> <s xml:id="echoid-s3334" xml:space="preserve">quemadmodum in adiecta figura contemplari licet. </s> <s xml:id="echoid-s3335" xml:space="preserve">Inferius <lb/>verò cum de motu terræ ſermo fuerit, Authores huius ſubtiliſſimi commenti, necnon eorum ſenten-<lb/>tiam latius aperiemus.</s> <s xml:id="echoid-s3336" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div68" type="section" level="1" n="45"> <head xml:id="echoid-head47" style="it" xml:space="preserve">Systema Mundi ſecundum Philolaum Phthagoricum, & eius ſectatores.</head> <figure> <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01"/> </figure> </div> <div xml:id="echoid-div69" type="section" level="1" n="46"> <head xml:id="echoid-head48" style="it" xml:space="preserve">De figura partis Elementarijs. Cap II.</head> <p> <s xml:id="echoid-s3337" xml:space="preserve">EXiſtimo partem hanc mundi Sublunarem, atq; </s> <s xml:id="echoid-s3338" xml:space="preserve">Elementarem eſſe ſphæricam; </s> <s xml:id="echoid-s3339" xml:space="preserve">Primo, quia intra Lu-<lb/>næ circulationes, ſeu intra concauum cæli, ſeu regionis Lunæ compræhenditur, quæ circulationes in <lb/>modum ſphæricum aguntur, ergo erit illud etiam, quod abillis ambitur, ſphæricum. </s> <s xml:id="echoid-s3340" xml:space="preserve">Secundo, quia cum <lb/>vt poſtea patebit, terra, & </s> <s xml:id="echoid-s3341" xml:space="preserve">aqua globum rotundum conſtituant, circa quem aerſphæricè aſſiſtat, veriſimi-<lb/>le eſt, reliquum etiam corpus vſq; </s> <s xml:id="echoid-s3342" xml:space="preserve">ad Lunam, in modum ſphæræ circumfundi.</s> <s xml:id="echoid-s3343" xml:space="preserve"/> </p> <pb o="34" file="0050" n="50" rhead="De Mundi Fabrica."/> </div> <div xml:id="echoid-div70" type="section" level="1" n="47"> <head xml:id="echoid-head49" style="it" xml:space="preserve">De motu Sphæra Elementaris. Cap. III.</head> <p> <s xml:id="echoid-s3344" xml:space="preserve">TRes ſuntſecundum Phyſiologos motus ſimplices, circularis, rectus ſurſum, qui & </s> <s xml:id="echoid-s3345" xml:space="preserve">aſcenſus dicitur; </s> <s xml:id="echoid-s3346" xml:space="preserve">& </s> <s xml:id="echoid-s3347" xml:space="preserve"><lb/>rectus deorſum, qui & </s> <s xml:id="echoid-s3348" xml:space="preserve">deſcenſus; </s> <s xml:id="echoid-s3349" xml:space="preserve">reliqui motus mixti dicuntur. </s> <s xml:id="echoid-s3350" xml:space="preserve">Circularis primo hac ratione huic fe-<lb/>rè toti ſphæræ ineſſe videtur, nam Mare Oceanum, vt nonnulli tradunt, & </s> <s xml:id="echoid-s3351" xml:space="preserve">nos ſuperius explicauimus in <lb/>mundi motu, ab ortu in occaſum motu primi mobilis quamuis lentè, videtur tamen cieri. </s> <s xml:id="echoid-s3352" xml:space="preserve">Secundo quia <lb/>veriſimile eſt cęlum Lunæ circulariter moueri, ergo etiam veriſimile eſt ſupremam huius ſphęræ partem, <lb/>quæ cælum Lunæ contingens eſt, illud in gyrum ſubſequi. </s> <s xml:id="echoid-s3353" xml:space="preserve">Motus rectum deorſum, ideſt, deſcenſus cer-<lb/>nitur manifeſtè in omnibus grauibus, quæ niſi impediantur deſcendunt, vt aqua, & </s> <s xml:id="echoid-s3354" xml:space="preserve">terræ partes, lapides, <lb/>grandines, &</s> <s xml:id="echoid-s3355" xml:space="preserve">c. </s> <s xml:id="echoid-s3356" xml:space="preserve">Motus autem rectus ſurſum, ideſt, aſcenſus manifeſtè apparet in rebus leuibus, vt in bullis <lb/>aeris, quæ in aqua aſcendunt, in fumis, vaporibus, & </s> <s xml:id="echoid-s3357" xml:space="preserve">omnibus halitibus, &</s> <s xml:id="echoid-s3358" xml:space="preserve">c. </s> <s xml:id="echoid-s3359" xml:space="preserve">quæ omnino ob leuitatem <lb/>ſumma petunt.</s> <s xml:id="echoid-s3360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3361" xml:space="preserve">Vt autem perfectè Tyrones intelligant, qua ratione hi motus in hac Elementari ſphæra peragantur, in-<lb/>ſpiciendum eſt appoſitum ſchema; </s> <s xml:id="echoid-s3362" xml:space="preserve">in quo terra, & </s> <s xml:id="echoid-s3363" xml:space="preserve">centrum eius ſit vbi C. </s> <s xml:id="echoid-s3364" xml:space="preserve">cælum Lunæ A D B E. </s> <s xml:id="echoid-s3365" xml:space="preserve">motus <lb/>igitur circularis fit circa centrum C. </s> <s xml:id="echoid-s3366" xml:space="preserve">vti ſi quid moueretur per prædictam circumferentiam ab A. </s> <s xml:id="echoid-s3367" xml:space="preserve">in F. </s> <s xml:id="echoid-s3368" xml:space="preserve">& </s> <s xml:id="echoid-s3369" xml:space="preserve"><lb/>ab F. </s> <s xml:id="echoid-s3370" xml:space="preserve">in E. </s> <s xml:id="echoid-s3371" xml:space="preserve">atq; </s> <s xml:id="echoid-s3372" xml:space="preserve">hinc in G. </s> <s xml:id="echoid-s3373" xml:space="preserve">inde in B. </s> <s xml:id="echoid-s3374" xml:space="preserve">& </s> <s xml:id="echoid-s3375" xml:space="preserve">ſic deinceps.</s> <s xml:id="echoid-s3376" xml:space="preserve"/> </p> <figure> <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-01"/> </figure> <p> <s xml:id="echoid-s3377" xml:space="preserve">Deſcenſus verò incipit à parte ſuperiori, ideſt, à quolibet cę-<lb/>li puncto, & </s> <s xml:id="echoid-s3378" xml:space="preserve">tendit verſus C. </s> <s xml:id="echoid-s3379" xml:space="preserve">& </s> <s xml:id="echoid-s3380" xml:space="preserve">quidem per lineas rectas in C. <lb/></s> <s xml:id="echoid-s3381" xml:space="preserve">concurrentes: </s> <s xml:id="echoid-s3382" xml:space="preserve">quare ſi plura grauia ſint in punctis A. </s> <s xml:id="echoid-s3383" xml:space="preserve">F. </s> <s xml:id="echoid-s3384" xml:space="preserve">D. </s> <s xml:id="echoid-s3385" xml:space="preserve">B. </s> <s xml:id="echoid-s3386" xml:space="preserve">& </s> <s xml:id="echoid-s3387" xml:space="preserve">c. </s> <s xml:id="echoid-s3388" xml:space="preserve"><lb/>quæ ſuę inclinationi libera relinquantur, ſuapte natura deſcen-<lb/>dent per lineas rectas A F. </s> <s xml:id="echoid-s3389" xml:space="preserve">F C. </s> <s xml:id="echoid-s3390" xml:space="preserve">& </s> <s xml:id="echoid-s3391" xml:space="preserve">c. </s> <s xml:id="echoid-s3392" xml:space="preserve">ad medium quare deſcenſus <lb/>hic in C. </s> <s xml:id="echoid-s3393" xml:space="preserve">tandem deſinit. </s> <s xml:id="echoid-s3394" xml:space="preserve">quod ſi graue ob impetum in deſcenſi <lb/>aqui<unsure/>ſitum vltra C. </s> <s xml:id="echoid-s3395" xml:space="preserve">procederet, non amplius deſcenderet, ſed <lb/>aſcenderet. </s> <s xml:id="echoid-s3396" xml:space="preserve">Aſcenſus demum rectus è contrario incipit à me-<lb/>dio C. </s> <s xml:id="echoid-s3397" xml:space="preserve">& </s> <s xml:id="echoid-s3398" xml:space="preserve">quoquouerſus recta tendit ad quælibet cæli puncta, <lb/>cælum enim (vt ille cecinit) vndiq; </s> <s xml:id="echoid-s3399" xml:space="preserve">ſurſum: </s> <s xml:id="echoid-s3400" xml:space="preserve">ſic leuè quodpiam <lb/>ex C. </s> <s xml:id="echoid-s3401" xml:space="preserve">ſuæ ſponti relictum aſcendit æquè ad A. </s> <s xml:id="echoid-s3402" xml:space="preserve">per rectam C @. </s> <s xml:id="echoid-s3403" xml:space="preserve"><lb/>atq; </s> <s xml:id="echoid-s3404" xml:space="preserve">ad B. </s> <s xml:id="echoid-s3405" xml:space="preserve">per rectam C B. </s> <s xml:id="echoid-s3406" xml:space="preserve">prout illi liberum fuerit.</s> <s xml:id="echoid-s3407" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3408" xml:space="preserve">Iuuenes igitur puerilem, ac vulgarem illam opinationem, <lb/>atq; </s> <s xml:id="echoid-s3409" xml:space="preserve">imaginationem corrigant, qua grauia ablatis impedimen-<lb/>tis perpetuò deſcenſura putant. </s> <s xml:id="echoid-s3410" xml:space="preserve">ſimiliter animaduertant ho@ <lb/>motus minime effici per lineas paralellas, verum per lineas ad <lb/>mundi medium ſeu centrum concurrentes, contra quam pueri, <lb/>ac ignarum vulgus opinantur; </s> <s xml:id="echoid-s3411" xml:space="preserve">ij enim putant mundum inſtar <lb/>furni eſſe, vt in adiecta figura repræſentatur, terramque vndi-<lb/>que cælum contingere, grauiaque in perpetuum, ni impedirentur, deſcenſura eſſe, & </s> <s xml:id="echoid-s3412" xml:space="preserve">quidem per lineas <lb/>paralellas, v. </s> <s xml:id="echoid-s3413" xml:space="preserve">g. </s> <s xml:id="echoid-s3414" xml:space="preserve">grauia duo, G. </s> <s xml:id="echoid-s3415" xml:space="preserve">& </s> <s xml:id="echoid-s3416" xml:space="preserve">F. </s> <s xml:id="echoid-s3417" xml:space="preserve">putant deſcenſura deorſum in perpetuum per lineas paralellas infini-<lb/>tas G H. </s> <s xml:id="echoid-s3418" xml:space="preserve">F I. </s> <s xml:id="echoid-s3419" xml:space="preserve">Exiſtimant etiam homines terræ inſidere ſecundum lineas inuicem paralellas, hoc eſ@ ho-<lb/>mines ſtantes, & </s> <s xml:id="echoid-s3420" xml:space="preserve">erectos, eſſe inuicem paralellos, quæ omnia figmenta ſunt ex mera inſcitia. </s> <s xml:id="echoid-s3421" xml:space="preserve">Hæc autem <lb/>omnia probantur experientia, quia in quouis loco terræ, etiam apud Antipodes, grauia tendunt verſus <lb/>centrum terræ per lineam rectam, ni impediantur; </s> <s xml:id="echoid-s3422" xml:space="preserve">leuia verò vbique terrarum aſcendunt, ni quid obeſt <lb/>per lineam rectam: </s> <s xml:id="echoid-s3423" xml:space="preserve">cum autem terra ſit ſphærica vt patebit, manifeſtum eſt hoſce motus fieri ſicuti di-<lb/>ximus.</s> <s xml:id="echoid-s3424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3425" xml:space="preserve">Vt autem adhuc perfectius grauium deſcenſus percipiatur, ſciendum eſt in quouis corpore graui reperi-<lb/>ri duo centra, centrum videlicet magnitudinis, & </s> <s xml:id="echoid-s3426" xml:space="preserve">centrum grauitatis. </s> <s xml:id="echoid-s3427" xml:space="preserve">Centrum magnitudinis eſt pun-<lb/> <anchor type="figure" xlink:label="fig-0050-02a" xlink:href="fig-0050-02"/> ctum æqualiter ab extremitatibus remotum, quod propriè in corpo-<lb/>ribus regularibus reperitur vti ſunt Sphæra, Pyramis, Cubus, Cy-<lb/>lyndrus, Octaedrum, & </s> <s xml:id="echoid-s3428" xml:space="preserve">c. </s> <s xml:id="echoid-s3429" xml:space="preserve">Grauitatis centrum punctum eſt, in quo <lb/>ſi graue ſuſpendatur in æquilibrio manet, etiamſi huc illuc trasfera-<lb/>tur, ideſt, ſeruat eandem poſitionem, quam antea habebat; </s> <s xml:id="echoid-s3430" xml:space="preserve">cuius cau-<lb/>ſa eſt, quia vndique ab illo puncto ſunt æqualia momenta, vt tradit <lb/>Pappus Alexandrinus lib. </s> <s xml:id="echoid-s3431" xml:space="preserve">8. </s> <s xml:id="echoid-s3432" xml:space="preserve">Collect. </s> <s xml:id="echoid-s3433" xml:space="preserve">Mathem. </s> <s xml:id="echoid-s3434" xml:space="preserve">vnde ſequitur, vt cum <lb/>graue rectè deſcendit, ita deſcendat vt eius centrum grauitatis, re-<lb/>cta, ſeu ſecundum perpendiculum ad centrum vniuerſi deferatur. </s> <s xml:id="echoid-s3435" xml:space="preserve">il-<lb/>la autem linea per quam centrum grauitatis deſcendit, dicitur linea <lb/>directionis, reliquæ verò eius partes per lineas, lineæ directionis pa-<lb/>ralellas, vt in Prima ſuperiori figura, ſi corporis graui Z L. </s> <s xml:id="echoid-s3436" xml:space="preserve">centrum <lb/>grauitatis fuerit Q. </s> <s xml:id="echoid-s3437" xml:space="preserve">in deſcenſu, punctum Q. </s> <s xml:id="echoid-s3438" xml:space="preserve">ſemper delabetur per li-<lb/>neam QC. </s> <s xml:id="echoid-s3439" xml:space="preserve">ipſaque erit linea directionis; </s> <s xml:id="echoid-s3440" xml:space="preserve">partes vero Z. </s> <s xml:id="echoid-s3441" xml:space="preserve">& </s> <s xml:id="echoid-s3442" xml:space="preserve">L. </s> <s xml:id="echoid-s3443" xml:space="preserve">per pa-<lb/>ralellas illi in eodem ſemper ſitu prolabentur. </s> <s xml:id="echoid-s3444" xml:space="preserve">Quo verò loco cen-<lb/>trum grauitatis in quouis corpore collocetur, ſubtiliſſima noſtra <lb/>ætate Federicus Commẽdinus, & </s> <s xml:id="echoid-s3445" xml:space="preserve">Lucas Valerius infignes Mathem.</s> <s xml:id="echoid-s3446" xml:space="preserve"> <pb o="35" file="0051" n="51" rhead="Liber Tertius."/> explorarunt: </s> <s xml:id="echoid-s3447" xml:space="preserve">Nos autem hoe illud, ſinon tam exactè, facilius tamen, iuxta inſtitutum noſtrum, indaga-<lb/>bimus hac ratione; </s> <s xml:id="echoid-s3448" xml:space="preserve">ſuſpendatur liberè corpus, & </s> <s xml:id="echoid-s3449" xml:space="preserve">a ſuſpenſionis loco cadat filium perpendiculi iuxta cor-<lb/>pus, noteturque linea, quam filum perpendiculi in corpore deſignat. </s> <s xml:id="echoid-s3450" xml:space="preserve">rurſus ex alia parteidem corpus li-<lb/>berè pendeat, atqueiterum à ſuſpenſionis puncto perpendiculi filum deſcendens, alteram lineam eidem <lb/>corpori inurat: </s> <s xml:id="echoid-s3451" xml:space="preserve">hæc ſecunda linea priorem neceſſario ſecabit; </s> <s xml:id="echoid-s3452" xml:space="preserve">nam cum centru<unsure/>m grauitatis ſit ſemper <lb/>iuxta lineam illam perpendiculi, neceſſe eſt vtramque lineam a perpendiculo delineatam iuta grauita-<lb/>tis centrum tranſire, atque adeò in illud idem punctum coacurrere; </s> <s xml:id="echoid-s3453" xml:space="preserve">quapropter neceſſe eſt, punctum il-<lb/>lud, quod earum communis eſt ſectio, cent um grauitatis deſignare. </s> <s xml:id="echoid-s3454" xml:space="preserve">exempli gr. </s> <s xml:id="echoid-s3455" xml:space="preserve">ſit corpus A B D E. </s> <s xml:id="echoid-s3456" xml:space="preserve">cu-<lb/> <anchor type="figure" xlink:label="fig-0051-01a" xlink:href="fig-0051-01"/> ius centrum g@auitatis ſic inuenies; </s> <s xml:id="echoid-s3457" xml:space="preserve">Primo ex A. </s> <s xml:id="echoid-s3458" xml:space="preserve">libere ſuſpendatur, <lb/>filumque perpendiculi illi adhærens deſignet lineam A D. </s> <s xml:id="echoid-s3459" xml:space="preserve">ſecundo <lb/>pendeat ex B. </s> <s xml:id="echoid-s3460" xml:space="preserve">lineaque perpendiculi ſit B E. </s> <s xml:id="echoid-s3461" xml:space="preserve">quæ ſe viciſſim ſecent <lb/>in C. </s> <s xml:id="echoid-s3462" xml:space="preserve">erit C. </s> <s xml:id="echoid-s3463" xml:space="preserve">punctum indicans centrum grauitatis. </s> <s xml:id="echoid-s3464" xml:space="preserve">quod quidem ali-<lb/>quando eſſe poteſt non in ipſo C. </s> <s xml:id="echoid-s3465" xml:space="preserve">ſed tamen è regione illius ſemper <lb/>erit intra, aut extra corporis ſoliditatem; </s> <s xml:id="echoid-s3466" xml:space="preserve">cum enim vtraque linea <lb/>per centrum grauitatis, aut iuxta illud tranſeat, neceſſario C. </s> <s xml:id="echoid-s3467" xml:space="preserve">per <lb/>quod vtraque tranſit, erit grauitatis centrum quæſitum. </s> <s xml:id="echoid-s3468" xml:space="preserve">Poſtremò <lb/>eſt illud notandum, ſi grauè ad centrum mundi liberè dilabatur, num-<lb/>quam quieturum, niſi eius centrum grauitatis, mundi centro con-<lb/>gruat; </s> <s xml:id="echoid-s3469" xml:space="preserve">ſic enim erit in æquilibrio, nec pars altera, alteram propel-<lb/>let amplius. </s> <s xml:id="echoid-s3470" xml:space="preserve">ſi cum impetu deſcenderet, vltrò citroq; </s> <s xml:id="echoid-s3471" xml:space="preserve">centrum mun-<lb/>di ob impetum ſæpius reciprocaretur, ſed paulatim ceſſante impetu, <lb/>tandem centrum grauitatis, com centro mundi coincideret. </s> <s xml:id="echoid-s3472" xml:space="preserve">Hacte-<lb/>nus de tribus ſimplicibus motibus dictum ſit: </s> <s xml:id="echoid-s3473" xml:space="preserve">nunc de mixto motu, <lb/>qui in hac Elementari parte cernitur pauca ſuperſunt dicenda. </s> <s xml:id="echoid-s3474" xml:space="preserve">tunc igitur aliquid mixto motu mouetur, <lb/>cum mobile illud impeditur ab aliqua re, ne ſuo naturali, ac ſimplici motu moueatur, v. </s> <s xml:id="echoid-s3475" xml:space="preserve">g. </s> <s xml:id="echoid-s3476" xml:space="preserve">gutta aquæ <lb/>pluentis ſuapte natura rectà deorſum petit, & </s> <s xml:id="echoid-s3477" xml:space="preserve">quidem ſuo motu ſimplici, qui rectus eſt; </s> <s xml:id="echoid-s3478" xml:space="preserve">ſed accidit vt à <lb/>vento tranſuerſim ſtante ab illa rectitudine deturbetur, & </s> <s xml:id="echoid-s3479" xml:space="preserve">in tranſuerſum, atque obliquè transferatur-<lb/>huiuſmodi motus eſt illi accidentalis, ac præter naturam; </s> <s xml:id="echoid-s3480" xml:space="preserve">& </s> <s xml:id="echoid-s3481" xml:space="preserve">dicitur mixtus, quòd duobus aduerſis moto-<lb/>ribus efficiatur, ſitque neutrius eorum proprius, & </s> <s xml:id="echoid-s3482" xml:space="preserve">naturalis; </s> <s xml:id="echoid-s3483" xml:space="preserve">in exemplo allato, motus illius guttæ à ven-<lb/>to actæ partim deſcenſus eſt, partim tranſuerſalis: </s> <s xml:id="echoid-s3484" xml:space="preserve">quatenus deſcendit participat motum rectum aquæ <lb/>proprium; </s> <s xml:id="echoid-s3485" xml:space="preserve">quatenus verò in tranſuerſum agitur, participat motum venti proprium, aut circularis, aut <lb/>rectus eſt. </s> <s xml:id="echoid-s3486" xml:space="preserve">eodem etiam modo aliquid, dum circulari, ac ſimplici motu fertur, poteſt abeo deturbari ab <lb/>a<unsure/>liquo extrinſeco, vnde poſtea mixtis deferatur. </s> <s xml:id="echoid-s3487" xml:space="preserve">Atque de his ſatis.</s> <s xml:id="echoid-s3488" xml:space="preserve"/> </p> <div xml:id="echoid-div70" type="float" level="2" n="1"> <figure xlink:label="fig-0050-02" xlink:href="fig-0050-02a"> <image file="0050-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-02"/> </figure> <figure xlink:label="fig-0051-01" xlink:href="fig-0051-01a"> <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0051-01"/> </figure> </div> </div> <div xml:id="echoid-div72" type="section" level="1" n="48"> <head xml:id="echoid-head50" style="it" xml:space="preserve">De Magnitudine Sphæræ Elementaris. Cap. IIII.</head> <p> <s xml:id="echoid-s3489" xml:space="preserve">NOnniſi ex quantitate terræ prius exploratæ, in quantitatis reliquorum Elementorum, ac proinde <lb/>totius Elementaris globi cognitionem iri poteſt. </s> <s xml:id="echoid-s3490" xml:space="preserve">quapropter hoc loco, nihil certi ſtatuere debemus, <lb/>infra tamen maniſeſtè oſtendemus diametrum Elemen. </s> <s xml:id="echoid-s3491" xml:space="preserve">ſphæræ continere terrenas diametros 52. </s> <s xml:id="echoid-s3492" xml:space="preserve">quæ <lb/>efficiunt milliaria Aſtronomica 357. </s> <s xml:id="echoid-s3493" xml:space="preserve">396. </s> <s xml:id="echoid-s3494" xml:space="preserve">milliare autem Aſtronomicum, vti poſtea dicemus, eſt ſexage-<lb/>@@ma pars vnius gradus terreſtris circumferentiæ; </s> <s xml:id="echoid-s3495" xml:space="preserve">eſtque idem, ac milliare commune, & </s> <s xml:id="echoid-s3496" xml:space="preserve">vulgare.</s> <s xml:id="echoid-s3497" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3498" xml:space="preserve">De lumine, & </s> <s xml:id="echoid-s3499" xml:space="preserve">vmbra huius ſphæræ, nihil peculiare hoc loco occurit.</s> <s xml:id="echoid-s3500" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div73" type="section" level="1" n="49"> <head xml:id="echoid-head51" xml:space="preserve">Finis Libri Tertij@</head> <pb o="36" file="0052" n="52"/> </div> <div xml:id="echoid-div74" type="section" level="1" n="50"> <head xml:id="echoid-head52" xml:space="preserve">LIBER QVARTVS DE TERRA</head> <head xml:id="echoid-head53" style="it" xml:space="preserve">De loco Terræ. # Cap. I.</head> <p> <s xml:id="echoid-s3501" xml:space="preserve">DIcimus terram eſſe in medio Sphæræ mundi, ſeu Firmamenti, ita vt medium ſiue <lb/>centrum eius ſit vnum, & </s> <s xml:id="echoid-s3502" xml:space="preserve">idem cum medio, ſiue centro Mundi, & </s> <s xml:id="echoid-s3503" xml:space="preserve">Firmamenti. <lb/></s> <s xml:id="echoid-s3504" xml:space="preserve">quod primus omnium Parmenides Eleates ante Chriſti natiuitatem ann. </s> <s xml:id="echoid-s3505" xml:space="preserve">452. </s> <s xml:id="echoid-s3506" xml:space="preserve"><lb/>circiter animaduerit.</s> <s xml:id="echoid-s3507" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3508" xml:space="preserve">Prima ratio ſit, quia exiſtẽtibus nobis in quouis ſuperficiei terreſtris loco, ſtel-<lb/>læ eiuſdem ſemper magnitudinis cum ad meridianum peruenerint, ſecluſis va-<lb/>poribus, ac nebulis, apparent: </s> <s xml:id="echoid-s3509" xml:space="preserve">quod non accideret, niſi æqualiter vndique ab om-<lb/>nibus cæli partibus, ſeu ſtellis diſtaremus: </s> <s xml:id="echoid-s3510" xml:space="preserve">cum autem Firmamentum ſit ſphæri-<lb/>cum, in eoque ſtellæ infigantur, à quibus æque vndique abſcendimus, neceſſa-<lb/>rio ſequitur, nos in medio eius, ſiue apud eius centrum reſidere; </s> <s xml:id="echoid-s3511" xml:space="preserve">ac propterea <lb/>Terra cui inſiſtimus medium mundi obtinebit.</s> <s xml:id="echoid-s3512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3513" xml:space="preserve">2 Vbique terrarum cæli medietas vna ſemper ſpectatur, altera ſemper infrà horizontem occultatur: <lb/></s> <s xml:id="echoid-s3514" xml:space="preserve">videmus namque ſemper ſex ſigna Zodiaci, quæ cæli dimidium in gyrum occupant, ſupra horizontem, <lb/>reliqua verò ſex infra latere: </s> <s xml:id="echoid-s3515" xml:space="preserve">quod quidem neutiquam contingeret, terra extra mundi medium ſita. </s> <s xml:id="echoid-s3516" xml:space="preserve">Idem <lb/>etiam inde patet, quia cum luminaria ſunt ex diametro oppoſita, quod accidit in perfecto plenilunio, eo-<lb/>rum vno occidente, alterum oritur, ideſt, ambo in horizonte ſpectantur, atqui horizon mundum bitariam <lb/>ſecat, igitur mundi ſemiſſis ſupra horizontem exiſtit.</s> <s xml:id="echoid-s3517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3518" xml:space="preserve">Porrò ſicuti in cap. </s> <s xml:id="echoid-s3519" xml:space="preserve">de horizonte dictum eſt, horizon Phyſicus, & </s> <s xml:id="echoid-s3520" xml:space="preserve">Aſtronomicus in cælo inſenſibiliter <lb/>differunt: </s> <s xml:id="echoid-s3521" xml:space="preserve">ob nimiam enim cæli à terra diſtantiam, differentiam eorum inibi inſenſibilis euadit. </s> <s xml:id="echoid-s3522" xml:space="preserve">vnde quã-<lb/>uis allatæ rationes ad horizontem Phyſicum referantur, qui exacte mundum bifariam non ſecat, validæ <lb/>nihilominus ſunt, quia eum bifariam phyſicè partitur.</s> <s xml:id="echoid-s3523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3524" xml:space="preserve">3 Ratio deſumitur ab Eclypſibus Lunæ; </s> <s xml:id="echoid-s3525" xml:space="preserve">quando enim Luna eclypſatur, Soli perfectè diametralite@ <lb/>opponitur, vt, & </s> <s xml:id="echoid-s3526" xml:space="preserve">experientia, & </s> <s xml:id="echoid-s3527" xml:space="preserve">Aſtronomorum calculationes oſtendunt. </s> <s xml:id="echoid-s3528" xml:space="preserve">priuatur autem lumine, quia <lb/>in vmbram terræ incurrit, ſicque obiectu terræ Solis lumen inhibetur; </s> <s xml:id="echoid-s3529" xml:space="preserve">neceſiario igitur terra tunc erit in-<lb/> <anchor type="figure" xlink:label="fig-0052-01a" xlink:href="fig-0052-01"/> ter Solem, & </s> <s xml:id="echoid-s3530" xml:space="preserve">Lunam; </s> <s xml:id="echoid-s3531" xml:space="preserve">experientia enim docet, corpus vmbro-<lb/>ſum medium eſſe inter luminoſum, & </s> <s xml:id="echoid-s3532" xml:space="preserve">obumbratum; </s> <s xml:id="echoid-s3533" xml:space="preserve">erit igitur <lb/>terra inter Solem, & </s> <s xml:id="echoid-s3534" xml:space="preserve">Lunam, ac proinde in mundi diametro in <lb/>quapiam Eclypſis, quæ in appoſita figura fit A B C. </s> <s xml:id="echoid-s3535" xml:space="preserve">ſimiliter <lb/>in altera quauis Eclypſi, ideſt, quæ in alio Zodiaci loco contin-<lb/>gat, terra neceſſario erit in mundana diame@ro, v. </s> <s xml:id="echoid-s3536" xml:space="preserve">g. </s> <s xml:id="echoid-s3537" xml:space="preserve">in Eclypſi <lb/>D B E. </s> <s xml:id="echoid-s3538" xml:space="preserve">in vtraque igitur fuit in mundi diametro, ergo etiam <lb/>in loco B. </s> <s xml:id="echoid-s3539" xml:space="preserve">qui ſolus in vtraque diametro eſt: </s> <s xml:id="echoid-s3540" xml:space="preserve">idem accidit in <lb/>omnibus Lunæ defectibus; </s> <s xml:id="echoid-s3541" xml:space="preserve">ſed locus B. </s> <s xml:id="echoid-s3542" xml:space="preserve">eſt in mundi medio, in <lb/>eo enim ſe mutuo diametriſecant: </s> <s xml:id="echoid-s3543" xml:space="preserve">terra igitur medium, ac cen <lb/>trum illud obſidet. </s> <s xml:id="echoid-s3544" xml:space="preserve">Hæ autem rationes, euidenter propoſi-<lb/>tum concludere videntur.</s> <s xml:id="echoid-s3545" xml:space="preserve"/> </p> <div xml:id="echoid-div74" type="float" level="2" n="1"> <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a"> <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0052-01"/> </figure> </div> <p> <s xml:id="echoid-s3546" xml:space="preserve">4 Inſtrumenta omnia Aſtronomorum ſupponunt terram <lb/>eſſe in centro mundi, v.</s> <s xml:id="echoid-s3547" xml:space="preserve">g. </s> <s xml:id="echoid-s3548" xml:space="preserve">ſupponunt Horologium ſolare eſſe <lb/>in centro, imò apicem ſtyli illius eſſe ipſum mundi centrum: <lb/></s> <s xml:id="echoid-s3549" xml:space="preserve">conſtruuntque illud ipſum perinde, ac ſi eſſemus in centro, eo-<lb/>demque vtuntur eadem hypotheſi, ex qua nullum ſequitur in-<lb/>conueniens, quinimò omnia veritate conſona ſuccedunt; </s> <s xml:id="echoid-s3550" xml:space="preserve">vide-<lb/>mus enim prædicta horologia rectè horas perpetuo indicare. </s> <s xml:id="echoid-s3551" xml:space="preserve"><lb/>hæ ſunt rationes Aſtronomicæ. </s> <s xml:id="echoid-s3552" xml:space="preserve">Phyſicæ ſunt ſequentes.</s> <s xml:id="echoid-s3553" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3554" xml:space="preserve">5 Ratio Phyſicorum eſt. </s> <s xml:id="echoid-s3555" xml:space="preserve">grauia omnia deorſum tendunt, ergo terra omnium Elementorum grauiſ-<lb/>fima, infra ea deſcendet, atque in infimo loco, nempe a cælo remotiſſimo, quod eſt eius centrum, reſide-<lb/>bit: </s> <s xml:id="echoid-s3556" xml:space="preserve">quæ ratio non conuincit relipſa terram inibi eſſe ſed tantummodo in eſie debere; </s> <s xml:id="echoid-s3557" xml:space="preserve">eſt tamen vera cauſa <lb/>poſitus terræ. </s> <s xml:id="echoid-s3558" xml:space="preserve">Cæterum meritò homines mirantur, cum intelligunt terram in medio mundi ſitam, aere <lb/>circumfuſam nullo fultam fulcimento pendere, ſed hanc illi naturam conditor eius ſapientiſſimus indi-<lb/>dit, quippe qui, vt aiunt ſacræ literæ, firmauit orbem terræ, qui non conmouehitur, quam immobilita-<lb/>tem Ouidius eleganter ſic cecinit;</s> <s xml:id="echoid-s3559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3560" xml:space="preserve">stat viterraſua: </s> <s xml:id="echoid-s3561" xml:space="preserve">& </s> <s xml:id="echoid-s3562" xml:space="preserve">alibi, <lb/>Ponderibus librata ſuis immobilis bæret.</s> <s xml:id="echoid-s3563" xml:space="preserve"/> </p> <pb o="37" file="0053" n="53" rhead="Liber Quartus."/> <p> <s xml:id="echoid-s3564" xml:space="preserve">Nec minus eleganter Manilius, ſic,</s> </p> <p style="it"> <s xml:id="echoid-s3565" xml:space="preserve">Nec vero tibi natura admiranda videri <lb/>Pendentis terræ debet, cum pendeat ipſe <lb/>Mundus, & </s> <s xml:id="echoid-s3566" xml:space="preserve">in nullo ponat vestigia fundo.</s> <s xml:id="echoid-s3567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3568" xml:space="preserve">Neq; </s> <s xml:id="echoid-s3569" xml:space="preserve">tandem alterius Aſtronomorũ ſectę ſententia hocloco ſilentio prętereunda eſt, qui terr am quidem <lb/>in medio elementaris ſphæræ collocant, at verò ipſam elementarem ſphærã, ac proinde terram extra mun-<lb/>di medium inter errantia ſydera euehunt, vt ſuperius iam expoſuimus, & </s> <s xml:id="echoid-s3570" xml:space="preserve">quam infra refellemus.</s> <s xml:id="echoid-s3571" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div76" type="section" level="1" n="51"> <head xml:id="echoid-head54" style="it" xml:space="preserve">De Motu Terræ. Cap. II.</head> <p> <s xml:id="echoid-s3572" xml:space="preserve">NOn de terræmotu, ſed de motu terræ hicagendum eſt: </s> <s xml:id="echoid-s3573" xml:space="preserve">ille enim nihil habet Aſtronomicum, ac proin-<lb/>de totus phyſicis relinquendus eſt:</s> <s xml:id="echoid-s3574" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3575" xml:space="preserve">Primo igitur certum eſt totam terram non moueri motu recto, ita vt à mundi medio cælum verſus aſcen-<lb/>dat: </s> <s xml:id="echoid-s3576" xml:space="preserve">in præcedenti enim cap. </s> <s xml:id="echoid-s3577" xml:space="preserve">probatum eſt eam in mundi centro quieſcere. </s> <s xml:id="echoid-s3578" xml:space="preserve">quælibet tamen eius pars ſi libe-<lb/>rè demittatur rect@ deorſum ad vniuerſi medium delabitur, vt experientia docet.</s> <s xml:id="echoid-s3579" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3580" xml:space="preserve">2 Neq; </s> <s xml:id="echoid-s3581" xml:space="preserve">terram in eodem loco manentem, orbiculariter circa ſuum centrum conuolui opinamur: </s> <s xml:id="echoid-s3582" xml:space="preserve">nam <lb/>ſi quod graue corpus, v.</s> <s xml:id="echoid-s3583" xml:space="preserve">g. </s> <s xml:id="echoid-s3584" xml:space="preserve">lapis, ex edito loco demittatur, deorſum recta deſcendens, in eum locum decidit, <lb/>cui antea directè, atq; </s> <s xml:id="echoid-s3585" xml:space="preserve">ad perpendiculum iminebat; </s> <s xml:id="echoid-s3586" xml:space="preserve">quod quidem nullo pacto accideret, ſi terra in gyrum <lb/>raperetur, tunc enim dum lapis deſcenderet, terra interim commota locum illum, cui antea lapis immine-<lb/>bat, deferret alio. </s> <s xml:id="echoid-s3587" xml:space="preserve">quæ ratio probat terram nullam ad partem circumuerti.</s> <s xml:id="echoid-s3588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3589" xml:space="preserve">3 At verò non moueri à Septentrione in Meridiem, aut contra, peculiaris occurrit ratio; </s> <s xml:id="echoid-s3590" xml:space="preserve">quia ſcilicet <lb/>poli altitudines vbiq; </s> <s xml:id="echoid-s3591" xml:space="preserve">perpetuo variarentur: </s> <s xml:id="echoid-s3592" xml:space="preserve">ſi enim polum verſus verteretur, idem nobis accideret, ac ſi ver-<lb/>ſus polum progrederemur; </s> <s xml:id="echoid-s3593" xml:space="preserve">polus videlicet magis, ac magis eleuaretur, quò magis in Septentrionem profi-<lb/>ciſceremur, vti illorſum ambulantibus quotidie contingit: </s> <s xml:id="echoid-s3594" xml:space="preserve">Atqui numquam poli altitudines vſquam, ne-<lb/>que ſtellarum ad eadem loca habitudines mutantur, ex quibus euidens eſt, terram hoc motu minimè com-<lb/>moueri.</s> <s xml:id="echoid-s3595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3596" xml:space="preserve">4 Cùm terra ſit omnium Elementorum grauiſſima, ac propterea (vt vidimus) omnium infima, conue-<lb/>niens eſt, eam quoq; </s> <s xml:id="echoid-s3597" xml:space="preserve">ab omni motu immunem exiſtere, grauitas enim motui obſiſtit, quæ in terra maxima <lb/>eſt; </s> <s xml:id="echoid-s3598" xml:space="preserve">quare grauitas erit cauſa terrenæ quietis, & </s> <s xml:id="echoid-s3599" xml:space="preserve">immobilitatis.</s> <s xml:id="echoid-s3600" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3601" xml:space="preserve">5 Accedat tandem communis Philoſophorum, ac Mathematicorum ferè omnium authoritas, qui eam <lb/>in mundi medio prorſus immobilem confingunt.</s> <s xml:id="echoid-s3602" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3603" xml:space="preserve">6 Dixi ferè omnium, quoniam nonnulli tum veteres, tum recentiores Aſtronomi terram moueri exiſti-<lb/>runt. </s> <s xml:id="echoid-s3604" xml:space="preserve">ex veteribus primus Nicetas Syracuſanus (teſtè Cicerone primo Tuſcula:) </s> <s xml:id="echoid-s3605" xml:space="preserve">terram moueri ſenſit; </s> <s xml:id="echoid-s3606" xml:space="preserve">cu-<lb/>ius poſtea ſententiam ſecuti ſunt (teſte Plutarcho de placitis Philo:) </s> <s xml:id="echoid-s3607" xml:space="preserve">Heraclides Ponticus, atq; </s> <s xml:id="echoid-s3608" xml:space="preserve">Ecphantus <lb/>Pythagoricus, in medio mundi terram circa proprium centrum reuoluentes: </s> <s xml:id="echoid-s3609" xml:space="preserve">exiſtimabant enim apparere <lb/>ſtellas oriri, non quòd ipſæ ab ortu in occaſum circa ſtabilem terram mouerentur: </s> <s xml:id="echoid-s3610" xml:space="preserve">verum quòd ipſis manen-<lb/>tibus terra ab occaſu in ortum, ſpatio 24. </s> <s xml:id="echoid-s3611" xml:space="preserve">horarum circum verſaretur; </s> <s xml:id="echoid-s3612" xml:space="preserve">hoc enim poſito, non minus ſtellas mo <lb/>ueri videremus, quam ſi verè mouerentur. </s> <s xml:id="echoid-s3613" xml:space="preserve">Philolaus præterea Pythagoricus (eodem Plutarcho teſte,) ali-<lb/>ter terram collocabat, ac commouebat, nam præter diurnam cõuerſionem, volebat eam in gyrum localiter <lb/>moueri ſecundum Zodiacum motu annuo, quemadmodum Solem, ac Lunam moueri putamus, vnamq; </s> <s xml:id="echoid-s3614" xml:space="preserve">vnã <lb/>eſſe ex ſtellis. </s> <s xml:id="echoid-s3615" xml:space="preserve">Philolaus ſequutus eſt Ariſtarchus Samius, qui vt tradit Archimedes initio libelli de arenæ <lb/>numero, poſuit ſtellas inerrantes, atq; </s> <s xml:id="echoid-s3616" xml:space="preserve">Solem immobiles permanere, terram verò ipſam circa manentem So-<lb/>lem circumferri; </s> <s xml:id="echoid-s3617" xml:space="preserve">& </s> <s xml:id="echoid-s3618" xml:space="preserve">quidem ſecundum circumferentiam circuli, qui eſt in medio curſu conſtitutus, ideſt, ſe-<lb/>cundum Eclypticam; </s> <s xml:id="echoid-s3619" xml:space="preserve">Sphæram autem inerrantium ſtellarum circa idem centrum cum Sole fixam, cuius <lb/>commenti imaginem qualemcumq; </s> <s xml:id="echoid-s3620" xml:space="preserve">appoluimus cap. </s> <s xml:id="echoid-s3621" xml:space="preserve">1. </s> <s xml:id="echoid-s3622" xml:space="preserve">tractatus ſecundus de loco partis Elementaris: </s> <s xml:id="echoid-s3623" xml:space="preserve">quam <lb/>nunc reuiſere conſultum fuerit. </s> <s xml:id="echoid-s3624" xml:space="preserve">qua hypoteſi omnia phænomena, non minus quam alij excuſabat, vtinfe-<lb/>rius dicemus.</s> <s xml:id="echoid-s3625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3626" xml:space="preserve">Hanc veterum de motu, ac loco terræ ſententiam ſuperiori ſeculo Nicolaus Copernicus, vir acri ingenio <lb/>præditus, atq; </s> <s xml:id="echoid-s3627" xml:space="preserve">Aſtronomiæ reſtaurator, ab inferis iterum excitauit, atq; </s> <s xml:id="echoid-s3628" xml:space="preserve">contra aliorum ratione tutatus eſt; <lb/></s> <s xml:id="echoid-s3629" xml:space="preserve">hanc hodie nonnulli etiam celebres Mathematici vti lo: </s> <s xml:id="echoid-s3630" xml:space="preserve">Keplerus, Ghilelmus Gilbertus de Magnetica Phi-<lb/>loſophia, & </s> <s xml:id="echoid-s3631" xml:space="preserve">alij, mordicus tuentur; </s> <s xml:id="echoid-s3632" xml:space="preserve">cæteri vero omnes eam veiuti abſurdiſſimam reijciunt. </s> <s xml:id="echoid-s3633" xml:space="preserve">Addit tamen <lb/>Copernicus vna cum recentioribus, non ſolum terram ſecus Eclypticam moueri, ſed vna cũ ea moueri etiam <lb/>aquam, & </s> <s xml:id="echoid-s3634" xml:space="preserve">aerem, ac totam deniq; </s> <s xml:id="echoid-s3635" xml:space="preserve">ſphęram interlunarem, ijſdem prorſus lationibus, quibus ipſa terra affici; </s> <s xml:id="echoid-s3636" xml:space="preserve"><lb/>qua hypotheſi non ſolum omnes ſaluantapparentias, verum etiam omnium aduerſariorum argumenta faci-<lb/>lè ſe eludere putant. </s> <s xml:id="echoid-s3637" xml:space="preserve">Porrò hanc opinionem falſam eſſe, ac reijciendam (etiamſi ſuperioribus rationibus, & </s> <s xml:id="echoid-s3638" xml:space="preserve"><lb/>authoritatibus manifeſtum ſit) multo tamen certius euaſit hac tæpeſtate, qua Eccleſiaſtica authoritate, tan-<lb/>quam ſacris literis aduerſa, inhibita eſt.</s> <s xml:id="echoid-s3639" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3640" xml:space="preserve">7 Alij aliam quandam terræ notionem, quamuis inſenſibilem ineſſe contendunt, inter quos eſt noſter <lb/>Vaſquez, in prima ſecundæ, diſp. </s> <s xml:id="echoid-s3641" xml:space="preserve">81. </s> <s xml:id="echoid-s3642" xml:space="preserve">cap. </s> <s xml:id="echoid-s3643" xml:space="preserve">3. </s> <s xml:id="echoid-s3644" xml:space="preserve">hac autem vtuntur ratiocinatione. </s> <s xml:id="echoid-s3645" xml:space="preserve">Terræ moles ita circa mundi <lb/>centrum conſtituta eſt, vt in æquilibrio ſita ſit, ideſt, partes eius circa mundi centrum æque ponderent, ac <lb/>propterea immota conſiſtat: </s> <s xml:id="echoid-s3646" xml:space="preserve">quæ verò in æquilibrio manent, quouis minimo ex vna parte addito, vel ablato <lb/>pondere, ab æquilibrij ſitu dimouentur, vt experientia quotidiana in lancibus, ac ſtateris oſtendit, & </s> <s xml:id="echoid-s3647" xml:space="preserve">ratio-<lb/>nes Mechanicorũ<unsure/> euincunt. </s> <s xml:id="echoid-s3648" xml:space="preserve">cum igitur perpetuò circa rerram, res variæ modò illi addantur, modo deman- <pb o="38" file="0054" n="54" rhead="De Mundi Fabrica."/> tur (vt cum lapis in altum proijcitur, vel cum aues ab ea auolant, & </s> <s xml:id="echoid-s3649" xml:space="preserve">ad eandem aduolant, aut eum aliquid ſu-<lb/>per eam ſaltat) neceſſariũ eſſe videtur ipſam in perpetua quadam trepidatione inſenſibili tamen titubare, ac <lb/>vacillare. </s> <s xml:id="echoid-s3650" xml:space="preserve">Verum enim verò contra hanc terræ vacillationem ſic obijcio; </s> <s xml:id="echoid-s3651" xml:space="preserve">ſi iſthæc vera eſſent, oporteret vt <lb/>terra à validis ventis, qui in montes, arbores, turreſq; </s> <s xml:id="echoid-s3652" xml:space="preserve">magna vi impingunt, ſenſibiliter admodum rotaretur. <lb/></s> <s xml:id="echoid-s3653" xml:space="preserve">quod tamen nullatenus contingere videmus; </s> <s xml:id="echoid-s3654" xml:space="preserve">ergo trepidatio illa, ita trepidat, vt nulla ſit. </s> <s xml:id="echoid-s3655" xml:space="preserve">huic tamen obie-<lb/>ctioni, quidam ſatis acutè ſic reſpondit; </s> <s xml:id="echoid-s3656" xml:space="preserve">difficilius, videlicet, eſſe terram motu circulari quam recto ſurſum, <lb/>ac deorſum commouere; </s> <s xml:id="echoid-s3657" xml:space="preserve">quia cum quodlibet pondus terrę additur ex vna parte, centrum eius grauitatis va-<lb/>riatur, quo variato, terra naturaliter mouebitur, quia centrum grauitatis nouum, ad mundi centrum nutat, <lb/>quare terra naturaliter mouebitur, donec iſtud centrum eius grauitatis, centro mundi congruat. </s> <s xml:id="echoid-s3658" xml:space="preserve">At verò ad <lb/>motum circularem, nullam terra habet aptitudinem, illiq; </s> <s xml:id="echoid-s3659" xml:space="preserve">propterea repugnat, ac reſiſtit: </s> <s xml:id="echoid-s3660" xml:space="preserve">quare vis venti <lb/>in gyrum minimè poteſt circumuertere, niſi tanta ſit, quæ totum terræ pondus ſuperet; </s> <s xml:id="echoid-s3661" xml:space="preserve">requiritur igitur vis <lb/>tota terræ grauitate maior, quæ eam in gyrum actura eſt. </s> <s xml:id="echoid-s3662" xml:space="preserve">quare adhuc prædicta terræ vacillatio videtur <lb/>ſubſiſtere.</s> <s xml:id="echoid-s3663" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3664" xml:space="preserve">Aduertendum prædicta omnla etiam in mare quadrare.</s> <s xml:id="echoid-s3665" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div77" type="section" level="1" n="52"> <head xml:id="echoid-head55" style="it" xml:space="preserve">De Terræ illuminatione, & vmbra. Cap. III.</head> <p> <s xml:id="echoid-s3666" xml:space="preserve">1 SOlem terram illuminare, luce clarius eſt, cum quotidie hanc illuminationem videamus, quid enim@ <lb/>aliud eſt ipſa dies, quam terreſtris globus à Sole colluſtratus? </s> <s xml:id="echoid-s3667" xml:space="preserve">Enimuerò cum terra ſit corpus opa-<lb/>cum, ac denſum, lumen Solis ſiſtit, ac reflectit; </s> <s xml:id="echoid-s3668" xml:space="preserve">hacq; </s> <s xml:id="echoid-s3669" xml:space="preserve">ratione ex parte Soli aduerſa lumine eius perfunditur, <lb/>atq; </s> <s xml:id="echoid-s3670" xml:space="preserve">clareſcit, quam claritatem, ac ſplendorem, diem appellamus. </s> <s xml:id="echoid-s3671" xml:space="preserve">Porro hanc lucem à Sole mutuatam, terra<unsure/> <lb/>ad Lunam vſq; </s> <s xml:id="echoid-s3672" xml:space="preserve">reflectit, eamque, à qua noctu viciſſim Solis lumine reflexo perfunditur, grata vice, ac per-<lb/>mutatione eiuſdem ſolaris luminis, illuſtrat. </s> <s xml:id="echoid-s3673" xml:space="preserve">quod præcipuè circa nouilunia perſpicitur; </s> <s xml:id="echoid-s3674" xml:space="preserve">ea enim pars Lunæ, <lb/>quæ tunc temporis nondum à Sole illuminata eſt, & </s> <s xml:id="echoid-s3675" xml:space="preserve">tamen videtur, ideo videtur, quia Sole lumine à terra il-<lb/>luc repercuſſo, aliquo modo clareſcit, ſicque apparere poteſt: </s> <s xml:id="echoid-s3676" xml:space="preserve">verum hac de re oportunius in tractatu de Lu-<lb/>na agendum erit.</s> <s xml:id="echoid-s3677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3678" xml:space="preserve">2 Terreſtrem globum à Sole vmbram proijcere manifeſtum eſt; </s> <s xml:id="echoid-s3679" xml:space="preserve">quid enim aliud nox ipſa eſt, quam ter-<lb/>ræ vmbra? </s> <s xml:id="echoid-s3680" xml:space="preserve">quæ circa terram alternatim cum illuminatione, ſeu cum die promouetur. </s> <s xml:id="echoid-s3681" xml:space="preserve">cum enim terra ſit cor <lb/>pus opacum, ac proinde lumini ſit imperuium, neceſſario ex parte Soli auerſa, lumine priuabitur, ſicq; </s> <s xml:id="echoid-s3682" xml:space="preserve">tene-<lb/>bras, & </s> <s xml:id="echoid-s3683" xml:space="preserve">vmbram, quæ nihil aliud ſunt, quam lucis priuationes, ex illa parte effundet. </s> <s xml:id="echoid-s3684" xml:space="preserve">hanc etiam vmbram <lb/>lunares Eclypſes manifeſtam reddunt; </s> <s xml:id="echoid-s3685" xml:space="preserve">nihil enim eſt aliud Lunaris Eclypſis, quam defectes luminis Solaris <lb/>in Luna, qui ei accidit, eò quòd in vmbram terræ incurrat: </s> <s xml:id="echoid-s3686" xml:space="preserve">cuius rei euidens eſt ſignum, quod quoties Luna <lb/>defectum patitur, lbi @emper eſſe comperitur, vbi directè vmbra terræ proijcitur; </s> <s xml:id="echoid-s3687" xml:space="preserve">eſt enim Luna deficiens <lb/>ſemper ex ea terræ parte Soli auerſa, quæ vmbram efficit, eſtque ſemper Soli è diametro penitus oppofita, <lb/>quam etiam in partem vmbra proijcitur. </s> <s xml:id="echoid-s3688" xml:space="preserve">quod præterea Aſtronomorum obſeruationcs, & </s> <s xml:id="echoid-s3689" xml:space="preserve">Eclypſium cal-<lb/>culationes, ac certæ prædictiones ſupponunt, atq; </s> <s xml:id="echoid-s3690" xml:space="preserve">demonſtrant.</s> <s xml:id="echoid-s3691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3692" xml:space="preserve">3 Hæc vmbra terreſtris eſt conica; </s> <s xml:id="echoid-s3693" xml:space="preserve">(quod vt probè percipiatur repetendum eſt cap. </s> <s xml:id="echoid-s3694" xml:space="preserve">5. </s> <s xml:id="echoid-s3695" xml:space="preserve">de Lumine, & </s> <s xml:id="echoid-s3696" xml:space="preserve">Vm <lb/>bra ex tractatu de Mundo.) </s> <s xml:id="echoid-s3697" xml:space="preserve">quod inde patet, quia hæc vmbra eſt finita, non enim aſcendit vſq; </s> <s xml:id="echoid-s3698" xml:space="preserve">ad cælum ſu-<lb/>periorum Planetarum, Martis, &</s> <s xml:id="echoid-s3699" xml:space="preserve">c. </s> <s xml:id="echoid-s3700" xml:space="preserve">ſi enim illuc aſcenderet Planetas illos obumbraret, lumineq; </s> <s xml:id="echoid-s3701" xml:space="preserve">eos non ſe-<lb/>cus, ac Lunam priuaret; </s> <s xml:id="echoid-s3702" xml:space="preserve">quod tamen non contingit; </s> <s xml:id="echoid-s3703" xml:space="preserve">erit igitur hæc vmbra finita. </s> <s xml:id="echoid-s3704" xml:space="preserve">præterea eſt etiam rotun-<lb/>da, nam in facie Lunæ defi ientis, confinium vmbræ, ſeu defectus, cum parte non deficiente, eſt ſemper linea <lb/>circularis, quæ curu tas aliunde prouenire nequit, quam ab vmbræ rotunditate; </s> <s xml:id="echoid-s3705" xml:space="preserve">quod euidens ſignum eſt vm <lb/>bram hanc eſſe non ſolum longam, ſed etiam rotundam: </s> <s xml:id="echoid-s3706" xml:space="preserve">ſed cum ſit etiam finita, ſequitur neceſſario eam eſ-<lb/>ſe conicam, idelt, veluti corpus quoddam oblongum, rotundum, atq; </s> <s xml:id="echoid-s3707" xml:space="preserve">acuminatum; </s> <s xml:id="echoid-s3708" xml:space="preserve">ſicuti ſecunda figura <lb/>num. </s> <s xml:id="echoid-s3709" xml:space="preserve">7. </s> <s xml:id="echoid-s3710" xml:space="preserve">citati cap. </s> <s xml:id="echoid-s3711" xml:space="preserve">repræſentat.</s> <s xml:id="echoid-s3712" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3713" xml:space="preserve">4 Porro ex hoc vmbræcono, duo conſequuntur maximè notanda: </s> <s xml:id="echoid-s3714" xml:space="preserve">vnum eſt terram eſſe rotundam: </s> <s xml:id="echoid-s3715" xml:space="preserve">al-<lb/>terum, Solem eſſe terra maiorem: </s> <s xml:id="echoid-s3716" xml:space="preserve">vt patet ex eodem num. </s> <s xml:id="echoid-s3717" xml:space="preserve">7. </s> <s xml:id="echoid-s3718" xml:space="preserve">cap. </s> <s xml:id="echoid-s3719" xml:space="preserve">5. </s> <s xml:id="echoid-s3720" xml:space="preserve">de quibus conſectarijs ſuis locis tracta-<lb/>bimus.</s> <s xml:id="echoid-s3721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3722" xml:space="preserve">5 Cùm igitur Sol ſit terra maior, illuminabit pluſquam hemiphærium, ſeu pluſquam dimidium eius; </s> <s xml:id="echoid-s3723" xml:space="preserve">v@ <lb/>patet ex præallegato loco: </s> <s xml:id="echoid-s3724" xml:space="preserve">quantum autem illud ſit, quod vltra hemiphę<unsure/>ium colluſtratur, perpulchrè doce@ <lb/>@cumen, ſiue angulus vmbræ, quantus enim eſt ipſe angulus, tantus eſt exceſſus ille colluſtratus, quod ex ſe-<lb/> <anchor type="figure" xlink:label="fig-0054-01a" xlink:href="fig-0054-01"/> quen@i deſcriptio-<lb/>ne, quamuis mi-<lb/>nimèvera, ideſt, <lb/>quamuis non ha-<lb/>beat reapſe, veras <lb/>proportiones, ſic <lb/>demonſtro, Sol ſit <lb/>circa A. </s> <s xml:id="echoid-s3725" xml:space="preserve">centrũ. </s> <s xml:id="echoid-s3726" xml:space="preserve">ter <lb/>ra ſit R N E F M. <lb/></s> <s xml:id="echoid-s3727" xml:space="preserve">eius centrũ l. </s> <s xml:id="echoid-s3728" xml:space="preserve">dia-<lb/>meter N M. </s> <s xml:id="echoid-s3729" xml:space="preserve">diri-<lb/>mathemiſphæriũ</s> </p> <div xml:id="echoid-div77" type="float" level="2" n="1"> <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a"> <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0054-01"/> </figure> </div> <pb file="0055" n="55"/> <pb file="0055a" n="56"/> <figure> <image file="0055a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0055a-01"/> </figure> </div> <div xml:id="echoid-div79" type="section" level="1" n="53"> <head xml:id="echoid-head56" xml:space="preserve">PAGINAS 38. & 39.</head> <p style="it"> <s xml:id="echoid-s3730" xml:space="preserve">peri quantitatem vmbræ lunaris, quam depictam vides apud vmbram T. </s> <s xml:id="echoid-s3731" xml:space="preserve">extenditurque à Luna perigæa verſus Terram, ea@que ſemidiam. </s> <s xml:id="echoid-s3732" xml:space="preserve">5. </s> <s xml:id="echoid-s3733" xml:space="preserve">tranſcendit. </s> <s xml:id="echoid-s3734" xml:space="preserve">ea-<lb/>demque ratione apponi poſſunt vmbra reliquorum ſyderum, ſed aduertendum eſt vmbram T. </s> <s xml:id="echoid-s3735" xml:space="preserve">mucronem dirigere verſus Solem, à quo eum deberet auertere, <lb/>quod ideo feci, ne figuralongior euaderet. </s> <s xml:id="echoid-s3736" xml:space="preserve">eadem ratione ex distantijs, & </s> <s xml:id="echoid-s3737" xml:space="preserve">proportionibus ſyderum tradendis (atque in Tabellis proprijs ad finem Firmamen-<lb/>ti exponendis) poterit quilibet figur am hanc vſque ad Firmamentum extendere, ideſt, in prælonga carta Zona Mundi ſemidiametrum ducere, quæ constet T. <lb/></s> <s xml:id="echoid-s3738" xml:space="preserve">ſemidiam. </s> <s xml:id="echoid-s3739" xml:space="preserve">14000. </s> <s xml:id="echoid-s3740" xml:space="preserve">atque in ea deſcribere omnia ſydera, ad proprias perigæorum, & </s> <s xml:id="echoid-s3741" xml:space="preserve">apogæorum diſtantias, cum ſuis magnitudinibus ad T. </s> <s xml:id="echoid-s3742" xml:space="preserve">relatis, necnon <lb/>cum ſuis vmbris; </s> <s xml:id="echoid-s3743" xml:space="preserve">ſicuti factum eſt in præſenti figura vſque ad Solem. </s> <s xml:id="echoid-s3744" xml:space="preserve">hæc autem conſtructio pendet, ex dicendis de diſtantijs, & </s> <s xml:id="echoid-s3745" xml:space="preserve">diametris ſingulorum rela-<lb/>tis ad T. </s> <s xml:id="echoid-s3746" xml:space="preserve">porrò ex huiuſmodi delineationem, admirandam huius mundanæ fabricæ ſymmetriam, abſque vllaimaginationis molestia, aut fallacia, verum ma-<lb/>gna animi voluptate contemplari licebit.</s> <s xml:id="echoid-s3747" xml:space="preserve"/> </p> <pb file="0055b" n="57"/> <pb file="0056" n="58"/> <pb file="0057" n="59"/> <pb file="0057a" n="60"/> <figure> <image file="0057a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0057a-01"/> </figure> </div> <div xml:id="echoid-div80" type="section" level="1" n="54"> <head xml:id="echoid-head57" xml:space="preserve">EXPLANATIO, ETCONSTRVCTIO FIGVRAE PONENDAE INTER</head> <p style="it"> <s xml:id="echoid-s3748" xml:space="preserve">COn ſtat præſens figura paralellis quatuor lineis rectis, & </s> <s xml:id="echoid-s3749" xml:space="preserve">pluſquam dimidia: </s> <s xml:id="echoid-s3750" xml:space="preserve">quæ omnes tamen (ſaltem per imaginationem) constituendæ ſunt in directum <lb/>ad vnam tantum rectam lineam efficiendam; </s> <s xml:id="echoid-s3751" xml:space="preserve">ſicuti ego prius eam in longa papyri Zona deſcripſeram; </s> <s xml:id="echoid-s3752" xml:space="preserve">ſed quod præ longitudine Bibliopolis eßeti commo-<lb/>do, eam in haſce quinque partes diuiſam ad banc breuitatem contraxi; </s> <s xml:id="echoid-s3753" xml:space="preserve">quas tamen quilibet poterit ab inuicem prius diſſectas vnam post alteram ſecundum nu-<lb/>merorum ſeriem iterum in longum connectere, atque in pristinum ſtatum reſtituere: </s> <s xml:id="echoid-s3754" xml:space="preserve">quod quidem Lectori conſulo, vt maiorem ex ea fructum, ac volupta-<lb/>tem percipiat. </s> <s xml:id="echoid-s3755" xml:space="preserve">porrò tota hæc linea refert diſtantiam à centro Terræ, vſque ad ſummum apogæum cæli Solis; </s> <s xml:id="echoid-s3756" xml:space="preserve">ſeu eſt ſemidiameter conuexi eius. </s> <s xml:id="echoid-s3757" xml:space="preserve">quæ conſtat, <lb/>vt postea patebit, ſemidiametris Terræ 1182. </s> <s xml:id="echoid-s3758" xml:space="preserve">atque in ea poſita ſunt ſuis locis corpora Planetarum, necnon vmbra Terræ, & </s> <s xml:id="echoid-s3759" xml:space="preserve">Lunæ, omnia cum veris, ac <lb/>mutuis eorum proportionibus. </s> <s xml:id="echoid-s3760" xml:space="preserve">Eam autem ſic conſtruxi, primo deſcripſi globulum Terræ, quem initio totius lineæ vices notatum litera T. </s> <s xml:id="echoid-s3761" xml:space="preserve">quoniam vero ſe-<lb/>midiametro Terræ vtuntur Aſtronomis pro cæterarum magnitudinum, ac diſtantiarum menſura; </s> <s xml:id="echoid-s3762" xml:space="preserve">ideo in prima linea ſinistrorſum numeraui 52. </s> <s xml:id="echoid-s3763" xml:space="preserve">huius Terræ <lb/>ſemidiametros, quæ eſt finitimæ Lunæ diſtantia, ſeueft Lunæ perigæum, ibique Lunæ ſphærulam, ad Terram comparatam depinxi: </s> <s xml:id="echoid-s3764" xml:space="preserve">inde<unsure/> ad 68. </s> <s xml:id="echoid-s3765" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s3766" xml:space="preserve">quæ <lb/>eſt ſupremæ Lunæ à T. </s> <s xml:id="echoid-s3767" xml:space="preserve">remotio, ſeu apogæum, iterum poſui lunulam. </s> <s xml:id="echoid-s3768" xml:space="preserve">hinc vſque ad 254. </s> <s xml:id="echoid-s3769" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s3770" xml:space="preserve">poſui terminum lineæ, ac ſimul vmbræ terrestris, quam vi-<lb/>des à terra illuc vſque in acutum deſinere. </s> <s xml:id="echoid-s3771" xml:space="preserve">postea ad ſecundam lineam, ex eadem parte, facto gradu, ac dextrorſum procedendo ad ſemid. </s> <s xml:id="echoid-s3772" xml:space="preserve">285. </s> <s xml:id="echoid-s3773" xml:space="preserve">occurrit <lb/>Veneris perigæum. </s> <s xml:id="echoid-s3774" xml:space="preserve">inde pariter dextrorſum ad tertiam lineam flectendo, atque per eam ſiniſtrorſum redeunti, ad ſemid. </s> <s xml:id="echoid-s3775" xml:space="preserve">571. </s> <s xml:id="echoid-s3776" xml:space="preserve">perigæum Mercurij, & </s> <s xml:id="echoid-s3777" xml:space="preserve">po-<lb/>stea ad 761. </s> <s xml:id="echoid-s3778" xml:space="preserve">Mars perigæus fiunt obuiam. </s> <s xml:id="echoid-s3779" xml:space="preserve">hinc per quartam lineam, nulla re inſignitam tranſcendimus ad quintam, in qua ad 1102. </s> <s xml:id="echoid-s3780" xml:space="preserve">ſemid in Solem peri-<lb/>gæum incidimus. </s> <s xml:id="echoid-s3781" xml:space="preserve">deinde ad 1142. </s> <s xml:id="echoid-s3782" xml:space="preserve">ad Solem ipſum in mediocri diſtantia ſitum peruenimus. </s> <s xml:id="echoid-s3783" xml:space="preserve">cuius ſphæra ibi depicta habet ſemidiametrum constantem ex ſe-<lb/>midiam. </s> <s xml:id="echoid-s3784" xml:space="preserve">T 5 {1/2}. </s> <s xml:id="echoid-s3785" xml:space="preserve">vt habeat veram cum Terrę proportionem. </s> <s xml:id="echoid-s3786" xml:space="preserve">ſicuti etiam globuli Lunæ, Ven. </s> <s xml:id="echoid-s3787" xml:space="preserve">Merc. </s> <s xml:id="echoid-s3788" xml:space="preserve">& </s> <s xml:id="echoid-s3789" xml:space="preserve">Mart. </s> <s xml:id="echoid-s3790" xml:space="preserve">habent ſemidiam. </s> <s xml:id="echoid-s3791" xml:space="preserve">ad ſemidiam. </s> <s xml:id="echoid-s3792" xml:space="preserve">T. </s> <s xml:id="echoid-s3793" xml:space="preserve">relatas; </s> <s xml:id="echoid-s3794" xml:space="preserve">qua-<lb/>les exponuntur in Tabella ſecunda ad finem Firmamenti.</s> <s xml:id="echoid-s3795" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3796" xml:space="preserve">Quando igitur hæc figura erat vnica linea in longa papyri faſcia extenſa, duxi duas lineas Solem, ac Teuram hinc inde tangentes, quæ ibi concurrerunt <lb/>vbi nunc est vmbra T. </s> <s xml:id="echoid-s3797" xml:space="preserve">apex, ideſt ad num. </s> <s xml:id="echoid-s3798" xml:space="preserve">254. </s> <s xml:id="echoid-s3799" xml:space="preserve">ſicque eius longitudinem denotarunt: </s> <s xml:id="echoid-s3800" xml:space="preserve">vt patet ex ſuperiori tractatu de lumine, & </s> <s xml:id="echoid-s3801" xml:space="preserve">vmbra. </s> <s xml:id="echoid-s3802" xml:space="preserve">eodem modo re-</s> </p> <pb file="0057b" n="61"/> <pb file="0058" n="62"/> <pb o="39" file="0059" n="63" rhead="Liber Quartus."/> <p> <s xml:id="echoid-s3803" xml:space="preserve">illuminatum M R N. </s> <s xml:id="echoid-s3804" xml:space="preserve">verſus Solem: </s> <s xml:id="echoid-s3805" xml:space="preserve">linea E F. </s> <s xml:id="echoid-s3806" xml:space="preserve">ſit diametro paralella, claudatq; </s> <s xml:id="echoid-s3807" xml:space="preserve">portionem terræ N E F M. <lb/></s> <s xml:id="echoid-s3808" xml:space="preserve">quam vltra hemiſphærium Sol illuſtrat; </s> <s xml:id="echoid-s3809" xml:space="preserve">hæc autem terræ portio eſt inſtar faſciolæ cuiuſdam terræ præcin-<lb/>gentis, cuius latitudo erit arcus N E. </s> <s xml:id="echoid-s3810" xml:space="preserve">vel M F. </s> <s xml:id="echoid-s3811" xml:space="preserve">quæritur nunc quantus ſit hic arcus, hic enim eſt quantitas por <lb/>tionis illius. </s> <s xml:id="echoid-s3812" xml:space="preserve">pars autem terræ E F. </s> <s xml:id="echoid-s3813" xml:space="preserve">vmbroſa eri<unsure/>t, vmbraq; </s> <s xml:id="echoid-s3814" xml:space="preserve">terræ erit E F C. </s> <s xml:id="echoid-s3815" xml:space="preserve">lam dico angulum vmbræ C. </s> <s xml:id="echoid-s3816" xml:space="preserve">tot <lb/>gradus aut minuta continere, quotſunt in duobus arcubus ſimul N E. </s> <s xml:id="echoid-s3817" xml:space="preserve">M F. </s> <s xml:id="echoid-s3818" xml:space="preserve">ideſt, eund m arcum angulo C. </s> <s xml:id="echoid-s3819" xml:space="preserve"><lb/>ſubtendi: </s> <s xml:id="echoid-s3820" xml:space="preserve">hoc autem eſt nihil aliud quam angulum C. </s> <s xml:id="echoid-s3821" xml:space="preserve">quantitatem illam continere: </s> <s xml:id="echoid-s3822" xml:space="preserve">quod ſic patebit; </s> <s xml:id="echoid-s3823" xml:space="preserve">conſi-<lb/>deretur quadrilaterum I E C F. </s> <s xml:id="echoid-s3824" xml:space="preserve">in quo duo anguli ad E. </s> <s xml:id="echoid-s3825" xml:space="preserve">& </s> <s xml:id="echoid-s3826" xml:space="preserve">F. </s> <s xml:id="echoid-s3827" xml:space="preserve">ſunt recti per 18. </s> <s xml:id="echoid-s3828" xml:space="preserve">3. </s> <s xml:id="echoid-s3829" xml:space="preserve">Elem. </s> <s xml:id="echoid-s3830" xml:space="preserve">ergo reliqui duo an-<lb/>guli ad I. </s> <s xml:id="echoid-s3831" xml:space="preserve">& </s> <s xml:id="echoid-s3832" xml:space="preserve">C. </s> <s xml:id="echoid-s3833" xml:space="preserve">ſunt ſimul æquales duobus rectis, quia quodlibet quadrilaterum habet ſuos 4. </s> <s xml:id="echoid-s3834" xml:space="preserve">angulos ſimul <lb/>æquales quatuor rectis, ex ſchol. </s> <s xml:id="echoid-s3835" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s3836" xml:space="preserve">32. </s> <s xml:id="echoid-s3837" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s3838" xml:space="preserve">quare angulus I. </s> <s xml:id="echoid-s3839" xml:space="preserve">tãto minor erit duobus rectis, quan-<lb/>tus fuerit angulus C. </s> <s xml:id="echoid-s3840" xml:space="preserve">ſiue minor erit duobus rectis, quantitate anguli C. </s> <s xml:id="echoid-s3841" xml:space="preserve">quare arcus E F. </s> <s xml:id="echoid-s3842" xml:space="preserve">qui angulo I. </s> <s xml:id="echoid-s3843" xml:space="preserve">ſubten-<lb/>ditur ex centro, ac propterea eius quantitatem indicat, tanto minor erit duobus angulis rectis, hoc eſt tanto <lb/>minor erit gr. </s> <s xml:id="echoid-s3844" xml:space="preserve">180. </s> <s xml:id="echoid-s3845" xml:space="preserve">ſiue ſemicirculo N E F M. </s> <s xml:id="echoid-s3846" xml:space="preserve">quantus fuerit angulus C. </s> <s xml:id="echoid-s3847" xml:space="preserve">ſiue dixer s, tanti erunt duo arcus ſi-<lb/>mul N E. </s> <s xml:id="echoid-s3848" xml:space="preserve">M F. </s> <s xml:id="echoid-s3849" xml:space="preserve">qui conflant exceſſum vltra dimidium illuſtratũ. </s> <s xml:id="echoid-s3850" xml:space="preserve">qui exceſſus duplus ex aſtronomicis demon-<lb/>ſtrationibus, & </s> <s xml:id="echoid-s3851" xml:space="preserve">calculis reperitur eſſe minuta 28. </s> <s xml:id="echoid-s3852" xml:space="preserve">quaretotus arcus E R F. </s> <s xml:id="echoid-s3853" xml:space="preserve">illuſtratus, erit gr. </s> <s xml:id="echoid-s3854" xml:space="preserve">180. </s> <s xml:id="echoid-s3855" xml:space="preserve">28′. </s> <s xml:id="echoid-s3856" xml:space="preserve">arcus ve <lb/>rò N E. </s> <s xml:id="echoid-s3857" xml:space="preserve">& </s> <s xml:id="echoid-s3858" xml:space="preserve">M F. </s> <s xml:id="echoid-s3859" xml:space="preserve">ſinguli e unt 14′. </s> <s xml:id="echoid-s3860" xml:space="preserve">min. </s> <s xml:id="echoid-s3861" xml:space="preserve">quare Zonula illa N E F M. </s> <s xml:id="echoid-s3862" xml:space="preserve">lata erit tantummodo min. </s> <s xml:id="echoid-s3863" xml:space="preserve">14′. </s> <s xml:id="echoid-s3864" xml:space="preserve">ideſt, quar <lb/>ta ferè pars gradus, quæ erunt milliaria aſtronomica 15. </s> <s xml:id="echoid-s3865" xml:space="preserve">Sol igitur vltra terræ hemiſphærium illuminat hinc <lb/>in gyrum milliaria 15. </s> <s xml:id="echoid-s3866" xml:space="preserve">aſtr<unsure/>onomica, quæ omnia probari poſſunt etiam oracticè, vt in apparatu docui; </s> <s xml:id="echoid-s3867" xml:space="preserve">cõſtru-<lb/>cta enim qualibet figura in qua corpus @uminans ſit vtcumq; </s> <s xml:id="echoid-s3868" xml:space="preserve">maius illuminato, & </s> <s xml:id="echoid-s3869" xml:space="preserve">ductis reliquis lineis, & </s> <s xml:id="echoid-s3870" xml:space="preserve"><lb/>vmbra etiam delineata, ſemper reperies (ſi per circinum rectè acuminatum diligenter operatus fueris) an-<lb/>gulum vmbræ, tot gradus, vel min. </s> <s xml:id="echoid-s3871" xml:space="preserve">compræhendere, quot fuerint in exce<unsure/>ſſu, vltra hemiſphærium illuſtrato. </s> <s xml:id="echoid-s3872" xml:space="preserve"><lb/>6 Quantitatem vmbræ terreſtris, ſeu longitudinem explorare oportet. </s> <s xml:id="echoid-s3873" xml:space="preserve">huius rei gratia duo ſupponere <lb/>oportet, quæ inferius ſuo loco erunt demonſtranda. </s> <s xml:id="echoid-s3874" xml:space="preserve">quorum primum eſt, Solis centrum a centro terræ di-<lb/>ſtare, in mediocri diſtantia, ſemidiametris terræ 1142. </s> <s xml:id="echoid-s3875" xml:space="preserve">alterum eſt ſemidiametrum Solis ad ſemidiametrum <lb/>terræ habere proportionem quam habet 5 {1/2}. </s> <s xml:id="echoid-s3876" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s3877" xml:space="preserve">ſi igitur accuratè figura deſcribatur, quæ haſce habeat ra-<lb/>tiones, qualis eſt præſens ad ſiniſtrã, ſlatim apparebit vmbræ longitudo exploranda; </s> <s xml:id="echoid-s3878" xml:space="preserve">ibi enim vmbra in acu-<lb/>tum deſinet, vbi radij Solis extremi terram contingentes concurrent, reperieſq; </s> <s xml:id="echoid-s3879" xml:space="preserve">vmbram elongari per ter-<lb/>ræ ſemidiametros ferè 254. </s> <s xml:id="echoid-s3880" xml:space="preserve">✠</s> </p> <p> <s xml:id="echoid-s3881" xml:space="preserve">Idem autem Geometricè ijſdem ſuppoſitis aſſequeris in hunc modum, in figura ſuperiori, qua vſi ſumus <lb/>ad illuminationem terræ inueſtigandam, ducatur linea O I. </s> <s xml:id="echoid-s3882" xml:space="preserve">paraleila ipſi B E. </s> <s xml:id="echoid-s3883" xml:space="preserve">eritq; </s> <s xml:id="echoid-s3884" xml:space="preserve">paralellogranũ B E I O. <lb/></s> <s xml:id="echoid-s3885" xml:space="preserve">nam etiam duæ O B. </s> <s xml:id="echoid-s3886" xml:space="preserve">I E. </s> <s xml:id="echoid-s3887" xml:space="preserve">ſunt paralellæ, quia perpendiculares ſunt eidem B E. </s> <s xml:id="echoid-s3888" xml:space="preserve">per 18. </s> <s xml:id="echoid-s3889" xml:space="preserve">3. </s> <s xml:id="echoid-s3890" xml:space="preserve">Elem. </s> <s xml:id="echoid-s3891" xml:space="preserve">conſiderentur <lb/>præterea duo trianguia A B C. </s> <s xml:id="echoid-s3892" xml:space="preserve">& </s> <s xml:id="echoid-s3893" xml:space="preserve">A O I. </s> <s xml:id="echoid-s3894" xml:space="preserve">quæ ſimilia ſunt, per coroll. </s> <s xml:id="echoid-s3895" xml:space="preserve">4. </s> <s xml:id="echoid-s3896" xml:space="preserve">ſexti<unsure/>; </s> <s xml:id="echoid-s3897" xml:space="preserve">igitur perquartam ſexti, eſt vt <lb/>A C. </s> <s xml:id="echoid-s3898" xml:space="preserve">ad I C. </s> <s xml:id="echoid-s3899" xml:space="preserve">i<unsure/>ta A B. </s> <s xml:id="echoid-s3900" xml:space="preserve">ad O B. </s> <s xml:id="echoid-s3901" xml:space="preserve">ſiue ad ipſi æqualem I E. </s> <s xml:id="echoid-s3902" xml:space="preserve">& </s> <s xml:id="echoid-s3903" xml:space="preserve">diuidendo vt A I. </s> <s xml:id="echoid-s3904" xml:space="preserve">ad I C. </s> <s xml:id="echoid-s3905" xml:space="preserve">ita A O. </s> <s xml:id="echoid-s3906" xml:space="preserve">ad O B. </s> <s xml:id="echoid-s3907" xml:space="preserve">ſiue I E. </s> <s xml:id="echoid-s3908" xml:space="preserve">eſt <lb/>autem ex ſuppoſitione A B. </s> <s xml:id="echoid-s3909" xml:space="preserve">5 {1/2}. </s> <s xml:id="echoid-s3910" xml:space="preserve">partium, qualium I E. </s> <s xml:id="echoid-s3911" xml:space="preserve">eſt vna; </s> <s xml:id="echoid-s3912" xml:space="preserve">quare A O. </s> <s xml:id="echoid-s3913" xml:space="preserve">erit 4 {1/2}. </s> <s xml:id="echoid-s3914" xml:space="preserve">eſt igitur eadem ratio 4 {1/2}. </s> <s xml:id="echoid-s3915" xml:space="preserve"><lb/>ad 1. </s> <s xml:id="echoid-s3916" xml:space="preserve">quæ lineæ A I. </s> <s xml:id="echoid-s3917" xml:space="preserve">quæ continet ſemidiametros trrræ 1142. </s> <s xml:id="echoid-s3918" xml:space="preserve">ad alium numerum, qui explicet quantitatem <lb/>vmbræ terreſtris, qui per regulam auream reperitur eſſe quaſi 254. </s> <s xml:id="echoid-s3919" xml:space="preserve">ſcili<unsure/>cet ſemid. </s> <s xml:id="echoid-s3920" xml:space="preserve">terræ tanta igitur eſt ter-<lb/>reſtris vmbrę a terra proceritas, cum igitur inueſtiganda eſt a@icui<unsure/>us aſtri vmbra, fiat vt exceſlus diametri So-<lb/>lis ab aſtro ad aliud per auream regulam, illud enim erit vmbræ longitudo. </s> <s xml:id="echoid-s3921" xml:space="preserve">vide infra in cap. </s> <s xml:id="echoid-s3922" xml:space="preserve">de Lunæ ma-<lb/>gnitudine; </s> <s xml:id="echoid-s3923" xml:space="preserve">necnon in cap. </s> <s xml:id="echoid-s3924" xml:space="preserve">de loco Solis; </s> <s xml:id="echoid-s3925" xml:space="preserve">vbi plura de hac vmbra, & </s> <s xml:id="echoid-s3926" xml:space="preserve">modo eam deſcribendi traduntur. </s> <s xml:id="echoid-s3927" xml:space="preserve">Tan-<lb/>dem conſiderandus eſt huius vmbrę motus; </s> <s xml:id="echoid-s3928" xml:space="preserve">cum enim ea ſit penitus Soliauerſa, erit ſemper eius apex in gra-<lb/>du Eclypticæ Solis oppoſito, progredieturq; </s> <s xml:id="echoid-s3929" xml:space="preserve">conſequenter ad motum Solis ſecundum ſignorum ordinem, <lb/>atq; </s> <s xml:id="echoid-s3930" xml:space="preserve">hæc ad hanc vmbram colluſtrandam ſufficiant.</s> <s xml:id="echoid-s3931" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div81" type="section" level="1" n="55"> <head xml:id="echoid-head58" style="it" xml:space="preserve">De Terræ figura. Cap. IV.</head> <p> <s xml:id="echoid-s3932" xml:space="preserve">PVeri, atq; </s> <s xml:id="echoid-s3933" xml:space="preserve">imperitum vulgus, ſenſus æſtimatione perſuaſi, terram eſſe planum quoddam ad cælum vn-<lb/>diq; </s> <s xml:id="echoid-s3934" xml:space="preserve">attinens, falsò exiſtimant: </s> <s xml:id="echoid-s3935" xml:space="preserve">quorum mundi fabricam habes in ſecunda gura cap. </s> <s xml:id="echoid-s3936" xml:space="preserve">1. </s> <s xml:id="echoid-s3937" xml:space="preserve">de S<unsure/>phæra. <lb/></s> <s xml:id="echoid-s3938" xml:space="preserve">Elementari, in qua terra ſecundum eos eſſet planum A C. </s> <s xml:id="echoid-s3939" xml:space="preserve">cælum vero efſet circulus A B C. </s> <s xml:id="echoid-s3940" xml:space="preserve">&</s> <s xml:id="echoid-s3941" xml:space="preserve">c. </s> <s xml:id="echoid-s3942" xml:space="preserve">ſi enim id <lb/>eſſet; </s> <s xml:id="echoid-s3943" xml:space="preserve">primo ſequeretur magnum inconueniens, neminem ſcilicet (præter vnum) in tali terræ planitie ha-<lb/>bitare, aut conſiſtere poſſe (quod prima facie mirum videbitur) nam ſi terra eſſet tale planum, in medio eius <lb/>medio eſſet centrum mundi, quia huiuſmodi planum ſecat cælum, ac mundum bifariam. </s> <s xml:id="echoid-s3944" xml:space="preserve">atqui omnia gra-<lb/>uia deſcendunt ad centrum mundi niſi impediantur: </s> <s xml:id="echoid-s3945" xml:space="preserve">igitur quoduis graue poſitum in illa planitie extra cen <lb/>trum illud, ad illud delaberetur, quia nihil obſtaret. </s> <s xml:id="echoid-s3946" xml:space="preserve">quare ſolus ille habitator, qui in medio terræ, atq; </s> <s xml:id="echoid-s3947" xml:space="preserve">adeo <lb/>in centro eſſet, ibi manere, accon ſtere poſiet, isenim centro mundi hæreret. </s> <s xml:id="echoid-s3948" xml:space="preserve">cæteri vero in plano illo non <lb/>poſſent erecti inſiſtere, quia vt erecti inſiſtamus, neceſſe eſt noſtri corporis longitudinem eſſe in linea per-<lb/>pendiculari, quæ directionis dicitur, ita vt pedes centrum aſpiciant, caput vero ſurſum ad cælum. </s> <s xml:id="echoid-s3949" xml:space="preserve">Secundo <lb/>ſequeretur eodem temporis momento Solem, ac cætera ſydera omnibus tam orientalibus, quam occidenta-<lb/>libus oriri atq; </s> <s xml:id="echoid-s3950" xml:space="preserve">occidere, omnes enim vnicum haberent horizontem, planum illud videlicet terræ: </s> <s xml:id="echoid-s3951" xml:space="preserve">quod ta-<lb/>men aliter contingit; </s> <s xml:id="echoid-s3952" xml:space="preserve">nam primo orientalibus, deinde alijs locis ſucceſſiuè, & </s> <s xml:id="echoid-s3953" xml:space="preserve">poſtremo occidentalibus ap-<lb/>paret, & </s> <s xml:id="echoid-s3954" xml:space="preserve">occultatur vt manifeſtè<unsure/> in Eclypſibus cernitur; </s> <s xml:id="echoid-s3955" xml:space="preserve">nam ſi nobis, v. </s> <s xml:id="echoid-s3956" xml:space="preserve">g. </s> <s xml:id="echoid-s3957" xml:space="preserve">in meridie Sol eclypſetur, orien-<lb/>talibus eadem, ecly@ſis poſt meridiem accider, & </s> <s xml:id="echoid-s3958" xml:space="preserve">tanto poſt meridiem tardius, quantoij fuerin<unsure/>t orientalio-<lb/>res. </s> <s xml:id="echoid-s3959" xml:space="preserve">idem et@ã accidit in Lunæ defectibus. </s> <s xml:id="echoid-s3960" xml:space="preserve">conſtat autem ex cercis relationibus tardius eas apparere ad orien <lb/>tem, quam ad occidentem, tardius, ideſt, plur<unsure/>ibus horis ſecundum horologium, illius loci orientalioris: </s> <s xml:id="echoid-s3961" xml:space="preserve">ab-<lb/>ſoluto<unsure/>enim omnibus eodem temporis momento fiunt. </s> <s xml:id="echoid-s3962" xml:space="preserve">imo Aſtronomi prædicunt quot horis prius vni lo <pb o="40" file="0060" n="64" rhead="De Mundi Fabrica"/> co, quam alteri apparitura fit. </s> <s xml:id="echoid-s3963" xml:space="preserve">qui etiam ex hac eclypſium varia apparitione, explorant, quæ nam loca ſint <lb/>alijs locis orientaliora, & </s> <s xml:id="echoid-s3964" xml:space="preserve">quanto, quod eſt longitudinem regionum explicare. </s> <s xml:id="echoid-s3965" xml:space="preserve">quæ omnia ſi terra plana eſ-<lb/>ſet aliter ſe haberent: </s> <s xml:id="echoid-s3966" xml:space="preserve">ſed quſa rotunda eſt, vt mox patebit, & </s> <s xml:id="echoid-s3967" xml:space="preserve">Sol circa eam vniformiter, & </s> <s xml:id="echoid-s3968" xml:space="preserve">ſucceſſiuè reuol-<lb/>uitur, ideo prius vnis, quam alteris oritur, & </s> <s xml:id="echoid-s3969" xml:space="preserve">occidit. </s> <s xml:id="echoid-s3970" xml:space="preserve">Tertiò ſi eſſet tantum vnus horizon, omnes eaſdem ſtel-<lb/>las videremus: </s> <s xml:id="echoid-s3971" xml:space="preserve">atqui certum eſt ſtellas alias videre eos, qui magis ad Auſtrum habitãt, v.</s> <s xml:id="echoid-s3972" xml:space="preserve">g. </s> <s xml:id="echoid-s3973" xml:space="preserve">ſtellam Canopum <lb/>vident Aegyptij, quam nos minimè conſpicimus. </s> <s xml:id="echoid-s3974" xml:space="preserve">terra igitur nullo modo planum eſt.</s> <s xml:id="echoid-s3975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3976" xml:space="preserve">2 Dicendum igitur terram eſſe rotundam, ac ſphæricam, non quidem Geometricè, ſed rudi, quodam-<lb/>modo, cum eius ſuperficium valles, ac montes aſperam reddant. </s> <s xml:id="echoid-s3977" xml:space="preserve">cuius primum ſit argumentum, quod vt mo-<lb/>do dicebamus, Sol, Stellæ, Eclypſes, circa terram omnibus habitatoribus ita ſucceſſiue apparent, perinde ac <lb/>ſi circa ſphęram rotundiſſimam mouerentur, hoc eſt regulariter, & </s> <s xml:id="echoid-s3978" xml:space="preserve">vniformiter, ita vt locis, v.</s> <s xml:id="echoid-s3979" xml:space="preserve">g. </s> <s xml:id="echoid-s3980" xml:space="preserve">per 15. </s> <s xml:id="echoid-s3981" xml:space="preserve">gra-<lb/>dus magis orientalibus, vna hora prius appareant: </s> <s xml:id="echoid-s3982" xml:space="preserve">atq; </s> <s xml:id="echoid-s3983" xml:space="preserve">hoc accidit, vbiq; </s> <s xml:id="echoid-s3984" xml:space="preserve">terrarum ſecundum terræ gyrum <lb/>ab oriente in occaſum productum. </s> <s xml:id="echoid-s3985" xml:space="preserve">quod patet ex eclypſium prædictione infallibi, ſecundum quam non om-<lb/>nibus eadem hora, ſed diuerſis apparituræ prænunciantur; </s> <s xml:id="echoid-s3986" xml:space="preserve">quæ certa prædictio ſupponit terram eſſe rotun-<lb/>dam. </s> <s xml:id="echoid-s3987" xml:space="preserve">accedit etiam experient a nautarum Luſitanorum, & </s> <s xml:id="echoid-s3988" xml:space="preserve">aliorum, qui dum totum terrę ambitum circum-<lb/>nauigant, eandem ſtellarum vniformem, ac regularem apparitionem vbiq; </s> <s xml:id="echoid-s3989" xml:space="preserve">obſeruant. </s> <s xml:id="echoid-s3990" xml:space="preserve">quæ omnia euincunt <lb/>terram, & </s> <s xml:id="echoid-s3991" xml:space="preserve">quidem maximè ab oriente in occidentem eſſe rotundam.</s> <s xml:id="echoid-s3992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3993" xml:space="preserve">Quod verò ſit etiam a Septentrione in Auſtrum rotunda, ſimilis præcedentibus ratio perſuadet, nam am-<lb/>bulantibus nobis, v.</s> <s xml:id="echoid-s3994" xml:space="preserve">g. </s> <s xml:id="echoid-s3995" xml:space="preserve">Septentrionem verſus altitudines poli regulariter, ac vniformiter creſcunt, perinde <lb/>ac ſi circa ſphæram progrederemur. </s> <s xml:id="echoid-s3996" xml:space="preserve">hac ratione ſi Parma, vbi polus arcticus eleuatur ferè gr. </s> <s xml:id="echoid-s3997" xml:space="preserve">45. </s> <s xml:id="echoid-s3998" xml:space="preserve">ad Boream <lb/>milliarijs 60. </s> <s xml:id="echoid-s3999" xml:space="preserve">quæ gradum vnum efficiant, proficiſcamur, pariter polus gradu vno amplius eleuabitur ſupra <lb/>horizontem, eritq; </s> <s xml:id="echoid-s4000" xml:space="preserve">propterea eleuatus gr. </s> <s xml:id="echoid-s4001" xml:space="preserve">46 quod ſi alia 60. </s> <s xml:id="echoid-s4002" xml:space="preserve">milliaria vlterius perrexerimus, alio itidem gra-<lb/>du eleuabitur, eritq; </s> <s xml:id="echoid-s4003" xml:space="preserve">eleuatio gr. </s> <s xml:id="echoid-s4004" xml:space="preserve">47. </s> <s xml:id="echoid-s4005" xml:space="preserve">idem accidit proficiſcentibus ad alterum polum. </s> <s xml:id="echoid-s4006" xml:space="preserve">idque non in Europa <lb/>ſolum, ſed in Africa, Aſia, Nouo orbe, & </s> <s xml:id="echoid-s4007" xml:space="preserve">vbiq; </s> <s xml:id="echoid-s4008" xml:space="preserve">terrarum, vt quotid anæ nautarum, ac viatorum relationes <lb/>teſtatiſſimæ comprobant: </s> <s xml:id="echoid-s4009" xml:space="preserve">Terra igitur non ſolum ab oriente in occaſum, verum etiam a Borea, in Meri-<lb/>diem, ac proinde vſquequaque ſphærica eſt.</s> <s xml:id="echoid-s4010" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4011" xml:space="preserve">3 Vmbra terræ vt ſupra oſtendimus, conica eſt, & </s> <s xml:id="echoid-s4012" xml:space="preserve">probauimus ab eclypſibus; </s> <s xml:id="echoid-s4013" xml:space="preserve">quæ eclypſes fiunt circa <lb/>ferè omnes terræ partes, igituriterra efficit vmbram co nicam ad omnes partes; </s> <s xml:id="echoid-s4014" xml:space="preserve">vnde neceſiario ſequitur ip-<lb/>ſam eſſe vndique rotundam: </s> <s xml:id="echoid-s4015" xml:space="preserve">vmbra enim conica cùm habeat rotunditatem, habebit neceſſario pro baſi vm-<lb/>broſum corpus etiam rotundum; </s> <s xml:id="echoid-s4016" xml:space="preserve">ſed cum hic conus vndique à terra proijciatur, fit vt terra neceſſario ſit vn-<lb/>dique pariter rotunda.</s> <s xml:id="echoid-s4017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4018" xml:space="preserve">4 Idem ex plurimis itinerum, ac nauigationum, quæ hac tempeſtate, circa maria, ac terras habentur, re-<lb/>lationibus comprobatur: </s> <s xml:id="echoid-s4019" xml:space="preserve">qui enim totam per Antipodas terram circumnauigant ac tandem ad eundem lo-<lb/>cum aliunde reuertuntur ad eandem vbique terrenæ molis faciem, & </s> <s xml:id="echoid-s4020" xml:space="preserve">figuram conſpiciunt, ijſque ſemper, & </s> <s xml:id="echoid-s4021" xml:space="preserve"><lb/>vbique omnia circa ſtellarum ortus, & </s> <s xml:id="echoid-s4022" xml:space="preserve">occaſus vniformiter, ac regulariter apparuerunt: </s> <s xml:id="echoid-s4023" xml:space="preserve">quæ nullo modo <lb/>fieri poſſent, niſi terra eſſet ſpærica.</s> <s xml:id="echoid-s4024" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4025" xml:space="preserve">5 Tandem ratio phyſica idem atteſtatur, cum enim terra ſit grauiſſima, ac ideò omnes eius partes pari-<lb/>ter deorſum, ideſt, ad centrum mundi grauitent, fit vt ſingulæ quantum poſſunt, deſcendere conentur; </s> <s xml:id="echoid-s4026" xml:space="preserve">ex <lb/>quo ſequitur extremarum atque extimarum partium a centro æquidiſtantia, quæ aliud nihil eſt, quam ſphæ-<lb/>ricitas. </s> <s xml:id="echoid-s4027" xml:space="preserve">Porrò quamuis montes hanc ſphæricitatem impolitam efficiant, quia tamen ſumma eorum altitu-<lb/>do reſpectu totius terrenæ molis, vt oſtendemus infra, eſt peuè inſenſibilis, ſphærica nihilominus; </s> <s xml:id="echoid-s4028" xml:space="preserve">ſaltem <lb/>phyſicè appellãda eſt. </s> <s xml:id="echoid-s4029" xml:space="preserve">Illud etiam notandum omnes allatas rationes, poſſe etiam probare extimam aquæ, ſeu <lb/>maris ſuperficiem eſſe ſphæricam. </s> <s xml:id="echoid-s4030" xml:space="preserve">Demum, & </s> <s xml:id="echoid-s4031" xml:space="preserve">illud ſcitu dignum, Parmenidem Eleatem primum omnium <lb/>ante Chriſti natiuitatẽ anno circiter 452. </s> <s xml:id="echoid-s4032" xml:space="preserve">hanc terræ globoſitatẽ demonſtraſſe: </s> <s xml:id="echoid-s4033" xml:space="preserve">ex noſtra Mathem. </s> <s xml:id="echoid-s4034" xml:space="preserve">Chronol.</s> <s xml:id="echoid-s4035" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div82" type="section" level="1" n="56"> <head xml:id="echoid-head59" style="it" xml:space="preserve">De Mutatione rotunditatis terræ. Corrollarium.</head> <p> <s xml:id="echoid-s4036" xml:space="preserve">PErgratum lectori forè ex@ſtimaui, ſi rem ſcitu digniſſimam expoſuero, quam pridem ac diu obſeruari, <lb/>præſertim cum nullus, quod ſciam, eam literis mandauerit: </s> <s xml:id="echoid-s4037" xml:space="preserve">nos de ea in locis Ariſt. </s> <s xml:id="echoid-s4038" xml:space="preserve">Mathematicis pri-<lb/>mum ſatis fusè tractauimus; </s> <s xml:id="echoid-s4039" xml:space="preserve">vnde quæ ſequuntur ſummatim deſcribemus; </s> <s xml:id="echoid-s4040" xml:space="preserve">Ea igitur eſt, Terræ totius ſuper-<lb/>ficiem, quæ ob montes, ac valles aſpera, atque ruditer ſphærica, eſt in dies iam inde à mundi exordio paula-<lb/>tim reduci ad perfectam ſpæricitatem, itaut aliquando naturaliter neceſsè futurum ſit eam a mari inundari, <lb/>atque inhabitabilem reddi. </s> <s xml:id="echoid-s4041" xml:space="preserve">Primum igitur vt re cauſas probe teneamus, illud ex ſacris literis ſtatuendum; <lb/></s> <s xml:id="echoid-s4042" xml:space="preserve">Orbem terræ in ſuo primordio, fuiſſe perfectiori ſphærica figura præd ctum, ideſt, abſque montium, ac val-<lb/>lium inæqualitatibus; </s> <s xml:id="echoid-s4043" xml:space="preserve">tunc enim tota mari obtegebatur, mi<unsure/>nimeque ideo apta animantium terreſtrium ha-<lb/>bitationi; </s> <s xml:id="echoid-s4044" xml:space="preserve">tunc autem habitabilis reddi<unsure/>ta eſt, cum ipſius conditoris nutu, maxima terræ pars ex vnoloco in <lb/>alium translata eſt, vnde illic marium concauitates, iſtic verò montium ſublimitates apparuerunt: </s> <s xml:id="echoid-s4045" xml:space="preserve">quo facto <lb/>aquæ omnes, quæ prius totam terræ faciem tegebant, in loca illa decliuiora, ac concaua receſſerunt; </s> <s xml:id="echoid-s4046" xml:space="preserve">quæ <lb/>aquarum congregatio mare apellatum eſt. </s> <s xml:id="echoid-s4047" xml:space="preserve">hinc nonnulli authores grauiſſimi aſſerere non dubitarunt, mon-<lb/>tes ex illa terra conflatos eſſe, quæ maris concauitatem prius occupabat. </s> <s xml:id="echoid-s4048" xml:space="preserve">ex quibus ſequitur terram ſic mon-<lb/>tuoſam, eſſe extra naturalem ſuam figuram, atq; </s> <s xml:id="echoid-s4049" xml:space="preserve">in ſtatu quodam violento. </s> <s xml:id="echoid-s4050" xml:space="preserve">pręterea cum terra ſit grauior <lb/>quam aqua, nullæ ipſius partes deberent eſſe eminentiores quam ſit maris ſuperficies, & </s> <s xml:id="echoid-s4051" xml:space="preserve">tamen re vera ter-<lb/>ra mari altior eſt maximè verò montanæ regiones, quæ altera violentia terræ, & </s> <s xml:id="echoid-s4052" xml:space="preserve">aquæ ineſt: </s> <s xml:id="echoid-s4053" xml:space="preserve">quare vtique <lb/>valde conueniens eſt, terram, & </s> <s xml:id="echoid-s4054" xml:space="preserve">aquam ad earum primigenium ſtatum, ac figuram quotidie reuerti.</s> <s xml:id="echoid-s4055" xml:space="preserve"/> </p> <pb o="41" file="0061" n="65" rhead="Liber Quartus."/> <p> <s xml:id="echoid-s4056" xml:space="preserve">Porrò cauſam huius reſtaurationis dicimus eſſe aquas, tum fluniales, tum etiam pluuiales, vt ex ſequenti-<lb/>bus obſeruationibus fiet manifeſtum.</s> <s xml:id="echoid-s4057" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4058" xml:space="preserve">Primo videmus flumina quotidie montium radices corrodere, ac ſuffodere, ita vt paſſim ex omnibus mon <lb/>tibus magnas efficiant ruinas, ac præcipitia, ſicq; </s> <s xml:id="echoid-s4059" xml:space="preserve">terra (vt eſt apud Iobum cap. </s> <s xml:id="echoid-s4060" xml:space="preserve">14.) </s> <s xml:id="echoid-s4061" xml:space="preserve">alluuione paulatim con-<lb/>ſumitur. </s> <s xml:id="echoid-s4062" xml:space="preserve">humum vero illam ex montibus delapſam ſemper ad loca humiliora fluuij deducunt.</s> <s xml:id="echoid-s4063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4064" xml:space="preserve">Ex his fluminum corroſionibus naſcuntur tardiffimæ illæ, ſed tamen magnæ ruinæ, quæ Labinæ à laben-<lb/>do dicuntur; </s> <s xml:id="echoid-s4065" xml:space="preserve">quibus non rarò pagi, ac vici integri in fluuios præcipites delabuntur.</s> <s xml:id="echoid-s4066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4067" xml:space="preserve">2 Quotidie cernimus aquas pluuias montium ſuperficies ad ima deducere; </s> <s xml:id="echoid-s4068" xml:space="preserve">hinc fit vt altiores mõtes ſint <lb/>etiã cæteris duriores, ac lapidoſi magis, qua duritie aquis me@ius reſiſtunt. </s> <s xml:id="echoid-s4069" xml:space="preserve">hinc pariter fit vt antiqua in mon-<lb/>tibus ædificia, fundamentis eorum paulatim detectis, non admodum diuturna euadant. </s> <s xml:id="echoid-s4070" xml:space="preserve">hac de cauſa Ro-<lb/>mani Capitolij fundamenta modo tota ſupra terram extant, quæ olim altè ſub terram deſcendebant. </s> <s xml:id="echoid-s4071" xml:space="preserve">vide <lb/>hac de re Georgium Agricolam lib. </s> <s xml:id="echoid-s4072" xml:space="preserve">3. </s> <s xml:id="echoid-s4073" xml:space="preserve">cap. </s> <s xml:id="echoid-s4074" xml:space="preserve">1. </s> <s xml:id="echoid-s4075" xml:space="preserve">vbi plura ſcitu digna reperies. </s> <s xml:id="echoid-s4076" xml:space="preserve">ſed iam ad plana deſcendamus.</s> <s xml:id="echoid-s4077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4078" xml:space="preserve">3 In planis igitur contrarium omnino accedere videmus, atq; </s> <s xml:id="echoid-s4079" xml:space="preserve">in montibus plana videlicet loca quoti-<lb/>die magis eleuari, quoniam aquæ terram, quam ſecum ex montanis detrahunt, in planis, & </s> <s xml:id="echoid-s4080" xml:space="preserve">alijs etiam de-<lb/>cliuioribus locis deponunt. </s> <s xml:id="echoid-s4081" xml:space="preserve">hinc cernimus antiqua in hiſce locis ædificia, eſſe iam penè tota ſepulta, contra <lb/>quam in editionibus locis accidat: </s> <s xml:id="echoid-s4082" xml:space="preserve">ſic Romæ ad radices ipſius Capitolij montis, cernere eſt triumph alem ar-<lb/>cum Septimij iam penè totum terra obrutum. </s> <s xml:id="echoid-s4083" xml:space="preserve">eadem de cauſa in Pantheona nunc deſcenditur, in quem mul <lb/>tis gradibus olim aſcendebatur@ſic etiã Epiſcopalia templa vetuſtiora, ſatis infra terram conſpiciuntur. </s> <s xml:id="echoid-s4084" xml:space="preserve">hinc <lb/>etiam paſſim in antiquioribus vrbium domibus portæ complures occluſæ cernuntur parum ſupra ſolum ex-<lb/>tantes, quæ cauſam ignorantibus, magnæ ſunt admirationi.</s> <s xml:id="echoid-s4085" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4086" xml:space="preserve">Ex quibus patet hanc ędificiorum demerſionem in terram manifeſtum eſſe ſignum eorum antiquitatis eo <lb/>maioris, quo altius in terram defoſſa ſunt, v. </s> <s xml:id="echoid-s4087" xml:space="preserve">g. </s> <s xml:id="echoid-s4088" xml:space="preserve">Bononiæ viſuntur plures antiquę vrbis Portæ, quas vulgò Bo-<lb/>nonienſes appellant Torreſotti, valde demerſæ, ideo certum earum antiquitatis argumentum eſt; </s> <s xml:id="echoid-s4089" xml:space="preserve">ac proin-<lb/>de verum eſſe, quod tradũt hiſtoriæ, eas tempore S. </s> <s xml:id="echoid-s4090" xml:space="preserve">Petronij, ſcilicet 1200. </s> <s xml:id="echoid-s4091" xml:space="preserve">ab hinc ferè annis fuiſſe extructas. <lb/></s> <s xml:id="echoid-s4092" xml:space="preserve">Idem de cæteris quoq; </s> <s xml:id="echoid-s4093" xml:space="preserve">fabricis iudicium haberi debet. </s> <s xml:id="echoid-s4094" xml:space="preserve">animaduertendum tamen eſt cæteris paribus, eas al-<lb/>tius eſſe demerſas, quæ in humiliori loco, quam quæ in editiori conſtructæ ſunt, ob allatam ſuperius rationẽ. </s> <s xml:id="echoid-s4095" xml:space="preserve"><lb/>ſic Bononiæ pariter Porta illa vetus quæ dicitur, il Torreſotto di S. </s> <s xml:id="echoid-s4096" xml:space="preserve">Giorgio, altius obruta eſt, quam quæ di-<lb/>citur, il Torreſotto di Stracaſtiglione, quia enim illa in humiliori loco ſita eſt, propterea circa ipſam humus <lb/>facilius congeſta accreuit.</s> <s xml:id="echoid-s4097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4098" xml:space="preserve">4 Idem affirmant Architectores, qui dum fundamenta defodiunt, primò vbiq; </s> <s xml:id="echoid-s4099" xml:space="preserve">in planis excauant terrã, <lb/>quam commotam appellant, quæ lignis, ferramentis, ruderibus, numiſmatis, antiquis ſepulchris, alijſq; </s> <s xml:id="echoid-s4100" xml:space="preserve">re-<lb/>bus permixta eſt: </s> <s xml:id="echoid-s4101" xml:space="preserve">hac autem eruta, humum aliam, effodiunt numquam antea commotam, ſed ſolidam, ac be-<lb/>nè compactam, nulliſq; </s> <s xml:id="echoid-s4102" xml:space="preserve">alienis rebus, præſertim artificiatis, commixtam. </s> <s xml:id="echoid-s4103" xml:space="preserve">terra igitur illa commota, & </s> <s xml:id="echoid-s4104" xml:space="preserve">im-<lb/>pura, ea eſt, quam ex altioribus locis, aquæ in depreſſiora paulatim deportauerunt; </s> <s xml:id="echoid-s4105" xml:space="preserve">quæ non vbiq; </s> <s xml:id="echoid-s4106" xml:space="preserve">eiuſdem <lb/>eſt altitudinis. </s> <s xml:id="echoid-s4107" xml:space="preserve">quoniam verò in montibus nuſquam reperitur huiuſmodi terra mota, aut noua, vt patet ex-<lb/>perientia Architectorum, manifeſtum eſt montes nullo modo creſcere, vt nonnulli ſomniant.</s> <s xml:id="echoid-s4108" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4109" xml:space="preserve">5 Comprobatur tandem noſtra obſeruatio, ex illa arte, quæ nunc viget, qua ſcilicet, per aquas fluuiales <lb/>aggerando loca depræſſiora attollunt; </s> <s xml:id="echoid-s4110" xml:space="preserve">altiora verò corrodendo deprimunt, atq; </s> <s xml:id="echoid-s4111" xml:space="preserve">hæc de terra.</s> <s xml:id="echoid-s4112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4113" xml:space="preserve">Circa mare verò eadem contingunt; </s> <s xml:id="echoid-s4114" xml:space="preserve">cum enim maris fundum ſit terreſtri ſuperficie depreſſius, atque in <lb/>mare ingentia omnia flumina ſe exonerent, ſecumq; </s> <s xml:id="echoid-s4115" xml:space="preserve">magnam terræ, ac arenæ copiam inferant, continuo, <lb/>fiunt circa maris litora propè oſtia fluminum, magnæ aggerationes, quibus multum litora in mare creſcunt, <lb/>illudq; </s> <s xml:id="echoid-s4116" xml:space="preserve">recedere propterea cogunt.</s> <s xml:id="echoid-s4117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4118" xml:space="preserve">Primo id quidem probatur authoritate Ariſt. </s> <s xml:id="echoid-s4119" xml:space="preserve">lib. </s> <s xml:id="echoid-s4120" xml:space="preserve">1. </s> <s xml:id="echoid-s4121" xml:space="preserve">Meteor. </s> <s xml:id="echoid-s4122" xml:space="preserve">cap. </s> <s xml:id="echoid-s4123" xml:space="preserve">de permutatione terræ, ac maris; </s> <s xml:id="echoid-s4124" xml:space="preserve">necnort <lb/>authoritate veterum Geographorum, & </s> <s xml:id="echoid-s4125" xml:space="preserve">Hiſtoricorum. </s> <s xml:id="echoid-s4126" xml:space="preserve">Ariſtoteles igitur ibi in comprobationem huius ad-<lb/>ducit primo magnam illam Aegypti aggerationem a Nilo flumine factam, pars enim illa Aegypti, quę Del-<lb/>ta, Niliq; </s> <s xml:id="echoid-s4127" xml:space="preserve">donum appellatur, ab Herodoto, ex arenis, & </s> <s xml:id="echoid-s4128" xml:space="preserve">limo ex Aethiopiæ montibus ſimul cum aquis Nili <lb/>delabentibus, eſt conflata, atq; </s> <s xml:id="echoid-s4129" xml:space="preserve">antiquo litori addita, cui locum paulatim inare ceſſit, eſtque propterea Nili <lb/>donum appellata. </s> <s xml:id="echoid-s4130" xml:space="preserve">Secundum Ariſtotelis exemplum eſt Ammonia Regio: </s> <s xml:id="echoid-s4131" xml:space="preserve">cuius humiliora loca, ſcilicet ma-<lb/>ritima, palam, inquit, eſt quod aggeratione facta, fiunt ſtagna, & </s> <s xml:id="echoid-s4132" xml:space="preserve">continens; </s> <s xml:id="echoid-s4133" xml:space="preserve">& </s> <s xml:id="echoid-s4134" xml:space="preserve">ſuccedente tempore aqua ſta-<lb/>gnans exſiccata eſt, & </s> <s xml:id="echoid-s4135" xml:space="preserve">iam ob aggerationem annihilata. </s> <s xml:id="echoid-s4136" xml:space="preserve">Tertium exemplum eſt Meotidis Paludis; </s> <s xml:id="echoid-s4137" xml:space="preserve">at verò <lb/>ait, & </s> <s xml:id="echoid-s4138" xml:space="preserve">quæ ſunt circa Meotidem paludem creuerunt alluuione fluuiorum tantum, vt multo minores magni-<lb/>tudine naues, nunc innare poſſint, quam anno ab hinc 60. </s> <s xml:id="echoid-s4139" xml:space="preserve">quare ex hoc facilè eſt ratiocinari, vt multa ſtagno-<lb/>rum, ita, & </s> <s xml:id="echoid-s4140" xml:space="preserve">hoc opus eſſe fluuiorum, & </s> <s xml:id="echoid-s4141" xml:space="preserve">tandem neceſſe eſt, totum fieri ſiccum. </s> <s xml:id="echoid-s4142" xml:space="preserve">vide Polybium lib. </s> <s xml:id="echoid-s4143" xml:space="preserve">4. </s> <s xml:id="echoid-s4144" xml:space="preserve">pag. </s> <s xml:id="echoid-s4145" xml:space="preserve">317. <lb/></s> <s xml:id="echoid-s4146" xml:space="preserve">Quartum eſt Boſphorus Thracius, quod apud ipſum, breuitatis cauſa videas. </s> <s xml:id="echoid-s4147" xml:space="preserve">Quinto accedat Plinij teſtimo-<lb/>nium, qui tradit multas terras naſci, non ſolũ fluminum inuectu, ſed etiam marium receſſu; </s> <s xml:id="echoid-s4148" xml:space="preserve">ſic mare ab Am-<lb/>braciæ portu 10. </s> <s xml:id="echoid-s4149" xml:space="preserve">millia paſſuum, ab Athenarum verò 5. </s> <s xml:id="echoid-s4150" xml:space="preserve">millia; </s> <s xml:id="echoid-s4151" xml:space="preserve">& </s> <s xml:id="echoid-s4152" xml:space="preserve">alijs in locis plus minuſuè receſſiſſe ſcribit. </s> <s xml:id="echoid-s4153" xml:space="preserve"><lb/>huc facit locus Strabonius lib. </s> <s xml:id="echoid-s4154" xml:space="preserve">12. </s> <s xml:id="echoid-s4155" xml:space="preserve">de Pyramo Ciliciæ fluuio; </s> <s xml:id="echoid-s4156" xml:space="preserve">montes vero, inquit, egreſſus tantum limum in <lb/>mare deducit, partim ex Cataonia, partim ex Ciliciæ campis, vt huiuſmodi de eo oraculum feratut.</s> <s xml:id="echoid-s4157" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4158" xml:space="preserve">Tempus erit rapidis olim cum Pyramus vndis, <lb/>In ſacram veniet congeſto litto@e, Cyprum.</s> <s xml:id="echoid-s4159" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4160" xml:space="preserve">Hicenim fluuius è regione Cypri inſulæ in mare influit: </s> <s xml:id="echoid-s4161" xml:space="preserve">hæc Strabo, apud quem plura huc ſpectantia, ac <lb/>ſcit@ digna reperies.</s> <s xml:id="echoid-s4162" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4163" xml:space="preserve">6 Verum recentiora, ac propiora non deſunt experimenta. </s> <s xml:id="echoid-s4164" xml:space="preserve">Rauenna olim erat extremo littori adhæ- <pb o="42" file="0062" n="66" rhead="De Mundi Fabrica."/> rens, nunc ob aggerationem mare ab ea multum receſſit. </s> <s xml:id="echoid-s4165" xml:space="preserve">Patauium mare alluebat, quod nunc 25. </s> <s xml:id="echoid-s4166" xml:space="preserve">millia pa@-<lb/>ſuum diſtat. </s> <s xml:id="echoid-s4167" xml:space="preserve">Aeſtuarium ipſum Venetum ob arenas à<unsure/> fluuijs hinc inde inuectas, fundum adeo extulit, vt vix <lb/>amplius nauigationi ſit idoneum: </s> <s xml:id="echoid-s4168" xml:space="preserve">periculumq; </s> <s xml:id="echoid-s4169" xml:space="preserve">immineat ne Venetiarum mirabilis locus ex maritimo fiat <lb/>terreſtris. </s> <s xml:id="echoid-s4170" xml:space="preserve">demum noſter Bononienſium Rhenus, quamuis exiguus torrẽs paucis tamen annis quibus in Pa-<lb/>dum, in quem arte immiſlus, influxit, eum ita arena, atq; </s> <s xml:id="echoid-s4171" xml:space="preserve">limo compleuit, vt & </s> <s xml:id="echoid-s4172" xml:space="preserve">Pado, & </s> <s xml:id="echoid-s4173" xml:space="preserve">fibi magno agrorũ <lb/>damno, viam in mare obſtruxerit. </s> <s xml:id="echoid-s4174" xml:space="preserve">Cum igitur ob varias aggerationes mare cogatur magis quotidie rece-<lb/>dere, fiatque alueus ipſius anguſtor, & </s> <s xml:id="echoid-s4175" xml:space="preserve">e@atior, neceſſe eſt aliquando futurum, vt exundare incipiat. </s> <s xml:id="echoid-s4176" xml:space="preserve">quod iam <lb/>pleriſq; </s> <s xml:id="echoid-s4177" xml:space="preserve">in locis accidit, vt in littore Baltico, Danico, & </s> <s xml:id="echoid-s4178" xml:space="preserve">Hollandico; </s> <s xml:id="echoid-s4179" xml:space="preserve">quibus in locis iam pridem ſunt extru-<lb/>cti prælongi, ac præalti aggeres contra maritimas exundationes: </s> <s xml:id="echoid-s4180" xml:space="preserve">quibus antiquitus minimè opus fuiſſe Hi-<lb/>ſtoricorum, & </s> <s xml:id="echoid-s4181" xml:space="preserve">Geographorum ſilentium comprobat. </s> <s xml:id="echoid-s4182" xml:space="preserve">Hoc igitur modo terra ea, quæ montes conflat, pau-<lb/>latim ab aquis in maris concauitates deducta, cauſa eſt vt mare ſenſim modo hac, modo illac, terræ ſuperfi-<lb/>ciei ſuperfundatur; </s> <s xml:id="echoid-s4183" xml:space="preserve">ſicq; </s> <s xml:id="echoid-s4184" xml:space="preserve">iterum terræ globus, vti erat exordio mundi inhabitabilis ob aquarum effuſionem <lb/>reddatur: </s> <s xml:id="echoid-s4185" xml:space="preserve">atq; </s> <s xml:id="echoid-s4186" xml:space="preserve">omnino ad priſtinum ſtatum, & </s> <s xml:id="echoid-s4187" xml:space="preserve">figuram terra, & </s> <s xml:id="echoid-s4188" xml:space="preserve">aqua reuertantur, in quo naturaliter quie-<lb/>ſcere debent. </s> <s xml:id="echoid-s4189" xml:space="preserve">Quod probare volebam.</s> <s xml:id="echoid-s4190" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div83" type="section" level="1" n="57"> <head xml:id="echoid-head60" style="it" xml:space="preserve">Tantum æui mutare poteſt longæ@a vetuſtas.</head> <p> <s xml:id="echoid-s4191" xml:space="preserve">Hinc nonnulla deducuntur conſectari<unsure/>a ſcitu digniſſima; </s> <s xml:id="echoid-s4192" xml:space="preserve">Mundum videlicet, vel ſaltem terram ab æter-<lb/>no non fuiſſe figura hac præditam, quam nunc videmus, nec mundum perpetuo duraturum: </s> <s xml:id="echoid-s4193" xml:space="preserve">nam ſi hæc illi <lb/>montuoſa figura ab æterno ineſiet, iam pri<unsure/>dem tota illa montium tuberoſitas fuiflet ab aquis exeſa, & </s> <s xml:id="echoid-s4194" xml:space="preserve">con-<lb/>ſumpta: </s> <s xml:id="echoid-s4195" xml:space="preserve">neq; </s> <s xml:id="echoid-s4196" xml:space="preserve">æterna eſſe poterit, quia, vt probauimus, ſucceſſu temporis, reducetur ad perfectam rotundi-<lb/>tatem, atq; </s> <s xml:id="echoid-s4197" xml:space="preserve">a mari inundabitur, vnde fiet inhabitabilis; </s> <s xml:id="echoid-s4198" xml:space="preserve">indeq; </s> <s xml:id="echoid-s4199" xml:space="preserve">neceſſario mortalium genus interibit qua-<lb/>propter niſi igneo illo, quem ſacræ literæ innuunt, cataclyſmo ille præueniretur, aqua nihilominus interi-<lb/>turum eſſet. </s> <s xml:id="echoid-s4200" xml:space="preserve">ſi plura deſideras conſule opus noſtrum de locis Mathematicis apud Ariſtotelem. </s> <s xml:id="echoid-s4201" xml:space="preserve">multo poſt <lb/>tempore a quo hæc literis mandaueram, incidi in libellum Philonis Hebræi de mundo. </s> <s xml:id="echoid-s4202" xml:space="preserve">vbi ipſe hanc rem <lb/>pauciſiſſimis ac obſcurè tangit.</s> <s xml:id="echoid-s4203" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div84" type="section" level="1" n="58"> <head xml:id="echoid-head61" style="it" xml:space="preserve">De Magnitudine. Cap. V.</head> <p> <s xml:id="echoid-s4204" xml:space="preserve">DV pliciter telluris magnitudo conſideranda eſt, comparatè videlicet, & </s> <s xml:id="echoid-s4205" xml:space="preserve">abſolutè. </s> <s xml:id="echoid-s4206" xml:space="preserve">Terra igitur ſupremo <lb/>cælo, ac toti mundo comparata eſt inſtar puncti, ac illius veluti centrum inſenſibile in eius medio reſi-<lb/>dens quod quidem ex eo patet, quod vt ſupra probauimus ex quouis terræ ſuperficiei loco, non minus cæli <lb/>climidium, quam ſi in eius centro eſſemus, videamus; </s> <s xml:id="echoid-s4207" xml:space="preserve">argumentum ſanè euidens terræ craſſitiem nullatenus <lb/>obſtare, qui<unsure/>n mundi hemiſphærium, ſeu ſemimundum ſpectemus, ac proinde ipſius molem ad totum mun-<lb/>clum collatam inſenfibilem omnino euadere. </s> <s xml:id="echoid-s4208" xml:space="preserve">inſpiciatur figura ſeq. </s> <s xml:id="echoid-s4209" xml:space="preserve">pag. </s> <s xml:id="echoid-s4210" xml:space="preserve">88. </s> <s xml:id="echoid-s4211" xml:space="preserve">vbi quia terra maior eſt quã opor <lb/>teret ideo horizon phyficus K L. </s> <s xml:id="echoid-s4212" xml:space="preserve">non dirimit cęlum in partes æquas, nam pars K C L. </s> <s xml:id="echoid-s4213" xml:space="preserve">ſupra dictum horizon <lb/>tem, quæ ſola à ſuo habitatore vi deri poteſt, multò minor eſt ſemimundo.</s> <s xml:id="echoid-s4214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4215" xml:space="preserve">Quod ſi terra ibi depicta eſſet adeò parua, vt centro ſuo ibi depicto æqualis eſſet, tunc horizon K L. </s> <s xml:id="echoid-s4216" xml:space="preserve">coin-<lb/>cideret ferè cum horizonte aſtronomico A D. </s> <s xml:id="echoid-s4217" xml:space="preserve">ac proinde cælum in partes ad ſenſum æquas ſecaret, nõ aliter <lb/>ac ipſa terra faciat. </s> <s xml:id="echoid-s4218" xml:space="preserve">exiſtimandum igitur eam ad cælum nullius eſſe magnitudin s.</s> <s xml:id="echoid-s4219" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4220" xml:space="preserve">2 Ex probatiſſimorum Aſtronorum ſententia, vt poſtea videbimus inerrantium ſphæra, ſiue firmamen-<lb/>tum ad terram collatum, eam ſaltem habet rationem, quam 2. </s> <s xml:id="echoid-s4221" xml:space="preserve">milliones millionum, & </s> <s xml:id="echoid-s4222" xml:space="preserve">c. </s> <s xml:id="echoid-s4223" xml:space="preserve">(vt aiunt) habent ad <lb/>1. </s> <s xml:id="echoid-s4224" xml:space="preserve">ideſt, 2, 744, 000, 000, 000, ad 1. </s> <s xml:id="echoid-s4225" xml:space="preserve">hoc eſt intra firmamenti concauitatem continerentur duo milliones mil-<lb/>lionum, &</s> <s xml:id="echoid-s4226" xml:space="preserve">c. </s> <s xml:id="echoid-s4227" xml:space="preserve">Terrarum, quare merito dicendum eſt, eam inſenſibilem euadere ſi cum firmamento compare-<lb/>tur, um vnitas ad tantum numerum ſit pené<unsure/> nihil.</s> <s xml:id="echoid-s4228" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4229" xml:space="preserve">3 Idem oſtenditur ex Aſtronomicis inſtrumẽtis, vti ſunt ſolaria horologia; </s> <s xml:id="echoid-s4230" xml:space="preserve">quando enim ea conſtruunt <lb/>Aſtronomi, ſupponunt ſtyli apicem eſſe præcisè in centro terrę ac mundi, cum tamen poſtea eo vtimur, non <lb/>in centro mundi, vel terræ, ſed valdè ab eo diſtantes, videlicet in terræ ſuperficie lumus; </s> <s xml:id="echoid-s4231" xml:space="preserve">nihilominus tamen <lb/>horas adeo exactè indicat, ac ſi in centro exiſteret. </s> <s xml:id="echoid-s4232" xml:space="preserve">quod euidens indicium eſt, Telluris globum non ſolum <lb/>ad totius vniuerſi machinam, verum etiam ad cæleſtem Solis regionem indiuidui puncti vicem obtinere; <lb/></s> <s xml:id="echoid-s4233" xml:space="preserve">quandoquidem Sol circa ſtyli apicem ſupra terram exiſtentem, eadem efficit, quæ ſi in eius centro eſſet, ef-<lb/>ficeret.</s> <s xml:id="echoid-s4234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4235" xml:space="preserve">4 Argumenta illa omnia ſuperius allata, quæ terram in medio mundi eſſe conuincunt, eandem quoque <lb/>eſle inſtar puncti demonſtrant: </s> <s xml:id="echoid-s4236" xml:space="preserve">oſtendunt enim primo terræ ſuperficiem in centro mundi exiſtere. </s> <s xml:id="echoid-s4237" xml:space="preserve">Illud po-<lb/>ſtremo notandum quatuor has rationes pro terræ paruitate allatas, conuenire etiam, & </s> <s xml:id="echoid-s4238" xml:space="preserve">applicari poſſe Ele-<lb/>mento aquæ, ſiue mari, vt conſideranti fac@lè patebit.</s> <s xml:id="echoid-s4239" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div85" type="section" level="1" n="59"> <head xml:id="echoid-head62" style="it" xml:space="preserve">Terræ<unsure/> magnitudo abſoluta.</head> <p> <s xml:id="echoid-s4240" xml:space="preserve">Iam tandem ad hanc ſubtiliſſimam Aſtronomorum indagationem, atq; </s> <s xml:id="echoid-s4241" xml:space="preserve">vt ita dicam, ad primum Aſtro-<lb/>nom@æ miraculum peruenimus: </s> <s xml:id="echoid-s4242" xml:space="preserve">Enimuero non ſolum illiteratorum vulgus, verum etiam philoſophan-<lb/>tium complures ſæpius audiui, præclaram hanc atq; </s> <s xml:id="echoid-s4243" xml:space="preserve">abſtruſam cognitionem humani ingenij viribus impa-<lb/>rem exiſtimantes. </s> <s xml:id="echoid-s4244" xml:space="preserve">quis enim, aiunt, eam metiens obiuit, aut ambire potuit, pelagus, lacubus, montibus cir-<lb/>cumambulantẽ impedientibus. </s> <s xml:id="echoid-s4245" xml:space="preserve">Verum enimuerò Aſtronomi non pedibus, ſed ingenio, ac ſolertia ſublimius <lb/>incedentes, eam circumluſtrarunt. </s> <s xml:id="echoid-s4246" xml:space="preserve">Rem autem aggrediamur. </s> <s xml:id="echoid-s4247" xml:space="preserve">Quadruplicem in quauis ſphæra, vti terra eſt, <pb o="43" file="0063" n="67" rhead="Liber Quartus."/> quantitatem conſiderare Geometræ ſolet; </s> <s xml:id="echoid-s4248" xml:space="preserve">diametrum videlicet eius, peripherlam elus eirculi maximi, ſu-<lb/>perficiem conuexam, vltimo ſoliditatem. </s> <s xml:id="echoid-s4249" xml:space="preserve">ſed priuſquam prædictas terræ quantitates indagemus, aut me-<lb/>tiamu r, de menſuris ipſis nonnulla præmittere oportet.</s> <s xml:id="echoid-s4250" xml:space="preserve"/> </p> <figure> <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-01"/> </figure> <p> <s xml:id="echoid-s4251" xml:space="preserve">Pes Romanus erat duplo maior quam linea A B. </s> <s xml:id="echoid-s4252" xml:space="preserve">in margine adſcripta, quem ex P. </s> <s xml:id="echoid-s4253" xml:space="preserve">Vilalpando <lb/>de Templo Salom. </s> <s xml:id="echoid-s4254" xml:space="preserve">deſumpſimus. </s> <s xml:id="echoid-s4255" xml:space="preserve">Pes autem continet digitos 16.</s> <s xml:id="echoid-s4256" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4257" xml:space="preserve">Paſſus Geometricus continebat pedes quinque. </s> <s xml:id="echoid-s4258" xml:space="preserve">eſt autem interuallum intus eiuſdem pedis ve-<lb/>ſtigia duo ambulamus. </s> <s xml:id="echoid-s4259" xml:space="preserve">ideſt, ab eleuatione eiuſdem incluſiuè plantæ vſque ad eiuſdem poſitionem <lb/>excluſiue.</s> <s xml:id="echoid-s4260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4261" xml:space="preserve">Stadium continet paſſus Geometricos 125. </s> <s xml:id="echoid-s4262" xml:space="preserve">vel pedes 625.</s> <s xml:id="echoid-s4263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4264" xml:space="preserve">Milliaria ſiue milliare continet 8. </s> <s xml:id="echoid-s4265" xml:space="preserve">ſtadia; </s> <s xml:id="echoid-s4266" xml:space="preserve">ſed paſſus Geometricos mille, vnde & </s> <s xml:id="echoid-s4267" xml:space="preserve">milliarium de-<lb/>nominatur.</s> <s xml:id="echoid-s4268" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4269" xml:space="preserve">Leuca Gallica, & </s> <s xml:id="echoid-s4270" xml:space="preserve">Hiſpanica continet ſeſquimilliarium, ideſt vnum cum dimidio.</s> <s xml:id="echoid-s4271" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4272" xml:space="preserve">Leuca Germanica communis conſtat milliar. </s> <s xml:id="echoid-s4273" xml:space="preserve">4.</s> <s xml:id="echoid-s4274" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4275" xml:space="preserve">Valor autem harum menſurarum ſumitur penes longitudinem, ac propterea terreſtres longi-<lb/>tudine veluti itinere, per eas metimur. </s> <s xml:id="echoid-s4276" xml:space="preserve">ſolent præterea hæ menſuræ ſumi etiam ſecundum latitu-<lb/>dinem, ideſt, ſecundum ſuperficiem, in qua acceptione euadunt ſuperficies quadratæ, ſiue qua-<lb/>drata; </s> <s xml:id="echoid-s4277" xml:space="preserve">ſic pes quadratus, paſſus quadratus; </s> <s xml:id="echoid-s4278" xml:space="preserve">ſtadium quadratum, milliare quadratum, ſunt quadratæ <lb/>ſuperficies, quarum quatuor latera ſunt æqualia quatuor pedibus linearibus; </s> <s xml:id="echoid-s4279" xml:space="preserve">vel quatuor paſſibus, <lb/>ſtadijs, aut milliarijs linearibus. </s> <s xml:id="echoid-s4280" xml:space="preserve">in qua acceptione non habent inuicem eaſdem proportiones quas <lb/>habent latera eorum, ſiue quas habent quando vti lineæ ſumuntur. </s> <s xml:id="echoid-s4281" xml:space="preserve">hiſce autem quadratis ſuperfi-<lb/>ciebus vtuntur ad alias ſuperficies menſurandas.</s> <s xml:id="echoid-s4282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4283" xml:space="preserve">Sumuntur etiam pro ſolidis menſuris, qua ratione ſunt omnes Cubi, quorum ſex ſuperficies cos <lb/>terminantes, & </s> <s xml:id="echoid-s4284" xml:space="preserve">ambientes ſunt 6. </s> <s xml:id="echoid-s4285" xml:space="preserve">æqualia quadrata modo explicata: </s> <s xml:id="echoid-s4286" xml:space="preserve">ſic pes cubicus, paſſus cubicus, <lb/>milliare cubicum, &</s> <s xml:id="echoid-s4287" xml:space="preserve">c. </s> <s xml:id="echoid-s4288" xml:space="preserve">ſunt cubi, quos 6. </s> <s xml:id="echoid-s4289" xml:space="preserve">pedes quadrati, vel 6. </s> <s xml:id="echoid-s4290" xml:space="preserve">paſſus quadrati, &</s> <s xml:id="echoid-s4291" xml:space="preserve">c. </s> <s xml:id="echoid-s4292" xml:space="preserve">ambiunt. </s> <s xml:id="echoid-s4293" xml:space="preserve">atq; </s> <s xml:id="echoid-s4294" xml:space="preserve">hi-<lb/>ſce cubis ſolida corpora menſurantur. </s> <s xml:id="echoid-s4295" xml:space="preserve">quare pes linearis menſurat alias lineas; </s> <s xml:id="echoid-s4296" xml:space="preserve">pes quadratus ſu-<lb/>perficialis, metitur ſuperficies: </s> <s xml:id="echoid-s4297" xml:space="preserve">Pes cubicus ſolidus, eſt ſolidarum menſura. </s> <s xml:id="echoid-s4298" xml:space="preserve">his prænotatis varios, <lb/>eoſque acutiſſimos modos explicemus, quibus Aſtronomi quadruplicem terræ quantitatem ſunt <lb/>perſcrutati.</s> <s xml:id="echoid-s4299" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4300" xml:space="preserve">Aſtronomorum veterrimi, vti Ptolemæus in Geographia tradit, hanc inibant rationem. </s> <s xml:id="echoid-s4301" xml:space="preserve">pri-<lb/>mo conſiderabant quod cum terra ſit rotunda, atque in medio ſirmamenti ſita, cumque ambitus <lb/>tam terræ, quam firmamenti maximus intelligatur ab Aſtronomis diuiſus in partes 360. </s> <s xml:id="echoid-s4302" xml:space="preserve">quas gra-<lb/>dus appellauimus, neceſſario ſequitur ſingulis cæli gradibus ſingulos terræ gradus reſpondere; </s> <s xml:id="echoid-s4303" xml:space="preserve">vt <lb/>in ſequenti figura, ſi inter duo loca in terra G H. </s> <s xml:id="echoid-s4304" xml:space="preserve">ſint duo, aut tres gradus, pariter in cælo in arcu <lb/>C S. </s> <s xml:id="echoid-s4305" xml:space="preserve">illi reſpondebunt gradus duo, vel tres, &</s> <s xml:id="echoid-s4306" xml:space="preserve">c. </s> <s xml:id="echoid-s4307" xml:space="preserve">duæ enim lineæ X C. </s> <s xml:id="echoid-s4308" xml:space="preserve">X S. </s> <s xml:id="echoid-s4309" xml:space="preserve">è centro ingredientes <lb/>intercipiunt arcus G H. </s> <s xml:id="echoid-s4310" xml:space="preserve">C S. </s> <s xml:id="echoid-s4311" xml:space="preserve">ſimiles, ſeu proportionales, ideſt, quota pars eſt arcus G H. </s> <s xml:id="echoid-s4312" xml:space="preserve">terreni <lb/>ambitus, tanta erit etiam arcus C S. </s> <s xml:id="echoid-s4313" xml:space="preserve">cæleſtis peripheriæ, vt propoſitione prima Appar. </s> <s xml:id="echoid-s4314" xml:space="preserve">probaui-<lb/>mus, aſſumebant deinde duo loca ſub eodem meridiano poſita, v. </s> <s xml:id="echoid-s4315" xml:space="preserve">g. </s> <s xml:id="echoid-s4316" xml:space="preserve">duo G H. </s> <s xml:id="echoid-s4317" xml:space="preserve">& </s> <s xml:id="echoid-s4318" xml:space="preserve">præterea duas <lb/>ſtellas fixas, quæ ijſdem locis eſſent verticales; </s> <s xml:id="echoid-s4319" xml:space="preserve">earum diſtantiam diligenter per quadrantem ob-<lb/>ſeruabant, quot ſcilicet gradus in meridiano inter vtramq; </s> <s xml:id="echoid-s4320" xml:space="preserve">interciperentur, ſeu quantus eſſet ar-<lb/>cus meridiani inter vertices aſſumptorum locorum. </s> <s xml:id="echoid-s4321" xml:space="preserve">& </s> <s xml:id="echoid-s4322" xml:space="preserve">quamuis hæc obſeruatio ſieret in ſuperfi-<lb/>cie terræ, ob exiguam tamen eius paruitatem reſpectu firmamenti, perinde eſt, ac ſi in centro ha-<lb/>berentur. </s> <s xml:id="echoid-s4323" xml:space="preserve">eundem propterea arcum C S. </s> <s xml:id="echoid-s4324" xml:space="preserve">in cælo duo radij opſici, ſeu viſiui, ad ſenſum compræ-<lb/> <anchor type="figure" xlink:label="fig-0063-02a" xlink:href="fig-0063-02"/> hendunt, ſiue ex G. </s> <s xml:id="echoid-s4325" xml:space="preserve">in ſuperficie, ſiue ex cen-<lb/>tro X. </s> <s xml:id="echoid-s4326" xml:space="preserve">egrediantur. </s> <s xml:id="echoid-s4327" xml:space="preserve">quot igitur gradus inar-<lb/>cu C S. </s> <s xml:id="echoid-s4328" xml:space="preserve">inueniebant, tot etiam in arcu terre-<lb/>ſtri G H. </s> <s xml:id="echoid-s4329" xml:space="preserve">contineri neceſſario concludebant; <lb/></s> <s xml:id="echoid-s4330" xml:space="preserve">ponamus, v. </s> <s xml:id="echoid-s4331" xml:space="preserve">g. </s> <s xml:id="echoid-s4332" xml:space="preserve">fuiſſe gr. </s> <s xml:id="echoid-s4333" xml:space="preserve">3. </s> <s xml:id="echoid-s4334" xml:space="preserve">in arcu C S. </s> <s xml:id="echoid-s4335" xml:space="preserve">igitur <lb/>tres quoque in arcu G H. </s> <s xml:id="echoid-s4336" xml:space="preserve">terreſtri contine-<lb/>bantur: </s> <s xml:id="echoid-s4337" xml:space="preserve">quo in tres æquas partes diuiſo, gra-<lb/>dum etiam vnum in terra exploratũ habue-<lb/>runt. </s> <s xml:id="echoid-s4338" xml:space="preserve">hunc igitur ſic cognitum poſtea per ſta-<lb/>dia metiebantur: </s> <s xml:id="echoid-s4339" xml:space="preserve">ei quæ vni conuenere ſta-<lb/>dia ferè 1111. </s> <s xml:id="echoid-s4340" xml:space="preserve">milliaria verò prope 138. </s> <s xml:id="echoid-s4341" xml:space="preserve">quia <lb/>vero maximus terræ ambitus conſtat 360. </s> <s xml:id="echoid-s4342" xml:space="preserve">par <lb/>tibus, ideo prædictum numerum ſtadiorum <lb/>multiplicantes per 360. </s> <s xml:id="echoid-s4343" xml:space="preserve">totius terreni circuli <lb/>ambitum continere reperunt ſtadia 400,000. </s> <s xml:id="echoid-s4344" xml:space="preserve"><lb/>ideſt, quadringenta millia, quæ efficiunt mil-<lb/>liaria 50.</s> <s xml:id="echoid-s4345" xml:space="preserve">000. </s> <s xml:id="echoid-s4346" xml:space="preserve">ideſt, quinquaginta millia; </s> <s xml:id="echoid-s4347" xml:space="preserve">vt <lb/>Ariſt. </s> <s xml:id="echoid-s4348" xml:space="preserve">ad finẽ 2. </s> <s xml:id="echoid-s4349" xml:space="preserve">de cælo ſic refert; </s> <s xml:id="echoid-s4350" xml:space="preserve">Mathema-<lb/>ticorum etiam, inquit, qui circumferentiæ <lb/>magnitudinem ratiocinari tentant ad 400. </s> <s xml:id="echoid-s4351" xml:space="preserve"><lb/>dicunt eſſe ſtadiorum millia.</s> <s xml:id="echoid-s4352" xml:space="preserve"/> </p> <div xml:id="echoid-div85" type="float" level="2" n="1"> <figure xlink:label="fig-0063-02" xlink:href="fig-0063-02a"> <image file="0063-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-02"/> </figure> </div> <pb o="44" file="0064" n="68" rhead="De Mundi Fabrica"/> <p> <s xml:id="echoid-s4353" xml:space="preserve">Eandem quantitatem veteres alij ſyderum obſeruatores alia, ſimili tamen via compererunt; </s> <s xml:id="echoid-s4354" xml:space="preserve">nam ex duo-<lb/>bus diuerſis locis Poli altitudines obſeruarent, eo modo quem in meridiano circulo expoſuimus; </s> <s xml:id="echoid-s4355" xml:space="preserve">quæ binæ <lb/>altitudines neceſſario tanto meridiani arcu diſcrepabant, quantus quoque erat arcus terreſtris meridiani in-<lb/>ter eadem duo loca interiectus; </s> <s xml:id="echoid-s4356" xml:space="preserve">qualis in eadem figura eſlet arcus S D, differentiam altitudinum poli loco-<lb/>rum H I, qui tantus eſt, quantus eſt arcus H I, inter eadem loca contentus; </s> <s xml:id="echoid-s4357" xml:space="preserve">quot enim gradus quiſ piam am-<lb/>bulans ab H, in I, in terra obiret, totidem gradib. </s> <s xml:id="echoid-s4358" xml:space="preserve">ei polus D, ſupra alium horizontem C F, eleuaretur; </s> <s xml:id="echoid-s4359" xml:space="preserve">quin <lb/>etiam eidem horizon ſucceſſiuè permutatur, quouſque ſit in horizonte C F. </s> <s xml:id="echoid-s4360" xml:space="preserve">cognito igitur per quadrantem <lb/>arcu S D. </s> <s xml:id="echoid-s4361" xml:space="preserve">cognitus quoque erit arcus H I, in gradibus. </s> <s xml:id="echoid-s4362" xml:space="preserve">dimenſo igitur arcu H I, per ſtadia, vel per millia-<lb/>ria, patebat quot vnus gradus milliaria contineret. </s> <s xml:id="echoid-s4363" xml:space="preserve">atque hi duo modi vti faciliores, ita priſcis illis, ac mi-<lb/>nus exercitatis prius occurrerunt.</s> <s xml:id="echoid-s4364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4365" xml:space="preserve">Verum poſt priſcos hoſce indagatores ſubtiliori ad modum via terreſtrem ambitum Eratoſthenes inda-<lb/>gauit: </s> <s xml:id="echoid-s4366" xml:space="preserve">is autem Alexandriæ in Ægypto ante Chriſti natalem annis circiter 250. </s> <s xml:id="echoid-s4367" xml:space="preserve">Syderali ſcientiæ nauabat <lb/>operam. </s> <s xml:id="echoid-s4368" xml:space="preserve">huius igitur rei cauſa, duas elegit vrbes, quæ ſub eodem eſſent meridiano, Alexandriam, & </s> <s xml:id="echoid-s4369" xml:space="preserve">Syenem; <lb/></s> <s xml:id="echoid-s4370" xml:space="preserve">quarum Syene quæ auſtralior eſt, ſita eſt præcisè ſub Cancri tropico. </s> <s xml:id="echoid-s4371" xml:space="preserve">Alexandriæ deinde in platea quapiam <lb/>ſatis magna, haſtam horizonti perpendicularem erexit; </s> <s xml:id="echoid-s4372" xml:space="preserve">poſtea æſtiui ſolſtitij tempore, quo ſcilicet ſol Can-<lb/>cri tropicum percurrit, ac proinde in meridie directè ſupra Syenem imminet, ſiue ei fit verticalis, vnde, & </s> <s xml:id="echoid-s4373" xml:space="preserve"><lb/>radios ei perpendiculariter demittit, eodem inquam tempore, & </s> <s xml:id="echoid-s4374" xml:space="preserve">quidem exactè meridiano, meridianam <lb/>haſtæ illius Alexandriæ erectæ vmbram obſeruauit, & </s> <s xml:id="echoid-s4375" xml:space="preserve">diligenter angulum notauit, quem ſolis radius per <lb/>haſtæ verticem tranſiens, cum ipſa haſta conſtituebat; </s> <s xml:id="echoid-s4376" xml:space="preserve">eumq; </s> <s xml:id="echoid-s4377" xml:space="preserve">quot gradib. </s> <s xml:id="echoid-s4378" xml:space="preserve">conſtaret accuratè expendit. </s> <s xml:id="echoid-s4379" xml:space="preserve">quæ <lb/>vt probè præcipiantur ſit figura ſequens in qua Sol, E F, terra G A B, ſitque arcus G A B, ſub meridiano Ale-<lb/>xandriæ, & </s> <s xml:id="echoid-s4380" xml:space="preserve">Syenes communi. </s> <s xml:id="echoid-s4381" xml:space="preserve">Alexandria ſit vbi A. </s> <s xml:id="echoid-s4382" xml:space="preserve">Syene vbi B, Cancro. </s> <s xml:id="echoid-s4383" xml:space="preserve">Sole igitur Cancri tropicum ob-<lb/> <anchor type="figure" xlink:label="fig-0064-01a" xlink:href="fig-0064-01"/> eunte, erit ſolis radius in meridie ipſi Syene ad perpendiculum, <lb/>qui ſit in figura F B, deſcendatque vſque ad centrum terræ C. </s> <s xml:id="echoid-s4384" xml:space="preserve">Ha-<lb/>ſta Alexandriæ erecta ſit A D, quæ ſimiliter ad centrum C, cum <lb/>radio F B C. </s> <s xml:id="echoid-s4385" xml:space="preserve">concurrat: </s> <s xml:id="echoid-s4386" xml:space="preserve">eodem tempore ſolis alter radius per ha-<lb/>ſtæ apicem D. </s> <s xml:id="echoid-s4387" xml:space="preserve">tranſiens ſit E D G. </s> <s xml:id="echoid-s4388" xml:space="preserve">duos hoſce radios abſque ſenſi-<lb/>bili errore, ob nimiam ſolis à terra diſtantiam ſupponebat eſſe pa-<lb/>ralellos quibus prænotatis ſic ratiocinabatur; </s> <s xml:id="echoid-s4389" xml:space="preserve">cum linea D A C. <lb/></s> <s xml:id="echoid-s4390" xml:space="preserve">incidat in duas paralellas E D G. </s> <s xml:id="echoid-s4391" xml:space="preserve">F B C. </s> <s xml:id="echoid-s4392" xml:space="preserve">erunt per 29. </s> <s xml:id="echoid-s4393" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s4394" xml:space="preserve"><lb/>duo anguli alterni G D A. </s> <s xml:id="echoid-s4395" xml:space="preserve">A C B. </s> <s xml:id="echoid-s4396" xml:space="preserve">æquales. </s> <s xml:id="echoid-s4397" xml:space="preserve">quod etiam patebit ſi <lb/>vterque expendatur per propoſ. </s> <s xml:id="echoid-s4398" xml:space="preserve">2. </s> <s xml:id="echoid-s4399" xml:space="preserve">Appar. </s> <s xml:id="echoid-s4400" xml:space="preserve">deſcripto videlicet arcu, <lb/>A I. </s> <s xml:id="echoid-s4401" xml:space="preserve">ex centro D. </s> <s xml:id="echoid-s4402" xml:space="preserve">eoque in gradus diuiſo; </s> <s xml:id="echoid-s4403" xml:space="preserve">quot enim gradus in eo <lb/>erunt, tot neceſſario in arcu terræ A B. </s> <s xml:id="echoid-s4404" xml:space="preserve">eſſe neceſſe eſt, cum angu-<lb/>lo D. </s> <s xml:id="echoid-s4405" xml:space="preserve">æqualis eſt; </s> <s xml:id="echoid-s4406" xml:space="preserve">& </s> <s xml:id="echoid-s4407" xml:space="preserve">proinde erunt arcus ſimiles, vt in prima pro-<lb/>poſitione Apparatus explicatum eſt. </s> <s xml:id="echoid-s4408" xml:space="preserve">cognito igitur angulo D. </s> <s xml:id="echoid-s4409" xml:space="preserve">ad <lb/>haſlæ verticem, cognoſcitur etiam, quod ſanè mirum eſt, angulus <lb/>C. </s> <s xml:id="echoid-s4410" xml:space="preserve">quamuis ſit in terræ centro, atque abyſſo detruſus; </s> <s xml:id="echoid-s4411" xml:space="preserve">quare etiam <lb/>innoteſcit quantitas arcus A B. </s> <s xml:id="echoid-s4412" xml:space="preserve">meridiani inter Alexandriam, & </s> <s xml:id="echoid-s4413" xml:space="preserve"><lb/>Syenem, quot ſcilicet gradus contineat. </s> <s xml:id="echoid-s4414" xml:space="preserve">tradit autem Cleomedes <lb/>in ſuis Meteoris, Eratoſthenem reperiſſe hunc arcum gradum 8. </s> <s xml:id="echoid-s4415" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s4416" xml:space="preserve">4. </s> <s xml:id="echoid-s4417" xml:space="preserve">quintas. </s> <s xml:id="echoid-s4418" xml:space="preserve">idem arcus A B. </s> <s xml:id="echoid-s4419" xml:space="preserve">quæ eſt diſtantia prædictarum vr-<lb/>bium, cognitus erat etiam in ſtadij, continebat enim ſtadia 6183. </s> <s xml:id="echoid-s4420" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s4421" xml:space="preserve">1. </s> <s xml:id="echoid-s4422" xml:space="preserve">tertiam. </s> <s xml:id="echoid-s4423" xml:space="preserve">vnde arithmeticis rationibus vni gradui 700. </s> <s xml:id="echoid-s4424" xml:space="preserve">ſtadia, <lb/>ac proinde toti terræ perimetro 252, 000. </s> <s xml:id="echoid-s4425" xml:space="preserve">ſtadia attribuit. </s> <s xml:id="echoid-s4426" xml:space="preserve">quæ ef-<lb/>ficiunt milliaria aſtronomica 31, 500.</s> <s xml:id="echoid-s4427" xml:space="preserve"/> </p> <div xml:id="echoid-div86" type="float" level="2" n="2"> <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a"> <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0064-01"/> </figure> </div> <p> <s xml:id="echoid-s4428" xml:space="preserve">Poſt Eratoſthenem Poſſidonius ille Philoſophus (cuius lanuæ, <lb/>cum ad eum audiendum Pompeius Magnus adiret, Imperij faſces <lb/>ſubmiſſit) nouam de eadem re rationem excogitauit; </s> <s xml:id="echoid-s4429" xml:space="preserve">duo enim <lb/>loca ſub eodem meridiano ſita aſſumpſit, Rhodum vbi ipſe dege-<lb/>bat, & </s> <s xml:id="echoid-s4430" xml:space="preserve">Alexandriam; </s> <s xml:id="echoid-s4431" xml:space="preserve">quorum itinerum interuallum iam explo-<lb/>ratum habebat; </s> <s xml:id="echoid-s4432" xml:space="preserve">atque vtrobique inſignis illius ſtellæ, quæ Cano-<lb/>pus dicitur, quæque in Argus temone fulget, meridianam alti-<lb/>tudinem depræhendit. </s> <s xml:id="echoid-s4433" xml:space="preserve">hæc porrò Rhodi horizontem vix aſcen-<lb/>dit, ſed eum leuiter ita perſtringit, vt ex editioribus tantum lo-<lb/>cis videri queat: </s> <s xml:id="echoid-s4434" xml:space="preserve">illinc vero Alexandriam procedenti fit ea ſem-<lb/>per ſublimior, donec Alexandriæ eleuetur in meridiano circu-<lb/>lo partibus 7 {1/2}. </s> <s xml:id="echoid-s4435" xml:space="preserve">rectè igitur concluſit aſlumpta@ vrbes terrenum. <lb/></s> <s xml:id="echoid-s4436" xml:space="preserve">meridiani arcum inter cipere totidem partium; </s> <s xml:id="echoid-s4437" xml:space="preserve">eadem videlicet argumentatione qua vſi fuerant maiores in <lb/>poli eleuatione, eadem fini, obſeruanda: </s> <s xml:id="echoid-s4438" xml:space="preserve">atqui Rhodum inter, & </s> <s xml:id="echoid-s4439" xml:space="preserve">Alexandriam compertum illi erat conti-<lb/>neri ſtadiorum 5, 000. </s> <s xml:id="echoid-s4440" xml:space="preserve">quare cum partes 7 {1/2}. </s> <s xml:id="echoid-s4441" xml:space="preserve">ſint totius maximi circuli pars 48. </s> <s xml:id="echoid-s4442" xml:space="preserve">fit vt ſi 5, 000. </s> <s xml:id="echoid-s4443" xml:space="preserve">multiplicen-<lb/>tur per 48. </s> <s xml:id="echoid-s4444" xml:space="preserve">producatur numerus ſtadiorum totius terreni ambitus, videlicet 240, 000. </s> <s xml:id="echoid-s4445" xml:space="preserve">ideſt, ducenta qua-<lb/>draginta millia; </s> <s xml:id="echoid-s4446" xml:space="preserve">quæ efficiunt milliaria aſtronomica 30.</s> <s xml:id="echoid-s4447" xml:space="preserve">000, ex Cleomede. </s> <s xml:id="echoid-s4448" xml:space="preserve">idem obtineri poteſt ex cuiuluis <lb/>alius ſtellæ fixæ obſeruatione. </s> <s xml:id="echoid-s4449" xml:space="preserve">Hipparcus etiam, teſte Plinio Aſtronomiæ conſultiſſimus, quippe qui pri- <pb o="45" file="0065" n="69" rhead="Liber Quartus."/> mus accuratè ſtellis omnibus numeros, & </s> <s xml:id="echoid-s4450" xml:space="preserve">nomina fecit, maiorum vijs inſiſtens. </s> <s xml:id="echoid-s4451" xml:space="preserve">affirmauit terræ ambitum <lb/>continere ſtadia 277, 000, quæ efficiunt milliaria 34. </s> <s xml:id="echoid-s4452" xml:space="preserve">625.</s> <s xml:id="echoid-s4453" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4454" xml:space="preserve">Prolemæus deinde Aſtronomorum princeps, ijſdem modis terreſtri peripheriæ ſtadia 180’ 000. </s> <s xml:id="echoid-s4455" xml:space="preserve">ſeu mil-<lb/>liaria 22. </s> <s xml:id="echoid-s4456" xml:space="preserve">500, attribuit.</s> <s xml:id="echoid-s4457" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4458" xml:space="preserve">Cum deinde litteræ ac præcipue Aſtronomica ſtudia apud Arabes florerent, extitit Almamon rex Ara-<lb/>bum regalibus hiſce ſtudijs oblectatus, cuius præcepto, vti narrat Abifeldea pariter Arabs initio ſuæ Geo-<lb/>graphiæ, nonnulli ablegati fuerunt, qui in Campis Singar, & </s> <s xml:id="echoid-s4459" xml:space="preserve">vicinis maribus iuxta rectum iter, & </s> <s xml:id="echoid-s4460" xml:space="preserve">poli ſi-<lb/>tum, obſeruarunt quot milliaria reſponderent vni gradui cæleſti, & </s> <s xml:id="echoid-s4461" xml:space="preserve">depræhenſum fuiſſe ab illis in vno gra-<lb/>du conficiendo milliaria 56. </s> <s xml:id="echoid-s4462" xml:space="preserve">& </s> <s xml:id="echoid-s4463" xml:space="preserve">duo tertia per tranſiri, ac proinde totum terræ ambitum conſtare millia-<lb/>ribus 20.</s> <s xml:id="echoid-s4464" xml:space="preserve">400. </s> <s xml:id="echoid-s4465" xml:space="preserve">quam magnitudindem cæteri<unsure/> Arabes, Alfraganus, Thebitus, &</s> <s xml:id="echoid-s4466" xml:space="preserve">c. </s> <s xml:id="echoid-s4467" xml:space="preserve">complexi ſunt.</s> <s xml:id="echoid-s4468" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4469" xml:space="preserve">Neque vero in præclara adeo inquiſitione deceſſe tandem aliqua experientia debuit; </s> <s xml:id="echoid-s4470" xml:space="preserve">recentiores enim <lb/>Argonautæ rerum Aſtronomicarum ſatis gnari, qui iam ſæpius totum Oceanum magno ac fælici auſu cir-<lb/>cumnauigarunt, quantum ipſi experiri potuerunt, exiſtimant totum terreni Globi circuitum complecti <lb/>milliaria 19′080. </s> <s xml:id="echoid-s4471" xml:space="preserve">ſic autem vni gradui cedunt milliaria 53.</s> <s xml:id="echoid-s4472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4473" xml:space="preserve">Omnes porrò prædicti indagatores primo terræ ambitum præueſtigarunt, vnde poſtea cæteras quantita-<lb/>tes habere poſſent; </s> <s xml:id="echoid-s4474" xml:space="preserve">vt paulo poſt oſtendam.</s> <s xml:id="echoid-s4475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4476" xml:space="preserve">Illud tandem conſideratione dignum videtur, quanto videlicet antiquiores ſunt prædicti obſeruatores, <lb/>eo facere terræ ambitum maiorem, ita vt ſemper a priſcis illis, vſq; </s> <s xml:id="echoid-s4477" xml:space="preserve">ad noſtra tempora hic ambitus decreue-<lb/>rit. </s> <s xml:id="echoid-s4478" xml:space="preserve">quod non niſi ex rudioribus obſeruationibus, quæ quotidie exactiores euadunt, vel ex ſtadiorum, aut mil <lb/>liariorum varietate accidiſſe exiſtimo: </s> <s xml:id="echoid-s4479" xml:space="preserve">videmus enim, quod ad hanc varietatem attinet, ſingulas nationes, <lb/>imo etiam prouincias ab inuicem valde diſcrepare. </s> <s xml:id="echoid-s4480" xml:space="preserve">qua propter vt hæc varietas, ac proinde veritatis obum-<lb/>bratio tollatur, libenter Aſtronomis auctor eſſe velim, vt deinceps omnes pro vno milliario intelligãt vnius <lb/>terreſtris gradus partem ſexageſimam. </s> <s xml:id="echoid-s4481" xml:space="preserve">quamuis enim talis pars nondum ſit determinata, nec ſatis cognita, <lb/>facile tamen eſt eam cognoſcere; </s> <s xml:id="echoid-s4482" xml:space="preserve">quidni enim Princeps quiſpiam nobiliſſimo hoc ſtudio delectatus, ceu al-<lb/>ter Almamon poterit exquiſitè gradum vnum in planitie quapiam, vel in ora maritima explorare; </s> <s xml:id="echoid-s4483" xml:space="preserve">ac pro-<lb/>inde eius ſexageſimam partem accuratè metiri; </s> <s xml:id="echoid-s4484" xml:space="preserve">quam poſtea milliarium aſtronomicum in poſterum ſtatuat, <lb/>atq; </s> <s xml:id="echoid-s4485" xml:space="preserve">determinet. </s> <s xml:id="echoid-s4486" xml:space="preserve">quod quidem valde conueniens eſſet, tum quia nonnulli iam ex antiquis vni gradui millia-<lb/>ria 60. </s> <s xml:id="echoid-s4487" xml:space="preserve">attribuerunt, cum alij plura alij pauciora attribuerent: </s> <s xml:id="echoid-s4488" xml:space="preserve">quapropter erit hoc milliare Aſtronomicum <lb/>idem fere ac milliare commune, tũ etiam quia ſexagenarius numerus ob varias ſui ipſius commoditates val-<lb/>de familiaris eſt Aſtronomis.</s> <s xml:id="echoid-s4489" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4490" xml:space="preserve">Poſtremus omnium ſuperiori ſeculo Franciſcus Maurolycus Abbas Syracuſanus, acutiſſimam rationem <lb/>adinuenit, qua primo, non ambitus, vt à<unsure/> cæteris factum eſt, ſed diameter terreni orbis explorari poſſit: </s> <s xml:id="echoid-s4491" xml:space="preserve">Eli-<lb/>gendus eſt (inquit in ſua Coſmographia) in primis mons editiſſimus, vnde maris proſpectus longè pateat; <lb/></s> <s xml:id="echoid-s4492" xml:space="preserve">exiſtimo Aethnam montem huic negotio aptiſſimum, nam ex eius apice per plura quam ducenta paſſuum <lb/>millia in pelago viſus pro@enditur. </s> <s xml:id="echoid-s4493" xml:space="preserve">Oportet igitur vt montis altitudo perpendicularis ab eius vertice, vſq; </s> <s xml:id="echoid-s4494" xml:space="preserve"><lb/>ad maris æquilibrium (ideſt, vſq; </s> <s xml:id="echoid-s4495" xml:space="preserve">ad maris ſuperficiem, quæ fi extenderetur ſub monte eſſet) nota ſit in paſ <lb/>ſibus. </s> <s xml:id="echoid-s4496" xml:space="preserve">(qua vero ratione hæ montium altitudines menſurentur, in ſequenti appendice oſtendemus) deinde <lb/>ex ipſius vertice metiemur interuallum vſq; </s> <s xml:id="echoid-s4497" xml:space="preserve">ad extremam horizontis periphæriam, quod quidem non ſolũ <lb/>Geometricè, vt ipſe Maurolycus ſupponit oſtendemus, verum etiam Mechanicè prædictum interuallum. </s> <s xml:id="echoid-s4498" xml:space="preserve"><lb/>vſq; </s> <s xml:id="echoid-s4499" xml:space="preserve">ad aliquod vltimum in horizonte viſum, menſurabimus, videlicet per decempedam, qua practici men-<lb/>ſores vtuntur. </s> <s xml:id="echoid-s4500" xml:space="preserve">quibus paratis intelligantur iam hæc in præſenti figura; </s> <s xml:id="echoid-s4501" xml:space="preserve">ſit circulus terræ C B. </s> <s xml:id="echoid-s4502" xml:space="preserve">ex centro D. </s> <s xml:id="echoid-s4503" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0065-01a" xlink:href="fig-0065-01"/> deſcriptus: </s> <s xml:id="echoid-s4504" xml:space="preserve">linea A B. </s> <s xml:id="echoid-s4505" xml:space="preserve">ſit pro altitudine montis perpendiculari, quę extendantur vſq; <lb/></s> <s xml:id="echoid-s4506" xml:space="preserve">ad centrum terræ D. </s> <s xml:id="echoid-s4507" xml:space="preserve">linea A C. </s> <s xml:id="echoid-s4508" xml:space="preserve">ſit radius viſiuus ad vltimum vſq; </s> <s xml:id="echoid-s4509" xml:space="preserve">horizontem C. </s> <s xml:id="echoid-s4510" xml:space="preserve">de-<lb/>ſinens, ac proinde tangens terram in puncto C. </s> <s xml:id="echoid-s4511" xml:space="preserve">ducanturque C D. </s> <s xml:id="echoid-s4512" xml:space="preserve">& </s> <s xml:id="echoid-s4513" xml:space="preserve">C B. </s> <s xml:id="echoid-s4514" xml:space="preserve">propoſitum <lb/>eſt igitur ex prænotatis cognoſcere lineam B D. </s> <s xml:id="echoid-s4515" xml:space="preserve">ſemidiametrũ videlicet terræ. </s> <s xml:id="echoid-s4516" xml:space="preserve">con-<lb/>ſidero igitur triangulum A C D. </s> <s xml:id="echoid-s4517" xml:space="preserve">in quo ex præmiſſis cognitum eſt latus C C. </s> <s xml:id="echoid-s4518" xml:space="preserve">ad ſen-<lb/>ſum enim æquale eſt ipſi C B. </s> <s xml:id="echoid-s4519" xml:space="preserve">iam in paſſibus cognito. </s> <s xml:id="echoid-s4520" xml:space="preserve">duo præterea anguli manife-<lb/>ſti ſunt, angulus enim ad C. </s> <s xml:id="echoid-s4521" xml:space="preserve">eſt rectus per 18. </s> <s xml:id="echoid-s4522" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4523" xml:space="preserve">3. </s> <s xml:id="echoid-s4524" xml:space="preserve">Elementi. </s> <s xml:id="echoid-s4525" xml:space="preserve">Angulus vero ad <lb/>A. </s> <s xml:id="echoid-s4526" xml:space="preserve">cognoſcitur ex inſtrumento, veluti ex quadrante noſtro, per cuius dioptram ex A. </s> <s xml:id="echoid-s4527" xml:space="preserve"><lb/>collimandum eſt in C. </s> <s xml:id="echoid-s4528" xml:space="preserve">per 5. </s> <s xml:id="echoid-s4529" xml:space="preserve">igitur Appar. </s> <s xml:id="echoid-s4530" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4531" xml:space="preserve">conſtruatur in papyro triangulum <lb/>ſimile triangulo huic A C D. </s> <s xml:id="echoid-s4532" xml:space="preserve">cx quo per 6. </s> <s xml:id="echoid-s4533" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s4534" xml:space="preserve">eiuſdem Appar. </s> <s xml:id="echoid-s4535" xml:space="preserve">veniemus in co-<lb/>gnitione proportionis, quæ eſt inter latera C A. </s> <s xml:id="echoid-s4536" xml:space="preserve">C D. </s> <s xml:id="echoid-s4537" xml:space="preserve">ideſt, in@oteſcet quoties C A. </s> <s xml:id="echoid-s4538" xml:space="preserve"><lb/>contineatur in C D. </s> <s xml:id="echoid-s4539" xml:space="preserve">cum autem C A. </s> <s xml:id="echoid-s4540" xml:space="preserve">cognita ſit in paſſionis, neceſſario ipſa quoque <lb/>C D. </s> <s xml:id="echoid-s4541" xml:space="preserve">terræ ſemidiameter in paſſibus manifeſta erit. </s> <s xml:id="echoid-s4542" xml:space="preserve">quod porrò attinet ad interuallum C B. </s> <s xml:id="echoid-s4543" xml:space="preserve">menſurandum, <lb/>ſatius fortaſſe eſſet illud non ex montis apice A. </s> <s xml:id="echoid-s4544" xml:space="preserve">verum ex C. </s> <s xml:id="echoid-s4545" xml:space="preserve">prænotare. </s> <s xml:id="echoid-s4546" xml:space="preserve">eſt autem C. </s> <s xml:id="echoid-s4547" xml:space="preserve">primo horizontis pun <lb/>ctum, ex quo Aethnæ vertex igniuomus primo ſpectatur: </s> <s xml:id="echoid-s4548" xml:space="preserve">quare eſſet id Nautis admodum facilè, quibus no-<lb/>ctu is vertex, cũ ſit igniuomus, ac ſplendidus in mari a longe conſpicuus eſt; </s> <s xml:id="echoid-s4549" xml:space="preserve">a loco enim in quo primus con-<lb/>ſpicitur, menſurandum eſſet vſque ad montis perpendiculum. </s> <s xml:id="echoid-s4550" xml:space="preserve">Atq; </s> <s xml:id="echoid-s4551" xml:space="preserve">hic eſto modus iuxta noſtram demon-<lb/>ſtrandi methodum. </s> <s xml:id="echoid-s4552" xml:space="preserve">magis vero geometricè cum ipſo Maurolyco in hunc modum; </s> <s xml:id="echoid-s4553" xml:space="preserve">in eadẽ figura linea C B. </s> <s xml:id="echoid-s4554" xml:space="preserve"><lb/>quamuis re vera ſit curua, ſi tamen pro recta capiatur, in tam pauca circuli terreſtris portione, nihil erroris <lb/>ſenſibus ingeret. </s> <s xml:id="echoid-s4555" xml:space="preserve">Cũ igitur in triangulo A B C. </s> <s xml:id="echoid-s4556" xml:space="preserve">angulus ad B. </s> <s xml:id="echoid-s4557" xml:space="preserve">ſit rectus, & </s> <s xml:id="echoid-s4558" xml:space="preserve">rectæ C B. </s> <s xml:id="echoid-s4559" xml:space="preserve">B A. </s> <s xml:id="echoid-s4560" xml:space="preserve">notæ ſint ex men-<lb/>ſuratione; </s> <s xml:id="echoid-s4561" xml:space="preserve">eorum quadrata capiantur, ideſt, numeri, paſſuum earum in ſeipſos ducãtur; </s> <s xml:id="echoid-s4562" xml:space="preserve">horum numerorum <lb/>quadra@orum ſumma æqualis erit quadrato lineæ A C. </s> <s xml:id="echoid-s4563" xml:space="preserve">per 47. </s> <s xml:id="echoid-s4564" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s4565" xml:space="preserve">quare & </s> <s xml:id="echoid-s4566" xml:space="preserve">ipſa nota erit in paſſi- <pb o="46" file="0066" n="70" rhead="De Mundi Fabrica."/> bus; </s> <s xml:id="echoid-s4567" xml:space="preserve">ſi enim radix quadrata huius ſummæ per Arithmetices præcepta extrahatur, erit ipſa linea A C. </s> <s xml:id="echoid-s4568" xml:space="preserve">ide@, <lb/>numerus paſſuum radicis extractæ, erit idem ac numerus paſſuum in linea A C. </s> <s xml:id="echoid-s4569" xml:space="preserve">contentorum. </s> <s xml:id="echoid-s4570" xml:space="preserve">quoniam ve-<lb/>ro A C. </s> <s xml:id="echoid-s4571" xml:space="preserve">tangit circulum in C. </s> <s xml:id="echoid-s4572" xml:space="preserve">erit per penult. </s> <s xml:id="echoid-s4573" xml:space="preserve">3. </s> <s xml:id="echoid-s4574" xml:space="preserve">Elem. </s> <s xml:id="echoid-s4575" xml:space="preserve">quadratum eius ęquale rectangulo contento ſub linei<unsure/>s <lb/>A G. </s> <s xml:id="echoid-s4576" xml:space="preserve">A B. </s> <s xml:id="echoid-s4577" xml:space="preserve">quale in figura eſt rectangulum A G E F. </s> <s xml:id="echoid-s4578" xml:space="preserve">quare & </s> <s xml:id="echoid-s4579" xml:space="preserve">ipſum cognitum. </s> <s xml:id="echoid-s4580" xml:space="preserve">ſi ergo numerus quadratus, <lb/>qui numero rectanguli huius eſt æqualis, diuidatur per numerum lineæ A F. </s> <s xml:id="echoid-s4581" xml:space="preserve">alterum latus A G. </s> <s xml:id="echoid-s4582" xml:space="preserve">cognoſcetur <lb/>in paſſibus; </s> <s xml:id="echoid-s4583" xml:space="preserve">ex numero autem lateris A G. </s> <s xml:id="echoid-s4584" xml:space="preserve">detracta montis altitudine A B. </s> <s xml:id="echoid-s4585" xml:space="preserve">reliqua B G. </s> <s xml:id="echoid-s4586" xml:space="preserve">erit terræ diameter <lb/>quæſita. </s> <s xml:id="echoid-s4587" xml:space="preserve">hic eſt modus Maurolyci, quem in praxim non videtur deduxiſſe, cum inde nullam aſſerat ſemidia-<lb/>metri quantitatem, neq; </s> <s xml:id="echoid-s4588" xml:space="preserve">vllam montis altitudinem certam ponat. </s> <s xml:id="echoid-s4589" xml:space="preserve">Cum tamen ipſe dicat lineam B C. </s> <s xml:id="echoid-s4590" xml:space="preserve">eſſe <lb/>plus quam ducenta milliaria, ponatur, breuitatis gratia C A, ipſi ſenſibiliter æqualis, eritq; </s> <s xml:id="echoid-s4591" xml:space="preserve">quadratum eius <lb/>40.</s> <s xml:id="echoid-s4592" xml:space="preserve">000. </s> <s xml:id="echoid-s4593" xml:space="preserve">quod æquale eſt rectangulo A E. </s> <s xml:id="echoid-s4594" xml:space="preserve">ponamus etiam montis altitudinem A B. </s> <s xml:id="echoid-s4595" xml:space="preserve">ad ſummum eſſe duorum <lb/>milliariorum, diuidatur igitur rectangulum 40.</s> <s xml:id="echoid-s4596" xml:space="preserve">000. </s> <s xml:id="echoid-s4597" xml:space="preserve">per 2. </s> <s xml:id="echoid-s4598" xml:space="preserve">& </s> <s xml:id="echoid-s4599" xml:space="preserve">erit quoties num. </s> <s xml:id="echoid-s4600" xml:space="preserve">20.</s> <s xml:id="echoid-s4601" xml:space="preserve">000. </s> <s xml:id="echoid-s4602" xml:space="preserve">pro tota A G. </s> <s xml:id="echoid-s4603" xml:space="preserve">ex qua <lb/>detracta A B. </s> <s xml:id="echoid-s4604" xml:space="preserve">quæ eſt 2. </s> <s xml:id="echoid-s4605" xml:space="preserve">remanet 19, 998. </s> <s xml:id="echoid-s4606" xml:space="preserve">pro terrena diametro, quæ a ſuperiorum Aſtronomorum quan-<lb/>titatibus, parum diſcrepat, quare ſequitur lineam B C. </s> <s xml:id="echoid-s4607" xml:space="preserve">eſſe tot milliariorum ferè, quot a Maurolyco aſ-<lb/>ſumitur.</s> <s xml:id="echoid-s4608" xml:space="preserve"/> </p> <div xml:id="echoid-div87" type="float" level="2" n="3"> <figure xlink:label="fig-0065-01" xlink:href="fig-0065-01a"> <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/> </figure> </div> <p> <s xml:id="echoid-s4609" xml:space="preserve">Quoniam verò milliare Aſtronomum, de quo ſupra egimus, idoneum eſt rebus Aſtronomicis menſuran-<lb/>dis, proinde ſi eo vti libuerit, erunt in toto telluris circuitu milliaria 21, 600. </s> <s xml:id="echoid-s4610" xml:space="preserve">ſiquidem vni 60. </s> <s xml:id="echoid-s4611" xml:space="preserve">competunt; <lb/></s> <s xml:id="echoid-s4612" xml:space="preserve">quæ inter Ptolemæi, & </s> <s xml:id="echoid-s4613" xml:space="preserve">recentiorum quantitates, quæ cæteris veriſimiliores ſunt, media eſt.</s> <s xml:id="echoid-s4614" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4615" xml:space="preserve">Atq; </s> <s xml:id="echoid-s4616" xml:space="preserve">hæc ſunt, vt cum Plinio loquamur, quæ de terra circuitu digna memoratu putem, magna ſubtilita-<lb/>te, atq; </s> <s xml:id="echoid-s4617" xml:space="preserve">ingeniorum ſolertia literis prodita; </s> <s xml:id="echoid-s4618" xml:space="preserve">improbum equidem auſum, verum ita ſubtili argumentatione <lb/>comprehenſum, vt pudeat non credere.</s> <s xml:id="echoid-s4619" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4620" xml:space="preserve">Perſpecto igitur telluris gyro in Aſtron. </s> <s xml:id="echoid-s4621" xml:space="preserve">milliar. </s> <s xml:id="echoid-s4622" xml:space="preserve">reliquas iam quantitates, ex ijs, quæ Archimedes partim <lb/>de circulo, partim de ſphæra, & </s> <s xml:id="echoid-s4623" xml:space="preserve">cylindro demonſtrauit, facilè obtinere poterimus; </s> <s xml:id="echoid-s4624" xml:space="preserve">cum enim (per ipſum) <lb/>circuli peripheria ad ſuum diametrum eam habeant ferè rationem, quam 22. </s> <s xml:id="echoid-s4625" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s4626" xml:space="preserve">(quod etiam experientia <lb/>probari poteſt) ſi per auream Arithmeticorũ regula fiat, vt 22. </s> <s xml:id="echoid-s4627" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s4628" xml:space="preserve">ita 21, 600. </s> <s xml:id="echoid-s4629" xml:space="preserve">milliaria peripherie<unsure/> ad aliud, <lb/>procreabitur numerus 6,873. </s> <s xml:id="echoid-s4630" xml:space="preserve">milliariorum totius diametri terreſtris. </s> <s xml:id="echoid-s4631" xml:space="preserve">cuius dimidium 3. </s> <s xml:id="echoid-s4632" xml:space="preserve">43 6 {1/2}. </s> <s xml:id="echoid-s4633" xml:space="preserve">erit eiuſdem <lb/>ſemidiameter, diſtantia videlicet a terræ ſuperficie vſque ad eius centrum; </s> <s xml:id="echoid-s4634" xml:space="preserve">qui locus profundiſſima abyſſus <lb/>dicitur. </s> <s xml:id="echoid-s4635" xml:space="preserve">hæc porrò cognitio adeò abſtruſa, ac recondita eſt, vt nihil magis; </s> <s xml:id="echoid-s4636" xml:space="preserve">vnde & </s> <s xml:id="echoid-s4637" xml:space="preserve">ſacrę litteræ merito quaſi <lb/>mirabundæ dicant, profunditatem abyſſi quis dimenſus eſt? </s> <s xml:id="echoid-s4638" xml:space="preserve">vide lib. </s> <s xml:id="echoid-s4639" xml:space="preserve">4. </s> <s xml:id="echoid-s4640" xml:space="preserve">Geomet. </s> <s xml:id="echoid-s4641" xml:space="preserve">pract. </s> <s xml:id="echoid-s4642" xml:space="preserve">P. </s> <s xml:id="echoid-s4643" xml:space="preserve">Clauij.</s> <s xml:id="echoid-s4644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4645" xml:space="preserve">Superficiem verò conuexam totius orbis terræ, ac maris ſimul ſic habebimus; </s> <s xml:id="echoid-s4646" xml:space="preserve">multiplicentur inuicem cir-<lb/>cumferentia, & </s> <s xml:id="echoid-s4647" xml:space="preserve">diameter, productus enim erit numerus quadratorum milliariorũ, quæ totam terræ, & </s> <s xml:id="echoid-s4648" xml:space="preserve">quæ <lb/>faciem conſtituunt; </s> <s xml:id="echoid-s4649" xml:space="preserve">is autem eſt 148, 456, 800. </s> <s xml:id="echoid-s4650" xml:space="preserve">vide lib. </s> <s xml:id="echoid-s4651" xml:space="preserve">1. </s> <s xml:id="echoid-s4652" xml:space="preserve">Geom. </s> <s xml:id="echoid-s4653" xml:space="preserve">pract. </s> <s xml:id="echoid-s4654" xml:space="preserve">P. </s> <s xml:id="echoid-s4655" xml:space="preserve">Clauij.</s> <s xml:id="echoid-s4656" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4657" xml:space="preserve">Demum globi terreſtris ſoliditas ſic conſtabit: </s> <s xml:id="echoid-s4658" xml:space="preserve">ducantur inuicem ſemidiameter terræ, videlicet 3. </s> <s xml:id="echoid-s4659" xml:space="preserve">436 {1/2}. <lb/></s> <s xml:id="echoid-s4660" xml:space="preserve">& </s> <s xml:id="echoid-s4661" xml:space="preserve">tertia pars ſuperficialis circumferentiæ modò inuẽtæ, quæ eſt 49, 485, 600. </s> <s xml:id="echoid-s4662" xml:space="preserve">nam producetur numerus h@c <lb/>170, 032, 521, 600. </s> <s xml:id="echoid-s4663" xml:space="preserve">milliariorum cubicorum, quæ totam terræ craſſitiem conflarent. </s> <s xml:id="echoid-s4664" xml:space="preserve">vide lib. </s> <s xml:id="echoid-s4665" xml:space="preserve">5. </s> <s xml:id="echoid-s4666" xml:space="preserve">Geometricæ <lb/>pract. </s> <s xml:id="echoid-s4667" xml:space="preserve">P. </s> <s xml:id="echoid-s4668" xml:space="preserve">Clauij. </s> <s xml:id="echoid-s4669" xml:space="preserve">ſi verò quis addubitet hanc terrę corporeitatem iuſto minorem eſſe, propterca quod in hanc <lb/>computationem colles ac montes non venerint, is oculos Mari obuertat, quod loco montium, & </s> <s xml:id="echoid-s4670" xml:space="preserve">collium <lb/>ſubſtituimus; </s> <s xml:id="echoid-s4671" xml:space="preserve">neque equidem abſque ratione, quandoquidem vt infra patebit, veriſimile eſt montium, & </s> <s xml:id="echoid-s4672" xml:space="preserve"><lb/>maris corporeitates eſſe æquales.</s> <s xml:id="echoid-s4673" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div89" type="section" level="1" n="60"> <head xml:id="echoid-head63" style="it" xml:space="preserve">De altitudine Montium. Cap. VI.</head> <p> <s xml:id="echoid-s4674" xml:space="preserve">VT tractatio de terræ quautitate omnibus numeris abſoluta euadat, minimè omittenda videtur mõtium <lb/>altitudo, quandoquidem, & </s> <s xml:id="echoid-s4675" xml:space="preserve">ipſi altiores terræ ſunt partes, & </s> <s xml:id="echoid-s4676" xml:space="preserve">eius perſcrutatio ſubtilis æque, ac iucunda <lb/>eſt. </s> <s xml:id="echoid-s4677" xml:space="preserve">litteris igitur proditum eſt, inquit Plin. </s> <s xml:id="echoid-s4678" xml:space="preserve">lib. </s> <s xml:id="echoid-s4679" xml:space="preserve">2. </s> <s xml:id="echoid-s4680" xml:space="preserve">cap. </s> <s xml:id="echoid-s4681" xml:space="preserve">67. </s> <s xml:id="echoid-s4682" xml:space="preserve">Dicearchum Siculum Ariſtotelis diſcipulum, pri-<lb/>mum perpendicularem montium altitudinem dimenſum eſſe, altiffimumq; </s> <s xml:id="echoid-s4683" xml:space="preserve">prodidiſſe Pelion, eiuſque per-<lb/>pendiculum aſſeruiſſe 1, 250. </s> <s xml:id="echoid-s4684" xml:space="preserve">paſſus; </s> <s xml:id="echoid-s4685" xml:space="preserve">vnde concludere licet montium altitudinem multo minorem eſſe ſeſ-<lb/>quimilliari. </s> <s xml:id="echoid-s4686" xml:space="preserve">Notandum vero montium altitudines quotidie magis decreſcere, vti manifeſtè probauimus <lb/>ſupra in Corollario de permutatione rotunditatis terræ, Geometrę autem hoc modo altitudinem hanc me-<lb/>tiuntur: </s> <s xml:id="echoid-s4687" xml:space="preserve">in plano quopiam mõti proximo, ſupra quod mons attollitur, quadratum quod vltima Appar, pro-<lb/>poſitione conſtruximus, ita in cultrum ſtatuunt, vt latus A B. </s> <s xml:id="echoid-s4688" xml:space="preserve">horizonti æquidiſtet; </s> <s xml:id="echoid-s4689" xml:space="preserve">latus vero B E. </s> <s xml:id="echoid-s4690" xml:space="preserve">ad mon-<lb/>tem reſpiciat; </s> <s xml:id="echoid-s4691" xml:space="preserve">perpendiculum autem C I. </s> <s xml:id="echoid-s4692" xml:space="preserve">lateri, C A. </s> <s xml:id="echoid-s4693" xml:space="preserve">appenſum debet ſuæ lineæ reſpondere exactè; </s> <s xml:id="echoid-s4694" xml:space="preserve">ho c <lb/>enim modo inſtrumentum erit in cultrum poſitum, ſiue horizonti perpendiculare. </s> <s xml:id="echoid-s4695" xml:space="preserve">deinde menſor inſpi-<lb/>ciens per pinnulas dioptræ verſus apicem montis, eam ſuſque deque eleuet, donec exactè ipſius apicem per <lb/>rimulas pinnularum inſpiciat; </s> <s xml:id="echoid-s4696" xml:space="preserve">in quo ſitu dioptram ſiſtat; </s> <s xml:id="echoid-s4697" xml:space="preserve">& </s> <s xml:id="echoid-s4698" xml:space="preserve">conſideret triangulum in inſtrumento factum, <lb/>v. </s> <s xml:id="echoid-s4699" xml:space="preserve">g. </s> <s xml:id="echoid-s4700" xml:space="preserve">ſit altitudo alicuius montis perpendicularis E F. </s> <s xml:id="echoid-s4701" xml:space="preserve">menſuranda, & </s> <s xml:id="echoid-s4702" xml:space="preserve">quadratũ cum dioptra ad apicem mon-<lb/>tis ſit directa, vt apparet in figura ſequenti, in qua conſidera duo triangula ſimilia, primum, & </s> <s xml:id="echoid-s4703" xml:space="preserve">maius A E F. <lb/></s> <s xml:id="echoid-s4704" xml:space="preserve">quod faciunt diſtantia A F. </s> <s xml:id="echoid-s4705" xml:space="preserve">altitudo F E. </s> <s xml:id="echoid-s4706" xml:space="preserve">& </s> <s xml:id="echoid-s4707" xml:space="preserve">radius viſiuus A E. </s> <s xml:id="echoid-s4708" xml:space="preserve">alternm minus eſt in inſtrumento triangulũ, <lb/>videlicet A B D. </s> <s xml:id="echoid-s4709" xml:space="preserve">quod æquiangulum eſt maiori; </s> <s xml:id="echoid-s4710" xml:space="preserve">nam anguli ad F. </s> <s xml:id="echoid-s4711" xml:space="preserve">& </s> <s xml:id="echoid-s4712" xml:space="preserve">F. </s> <s xml:id="echoid-s4713" xml:space="preserve">ſunt recti, angulus vero ad A. </s> <s xml:id="echoid-s4714" xml:space="preserve">eſt com-<lb/>munis igitur, & </s> <s xml:id="echoid-s4715" xml:space="preserve">reliqui anguli æquales erunt, ergo triangula erunt proportionalia, ideſt, erit vt latus A B. </s> <s xml:id="echoid-s4716" xml:space="preserve"><lb/>ad B D. </s> <s xml:id="echoid-s4717" xml:space="preserve">in paruo triangulo, ita in magno, diſtantia A F. </s> <s xml:id="echoid-s4718" xml:space="preserve">ad altitudinem F E. </s> <s xml:id="echoid-s4719" xml:space="preserve">ſi igitur diſtantia ſit nota in <lb/>paſſibus, vel milliarijs, facilè erit cognoſcere altitudinem F E. </s> <s xml:id="echoid-s4720" xml:space="preserve">quæ enim pars fuerit latus B D. </s> <s xml:id="echoid-s4721" xml:space="preserve">lateris A B. </s> <s xml:id="echoid-s4722" xml:space="preserve"><lb/>eadem pars erit altitudo F E. </s> <s xml:id="echoid-s4723" xml:space="preserve">diſtãtiæ A F. </s> <s xml:id="echoid-s4724" xml:space="preserve">v. </s> <s xml:id="echoid-s4725" xml:space="preserve">g. </s> <s xml:id="echoid-s4726" xml:space="preserve">ſi B D. </s> <s xml:id="echoid-s4727" xml:space="preserve">fuerit pars decima, ipſius A B. </s> <s xml:id="echoid-s4728" xml:space="preserve">F E. </s> <s xml:id="echoid-s4729" xml:space="preserve">altitudo erit pars <lb/>10. </s> <s xml:id="echoid-s4730" xml:space="preserve">diſtantiæ A F. </s> <s xml:id="echoid-s4731" xml:space="preserve">quare ſi diſtantia A F. </s> <s xml:id="echoid-s4732" xml:space="preserve">eſſet milliaria 10. </s> <s xml:id="echoid-s4733" xml:space="preserve">eſſet F E. </s> <s xml:id="echoid-s4734" xml:space="preserve">milliare vnum, pars ſcilicet decima, vt <pb o="47" file="0067" n="71" rhead="Liber Quarius."/> <anchor type="figure" xlink:label="fig-0067-01a" xlink:href="fig-0067-01"/> patet ex Appar. </s> <s xml:id="echoid-s4735" xml:space="preserve">Ego Parmæ <lb/>exiſtens montẽ Baldũ totius <lb/>Lombardiæ altiſſimũ in agro <lb/>Veronenſi ſitum, diſtantemq: <lb/></s> <s xml:id="echoid-s4736" xml:space="preserve">Parma milliar. </s> <s xml:id="echoid-s4737" xml:space="preserve">70. </s> <s xml:id="echoid-s4738" xml:space="preserve">menſuraui <lb/>per quadratum, reperique la-<lb/>tus B D. </s> <s xml:id="echoid-s4739" xml:space="preserve">parui trianguli con-<lb/>tineri ferè octuagies ſepties <lb/>in latere A B. </s> <s xml:id="echoid-s4740" xml:space="preserve">quare concluſi <lb/>altitudinem eius perpendicu-<lb/>larem contineri in diſtantia <lb/>ctiam octuagies ſepties; </s> <s xml:id="echoid-s4741" xml:space="preserve">di-<lb/>ſtantia autem eſt paſſuum 70. </s> <s xml:id="echoid-s4742" xml:space="preserve"><lb/>000. </s> <s xml:id="echoid-s4743" xml:space="preserve">quæ diuiſa per 87. </s> <s xml:id="echoid-s4744" xml:space="preserve">exhi-<lb/>bet quotientem 804. </s> <s xml:id="echoid-s4745" xml:space="preserve">altitudi-<lb/>nem nempe quęſitam. </s> <s xml:id="echoid-s4746" xml:space="preserve">Si ve-<lb/>ro d ſtantia ſit ignota, eam ſic <lb/>dignoſcunt à loco A. </s> <s xml:id="echoid-s4747" xml:space="preserve">intelli-<lb/>gitur duas lineas, vnam ipſam diſtantiam A F. </s> <s xml:id="echoid-s4748" xml:space="preserve">alteram vero, quam ipſi ambulando ducunt à loco A. </s> <s xml:id="echoid-s4749" xml:space="preserve">priori <lb/>lineæ perpendicularem, cuius longitudinem paſſibus ambulantes obſeruant recedũt, v. </s> <s xml:id="echoid-s4750" xml:space="preserve">g. </s> <s xml:id="echoid-s4751" xml:space="preserve">ab eo loco per 40. </s> <s xml:id="echoid-s4752" xml:space="preserve"><lb/>vel 50. </s> <s xml:id="echoid-s4753" xml:space="preserve">paſſus per lineam A H. </s> <s xml:id="echoid-s4754" xml:space="preserve">poſtea ex loco H. </s> <s xml:id="echoid-s4755" xml:space="preserve">verſus montis medium deſignant tertiam lineam H F. </s> <s xml:id="echoid-s4756" xml:space="preserve">huic <lb/>ergo triangulo magno A F H. </s> <s xml:id="echoid-s4757" xml:space="preserve">conſtruunt triangulum proportionale, iuxto Appar. </s> <s xml:id="echoid-s4758" xml:space="preserve">doctrinam, ducta ſcili-<lb/>cet linea I K. </s> <s xml:id="echoid-s4759" xml:space="preserve">perpendiculari ad A H. </s> <s xml:id="echoid-s4760" xml:space="preserve">ſic enim triangulum H I K. </s> <s xml:id="echoid-s4761" xml:space="preserve">æquiangulum, & </s> <s xml:id="echoid-s4762" xml:space="preserve">proportionale erit ma-<lb/>gno triangulo H A F. </s> <s xml:id="echoid-s4763" xml:space="preserve">& </s> <s xml:id="echoid-s4764" xml:space="preserve">quoties H I. </s> <s xml:id="echoid-s4765" xml:space="preserve">continebitur in I K. </s> <s xml:id="echoid-s4766" xml:space="preserve">toties A H. </s> <s xml:id="echoid-s4767" xml:space="preserve">40. </s> <s xml:id="echoid-s4768" xml:space="preserve">paſſuum continebitur in diſtantia <lb/>A F. </s> <s xml:id="echoid-s4769" xml:space="preserve">eamq; </s> <s xml:id="echoid-s4770" xml:space="preserve">propterea cognitam reddet. </s> <s xml:id="echoid-s4771" xml:space="preserve">vide tractationem noſtram de altitudine montis Caucaſi, in lib. </s> <s xml:id="echoid-s4772" xml:space="preserve"><lb/>noſtro de locis Mathematicis apud Ariſt. </s> <s xml:id="echoid-s4773" xml:space="preserve">lib. </s> <s xml:id="echoid-s4774" xml:space="preserve">1. </s> <s xml:id="echoid-s4775" xml:space="preserve">Meteorum, ad num. </s> <s xml:id="echoid-s4776" xml:space="preserve">184. </s> <s xml:id="echoid-s4777" xml:space="preserve">marginalem, vbi plura de montium <lb/>altitudine ſcitu digniſſima, & </s> <s xml:id="echoid-s4778" xml:space="preserve">iucundiſſima reperies.</s> <s xml:id="echoid-s4779" xml:space="preserve"/> </p> <div xml:id="echoid-div89" type="float" level="2" n="1"> <figure xlink:label="fig-0067-01" xlink:href="fig-0067-01a"> <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/> </figure> </div> </div> <div xml:id="echoid-div91" type="section" level="1" n="61"> <head xml:id="echoid-head64" style="it" xml:space="preserve">Corollarium de Arenæ numero. Cap. VII.</head> <p> <s xml:id="echoid-s4780" xml:space="preserve">NOn alienum ab inſtituto videtur acutiſſimam Archimedis de arenæ numero diſputationem huc acco@ <lb/>modare, cum arenæ ipſæ telluris particulæ ſint, earumque multitudo indaganda proponatur. </s> <s xml:id="echoid-s4781" xml:space="preserve">Qua <lb/>igitur tempeſtate rex Gelon Siciliæ regnum adminiſtrabat, Philoſophi complures, inter quos, ille ingenio-<lb/>rum phœnix Archimedes, verſabatur, Regis aulam frequentabant. </s> <s xml:id="echoid-s4782" xml:space="preserve">cumque varijs eorum diſſertationibus <lb/>Rex ille ſæpius oblectaretur, factum eſt aliquando vt inter eos de numero arenæ maris oriretur diſputatio; <lb/></s> <s xml:id="echoid-s4783" xml:space="preserve">quod ipſemet refert Archimedes. </s> <s xml:id="echoid-s4784" xml:space="preserve">eorum igitur nõnulli arenæ numerum, non ſolum eius quæ toto orbe, ſed <lb/>cius etiam, quæ littoribus tantum Syracuſanis contineretur, infinitum eſſe arbitrabantur: </s> <s xml:id="echoid-s4785" xml:space="preserve">alij vero è contra, <lb/>cum infinitum eſſe negantes, propterea quod infinitum omnem tollerent, aiebant tamen nullum poſſe re-<lb/>periri determinatum numerum, qui illius arenæ multitudini explicandæ par eſſet, ita vt quamuis quiſpiam <lb/>per mille annos continenter proferret milliones millionum millionum, & </s> <s xml:id="echoid-s4786" xml:space="preserve">numquam, tamen ſatis magnum <lb/>numerum prolatũ haberet. </s> <s xml:id="echoid-s4787" xml:space="preserve">diu iam proceſſerat diſputatio, nec tamen certi quidquam ſtatui videbatur: </s> <s xml:id="echoid-s4788" xml:space="preserve">cum <lb/>rex Archimedis rogauit ſententiam, cui ſic ille reſpondit: </s> <s xml:id="echoid-s4789" xml:space="preserve">Sapientiſſime rex, quæſtio hæc Mathematicis ra-<lb/>tionibus diſsolui poteſt, ijs enim oſtendi poteſt, non ſolum inueniri poſſe numerum, qui totam totius orbis <lb/>terræ arenam complectatur, verum etiamſi totus mundus, quantus quantus eſt, minutiſſimis arenulis com-<lb/>pleretur, eandem multitudinem numero definiri poſſe contendimus, quod quidem, & </s> <s xml:id="echoid-s4790" xml:space="preserve">Regi, Philoſophiſ-<lb/>que illis omni admiratione ac fide maius videbatur: </s> <s xml:id="echoid-s4791" xml:space="preserve">apud quos in hunc ferè modum ratiocinatus eſt. </s> <s xml:id="echoid-s4792" xml:space="preserve">vt pro-<lb/>poſitæ quæſtioni ſatis a me fieri poſſit, neceſſe habeo nonnulla præmittere.</s> <s xml:id="echoid-s4793" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4794" xml:space="preserve">1 Primum iſtud ſit; </s> <s xml:id="echoid-s4795" xml:space="preserve">aſſumo pro fundamento omnium, quæ dicturus ſum, granum papaueris, ſiue ſphæ-<lb/>rulam illi æqualem cõtinere arenulas 100. </s> <s xml:id="echoid-s4796" xml:space="preserve">eſt autem granum papaueris hoc (ſimulque illud oſcendebat) quod <lb/>vix oculorum acies aſſequi valet: </s> <s xml:id="echoid-s4797" xml:space="preserve">quod cũ arenulas 100. </s> <s xml:id="echoid-s4798" xml:space="preserve">continere ponamus, conſequens eſt huiuſmodi are-<lb/>nulas eſſe minutiſſimi pulueris inſtar, minor@ſque quam vſpiam inueniri queant.</s> <s xml:id="echoid-s4799" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4800" xml:space="preserve">2 Suppono, grana papaueris 40. </s> <s xml:id="echoid-s4801" xml:space="preserve">in recta linea diſpoſita, ſeque inuicem tangentia, vnius digiti Geome-<lb/>trici longitudinem hane; </s> <s xml:id="echoid-s4802" xml:space="preserve">-- non ſuperare, quamuis eam re vera multum extendant.</s> <s xml:id="echoid-s4803" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4804" xml:space="preserve">3 Milliare vnum continere digitas 80.</s> <s xml:id="echoid-s4805" xml:space="preserve">000. </s> <s xml:id="echoid-s4806" xml:space="preserve">pes enim cont net 16. </s> <s xml:id="echoid-s4807" xml:space="preserve">digitos; </s> <s xml:id="echoid-s4808" xml:space="preserve">paſſus vero pedes 5. </s> <s xml:id="echoid-s4809" xml:space="preserve">milliare <lb/>paſſus 1000. </s> <s xml:id="echoid-s4810" xml:space="preserve">ex quibus arithmetica multiplicatione patet, quod ſuppono.</s> <s xml:id="echoid-s4811" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4812" xml:space="preserve">4 Diametrum terræ continere milliaria 7.</s> <s xml:id="echoid-s4813" xml:space="preserve">000. </s> <s xml:id="echoid-s4814" xml:space="preserve">plura ſcilicet aliquanto, quã Aſtronomi communiter ſen <lb/>tiant; </s> <s xml:id="echoid-s4815" xml:space="preserve">diametrum vero totius mundi continere diamecios terræ 14.</s> <s xml:id="echoid-s4816" xml:space="preserve">000.</s> <s xml:id="echoid-s4817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4818" xml:space="preserve">5 Tandem poſitio ſit; </s> <s xml:id="echoid-s4819" xml:space="preserve">iphæras habere inuicem triplicatam ſuarum diametrorum proportionem ex 18. <lb/></s> <s xml:id="echoid-s4820" xml:space="preserve">propoſitione 12. </s> <s xml:id="echoid-s4821" xml:space="preserve">Elem. </s> <s xml:id="echoid-s4822" xml:space="preserve">v. </s> <s xml:id="echoid-s4823" xml:space="preserve">g. </s> <s xml:id="echoid-s4824" xml:space="preserve">ſint duæ ſphæræ, quarum diainetrorum notæ ſint rationes, & </s> <s xml:id="echoid-s4825" xml:space="preserve">ſit, v. </s> <s xml:id="echoid-s4826" xml:space="preserve">g. </s> <s xml:id="echoid-s4827" xml:space="preserve">diame-<lb/>ter vnius diametri alterius dimidia, ideſt, ſint in ratione ſubdupla, quali eſt hæc 1. </s> <s xml:id="echoid-s4828" xml:space="preserve">2. </s> <s xml:id="echoid-s4829" xml:space="preserve">iam ſi hæc ratio tripli-<lb/>cetur, ideſt, ſi accipiantur hi numeri, 1. </s> <s xml:id="echoid-s4830" xml:space="preserve">2. </s> <s xml:id="echoid-s4831" xml:space="preserve">4. </s> <s xml:id="echoid-s4832" xml:space="preserve">8. </s> <s xml:id="echoid-s4833" xml:space="preserve">inter quos eadem dupla ratio ter contineratur, erit inter pri-<lb/>mum numerum 1. </s> <s xml:id="echoid-s4834" xml:space="preserve">& </s> <s xml:id="echoid-s4835" xml:space="preserve">vltimum 8. </s> <s xml:id="echoid-s4836" xml:space="preserve">ratio triplicata rationis ſubduplæ: </s> <s xml:id="echoid-s4837" xml:space="preserve">& </s> <s xml:id="echoid-s4838" xml:space="preserve">ſphęrę pariter quarum diametri erant <pb o="48" file="0068" n="72" rhead="De Mundi Fabrica."/> in ratione ſubdupla, habebunt inuicem rationem eam, quam habebunt numeri 1,8. </s> <s xml:id="echoid-s4839" xml:space="preserve">ideſt, ea cuius diameter <lb/>erat diametro alterius dupla, eam octies continebit.</s> <s xml:id="echoid-s4840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4841" xml:space="preserve">Hiſce ita præmiſſis, cum diametri harum ſphęrarum, grani papaueris, ſphæræ digitalis, ſphæræ milliariæ, <lb/>ſphæræ globi terreſtris, & </s> <s xml:id="echoid-s4842" xml:space="preserve">tandem totius mundi ſint notæ, neque latere poterunt earumdem ſphærarum <lb/>mutuæ proportiones; </s> <s xml:id="echoid-s4843" xml:space="preserve">quare notum erit quoties quælibet maior minorem contineat. </s> <s xml:id="echoid-s4844" xml:space="preserve">verum per ſingulas <lb/>ratiocinemur.</s> <s xml:id="echoid-s4845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4846" xml:space="preserve">Quoniam igitur diameter grani papaueris, ad diametrum ſphæræ digitalis habet rationem, quæ eſt in-<lb/>ter 1. </s> <s xml:id="echoid-s4847" xml:space="preserve">& </s> <s xml:id="echoid-s4848" xml:space="preserve">40. </s> <s xml:id="echoid-s4849" xml:space="preserve">habebunt iſtæ ſphæræ huius triplicatam rationem; </s> <s xml:id="echoid-s4850" xml:space="preserve">ſi autem illa triplicentur exhibebit hos nu-<lb/>meros. </s> <s xml:id="echoid-s4851" xml:space="preserve">1, 40, 16, 00, 64, 000. </s> <s xml:id="echoid-s4852" xml:space="preserve">igitur inter extremos numeros 1. </s> <s xml:id="echoid-s4853" xml:space="preserve">& </s> <s xml:id="echoid-s4854" xml:space="preserve">64.</s> <s xml:id="echoid-s4855" xml:space="preserve">000. </s> <s xml:id="echoid-s4856" xml:space="preserve">eſt ratio triplicata quæſita, quam <lb/>ſpæræ inuicem habent: </s> <s xml:id="echoid-s4857" xml:space="preserve">hoc eſt ſphæra digitalis continent grana papaueris. </s> <s xml:id="echoid-s4858" xml:space="preserve">64,000. </s> <s xml:id="echoid-s4859" xml:space="preserve">quia vero granum vnum <lb/>pap. </s> <s xml:id="echoid-s4860" xml:space="preserve">continet arenulas 100. </s> <s xml:id="echoid-s4861" xml:space="preserve">ſequitur ſphæram digitalem continere arenulas, 6,400,000. </s> <s xml:id="echoid-s4862" xml:space="preserve">qui numerus pro-<lb/>ducitur multiplicando 100. </s> <s xml:id="echoid-s4863" xml:space="preserve">in 64, 000.</s> <s xml:id="echoid-s4864" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4865" xml:space="preserve">Rurſus quoniam diameter ſphæræ digitalis ad diametrum ſphæræ milliariæ, habet rationem, quam ha-<lb/>bent 1, 80, 000. </s> <s xml:id="echoid-s4866" xml:space="preserve">quæ ratio triplicata dat hoſce terminos; </s> <s xml:id="echoid-s4867" xml:space="preserve">1, 80, 000, 6, 400, 000, 000, 512, 000, 000, 000, 000. <lb/></s> <s xml:id="echoid-s4868" xml:space="preserve">propterea ratio primi ad vltimum eſt proportio ſpærarum: </s> <s xml:id="echoid-s4869" xml:space="preserve">quare ſphæra milliaria continet tot ſphæras di-<lb/>gitales, quot quartus numerus continet vnitates, & </s> <s xml:id="echoid-s4870" xml:space="preserve">quia ſphæra digitalis continet arenulas 6. </s> <s xml:id="echoid-s4871" xml:space="preserve">400.</s> <s xml:id="echoid-s4872" xml:space="preserve">000. </s> <s xml:id="echoid-s4873" xml:space="preserve">ſi hic <lb/>numerus in quartum prædictum multiplicetur, producetur numerus 3, 276, 800, 000, 000, 000, 000, 000. </s> <s xml:id="echoid-s4874" xml:space="preserve">nu-<lb/>merus videlicet arenularum in milliario globo contentarum.</s> <s xml:id="echoid-s4875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4876" xml:space="preserve">Præterea quia diameter terreſtris ſphæræ continet 7, 000. </s> <s xml:id="echoid-s4877" xml:space="preserve">erit eius habitudo ad diametrum globi millia-<lb/>rij, quæ 1. </s> <s xml:id="echoid-s4878" xml:space="preserve">ad 7, 000. </s> <s xml:id="echoid-s4879" xml:space="preserve">cuius triplicata eſt in his numeris 1, 7, 000, 49, 000, 000, 343, 000, 000, 000. </s> <s xml:id="echoid-s4880" xml:space="preserve">Tota igitur <lb/>terra ad ſphæram milliariam collata eſt ſicuti quartus num. </s> <s xml:id="echoid-s4881" xml:space="preserve">1. </s> <s xml:id="echoid-s4882" xml:space="preserve">Iam vero ſi num. </s> <s xml:id="echoid-s4883" xml:space="preserve">arenularum vnius giobi mil-<lb/>liarij, quem ante inuenimus, ducatur in hũc quartum numerum, productus numerus indicabit arenulas om-<lb/>nes in tota terræ mole contentas: </s> <s xml:id="echoid-s4884" xml:space="preserve">is autem eſt hic; </s> <s xml:id="echoid-s4885" xml:space="preserve">1, 123, 942, 400, 000, 000, 000, 000, 000, 000, 000, 000. <lb/></s> <s xml:id="echoid-s4886" xml:space="preserve">vnde iam ſatis patere poteſt, illorum Philoſophorum opinionũ minimè ſubſiſtere, qui arenarum omnium <lb/>per maria diſperſarum adeò magnum eſſe numerum opinabantur, vt nullo pacto ſcribi, aut proferri poſſet. </s> <s xml:id="echoid-s4887" xml:space="preserve"><lb/>atque hæc ſatis in præſentia videri poſſent, cum tractationem quantitatis terræ ſapiant, eamque minime <lb/>excedant.</s> <s xml:id="echoid-s4888" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4889" xml:space="preserve">Verumtamen ne Archimedis diſcurſus ſubtiliſſimus obtruncetur, pauca quæ ſuperſunt afferam. </s> <s xml:id="echoid-s4890" xml:space="preserve">ſtatutum <lb/>eſt ſupra diametrum terræ ad diametrum mundi eſſe ficut 1. </s> <s xml:id="echoid-s4891" xml:space="preserve">ad 14,000. </s> <s xml:id="echoid-s4892" xml:space="preserve">quæ analogia ſi triplicetur dabit ho-<lb/>ſce numeros, 1,14,000. </s> <s xml:id="echoid-s4893" xml:space="preserve">196,000,000. </s> <s xml:id="echoid-s4894" xml:space="preserve">2,744,000,000,000. </s> <s xml:id="echoid-s4895" xml:space="preserve">terra igitur ad totam mundi ſphæram eſt ſicut 1. </s> <s xml:id="echoid-s4896" xml:space="preserve">ad <lb/>quartum numerum. </s> <s xml:id="echoid-s4897" xml:space="preserve">& </s> <s xml:id="echoid-s4898" xml:space="preserve">quoniam numerus arenularum totius globi terreſtri paulò ante repertus eſt, ſi is du-<lb/>catur in hunc quartum numerum, producetur numerus ille admirabilis omnium arenularum, quæ totam <lb/>mundi ſphęram complerent, is autem eſt huiuſmodi, 3,084,097,945,6000,000,000,000,000,000,000,000,000, <lb/>000,000,000. </s> <s xml:id="echoid-s4899" xml:space="preserve">qui numerus conſtat tantummodo figuris quadraginta ſex, qui tamen multo maior iuſto fit, <lb/>neceſſe eſt, cùm multa aduerſarijs dederimus, vt illuſtrior, ac admirabilior noſtra euaderet diſputatio.</s> <s xml:id="echoid-s4900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4901" xml:space="preserve">Atque hæc eſt illa Archimedis de arenæ numero mira perueſtigatio, quam ſummopere tota antiqui-<lb/>tas ſimul, ac poſteritas admirata eſt.</s> <s xml:id="echoid-s4902" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div92" type="section" level="1" n="62"> <head xml:id="echoid-head65" xml:space="preserve">LIBER QVINTVS</head> <head xml:id="echoid-head66" xml:space="preserve">De Aqua Elementari, ſiue de Mari.</head> <head xml:id="echoid-head67" style="it" xml:space="preserve">De loco Aque Mariſuè. Cap. I.</head> <p> <s xml:id="echoid-s4903" xml:space="preserve">QVem locum Mare in ordine Elementorum occupet, ſenſu manifeſtum eſt, videmus enim <lb/>ipſum proximè ſupra terram collocatum eſſe, non tamen ita, vt totam ambiat, ſed dimidiã<unsure/> <lb/>ferè ſuperficiem, tantum contingat. </s> <s xml:id="echoid-s4904" xml:space="preserve">quod factum eſt, quia terra non eſt perſectè rotunda, <lb/>ſed habet plurimas, ac magnas cauitates, in quas omnis aquarum copia receſſit: </s> <s xml:id="echoid-s4905" xml:space="preserve">ibiq; </s> <s xml:id="echoid-s4906" xml:space="preserve">ſubſi-<lb/>det: </s> <s xml:id="echoid-s4907" xml:space="preserve">ſi enim eſſet perfectè rotũda deberent aquæ iuxta naturalem earum ſtatum ſupra vni-<lb/>uerſam terræ faciem circunfundi, eamque complecti, cum elementum aquæ ſit elemento <lb/>terræ leuius. </s> <s xml:id="echoid-s4908" xml:space="preserve">vnde nonnulli magnę auctoritatis Theologi, terram initio mundi à Deo om-<lb/>nino rotundam, ſiue vllis cauitatibus, aut eminentijs factam, ac proinde totam aquis circumfuſam fuiſſe exi-<lb/>ſtimant. </s> <s xml:id="echoid-s4909" xml:space="preserve">Cùm vero Deus dixit; </s> <s xml:id="echoid-s4910" xml:space="preserve">congregentur aquæ in locum vnum, vt appareat arida; </s> <s xml:id="echoid-s4911" xml:space="preserve">ob animantium ſci-<lb/>licet terreſtrium vitam, tũc diuino iuſſu cauitates latè patentes in terras factas eſſe, in quas omnem aquarum <lb/>vim ſua naturali propenſione, qua ad decliuiora loca deſcendunt, tanquam in ſuas congregationes conceſ-<lb/>ſiſſe, ſicq; </s> <s xml:id="echoid-s4912" xml:space="preserve">varia maria in diuerſis terræ partibus exorta eſſe porrò ex partibus illis terrę inde extractis, mon-<lb/>tes eſſe conſtructos veriſimile eſſe parires opinantur. </s> <s xml:id="echoid-s4913" xml:space="preserve">quod inde colligunt, quia quanta eſt montium altitu-<lb/>do, tanta eſt etiam maris profunditas, vt de mari nautæ; </s> <s xml:id="echoid-s4914" xml:space="preserve">de montibus vero Geometræ obſeruarunt.</s> <s xml:id="echoid-s4915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4916" xml:space="preserve">Pręterea rationi conſentaneũ eſt, vt aqua ſecundum à terra locum obtineat, cùm ſit proximè leuior terra, <pb o="49" file="0069" n="73" rhead="Liber Quintus."/> aere vero proxime grauior. </s> <s xml:id="echoid-s4917" xml:space="preserve">terra enim infra aerem & </s> <s xml:id="echoid-s4918" xml:space="preserve">aquan deſcendit, ac ſubſidet. </s> <s xml:id="echoid-s4919" xml:space="preserve">aer vero proxime gra-<lb/>uior. </s> <s xml:id="echoid-s4920" xml:space="preserve">terra enim infra aerem & </s> <s xml:id="echoid-s4921" xml:space="preserve">aquam deſcendit, ac ſubſidet. </s> <s xml:id="echoid-s4922" xml:space="preserve">aer vero infra aquam detruſus, ſi poſſit recta <lb/>ſtatim ſumma petit, vt patet in bullis aeris, quæ ab imo aquæ celerrimè aſcendunt. </s> <s xml:id="echoid-s4923" xml:space="preserve">id facile eſt experiri hoc <lb/>pacto; </s> <s xml:id="echoid-s4924" xml:space="preserve">cyathum inuerſum, ideſt, ore deorſum in aquam immitte, ſic enim aer incluſus ſub aquam detrude-<lb/>tur; </s> <s xml:id="echoid-s4925" xml:space="preserve">deinde pedem cyathi in partem aliquam deflecte, ſic enim aer demerſus incipiet exilire, ac ſumma cele-<lb/>ritate rectà petere.</s> <s xml:id="echoid-s4926" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4927" xml:space="preserve">Ita tamen aqua ſecundum locum occupat, vt ſuprema maris ſuperficies ſupra terræ ſuperficiem ſupremã <lb/>non eleuetur, ſed vtraq; </s> <s xml:id="echoid-s4928" xml:space="preserve">ſuperficies vnius globi ſuperficiem componat; </s> <s xml:id="echoid-s4929" xml:space="preserve">vt partim ſupra, partim etiam infra <lb/>probabitur. </s> <s xml:id="echoid-s4930" xml:space="preserve">Qua vero ratione mare ſupra terræ faciem ſit in varias veluti ſtationes diſtributum, vnde varia <lb/>marium nomina, Oceanum, Mediterraneum, Caſpium, & </s> <s xml:id="echoid-s4931" xml:space="preserve">c. </s> <s xml:id="echoid-s4932" xml:space="preserve">emerſerint, Geographi munus eſt explicare. <lb/></s> <s xml:id="echoid-s4933" xml:space="preserve">Illud notatu d@gnum eſt; </s> <s xml:id="echoid-s4934" xml:space="preserve">Maria omnia alicubi coniuncta eſſe, ac ſimul communicare; </s> <s xml:id="echoid-s4935" xml:space="preserve">præter mare Caſpium, <lb/>quod intra Aſiæ mediteranea ſitum eſt, ac proinde verè Mediterraneum eſt.</s> <s xml:id="echoid-s4936" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div93" type="section" level="1" n="63"> <head xml:id="echoid-head68" style="it" xml:space="preserve">De motu Aquæ Mariſue. Cap. II.</head> <p> <s xml:id="echoid-s4937" xml:space="preserve">PRimo, & </s> <s xml:id="echoid-s4938" xml:space="preserve">ex natura Aquæ ineſt ipſi mótus rectus deorſum, ideſt, deſcenſus; </s> <s xml:id="echoid-s4939" xml:space="preserve">quæ ſi libera ſit directè, ſeu ad <lb/>perpendiculum deſcendit ad mundi medium, ſeu centrum; </s> <s xml:id="echoid-s4940" xml:space="preserve">vt apparet in guttis pluentibus, quæ niſi aeris <lb/>agitatione imped@antur perpendiculariter delabuntur. </s> <s xml:id="echoid-s4941" xml:space="preserve">quod ſi nequeant recta deſcende-<lb/> <anchor type="figure" xlink:label="fig-0069-01a" xlink:href="fig-0069-01"/> re; </s> <s xml:id="echoid-s4942" xml:space="preserve">ad loca tamen decliuiora defluere.</s> <s xml:id="echoid-s4943" xml:space="preserve"/> </p> <div xml:id="echoid-div93" type="float" level="2" n="1"> <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a"> <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0069-01"/> </figure> </div> <p> <s xml:id="echoid-s4944" xml:space="preserve">2 Etiam aſcenſus aquæ ſecundum partes ineſt, quantum enim ex vna parte deſcendit, <lb/>tantum ex altera aſcendit, ſi tamen per tubum clauſa fluat. </s> <s xml:id="echoid-s4945" xml:space="preserve">fit tubus A B C. </s> <s xml:id="echoid-s4946" xml:space="preserve">in quem ex par-<lb/>te A. </s> <s xml:id="echoid-s4947" xml:space="preserve">infundatur aqua, vſque ad D E. </s> <s xml:id="echoid-s4948" xml:space="preserve">etiam cx altera parte aſcendet vſque ad lineam E F. <lb/></s> <s xml:id="echoid-s4949" xml:space="preserve">quæ in eodem eſt æquilibrio cum D E. </s> <s xml:id="echoid-s4950" xml:space="preserve">& </s> <s xml:id="echoid-s4951" xml:space="preserve">quamuis pars A B. </s> <s xml:id="echoid-s4952" xml:space="preserve">ſit multo latior, & </s> <s xml:id="echoid-s4953" xml:space="preserve">capacior, <lb/>quam altera, quæ gracilior eſſe poteſt; </s> <s xml:id="echoid-s4954" xml:space="preserve">tamen tota aqua in A B. </s> <s xml:id="echoid-s4955" xml:space="preserve">non propellet modicã aquam <lb/>B C. </s> <s xml:id="echoid-s4956" xml:space="preserve">ſupra æquilibrium D E F.</s> <s xml:id="echoid-s4957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4958" xml:space="preserve">3 Similiter non minus vult deſcendere, quam aſcendet: </s> <s xml:id="echoid-s4959" xml:space="preserve">ſit in vaſe aqua vſque ab A B. <lb/></s> <s xml:id="echoid-s4960" xml:space="preserve">fitque tubus inflexus ſiue ſipho D E N C F. </s> <s xml:id="echoid-s4961" xml:space="preserve">ex parte D. </s> <s xml:id="echoid-s4962" xml:space="preserve">in aqua demerſus, ex altera F. </s> <s xml:id="echoid-s4963" xml:space="preserve">de-<lb/>ſcendat A B C. </s> <s xml:id="echoid-s4964" xml:space="preserve">nam ſi per exſuctionem, aut alio modo aqua extraha@ur vſque ad F. </s> <s xml:id="echoid-s4965" xml:space="preserve">continuò ex F. </s> <s xml:id="echoid-s4966" xml:space="preserve">effluet, do-<lb/>nec A B. </s> <s xml:id="echoid-s4967" xml:space="preserve">ſuperficies aquæ deſcenderit ad æquilibrium ipſius F. </s> <s xml:id="echoid-s4968" xml:space="preserve">in quo ſitu non amplius fluet, ideſt, ſi os F. </s> <s xml:id="echoid-s4969" xml:space="preserve">ſit <lb/> <anchor type="figure" xlink:label="fig-0069-02a" xlink:href="fig-0069-02"/> exactè in æquilibrio aquæ A B. </s> <s xml:id="echoid-s4970" xml:space="preserve">nullus ſequetur fluxus, ſed aqua in pleno ſiphone <lb/>manebit. </s> <s xml:id="echoid-s4971" xml:space="preserve">Quod ſi os F. </s> <s xml:id="echoid-s4972" xml:space="preserve">ſit ſupra aquæ æquilibrium, vt ſi fuerit in N. </s> <s xml:id="echoid-s4973" xml:space="preserve">non ſolum non <lb/>fluet, ſed intus iterum in vas refluet.</s> <s xml:id="echoid-s4974" xml:space="preserve"/> </p> <div xml:id="echoid-div94" type="float" level="2" n="2"> <figure xlink:label="fig-0069-02" xlink:href="fig-0069-02a"> <image file="0069-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0069-02"/> </figure> </div> <p> <s xml:id="echoid-s4975" xml:space="preserve">Et quamuis pars tubi E N. </s> <s xml:id="echoid-s4976" xml:space="preserve">exterior ſit multo latior, & </s> <s xml:id="echoid-s4977" xml:space="preserve">capacior, quam altera D E. <lb/></s> <s xml:id="echoid-s4978" xml:space="preserve">non propterea tamen pondus aquæ maioris trahet aquam minorem, quæ eſt in D E. </s> <s xml:id="echoid-s4979" xml:space="preserve"><lb/>vt experientia quotidiana patefacit.</s> <s xml:id="echoid-s4980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4981" xml:space="preserve">4 Mare Oceanum præſertim ſub torrida Zona, motu diurno, ideſt, ab oriente in <lb/>occidentẽ quamuis tardè promouetur; </s> <s xml:id="echoid-s4982" xml:space="preserve">vt P. </s> <s xml:id="echoid-s4983" xml:space="preserve">Acoſta noſtræ Soc. </s> <s xml:id="echoid-s4984" xml:space="preserve">ab experientijs nau-<lb/>tarum edoctus, tradidit; </s> <s xml:id="echoid-s4985" xml:space="preserve">& </s> <s xml:id="echoid-s4986" xml:space="preserve">nos ſupra de motu Sphæræ Elementaris retulimus, at 10. <lb/></s> <s xml:id="echoid-s4987" xml:space="preserve">Baptiſta Porta putat eſſe motum aeris, ob ventos ab ortu in occaſum flantes.</s> <s xml:id="echoid-s4988" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div96" type="section" level="1" n="64"> <head xml:id="echoid-head69" style="it" xml:space="preserve">Maris fluxus, ac refluxus.</head> <p> <s xml:id="echoid-s4989" xml:space="preserve">MAria tam Mediterranea, quam Oceanum, motu fluxus ac refluxus cientur: </s> <s xml:id="echoid-s4990" xml:space="preserve">quo motu ſex ferè horis Ma-<lb/>re niſi quid obeſt, fluit ad littora, totidemq; </s> <s xml:id="echoid-s4991" xml:space="preserve">a littoribus in altum recipitur. </s> <s xml:id="echoid-s4992" xml:space="preserve">qui motus quoniam à Luna <lb/>pendet, ſequiturque Lunares periodos, atq; </s> <s xml:id="echoid-s4993" xml:space="preserve">aſpectus Lunæad Solem, idcirco Aſtronomicus, atque ſub iure <lb/>Aſtronomico cenſeri debet. </s> <s xml:id="echoid-s4994" xml:space="preserve">De eo igitur iure noſtro hocloco agimus. </s> <s xml:id="echoid-s4995" xml:space="preserve">quoniam vero hac de re fusè egimus <lb/>in locis mathematicis apud Ariſt. </s> <s xml:id="echoid-s4996" xml:space="preserve">ad cap. </s> <s xml:id="echoid-s4997" xml:space="preserve">3. </s> <s xml:id="echoid-s4998" xml:space="preserve">lib. </s> <s xml:id="echoid-s4999" xml:space="preserve">de Mũdo ad Alex. </s> <s xml:id="echoid-s5000" xml:space="preserve">ideo ſummatim inde nonnulla decerpemus, <lb/>quæ præſenti inſtituto ſatisfaciant. </s> <s xml:id="echoid-s5001" xml:space="preserve">Quoniam igitur fluxus, ac refluxus maris prouenit ab æſtu maris, dicen-<lb/>dum prius, quid ſit maris æſtus; </s> <s xml:id="echoid-s5002" xml:space="preserve">is igitur eſt quædam maris ebullitio, ob quam, vt ſolet in ebullientibus aquis <lb/>mare intumeſcit. </s> <s xml:id="echoid-s5003" xml:space="preserve">fiunt autem in toto mundo, duobus tamen in locis diametraliter oppoſitis, duos æſtus, & </s> <s xml:id="echoid-s5004" xml:space="preserve"><lb/>proinde duo tumores, quales in ſequenti figura præuidere eſt. </s> <s xml:id="echoid-s5005" xml:space="preserve">quorum vnus directe Lunæ ſubeſt, alter vero <lb/>in auerſa terræ parte; </s> <s xml:id="echoid-s5006" xml:space="preserve">ex his tumoribus fit vt aquæ maris, quæ natura ſua decliuiora petunt, quafi exundantes <lb/>ad litora difluant; </s> <s xml:id="echoid-s5007" xml:space="preserve">qui maris curſus dicitur, vulgo fluxus. </s> <s xml:id="echoid-s5008" xml:space="preserve">decreſcente deinde maris æſtu ac tumore ex receſſu <lb/>Lunæ, aquæ iterum decliuiora repetentes, | ad maris medium refluunt, qui curſus maris refluxus meritò nun-<lb/>cupatur. </s> <s xml:id="echoid-s5009" xml:space="preserve">cum autem in integro die ſint horæ 24. </s> <s xml:id="echoid-s5010" xml:space="preserve">ſemperq; </s> <s xml:id="echoid-s5011" xml:space="preserve">fint duo tumores oppoſiti, ſequitur etiam ſemper <lb/>eſſe duos fluxus, & </s> <s xml:id="echoid-s5012" xml:space="preserve">in alijs duobus locis oppoſitis diſtantibus per quadrantẽ à tumoribus, eſſe duas maris ſub-<lb/>ſidẽtias, & </s> <s xml:id="echoid-s5013" xml:space="preserve">proinde duos refluxus; </s> <s xml:id="echoid-s5014" xml:space="preserve">quare totus maris, gyrus erit diſtributus in quatuor partes, ſcilicet in duos <lb/>fluxus, duoſq; </s> <s xml:id="echoid-s5015" xml:space="preserve">refluxus; </s> <s xml:id="echoid-s5016" xml:space="preserve">qui perpetuo circa terrenum globum cum Luna, ſeu Lunam ſubſequentes, circunſe-<lb/>runtur, vt Ariſt. </s> <s xml:id="echoid-s5017" xml:space="preserve">in 3. </s> <s xml:id="echoid-s5018" xml:space="preserve">cap. </s> <s xml:id="echoid-s5019" xml:space="preserve">ad Alex. </s> <s xml:id="echoid-s5020" xml:space="preserve">teſtatur; </s> <s xml:id="echoid-s5021" xml:space="preserve">& </s> <s xml:id="echoid-s5022" xml:space="preserve">experientia quotidiana comprobat. </s> <s xml:id="echoid-s5023" xml:space="preserve">hinc fit vt 6. </s> <s xml:id="echoid-s5024" xml:space="preserve">ferè horis <lb/>reſpectu eiuſdem horizontis aduentante Luna duret fluxus; </s> <s xml:id="echoid-s5025" xml:space="preserve">ſex alijs refluxus, alijs 6. </s> <s xml:id="echoid-s5026" xml:space="preserve">iterum fluxus ob tumo-<lb/>rem Lunæ antipodum, & </s> <s xml:id="echoid-s5027" xml:space="preserve">poſtremo 6. </s> <s xml:id="echoid-s5028" xml:space="preserve">alijs refluxus: </s> <s xml:id="echoid-s5029" xml:space="preserve">tota tamen hæc fluxuum, & </s> <s xml:id="echoid-s5030" xml:space="preserve">refluxuum periodus non ab-<lb/>ſoluitur niſi ſpatio ferè 25. </s> <s xml:id="echoid-s5031" xml:space="preserve">horarum; </s> <s xml:id="echoid-s5032" xml:space="preserve">cuius cauſa eſt motus Lunæ proprius, quo ad orientem contra motum <lb/>diurnum pergens, fit quotidie magis tanto orientalior, quantum ferè ſufficit, vt hora vna quotidie tardius <pb o="50" file="0070" n="74" rhead="De Mundi Fabrica"/> oriatur: </s> <s xml:id="echoid-s5033" xml:space="preserve">hoc autem euidens ſignum eſt à Luna effici: </s> <s xml:id="echoid-s5034" xml:space="preserve">qua quidem certiſſima experientia inducti veteres om-<lb/>nes ſcriptores cauſam huius in Lunam retulerunt; </s> <s xml:id="echoid-s5035" xml:space="preserve">vt primus omnium Ariſt. </s> <s xml:id="echoid-s5036" xml:space="preserve">loco citato, Poſſidonius, deinde <lb/>Strabo, Pompon@us Mela, Plinius, Solinus, & </s> <s xml:id="echoid-s5037" xml:space="preserve">alij complures ſenſerunt; </s> <s xml:id="echoid-s5038" xml:space="preserve">Lunam videlicet eam habere vim in <lb/>mare, vt eius pars quæ Lunæ ſupponitur, necnon ea quæ huic oppoſita eſt, quamuis tota terra interponatur, <lb/>æſtuet, & </s> <s xml:id="echoid-s5039" xml:space="preserve">vrgeat ac proinde fluxum eſſiciat; </s> <s xml:id="echoid-s5040" xml:space="preserve">vnde & </s> <s xml:id="echoid-s5041" xml:space="preserve">alij duo refluxus ſequantur. </s> <s xml:id="echoid-s5042" xml:space="preserve">vbi notandum eſt æſtum illũ <lb/>antipodum eſſe ſemper altero minorem. </s> <s xml:id="echoid-s5043" xml:space="preserve">ſed hæc melius ex figura percipientur, vbi infra Lunam vides tu-<lb/> <anchor type="figure" xlink:label="fig-0070-01a" xlink:href="fig-0070-01"/> morem, A. </s> <s xml:id="echoid-s5044" xml:space="preserve">pariter in par-<lb/>te aduerſa tumorem B. </s> <s xml:id="echoid-s5045" xml:space="preserve">ali-<lb/>quanto minorem: </s> <s xml:id="echoid-s5046" xml:space="preserve">ex qui-<lb/>bus fiunt duo fluxus ad lito-<lb/>ra. </s> <s xml:id="echoid-s5047" xml:space="preserve">in alijs vero duobus ter <lb/>ræ lateribus C D. </s> <s xml:id="echoid-s5048" xml:space="preserve">quæ Lu-<lb/>na radijs nulla impetere <lb/>poteſt, ſed tan@ummodo <lb/>leuiter tangere, nulli fiunt <lb/>tumores, ſed potius ob æ-<lb/>ſtus ceſſationem fit refrige <lb/>ratio, & </s> <s xml:id="echoid-s5049" xml:space="preserve">perinde ſubſiden-<lb/>tia, & </s> <s xml:id="echoid-s5050" xml:space="preserve">decliuitas, vnde ſe-<lb/>quitur aquas ad ea reflue-<lb/>re, fierique duos refluxus <lb/>C D. </s> <s xml:id="echoid-s5051" xml:space="preserve">ita vt in vniuerſo ma-<lb/>ri ſint ſemper hi quatuor <lb/>effectus, qui ſimul cum Lu-<lb/>na, teſte experientia, circa <lb/>terram circumaguntur. </s> <s xml:id="echoid-s5052" xml:space="preserve">ſic <lb/>quando Luna, quæ in figu-<lb/>ra eſt in parte auſtrali ve-<lb/>nietad occidẽtem E. </s> <s xml:id="echoid-s5053" xml:space="preserve">eam <lb/>fluxus A. </s> <s xml:id="echoid-s5054" xml:space="preserve">ſubſequetur, erit-<lb/>que vbi modo eſt D. </s> <s xml:id="echoid-s5055" xml:space="preserve">pari-<lb/>ter fluxus B. </s> <s xml:id="echoid-s5056" xml:space="preserve">promouebitur <lb/>ad C. </s> <s xml:id="echoid-s5057" xml:space="preserve">refluxus vero C. </s> <s xml:id="echoid-s5058" xml:space="preserve">ve-<lb/>niet ad A. </s> <s xml:id="echoid-s5059" xml:space="preserve">ſicque ſpatio 25. <lb/></s> <s xml:id="echoid-s5060" xml:space="preserve">horarũ abſoluetur perio-<lb/>dus quæ conſequentia ad <lb/>Lunam perpetua, manife-<lb/>ſtum facit, hunc fluxum, & </s> <s xml:id="echoid-s5061" xml:space="preserve"><lb/>refluxum non aliunde, quã <lb/>ab ea, manare: </s> <s xml:id="echoid-s5062" xml:space="preserve">præſertim <lb/>cum certò videamus, quod quanto Luna tardius quotidie reuertitur, tanto etiam hi effectus tardius cum ea re-<lb/>ſtituuntur. </s> <s xml:id="echoid-s5063" xml:space="preserve">Sed præſtat audire Poſſidonium apud Strabonem ſic loquentem: </s> <s xml:id="echoid-s5064" xml:space="preserve">Oceani vero motus ſyderis ſu-<lb/>bit circui tum, quemdam quidem diurnum, quemdam menſtruum, quemdam annuum, vt Lunę etiam contin-<lb/>git. </s> <s xml:id="echoid-s5065" xml:space="preserve">quo enim tempore iſta horizontem aſcendit, mare terram aſcendere incipit, ſenſu teſte, quouſq; </s> <s xml:id="echoid-s5066" xml:space="preserve">ad cæli <lb/>medium Luna conſcenderit. </s> <s xml:id="echoid-s5067" xml:space="preserve">vbi vero declinare ſydus ipſum cæperit, ſenſim rurſus a terra pelagus ad mediũ <lb/>mare relabitur, donec ad occidentis punctum Luna deſcenderit. </s> <s xml:id="echoid-s5068" xml:space="preserve">poſtea rurſus mare aſcendit, quouſq; </s> <s xml:id="echoid-s5069" xml:space="preserve">ſub tel-<lb/>lurem in medio, & </s> <s xml:id="echoid-s5070" xml:space="preserve">imo cæli ſit Luna; </s> <s xml:id="echoid-s5071" xml:space="preserve">deinde mare à litore ad medium maris regredi, quoad iterum Luna ad <lb/>orientem procedat, ac eleuetur, rurſuſque mare terras influat. </s> <s xml:id="echoid-s5072" xml:space="preserve">poſtea explicat qua ratione alijs etiam motibus <lb/>menſtruo, & </s> <s xml:id="echoid-s5073" xml:space="preserve">annuo, Luna mare percellat. </s> <s xml:id="echoid-s5074" xml:space="preserve">Eadem habens Plinius ac veteres omnes: </s> <s xml:id="echoid-s5075" xml:space="preserve">vnde mirum ſit, curè re-<lb/>centioribus nonnulli, contra veterum omnium ſententiam, necnon contra quotidianam experientiam, nulla <lb/>euidenti ratione aut experiẽtia nixi, hanc maris affectionem a Luna minimè procedere auſi ſint aſſerere. </s> <s xml:id="echoid-s5076" xml:space="preserve">Ve-<lb/>rum ipſi duabus de cauſis id negarunt.</s> <s xml:id="echoid-s5077" xml:space="preserve"/> </p> <div xml:id="echoid-div96" type="float" level="2" n="1"> <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a"> <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0070-01"/> </figure> </div> <p> <s xml:id="echoid-s5078" xml:space="preserve">Prima eſt quod vario modo, & </s> <s xml:id="echoid-s5079" xml:space="preserve">tempore in diuerſis maribus hæc accidant: </s> <s xml:id="echoid-s5080" xml:space="preserve">imo in aliquibus nihil horum <lb/>appareat. </s> <s xml:id="echoid-s5081" xml:space="preserve">huic reſpondendum eſt, id ex varia marium diſpoſitione, tum etiam vario ſitu quo Lunã reſpiciunt <lb/>prouenire. </s> <s xml:id="echoid-s5082" xml:space="preserve">hac ratione videmus in toto terrarum orbe, varijs modis varijſque temporibus effici dies, ac no-<lb/>ctes, æſtatem, ac hyemem, cum tamen certum ſit Solem iſta omnia efficere. </s> <s xml:id="echoid-s5083" xml:space="preserve">ſed melius etiam occurre-<lb/>mus ex certa experientia, & </s> <s xml:id="echoid-s5084" xml:space="preserve">regulis artis nauticæ. </s> <s xml:id="echoid-s5085" xml:space="preserve">nam libri nautici ſine vlla dubitatione Lunæ hæc omnia <lb/>aſcribunt; </s> <s xml:id="echoid-s5086" xml:space="preserve">tradunt enim quaſdam regulas, eas tamen pro varijs maribus varias, quibus per ætatem Lunæ ſitũ-<lb/>que ipſius ſupra horizontem illius maris certo certius horam fluxus, & </s> <s xml:id="echoid-s5087" xml:space="preserve">refluxus, atq; </s> <s xml:id="echoid-s5088" xml:space="preserve">etiam eorum magnitu-<lb/>dinem prædicunt, huiuſmodi lib. </s> <s xml:id="echoid-s5089" xml:space="preserve">vidi Auguſtino Cæſareo authore, ſed manu ſcriptum. </s> <s xml:id="echoid-s5090" xml:space="preserve">quod ſi hi effectus à <lb/>Luna non penderent, nulla ratione regulæ illę adeo infallibiles conſtrui potuiſſent, quibus per Lunæ ætatem <lb/>ac ſitum, eos tuto diuinare poſſent.</s> <s xml:id="echoid-s5091" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5092" xml:space="preserve">Præterea quærunt, qua nam ratione à Luna effici poſſit tumor ille B. </s> <s xml:id="echoid-s5093" xml:space="preserve">ad partes auerſas, cum tota terræ mo- <pb o="51" file="0071" n="75" rhead="Liber Quintus."/> les obſtare videatur. </s> <s xml:id="echoid-s5094" xml:space="preserve">cui dubitationi vt rectè occurramus, primo ſciendum eſt, Lunam multum à Sole iu<unsure/>uari <lb/>in hoc æſtu ciendo, conſtat enim ex obſeruatione maiorem tunc fieri fluxum, cum ſimul luminaria ſunt con-<lb/>iuncta, vt accidit in nouilunijs quam vnquam alias; </s> <s xml:id="echoid-s5095" xml:space="preserve">ſimiliter quando ſunt oppoſita, vt in plenilunijs; </s> <s xml:id="echoid-s5096" xml:space="preserve">qu@a tũc <lb/>ctiam radij vniuntur magis, ſed vnius directi, alterius vero reflexi, vt mox patebit. </s> <s xml:id="echoid-s5097" xml:space="preserve">Secundo prænotandum <lb/>eſt radios tanto eſſe efficaciores, quanto ſunt rei, cui accidũt, perpendiculariores: </s> <s xml:id="echoid-s5098" xml:space="preserve">ſint ergo Sol, & </s> <s xml:id="echoid-s5099" xml:space="preserve">Luna ſimul, <lb/>vt in figura apparet: </s> <s xml:id="echoid-s5100" xml:space="preserve">ſitque octauæ ſphæræ adhærentium ſtellarũ portio F G H I E. </s> <s xml:id="echoid-s5101" xml:space="preserve">innumeris ſyderibus con-<lb/>ſtipata, vt patet adhibito nouo illo, ſed admirabili Teleſcopij inuento. </s> <s xml:id="echoid-s5102" xml:space="preserve">iam vt patet ex opticorum doctrina <lb/>omnes Stellæ, & </s> <s xml:id="echoid-s5103" xml:space="preserve">Plane<unsure/>tę illuminantur a Sole, & </s> <s xml:id="echoid-s5104" xml:space="preserve">lumen illud ad terram quandoque reflectunt; </s> <s xml:id="echoid-s5105" xml:space="preserve">pars tamen eo-<lb/>rum illuminata ſemper ad Solem vergit; </s> <s xml:id="echoid-s5106" xml:space="preserve">vt in figura apparet, in qua ſtel æ omnes, qua parte ſunt illuſtratæ, <lb/>eadem Solem, ac Lunam reſpiciun@. </s> <s xml:id="echoid-s5107" xml:space="preserve">vbi rurſus conſide@andum eſt plures ſtellas, quæ videlicet ſunt in portio-<lb/>ne G H I. </s> <s xml:id="echoid-s5108" xml:space="preserve">obuertere partem ſui illuſtram non ſolum ad luminaria, verum etiam ad partem terræ B. </s> <s xml:id="echoid-s5109" xml:space="preserve">hacq; </s> <s xml:id="echoid-s5110" xml:space="preserve">ra-<lb/>tione lumen, ſeu virtutem luminarium ad æſtum B. </s> <s xml:id="echoid-s5111" xml:space="preserve">excitandum reflectere; </s> <s xml:id="echoid-s5112" xml:space="preserve">reliquas vero circa F. </s> <s xml:id="echoid-s5113" xml:space="preserve">& </s> <s xml:id="echoid-s5114" xml:space="preserve">E. </s> <s xml:id="echoid-s5115" xml:space="preserve">parum <lb/>ſui luminis ad terram remittere: </s> <s xml:id="echoid-s5116" xml:space="preserve">reliquas vero quæ ſunt in reliqua cæli parte, nihil ſui luminis ad terras, ſed <lb/>totum ſurſus verſus luminaria obuertere. </s> <s xml:id="echoid-s5117" xml:space="preserve">quando igitur luminaria ſunt ſimul tunc eorum radij ex ſyderibus <lb/>circa G H I. </s> <s xml:id="echoid-s5118" xml:space="preserve">ſimul coniuncti, ac proinde fortiores ad partem terræ B. </s> <s xml:id="echoid-s5119" xml:space="preserve">auerſam remittuntur ab ipſis, ſicque ibi <lb/>æſtum excitant. </s> <s xml:id="echoid-s5120" xml:space="preserve">ſimiliter in parte A. </s> <s xml:id="echoid-s5121" xml:space="preserve">lumine directo & </s> <s xml:id="echoid-s5122" xml:space="preserve">fortiori, quia vnita virtus for@ior æſtum, & </s> <s xml:id="echoid-s5123" xml:space="preserve">ebullitio-<lb/>nem maris ma@ores, quam alias efficiunt. </s> <s xml:id="echoid-s5124" xml:space="preserve">porrò in partibus terræ C D. </s> <s xml:id="echoid-s5125" xml:space="preserve">non excitantur fluxus, imò ibi reflu-<lb/>xus aguntur, quia ad partes illas nullum ferè lumen, nec reflexum ſtellis, nec directum ex luminaribus, attin-<lb/>git: </s> <s xml:id="echoid-s5126" xml:space="preserve">quod ſi qui radij illuc perueniant, ij non directi, ſeu perpendiculares, qui efficaces ſunt; </s> <s xml:id="echoid-s5127" xml:space="preserve">ſed valde obliqui, <lb/>atq,<unsure/> tangentes tantummodo, qui nullius roboris ſunt, perueniunt.</s> <s xml:id="echoid-s5128" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5129" xml:space="preserve">Quando autem luminaria ſunt oppoſita, vt in plenilunio, v. </s> <s xml:id="echoid-s5130" xml:space="preserve">g. </s> <s xml:id="echoid-s5131" xml:space="preserve">ſi Luna ſit in H. </s> <s xml:id="echoid-s5132" xml:space="preserve">tunc pariter maiore vi ma-<lb/>ria percelluntur, maioreſq; </s> <s xml:id="echoid-s5133" xml:space="preserve">fl@xus ac refluxus ſequuntur, quia virtutes eorum in hoc etiam aſpectu vniuntur; <lb/></s> <s xml:id="echoid-s5134" xml:space="preserve">tunc enim Luna directè, Sol vero lumine reflexo, feriunt ad B. </s> <s xml:id="echoid-s5135" xml:space="preserve">æſ@tum vero A. </s> <s xml:id="echoid-s5136" xml:space="preserve">Luna lumine reflexo, Sol vero <lb/>directo excitant; </s> <s xml:id="echoid-s5137" xml:space="preserve">ſicq; </s> <s xml:id="echoid-s5138" xml:space="preserve">maiores hi omnes effectus redduntur. </s> <s xml:id="echoid-s5139" xml:space="preserve">exiſtentibus autem luminaribus in alio aſpectu, <lb/>vt in quadrato, vt ſi Luna eſſet in F. </s> <s xml:id="echoid-s5140" xml:space="preserve">exigui fiunt fluxus, & </s> <s xml:id="echoid-s5141" xml:space="preserve">reſluxus, quia eorum vires non ſunt vnitæ, ſed ſepa-<lb/>ratæ, quæ maria in diuerſas partes diſtrahunt.</s> <s xml:id="echoid-s5142" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5143" xml:space="preserve">Iſthæc omnia confirmantur ex fiuxu, ac refi<unsure/>uxu cuiuſdam laci apud Sinas, vt qui narrat P. </s> <s xml:id="echoid-s5144" xml:space="preserve">Nicolaus Tri-<lb/>gautius è noſtra Soc. </s> <s xml:id="echoid-s5145" xml:space="preserve">lib. </s> <s xml:id="echoid-s5146" xml:space="preserve">3. </s> <s xml:id="echoid-s5147" xml:space="preserve">cap. </s> <s xml:id="echoid-s5148" xml:space="preserve">9. </s> <s xml:id="echoid-s5149" xml:space="preserve">de Chriſtiana exped. </s> <s xml:id="echoid-s5150" xml:space="preserve">ad Sinas, in nouilunijs, ac plenilunijs tantum, fi<unsure/>uxum, <lb/>ac refluxum more maris patitur: </s> <s xml:id="echoid-s5151" xml:space="preserve">cuius viciffim ratio redditur, quia videlicet tũc temporis Luna fortius agit, <lb/>ac propterea laci illius diſpoſitiones quamuis adeò exiguæ ſint, vt alias non recipiant virtutem Lunæ, eam <lb/>tamen in plenilunijs, ac nouilunijs, cum vehementio@ eſt perſentiſcere coguntur, quibus addenda ſunt, quæ <lb/>apud P. </s> <s xml:id="echoid-s5152" xml:space="preserve">noſtrum Godignum de rebus Abaſſinorum pag. </s> <s xml:id="echoid-s5153" xml:space="preserve">69. </s> <s xml:id="echoid-s5154" xml:space="preserve">leguntu<unsure/>r: </s> <s xml:id="echoid-s5155" xml:space="preserve">expertus ſum hoc fretum (loqu@tu<unsure/>r de <lb/>Erythræo mari) ab ortu Lunæ vſque ad plenitudinem 14. </s> <s xml:id="echoid-s5156" xml:space="preserve">continuos dies fuere, & </s> <s xml:id="echoid-s5157" xml:space="preserve">dies totidem ad eiuſdem.</s> <s xml:id="echoid-s5158" xml:space="preserve"><unsure/> <lb/>Lunæ decrementum continenter refiuere: </s> <s xml:id="echoid-s5159" xml:space="preserve">vt@onge mihi falli videantui male feriati quidam Philoſophiæ <lb/>profeſſores, qui æſtus marini cauſam, aliò quam ad Lunæ motum referunt. </s> <s xml:id="echoid-s5160" xml:space="preserve">tandem notandum eſt fluxum an-<lb/>tipodum ad B. </s> <s xml:id="echoid-s5161" xml:space="preserve">eſſe altero minorem, quia efficitur à lumine reflexo Lunæ, quæ primas in hoc negotio te<unsure/>net; <lb/></s> <s xml:id="echoid-s5162" xml:space="preserve">lumen autem refl<unsure/>exum, vt docent perſpectini, debilius eſt directo vnde & </s> <s xml:id="echoid-s5163" xml:space="preserve">debilior effectus ſequi oportet. </s> <s xml:id="echoid-s5164" xml:space="preserve">por <lb/>rò non in omni mari hæc accidunt ob eorum aliquem defectum, v. </s> <s xml:id="echoid-s5165" xml:space="preserve">g. </s> <s xml:id="echoid-s5166" xml:space="preserve">quia carent quibuſdam flatibus, aut ſpi-<lb/>ritibus, qui facilè a lumine Lunę excitantur, & </s> <s xml:id="echoid-s5167" xml:space="preserve">æſtuant, quod Ariſtotiles videtur ſentire; </s> <s xml:id="echoid-s5168" xml:space="preserve">ſiue alia de cauſa no-<lb/>bis occulta. </s> <s xml:id="echoid-s5169" xml:space="preserve">Atque hæc eſt non ſolum mea de hac re ſententia circa fluxum illum ad B. </s> <s xml:id="echoid-s5170" xml:space="preserve">ſed etiam ſubciliſſimi <lb/>Scoti in primo ſententiarum, atq; </s> <s xml:id="echoid-s5171" xml:space="preserve">Rogerij Bachon soptici probatiſſimi, cap. </s> <s xml:id="echoid-s5172" xml:space="preserve">5. </s> <s xml:id="echoid-s5173" xml:space="preserve">de Speculis Mathematicis. </s> <s xml:id="echoid-s5174" xml:space="preserve"><lb/>Qua tandem virtute id Luna ef@@ciat, luminene, an calore, an influentia quappiam incompertum m@hi eſt, <lb/>munuſq; </s> <s xml:id="echoid-s5175" xml:space="preserve">Philoſophi eſt id inueſtigare.</s> <s xml:id="echoid-s5176" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5177" xml:space="preserve">Aliorum tamen commentitias opinationes, ſiue Angelo cuidam, ſiue virtuti totam terram peruadenti, <lb/>@unc æſtum aſcribentium, non eſt meum refellere, neque puto neceſſarium. </s> <s xml:id="echoid-s5178" xml:space="preserve">in hoc igitur effectu, hæc eſt ſe-<lb/>ries cauſarum, fluxus a tumore, tumor ab æſtu, æſtus a flatibus, flatus a vi Lunæ exciti, vis illa a Luna. </s> <s xml:id="echoid-s5179" xml:space="preserve">vide <lb/>Ariſt. </s> <s xml:id="echoid-s5180" xml:space="preserve">lib. </s> <s xml:id="echoid-s5181" xml:space="preserve">4. </s> <s xml:id="echoid-s5182" xml:space="preserve">de generatione anim. </s> <s xml:id="echoid-s5183" xml:space="preserve">in fine.</s> <s xml:id="echoid-s5184" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div98" type="section" level="1" n="65"> <head xml:id="echoid-head70" style="it" xml:space="preserve">De figura Maris. Cap. III.</head> <p> <s xml:id="echoid-s5185" xml:space="preserve">SVperficies Maris ſuperior, ac conuexa, ſphærica eſt: </s> <s xml:id="echoid-s5186" xml:space="preserve">quamuis non per ſe ſolam, totam ſphæram cõpleat, <lb/>ſed ſimul cum terræ ſuperficie terreſtrem ſphæram integret: </s> <s xml:id="echoid-s5187" xml:space="preserve">quod quidem probatur primo omnibus illis <lb/>rationibus, quibus etiam terræ rotunditas aſſeritur. </s> <s xml:id="echoid-s5188" xml:space="preserve">& </s> <s xml:id="echoid-s5189" xml:space="preserve">præterea peculiaribus, quarum. </s> <s xml:id="echoid-s5190" xml:space="preserve">Prima, ſit experientia <lb/>viſus, in quauis enim parte fuerimus, nũquam videmus Mare ſupra terræ ſuperficiem aſſurgere, ſed eandem <lb/>vbique ſemper faciem exhibere. </s> <s xml:id="echoid-s5191" xml:space="preserve">Secunda, ſi Mare eſſet terra altius, vt nonnulli opinantur, naues tard@us à <lb/>litore in altum nauigarent, velociuſque ab alto ad litora deſcenderet; </s> <s xml:id="echoid-s5192" xml:space="preserve">quod tamen experimento quotid@ano <lb/>repugnat. </s> <s xml:id="echoid-s5193" xml:space="preserve">Tertia, præterea cùm eſſemus in medio Mari, terram, totas turres, montes totos, conſpiceremus, <lb/>quod tamen non experimur; </s> <s xml:id="echoid-s5194" xml:space="preserve">imo contrarium accidit, nam accedentibus ad terram apparent prius montium <lb/>ac turrium ſummitates, deinde paulatim mediæ eorũ partes emergunt, & </s> <s xml:id="echoid-s5195" xml:space="preserve">ſenſim eo plures, quo magis ijs ap-<lb/>propinquamus: </s> <s xml:id="echoid-s5196" xml:space="preserve">cuius nulla alia occurrit cauſa, quam Maris rotunditas, ac proinde tumor, qu@pr@mo inter <lb/>ocuios nautarum, & </s> <s xml:id="echoid-s5197" xml:space="preserve">terras aſſurgens interponitur, & </s> <s xml:id="echoid-s5198" xml:space="preserve">poſtea paulatim à Naui ſuperatnr, ac de medio @ollitur, <lb/>@icque montes, ac turres per partes ſucceffiuè de eguntur, & </s> <s xml:id="echoid-s5199" xml:space="preserve">tandem totæ apparent. </s> <s xml:id="echoid-s5200" xml:space="preserve">Quarta, in omnibus <lb/>Maribus paſſim Inſulæ emergunt, quæ fidem faciunt Mare non eſſe terra altius, ac proinde in eundem cum <pb o="52" file="0072" n="76" rhead="De Mundi Fabrica"/> ipſa globum conformari. </s> <s xml:id="echoid-s5201" xml:space="preserve">Quinta, vbique terra, & </s> <s xml:id="echoid-s5202" xml:space="preserve">aqua, per eandem lineam perpendicularem deſcendunt, <lb/>ergo ad idem centrum, quod eſt Mundi medium, ergo etiam vnum eumdemque ſimul globum conſtituere <lb/>debent. </s> <s xml:id="echoid-s5203" xml:space="preserve">Sexta, eſt quam Ariſtoteles ſecundo de cælo affert, quæ ſumitur a liquiditate, & </s> <s xml:id="echoid-s5204" xml:space="preserve">fluiditate aquæ, <lb/>ob quam trahente ipſius grauitate, ad loca decliuiora ſemper deuoluitur; </s> <s xml:id="echoid-s5205" xml:space="preserve">quare neceſſe eſt in Mari nuli<unsure/>am <lb/>eſſe partem al era eminentiorem; </s> <s xml:id="echoid-s5206" xml:space="preserve">quia ſi eſſet ſtatim ad humiliorem deflueret partem; </s> <s xml:id="echoid-s5207" xml:space="preserve">cum igitur nulla ſit al-<lb/>tera altior, neceſſario ſequitur vt omnes eius ſupremæ partes à Mundi centro æquidiſtent, ac proinde rotun-<lb/>ditatem acquirant. </s> <s xml:id="echoid-s5208" xml:space="preserve">Hinc illud minime prætereundum deducitur, neceſſario ſcilicet omnia maria exactè eſſe <lb/>æquè alta, cùm enim omnia maria inuicem aliquatenus ſaltem coniungantur (excepto Hircano) neceſſe eſt <lb/>ſupremam eorum ſuperſiciem a centro Mundi æquidiſtare ob dictam fluiditatem, qu a ſi vnum eſſet altius <lb/>altero, altius in inferius influeret. </s> <s xml:id="echoid-s5209" xml:space="preserve">quocirca conſtat illos Seſoſtris Regis Aegypti conſiliarios hallucinatos eſ-<lb/>ſe, dum ei Aegyptiaci Iſthmi ſectionem diſſuaderent, quod dicerent Mare rubrũ altius eſſe Mari noſtro Me-<lb/>diterraneo, ac proinde fore, vt totam Græciam, ac parte Aſiæ, ſi Iſtmo perfoſſo, porta ei aperiretur, inuade-<lb/>ret, ac ſubmergeret. </s> <s xml:id="echoid-s5210" xml:space="preserve">Septimam, & </s> <s xml:id="echoid-s5211" xml:space="preserve">vltimo loco addamus ſubtiliſſimam Archimedis demonſtrationem ex li-<lb/>bro de ijs, quæ in aqua vehuntur. </s> <s xml:id="echoid-s5212" xml:space="preserve">quæ quidem pręce dentem Ariſtotelis rationem reducit ad formam Geome-<lb/>tricam: </s> <s xml:id="echoid-s5213" xml:space="preserve">ſupponit autem primo humidi eam eſſe naturam, vt partibus eius ex æquo iacentibus, & </s> <s xml:id="echoid-s5214" xml:space="preserve">inuicem con-<lb/>tinuatis, minus preſſa, a magis preſſa expellatur: </s> <s xml:id="echoid-s5215" xml:space="preserve">vna quæq; </s> <s xml:id="echoid-s5216" xml:space="preserve">aurem pars pręmitur humido ſupra ipſam exiſten-<lb/>te ad perpendiculum, ſi humidum ſit deſcendens in aliquo, aut ab aliquo alio preſſum. </s> <s xml:id="echoid-s5217" xml:space="preserve">ſecundo demonſtrat <lb/>ſequentem propoſitionem.</s> <s xml:id="echoid-s5218" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div99" type="section" level="1" n="66"> <head xml:id="echoid-head71" style="it" xml:space="preserve">Si ſuperficies aliqua plano ſecetur per idem ſemper punctum, ſitq; ſectio ſemper circuli circum-<lb/>ferentia, centrum habens punctum illud per quod planum ſecans tran-<lb/>ſit, ea Sphæræ ſuperficies erit.</head> <p> <s xml:id="echoid-s5219" xml:space="preserve">SEcetur ſuperficies aliqua B E D F. </s> <s xml:id="echoid-s5220" xml:space="preserve">plano per C. </s> <s xml:id="echoid-s5221" xml:space="preserve">punctum tran-<lb/> <anchor type="figure" xlink:label="fig-0072-01a" xlink:href="fig-0072-01"/> ſeunte, & </s> <s xml:id="echoid-s5222" xml:space="preserve">ſic ſectio ſemper circuli circumferentia, prima ſit, <lb/>v. </s> <s xml:id="echoid-s5223" xml:space="preserve">g. </s> <s xml:id="echoid-s5224" xml:space="preserve">G H I. </s> <s xml:id="echoid-s5225" xml:space="preserve">ſecunda ſit E A F. </s> <s xml:id="echoid-s5226" xml:space="preserve">& </s> <s xml:id="echoid-s5227" xml:space="preserve">ſimiliter aliæ omnes ſint circu-<lb/>li circumferentiæ. </s> <s xml:id="echoid-s5228" xml:space="preserve">Dico ſuperficiem B E D F. </s> <s xml:id="echoid-s5229" xml:space="preserve">eſſe Sphæricam, <lb/>cuius centrum C. </s> <s xml:id="echoid-s5230" xml:space="preserve">ſi enim non eſt Sphærica, rectæ quæ à C. </s> <s xml:id="echoid-s5231" xml:space="preserve">ad <lb/>eam ducuntur non erunt omnes æquales: </s> <s xml:id="echoid-s5232" xml:space="preserve">ſint igitur ſi fieri po-<lb/>teſt inæquales lineæ C A. </s> <s xml:id="echoid-s5233" xml:space="preserve">C D. </s> <s xml:id="echoid-s5234" xml:space="preserve">& </s> <s xml:id="echoid-s5235" xml:space="preserve">per ipſas C A. </s> <s xml:id="echoid-s5236" xml:space="preserve">C D. </s> <s xml:id="echoid-s5237" xml:space="preserve">planum <lb/>ducatur faciens in ea ſectionem B A D. </s> <s xml:id="echoid-s5238" xml:space="preserve">ergo ex hypotheſi ſe-<lb/>ctio illa erit circuli portio cuius centrum C. </s> <s xml:id="echoid-s5239" xml:space="preserve">ergo æquales inui-<lb/>cem ſunt C A. </s> <s xml:id="echoid-s5240" xml:space="preserve">C D. </s> <s xml:id="echoid-s5241" xml:space="preserve">atqui modo dicebantur inæquales, quod eſt <lb/>abſurdum; </s> <s xml:id="echoid-s5242" xml:space="preserve">ergo propoſita ſuperficies B E D E. </s> <s xml:id="echoid-s5243" xml:space="preserve">Sphærica eſt. </s> <s xml:id="echoid-s5244" xml:space="preserve">his <lb/>præmiſſus probat prinicipalem propoſitionem, nimirum.</s> <s xml:id="echoid-s5245" xml:space="preserve"/> </p> <div xml:id="echoid-div99" type="float" level="2" n="1"> <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a"> <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-01"/> </figure> </div> </div> <div xml:id="echoid-div101" type="section" level="1" n="67"> <head xml:id="echoid-head72" style="it" xml:space="preserve">Omnes humidi conſiſtentis, ac manentis ſuperficies ſph@@ <lb/>rica@st, cuius ſphæræ centrum eſt idem, <lb/>quod centrum terræ.</head> <p> <s xml:id="echoid-s5246" xml:space="preserve">INtelligatur humidum conſiſtens, manenſque, ſeceturque eius <lb/>ſuperſicies plano per centrum terræ K. </s> <s xml:id="echoid-s5247" xml:space="preserve">ducto, ſectio a@@em ſi@ <lb/>in ſuperſicie linea A B C D. </s> <s xml:id="echoid-s5248" xml:space="preserve">quam dico eſſe circuli peripheriam, <lb/>cuius centrum K. </s> <s xml:id="echoid-s5249" xml:space="preserve">nam ſi negetur, erunt ergo à K. </s> <s xml:id="echoid-s5250" xml:space="preserve">ad eam ductæ lineę inæquales, v. </s> <s xml:id="echoid-s5251" xml:space="preserve">g. </s> <s xml:id="echoid-s5252" xml:space="preserve">K A. </s> <s xml:id="echoid-s5253" xml:space="preserve">minor quam K C. <lb/></s> <s xml:id="echoid-s5254" xml:space="preserve">ſumatur igitur recta K B. </s> <s xml:id="echoid-s5255" xml:space="preserve">inter eas media; </s> <s xml:id="echoid-s5256" xml:space="preserve">cuius interuallo ducatur circuli portio F B H E. </s> <s xml:id="echoid-s5257" xml:space="preserve">eius igitur pars vna <lb/>erit extra circulũ A B C D. </s> <s xml:id="echoid-s5258" xml:space="preserve">pars vero altera intra. </s> <s xml:id="echoid-s5259" xml:space="preserve">iungantur rectæ F K. </s> <s xml:id="echoid-s5260" xml:space="preserve">B K. </s> <s xml:id="echoid-s5261" xml:space="preserve">C K. </s> <s xml:id="echoid-s5262" xml:space="preserve">quæ angulos ad K. </s> <s xml:id="echoid-s5263" xml:space="preserve">æqua-<lb/> <anchor type="figure" xlink:label="fig-0072-02a" xlink:href="fig-0072-02"/> les facient. </s> <s xml:id="echoid-s5264" xml:space="preserve">deſcribatur etiam circumferentia X O P. </s> <s xml:id="echoid-s5265" xml:space="preserve">in plano ſecan-<lb/>te. </s> <s xml:id="echoid-s5266" xml:space="preserve">ergo partes humidi, quæ ſunt ad circumferentiam X O P. </s> <s xml:id="echoid-s5267" xml:space="preserve">æqua-<lb/>liter iacent, ac continuatæ inuicem ſunt: </s> <s xml:id="echoid-s5268" xml:space="preserve">& </s> <s xml:id="echoid-s5269" xml:space="preserve">pręmuntur partes humi-<lb/>di quæ ſunt ſub X O. </s> <s xml:id="echoid-s5270" xml:space="preserve">humido quod loco A B X O. </s> <s xml:id="echoid-s5271" xml:space="preserve">continetur quæ <lb/>vero ſub O P. </s> <s xml:id="echoid-s5272" xml:space="preserve">premuntur humido exiſtente in B C P O. </s> <s xml:id="echoid-s5273" xml:space="preserve">inæqualiter <lb/>igitur præmuntur, magis enim premuntur partes, quæ ſub O P. </s> <s xml:id="echoid-s5274" xml:space="preserve">qua <lb/>quæ ſub O X. </s> <s xml:id="echoid-s5275" xml:space="preserve">exiſtunt, quare partes ſub X O. </s> <s xml:id="echoid-s5276" xml:space="preserve">minus preſſæ a partibus <lb/>ſub O P. </s> <s xml:id="echoid-s5277" xml:space="preserve">magis preſſis, expelluntur. </s> <s xml:id="echoid-s5278" xml:space="preserve">non ergo humidum conſiſtens <lb/>ac manens eſt, quod eſt contra hypotheſim, & </s> <s xml:id="echoid-s5279" xml:space="preserve">proinde abſurdum. <lb/></s> <s xml:id="echoid-s5280" xml:space="preserve">neceſſarium igitur eſt lineam A B C D. </s> <s xml:id="echoid-s5281" xml:space="preserve">eſſe circuli circumferẽtiam, <lb/>cuius centrum K. </s> <s xml:id="echoid-s5282" xml:space="preserve">hoc enim negato ſequitur abſurdum. </s> <s xml:id="echoid-s5283" xml:space="preserve">eodem mo-<lb/>do oſtendemus quamlibet aliam ſectionem humidi per centrum K. </s> <s xml:id="echoid-s5284" xml:space="preserve">tranſeuntem, eſſe circuli portionem, cu-<lb/>ius centrum K. </s> <s xml:id="echoid-s5285" xml:space="preserve">ex quibus per præcedentem propoſitionẽ ſequitur omnis humidi conſiſtentis, ſeu non fluen- <pb o="53" file="0073" n="77" rhead="Liber Quintus."/> tis ſuperficiem eſſe ſphæricam, cuius centrum eſt idem ac centrum terræ: </s> <s xml:id="echoid-s5286" xml:space="preserve">quod erat demonſtrandum. </s> <s xml:id="echoid-s5287" xml:space="preserve">atque <lb/>hæc de ſuperficie maris conuexa, & </s> <s xml:id="echoid-s5288" xml:space="preserve">ſuprema.</s> <s xml:id="echoid-s5289" xml:space="preserve"/> </p> <div xml:id="echoid-div101" type="float" level="2" n="1"> <figure xlink:label="fig-0072-02" xlink:href="fig-0072-02a"> <image file="0072-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-02"/> </figure> </div> <p> <s xml:id="echoid-s5290" xml:space="preserve">Quod vero attinet ad inferiorem maris ſuperficiem quæ concaua eſt, qua ſcilicet marifundum contingit, <lb/>variam admodum atque irregularem eam eſſe oportet; </s> <s xml:id="echoid-s5291" xml:space="preserve">terminatur enim a terra, quæ fundum, & </s> <s xml:id="echoid-s5292" xml:space="preserve">alueum ma-<lb/>ri præbet, quam inęqualem admodum eſſe appartet, plenam nimirum ſcopulis, inſulis, vorticibus, & </s> <s xml:id="echoid-s5293" xml:space="preserve">mo-<lb/>do altiorem, modo depreſſiorem, quare ad earumdem inequalitates, neceſſe eſt configurari maris inferio-<lb/>rem concauam ſuperficiem.</s> <s xml:id="echoid-s5294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5295" xml:space="preserve">Cum verò mare non totam terræ faciem tegat, ſed eam interruptè modo hac, modo illac inuadat, ſequi-<lb/>tur eius figuram eſſe corpus ſolidum orbiculare, ſed valde interruptum, & </s> <s xml:id="echoid-s5296" xml:space="preserve">confractum, cuius craſſities ſit ad <lb/>ſummum ſeſquimilliaris, vt ſequenti capite videbimus.</s> <s xml:id="echoid-s5297" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5298" xml:space="preserve">Ex ijs quæ de terra, & </s> <s xml:id="echoid-s5299" xml:space="preserve">aqua demonſtrata ſunt, manifeſtè conſequitur Terram, & </s> <s xml:id="echoid-s5300" xml:space="preserve">Aquam vnicum globum <lb/>conſtituere, cuius ſit idem centrum cum Mundi centro ac medio.</s> <s xml:id="echoid-s5301" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div103" type="section" level="1" n="68"> <head xml:id="echoid-head73" style="it" xml:space="preserve">De quantitate Aquæ Mariſuè. Cap. IIII.</head> <p> <s xml:id="echoid-s5302" xml:space="preserve">TRiplex in mari quantitas inueſtiganda eſt. </s> <s xml:id="echoid-s5303" xml:space="preserve">Prima eſt eius altitudo, ſeu profunditas. </s> <s xml:id="echoid-s5304" xml:space="preserve">Secunda ſuperficies <lb/>ſecundum milliaria quadrata. </s> <s xml:id="echoid-s5305" xml:space="preserve">Tertia, ſoliditas eius tota ſecundum milliaria cubica.</s> <s xml:id="echoid-s5306" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5307" xml:space="preserve">Quod igitur ad profunditatem attinet, eam exiſtimo eſſe ad ſummum vnius ſeſquimilliaris, idque paucis <lb/>in locis: </s> <s xml:id="echoid-s5308" xml:space="preserve">ordinariam verò eſſe ſemimilliaris; </s> <s xml:id="echoid-s5309" xml:space="preserve">nautæ enim noſtræ tempeſtatis, qui totum ferè Oceanum Boli. <lb/></s> <s xml:id="echoid-s5310" xml:space="preserve">de perſcrutati ſunt, vbique fundum repererunt, illudque ad ſummum, & </s> <s xml:id="echoid-s5311" xml:space="preserve">perraro ſeſqu@milliare tantum de-<lb/>ſcendere. </s> <s xml:id="echoid-s5312" xml:space="preserve">ordinarie verò, & </s> <s xml:id="echoid-s5313" xml:space="preserve">ferè vbique ad dimidij profunditatem circiter prouenire.</s> <s xml:id="echoid-s5314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5315" xml:space="preserve">Idem confirmatur ex ſententia eorum Theologorum, qui veriſimiliter valde exiſtimant, maris profundi-<lb/>tatem, & </s> <s xml:id="echoid-s5316" xml:space="preserve">montium altitudinem æquales eſſe, ſibique inuicem reſpondere; </s> <s xml:id="echoid-s5317" xml:space="preserve">vti ſuperius explicatum eſt.</s> <s xml:id="echoid-s5318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5319" xml:space="preserve">Modus autem menſurandi hanc profunditatem ordinarius eſt per Bolidem, inſtrumentum nauticum.</s> <s xml:id="echoid-s5320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5321" xml:space="preserve">Alium vero modum, & </s> <s xml:id="echoid-s5322" xml:space="preserve">quidem ſubtiliorem Leo Baptiſta Albertus nobilis Architector, in ſuo de Archi-<lb/>tectura opere excogitauit ad hanc maris profunditatem expiſcandam, qui ſic ſe habet: </s> <s xml:id="echoid-s5323" xml:space="preserve">Primo paratum ſi@ <lb/>vas aqua plenum in cuius fundo ſit exiguum foramem, per quod aqua in aliud ſubiectum vas cum oportue-<lb/>@it, effluat. </s> <s xml:id="echoid-s5324" xml:space="preserve">Secundo adſit galla, vel ſphærula ex ſubere, cui infixa ſit acus vncinata, vt in figura apparet. <lb/></s> <s xml:id="echoid-s5325" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0073-01a" xlink:href="fig-0073-01"/> Tertio habeas nonnulla corpora plumbea, quę <lb/>hãc 7. </s> <s xml:id="echoid-s5326" xml:space="preserve">ſeptenarij figuram referant, ſintque om-<lb/>nia æqualis inuicem ponderis, & </s> <s xml:id="echoid-s5327" xml:space="preserve">tanti, vt gal-<lb/>lam, vel ſuber valeant ſecum ſub mare demer-<lb/>gere, debet enim galla breuiori parti corporis <lb/>plumbei per vncinum inſeri, ſed laxè vt exire <lb/>poſtea poſſit.</s> <s xml:id="echoid-s5328" xml:space="preserve"/> </p> <div xml:id="echoid-div103" type="float" level="2" n="1"> <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a"> <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0073-01"/> </figure> </div> <p> <s xml:id="echoid-s5329" xml:space="preserve">4 Adſit tãdem mare quodpiam, cuius pro-<lb/>funditatem habeas probè per funẽ aut bolidem <lb/>exploratam, ſitque, v. </s> <s xml:id="echoid-s5330" xml:space="preserve">g. </s> <s xml:id="echoid-s5331" xml:space="preserve">paſſus 300. </s> <s xml:id="echoid-s5332" xml:space="preserve">poſt hæc <lb/>eodem temporis momento duo debes facere, <lb/>vnum eſt plumbum cum galla demergere, ita <lb/>vt ad fundum deſcendat; </s> <s xml:id="echoid-s5333" xml:space="preserve">alterum eſt aquæ fo-<lb/>ramem exiguum aperire, vt eodem tempore <lb/>fluere incipiat, quo plumbum deſcendere pari-<lb/>ter incipit. </s> <s xml:id="echoid-s5334" xml:space="preserve">interim dum effluit aqua plumbum <lb/>deſcendit, fundumq; </s> <s xml:id="echoid-s5335" xml:space="preserve">tanget parte ima B. </s> <s xml:id="echoid-s5336" xml:space="preserve">quia <lb/>altera leuior eſt propter gallã; </s> <s xml:id="echoid-s5337" xml:space="preserve">ad fundi tactum <lb/>proſternetur, ita vt angulus eius deorſum ver-<lb/>gat; </s> <s xml:id="echoid-s5338" xml:space="preserve">pars vero in qua eſt galla, ſurſum quia le-<lb/>uior eſt eleuabitur, quapropter poterit galla fa-<lb/>cile ab ea liberari, & </s> <s xml:id="echoid-s5339" xml:space="preserve">ſurſum exilire. </s> <s xml:id="echoid-s5340" xml:space="preserve">ſtatim igi-<lb/>@@@ ac videris gallam emergentem, claude vaſis foramen: </s> <s xml:id="echoid-s5341" xml:space="preserve">& </s> <s xml:id="echoid-s5342" xml:space="preserve">aquam quæ interim efluxit diligenter ponde-<lb/>ra, ſitque v. </s> <s xml:id="echoid-s5343" xml:space="preserve">g. </s> <s xml:id="echoid-s5344" xml:space="preserve">vnciarum 4. </s> <s xml:id="echoid-s5345" xml:space="preserve">eiuſque pondus vnc. </s> <s xml:id="echoid-s5346" xml:space="preserve">4. </s> <s xml:id="echoid-s5347" xml:space="preserve">necnon maris huius altitudinem paſsuum 300. </s> <s xml:id="echoid-s5348" xml:space="preserve">memoriæ, <lb/>aut ſcripto commenda. </s> <s xml:id="echoid-s5349" xml:space="preserve">hæc igitur omnia erunt veluti apparatus quidam ad cuiuſuis profundiſſimi Oceani <lb/>altitudinem perſcrutandam. </s> <s xml:id="echoid-s5350" xml:space="preserve">ſit iam igitur aliquod mare valde profundum menſurandum. </s> <s xml:id="echoid-s5351" xml:space="preserve">eo adito, eodem <lb/>tempore, & </s> <s xml:id="echoid-s5352" xml:space="preserve">aliud plumbum priori æquale cum galla demerge, & </s> <s xml:id="echoid-s5353" xml:space="preserve">ſimul aquæ fluxum reſera; </s> <s xml:id="echoid-s5354" xml:space="preserve">galla vt prius <lb/>relicto deorſum plumbo enatabit: </s> <s xml:id="echoid-s5355" xml:space="preserve">qua ſtatim conſpecta fluxum aquæ ſiſte, diligenterquè aquam interim de-<lb/>fluxam pondera ſit, v. </s> <s xml:id="echoid-s5356" xml:space="preserve">g. </s> <s xml:id="echoid-s5357" xml:space="preserve">vnc. </s> <s xml:id="echoid-s5358" xml:space="preserve">10. </s> <s xml:id="echoid-s5359" xml:space="preserve">poſtea ſic ratiocinare, vt ſe habet pondus prioris aquæ vnc. </s> <s xml:id="echoid-s5360" xml:space="preserve">4. </s> <s xml:id="echoid-s5361" xml:space="preserve">ad paſſus 300. <lb/></s> <s xml:id="echoid-s5362" xml:space="preserve">altitudinis prioris mari; </s> <s xml:id="echoid-s5363" xml:space="preserve">ita ſe debet habere pondus vnc. </s> <s xml:id="echoid-s5364" xml:space="preserve">10. </s> <s xml:id="echoid-s5365" xml:space="preserve">ad altitudinem huius maris; </s> <s xml:id="echoid-s5366" xml:space="preserve">quare per auream <lb/>trium regulam ex cognitis iam tribus analogiæ, quartus inueniri poterit hoc modo, ſi vnc. </s> <s xml:id="echoid-s5367" xml:space="preserve">4. </s> <s xml:id="echoid-s5368" xml:space="preserve">dant altitudi-<lb/>nem 300. </s> <s xml:id="echoid-s5369" xml:space="preserve">ergo vnc. </s> <s xml:id="echoid-s5370" xml:space="preserve">10 dabunt altitudinem 750. </s> <s xml:id="echoid-s5371" xml:space="preserve">igitur maris vltimi profunditas erit paſſuum 750.</s> <s xml:id="echoid-s5372" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5373" xml:space="preserve">Quod vero ad ſuperficialem eius quantitatem ſpectat, ea ex Geographia petenda eſt: </s> <s xml:id="echoid-s5374" xml:space="preserve">recentiores autem <lb/>Geographi, qui totum ferè terræ orbem in globo depingunt, ſuperficiem aquæ æqualem propè ſuperficiei <lb/>@erræ faciunt; </s> <s xml:id="echoid-s5375" xml:space="preserve">quamuis hoc exactè nondũ perſpici potuerit, ob aliquam adhuc Geographiæ imperfectionem.</s> <s xml:id="echoid-s5376" xml:space="preserve"/> </p> <pb o="54" file="0074" n="78" rhead="De Mundi Fabrica."/> <p> <s xml:id="echoid-s5377" xml:space="preserve">Cum igitur tota totius terreſtris globi ex aqua, & </s> <s xml:id="echoid-s5378" xml:space="preserve">terra conflati ſuperficies ſupra in tractatu de quantita-<lb/>te terræ innotuerit, videlicet quadrata milliaria 148,456,800. </s> <s xml:id="echoid-s5379" xml:space="preserve">ſi eius dimidium accipiatur, videlicet 74,228, <lb/>400. </s> <s xml:id="echoid-s5380" xml:space="preserve">id erit marinæ ſuperficiei in quadratis milliaribus quantitas. </s> <s xml:id="echoid-s5381" xml:space="preserve">antiqui vero ſcriptores omnes, etiam Geo-<lb/>graphi, hanc maris ſuperficiem multo quam terræ maiorem opinantur, verum id eis ob magnam veteri@ <lb/>Geographiæ imperfectionem condonandum eſt; </s> <s xml:id="echoid-s5382" xml:space="preserve">tunc enim vix quarta pars terreni huius globi Geographi@ <lb/>perſpecta erat.</s> <s xml:id="echoid-s5383" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5384" xml:space="preserve">Tandem maris ſoliditatem metiri conuenit. </s> <s xml:id="echoid-s5385" xml:space="preserve">cum igitur oſtenſum ſit ſuperficiem eius continere quadrata <lb/>milliaria 74,228,400. </s> <s xml:id="echoid-s5386" xml:space="preserve">conſtet etiam eius profunditatem rarò maiorem eſſe v@o milliari, ſed vbique ferè eſſe <lb/>ſemimilliariam, ponamus tamen, vt ſic etiam omnium paludum, lacu@m, ac fluminum aquas compute-<lb/>mus, eam eſſe vbique milliariam: </s> <s xml:id="echoid-s5387" xml:space="preserve">hoc enim poſito manifeſtum ſtatim fit maris ſoliditatem continere mil-<lb/>liaria cubica totidem, videlicet 74,228,400. </s> <s xml:id="echoid-s5388" xml:space="preserve">quodlibet enim milliare ſuperficiale continet ſub ſe vnum fe-<lb/>re milliare cubicum.</s> <s xml:id="echoid-s5389" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div105" type="section" level="1" n="69"> <head xml:id="echoid-head74" style="it" xml:space="preserve">Conſectarium.</head> <p> <s xml:id="echoid-s5390" xml:space="preserve">EX demonſtratis facilè innoteſcit proportio terræ, & </s> <s xml:id="echoid-s5391" xml:space="preserve">aquæ.</s> <s xml:id="echoid-s5392" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5393" xml:space="preserve">Terra enim continet milliaria cubica 170,232,521,600.</s> <s xml:id="echoid-s5394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5395" xml:space="preserve">Aqua continet milliaria cubica 170,228,400.</s> <s xml:id="echoid-s5396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5397" xml:space="preserve">Horum numerorum ratio eſt ſicuti ferè 2,290. </s> <s xml:id="echoid-s5398" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s5399" xml:space="preserve">vt patet diuidendo maiorem per minorem, dixi fere o <lb/>fractionem in quotic<unsure/>nte ommiſſam. </s> <s xml:id="echoid-s5400" xml:space="preserve">Terra igitur totius continet aquam, quoties numerus 2,290. </s> <s xml:id="echoid-s5401" xml:space="preserve">contine@ <lb/>vnitatem.</s> <s xml:id="echoid-s5402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5403" xml:space="preserve">De Maris illuminatione, & </s> <s xml:id="echoid-s5404" xml:space="preserve">vmbra nihil ſupereſt dicendum, præter id, quod dictum eſt de illuminatio-<lb/>ne, & </s> <s xml:id="echoid-s5405" xml:space="preserve">vmbra totius terreni globi, quem integrat ſimul cum terra, ac proinde ſimul ad eiuſdem globiillu-<lb/>minationem, & </s> <s xml:id="echoid-s5406" xml:space="preserve">vmbram concurrit.</s> <s xml:id="echoid-s5407" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div106" type="section" level="1" n="70"> <head xml:id="echoid-head75" xml:space="preserve">LIBER SEXTVS <lb/>DE AERE.</head> <head xml:id="echoid-head76" style="it" xml:space="preserve">De loco Aeris. Cap. I.</head> <p> <s xml:id="echoid-s5408" xml:space="preserve">SEnſu manifeſtum eſt aerem proximè terrenum globum, ex aqua, & </s> <s xml:id="echoid-s5409" xml:space="preserve">terra conſtantem <lb/> <anchor type="figure" xlink:label="fig-0074-01a" xlink:href="fig-0074-01"/> circumfundi, eumque complecti. </s> <s xml:id="echoid-s5410" xml:space="preserve">qui locus ei iure naturæ debetur, cum ſit terra, & </s> <s xml:id="echoid-s5411" xml:space="preserve"><lb/>aqua leuior, vt patet in bullis aeris ſurſum in aqua aſcendentibus, de quibus ſequenti cap. <lb/></s> <s xml:id="echoid-s5412" xml:space="preserve">dicitur; </s> <s xml:id="echoid-s5413" xml:space="preserve">quare cum aer ſit illis leuior, conſequens eſt etiam altiorem locum, quam illis con-<lb/>uenire.</s> <s xml:id="echoid-s5414" xml:space="preserve"/> </p> <div xml:id="echoid-div106" type="float" level="2" n="1"> <figure xlink:label="fig-0074-01" xlink:href="fig-0074-01a"> <image file="0074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0074-01"/> </figure> </div> <p> <s xml:id="echoid-s5415" xml:space="preserve">Pulchrè autem mutuus hic aquæ, & </s> <s xml:id="echoid-s5416" xml:space="preserve">aeris aſcenſus, & </s> <s xml:id="echoid-s5417" xml:space="preserve">deſcenuſs cernitur in vitrea quadam <lb/>ampulla vndique clauſa, cuius collum ſit oblungum, & </s> <s xml:id="echoid-s5418" xml:space="preserve">gracile, in qua aer, & </s> <s xml:id="echoid-s5419" xml:space="preserve">aqua ſimul <lb/>ſint occluſa: </s> <s xml:id="echoid-s5420" xml:space="preserve">figuram eius aſpice, aqua ſit A B C @eliquum aer occupet, ne vacuum ſit; </s> <s xml:id="echoid-s5421" xml:space="preserve">iam <lb/>ſi inuertatur, vt pars A B C. </s> <s xml:id="echoid-s5422" xml:space="preserve">ſurſum, collum vero deorſum vergat, illico videre eſt aquam <lb/>per latera fiſtulæ deſcendere, aerem vero contra eodem tempore per medium aquæ, & </s> <s xml:id="echoid-s5423" xml:space="preserve">fiſtu-<lb/>læ, ideſt, vndique aqua circundatum, aſcendere.</s> <s xml:id="echoid-s5424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div108" type="section" level="1" n="71"> <head xml:id="echoid-head77" style="it" xml:space="preserve">De motu Aeris. Cap. II.</head> <p> <s xml:id="echoid-s5425" xml:space="preserve">1 AEr natura ſua mouetur motu recto ſurſum, qui aſcenſus dicitur, vt patet in bullis aeris infra aquam <lb/>aliquando vi illatis, quæ ſl<unsure/>atim ac libertate donantur ſurſum celeriter, ac directè petunt; </s> <s xml:id="echoid-s5426" xml:space="preserve">vt etiam ſu-<lb/>perius explicatum eſt in loco aquæ.</s> <s xml:id="echoid-s5427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5428" xml:space="preserve">2 Par eſt credere aerem diurno motu aliquatenus circumuolui præſertim ſub torrida zona; </s> <s xml:id="echoid-s5429" xml:space="preserve">ſi enim ve-<lb/>rum eſt Oceanum eodem motu promoueri, multo magis verum erit aerem, qui fluidior eſt quam aqua, non <lb/>ſolum moueri verum etiam velocius, quod conſirmat loan. </s> <s xml:id="echoid-s5430" xml:space="preserve">Baptiſ@a Porta, de aeris tranſm. </s> <s xml:id="echoid-s5431" xml:space="preserve">quia aſſerit hunc <lb/>motum ab experientijs nautarum, qui auxilio huius motus aeris, ſeu venti, citius nauigant verſus occidentẽ <lb/>quam verſus orientem. </s> <s xml:id="echoid-s5432" xml:space="preserve">Nonnulli ex diurno Cometarum motu, quos in ſupremo aere collocabant, hunc <lb/>acris motum rectè colligi opinabantur; </s> <s xml:id="echoid-s5433" xml:space="preserve">verum Cometas multo altius incedere poſtea compertum eſt, vt ſuo <lb/>loco videbimus, & </s> <s xml:id="echoid-s5434" xml:space="preserve">in opere de locis Mathematicis apud Ariſt. </s> <s xml:id="echoid-s5435" xml:space="preserve">iam explicauimus.</s> <s xml:id="echoid-s5436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5437" xml:space="preserve">3 Ineſt alius aeri motus, quo idem aer aliquando minor, aliquando maior euadit, ſeu ſuam auget, & </s> <s xml:id="echoid-s5438" xml:space="preserve"><lb/>minuit magnitudinem, idque nullo extrinſecus additamento; </s> <s xml:id="echoid-s5439" xml:space="preserve">hunc phyſici rarefactionem, & </s> <s xml:id="echoid-s5440" xml:space="preserve">condenſ<unsure/>a-<lb/>tionem appellant. </s> <s xml:id="echoid-s5441" xml:space="preserve">quod etſi multis conſtet experientijs, libet tamen pulcherrimam nunc æque ac euiden-<lb/>tiſſimam afferre: </s> <s xml:id="echoid-s5442" xml:space="preserve">conſtruatur, vitrea ampulla, vti in figura vides; </s> <s xml:id="echoid-s5443" xml:space="preserve">cuius venter B. </s> <s xml:id="echoid-s5444" xml:space="preserve">collum vero E A. </s> <s xml:id="echoid-s5445" xml:space="preserve">ſit gra- <pb o="55" file="0075" n="79" rhead="Liber Sextus."/> ciliſſima fiſi<unsure/>ula: </s> <s xml:id="echoid-s5446" xml:space="preserve">in hac igitur ampulla nihil ſit præter @@rem, in parte tamen inferiori A C. </s> <s xml:id="echoid-s5447" xml:space="preserve">ſit <lb/> <anchor type="figure" xlink:label="fig-0075-01a" xlink:href="fig-0075-01"/> aqua colore aliquo ſatis perſpicuo tincta, quæ ex ſuppoſito vaſe D. </s> <s xml:id="echoid-s5448" xml:space="preserve">ſurſum aſcendat, ac deſcen-<lb/>dat. </s> <s xml:id="echoid-s5449" xml:space="preserve">Iam ſi prædictæ ampullæ capiti B. </s> <s xml:id="echoid-s5450" xml:space="preserve">manum aut digitum admoueris, illico videbis aquam <lb/>A C. </s> <s xml:id="echoid-s5451" xml:space="preserve">deſcendere: </s> <s xml:id="echoid-s5452" xml:space="preserve">cauſa eſt calor manus, quo aer incluſus citiſſime rareſcit, ſitque maior, ac pro-<lb/>inde dilatatur per ſiſt<unsure/>ulam E C. </s> <s xml:id="echoid-s5453" xml:space="preserve">ſicque aquam deorſum pellit. </s> <s xml:id="echoid-s5454" xml:space="preserve">quod ſi ampullę aliquod frigid@m <lb/>admoueris, aer incluſus ſtatim condenſabitur, ac ſeſe contrahet, ac propcerea ne vacuum exi-<lb/>ſtat, aqua A C. </s> <s xml:id="echoid-s5455" xml:space="preserve">aeris receſſum ſupplens, ſurſum aſcendet. </s> <s xml:id="echoid-s5456" xml:space="preserve">auxilio huius inſtrumenti, quod c<unsure/>go <lb/>Thermoſcopium libenter appellarem, multa ad aeris naturam ſpectantia, in d<unsure/>agari poſſunt. </s> <s xml:id="echoid-s5457" xml:space="preserve">au-<lb/>diui Doctorem quendam Medicum@ Patauij degentem, qui Santorius cognominatur huius eſi<unsure/>e <lb/>inuentorem.</s> <s xml:id="echoid-s5458" xml:space="preserve"/> </p> <div xml:id="echoid-div108" type="float" level="2" n="1"> <figure xlink:label="fig-0075-01" xlink:href="fig-0075-01a"> <image file="0075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0075-01"/> </figure> </div> <p> <s xml:id="echoid-s5459" xml:space="preserve">4 Ventorum agitatio nihil Aſtronomicum ſapit, ideo Philoſophicis diſquifitionibus reli-<lb/>quanda eſt.</s> <s xml:id="echoid-s5460" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div110" type="section" level="1" n="72"> <head xml:id="echoid-head78" style="it" xml:space="preserve">De Aeris figura. Cap. III.</head> <p> <s xml:id="echoid-s5461" xml:space="preserve">IAm dictum ſuperius eſt in quo ſphæra, & </s> <s xml:id="echoid-s5462" xml:space="preserve">orbis diſcrepent; </s> <s xml:id="echoid-s5463" xml:space="preserve">quod nunc in memoriam reuocan-<lb/>dum eſt. </s> <s xml:id="echoid-s5464" xml:space="preserve">Aio igitur aerem orbis figuræ præditum eſſe: </s> <s xml:id="echoid-s5465" xml:space="preserve">cum enim circa terrenum globum ef-<lb/>fuſus ſit, eumque vndique ambiat, neceſſario concauam ſuperſiciem habebit, eamque ſphæricam <lb/>iuxta ſphæricitatem terreni globi, circa quem configuratur. </s> <s xml:id="echoid-s5466" xml:space="preserve">pariter eum habere ſuperficiem ſu-<lb/>premam, & </s> <s xml:id="echoid-s5467" xml:space="preserve">conuexam, quæ ſphærica ſit, inde collig@ poteſt, quia aer cum ſit fl@@dus, ac leuis, & </s> <s xml:id="echoid-s5468" xml:space="preserve"><lb/>proinde ſurſum ad omnes partes æqualiter aſcendat, neceſſario in ſphæricam figuram deſinit, <lb/>quia à centro Mundiæqualiter vndique aſcendens recedit: </s> <s xml:id="echoid-s5469" xml:space="preserve">ſicuti enim è contrario aqua quia <lb/>fluida eſt, & </s> <s xml:id="echoid-s5470" xml:space="preserve">grauis deſcendendo ſphæricitatem acquirit, ita etiam aerem, quia fluidus, & </s> <s xml:id="echoid-s5471" xml:space="preserve">leuis <lb/>eſt, par eſt ſphæricitatem aſcendendo conſequi.</s> <s xml:id="echoid-s5472" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div111" type="section" level="1" n="73"> <head xml:id="echoid-head79" style="it" xml:space="preserve">De Aeris illuminatione. Cap. IIII.</head> <p> <s xml:id="echoid-s5473" xml:space="preserve">AEr purus, ideſt, abſque vlla exhalatione, aut vapore eſt omnino diaphanus, & </s> <s xml:id="echoid-s5474" xml:space="preserve">tranſparens, <lb/>quare lumen Solis nullo modo ſiſtit, ſed illud præterire permittit: </s> <s xml:id="echoid-s5475" xml:space="preserve">vnde ſequitur eum nullo <lb/>modo, quamuis toto lumine profundatur, fieri conſpicuum, ſeu videri poſſe.</s> <s xml:id="echoid-s5476" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5477" xml:space="preserve">Aer vero impurus qui terræ proximior eſt, ob terreſtres halitus, qui ei perpetuo admiſcentur, <lb/>impurior ac craſſior euadit, vnde aptè Atmoſphæra, ideſt, halituum ſphæra nominatur; </s> <s xml:id="echoid-s5478" xml:space="preserve">hæc in-<lb/>quam Atmoſphæra, cum imperfectè tranſpareat, abundetque prædictis halitibus, quæ opacita-<lb/>tem aliquam illi inferunt, fit vt lumen Solis per ipſam diffuſum, partim tranſmittat, partim de-<lb/>tineat ac reſi<unsure/>ectat, eoque illuſtretur, ac proinde reddatur conſpicuus, lucemque Solis, quæ diem <lb/>efficit, vniuerſæ terræ communicet. </s> <s xml:id="echoid-s5479" xml:space="preserve">imo crepuiculum, quod d ei initiũ eſt, nihil aliud eſt quam <lb/>huiuſmodi halitus in extremo, orientalique horizonte illuminati, vt ſequenti cap. </s> <s xml:id="echoid-s5480" xml:space="preserve">patebit. </s> <s xml:id="echoid-s5481" xml:space="preserve">quæ ex opticorũ <lb/>doctrina deſumpta ſunt.</s> <s xml:id="echoid-s5482" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div112" type="section" level="1" n="74"> <head xml:id="echoid-head80" style="it" xml:space="preserve">De Aeris quantitate. Cap. V.</head> <p> <s xml:id="echoid-s5483" xml:space="preserve">ALhazenus vir Arabs acutiſſime ex crepuſcu <lb/> <anchor type="figure" xlink:label="fig-0075-02a" xlink:href="fig-0075-02"/> lorum contemplatione aeris, ſeu potius At-<lb/>moſphæræ altitudinem rimatus eſt. </s> <s xml:id="echoid-s5484" xml:space="preserve">crepuſcu-<lb/>lum autem eſt lux illa crepera, ſeu dubia, quę an-<lb/>te Solis ortum, & </s> <s xml:id="echoid-s5485" xml:space="preserve">poſt Solis occaſum, videtur: </s> <s xml:id="echoid-s5486" xml:space="preserve">il-<lb/>lud matutinum, iſtud veſpertinum appellatur. <lb/></s> <s xml:id="echoid-s5487" xml:space="preserve">Cauſa autem crepuſculi hæc eſt; </s> <s xml:id="echoid-s5488" xml:space="preserve">circa terram <lb/>eleuantur variæ euaporationes, quæ ſola in aere <lb/>ſpectantur, aer enim purus, vt ante dictum eſt, <lb/>videri nequit. </s> <s xml:id="echoid-s5489" xml:space="preserve">quapropter prima illa lux ſubal-<lb/>bida, quam initio crepuſculi videmus, quamque <lb/>Albam vulgo, & </s> <s xml:id="echoid-s5490" xml:space="preserve">paulò poſt Aurorã nuncupant, <lb/>nihil eſt aliud, quam halitus illi qui ſunt in no-<lb/>ſtri horizontis phyſici, & </s> <s xml:id="echoid-s5491" xml:space="preserve">orientalis ex tremita-<lb/>te, quos primum radij Solis attingunt, & </s> <s xml:id="echoid-s5492" xml:space="preserve">illumi-<lb/>nant, ac proinde à nobis videri poſſunt. </s> <s xml:id="echoid-s5493" xml:space="preserve">quæ vt <lb/>planius percipiantur, ſit ſequens figura, in qua <lb/>circulus F E G. </s> <s xml:id="echoid-s5494" xml:space="preserve">ſit terra, circulus vero M X N. </s> <s xml:id="echoid-s5495" xml:space="preserve"><lb/>tranſeat per ſummas vaporum altitudines, ho-<lb/>rizõ phyſicus Q F R. </s> <s xml:id="echoid-s5496" xml:space="preserve">aſtronomicus O H P. </s> <s xml:id="echoid-s5497" xml:space="preserve">ocu-<lb/>lus igitur erit in F. </s> <s xml:id="echoid-s5498" xml:space="preserve">medio horizõtis phyſici. </s> <s xml:id="echoid-s5499" xml:space="preserve">cir-<lb/>culus autem maior O S P A. </s> <s xml:id="echoid-s5500" xml:space="preserve">ſit verticalis circu-<lb/>lus tranſiens per verticem S. </s> <s xml:id="echoid-s5501" xml:space="preserve">& </s> <s xml:id="echoid-s5502" xml:space="preserve">Solem D. </s> <s xml:id="echoid-s5503" xml:space="preserve">radius <lb/>Solis incipiens illuſtrare extremos noſtri hori- <pb o="56" file="0076" n="80" rhead="De Mundi Fabrica."/> zontis halitus, qui ſunt apud K. </s> <s xml:id="echoid-s5504" xml:space="preserve">ſit C I V. </s> <s xml:id="echoid-s5505" xml:space="preserve">qui terram tangat in I. </s> <s xml:id="echoid-s5506" xml:space="preserve">iam ſic diſcurrendum eſt, noctu ante c<unsure/>repu-<lb/>ſculum vapores, qui ſunt ſupra horizontem F K. </s> <s xml:id="echoid-s5507" xml:space="preserve">non videbantur quia nondum illuſtrabantur, primus enim <lb/>radius C I K. </s> <s xml:id="echoid-s5508" xml:space="preserve">non prouenerat nec ad I. </s> <s xml:id="echoid-s5509" xml:space="preserve">nec ad K. </s> <s xml:id="echoid-s5510" xml:space="preserve">ſed infra I. </s> <s xml:id="echoid-s5511" xml:space="preserve">tangebat terram; </s> <s xml:id="echoid-s5512" xml:space="preserve">& </s> <s xml:id="echoid-s5513" xml:space="preserve">vltra K. </s> <s xml:id="echoid-s5514" xml:space="preserve">per aerem purum <lb/>extendebatur. </s> <s xml:id="echoid-s5515" xml:space="preserve">nihil etiam videbatur vltra punctu@ K. </s> <s xml:id="echoid-s5516" xml:space="preserve">quamuis ibi radij Solis plures excurrerent, ob aeris <lb/>meram diaphaneitatem, quæ nullam efficit viſionem. </s> <s xml:id="echoid-s5517" xml:space="preserve">tunc igitur tantum neceſſario incipimus aliquid in ho-<lb/>rizonte videre, cum radius primus C I K. </s> <s xml:id="echoid-s5518" xml:space="preserve">ad punctum K. </s> <s xml:id="echoid-s5519" xml:space="preserve">vbi ſunt extremi vapores, & </s> <s xml:id="echoid-s5520" xml:space="preserve">vbi circumferentia@ <lb/>Atmoſphæræ ſecatur ab horizonte phyſico F K. </s> <s xml:id="echoid-s5521" xml:space="preserve">quæ prima viſio dicitur crepuſculum.</s> <s xml:id="echoid-s5522" xml:space="preserve"/> </p> <div xml:id="echoid-div112" type="float" level="2" n="1"> <figure xlink:label="fig-0075-02" xlink:href="fig-0075-02a"> <image file="0075-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0075-02"/> </figure> </div> <p> <s xml:id="echoid-s5523" xml:space="preserve">Notandum poſtea ex Aſtro<unsure/>nomorum obſeruationibus, in initio crepuſculi, Solem eſſe infrà Aſtronomi-<lb/>cum horizontem gr. </s> <s xml:id="echoid-s5524" xml:space="preserve">18. </s> <s xml:id="echoid-s5525" xml:space="preserve">in circulo verticali O S P D. </s> <s xml:id="echoid-s5526" xml:space="preserve">vel in arcu terræ G T. </s> <s xml:id="echoid-s5527" xml:space="preserve">v. </s> <s xml:id="echoid-s5528" xml:space="preserve">g. </s> <s xml:id="echoid-s5529" xml:space="preserve">ſi arcus P D. </s> <s xml:id="echoid-s5530" xml:space="preserve">fuerit gr. </s> <s xml:id="echoid-s5531" xml:space="preserve">18. </s> <s xml:id="echoid-s5532" xml:space="preserve">tũc <lb/>incipit crepuſculũ. </s> <s xml:id="echoid-s5533" xml:space="preserve">vltimo notandum Solem illuminare pluſquam terrę dimidium, vt in cap. </s> <s xml:id="echoid-s5534" xml:space="preserve">de terræ illumi-<lb/>natione oſtenſum eſt; </s> <s xml:id="echoid-s5535" xml:space="preserve">illuminat enim vltra gr. </s> <s xml:id="echoid-s5536" xml:space="preserve">180. </s> <s xml:id="echoid-s5537" xml:space="preserve">etiam min. </s> <s xml:id="echoid-s5538" xml:space="preserve">28. </s> <s xml:id="echoid-s5539" xml:space="preserve">cuius dimidium eſt gr. </s> <s xml:id="echoid-s5540" xml:space="preserve">90. </s> <s xml:id="echoid-s5541" xml:space="preserve">m<unsure/>n. </s> <s xml:id="echoid-s5542" xml:space="preserve">14. </s> <s xml:id="echoid-s5543" xml:space="preserve">& </s> <s xml:id="echoid-s5544" xml:space="preserve">repræ-<lb/>ſentatur in arcu T I. </s> <s xml:id="echoid-s5545" xml:space="preserve">intelligantur etiam lineæ H F X F. </s> <s xml:id="echoid-s5546" xml:space="preserve">H L K. </s> <s xml:id="echoid-s5547" xml:space="preserve">H I. </s> <s xml:id="echoid-s5548" xml:space="preserve">H C. </s> <s xml:id="echoid-s5549" xml:space="preserve">propoſitum eſt igitur inueſtiga-<lb/>re quantitatem lineæ L K. </s> <s xml:id="echoid-s5550" xml:space="preserve">hæc enim eſt maxima halituum altitudo: </s> <s xml:id="echoid-s5551" xml:space="preserve">arcus itaque F G. </s> <s xml:id="echoid-s5552" xml:space="preserve">eſt quadrans, ſcilice@ <lb/>gr. </s> <s xml:id="echoid-s5553" xml:space="preserve">90. </s> <s xml:id="echoid-s5554" xml:space="preserve">arcus veto G T. </s> <s xml:id="echoid-s5555" xml:space="preserve">eſt gr. </s> <s xml:id="echoid-s5556" xml:space="preserve">18. </s> <s xml:id="echoid-s5557" xml:space="preserve">tot enim gradibus Sol in crepuſcu@i initio infra horizontem O H P. </s> <s xml:id="echoid-s5558" xml:space="preserve">depri-<lb/>mitur: </s> <s xml:id="echoid-s5559" xml:space="preserve">qui arcus tot gradus continet, quot etiam ſunt in arcu P D. </s> <s xml:id="echoid-s5560" xml:space="preserve">ex prima propoſitione appar. </s> <s xml:id="echoid-s5561" xml:space="preserve">totus igitur <lb/>arcus F I T. </s> <s xml:id="echoid-s5562" xml:space="preserve">eſt gr. </s> <s xml:id="echoid-s5563" xml:space="preserve">108. </s> <s xml:id="echoid-s5564" xml:space="preserve">à quo ſi dematur, arcus T I. </s> <s xml:id="echoid-s5565" xml:space="preserve">quem diximus eſſe gr. </s> <s xml:id="echoid-s5566" xml:space="preserve">90. </s> <s xml:id="echoid-s5567" xml:space="preserve">14′. </s> <s xml:id="echoid-s5568" xml:space="preserve">remanet arcus F I. </s> <s xml:id="echoid-s5569" xml:space="preserve">gr. </s> <s xml:id="echoid-s5570" xml:space="preserve">17. </s> <s xml:id="echoid-s5571" xml:space="preserve">46′. <lb/></s> <s xml:id="echoid-s5572" xml:space="preserve">cuius dimidium eſt arcus F L. </s> <s xml:id="echoid-s5573" xml:space="preserve">eritq; </s> <s xml:id="echoid-s5574" xml:space="preserve">gr. </s> <s xml:id="echoid-s5575" xml:space="preserve">8. </s> <s xml:id="echoid-s5576" xml:space="preserve">53′. </s> <s xml:id="echoid-s5577" xml:space="preserve">quare etiam angulus F H L. </s> <s xml:id="echoid-s5578" xml:space="preserve">quem ſubtendit, erit eorumdem. </s> <s xml:id="echoid-s5579" xml:space="preserve"><lb/>gr. </s> <s xml:id="echoid-s5580" xml:space="preserve">8. </s> <s xml:id="echoid-s5581" xml:space="preserve">53′. </s> <s xml:id="echoid-s5582" xml:space="preserve">ſicq; </s> <s xml:id="echoid-s5583" xml:space="preserve">in triangulo F H K. </s> <s xml:id="echoid-s5584" xml:space="preserve">iam duo anguli ſunt noti, cum angulus H F K. </s> <s xml:id="echoid-s5585" xml:space="preserve">ſit rectus, notum etiam eſt <lb/>latus H F. </s> <s xml:id="echoid-s5586" xml:space="preserve">cũ ſit terræ ſemidiameter, quam ſupra in milliarijs metiti ſumus: </s> <s xml:id="echoid-s5587" xml:space="preserve">quare per 5. </s> <s xml:id="echoid-s5588" xml:space="preserve">& </s> <s xml:id="echoid-s5589" xml:space="preserve">6. </s> <s xml:id="echoid-s5590" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s5591" xml:space="preserve">Appar. </s> <s xml:id="echoid-s5592" xml:space="preserve"><lb/>veniemus in cognitionem reliqui lateris H K. </s> <s xml:id="echoid-s5593" xml:space="preserve">eumque reperiemus milliariorum ferè 3′479. </s> <s xml:id="echoid-s5594" xml:space="preserve">iuxta noſtram@ <lb/>terrenæ ſemidiametri menſuram. </s> <s xml:id="echoid-s5595" xml:space="preserve">iam ex linea H K. </s> <s xml:id="echoid-s5596" xml:space="preserve">detracta terræ ſemidiametro H L. </s> <s xml:id="echoid-s5597" xml:space="preserve">quæ eſt 3,426. </s> <s xml:id="echoid-s5598" xml:space="preserve">rema-<lb/>net L K. </s> <s xml:id="echoid-s5599" xml:space="preserve">milliaria 43. </s> <s xml:id="echoid-s5600" xml:space="preserve">ferè. </s> <s xml:id="echoid-s5601" xml:space="preserve">alij aliam quantitatem reperiunt, vt Alhazenus, qui eam reperit 52. </s> <s xml:id="echoid-s5602" xml:space="preserve">quod oritur <lb/>ex varia ſuppoſitione diametrorum Solis, & </s> <s xml:id="echoid-s5603" xml:space="preserve">terræ, & </s> <s xml:id="echoid-s5604" xml:space="preserve">diſtantia eorum, necnon depreſſionis Solis infra hori-<lb/>zontem initio crepuſculi. </s> <s xml:id="echoid-s5605" xml:space="preserve">Cæterum cum ex communi Philoſophorum ſententia veriſimile ſit aeream re-<lb/>gionem, eam eſſe tantummodo in qua euaporationes, & </s> <s xml:id="echoid-s5606" xml:space="preserve">halitus, vel ſubtiliſſimi, ex terreſtri globo aſcenden-<lb/>tes ſpatiantur (non enim ratio vlla apparet cur non altius aſcendant, ſi altius aer attollatur) videretur iuxta <lb/>hanc opinionem Elemẽtum aeris attolli tantummodo milliaria 43. </s> <s xml:id="echoid-s5607" xml:space="preserve">vel ſi dixerimus aerem adhuc altius eue-<lb/>@i, ſaltem manifeſtè oſtenſum erit Atmoſphæræ altitudinem circa terram eſſe prædicta milliaria 43. </s> <s xml:id="echoid-s5608" xml:space="preserve">circi-<lb/>ter; </s> <s xml:id="echoid-s5609" xml:space="preserve">ita vt tanto interuallo à<unsure/> terra fit aeris, aut Atmoſphæræ ſuprema, & </s> <s xml:id="echoid-s5610" xml:space="preserve">conuexa ſuperficies. </s> <s xml:id="echoid-s5611" xml:space="preserve">ex hac altitu-<lb/>dine facile eſt totius aeris ſoliditatem rudi ſaltem Minerua colligere ſecundum milliaria cubica; </s> <s xml:id="echoid-s5612" xml:space="preserve">hac ratio-<lb/>ne, aqua tota vt viſum eſt, ad totam terram habet eam rationem, quam 1. </s> <s xml:id="echoid-s5613" xml:space="preserve">ad 2,290. </s> <s xml:id="echoid-s5614" xml:space="preserve">& </s> <s xml:id="echoid-s5615" xml:space="preserve">tamen dimidium tantũ <lb/>ſuperſiciei terræ cooperit, ſi igitur totam terram cooperiret, haberet rationem ad terram, quam 2. </s> <s xml:id="echoid-s5616" xml:space="preserve">ad 2 ′290. </s> <s xml:id="echoid-s5617" xml:space="preserve"><lb/>quia vero aer eſt altior quam aqua quadragies, & </s> <s xml:id="echoid-s5618" xml:space="preserve">ter, erit etiã tota ipſius corporeitas, quadragies, & </s> <s xml:id="echoid-s5619" xml:space="preserve">ter ma-<lb/>ior, quam eſſet aqua, quæ totam terram occuparet in altitudine vnius milliarij; </s> <s xml:id="echoid-s5620" xml:space="preserve">atqui talis aqua eſſet ad terrã <lb/>vt 2. </s> <s xml:id="echoid-s5621" xml:space="preserve">ad 2,290. </s> <s xml:id="echoid-s5622" xml:space="preserve">ergo aer qui eſt ad talem aquam vt 42. </s> <s xml:id="echoid-s5623" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s5624" xml:space="preserve">erit ad veram aquam vt 86. </s> <s xml:id="echoid-s5625" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s5626" xml:space="preserve">ad terram verò vt <lb/>86. </s> <s xml:id="echoid-s5627" xml:space="preserve">ad 2,299<unsure/>. </s> <s xml:id="echoid-s5628" xml:space="preserve">ſeu ferè 1. </s> <s xml:id="echoid-s5629" xml:space="preserve">ad 27.</s> <s xml:id="echoid-s5630" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5631" xml:space="preserve">Aliter ſuperficies @otius globi terrenæ habet milliaria quadrata 148′456′800. </s> <s xml:id="echoid-s5632" xml:space="preserve">hunc <lb/> <anchor type="note" xlink:label="note-0076-01a" xlink:href="note-0076-01"/> numerum multiplica per 43. </s> <s xml:id="echoid-s5633" xml:space="preserve">altitudinem aeris, & </s> <s xml:id="echoid-s5634" xml:space="preserve">producentur milliaria cubica to-<lb/>tius aeris, ſed vero pauciora, quia altio<unsure/>ra magis ampliantur, & </s> <s xml:id="echoid-s5635" xml:space="preserve">fiunt maiora, quo al-<lb/>tiora. </s> <s xml:id="echoid-s5636" xml:space="preserve">numerus autem productus eſt 6,373,642,400. </s> <s xml:id="echoid-s5637" xml:space="preserve">qui ad numerum cuborum totius <lb/>terrenæ ſoliditatis habet rationem quam 1. </s> <s xml:id="echoid-s5638" xml:space="preserve">ad 27. </s> <s xml:id="echoid-s5639" xml:space="preserve">quare terreſtris globus continet totam Atmoſphæram@ <lb/>vicies, & </s> <s xml:id="echoid-s5640" xml:space="preserve">ſepties. </s> <s xml:id="echoid-s5641" xml:space="preserve">tantus igitur eſt aer.</s> <s xml:id="echoid-s5642" xml:space="preserve"/> </p> <div xml:id="echoid-div113" type="float" level="2" n="2"> <note position="right" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve"> <lb/>Terra # 2,290. <lb/>Aqua # 1. <lb/>Aer # 86. <lb/></note> </div> </div> <div xml:id="echoid-div115" type="section" level="1" n="75"> <head xml:id="echoid-head81" xml:space="preserve">LIBER SEPTIMVS</head> <head xml:id="echoid-head82" xml:space="preserve">De Æthere ſeu mauis putato Igne.</head> <p> <s xml:id="echoid-s5643" xml:space="preserve">EA mundi pars quæ inter aerem vel Atmoſphæram, cælumq; </s> <s xml:id="echoid-s5644" xml:space="preserve">intereſt, à plurimis ſcriptoribus <lb/>tam prophanis, quam Sacris appellatur Æther; </s> <s xml:id="echoid-s5645" xml:space="preserve">ſic. </s> <s xml:id="echoid-s5646" xml:space="preserve">S. </s> <s xml:id="echoid-s5647" xml:space="preserve">Gregorius Papa, Hom. </s> <s xml:id="echoid-s5648" xml:space="preserve">29. </s> <s xml:id="echoid-s5649" xml:space="preserve">ait aliud eſt <lb/>cælũ aereum, aliud æthereum; </s> <s xml:id="echoid-s5650" xml:space="preserve">vbi perſpicuè ſupra aerem ſtatim collocat æthera. </s> <s xml:id="echoid-s5651" xml:space="preserve">alij ignem <lb/>ibi quemdam collocant. </s> <s xml:id="echoid-s5652" xml:space="preserve">nonnulli aerem vſque ad lunares circuitus extollunt. </s> <s xml:id="echoid-s5653" xml:space="preserve">quidquid ſi@ <lb/>non eſt noſtrum definire, ſed eius locum, ſiguram, magnitudinem, motum, illuminationem, <lb/>v@in præcedentibus factum eſt, explicare. </s> <s xml:id="echoid-s5654" xml:space="preserve">diſtinctionis tamen gratia illud Æthera libenter <lb/>appellarem, cum id quod ſuperius eſt, & </s> <s xml:id="echoid-s5655" xml:space="preserve">in quo planetæ ac ſydera verſantur, cælum dicatur.</s> <s xml:id="echoid-s5656" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div116" type="section" level="1" n="76"> <head xml:id="echoid-head83" style="it" xml:space="preserve">De loco Aetheris. Cap. I.</head> <p> <s xml:id="echoid-s5657" xml:space="preserve">LOcus eius<unsure/> ex præmiſſis ſatis manifeſtus eſt, videlicet ſupra aerem, & </s> <s xml:id="echoid-s5658" xml:space="preserve">infra lunares regiones.</s> <s xml:id="echoid-s5659" xml:space="preserve"/> </p> <pb o="57" file="0077" n="81" rhead="Liber Septimus."/> </div> <div xml:id="echoid-div117" type="section" level="1" n="77"> <head xml:id="echoid-head84" style="it" xml:space="preserve">De figura Aetheris. Cap. II.</head> <p> <s xml:id="echoid-s5660" xml:space="preserve">FIguram eius orbicularem eſſe oportet, habet enim concauam ſuperficiem, qua aeri conterminus eſt; </s> <s xml:id="echoid-s5661" xml:space="preserve">ha-<lb/>bet etiam conuexam ſuperficiem qua cęlo Lunæ ſubijcitur, ac cõmicitur: </s> <s xml:id="echoid-s5662" xml:space="preserve">Ætheris igitur figura orbis eſt.</s> <s xml:id="echoid-s5663" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div118" type="section" level="1" n="78"> <head xml:id="echoid-head85" style="it" xml:space="preserve">De Aetheris motu. Cap. III.</head> <p> <s xml:id="echoid-s5664" xml:space="preserve">SI verum eſt oceanum diurno motu affici, ob quandam à cęlo ſibi inditam circu mductionem; </s> <s xml:id="echoid-s5665" xml:space="preserve">etiam par eſt <lb/>credere non ſolum aerem, ſed etiam æthera eadem conuerſione cieri: </s> <s xml:id="echoid-s5666" xml:space="preserve">pręſertim verò cum æther ſi@ Lunę <lb/>cęlo contiguus; </s> <s xml:id="echoid-s5667" xml:space="preserve">quod etiam veriſimile eſt eadem motione circumuerti, ſecumque proinde Aethera raptare.</s> <s xml:id="echoid-s5668" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div119" type="section" level="1" n="79"> <head xml:id="echoid-head86" style="it" xml:space="preserve">De illuminatione Aetheris. Cap. IIII.</head> <p> <s xml:id="echoid-s5669" xml:space="preserve">CVm Aether ſit ſupra Atmoſphęram, quo halitus non aſcendunt, erit omnino defæcatus, ac purus, ac pro-<lb/>inde omnino diaphanus; </s> <s xml:id="echoid-s5670" xml:space="preserve">quare nullo modo etiamſi totus lumine perfunda@ur, co @ſpicuus redditur, <lb/>nihilque in toto hoc Aethere reperitur quod ſplendeat, niſi in ſuprema eius parte aliquando Co@etæ efful-<lb/>geant, quod fieri poſſe exiſtimo; </s> <s xml:id="echoid-s5671" xml:space="preserve">vt ſuo loco demonſtrabo.</s> <s xml:id="echoid-s5672" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div120" type="section" level="1" n="80"> <head xml:id="echoid-head87" style="it" xml:space="preserve">De quantitate Aetheris. Cap. V.</head> <p> <s xml:id="echoid-s5673" xml:space="preserve">VT Aetheris quantitatem aſſequamur, nobis opus eſt prius diſtãtiam concaui regionis Lunæ à centro ter-<lb/>ræ perſcrutari: </s> <s xml:id="echoid-s5674" xml:space="preserve">quæ quidem perſcrutatio omnibus adeo ſemper mirabilis viſa eſt, vt etiam eorum com-<lb/>plures, qui ſapientes haberi volunt eam humani viribus ingenij imparem putent; </s> <s xml:id="echoid-s5675" xml:space="preserve">pręſertim cum ſacræ etiam <lb/>litteræ eam admirari vi<unsure/>deantur; </s> <s xml:id="echoid-s5676" xml:space="preserve">altitudinem enim cæli quis dimenſus eſt, ait ſapiens.</s> <s xml:id="echoid-s5677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5678" xml:space="preserve">Verum enim vero breuiter ac facile oſtendi poteſt qua ratione Aſtronomi, ſolertia vtique magna, eam di-<lb/>menſi fuerint. </s> <s xml:id="echoid-s5679" xml:space="preserve">primo itaque præſcire oportet Lunam non ſemper eandem diſtantiam a centro terræ ſerua-<lb/>re; </s> <s xml:id="echoid-s5680" xml:space="preserve">quod Aſtronomi ex colligunt, quodipſa aliquando maior aliquando minor, cæteris paribus, appareat. <lb/></s> <s xml:id="echoid-s5681" xml:space="preserve">obſeruant igitur eam cum maxima apparet, quod accidit in quadrato eius ad ſolem aſpectu, tunc enim terris <lb/>proximior fit; </s> <s xml:id="echoid-s5682" xml:space="preserve">ac proinde probabile eſt eam prope confinium cæli, atque ætheri attingere. </s> <s xml:id="echoid-s5683" xml:space="preserve">2. </s> <s xml:id="echoid-s5684" xml:space="preserve">aſſumunt eam <lb/>quando eſt in aliquo certo Eclypticæ gradu, v. </s> <s xml:id="echoid-s5685" xml:space="preserve">g. </s> <s xml:id="echoid-s5686" xml:space="preserve">tempore alicuius Eclypſis lunaris, tunc enim certum eſt <lb/>eam eſſe in oppoſito Solis gradu: </s> <s xml:id="echoid-s5687" xml:space="preserve">quod ſi hoc @cire non poſſent, numquam adeo exacte lunares Eclypſes <lb/>prædicerent.</s> <s xml:id="echoid-s5688" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5689" xml:space="preserve">Gradus igitur ille cum ſit notus, notam etiam habebit diſtantiam à vertice illius loci, in quo debet fieri hęc <lb/>inueſtigatio; </s> <s xml:id="echoid-s5690" xml:space="preserve">quam diſtantiam ſuppono facilitatis gratia eſſe ſub meridiano illius loci quandoquidem hoc <lb/>fieri poteſt, vt ſcilicet Luna ſit ſimul, & </s> <s xml:id="echoid-s5691" xml:space="preserve">in meridiano, & </s> <s xml:id="echoid-s5692" xml:space="preserve">in gradu Eclyp. </s> <s xml:id="echoid-s5693" xml:space="preserve">certo. </s> <s xml:id="echoid-s5694" xml:space="preserve">ſit igitur figura in qua terra <lb/>A C. </s> <s xml:id="echoid-s5695" xml:space="preserve">concauum Lunæ citimæ ſit D E. </s> <s xml:id="echoid-s5696" xml:space="preserve">ſimulque idem arcus D E. </s> <s xml:id="echoid-s5697" xml:space="preserve">referat meridianum in quo Lunam poni-<lb/> <anchor type="figure" xlink:label="fig-0077-01a" xlink:href="fig-0077-01"/> mus apud E. </s> <s xml:id="echoid-s5698" xml:space="preserve">ſitque, exempli gratia, in primo gradu ♈. </s> <s xml:id="echoid-s5699" xml:space="preserve">ac proin-<lb/>de in æquatore. </s> <s xml:id="echoid-s5700" xml:space="preserve">intelligatur etiam triangulum C A E. </s> <s xml:id="echoid-s5701" xml:space="preserve">in quo con-<lb/>ſidero angulum C. </s> <s xml:id="echoid-s5702" xml:space="preserve">qui notus euadit ex nota diſtantia puncti E. <lb/></s> <s xml:id="echoid-s5703" xml:space="preserve">æquatoris a vertice D. </s> <s xml:id="echoid-s5704" xml:space="preserve">illius loci, i. </s> <s xml:id="echoid-s5705" xml:space="preserve">ex noto arcu D E. </s> <s xml:id="echoid-s5706" xml:space="preserve">cognoſcitur <lb/>angulus C. </s> <s xml:id="echoid-s5707" xml:space="preserve">illi ex ce tro inſiſtens, ex 1. </s> <s xml:id="echoid-s5708" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s5709" xml:space="preserve">Appar. </s> <s xml:id="echoid-s5710" xml:space="preserve">deinde con-<lb/>ſidero angulum C A E. </s> <s xml:id="echoid-s5711" xml:space="preserve">quem Aſtronomus obſeruator cognoſce-<lb/>re poteſt per inſtrumentum, quo vtetur in hac obſeruatione, v. </s> <s xml:id="echoid-s5712" xml:space="preserve">g. </s> <s xml:id="echoid-s5713" xml:space="preserve"><lb/>per Quadrantem; </s> <s xml:id="echoid-s5714" xml:space="preserve">latus enim A D. </s> <s xml:id="echoid-s5715" xml:space="preserve">Quadrantis noſtri congruet li-<lb/>neæ A D. </s> <s xml:id="echoid-s5716" xml:space="preserve">quo tempore Dioptra, per quam collimabitur in Lunam <lb/>erit in linea A E. </s> <s xml:id="echoid-s5717" xml:space="preserve">quare arcus Quadrantis inter Dioptram<unsure/>, & </s> <s xml:id="echoid-s5718" xml:space="preserve">latus <lb/>A D. </s> <s xml:id="echoid-s5719" xml:space="preserve">incluſus, qualis eſi<unsure/>et B F. </s> <s xml:id="echoid-s5720" xml:space="preserve">manifeſtabit angulum D A E. </s> <s xml:id="echoid-s5721" xml:space="preserve">trian-<lb/>guli extrinſecum; </s> <s xml:id="echoid-s5722" xml:space="preserve">quo cognito cognoſcitur etiam angulus intrinſecus C A E. </s> <s xml:id="echoid-s5723" xml:space="preserve">illi deinceps; </s> <s xml:id="echoid-s5724" xml:space="preserve">ambo enim ſi-<lb/>mulæquales ſunt duobus rectis, ſeu contineat gr. </s> <s xml:id="echoid-s5725" xml:space="preserve">180. </s> <s xml:id="echoid-s5726" xml:space="preserve">ſi igitur angulus extrinſecus detrahatur a gr. </s> <s xml:id="echoid-s5727" xml:space="preserve">180. </s> <s xml:id="echoid-s5728" xml:space="preserve">re-<lb/>manebit quantitas anguli interni C A E. </s> <s xml:id="echoid-s5729" xml:space="preserve">nota. </s> <s xml:id="echoid-s5730" xml:space="preserve">notũ præterea eſt latus A C. </s> <s xml:id="echoid-s5731" xml:space="preserve">cum ſi@ſemid@ameter terræ, quam <lb/>ſupra indagauimus; </s> <s xml:id="echoid-s5732" xml:space="preserve">quare per 6. </s> <s xml:id="echoid-s5733" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s5734" xml:space="preserve">Appar. </s> <s xml:id="echoid-s5735" xml:space="preserve">notum etiam erit latus C E. </s> <s xml:id="echoid-s5736" xml:space="preserve">quia patebit quoties latus A C. </s> <s xml:id="echoid-s5737" xml:space="preserve"><lb/>cognitum contineatur in C E. </s> <s xml:id="echoid-s5738" xml:space="preserve">quæ eſt diſtantia Lunæ à centro terræ. </s> <s xml:id="echoid-s5739" xml:space="preserve">quam Copernicus, & </s> <s xml:id="echoid-s5740" xml:space="preserve">Tycho exquiſitis <lb/>inſtrumentis reperere continere ſemidiametros terræ 52. </s> <s xml:id="echoid-s5741" xml:space="preserve">toties enim latus A C. </s> <s xml:id="echoid-s5742" xml:space="preserve">in triangulo ſimili ingredi-<lb/>tur in latus C E. </s> <s xml:id="echoid-s5743" xml:space="preserve">ſemidiameter igitur totius ſphæræ elementaris, ſeu ſub@unaris tanta eſt, a qua ſi detrahatur <lb/>ſemidiameter terræ, necnon altitudo aeris, remanebit diſtantia ab aere ad citimam Lun@@, quæ eſt Aethe-<lb/>ris altitudo, quam inueſtigare propoſuimns. </s> <s xml:id="echoid-s5744" xml:space="preserve">ſemidiametri verò terræ 52. </s> <s xml:id="echoid-s5745" xml:space="preserve">efficiunt milliaria Aſtronomica <lb/>176,698. </s> <s xml:id="echoid-s5746" xml:space="preserve">quod patet multiplicando numer@m milliariorum vnius ſemidiametr@ per 52. </s> <s xml:id="echoid-s5747" xml:space="preserve">ab hiſce milliarijs ſi <lb/>detrahatur ſemidiameter terræ, vna cũ ae@is altitudine, quæ ſimul efficiunt, vt vidimus milliaria ferè 3,479. </s> <s xml:id="echoid-s5748" xml:space="preserve"><lb/>relinquetur hic numerus 175,219. </s> <s xml:id="echoid-s5749" xml:space="preserve">milliariorum; </s> <s xml:id="echoid-s5750" xml:space="preserve">interuallum videlicet a conuexo aeris ad concauum cęli Lu-<lb/>næ; </s> <s xml:id="echoid-s5751" xml:space="preserve">quæ eſt altitudo Aetheris@ quam indagare volebamus.</s> <s xml:id="echoid-s5752" xml:space="preserve"/> </p> <div xml:id="echoid-div120" type="float" level="2" n="1"> <figure xlink:label="fig-0077-01" xlink:href="fig-0077-01a"> <image file="0077-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0077-01"/> </figure> </div> <p> <s xml:id="echoid-s5753" xml:space="preserve">Habita ſphæræ totius elementaris ſem@diametro, cognoſcitur etiam quoties ſphęra elementaris ſphæram <lb/>terræ @o@t<unsure/>ineat: </s> <s xml:id="echoid-s5754" xml:space="preserve">cognitis<unsure/> enim diametris duarum ſphærarum, cognoſcit@@ etiam earumdem proportio ſe- <pb o="58" file="0078" n="82" rhead="De Mundi Fabrica"/> cundum ſoliditates, hoc modo, numeri in quibus noti ſunt diametri ſcribuntur ſic 1,52. </s> <s xml:id="echoid-s5755" xml:space="preserve">horũ proportio con-<lb/>tinuatur vſque ad quatuor terminos ſic 1. </s> <s xml:id="echoid-s5756" xml:space="preserve">52. </s> <s xml:id="echoid-s5757" xml:space="preserve">2,704. </s> <s xml:id="echoid-s5758" xml:space="preserve">140,608. </s> <s xml:id="echoid-s5759" xml:space="preserve">ideſt ita vt ſit eadẽ ratio primi ad ſecundum, quę <lb/>ſecundi ad tertium, & </s> <s xml:id="echoid-s5760" xml:space="preserve">tertij ad quartum, ſicuti eſt in iſtis. </s> <s xml:id="echoid-s5761" xml:space="preserve">Iam vt Euclides propoſ. </s> <s xml:id="echoid-s5762" xml:space="preserve">18. </s> <s xml:id="echoid-s5763" xml:space="preserve">12. </s> <s xml:id="echoid-s5764" xml:space="preserve">Elem. </s> <s xml:id="echoid-s5765" xml:space="preserve">demonſtrat, <lb/>eadem cſt proportio primi, 1. </s> <s xml:id="echoid-s5766" xml:space="preserve">ad vltimum 140,608. </s> <s xml:id="echoid-s5767" xml:space="preserve">quæ minoris ſphærę ad maiorem, ideſt quartum ſemidia-<lb/>metri ſunt vt 1. </s> <s xml:id="echoid-s5768" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s5769" xml:space="preserve">quare tota ſphæra ſublunar@s toties continet terræ globum, quoties num. </s> <s xml:id="echoid-s5770" xml:space="preserve">140,608. </s> <s xml:id="echoid-s5771" xml:space="preserve">con-<lb/> <anchor type="note" xlink:label="note-0078-01a" xlink:href="note-0078-01"/> tinet vnitatem. </s> <s xml:id="echoid-s5772" xml:space="preserve">eodem modo ad reliqua elementa, aquam, aerem, &</s> <s xml:id="echoid-s5773" xml:space="preserve">c. </s> <s xml:id="echoid-s5774" xml:space="preserve">compara-<lb/>tiones haberi poſſunt ſupra<unsure/> innuimus terram, aquam, & </s> <s xml:id="echoid-s5775" xml:space="preserve">aerem eſſe inter ſe, vt <lb/>ſunt appoſiti num. </s> <s xml:id="echoid-s5776" xml:space="preserve">nunc vero oſtẽdimus Aetherem qui ferè totam ſphæram ele-<lb/>mentarem occupat. </s> <s xml:id="echoid-s5777" xml:space="preserve">eſſe ad terram ferè vt 140,608. </s> <s xml:id="echoid-s5778" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s5779" xml:space="preserve">ſi igitur multiplicaueri-<lb/>mus hunc num. </s> <s xml:id="echoid-s5780" xml:space="preserve">per 2,290. </s> <s xml:id="echoid-s5781" xml:space="preserve">producetur num. </s> <s xml:id="echoid-s5782" xml:space="preserve">321,992,320. </s> <s xml:id="echoid-s5783" xml:space="preserve">qui erit in eadem ratio-<lb/>ne ad 2,290. </s> <s xml:id="echoid-s5784" xml:space="preserve">in qua eſt Aether ad terram; </s> <s xml:id="echoid-s5785" xml:space="preserve">exponantur igitur num. </s> <s xml:id="echoid-s5786" xml:space="preserve">quatuor, pro-<lb/>portiones quatuor elementorum inuicem habentes.</s> <s xml:id="echoid-s5787" xml:space="preserve"/> </p> <div xml:id="echoid-div121" type="float" level="2" n="2"> <note position="right" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve"> <lb/>Terra # 2′290. <lb/>Aqua # 1. <lb/>Aer # 86. <lb/>Aether # 321′992′320. <lb/></note> </div> </div> <div xml:id="echoid-div123" type="section" level="1" n="81"> <head xml:id="echoid-head88" style="it" xml:space="preserve">Conſectarium.</head> <p> <s xml:id="echoid-s5788" xml:space="preserve">EX demonſtratis de horum quatuor corporum elementarem ſphæram conflantium, quantitatibus, mani<unsure/> <lb/>feſtum eſt decuplam illam elementorum analogiam, quam nonnulli Ariſtoteli imponere contendunt<unsure/> <lb/>omnino commentitiam eſſe, ac proinde reijciendam.</s> <s xml:id="echoid-s5789" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div124" type="section" level="1" n="82"> <head xml:id="echoid-head89" style="it" xml:space="preserve">Cap. VI. Appendix, in qua problemata aliquot non iniucunda, ex hactenus traditis ſoluenda<unsure/> <lb/>proponuntur, quibus ingenium vtiliter, ac variè exercetur, atq; acuitur.</head> <p> <s xml:id="echoid-s5790" xml:space="preserve">1 POnamus Deum abſtuliſſe totum illud terræ hemiſphæriũ, quod eſt ſupra noſtrum horizontem Aſtro-<lb/>nomicum, quod nos vulgò ſuperius appellamus, altero inferiori antipodum hemiſphæro nihil immu-<lb/>tato: </s> <s xml:id="echoid-s5791" xml:space="preserve">hoc enim facto remaneret plana, ac rotunda terræ ſuperficies. </s> <s xml:id="echoid-s5792" xml:space="preserve">Iam quæritur an homines poſſent in il-<lb/>la magna planitie degere, & </s> <s xml:id="echoid-s5793" xml:space="preserve">inhabitare? </s> <s xml:id="echoid-s5794" xml:space="preserve">Reſpondeo negando inibi homines vno excepto conſiſtere poſſe, <lb/>ſolus enim ille vnus qui pedibus centrũ illius plani, quod eſt centrum pariter terræ calcaret, in illo plano exi-<lb/>ſtere poſſet. </s> <s xml:id="echoid-s5795" xml:space="preserve">cæteri vero omnes, quos alibi extra illud centrum ſtare poſſe imaginamur, nullo modo ibi inſi-<lb/>ſtere poſſent, ſed verſus centrum illius plani vndiq; </s> <s xml:id="echoid-s5796" xml:space="preserve">delabarentur; </s> <s xml:id="echoid-s5797" xml:space="preserve">quia omne graue deorſum tendit niſi quid <lb/>obſtet. </s> <s xml:id="echoid-s5798" xml:space="preserve">planior autem ſolutio euadit, ſi cogitemus ablatum eſſe non noſtrum hæmiſphęrium, ſed hæmiſphæ-<lb/>rium, v. </s> <s xml:id="echoid-s5799" xml:space="preserve">g. </s> <s xml:id="echoid-s5800" xml:space="preserve">orientale; </s> <s xml:id="echoid-s5801" xml:space="preserve">ſic enim planities illa terræ tranſiret ſub noſtris pedibus, eamque intuentes videremus <lb/>abyſſum, aut præcipitium horrendum, vſque ad antipodas recta deſcendere, in cuius medio eſſet centrum <lb/>mundi, quo intuitu ſtatim intelligeremus nullos homines ei pedibus affixos, ac perpẽdiculares inhærere p<unsure/>oſ-<lb/>ſe, præter illum qui centro infiſteret. </s> <s xml:id="echoid-s5802" xml:space="preserve">Hinc patet fieri nullo modo poſſe, vt terra ſit ſuperficies quædam qua-<lb/>drata, vti Sinæ opinantur, vnicum enim tantum pateretur habitatorem.</s> <s xml:id="echoid-s5803" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5804" xml:space="preserve">2 Qua ratione pons lapideus aut latericius architectari poſſet, qui nullis pylis, aut fulcimentis terrã con-<lb/>tingeret, ſed totus in aere pendulus exiſteret. </s> <s xml:id="echoid-s5805" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5806" xml:space="preserve">ſi circa ambitum terræ maximum pons vniformis craſſi-<lb/>tie, ac ponderis prius ſuper fulcris ligneis per parte extrueretur, eoq; </s> <s xml:id="echoid-s5807" xml:space="preserve">abſoluto fulcra omnia ſubtraherentur, <lb/>nullo modo pons corrueret, quia vndiq; </s> <s xml:id="echoid-s5808" xml:space="preserve">ad centrum mundi æqualiter grauitaret, atq; </s> <s xml:id="echoid-s5809" xml:space="preserve">vrgeret, vnde ſibi ipſi <lb/>eſſet impedimento, ne ex vna parte potius, quam ex altera ſubſiderct. </s> <s xml:id="echoid-s5810" xml:space="preserve">eadem de cauſa @ornices, & </s> <s xml:id="echoid-s5811" xml:space="preserve">concamera-<lb/>tionesconſiſtu nt.</s> <s xml:id="echoid-s5812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5813" xml:space="preserve">3 Sit in noſtro horizonte ſenſibili pauimentum aliquod rectum, & </s> <s xml:id="echoid-s5814" xml:space="preserve">oblungũ, ita vt cælum vſque & </s> <s xml:id="echoid-s5815" xml:space="preserve">vtrin-<lb/> <anchor type="figure" xlink:label="fig-0078-01a" xlink:href="fig-0078-01"/> que pertingat, vti eſt A B. </s> <s xml:id="echoid-s5816" xml:space="preserve">in figura; </s> <s xml:id="echoid-s5817" xml:space="preserve">quæritur <lb/>num per illud quantũlibet ambulare poſſemus. <lb/></s> <s xml:id="echoid-s5818" xml:space="preserve">Reſpondeo, nequaquam quantumlibet ambu-<lb/>laremus, ſed ad aliquod tantum interual@um. </s> <s xml:id="echoid-s5819" xml:space="preserve"><lb/>ratio eſt, quia ſic homines aſcenderẽt, fieretque <lb/>ſemper magis aſcenſus ille acliuis, ita vt aliquã-<lb/>do non amplius recti illi inſiſterent, ſed proni, <lb/>& </s> <s xml:id="echoid-s5820" xml:space="preserve">inclinati reperent, non enim conſiſtere poſ-<lb/>ſumus niſi lõgitudo corporis noſtri, ſit in linea <lb/>directionis quæ tendit ad centrum, & </s> <s xml:id="echoid-s5821" xml:space="preserve">de qua <lb/>ſuperius dixi in cap. </s> <s xml:id="echoid-s5822" xml:space="preserve">de motu ſphęræ elementa-<lb/>ris. </s> <s xml:id="echoid-s5823" xml:space="preserve">melius id percipitur ſi imaginemur tale pa-<lb/>uimentum extructum eſſe in horizonte diſtanti <lb/>à noſtra hab tatione per terreſtris circuli qua-<lb/>drantem, quale eſt in figura C D. </s> <s xml:id="echoid-s5824" xml:space="preserve">intelligimus<unsure/> <lb/>enim ſtatim id eſſe turris inſtar cęlũ vſq; </s> <s xml:id="echoid-s5825" xml:space="preserve">aſcen-<lb/>dentis, in cui<unsure/>us parietibus homines fruſtra co-<lb/>narentur reptare.</s> <s xml:id="echoid-s5826" xml:space="preserve"/> </p> <div xml:id="echoid-div124" type="float" level="2" n="1"> <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a"> <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0078-01"/> </figure> </div> <p> <s xml:id="echoid-s5827" xml:space="preserve">4 Sit tabula plana perfectè, atque in noſtro horizonte ad æqui@ibrium conſtituta qualem linea A B. </s> <s xml:id="echoid-s5828" xml:space="preserve">refe-<lb/>rat; </s> <s xml:id="echoid-s5829" xml:space="preserve">ſupra qu@m@ ponatur ſphæra perfectè rotunda, hæc ſphæra maneb@tne an reuoluetur? </s> <s xml:id="echoid-s5830" xml:space="preserve">Reſpondeo, ſi po- <pb o="59" file="0079" n="83" rhead="Liber Septimus."/> <anchor type="figure" xlink:label="fig-0079-01a" xlink:href="fig-0079-01"/> naturin medio, v. </s> <s xml:id="echoid-s5831" xml:space="preserve">g. </s> <s xml:id="echoid-s5832" xml:space="preserve">in D. </s> <s xml:id="echoid-s5833" xml:space="preserve">ibi quieſcet, quia punctum illud eſt cen-<lb/>tro mundi propinquius, quam ſit aliud quiduis punctum; </s> <s xml:id="echoid-s5834" xml:space="preserve">& </s> <s xml:id="echoid-s5835" xml:space="preserve">ideo cæ-<lb/>teris punctis inferius eſt. </s> <s xml:id="echoid-s5836" xml:space="preserve">alibi vero poſita deuoluetur ad D. </s> <s xml:id="echoid-s5837" xml:space="preserve">quia de-<lb/>cliuius eſt, v. </s> <s xml:id="echoid-s5838" xml:space="preserve">g. </s> <s xml:id="echoid-s5839" xml:space="preserve">poſita in B. </s> <s xml:id="echoid-s5840" xml:space="preserve">deuoluetur ad D. </s> <s xml:id="echoid-s5841" xml:space="preserve">quia linea eius directio-<lb/>nis eſt, nec C E. </s> <s xml:id="echoid-s5842" xml:space="preserve">E. </s> <s xml:id="echoid-s5843" xml:space="preserve">vero eſt centrum grauitatis eius, infra quod nul-<lb/>lum directè ſubeſt fulcimentum, quare centrum E. </s> <s xml:id="echoid-s5844" xml:space="preserve">deuoluetur ver-<lb/>ſus D.</s> <s xml:id="echoid-s5845" xml:space="preserve"/> </p> <div xml:id="echoid-div125" type="float" level="2" n="2"> <figure xlink:label="fig-0079-01" xlink:href="fig-0079-01a"> <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-01"/> </figure> </div> <p> <s xml:id="echoid-s5846" xml:space="preserve">5 Cur homines, turres, plantæ, &</s> <s xml:id="echoid-s5847" xml:space="preserve">c. </s> <s xml:id="echoid-s5848" xml:space="preserve">quę recta vt plurimum aſſur-<lb/>gunt, ſi inclinentur, aliquando cadunt, aliquando vero minimè. </s> <s xml:id="echoid-s5849" xml:space="preserve">Bo-<lb/>noniæ videre eſt communi omnium admiratione turrem illã quam <lb/>vocant Gariſendam admodum inclinatam, quæ tamen à 500. </s> <s xml:id="echoid-s5850" xml:space="preserve">iam <lb/>annis immota non cadit. </s> <s xml:id="echoid-s5851" xml:space="preserve">Reſpondeo hæc omnia nõ proſterni quo-<lb/>ties linea directionis tranſit per baſim eorum, v. </s> <s xml:id="echoid-s5852" xml:space="preserve">g. </s> <s xml:id="echoid-s5853" xml:space="preserve">turris illa non cadit quia linea directionis E C. </s> <s xml:id="echoid-s5854" xml:space="preserve">quæ à<unsure/> cen-<lb/>tro grauitatis eius ad centrum mundi ducitur, tranſit per baſim turris A D. </s> <s xml:id="echoid-s5855" xml:space="preserve">ideſt, quia centrum grauit E. </s> <s xml:id="echoid-s5856" xml:space="preserve">ſe-<lb/> <anchor type="figure" xlink:label="fig-0079-02a" xlink:href="fig-0079-02"/> cundum quod grauia mouentur, ſuſtinetur a partibus turris infra <lb/>ipſum poſitis iuxta lineam directionis, quare tota turris grauitas, <lb/>quæ circa centrum illud ęque ponderat, ipſo fulto moueri nequit; <lb/></s> <s xml:id="echoid-s5857" xml:space="preserve">nam ponderibus librata, ſuis immobilis hæret. </s> <s xml:id="echoid-s5858" xml:space="preserve">quod ſi linea E C. </s> <s xml:id="echoid-s5859" xml:space="preserve"><lb/>extra baſim A D. </s> <s xml:id="echoid-s5860" xml:space="preserve">exiret, nimia eſſet inclinatio, ac proinde turris <lb/>ſterneretur. </s> <s xml:id="echoid-s5861" xml:space="preserve">Eadem de cauſa homines, ſecundum quandam incli-<lb/>nationem ſtant; </s> <s xml:id="echoid-s5862" xml:space="preserve">quod ſi eorum linea directionis extra plantas ca-<lb/>dat, & </s> <s xml:id="echoid-s5863" xml:space="preserve">ipſi cadunt.</s> <s xml:id="echoid-s5864" xml:space="preserve"/> </p> <div xml:id="echoid-div126" type="float" level="2" n="3"> <figure xlink:label="fig-0079-02" xlink:href="fig-0079-02a"> <image file="0079-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-02"/> </figure> </div> <p> <s xml:id="echoid-s5865" xml:space="preserve">Sic ſuper parietes ſcandere nequimus, quia nullum ibi eſt cen-<lb/>tro grauitatis fulcimentum.</s> <s xml:id="echoid-s5866" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5867" xml:space="preserve">6 Cur caſuri in partem vnam, in alteram brachiũ naturali in-<lb/>ſtinctu extendimus? </s> <s xml:id="echoid-s5868" xml:space="preserve">Reſpondeo, vt ſcilicet brachij extenſione, <lb/>& </s> <s xml:id="echoid-s5869" xml:space="preserve">remotione a reliquo corpore fiat æquilibriu<unsure/>m; </s> <s xml:id="echoid-s5870" xml:space="preserve">brachium enim <lb/>extenſum plus grauitat, quam contractum; </s> <s xml:id="echoid-s5871" xml:space="preserve">ſicut in ſtatera æqui-<lb/>pondium plus grauitata trutina remotũ; </s> <s xml:id="echoid-s5872" xml:space="preserve">quam proximum. </s> <s xml:id="echoid-s5873" xml:space="preserve">in ca-<lb/>ſuro homine linea directionis extra baſim fertur, ſed brachij extenſione centrum grauitatis acced@tad partẽ <lb/>camdem, ac proinde linea directionis inter plantas retrahitur.</s> <s xml:id="echoid-s5874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5875" xml:space="preserve">7 Cur gibboſi ſenes genua antrorſum valde incuruant? </s> <s xml:id="echoid-s5876" xml:space="preserve">Reſpondeo, vt nimirum crura gibbo æquipon-<lb/>dium faciant: </s> <s xml:id="echoid-s5877" xml:space="preserve">aliter ſtare non poſſent, ſed antrorſum deciderent, trahente eos parte corporis prona.</s> <s xml:id="echoid-s5878" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5879" xml:space="preserve">8 Cur ſedentes cum ſeſſu ſurgere volunt retrorſum crura, antrorſum caput ac pectus inclinant reſpon-<lb/>deo. </s> <s xml:id="echoid-s5880" xml:space="preserve">ſimilis eſt ratio vt in prædictis.</s> <s xml:id="echoid-s5881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5882" xml:space="preserve">9 Cum montium conuexa ſuperficies ſit multo maior quam ſit plana, illa ſuperficies cui inſiſtunt, quæq; <lb/></s> <s xml:id="echoid-s5883" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0079-03a" xlink:href="fig-0079-03"/> eorum baſis dicitur, poſſunt ne plures homines habitare in ſuperficie iſ-<lb/>la conuexa, an in baſi? </s> <s xml:id="echoid-s5884" xml:space="preserve">Reſpondeo totidem, & </s> <s xml:id="echoid-s5885" xml:space="preserve">non plures in illa, quam <lb/>in hac conſiſtere poſſe. </s> <s xml:id="echoid-s5886" xml:space="preserve">cuius ratio eſt, quia hominum corpora debent <lb/>ſemper conſtitui in rectitudine lineæ directionis, quæ ad centrum ten-<lb/>dit, vnde fit vt ſingulis habitatoribus baſis, ſinguli habitatores conuexi <lb/>reſpondeant, vt ex contemplatione figuræ inte@ligi poteſt. </s> <s xml:id="echoid-s5887" xml:space="preserve">plures in <lb/>conuexo degerent, ſi poſſent illi conuexo perpendiculariter inſiſtere.</s> <s xml:id="echoid-s5888" xml:space="preserve"/> </p> <div xml:id="echoid-div127" type="float" level="2" n="4"> <figure xlink:label="fig-0079-03" xlink:href="fig-0079-03a"> <image file="0079-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-03"/> </figure> </div> <p> <s xml:id="echoid-s5889" xml:space="preserve">10 Si turres ad perpend@culum conſtruantur<unsure/>, aut putei ex@auentur; <lb/></s> <s xml:id="echoid-s5890" xml:space="preserve">eruntne eorum parietes aut latera paralella? </s> <s xml:id="echoid-s5891" xml:space="preserve">Reſpondeo turres eſſent <lb/>in ſummo latiores, in imo vero contractiores: </s> <s xml:id="echoid-s5892" xml:space="preserve">idem puteis accideret. </s> <s xml:id="echoid-s5893" xml:space="preserve"><lb/>perpendicula enim quibus parietes diriguntur non ſunt lineæ æquidiſtantes, ſed concurrentes ad centrum <lb/>mundi, ſi eovſq; </s> <s xml:id="echoid-s5894" xml:space="preserve">producerentur.</s> <s xml:id="echoid-s5895" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5896" xml:space="preserve">11 Qua ratione quiſpiam ſolius vnius agelli A B C D. </s> <s xml:id="echoid-s5897" xml:space="preserve">dominus ſit verè poteſt dice-<lb/> <anchor type="figure" xlink:label="fig-0079-04a" xlink:href="fig-0079-04"/> re ſe poſſe per ſuum agellum ambulare, & </s> <s xml:id="echoid-s5898" xml:space="preserve">quidem ſemper in directum pluſquam 3000. <lb/></s> <s xml:id="echoid-s5899" xml:space="preserve">milliariorum. </s> <s xml:id="echoid-s5900" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5901" xml:space="preserve">conſiderandum eſt nos non ſolum agri ſuperficiem poſſidere, ſed <lb/>etiam totam illam terram, quæ ſuperficiei illius directè ſubeſt vſque ad centrum terræ; </s> <s xml:id="echoid-s5902" xml:space="preserve"><lb/>omnes agri hoc modo accepti ſunt totidem@yramides; </s> <s xml:id="echoid-s5903" xml:space="preserve">quorum cuſpides ad centrum <lb/>terræ coeunt, baſis vero eo<unsure/>rum eſt agri ſuperficies: </s> <s xml:id="echoid-s5904" xml:space="preserve">a baſi igitur vſq; </s> <s xml:id="echoid-s5905" xml:space="preserve">ad verticem ſeu cen-<lb/>trum terræ interſunt milliariorum pluſquam 3,000. </s> <s xml:id="echoid-s5906" xml:space="preserve">tota enim terræ ſemidiameter eua-<lb/>dit harum pyramidum longitudo. </s> <s xml:id="echoid-s5907" xml:space="preserve">ſit i<unsure/>n figura ager ſuperficialis A B C D. </s> <s xml:id="echoid-s5908" xml:space="preserve">ſolidus autem <lb/>erit pyramis protenſa vertice E. </s> <s xml:id="echoid-s5909" xml:space="preserve">ad terræ medium E. </s> <s xml:id="echoid-s5910" xml:space="preserve">@ille igitur huius poſſeſſor agelli <lb/>nequaquam impoſſibilia comminiſcebatur. </s> <s xml:id="echoid-s5911" xml:space="preserve">quid ſi inibi Theſaurus inueniretur? </s> <s xml:id="echoid-s5912" xml:space="preserve">conſu-<lb/>lendi ſunt legulei, qui cum Principi ad@udicant.</s> <s xml:id="echoid-s5913" xml:space="preserve"/> </p> <div xml:id="echoid-div128" type="float" level="2" n="5"> <figure xlink:label="fig-0079-04" xlink:href="fig-0079-04a"> <image file="0079-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-04"/> </figure> </div> <p> <s xml:id="echoid-s5914" xml:space="preserve">11 Si magnum pauimentum libellatim extendatur, eritne plana ſuperficies? </s> <s xml:id="echoid-s5915" xml:space="preserve">Reſp. <lb/></s> <s xml:id="echoid-s5916" xml:space="preserve">quamuis parua pauimenta ad ſenſum plana videantur, ſi tamen magna fierent @otundi-<lb/>@@tem præ ſe ferrent aliquam, cogitemus enim totam terræ ſuperficiem @pauimento ad libellam facto poſ-<lb/>ſe pauiri: </s> <s xml:id="echoid-s5917" xml:space="preserve">Libella enim vbique terrarum terræ ſphæricitatem in puncto tangit, eiuſque perpendiculum ad <pb o="60" file="0080" n="84" rhead="De Mundi Fabrica,"/> terræ centrum pendet; </s> <s xml:id="echoid-s5918" xml:space="preserve">quapropter ſphæricum fieret libellando vbique pauimentum, cuius portiones parua <lb/>pauimenta ſunt exiſtimandæ.</s> <s xml:id="echoid-s5919" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5920" xml:space="preserve">13 Cur dici ſo@et caput pluſquam pedes ambulare? </s> <s xml:id="echoid-s5921" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5922" xml:space="preserve">ſi quis totius terræ gyrũ peregiſſet, duas ſimul <lb/>peripherias, vnam pedibus, alteram capite deſcripſiſſet: </s> <s xml:id="echoid-s5923" xml:space="preserve">quarũ proculdubio illa maior eſſet, quam caput cir-<lb/>cinauit, quippe qui magis a centro diſtat: </s> <s xml:id="echoid-s5924" xml:space="preserve">vnde ſolutio quæſtionis habetur.</s> <s xml:id="echoid-s5925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5926" xml:space="preserve">14 Cur dicunt Cyathum plus vini continere in cellario, quã <lb/> <anchor type="figure" xlink:label="fig-0080-01a" xlink:href="fig-0080-01"/> in tecti culmine. </s> <s xml:id="echoid-s5927" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5928" xml:space="preserve">quia humores omnes vbicumque tuerint, <lb/>dum quieſcunt, ſecundum ſupremã ſuperficiem contrahunt ro-<lb/>tunditatem, cuius centrum eſt centrũ terræ. </s> <s xml:id="echoid-s5929" xml:space="preserve">quanto autem Cya-<lb/>thus fuerit inferior, tanto erit rotunditas humidi portio mino-<lb/>ris ſphæræ; </s> <s xml:id="echoid-s5930" xml:space="preserve">minor autem ſphæra curuiorem habet conuexitatẽ, <lb/>& </s> <s xml:id="echoid-s5931" xml:space="preserve">proinde capaciorem, quia magis ſupra Cyathi ora incuruatur: <lb/></s> <s xml:id="echoid-s5932" xml:space="preserve">vt in figuris videre eſt; </s> <s xml:id="echoid-s5933" xml:space="preserve">in qua C. </s> <s xml:id="echoid-s5934" xml:space="preserve">eſt centrum terræ, circa quod <lb/> <anchor type="figure" xlink:label="fig-0080-02a" xlink:href="fig-0080-02"/> humidum Cyathi inferioris C D. </s> <s xml:id="echoid-s5935" xml:space="preserve">magis curuatnr, & </s> <s xml:id="echoid-s5936" xml:space="preserve">proinde ca-<lb/>pacius eſt: </s> <s xml:id="echoid-s5937" xml:space="preserve">altioris vero Cyathi humidum A B. </s> <s xml:id="echoid-s5938" xml:space="preserve">minus curuatur, & </s> <s xml:id="echoid-s5939" xml:space="preserve"><lb/>ideo minus continet.</s> <s xml:id="echoid-s5940" xml:space="preserve"/> </p> <div xml:id="echoid-div129" type="float" level="2" n="6"> <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a"> <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-01"/> </figure> <figure xlink:label="fig-0080-02" xlink:href="fig-0080-02a"> <image file="0080-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-02"/> </figure> </div> <p> <s xml:id="echoid-s5941" xml:space="preserve">15 Vt lacus quiſpiam, aut mare conſiſtat opuſne eſt ſpondis, <lb/>aut cauitatibus vllis? </s> <s xml:id="echoid-s5942" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5943" xml:space="preserve">minime opus eſſe, nam ſi cogitemus <lb/>portionem aliquam terrę a plano quodam ſecante, eſſe reſectam, <lb/>relinquetur quædam planities: </s> <s xml:id="echoid-s5944" xml:space="preserve">in hanc planitiem ſi aquæ tantumdem loco terrę auulſæ inferatur, extra eam <lb/>planitiem non effluet, ſed configuratur ſuperiori ſuperficie ſphærica reſpectu centri mundi, quare naturale <lb/>eſt mare abſque altis litoribus, ſeu ſpondis conſiſtere.</s> <s xml:id="echoid-s5945" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5946" xml:space="preserve">16 Sunt duo montes proximi, & </s> <s xml:id="echoid-s5947" xml:space="preserve">in vertice vnius eſt fons viuus, in vertice alterius ſunt quidam habita-<lb/>tores, qui aquæ inopia laborant, ac propterea illius fontis aquam ad verticem alterius montis deducere vel-<lb/>lent: </s> <s xml:id="echoid-s5948" xml:space="preserve">neq; </s> <s xml:id="echoid-s5949" xml:space="preserve">vero ob nimios ſumptus Aquæductũ ſuper fornicibus plurimis fabricare poſſunt; </s> <s xml:id="echoid-s5950" xml:space="preserve">quid igitur agen <lb/>dum? </s> <s xml:id="echoid-s5951" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5952" xml:space="preserve">fiat tubus plumbeus à fonte deſcendens per vallem atq; </s> <s xml:id="echoid-s5953" xml:space="preserve">ad alterius verticem ſcandens, per hunc <lb/>enim aqua deſcendet, & </s> <s xml:id="echoid-s5954" xml:space="preserve">iterum tantumdem aſcendet.</s> <s xml:id="echoid-s5955" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5956" xml:space="preserve">17 Eſt mons ad cuius radices eſt fons ſcaturiens, ex altera vero partes pariter ad radices ſunt habitatores <lb/>illa aqua indigentes, qui ſolummodo per montis verticem fontem adire poſſunt, quid illis faciẽdum? </s> <s xml:id="echoid-s5957" xml:space="preserve">Reſp. <lb/></s> <s xml:id="echoid-s5958" xml:space="preserve">conſtruatur tubus plumbeus aſcendens à fonte ſuper verticem montis, indeq; </s> <s xml:id="echoid-s5959" xml:space="preserve">ad habitatores illos deſcendẽs <lb/>initium eius fonti immergi debet, fin is eius paulo depræſſior ſit quam initium, vtrumque os obturetur; </s> <s xml:id="echoid-s5960" xml:space="preserve">de-<lb/>inde tubus in ſummitate montis perforetur, ac per foramen ſemel totus aqua impleatur; </s> <s xml:id="echoid-s5961" xml:space="preserve">poſtea foramen di-<lb/>ligenter obturetur. </s> <s xml:id="echoid-s5962" xml:space="preserve">vltimo vtrumque os tubi eodem tempore aperiantur, vel certe primo aperiatur os fonti <lb/>immerſum; </s> <s xml:id="echoid-s5963" xml:space="preserve">hoc enim modo aqua perpetuo prædictis habitatoribus effluere debet: </s> <s xml:id="echoid-s5964" xml:space="preserve">vt conſtat ex dictis de <lb/>motu aquæ.</s> <s xml:id="echoid-s5965" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5966" xml:space="preserve">18 Eſt dolium humido non omnino plenum, ſcire libet quantum humidi contineat abſque apertione ſu <lb/>perioris, atque vlla dolij perforatione. </s> <s xml:id="echoid-s5967" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5968" xml:space="preserve">fiat canna vitrea gracilis, in imo curua, ſecũdum quam partem <lb/>immittatur in dolij fiſtulam, per quam ordinariè ſolet humidum hauriri. </s> <s xml:id="echoid-s5969" xml:space="preserve">reliqua pars @urſum erigatur iuxta <lb/>dolium; </s> <s xml:id="echoid-s5970" xml:space="preserve">ſtatim enim per ca@nam vitream tantum liquor aſcendet, quantum intra dolium attollitur.</s> <s xml:id="echoid-s5971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5972" xml:space="preserve">19 Eodem inſtrumento, & </s> <s xml:id="echoid-s5973" xml:space="preserve">modo, licebit dolium implere, aut humidum addere, non per os ſuperius, vt <lb/>fieri ſolet.</s> <s xml:id="echoid-s5974" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5975" xml:space="preserve">20 Sit puteus vſque ad antipodas excauatus ac neceſſario per centrum terræ tranſiens, quæritur primo; <lb/></s> <s xml:id="echoid-s5976" xml:space="preserve">graue per ipſum deſ@endens quid tandem ageret? </s> <s xml:id="echoid-s5977" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5978" xml:space="preserve">ob impetum in deſcenſu acquiſitum, vltra citraq; </s> <s xml:id="echoid-s5979" xml:space="preserve"><lb/>@undi centrum aliquoties reciprocaretur, ſed tandem centrũ eius grauitatis centro mundi congrueret, ſicq; </s> <s xml:id="echoid-s5980" xml:space="preserve"><lb/>@uieſceret.</s> <s xml:id="echoid-s5981" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5982" xml:space="preserve">21 Ignis in centro prædicto accenſus flammam in orbem conglobaret: </s> <s xml:id="echoid-s5983" xml:space="preserve">fumum verò partim ad nos, par-<lb/>t<unsure/>im ad antipodas exhalaret.</s> <s xml:id="echoid-s5984" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5985" xml:space="preserve">22 Aqua in prædictum puteum proiecta, tandem circa centrum in globum conquieſceret.</s> <s xml:id="echoid-s5986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5987" xml:space="preserve">23 Bilianx per hunc puteum demiſſa dum deſcenderent magis ſemper, lances contraheret. </s> <s xml:id="echoid-s5988" xml:space="preserve">quouſqũe ad <lb/>centrum mundi deueniret, vbi lances brachio bilancis adhærerent.</s> <s xml:id="echoid-s5989" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5990" xml:space="preserve">24 Ponamus haſtam plumbeam vniformis ponderis A B. </s> <s xml:id="echoid-s5991" xml:space="preserve">in figura, cu-<lb/> <anchor type="figure" xlink:label="fig-0080-03a" xlink:href="fig-0080-03"/> ius centrum grauit C. </s> <s xml:id="echoid-s5992" xml:space="preserve">ex quo ſuſpenſa maneat non in æquilibrio, ſed obli-<lb/>quata; </s> <s xml:id="echoid-s5993" xml:space="preserve">cum hæc deuenerit ad horizontem aſtronomicum D E. </s> <s xml:id="echoid-s5994" xml:space="preserve">tranſeuntem <lb/>per centrum mundi F. </s> <s xml:id="echoid-s5995" xml:space="preserve">ita vt pars eius inferior attingat hunc horizontem, <lb/>aut iam aliquantulum pertranſierit, quid fiet? </s> <s xml:id="echoid-s5996" xml:space="preserve">deſcendens ne ſeruat eãdem <lb/>poſitionem, an aliquatenus reuoluetur. </s> <s xml:id="echoid-s5997" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s5998" xml:space="preserve">me nunc tantum alijs Mathe-<lb/>maticis hoc problema ſoluendum proponere, nondum enim apud me eius <lb/>ſolutio abſoluta eſt.</s> <s xml:id="echoid-s5999" xml:space="preserve"/> </p> <div xml:id="echoid-div130" type="float" level="2" n="7"> <figure xlink:label="fig-0080-03" xlink:href="fig-0080-03a"> <image file="0080-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-03"/> </figure> </div> <p> <s xml:id="echoid-s6000" xml:space="preserve">25 Qua induſtria conſtruere oportet ſcalã, ita vt per eam duo pariter aſcendant, & </s> <s xml:id="echoid-s6001" xml:space="preserve">tamen, ſimul in con-<lb/>tr<unsure/>arias partes tendant? </s> <s xml:id="echoid-s6002" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s6003" xml:space="preserve">ſcala quæpiam in prædicto puteo ita collocetur vt dimidia ſit citra, dimidiaq; <lb/></s> <s xml:id="echoid-s6004" xml:space="preserve">vltra centrum mundi; </s> <s xml:id="echoid-s6005" xml:space="preserve">iam duo a centro, ſimulque à medio ſcalę ſcandere incipiant, vnus ad nos, alter ad an@-<lb/>podas: </s> <s xml:id="echoid-s6006" xml:space="preserve">ambo enim aſcendent, ſed tamen ad partes oppoſitas in eadem ſcala.</s> <s xml:id="echoid-s6007" xml:space="preserve"/> </p> <pb o="61" file="0081" n="85" rhead="Liber Septimus."/> <p> <s xml:id="echoid-s6008" xml:space="preserve">26 Puer per iocum interrogatus vtra grauior eſſet, librane vna plumbi, an vna aquæ, vel ſtupæ; </s> <s xml:id="echoid-s6009" xml:space="preserve">reſpon-<lb/>dit grauiorem eſſe cæteris libram plumbi, ob idque adſtantes ſubriſere: </s> <s xml:id="echoid-s6010" xml:space="preserve">Verum enim vero reſponſionem <lb/>eius tueri hac ratione poſſumus. </s> <s xml:id="echoid-s6011" xml:space="preserve">ſciendum enim eſt duplicem eſſe alicuius corporis grauitatem; </s> <s xml:id="echoid-s6012" xml:space="preserve">vnam ipſius <lb/>particularem, & </s> <s xml:id="echoid-s6013" xml:space="preserve">propriam, ſecundum quam dicimus hæc plumbea ſphæra pendet libras 10. </s> <s xml:id="echoid-s6014" xml:space="preserve">vel vnam, &</s> <s xml:id="echoid-s6015" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s6016" xml:space="preserve">Alteram vero non ipſius corporis propriam ſed totius generis, aut naturæ communem, ſecundum quam di-<lb/>ci ſolet plumbum eſt grauius ligno, ferro, aqua, &</s> <s xml:id="echoid-s6017" xml:space="preserve">c. </s> <s xml:id="echoid-s6018" xml:space="preserve">tunc autem genus vnum grauius altero cenſetur, cum <lb/>accepta ex vtroque æquali mole, altera grauior ſit: </s> <s xml:id="echoid-s6019" xml:space="preserve">ſic quia ex duabus æqualibus ſphæris, vna plumbea, lignea <lb/>altera, plus pendit ſiue grauior eſt plumbea, ideo dicimus naturam plumbi grauiorem eſſe natura ligni, ferri, <lb/>aquæ, &</s> <s xml:id="echoid-s6020" xml:space="preserve">c. </s> <s xml:id="echoid-s6021" xml:space="preserve">qua diſtinctione allata dicam Puerum loquutum eſſe de grauitate generica, non autem de particu-<lb/>lari. </s> <s xml:id="echoid-s6022" xml:space="preserve">prætera ſi in codem vaſe ſimul vna libra aquæ, & </s> <s xml:id="echoid-s6023" xml:space="preserve">vna libra plumbi ponantur, nonne plumbum infra <lb/>aquam deſcendet? </s> <s xml:id="echoid-s6024" xml:space="preserve">nonne igitur libra plumbi libra aquæ grauior?</s> <s xml:id="echoid-s6025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6026" xml:space="preserve">27 Eſt ne idem corpusæque graue in aere, & </s> <s xml:id="echoid-s6027" xml:space="preserve">in aqua, alioue humido? </s> <s xml:id="echoid-s6028" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s6029" xml:space="preserve">grauius eſſe in aere leuius <lb/>in aqua, in aqua enim demerſa leuiora ſunt quam in aere, quantum eſt pondus tantũdem aquæ, ſiue quantum <lb/>eſt pondus aquæ æqualis molis cum illo corpore graui, ſiue quæ occuparet eundem locum, quem graue illud <lb/>occupat porrò grauia triplicia ſunt; </s> <s xml:id="echoid-s6030" xml:space="preserve">alia in aqua omnino demerguntur, atque hæc ſunt natura grauiora quam <lb/>aqua; </s> <s xml:id="echoid-s6031" xml:space="preserve">alia in aqua nec deſcendunt ad fundum, neque parte vlla ſupra aquam eminent, vbicumque poſita <lb/>fuerint; </s> <s xml:id="echoid-s6032" xml:space="preserve">quæ quidem æque grauia eſſe, atque aqua neceſſe eſt. </s> <s xml:id="echoid-s6033" xml:space="preserve">tertia partim eminent atque in genere leuio-<lb/>ra ſunt aqua: </s> <s xml:id="echoid-s6034" xml:space="preserve">hiſce tamen tantumdem aquæ, quanta eſt pars corporis demerſa, ſiue quantum eſt totum cor-<lb/>pus totaliter demerſum, toti graui æqueponderat. </s> <s xml:id="echoid-s6035" xml:space="preserve">hęc omnia quamuis Archimedes in lib. </s> <s xml:id="echoid-s6036" xml:space="preserve">de ijs quæ vehun-<lb/>tur in aqua acutiſſime demonſtrauerit, poſſumus tamen nos eadem practice comprobare, ponderando vide-<lb/>licet iſthæc grauia ſolida in aqua, hoc modo. </s> <s xml:id="echoid-s6037" xml:space="preserve">Corpus quod ponderandum eſt ſeta equina ex altera librę lance <lb/>appendatur, in altera vero lance ponantur pondera; </s> <s xml:id="echoid-s6038" xml:space="preserve">ſic corpus appenſum demittatur in aquam, ita vt libe-<lb/>rè pendeat, reliqua vero tota libra aquam minime contingat, in quo ſtatu diligenter corpus illud pondere-<lb/>tur ac ſi in aere eſſet; </s> <s xml:id="echoid-s6039" xml:space="preserve">manifeſtũ enim apparebit illud minus quam in aere pendere, quantum eſt pondus aquę <lb/>æqualis molis. </s> <s xml:id="echoid-s6040" xml:space="preserve">ſi totum demergatur, & </s> <s xml:id="echoid-s6041" xml:space="preserve">tamen nihil pendat, ſig num eſt eſſe in genere æquè graue, atq; </s> <s xml:id="echoid-s6042" xml:space="preserve">humi-<lb/>dum. </s> <s xml:id="echoid-s6043" xml:space="preserve">ſi partim extiterit, pariter lancem non trahet deorſum. </s> <s xml:id="echoid-s6044" xml:space="preserve">ex Marino Ghetaldo in Promoto Archimede. <lb/></s> <s xml:id="echoid-s6045" xml:space="preserve">ſeta equina æquè grauis eſt atq; </s> <s xml:id="echoid-s6046" xml:space="preserve">aqua, ideo nihil variabit corporis ponderandi grauitatem.</s> <s xml:id="echoid-s6047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6048" xml:space="preserve">28 Qua ratione ſciri poteſt cuiuſuis humidi pondus, etiamſi ipſum non ponderetur? </s> <s xml:id="echoid-s6049" xml:space="preserve">Reſpondeo cor-<lb/>pus ſolidum dato humido grauius ponderetur in aere prius, deinde in humido: </s> <s xml:id="echoid-s6050" xml:space="preserve">quanto enim in humido <lb/>minus pendet, tantumdem etiam pendet alterum tantum illius humidi, quantum eſt ipſum. </s> <s xml:id="echoid-s6051" xml:space="preserve">hac ratione <lb/>poſſumus plurium aquarum pondus experiri, vt quæ ſit leuior, ac proinde ſanior conſtet, ea enim leui or <lb/>erit in qua idem pondus pluſquam in alijs grauitabit. </s> <s xml:id="echoid-s6052" xml:space="preserve">2. </s> <s xml:id="echoid-s6053" xml:space="preserve">Sic corpus aqua leuius in pluribus aquis immitta-<lb/>tur, in qua enim magis demerg etur, ea leuior cæteris erit; </s> <s xml:id="echoid-s6054" xml:space="preserve">in qua vero plus emerget, ea grauior. </s> <s xml:id="echoid-s6055" xml:space="preserve">Sic & </s> <s xml:id="echoid-s6056" xml:space="preserve">qui-<lb/>dem exactiſſimè, adſit primo vas humido quopiam plenum: </s> <s xml:id="echoid-s6057" xml:space="preserve">globulo deinde cereo tantum plumbi addatur, <lb/>vtin eo humido nec ſupernatet, nec deſcendat, ſed vbiq; </s> <s xml:id="echoid-s6058" xml:space="preserve">in eo quieſcat; </s> <s xml:id="echoid-s6059" xml:space="preserve">ſic enim erit æquè grauis ac humi-<lb/>dum. </s> <s xml:id="echoid-s6060" xml:space="preserve">iam ſi in alio quouis humore poſitus, deſcenderit, is erit priori humido leuior; </s> <s xml:id="echoid-s6061" xml:space="preserve">ſi vero ſupernatauerit <lb/>grauior, ſi quieuerit, æquè grauis. </s> <s xml:id="echoid-s6062" xml:space="preserve">imo hac ratione experiri poteris eandem aquam, modo grauiorem eſſe, <lb/>modo leuiorem, pro ambientis aeris frigore, aut calore. </s> <s xml:id="echoid-s6063" xml:space="preserve">Ex prædictis manifeſta eſt cauſa, cur Hydria dum <lb/>ex puteo aqua hauritur non grauitet, quouſque extra aquam emerſerit.</s> <s xml:id="echoid-s6064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6065" xml:space="preserve">29 Cur vas plumbeum, & </s> <s xml:id="echoid-s6066" xml:space="preserve">concauum, quamuis ſit aqua grauius, tamen ſupernatat. </s> <s xml:id="echoid-s6067" xml:space="preserve">Reſpondeo quia <lb/>aer in concauo contentus leuior eſt aqua, quare ex plumbo grauiori, aere vero leuiori, fit compoſicum aqua <lb/>leuius.</s> <s xml:id="echoid-s6068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6069" xml:space="preserve">30 Sit columna marmorea è lacunari perpendiculariter pendens, ei vas aliquod manibus ſuppone, & </s> <s xml:id="echoid-s6070" xml:space="preserve"><lb/>ſuſtine tantæ capacitatis, vt imum columnæ intra ſe contineat, ita tamen vt eam nontangat, proximum ta-<lb/>men ei vndique ſit: </s> <s xml:id="echoid-s6071" xml:space="preserve">inijciatur intra vas tantum aquæ, vt vacuum inter vas, & </s> <s xml:id="echoid-s6072" xml:space="preserve">columnam repleat; </s> <s xml:id="echoid-s6073" xml:space="preserve">hæc igitur <lb/>aqua quamuis modica ſit, mirum tamen quantũ pendeat, & </s> <s xml:id="echoid-s6074" xml:space="preserve">grauitet. </s> <s xml:id="echoid-s6075" xml:space="preserve">Reſpondeo ex dictis num. </s> <s xml:id="echoid-s6076" xml:space="preserve">27. </s> <s xml:id="echoid-s6077" xml:space="preserve">ſolutio ha-<lb/>beri poteſt, cum enim ea pars columnæ, quæ immergitur, tanto leuior fiat, quantum eſt grauitas tantundem <lb/>aquæ, cumque ea grauitas non habeat in nihilum, neceſſe eſt eam grauitati reliquę aquæ commiſceri, ae pro-<lb/>inde ac ſi to tum vas eſſet aqua plenum, in ipſum vas grauitare, ab eoque ſuſtineri.</s> <s xml:id="echoid-s6078" xml:space="preserve"/> </p> <figure> <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01"/> </figure> <p> <s xml:id="echoid-s6079" xml:space="preserve">31 Qua induſtria fieri poteſt, vt aquæ modicum, v.</s> <s xml:id="echoid-s6080" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s6081" xml:space="preserve">vna libra, attollat, ac ſuſtineat quoduis ingens pondus, v.</s> <s xml:id="echoid-s6082" xml:space="preserve">g. </s> <s xml:id="echoid-s6083" xml:space="preserve"><lb/>librarum 1,000. </s> <s xml:id="echoid-s6084" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s6085" xml:space="preserve">accipiatur corpus ſolidum cuiuſuis <lb/>ponderis, quod tamen ſit de genere eorum quæ aqua ſunt <lb/>leuiora; </s> <s xml:id="echoid-s6086" xml:space="preserve">ac propterea in ea ſupernatant. </s> <s xml:id="echoid-s6087" xml:space="preserve">corpus hoc pona-<lb/>tur in aliquo vaſe talis ſiguræ, vt concauum eius congruat <lb/>ferè conuexo corporis ſolidi: </s> <s xml:id="echoid-s6088" xml:space="preserve">tamen inter vas, & </s> <s xml:id="echoid-s6089" xml:space="preserve">ſolidum, <lb/>aqua infundatur, quæ exigua admodum erit; </s> <s xml:id="echoid-s6090" xml:space="preserve">hæc tamen <lb/>deorſum deſcendens infra, ac circa ſolidum circunfuſa, il-<lb/>lud eleuabit, ac natare faciet.</s> <s xml:id="echoid-s6091" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6092" xml:space="preserve">32 Qua arte efficitur vt libra vna aquæ, libris 10. </s> <s xml:id="echoid-s6093" xml:space="preserve">aut 12. <lb/></s> <s xml:id="echoid-s6094" xml:space="preserve">in pari lance æquiponderet? </s> <s xml:id="echoid-s6095" xml:space="preserve">Reſpondeo, ex clauo A. </s> <s xml:id="echoid-s6096" xml:space="preserve"><lb/>parieti affixo ſuſpende Bilancem B C. </s> <s xml:id="echoid-s6097" xml:space="preserve">cui impone bina va-<lb/>ſcula D E. </s> <s xml:id="echoid-s6098" xml:space="preserve">æqualia, capacia, v.</s> <s xml:id="echoid-s6099" xml:space="preserve">g. </s> <s xml:id="echoid-s6100" xml:space="preserve">12. </s> <s xml:id="echoid-s6101" xml:space="preserve">vnciarum aquæ. </s> <s xml:id="echoid-s6102" xml:space="preserve">dein- <pb o="62" file="0082" n="86" rhead="De Mundi Fabrica,"/> de ex altero clauo G. </s> <s xml:id="echoid-s6103" xml:space="preserve">parieti eidem infixo ſuſpendatur ſolidum F. </s> <s xml:id="echoid-s6104" xml:space="preserve">aqua grauius, v.</s> <s xml:id="echoid-s6105" xml:space="preserve">g. </s> <s xml:id="echoid-s6106" xml:space="preserve">ex metallo quopiam, eius <lb/>magnitudinis ac figuræ, vt in vaſculum D. </s> <s xml:id="echoid-s6107" xml:space="preserve">immiſſum, illud ferè impleat, ſed tamen nullo modo illud con-<lb/>tingat; </s> <s xml:id="echoid-s6108" xml:space="preserve">quare inter illud, & </s> <s xml:id="echoid-s6109" xml:space="preserve">concauum vaſis relinquetur exiguum interuallum. </s> <s xml:id="echoid-s6110" xml:space="preserve">lam vaſculum E. </s> <s xml:id="echoid-s6111" xml:space="preserve">repleatur <lb/>totum vncijs 12. </s> <s xml:id="echoid-s6112" xml:space="preserve">alterum etiam D. </s> <s xml:id="echoid-s6113" xml:space="preserve">repleatur aqua ſecundum illud vacuum, quod in eo eſt, quodq; </s> <s xml:id="echoid-s6114" xml:space="preserve">vnius tan-<lb/>tum vnciæ capax eſt; </s> <s xml:id="echoid-s6115" xml:space="preserve">& </s> <s xml:id="echoid-s6116" xml:space="preserve">mirum omnino videbis, hanc ſcilicet aquæ vnciam vncijs duodecim æquè pondera-<lb/>re, atque æquilibrium facere, ratio patet ex prædictis.</s> <s xml:id="echoid-s6117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6118" xml:space="preserve">33 Qua induſtria effici poteſt, vt quoduis corpus ex ijs, quæ ſolẽt in humido demergi, vti ſunt metalla, & </s> <s xml:id="echoid-s6119" xml:space="preserve"><lb/>lapides, in ea ſupernatet, etiã ſi ſuperius minime ſit concauũ, ſed rectum & </s> <s xml:id="echoid-s6120" xml:space="preserve">planum, cuiuſmodi ſunt acus fer-<lb/>reæ, laminę aureæ, plumbeæ, &</s> <s xml:id="echoid-s6121" xml:space="preserve">c. </s> <s xml:id="echoid-s6122" xml:space="preserve">ramenta etiã horum metallorũ minutiſſima. </s> <s xml:id="echoid-s6123" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s6124" xml:space="preserve">primo neceſſe eſſe præ-<lb/>dicta corpora habere quandã tenuitatem determinatã, quã ſi exceſſerint nũquam innare poterunt. </s> <s xml:id="echoid-s6125" xml:space="preserve">2. </s> <s xml:id="echoid-s6126" xml:space="preserve">oporte-<lb/>re vt ſint omnino arida & </s> <s xml:id="echoid-s6127" xml:space="preserve">ſicca, aliter aqua ſuper ea effundetur, vnde & </s> <s xml:id="echoid-s6128" xml:space="preserve">demergẽtur. </s> <s xml:id="echoid-s6129" xml:space="preserve">3. </s> <s xml:id="echoid-s6130" xml:space="preserve">magna dexteritate in <lb/>aquæ ſuperficie ſecundũ aquæ æquilibriũ ſunt collocanda, ideſt, ne ex vna parte prius, quam ex altera aquam <lb/>contingant: </s> <s xml:id="echoid-s6131" xml:space="preserve">hac enim diligentia adhibita omnia natare queũt, vt plurimis experientijs conſtat. </s> <s xml:id="echoid-s6132" xml:space="preserve">debent autẽ <lb/>eſſe tenuuia, ſeu minimam habere altitudinem, quia aliter non poſſunt concurrere ad leuitatem huic nego-<lb/>tio neceſſariam, vt mox conſtabit: </s> <s xml:id="echoid-s6133" xml:space="preserve">ex maiori enim craſſitie ſequitur & </s> <s xml:id="echoid-s6134" xml:space="preserve">maius pondus. </s> <s xml:id="echoid-s6135" xml:space="preserve">debent eſſe ſicca, ſecus <lb/>enim aqua in quam ponuntur ſuper ea accurrit, ac aerem illis adhærentem, ac leuitatem expellens, cauſa eſt <lb/>vt demergantur. </s> <s xml:id="echoid-s6136" xml:space="preserve">ſi vero ſicca ſint, aqua ſuper ea non effunditur, ſed circa eorum extremitates paululum in <lb/>gyrum intumeſcens paruum aggerem ſatis tamen viſibilem efficit, intra quem aerem contineri neceſſe eſt; <lb/></s> <s xml:id="echoid-s6137" xml:space="preserve">quare perinde eſt, ac ſi concaua eſſent, aut ſi ſpondas haberent, intra quas aer exiſtens, & </s> <s xml:id="echoid-s6138" xml:space="preserve">leuitans ſimul cum <lb/>eis facit compoſitum aqua leuius ac natare potens, vti num. </s> <s xml:id="echoid-s6139" xml:space="preserve">30. </s> <s xml:id="echoid-s6140" xml:space="preserve">dictum eſt. </s> <s xml:id="echoid-s6141" xml:space="preserve">Vbi notandum eſt, quod cum te-<lb/>nuitas requiſita aderit, tunc laminæ, & </s> <s xml:id="echoid-s6142" xml:space="preserve">bracteæ quantumuis latę, & </s> <s xml:id="echoid-s6143" xml:space="preserve">quantumuis anguſtæ; </s> <s xml:id="echoid-s6144" xml:space="preserve">ſimiliter acus quan-<lb/>tumlibet longæ, aut breuiſſimæ ſint, ſupernatant. </s> <s xml:id="echoid-s6145" xml:space="preserve">vnde ſequitur quamlibet natãtis bracteæ, aut acus, partem <lb/>pariter natare poſſe, quod etiam experientia comprobat: </s> <s xml:id="echoid-s6146" xml:space="preserve">imo acus ex ebeno eiuſdem longitudinis, cum alti-<lb/>tudine natantis aſſerculi ex ebeno, etiamſi ponatur in aqua acumine deorſum ita vt erectæ horizonti conſi-<lb/>ſtant, non merguntur, ſed ex paruulo aggere, & </s> <s xml:id="echoid-s6147" xml:space="preserve">aere ſuſpenduntur. </s> <s xml:id="echoid-s6148" xml:space="preserve">hæc mihi occurrerunt, alij alias cauſas <lb/>pro libito afferant.</s> <s xml:id="echoid-s6149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6150" xml:space="preserve">34 Fieri ne poteſt, vt duo pueri eodem loco ac tempore nati, poſtea in numero dierum diſcrepent? </s> <s xml:id="echoid-s6151" xml:space="preserve">ideſt, <lb/>vnus eorum ſuæ ætatis dies plures, quam alter verè numeret? </s> <s xml:id="echoid-s6152" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s6153" xml:space="preserve">hoc quidem magnum videri parado-<lb/>xum, verumtamen verè aliquando accidere, quod vt cito ac rectè intelligatur, conſidera hanc figuram, in qua <lb/>ſphæra illa terra eſt, in qua oriens, & </s> <s xml:id="echoid-s6154" xml:space="preserve">occidens vt vides; </s> <s xml:id="echoid-s6155" xml:space="preserve">Gemelli in eodem loco nati ſint A B. </s> <s xml:id="echoid-s6156" xml:space="preserve">pergat igitur <lb/> <anchor type="figure" xlink:label="fig-0082-01a" xlink:href="fig-0082-01"/> B. </s> <s xml:id="echoid-s6157" xml:space="preserve">verſus occidentem, A. </s> <s xml:id="echoid-s6158" xml:space="preserve">verò orientem verſus, ambo vſque ad <lb/>antipodas. </s> <s xml:id="echoid-s6159" xml:space="preserve">Aio quod cum inuicem occurrerint in numero die-<lb/>rum diſcrepabunt; </s> <s xml:id="echoid-s6160" xml:space="preserve">& </s> <s xml:id="echoid-s6161" xml:space="preserve">B. </s> <s xml:id="echoid-s6162" xml:space="preserve">qui occidẽtale itet peregit die vno ab A. <lb/></s> <s xml:id="echoid-s6163" xml:space="preserve">orientali deficiet. </s> <s xml:id="echoid-s6164" xml:space="preserve">ratio huius eſt quoniam progreſſus occidenta-<lb/>lis Soiem ſequitur, & </s> <s xml:id="echoid-s6165" xml:space="preserve">proinde dies ei naturales longiores fiunt, <lb/>ac proinde in toto ſemicirculo B C B pauciores, qui defectus tan-<lb/>tus eſſe poteſt, quantũ ſemicirculus prædictus, qui gr. </s> <s xml:id="echoid-s6166" xml:space="preserve">180. </s> <s xml:id="echoid-s6167" xml:space="preserve">conti-<lb/>net, infert, porrò cum gr. </s> <s xml:id="echoid-s6168" xml:space="preserve">15. </s> <s xml:id="echoid-s6169" xml:space="preserve">vnam horam efficiant, gr. </s> <s xml:id="echoid-s6170" xml:space="preserve">180. </s> <s xml:id="echoid-s6171" xml:space="preserve">horas <lb/>12. </s> <s xml:id="echoid-s6172" xml:space="preserve">ſiue dimidium diem efficient; </s> <s xml:id="echoid-s6173" xml:space="preserve">quapropter defectus dierũ, huic <lb/>erit dimidij diei, qui defectus o@itur ex quotidianis dierũ incre-<lb/>mentis. </s> <s xml:id="echoid-s6174" xml:space="preserve">e contra A. </s> <s xml:id="echoid-s6175" xml:space="preserve">quia aduerſo Sole perficiſcitur dies naturales <lb/>breuioris in toto ſemicirculo A D A. </s> <s xml:id="echoid-s6176" xml:space="preserve">ſortitur, ac proinde plures: </s> <s xml:id="echoid-s6177" xml:space="preserve"><lb/>qui exc @@us erit neceſia@io tantus quantus in ſemicirculo gr. </s> <s xml:id="echoid-s6178" xml:space="preserve">180. </s> <s xml:id="echoid-s6179" xml:space="preserve"><lb/>oriri pote@t; </s> <s xml:id="echoid-s6180" xml:space="preserve">qui pariter eſt horarum 12. </s> <s xml:id="echoid-s6181" xml:space="preserve">ſiue diei dimidij. </s> <s xml:id="echoid-s6182" xml:space="preserve">qui de-<lb/>fectus oritur ex quotidianis dierum defectibus. </s> <s xml:id="echoid-s6183" xml:space="preserve">cùm igitur occi-<lb/>dentales dies deficiant horis 12. </s> <s xml:id="echoid-s6184" xml:space="preserve">ab ordinarijs diebus; </s> <s xml:id="echoid-s6185" xml:space="preserve">orientales <lb/>vero totidem eoſdem ſuperent, conſequetur neceſſario dies oc-<lb/>cidentales horis 24. </s> <s xml:id="echoid-s6186" xml:space="preserve">ideſt, integro die à diebus orientalibus deficere. </s> <s xml:id="echoid-s6187" xml:space="preserve">A, igitur vno die natu maior erit quam <lb/>B. </s> <s xml:id="echoid-s6188" xml:space="preserve">quod omnino videbatur impoſſibile. </s> <s xml:id="echoid-s6189" xml:space="preserve">quamuis autem dies ſint impares, ętates tamen eorum æquales ſunt: </s> <s xml:id="echoid-s6190" xml:space="preserve"><lb/>differentia enim oritur ex longioribus ac breuioribus diebus. </s> <s xml:id="echoid-s6191" xml:space="preserve">Quod ſi ijſdem continuatis contrarijs itine-<lb/>ribus ad natiuum locum reuertentur, tunc per duos integros dies ab inuicem diſcreparent. </s> <s xml:id="echoid-s6192" xml:space="preserve">Hinc manife-<lb/>ſta eſſe cauſa poteſt illius putati erroris in dierum numeratione, in quem initio Indicarum nauigationum <lb/>ſæpe Europæi in contrarias partes ſoluentes, ac ſibi mutuo ad antipodas occurrentes, magna cum admira-<lb/>tione incidebant.</s> <s xml:id="echoid-s6193" xml:space="preserve"/> </p> <div xml:id="echoid-div131" type="float" level="2" n="8"> <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a"> <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0082-01"/> </figure> </div> <p> <s xml:id="echoid-s6194" xml:space="preserve">35 Qua arte diuerſorum cubiculorum calorem, aut frigus exactè expendere poſſumus? </s> <s xml:id="echoid-s6195" xml:space="preserve">Reſpondeo ſu-<lb/>me ampullam de qua in capite de motu aeris egi, & </s> <s xml:id="echoid-s6196" xml:space="preserve">ingredere diuerſa cubicula, in quo enim plus aqua A C. <lb/></s> <s xml:id="echoid-s6197" xml:space="preserve">deſcendet illud erit calidius; </s> <s xml:id="echoid-s6198" xml:space="preserve">in quo vero mag is aſcendet<unsure/> frigidius erit. </s> <s xml:id="echoid-s6199" xml:space="preserve">hinc patet ampullam hanc Thermo-<lb/>ſcopium non ineptè appellari poſſe.</s> <s xml:id="echoid-s6200" xml:space="preserve"/> </p> <pb o="63" file="0083" n="87"/> </div> <div xml:id="echoid-div133" type="section" level="1" n="83"> <head xml:id="echoid-head90" xml:space="preserve">LIBER OCTAVVS</head> <head xml:id="echoid-head91" xml:space="preserve">DE CÆLO VNIVERSE@.</head> <head xml:id="echoid-head92" style="it" xml:space="preserve">De loco Calestis regionis. Cap. I.</head> <p> <s xml:id="echoid-s6201" xml:space="preserve">MAnifeſtum eſt locum huius nobiliſſimæ Mundi partis eſſe pariter nobiliſſimum, altiſſimum <lb/>videlicet ac ſupra cæteras Mundi partes Elementares, quandoquidem hæc ſuprema pars to-<lb/>tam illam intra ſe, veluti proprio ſinu complectitur atque circundat, ex quouis namque ter-<lb/>ræ loco videmus cæleſtia corpora, luminaria nempè, & </s> <s xml:id="echoid-s6202" xml:space="preserve">ſydera omnia ſupra hanc infimam. <lb/></s> <s xml:id="echoid-s6203" xml:space="preserve">Mundi portionem circumferri.</s> <s xml:id="echoid-s6204" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div134" type="section" level="1" n="84"> <head xml:id="echoid-head93" style="it" xml:space="preserve">De Cæli figura. Cap. II.</head> <p> <s xml:id="echoid-s6205" xml:space="preserve">PErſpicuum quoque ex præmiſſis, tum de figura Sphæræ Elementaris, tum de figura totius Mundi eſſe <lb/>poteſt Cæli figuram eſſe orbem. </s> <s xml:id="echoid-s6206" xml:space="preserve">habet enim ſupremam; </s> <s xml:id="echoid-s6207" xml:space="preserve">ac conuexam ſuperficiem ſphæricam, quæ eſt <lb/>eadem cum totius vniuerſi figura, quam ſphæricam eſſe iam probauimus. </s> <s xml:id="echoid-s6208" xml:space="preserve">habet etiam concauam, quæ con-<lb/>uexam ſphæræ ſublunaris contingit, quam itidem ſphæricam eſſe oſtendimus. </s> <s xml:id="echoid-s6209" xml:space="preserve">vnde ſequitur illud quoque <lb/>concauum, quod huic congruit, & </s> <s xml:id="echoid-s6210" xml:space="preserve">coaptatur eſſe pariter ſphæricum. </s> <s xml:id="echoid-s6211" xml:space="preserve">cum ergo pars hæc cæleſtis binis ter-<lb/>@inetur ſuperficiebus conuexa, & </s> <s xml:id="echoid-s6212" xml:space="preserve">concaua, figura orbiculari prædicta ſit oportet.</s> <s xml:id="echoid-s6213" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6214" xml:space="preserve">Idem ex motibus, quibus reuoluitur conſtare poteſt, ſunt enim vt ſenſus teſtatur, & </s> <s xml:id="echoid-s6215" xml:space="preserve">mox dicemus, circu-<lb/>lares & </s> <s xml:id="echoid-s6216" xml:space="preserve">ſphærici, quique orbiculari figuræ maxime competant.</s> <s xml:id="echoid-s6217" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div135" type="section" level="1" n="85"> <head xml:id="echoid-head94" style="it" xml:space="preserve">De Cæli motibus. Cap. III.</head> <p> <s xml:id="echoid-s6218" xml:space="preserve">IN cęleſti regione motum exiſtere, vel vulgo manifeſtum eſt; </s> <s xml:id="echoid-s6219" xml:space="preserve">cum omnes Planetas, ac ſydera perpetuo cir-<lb/>cumagi videamus. </s> <s xml:id="echoid-s6220" xml:space="preserve">quis tamen ſit eorum motus, quaque ratione fiat, haud ita facile eſt explicatu. </s> <s xml:id="echoid-s6221" xml:space="preserve">Eſt enim <lb/>hac ſyderum gyratio non ſimplex motus circularis, quo per eundem ſemper gyrum recurrãt, ſed eſt motus, <lb/>vt opinantur mixtus, non perfectè circularis, ſed ſpir@lis, ac ſphæricus. </s> <s xml:id="echoid-s6222" xml:space="preserve">ſpiræ autem ſunt reuolutiones, ſeu <lb/>glomerationes, quæ in ſe ipſas non recurrunt. </s> <s xml:id="echoid-s6223" xml:space="preserve">talis eſt linea, ſeu reuolutio torcularis, quam & </s> <s xml:id="echoid-s6224" xml:space="preserve">helicem, & </s> <s xml:id="echoid-s6225" xml:space="preserve">co-<lb/>chleam ob ſimilitudinem appellant. </s> <s xml:id="echoid-s6226" xml:space="preserve">talem etiam ſpiram efficit ductarius ſucculæ funis: </s> <s xml:id="echoid-s6227" xml:space="preserve">is enim ab vna ſuc-<lb/>culæ parte per ſucculam ſpiratim agglomeratur, ideſt, gyris vno poſt alterum ſucceſſiuè, vſque ad alterum <lb/>extremum procedentibus; </s> <s xml:id="echoid-s6228" xml:space="preserve">vnde iterum reflexa conuolutione ad priorem partem reuertitur. </s> <s xml:id="echoid-s6229" xml:space="preserve">Porrò hæſpi-<lb/>@ales lineæ<unsure/>, à locis in quibus deſcr buntur denominantur; </s> <s xml:id="echoid-s6230" xml:space="preserve">ſic ea quæ in cylindri ſuperficie ducitur, cylindri-<lb/>ca ſpira cognominatur; </s> <s xml:id="echoid-s6231" xml:space="preserve">qualis eſt torculi cochlea: </s> <s xml:id="echoid-s6232" xml:space="preserve">quæ vero in conica ſuperficie, dicitur conica, vti ferè in li-<lb/>macum teſtis apparent. </s> <s xml:id="echoid-s6233" xml:space="preserve">quæ in ſphærica ſuperficie ſpiralis ſphærica nuncupatur, quales eſſe etiam oportet <lb/>eas, quas Planetæ præcipuè deſcribunt, ipſorum enim motus ſphærici, ac ſpirales exiſtunt. </s> <s xml:id="echoid-s6234" xml:space="preserve">id enim manife-<lb/>ſte apparet in luminaribus Sole, videlicet ac Luna, ac reliquis Planetis; </s> <s xml:id="echoid-s6235" xml:space="preserve">ij enim conſpiciuntur ab vno ad al-<lb/>terum Tropicũ vltro citroque continuo per continuas ſpiras remeare. </s> <s xml:id="echoid-s6236" xml:space="preserve">ſic videmus Solem hyeme ſecus Ca-<lb/>pricorni Tropicum incedere; </s> <s xml:id="echoid-s6237" xml:space="preserve">deinde ſenſim, ac ſpiratim altius ferri, ac proinde quotidie ſupra horizontem <lb/>eleuari, noſtroque vertici appropinquare, quouſque Cancri tropen attingat; </s> <s xml:id="echoid-s6238" xml:space="preserve">vnde iterum aliam ſpiram re-<lb/>texendo ad brumalem tropen relabitur. </s> <s xml:id="echoid-s6239" xml:space="preserve">hanc ſpiram materialis ſphæræ auxilio rectè percipies hoc modo: <lb/></s> <s xml:id="echoid-s6240" xml:space="preserve">Soiem illum materialem, quem circulo ſecundi motus affiximus, colloca ſub altero Tropicorum, v.</s> <s xml:id="echoid-s6241" xml:space="preserve">g. </s> <s xml:id="echoid-s6242" xml:space="preserve">ſub ini-<lb/>@io Cancri, deinde fac vt tardè ſecundum ſignorum conſequentiã, ideſt, verſus Leonem incedat, eo ſic tardè <lb/>incedente, fac vt ſimul ea ſphæræ pars quæ primum mobile dicitur, ab oriente in occidentem velociter re-<lb/>uoluatur: </s> <s xml:id="echoid-s6243" xml:space="preserve">videbis enim concurrentibus in vnum duobus hiſce motibus, Solem illum materialem paulatim <lb/>per lineam ſpiralem verſus Aequatorem, atque alterum Tropicum deuo lui. </s> <s xml:id="echoid-s6244" xml:space="preserve">vel ſic, imaginare formicam in <lb/>Eclyptica tardiſſimè ſecundum ſignorum ſequelam progredi, vti a primo gradu Cancri ad ſecundum, & </s> <s xml:id="echoid-s6245" xml:space="preserve">ſic <lb/>deinceps, qua ſic pergente, interim primum mobile ſuper mundi polis motu diurno, ideſt, ab oriente ad <lb/>occaſum cito reuoluatur, intelliges enim formicam illam ſpiratim, ac ſenſim ad alteram tropen deſcendere. </s> <s xml:id="echoid-s6246" xml:space="preserve"><lb/>atque hic eſt ille motus mixtus, quo omnes errantes, atque inerrantes ſtellæ prouoluuntur; </s> <s xml:id="echoid-s6247" xml:space="preserve">qui etiam ſolet <lb/>explicari per duos ſimplices motus circulares; </s> <s xml:id="echoid-s6248" xml:space="preserve">ſolet enim dici Planeta mouetur motu diurno ab oriente in <lb/>occidentem ſpatio 24. </s> <s xml:id="echoid-s6249" xml:space="preserve">horarum, motu proprio ab occidente in orientem per Zodiacum. </s> <s xml:id="echoid-s6250" xml:space="preserve">qui duo motus, qua <lb/>ratione in vnum eundemq; </s> <s xml:id="echoid-s6251" xml:space="preserve">ſpiralem mo@um coaleſcant, exemplis tum ſolis materialis, tum formicæ modò <lb/>allatis, probè poteſt intelligi.</s> <s xml:id="echoid-s6252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6253" xml:space="preserve">Iam verò præter hos duos partiales motus diurnum ſcilicet, & </s> <s xml:id="echoid-s6254" xml:space="preserve">proprium, ſeu primum, & </s> <s xml:id="echoid-s6255" xml:space="preserve">ſecundum; </s> <s xml:id="echoid-s6256" xml:space="preserve">ſeu <lb/>primi mobilis, & </s> <s xml:id="echoid-s6257" xml:space="preserve">ſecundorum mobilium, ideſt, Planetarum; </s> <s xml:id="echoid-s6258" xml:space="preserve">reperitur etiam tertius qui trepidationis, ſeu <lb/>acceſſus, & </s> <s xml:id="echoid-s6259" xml:space="preserve">receſſus dicitur, qui motus non integrum abſoluit circulum, ſed eſt quædam veluti tardiſſima <lb/>mundi libratio, qua poli Eclypticæ, ac proinde tota cæleſtis regio à Septentrione in Auſtrum, & </s> <s xml:id="echoid-s6260" xml:space="preserve">è contra <pb o="64" file="0084" n="88" rhead="De Mundi Fabrica,"/> per 24. </s> <s xml:id="echoid-s6261" xml:space="preserve">minuta in coluro ſolſtitiorum reciprocatur; </s> <s xml:id="echoid-s6262" xml:space="preserve">vti latius cùm de Stellis inerrantibus agetur, explicabi-<lb/>tur. </s> <s xml:id="echoid-s6263" xml:space="preserve">hac vero libratione fieri neceſſe eſt, vt ſpirales prædicti ſyderum motus ſubinde varientur, atq; </s> <s xml:id="echoid-s6264" xml:space="preserve">aliquan-<lb/>do per 24. </s> <s xml:id="echoid-s6265" xml:space="preserve">min. </s> <s xml:id="echoid-s6266" xml:space="preserve">hinc inde ad vtramq; </s> <s xml:id="echoid-s6267" xml:space="preserve">tropen augeatur, ac minuatur. </s> <s xml:id="echoid-s6268" xml:space="preserve">ſunt igitur omnino tres in cælis motio-<lb/>nes, quas concipimus in vnum, eundemq; </s> <s xml:id="echoid-s6269" xml:space="preserve">ſpiralem motum coaleſcere, quo omnia ſydera circa mundum ſpi-<lb/>ratim circumferuntur.</s> <s xml:id="echoid-s6270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6271" xml:space="preserve">Demum aduertendum eſt hac ſpirali latione ſydera ſemper moueri ab oriente per meridiem in occiden-<lb/>tem, ideſt, ſemper magis accedere ad partes occidentales. </s> <s xml:id="echoid-s6272" xml:space="preserve">quando itaque nonnulli dicunt Planetas moueri <lb/>motibus contrarijs, ideſt, motu diurno ab oriente ad occidentem: </s> <s xml:id="echoid-s6273" xml:space="preserve">& </s> <s xml:id="echoid-s6274" xml:space="preserve">è contra, motu proprio ab occidente <lb/>in orientem, non ita intelligendi ſunt, vt velint eundem planetam eodem tempore appropinquare occiden-<lb/>ti, & </s> <s xml:id="echoid-s6275" xml:space="preserve">orienti; </s> <s xml:id="echoid-s6276" xml:space="preserve">hoc enim eſt omnino impoſſibile, nec vllo modo intelligi poteſt: </s> <s xml:id="echoid-s6277" xml:space="preserve">ſed intelligendum eſt plane-<lb/>tas ſpirali motu, qui ex prædictis coaleſcit, ſemper ad occidentem properare. </s> <s xml:id="echoid-s6278" xml:space="preserve">quia talis eſt hic ſpiralis mo-<lb/>tus, ac ſi oriretur à duobus motoribus, quorum vnus aſtrum tardè verſus orientem ſub Zodiaco, alter vero <lb/>ocy ſſimè è contra ab oriente in occidentem motu diurno propelleret.</s> <s xml:id="echoid-s6279" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6280" xml:space="preserve">Vtrum autem ſola ſydera, an etiam ipſi cæli, aut cæleſtis regio hiſce circuitibus ac ſpiris commoueatur, <lb/>certo ac euidenter affirmare non auſim. </s> <s xml:id="echoid-s6281" xml:space="preserve">probabile tamen admodum videtur regionem illam affixarum ſtel-<lb/>larum, quæ Firmamento merito appellatur vna cum ſibi infixis ſyderibus conuolui; </s> <s xml:id="echoid-s6282" xml:space="preserve">quandoquidem tot lu-<lb/>minum myriades certo ac perpetuo ab initio mundi ordine, quaſi in aciem diſtributæ, videntur aliquo ege-<lb/>re fundo, cui dum adeo ſtabili concordia prouoluuntur, fixæ inhæreant. </s> <s xml:id="echoid-s6283" xml:space="preserve">Cæteri vero errones num liberi ceu <lb/>Piſces in aqua, aut aues in aere ferantur, incompertum mihi eſt.</s> <s xml:id="echoid-s6284" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6285" xml:space="preserve">Porrò qua ratione Aſtronomi diurnum motum in aſtris poſuerint nihil eſt dicẽdum, cum id ſit vulgo no-<lb/>tum, ac proinde inſtar principij. </s> <s xml:id="echoid-s6286" xml:space="preserve">quibus vero obſeruationibus, ac apparentijs planetas ſub Zodiaco motibus <lb/>proprijs ſecundum ſignorum ordinem, ſeu orientem verſus progredi depræhenderint, dicendum eſt breui-<lb/>ter. </s> <s xml:id="echoid-s6287" xml:space="preserve">Primo igitur obleruarunt Lunam nouam quotidie veſperi magis à Sole recedere verſus orientem, do-<lb/>nec ei opponatur, ac pleno lumine reſplendeat. </s> <s xml:id="echoid-s6288" xml:space="preserve">poſtea vlterius pergens ad Solem accedere quotidie magis. <lb/></s> <s xml:id="echoid-s6289" xml:space="preserve">quouſque ipſum denuo aſſequatur. </s> <s xml:id="echoid-s6290" xml:space="preserve">2. </s> <s xml:id="echoid-s6291" xml:space="preserve">obſeruauerunt Lunam, cæteroſque planetas collatos ad fixas ſtellas, eas <lb/>paulatim verſus orientem præterire. </s> <s xml:id="echoid-s6292" xml:space="preserve">3. </s> <s xml:id="echoid-s6293" xml:space="preserve">Idem in ſtellis Firmamenti, ſed tamen ſerius, ac difficilius compere-<lb/>runt; </s> <s xml:id="echoid-s6294" xml:space="preserve">notarunt enim quaſdam ſtellas parum ante puncta æquinoctialia Arietis, & </s> <s xml:id="echoid-s6295" xml:space="preserve">Libræ, eaſque depræhen-<lb/>derunt ijſdem punctis fieri propiores, donec tandem illa prætergrederentur. </s> <s xml:id="echoid-s6296" xml:space="preserve">ſpica Virginis, quæ olim gra-<lb/>dibus 8. </s> <s xml:id="echoid-s6297" xml:space="preserve">æquinoctium autumnale, ſeu initium Libræ præcedebat, modo illud gradibus 18. </s> <s xml:id="echoid-s6298" xml:space="preserve">ſubſequ. </s> <s xml:id="echoid-s6299" xml:space="preserve">qua de r@ <lb/>vberius cum de octaua Sphæra, ſeu Firmamento tractandum erit. </s> <s xml:id="echoid-s6300" xml:space="preserve">4. </s> <s xml:id="echoid-s6301" xml:space="preserve">Inſtrumentis fabrefactis, ac magnis de-<lb/>præhenderunt planetarum, ac ſtellarum declinationes, ideſt, earum diſtantias ab æquatore variari, ſed ea ta-<lb/>men lege, vt eaſdem quas habet Zodiacus declinationes, ſemper ſubirent. </s> <s xml:id="echoid-s6302" xml:space="preserve">quapropter con cluſerunt eos hoc <lb/>ſecundo motu perpetuo moueri ſub quadam faſcia, quam poſtea Zodiacum appellarunt; </s> <s xml:id="echoid-s6303" xml:space="preserve">cuius poli diſtant à <lb/>polis æquatoris gr. </s> <s xml:id="echoid-s6304" xml:space="preserve">23. </s> <s xml:id="echoid-s6305" xml:space="preserve">30′. </s> <s xml:id="echoid-s6306" xml:space="preserve">vti ſupra diximus. </s> <s xml:id="echoid-s6307" xml:space="preserve">Idem confirmatur ex obſeruatione varij ortus, & </s> <s xml:id="echoid-s6308" xml:space="preserve">occaſus ſy-<lb/>derum in horizonte, habent enim latitudinem ortiuam, & </s> <s xml:id="echoid-s6309" xml:space="preserve">occiduam in horizonte inter vtrumque Tropicũ <lb/>intercepto: </s> <s xml:id="echoid-s6310" xml:space="preserve">oriuntur enim & </s> <s xml:id="echoid-s6311" xml:space="preserve">occidunt in toto illo horizontis arcu, qui etiam varius eſt pro var<unsure/>ia eleua-<lb/>tione poli: </s> <s xml:id="echoid-s6312" xml:space="preserve">eundem namq; </s> <s xml:id="echoid-s6313" xml:space="preserve">arcum horizontis Zodiacus tortuosè radit. </s> <s xml:id="echoid-s6314" xml:space="preserve">variæ pariter altitudines meridianæ <lb/>idem comprobant, modo enim in eo propè horizontem incedunt, & </s> <s xml:id="echoid-s6315" xml:space="preserve">paulatim ſuccedentibus diebus attol-<lb/>luntur, donec ad ſummas altitudines aſcenderint, vnde iterum deſcendere incipiunt; </s> <s xml:id="echoid-s6316" xml:space="preserve">in quo etiam ductum <lb/>Zodiaci manifeſtè ſequuntur.</s> <s xml:id="echoid-s6317" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6318" xml:space="preserve">Tandem ad perfectam horum motuum intelligentiam, conſiderandum eſt, quod ſi mundus à diurna con-<lb/>uerſione ceſſaret, planetæ tamen, & </s> <s xml:id="echoid-s6319" xml:space="preserve">ſtellæ orirentur, ſed in occidente, & </s> <s xml:id="echoid-s6320" xml:space="preserve">progrederentur ad orientem oblie <lb/>què ſecundum Zodiaci obliquitatem, ideſt, non ſecundum lationes æquatori paralellas, ſemperque magis <lb/>orienti appeterent, contra quam nunc facian@; </s> <s xml:id="echoid-s6321" xml:space="preserve">diuque ſupra horizontem ſecundum medias eorum periodo@ <lb/>detinerentur, Sol enim ſex menſibus, Luna diebus 14. </s> <s xml:id="echoid-s6322" xml:space="preserve">&</s> <s xml:id="echoid-s6323" xml:space="preserve">c. </s> <s xml:id="echoid-s6324" xml:space="preserve">ſupra horizontem perpetuo exiſterent antequam <lb/>ab occidente vnde orirenturad orientem peruenirent, vbi occiderent; </s> <s xml:id="echoid-s6325" xml:space="preserve">atque per totidem dies ſub horizon@ <lb/>te latitarent: </s> <s xml:id="echoid-s6326" xml:space="preserve">Quod ſi è contra motu proprio deſtituerentur, non autem diurno, tunc perpetuo directè a@ <lb/>oriente vbi orirentut, in occidentem vbi occiderent promoti, ſpatio vnius diei artificialis, peruenireni, a@ <lb/>ſemper directè per eundem circulum, non autem ſpiram, æquatori paralellum, ſpatio 24. </s> <s xml:id="echoid-s6327" xml:space="preserve">horarum, recurre-<lb/>rent, ſemperq; </s> <s xml:id="echoid-s6328" xml:space="preserve">in eiſdem horizontis punctis orirentur, atque occiderent: </s> <s xml:id="echoid-s6329" xml:space="preserve">neque ab vno Tropico ad alterum <lb/>reuerterentur. </s> <s xml:id="echoid-s6330" xml:space="preserve">Pariter poſſumus trepidationis motum per ſe ſolum conſiderare, quo omnia ſydera per 24. <lb/></s> <s xml:id="echoid-s6331" xml:space="preserve">minuta ab Auſtro in Boream, & </s> <s xml:id="echoid-s6332" xml:space="preserve">a Borea in Auſtrum tardiſſime titubarent.</s> <s xml:id="echoid-s6333" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6334" xml:space="preserve">Non me latet a recentioribus Aſtronomis alium quartum motum cælo attribui, quo tanquamdibratio-<lb/>ne quadam in mundi latera, ſeu ab oriente in occidentem, & </s> <s xml:id="echoid-s6335" xml:space="preserve">contra, ad modicum interuallum titubat, atque <lb/>reciprocatur: </s> <s xml:id="echoid-s6336" xml:space="preserve">ſed quoniam eum nondum ſatis exploratum exiſtimo, ideo ne, quam inſtitutum meum patia-<lb/>tur, longior ſim, eum prætermittendum cenſui.</s> <s xml:id="echoid-s6337" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6338" xml:space="preserve">Hæc igitur de tribus cæli motibus ſimplicibus, ac partialibus, dicta ſufficiant, qui in vnum mixtum, & </s> <s xml:id="echoid-s6339" xml:space="preserve"><lb/>ſpiralem coaleſcunt, quo tandem vltimo ſydera circumferri videmus. </s> <s xml:id="echoid-s6340" xml:space="preserve">Neque vero cuique impoſſibile vi-<lb/>deri debet idem corpus motu mixto, ideſt, qui ex pluribus miſceatur agitari poſſe, videmus enim Trochũ, <lb/>quem pueri ludentes circumagunt, tali motu percelli, nam eodem tempore Trochus gyrat, ſaltat, titubat, <lb/>a@tortuosè progreditur. </s> <s xml:id="echoid-s6341" xml:space="preserve">cum autem de ſingulis Planetis, & </s> <s xml:id="echoid-s6342" xml:space="preserve">Firmamento tractabitur, tunc hæc omnia ex-<lb/>piicatius tradentur.</s> <s xml:id="echoid-s6343" xml:space="preserve"/> </p> <pb o="65" file="0085" n="89" rhead="Liber Octauus."/> </div> <div xml:id="echoid-div136" type="section" level="1" n="86"> <head xml:id="echoid-head95" style="it" xml:space="preserve">Cap. IIII. Seu de numero Cælorum, & Magnitudine.</head> <p> <s xml:id="echoid-s6344" xml:space="preserve">AN tota cæleſtis regio in plures cælos re ipſa diſtinctos diuidatur, haud ita facile eſt determinare, vt non-<lb/>nulli exiſtimant; </s> <s xml:id="echoid-s6345" xml:space="preserve">qua de ie nonnullorum Philoſophorum rogatu, nonnulla ex aliorum ſententia, @n me-<lb/>dium afferam, non vt ego quidquam de ea ſtatuam, ſed vt ipſi, quorum id munus eſt, de ea ſententiam tãdem <lb/>aliquam ferre valeant. </s> <s xml:id="echoid-s6346" xml:space="preserve">ſciendum igitur primo eſt veteres Aſtronomos, Hipparchum, Ptolomæu@n, & </s> <s xml:id="echoid-s6347" xml:space="preserve">alios <lb/>de hac cælorum diſtinctione, nihil certi loquutos eſſe, vt videre eſt apud Ptolemæum, & </s> <s xml:id="echoid-s6348" xml:space="preserve">alios; </s> <s xml:id="echoid-s6349" xml:space="preserve">verum ipſi <lb/>hypotheticè loquebantur, nam poſita tali cælorum diuifione aut numero excuſantur apparentiæ, & </s> <s xml:id="echoid-s6350" xml:space="preserve">obſer-<lb/>uationes. </s> <s xml:id="echoid-s6351" xml:space="preserve">imo ipſi vt videre eſt apud Ptolemæum, & </s> <s xml:id="echoid-s6352" xml:space="preserve">Proclum, haſce cælorũ fabricas hypotheſes vocabant, <lb/>hodieque eruditiores vocant. </s> <s xml:id="echoid-s6353" xml:space="preserve">Hanc vero opinionem de reali cælorum diſtinctione in populum ſparſere <lb/>olim Eudoxus, & </s> <s xml:id="echoid-s6354" xml:space="preserve">Calippus, & </s> <s xml:id="echoid-s6355" xml:space="preserve">poſtea ſemipriſci, ac ſemibarbari ſcriptores tractatuũ de Sphęra, aut de Theo-<lb/>ricis planetarum, qui vt populo, atque alijs Aſtronomiæ ignaris res miras venditarent, tales cælorum con-<lb/>ſtructiones eccentricis, atque epicylis veris, & </s> <s xml:id="echoid-s6356" xml:space="preserve">realibus refertas propalarunt; </s> <s xml:id="echoid-s6357" xml:space="preserve">& </s> <s xml:id="echoid-s6358" xml:space="preserve">quas veteres hypotheſes ap-<lb/>pellabant, ipſi ſucceſſu temporis tanquam aſſertiones ſine vlla euidenti ratione enunciarunt; </s> <s xml:id="echoid-s6359" xml:space="preserve">ijſque ſimpli-<lb/>ciores, ac rudiores fidem vltro adhibuerũt, adeo vt Philoſophorum etiam complures ijſdem paulatim aſſen-<lb/>ſerint. </s> <s xml:id="echoid-s6360" xml:space="preserve">Ex hac cælorum hypotheſi in aſſertionem transformata, factum eſt etiam, vt complures cælos ad in-<lb/>uicem non ſolum diuiſos, ſed etiam duros eſſe deduxerint: </s> <s xml:id="echoid-s6361" xml:space="preserve">dum enim intelligebant cælorum diſtinctionem <lb/>atque eorum munia in aſtris deferen@is, conſequenter etiam de eorum ſoliditate philoſophati ſunt. </s> <s xml:id="echoid-s6362" xml:space="preserve">Verum <lb/>enim vero antiquorum ac recentiorum doctiſſimi, vti ſunt Ptolemæus, Copernicus, Tycho, & </s> <s xml:id="echoid-s6363" xml:space="preserve">al@j, per ſolas <lb/>lineas, aut circulos motus planetarum optimè explicarunt, vt in eorum monumentis videre eſt. </s> <s xml:id="echoid-s6364" xml:space="preserve">Omnes ta-<lb/>men merito exiſtimant octauam Sphæram, ſeu Firmamentũ eſſe corpus ſolidum, ac conſtans, cum in eo ſy-<lb/>dera veluti confixa, eundem perpetuo ordinem, mutuas diſtantias, ac poſitiones tueantur, atq; </s> <s xml:id="echoid-s6365" xml:space="preserve">in eo, ſeu po-<lb/>tius ab eo irrequieta vertigine reuoluantur. </s> <s xml:id="echoid-s6366" xml:space="preserve">qua ratione putandum eſt Firmamentum ab inferiori planeta-<lb/>rum regione eſſe aliquo modo diſtinctum, & </s> <s xml:id="echoid-s6367" xml:space="preserve">diuiſum: </s> <s xml:id="echoid-s6368" xml:space="preserve">hæc itaq; </s> <s xml:id="echoid-s6369" xml:space="preserve">ſunt huius ſententiæ fundamenta.</s> <s xml:id="echoid-s6370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6371" xml:space="preserve">Ex aduerſo autem multa ſunt quibus recentiores Aſtronomi ſuadent planetarũ regionem non eſſe reapſe <lb/>in varios cælos diſtinctam. </s> <s xml:id="echoid-s6372" xml:space="preserve">in qua ſententia fuerunt etiam veterum nonnulli; </s> <s xml:id="echoid-s6373" xml:space="preserve">nam vt Vitruuius, & </s> <s xml:id="echoid-s6374" xml:space="preserve">Martia-<lb/>nus Capella ex veterum Aſtronomorum ſententias litteris mandarunt, Mercurium, ac Venerem circa So-<lb/>lem ita circulari, vt aliquando ſupra eum, aliquando vero infra ferantur, exiſtimarunt. </s> <s xml:id="echoid-s6375" xml:space="preserve">quorum fundamenta <lb/>ſunt ſequentia: </s> <s xml:id="echoid-s6376" xml:space="preserve">primo, qua ratione, hi duo planetæ in proprijs cælis à cælo Solis, necnon ad inuicem diſtin-<lb/>ctis ferrentur? </s> <s xml:id="echoid-s6377" xml:space="preserve">potius aſſerendum videretur eos in eodem ſolis cælo, cum Sole ſpatiari. </s> <s xml:id="echoid-s6378" xml:space="preserve">Martis ſtellam ali-<lb/>quando infra Solis circuitus deſcendere certum eſt ex Tychone, quo igitur iure in alienum cælum ingre-<lb/>ditur? </s> <s xml:id="echoid-s6379" xml:space="preserve">quo modo illud perforat? </s> <s xml:id="echoid-s6380" xml:space="preserve">3. </s> <s xml:id="echoid-s6381" xml:space="preserve">Nonne inquiunt in eodem Iouis cælo alij quatuor planetæ ipſius aſſeclæ <lb/>eum perpetuo comitantur? </s> <s xml:id="echoid-s6382" xml:space="preserve">Demum eodem ſpectant Cometæ, qui ſupra Lunam in planetaria regione efful-<lb/>gent, atq; </s> <s xml:id="echoid-s6383" xml:space="preserve">in tranſuerſum proprijs motibus gradiuntur: </s> <s xml:id="echoid-s6384" xml:space="preserve">(Porrò quæ hic de Planetis, & </s> <s xml:id="echoid-s6385" xml:space="preserve">Cometis aſſumũtur, <lb/>ſuis locis oſtendentur.) </s> <s xml:id="echoid-s6386" xml:space="preserve">Quapropter ex prænotatis deducunt cælos planetarum eſſe tantummodo quaſdam <lb/>cæli regiones aut partes, in quibus ipſi ſuos circuitus ducũt, quas partes non neceſſe ſit eſſe re ipſa aliquo con-<lb/>finio inuicem diſtinctas, & </s> <s xml:id="echoid-s6387" xml:space="preserve">diuiſas, quæ mutuo ob proprios motus perpetuo confricentur. </s> <s xml:id="echoid-s6388" xml:space="preserve">Lectores igitur ex <lb/>his, atq; </s> <s xml:id="echoid-s6389" xml:space="preserve">etiam alijs ſtatuant, quod mag is veritati conſonum videatur.</s> <s xml:id="echoid-s6390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6391" xml:space="preserve">Quod ſpectat ad totius cæli magnitudinem, impoſſibile eſt eam hoc loco vllatenus determinare, cum ea <lb/>ex ſingulorum cęlorum tanquam partium magnitudinibus per partes inueſtigetur; </s> <s xml:id="echoid-s6392" xml:space="preserve">inueſtigandæ igitur ſunt <lb/>prius ſingulorum craſſities, antequam totius cæli craſſitiem, ac proinde magnitudinem aſſequamur. </s> <s xml:id="echoid-s6393" xml:space="preserve">Erit <lb/>autem craſſities eius ſemidiametr. </s> <s xml:id="echoid-s6394" xml:space="preserve">terræ ſaltem 13,<unsure/>948,<unsure/>.</s> <s xml:id="echoid-s6395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6396" xml:space="preserve">De lumine Cæleſtis regionis, nihil noui occurrit, præter id, quod in tract. </s> <s xml:id="echoid-s6397" xml:space="preserve">de Mundo dictum eſt.</s> <s xml:id="echoid-s6398" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div137" type="section" level="1" n="87"> <head xml:id="echoid-head96" xml:space="preserve">LIBER NONVS <lb/>DELVNA.</head> <p> <s xml:id="echoid-s6399" xml:space="preserve">ABſoluta iam Elementari Mundi parte, atque etiam generali Cæli tractatione conſequens eſt, vt <lb/>ad particularem conſcendamus; </s> <s xml:id="echoid-s6400" xml:space="preserve">in qua primo Luna occurrit, alterum vniuerſi luminare, quod <lb/>veluti nocturnus Sol noctem lumine perfundit, quodque ſecundas inter cæleſtia corpora digni-<lb/>tatis partes obtinet.</s> <s xml:id="echoid-s6401" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div138" type="section" level="1" n="88"> <head xml:id="echoid-head97" style="it" xml:space="preserve">De loco Lunæ. Cap. I.</head> <p> <s xml:id="echoid-s6402" xml:space="preserve">1 LVnam ſuas reuolutiones ſupra Sphæram Elementarem, atque etiam Aetherem proximè peragere, & </s> <s xml:id="echoid-s6403" xml:space="preserve"><lb/>proinde eam inter planetas ordine primam ac citimam ſupra innuimus; </s> <s xml:id="echoid-s6404" xml:space="preserve">nunc autem probare conten-<lb/>dimus. </s> <s xml:id="echoid-s6405" xml:space="preserve">Et primo quidem euidentiſſima eſt illa ratio, quæ deſumitur ab eclypſibus, ſeu occultationibus plane-<lb/>tarum: </s> <s xml:id="echoid-s6406" xml:space="preserve">manifeſtum enim eſt planetam illum qui alterum nobis occultat eo eſſe inferiorem, ideo enim eum <pb o="66" file="0086" n="90" rhead="De Mundi Fabrica,"/> occultat quia ſub ipſo tunc temporis pertranſit; </s> <s xml:id="echoid-s6407" xml:space="preserve">ſiue quia inter oculum noſtrum, & </s> <s xml:id="echoid-s6408" xml:space="preserve">eum interponitur. </s> <s xml:id="echoid-s6409" xml:space="preserve">At ve-<lb/>ro Luna nobis Solem eclypſat, reliquoſque planetas, ac ſtellas omnes occulit, igitur indubitato aſſerendum <lb/>eſt Lunam omnium errantium atq; </s> <s xml:id="echoid-s6410" xml:space="preserve">inerrantium ſyderum Telluri proximam circumferri.</s> <s xml:id="echoid-s6411" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6412" xml:space="preserve">2 Luna ex omnibus aſtris ſola in vmbram terræincurrit, vt conſtat ex ipſius defectibus; </s> <s xml:id="echoid-s6413" xml:space="preserve">ideo enim vt <lb/>mox dicemus aliquando Luna eclypſim patitur, quod in vmbram terræ inuadat, propterea autem cæteri <lb/>planetæ ab vmbra terræ non obſcurantur, quod ea ſuperiores, ac altiores incedant; </s> <s xml:id="echoid-s6414" xml:space="preserve">igitur Luna omnium ci-<lb/>tima eſt.</s> <s xml:id="echoid-s6415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6416" xml:space="preserve">3 Ratio deducitur ab vmbris Solis, & </s> <s xml:id="echoid-s6417" xml:space="preserve">Lunæ inuicem collatis, hoc modo, oportet vt Sol, & </s> <s xml:id="echoid-s6418" xml:space="preserve">Luna ſint in <lb/>eadem altitudine ſupra horizontem Aſtronomicum, quando eorum vmbrę denotantur, etiamſi obſeruatio-<lb/> <anchor type="figure" xlink:label="fig-0086-01a" xlink:href="fig-0086-01"/> nes fiant in diuerſis temporibus, v.</s> <s xml:id="echoid-s6419" xml:space="preserve">g. </s> <s xml:id="echoid-s6420" xml:space="preserve">fit in figura horizon Aſtrono-<lb/>micus G D H. </s> <s xml:id="echoid-s6421" xml:space="preserve">& </s> <s xml:id="echoid-s6422" xml:space="preserve">in eadem linea C D. </s> <s xml:id="echoid-s6423" xml:space="preserve">hoc eſt in eadem altitudine <lb/>ſint Sol, & </s> <s xml:id="echoid-s6424" xml:space="preserve">Luna in punctis C B. </s> <s xml:id="echoid-s6425" xml:space="preserve">ſed ignoretur vter eorum ſit altior. <lb/></s> <s xml:id="echoid-s6426" xml:space="preserve">erecto igitur Gnomone D A. </s> <s xml:id="echoid-s6427" xml:space="preserve">notentur vtriuſque vmbræ in plano <lb/>horizõtali; </s> <s xml:id="echoid-s6428" xml:space="preserve">ſitque aſtri B. </s> <s xml:id="echoid-s6429" xml:space="preserve">vmbra D F. </s> <s xml:id="echoid-s6430" xml:space="preserve">aſtri etiam C. </s> <s xml:id="echoid-s6431" xml:space="preserve">vmbra ſit D E. </s> <s xml:id="echoid-s6432" xml:space="preserve"><lb/>radius aſtri B. </s> <s xml:id="echoid-s6433" xml:space="preserve">erit F A B. </s> <s xml:id="echoid-s6434" xml:space="preserve">radius autem aſtri C. </s> <s xml:id="echoid-s6435" xml:space="preserve">erit E A C. </s> <s xml:id="echoid-s6436" xml:space="preserve">qui altius <lb/>euehitur quam alter radius, ac proinde manifeſtum facit aſtrum C. </s> <s xml:id="echoid-s6437" xml:space="preserve"><lb/>qui Solem refert eſſe à centro D. </s> <s xml:id="echoid-s6438" xml:space="preserve">remotius, quàm aſtrum B. </s> <s xml:id="echoid-s6439" xml:space="preserve">qui Lu-<lb/>næ gerit vices. </s> <s xml:id="echoid-s6440" xml:space="preserve">ſi quis hanc obſeruationem habere velit, Lunæ mo-<lb/>tum probæ perſpectum habeat oportet, aliunde quam per noſtrum <lb/>Quadrantem; </s> <s xml:id="echoid-s6441" xml:space="preserve">Luna enim parallaxim exhibet, ideſt, aſpectus varia-<lb/>tionem à vero ipſius loco, vt paulo poſt patebit. </s> <s xml:id="echoid-s6442" xml:space="preserve">Calculus tamen Aſtronomicus verum eius locum, ac pro-<lb/>inde veram eius altitudinem ſupra horizontem Aſtronomicum manifeſtat. </s> <s xml:id="echoid-s6443" xml:space="preserve">habita igitur altitudine eius ſu-<lb/>pra horizontem, notetur eius vmbra: </s> <s xml:id="echoid-s6444" xml:space="preserve">poſtea cum Sol eãdem altitudinem ſortitus fuerit, eius pariter vmbra <lb/>notetur, quæ perpetuo Lunari vmbra minor erit, ac conſequenter Sol, quam Luna altior conuincetur.</s> <s xml:id="echoid-s6445" xml:space="preserve"/> </p> <div xml:id="echoid-div138" type="float" level="2" n="1"> <figure xlink:label="fig-0086-01" xlink:href="fig-0086-01a"> <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0086-01"/> </figure> </div> <p> <s xml:id="echoid-s6446" xml:space="preserve">Porrò quamuis hæc ratiocinatio præ cæteris melius Soli accommodetur, poterit tamen ad cæteros quo-<lb/>que planetas transferri, quamuis enim non ita ſplendeant, vt ab ipſis vmbræ corporum proijciantur, vti à <lb/>Sole, & </s> <s xml:id="echoid-s6447" xml:space="preserve">Luna; </s> <s xml:id="echoid-s6448" xml:space="preserve">eorum tamen radij qui per verticem Gnomonis tranſeuntes vmbras efficerent, non poſſunt <lb/>ignorari; </s> <s xml:id="echoid-s6449" xml:space="preserve">poſſumus enim loco radiorum accipere radios viſiuos, qui ab oculo noſtro per verticem ſtyli, & </s> <s xml:id="echoid-s6450" xml:space="preserve"><lb/>centrum aſtri ducuntur, ijſque vſque ad horizontale planum productis longitudines vmbrarum illis debita-<lb/>rum inueſtigare.</s> <s xml:id="echoid-s6451" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6452" xml:space="preserve">4 Planeta ille cuius proprius motus magis aduerſatur, ac magis cõtranititur aduerſus motum primi mo-<lb/>bilis, ideſt, motum diurnum, tanto etiam magis ab eodem primo mobili abſcedere, ac remoueri conueniens <lb/>eſt ad maiorem vniuerſi concordia: </s> <s xml:id="echoid-s6453" xml:space="preserve">ille autem magis primo mobili aduerſatur, (ideſt, motui diurno, qui ve-<lb/>lociſſimè ab oriente ad occidentem perficitur) qui proprio motu contra ab occidente in orientem velocio@ <lb/>eſt; </s> <s xml:id="echoid-s6454" xml:space="preserve">vt conſideranti patet. </s> <s xml:id="echoid-s6455" xml:space="preserve">Ex aduerſo planeta ille cuius proprius motus tardior eſt cæteris, minus motui pr@-<lb/>mi mobilis aduerſatur, ac repugnat; </s> <s xml:id="echoid-s6456" xml:space="preserve">& </s> <s xml:id="echoid-s6457" xml:space="preserve">ideo conſentaneum eſt eum veluti primo mobili conformiorem, ac <lb/>amiciorem, eſſe etiam proximiorem. </s> <s xml:id="echoid-s6458" xml:space="preserve">Quapropter Saturnus qui cæteris proprio motu tardior eſt, eſt etiam <lb/>primo mobili propinquior, ac proinde cæteris altior: </s> <s xml:id="echoid-s6459" xml:space="preserve">ſub eo lupiter merito deinde collocatur, quia ſicuti eſt <lb/>Saturno proxime velocior, ita etiam ſit illi propinquior. </s> <s xml:id="echoid-s6460" xml:space="preserve">Eadem ratione Mars, qui adhuc velocior eſt, Io-<lb/>uem ſubſequitur. </s> <s xml:id="echoid-s6461" xml:space="preserve">quarto loco Sol ſuccedit, &</s> <s xml:id="echoid-s6462" xml:space="preserve">c. </s> <s xml:id="echoid-s6463" xml:space="preserve">tandem Luna omnium cit ſſima, omniumq; </s> <s xml:id="echoid-s6464" xml:space="preserve">quoque citima <lb/>ſit neceſſe eſt. </s> <s xml:id="echoid-s6465" xml:space="preserve">Cęterum hæc ratio ſic, vt communiter fit ab Aſtronomis, allata, indiget animaduerſione. </s> <s xml:id="echoid-s6466" xml:space="preserve">non <lb/>enim abſolute verum eſt ſydus illud velocius cæteris eſſe, quod citius proprium curſum, per Zodiacum ab-<lb/>ſoluit. </s> <s xml:id="echoid-s6467" xml:space="preserve">ſi enim gy@us illius ſit tanto cæteris minor, vt æquali, ſeu eodem tempore de eo minus ſpatium conſi-<lb/>ficiat, quam cætera aſtra de ſuis gyris conficiant, erit ſydus illud abſolutè, tardius, v. </s> <s xml:id="echoid-s6468" xml:space="preserve">g. </s> <s xml:id="echoid-s6469" xml:space="preserve">quia cælum ſeu gyrus <lb/>Lunæ minor eſt vndeuicies gyro Solis, fit vt etiamſi ipſa eodem tempore, ideſt, anno vno pluſquam duode-<lb/>cies Zodiacum percurrat, quo tempore eundem Sol ſemel percurrit, non tamen dicenda ſit ſimpliciter velo-<lb/>cior, ſed tardior. </s> <s xml:id="echoid-s6470" xml:space="preserve">qu a nimirum eodem tempore minus ſpatium conficit quam Sol, cùm circuitus eius ſit vn-<lb/>deuicies minor circuitu ſolari, ac propterea quamuis eodem tempore duodecies, quo Sol ſuum ſemel, abſol-<lb/>uat, tamen a dhuc re vera tardior eſt; </s> <s xml:id="echoid-s6471" xml:space="preserve">quod ſi eum vndeuicies eodem tempore recurreret, tũc æquale ſpatium <lb/>cum ſpatio Sol spercurreret, eſſetque propterea æqueuelox, acille. </s> <s xml:id="echoid-s6472" xml:space="preserve">Luna igitur hac ratione erit non ſo-<lb/>lum Soli, ſed cæteris planetis abſolutè tardior: </s> <s xml:id="echoid-s6473" xml:space="preserve">quæ priori tamen ac vulgari modo conſiderata velociot <lb/>putabatur.</s> <s xml:id="echoid-s6474" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6475" xml:space="preserve">5 Ratio ſumitur à parallaxi, ſeu euariatione, aut commutatione aſpectus de ea igitur in primis non nihil <lb/>agendum eſt, quæ vt facilius intelligantur, repetenda ſunt ea, quæ ſupra diximus dum Lunæ a terra altitu-<lb/>dinẽ indagauimus. </s> <s xml:id="echoid-s6476" xml:space="preserve">poſtea figura præſens inſpicienda eſt, in qua terræ ſemidiameter eſt A C. </s> <s xml:id="echoid-s6477" xml:space="preserve">horizon Aſtro-<lb/>nomicus C I. </s> <s xml:id="echoid-s6478" xml:space="preserve">quadrans F I. </s> <s xml:id="echoid-s6479" xml:space="preserve">ſit quadrans meridiani in firmamento, ſeu extimo cælo, in quo loca planetarum <lb/>conſiderantur. </s> <s xml:id="echoid-s6480" xml:space="preserve">circuli B B. </s> <s xml:id="echoid-s6481" xml:space="preserve">& </s> <s xml:id="echoid-s6482" xml:space="preserve">E E. </s> <s xml:id="echoid-s6483" xml:space="preserve">ſint duo cæli. </s> <s xml:id="echoid-s6484" xml:space="preserve">in quo ſit duo planetæ B. </s> <s xml:id="echoid-s6485" xml:space="preserve">& </s> <s xml:id="echoid-s6486" xml:space="preserve">E. </s> <s xml:id="echoid-s6487" xml:space="preserve">vterque in duobus locis ſui <lb/>ci@culi. </s> <s xml:id="echoid-s6488" xml:space="preserve">linea C A F. </s> <s xml:id="echoid-s6489" xml:space="preserve">aſcendet vſque ad polum horizontis, ſiue verticem F. </s> <s xml:id="echoid-s6490" xml:space="preserve">ducantur etiam reliquæ lineæ, à <lb/>centro terræ C. </s> <s xml:id="echoid-s6491" xml:space="preserve">necnon ab oculo noſtro A. </s> <s xml:id="echoid-s6492" xml:space="preserve">tranſeuntes per centra plan@tarum E B. </s> <s xml:id="echoid-s6493" xml:space="preserve">vſque ad ſirmamentum, <lb/>ſintque primæ C E|B M. </s> <s xml:id="echoid-s6494" xml:space="preserve">A E O. </s> <s xml:id="echoid-s6495" xml:space="preserve">A B N. </s> <s xml:id="echoid-s6496" xml:space="preserve">aliæ vero ſint C E B G. </s> <s xml:id="echoid-s6497" xml:space="preserve">A E H. </s> <s xml:id="echoid-s6498" xml:space="preserve">A B K. </s> <s xml:id="echoid-s6499" xml:space="preserve">h s pręſtructis explicandus <lb/>eſt quis ſit locus aſtri viſus, & </s> <s xml:id="echoid-s6500" xml:space="preserve">quis verus. </s> <s xml:id="echoid-s6501" xml:space="preserve">linea igitur ex centro Mundi C. </s> <s xml:id="echoid-s6502" xml:space="preserve">ducta tranſiens per aſtrum vſque <lb/>ad ſupremum cælum, locum eius verum in eo indicat. </s> <s xml:id="echoid-s6503" xml:space="preserve">v.</s> <s xml:id="echoid-s6504" xml:space="preserve">g. </s> <s xml:id="echoid-s6505" xml:space="preserve">linea C E B M. </s> <s xml:id="echoid-s6506" xml:space="preserve">tranſiens per ſydus E. </s> <s xml:id="echoid-s6507" xml:space="preserve">vel B. </s> <s xml:id="echoid-s6508" xml:space="preserve">indi-<lb/>cat eorum locum in firmamento eſſe punctum M. </s> <s xml:id="echoid-s6509" xml:space="preserve">linea vero A E O. </s> <s xml:id="echoid-s6510" xml:space="preserve">ducta ab oculo, noſtro A. </s> <s xml:id="echoid-s6511" xml:space="preserve">per ſydus E.</s> <s xml:id="echoid-s6512" xml:space="preserve"> <pb o="67" file="0087" n="91" rhead="Liber Nonus."/> oſtendit locum eius viſum eſſe O. </s> <s xml:id="echoid-s6513" xml:space="preserve">in firmamento; </s> <s xml:id="echoid-s6514" xml:space="preserve">ſicnti etiam linea A B. </s> <s xml:id="echoid-s6515" xml:space="preserve">terminatur ad N. </s> <s xml:id="echoid-s6516" xml:space="preserve">locum viſum aſtri <lb/>B. </s> <s xml:id="echoid-s6517" xml:space="preserve">Iam videndum quid ſit parallaxis, ſiue aſpectus diuerſitas, quæ nihil aliud eſt, quam arcus firmamenti in-<lb/> <anchor type="figure" xlink:label="fig-0087-01a" xlink:href="fig-0087-01"/> terceptus inter locum verum, & </s> <s xml:id="echoid-s6518" xml:space="preserve">viſum; </s> <s xml:id="echoid-s6519" xml:space="preserve">quo <lb/>videlicetilla duo loca differũt, qualis eſt ar-<lb/>cus M O. </s> <s xml:id="echoid-s6520" xml:space="preserve">reſpectu aſtri E. </s> <s xml:id="echoid-s6521" xml:space="preserve">& </s> <s xml:id="echoid-s6522" xml:space="preserve">arcus M N. </s> <s xml:id="echoid-s6523" xml:space="preserve">re-<lb/>ſpectu aſtri B. </s> <s xml:id="echoid-s6524" xml:space="preserve">ſciendum quoq; </s> <s xml:id="echoid-s6525" xml:space="preserve">eſt Aſtrono-<lb/>mos appellare parallaxim non ſolum prædi-<lb/>ctum arcum, verum & </s> <s xml:id="echoid-s6526" xml:space="preserve">angulũ, qui ſit a præ-<lb/>dictis lineis in centro aſtri, qualis eſt angu-<lb/>lus M E O. </s> <s xml:id="echoid-s6527" xml:space="preserve">ſeu angulus A E C. </s> <s xml:id="echoid-s6528" xml:space="preserve">illi ad verti-<lb/>cem, ac proinde ei æqualis, quia quantus eſt <lb/>arcus M O. </s> <s xml:id="echoid-s6529" xml:space="preserve">ſecundũ gradus, ideſt, quot gra-<lb/>dus continet arcus M O. </s> <s xml:id="echoid-s6530" xml:space="preserve">totidem etiam con-<lb/>tinet prædictus angulus. </s> <s xml:id="echoid-s6531" xml:space="preserve">quod quidem geo-<lb/>metricè verum non eſt, cum arcus M O. </s> <s xml:id="echoid-s6532" xml:space="preserve">non <lb/>ſit ex E. </s> <s xml:id="echoid-s6533" xml:space="preserve">angulo tanquam centro deſcriptus, <lb/>vti oporteret; </s> <s xml:id="echoid-s6534" xml:space="preserve">tamen ob immodicam anguli <lb/>E. </s> <s xml:id="echoid-s6535" xml:space="preserve">ad firmamentuin M O. </s> <s xml:id="echoid-s6536" xml:space="preserve">diſtantiam non <lb/>incurritur error sẽſibilis, ſi ſupponamus an-<lb/>gulum E. </s> <s xml:id="echoid-s6537" xml:space="preserve">eſſe centrum arcus M O. </s> <s xml:id="echoid-s6538" xml:space="preserve">acconſe-<lb/>quenter ſuam quantitatem ab arcu M O. </s> <s xml:id="echoid-s6539" xml:space="preserve">accipere. </s> <s xml:id="echoid-s6540" xml:space="preserve">parallaxis, eſt tam arcus M O. </s> <s xml:id="echoid-s6541" xml:space="preserve">quam angulus A E C. </s> <s xml:id="echoid-s6542" xml:space="preserve">Iam <lb/>vero ſi duorum aſtrorum E. </s> <s xml:id="echoid-s6543" xml:space="preserve">& </s> <s xml:id="echoid-s6544" xml:space="preserve">B. </s> <s xml:id="echoid-s6545" xml:space="preserve">parallaxes inuicem conferamus, videbimus ſuperius aſtrum B. </s> <s xml:id="echoid-s6546" xml:space="preserve">minorem <lb/>efficere parallaxim, minor enim eſt arcus M N. </s> <s xml:id="echoid-s6547" xml:space="preserve">arcu M O. </s> <s xml:id="echoid-s6548" xml:space="preserve">cauſamque ſimul in figura licebit intueri. </s> <s xml:id="echoid-s6549" xml:space="preserve">vnde ex <lb/>oppoſito inferre licebit aſtrum, quod ſuperius alio aſtro ſit, minorem exhibere parallaxim. </s> <s xml:id="echoid-s6550" xml:space="preserve">cum igitur, vt <lb/>conſtat ex communi Aſtronomorum conſenſu, Lunæ parallaxes ſint maiores, quam aliorum planetarum, <lb/>manifeſtum erit eam omnium eſſe infimam: </s> <s xml:id="echoid-s6551" xml:space="preserve">quod præcipuè intendebamus.</s> <s xml:id="echoid-s6552" xml:space="preserve"/> </p> <div xml:id="echoid-div139" type="float" level="2" n="2"> <figure xlink:label="fig-0087-01" xlink:href="fig-0087-01a"> <image file="0087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0087-01"/> </figure> </div> <p> <s xml:id="echoid-s6553" xml:space="preserve">Aduertẽdum etiam eſt idem aſtrum in eadem à terra remotione maiorem exhibere parallaxim, quo pro-<lb/>pius horizonti fuerit; </s> <s xml:id="echoid-s6554" xml:space="preserve">ſic aſtrum E. </s> <s xml:id="echoid-s6555" xml:space="preserve">propè horizontem efficit parallaxim M O. </s> <s xml:id="echoid-s6556" xml:space="preserve">altius vero horizonte exhibet <lb/>parallaxim G H. </s> <s xml:id="echoid-s6557" xml:space="preserve">quæ minor eſt quam M O. </s> <s xml:id="echoid-s6558" xml:space="preserve">tandem in ipſo F. </s> <s xml:id="echoid-s6559" xml:space="preserve">vertice, nulla contingit parallaxis, quia duæ <lb/>ibi lineæ viſa, & </s> <s xml:id="echoid-s6560" xml:space="preserve">vera ſimul vniuntur.</s> <s xml:id="echoid-s6561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6562" xml:space="preserve">Qua vero ratione ſint parallaxes rimandæ, dictum eſt ſupra, cum de Ætheris quantitate actum eſt: </s> <s xml:id="echoid-s6563" xml:space="preserve">vbi di-<lb/>ftantiam Lunæ à terra inueſtigauimus ex cognitione illius trianguli, qui acutiſſimum angulum A E C. </s> <s xml:id="echoid-s6564" xml:space="preserve">in cen <lb/>@rum Lunæ emittebat: </s> <s xml:id="echoid-s6565" xml:space="preserve">ille enim angulus in Luna deſinens eſt ipſa parallaxis, quamuis ibi nomen parallaxis <lb/>reticuerimus.</s> <s xml:id="echoid-s6566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6567" xml:space="preserve">Aliter parallaxis Lunaris deprehenditur, cognita prius eius latitudine, & </s> <s xml:id="echoid-s6568" xml:space="preserve">declinatione per calculum, co <lb/>@empore, quo ea meridianum pertranſit; </s> <s xml:id="echoid-s6569" xml:space="preserve">tunc enim non later eius altitudo ſupra horizontem aſtronomicum <lb/>quare tunc pariter eiuſdem altitudo per inſtrumentum notatur, quæ obſeruatio Lunam horizonti vicinio-<lb/>rem oſtendet: </s> <s xml:id="echoid-s6570" xml:space="preserve">differentia igitur harum duarum altitudinum erit parallaxis verum hic modus ad vſum reuo-<lb/>cari nequit, niſi poſt explicationem Lunaris calculi. </s> <s xml:id="echoid-s6571" xml:space="preserve">parallaxium autem cauſa eſt diameter terræ, quando eſt <lb/>ſenſibilis quantitatis cum diſtantia aſtri a centro terræ; </s> <s xml:id="echoid-s6572" xml:space="preserve">ſi enim eius quantitas reſpectu diſtantiæ aſtri ſit in-<lb/>ſenſibilis, nulla percipitur parallaxis. </s> <s xml:id="echoid-s6573" xml:space="preserve">hac de cauſa ſtellæ fixæ nullam patiuntur parallaxim. </s> <s xml:id="echoid-s6574" xml:space="preserve">Illud tandem in <lb/>collatione parallaxium diuerſorum planetarum obſeruandum eſt, vt ſcilicet vterque aſtrum ſit in eadem al-<lb/>titudine ſupra horizontem aſtronomicum quando eorum parallaxes obſeruantur, etiamſi id fiat in diuerſis <lb/>@emporibus, vt infra de loco ſolis fuſius expli cabitur.</s> <s xml:id="echoid-s6575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6576" xml:space="preserve">Demum ſciendum eſt Tychonem Brahe obſeruaſse minimã, & </s> <s xml:id="echoid-s6577" xml:space="preserve">maximam Lunæ parallaxim quando ipſa <lb/>eleuata eſt ſupra horizontem aſtronom. </s> <s xml:id="echoid-s6578" xml:space="preserve">gradibus 8. </s> <s xml:id="echoid-s6579" xml:space="preserve">reperiſſeq; </s> <s xml:id="echoid-s6580" xml:space="preserve">minimam parallaxim eſſe minuta, 56′. </s> <s xml:id="echoid-s6581" xml:space="preserve">44″-<lb/>maximam autem eſſe minuta 65′. </s> <s xml:id="echoid-s6582" xml:space="preserve">36″. </s> <s xml:id="echoid-s6583" xml:space="preserve">ſiue dicamus angulum minimum, & </s> <s xml:id="echoid-s6584" xml:space="preserve">maximum euitato refractionum <lb/>@rrore. </s> <s xml:id="echoid-s6585" xml:space="preserve">ex quibus cognito triangulo A C E. </s> <s xml:id="echoid-s6586" xml:space="preserve">cognouit latus A C. </s> <s xml:id="echoid-s6587" xml:space="preserve">ſub maxima parallaxi in gredi in latus C E. <lb/></s> <s xml:id="echoid-s6588" xml:space="preserve">52. </s> <s xml:id="echoid-s6589" xml:space="preserve">vicibus ſub minima vero parallaxi, vti ſi Luna eſſet in B. </s> <s xml:id="echoid-s6590" xml:space="preserve">deprehendit latus A C. </s> <s xml:id="echoid-s6591" xml:space="preserve">ingredi in latus C B. </s> <s xml:id="echoid-s6592" xml:space="preserve">61, <lb/>vicibus. </s> <s xml:id="echoid-s6593" xml:space="preserve">vnde patuit Lunam accedere, & </s> <s xml:id="echoid-s6594" xml:space="preserve">recedere a terris ad interuallum ferè 9. </s> <s xml:id="echoid-s6595" xml:space="preserve">ſemidiametrorum terræ. </s> <s xml:id="echoid-s6596" xml:space="preserve">ac <lb/>proinde cælum Lunæ, ſiue regionem Lunarem habere craſſitiem ſaltem 9. </s> <s xml:id="echoid-s6597" xml:space="preserve">ſemidiam. </s> <s xml:id="echoid-s6598" xml:space="preserve">terræ. </s> <s xml:id="echoid-s6599" xml:space="preserve">Tyconicas au-<lb/>tem obſeruationes tanquam exactiores, & </s> <s xml:id="echoid-s6600" xml:space="preserve">accurationes libenter omnes huius tempeſtatis aſtronomi ample-<lb/>c<unsure/>tuntur. </s> <s xml:id="echoid-s6601" xml:space="preserve">ex quibus ſatis diſtantia ſiue locus Lunæ cognitus euadit. </s> <s xml:id="echoid-s6602" xml:space="preserve">An vero Lunæ cælum, ſiue regio extra <lb/>hos 9. </s> <s xml:id="echoid-s6603" xml:space="preserve">terræ ſemid. </s> <s xml:id="echoid-s6604" xml:space="preserve">tam ſupra, quam infra excurrat, neminem puto. </s> <s xml:id="echoid-s6605" xml:space="preserve">indubitanter affirmare poſſe.</s> <s xml:id="echoid-s6606" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div141" type="section" level="1" n="89"> <head xml:id="echoid-head98" style="it" xml:space="preserve">De motibus Lunæ<unsure/>. Cap. II.</head> <p> <s xml:id="echoid-s6607" xml:space="preserve">VT motum Lunę rectè intelligamus in primis neceſſe eſt circulum aſſignare per quem iter ſuum conficit, <lb/>atque hunc circulum, qui ipſius eſt via in cælo probè imaginari. </s> <s xml:id="echoid-s6608" xml:space="preserve">habeat igitur lector ob oculos ſphæram <lb/>materia. </s> <s xml:id="echoid-s6609" xml:space="preserve">em; </s> <s xml:id="echoid-s6610" xml:space="preserve">& </s> <s xml:id="echoid-s6611" xml:space="preserve">zodiacum intuens imaginetur in eo alteram, vt ita dicam eclyptica, ſiue potius circulum, qui <lb/>totam zodiaci longitudinem ſecet, ſed non per medium vti facit eclyptica; </s> <s xml:id="echoid-s6612" xml:space="preserve">verum ipſam eclypticam ſecet <lb/>in duobus punctis oppoſitis, ita vt vna ipſius medietas reſpectu eclypticæ ſit borealis, altera vero auſtralis; </s> <s xml:id="echoid-s6613" xml:space="preserve">& </s> <s xml:id="echoid-s6614" xml:space="preserve"><lb/>vtrinque ab eclyptica, tam in boream, quam in auſtrum, ad ſummum recedat per grad. </s> <s xml:id="echoid-s6615" xml:space="preserve">5. </s> <s xml:id="echoid-s6616" xml:space="preserve">Quemadmodum <pb o="68" file="0088" n="92" rhead="De Mundi Fabrica,"/> enim eclyptica ſecat æquatorem in duobus punctis oppoſitis, ita hæc Lunaris linea ipſam eclypticam in op-<lb/>poſitis locis dirimit, & </s> <s xml:id="echoid-s6617" xml:space="preserve">ſicuti eclyptica recedit ab æquatore plurimum grad. </s> <s xml:id="echoid-s6618" xml:space="preserve">23. </s> <s xml:id="echoid-s6619" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s6620" xml:space="preserve">ita hæ Lunaris orbita ab <lb/>ipſa eclyptica plurimum abſcedit, grad. </s> <s xml:id="echoid-s6621" xml:space="preserve">5. </s> <s xml:id="echoid-s6622" xml:space="preserve">duæ illæ interſectiones cum eclyptica dicuntura Græcis nodi, <lb/>quorum @@le dicitur nodus boreus, & </s> <s xml:id="echoid-s6623" xml:space="preserve">aſcendens, per quem Luna motu proprio tranſiens efficitur borealis. </s> <s xml:id="echoid-s6624" xml:space="preserve">al-<lb/>ter huic oppoſitus per quem Luna ſit auſtralis dicitur nodus auſtralis, & </s> <s xml:id="echoid-s6625" xml:space="preserve">deſcendens. </s> <s xml:id="echoid-s6626" xml:space="preserve">Arabes illũ caput Dra-<lb/>conis, hunc caudam appellant. </s> <s xml:id="echoid-s6627" xml:space="preserve">pro nodo boreo vtuntur hoc charactere ♌. </s> <s xml:id="echoid-s6628" xml:space="preserve">pro auſtrino eodem inuerſo ☋. </s> <s xml:id="echoid-s6629" xml:space="preserve">lo-<lb/>ca vero illa duo, ſiue puncta, quæ maximè ab eclyptica abſcedunt, ſeu quæ maximam ſortiuntur latitudinem <lb/>gr. </s> <s xml:id="echoid-s6630" xml:space="preserve">5. </s> <s xml:id="echoid-s6631" xml:space="preserve">vnum boream, alterum auſtrinam, dicuntur limites, eo quod ſint maximæ latitudinis Lunæ limites, <lb/>vnus boreus, alter auſtrinus quæ duo puncta diſtant à nodi gr. </s> <s xml:id="echoid-s6632" xml:space="preserve">90. </s> <s xml:id="echoid-s6633" xml:space="preserve">non aliter ac puncta eclypticæ ſolſtitialia <lb/>diſtant per quadrantem à punctis æquinoctialibus. </s> <s xml:id="echoid-s6634" xml:space="preserve">hi duo limites Arabicè dicuntur ventres Draconis. </s> <s xml:id="echoid-s6635" xml:space="preserve">Porrò <lb/>ſciendum eſt hanc Lunæ orbitã non ſemper ſecare ecly pticam in ijſdem duobus locis, ſed perpetuo hæ duæ <lb/>ſectiones, ſeu nodi mouentur tardiſſimè contra ſignorum ordinem, manente tamen ſemper eadem totius <lb/>orb tæ obliquitate ad eclypticam gr. </s> <s xml:id="echoid-s6636" xml:space="preserve">5. </s> <s xml:id="echoid-s6637" xml:space="preserve">quare ſi modo nodi eſſent in 30. </s> <s xml:id="echoid-s6638" xml:space="preserve">gradu Cancri, & </s> <s xml:id="echoid-s6639" xml:space="preserve">Capricorni. </s> <s xml:id="echoid-s6640" xml:space="preserve">poſt ali-<lb/>quod tem pus futuri ſint in gr. </s> <s xml:id="echoid-s6641" xml:space="preserve">29. </s> <s xml:id="echoid-s6642" xml:space="preserve">eorumdem quare hic Lunaris circulus ſecundũ ſe totum traſuerſim, & </s> <s xml:id="echoid-s6643" xml:space="preserve">obli <lb/>què in zodiaco retrogreditur, ac retorquetur: </s> <s xml:id="echoid-s6644" xml:space="preserve">vnde etiam limites eodem modo retrocedunt. </s> <s xml:id="echoid-s6645" xml:space="preserve">hunc motum <lb/>inde collegerunt, quod eclypſes, quænon niſi apud prædictos nodos contingunt, non ſemper contingunt <lb/>in locis ijſdem, ſed perpetuo in locis zodiaci occidentalioribus. </s> <s xml:id="echoid-s6646" xml:space="preserve">ſimiliter maximę Lunæ latitudines, quæ per <lb/>obſeruationem inueſtigantur, ſemper eodem modo contra ſignorum ſequelam promouentur. </s> <s xml:id="echoid-s6647" xml:space="preserve">Porrò to@@m <lb/>zodiacum hæc Lunaris orbita hoc modo recurrit, motu regulari, ſeu vniformi in annis Ægyptijs, 18. </s> <s xml:id="echoid-s6648" xml:space="preserve">die-<lb/>bus 223. </s> <s xml:id="echoid-s6649" xml:space="preserve">Quare quotidie mouetur tantum 3′. </s> <s xml:id="echoid-s6650" xml:space="preserve">min. </s> <s xml:id="echoid-s6651" xml:space="preserve">& </s> <s xml:id="echoid-s6652" xml:space="preserve">10″. </s> <s xml:id="echoid-s6653" xml:space="preserve">ſecundis annuo vero motu, ſiue anno vno, facit gr. <lb/></s> <s xml:id="echoid-s6654" xml:space="preserve">19. </s> <s xml:id="echoid-s6655" xml:space="preserve">20. </s> <s xml:id="echoid-s6656" xml:space="preserve">33″. </s> <s xml:id="echoid-s6657" xml:space="preserve">Annus autem Ægyptius, quo libenter, ac paſſim aſtronomi vtuntur, continet præcisè dies in-<lb/>tegros 365.</s> <s xml:id="echoid-s6658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6659" xml:space="preserve">Notandum etiam motum regularem eum eſſe, qui æqualibus temporibus, æqualia ſpacia conficit; </s> <s xml:id="echoid-s6660" xml:space="preserve">ſiue <lb/>qui ſemper eſt vniformis, ſeu æquè velox: </s> <s xml:id="echoid-s6661" xml:space="preserve">irregularem e contra, qui non eſt vniformis. </s> <s xml:id="echoid-s6662" xml:space="preserve">&</s> <s xml:id="echoid-s6663" xml:space="preserve">c.</s> <s xml:id="echoid-s6664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6665" xml:space="preserve">Huius autem Lunaris itineris maximam ab eclyptica latitudinem deduxerunt ab ipſa Lunæ latitudine <lb/>maxima, quam per inſtrumenta veluti per noſtrum Quadrantem, diligenter ſæpius obſeruarunt: </s> <s xml:id="echoid-s6666" xml:space="preserve">quod qui-<lb/>dem facile eſt, cum Luna ſingulis menſibus percurrens zodiacum totum, percurrat etiam ſuam hanc viam, <lb/>ac proinde adeat bis quolibet menſe limitem vtrumque, ideſt, bis ſortiatur maximam latitudinem. </s> <s xml:id="echoid-s6667" xml:space="preserve">Verum-<lb/>tamẽ ob Lunę parallaxim difficile eſt veram eius latitudinem percipere, quia parallaxis efficit, vt eam videa-<lb/>mus depreſſiorem, quam re vera ſit. </s> <s xml:id="echoid-s6668" xml:space="preserve">Quopropter exactius in regionibus, vbi minus eleuatur polus, eam <lb/>deprehendere poſſumus, qui illis cum vertici appropinquat, nullam ſubit parallaxim. </s> <s xml:id="echoid-s6669" xml:space="preserve">propterea Ptolemæus <lb/>eam percommodè rimatus eſt Alexandriæ, vbi Polus eleuatur ferè gra. </s> <s xml:id="echoid-s6670" xml:space="preserve">31. </s> <s xml:id="echoid-s6671" xml:space="preserve">Lunam enim attendebat quando <lb/>maximè acceſſura eſſet ad verticem. </s> <s xml:id="echoid-s6672" xml:space="preserve">dum videlicet ea eſſet in principio Cancri, ſimulque eſſet in boreo limi-<lb/>te, in quo maximam habet latitudinem, quæ ex calculo aſtronomico optimè prænouerat. </s> <s xml:id="echoid-s6673" xml:space="preserve">inuenit igitur eam <lb/>tunc per inſtrumentum diſtare a vertice gr. </s> <s xml:id="echoid-s6674" xml:space="preserve">2.</s> <s xml:id="echoid-s6675" xml:space="preserve">7′. </s> <s xml:id="echoid-s6676" xml:space="preserve">in quo loco nullam pati poterat parallaxim ſenſibilem, cùm <lb/>vti ſupra dixi, quo propius vertici ſydus eſt eo minorem habeat parallaxim, & </s> <s xml:id="echoid-s6677" xml:space="preserve">in ipſo vertice nullam. </s> <s xml:id="echoid-s6678" xml:space="preserve">Cum <lb/>vero tanta ſit poli altitudo, quanta eſt latitudo loci: </s> <s xml:id="echoid-s6679" xml:space="preserve">erat latitudo Alexandriæ grad. </s> <s xml:id="echoid-s6680" xml:space="preserve">31. </s> <s xml:id="echoid-s6681" xml:space="preserve">diſtantia ſcilicet ab <lb/>æquatore: </s> <s xml:id="echoid-s6682" xml:space="preserve">quare detractis gr. </s> <s xml:id="echoid-s6683" xml:space="preserve">2.</s> <s xml:id="echoid-s6684" xml:space="preserve">7<emph style="super">′</emph>. </s> <s xml:id="echoid-s6685" xml:space="preserve">ab 31. </s> <s xml:id="echoid-s6686" xml:space="preserve">remanſerunt ferè gr. </s> <s xml:id="echoid-s6687" xml:space="preserve">29. </s> <s xml:id="echoid-s6688" xml:space="preserve">quibus diſtabat Luna ab æquatore dum eſſet <lb/>in principio Cancri, atque in boreo limite. </s> <s xml:id="echoid-s6689" xml:space="preserve">diſtabat autem tunc temporis principium Cancri ab æquatore <lb/>gr. </s> <s xml:id="echoid-s6690" xml:space="preserve">ferè 24. </s> <s xml:id="echoid-s6691" xml:space="preserve">hoc eſt tãta erat maxima declinatio eclypticę, quare Luna magis diſtabat ab æquatore quam ecly-<lb/>ptica in eo loco per gr. </s> <s xml:id="echoid-s6692" xml:space="preserve">5. </s> <s xml:id="echoid-s6693" xml:space="preserve">integros: </s> <s xml:id="echoid-s6694" xml:space="preserve">quod ipſe inquirere ſatagebat. </s> <s xml:id="echoid-s6695" xml:space="preserve">non ignorandum Tychonem facere hanc <lb/>maximam latitudinem part. </s> <s xml:id="echoid-s6696" xml:space="preserve">5. </s> <s xml:id="echoid-s6697" xml:space="preserve">17′. </s> <s xml:id="echoid-s6698" xml:space="preserve">cum igitur Lunæ latitudo maxima ſit gr. </s> <s xml:id="echoid-s6699" xml:space="preserve">5. </s> <s xml:id="echoid-s6700" xml:space="preserve">neceſſario tanta erit etiam Lu-<lb/>naris orbitæ ab eclyptica diſtantia. </s> <s xml:id="echoid-s6701" xml:space="preserve">Porrò ad imi ationem Ptolæmei, aut alia ſolertia, poterit quiſque nego-<lb/>tium iſtud pertractare. </s> <s xml:id="echoid-s6702" xml:space="preserve">cognita autem maxima latitudine viæ Lunaris, cognoſcentur aliæ latitudines aliorum <lb/>partium à nodis vtcumque, nam ſi talis via in Zodiaco deſcribatur declinans gr. </s> <s xml:id="echoid-s6703" xml:space="preserve">5. </s> <s xml:id="echoid-s6704" xml:space="preserve">ſtatim apparebunt reliqua-<lb/>rum partium latitudines. </s> <s xml:id="echoid-s6705" xml:space="preserve">Hactenus viam Lunæ in Zodiaco deſignauimus qui aut in Firmamento, aut pri-<lb/>mo mobili eſſe concipitur. </s> <s xml:id="echoid-s6706" xml:space="preserve">cum autem Luna plurimum infra primum mobile ſuas exerceat reuolutiones, <lb/>quippè quæ omnium planetarum terris citima ſi, ſequitur vt videamus qua ratione ſemitam prædictam re-<lb/>ſpiciat. </s> <s xml:id="echoid-s6707" xml:space="preserve">debemus igitur imaginari Lunam in ſuo cælo, proprio motu ſemper moueri directè ſub prædicta <lb/>orbita, ita vt ſi ducatur linea recta a centro Mundi per centrum Lunæ, ſemper hæc linea producta pertineat <lb/>vſque ad prædictam ſemitam in Zodiaco deſignatam.</s> <s xml:id="echoid-s6708" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6709" xml:space="preserve">Reliquum eſt videre qualis ſit Lunę motus ſub aſſignata linea. </s> <s xml:id="echoid-s6710" xml:space="preserve">mouetur igitur Luna ſub ea motu proprio, <lb/>ideſt, ſecundum ſignorum ſequelam, & </s> <s xml:id="echoid-s6711" xml:space="preserve">quidem reſpectu centri mundi irregulariter, ideſt, modo velocius, <lb/>modo tardius. </s> <s xml:id="echoid-s6712" xml:space="preserve">Quoniam vero Philoſophi, ac Aſtronomi pariter abſurdum exiſtimant cæleſtia corpora ab-<lb/>ſolutè irregulariter moueri, quamuis ad ſenſum ita appareant, ſed regularia eſſe ſecundum naturales latio-<lb/>nes; </s> <s xml:id="echoid-s6713" xml:space="preserve">idcirco irregularitatem hanc ad vniformitatem in geniosè admodum reuocarunt. </s> <s xml:id="echoid-s6714" xml:space="preserve">Confinxerunt igitur <lb/>eam per huiuſmodi circulos agitari, dum prædictum ſuum iter ſub Zodiaco peragit. </s> <s xml:id="echoid-s6715" xml:space="preserve">Egrediatur è centro <lb/>mundi linea tendens directè ad Lunarem viam, ſitq; </s> <s xml:id="echoid-s6716" xml:space="preserve">alta 56. </s> <s xml:id="echoid-s6717" xml:space="preserve">terræ ſemidiametris (tanta eſt enim mediocris <lb/>Lunæ a terra diſtantia) qualis eſt in ſequenti figura linea A B. </s> <s xml:id="echoid-s6718" xml:space="preserve">in cu us vertice ſit deſcriptus circulus, quem <lb/>epicyclum vocant, cuius ſemidiameter conſtet ex prædictis ſemidiameter 4 {1/2}. </s> <s xml:id="echoid-s6719" xml:space="preserve">qualis eſt F C D. </s> <s xml:id="echoid-s6720" xml:space="preserve">in cuius peri-<lb/>pheria ſit Lunare corpus, quaſi in proprio loculo inſertum. </s> <s xml:id="echoid-s6721" xml:space="preserve">Quantitas autem prædicta ſemidiametri epicy-<lb/>cli reperta eſt maxima, & </s> <s xml:id="echoid-s6722" xml:space="preserve">minima diſtantia Lunæ à terra, de qua ſupra: </s> <s xml:id="echoid-s6723" xml:space="preserve">cum enim viderent Lunam maximè, <lb/>ac minimè, item mediocriter attolli, merito poſuerunt centrum, epicycli debere eſſe in ſublimitate media, <pb o="69" file="0089" n="93" rhead="Liber Nonus."/> à qua vſque ad maximam, & </s> <s xml:id="echoid-s6724" xml:space="preserve">minimam eſſet ſemidiameter epicycli, porrò tota ſemidiameter ſubtendit in <lb/>cælo gr. </s> <s xml:id="echoid-s6725" xml:space="preserve">7. </s> <s xml:id="echoid-s6726" xml:space="preserve">40′. </s> <s xml:id="echoid-s6727" xml:space="preserve">ex Copernico pagina 110. </s> <s xml:id="echoid-s6728" xml:space="preserve">quæ dicitur maxima æquatio, vt infra explicabitur. </s> <s xml:id="echoid-s6729" xml:space="preserve">ſupponunt igi-<lb/>tur centrum B. </s> <s xml:id="echoid-s6730" xml:space="preserve">epicycli moueri regulariter ſecundum ſignorum ordinem directe ſub præſcripta iam orbita, <lb/>ſuoque motu deſcribere circulum B H G K. </s> <s xml:id="echoid-s6731" xml:space="preserve">cuius ſemidiameter ſit A B. </s> <s xml:id="echoid-s6732" xml:space="preserve">Porrò hunc centri cpicycli motum <lb/>appellant motum Lunæ medium, quod inter velocem, ac tardum medius fit; </s> <s xml:id="echoid-s6733" xml:space="preserve">qui motus ſortitur varia no-<lb/>mina, ac<unsure/> varias quantitates, prout ex varijs principijs numeratur.</s> <s xml:id="echoid-s6734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6735" xml:space="preserve">Nam ſi referatur ad nodos, vel <lb/> <anchor type="figure" xlink:label="fig-0089-01a" xlink:href="fig-0089-01"/> ad limites ſemitæ Lunaris, dici-<lb/>tur motus medius Lunæ in lati-<lb/>tudinem; </s> <s xml:id="echoid-s6736" xml:space="preserve">hinc enim latitudinem <lb/>Luna acquirit. </s> <s xml:id="echoid-s6737" xml:space="preserve">& </s> <s xml:id="echoid-s6738" xml:space="preserve">ab eis diſcedit <lb/>quotidie gr. </s> <s xml:id="echoid-s6739" xml:space="preserve">13. </s> <s xml:id="echoid-s6740" xml:space="preserve">13″. </s> <s xml:id="echoid-s6741" xml:space="preserve">54″. </s> <s xml:id="echoid-s6742" xml:space="preserve">quare <lb/>ad eundem nodũ reuertitur die-<lb/>bus 27. </s> <s xml:id="echoid-s6743" xml:space="preserve">horis 5 {1/2}. </s> <s xml:id="echoid-s6744" xml:space="preserve">ſi vero referatur <lb/>ad Zodiacum, eum abſoluit die-<lb/>bus 27. </s> <s xml:id="echoid-s6745" xml:space="preserve">hor. </s> <s xml:id="echoid-s6746" xml:space="preserve">7. </s> <s xml:id="echoid-s6747" xml:space="preserve">43′. </s> <s xml:id="echoid-s6748" xml:space="preserve">quod tempus <lb/>dicitur menſis periodicus, quòd <lb/>integram Zodiaci periodum eo <lb/>tẽpore abſoluat; </s> <s xml:id="echoid-s6749" xml:space="preserve">ac ſingulis die-<lb/>bus cõficit in Zodiaco gr. </s> <s xml:id="echoid-s6750" xml:space="preserve">13. </s> <s xml:id="echoid-s6751" xml:space="preserve">10′. <lb/></s> <s xml:id="echoid-s6752" xml:space="preserve">33′. </s> <s xml:id="echoid-s6753" xml:space="preserve">numeraturque a princioio ſi-<lb/>gni Arietis, non Aſteriſmi; </s> <s xml:id="echoid-s6754" xml:space="preserve">dici-<lb/>turq; </s> <s xml:id="echoid-s6755" xml:space="preserve">motus Lunæ in longitudi-<lb/>nem eo, quod hinc lõgitudinem <lb/>Zodiaci acquirat.</s> <s xml:id="echoid-s6756" xml:space="preserve"/> </p> <div xml:id="echoid-div141" type="float" level="2" n="1"> <figure xlink:label="fig-0089-01" xlink:href="fig-0089-01a"> <image file="0089-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0089-01"/> </figure> </div> <p> <s xml:id="echoid-s6757" xml:space="preserve">Si referatur ad Solem, dicitur <lb/>elongatio Lunæ a Sole, & </s> <s xml:id="echoid-s6758" xml:space="preserve">ab eo <lb/>diſcedit quotidie gr. </s> <s xml:id="echoid-s6759" xml:space="preserve">12. </s> <s xml:id="echoid-s6760" xml:space="preserve">11′. </s> <s xml:id="echoid-s6761" xml:space="preserve">26″. <lb/></s> <s xml:id="echoid-s6762" xml:space="preserve">Solemque iterum aſſequitur die-<lb/>bus 29. </s> <s xml:id="echoid-s6763" xml:space="preserve">hor. </s> <s xml:id="echoid-s6764" xml:space="preserve">12. </s> <s xml:id="echoid-s6765" xml:space="preserve">44′. </s> <s xml:id="echoid-s6766" xml:space="preserve">quod tempo-<lb/>ris ſpatium dicitur menſis ſyno-<lb/>dicus, ideſt, vnitiuus, quod Lu-<lb/>nam iterũ Soli coniungatur. </s> <s xml:id="echoid-s6767" xml:space="preserve">hoc <lb/>igitur motu centri B. </s> <s xml:id="echoid-s6768" xml:space="preserve">defertur ſi-<lb/>mul epicyclus cum Luna per Zo <lb/>diacum ſecundum ordinẽ ſigno-<lb/>rum. </s> <s xml:id="echoid-s6769" xml:space="preserve">quem motum, vt alias dixi, <lb/>poſſumus ſine exacta obſeruatio-<lb/>@e percipere quotidie naturali oculorum inſpectione; </s> <s xml:id="echoid-s6770" xml:space="preserve">ſi enim Lunam apud quampiam Stellam fixam nota-<lb/>uerimus, & </s> <s xml:id="echoid-s6771" xml:space="preserve">poſt aliquot horas eam iterum aſpexerimus, vidcbimus eam ab illa ſixa aliquantulũ verſus orien-<lb/>tem receſſiſſe, & </s> <s xml:id="echoid-s6772" xml:space="preserve">ſequenti nocte ab eadem magno ſpatio (quod eſt ferè 13. </s> <s xml:id="echoid-s6773" xml:space="preserve">graduum) in orientem abijſſe: </s> <s xml:id="echoid-s6774" xml:space="preserve"><lb/>quo motu, ſpatio menſis periodici, omnes ſtellas aſſequitur, ac præterit. </s> <s xml:id="echoid-s6775" xml:space="preserve">ſimll ter eam ad Solem obſeruare <lb/>facile eſt</s> </p> <p> <s xml:id="echoid-s6776" xml:space="preserve">Cæterum ſi Luna hoc tantum motu medio moueretur, vniformiter moueretur, ſed mouetur irregulari-<lb/>@er, vt experientia docet: </s> <s xml:id="echoid-s6777" xml:space="preserve">propterea vt hanc irregularitatem excuſemus, debemus imaginari, quod dum cen-<lb/>@rum B. </s> <s xml:id="echoid-s6778" xml:space="preserve">epi. </s> <s xml:id="echoid-s6779" xml:space="preserve">motu mediocri progreditur, vti dictum eſt interim circumferentia eius circa ſuum centrum B. <lb/></s> <s xml:id="echoid-s6780" xml:space="preserve">regulariter reuoluitur, ſecumque Lunare corpus ſibi impactum reuoluit, ita vt in ſuperiori parte F C D. </s> <s xml:id="echoid-s6781" xml:space="preserve">epi. </s> <s xml:id="echoid-s6782" xml:space="preserve"><lb/>contra ordinem ſignorum, hoc eſt, ab F. </s> <s xml:id="echoid-s6783" xml:space="preserve">in C. </s> <s xml:id="echoid-s6784" xml:space="preserve">& </s> <s xml:id="echoid-s6785" xml:space="preserve">a C. </s> <s xml:id="echoid-s6786" xml:space="preserve">in D. </s> <s xml:id="echoid-s6787" xml:space="preserve">Lunam deferat. </s> <s xml:id="echoid-s6788" xml:space="preserve">In inferiori vero parte D E F. </s> <s xml:id="echoid-s6789" xml:space="preserve"><lb/>ſ<unsure/>ecundum ordinem ſingorum, ideſta D. </s> <s xml:id="echoid-s6790" xml:space="preserve">in E. </s> <s xml:id="echoid-s6791" xml:space="preserve">& </s> <s xml:id="echoid-s6792" xml:space="preserve">ab E. </s> <s xml:id="echoid-s6793" xml:space="preserve">ad F. </s> <s xml:id="echoid-s6794" xml:space="preserve">reſtituat. </s> <s xml:id="echoid-s6795" xml:space="preserve">abſoluit autem hanc periodum diebus <lb/>@7. </s> <s xml:id="echoid-s6796" xml:space="preserve">hor. </s> <s xml:id="echoid-s6797" xml:space="preserve">13. </s> <s xml:id="echoid-s6798" xml:space="preserve">18′. </s> <s xml:id="echoid-s6799" xml:space="preserve">35″. </s> <s xml:id="echoid-s6800" xml:space="preserve">& </s> <s xml:id="echoid-s6801" xml:space="preserve">numeratio eius incipit à ſupremo puncto C. </s> <s xml:id="echoid-s6802" xml:space="preserve">Quotidie vero Luna percurrit de circum-<lb/>ferentia, ſiue defertur ab ipſa circũferentia gradibus 13. </s> <s xml:id="echoid-s6803" xml:space="preserve">3′. </s> <s xml:id="echoid-s6804" xml:space="preserve">54″. </s> <s xml:id="echoid-s6805" xml:space="preserve">ideſt, eſt motus diurnus Lunæ in peripheria <lb/>epi. </s> <s xml:id="echoid-s6806" xml:space="preserve">porrò ex hac Lunæ circa centrum huius epi. </s> <s xml:id="echoid-s6807" xml:space="preserve">gyratione, ſaluantur apparentiæ, & </s> <s xml:id="echoid-s6808" xml:space="preserve">irregularitates e@us. </s> <s xml:id="echoid-s6809" xml:space="preserve">hic <lb/>autem motus dicitur Aſtronomis Anomaliæ, ideſt, irregularitatis motus, quod eam ipſe efficiat: </s> <s xml:id="echoid-s6810" xml:space="preserve">nam quan-<lb/>do Luna verſatur in ſuperiori parte epi. </s> <s xml:id="echoid-s6811" xml:space="preserve">vt dictum eſt, mouetur contra ordinem ſignorum, quare mouetur <lb/>motu contrario ei, quo centrum epi. </s> <s xml:id="echoid-s6812" xml:space="preserve">ſecundum ſequelam ſignorum procedit; </s> <s xml:id="echoid-s6813" xml:space="preserve">quapropter fit vt ipſa Luna <lb/>feratur contrarijs motibus, vno ſecundum ordinem ſignorum, altero contra; </s> <s xml:id="echoid-s6814" xml:space="preserve">quapropter tardè admodum <lb/>videtur progredi in conſequentia, quia motus cẽtri B. </s> <s xml:id="echoid-s6815" xml:space="preserve">paulò velocior eſt, quam ſit Luna in periph. </s> <s xml:id="echoid-s6816" xml:space="preserve">epic. </s> <s xml:id="echoid-s6817" xml:space="preserve">quan-<lb/>do vero verſatur in inferiori parte epi. </s> <s xml:id="echoid-s6818" xml:space="preserve">tunc tendit ad eaſdem partes cũ motu centri B. </s> <s xml:id="echoid-s6819" xml:space="preserve">quare ob motum am-<lb/>borum concordiam velox ad orientem progreditur. </s> <s xml:id="echoid-s6820" xml:space="preserve">in lateribus autem epi. </s> <s xml:id="echoid-s6821" xml:space="preserve">propè punctu F D. </s> <s xml:id="echoid-s6822" xml:space="preserve">motus Lunæ <lb/>mediocris, ſeu medius apparet; </s> <s xml:id="echoid-s6823" xml:space="preserve">quia inibi circulatio Lunæ in epi. </s> <s xml:id="echoid-s6824" xml:space="preserve">nec aduerſatur, nec iuuat motum centri B. </s> <s xml:id="echoid-s6825" xml:space="preserve"><lb/>in longitudinem. </s> <s xml:id="echoid-s6826" xml:space="preserve">Notanda ſunt in epi. </s> <s xml:id="echoid-s6827" xml:space="preserve">quatuor puncta. </s> <s xml:id="echoid-s6828" xml:space="preserve">punctum eius ſupremum C. </s> <s xml:id="echoid-s6829" xml:space="preserve">dicitur Apogæum, ideſt, <lb/>à terra altiſſimum a quo incipit numerari motus Anomaliæ. </s> <s xml:id="echoid-s6830" xml:space="preserve">punctum E. </s> <s xml:id="echoid-s6831" xml:space="preserve">dicitur perigæum, ideſt, terræ pro-<lb/>@imum. </s> <s xml:id="echoid-s6832" xml:space="preserve">puncta F D. </s> <s xml:id="echoid-s6833" xml:space="preserve">dicuntur mediæ diſtantiæ; </s> <s xml:id="echoid-s6834" xml:space="preserve">& </s> <s xml:id="echoid-s6835" xml:space="preserve">determinantur à duabus lineis A F D. </s> <s xml:id="echoid-s6836" xml:space="preserve">tangentibus epicyl.</s> <s xml:id="echoid-s6837" xml:space="preserve"> <pb o="70" file="0090" n="94" rhead="De Mundi Fabrica,"/> Hinc rellqua quoque excuſantur phænomena; </s> <s xml:id="echoid-s6838" xml:space="preserve">aliquando enim Luna maior videtur, ita vt eius apparens dia-<lb/>meter ſit 36. </s> <s xml:id="echoid-s6839" xml:space="preserve">min. </s> <s xml:id="echoid-s6840" xml:space="preserve">quod ei accidit quod ſit in perigæo E. </s> <s xml:id="echoid-s6841" xml:space="preserve">oculis noſtris propior. </s> <s xml:id="echoid-s6842" xml:space="preserve">aliquando minor videtur mi-<lb/>nutorum ſcilicet 32. </s> <s xml:id="echoid-s6843" xml:space="preserve">quia videlicet remotior eſt in C. </s> <s xml:id="echoid-s6844" xml:space="preserve">Apogæo. </s> <s xml:id="echoid-s6845" xml:space="preserve">Aliquando mediocris apparet in punctis ni-<lb/>mirum F D. </s> <s xml:id="echoid-s6846" xml:space="preserve">mediæ remotionis.</s> <s xml:id="echoid-s6847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6848" xml:space="preserve">Non mireris quæſo lector ſi aliũ minorem epicyclũ huic noſtro epicyclo non ſuperaddo, illũ enim de in-<lb/>duſtria omitto, ne videlicet longior, atque impeditior hæc euadat tractatio, quam inſtituto conueniat. </s> <s xml:id="echoid-s6849" xml:space="preserve">neque <lb/>enim ſphæræ ſcriptores minutiſſima quæque perſequi debent: </s> <s xml:id="echoid-s6850" xml:space="preserve">nobis autem ſatis eſt præcipua, ac pulchriora <lb/>perſequi. </s> <s xml:id="echoid-s6851" xml:space="preserve">Præterea moneo te vt parum ſolicitus ſis de fabrica horum circulorum, epicyclorum, aut eccen-<lb/>tricorum; </s> <s xml:id="echoid-s6852" xml:space="preserve">num videlicet ſint orbes reales ab inuicem diſtincti, num duri, aut teneri, & </s> <s xml:id="echoid-s6853" xml:space="preserve">an cælum Lunæ mo-<lb/>uea tur cum Luna, an Luna ſine ipſo, & </s> <s xml:id="echoid-s6854" xml:space="preserve">alia huiuſmodi, quæſatius eſt fateri nos ignorare, quam fabuloſam <lb/>quandam Philoſophiam iunioribus tradere. </s> <s xml:id="echoid-s6855" xml:space="preserve">Ptolemæus Aſtronomorum princeps, quem ſequuntur Coper. <lb/></s> <s xml:id="echoid-s6856" xml:space="preserve">& </s> <s xml:id="echoid-s6857" xml:space="preserve">Tycho ſummi pariter aſtronomi; </s> <s xml:id="echoid-s6858" xml:space="preserve">totam cælorum fabricam per ſolas lineas tradidit, ideſt, per ſolos circu-<lb/>los, ſola centra, abſque vlla eorum craſſitie, aut duritie, motus ſyderum explicauit; </s> <s xml:id="echoid-s6859" xml:space="preserve">eaſque res hypotheſes ap-<lb/>pellauit. </s> <s xml:id="echoid-s6860" xml:space="preserve">Quaproter toti eſſe debemus in ipſorum planetarũ, & </s> <s xml:id="echoid-s6861" xml:space="preserve">affixarum accidentibus diſquirendis, hoc eſt <lb/>enim verum, ac præcipuum aſtronomiæ ſtudium.</s> <s xml:id="echoid-s6862" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6863" xml:space="preserve">Sed iterum in motu Lunæ pergamus. </s> <s xml:id="echoid-s6864" xml:space="preserve">Imaginati hactenus ſumus Lunam moueri duplici motu, altero <lb/>quem diximus anomaliæ in peripheria epicycli neceſſe igitur eſt, vt tertius ex his duobus reſultet motus, cũ <lb/>impoffibile ſit, idem corpus moueri pluribus ab inuicem reapſe diſtinctis motibus, niſi in vnũ mixtum coale-<lb/>ſcant. </s> <s xml:id="echoid-s6865" xml:space="preserve">hunc in re præſenti ſic concipiemus, ſi conſideremus quod quando eſt in apogæo magis diſtat à cẽtro, <lb/>quam in perigeo, in medijs locis proportionaliter ſe habeat; </s> <s xml:id="echoid-s6866" xml:space="preserve">quare Luna ipſa, hac ratione, deſcribit circulum <lb/>mundo eccentricum, ideſt, cuius centrum eſt extra centrum mundi, talem eccentricum in figura refert linea <lb/>C H I K L. </s> <s xml:id="echoid-s6867" xml:space="preserve">quod benè ſic percipiemus; </s> <s xml:id="echoid-s6868" xml:space="preserve">ponamus Lunam initio vtriuſque motus eſſe in Apogæo C. </s> <s xml:id="echoid-s6869" xml:space="preserve">dum igi-<lb/>tur B. </s> <s xml:id="echoid-s6870" xml:space="preserve">mouetur per ſuam Lunares orbitam in conſequentia, interim Luna ab Apogæo deſcendit verſus D. <lb/></s> <s xml:id="echoid-s6871" xml:space="preserve">quare cum B. </s> <s xml:id="echoid-s6872" xml:space="preserve">fuerit apud H. </s> <s xml:id="echoid-s6873" xml:space="preserve">Luna in epi. </s> <s xml:id="echoid-s6874" xml:space="preserve">erit ad D. </s> <s xml:id="echoid-s6875" xml:space="preserve">& </s> <s xml:id="echoid-s6876" xml:space="preserve">cum, B. </s> <s xml:id="echoid-s6877" xml:space="preserve">fuerit ad G. </s> <s xml:id="echoid-s6878" xml:space="preserve">Luna erit ferè in perigæo E. </s> <s xml:id="echoid-s6879" xml:space="preserve">quod <lb/>tunc congruet puncto I. </s> <s xml:id="echoid-s6880" xml:space="preserve">cum B. </s> <s xml:id="echoid-s6881" xml:space="preserve">fuerit ad K. </s> <s xml:id="echoid-s6882" xml:space="preserve">Luna ad F. </s> <s xml:id="echoid-s6883" xml:space="preserve">aſcenderit. </s> <s xml:id="echoid-s6884" xml:space="preserve">tandem epi. </s> <s xml:id="echoid-s6885" xml:space="preserve">ad idem punctum Zodiaci re-<lb/>uerſo, Luna nondum redierit ad Apogæum, C. </s> <s xml:id="echoid-s6886" xml:space="preserve">quia motus eius Anomaliæ ſiue in periphæria epic. </s> <s xml:id="echoid-s6887" xml:space="preserve">ſex ferè <lb/>horis tardior eſt, quàm motus centri. </s> <s xml:id="echoid-s6888" xml:space="preserve">epic. </s> <s xml:id="echoid-s6889" xml:space="preserve">in conſequentia, ſiue menſe periodico: </s> <s xml:id="echoid-s6890" xml:space="preserve">quare abſoluta reuolutione <lb/>centri B. </s> <s xml:id="echoid-s6891" xml:space="preserve">Luna nondum erit in C. </s> <s xml:id="echoid-s6892" xml:space="preserve">niſi poſt horas 6. </s> <s xml:id="echoid-s6893" xml:space="preserve">circa punctum L. </s> <s xml:id="echoid-s6894" xml:space="preserve">ſub quo etiam centrũ B. </s> <s xml:id="echoid-s6895" xml:space="preserve">vltra integram <lb/>periodum proceſſerit; </s> <s xml:id="echoid-s6896" xml:space="preserve">quare in L. </s> <s xml:id="echoid-s6897" xml:space="preserve">deſinet motus anomaliæ igitur via propria Lunaris corporis in ſua regio-<lb/>ne erit, C H I K L. </s> <s xml:id="echoid-s6898" xml:space="preserve">qua finita alia ſimils deſcribetur. </s> <s xml:id="echoid-s6899" xml:space="preserve">quę quidem omnia ita ſe haberent, niſi motus primi mo-<lb/>bilis, ſiue diurnus Lumæ ſuperueniret. </s> <s xml:id="echoid-s6900" xml:space="preserve">imo cũ Meſſahala Arabe notandum eſt, quod ſi Luna prædicto mo-<lb/>tu ſolum moueretur, ideſt, ſi a diurna cõuerſione non reuolueretur ab oriente in occid. </s> <s xml:id="echoid-s6901" xml:space="preserve">videremus primo Lu-<lb/>nam nouam oriri in occidente, & </s> <s xml:id="echoid-s6902" xml:space="preserve">paulatim progredi ad ortum, ita vt per 14. </s> <s xml:id="echoid-s6903" xml:space="preserve">ferè dies continuos eam diu, ac <lb/>noctu ſupra noſtrum finitorem ſpectaremus; </s> <s xml:id="echoid-s6904" xml:space="preserve">eamque tandem plenam in oriente contra naturæ leges occide-<lb/>re. </s> <s xml:id="echoid-s6905" xml:space="preserve">ij tamen qui ſub polis Lunaris orbitæ degerent, eam ſemper circa ſuos horizontes gyrare conſpicerent. </s> <s xml:id="echoid-s6906" xml:space="preserve"><lb/>Atque hic eſſet propria Lunæ in ſua regione reuolutio, niſi ei interim diurna reuolutio ſuperueniret, quæ <lb/>eam, vt videmus omnes, defert ab oriente in occidentem ſpatio ferè 25. </s> <s xml:id="echoid-s6907" xml:space="preserve">horarum quamuis enim diurna con-<lb/>uerſio omnes part@s primi mobilis 24. </s> <s xml:id="echoid-s6908" xml:space="preserve">hor. </s> <s xml:id="echoid-s6909" xml:space="preserve">perfectè reuoluat, planetæ tamen ob motum proprium, quo in-<lb/>terim ad orientem feruntur, non omnino primo mobili obtemperant, ſed tanto tardius diurnam conue rſio-<lb/>nem abſoluunt, quantum importat ſpatium illud, quod interim, ad orientem contra motum diurnum perfi-<lb/>ciunt. </s> <s xml:id="echoid-s6910" xml:space="preserve">Et quoniam Luna ſuo motu diurno ſeu diario proprio mouetur ad orientem gr. </s> <s xml:id="echoid-s6911" xml:space="preserve">13. </s> <s xml:id="echoid-s6912" xml:space="preserve">qui ferè horam <lb/>vnam in motu diurno primi mobilis efficiunt, ideo Luna hanc diurnam conuerſionem nõ niſi ſpatio 25. </s> <s xml:id="echoid-s6913" xml:space="preserve">qua-<lb/>ſi horarum peragit. </s> <s xml:id="echoid-s6914" xml:space="preserve">Atque hæc eſt cauſa cur ſingulis noctibus eam vna hora tardius oriri cernamus: </s> <s xml:id="echoid-s6915" xml:space="preserve">& </s> <s xml:id="echoid-s6916" xml:space="preserve">cor <lb/>ſequenter maris æſtus vna etiam hora tard us reuertantur: </s> <s xml:id="echoid-s6917" xml:space="preserve">vti ſupra diximus.</s> <s xml:id="echoid-s6918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6919" xml:space="preserve">Conſidera@dum eſt igi@ur qua rátione ex motu proprio, atque ex motu diurno ſupeueniente, Luna tertio <lb/>quodam motu mixto, ac vltimo moueatur, qui motus eſt ſpirali, vt alias explicaui, ab vno tropico ad alterum, <lb/>dum enim Luna in ſua orbita ſub Zodiaco proficiſcitur, ſpatio 27. </s> <s xml:id="echoid-s6920" xml:space="preserve">dierum; </s> <s xml:id="echoid-s6921" xml:space="preserve">interim quotidie cogitur diur-<lb/>nam reuolutionem peragere. </s> <s xml:id="echoid-s6922" xml:space="preserve">Cogitemus lineam Lunæ C H I K L. </s> <s xml:id="echoid-s6923" xml:space="preserve">eſſe ſub Zodiaco, Lunamqu@ eam inci-<lb/> <anchor type="figure" xlink:label="fig-0090-01a" xlink:href="fig-0090-01"/> pere in principio Cancri, & </s> <s xml:id="echoid-s6924" xml:space="preserve">dum in ea percurrit in conſequen-<lb/>tia gr. </s> <s xml:id="echoid-s6925" xml:space="preserve">13. </s> <s xml:id="echoid-s6926" xml:space="preserve">interim ſimul diurna conuerſio eam in contrarias par <lb/>tes vertat, ac reuoluat, & </s> <s xml:id="echoid-s6927" xml:space="preserve">quidem magis ſemper accedendo ad <lb/>alterum Tropicum ob Zodiaci obliquitatem. </s> <s xml:id="echoid-s6928" xml:space="preserve">quare Luna hac <lb/>diurna conuerſione nõ circulum in ſe redeuntem, ſed ſpiralem <lb/>lineam, aut helicem, ſeu glomerationem quandam delineabit <lb/>verſus alterum Tropicum. </s> <s xml:id="echoid-s6929" xml:space="preserve">ſequenti die idem efficit, & </s> <s xml:id="echoid-s6930" xml:space="preserve">ſic dein-<lb/>ceps quare diebus 14. </s> <s xml:id="echoid-s6931" xml:space="preserve">ferè, ad alterum Tropicum ſpiratim per-<lb/>ueniet: </s> <s xml:id="echoid-s6932" xml:space="preserve">& </s> <s xml:id="echoid-s6933" xml:space="preserve">inde ſpiras iterum nouas reciprocans ad Tropicum <lb/>Cancri integram, & </s> <s xml:id="echoid-s6934" xml:space="preserve">menſtruam deducet helicem. </s> <s xml:id="echoid-s6935" xml:space="preserve">quamuis au-<lb/>tem hæc difficilè pingantur, aliquam tamen huius ſpiræ accipe <lb/>figuram, in qua A B. </s> <s xml:id="echoid-s6936" xml:space="preserve">prima ac diurna ſpira fit in principio Can-<lb/>cri, atqne in limite boreo; </s> <s xml:id="echoid-s6937" xml:space="preserve">vltima vero C D. </s> <s xml:id="echoid-s6938" xml:space="preserve">ſit vltra Tropicum <lb/>Capricorni in auſtrali limite, ſunt omnes ſpiræ 13. </s> <s xml:id="echoid-s6939" xml:space="preserve">cum dimidia; </s> <s xml:id="echoid-s6940" xml:space="preserve">totidem enim diebus interuallum illud de-<lb/>curritur, non eſt æqualis craffitiei, aut corpulentiæ, ſed circa A B. </s> <s xml:id="echoid-s6941" xml:space="preserve">laxior, quam ad D D. </s> <s xml:id="echoid-s6942" xml:space="preserve">vbi anguſtior; </s> <s xml:id="echoid-s6943" xml:space="preserve">quia ſi <pb o="71" file="0091" n="95" rhead="Liber Nonus."/> Luna fit in Apogæo dum facit ſpiram A B. </s> <s xml:id="echoid-s6944" xml:space="preserve">eam ampliorem efficiet: </s> <s xml:id="echoid-s6945" xml:space="preserve">ſi ſit in perigæo dum recurrit per D C. <lb/></s> <s xml:id="echoid-s6946" xml:space="preserve">eam contractiorem reddet. </s> <s xml:id="echoid-s6947" xml:space="preserve">Atque hictandem ſpiralis motus eſt ille vltimus, ad quem Luna peragendum à <lb/>naturæ opifice deſtinata eſt; </s> <s xml:id="echoid-s6948" xml:space="preserve">& </s> <s xml:id="echoid-s6949" xml:space="preserve">cuius gratia cę@eri prius explicati ſunt; </s> <s xml:id="echoid-s6950" xml:space="preserve">ex ijs enim videtur nobis hanc vltimam <lb/>ſpiram elaborandam eſſe. </s> <s xml:id="echoid-s6951" xml:space="preserve">crediderim tamen libentius Lunam ipſa ſuapte naturali hac motione primo per-<lb/>celli. </s> <s xml:id="echoid-s6952" xml:space="preserve">illud notatu dignum eſt, in omnibus niſce Lunæ conuolutionibus, eandem ſemper eius partem eodem <lb/>ſitu Telluri obuerti, maculas nimirum illas, quę humanam faciem ruditer imitantur; </s> <s xml:id="echoid-s6953" xml:space="preserve">vnde conijci poteſt eam <lb/>nullis epicycli vinculis conſtrictam, ſed liberè circumuolui.</s> <s xml:id="echoid-s6954" xml:space="preserve"/> </p> <div xml:id="echoid-div142" type="float" level="2" n="2"> <figure xlink:label="fig-0090-01" xlink:href="fig-0090-01a"> <image file="0090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0090-01"/> </figure> </div> <p> <s xml:id="echoid-s6955" xml:space="preserve">Sed adhuc explicare oportet, qua ratione Aſtronomi ſuperiores motus medios explorauerint. </s> <s xml:id="echoid-s6956" xml:space="preserve">ſciendum. <lb/></s> <s xml:id="echoid-s6957" xml:space="preserve">igitur eſt eos per Lunares eclypſes obſcuriſlima quæque, ac difficillima ſuperaſſe. </s> <s xml:id="echoid-s6958" xml:space="preserve">Hipparchus itaque hu-<lb/>ius rei gratia, accepit duas Lunæ eclypſes omnino ſimiles, ideſt, in quibus Luna eſſet in eodem epicycli pun-<lb/>cto, quod ex motu Lunæ tardo, veloci, aut mediocri, cognoſcere poterat; </s> <s xml:id="echoid-s6959" xml:space="preserve">necnon ex apparente eius magni-<lb/>tudine. </s> <s xml:id="echoid-s6960" xml:space="preserve">erant autem hæ duæ<unsure/> eclypſes per annos ægyptios 345. </s> <s xml:id="echoid-s6961" xml:space="preserve">dies 82. </s> <s xml:id="echoid-s6962" xml:space="preserve">& </s> <s xml:id="echoid-s6963" xml:space="preserve">hor. </s> <s xml:id="echoid-s6964" xml:space="preserve">vnã, quæ efficiunt dies 126,007. </s> <s xml:id="echoid-s6965" xml:space="preserve"><lb/>abinuicem diſtantes. </s> <s xml:id="echoid-s6966" xml:space="preserve">quarũ prima obſeruata, ac denotata fuerata Chaldęis. </s> <s xml:id="echoid-s6967" xml:space="preserve">alteram ipſemet ſuis organis an-<lb/>notauit, quia ergo eclypſes erant omnino ſimiles, Lunaque erat in eodem epic. </s> <s xml:id="echoid-s6968" xml:space="preserve">puncto in ſecunda, ac prima, <lb/>neceſſe eſt in prædicto temporis interuallo, factas eſſe Lunationes integras: </s> <s xml:id="echoid-s6969" xml:space="preserve">& </s> <s xml:id="echoid-s6970" xml:space="preserve">pariter Anomaliæ reuolutio-<lb/>nes integras, cum ab vno plenilunio ad aliud, & </s> <s xml:id="echoid-s6971" xml:space="preserve">ab eodem Anomaliæ puncto ad idem Luna redierit. </s> <s xml:id="echoid-s6972" xml:space="preserve">fuerunt <lb/>autem in prædicto dierum numero Lunationes, ſiue menſes Lunares ſynodici 4, 267. </s> <s xml:id="echoid-s6973" xml:space="preserve">quod facilè ex nouilu-<lb/>niorum præteritorum numeratione a maioribus habita conſtitit. </s> <s xml:id="echoid-s6974" xml:space="preserve">his paratis diuiſit numerũ d@erum 126, 007. </s> <s xml:id="echoid-s6975" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s6976" xml:space="preserve">horam vnam qui a prima eclypſi ad vltimam excurrerunt, per numerum menſium 4, 267. </s> <s xml:id="echoid-s6977" xml:space="preserve">& </s> <s xml:id="echoid-s6978" xml:space="preserve">ſic patuit vni <lb/>Lunationi mediæconuenire dies 29. </s> <s xml:id="echoid-s6979" xml:space="preserve">horas 12. </s> <s xml:id="echoid-s6980" xml:space="preserve">ac minuta 44. </s> <s xml:id="echoid-s6981" xml:space="preserve">horarum; </s> <s xml:id="echoid-s6982" xml:space="preserve">vti ſupra dictum eſt. </s> <s xml:id="echoid-s6983" xml:space="preserve">dixi Lunationi <lb/>mediæ, quia in toto illo dierum interuallo, Lunationes re vera non fuerunt inuicem ęquales, cùm Luna irre-<lb/>gulariter moueatur; </s> <s xml:id="echoid-s6984" xml:space="preserve">ſupponuntur tamen æqua@es, ſiue mediæ inter maiores, ac minores. </s> <s xml:id="echoid-s6985" xml:space="preserve">Rurſus in eodem. </s> <s xml:id="echoid-s6986" xml:space="preserve"><lb/>interualio fuerunt Anomaliæ reuolutiones 4,573. </s> <s xml:id="echoid-s6987" xml:space="preserve">quod per Lunæ irregular tates repetitas, ac numeratas a ſu-<lb/>perioribus Aſtronomis patuit. </s> <s xml:id="echoid-s6988" xml:space="preserve">diu@ſis igitur @jidem diebus 126,007. </s> <s xml:id="echoid-s6989" xml:space="preserve">& </s> <s xml:id="echoid-s6990" xml:space="preserve">horam vnam per 4,573. </s> <s xml:id="echoid-s6991" xml:space="preserve">vni Anomalię <lb/>competunt dies 27. </s> <s xml:id="echoid-s6992" xml:space="preserve">horæ 13. </s> <s xml:id="echoid-s6993" xml:space="preserve">18′.</s> <s xml:id="echoid-s6994" xml:space="preserve">35″. </s> <s xml:id="echoid-s6995" xml:space="preserve">hac ratione, aut paulo aliter per eclypſes admodum diſtantes (quanto <lb/>enim maius interceſſerit interuallum, melius eſt) alias quoque medias periodos, ſiue media tempora, Aſtro-<lb/>nomi compererunt. </s> <s xml:id="echoid-s6996" xml:space="preserve">ſic menſis perio @icus conſtitit diebus 27. </s> <s xml:id="echoid-s6997" xml:space="preserve">hor. </s> <s xml:id="echoid-s6998" xml:space="preserve">7. </s> <s xml:id="echoid-s6999" xml:space="preserve">min. </s> <s xml:id="echoid-s7000" xml:space="preserve">43′. </s> <s xml:id="echoid-s7001" xml:space="preserve">ſic motus in latitudinem, & </s> <s xml:id="echoid-s7002" xml:space="preserve">mo-<lb/>tus etiam nodorum, vti ſupra definitum eſt, explorati ſunt.</s> <s xml:id="echoid-s7003" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7004" xml:space="preserve">Quibus temporibus habitis quæſierunt motus medios prædictos ad ſingula tempora, v.</s> <s xml:id="echoid-s7005" xml:space="preserve">g. </s> <s xml:id="echoid-s7006" xml:space="preserve">motum diurnum <lb/>Lunæ in latitudinem, aut eiongationem eius diurnam à Sole, aut diariam Anomaliam, &</s> <s xml:id="echoid-s7007" xml:space="preserve">c. </s> <s xml:id="echoid-s7008" xml:space="preserve">quos ſic ſunt aſſe-<lb/>quuti, v.</s> <s xml:id="echoid-s7009" xml:space="preserve">g. </s> <s xml:id="echoid-s7010" xml:space="preserve">volentes ſcire motum diarium Lunæ ſecundum longitudinem Zodiaci, diuiſerunt totum Zodia-<lb/>cum, ideſt, gr. </s> <s xml:id="echoid-s7011" xml:space="preserve">360. </s> <s xml:id="echoid-s7012" xml:space="preserve">per numerum dierum, & </s> <s xml:id="echoid-s7013" xml:space="preserve">horarum vnins menſis periodici, nimirũ per dies 27. </s> <s xml:id="echoid-s7014" xml:space="preserve">hor. </s> <s xml:id="echoid-s7015" xml:space="preserve">7. </s> <s xml:id="echoid-s7016" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s7017" xml:space="preserve">43′. </s> <s xml:id="echoid-s7018" xml:space="preserve">& </s> <s xml:id="echoid-s7019" xml:space="preserve">in quotiente prouenerunt gradus, & </s> <s xml:id="echoid-s7020" xml:space="preserve">minuta diurnæ longitudines Lunæ, qui ſunt, vt ſupra diximus gr. </s> <s xml:id="echoid-s7021" xml:space="preserve"><lb/>13. </s> <s xml:id="echoid-s7022" xml:space="preserve">10′. </s> <s xml:id="echoid-s7023" xml:space="preserve">35″. </s> <s xml:id="echoid-s7024" xml:space="preserve">ſimili ratione, & </s> <s xml:id="echoid-s7025" xml:space="preserve">alijs etiam modis, quos breuitatis cauſa prætereo, alios diarios motus æquales <lb/>repererunt. </s> <s xml:id="echoid-s7026" xml:space="preserve">quibus compercis ſaci@e fuit poſtea motus etiam horarios, qui ſunt partes 24. </s> <s xml:id="echoid-s7027" xml:space="preserve">motuum diurnorũ <lb/>per diuiſionem ipſorum per 24. </s> <s xml:id="echoid-s7028" xml:space="preserve">obtinere. </s> <s xml:id="echoid-s7029" xml:space="preserve">ſimiliter & </s> <s xml:id="echoid-s7030" xml:space="preserve">aunuos per multiplicationem diurnorum habere. </s> <s xml:id="echoid-s7031" xml:space="preserve">vnde <lb/>poſtea Tabulas Aſtronomicas condidere de quibus paulo poſt.</s> <s xml:id="echoid-s7032" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div144" type="section" level="1" n="90"> <head xml:id="echoid-head99" style="it" xml:space="preserve">De motibus Lunæ veris, & apparentibus.</head> <p> <s xml:id="echoid-s7033" xml:space="preserve">IN figura ſuperiori linea A B. </s> <s xml:id="echoid-s7034" xml:space="preserve">dicitur linea medij motus, quia vbi ipſa in Zodiaco fuerit ibi deſinit medius <lb/>quilibet motus ex ſupradictis. </s> <s xml:id="echoid-s7035" xml:space="preserve">linea vero A M. </s> <s xml:id="echoid-s7036" xml:space="preserve">tranſiens per Lunam deſignat in Zodiaco locum verũ Lu-<lb/>næ; </s> <s xml:id="echoid-s7037" xml:space="preserve">& </s> <s xml:id="echoid-s7038" xml:space="preserve">conſequentur etiam motus omnes veri ipſi abſoluuntur, vbi ipſa in Zodiaco fuerit, v.</s> <s xml:id="echoid-s7039" xml:space="preserve">g. </s> <s xml:id="echoid-s7040" xml:space="preserve">ſi ipſa fuerit 15. <lb/></s> <s xml:id="echoid-s7041" xml:space="preserve">grad. </s> <s xml:id="echoid-s7042" xml:space="preserve">♈. </s> <s xml:id="echoid-s7043" xml:space="preserve">erit motus verus longitudinis Lunæ gr. </s> <s xml:id="echoid-s7044" xml:space="preserve">15. </s> <s xml:id="echoid-s7045" xml:space="preserve">motus enim iſti ſunt arcus numerati, vel ab Ariete, vel à <lb/>Sole, vel a Nodis, vſque ad lineam medij motus, aut veri. </s> <s xml:id="echoid-s7046" xml:space="preserve">Conſideratur præterea aliquando motus apparens, <lb/>qui eſt arcus Zodiaci, aliunde numeratus vſque ad illum Zodiaci gradum, ad quem linea motus apparentis <lb/>applicuerit. </s> <s xml:id="echoid-s7047" xml:space="preserve">linea autem motus apparentis eſt quæ ducitur ab oculo noſtro per Lunam vſque ad Zodiacum, <lb/>vbi deſignat locum Lunæ viſum, difterentem a vero, vti alias explicatum eſt. </s> <s xml:id="echoid-s7048" xml:space="preserve">motus verus reperitur, per cal-<lb/>culum Aſtronomicum, de quo mox: </s> <s xml:id="echoid-s7049" xml:space="preserve">motus apparens reperitur per obſeruationem inſtrument@s adh@bitis. </s> <s xml:id="echoid-s7050" xml:space="preserve"><lb/>Sed quæres quot milliaria Aſtronomica ſingulis ho@is ob diurnam conuerſionem peragit Luna? </s> <s xml:id="echoid-s7051" xml:space="preserve">Reſpon-<lb/>deo eam, quando eſt in mediocri à terra diſtantia conficere milliariorum 50, 400. </s> <s xml:id="echoid-s7052" xml:space="preserve">nam cũ in mediocri remo-<lb/>tione diameter circuitus Lunaris contineat diametros terræ 56. </s> <s xml:id="echoid-s7053" xml:space="preserve">continebit pariter circuitus ille terræ peri-<lb/>pheria 56. </s> <s xml:id="echoid-s7054" xml:space="preserve">vicibus; </s> <s xml:id="echoid-s7055" xml:space="preserve">nam vt ſe habet diameter ad diametrum, ita circumferentia ad circumferentiam (ex Papi <lb/>Alex@ndrini lib. </s> <s xml:id="echoid-s7056" xml:space="preserve">5. </s> <s xml:id="echoid-s7057" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s7058" xml:space="preserve">11. </s> <s xml:id="echoid-s7059" xml:space="preserve">& </s> <s xml:id="echoid-s7060" xml:space="preserve">ex Geom. </s> <s xml:id="echoid-s7061" xml:space="preserve">pract. </s> <s xml:id="echoid-s7062" xml:space="preserve">Clauij lib. </s> <s xml:id="echoid-s7063" xml:space="preserve">4. </s> <s xml:id="echoid-s7064" xml:space="preserve">& </s> <s xml:id="echoid-s7065" xml:space="preserve">8.) </s> <s xml:id="echoid-s7066" xml:space="preserve">quare cùm in ambitu terræ ſint millia-<lb/>ria Aſtronomica 21, 600. </s> <s xml:id="echoid-s7067" xml:space="preserve">ſi eam multiplicentur per 56. </s> <s xml:id="echoid-s7068" xml:space="preserve">producitur num. </s> <s xml:id="echoid-s7069" xml:space="preserve">milliariorum circuitus Lunaris, is <lb/>autem eſt 1,200,600. </s> <s xml:id="echoid-s7070" xml:space="preserve">qui numerus diui@us per 24. </s> <s xml:id="echoid-s7071" xml:space="preserve">horas, dab@t 50,400. </s> <s xml:id="echoid-s7072" xml:space="preserve">milliar. </s> <s xml:id="echoid-s7073" xml:space="preserve">vnicuique horæ; </s> <s xml:id="echoid-s7074" xml:space="preserve">tantuſque id-<lb/>circo erit motus Lunæ horarius ſecundum d@urnam lationem primi mobilis. </s> <s xml:id="echoid-s7075" xml:space="preserve">Atq; </s> <s xml:id="echoid-s7076" xml:space="preserve">hæc de Lunæ motu pro <lb/>inſtituta breuitate ſufficiant.</s> <s xml:id="echoid-s7077" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div145" type="section" level="1" n="91"> <head xml:id="echoid-head100" style="it" xml:space="preserve">De Lunæ Illuminatione. Cap. III.</head> <p> <s xml:id="echoid-s7078" xml:space="preserve">ANaximander Mileſius Aſtronomorum vetuſtiſſimus abhinc bis mille, & </s> <s xml:id="echoid-s7079" xml:space="preserve">ducentis annis, & </s> <s xml:id="echoid-s7080" xml:space="preserve">amplius, te-<lb/>ſte Plinio omnium primus docuit Lunam lumen a Sole mutuare, ac proinde, vt alius quoque dixit, lu-<lb/>ce aliena lucere; </s> <s xml:id="echoid-s7081" xml:space="preserve">cuius rei hæc forte argumenta illi occurrere.</s> <s xml:id="echoid-s7082" xml:space="preserve"/> </p> <pb o="72" file="0092" n="96" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s7083" xml:space="preserve">Primo, cum Sol lumen ſuum in orbem, ac quoquouerſus diffundat, neceſſario etiam in Lunam illud emit-<lb/>ter, ac proinde illam Lunæ partem, quæ ſibi obijcitur, illuminabit: </s> <s xml:id="echoid-s7084" xml:space="preserve">quod quidem ex eo maximè comproba-<lb/>tur, quod videamus eam Lunæ partem, quæ ſplendet, ſemper Soli aduerſam eſſe, eam vero quæ obſcura eſt, <lb/>ſemper eſſe a Sole auerſam. </s> <s xml:id="echoid-s7085" xml:space="preserve">atque hinc etiam pateſcit cur ea creſcens, ſemper auerſis a Sole cornibus luceat.</s> <s xml:id="echoid-s7086" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7087" xml:space="preserve">2 Eam perpetuo ſplendere cernimus, niſi quãdo ei terra impedimento eſt ne lumẽ a Sole recipiat. </s> <s xml:id="echoid-s7088" xml:space="preserve">quod <lb/>accidit in Lunæ eclypſibus præſertim cum tota deficit, eam enim horribiliter nigricantem, atq; </s> <s xml:id="echoid-s7089" xml:space="preserve">omni ſplen-<lb/>dore deſtitutam ſpectamus; </s> <s xml:id="echoid-s7090" xml:space="preserve">certum autem eſt, vt paulo poſt conſtabit, eam tunc temporis obiectu terræ ob-<lb/>umbrari. </s> <s xml:id="echoid-s7091" xml:space="preserve">Quapropter certum ſit eam a Sole colluſtrari, ac proinde Solare lumen ad nos reflectere. </s> <s xml:id="echoid-s7092" xml:space="preserve">cum igi-<lb/>tur conſtet eam à Sole colluſtrari, deinceps, videndum eſt, qua ratioue id efficiatur, & </s> <s xml:id="echoid-s7093" xml:space="preserve">cur corniculata, dimi-<lb/>diata, plena, ſubinde effulgeat. </s> <s xml:id="echoid-s7094" xml:space="preserve">Dicimus igitur huiuſmodi Lunæ phaſes inde prouenire, quod Luna, vt ait <lb/>Ariſtoteles, ſpæricè illuminetur, ideſt eo modo quo ſphæra illuminatur. </s> <s xml:id="echoid-s7095" xml:space="preserve">quod vt rectè percipiatur, ſciendum <lb/>eſt, Lunam ſemper exceptis eclypſibus, à Sole eodem ſemper modo iluminari, ideſt, Solem eam Lunæ par-<lb/>tem, quæ illi opponitur ſemper illuſtrare, quæ pars eſt paulo plus quam hæmiſpherium: </s> <s xml:id="echoid-s7096" xml:space="preserve">quia vero nos valde <lb/>exiſtimus infra Lunam, Luna autem infra Solem, ac proinde ipſa infra Solem, ſed ſupra oculum noſtrum <lb/>mo@u proprio fertur; </s> <s xml:id="echoid-s7097" xml:space="preserve">hinc fit vt totum illud illuminatum hæmiſpherium non ſemper videamus, ſed aliquan-<lb/>do dimidium, vt in Lunæ quartis; </s> <s xml:id="echoid-s7098" xml:space="preserve">aliquando totum, vt in plenilunijs. </s> <s xml:id="echoid-s7099" xml:space="preserve">quod vt ſine labore, imo iucunde intelli-<lb/>gas, hanc pulcherrimam adhibe experientiam. </s> <s xml:id="echoid-s7100" xml:space="preserve">Cape ſphæram quampiam ſolidam, cuius ſuperficies ſit per-<lb/>fectè terſa, qualis eſſet vitrea, aut marmorea. </s> <s xml:id="echoid-s7101" xml:space="preserve">deinde pone lumen ſeorſum ad partem cubiculi, ſupra menſam; <lb/></s> <s xml:id="echoid-s7102" xml:space="preserve">tu vero ſtans in medio cubiculi manuque ſphæram tenens, eam extenſo omnino brachio lumini oppone, ita <lb/>vt ipſa inter oculum tuum, & </s> <s xml:id="echoid-s7103" xml:space="preserve">lumen interponatur, quo in ſitu, quamuis eius ferè dimidium illuminetur, nihil <lb/>tamen de illuminatione videbis. </s> <s xml:id="echoid-s7104" xml:space="preserve">deinde ibidem manens conuerte te ipſum paulatim, extenſo tamen ſemper <lb/>brachio, & </s> <s xml:id="echoid-s7105" xml:space="preserve">illico videre incipies illuminationis quidpiam, quod erit inſtar primæ, ac nouiſſimæ Lunæ falca-<lb/>tum, accorniculatum, cornuaq; </s> <s xml:id="echoid-s7106" xml:space="preserve">à lumine auertet: </s> <s xml:id="echoid-s7107" xml:space="preserve">pergente adhuc conuerſione oculo tuo creſcet illuminatio <lb/>magis ſemper, donec eam ſimilem Lunæ dimidiatæ videas; </s> <s xml:id="echoid-s7108" xml:space="preserve">& </s> <s xml:id="echoid-s7109" xml:space="preserve">ſic paulatim plus de illuminatione ſpectabis <lb/>quouſque totam videas, eritque tibi inſtar plenæ Lunæ, ſiue plenilunij, idque tunc accidet cũ ipſa directè fue-<lb/>ri@in ea rectitudine in qua eſt oculus, & </s> <s xml:id="echoid-s7110" xml:space="preserve">lumen.</s> <s xml:id="echoid-s7111" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7112" xml:space="preserve">Vlterius te conuerte videbiſque illuminationem oculo tuo minui paulatim donec iterum ordine inuerſo, <lb/>eædem illuminationes reſtituantur, quæ iam præceſſerint, eritque iterum dimidiata, & </s> <s xml:id="echoid-s7113" xml:space="preserve">falcata, quouſque to-<lb/> <anchor type="figure" xlink:label="fig-0092-01a" xlink:href="fig-0092-01"/> ta ab oculo tuo auertatur, iterumque contingat interlunium. </s> <s xml:id="echoid-s7114" xml:space="preserve">Atq; <lb/></s> <s xml:id="echoid-s7115" xml:space="preserve">hoc quidem eſt ſphæricè, ideſt, in modum ſphæræ illuminari; </s> <s xml:id="echoid-s7116" xml:space="preserve">quo <lb/>modo Lunam ipſam illuminari, vulgo etiam notum eſt. </s> <s xml:id="echoid-s7117" xml:space="preserve">ſolent au-<lb/>tem Aſtronomi hac Lunæ illuminationem ex appoſita figura ex-<lb/>plicare, in qua oculus ſit vbi A. </s> <s xml:id="echoid-s7118" xml:space="preserve">in centro Mundi. </s> <s xml:id="echoid-s7119" xml:space="preserve">Cælum Lunæ ſit <lb/>gyrusille, in quo Luna variè depicta eſt: </s> <s xml:id="echoid-s7120" xml:space="preserve">ſupra quod ſit Sol illumi-<lb/>nans Lunam ſemper eodem modo. </s> <s xml:id="echoid-s7121" xml:space="preserve">Luna in B. </s> <s xml:id="echoid-s7122" xml:space="preserve">nihil oculo de ſua <lb/> <anchor type="figure" xlink:label="fig-0092-02a" xlink:href="fig-0092-02"/> illuminatione oſtendit. </s> <s xml:id="echoid-s7123" xml:space="preserve">Luna in C. </s> <s xml:id="echoid-s7124" xml:space="preserve">oſtendit oculo A. </s> <s xml:id="echoid-s7125" xml:space="preserve">partem illu-<lb/>minationis exiguam & </s> <s xml:id="echoid-s7126" xml:space="preserve">corniculatam. </s> <s xml:id="echoid-s7127" xml:space="preserve">in D. </s> <s xml:id="echoid-s7128" xml:space="preserve">dimidiata apparet. </s> <s xml:id="echoid-s7129" xml:space="preserve">in <lb/>E. </s> <s xml:id="echoid-s7130" xml:space="preserve">gibboſa. </s> <s xml:id="echoid-s7131" xml:space="preserve">tandem in F. </s> <s xml:id="echoid-s7132" xml:space="preserve">plenilunium efficit, quoniam totam illu-<lb/>minationẽ oculo A. </s> <s xml:id="echoid-s7133" xml:space="preserve">obuertit. </s> <s xml:id="echoid-s7134" xml:space="preserve">poſtea in G H I. </s> <s xml:id="echoid-s7135" xml:space="preserve">decreſcens eaſdem, <lb/>inuerſe tamen, phaſes iterat, donec in B. </s> <s xml:id="echoid-s7136" xml:space="preserve">omnino ſeneſcat.</s> <s xml:id="echoid-s7137" xml:space="preserve"/> </p> <div xml:id="echoid-div145" type="float" level="2" n="1"> <figure xlink:label="fig-0092-01" xlink:href="fig-0092-01a"> <image file="0092-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0092-01"/> </figure> <figure xlink:label="fig-0092-02" xlink:href="fig-0092-02a"> <image file="0092-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0092-02"/> </figure> </div> <p> <s xml:id="echoid-s7138" xml:space="preserve">Porrò tota hæc illuminationũ periodus dicitur lunatio, & </s> <s xml:id="echoid-s7139" xml:space="preserve">men-<lb/>ſis ſinodicus, ideſt, coniunctiuus, quod Lunam Soli iterum coniun-<lb/>gat in nouilunio: </s> <s xml:id="echoid-s7140" xml:space="preserve">abſoluiturque ſpatio 29. </s> <s xml:id="echoid-s7141" xml:space="preserve">dierum cum dimidio fe-<lb/>rè: </s> <s xml:id="echoid-s7142" xml:space="preserve">in qua Luna ſccundum varias illuminationes, ſiue apparentias <lb/>variat ſortitur nomina, & </s> <s xml:id="echoid-s7143" xml:space="preserve">alpectus; </s> <s xml:id="echoid-s7144" xml:space="preserve">nam in B. </s> <s xml:id="echoid-s7145" xml:space="preserve">dicitur nouilunium, <lb/>inter luminum, Luna ſilens, ſitque eius cum Sole coniunctio, quæ <lb/>hoc charactere pingitur, ☌</s> </p> <p> <s xml:id="echoid-s7146" xml:space="preserve">In C. </s> <s xml:id="echoid-s7147" xml:space="preserve">dicitur falcata, corniculata, diſtatque à Sole per ſextan-<lb/>tem Zodiaci, quæ habitudo dicitur ſęxtilis aſpectus, ſicque pin-<lb/>gitur, *</s> </p> <p> <s xml:id="echoid-s7148" xml:space="preserve">In D. </s> <s xml:id="echoid-s7149" xml:space="preserve">dimidiata, reſpicitque Soiem aſpectuquadrato, diſtat enim ab eo Zodiaci ferè quadrante, cuiu@ <lb/>ſignum, eſt ſimile omnino cubo ſeu teſſeræ luſoniæ.</s> <s xml:id="echoid-s7150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7151" xml:space="preserve">In E. </s> <s xml:id="echoid-s7152" xml:space="preserve">vtrinque gibboſa: </s> <s xml:id="echoid-s7153" xml:space="preserve">diſtatque a Sole Zodiaci triente, qui aſpectus dicitur trinus, ſiue trigonus, cuius <lb/>eſt figura, triangulum æquilaterum.</s> <s xml:id="echoid-s7154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7155" xml:space="preserve">In F. </s> <s xml:id="echoid-s7156" xml:space="preserve">eſt plenilunium: </s> <s xml:id="echoid-s7157" xml:space="preserve">eſtque oppoſitio, cuius hæc pictura, ☍</s> </p> <p> <s xml:id="echoid-s7158" xml:space="preserve">Tandem in G H l. </s> <s xml:id="echoid-s7159" xml:space="preserve">reſtiruuntur eædem appellationes, atque aſpectus, ſed ſecundæ ac ſecundi dicuntur.</s> <s xml:id="echoid-s7160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7161" xml:space="preserve">Demum addimus, Solem pluſquam hæmiſpherium Lunæ illuminare; </s> <s xml:id="echoid-s7162" xml:space="preserve">quod perſpicuè ſequitur ex dictis in <lb/>tract. </s> <s xml:id="echoid-s7163" xml:space="preserve">de mundo cap. </s> <s xml:id="echoid-s7164" xml:space="preserve">de lumine: </s> <s xml:id="echoid-s7165" xml:space="preserve">Etenim Sol lunari o@be multis partibus maioreſt: </s> <s xml:id="echoid-s7166" xml:space="preserve">itaq; </s> <s xml:id="echoid-s7167" xml:space="preserve">radij ab ambitu So-<lb/>lis profuſi maiorem Lunæ portionem compræhendunt.</s> <s xml:id="echoid-s7168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7169" xml:space="preserve">Sed cur non ſtatim ab oppoſitione Solis, Luna maniſeſtè decreſcere incipit? </s> <s xml:id="echoid-s7170" xml:space="preserve">verum etiam altero ab oppo-<lb/>ſitione die, adhuc plena, ac rotunda perſeuerat? </s> <s xml:id="echoid-s7171" xml:space="preserve">cauſa eſt, quia Sol, vt dixi, pluſquam Lunæ dimidium illu-<lb/>ſtrat; </s> <s xml:id="echoid-s7172" xml:space="preserve">è contra vero oculus noſter minus quam Lunæ dimidium cer ere valet, cum inſtar puncti ſit reſpectu <lb/>Lanæ, vt optici oſtendunt. </s> <s xml:id="echoid-s7173" xml:space="preserve">cum ergo pars illuminata ſit maior parte viſa fit, vt in ea laxè contineatur: </s> <s xml:id="echoid-s7174" xml:space="preserve">ac pro- <pb o="71" file="0093" n="97" rhead="Liber Nonus."/> inde quamuis ab oppoſitione Luna aliquantulum recedat, non tamen ſtatim pars viſa exra partem illumina-<lb/>tam ſe maiorem, excurrere incipit, ſed tota intra eam diutius continetur.</s> <s xml:id="echoid-s7175" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div147" type="section" level="1" n="92"> <head xml:id="echoid-head101" style="it" xml:space="preserve">PARADOXVM.</head> <head xml:id="echoid-head102" style="it" xml:space="preserve">Luna nunquam minus illustratur qua cum plena est.</head> <p> <s xml:id="echoid-s7176" xml:space="preserve">EA vulgi æſtimatio Lunam tum maximè Solis fulgore perfundi, cum plenitudinẽ fuerit adepta; </s> <s xml:id="echoid-s7177" xml:space="preserve">verum. <lb/></s> <s xml:id="echoid-s7178" xml:space="preserve">aliter ſe res habet, nam ea Lunæ portio@quæ lumine Solis illuſtratur, non ſemper æqualis eſt: </s> <s xml:id="echoid-s7179" xml:space="preserve">cums cau-<lb/>ſa eſt varia Lunæ a Sole remotio; </s> <s xml:id="echoid-s7180" xml:space="preserve">pro@ant enim optici, & </s> <s xml:id="echoid-s7181" xml:space="preserve">nos ſupra in cap. </s> <s xml:id="echoid-s7182" xml:space="preserve">de lumine, & </s> <s xml:id="echoid-s7183" xml:space="preserve">vmbrainnaimus; </s> <s xml:id="echoid-s7184" xml:space="preserve"><lb/>quod ſphæra maior luminoſa è propinquo ampliorem partem minoris ſphæræ illuſtrat, quam è remoto: </s> <s xml:id="echoid-s7185" xml:space="preserve">cũ <lb/>igitur Luna in plenilunio à Sole remotiſſima ſit, quippe quæ è diametro illi opponatur, & </s> <s xml:id="echoid-s7186" xml:space="preserve">vt plurimum in <lb/>auge eodem tempore verſetur, conſequens eſt Lunam numquam illuſtrari minus, quam cum eſt plena; </s> <s xml:id="echoid-s7187" xml:space="preserve">quod <lb/>erat oſtendendum. </s> <s xml:id="echoid-s7188" xml:space="preserve">Vide Aguillonium lib. </s> <s xml:id="echoid-s7189" xml:space="preserve">5. </s> <s xml:id="echoid-s7190" xml:space="preserve">opticorum.</s> <s xml:id="echoid-s7191" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7192" xml:space="preserve">Atq; </s> <s xml:id="echoid-s7193" xml:space="preserve">in hunc modum hæ illuminationes ſine vllo artiſicio omnibus conſpicuæ ſunt. </s> <s xml:id="echoid-s7194" xml:space="preserve">quòd ſi per Teleſco-<lb/>pium obſeruentur alia complura mira æquè, ac pulchra ſpectantur, a@primo quidem creſcente Luna appa-<lb/>retſemper confinium illuminatæ partis, & </s> <s xml:id="echoid-s7195" xml:space="preserve">vmbroſæ eſſe lineam an fractuoſam, ac denticulatam, atque aſpe-<lb/>ram, vti apparet in ſequenti ſchemate linea A B C D E. </s> <s xml:id="echoid-s7196" xml:space="preserve">ſecun <lb/> <anchor type="figure" xlink:label="fig-0093-01a" xlink:href="fig-0093-01"/> do, intra partem vmbroſam non procul à confinio apparent <lb/>quædam exiguæ illuminationes, quaſi vertices quidam lumi-<lb/>noſi; </s> <s xml:id="echoid-s7197" xml:space="preserve">quarũ vna eſt F. </s> <s xml:id="echoid-s7198" xml:space="preserve">quæ poſtea paulatim maiores fiunt Lu-<lb/>na a Sole recedente, & </s> <s xml:id="echoid-s7199" xml:space="preserve">tandem parti luminoſæ coniungun-<lb/>tur. </s> <s xml:id="echoid-s7200" xml:space="preserve">tertio, in parte colluſtrata prope pariter terminũ lucis, <lb/>& </s> <s xml:id="echoid-s7201" xml:space="preserve">vmbræ, apparent areolæ quædam rotundæ, & </s> <s xml:id="echoid-s7202" xml:space="preserve">quidem per <lb/>multæ, vti ſunt in ſchemate I L M N O P. </s> <s xml:id="echoid-s7203" xml:space="preserve">quarum pars Soli <lb/>propinquior ſiue occidẽtalis, & </s> <s xml:id="echoid-s7204" xml:space="preserve">quę in figura eſt dextera, ſem-<lb/>per eſt tenebroſa; </s> <s xml:id="echoid-s7205" xml:space="preserve">altera, quæ orientalis eſt, ac magis Soli ex-<lb/>poſita illuſtrata eſt, recedente autem Luna à Sole tenebræ, <lb/>ſiue potius vmbræ illę minuuntur, quouſque totæ illuſtren-<lb/>tur; </s> <s xml:id="echoid-s7206" xml:space="preserve">quia ſic magis Soli obuertuntur; </s> <s xml:id="echoid-s7207" xml:space="preserve">illuminantur enim ac ſi <lb/>valles, aut concaua quædam magna eſſent, quæ Sol ſucceſſiuè <lb/>lumine perfundit. </s> <s xml:id="echoid-s7208" xml:space="preserve">in plenilunio vero nullæ huiuſmodi areo-<lb/>@@ cernũtur, quia omnes Lunæ concauitates Soli directè obuertuntur, ac proinde totæ illuminantur. </s> <s xml:id="echoid-s7209" xml:space="preserve">In Lu-<lb/>na tandem nouiſſima quando eius cornua acutiſſima ſunt, apparent propè acumina cornuum in ipſa Lunæ <lb/>peripheria, particulæ quædam lucidæ, acſeorſim ſeparatæ, quaſi adamantes quidam ſplendidi.</s> <s xml:id="echoid-s7210" xml:space="preserve"/> </p> <div xml:id="echoid-div147" type="float" level="2" n="1"> <figure xlink:label="fig-0093-01" xlink:href="fig-0093-01a"> <image file="0093-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0093-01"/> </figure> </div> </div> <div xml:id="echoid-div149" type="section" level="1" n="93"> <head xml:id="echoid-head103" style="it" xml:space="preserve">Mac@læ Lunares. Cap. IV.</head> <p> <s xml:id="echoid-s7211" xml:space="preserve">IN Lunari diſco omnibus maculæ quædam conſpicuæ, ſunt, quæ rudem quandam hominis faciem repræ, <lb/>ſentant: </s> <s xml:id="echoid-s7212" xml:space="preserve">præter eas autem Teleſcopium plures alias, ſed minores nobis oſtendit. </s> <s xml:id="echoid-s7213" xml:space="preserve">Communis autem Phi-<lb/>loſophorum ſententia eſt, haſce maculas eſſe partes Lunæ rariores, ſeu magis tranſparentes, quæ propteril-<lb/>lam tranſparentiam lumen Solis admittunt quidem, ſed non ſiſtunt, ac pro nde illius parũ nobis reflectunt. <lb/></s> <s xml:id="echoid-s7214" xml:space="preserve">vnde & </s> <s xml:id="echoid-s7215" xml:space="preserve">minus luminoſæ, ſeu nigriores cæteris partibus, quæ ob denſitatem melius lumen reflectant, ac pro-<lb/>inde magis illuſtratæ cernuntur, apparent. </s> <s xml:id="echoid-s7216" xml:space="preserve">ſimili de cauſa in albo pariete feneſtellæ, & </s> <s xml:id="echoid-s7217" xml:space="preserve">foramina videntur <lb/>nigra, ſeu maculæ nigriores. </s> <s xml:id="echoid-s7218" xml:space="preserve">Vide Nuncium ſydereum Galilæi, qui noua alia complura annunciat. </s> <s xml:id="echoid-s7219" xml:space="preserve">hic obi-<lb/>ter monere lectorem volo, in figuris rerum cęleſtium, vti ſupra obſeruaui, partem dexteram referre occiden-<lb/>@em, ſi niſtram vero orientem; </s> <s xml:id="echoid-s7220" xml:space="preserve">voco autem dexteram, quę nobis à dextera eſt, cuius ratio eſt quia Aſtronomi <lb/>ſolent in ſuis contemplationibus, atque obſeruationibus ad meridiem, qua planetæ pertranſeunt, ſe conuer-<lb/>s<unsure/>ere, ſicq; </s> <s xml:id="echoid-s7221" xml:space="preserve">illis occidens eſt ad dexteram, oriens ad ſiniſtram. </s> <s xml:id="echoid-s7222" xml:space="preserve">Contrarium contraria de cauſa accidit in Geo-<lb/>g<unsure/>raphorum picturis, vt poſtea ſuo loco dicetur.</s> <s xml:id="echoid-s7223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7224" xml:space="preserve">Poſtremo obſeruatione ſimul, ac admiratione dignum eſt, in nouis Lunis partem eam Lunę, quæ nondum <lb/>à<unsure/> Solis illuſtrata eſt, apparere admodum albicantem, & </s> <s xml:id="echoid-s7225" xml:space="preserve">conſpicuam, idq; </s> <s xml:id="echoid-s7226" xml:space="preserve">multo magis, quam alias in proue-<lb/>c<unsure/>ta Luna. </s> <s xml:id="echoid-s7227" xml:space="preserve">Obſeruetur igitur dum adhuc noua eſt, in eo ſitu, ac loco, vt pars Lunæ à Sole illuſtrata, quæ falca-<lb/>@@ eſt, lateat poſt faſtigiũ alicuius turris, vel domus diſtantis a nobis ſaltem per 60. </s> <s xml:id="echoid-s7228" xml:space="preserve">aut 80. </s> <s xml:id="echoid-s7229" xml:space="preserve">vlnas, reliqua enim <lb/>pa@, quamuis nondũ ſolari radio perfuſa, apparebit tamen, quaſi eſſet illuſtrata. </s> <s xml:id="echoid-s7230" xml:space="preserve">quæ experientia ita me ali-<lb/>quando feſellit, vt in hunc fulgorem caſu, ac repente incidens, exiſtimarim nouo quopiam miraculo, tempo-<lb/>@e adoleſcentis Lunæ, factum eſſe plenilunium. </s> <s xml:id="echoid-s7231" xml:space="preserve">Sunt qui putent hanc Lunæ lucem, eſſe lucem, quam terra à <lb/>Sole acceptam in Lunam reflectat, eamque hac ratione illuminet: </s> <s xml:id="echoid-s7232" xml:space="preserve">ita vt quadam luminis permutatione ter-<lb/>ra, & </s> <s xml:id="echoid-s7233" xml:space="preserve">Luna Solis lumen ſibi inuicem reuerberent, ſeque inuicem illuſtrent. </s> <s xml:id="echoid-s7234" xml:space="preserve">quod confirmant inde, quia pro-<lb/>pè nouilunium lumen a<unsure/> terra reflexum, ad Lunam natura ſua reuertitur; </s> <s xml:id="echoid-s7235" xml:space="preserve">ſunt enim tune Sol, & </s> <s xml:id="echoid-s7236" xml:space="preserve">Luna in eo-<lb/>dem cæli loco, ad quem ſit reſtexio. </s> <s xml:id="echoid-s7237" xml:space="preserve">Poſtea recedens Luna a<unsure/> Sole minus participat de terræ reflexione, quia <lb/>@eflexio @aior tendit ad partes Solis, à quibus Luna receſſit, ac proinde minora terra reflexio Lunæ cedit. <lb/></s> <s xml:id="echoid-s7238" xml:space="preserve">@@@@s ſ@@tent@@ eſt Galil@us.</s> <s xml:id="echoid-s7239" xml:space="preserve"/> </p> <pb o="72" file="0094" n="98" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s7240" xml:space="preserve">Al@orum ſententia eſt Lunam eſſe corpus ſemidiaphanum, ideſt, necomnino opacũ, nec omnino tranſpa <lb/>rens; </s> <s xml:id="echoid-s7241" xml:space="preserve">ex qua ſemidiaphaneitate ſit vt aliquatenus Solis lumine imbibatur, eoque lumine conſpicuam fieri par <lb/>tem illam Lunæ a Sole auerſam. </s> <s xml:id="echoid-s7242" xml:space="preserve">probatid P. </s> <s xml:id="echoid-s7243" xml:space="preserve">Chriſtophorus Scheinerè noſtra Societate in ſui<unsure/>s Mathemati-<lb/>cis diſquiſitionibus, hac obſeruatione; </s> <s xml:id="echoid-s7244" xml:space="preserve">in quadam eclypſi Solis, ea Lunæ pars, quæ Sol@ ſupponebatur, per-<lb/>ſpicuè cernebatur, quaſi ſolari luce traluceret; </s> <s xml:id="echoid-s7245" xml:space="preserve">quæ vero extra Solem porrigebatur omnino inuiſa latebat; <lb/></s> <s xml:id="echoid-s7246" xml:space="preserve">quoniam radij Solis eam peruadentes alio quam ad noſtrum oculum dirigebantur, vt conſideranti manife-<lb/>ſtum eſt.</s> <s xml:id="echoid-s7247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7248" xml:space="preserve">Idem a ſimili quorumdam corporum comprobatur. </s> <s xml:id="echoid-s7249" xml:space="preserve">aqua enim, &</s> <s xml:id="echoid-s7250" xml:space="preserve">c. </s> <s xml:id="echoid-s7251" xml:space="preserve">ſemidiaphana, criſtallus, vitrum, pila <lb/>vitrea Soli obiecta vtramque Lunæ illuminationem imitatur. </s> <s xml:id="echoid-s7252" xml:space="preserve">huius ſententiæ fuerunt antiquitus Poſſidonius <lb/>ille celeberrimus, Cleomedes in Meteoris; </s> <s xml:id="echoid-s7253" xml:space="preserve">ex ſemipriſcis Vitellio, Eraſmus Reinoldus in Theoricas Purba-<lb/>chij; </s> <s xml:id="echoid-s7254" xml:space="preserve">ex recentibus P. </s> <s xml:id="echoid-s7255" xml:space="preserve">Chriſtophorus prędictus, necnõ P. </s> <s xml:id="echoid-s7256" xml:space="preserve">Aguillonius noſtræ pariter Societatis in ſuis opticis. <lb/></s> <s xml:id="echoid-s7257" xml:space="preserve">Vtra autem harum opinionum veritati propior ſit, melioris eſto iudicij.</s> <s xml:id="echoid-s7258" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div150" type="section" level="1" n="94"> <head xml:id="echoid-head104" style="it" xml:space="preserve">Lunares Eclypſes. Cap. V.</head> <p> <s xml:id="echoid-s7259" xml:space="preserve">NOn hic agendum eſt de eo lumin@s defectu, qui in Luna ſingulis interlunijs apparet, qui verus defectu@ <lb/>non eſt, ſed apparens, Luna enim tunc temporis ſupernè illuminatur; </s> <s xml:id="echoid-s7260" xml:space="preserve">vnde fit vt ipſius ſplendor ſurſum <lb/>Solem aſpiciat, ac propterea a nobis aſpici nequeat. </s> <s xml:id="echoid-s7261" xml:space="preserve">ſed agemus de eo defectu, qui ſæpe in plenilunijs ſpecta-<lb/>tur, veruſque eſt lucis defectus, & </s> <s xml:id="echoid-s7262" xml:space="preserve">communiter <lb/> <anchor type="figure" xlink:label="fig-0094-01a" xlink:href="fig-0094-01"/> Lunæ eclypſis dicitur: </s> <s xml:id="echoid-s7263" xml:space="preserve">deficit igitur tunc Luna <lb/>hanc obcauſam, quia videlicet in vmbram ter <lb/>ræ incurrit, vt in præſenti figuratione, ſit Sol, <lb/>terra, & </s> <s xml:id="echoid-s7264" xml:space="preserve">vmbra terræ, vt apparet, in quam Lu-<lb/>na inuaſerit. </s> <s xml:id="echoid-s7265" xml:space="preserve">oportet, vt terra directè inter So-<lb/>lem, & </s> <s xml:id="echoid-s7266" xml:space="preserve">Lunam interponatur, ſic enim fit vt vm <lb/>bra terrę Lunam obtegere queat. </s> <s xml:id="echoid-s7267" xml:space="preserve">quod nõ niſi <lb/>in plenilunio accidere poteſt, quia tunc ſolum <lb/>Luna Soli directè opponitur. </s> <s xml:id="echoid-s7268" xml:space="preserve">hanc autem eſſe <lb/>eclypſis cauſam, hinc probant Aſtronom. </s> <s xml:id="echoid-s7269" xml:space="preserve">pri-<lb/>mo enim obſeruatum eſt, Lunam nunquam. <lb/></s> <s xml:id="echoid-s7270" xml:space="preserve">eclypſari, niſi cum Soli in plenilunio è diame-<lb/>tro ſerè opponitur, hoc eſt, niſi quando in eo <lb/>Zodiaci loco fuerit, ad quem vmbra terræ ne-<lb/>ceſſario ad partes Soli diametraliter oppoſitas <lb/>tendit, cum terra ſit in centro mundi, vt ex fi-<lb/>gura percipi poteſt: </s> <s xml:id="echoid-s7271" xml:space="preserve">atqui Luna, quando ecly-<lb/>pſatur, ſemper in eadem parte ſoli oppoſita, in qua vmbra extenditur, exiſtit: </s> <s xml:id="echoid-s7272" xml:space="preserve">merito igitur concluſerunt Lu-<lb/>næ defectum prouenire ab vmbra interiectæ terræ. </s> <s xml:id="echoid-s7273" xml:space="preserve">quod etiam euidenter confirmatur ex certa eclypſium. </s> <s xml:id="echoid-s7274" xml:space="preserve"><lb/>prædictione, in qua ſupponunt Lunam cum ad vmbræ locum peruenerit defecturam; </s> <s xml:id="echoid-s7275" xml:space="preserve">quod re vera ſuccedit, <lb/>neq; </s> <s xml:id="echoid-s7276" xml:space="preserve">tandem alia huius defectus cauſa reperiri poteſt. </s> <s xml:id="echoid-s7277" xml:space="preserve">certum igitur ſit Lunam præ@icta de cauſa priuari lu-<lb/>mine. </s> <s xml:id="echoid-s7278" xml:space="preserve">Sed quæret quiſpiam cur in omni Lunæ plenilunio, aut oppoſitione non fiant eclypſes, cui reſpon-<lb/>dendum eſt, cauſam eſſe quia iter Lunæ proprium, quo ſub Zodiaco ſecundum ſignorum ordinem incedit, <lb/>non eſt ſub eclyptica, verum eam duobus in locis ſecat, atque ab ea, tam in Septentrione quam in Auſtrum. </s> <s xml:id="echoid-s7279" xml:space="preserve"><lb/>deflectit ad gradus quinque, quas ſectiones ſupra diximus appellari Nodũ Boreum ☊. </s> <s xml:id="echoid-s7280" xml:space="preserve">& </s> <s xml:id="echoid-s7281" xml:space="preserve">Auſtralem ☋. </s> <s xml:id="echoid-s7282" xml:space="preserve">Ara-<lb/>bicè caput, & </s> <s xml:id="echoid-s7283" xml:space="preserve">cauda Draconis. </s> <s xml:id="echoid-s7284" xml:space="preserve">Vnde ſequitur Lunam opponi tantum Soli è diametro in plenilunijs illis, quę <lb/>continguntapud illas duas ſectiones, ſeu apud illa duo quadriuia Solis, & </s> <s xml:id="echoid-s7285" xml:space="preserve">Lunæ, in quibus vmbra terræ, & </s> <s xml:id="echoid-s7286" xml:space="preserve"><lb/>Luna, ita ſibi occurrunt, vt altera alteri de via omnino cedere nequeat, ſed neceſſe ſit Lunam, aut totam, aut <lb/>partem in vmbram incurrere. </s> <s xml:id="echoid-s7287" xml:space="preserve">cauſa igitur cur non omne plenilunium ſit eclypticum, eſt imperfecta lumi-<lb/>narium oppoſitio, quæ oritura viarum ipſarum euariatione. </s> <s xml:id="echoid-s7288" xml:space="preserve">omnis autem vera oppoſitio eclyptica fit, aut <lb/>in prædictis viarum quadriuijs, aut ſaltem intra diſtantiam vtrinque ab eis 12. </s> <s xml:id="echoid-s7289" xml:space="preserve">graduum. </s> <s xml:id="echoid-s7290" xml:space="preserve">oppoſitio autem <lb/>media eclyptica ad ſummum diſtat gr. </s> <s xml:id="echoid-s7291" xml:space="preserve">15. </s> <s xml:id="echoid-s7292" xml:space="preserve">12′. </s> <s xml:id="echoid-s7293" xml:space="preserve">extra hos terminos, earũ viæ adeo ab inuicem recedunt, vt Lu-<lb/>na vmbram ablq; </s> <s xml:id="echoid-s7294" xml:space="preserve">ipſius contactu, prætergrediatur. </s> <s xml:id="echoid-s7295" xml:space="preserve">quid media, & </s> <s xml:id="echoid-s7296" xml:space="preserve">vera ſit oppoſitio poſtea dicetur.</s> <s xml:id="echoid-s7297" xml:space="preserve"/> </p> <div xml:id="echoid-div150" type="float" level="2" n="1"> <figure xlink:label="fig-0094-01" xlink:href="fig-0094-01a"> <image file="0094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0094-01"/> </figure> </div> <p> <s xml:id="echoid-s7298" xml:space="preserve">Ex hac via rum inclinatione oriuntur etiam varia eclypſium genera; </s> <s xml:id="echoid-s7299" xml:space="preserve">totales enim ſunt cum tota Luna <lb/>eclyplatur; </s> <s xml:id="echoid-s7300" xml:space="preserve">quæ contingunt aut in ſectionibus ipſis, aut propè. </s> <s xml:id="echoid-s7301" xml:space="preserve">aliæ totales cum mora, in quibus Luna tota <lb/>eclypſata in vmbra moras diu trahit. </s> <s xml:id="echoid-s7302" xml:space="preserve">aliæ totales ſine mora, in quibus Luna tota quidem deficit, ſed non mo-<lb/>ratur in vmbra. </s> <s xml:id="echoid-s7303" xml:space="preserve">hæ contingunt paulò remotius à ſectionibus. </s> <s xml:id="echoid-s7304" xml:space="preserve">aliæ partiales, quibus non tota Luna, ſed pars <lb/>eius tantum obſcuratur, tantoque minor, quanto longius a ſectionibus diſtiterint, dummodo ſint inter præ-<lb/>dictos terminos.</s> <s xml:id="echoid-s7305" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7306" xml:space="preserve">Porrò hæc defectum varietas, ſubit aliam varietatem, nam defectus in eadem à ſectionibus diſtantia con-<lb/>tingentes, non ſunt ſemper æquales, quia vmbra terræ non eſt ſemper eiuſdem craſſitiei, ſed nodo amplior, <lb/>modo gracilior, prout Sol fuerit terræ propinquor, vel altior. </s> <s xml:id="echoid-s7307" xml:space="preserve">præterea quia ipſa quoque Luna variam for-<lb/>titura terra diſtantiam, quæ cauſa ſunt, vtipſa ingrediatur vmbram aliquando in ſublimiori loco, & </s> <s xml:id="echoid-s7308" xml:space="preserve">proin- <pb o="73" file="0095" n="99" rhead="Liber Nonus."/> de gracilior, vnde, & </s> <s xml:id="echoid-s7309" xml:space="preserve">eclypſis minor, & </s> <s xml:id="echoid-s7310" xml:space="preserve">breuior: </s> <s xml:id="echoid-s7311" xml:space="preserve">aliquando in inferiori, vnde eclypſis maior, ac diuturnior, <lb/>quæ melius intelligentur, cum de motu etiam Solis tractatum fuerit.</s> <s xml:id="echoid-s7312" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7313" xml:space="preserve">Tandem non prætereundum Lunarium eclypſium loca non eſſe ſemper eadẽ, ſed perpetuo quamuis len-<lb/>rè mutari contra ſignorum ſucceſſionem, cuius cauſa redditur, quia illi viarum occurſus ſeu Nodi apud quos <lb/>fiunt eclypſes, mouentur contra ſignorum ordinem; </s> <s xml:id="echoid-s7314" xml:space="preserve">totumque Zodiacum peragrant in annis 19. </s> <s xml:id="echoid-s7315" xml:space="preserve">circiter, <lb/>vti ſupra patuit: </s> <s xml:id="echoid-s7316" xml:space="preserve">quarefit vtipſa eclypſium loca pariter permutentur.</s> <s xml:id="echoid-s7317" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div152" type="section" level="1" n="95"> <head xml:id="echoid-head105" style="it" xml:space="preserve">Vmbra Lunæ. Cap. VI.</head> <p> <s xml:id="echoid-s7318" xml:space="preserve">CVm Lunæ corpus non ſit omnino diaphanum, vti probatum eſt, atque ex vna parte lumen Solis ſiſtat, <lb/>ac reuerberet, neceſſario ex altera parte vmbram proijciet atque hæc ſit cauſa. </s> <s xml:id="echoid-s7319" xml:space="preserve">neque vero deeſt expe-<lb/>rientia, nam quando Sol eclypſatur ſeu eclypſari videtur, id accidit quia Luna Soli ita ſupponitur, vt lumen <lb/>Solis nobis auferat, ac proinde vmbram ſupra nos demittat. </s> <s xml:id="echoid-s7320" xml:space="preserve">Quamobrem in hoc ſolari defectu, nos ipſi verè <lb/>lumine priuamur, eo quod ſub vmbra Lunæ ſimus. </s> <s xml:id="echoid-s7321" xml:space="preserve">quod melius pateſcet cum oſtenderimus prædicto Lunæ <lb/>obiectu Solem nobis auferri. </s> <s xml:id="echoid-s7322" xml:space="preserve">Manifeſta eſt igitur vmbra Lunæ.</s> <s xml:id="echoid-s7323" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7324" xml:space="preserve">Iam vero qualis, quantaque ſit, vt determinetur, neceſſe eſt hæc præſcire. </s> <s xml:id="echoid-s7325" xml:space="preserve">Primo proportionem corporis <lb/>Lunæ, ac Solis. </s> <s xml:id="echoid-s7326" xml:space="preserve">Secundo earum ab inuicem diſtantiam. </s> <s xml:id="echoid-s7327" xml:space="preserve">Tertio, vtrumque eſſe ſphæricum. </s> <s xml:id="echoid-s7328" xml:space="preserve">quibus habitis <lb/>poſſumus conſtruere ſiguram habentem veras proportiones, in qua duæ lineæ tangentes vtrinque Solem, & </s> <s xml:id="echoid-s7329" xml:space="preserve"><lb/>Lunam, concurrent vltra Lunam, quia Sole minor eſt, & </s> <s xml:id="echoid-s7330" xml:space="preserve">oſtendent quantitatem, ac figuram Lunaris vmbræ. <lb/></s> <s xml:id="echoid-s7331" xml:space="preserve">ſic fecimus in conſtructione veræ figuræ pag. </s> <s xml:id="echoid-s7332" xml:space="preserve">79. </s> <s xml:id="echoid-s7333" xml:space="preserve">in vmbra terræ, vbi apparet hanc vmbram eſſe conicam, ea-<lb/>dem ratione, qua vmbram terræ. </s> <s xml:id="echoid-s7334" xml:space="preserve">apparet etiam longam eſſe ſemid. </s> <s xml:id="echoid-s7335" xml:space="preserve">terræ ferè 60. </s> <s xml:id="echoid-s7336" xml:space="preserve">exiſtente Luna inter nos, <lb/>& </s> <s xml:id="echoid-s7337" xml:space="preserve">Solem in mediocri diſtantia. </s> <s xml:id="echoid-s7338" xml:space="preserve">quæ longitudo exactè per circinum examinatur, ex qua conſtat vmbræ huius <lb/>longitudinem tranſcendere terram aliquot ſemidiametris ipſius terræ; </s> <s xml:id="echoid-s7339" xml:space="preserve">ac proinde poſſe aliquando terram, <lb/>non tamen totam obumbrare; </s> <s xml:id="echoid-s7340" xml:space="preserve">vt facit in Solis defectibus. </s> <s xml:id="echoid-s7341" xml:space="preserve">non totam obũbrat quia Luna eſt minor terra qua-<lb/>dragies; </s> <s xml:id="echoid-s7342" xml:space="preserve">idcirco vmbra gracilior erit quam terra, maxime vero a pud verticem, qua terra inumbrat. </s> <s xml:id="echoid-s7343" xml:space="preserve">reliqua <lb/>in tract. </s> <s xml:id="echoid-s7344" xml:space="preserve">de eclypſi Solis. </s> <s xml:id="echoid-s7345" xml:space="preserve">quando vero Luna Soli opponitur longiſſimam vmbram emittit, cuius longitudinẽ <lb/>eadem via inueſtigabis. </s> <s xml:id="echoid-s7346" xml:space="preserve">præterea etiam Geometricè, ſicuti in vmbra terræ factum eſt. </s> <s xml:id="echoid-s7347" xml:space="preserve">exiſtente Luna in op-<lb/>poſitione eius, maxima a Sole diſtantia erit ſemidiametrum terræ 1247. </s> <s xml:id="echoid-s7348" xml:space="preserve">diameter Solis ad diametrum Lunæ <lb/>eſt ſicuti 26. </s> <s xml:id="echoid-s7349" xml:space="preserve">ad {1/3}. </s> <s xml:id="echoid-s7350" xml:space="preserve">ex quibus ſicuti in vmbra terræ inueſtiganda per regulam proportionum feci, vt 24 {2/3}. </s> <s xml:id="echoid-s7351" xml:space="preserve">ad 1 {3/1} <lb/>ideſt, vt excelſus diametri Solis ſupra diametrum Lunæ, ita diſtantia 1247. </s> <s xml:id="echoid-s7352" xml:space="preserve">ad 67. </s> <s xml:id="echoid-s7353" xml:space="preserve">quare ibi vmbra Luna elon. </s> <s xml:id="echoid-s7354" xml:space="preserve"><lb/>gabitur ſemid. </s> <s xml:id="echoid-s7355" xml:space="preserve">terræ 67. </s> <s xml:id="echoid-s7356" xml:space="preserve">& </s> <s xml:id="echoid-s7357" xml:space="preserve">quia Luna ipſa diſtat tunc a terra ſemid. </s> <s xml:id="echoid-s7358" xml:space="preserve">56. </s> <s xml:id="echoid-s7359" xml:space="preserve">circiter, ideo apex vmbræ à terra di-<lb/>ſtabit ſemid. </s> <s xml:id="echoid-s7360" xml:space="preserve">132. </s> <s xml:id="echoid-s7361" xml:space="preserve">vnde colligitur Martem ab vmbra Lunæ minimè eclypſari poſſe, cum à terra diſter ſemi-<lb/>diametris 761. </s> <s xml:id="echoid-s7362" xml:space="preserve">minimum.</s> <s xml:id="echoid-s7363" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div153" type="section" level="1" n="96"> <head xml:id="echoid-head106" style="it" xml:space="preserve">De Figura Lunæ. Cap. VII.</head> <p> <s xml:id="echoid-s7364" xml:space="preserve">CVm oſtenſum ſit Lunam ſphæricè, ſeu in ſphæræ modum illuminari, neceſſario cogimur aſſerere eam <lb/>quoque ſphæricam eſſe, aliter enim ad eum, quem vidimus modum neutiquam varias exhiberet illumi-<lb/>nationes. </s> <s xml:id="echoid-s7365" xml:space="preserve">Porrò ſuperiores Aſtronomi exiſtimarunt eam eſſe perfectè ſphæricam, ideſt, habere ſuperſiciem <lb/>terſam, ac læuigatam, cum eam cernerent, ſpeculi inſtar perpoliti, lumen reuerberare: </s> <s xml:id="echoid-s7366" xml:space="preserve">tum etiam quia opina-<lb/>bantur cæleſtia corpora perfectis, ſeu geometricis figuris eſſe prædita. </s> <s xml:id="echoid-s7367" xml:space="preserve">Præterea quia linea illa, quæ terminus <lb/>eſt partis illuſtratæ, ac tenebroſæ, putabatur ab eis minimè eſſe anfractuoſa, & </s> <s xml:id="echoid-s7368" xml:space="preserve">aſpera, ſed eſſe linea curua, cir-<lb/>cularis, vniformis, ac regularis (vti ſolet eſſe circuli peripheria in globo deſcripta) talis enim viſui apparet. <lb/></s> <s xml:id="echoid-s7369" xml:space="preserve">at vero noſtra tempeſtate Teleſcopij auxilio rem aliter ſe habere ſupra oſtendimus.</s> <s xml:id="echoid-s7370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7371" xml:space="preserve">Dicimus igitur Lunæ ſphæricitatem non eſſe perfectam, ſed aſperam, & </s> <s xml:id="echoid-s7372" xml:space="preserve">inæqualem, vti etiam eſt terræ. <lb/></s> <s xml:id="echoid-s7373" xml:space="preserve">quod ab inæqualitate, ac tortuoſitate prædicti confinij conuincitur; </s> <s xml:id="echoid-s7374" xml:space="preserve">quæ aliunde oriri nequit, quam ex Lunæ <lb/>partibus, tum altioribus, tũ depreſſioribus, quæ Solis propterea lumen inæqualiter, ac diſſormiter excipiunt. </s> <s xml:id="echoid-s7375" xml:space="preserve"><lb/>ſicuti videre eſt in pila ruida, & </s> <s xml:id="echoid-s7376" xml:space="preserve">montuoſa Soli expoſita. </s> <s xml:id="echoid-s7377" xml:space="preserve">Secundo, idem confirmantareolæ illæ, in parte ad-<lb/>huc tenebroſa exiſtentes, & </s> <s xml:id="echoid-s7378" xml:space="preserve">tamen illuminatæ, quæ nihil aliud eſſe poſſe videntur, quam vertices quidam re-<lb/>liquis partibus altiores, qui propterea prius lumen recipiant. </s> <s xml:id="echoid-s7379" xml:space="preserve">Tertio idem probant areolæ aliæ rotundæ in <lb/>parte luminoſa propè confinium conſpectæ, quarum parsoccidentalis, ideſt, quæ Soli propior eſt, vmbroſa <lb/>eſt, quia videlicet ſunt concauitates quædam quarum profunditates non ſtatim Sol illuminat, ſed prius par-<lb/>tem orientalem, quia Soli prius exponitur; </s> <s xml:id="echoid-s7380" xml:space="preserve">poſtremo partem occidentalem, quia vltima Soli obuertitur: </s> <s xml:id="echoid-s7381" xml:space="preserve">ſicu-<lb/>ti proporcionaliter accidit in illuminatione vallium terreſtrium. </s> <s xml:id="echoid-s7382" xml:space="preserve">quod in pila parua concauitates habentes <lb/>experiri potes. </s> <s xml:id="echoid-s7383" xml:space="preserve">Quarto denique qu@a, ſi eſſet geometricè rotunda, lumen Solis a ſe reflexum adeo in varias <lb/>partes diſpergeret, vt nos aut nihil de eo, aut ferè nihil, videremus. </s> <s xml:id="echoid-s7384" xml:space="preserve">Simile quotidie obſeruo in ſphęris æneis, <lb/>quæ in campananiorum ſummitatibus lumẽ Solis reflectũt, quæ quo ſunt perfectiores, ac terſiores, eò minus <lb/>de Solis lumine, ad meum oculum reflectunt; </s> <s xml:id="echoid-s7385" xml:space="preserve">vnde etiamſi magnæ ſint, illuminatio tamen earum reflexa ad <lb/>eundem oculum, exigua eſt. </s> <s xml:id="echoid-s7386" xml:space="preserve">quanto autem aſperiores, ac ruidiores ſunt, tanto maiorem mihi exhibent illu-<lb/>minationem. </s> <s xml:id="echoid-s7387" xml:space="preserve">in hunc igitur finem Luna montuoſa, & </s> <s xml:id="echoid-s7388" xml:space="preserve">aſpera eſt, vt plenius, ac maius lumen terræ ſibi cogna-<lb/>tæ reuerberet. </s> <s xml:id="echoid-s7389" xml:space="preserve">Quinto, ſi eſſet perfectè rotunda, eſſet ſpeculum conuexum, cuius eſt (vt Catoptrica docet, ac <lb/>experientia conſtat) rerum imagines parua reddere, ſic Luna Solis imaginem exiguam valde, ac ferè pun-<lb/>ctualem nobis reuerberaret. </s> <s xml:id="echoid-s7390" xml:space="preserve">ex Aguillonio. </s> <s xml:id="echoid-s7391" xml:space="preserve">Cur ergo non ſphærica, ſed plana à nobis iudicatur? </s> <s xml:id="echoid-s7392" xml:space="preserve">reſpondent <pb o="74" file="0096" n="100" rhead="De Mundi Fabrica,"/> ci, id ex nimia à nobís remotíone prouenire, quæ in cauſa eſt, vt tumor ille tam pro@ul non appare at.</s> <s xml:id="echoid-s7393" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7394" xml:space="preserve">Poſtremò animaduerſione dignum eſt, allatas rationes pro Lunæſphæricitate non conuincere Lunam eſ-<lb/>ſe integram ſphæram, ſed tantummodo hemiſphærium; </s> <s xml:id="echoid-s7395" xml:space="preserve">videmus enim nos ipſius vnum tantum, & </s> <s xml:id="echoid-s7396" xml:space="preserve">idem he-<lb/>miſphærium, illud nimirum. </s> <s xml:id="echoid-s7397" xml:space="preserve">in quo ſunt veteres maculæ, faciem humanam aliquatenus referentes, eas enim <lb/>in omnibus ſuis reuolutionibua ſemper Luna nobis obuertir.</s> <s xml:id="echoid-s7398" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div154" type="section" level="1" n="97"> <head xml:id="echoid-head107" style="it" xml:space="preserve">De Luna Magnitudine. Cap. VIII.</head> <p> <s xml:id="echoid-s7399" xml:space="preserve">1 AIo Lunam eſſe minorem terra, cuius euidens argumentum eſt, quod in Lunaribus eclypſibus, ipſa in <lb/>vmbra terræ aliquando tandiu immoratur, vt neceſl<unsure/>e ſit diametrum Lunæ, diametrum vmbræ inibi <lb/>bis, teruè metiri. </s> <s xml:id="echoid-s7400" xml:space="preserve">cum autem vmbra, vt oſtendimus, ſit conica, erit ibidem vbi Luna pertranſit, diameter vm-<lb/>bræ minor diametro terræ; </s> <s xml:id="echoid-s7401" xml:space="preserve">quia vmbra conica ſemper gracileſcit. </s> <s xml:id="echoid-s7402" xml:space="preserve">vnde neceſſario ſequitur Lunæ quoque <lb/>diametrum multo minorem eſſe, quam ſit terræ diameter, ac proinde ipſam quoque Lunam terra eſſe mi-<lb/>norem.</s> <s xml:id="echoid-s7403" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7404" xml:space="preserve">2 Aio Lunam eſſe longo interuallo Sole minorem, cuius ſignum euidens ſunt Solis eclypſes, in quibus, <lb/>quamuis Luna ſit multis partibus Sole inferior, nobiſque propior, nihilominus aliquando Solẽ nobis ita oc-<lb/>cultat, vt eo ſe multo minorem prodat; </s> <s xml:id="echoid-s7405" xml:space="preserve">nam vti refert P. </s> <s xml:id="echoid-s7406" xml:space="preserve">A guillonius in opticis lib. </s> <s xml:id="echoid-s7407" xml:space="preserve">6. </s> <s xml:id="echoid-s7408" xml:space="preserve">anno 1567. </s> <s xml:id="echoid-s7409" xml:space="preserve">facta eſt ecly-<lb/>pſis, in qua, quamuis Luna directe<unsure/> inter viſum, & </s> <s xml:id="echoid-s7410" xml:space="preserve">Solem interponebatur, non tamen totũ Solem obſcurabat, <lb/>ſed relinquebatur circumquaque de Sole circulus quidam lucidus, qui Lunæ diſcum, in coronæ modum, cir-<lb/>cumuergebat. </s> <s xml:id="echoid-s7411" xml:space="preserve">hinc ſanè efficitur Solem Luna maiorem eſſe; </s> <s xml:id="echoid-s7412" xml:space="preserve">quoniã enim radij optici, ſiue lineæ viſiuæ, quæ <lb/>ab oculo noſtro productæ, lunare corpus hinc inde tangebant, altius vſque ad Solem per magnum illud in-<lb/>teruallum extenſæ ſemper magis, ac magis à ſe inuicem diuellebantur, maius profecto eſſe oporter corpus il-<lb/>lud Solis, quod in tanta remotione prædictarum linearum diſtantiam adimplebat, quam ſit Luna, quę earum-<lb/>dem linearum longè minorem diſtantiam occupabat. </s> <s xml:id="echoid-s7413" xml:space="preserve">Præterea, Luna eſt minor quam terra. </s> <s xml:id="echoid-s7414" xml:space="preserve">Terra autem <lb/>eſt minor Sole, vt patet ex vmbra eius conica, quare Luna multo magis erit minor ipſo Sole.</s> <s xml:id="echoid-s7415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7416" xml:space="preserve">3 Hæc autem leui brachio ſint dicta. </s> <s xml:id="echoid-s7417" xml:space="preserve">Verum, vt exactè Lunæ magnitudinem oſtendamus, eam nimirum <lb/>eſſe terræ partem quadrageſimam, ſiue eam eſſe ad terram vt 1. </s> <s xml:id="echoid-s7418" xml:space="preserve">ad 40. </s> <s xml:id="echoid-s7419" xml:space="preserve">duo prius ſunt præcognoſce nda. </s> <s xml:id="echoid-s7420" xml:space="preserve">Pri-<lb/>mum eſt diſtantia ipſius à terra. </s> <s xml:id="echoid-s7421" xml:space="preserve">Secundũ eſt diameter eius viſibilis, ſiue apparens, ſiue etiam angulus ſub quo <lb/>videtur, quæ duo pariter in cæterorum ſyderum magnitudine perſcrutanda, præſcire neceſſe erit. </s> <s xml:id="echoid-s7422" xml:space="preserve">qua porro <lb/>ratione diſtantia Lunę a<unsure/> terris inueſtigetur, iam ſuperius oſtenſum eſt. </s> <s xml:id="echoid-s7423" xml:space="preserve">Reſtat igitur, vt de eius apparenti dia-<lb/>metro cognoſcenda tractemus. </s> <s xml:id="echoid-s7424" xml:space="preserve">Primus modus ſit per noſtrum quadrantem, magna cura, aſtronomicè collo-<lb/>catum. </s> <s xml:id="echoid-s7425" xml:space="preserve">quo ſic conſtituto, per foramina, aut rimulas dioptræ, collimandum eſt diligenter in ſupremum Lu-<lb/>næ @mbum, cum ea meridianum pertranſit; </s> <s xml:id="echoid-s7426" xml:space="preserve">& </s> <s xml:id="echoid-s7427" xml:space="preserve">ſtatim in inferiorem etiam limbum; </s> <s xml:id="echoid-s7428" xml:space="preserve">atque notanda ſunt duo <lb/>loca dioptræ in arcu quadrantis; </s> <s xml:id="echoid-s7429" xml:space="preserve">nã diſtantia, ſiue arcus quadrantis inter hæc duo loca interceptus, erit quan-<lb/>titas apparentis diametri Lunæ. </s> <s xml:id="echoid-s7430" xml:space="preserve">ideſt, exhibebit tot minuta anguli, ſub quo Luna videtur. </s> <s xml:id="echoid-s7431" xml:space="preserve">hæc obſeruatio <lb/>accuratioreuadet ſi fuerint duo obſeruatores ſimul, qui per duos quadrantes colliment, vnus ad ſuperiorem <lb/>limbũ, differentia enim eorum erit quędã quantitas. </s> <s xml:id="echoid-s7432" xml:space="preserve">Secundus modus eſt Hipparchi, qui ob id dioptrã quan-<lb/>dam, quam ideo Hipparchi appellant, excogitauit, cuius conſtructionem, & </s> <s xml:id="echoid-s7433" xml:space="preserve">vſus docet Proclus Diadochus in <lb/> <anchor type="figure" xlink:label="fig-0096-01a" xlink:href="fig-0096-01"/> Hypothes: </s> <s xml:id="echoid-s7434" xml:space="preserve">Aſtron. </s> <s xml:id="echoid-s7435" xml:space="preserve">in hunc modum: </s> <s xml:id="echoid-s7436" xml:space="preserve">ſit <lb/>regula inflexibilis quatuor cubitis lon-<lb/>ga, vt in figura A B. </s> <s xml:id="echoid-s7437" xml:space="preserve">in in qua ad partem <lb/>A. </s> <s xml:id="echoid-s7438" xml:space="preserve">infixit, erexitq; </s> <s xml:id="echoid-s7439" xml:space="preserve">orthogonaliter pin-<lb/>nulam D C. </s> <s xml:id="echoid-s7440" xml:space="preserve">immobilem, in qua eſſet par <lb/>uum foramen D. </s> <s xml:id="echoid-s7441" xml:space="preserve">alteram ſimiliter E F. <lb/></s> <s xml:id="echoid-s7442" xml:space="preserve">pinnulam orthogonaliter ei<unsure/>dem regu-<lb/>læ erexit, ſed quæ per ſubſcudem in ca-<lb/>naliculo A B. </s> <s xml:id="echoid-s7443" xml:space="preserve">inſerta, ſurſum, ac deor-<lb/>ſum manens perpendiculariter, moueri <lb/>poſſet. </s> <s xml:id="echoid-s7444" xml:space="preserve">in ea fecit duo foramina parua E F. </s> <s xml:id="echoid-s7445" xml:space="preserve">quę ita alteri foramini D. </s> <s xml:id="echoid-s7446" xml:space="preserve">reſponderent, vt D. </s> <s xml:id="echoid-s7447" xml:space="preserve">mediũ eorum obti-<lb/>neret, ſicuti apparet in figura. </s> <s xml:id="echoid-s7448" xml:space="preserve">vſus hic erit, cum Solis, aut Lunæ diametrum apparentem accipere licet; </s> <s xml:id="echoid-s7449" xml:space="preserve">con-<lb/>ſtituatur dioptra ad Lunam, aut Solem, quantum fieri poteſt ab horizontem eleuatum, vt ſidus ſit puriſſimũ<unsure/>, <lb/>& </s> <s xml:id="echoid-s7450" xml:space="preserve">ab omni refractionum errore immune. </s> <s xml:id="echoid-s7451" xml:space="preserve">pars autem B. </s> <s xml:id="echoid-s7452" xml:space="preserve">ſyderi obuertatur, in qua eſt pinnacidium mobile. </s> <s xml:id="echoid-s7453" xml:space="preserve"><lb/>iam per foramen D. </s> <s xml:id="echoid-s7454" xml:space="preserve">oculus inſpiciens ad ſydus, ita pinnulam E F. </s> <s xml:id="echoid-s7455" xml:space="preserve">vltro, citroque promoueat, quouſque per <lb/>duo foramina deſpiciat luminaris limbum ſuperiorem, & </s> <s xml:id="echoid-s7456" xml:space="preserve">inferiorem ſimul, ideſt, radius vnus viſiuus tran-<lb/>ſiens per foramina D E. </s> <s xml:id="echoid-s7457" xml:space="preserve">videat inferiorem Lunæ marginem; </s> <s xml:id="echoid-s7458" xml:space="preserve">alter radius per foramina D E. </s> <s xml:id="echoid-s7459" xml:space="preserve">videat ſuperio-<lb/>rem marginem. </s> <s xml:id="echoid-s7460" xml:space="preserve">hac enim ratione extrema diametri Lunæ compræhenduntur ad huiuſmodi radijs, fitq; </s> <s xml:id="echoid-s7461" xml:space="preserve">ab <lb/>e<unsure/>is angulus E D F. </s> <s xml:id="echoid-s7462" xml:space="preserve">ſub quo eadem diameter ſpectatur, ſiue cui diameter ſubtenditur. </s> <s xml:id="echoid-s7463" xml:space="preserve">hic ergo angulus expen <lb/>dendus eſt, per propoſ. </s> <s xml:id="echoid-s7464" xml:space="preserve">2. </s> <s xml:id="echoid-s7465" xml:space="preserve">Appar. </s> <s xml:id="echoid-s7466" xml:space="preserve">quot enim minuta ille continebit, totidem etiam minutorum eri@ apparens <lb/>diameter obſeruata. </s> <s xml:id="echoid-s7467" xml:space="preserve">hoc eodem modo, & </s> <s xml:id="echoid-s7468" xml:space="preserve">dioptra vtebatur etiam Ptolæmeus, cap. </s> <s xml:id="echoid-s7469" xml:space="preserve">14. </s> <s xml:id="echoid-s7470" xml:space="preserve">lib. </s> <s xml:id="echoid-s7471" xml:space="preserve">5. </s> <s xml:id="echoid-s7472" xml:space="preserve">magnæ conſt. </s> <s xml:id="echoid-s7473" xml:space="preserve">ad <lb/>luminarium diametros capiendas.</s> <s xml:id="echoid-s7474" xml:space="preserve"/> </p> <div xml:id="echoid-div154" type="float" level="2" n="1"> <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a"> <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0096-01"/> </figure> </div> <p> <s xml:id="echoid-s7475" xml:space="preserve">Modus tertius eſt per craſſitiem vmbræ terræ in loco, vbi eam Luna attingit. </s> <s xml:id="echoid-s7476" xml:space="preserve">Primo autem vmbræ c<unsure/>raſ-<lb/>ſitiem ſagaciter ſic inueſtigant, obſeruant eclypſim, in q@a obſcuretur Lunæ dimidium, quo etiam tempore <lb/>Lunæ latitudinem exploratam, aut ex obſeruatione, aut ex calculo, habent. </s> <s xml:id="echoid-s7477" xml:space="preserve">ſit in figura circulus D B E C.</s> <s xml:id="echoid-s7478" xml:space="preserve"> <pb o="75" file="0097" n="101" rhead="Liber Nonus."/> recta vmbræ ſectio, in loco tranſitus Lunæ; </s> <s xml:id="echoid-s7479" xml:space="preserve">ita vt diameter eius B C. </s> <s xml:id="echoid-s7480" xml:space="preserve">refe-<lb/> <anchor type="figure" xlink:label="fig-0097-01a" xlink:href="fig-0097-01"/> ram craſſitiem illam vmbræ. </s> <s xml:id="echoid-s7481" xml:space="preserve">linea autem D A E. </s> <s xml:id="echoid-s7482" xml:space="preserve">referat eclypticam. </s> <s xml:id="echoid-s7483" xml:space="preserve">fit Lu-<lb/>na vbi B. </s> <s xml:id="echoid-s7484" xml:space="preserve">vſque ad dimidium eclypſata. </s> <s xml:id="echoid-s7485" xml:space="preserve">quia igitur Lunæ latitudo nota eſt, <lb/>nota erit linea A B. </s> <s xml:id="echoid-s7486" xml:space="preserve">quæ ipſam refert; </s> <s xml:id="echoid-s7487" xml:space="preserve">& </s> <s xml:id="echoid-s7488" xml:space="preserve">conſequenter nota erit vmbræ ſe-<lb/>midiameter B A. </s> <s xml:id="echoid-s7489" xml:space="preserve">ſi igitur latitudo Lunæ fuiſſet 43. </s> <s xml:id="echoid-s7490" xml:space="preserve">min. </s> <s xml:id="echoid-s7491" xml:space="preserve">totidem eſſet ſemi-<lb/>diameter B A. </s> <s xml:id="echoid-s7492" xml:space="preserve">tota autem diameter B C. </s> <s xml:id="echoid-s7493" xml:space="preserve">86. </s> <s xml:id="echoid-s7494" xml:space="preserve">min. </s> <s xml:id="echoid-s7495" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s7496" xml:space="preserve">vmbræ minima in <lb/>loco Lunæ eſt 45. </s> <s xml:id="echoid-s7497" xml:space="preserve">min. </s> <s xml:id="echoid-s7498" xml:space="preserve">maxima eſt 47. </s> <s xml:id="echoid-s7499" xml:space="preserve">min. </s> <s xml:id="echoid-s7500" xml:space="preserve">ex Tich. </s> <s xml:id="echoid-s7501" xml:space="preserve">Inuenta hac ratione <lb/>craſſitie vmbræ, aliam poſtea eclypſim notant, in qua ſint eædem diſtantiæ <lb/>Solis, & </s> <s xml:id="echoid-s7502" xml:space="preserve">Lunæ à terra. </s> <s xml:id="echoid-s7503" xml:space="preserve">ac per eam ſic Lunę diametrum apparentem ſcrutan-<lb/>tur, ſit v.</s> <s xml:id="echoid-s7504" xml:space="preserve">g. </s> <s xml:id="echoid-s7505" xml:space="preserve">in eadem figura Luna F. </s> <s xml:id="echoid-s7506" xml:space="preserve">cuius quarta pars C @. </s> <s xml:id="echoid-s7507" xml:space="preserve">ſit obſcurata. </s> <s xml:id="echoid-s7508" xml:space="preserve">lati<unsure/>-<lb/>tudinem etiam Lunæ compertam habent, v. </s> <s xml:id="echoid-s7509" xml:space="preserve">g. </s> <s xml:id="echoid-s7510" xml:space="preserve">51. </s> <s xml:id="echoid-s7511" xml:space="preserve">min. </s> <s xml:id="echoid-s7512" xml:space="preserve">quæ eſt linea A F. <lb/></s> <s xml:id="echoid-s7513" xml:space="preserve">nota eſt etiam ex præcedenti obſeruatione linea A C. </s> <s xml:id="echoid-s7514" xml:space="preserve">min. </s> <s xml:id="echoid-s7515" xml:space="preserve">42. </s> <s xml:id="echoid-s7516" xml:space="preserve">igitur detra-<lb/>cta A C. </s> <s xml:id="echoid-s7517" xml:space="preserve">ab A F. </s> <s xml:id="echoid-s7518" xml:space="preserve">remanebit C F. </s> <s xml:id="echoid-s7519" xml:space="preserve">nota min. </s> <s xml:id="echoid-s7520" xml:space="preserve">8. </s> <s xml:id="echoid-s7521" xml:space="preserve">quę eſt quarta pars diametri Lu-<lb/>@æ, ergo tota diameter erit 32. </s> <s xml:id="echoid-s7522" xml:space="preserve">min. </s> <s xml:id="echoid-s7523" xml:space="preserve">in minima diſtantia Lunæ, quæ eſt ſemid. </s> <s xml:id="echoid-s7524" xml:space="preserve">T. </s> <s xml:id="echoid-s7525" xml:space="preserve">52. </s> <s xml:id="echoid-s7526" xml:space="preserve">apparens eius diam. </s> <s xml:id="echoid-s7527" xml:space="preserve">eſt <lb/>36′. </s> <s xml:id="echoid-s7528" xml:space="preserve">in maxima diſtantia quæ eſt ſemid. </s> <s xml:id="echoid-s7529" xml:space="preserve">T. </s> <s xml:id="echoid-s7530" xml:space="preserve">60. </s> <s xml:id="echoid-s7531" xml:space="preserve">apparens diam. </s> <s xml:id="echoid-s7532" xml:space="preserve">eſt 33′. </s> <s xml:id="echoid-s7533" xml:space="preserve">ex Tychone. </s> <s xml:id="echoid-s7534" xml:space="preserve">Obiter notandum, quod <lb/>habita diam. </s> <s xml:id="echoid-s7535" xml:space="preserve">vm-<lb/> <anchor type="figure" xlink:label="fig-0097-02a" xlink:href="fig-0097-02"/> bræ apparente in <lb/>tranſitu Lunę, poſ <lb/>ſumus vmbrã ter-<lb/>ræ delincare, de-<lb/>ſcribẽdo figuram, <lb/>quæ veras habeat <lb/>proportiones, hoc modo, accepta terrę ſemid. </s> <s xml:id="echoid-s7536" xml:space="preserve">A E. </s> <s xml:id="echoid-s7537" xml:space="preserve">cuiuſuis magnitudinis ducantur ab A. </s> <s xml:id="echoid-s7538" xml:space="preserve">centro terrę binæ <lb/>lineę conſtituentes angulum tot min. </s> <s xml:id="echoid-s7539" xml:space="preserve">quot ſunt in vmbra apparente, vt in figura angulus B A C. </s> <s xml:id="echoid-s7540" xml:space="preserve">fit 40′. </s> <s xml:id="echoid-s7541" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s7542" xml:space="preserve">linea vero A B, vel A C. </s> <s xml:id="echoid-s7543" xml:space="preserve">contineat aſſumptus ſemid. </s> <s xml:id="echoid-s7544" xml:space="preserve">terrę A E. </s> <s xml:id="echoid-s7545" xml:space="preserve">v.</s> <s xml:id="echoid-s7546" xml:space="preserve">g. </s> <s xml:id="echoid-s7547" xml:space="preserve">52′. </s> <s xml:id="echoid-s7548" xml:space="preserve">& </s> <s xml:id="echoid-s7549" xml:space="preserve">earum extremitas ſit vbi B C. </s> <s xml:id="echoid-s7550" xml:space="preserve">du-<lb/>ctis iam duabus lineis E B D. </s> <s xml:id="echoid-s7551" xml:space="preserve">F C D. </s> <s xml:id="echoid-s7552" xml:space="preserve">vmbram terrę repręſentabunt, vt ex ſe pater.</s> <s xml:id="echoid-s7553" xml:space="preserve"/> </p> <div xml:id="echoid-div155" type="float" level="2" n="2"> <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a"> <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-01"/> </figure> <figure xlink:label="fig-0097-02" xlink:href="fig-0097-02a"> <image file="0097-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-02"/> </figure> </div> <figure> <image file="0097-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-03"/> </figure> <p> <s xml:id="echoid-s7554" xml:space="preserve">Modus 4. </s> <s xml:id="echoid-s7555" xml:space="preserve">pręrequirit diſtantiã Solis à<unsure/> terra, necnõ proportionem <lb/>corporis ſolaris ad terrã, quibus habitis conſtruenda eſt figura <lb/>vera proportionalis, quam ſupra pag. </s> <s xml:id="echoid-s7556" xml:space="preserve">38. </s> <s xml:id="echoid-s7557" xml:space="preserve">exhibuimus, in qua <lb/>vera vmbræ craſſitie practicè accipi poteſt in loco trãſitus Lu <lb/>næ, qui locus etiam cognitus eſt, quia cognita eſt diſtantia Lu-<lb/>næ a terra, vti ſupra patuit. </s> <s xml:id="echoid-s7558" xml:space="preserve">Idem per auream proportionum <lb/>regulam, & </s> <s xml:id="echoid-s7559" xml:space="preserve">triangulorum ſimilium aſſequemur hoc pacto; </s> <s xml:id="echoid-s7560" xml:space="preserve">fit vmbra terræ A B C. </s> <s xml:id="echoid-s7561" xml:space="preserve">tranſi@us Lunæ E D. </s> <s xml:id="echoid-s7562" xml:space="preserve">ſunt <lb/>igitur duo triangula, æquiangula videlicet A B C. </s> <s xml:id="echoid-s7563" xml:space="preserve">E B D. </s> <s xml:id="echoid-s7564" xml:space="preserve">erit ergo vt A B. </s> <s xml:id="echoid-s7565" xml:space="preserve">ad E B. </s> <s xml:id="echoid-s7566" xml:space="preserve">ad E B. </s> <s xml:id="echoid-s7567" xml:space="preserve">quę nota ſunt, ita <lb/>A C. </s> <s xml:id="echoid-s7568" xml:space="preserve">diameter terræ nota ad aliud, quod per regulam auream prodibit, eritq; </s> <s xml:id="echoid-s7569" xml:space="preserve">vmbræ diameter. </s> <s xml:id="echoid-s7570" xml:space="preserve">Eadem por-<lb/>rò opera manifeſta eſt proportio diametri terræ ad diametrum vmbræ. </s> <s xml:id="echoid-s7571" xml:space="preserve">Hiſce præcognitis.</s> <s xml:id="echoid-s7572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7573" xml:space="preserve">4 Aſſero Lunam eſſe adeò terra minorem, vt ſit eius pars quadrageſima; </s> <s xml:id="echoid-s7574" xml:space="preserve">quod patere poteſt. </s> <s xml:id="echoid-s7575" xml:space="preserve">Pri<unsure/>mo ſic; <lb/></s> <s xml:id="echoid-s7576" xml:space="preserve">habita proportione diametri terræ ad diametrum vmbrę, necnon diametri vmbræ ad diametrum Lunæ; </s> <s xml:id="echoid-s7577" xml:space="preserve">ha-<lb/>bebitur quoque proportio diametri terræ ad diametrum Lunæ. </s> <s xml:id="echoid-s7578" xml:space="preserve">habit<unsure/>a autem proportione diametrorum <lb/>duarum ſphærarum, inde quoque elicitur earundem ſphærarum proportio, vt paulo poſt explicabo. </s> <s xml:id="echoid-s7579" xml:space="preserve">Secun-<lb/>do ſic, ex diſtantia Lunæ a terra duplicata conflatur tota diameter cæli Lunæ; </s> <s xml:id="echoid-s7580" xml:space="preserve">deinde ex hac diametro elici-<lb/>tur tota cæli peripheria in terræ ſemidiametris; </s> <s xml:id="echoid-s7581" xml:space="preserve">quia nota eſt ratio peripheriæ ad ſuam diametrum, quæ eſt <lb/>ferè ſicuti 22. </s> <s xml:id="echoid-s7582" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s7583" xml:space="preserve">vti ſuperius ſatis explicauimus. </s> <s xml:id="echoid-s7584" xml:space="preserve">& </s> <s xml:id="echoid-s7585" xml:space="preserve">quia nota eſt apparens Lunæ diameter,<unsure/> ideſt, eſt notum <lb/>eſt quot minuta in cælo ſubt<unsure/>endat; </s> <s xml:id="echoid-s7586" xml:space="preserve">& </s> <s xml:id="echoid-s7587" xml:space="preserve">pariter notũſit quot min@ta, aut gradus vna terræ diameter contineat, <lb/>aut ſubtendat. </s> <s xml:id="echoid-s7588" xml:space="preserve">hinc harum diametrorum ratio cognoſcetur. </s> <s xml:id="echoid-s7589" xml:space="preserve">Exempli gratia, diſtet Luna à terra ſemid. </s> <s xml:id="echoid-s7590" xml:space="preserve">52. </s> <s xml:id="echoid-s7591" xml:space="preserve"><lb/>quibus duplicatis erit diameter huius lunaris gyri 104. </s> <s xml:id="echoid-s7592" xml:space="preserve">ſemidiametri terræ, fiat ergo vt 7. </s> <s xml:id="echoid-s7593" xml:space="preserve">ad 22. </s> <s xml:id="echoid-s7594" xml:space="preserve">ita 104. </s> <s xml:id="echoid-s7595" xml:space="preserve">ad fe-<lb/>rè 327. </s> <s xml:id="echoid-s7596" xml:space="preserve">ſemidiatros terræ, quæ gyrum Lunæ componunt. </s> <s xml:id="echoid-s7597" xml:space="preserve">In toto autẽ circuitu ſunt gr. </s> <s xml:id="echoid-s7598" xml:space="preserve">360. </s> <s xml:id="echoid-s7599" xml:space="preserve">ſiue min. </s> <s xml:id="echoid-s7600" xml:space="preserve">21600. </s> <s xml:id="echoid-s7601" xml:space="preserve"><lb/>quæ diuiſa per 327. </s> <s xml:id="echoid-s7602" xml:space="preserve">producunt 66. </s> <s xml:id="echoid-s7603" xml:space="preserve">minuta, & </s> <s xml:id="echoid-s7604" xml:space="preserve">amplius. </s> <s xml:id="echoid-s7605" xml:space="preserve">Ergo vna terræ ſemidiameter occupat minuta ferè <lb/>66. </s> <s xml:id="echoid-s7606" xml:space="preserve">ac proinde tota diameter occupabit 132′. </s> <s xml:id="echoid-s7607" xml:space="preserve">At vero apparens Lunæ diameter occupat 36. </s> <s xml:id="echoid-s7608" xml:space="preserve">min. </s> <s xml:id="echoid-s7609" xml:space="preserve">Eſt ergo <lb/>proportio diametri terræ ad diametrum Lunæ ſicuti 132. </s> <s xml:id="echoid-s7610" xml:space="preserve">ad 36. </s> <s xml:id="echoid-s7611" xml:space="preserve">hoc eſt quæ 3<emph style="super">2</emph><emph style="super">3</emph>. </s> <s xml:id="echoid-s7612" xml:space="preserve">ferè ad 1. </s> <s xml:id="echoid-s7613" xml:space="preserve">quare non latebit <lb/>ſphærarum proportio, vt mox dicam. </s> <s xml:id="echoid-s7614" xml:space="preserve">Tertio ſic, ac magis expeditè. </s> <s xml:id="echoid-s7615" xml:space="preserve">cognitis iam diſtantia Lunæ, necnon <lb/>diametro eius apparenti, conſtruatur trigonum Iſoſceles, cuius duo latera æqualia contineant angulum, ſub <lb/>quo diameter apparens apparet; </s> <s xml:id="echoid-s7616" xml:space="preserve">quæ duo latera ſint diuiſa in tot partes æquales, quot ſemidiametri terræ <lb/>confiant aſſumptam diſtantiam, v.</s> <s xml:id="echoid-s7617" xml:space="preserve">g. </s> <s xml:id="echoid-s7618" xml:space="preserve">in partes 52. </s> <s xml:id="echoid-s7619" xml:space="preserve">ſit in figura trigonum A B. </s> <s xml:id="echoid-s7620" xml:space="preserve">cuius angulus A. </s> <s xml:id="echoid-s7621" xml:space="preserve">fit min. </s> <s xml:id="echoid-s7622" xml:space="preserve">36. </s> <s xml:id="echoid-s7623" xml:space="preserve">quot <lb/>nimirum continet diameter apparens. </s> <s xml:id="echoid-s7624" xml:space="preserve">latus A B. </s> <s xml:id="echoid-s7625" xml:space="preserve">vel A C. </s> <s xml:id="echoid-s7626" xml:space="preserve">contineat partes æquales 52. </s> <s xml:id="echoid-s7627" xml:space="preserve">quot nimirum conti-<lb/>net diſtantia Lunæ, cum talem exhibet diametrum, erit enim tale triangulum æquiangulum, ac proportio-<lb/>nale triangulo magno, quod ab oculo noſtro vſque ad Lunæ latera extrema exporrigitur. </s> <s xml:id="echoid-s7628" xml:space="preserve">Quapropter li-<lb/> <anchor type="figure" xlink:label="fig-0097-04a" xlink:href="fig-0097-04"/> ce<unsure/>bit practicè accepta baſi B C. </s> <s xml:id="echoid-s7629" xml:space="preserve">quæ diametrum <lb/>refert per circinum, eam partibus conferre quæ <lb/>in latere A B. </s> <s xml:id="echoid-s7630" xml:space="preserve">referunt ſemidiametros terræ; </s> <s xml:id="echoid-s7631" xml:space="preserve">ac <lb/>perſpicere quam cum illis habeat rarionem. </s> <s xml:id="echoid-s7632" xml:space="preserve">fic-<lb/>que apparebit diametrum terræ continere dia-<lb/>metrum Lunæ ter, ac duas quintas, hoc eſt habe- <pb o="76" file="0098" n="102" rhead="De Mundi Fabrica,"/> read eam proportionem, quam habet 17. </s> <s xml:id="echoid-s7633" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s7634" xml:space="preserve">& </s> <s xml:id="echoid-s7635" xml:space="preserve">è contra, diametrum Lunæ ad diametrum terræ, vt 5. </s> <s xml:id="echoid-s7636" xml:space="preserve">ad 17. <lb/></s> <s xml:id="echoid-s7637" xml:space="preserve">habita igitur hac proportione eliciemus etiam ſphærarum proportionem. </s> <s xml:id="echoid-s7638" xml:space="preserve">Primò mechanicè ſic; </s> <s xml:id="echoid-s7639" xml:space="preserve">conſtruan-<lb/>tur duæ ſphæræ inæquales ex eadẽ materia, veluti ex plumbo, minoris diameter ſit 5. </s> <s xml:id="echoid-s7640" xml:space="preserve">digiti, maioris vero 17. </s> <s xml:id="echoid-s7641" xml:space="preserve"><lb/>iam vtriuſque pondus, earum proportionem manifeſtabit; </s> <s xml:id="echoid-s7642" xml:space="preserve">eritq; </s> <s xml:id="echoid-s7643" xml:space="preserve">minoris pondus vt 1. </s> <s xml:id="echoid-s7644" xml:space="preserve">maioris vero vt 40. </s> <s xml:id="echoid-s7645" xml:space="preserve"><lb/>Quapropter Luh<unsure/>a etiam quadragies à<unsure/> terra continebitur.</s> <s xml:id="echoid-s7646" xml:space="preserve"/> </p> <div xml:id="echoid-div156" type="float" level="2" n="3"> <figure xlink:label="fig-0097-04" xlink:href="fig-0097-04a"> <image file="0097-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-04"/> </figure> </div> <p> <s xml:id="echoid-s7647" xml:space="preserve">Secundo ve@o Geometricè per propoſ. </s> <s xml:id="echoid-s7648" xml:space="preserve">vlt. </s> <s xml:id="echoid-s7649" xml:space="preserve">12. </s> <s xml:id="echoid-s7650" xml:space="preserve">Elem. </s> <s xml:id="echoid-s7651" xml:space="preserve">vbi Euclides probat binas ſphæras habere inuicẽ, nõ <lb/>c<unsure/>andem proportionem, quam habent earum diametri, ſed longe diuerſam; </s> <s xml:id="echoid-s7652" xml:space="preserve">habere videlicet proportionem, <lb/>quæ eſt triplicata ſuarum diametrorum proportio, ideſt, ſi diametrorum proportio triplicetur, tunc euadet <lb/>proportio ſphærarum; </s> <s xml:id="echoid-s7653" xml:space="preserve">triplicatur autem quæuis proportio hoc modo, ſit v.</s> <s xml:id="echoid-s7654" xml:space="preserve">g. </s> <s xml:id="echoid-s7655" xml:space="preserve">propor@@o 1. </s> <s xml:id="echoid-s7656" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s7657" xml:space="preserve">triplicanda: <lb/></s> <s xml:id="echoid-s7658" xml:space="preserve">accipia@tur, ſiue ſubdantur alij duo termini eandem rationem continuãtes, ita vt ſint 4. </s> <s xml:id="echoid-s7659" xml:space="preserve">numeri tales; </s> <s xml:id="echoid-s7660" xml:space="preserve">1. </s> <s xml:id="echoid-s7661" xml:space="preserve">2. </s> <s xml:id="echoid-s7662" xml:space="preserve">4. </s> <s xml:id="echoid-s7663" xml:space="preserve">8. </s> <s xml:id="echoid-s7664" xml:space="preserve"><lb/>inter quos eſt eadem ratio, quæ inter duos priores; </s> <s xml:id="echoid-s7665" xml:space="preserve">eaque dicitur triplicata, quia ter ibi reperitur; </s> <s xml:id="echoid-s7666" xml:space="preserve">primo eſt <lb/>inter primos duos 1. </s> <s xml:id="echoid-s7667" xml:space="preserve">2. </s> <s xml:id="echoid-s7668" xml:space="preserve">ſecundo inter ſecundum, & </s> <s xml:id="echoid-s7669" xml:space="preserve">tertium 2. </s> <s xml:id="echoid-s7670" xml:space="preserve">4. </s> <s xml:id="echoid-s7671" xml:space="preserve">tertio inter tertium, & </s> <s xml:id="echoid-s7672" xml:space="preserve">quartum 4. </s> <s xml:id="echoid-s7673" xml:space="preserve">8. </s> <s xml:id="echoid-s7674" xml:space="preserve">propor-<lb/>tio igitur primi ad vltimum hoc eſt 1. </s> <s xml:id="echoid-s7675" xml:space="preserve">ad 8. </s> <s xml:id="echoid-s7676" xml:space="preserve">eſt triplicata proportionis 1. </s> <s xml:id="echoid-s7677" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s7678" xml:space="preserve">quamobrem ſi ſint duæ ſphæræ, <lb/>quarũ diametri ſint vt 1. </s> <s xml:id="echoid-s7679" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s7680" xml:space="preserve">ſphæræ ipſe erunt inuicem, vt 1. </s> <s xml:id="echoid-s7681" xml:space="preserve">ad 8. </s> <s xml:id="echoid-s7682" xml:space="preserve">ideſt minor a maiore octies adæquabitur. </s> <s xml:id="echoid-s7683" xml:space="preserve"><lb/>hanc Euclidis propoſitionem experiri facilè poſſumus in ſphæris eiuſdem materię, & </s> <s xml:id="echoid-s7684" xml:space="preserve">vniformis quantitatis,<unsure/> <lb/>quia in hoc caſu maior ſphæra octies idem penderet, quod minor ſemel.</s> <s xml:id="echoid-s7685" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7686" xml:space="preserve">Cum igitur iam conſtet diametrum Lunæ ad diametrum terræ eſſe, vt 5. </s> <s xml:id="echoid-s7687" xml:space="preserve">ad 17. </s> <s xml:id="echoid-s7688" xml:space="preserve">ſi hæc proportio triplice-<lb/>tur, vti modo docuimus, erunt hi 4. </s> <s xml:id="echoid-s7689" xml:space="preserve">numeri eam triplicantes 5. </s> <s xml:id="echoid-s7690" xml:space="preserve">17. </s> <s xml:id="echoid-s7691" xml:space="preserve">57<emph style="super">4</emph><emph style="super">5</emph>. </s> <s xml:id="echoid-s7692" xml:space="preserve">196. </s> <s xml:id="echoid-s7693" xml:space="preserve">ratio igitur primi 5. </s> <s xml:id="echoid-s7694" xml:space="preserve">ad vltimum <lb/>196. </s> <s xml:id="echoid-s7695" xml:space="preserve">erit triplicata priorum duorum, & </s> <s xml:id="echoid-s7696" xml:space="preserve">proinde erit proportio Lunę ad terram, vt 5. </s> <s xml:id="echoid-s7697" xml:space="preserve">ad 196. </s> <s xml:id="echoid-s7698" xml:space="preserve">primus autem 5. <lb/></s> <s xml:id="echoid-s7699" xml:space="preserve">continetur in ſecundo 196. </s> <s xml:id="echoid-s7700" xml:space="preserve">tricies, & </s> <s xml:id="echoid-s7701" xml:space="preserve">nouies, & </s> <s xml:id="echoid-s7702" xml:space="preserve">paulo plus, vt patet per diuiſionem maioris per minorem. </s> <s xml:id="echoid-s7703" xml:space="preserve"><lb/>Eſt igitur Lunæ globus quadrageſima ferè pars terreſtris globi, ſiu<unsure/>e terra adęquat Lunam quadragies. </s> <s xml:id="echoid-s7704" xml:space="preserve">quod <lb/>c<unsure/>rat vltimus ſcopus. </s> <s xml:id="echoid-s7705" xml:space="preserve">Cur ergo videtur tantum pedalis? </s> <s xml:id="echoid-s7706" xml:space="preserve">reſpondent optici id prouenire ex nimia a nobis di-<lb/>ſtantia, experimur enim quotidie, quæ a longè videntur parua videri, & </s> <s xml:id="echoid-s7707" xml:space="preserve">quò<unsure/> magis à longè, eo minora ap-<lb/>parere.</s> <s xml:id="echoid-s7708" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7709" xml:space="preserve">Cur præterea ſæpe prope horizontem, vel in nebula, vel fumo, maior ſpectatur? </s> <s xml:id="echoid-s7710" xml:space="preserve">reſpondent optici ea, <lb/>quæ videntur per diuerſa media, ideſt, diuerſæ tranſparentiæ, ita vt craſſius fit ad obiectum, rarius ad ocu-<lb/>lum, tunc maiora ſolito videri. </s> <s xml:id="echoid-s7711" xml:space="preserve">ſic quæ exiſtũt in aqua maiora quam ſint apparent, quia videntur per aquam <lb/>primo quæ craſſior eſt aere.</s> <s xml:id="echoid-s7712" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div158" type="section" level="1" n="98"> <head xml:id="echoid-head108" style="it" xml:space="preserve">De altitudine Lunarium Montium. Cap. I X.</head> <p> <s xml:id="echoid-s7713" xml:space="preserve">SV perius probauimus Lunæ faciem, quæ terras deſpectat eſſe montibus, ac concauitatibus aſperam. </s> <s xml:id="echoid-s7714" xml:space="preserve">ſunt <lb/>@amen nonnulli, qui adeo ab Lunæ inæqualitatibus abhorreant, vt propterea velint has eminentias, atq; <lb/></s> <s xml:id="echoid-s7715" xml:space="preserve">depreſſiones ſaluari poſſe per partes denſiores, ac rariores; </s> <s xml:id="echoid-s7716" xml:space="preserve">quæ omnes vnica Lunæ ſphæricitate cõpræhen-<lb/>dantur. </s> <s xml:id="echoid-s7717" xml:space="preserve">quidquid ſit haſce eminentias, ſiue montes, menſurare aggredimur. </s> <s xml:id="echoid-s7718" xml:space="preserve">Vtautem ſupra dictum eſt; </s> <s xml:id="echoid-s7719" xml:space="preserve">ver-<lb/>tices horum montium intra partem adhuc tenebroſam exiſtentes, lumine Solis præuenti, ſicque cęteris par-<lb/>@ibus prius illuſtrati, ſe produnt. </s> <s xml:id="echoid-s7720" xml:space="preserve">tantaq; </s> <s xml:id="echoid-s7721" xml:space="preserve">eſt eorum diſtantia a confinio luminis, & </s> <s xml:id="echoid-s7722" xml:space="preserve">vmbrę, vt ſit quaſi pars vi-<lb/>geſima totius lunaris diametri, vt diligenti inſpectori conſtare po-<lb/>reſt. </s> <s xml:id="echoid-s7723" xml:space="preserve">hoc aſſumpto intelligatur lunaris globus C A E. </s> <s xml:id="echoid-s7724" xml:space="preserve">centrũ E. </s> <s xml:id="echoid-s7725" xml:space="preserve">di-<lb/> <anchor type="figure" xlink:label="fig-0098-01a" xlink:href="fig-0098-01"/> metiens C F. </s> <s xml:id="echoid-s7726" xml:space="preserve">quę ad terrę diametrum eſt ferè, vt 2. </s> <s xml:id="echoid-s7727" xml:space="preserve">ad 7. </s> <s xml:id="echoid-s7728" xml:space="preserve">cum autem <lb/>terræ ſemidiam. </s> <s xml:id="echoid-s7729" xml:space="preserve">contineat milliar a aſtronomica 3,436, {1/2}. </s> <s xml:id="echoid-s7730" xml:space="preserve">erit ſemi-<lb/>diam. </s> <s xml:id="echoid-s7731" xml:space="preserve">E C. </s> <s xml:id="echoid-s7732" xml:space="preserve">iuxta allatam rationem 981. </s> <s xml:id="echoid-s7733" xml:space="preserve">milliaria. </s> <s xml:id="echoid-s7734" xml:space="preserve">ſit autem pars fi-<lb/>guræ vbi C. </s> <s xml:id="echoid-s7735" xml:space="preserve">ea Lunæ pars, quã nos<unsure/> quotidie videmus, ſeu quę deor-<lb/>ſum vergit, & </s> <s xml:id="echoid-s7736" xml:space="preserve">per punctum C. </s> <s xml:id="echoid-s7737" xml:space="preserve">tranſeat E C. </s> <s xml:id="echoid-s7738" xml:space="preserve">confinium lucis, & </s> <s xml:id="echoid-s7739" xml:space="preserve">te-<lb/>nebrarum. </s> <s xml:id="echoid-s7740" xml:space="preserve">linea G C D. </s> <s xml:id="echoid-s7741" xml:space="preserve">referat radium Sol<unsure/>is exiſtẽtis ad partes G. <lb/></s> <s xml:id="echoid-s7742" xml:space="preserve">tangentem Lunam in C. </s> <s xml:id="echoid-s7743" xml:space="preserve">vbi non ſunt montes; </s> <s xml:id="echoid-s7744" xml:space="preserve">qui vlterius produ-<lb/>ctus occurrat vertici D. </s> <s xml:id="echoid-s7745" xml:space="preserve">exiſtenti adhuc in parte tenebroſa, eumq; </s> <s xml:id="echoid-s7746" xml:space="preserve"><lb/>illuſtret. </s> <s xml:id="echoid-s7747" xml:space="preserve">ducatur linea E A D. </s> <s xml:id="echoid-s7748" xml:space="preserve">linea D C. </s> <s xml:id="echoid-s7749" xml:space="preserve">eſt diſtãtia verticis à<unsure/> con-<lb/>finio, quam ponimus eſſe partem vigeſimam totius C F. </s> <s xml:id="echoid-s7750" xml:space="preserve">ſiue deci-<lb/>mam ipſius C E. </s> <s xml:id="echoid-s7751" xml:space="preserve">erit igitur milliaria ferè 98. </s> <s xml:id="echoid-s7752" xml:space="preserve">cum tota E C. </s> <s xml:id="echoid-s7753" xml:space="preserve">ſit mil-<lb/>liaria 981. </s> <s xml:id="echoid-s7754" xml:space="preserve">in triangulo igitur E C D. </s> <s xml:id="echoid-s7755" xml:space="preserve">rectangulo, quia angulus ad C. </s> <s xml:id="echoid-s7756" xml:space="preserve">eſt rectus per 16. </s> <s xml:id="echoid-s7757" xml:space="preserve">tertij Elem. </s> <s xml:id="echoid-s7758" xml:space="preserve">notum eſt <lb/>latus E C. </s> <s xml:id="echoid-s7759" xml:space="preserve">981. </s> <s xml:id="echoid-s7760" xml:space="preserve">milliariorum. </s> <s xml:id="echoid-s7761" xml:space="preserve">latus vero C D. </s> <s xml:id="echoid-s7762" xml:space="preserve">98. </s> <s xml:id="echoid-s7763" xml:space="preserve">mill. </s> <s xml:id="echoid-s7764" xml:space="preserve">& </s> <s xml:id="echoid-s7765" xml:space="preserve">angulus ad C. </s> <s xml:id="echoid-s7766" xml:space="preserve">notus, quia rectus. </s> <s xml:id="echoid-s7767" xml:space="preserve">ſi igitur fiat trian-<lb/>gulum paruum rectangulum, habens latera circa angulum rectum prædictis analoga, erit totum triangulum <lb/>proport onale triangulo magno lunari per 6. </s> <s xml:id="echoid-s7768" xml:space="preserve">ſexti Elem. </s> <s xml:id="echoid-s7769" xml:space="preserve">quod etiam experientia conf@rmari poteſt. </s> <s xml:id="echoid-s7770" xml:space="preserve">in hoc <lb/>igitur paruo triangulo per circinum diligenter expendatur pars A D. </s> <s xml:id="echoid-s7771" xml:space="preserve">quot ſcilicet milliar. </s> <s xml:id="echoid-s7772" xml:space="preserve">contineat ex ijs, <lb/>quæ ſunt in latere D C. </s> <s xml:id="echoid-s7773" xml:space="preserve">vel E C. </s> <s xml:id="echoid-s7774" xml:space="preserve">parui trianguli, & </s> <s xml:id="echoid-s7775" xml:space="preserve">m<unsure/>anife<unsure/>ſta erit altitudo montis A D. </s> <s xml:id="echoid-s7776" xml:space="preserve">eritque quaſi mil-<lb/>liaria quatuor.</s> <s xml:id="echoid-s7777" xml:space="preserve"/> </p> <div xml:id="echoid-div158" type="float" level="2" n="1"> <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a"> <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0098-01"/> </figure> </div> <p> <s xml:id="echoid-s7778" xml:space="preserve">Aliter geometricè ſic; </s> <s xml:id="echoid-s7779" xml:space="preserve">quadrata laterum in numeris congnitorum E C. </s> <s xml:id="echoid-s7780" xml:space="preserve">C D. </s> <s xml:id="echoid-s7781" xml:space="preserve">accipiantur, ſimulque addan-<lb/>tur, efficientque hunc numer. </s> <s xml:id="echoid-s7782" xml:space="preserve">971,965. </s> <s xml:id="echoid-s7783" xml:space="preserve">qui per 47. </s> <s xml:id="echoid-s7784" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s7785" xml:space="preserve">erit æqualis quadra@o numero lineæ E D.</s> <s xml:id="echoid-s7786" xml:space="preserve"><unsure/> <lb/>qua propter radix quadrata prædicti numeri, quæ eſt 985. </s> <s xml:id="echoid-s7787" xml:space="preserve">ferè, erit ipſa linea E D. </s> <s xml:id="echoid-s7788" xml:space="preserve">continens mill<unsure/>iaria 985.</s> <s xml:id="echoid-s7789" xml:space="preserve"><unsure/> <lb/>à qua ab@ata linea E A. </s> <s xml:id="echoid-s7790" xml:space="preserve">milliaria 981. </s> <s xml:id="echoid-s7791" xml:space="preserve">remanet ipſa A D. </s> <s xml:id="echoid-s7792" xml:space="preserve">quatuor ferè miliar. </s> <s xml:id="echoid-s7793" xml:space="preserve">pro altitudine montis. </s> <s xml:id="echoid-s7794" xml:space="preserve">Eadem <lb/>ratiocinatione poſſumus inueſtigare profunditatem concauitatum illarum, quæ ſunt in parte illuminata <lb/>propè confinium.</s> <s xml:id="echoid-s7795" xml:space="preserve"/> </p> <pb o="77" file="0099" n="103" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div160" type="section" level="1" n="99"> <head xml:id="echoid-head109" style="it" xml:space="preserve">De Lunæ Temporibus. Cap. X.</head> <p> <s xml:id="echoid-s7796" xml:space="preserve">INter cæteros planetas, duo luminaria præcipua, hac dignitate fulgent, vt eorum motus, quoniam certis <lb/>periodis diſtinguuntur, aſſu mantur in tempora conſtatque ex ſacris litteris, ideo creata eſſe, vt mortalibus <lb/>eſſent in tempora. </s> <s xml:id="echoid-s7797" xml:space="preserve">Eſt igitur annus Lunaris duplex, Aſtronomicus, & </s> <s xml:id="echoid-s7798" xml:space="preserve">Ciuilis. </s> <s xml:id="echoid-s7799" xml:space="preserve">rurſus Aſtrom. </s> <s xml:id="echoid-s7800" xml:space="preserve">eſt duplex, <lb/>communis qui conſtat ex 12. </s> <s xml:id="echoid-s7801" xml:space="preserve">Lunationibus, quarum ſingulæ, vti ſupra dictum eſt, continent dies 29. </s> <s xml:id="echoid-s7802" xml:space="preserve">horas <lb/>12. </s> <s xml:id="echoid-s7803" xml:space="preserve">44′. </s> <s xml:id="echoid-s7804" xml:space="preserve">quare ipſe conſtat ex diebus 354. </s> <s xml:id="echoid-s7805" xml:space="preserve">horis 8. </s> <s xml:id="echoid-s7806" xml:space="preserve">48′. </s> <s xml:id="echoid-s7807" xml:space="preserve">alter dicitur Emboliſmicus, ideſt, inſititius, quod ei vna <lb/>Lunatio extraordinaria inſeratur. </s> <s xml:id="echoid-s7808" xml:space="preserve">Et ideo conſtat ex 13. </s> <s xml:id="echoid-s7809" xml:space="preserve">Lunationibus: </s> <s xml:id="echoid-s7810" xml:space="preserve">ac proinde diebus 383. </s> <s xml:id="echoid-s7811" xml:space="preserve">horis 21. </s> <s xml:id="echoid-s7812" xml:space="preserve">32′.</s> <s xml:id="echoid-s7813" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7814" xml:space="preserve">Lunationes autem dicuntur etiam menſes. </s> <s xml:id="echoid-s7815" xml:space="preserve">Vnde factum eſt vt a Luna menſes ortum ducant. </s> <s xml:id="echoid-s7816" xml:space="preserve">Annuſque <lb/>ideo in 12. </s> <s xml:id="echoid-s7817" xml:space="preserve">menſes diuidatur, quod in eo Lunationes 12. </s> <s xml:id="echoid-s7818" xml:space="preserve">vt plurimum contineantur: </s> <s xml:id="echoid-s7819" xml:space="preserve">hinc græcè Luna, & </s> <s xml:id="echoid-s7820" xml:space="preserve"><lb/>menſis, eodem quaſi vocabulo vocitantur.</s> <s xml:id="echoid-s7821" xml:space="preserve"><unsure/> Menſis enim <emph style="super">M</emph>{ιω}, Luna verò <emph style="super">M</emph>{ιω}ψ, dicitur. </s> <s xml:id="echoid-s7822" xml:space="preserve">Sol igitur vt poſtea <lb/>dicetur annum effecit; </s> <s xml:id="echoid-s7823" xml:space="preserve">Luna vero eum in menſes 12. </s> <s xml:id="echoid-s7824" xml:space="preserve">partita eſt. </s> <s xml:id="echoid-s7825" xml:space="preserve">Annus ciuilis, vt vulgari vſui idoneus ſit, non <lb/>conſiderat horas, nec minuta, quæ ſunt in aſtronomico; </s> <s xml:id="echoid-s7826" xml:space="preserve">ſic etiam ciuiles Lunationes, omiſſis dierum frag-<lb/>mentis, conſtant ex diebus integris. </s> <s xml:id="echoid-s7827" xml:space="preserve">ita vt ex 12. </s> <s xml:id="echoid-s7828" xml:space="preserve">vel 13. </s> <s xml:id="echoid-s7829" xml:space="preserve">anni Lunationibus prima ponatur dierum 30. </s> <s xml:id="echoid-s7830" xml:space="preserve">ſecun-<lb/>dicetur annum effecit; </s> <s xml:id="echoid-s7831" xml:space="preserve">Luna vero eum in menſes 12. </s> <s xml:id="echoid-s7832" xml:space="preserve">partita eſt. </s> <s xml:id="echoid-s7833" xml:space="preserve">Annus ciuilis, vt vulgari vſui idoneus ſit, non <lb/>conſiderat horas, nec minuta, quæ ſunt in aſtronomico; </s> <s xml:id="echoid-s7834" xml:space="preserve">ſic etiam ciuiles Lunationes, omiſſis dierum frag-<lb/>mentis, conſtant ex diebus integris. </s> <s xml:id="echoid-s7835" xml:space="preserve">ita vt ex 12. </s> <s xml:id="echoid-s7836" xml:space="preserve">vel 13. </s> <s xml:id="echoid-s7837" xml:space="preserve">anni Lunationibus prima ponatur dierum 30. </s> <s xml:id="echoid-s7838" xml:space="preserve">ſecun-<lb/>da dierum 29. </s> <s xml:id="echoid-s7839" xml:space="preserve">& </s> <s xml:id="echoid-s7840" xml:space="preserve">ſic alternatim vſq; </s> <s xml:id="echoid-s7841" xml:space="preserve">ad finem. </s> <s xml:id="echoid-s7842" xml:space="preserve">ſic vides in Calendario, & </s> <s xml:id="echoid-s7843" xml:space="preserve">Martyrologio hac alteratione Lu-<lb/>nas eſſe diſpoſitas, vt Luna Ianuarij ſit dierum 30. </s> <s xml:id="echoid-s7844" xml:space="preserve">Luna Februarij dierum 29. </s> <s xml:id="echoid-s7845" xml:space="preserve">& </s> <s xml:id="echoid-s7846" xml:space="preserve">ſic viciſſim deinceps vſq; </s> <s xml:id="echoid-s7847" xml:space="preserve">ad <lb/>finem anni. </s> <s xml:id="echoid-s7848" xml:space="preserve">Porrò ſolent Computiſtæ ex labentibus in cælo Lunationibus, eam cuique menſi attribuere, quę <lb/>in ipſo deſinit. </s> <s xml:id="echoid-s7849" xml:space="preserve">Vnde eorum verſus.</s> <s xml:id="echoid-s7850" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div161" type="section" level="1" n="100"> <head xml:id="echoid-head110" style="it" xml:space="preserve">In quo finitur Menſi Lunatio detur.</head> <p> <s xml:id="echoid-s7851" xml:space="preserve">Qua ratione aliquando contingit eundem menſem binas obtinere Lunationes. </s> <s xml:id="echoid-s7852" xml:space="preserve">Annus igitur ciuilis, aut <lb/>eſt communis, conſtatque integris dieb. </s> <s xml:id="echoid-s7853" xml:space="preserve">354. </s> <s xml:id="echoid-s7854" xml:space="preserve">& </s> <s xml:id="echoid-s7855" xml:space="preserve">aliquando diebus 353. </s> <s xml:id="echoid-s7856" xml:space="preserve">aut Emboliſmicus, continetque dies <lb/>@otos 384. </s> <s xml:id="echoid-s7857" xml:space="preserve">& </s> <s xml:id="echoid-s7858" xml:space="preserve">aliquando 383. </s> <s xml:id="echoid-s7859" xml:space="preserve">annis hiſce Lunarib. </s> <s xml:id="echoid-s7860" xml:space="preserve">vtebantur olim Hebræi, Græci; </s> <s xml:id="echoid-s7861" xml:space="preserve">nunc et<unsure/>iam Hebræi, Ara-<lb/>bes, Turcæ, Perſæ, ac Sinæ vtuntur, eoſque ita inſtitunt, vt cum ſolaribus annis congruere poſſint, ſolent <lb/>autem hi populi primam anni Lunam ſtatuere, quam nos Chriſtiani Lunam Paſchalem, ſeu Martij vocamus: <lb/></s> <s xml:id="echoid-s7862" xml:space="preserve">c<unsure/>a autem eſt cuius plenilunium propius eſt æquinoctio verno quod circa 21. </s> <s xml:id="echoid-s7863" xml:space="preserve">Martij contingit. </s> <s xml:id="echoid-s7864" xml:space="preserve">Vetuſtiſſimi <lb/>autem Aſtronomorum inquirentes anni lunaris cum ſolari congruentiam, primo annotarunt annum Lunæ <lb/>communem, cuius Lunæ alternatim conſtant diebus 30. </s> <s xml:id="echoid-s7865" xml:space="preserve">& </s> <s xml:id="echoid-s7866" xml:space="preserve">29. </s> <s xml:id="echoid-s7867" xml:space="preserve">continere dies 354. </s> <s xml:id="echoid-s7868" xml:space="preserve">ac propterea minorem <lb/>eſſe anno communi ſolari diebus 11. </s> <s xml:id="echoid-s7869" xml:space="preserve">is enim conſtat ex diebus præciſe 365. </s> <s xml:id="echoid-s7870" xml:space="preserve">vnde ſequi videbant vt nouilunia <lb/>ſequentis anni 11. </s> <s xml:id="echoid-s7871" xml:space="preserve">diebus prius contingerent, quàm in anno præcedenti; </s> <s xml:id="echoid-s7872" xml:space="preserve">hocque modo per annos 19. </s> <s xml:id="echoid-s7873" xml:space="preserve">noui-<lb/>lunia anticipare, donec iterum annis 19. </s> <s xml:id="echoid-s7874" xml:space="preserve">completis, eodem die, quo ante anno 19. </s> <s xml:id="echoid-s7875" xml:space="preserve">contingat nouiluminium. </s> <s xml:id="echoid-s7876" xml:space="preserve"><lb/>ratio huius eſt, quia omnes Lunæ, quæ in annis 19. </s> <s xml:id="echoid-s7877" xml:space="preserve">compręhenduntur tot dies continent quot anni ſolares <lb/>19. </s> <s xml:id="echoid-s7878" xml:space="preserve">anni vero 19. </s> <s xml:id="echoid-s7879" xml:space="preserve">ſolares continent dies 6939. </s> <s xml:id="echoid-s7880" xml:space="preserve">& </s> <s xml:id="echoid-s7881" xml:space="preserve">horas 18. </s> <s xml:id="echoid-s7882" xml:space="preserve">in ijſdem fiunt lunationes 235. </s> <s xml:id="echoid-s7883" xml:space="preserve">quæ dies exigunt <lb/>6,939. </s> <s xml:id="echoid-s7884" xml:space="preserve">horas 16 {1/2}. </s> <s xml:id="echoid-s7885" xml:space="preserve">vnde ſolaris periodus decemnouennalis ſuperat lunarem hora 1 {1/2}. </s> <s xml:id="echoid-s7886" xml:space="preserve">Hanc porrò lumi-<lb/>narium communem; </s> <s xml:id="echoid-s7887" xml:space="preserve">ac congruentem periodum, primus omnium Meton Athenienſis, ante Chriſti natiui-<lb/>t<unsure/>atem, annis circiter 431. </s> <s xml:id="echoid-s7888" xml:space="preserve">adinuenit: </s> <s xml:id="echoid-s7889" xml:space="preserve">ideoque annus magnus Metonicus appellatus eſt. </s> <s xml:id="echoid-s7890" xml:space="preserve">Et quomodo in hac <lb/>decemnouenali periodo lunationes 235. </s> <s xml:id="echoid-s7891" xml:space="preserve">æquantur annis ſolaribus 19. </s> <s xml:id="echoid-s7892" xml:space="preserve">ideo neceſſe eſt, vt in omnibus huiuſ-<lb/>modi periodis, nouilunia recurrant ijſdem diebus, quibus in prima contigerunt, v.</s> <s xml:id="echoid-s7893" xml:space="preserve">g. </s> <s xml:id="echoid-s7894" xml:space="preserve">ſi in primo anno perio-<lb/>di primæ nouilunia facta ſunt die ſecunda Ianuarij, & </s> <s xml:id="echoid-s7895" xml:space="preserve">prima Februarij, & </s> <s xml:id="echoid-s7896" xml:space="preserve">ſecunda Martij, & </s> <s xml:id="echoid-s7897" xml:space="preserve">prima Aprilis, <lb/>&</s> <s xml:id="echoid-s7898" xml:space="preserve">c. </s> <s xml:id="echoid-s7899" xml:space="preserve">Etiam in primo anno ſecundæ periodi ſient ijſdem diebus, ſecunda Ianuarij, prima Februarij, ſecunda <lb/>Martij, prima Aprilis, &</s> <s xml:id="echoid-s7900" xml:space="preserve">c. </s> <s xml:id="echoid-s7901" xml:space="preserve">ſic etiam anni ſecundi cuiuſuis periodi Metonicæ habebunt nouilunia ijſdẽ die-<lb/>bus. </s> <s xml:id="echoid-s7902" xml:space="preserve">fic quoque tertij anni, & </s> <s xml:id="echoid-s7903" xml:space="preserve">reliquorum vſque ad finem. </s> <s xml:id="echoid-s7904" xml:space="preserve">præterea quoniam Meton animaduert@t nouilu-<lb/>nia anticipare ſingulis annis, diebus 11. </s> <s xml:id="echoid-s7905" xml:space="preserve">ideo ſolerter excogitauit ex hac ſua decemnouenali periodo, nume-<lb/>rum hunc 19. </s> <s xml:id="echoid-s7906" xml:space="preserve">poſſe ſic in Calendario deſcribi, vt nouilunia indicet: </s> <s xml:id="echoid-s7907" xml:space="preserve">hac ratione, in primo anno ſcripſit 1. </s> <s xml:id="echoid-s7908" xml:space="preserve">in <lb/>ſingulis menſibus ad diem nouilunij. </s> <s xml:id="echoid-s7909" xml:space="preserve">in ſecundo anno poſuit 2. </s> <s xml:id="echoid-s7910" xml:space="preserve">diebus 11. </s> <s xml:id="echoid-s7911" xml:space="preserve">ante numerum 1. </s> <s xml:id="echoid-s7912" xml:space="preserve">præcedentis an-<lb/>ni, in ſingulis menſibus: </s> <s xml:id="echoid-s7913" xml:space="preserve">in 3. </s> <s xml:id="echoid-s7914" xml:space="preserve">anno poſuit 3. </s> <s xml:id="echoid-s7915" xml:space="preserve">eadem ratione. </s> <s xml:id="echoid-s7916" xml:space="preserve">idem fecit in 4. </s> <s xml:id="echoid-s7917" xml:space="preserve">& </s> <s xml:id="echoid-s7918" xml:space="preserve">reliquis vſque ad 19. </s> <s xml:id="echoid-s7919" xml:space="preserve">vltimum. </s> <s xml:id="echoid-s7920" xml:space="preserve"><lb/>deſcriptis fic numeris in Calendario, facilè erat cuique nouilunia præſcire, dummodo noſſet quiſnam laben-<lb/>tis anni numerus nouilunia indicaret. </s> <s xml:id="echoid-s7921" xml:space="preserve">Hic igitur numerus, quod aptiſſimus eſſet ad Lunarem cum Sole con-<lb/>gruentiam conſeruãdam, necnon ad nouilunia pręgnoſcenda, vtiliſſimas, ideo aureus numerus dictus eſt, au-<lb/>reiſque notis ſcribebatur, atque in foro præfigebatur, vt per eum populus non ſolum nouilunia, ſed etiam <lb/>ætatem ***, in promptu haberet. </s> <s xml:id="echoid-s7922" xml:space="preserve">currente aureo numero, v.</s> <s xml:id="echoid-s7923" xml:space="preserve">g. </s> <s xml:id="echoid-s7924" xml:space="preserve">4. </s> <s xml:id="echoid-s7925" xml:space="preserve">num. </s> <s xml:id="echoid-s7926" xml:space="preserve">4. </s> <s xml:id="echoid-s7927" xml:space="preserve">ſcribebatur aureo colore in publico <lb/>Calendario.</s> <s xml:id="echoid-s7928" xml:space="preserve"><unsure/> quare vbicumque erat aureus 4. </s> <s xml:id="echoid-s7929" xml:space="preserve">in Calendario ibi eo anno erant interlunia. </s> <s xml:id="echoid-s7930" xml:space="preserve">Vnde, & </s> <s xml:id="echoid-s7931" xml:space="preserve">plenilu-<lb/>nia, & </s> <s xml:id="echoid-s7932" xml:space="preserve">dies menſis lunaris, ſiue ætatẽ ***, facillimè cognoſcebant. </s> <s xml:id="echoid-s7933" xml:space="preserve">ſequenti anno currebat 5. </s> <s xml:id="echoid-s7934" xml:space="preserve">aureus; </s> <s xml:id="echoid-s7935" xml:space="preserve">& </s> <s xml:id="echoid-s7936" xml:space="preserve">ſic vſq; </s> <s xml:id="echoid-s7937" xml:space="preserve"><lb/>ad 19. </s> <s xml:id="echoid-s7938" xml:space="preserve">quo finito ad 1. </s> <s xml:id="echoid-s7939" xml:space="preserve">reuertebatur.</s> <s xml:id="echoid-s7940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7941" xml:space="preserve">Quoniam vero Luna in annis 19. </s> <s xml:id="echoid-s7942" xml:space="preserve">ſedes ſibi in Calendario conſtituta hora 1 {1/2}. </s> <s xml:id="echoid-s7943" xml:space="preserve">anteuertit, fit vt in 4. </s> <s xml:id="echoid-s7944" xml:space="preserve">annis <lb/>Metonicis decemnouenalibus, hoc eſt in annis 76. </s> <s xml:id="echoid-s7945" xml:space="preserve">Luna anticipet per horas 6. </s> <s xml:id="echoid-s7946" xml:space="preserve">quam annorum 76. </s> <s xml:id="echoid-s7947" xml:space="preserve">periodum <lb/>ab eius repertore Calippo, Calippicam dixere. </s> <s xml:id="echoid-s7948" xml:space="preserve">tandem compertum eſt Lunam in annis 312 {1/2}. </s> <s xml:id="echoid-s7949" xml:space="preserve">diem vnum <lb/>anticipare; </s> <s xml:id="echoid-s7950" xml:space="preserve">quamuis in annis tantum 304. </s> <s xml:id="echoid-s7951" xml:space="preserve">quæ ſunt quatuor periodi Calippicæ, id effici oporteret. </s> <s xml:id="echoid-s7952" xml:space="preserve">Hacte-<lb/>@us de periodis, ſeu Lunæ temporibus.</s> <s xml:id="echoid-s7953" xml:space="preserve"/> </p> <pb o="78" file="0100" n="104" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div162" type="section" level="1" n="101"> <head xml:id="echoid-head111" style="it" xml:space="preserve">De calculo Aſtronomico, & tabulis Aſtronomicis. Cap. XI.</head> <p> <s xml:id="echoid-s7954" xml:space="preserve">HAnc calculi appendicem ijs tantum ſcribimus, qui communium numerorum operationes vtcumq<unsure/>; </s> <s xml:id="echoid-s7955" xml:space="preserve">te-<lb/>nent: </s> <s xml:id="echoid-s7956" xml:space="preserve">imo ijs etiam, quibus per otium liceat Aſtronomiæ operam nauare, quare ſi cui libucrit hanc cal-<lb/>culi appendicem non ſolum in Luna, ſed in cæteris quoque planetis omittere, is nihilominus cætera omnia <lb/>æquè bene intelligere poterit.</s> <s xml:id="echoid-s7957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7958" xml:space="preserve">Scopus igitur calculi, eſt inuenire loca vera planetarum in Zodiaco, ad quodlibet temporis momentum, <lb/>abſque vlla inſpectione, aut organica obſeruatione in cælum, ſed ſolum per Tabulas aſtronomicas. </s> <s xml:id="echoid-s7959" xml:space="preserve">inquirũt <lb/>autem primo reſpectu alicuius certi meridiani; </s> <s xml:id="echoid-s7960" xml:space="preserve">ſecundo etiam reſpectu omnium meridianorum, ac proinde <lb/>omnium terræ locorum.</s> <s xml:id="echoid-s7961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7962" xml:space="preserve">Sunt autem duo genera Tabularum. </s> <s xml:id="echoid-s7963" xml:space="preserve">aliæ enim exhibent motus medios, & </s> <s xml:id="echoid-s7964" xml:space="preserve">dicuntur Tabulæ mediorum <lb/>motuum, quos ſupra expoſui. </s> <s xml:id="echoid-s7965" xml:space="preserve">aliæ dicuntur Tabula æquationum, quæ nobis exhibent differentias, quibus ad <lb/>datum tempus, v.</s> <s xml:id="echoid-s7966" xml:space="preserve">g. </s> <s xml:id="echoid-s7967" xml:space="preserve">nunc, medij motus iam inuenti diſcrepant à<unsure/> veris. </s> <s xml:id="echoid-s7968" xml:space="preserve">Æquationes autẽ hæ ſunt arcus ecly-<lb/>pticæ intercepti inter lineam medij motus, & </s> <s xml:id="echoid-s7969" xml:space="preserve">lineam veri motus planetę. </s> <s xml:id="echoid-s7970" xml:space="preserve">vt in figura poſita in cap. </s> <s xml:id="echoid-s7971" xml:space="preserve">de motu <lb/>***. </s> <s xml:id="echoid-s7972" xml:space="preserve">medius motus numeratus ab initio ♈. </s> <s xml:id="echoid-s7973" xml:space="preserve">vſque ad 25. </s> <s xml:id="echoid-s7974" xml:space="preserve">grad. </s> <s xml:id="echoid-s7975" xml:space="preserve">Scorpij, vbi eſt linea A N. </s> <s xml:id="echoid-s7976" xml:space="preserve">medij motus, verus <lb/>autem motus vſque ad lineam A N. </s> <s xml:id="echoid-s7977" xml:space="preserve">veri motus. </s> <s xml:id="echoid-s7978" xml:space="preserve">arcus igitur N M. </s> <s xml:id="echoid-s7979" xml:space="preserve">eſt æquatio; </s> <s xml:id="echoid-s7980" xml:space="preserve">tot igitur gradus continet <lb/>æquatio, quot ſunt in arcu N M. </s> <s xml:id="echoid-s7981" xml:space="preserve">hæc modo additur medio motui, modò demitur, vt verus locus habeatur; <lb/></s> <s xml:id="echoid-s7982" xml:space="preserve">vt propterea Proſthaphereſis a Græcis dicatur. </s> <s xml:id="echoid-s7983" xml:space="preserve">in caſu figuræ, æquatio N M. </s> <s xml:id="echoid-s7984" xml:space="preserve">eſſet demenda a medio mo-<lb/>tu, qui numeratur ab initio ♈. </s> <s xml:id="echoid-s7985" xml:space="preserve">vſque ad 25. </s> <s xml:id="echoid-s7986" xml:space="preserve">grad. </s> <s xml:id="echoid-s7987" xml:space="preserve">Scorpij. </s> <s xml:id="echoid-s7988" xml:space="preserve">quæ æquatio ſi ſit v.</s> <s xml:id="echoid-s7989" xml:space="preserve">g. </s> <s xml:id="echoid-s7990" xml:space="preserve">grad. </s> <s xml:id="echoid-s7991" xml:space="preserve">7. </s> <s xml:id="echoid-s7992" xml:space="preserve">& </s> <s xml:id="echoid-s7993" xml:space="preserve">auferatur à medio <lb/>motu, remanet verus motus Lunæ in gr. </s> <s xml:id="echoid-s7994" xml:space="preserve">18. </s> <s xml:id="echoid-s7995" xml:space="preserve">Scorpij. </s> <s xml:id="echoid-s7996" xml:space="preserve">addenda eſſet, ſi Luna eſſet in parte epicycli ſiniſtra, <lb/>vti ſub L. </s> <s xml:id="echoid-s7997" xml:space="preserve">@aliquando linea veri motus coincidit cum linea medij, tuncque nulla eſt æquatio. </s> <s xml:id="echoid-s7998" xml:space="preserve">Tandem ex Ta-<lb/>bulis medij motus, & </s> <s xml:id="echoid-s7999" xml:space="preserve">æquationum, conſtruuntur Ephemerides, quæ ſunt Tabulæ verorum motuum ad plu-<lb/>res annos.</s> <s xml:id="echoid-s8000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8001" xml:space="preserve">Tertio neceſſe eſt angulorum mediorũ motuum radices aliquas ſtatuere, ideſt, certo proponere in prin-<lb/>cipio alicuius celebris Chronologiæ, quantus fuerit ille medius motus v.</s> <s xml:id="echoid-s8002" xml:space="preserve">g. </s> <s xml:id="echoid-s8003" xml:space="preserve">initio annorum Chriſti, vel Vr-<lb/>bis conditæ, vel primæ Olimpiadis, quantus fuerit medius motus longitudinis Lunæ, ideſt, quantum diſti-<lb/>terit ab æquinoctio, ſeu in quo grad. </s> <s xml:id="echoid-s8004" xml:space="preserve">Zodi@ci fuerit. </s> <s xml:id="echoid-s8005" xml:space="preserve">Ego autem breuitatis cauſa, ponam radices mediorum <lb/>motum ad annum Domini 1600. </s> <s xml:id="echoid-s8006" xml:space="preserve">completum, ſiue ad initium anni 1601. </s> <s xml:id="echoid-s8007" xml:space="preserve">intelligo autem annum 1600. </s> <s xml:id="echoid-s8008" xml:space="preserve">com-<lb/>pleri in meridie vltimi diei qui eſt 31. </s> <s xml:id="echoid-s8009" xml:space="preserve">Decembris, ideſt in meridie peridie Kalen. </s> <s xml:id="echoid-s8010" xml:space="preserve">Ianuarij; </s> <s xml:id="echoid-s8011" xml:space="preserve">& </s> <s xml:id="echoid-s8012" xml:space="preserve">conſequenter <lb/>incipere eodem momento annum ſequ. </s> <s xml:id="echoid-s8013" xml:space="preserve">1601. </s> <s xml:id="echoid-s8014" xml:space="preserve">omnes pariter dies a meridie in meridiem abſoluuntur. </s> <s xml:id="echoid-s8015" xml:space="preserve">præfi-<lb/>gunt autem huiuſmodi radices hoc modo. </s> <s xml:id="echoid-s8016" xml:space="preserve">primo ad certum aliquod inſtans temporis, v. </s> <s xml:id="echoid-s8017" xml:space="preserve">g. </s> <s xml:id="echoid-s8018" xml:space="preserve">hodie in meridie <lb/>partim ex obſeruatione, partim ex ſubtili argument. </s> <s xml:id="echoid-s8019" xml:space="preserve">motum medium, v.</s> <s xml:id="echoid-s8020" xml:space="preserve">g. </s> <s xml:id="echoid-s8021" xml:space="preserve">longitudinis Lunæ habent explo-<lb/>ratum, quod maximè per eclypſes aſſequuntur; </s> <s xml:id="echoid-s8022" xml:space="preserve">nam ſi Luna ſit in Apogæo, aut Perigæo epicy. </s> <s xml:id="echoid-s8023" xml:space="preserve">ſciunt certo <lb/>æqualem motum coincidere cum vero, & </s> <s xml:id="echoid-s8024" xml:space="preserve">apparente: </s> <s xml:id="echoid-s8025" xml:space="preserve">cognito igitur motu medio longitudinis Lunæ hodie, <lb/>quæ eſt dies 19. </s> <s xml:id="echoid-s8026" xml:space="preserve">Iulij an. </s> <s xml:id="echoid-s8027" xml:space="preserve">1616. </s> <s xml:id="echoid-s8028" xml:space="preserve">iam ſi voluero figere radicem eius ad finem an. </s> <s xml:id="echoid-s8029" xml:space="preserve">1600. </s> <s xml:id="echoid-s8030" xml:space="preserve">debeo per calculum ex-<lb/>plorare, quantum in toto tempore elapſo ab an. </s> <s xml:id="echoid-s8031" xml:space="preserve">1600. </s> <s xml:id="echoid-s8032" xml:space="preserve">vſq; </s> <s xml:id="echoid-s8033" xml:space="preserve">ad præſens inſtans, Luna prædicto motu profece-<lb/>rit; </s> <s xml:id="echoid-s8034" xml:space="preserve">totumq; </s> <s xml:id="echoid-s8035" xml:space="preserve">hunc motum detrahere a motu huius diei v.</s> <s xml:id="echoid-s8036" xml:space="preserve">g. </s> <s xml:id="echoid-s8037" xml:space="preserve">ſit hodie Luna in principio ♎, motus autem tem-<lb/>poris elapſi an. </s> <s xml:id="echoid-s8038" xml:space="preserve">15. </s> <s xml:id="echoid-s8039" xml:space="preserve">& </s> <s xml:id="echoid-s8040" xml:space="preserve">menſium aliquot, &</s> <s xml:id="echoid-s8041" xml:space="preserve">c. </s> <s xml:id="echoid-s8042" xml:space="preserve">detrahatur à motu medio longitudinis, qui eſt gr. </s> <s xml:id="echoid-s8043" xml:space="preserve">180. </s> <s xml:id="echoid-s8044" xml:space="preserve">quia hic <lb/>motus numeratur ab ♈, ſeu ab æquinoctio Verno vſq; </s> <s xml:id="echoid-s8045" xml:space="preserve">ad initium ♎, per hanc enim detractionem retroce-<lb/>demus, ac quaſi Lunã faciemus retrogradam, vnde videamus vbinam extiterit in fine an. </s> <s xml:id="echoid-s8046" xml:space="preserve">1600. </s> <s xml:id="echoid-s8047" xml:space="preserve">Exemplum <lb/>facile, Luna hodie eſt in principio ♎, in meridie, volo figere rad. </s> <s xml:id="echoid-s8048" xml:space="preserve">eius ad diem 10. </s> <s xml:id="echoid-s8049" xml:space="preserve">huius menſis: </s> <s xml:id="echoid-s8050" xml:space="preserve">per calcu-<lb/>lum igitur retro Lunam agendo, inuenio eam hiſce 10. </s> <s xml:id="echoid-s8051" xml:space="preserve">diebus, peragraſſe gr. </s> <s xml:id="echoid-s8052" xml:space="preserve">109. </s> <s xml:id="echoid-s8053" xml:space="preserve">quibus ablatis à<unsure/> 180. </s> <s xml:id="echoid-s8054" xml:space="preserve">rema-<lb/>nent 71. </s> <s xml:id="echoid-s8055" xml:space="preserve">Ergo Luna die 10. </s> <s xml:id="echoid-s8056" xml:space="preserve">in meridie diſtabat ab initio ♈ gr. </s> <s xml:id="echoid-s8057" xml:space="preserve">71. </s> <s xml:id="echoid-s8058" xml:space="preserve">hoc eſt, erat in gr. </s> <s xml:id="echoid-s8059" xml:space="preserve">11. </s> <s xml:id="echoid-s8060" xml:space="preserve">Geminorum gradus<unsure/> <lb/>igitur 71. </s> <s xml:id="echoid-s8061" xml:space="preserve">eſt radix longitudinis ***. </s> <s xml:id="echoid-s8062" xml:space="preserve">ad diem 10. </s> <s xml:id="echoid-s8063" xml:space="preserve">Iulij 1616. </s> <s xml:id="echoid-s8064" xml:space="preserve">ſi figenda eſſet radix ad annum aliquem ſequen-<lb/>tem, motus Lunæ peractus in toto interuallo eſſet addendus motui præſentis diei 19. </s> <s xml:id="echoid-s8065" xml:space="preserve">ſic enim per calculum <lb/>manifeſtus ſit locus Lunæ medius in futuro anno, v. </s> <s xml:id="echoid-s8066" xml:space="preserve">g. </s> <s xml:id="echoid-s8067" xml:space="preserve">in fine anni 1620.</s> <s xml:id="echoid-s8068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8069" xml:space="preserve">4 Sicuti omnes calculi incipiunt ab aliqua radice, ſic etiã reſpiciunt primo aliquem certum, ac præfixum <lb/>meridianum, ideſt, ſecundum dies, horas, menſes, & </s> <s xml:id="echoid-s8070" xml:space="preserve">annos, quibus vtuntur ij, qui degunt ſub illo meridia-<lb/>no, fiunt calculationes motuum cęleſtium; </s> <s xml:id="echoid-s8071" xml:space="preserve">ideſt, exhibent motus planetarum ſecundum dies relatos ad illum <lb/>meridianum: </s> <s xml:id="echoid-s8072" xml:space="preserve">ſecundum enim prædicta@tempora præfixæ ſunt radices, de quibus antea: </s> <s xml:id="echoid-s8073" xml:space="preserve">nos itaque vtimur <lb/>diebus relatis ad meridianum Venetum, reſpectu cuius etiam radices conditæ ſunt, v.</s> <s xml:id="echoid-s8074" xml:space="preserve">g. </s> <s xml:id="echoid-s8075" xml:space="preserve">anni 1600. </s> <s xml:id="echoid-s8076" xml:space="preserve">incipien-<lb/>tis à meridiano Veneto, tantus erat motus longitudinis Lunæ, vt poſtea dicetur. </s> <s xml:id="echoid-s8077" xml:space="preserve">facta deinde calculatione <lb/>ad præfixum hunc meridianum, transferunt eam facile ad alios meridianos, quorum nota ſit longitudo re-<lb/>ſpectu primarij meridiani. </s> <s xml:id="echoid-s8078" xml:space="preserve">transfertur autem per operationem quam dicunt æquationem meridianorum. <lb/></s> <s xml:id="echoid-s8079" xml:space="preserve">quare hoc modo cognoſci poſſunt loca planetarum, & </s> <s xml:id="echoid-s8080" xml:space="preserve">aſpectus eorum; </s> <s xml:id="echoid-s8081" xml:space="preserve">& </s> <s xml:id="echoid-s8082" xml:space="preserve">eclypſes, qua hora ſint futuræ, nõ <lb/>ſolum reſpectu meridie<unsure/>i illi primarij, ſed reſpectu omnium, ac totius terræ. </s> <s xml:id="echoid-s8083" xml:space="preserve">quamuis enim vno, eodemq; </s> <s xml:id="echoid-s8084" xml:space="preserve">tem <lb/>poris momento hæc contingant, reſpectu tamen variorum meridianorum, non fiunt eadem hora denomi-<lb/>nata a varijs meridianis, v.</s> <s xml:id="echoid-s8085" xml:space="preserve">g. </s> <s xml:id="echoid-s8086" xml:space="preserve">quod fit in meridie Venetorũ, fit poſt meridiẽ, & </s> <s xml:id="echoid-s8087" xml:space="preserve">proinde tardius reſpectu ma-<lb/>gis orientalium; </s> <s xml:id="echoid-s8088" xml:space="preserve">ante meridiem autem idem contingit magis oecidentalibus. </s> <s xml:id="echoid-s8089" xml:space="preserve">cuius cauſa eſt motus Solis ſuc-<lb/>ceſſiuus circa terram, quo prius apparet orientalibus, deinde nobis, poſtea occidentalibus: </s> <s xml:id="echoid-s8090" xml:space="preserve">quare ſicuti non <lb/>eadem hora omnibus oritur, nec occidit, nec meridiatur; </s> <s xml:id="echoid-s8091" xml:space="preserve">ſic cætera, quæ in cælo fiunt diuerſis horis ſub <lb/>diuerſis terræ meridianis ſpectantur.</s> <s xml:id="echoid-s8092" xml:space="preserve"/> </p> <pb o="79" file="0101" n="105" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div163" type="section" level="1" n="102"> <head xml:id="echoid-head112" style="it" xml:space="preserve">Explicatio ſex ſequentium Tabular. Aſtronom. Lunæ, & primò de prima Tabula <lb/>Horarum, & minutorum. Cap. XII.</head> <p> <s xml:id="echoid-s8093" xml:space="preserve">SEd iam tempus eſt Tabulas ipſas mediorum motuũ exponere, ac breniter explicare. </s> <s xml:id="echoid-s8094" xml:space="preserve">eas igitur ſimul om-<lb/>nes commoditatis cauſa exponemus, quæ ſunt ſex ſequentes poſt præſentem earum explicationem; </s> <s xml:id="echoid-s8095" xml:space="preserve">qua-<lb/>rum. </s> <s xml:id="echoid-s8096" xml:space="preserve">prima ſit ea, quæ continet tres motus medios, in horis, & </s> <s xml:id="echoid-s8097" xml:space="preserve">min. </s> <s xml:id="echoid-s8098" xml:space="preserve">horarum in ea ſunt tres columnæ, prima <lb/>dicata eſt motui horario longitudinis @, ab æquinoctio. </s> <s xml:id="echoid-s8099" xml:space="preserve">2. </s> <s xml:id="echoid-s8100" xml:space="preserve">motui anomaliæ. </s> <s xml:id="echoid-s8101" xml:space="preserve">3. </s> <s xml:id="echoid-s8102" xml:space="preserve">☊, nodi borealis motui. </s> <s xml:id="echoid-s8103" xml:space="preserve">pri-<lb/>ma columna habet quatuor ordines, ſeu ſeries. </s> <s xml:id="echoid-s8104" xml:space="preserve">prima ſeries habet numeros horarum ſingularum vſque ad 30. <lb/></s> <s xml:id="echoid-s8105" xml:space="preserve">qui numeri accipiuntur aliquando tanquam minuta; </s> <s xml:id="echoid-s8106" xml:space="preserve">& </s> <s xml:id="echoid-s8107" xml:space="preserve">ideo in eadem ſerie in principio, poſitum eſt vtrum-<lb/>que vocabulum (horæ, minuta) hæc prima ſeries inſeruit, etiam reliquis duabus columnis. </s> <s xml:id="echoid-s8108" xml:space="preserve">omnes pręterea <lb/>columnæ habent 30. </s> <s xml:id="echoid-s8109" xml:space="preserve">verſus in primo verſu ſunt S. </s> <s xml:id="echoid-s8110" xml:space="preserve">G. </s> <s xml:id="echoid-s8111" xml:space="preserve">hoceſt ſigna, gradus, minuta in 2. </s> <s xml:id="echoid-s8112" xml:space="preserve">verſu ſunt Gra. </s> <s xml:id="echoid-s8113" xml:space="preserve">1. </s> <s xml:id="echoid-s8114" xml:space="preserve">11. </s> <s xml:id="echoid-s8115" xml:space="preserve"><lb/>hoc eſt gradus, minuta, ſecunda; </s> <s xml:id="echoid-s8116" xml:space="preserve">quæ vſum habent quando numeri primæ ſeriei ſumuntur tanquam minuta. </s> <s xml:id="echoid-s8117" xml:space="preserve"><lb/>in reliquis 32. </s> <s xml:id="echoid-s8118" xml:space="preserve">verſibus, ſunt numeri ſignorum graduum, min. </s> <s xml:id="echoid-s8119" xml:space="preserve">& </s> <s xml:id="echoid-s8120" xml:space="preserve">ſec. </s> <s xml:id="echoid-s8121" xml:space="preserve">reſpondentes ſingulis horis, aut minu-<lb/>tis primæ ſeriei, prout ſunt in eorum directum: </s> <s xml:id="echoid-s8122" xml:space="preserve">qui numeri ſunt numeri mediorum motuum in proprijs co-<lb/>lumnis. </s> <s xml:id="echoid-s8123" xml:space="preserve">Conſtructio huius tabulæ fit hoc modo. </s> <s xml:id="echoid-s8124" xml:space="preserve">inuento vti ſupra dictum eſt motu diario. </s> <s xml:id="echoid-s8125" xml:space="preserve">v. </s> <s xml:id="echoid-s8126" xml:space="preserve">gr. </s> <s xml:id="echoid-s8127" xml:space="preserve">longitudi-<lb/>nis Lunæ, aut anomaliæ, eum diuidunt in partes 24. </s> <s xml:id="echoid-s8128" xml:space="preserve">quare pars illa 24. </s> <s xml:id="echoid-s8129" xml:space="preserve">eſt motus horarius. </s> <s xml:id="echoid-s8130" xml:space="preserve">hunc ſcribunt è <lb/>regione horæ vnius, ſiue in 3. </s> <s xml:id="echoid-s8131" xml:space="preserve">verſu; </s> <s xml:id="echoid-s8132" xml:space="preserve">ſic motus horarius longitudinis ſiue vnius horæ eſt, Si.</s> <s xml:id="echoid-s8133" xml:space="preserve">o.</s> <s xml:id="echoid-s8134" xml:space="preserve">Gr.</s> <s xml:id="echoid-s8135" xml:space="preserve">o. </s> <s xml:id="echoid-s8136" xml:space="preserve">331 hora-<lb/>rius anomaliæ eſt. </s> <s xml:id="echoid-s8137" xml:space="preserve">Sig o. </s> <s xml:id="echoid-s8138" xml:space="preserve">Gra. </s> <s xml:id="echoid-s8139" xml:space="preserve">32′. </s> <s xml:id="echoid-s8140" xml:space="preserve">&</s> <s xml:id="echoid-s8141" xml:space="preserve">c. </s> <s xml:id="echoid-s8142" xml:space="preserve">hunc motum horarium duplicant, eumque ſcribuntè regione dua-<lb/>rum horarum. </s> <s xml:id="echoid-s8143" xml:space="preserve">triplicant pro tribus horis, & </s> <s xml:id="echoid-s8144" xml:space="preserve">ſic deinceps, donec confletur motus 24. </s> <s xml:id="echoid-s8145" xml:space="preserve">horar. </s> <s xml:id="echoid-s8146" xml:space="preserve">ideſt vnius diei. </s> <s xml:id="echoid-s8147" xml:space="preserve"><lb/>Porro ijdem numeri motuum reſpõdent etiam minutis horarum, quatenus ſubſtant his characteribus G.</s> <s xml:id="echoid-s8148" xml:space="preserve">′.</s> <s xml:id="echoid-s8149" xml:space="preserve">″. </s> <s xml:id="echoid-s8150" xml:space="preserve"><lb/>è regione vocabuli min. </s> <s xml:id="echoid-s8151" xml:space="preserve">& </s> <s xml:id="echoid-s8152" xml:space="preserve">2. </s> <s xml:id="echoid-s8153" xml:space="preserve">verſu ſcriptis; </s> <s xml:id="echoid-s8154" xml:space="preserve">quia quatenus afficiuntur iſtis characteribus, fiunt ſexageſimæ <lb/>ſui ipſarum exiſtentium ſub charact. </s> <s xml:id="echoid-s8155" xml:space="preserve">prioris verſus, ideſt, qui erant gradus, fiunt minuta: </s> <s xml:id="echoid-s8156" xml:space="preserve">& </s> <s xml:id="echoid-s8157" xml:space="preserve">quæ minuta, fiunt <lb/>″. </s> <s xml:id="echoid-s8158" xml:space="preserve">pariter min. </s> <s xml:id="echoid-s8159" xml:space="preserve">horarum ſunt ſexageſimæ horarum; </s> <s xml:id="echoid-s8160" xml:space="preserve">quapropter vt ſe habent horæ ad min. </s> <s xml:id="echoid-s8161" xml:space="preserve">ſic ijdem numeri <lb/>ſub primis characteribus, ad ſe ipſos ſub ſecundis characteribus.</s> <s xml:id="echoid-s8162" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div164" type="section" level="1" n="103"> <head xml:id="echoid-head113" style="it" xml:space="preserve">De ſecunda Tabula dierum.</head> <p> <s xml:id="echoid-s8163" xml:space="preserve">QVæcumque dicta ſunt de prima Tabula, applicari debent etiam reliquis. </s> <s xml:id="echoid-s8164" xml:space="preserve">hæc autem ſecunda continet <lb/>eoſdem motus medios diarios, quos prima horarios habet in prima ſerie ſunt dies 31. </s> <s xml:id="echoid-s8165" xml:space="preserve">quorum ſingu-<lb/>lis in directum reſpondent motus trium columnarum. </s> <s xml:id="echoid-s8166" xml:space="preserve">Et conſtructa eſt prædicta methodo, motus <lb/>enim diurni ſibi ipſis additi ſunt à primo die, vſq; </s> <s xml:id="echoid-s8167" xml:space="preserve">ad vltimum, vt conflentur motus menſtrui. </s> <s xml:id="echoid-s8168" xml:space="preserve">hi autem dies <lb/>incipiunt a meridie, & </s> <s xml:id="echoid-s8169" xml:space="preserve">in meridie deſinunt, vt ſupra dixi & </s> <s xml:id="echoid-s8170" xml:space="preserve">infra de radicibus dicam.</s> <s xml:id="echoid-s8171" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div165" type="section" level="1" n="104"> <head xml:id="echoid-head114" style="it" xml:space="preserve">De tertia Tabula menſium.</head> <p> <s xml:id="echoid-s8172" xml:space="preserve">COntinet hæc eoſdem motus medios, ſed menſtruos, ideſt, quos Luna efficit ſpacijs menſtruis. </s> <s xml:id="echoid-s8173" xml:space="preserve">conſtrui-<lb/>tur autem hæc ex tabula dierum; </s> <s xml:id="echoid-s8174" xml:space="preserve">ſic vides lanuarium habere motũ longit. </s> <s xml:id="echoid-s8175" xml:space="preserve">ſig. </s> <s xml:id="echoid-s8176" xml:space="preserve">1. </s> <s xml:id="echoid-s8177" xml:space="preserve">gr. </s> <s xml:id="echoid-s8178" xml:space="preserve">18. </s> <s xml:id="echoid-s8179" xml:space="preserve">28′. </s> <s xml:id="echoid-s8180" xml:space="preserve">qui eſt idem, <lb/>ad dierum 31. </s> <s xml:id="echoid-s8181" xml:space="preserve">Februarius habet motum qui debetur diebus 29. </s> <s xml:id="echoid-s8182" xml:space="preserve">& </s> <s xml:id="echoid-s8183" xml:space="preserve">ſic reliqui numeri reſpondent vltimo diei <lb/>menſis; </s> <s xml:id="echoid-s8184" xml:space="preserve">ita vt numerus vltimus è regione Decembris, ſit motus vnius anni. </s> <s xml:id="echoid-s8185" xml:space="preserve">eſt autẽ tabula diuiſa in duas par-<lb/>tes, in prima ſunt menſes anni communis. </s> <s xml:id="echoid-s8186" xml:space="preserve">in ſecunda menſes anni Biſſextilis. </s> <s xml:id="echoid-s8187" xml:space="preserve">reliqua ſolertiæ lectoris relin-<lb/>quuntur. </s> <s xml:id="echoid-s8188" xml:space="preserve">De Biſſexto agam in anno ſolari.</s> <s xml:id="echoid-s8189" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div166" type="section" level="1" n="105"> <head xml:id="echoid-head115" style="it" xml:space="preserve">De quarta Tabula Annorum.</head> <p> <s xml:id="echoid-s8190" xml:space="preserve">HÆc diuiſa eſt in tres partes, vt ex titulis eius conſtat. </s> <s xml:id="echoid-s8191" xml:space="preserve">in prima ſunt motus debiti ſingulis annis vſque ad <lb/>20. </s> <s xml:id="echoid-s8192" xml:space="preserve">quorum quartus quiſque eſt Biſſextilis, vt indicat littera B. </s> <s xml:id="echoid-s8193" xml:space="preserve">illis præſcripta. </s> <s xml:id="echoid-s8194" xml:space="preserve">in ſecunda ſunt anni ag-<lb/>gregati. </s> <s xml:id="echoid-s8195" xml:space="preserve">Primo per annorum vicenas, vſque ad 100. </s> <s xml:id="echoid-s8196" xml:space="preserve">deinde per annorum centurias vſque ad 1000. </s> <s xml:id="echoid-s8197" xml:space="preserve">ex his enim <lb/>omnibus, omnes anni ſuppleri poſſunt. </s> <s xml:id="echoid-s8198" xml:space="preserve">Cõſtructio eius pendet ex tabula menſium; </s> <s xml:id="echoid-s8199" xml:space="preserve">ſic vides è regione primi <lb/>anni qui eſt communis, ſcrptum eſſe motum annuum qui vltimo diei Decembris anni pariter adſcriptus eſt, <lb/>ſcilicet ſig. </s> <s xml:id="echoid-s8200" xml:space="preserve">4. </s> <s xml:id="echoid-s8201" xml:space="preserve">gr. </s> <s xml:id="echoid-s8202" xml:space="preserve">9. </s> <s xml:id="echoid-s8203" xml:space="preserve">23′. </s> <s xml:id="echoid-s8204" xml:space="preserve">pro longitudine, ſed pro Anomalia ſig. </s> <s xml:id="echoid-s8205" xml:space="preserve">2. </s> <s xml:id="echoid-s8206" xml:space="preserve">gr. </s> <s xml:id="echoid-s8207" xml:space="preserve">28. </s> <s xml:id="echoid-s8208" xml:space="preserve">43′. </s> <s xml:id="echoid-s8209" xml:space="preserve">tandẽ pro Nodo ſig. </s> <s xml:id="echoid-s8210" xml:space="preserve">o. </s> <s xml:id="echoid-s8211" xml:space="preserve">gr. </s> <s xml:id="echoid-s8212" xml:space="preserve">19. </s> <s xml:id="echoid-s8213" xml:space="preserve">20′. </s> <s xml:id="echoid-s8214" xml:space="preserve">in <lb/>tertia ſunt radices prædictorum motuum ad an. </s> <s xml:id="echoid-s8215" xml:space="preserve">Chriſti 1600. </s> <s xml:id="echoid-s8216" xml:space="preserve">quæ nihil aliud ſunt quam prædicti motus me-<lb/>dij, in fine illius ſæculi definiti, ac præfixi; </s> <s xml:id="echoid-s8217" xml:space="preserve">vt ab illis, tanquam à radicibus. </s> <s xml:id="echoid-s8218" xml:space="preserve">motus ſucce-<lb/> <anchor type="note" xlink:label="note-0101-01a" xlink:href="note-0101-01"/> dentium temporũ deriuari queant. </s> <s xml:id="echoid-s8219" xml:space="preserve">Tabulæ enim medij motus oſtendunt quantitates mo-<lb/>tuum reſpondentes temporibus indefinitis, & </s> <s xml:id="echoid-s8220" xml:space="preserve">indeterminatis v.</s> <s xml:id="echoid-s8221" xml:space="preserve">g. </s> <s xml:id="echoid-s8222" xml:space="preserve">oſtendunt motum ano-<lb/>maliæ reſpondentem annis centum indefinitis. </s> <s xml:id="echoid-s8223" xml:space="preserve">ſi vero anni 100. </s> <s xml:id="echoid-s8224" xml:space="preserve">ſumantur cum ſuo motu <lb/>Anomaliæ, qui eſt fig. </s> <s xml:id="echoid-s8225" xml:space="preserve">6. </s> <s xml:id="echoid-s8226" xml:space="preserve">gr. </s> <s xml:id="echoid-s8227" xml:space="preserve">18.</s> <s xml:id="echoid-s8228" xml:space="preserve">30′. </s> <s xml:id="echoid-s8229" xml:space="preserve">ita vt hoc tẽpus ſequatur poſt an. </s> <s xml:id="echoid-s8230" xml:space="preserve">1600. </s> <s xml:id="echoid-s8231" xml:space="preserve">vt efficiantur an. <lb/></s> <s xml:id="echoid-s8232" xml:space="preserve">1700. </s> <s xml:id="echoid-s8233" xml:space="preserve">& </s> <s xml:id="echoid-s8234" xml:space="preserve">pariter motus horum 100. </s> <s xml:id="echoid-s8235" xml:space="preserve">an. </s> <s xml:id="echoid-s8236" xml:space="preserve">ſequatur, & </s> <s xml:id="echoid-s8237" xml:space="preserve">quaſi oriatur à radice eiuſdẽ Anomaliæ, <lb/>quæ eſt ſig. </s> <s xml:id="echoid-s8238" xml:space="preserve">o. </s> <s xml:id="echoid-s8239" xml:space="preserve">gr. </s> <s xml:id="echoid-s8240" xml:space="preserve">6. </s> <s xml:id="echoid-s8241" xml:space="preserve">40′. </s> <s xml:id="echoid-s8242" xml:space="preserve">conflabitur motus medius Anom. </s> <s xml:id="echoid-s8243" xml:space="preserve">qui debetur an. </s> <s xml:id="echoid-s8244" xml:space="preserve">Chriſti completo <lb/>1700. </s> <s xml:id="echoid-s8245" xml:space="preserve">hic autem erit ſig. </s> <s xml:id="echoid-s8246" xml:space="preserve">6. </s> <s xml:id="echoid-s8247" xml:space="preserve">gr. </s> <s xml:id="echoid-s8248" xml:space="preserve">25. </s> <s xml:id="echoid-s8249" xml:space="preserve">10′. </s> <s xml:id="echoid-s8250" xml:space="preserve">ideſt Luna effecerit in periphetia epicy. </s> <s xml:id="echoid-s8251" xml:space="preserve">incipiendo ab <lb/>Apogeo 6. </s> <s xml:id="echoid-s8252" xml:space="preserve">ſigna, & </s> <s xml:id="echoid-s8253" xml:space="preserve">25. </s> <s xml:id="echoid-s8254" xml:space="preserve">gradus & </s> <s xml:id="echoid-s8255" xml:space="preserve">10′. </s> <s xml:id="echoid-s8256" xml:space="preserve">quare tranſactum erit perigęum per gr. </s> <s xml:id="echoid-s8257" xml:space="preserve">25. </s> <s xml:id="echoid-s8258" xml:space="preserve">10′. </s> <s xml:id="echoid-s8259" xml:space="preserve">vides igitur qua ratione <lb/>rempora, & </s> <s xml:id="echoid-s8260" xml:space="preserve">motus indefinita beneficio radicum deſini<unsure/>antur, ac determinentur.</s> <s xml:id="echoid-s8261" xml:space="preserve"/> </p> <div xml:id="echoid-div166" type="float" level="2" n="1"> <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve"> <lb/>### Sig. grad. <lb/>6. # 18. # 30. <lb/>0. # 6. # 40. <lb/>6. # 25. # 10. <lb/>## Anoma. media\\ an. 1700. cõpleti <lb/></note> </div> <pb o="78" file="0102" n="106" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div168" type="section" level="1" n="106"> <head xml:id="echoid-head116" style="it" xml:space="preserve">De quinta Tabula Aequationum Lunæ.</head> <p> <s xml:id="echoid-s8262" xml:space="preserve">HVius tabulæ titulus maximè conſiderandus eſt; </s> <s xml:id="echoid-s8263" xml:space="preserve">is enim nos admonet hanc tabulam non exhibere iuſtas <lb/>æquationes, niſi in nouilunijs, ac plenilunijs medijs, quod factum eſt, quoniam id plurimi refert in <lb/>prædicendis eclypſibus, quæ omnes in nouil. </s> <s xml:id="echoid-s8264" xml:space="preserve">aut plenil contingunt. </s> <s xml:id="echoid-s8265" xml:space="preserve">Porro ſciendum eſt has æquationes mi-<lb/>nores eſſe cæteris æquationibus, quæ extra nouiluna aut pleniluna contingunt. </s> <s xml:id="echoid-s8266" xml:space="preserve">adeo vtin Quadraturis ali-<lb/>quando æquationes maiores ſint noſtris æquation bus per gradus 2.</s> <s xml:id="echoid-s8267" xml:space="preserve">44′. </s> <s xml:id="echoid-s8268" xml:space="preserve">maxima enim æquatio aliquando ad <lb/>7. </s> <s xml:id="echoid-s8269" xml:space="preserve">gra. </s> <s xml:id="echoid-s8270" xml:space="preserve">cum dimidio excreſcit. </s> <s xml:id="echoid-s8271" xml:space="preserve">ſciendum igitur noſtras æquationes extra nouiluna eſſe iuſto minores, & </s> <s xml:id="echoid-s8272" xml:space="preserve">qui-<lb/>dem aliquando per grad. </s> <s xml:id="echoid-s8273" xml:space="preserve">2.</s> <s xml:id="echoid-s8274" xml:space="preserve">44′.</s> <s xml:id="echoid-s8275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8276" xml:space="preserve">Deinde cõſiderare oportet in figura pag. </s> <s xml:id="echoid-s8277" xml:space="preserve">69. </s> <s xml:id="echoid-s8278" xml:space="preserve">epicycli ſemicirculos, dexterum C D E. </s> <s xml:id="echoid-s8279" xml:space="preserve">& </s> <s xml:id="echoid-s8280" xml:space="preserve">ſiniſtrum C F E. <lb/></s> <s xml:id="echoid-s8281" xml:space="preserve">qui ab apogæo, & </s> <s xml:id="echoid-s8282" xml:space="preserve">perigęo diſcriminatur. </s> <s xml:id="echoid-s8283" xml:space="preserve">in his duobus ſemicirculis, gradus, qui ab apogæo hinc inde æqua-<lb/>liter diſtant, ſortiuntur æquales æquationes. </s> <s xml:id="echoid-s8284" xml:space="preserve">v. </s> <s xml:id="echoid-s8285" xml:space="preserve">g. </s> <s xml:id="echoid-s8286" xml:space="preserve">gradus D. </s> <s xml:id="echoid-s8287" xml:space="preserve">& </s> <s xml:id="echoid-s8288" xml:space="preserve">gradus F. </s> <s xml:id="echoid-s8289" xml:space="preserve">æqualiter ab apogæo diſtantes, ha-<lb/>bebunt æquales æquationes in Zodiaco, quæ in figura ſunt N Q. </s> <s xml:id="echoid-s8290" xml:space="preserve">& </s> <s xml:id="echoid-s8291" xml:space="preserve">N P. </s> <s xml:id="echoid-s8292" xml:space="preserve">ſimiliter, & </s> <s xml:id="echoid-s8293" xml:space="preserve">reliqui gradus ab apo-<lb/>gæo æquidiſtantes. </s> <s xml:id="echoid-s8294" xml:space="preserve">vnde factum eſt vt in tabula eædem æquationes inſeruiant vtrique ſemicirculo; </s> <s xml:id="echoid-s8295" xml:space="preserve">& </s> <s xml:id="echoid-s8296" xml:space="preserve">ideo <lb/>in fronte Tabulæ ſunt 6. </s> <s xml:id="echoid-s8297" xml:space="preserve">ſigna occidentalis, ſeu dexteri ſemicirculi, in calce vero ſunt ſigna 6. </s> <s xml:id="echoid-s8298" xml:space="preserve">alterius ſemi-<lb/>circuli: </s> <s xml:id="echoid-s8299" xml:space="preserve">eo ordine vt ſigna æquidiſtantia ab apogæo ſint in eadem columna, vnum in fronte, alterum in pe-<lb/>de ſic prima columna inſeruit primo ſigno, & </s> <s xml:id="echoid-s8300" xml:space="preserve">duodecimo quę ab apogæo hinc inde pariter recedunt; </s> <s xml:id="echoid-s8301" xml:space="preserve">ſecun-<lb/>da verò columna inſeruit ſecundo, & </s> <s xml:id="echoid-s8302" xml:space="preserve">vndecimo ſigno; </s> <s xml:id="echoid-s8303" xml:space="preserve">ſen continent eorum æquationes: </s> <s xml:id="echoid-s8304" xml:space="preserve">& </s> <s xml:id="echoid-s8305" xml:space="preserve">ſic de reliquis, <lb/>vt conſideranti lectori conſtabit.</s> <s xml:id="echoid-s8306" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8307" xml:space="preserve">Præterea ſciendum eſt in priore ſemicirculo æquationes ſemper eſſe demẽdas à motu medio, vt verus ha-<lb/>beatur. </s> <s xml:id="echoid-s8308" xml:space="preserve">ſic exiſtente luna in O. </s> <s xml:id="echoid-s8309" xml:space="preserve">epicycli puncto, æquatio N M. </s> <s xml:id="echoid-s8310" xml:space="preserve">eſſet auferenda à medio motu, vt verus, qui eſ-<lb/>ſet in gradu M. </s> <s xml:id="echoid-s8311" xml:space="preserve">haberetur. </s> <s xml:id="echoid-s8312" xml:space="preserve">in ſecundo vero ſemicirculo æquationes ſunt medio motui addendæ, quia tunc <lb/>Luna magis diſtat ab æquinoctio, quàm epicycli centrum; </s> <s xml:id="echoid-s8313" xml:space="preserve">vt ſi Luna eſſet in F. </s> <s xml:id="echoid-s8314" xml:space="preserve">æquatio F N. </s> <s xml:id="echoid-s8315" xml:space="preserve">medio motui <lb/>eſſet addenda, vt verus haberetur. </s> <s xml:id="echoid-s8316" xml:space="preserve">Luna autem apogæa, aut perigęa exiſtente, nulla fit æquatio; </s> <s xml:id="echoid-s8317" xml:space="preserve">quia linea <lb/>medij, & </s> <s xml:id="echoid-s8318" xml:space="preserve">veri motus vniuntur. </s> <s xml:id="echoid-s8319" xml:space="preserve">in hac tabula numeri primæ ſeriei ſunt gradus ſignorum ſex ſuperiorum in <lb/>fronte tabulæ ſcriptorum: </s> <s xml:id="echoid-s8320" xml:space="preserve">numeri vero in vltima, ac dextera ſerie, ſunt gradus ſex ſignorum inferiorum in <lb/>calce tabulæ. </s> <s xml:id="echoid-s8321" xml:space="preserve">habet autem ſex æquationum columnas, & </s> <s xml:id="echoid-s8322" xml:space="preserve">quælibet earum inſeruit duobus ſignis, ideſt, conti-<lb/>net numeros, ſeu æquat ones duorum ſignorum æquidiſtantium ab apogæo. </s> <s xml:id="echoid-s8323" xml:space="preserve">Primum ſignum inſcribitur <lb/>charactere. </s> <s xml:id="echoid-s8324" xml:space="preserve">o. </s> <s xml:id="echoid-s8325" xml:space="preserve">in fronte primæ columnæ, quia nondum eſt completum, niſi poſt gradus 30. </s> <s xml:id="echoid-s8326" xml:space="preserve">numeri vero in <lb/>ipſa columna ſunt æquationes reſpondentes gradibus primi ſigni, nec non duodecimi. </s> <s xml:id="echoid-s8327" xml:space="preserve">Secundæ columnæ <lb/>inſcribitur 1. </s> <s xml:id="echoid-s8328" xml:space="preserve">hoc eſt ſignum vnum iam completum in prima columna: </s> <s xml:id="echoid-s8329" xml:space="preserve">eſt tamen columna hæc ſecundi ſigni <lb/>nondum completi. </s> <s xml:id="echoid-s8330" xml:space="preserve">ſic reliqui numeri titulares ſig nificant ſigna iam completa in præcedenti columna, & </s> <s xml:id="echoid-s8331" xml:space="preserve"><lb/>columna ſub eis pertinet ad ſignum ſequentis numeri. </s> <s xml:id="echoid-s8332" xml:space="preserve">v. </s> <s xml:id="echoid-s8333" xml:space="preserve">g. </s> <s xml:id="echoid-s8334" xml:space="preserve">numerus 2. </s> <s xml:id="echoid-s8335" xml:space="preserve">ſupra tertiam columnam ſignificat <lb/>duo ſigna iam completa cum ſuis æquationibus, in præcedentibus duabus columnis; </s> <s xml:id="echoid-s8336" xml:space="preserve">columnam vero ſub iſto <lb/>2. </s> <s xml:id="echoid-s8337" xml:space="preserve">eſſe columnam æquationum ſigni tertij cuius gradus ſunt in prima ſerie; </s> <s xml:id="echoid-s8338" xml:space="preserve">& </s> <s xml:id="echoid-s8339" xml:space="preserve">finitur iſtud ſignum tertium <lb/>in fine tertiæ columnæ è regione gradus 30. </s> <s xml:id="echoid-s8340" xml:space="preserve">idem dicendum deſignis 6. </s> <s xml:id="echoid-s8341" xml:space="preserve">inferioribus reliqua vſus, & </s> <s xml:id="echoid-s8342" xml:space="preserve">exem-<lb/>pla docebunt.</s> <s xml:id="echoid-s8343" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div169" type="section" level="1" n="107"> <head xml:id="echoid-head117" style="it" xml:space="preserve">De ſexta Tabula latitudinis Lunæ.</head> <p> <s xml:id="echoid-s8344" xml:space="preserve">CIrca Tabulam latitudinis @, ſcias ſigna inſcripta, eſſe ſigna motus @, in latitudinem; </s> <s xml:id="echoid-s8345" xml:space="preserve">numeros vero in <lb/>columnis grad. </s> <s xml:id="echoid-s8346" xml:space="preserve">& </s> <s xml:id="echoid-s8347" xml:space="preserve">min: </s> <s xml:id="echoid-s8348" xml:space="preserve">eſſe latitudines @, ab eclyptica. </s> <s xml:id="echoid-s8349" xml:space="preserve">reliqua ex dictis de alijs tabulis diligens lector <lb/>percipiet. </s> <s xml:id="echoid-s8350" xml:space="preserve">Neque me latet Tychonem paulo diuerſam latitudinis lunaris Tabulam exhibere, ſed hæc noſtra, <lb/>noſtro inſtituto, accommodatior eſt.</s> <s xml:id="echoid-s8351" xml:space="preserve"/> </p> <pb o="79" file="0103" n="107" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div170" type="section" level="1" n="108"> <head xml:id="echoid-head118" style="it" xml:space="preserve">Prima Tabula mediorum motuum Lunæ in Horis, & Minutis.</head> <note position="right" xml:space="preserve"> <lb/>#### Longitudo ***. ab \\ Aequinoctio. # ### Anomalia ***. # ### Motus ☊. <lb/>Horæ # Sig. # Gra. # ′. # # Sig. # Gra. # ′. # # Sig. # Gra. # ′. <lb/>Min. # Gra. # ′. # ″. # # Gra. # ′. # ″. # # Gra. # ′. # ″ <lb/>1 # 0 # 0 # 33 # # 0 # 0 # 32 # # 0 # 0 # 0 <lb/>2 # 0 # 1 # 5 # # 0 # 1 # 5 # # 0 # 0 # 0 <lb/>3 # 0 # 2 # 38 # # 0 # 1 # 37 # # 0 # 0 # 0 <lb/>4 # 0 # 3 # 11 # # 0 # 3 # 10 # # 0 # 0 # 1 <lb/>5 # 0 # 3 # 44 # # 0 # 2 # 43 # # 0 # 0 # 1 <lb/>6 # 0 # 4 # 17 # # 0 # 3 # 15 # # 0 # 0 # 1 <lb/>7 # 0 # 4 # 50 # # 0 # 3 # 48 # # 0 # 0 # 1 <lb/>8 # 0 # 5 # 23 # # 0 # 4 # 21 # # 0 # 0 # 1 <lb/>9 # 0 # 5 # 56 # # 0 # 4 # 53 # # 0 # 0 # 1 <lb/>10 # 0 # 6 # 29 # # 0 # 5 # 26 # # 0 # 0 # 1 <lb/>11 # 0 # 6 # 2 # # 0 # 5 # 59 # # 0 # 0 # 1 <lb/>12 # 0 # 6 # 35 # # 0 # 6 # 31 # # 0 # 0 # 1 <lb/>13 # 0 # 7 # 8 # # 0 # 7 # 4 # # 0 # 0 # 2 <lb/>14 # 0 # 7 # 41 # # 0 # 7 # 37 # # 0 # 0 # 2 <lb/>15 # 0 # 8 # 14 # # 0 # 8 # 9 # # 0 # 0 # 2 <lb/>16 # 0 # 8 # 47 # # 0 # 8 # 42 # # 0 # 0 # 2 <lb/>17 # 0 # 9 # 19 # # 0 # 9 # 15 # # 0 # 0 # 2 <lb/>18 # 0 # 9 # 52 # # 0 # 9 # 47 # # 0 # 0 # 2 <lb/>19 # 0 # 10 # 25 # # 0 # 10 # 20 # # 0 # 0 # 2 <lb/>20 # 0 # 10 # 58 # # 0 # 10 # 59 # # 0 # 0 # 3 <lb/>21 # 0 # 11 # 31 # # 0 # 11 # 25 # # 0 # 0 # 3 <lb/>22 # 0 # 12 # 4 # # 0 # 11 # 58 # # 0 # 0 # 3 <lb/>23 # 0 # 12 # 37 # # 0 # 12 # 31 # # 0 # 0 # 3 <lb/>24 # 0 # 13 # 10 # # 0 # 13 # 3 # # 0 # 0 # 3 <lb/>25 # 0 # 13 # 43 # # 0 # 13 # 37 # # 0 # 0 # 3 <lb/>26 # 0 # 14 # 16 # # 0 # 14 # 9 # # 0 # 0 # 3 <lb/>27 # 0 # 14 # 49 # # 0 # 14 # 42 # # 0 # 0 # 4 <lb/>28 # 0 # 15 # 22 # # 0 # 15 # 15 # # 0 # 0 # 4 <lb/>29 # 0 # 15 # 55 # # 0 # 15 # 47 # # 0 # 0 # 4 <lb/>30 # 0 # 16 # 28 # # 0 # 16 # 20 # # 0 # 0 # 4 <lb/></note> <pb o="80" file="0104" n="108" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div171" type="section" level="1" n="109"> <head xml:id="echoid-head119" style="it" xml:space="preserve">Secunda Tabula mediorum motuum Lunæ in diebus.</head> <note position="right" xml:space="preserve"> <lb/>#### Longitudo ***. ab Æqui- \\ noctio. # ### Anomalia ***. # ### Motus ☊. <lb/>Dies # Sig. # Gra. # ′. # # Sig. # Gra. # ′. # # Sig. # Gra. # ′. <lb/>1 # 0 # 13 # 10 # # 0 # 13 # 4 # # 0 # 0 # 3 <lb/>2 # 0 # 26 # 21 # # 0 # 26 # 8 # # 0 # 0 # 6 <lb/>3 # 1 # 9 # 32 # # 1 # 9 # 12 # # 0 # 0 # 9 <lb/>4 # 1 # 22 # 42 # # 1 # 22 # 16 # # 0 # 0 # 13 <lb/>5 # 2 # 5 # 53 # # 2 # 5 # 19 # # 0 # 0 # 16 <lb/>6 # 2 # 19 # 3 # # 2 # 18 # 23 # # 0 # 0 # 19 <lb/>7 # 3 # 2 # 14 # # 3 # 1 # 27 # # 0 # 0 # 22 <lb/>8 # 3 # 15 # 24 # # 3 # 14 # 31 # # 0 # 0 # 25 <lb/>9 # 3 # 28 # 35 # # 3 # 27 # 35 # # 0 # 0 # 29 <lb/>10 # 4 # 11 # 46 # # 4 # 10 # 39 # # 0 # 0 # 32 <lb/>11 # 4 # 24 # 56 # # 4 # 23 # 43 # # 0 # 0 # 35 <lb/>12 # 5 # 8 # 7 # # 5 # 6 # 46 # # 0 # 0 # 38 <lb/>13 # 5 # 21 # 18 # # 5 # 19 # 50 # # 0 # 0 # 41 <lb/>14 # 0 # 4 # 28 # # 6 # 2 # 54 # # 0 # 0 # 44 <lb/>15 # 6 # 17 # 39 # # 6 # 15 # 58 # # 0 # 0 # 48 <lb/>16 # 7 # 0 # 49 # # 6 # 29 # 2 # # 0 # 0 # 51 <lb/>17 # 7 # 13 # 59 # # 7 # 12 # 6 # # 0 # 0 # 54 <lb/>18 # 7 # 27 # 10 # # 7 # 25 # 10 # # 0 # 0 # 57 <lb/>19 # 8 # 10 # 21 # # 8 # 8 # 14 # # 0 # 1 # 0 <lb/>20 # 8 # 23 # 32 # # 8 # 21 # 18 # # 0 # 1 # 3 <lb/>21 # 9 # 6 # 42 # # 9 # 4 # 22 # # 0 # 1 # 7 <lb/>22 # 9 # 19 # 53 # # 9 # 17 # 25 # # 0 # 1 # 10 <lb/>23 # 10 # 3 # 3 # # 10 # 0 # 29 # # 0 # 1 # 13 <lb/>24 # 10 # 16 # 14 # # 10 # 13 # 34 # # 0 # 1 # 16 <lb/>25 # 10 # 29 # 24 # # 10 # 26 # 17 # # 0 # 1 # 19 <lb/>26 # 11 # 12 # 35 # # 11 # 9 # 41 # # 0 # 1 # 23 <lb/>27 # 11 # 25 # 46 # # 11 # 22 # 45 # # 0 # 1 # 26 <lb/>28 # 0 # 8 # 56 # # 0 # 5 # 49 # # 0 # 1 # 29 <lb/>29 # 0 # 22 # 6 # # 0 # 18 # 53 # # 0 # 1 # 32 <lb/>30 # 1 # 5 # 17 # # 1 # 1 # 56 # # 0 # 1 # 35 <lb/>31 # 1 # 18 # 28 # # 1 # 15 # 0 # # 0 # 1 # 38 <lb/></note> <pb o="85" file="0105" n="109" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div172" type="section" level="1" n="110"> <head xml:id="echoid-head120" style="it" xml:space="preserve">Tertia Tabula mediorum Motuum Lunæ in Menſibus completis <lb/>Anni communis.</head> <note position="right" xml:space="preserve"> <lb/># ### Longitudo ***. ab \\ Æquinoctio. # ### Anomalia ***. # ### Motus ☊. <lb/># Sig. # Gra. # ′. # # Sig. # Gra. # ′. # # Sig. # Gra. # ′. <lb/>Ianu. # 1 # 18 # 28 # # 1 # 15 # 0 # # 0 # 1 # 38 <lb/>Febr. # 1 # 27 # 24 # # 1 # 20 # 50 # # 0 # 3 # 7 <lb/>Mart. # 3 # 15 # 52 # # 3 # 5 # 50 # # 0 # 4 # 45 <lb/>Apri. # 4 # 21 # 10 # # 4 # 7 # 47 # # 0 # 6 # 21 <lb/>Maiu. # 6 # 9 # 38 # # 5 # 22 # 48 # # 0 # 7 # 59 <lb/>Iuni. # 7 # 14 # 56 # # 6 # 24 # 45 # # 0 # 9 # 35 <lb/>Iulius # 9 # 3 # 24 # # 8 # 9 # 46 # # 0 # 11 # 13 <lb/>Aug. # 10 # 21 # 52 # # 9 # 24 # 47 # # 0 # 12 # 52 <lb/>Sept. # 11 # 27 # 9 # # 10 # 26 # 44 # # 0 # 14 # 27 <lb/>Octo. # 1 # 15 # 37 # # 0 # 11 # 45 # # 0 # 16 # 5 <lb/>Nou. # 2 # 20 # 55 # # 1 # 13 # 42 # # 0 # 17 # 41 <lb/>Dec. # 4 # 9 # 23 # # 2 # 28 # 43 # # 0 # 19 # 19 <lb/></note> <head xml:id="echoid-head121" xml:space="preserve">In Menſibus Anni Bißextilis.</head> <note position="right" xml:space="preserve">Ianu. # 1 # 18 # 28 # # 1 # 15 # 0 # # 0 # 1 # 38<lb/>Febr. # 2 # 10 # 35 # # 2 # 3 # 53 # # 0 # 3 # 10<lb/>Mart. # 3 # 29 # 3 # # 3 # 18 # 54 # # 0 # 4 # 49<lb/>Apr. # 5 # 4 # 20 # # 4 # 20 # 51 # # 0 # 6 # 24<lb/>Maiu. # 6 # 22 # 49 # # 6 # 5 # 52 # # 0 # 8 # 2<lb/>Iuni. # 7 # 28 # 6 # # 7 # 7 # 49 # # 0 # 9 # 38<lb/>Iulius # 9 # 16 # 34 # # 8 # 22 # 50 # # 0 # 11 # 16<lb/>Aug. # 11 # 5 # 2 # # 10 # 7 # 51 # # 0 # 12 # 55<lb/>Sept. # 0 # 10 # 20 # # 11 # 9 # 48 # # 0 # 14 # 30<lb/>Octo. # 1 # 28 # 48 # # 0 # 24 # 49 # # 0 # 16 # 9<lb/>Nou. # 3 # 4 # 6 # # 1 # 26 # 46 # # 0 # 17 # 24<lb/>Dec. # 4 # 22 # 34 # # 3 # 11 # 47 # # 0 # 19 # 22<lb/></note> <pb o="86" file="0106" n="110" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div173" type="section" level="1" n="111"> <head xml:id="echoid-head122" style="it" xml:space="preserve">Quaria Tabula mediorum motuum Lunæ in Annis ſingulis.</head> <note position="right" xml:space="preserve"> <lb/>##### Longitudo ***\\ ab Aequin. # #### Anomalia ***. # ### Motus ☊. <lb/># Anni # Sig. # Gra. # ′. # # Sig. # Gra. # ′. # # Sig. # Gra. # ′. <lb/># 1 # 4 # 9 # 23 # # 2 # 28 # 43 # # 0 # 19 # 20 <lb/># 2 # 8 # 18 # 46 # # 5 # 27 # 26 # # 1 # 8 # 39 <lb/># 3 # 0 # 28 # 9 # # 8 # 26 # 9 # # 1 # 27 # 59 <lb/>B # 4 # 5 # 20 # 43 # # 0 # 7 # 56 # # 2 # 17 # 22 <lb/># 5 # 10 # 0 # 6 # # 3 # 6 # 40 # # 3 # 6 # 42 <lb/># 6 # 2 # 9 # 29 # # 6 # 5 # 23 # # 3 # 26 # 1 <lb/># 7 # 6 # 18 # 52 # # 9 # 4 # 6 # # 4 # 15 # 21 <lb/>B # 8 # 11 # 11 # 26 # # 0 # 15 # 53 # # 5 # 4 # 44 <lb/># 9 # 3 # 20 # 48 # # 3 # 14 # 36 # # 5 # 24 # 4 <lb/># 10 # 8 # 0 # 12 # # 6 # 13 # 19 # # 6 # 13 # 23 <lb/># 11 # 0 # 9 # 35 # # 9 # 12 # 2 # # 7 # 2 # 43 <lb/>B # 12 # 5 # 2 # 8 # # 0 # 23 # 49 # # 7 # 22 # 6 <lb/># 13 # 9 # 11 # 31 # # 3 # 22 # 32 # # 8 # 11 # 25 <lb/># 14 # 1 # 20 # 54 # # 6 # 21 # 15 # # 9 # 0 # 45 <lb/># 15 # 6 # 0 # 17 # # 9 # 19 # 59 # # 9 # 20 # 5 <lb/>B # 16 # 10 # 21 # 51 # # 1 # 1 # 46 # # 10 # 9 # 28 <lb/># 17 # 3 # 2 # 14 # # 4 # 0 # 29 # # 10 # 28 # 48 <lb/># 18 # 7 # 11 # 37 # # 6 # 29 # 12 # # 11 # 18 # 8 <lb/># 19 # 11 # 21 # 0 # # 9 # 27 # 55 # # 0 # 7 # 27 <lb/>B # 20 # 4 # 13 # 34 # # 1 # 9 # 42 # # 0 # 26 # 50 <lb/># 40 # 8 # 27 # 8 # # 2 # 19 # 24 # # 1 # 23 # 40 <lb/>In # 60 # 1 # 10 # 42 # # 3 # 29 # 6 # # 2 # 20 # 30 <lb/># 80 # 5 # 24 # 16 # # 5 # 8 # 48 # # 3 # 17 # 20 <lb/># 100 # 10 # 7 # 50 # # 6 # 18 # 30 # # 4 # 14 # 10 <lb/>Annis # 200 # 8 # 15 # 40 # # 1 # 7 # 0 # # 8 # 28 # 20 <lb/># 300 # 6 # 23 # 30 # # 7 # 25 # 30 # # 1 # 12 # 30 <lb/># 400 # 5 # 1 # 20 # # 2 # 14 # 0 # # 5 # 26 # 40 <lb/># 500 # 3 # 9 # 10 # # 9 # 2 # 30 # # 10 # 10 # 50 <lb/>aggregatis. # 600 # 1 # 17 # 0 # # 3 # 21 # 0 # # 2 # 25 # 0 <lb/># 700 # 11 # 24 # 50 # # 10 # 9 # 30 # # 7 # 9 # 10 <lb/># 800 # 10 # 2 # 40 # # 4 # 28 # 0 # # 11 # 23 # 20 <lb/># 900 # 8 # 10 # 30 # # 11 # 16 # 30 # # 4 # 7 # 30 <lb/># 1000 # 6 # 18 # 20 # # 6 # 5 # 0 # # 8 # 21 # 40 <lb/># # # # # # # # # # 1 # 5 # 50 <lb/></note> <head xml:id="echoid-head123" xml:space="preserve">Radices æqualium motum ad Ann. Christi 1600. abſolutum in meridie vltimi Decembris, \\ ideſt, pridie Katend. Ianuarij Anni 1601.</head> <note position="right" xml:space="preserve"> <lb/>##### Radix longitudinis ***. # ### Radix Anomaliæ. # ### Radix nodi ☊.<lb/>B # 1600 # 7 # 25 # 9 # # 0 # 6 # 40 # # 9 # 12 # 0<lb/></note> <pb o="87" file="0107" n="111" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div174" type="section" level="1" n="112"> <head xml:id="echoid-head124" style="it" xml:space="preserve">Quinta Tabula Aequationum Lunæ in Nouilunijs, <lb/>& Plenilunijs.</head> <note position="right" xml:space="preserve"> <lb/>######## Priora ſex ſigna Anomaliæ in quibus Aequatio demitur. <lb/># 0 \\ Gra. ′. # 1 \\ Gra. ′. # 2 \\ Gra. ′. # 3 \\ Gra. ′. # 4 \\ Gra. ′. # 5 \\ Gra. ′. <lb/>1 # 0 5 # 2 30 # 4 17 # 4 58 # 4 20 # 2 29 # 29 <lb/>2 # 0 10 # 2 35 # 4 20 # 4 58 # 4 17 # 2 24 # 28 <lb/>3 # 0 15 # 2 39 # 4 23 # 4 58 # 4 14 # 2 19 # 27 <lb/>4 # 0 20 # 2 43 # 4 25 # 4 58 # 4 12 # 2 15 # 26 <lb/>5 # 0 25 # 2 47 # 4 27 # 4 58 # 4 9 # 2 10 # 25 <lb/>6 # 0 30 # 2 52 # 4 29 # 4 58 # 4 6 # 2 5 # 24 <lb/>7 # 0 35 # 2 56 # 4 32 # 4 57 # 4 3 # 2 0 # 23 <lb/>8 # 0 40 # 3 0 # 4 34 # 4 57 # 3 59 # 1 56 # 22 <lb/>9 # 0 45 # 3 4 # 4 30 # 4 56 # 3 56 # 1 50 # 21 <lb/>10 # 0 50 # 3 8 # 4 38 # 4 56 # 3 53 # 1 45 # 20 <lb/>11 # 0 55 # 3 12 # 4 39 # 4 54 # 3 50 # 1 40 # 19 <lb/>12 # 1 0 # 3 16 # 4 41 # 4 54 # 3 46 # 1 35 # 18 <lb/>13 # 1 5 # 3 20 # 4 43 # 4 53 # 3 43 # 1 30 # 17 <lb/>14 # 1 10 # 3 23 # 4 45 # 4 52 # 3 39 # 1 25 # 16 <lb/>15 # 1 15 # 3 27 # 4 46 # 4 50 # 3 38 # 1 20 # 15 <lb/>16 # 1 20 # 3 31 # 4 47 # 4 49 # 3 32 # 1 14 # 14 <lb/>17 # 1 25 # 3 34 # 4 49 # 4 48 # 3 28 # 1 9 # 13 <lb/>18 # 1 30 # 3 38 # 4 50 # 4 46 # 3 24 # 1 4 # 12 <lb/>19 # 1 35 # 3 41 # 4 51 # 4 45 # 3 20 # 0 5 # 11 <lb/>20 # 1 40 # 3 45 # 4 52 # 4 43 # 3 16 # 0 53 # 10 <lb/>21 # 1 44 # 3 48 # 4 53 # 4 42 # 3 12 # 0 48 # 9 <lb/>22 # 1 49 # 3 51 # 4 54 # 4 40 # 3 8 # 0 43 # 8 <lb/>23 # 1 53 # 3 54 # 4 55 # 4 38 # 3 4 # 0 38 # 7 <lb/>24 # 1 58 # 3 58 # 4 56 # 4 36 # 3 0 # 0 32 # 6 <lb/>25 # 2 3 # 4 1 # 4 56 # 4 34 # 2 56 # 0 27 # 5 <lb/>26 # 2 8 # 4 4 # 4 57 # 4 32 # 2 51 # 0 21 # 4 <lb/>27 # 2 12 # 4 6 # 4 57 # 4 29 # 2 47 # 0 16 # 3 <lb/>28 # 2 17 # 4 9 # 4 58 # 4 27 # 2 42 # 0 11 # 2 <lb/>29 # 2 21 # 4 12 # 4 58 # 4 25 # 2 38 # 0 5 # 1 <lb/>30 # 2 26 # 4 15 # 4 58 # 4 22 # 2 33 # 0 0 # 0 <lb/># 11 # 10 # 9 # 8 # 7 # 6 <lb/>######## Poſteriora ſex ſigna Anomaliæ in quibus Aequatio additur. <lb/></note> <pb o="88" file="0108" n="112" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div175" type="section" level="1" n="113"> <head xml:id="echoid-head125" style="it" xml:space="preserve">Sexta Tabula latitudinis Lunæ.</head> <note position="right" xml:space="preserve"> <lb/>######## Latitudo Borealis. <lb/>Sig. # 0 \\ Gra. ′. # 1 \\ Gra. ′. # 2 \\ Gra. ′. # 3 \\ Gra. ′. # 4 \\ Gra. ′. # 5 \\ Gra. ′. # Motus in \\ latitudinẽ. <lb/>1 # 0 5 # 2 34 # 4 22 # 5 0 # 4 17 # 2 25 # 29 <lb/>2 # 0 10 # 2 39 # 4 25 # 5 0 # 4 14 # 2 20 # 28 <lb/>3 # 0 16 # 2 43 # 4 27 # 5 0 # 4 11 # 2 16 # 27 <lb/>4 # 0 21 # 2 48 # 4 30 # 4 59 # 4 9 # 2 11 # 26 <lb/>5 # 0 26 # 2 52 # 4 31 # 4 59 # 4 6 # 2 7 # 25 <lb/>6 # 0 31 # 2 56 # 4 34 # 4 58 # 4 3 # 2 2 # 24 <lb/>7 # 0 37 # 3 0 # 4 36 # 4 58 # 3 39 # 1 57 # 23 <lb/>8 # 0 42 # 3 5 # 4 38 # 4 57 # 3 56 # 1 52 # 22 <lb/>9 # 0 47 # 3 9 # 4 40 # 4 50 # 3 53 # 1 47 # 21 <lb/>10 # 0 52 # 3 13 # 4 42 # 4 55 # 3 50 # 1 42 # 20 <lb/>11 # 0 57 # 3 17 # 4 44 # 4 54 # 3 46 # 1 38 # 19 <lb/>12 # 1 2 # 3 21 # 4 45 # 4 53 # 3 43 # 1 33 # 18 <lb/>13 # 1 7 # 3 24 # 4 47 # 4 52 # 3 39 # 1 28 # 17 <lb/>14 # 1 12 # 3 28 # 4 48 # 4 51 # 3 36 # 1 23 # 16 <lb/>15 # 1 18 # 3 32 # 4 50 # 4 50 # 3 32 # 1 18 # 15 <lb/>16 # 1 23 # 3 36 # 4 51 # 4 48 # 3 28 # 1 12 # 14 <lb/>17 # 1 28 # 3 39 # 4 52 # 4 47 # 3 24 # 1 7 # 13 <lb/>18 # 1 33 # 3 43 # 4 53 # 4 45 # 3 21 # 1 2 # 12 <lb/>19 # 1 38 # 3 46 # 4 54 # 4 44 # 3 17 # 0 57 # 11 <lb/>20 # 1 42 # 3 50 # 4 55 # 4 42 # 3 13 # 0 52 # 10 <lb/>21 # 1 47 # 3 53 # 4 56 # 4 40 # 3 9 # 0 47 # 9 <lb/>22 # 1 52 # 3 56 # 4 57 # 4 38 # 3 5 # 0 42 # 8 <lb/>23 # 1 57 # 3 59 # 4 58 # 4 36 # 3 0 # 0 37 # 7 <lb/>24 # 2 2 # 4 3 # 4 58 # 4 34 # 2 56 # 0 31 # 6 <lb/>25 # 2 7 # 4 6 # 4 59 # 4 32 # 2 52 # 0 26 # 5 <lb/>26 # 2 11 # 4 9 # 4 59 # 4 30 # 2 48 # 0 21 # 4 <lb/>27 # 2 16 # 4 11 # 5 0 # 4 27 # 2 43 # 0 16 # 3 <lb/>28 # 2 21 # 4 14 # 5 0 # 4 25 # 2 39 # 0 10 # 2 <lb/>29 # 2 25 # 4 17 # 5 0 # 4 22 # 2 34 # 0 5 # 1 <lb/>30 # 2 30 # 4 20 # 5 0 # 4 20 # 2 30 # 0 0 # 0 <lb/>Sig. # 11 # 10 # 9 # 8 # 7 # 6 # Motus in \\ latitudinẽ. <lb/>######## Latitudo Auſtralis. <lb/></note> <pb o="89" file="0109" n="113" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div176" type="section" level="1" n="114"> <head xml:id="echoid-head126" style="it" xml:space="preserve">De numeris Aſironomicis, & eorum vſu. Cap. XIII.</head> <p> <s xml:id="echoid-s8352" xml:space="preserve">VT igitur hiſce Tabulis, vti poſſimus ad abſolutum Lunę locum in Zodiaco inueniendũ, opus eſt præmit-<lb/>torę cõpendioſam tractatione de numeris Aſtronomicis. </s> <s xml:id="echoid-s8353" xml:space="preserve">Verum quoniã numeri Aſtronomici peculiarẽ <lb/>doctriuam requirunt. </s> <s xml:id="echoid-s8354" xml:space="preserve">ideo hic ea ſolum breuiter indicabo, quæ vſui nobis futura ſunt. </s> <s xml:id="echoid-s8355" xml:space="preserve">Signum igitur vnum <lb/>continet gr. </s> <s xml:id="echoid-s8356" xml:space="preserve">30. </s> <s xml:id="echoid-s8357" xml:space="preserve">Gr. </s> <s xml:id="echoid-s8358" xml:space="preserve">vnus continet 60. </s> <s xml:id="echoid-s8359" xml:space="preserve">min. </s> <s xml:id="echoid-s8360" xml:space="preserve">ſeu prima. </s> <s xml:id="echoid-s8361" xml:space="preserve">Min. </s> <s xml:id="echoid-s8362" xml:space="preserve">vnum continet 60. </s> <s xml:id="echoid-s8363" xml:space="preserve">ſecunda. </s> <s xml:id="echoid-s8364" xml:space="preserve">Secundum vnum 60. <lb/></s> <s xml:id="echoid-s8365" xml:space="preserve">tertia: </s> <s xml:id="echoid-s8366" xml:space="preserve">& </s> <s xml:id="echoid-s8367" xml:space="preserve">ſic deinceps per ſexagenariam ſubdiuiſionem. </s> <s xml:id="echoid-s8368" xml:space="preserve">Præter gradus diuidunt etiam dies, & </s> <s xml:id="echoid-s8369" xml:space="preserve">horas, & </s> <s xml:id="echoid-s8370" xml:space="preserve">alia, <lb/>in prima, ſecunda, &</s> <s xml:id="echoid-s8371" xml:space="preserve">c. </s> <s xml:id="echoid-s8372" xml:space="preserve">illud aut quod diuiditur in haſce ſexagenas particulas dicitur integrum.</s> <s xml:id="echoid-s8373" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div177" type="section" level="1" n="115"> <head xml:id="echoid-head127" style="it" xml:space="preserve">ADDITIO.</head> <p> <s xml:id="echoid-s8374" xml:space="preserve">OMnes numeri addendi, ſcribendi ſunt, ita vt qui ſunt eiuſdem ſpeciei, ſint in eadem ſerie, ideſt, ſigna ſub <lb/>ſignis, gradus ſub gradibus, minuta ſub minutis recta deſcribãtur, vt in appoſito exemplo. </s> <s xml:id="echoid-s8375" xml:space="preserve">deinde incho, <lb/>anda eſt additio a numeris dextris ſeu a tenuioribus, vti a ſecundis in exemplo, ad-<lb/> <anchor type="note" xlink:label="note-0109-01a" xlink:href="note-0109-01"/> duntur igitur omnia ſecunda ſimul, quæ in caſu noſtro ſunt 78. </s> <s xml:id="echoid-s8376" xml:space="preserve">quando autem colli-<lb/>gitur numerus maior quam 60. </s> <s xml:id="echoid-s8377" xml:space="preserve">pro ſingulis 60. </s> <s xml:id="echoid-s8378" xml:space="preserve">retinentur mente totidem vnita-<lb/>tates, & </s> <s xml:id="echoid-s8379" xml:space="preserve">reliquus numerus ſcribitur ſub ſua ſerie. </s> <s xml:id="echoid-s8380" xml:space="preserve">nunc igitur quia in 78. </s> <s xml:id="echoid-s8381" xml:space="preserve">ſemel conti-<lb/>netur 60. </s> <s xml:id="echoid-s8382" xml:space="preserve">quę faciunt minutum vnum; </s> <s xml:id="echoid-s8383" xml:space="preserve">ideo retineo mente vnam tantum vnitatem. <lb/></s> <s xml:id="echoid-s8384" xml:space="preserve">Et reliquum 18. </s> <s xml:id="echoid-s8385" xml:space="preserve">ſcribo ſub ſecundis. </s> <s xml:id="echoid-s8386" xml:space="preserve">poſtea procedo ad minuta quibus addo retentã <lb/>vnitatem, & </s> <s xml:id="echoid-s8387" xml:space="preserve">omnia ſimul efficiunt 88′. </s> <s xml:id="echoid-s8388" xml:space="preserve">ſcribo igitur 28. </s> <s xml:id="echoid-s8389" xml:space="preserve">vnumque retineo pro ſexa-<lb/>gena, quæ efficit gradum vnum: </s> <s xml:id="echoid-s8390" xml:space="preserve">ideo addo vnum gradibus, quibus ſimul collectis <lb/>fiunt gr.</s> <s xml:id="echoid-s8391" xml:space="preserve">, 8. </s> <s xml:id="echoid-s8392" xml:space="preserve">& </s> <s xml:id="echoid-s8393" xml:space="preserve">quoniam gr. </s> <s xml:id="echoid-s8394" xml:space="preserve">38. </s> <s xml:id="echoid-s8395" xml:space="preserve">conflant ſignum vnum, & </s> <s xml:id="echoid-s8396" xml:space="preserve">præterea gr. </s> <s xml:id="echoid-s8397" xml:space="preserve">8. </s> <s xml:id="echoid-s8398" xml:space="preserve">ideo ſcribo <lb/>8. </s> <s xml:id="echoid-s8399" xml:space="preserve">ſub gradibus: </s> <s xml:id="echoid-s8400" xml:space="preserve">& </s> <s xml:id="echoid-s8401" xml:space="preserve">poſtea vnum addo ſignis: </s> <s xml:id="echoid-s8402" xml:space="preserve">& </s> <s xml:id="echoid-s8403" xml:space="preserve">cõputo ſigna 19. </s> <s xml:id="echoid-s8404" xml:space="preserve">ſed tamen ſcribo tantum 7. </s> <s xml:id="echoid-s8405" xml:space="preserve">quia ſigna 12. </s> <s xml:id="echoid-s8406" xml:space="preserve">om-<lb/>nia conficiunt integrum circulum, qui numquam ſcribitur, quia inutilis eſt calculationi, vt poſtea melius pa-<lb/>tebit. </s> <s xml:id="echoid-s8407" xml:space="preserve">quapropter obſeruandum eſt, ne vnquam in ſeriebus ſecundorum, aut primorum, ſcribatur numerus <lb/>maior quam 59. </s> <s xml:id="echoid-s8408" xml:space="preserve">in ſerie graduum nullus ſit maior, quam 29. </s> <s xml:id="echoid-s8409" xml:space="preserve">in ſerie ſignorum, nullus maior, quam 11. </s> <s xml:id="echoid-s8410" xml:space="preserve">ſiue in-<lb/>ter minuta, & </s> <s xml:id="echoid-s8411" xml:space="preserve">ſecunda omnes numeri ſint infra 60. </s> <s xml:id="echoid-s8412" xml:space="preserve">inter gradus ſint infra 30. </s> <s xml:id="echoid-s8413" xml:space="preserve">inter ſigna ſint infra 12.</s> <s xml:id="echoid-s8414" xml:space="preserve"/> </p> <div xml:id="echoid-div177" type="float" level="2" n="1"> <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve"> <lb/>Sig. # Gra. # ′. # ″ <lb/>7 # 9 # 28 # 58 <lb/>11 # 15 # 44 # 20 <lb/>0 # 13 # 15 <lb/>7 # 8 # 28 # 18 <lb/></note> </div> </div> <div xml:id="echoid-div179" type="section" level="1" n="116"> <head xml:id="echoid-head128" style="it" xml:space="preserve">SVBTRACTIO.</head> <p> <s xml:id="echoid-s8415" xml:space="preserve">NVmerus ſubtrahendus ſcribendus eſt ſub altero, eadem ratione, qua in additione, deinceps inchoanda <lb/>eſt ſubtractio a dextris; </s> <s xml:id="echoid-s8416" xml:space="preserve">Et cum quiſpiam numerus maior eſt ſuo ſuperiori, augendus eſt ſuperior acce-<lb/>pta mutuo vna ſexagena, aut trigena, aut duodena, prout numerus ad ſiniſtram ſequens, fuerit; </s> <s xml:id="echoid-s8417" xml:space="preserve">exemplo pa-<lb/>tebit, in quo inferior numerus 3. </s> <s xml:id="echoid-s8418" xml:space="preserve">29. </s> <s xml:id="echoid-s8419" xml:space="preserve">30′. </s> <s xml:id="echoid-s8420" xml:space="preserve">3″. </s> <s xml:id="echoid-s8421" xml:space="preserve">quãuis ſit maior ſupe ioris 2. </s> <s xml:id="echoid-s8422" xml:space="preserve">28. </s> <s xml:id="echoid-s8423" xml:space="preserve">0′. </s> <s xml:id="echoid-s8424" xml:space="preserve">2″. <lb/></s> <s xml:id="echoid-s8425" xml:space="preserve"> <anchor type="note" xlink:label="note-0109-02a" xlink:href="note-0109-02"/> ſic tamen ab eo ſubtrahatur.</s> <s xml:id="echoid-s8426" xml:space="preserve"><unsure/> quia 3″. </s> <s xml:id="echoid-s8427" xml:space="preserve">non poſium detrahere a 2″. </s> <s xml:id="echoid-s8428" xml:space="preserve">ideo accedo ad ſi-<lb/>niſtrum locum primorum, & </s> <s xml:id="echoid-s8429" xml:space="preserve">inde mutuo accipio vnum primum, vt inde habeam <lb/>60″. </s> <s xml:id="echoid-s8430" xml:space="preserve">quæ cum 2″. </s> <s xml:id="echoid-s8431" xml:space="preserve">faciant 62. </s> <s xml:id="echoid-s8432" xml:space="preserve">a quibus detrahere poſſim 3″. </s> <s xml:id="echoid-s8433" xml:space="preserve">ſed quoniam locus pri-<lb/>morum eſt, 0′: </s> <s xml:id="echoid-s8434" xml:space="preserve">ideo procedo ad gr. </s> <s xml:id="echoid-s8435" xml:space="preserve">28. </s> <s xml:id="echoid-s8436" xml:space="preserve">& </s> <s xml:id="echoid-s8437" xml:space="preserve">inde accipio gr. </s> <s xml:id="echoid-s8438" xml:space="preserve">vnum, ideſt, 60′. </s> <s xml:id="echoid-s8439" xml:space="preserve">quæ pono <lb/>loco 0′. </s> <s xml:id="echoid-s8440" xml:space="preserve">ex his 60. </s> <s xml:id="echoid-s8441" xml:space="preserve">accipio vnum primum, ideſt, 60″. </s> <s xml:id="echoid-s8442" xml:space="preserve">quæ pono cum 2″. </s> <s xml:id="echoid-s8443" xml:space="preserve">ſicque poſ-<lb/>ſum ſubtrahere: </s> <s xml:id="echoid-s8444" xml:space="preserve">detraho igitur 3″. </s> <s xml:id="echoid-s8445" xml:space="preserve">a 62″. </s> <s xml:id="echoid-s8446" xml:space="preserve">& </s> <s xml:id="echoid-s8447" xml:space="preserve">remanent 59″. </s> <s xml:id="echoid-s8448" xml:space="preserve">ſubſcribenda. </s> <s xml:id="echoid-s8449" xml:space="preserve">numeri <lb/>13. </s> <s xml:id="echoid-s8450" xml:space="preserve">57. </s> <s xml:id="echoid-s8451" xml:space="preserve">59. </s> <s xml:id="echoid-s8452" xml:space="preserve">60. </s> <s xml:id="echoid-s8453" xml:space="preserve">ſunt poſi i ſupra numeros 2. </s> <s xml:id="echoid-s8454" xml:space="preserve">28. </s> <s xml:id="echoid-s8455" xml:space="preserve">0. </s> <s xml:id="echoid-s8456" xml:space="preserve">2. </s> <s xml:id="echoid-s8457" xml:space="preserve">ad iuuandam memoriam Lecto-<lb/>ris. </s> <s xml:id="echoid-s8458" xml:space="preserve">deinde detraho 30′. </s> <s xml:id="echoid-s8459" xml:space="preserve">non a 0. </s> <s xml:id="echoid-s8460" xml:space="preserve">ſed a 59. </s> <s xml:id="echoid-s8461" xml:space="preserve">quæ i<unsure/>bi mente collocauiantea, remanent-<lb/>que 29′. </s> <s xml:id="echoid-s8462" xml:space="preserve">ſubſcribenda. </s> <s xml:id="echoid-s8463" xml:space="preserve">poſtea quia non poſſum detrahere 29. </s> <s xml:id="echoid-s8464" xml:space="preserve">a 27. </s> <s xml:id="echoid-s8465" xml:space="preserve">remanſerunt enim 27. </s> <s xml:id="echoid-s8466" xml:space="preserve">ob gradum accom-<lb/>modatum; </s> <s xml:id="echoid-s8467" xml:space="preserve">addo igitur gradus 30. </s> <s xml:id="echoid-s8468" xml:space="preserve">quos mutuo accipio a ſignis 2. </s> <s xml:id="echoid-s8469" xml:space="preserve">accipio enim ſignum <lb/> <anchor type="note" xlink:label="note-0109-03a" xlink:href="note-0109-03"/> vnum, quod continet gradus 30. </s> <s xml:id="echoid-s8470" xml:space="preserve">& </s> <s xml:id="echoid-s8471" xml:space="preserve">fi<unsure/>unt grad. </s> <s xml:id="echoid-s8472" xml:space="preserve">57. </s> <s xml:id="echoid-s8473" xml:space="preserve">a quibus detractis 29. </s> <s xml:id="echoid-s8474" xml:space="preserve">reliqui ſunt 28. <lb/></s> <s xml:id="echoid-s8475" xml:space="preserve">quos ſubi<unsure/>cribo. </s> <s xml:id="echoid-s8476" xml:space="preserve">Tandem demo ſigna 3. </s> <s xml:id="echoid-s8477" xml:space="preserve">a ſtgnis 1. </s> <s xml:id="echoid-s8478" xml:space="preserve">remanſit enim ſignum vnum ob mutua-<lb/>tionem alterius ſigni; </s> <s xml:id="echoid-s8479" xml:space="preserve">quod vt efficiam, debeo addere ſigna 12. </s> <s xml:id="echoid-s8480" xml:space="preserve">ideſt, circulum integrum <lb/>vni ſigno relicto; </s> <s xml:id="echoid-s8481" xml:space="preserve">fiuntque ſigna 13. </s> <s xml:id="echoid-s8482" xml:space="preserve">a quibus demo. </s> <s xml:id="echoid-s8483" xml:space="preserve">3. </s> <s xml:id="echoid-s8484" xml:space="preserve">remanentque 10. </s> <s xml:id="echoid-s8485" xml:space="preserve">ſicque ſemper fa-<lb/>c<unsure/>iendum eſt.</s> <s xml:id="echoid-s8486" xml:space="preserve"/> </p> <div xml:id="echoid-div179" type="float" level="2" n="1"> <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve"> <lb/>Sig. # Gra. # ′. # ″ <lb/>13 # 57 # 59 # 60 <lb/>2 # 28 # 0 # 2 <lb/>3 # 29 # 30 # 3 <lb/>10 # 28 # 29 # 59 <lb/></note> <note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve"> <lb/>Sig. # Gra. # ′ <lb/>6 # 5 # 4 <lb/>4 # 3 # 4 <lb/>2 # 2 # 0 <lb/></note> </div> <p> <s xml:id="echoid-s8487" xml:space="preserve">Quod ſi numeri inferiores ſint æquales, aut minores ſuperioribus, facillima eſt opera-<lb/>tio; </s> <s xml:id="echoid-s8488" xml:space="preserve">quia ſinguli inferiores detrahuntur a ſuis ſuperioribus, & </s> <s xml:id="echoid-s8489" xml:space="preserve">reſidui ſubſcribuntur, vt <lb/>hic vides.</s> <s xml:id="echoid-s8490" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div181" type="section" level="1" n="117"> <head xml:id="echoid-head129" style="it" xml:space="preserve">MVLTIPLICATIO.</head> <p> <s xml:id="echoid-s8491" xml:space="preserve">1 IN hac operatione non conſiderantur ſigna, quatenus ſigna ſunt, verum ea reſoluenda ſunt in ſuos gra-<lb/>dus, i<unsure/>jque in loco graduum concipiendi ſunt, vt exemplo patebit.</s> <s xml:id="echoid-s8492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8493" xml:space="preserve">2 Præcipua difficultas eſt in inuenienda denominatione productorum, ſeu cognoſcenda ſpecie, ex mul-<lb/>tiplicatione, emergente. </s> <s xml:id="echoid-s8494" xml:space="preserve">ſit igitur hæc regula, quando duo numeri inuicem ducuntur, adde ſimul eorum de-<lb/>nominatores, ſeu apices, & </s> <s xml:id="echoid-s8495" xml:space="preserve">habebis denominationẽ producti, v. </s> <s xml:id="echoid-s8496" xml:space="preserve">g. </s> <s xml:id="echoid-s8497" xml:space="preserve">ſi multiplicentur inuicem: </s> <s xml:id="echoid-s8498" xml:space="preserve">20′. </s> <s xml:id="echoid-s8499" xml:space="preserve">& </s> <s xml:id="echoid-s8500" xml:space="preserve">4″. </s> <s xml:id="echoid-s8501" xml:space="preserve">pro-<lb/>creabuntur 40′″. </s> <s xml:id="echoid-s8502" xml:space="preserve">quia ex additione, ‘<unsure/>cum,”<unsure/> quæ ſunt denominationes, ſeu apices eorum, fiunt’<unsure/>”<unsure/>. </s> <s xml:id="echoid-s8503" xml:space="preserve">quæ ſunt <lb/>tertia. </s> <s xml:id="echoid-s8504" xml:space="preserve">igitur primo n@meri ipſi 10′. </s> <s xml:id="echoid-s8505" xml:space="preserve">& </s> <s xml:id="echoid-s8506" xml:space="preserve">4″. </s> <s xml:id="echoid-s8507" xml:space="preserve">multiplicantur tanquam numeri communes, & </s> <s xml:id="echoid-s8508" xml:space="preserve">fiunt 40″. </s> <s xml:id="echoid-s8509" xml:space="preserve">ſecun- <pb o="90" file="0110" n="114" rhead="De Mundi Fabrica,"/> dae orum apices additi ſcribuntur ſupra productum, ſicque peracta eſt multiplicatio. </s> <s xml:id="echoid-s8510" xml:space="preserve">Aduertendum ta-<lb/>men eſt, quod apex, ſeu denominatio integrorum, v. </s> <s xml:id="echoid-s8511" xml:space="preserve">g. </s> <s xml:id="echoid-s8512" xml:space="preserve">graduum, ſupponitur eſſe 0. </s> <s xml:id="echoid-s8513" xml:space="preserve">quæ addita aliorum <lb/>apicibus, eos non immutat: </s> <s xml:id="echoid-s8514" xml:space="preserve">quare quando ducuntur gradus, in alias ſexagenas, productus erit ſemper eiuſdem <lb/>apicis, cuius eſt illa ſexagena, vt ſi duco 3″. </s> <s xml:id="echoid-s8515" xml:space="preserve">in gr. </s> <s xml:id="echoid-s8516" xml:space="preserve">15. </s> <s xml:id="echoid-s8517" xml:space="preserve">fiunt 45″. </s> <s xml:id="echoid-s8518" xml:space="preserve">&</s> <s xml:id="echoid-s8519" xml:space="preserve">c. </s> <s xml:id="echoid-s8520" xml:space="preserve">ſic ductis inuicem gradibus producuntur <lb/>pariter gradus, quia 0. </s> <s xml:id="echoid-s8521" xml:space="preserve">addita cum alia 0. </s> <s xml:id="echoid-s8522" xml:space="preserve">facit 0.</s> <s xml:id="echoid-s8523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8524" xml:space="preserve">3 Quoties numerus productus eſt maior, quam 60. </s> <s xml:id="echoid-s8525" xml:space="preserve">tunc quoties in ipſo continetur numerus 60. </s> <s xml:id="echoid-s8526" xml:space="preserve">tot vnita-<lb/>tes ſunt addendæ loco ſequenti ad ſiniſtram, ſiue loco proxime minoris denominationis ſiue pauciorum api-<lb/>cum, v. </s> <s xml:id="echoid-s8527" xml:space="preserve">g. </s> <s xml:id="echoid-s8528" xml:space="preserve">ductus 3′. </s> <s xml:id="echoid-s8529" xml:space="preserve">in 25″. </s> <s xml:id="echoid-s8530" xml:space="preserve">productus eſt 75′″. </s> <s xml:id="echoid-s8531" xml:space="preserve">quæ omnia ſemel continent 60. </s> <s xml:id="echoid-s8532" xml:space="preserve">& </s> <s xml:id="echoid-s8533" xml:space="preserve">præterea 15. </s> <s xml:id="echoid-s8534" xml:space="preserve">ideo productus <lb/>ſic erit ſcribendus 1″. </s> <s xml:id="echoid-s8535" xml:space="preserve">15″. </s> <s xml:id="echoid-s8536" xml:space="preserve">ſub ſuis titulis. </s> <s xml:id="echoid-s8537" xml:space="preserve">ratio eſt quia 60. </s> <s xml:id="echoid-s8538" xml:space="preserve">ſcrupula maioris denominationis efficiunt vnum <lb/>tantum ſcrupulum minoris proximè appellationis.</s> <s xml:id="echoid-s8539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8540" xml:space="preserve">4 Oportet ſingulos numeros multiplicantes in ſingulos multiplicandos ducere. </s> <s xml:id="echoid-s8541" xml:space="preserve">exemplum. </s> <s xml:id="echoid-s8542" xml:space="preserve">ſint igitur hi <lb/>numeri inuicem ducendi, hoc eſt ſigna 1. </s> <s xml:id="echoid-s8543" xml:space="preserve">gr. </s> <s xml:id="echoid-s8544" xml:space="preserve">3. </s> <s xml:id="echoid-s8545" xml:space="preserve">25′. </s> <s xml:id="echoid-s8546" xml:space="preserve">35″. </s> <s xml:id="echoid-s8547" xml:space="preserve">multiplicanda per gr. </s> <s xml:id="echoid-s8548" xml:space="preserve">3. </s> <s xml:id="echoid-s8549" xml:space="preserve">2″. </s> <s xml:id="echoid-s8550" xml:space="preserve">ſcribantur vt in formu-<lb/> <anchor type="note" xlink:label="note-0110-01a" xlink:href="note-0110-01"/> <anchor type="note" xlink:label="note-0110-02a" xlink:href="note-0110-02"/> la apparct, ducta ſub eis linea quæ produ-<lb/>ctos ſeparat. </s> <s xml:id="echoid-s8551" xml:space="preserve">Primo igitur duco duo prima <lb/>in 35. </s> <s xml:id="echoid-s8552" xml:space="preserve">ſecunda, ideſt, 2′. </s> <s xml:id="echoid-s8553" xml:space="preserve">in 35′ ′. </s> <s xml:id="echoid-s8554" xml:space="preserve">fiũtque 70′″. <lb/></s> <s xml:id="echoid-s8555" xml:space="preserve">ex præſcriptis regulis: </s> <s xml:id="echoid-s8556" xml:space="preserve">in quibus quia ſemel <lb/>60. </s> <s xml:id="echoid-s8557" xml:space="preserve">continetur, ideo pono vnitatem ſub lo-<lb/>co proximè minoris apicis, ideſt, ſub ſecuu-<lb/>dis; </s> <s xml:id="echoid-s8558" xml:space="preserve">reliqua autem 10′″. </s> <s xml:id="echoid-s8559" xml:space="preserve">ſub tertijs, vt in For <lb/>mula vides. </s> <s xml:id="echoid-s8560" xml:space="preserve">poſtea duco 2′. </s> <s xml:id="echoid-s8561" xml:space="preserve">in 25. </s> <s xml:id="echoid-s8562" xml:space="preserve">fiuntque <lb/>50″. </s> <s xml:id="echoid-s8563" xml:space="preserve">ſecunda; </s> <s xml:id="echoid-s8564" xml:space="preserve">quia ſingulares apices additi <lb/>efficiunt ſecunda. </s> <s xml:id="echoid-s8565" xml:space="preserve">ſcribo igitur 50″. </s> <s xml:id="echoid-s8566" xml:space="preserve">ſub lo-<lb/>co ſecundorum. </s> <s xml:id="echoid-s8567" xml:space="preserve">deinde duco 2′. </s> <s xml:id="echoid-s8568" xml:space="preserve">in gr. </s> <s xml:id="echoid-s8569" xml:space="preserve">3. </s> <s xml:id="echoid-s8570" xml:space="preserve">pro-<lb/>ducitur 6. </s> <s xml:id="echoid-s8571" xml:space="preserve">prima, quia apex gr. </s> <s xml:id="echoid-s8572" xml:space="preserve">eſt 0. </s> <s xml:id="echoid-s8573" xml:space="preserve">qui ad-<lb/>ditus appici 1′. </s> <s xml:id="echoid-s8574" xml:space="preserve">eum non immutat: </s> <s xml:id="echoid-s8575" xml:space="preserve">Scribo <lb/>igitur 6. </s> <s xml:id="echoid-s8576" xml:space="preserve">ſub loco primorum. </s> <s xml:id="echoid-s8577" xml:space="preserve">tandẽ duco 2′. </s> <s xml:id="echoid-s8578" xml:space="preserve"><lb/>in ſignum 1. </s> <s xml:id="echoid-s8579" xml:space="preserve">hoc eſt gr. </s> <s xml:id="echoid-s8580" xml:space="preserve">30. </s> <s xml:id="echoid-s8581" xml:space="preserve">iuxtam primam re-<lb/>gulam; </s> <s xml:id="echoid-s8582" xml:space="preserve">fiuntque 60′. </s> <s xml:id="echoid-s8583" xml:space="preserve">prima, quæ, quia faciunt <lb/>gr. </s> <s xml:id="echoid-s8584" xml:space="preserve">1. </s> <s xml:id="echoid-s8585" xml:space="preserve">ideo ſubſcribo 1. </s> <s xml:id="echoid-s8586" xml:space="preserve">loco graduum; </s> <s xml:id="echoid-s8587" xml:space="preserve">ſicque numerus 2′. </s> <s xml:id="echoid-s8588" xml:space="preserve">functus eſt munere ſuo. </s> <s xml:id="echoid-s8589" xml:space="preserve">Alterum igitur numero-<lb/>rum, ideſt, gr. </s> <s xml:id="echoid-s8590" xml:space="preserve">3. </s> <s xml:id="echoid-s8591" xml:space="preserve">duco in ſi@gulos ſuperiores, eodem modo. </s> <s xml:id="echoid-s8592" xml:space="preserve">Primo in 35″. </s> <s xml:id="echoid-s8593" xml:space="preserve">producunturq; </s> <s xml:id="echoid-s8594" xml:space="preserve">105. </s> <s xml:id="echoid-s8595" xml:space="preserve">quo in nume-<lb/>ro continetur 60. </s> <s xml:id="echoid-s8596" xml:space="preserve">ſeme@. </s> <s xml:id="echoid-s8597" xml:space="preserve">Quareſcribo vnitatem loco primorum; </s> <s xml:id="echoid-s8598" xml:space="preserve">reliquum vero 45″. </s> <s xml:id="echoid-s8599" xml:space="preserve">ſub ſecundis. </s> <s xml:id="echoid-s8600" xml:space="preserve">deinde <lb/>ductis 3. </s> <s xml:id="echoid-s8601" xml:space="preserve">in 25′. </s> <s xml:id="echoid-s8602" xml:space="preserve">fiunt 75′. </s> <s xml:id="echoid-s8603" xml:space="preserve">hoc eſt gr. </s> <s xml:id="echoid-s8604" xml:space="preserve">1. </s> <s xml:id="echoid-s8605" xml:space="preserve">& </s> <s xml:id="echoid-s8606" xml:space="preserve">15′. </s> <s xml:id="echoid-s8607" xml:space="preserve">quæ ſuis locis adſcribo, vt vides in formula. </s> <s xml:id="echoid-s8608" xml:space="preserve">rurſus ductis 3. </s> <s xml:id="echoid-s8609" xml:space="preserve">in 3. </s> <s xml:id="echoid-s8610" xml:space="preserve"><lb/>fiunt 9. </s> <s xml:id="echoid-s8611" xml:space="preserve">ideſt gr. </s> <s xml:id="echoid-s8612" xml:space="preserve">9. </s> <s xml:id="echoid-s8613" xml:space="preserve">ſub loco graduum ponendi. </s> <s xml:id="echoid-s8614" xml:space="preserve">Tandem ductis 3. </s> <s xml:id="echoid-s8615" xml:space="preserve">in ſignum 1. </s> <s xml:id="echoid-s8616" xml:space="preserve">ſeu in gr. </s> <s xml:id="echoid-s8617" xml:space="preserve">30. </s> <s xml:id="echoid-s8618" xml:space="preserve">emergunt 90. </s> <s xml:id="echoid-s8619" xml:space="preserve">gra-<lb/>dus, ſeu ſigna 3. </s> <s xml:id="echoid-s8620" xml:space="preserve">quæ ſub titulo ſignorum ſunt ſubſcr@bẽda. </s> <s xml:id="echoid-s8621" xml:space="preserve">poſtremo hi omnes numeri in vnam ſummam ſunt <lb/>colligendi iuxta regulas Additionis; </s> <s xml:id="echoid-s8622" xml:space="preserve">conflaturque ſumma hæc; </s> <s xml:id="echoid-s8623" xml:space="preserve">Signa 3. </s> <s xml:id="echoid-s8624" xml:space="preserve">gr. </s> <s xml:id="echoid-s8625" xml:space="preserve">11. </s> <s xml:id="echoid-s8626" xml:space="preserve">23′. </s> <s xml:id="echoid-s8627" xml:space="preserve">36″. </s> <s xml:id="echoid-s8628" xml:space="preserve">10′″. </s> <s xml:id="echoid-s8629" xml:space="preserve">Huius autem <lb/>rei de<unsure/>monſtratio pendet ex fractionibus vulgarium numerorum. </s> <s xml:id="echoid-s8630" xml:space="preserve">Fractiones enim Aſtronomicę poſſunt re-<lb/>duci ad vulgares, qua ratione vnum primum eſt {1/60}. </s> <s xml:id="echoid-s8631" xml:space="preserve">integr: </s> <s xml:id="echoid-s8632" xml:space="preserve">vnum vero ſecundum eſt, {1/3600}. </s> <s xml:id="echoid-s8633" xml:space="preserve">& </s> <s xml:id="echoid-s8634" xml:space="preserve">ſic de cæteris: </s> <s xml:id="echoid-s8635" xml:space="preserve"><lb/>Si autem ſecundum regulas vulgariũ fractionum multiplicentur inuicem {1/60}. </s> <s xml:id="echoid-s8636" xml:space="preserve">{1/3600}. </s> <s xml:id="echoid-s8637" xml:space="preserve">producunt {1/360000}. </s> <s xml:id="echoid-s8638" xml:space="preserve">qui pro-<lb/>ductus æquiualet vni tertio. </s> <s xml:id="echoid-s8639" xml:space="preserve">qui etiam producitur ex multiplicatione 1′. </s> <s xml:id="echoid-s8640" xml:space="preserve">in 2″. </s> <s xml:id="echoid-s8641" xml:space="preserve">quia 1. </s> <s xml:id="echoid-s8642" xml:space="preserve">in 1. </s> <s xml:id="echoid-s8643" xml:space="preserve">facit 1. </s> <s xml:id="echoid-s8644" xml:space="preserve">& </s> <s xml:id="echoid-s8645" xml:space="preserve">eorum <lb/>apices additi faciunt′″. </s> <s xml:id="echoid-s8646" xml:space="preserve">ponendos ſupra productum, ſic 1′″. </s> <s xml:id="echoid-s8647" xml:space="preserve">eodem modo de reliquis Aſtrom. </s> <s xml:id="echoid-s8648" xml:space="preserve">fractionibus <lb/>æſtimandum eſt.</s> <s xml:id="echoid-s8649" xml:space="preserve"/> </p> <div xml:id="echoid-div181" type="float" level="2" n="1"> <note position="right" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve"> <lb/>Sig. # Gra. # ′. # ″. # ′″. <lb/>1 # 3 # 25 # 35 <lb/>0 # 3 # 2 # 0 <lb/># # # 1 # 10 <lb/># 1 # 6 # 50 <lb/># # 1 <lb/>3 # 1 # 15 # 45 <lb/># 9 <lb/>3 # 11 # 23 # 36 # 10 <lb/></note> <note position="right" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve"> <lb/>Multiplicandi \\ Multiplicant<unsure/>es <lb/>Producti. <lb/>Summa productorum <lb/></note> </div> <p> <s xml:id="echoid-s8650" xml:space="preserve">5 Scias tandem hanc multiplicationem poſſe fieri reductis omnibus partibus, tam numeri multiplican-<lb/>di<unsure/>, quam multiplicantis, ad eorum maximam dcnominationem, de qua reductione dicam in ſequenti tra-<lb/>ctatu de diuiſione num. </s> <s xml:id="echoid-s8651" xml:space="preserve">6.</s> <s xml:id="echoid-s8652" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div183" type="section" level="1" n="118"> <head xml:id="echoid-head130" style="it" xml:space="preserve">DIVISIO.</head> <p> <s xml:id="echoid-s8653" xml:space="preserve">1 SIcut in multiplicatione non conſiderantur ſigna, ſed in gradus reſoluenda ſunt, ita pariter in di-<lb/>uiſione.</s> <s xml:id="echoid-s8654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8655" xml:space="preserve">2 At in cognoſcenda denominatione quotientis, ſeu producti, contra hic agendũ eſt, ac in multiplica-<lb/>tione ibi enim per additionẽ apicum cõſtabatur apex producti: </s> <s xml:id="echoid-s8656" xml:space="preserve">hic vero per ſubtractionem. </s> <s xml:id="echoid-s8657" xml:space="preserve">nam in diuiſione <lb/>ſubtrahetur apex minor a maiori, & </s> <s xml:id="echoid-s8658" xml:space="preserve">reliquus apex erit dennminatio quotientis. </s> <s xml:id="echoid-s8659" xml:space="preserve">vb illud etiam repetendum, <lb/>apicem integrorum, v.</s> <s xml:id="echoid-s8660" xml:space="preserve">g. </s> <s xml:id="echoid-s8661" xml:space="preserve">graduum eſſe 0. </s> <s xml:id="echoid-s8662" xml:space="preserve">exemplum; </s> <s xml:id="echoid-s8663" xml:space="preserve">diuidantur 24″. </s> <s xml:id="echoid-s8664" xml:space="preserve">per 6′. </s> <s xml:id="echoid-s8665" xml:space="preserve">primo numeri ipſi diuidẽdi ſunt <lb/>vti vulgares numeri, eritque quotiens 4. </s> <s xml:id="echoid-s8666" xml:space="preserve">cuius denom. </s> <s xml:id="echoid-s8667" xml:space="preserve">ſeu apex habetur detrahendo′. </s> <s xml:id="echoid-s8668" xml:space="preserve">a″. </s> <s xml:id="echoid-s8669" xml:space="preserve">remanent enim 1. <lb/></s> <s xml:id="echoid-s8670" xml:space="preserve">apex quoti<unsure/>entis, ſcilicet 4′. </s> <s xml:id="echoid-s8671" xml:space="preserve">rurſuſ diuidẽda ſunt 18′. </s> <s xml:id="echoid-s8672" xml:space="preserve">per 9′. </s> <s xml:id="echoid-s8673" xml:space="preserve">erit quotiens. </s> <s xml:id="echoid-s8674" xml:space="preserve">2. </s> <s xml:id="echoid-s8675" xml:space="preserve">nam detracto′. </s> <s xml:id="echoid-s8676" xml:space="preserve">ab′. </s> <s xml:id="echoid-s8677" xml:space="preserve">remanet 0. </s> <s xml:id="echoid-s8678" xml:space="preserve">qui <lb/>apex eſt integri, v.</s> <s xml:id="echoid-s8679" xml:space="preserve">g. </s> <s xml:id="echoid-s8680" xml:space="preserve">gradus: </s> <s xml:id="echoid-s8681" xml:space="preserve">ergo quotiens erit 2. </s> <s xml:id="echoid-s8682" xml:space="preserve">ſeu gr. </s> <s xml:id="echoid-s8683" xml:space="preserve">2.</s> <s xml:id="echoid-s8684" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. # ′. # ″ <lb/>D´uideudus. # 1 # 2 # 30 # 24 <lb/>Diuiſor. # 0 # 6 # 0 # 0 <lb/>Quotiens. # # 6 # 5 # 4 <lb/></note> <p> <s xml:id="echoid-s8685" xml:space="preserve">2 Quando igitur Aſtronomicus numerus diuiden-<lb/>dus, non fuerit minor diuiſore, ſed ei æqualis, aut maior: <lb/></s> <s xml:id="echoid-s8686" xml:space="preserve">pariterque cum eo apex eius non fuerit minor apice di-<lb/>uiſoris ſed ei æqualis, aut maior; </s> <s xml:id="echoid-s8687" xml:space="preserve">& </s> <s xml:id="echoid-s8688" xml:space="preserve">præterea diuiſor ha-<lb/>neat vnicum membrum tũc facilima eſt partitio, v.</s> <s xml:id="echoid-s8689" xml:space="preserve">g. </s> <s xml:id="echoid-s8690" xml:space="preserve">ſint <lb/>diuidenda, vt in exemplo apparet, ſigna 1. </s> <s xml:id="echoid-s8691" xml:space="preserve">gr. </s> <s xml:id="echoid-s8692" xml:space="preserve">6. </s> <s xml:id="echoid-s8693" xml:space="preserve">30′. </s> <s xml:id="echoid-s8694" xml:space="preserve">24″. </s> <s xml:id="echoid-s8695" xml:space="preserve"><lb/>per gr. </s> <s xml:id="echoid-s8696" xml:space="preserve">{0/6}. </s> <s xml:id="echoid-s8697" xml:space="preserve">Primo diuido 24′. </s> <s xml:id="echoid-s8698" xml:space="preserve">per {0/6}. </s> <s xml:id="echoid-s8699" xml:space="preserve">proueniuni 4″. </s> <s xml:id="echoid-s8700" xml:space="preserve">quia <pb o="91" file="0111" n="115" rhead="Liber Nonus."/> minor apex graduumo. </s> <s xml:id="echoid-s8701" xml:space="preserve">detractus à maiori″. </s> <s xml:id="echoid-s8702" xml:space="preserve">nihil minuit. </s> <s xml:id="echoid-s8703" xml:space="preserve">ſcribo itaque 4. </s> <s xml:id="echoid-s8704" xml:space="preserve">ſubtirulo″. </s> <s xml:id="echoid-s8705" xml:space="preserve">eadem ratione diui-<lb/>ſis 30′. </s> <s xml:id="echoid-s8706" xml:space="preserve">per {0/6}. </s> <s xml:id="echoid-s8707" xml:space="preserve">producitur 5. </s> <s xml:id="echoid-s8708" xml:space="preserve">tandem diuiſis gr. </s> <s xml:id="echoid-s8709" xml:space="preserve">36. </s> <s xml:id="echoid-s8710" xml:space="preserve">(reſoluo enim ſignum 1. </s> <s xml:id="echoid-s8711" xml:space="preserve">in gr. </s> <s xml:id="echoid-s8712" xml:space="preserve">30. </s> <s xml:id="echoid-s8713" xml:space="preserve">qui cũ gr. </s> <s xml:id="echoid-s8714" xml:space="preserve">6. </s> <s xml:id="echoid-s8715" xml:space="preserve">efficiunt efficiunt <lb/>36. </s> <s xml:id="echoid-s8716" xml:space="preserve">per {0/6}. </s> <s xml:id="echoid-s8717" xml:space="preserve">producitur 6. </s> <s xml:id="echoid-s8718" xml:space="preserve">ideſt, ſex integra; </s> <s xml:id="echoid-s8719" xml:space="preserve">qui in exemplo ſunt gradus.</s> <s xml:id="echoid-s8720" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8721" xml:space="preserve">4 In reliquis caſibus, quando ſcilicet numerus, aut apex diuiſoris eſt maior numero, aut apice diuidendi, <lb/>& </s> <s xml:id="echoid-s8722" xml:space="preserve">vterque aut alter conſtat gradibus, primis, ſecundis, & </s> <s xml:id="echoid-s8723" xml:space="preserve">c. </s> <s xml:id="echoid-s8724" xml:space="preserve">tunc occurrunt variæ, ac magnę difficultates; </s> <s xml:id="echoid-s8725" xml:space="preserve">quas <lb/>hac vnica regula ſuperabis. </s> <s xml:id="echoid-s8726" xml:space="preserve">Quando numerus diuidendus minor eſt, quam diuiſor, cum toties multiplica per <lb/>60. </s> <s xml:id="echoid-s8727" xml:space="preserve">donec ſit ei æqualis, aut mai<unsure/>or. </s> <s xml:id="echoid-s8728" xml:space="preserve">ſimiliter ſi apex numeri diuidendi ſit minor apice diuiſoris, multiplica nu-<lb/>merum diuidendum toties per 60. </s> <s xml:id="echoid-s8729" xml:space="preserve">quouſque apex eius ſit æqualis, aut maior apice diuiſoris: </s> <s xml:id="echoid-s8730" xml:space="preserve">ex hac enim mul-<lb/>tiplicatione per 60. </s> <s xml:id="echoid-s8731" xml:space="preserve">grad. </s> <s xml:id="echoid-s8732" xml:space="preserve">fiunt prima, prima vero fiunt ſecunda, ſecunda euadunt tertia, &</s> <s xml:id="echoid-s8733" xml:space="preserve">c. </s> <s xml:id="echoid-s8734" xml:space="preserve">vt conſideranti ea, <lb/>quæ initio huius tractatus diximus, patere poteſt. </s> <s xml:id="echoid-s8735" xml:space="preserve">Exemplum. </s> <s xml:id="echoid-s8736" xml:space="preserve">ſint diuidenda 3′ per 6′. </s> <s xml:id="echoid-s8737" xml:space="preserve">quia numerus diuiden-<lb/>dus minor eſt, diu dente eum due in 60. </s> <s xml:id="echoid-s8738" xml:space="preserve">fientque 180″. </s> <s xml:id="echoid-s8739" xml:space="preserve">qui erit nouus diuidendus priori æqualis, aptus tamen <lb/>diuiſioni, diuiſis ig@tur 180″. </s> <s xml:id="echoid-s8740" xml:space="preserve">per 6′. </s> <s xml:id="echoid-s8741" xml:space="preserve">erit quotiens 30′. </s> <s xml:id="echoid-s8742" xml:space="preserve">cuius apexerit′. </s> <s xml:id="echoid-s8743" xml:space="preserve">iuxta ſecundam regulam. </s> <s xml:id="echoid-s8744" xml:space="preserve">rurſus diui-<lb/>denda ſint 4′. </s> <s xml:id="echoid-s8745" xml:space="preserve">per 2″. </s> <s xml:id="echoid-s8746" xml:space="preserve">quia apex diuidendi eſt minor altero, due 4′. </s> <s xml:id="echoid-s8747" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8748" xml:space="preserve">fientq; </s> <s xml:id="echoid-s8749" xml:space="preserve">240″. </s> <s xml:id="echoid-s8750" xml:space="preserve">ea iam diuide per 2″. <lb/></s> <s xml:id="echoid-s8751" xml:space="preserve">productus erit 120. </s> <s xml:id="echoid-s8752" xml:space="preserve">ideſt, gr. </s> <s xml:id="echoid-s8753" xml:space="preserve">120. </s> <s xml:id="echoid-s8754" xml:space="preserve">aut aliud genus integrorum; </s> <s xml:id="echoid-s8755" xml:space="preserve">quia detracto apice diuiſoris, qui eſt″. </s> <s xml:id="echoid-s8756" xml:space="preserve">ab apice <lb/>diuidẽdi″. </s> <s xml:id="echoid-s8757" xml:space="preserve">ei æquali relinquitur o. </s> <s xml:id="echoid-s8758" xml:space="preserve">apex quotientis. </s> <s xml:id="echoid-s8759" xml:space="preserve">Pręterea diuide gr. </s> <s xml:id="echoid-s8760" xml:space="preserve">30. </s> <s xml:id="echoid-s8761" xml:space="preserve">per 5′. </s> <s xml:id="echoid-s8762" xml:space="preserve">ductis 30. </s> <s xml:id="echoid-s8763" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8764" xml:space="preserve">fiunt 1800′. </s> <s xml:id="echoid-s8765" xml:space="preserve"><lb/>cùm iam ſintæquales apic s, diuide 1800′. </s> <s xml:id="echoid-s8766" xml:space="preserve">per 5′. </s> <s xml:id="echoid-s8767" xml:space="preserve">erit quotiens 360. </s> <s xml:id="echoid-s8768" xml:space="preserve">gr. </s> <s xml:id="echoid-s8769" xml:space="preserve">integra, ex præſcriptis regulis. </s> <s xml:id="echoid-s8770" xml:space="preserve">ſi tam <lb/>apex, quam numerus ſint minores, vtrumq; </s> <s xml:id="echoid-s8771" xml:space="preserve">augebis per eodem ductu in 60′. </s> <s xml:id="echoid-s8772" xml:space="preserve">vt ſi 3′. </s> <s xml:id="echoid-s8773" xml:space="preserve">diuidenda ſint in 12″. </s> <s xml:id="echoid-s8774" xml:space="preserve">du-<lb/>ctis 3′. </s> <s xml:id="echoid-s8775" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8776" xml:space="preserve">producuntur 180″. </s> <s xml:id="echoid-s8777" xml:space="preserve">quæ iam per 12″. </s> <s xml:id="echoid-s8778" xml:space="preserve">diuiſibilia ſunt, prouenitque ex diuiſione quotiens {0/15}. </s> <s xml:id="echoid-s8779" xml:space="preserve">in-<lb/>tegra. </s> <s xml:id="echoid-s8780" xml:space="preserve">Atque ſic agendum eſt cùm vterque numerus ſimplex eſt, vt in allatis exemplis.</s> <s xml:id="echoid-s8781" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8782" xml:space="preserve">5 Quod ſi plura habeant membra, ideſt, ſigna, gradus, prima, ſecunda, &</s> <s xml:id="echoid-s8783" xml:space="preserve">c. </s> <s xml:id="echoid-s8784" xml:space="preserve">tuncomnia illa membra reſol-<lb/>nenda ſunt per multiplicationem per 60′. </s> <s xml:id="echoid-s8785" xml:space="preserve">ad vltimam denominationem ſeu ad maiorem apicem, v.</s> <s xml:id="echoid-s8786" xml:space="preserve">g. </s> <s xml:id="echoid-s8787" xml:space="preserve">ſit diui-<lb/>dendus, aut diuiſor, numerus hic Sig. </s> <s xml:id="echoid-s8788" xml:space="preserve">1. </s> <s xml:id="echoid-s8789" xml:space="preserve">gr. </s> <s xml:id="echoid-s8790" xml:space="preserve">6. </s> <s xml:id="echoid-s8791" xml:space="preserve">4′. </s> <s xml:id="echoid-s8792" xml:space="preserve">5″. </s> <s xml:id="echoid-s8793" xml:space="preserve">ſed quia figna non conſid rantur niſi vt gradus, ideo erũt <lb/>gr. </s> <s xml:id="echoid-s8794" xml:space="preserve">36. </s> <s xml:id="echoid-s8795" xml:space="preserve">4′. </s> <s xml:id="echoid-s8796" xml:space="preserve">5″. </s> <s xml:id="echoid-s8797" xml:space="preserve">tria hæc membra reducenda ſunt ad vltimam denomioationem quæ eſt ſecundorum, ideſt, om-<lb/>nia ſunt conuertenda|in″. </s> <s xml:id="echoid-s8798" xml:space="preserve">per multipl. </s> <s xml:id="echoid-s8799" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8800" xml:space="preserve">ſic, duco gr. </s> <s xml:id="echoid-s8801" xml:space="preserve">36. </s> <s xml:id="echoid-s8802" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8803" xml:space="preserve">fiunt 2160′. </s> <s xml:id="echoid-s8804" xml:space="preserve">quibus addo 4′. </s> <s xml:id="echoid-s8805" xml:space="preserve">quę prius erãt <lb/>in ipſo numero fiuntque 2164′. </s> <s xml:id="echoid-s8806" xml:space="preserve">hæc rurſus duco in 60′. </s> <s xml:id="echoid-s8807" xml:space="preserve">fiuutque 129840″. </s> <s xml:id="echoid-s8808" xml:space="preserve">ſecunda. </s> <s xml:id="echoid-s8809" xml:space="preserve">quæ cum 5″. </s> <s xml:id="echoid-s8810" xml:space="preserve">prioribus ef-<lb/>ficiunt 129845″. </s> <s xml:id="echoid-s8811" xml:space="preserve">idem ſaciendum eſt cum diuidente ſi plures habeat partes. </s> <s xml:id="echoid-s8812" xml:space="preserve">facta hac reductionẽ ad vltimam <lb/>denominationem, ſi contingat diuidendum adhuc eſſe minorem, aut habere minorem denominationẽ quam <lb/>diuiſor, adhuc ducendus eſt in 60′. </s> <s xml:id="echoid-s8813" xml:space="preserve">vt diuiſore non ſit minor, nec minorem habeat apicem. </s> <s xml:id="echoid-s8814" xml:space="preserve">Exemplum. </s> <s xml:id="echoid-s8815" xml:space="preserve">ſint <lb/>gr. </s> <s xml:id="echoid-s8816" xml:space="preserve">1 {0/0}. </s> <s xml:id="echoid-s8817" xml:space="preserve">15′. </s> <s xml:id="echoid-s8818" xml:space="preserve">30″. </s> <s xml:id="echoid-s8819" xml:space="preserve">diuidenda per 15′. </s> <s xml:id="echoid-s8820" xml:space="preserve">quia diuidendus habet plures partes, quarum vltima eſt ſecundorum, ideo <lb/>reliquas omnes ad ſeci<unsure/> nda reduco, eas per 60′. </s> <s xml:id="echoid-s8821" xml:space="preserve">multiplicando, ſic; </s> <s xml:id="echoid-s8822" xml:space="preserve">ductis {0/10}. </s> <s xml:id="echoid-s8823" xml:space="preserve">in 60′. </s> <s xml:id="echoid-s8824" xml:space="preserve">fiunt 600′. </s> <s xml:id="echoid-s8825" xml:space="preserve">quæ cum prio-<lb/>ribus 15′. </s> <s xml:id="echoid-s8826" xml:space="preserve">erunt 615′. </s> <s xml:id="echoid-s8827" xml:space="preserve">quibus rurſum ductis in 60′. </s> <s xml:id="echoid-s8828" xml:space="preserve">proueniunt 36900″. </s> <s xml:id="echoid-s8829" xml:space="preserve">quę cũ prioribus 30″. </s> <s xml:id="echoid-s8830" xml:space="preserve">efficiunt 36930″. <lb/></s> <s xml:id="echoid-s8831" xml:space="preserve">quia vero diuiſor 15′. </s> <s xml:id="echoid-s8832" xml:space="preserve">eſt ſimplex, non eſt opus reductionem ad vltimam denominationem. </s> <s xml:id="echoid-s8833" xml:space="preserve">ſimiliter quia di-<lb/>uidendus reductus ad vltimam denominationem eſt maior diuiſore, habentque maiorem denominationem <lb/>non eſt opus vlteriori reductione. </s> <s xml:id="echoid-s8834" xml:space="preserve">iam igitur diuido 36930″. </s> <s xml:id="echoid-s8835" xml:space="preserve">per 15. </s> <s xml:id="echoid-s8836" xml:space="preserve">oriturque Quotiens 2464′. </s> <s xml:id="echoid-s8837" xml:space="preserve">quę ſunt pri-<lb/>ma, quia detracto apice diuiſoris, qui eſt′. </s> <s xml:id="echoid-s8838" xml:space="preserve">ab apice diuidendi qui eſt″. </s> <s xml:id="echoid-s8839" xml:space="preserve">relinquitur′. </s> <s xml:id="echoid-s8840" xml:space="preserve">apex quotientis, ex præ-<lb/>in@ffis regulis. </s> <s xml:id="echoid-s8841" xml:space="preserve">Quod ſi diuiſor 15″. </s> <s xml:id="echoid-s8842" xml:space="preserve">fuiſſet ſecundorum, quo iens fuiſſet graduum, ſeu integrorum {0/2462}. </s> <s xml:id="echoid-s8843" xml:space="preserve">quia <lb/>detractis ſecundis a ſecundis, relinquitur o. </s> <s xml:id="echoid-s8844" xml:space="preserve">quæ eſt graduum ſeu alterius integri appellatio.</s> <s xml:id="echoid-s8845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8846" xml:space="preserve">Quando autem quotiens eſt minor quam 60. </s> <s xml:id="echoid-s8847" xml:space="preserve">vt in noſtro exemplo, tunc diuidendus eſt per 60. </s> <s xml:id="echoid-s8848" xml:space="preserve">vt appareat <lb/>quotſcrupula contineat minoris proximè appellationis. </s> <s xml:id="echoid-s8849" xml:space="preserve">in caſu noſtro 2464′. </s> <s xml:id="echoid-s8850" xml:space="preserve">diuiſa per 60′. </s> <s xml:id="echoid-s8851" xml:space="preserve">producunt {0/411}. <lb/></s> <s xml:id="echoid-s8852" xml:space="preserve">gradus, nam@o. </s> <s xml:id="echoid-s8853" xml:space="preserve">prima efficiunt gr. </s> <s xml:id="echoid-s8854" xml:space="preserve">vnum. </s> <s xml:id="echoid-s8855" xml:space="preserve">pariter ſi eadem {0/462}. </s> <s xml:id="echoid-s8856" xml:space="preserve">ſint gradus, diuidenda ſunt per 30. </s> <s xml:id="echoid-s8857" xml:space="preserve">vt exhibeãt <lb/>ſigna omnia, quæ in ipſis continentur, eruntque ſigna 82. </s> <s xml:id="echoid-s8858" xml:space="preserve">& </s> <s xml:id="echoid-s8859" xml:space="preserve">gr. </s> <s xml:id="echoid-s8860" xml:space="preserve">2. </s> <s xml:id="echoid-s8861" xml:space="preserve">relinquentur.</s> <s xml:id="echoid-s8862" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8863" xml:space="preserve">6 Accidit aliquando diuiſorem eſſe maiorem diuidẽdo, ynde oritur quotiens qui eſt fractio vnius integri. <lb/></s> <s xml:id="echoid-s8864" xml:space="preserve">quæ fractio ſi bene perſpecta ſit, indicat an quotiens ſit primorum, an ſecundorum, & </s> <s xml:id="echoid-s8865" xml:space="preserve">c. </s> <s xml:id="echoid-s8866" xml:space="preserve">v.</s> <s xml:id="echoid-s8867" xml:space="preserve">g. </s> <s xml:id="echoid-s8868" xml:space="preserve">ſi diuidantur 6′. </s> <s xml:id="echoid-s8869" xml:space="preserve"><lb/>per 12′. </s> <s xml:id="echoid-s8870" xml:space="preserve">producentur {6/12}. </s> <s xml:id="echoid-s8871" xml:space="preserve">hoc eſt, per minutiarum depreſſionem {2/1}. </s> <s xml:id="echoid-s8872" xml:space="preserve">ideſt dimidius gradus, ſiue 30′. </s> <s xml:id="echoid-s8873" xml:space="preserve">ſimiliter ſi <lb/>2′. </s> <s xml:id="echoid-s8874" xml:space="preserve">diuidantur per {0/4}. </s> <s xml:id="echoid-s8875" xml:space="preserve">4′. </s> <s xml:id="echoid-s8876" xml:space="preserve">reſoluo diuiſorem in 244′. </s> <s xml:id="echoid-s8877" xml:space="preserve">diu@ſis iam 2. </s> <s xml:id="echoid-s8878" xml:space="preserve">per 244′. </s> <s xml:id="echoid-s8879" xml:space="preserve">ſic ſtabit quotiens 2@4. </s> <s xml:id="echoid-s8880" xml:space="preserve">vnius integri, <lb/>ſiue per minutiarum depreſſionem, 1 {1/22}. </s> <s xml:id="echoid-s8881" xml:space="preserve">vnius integri. </s> <s xml:id="echoid-s8882" xml:space="preserve">quæ fractio valet quaſi dimidium vnius primi, nã gra-<lb/>dus vnus continet 60. </s> <s xml:id="echoid-s8883" xml:space="preserve">quare dimidium vnius primi erit 1 {1/20}. </s> <s xml:id="echoid-s8884" xml:space="preserve">pars gradus. </s> <s xml:id="echoid-s8885" xml:space="preserve">ſimili ſpeculatione opus eſt in ſimili-<lb/>ac proinde prima eſſe ſexageeſimas gradus, ſecunda eſſe termilleſimas eiuſdem gradus, tertia eſſe ducenteſimas <lb/>ſex decemilleſimas grad. </s> <s xml:id="echoid-s8886" xml:space="preserve">&</s> <s xml:id="echoid-s8887" xml:space="preserve">c. </s> <s xml:id="echoid-s8888" xml:space="preserve">Ratio huius diuiſionis pendet ex diuiſione minutiarum communium, quemad-<lb/>modum etiam multiplicationis, atque hæc breuitati noſtræ ſufficiant.</s> <s xml:id="echoid-s8889" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div184" type="section" level="1" n="119"> <head xml:id="echoid-head131" style="it" xml:space="preserve">Vſus pramiſſarum Tabularum, ex quo calculus Lunæ fit. Cap. XIIII.</head> <p> <s xml:id="echoid-s8890" xml:space="preserve">EXemplis melius, quam præceptis multis, rem hanc percipiemus. </s> <s xml:id="echoid-s8891" xml:space="preserve">ſit igitur hæc propoſitio.</s> <s xml:id="echoid-s8892" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div185" type="section" level="1" n="120"> <head xml:id="echoid-head132" style="it" xml:space="preserve">Ad datum tempus, medium motum longitudinis Lunæreperire. Propoſ. 1.</head> <p> <s xml:id="echoid-s8893" xml:space="preserve">SItergo exempli cauſa, datum tempus, quo hæc ſcribimus, annus Chriſti 1616. </s> <s xml:id="echoid-s8894" xml:space="preserve">dies 16. </s> <s xml:id="echoid-s8895" xml:space="preserve">Iulij, hora vna poſt <lb/>meridiem cum minutis 15′. </s> <s xml:id="echoid-s8896" xml:space="preserve">ideſt ad inſtans vltimum huius temporis reperire diſtantiam centriepicycli ab <lb/>æquinoctio. </s> <s xml:id="echoid-s8897" xml:space="preserve">porrò in primis conſiderandũ eſt quid ſibi velit vulgare illud tempus, ſeu qua ratione illud Aſtro-<lb/>nomi accipiant. </s> <s xml:id="echoid-s8898" xml:space="preserve">Cum ergo vulgo dicitur anno Domini 1616. </s> <s xml:id="echoid-s8899" xml:space="preserve">die 16. </s> <s xml:id="echoid-s8900" xml:space="preserve">lulij, h. </s> <s xml:id="echoid-s8901" xml:space="preserve">1. </s> <s xml:id="echoid-s8902" xml:space="preserve">p.</s> <s xml:id="echoid-s8903" xml:space="preserve">m. </s> <s xml:id="echoid-s8904" xml:space="preserve">aduertendum eſt annum <lb/>1616. </s> <s xml:id="echoid-s8905" xml:space="preserve">nondum eſſe completum, ſed labentem. </s> <s xml:id="echoid-s8906" xml:space="preserve">ſimiliter lulius nondum eſt abſolutus, ſed dies eius 16. </s> <s xml:id="echoid-s8907" xml:space="preserve">tantum <pb o="92" file="0112" n="116" rhead="De Mundi Fabrica,"/> exacta eſt, & </s> <s xml:id="echoid-s8908" xml:space="preserve">pręterea hora 1. </s> <s xml:id="echoid-s8909" xml:space="preserve">quæ pertinet ad diem 17. </s> <s xml:id="echoid-s8910" xml:space="preserve">quapropter Aſtronomi omnes temporis ſpecies com-<lb/>pleta aſſumunt, tempuſque iſtud ſic Aſtronomicè ad calculum diſponetur, vt in formula; </s> <s xml:id="echoid-s8911" xml:space="preserve">vbi omnia comple-<lb/> <anchor type="note" xlink:label="note-0112-01a" xlink:href="note-0112-01"/> <anchor type="note" xlink:label="note-0112-02a" xlink:href="note-0112-02"/> ta eſie intelliguntur, ſicuti reuera ſunt. </s> <s xml:id="echoid-s8912" xml:space="preserve">ſecun-<lb/>do cõſiderandum eſt, an menſis completus ſit <lb/>anni communis, an biſſextilis. </s> <s xml:id="echoid-s8913" xml:space="preserve">in caſu noſtro <lb/>eſt biſſextilis, quia eſt menfis anni 1606. </s> <s xml:id="echoid-s8914" xml:space="preserve">laben-<lb/>tis, qui intercalaris eſt. </s> <s xml:id="echoid-s8915" xml:space="preserve">Ideo no. </s> <s xml:id="echoid-s8916" xml:space="preserve">andus eſt lit-<lb/>tera B. </s> <s xml:id="echoid-s8917" xml:space="preserve">de anno autem biſſex tili infra cap. </s> <s xml:id="echoid-s8918" xml:space="preserve">de <lb/>Sole agemus. </s> <s xml:id="echoid-s8919" xml:space="preserve">accommodato igitur hoc modo <lb/>tempore, eoque deſcripto ſeriatim, vt in for-<lb/>mula vides, iam per ſingulas ſpecies accipien-<lb/>di ſunt motus ex præmiſſis Tabulis, hac me-<lb/>thodo; </s> <s xml:id="echoid-s8920" xml:space="preserve">primo cum annis 1600. </s> <s xml:id="echoid-s8921" xml:space="preserve">qui ſunt noſtri <lb/>temporis Radix, accipio ex annorum Tabula <lb/>ſimiliter Radicem motuum ſcripta in fine co-<lb/>lumnæ longitudinis Lunæ quæ eſt ſigna 7. </s> <s xml:id="echoid-s8922" xml:space="preserve">gr. </s> <s xml:id="echoid-s8923" xml:space="preserve">25. </s> <s xml:id="echoid-s8924" xml:space="preserve">min. </s> <s xml:id="echoid-s8925" xml:space="preserve">91. </s> <s xml:id="echoid-s8926" xml:space="preserve">eamque ſcribo è regione annorum 1600. </s> <s xml:id="echoid-s8927" xml:space="preserve">vti factum <lb/>vides. </s> <s xml:id="echoid-s8928" xml:space="preserve">deinde cum annis 15. </s> <s xml:id="echoid-s8929" xml:space="preserve">ex eadem columna accipio 6. </s> <s xml:id="echoid-s8930" xml:space="preserve">0. </s> <s xml:id="echoid-s8931" xml:space="preserve">17′. </s> <s xml:id="echoid-s8932" xml:space="preserve">quę in formula in directum annorum 15. </s> <s xml:id="echoid-s8933" xml:space="preserve">de-<lb/>ſcribo. </s> <s xml:id="echoid-s8934" xml:space="preserve">poſtea ex Tabula menſium ex menſibus anni biſſextilis, è regione menſis Iunij, accipio 7. </s> <s xml:id="echoid-s8935" xml:space="preserve">28. </s> <s xml:id="echoid-s8936" xml:space="preserve">6′. </s> <s xml:id="echoid-s8937" xml:space="preserve">quæ <lb/>pariter in formula aſcribo menſi Iunio. </s> <s xml:id="echoid-s8938" xml:space="preserve">Quarto cum diebus 15. </s> <s xml:id="echoid-s8939" xml:space="preserve">ex Tabula dierum accipio 7. </s> <s xml:id="echoid-s8940" xml:space="preserve">0. </s> <s xml:id="echoid-s8941" xml:space="preserve">49′. </s> <s xml:id="echoid-s8942" xml:space="preserve">quæ pa-<lb/>riter diebus 16. </s> <s xml:id="echoid-s8943" xml:space="preserve">adſcribo. </s> <s xml:id="echoid-s8944" xml:space="preserve">Quinto idem facio cum hora vna ex horarum Tabula, cui cõuenit motus, min. </s> <s xml:id="echoid-s8945" xml:space="preserve">331. <lb/></s> <s xml:id="echoid-s8946" xml:space="preserve">quæ in formula refero. </s> <s xml:id="echoid-s8947" xml:space="preserve">poſtremo ex eadem Tabula cum min. </s> <s xml:id="echoid-s8948" xml:space="preserve">151. </s> <s xml:id="echoid-s8949" xml:space="preserve">è regione eorum, accipio min. </s> <s xml:id="echoid-s8950" xml:space="preserve">8′. </s> <s xml:id="echoid-s8951" xml:space="preserve">tempo-<lb/>ris, quibus in formulam relatis; </s> <s xml:id="echoid-s8952" xml:space="preserve">habeo iam omnes motus correſpondentes propoſitis temporis partibus. </s> <s xml:id="echoid-s8953" xml:space="preserve">re-<lb/>ſtat igitur vt omnes hi motus in vnam addantur ſummam, eo modo, quem ſupra docuimus, eritque ſumma <lb/>hæc Sig. </s> <s xml:id="echoid-s8954" xml:space="preserve">4. </s> <s xml:id="echoid-s8955" xml:space="preserve">gr. </s> <s xml:id="echoid-s8956" xml:space="preserve">25. </s> <s xml:id="echoid-s8957" xml:space="preserve">min. </s> <s xml:id="echoid-s8958" xml:space="preserve">2′. </s> <s xml:id="echoid-s8959" xml:space="preserve">ex qua colligo centrum epicy. </s> <s xml:id="echoid-s8960" xml:space="preserve">Lunæ eſſe in gr. </s> <s xml:id="echoid-s8961" xml:space="preserve">25. </s> <s xml:id="echoid-s8962" xml:space="preserve">ac 2′. </s> <s xml:id="echoid-s8963" xml:space="preserve">Leonis. </s> <s xml:id="echoid-s8964" xml:space="preserve">motus vero huius <lb/>centri dicitur motus medius Lunę. </s> <s xml:id="echoid-s8965" xml:space="preserve">quoniam vero in Tabula horarum ſunt tantũ min. </s> <s xml:id="echoid-s8966" xml:space="preserve">30′. </s> <s xml:id="echoid-s8967" xml:space="preserve">ſi darentur in tem-<lb/>pore plura, quam 30′. </s> <s xml:id="echoid-s8968" xml:space="preserve">tuac ex illis 30. </s> <s xml:id="echoid-s8969" xml:space="preserve">quæ ſunt in Tabula, ſupplendum eſſet per partes, v. </s> <s xml:id="echoid-s8970" xml:space="preserve">g. </s> <s xml:id="echoid-s8971" xml:space="preserve">ſi darentur 45. </s> <s xml:id="echoid-s8972" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s8973" xml:space="preserve">horæ, accipienda eſſent primo min. </s> <s xml:id="echoid-s8974" xml:space="preserve">30′. </s> <s xml:id="echoid-s8975" xml:space="preserve">deinde 15′. </s> <s xml:id="echoid-s8976" xml:space="preserve">& </s> <s xml:id="echoid-s8977" xml:space="preserve">ſic defectui tabulæ ſatis erit factum. </s> <s xml:id="echoid-s8978" xml:space="preserve">Quoniam. </s> <s xml:id="echoid-s8979" xml:space="preserve"><lb/>vero ſcopus calculi non eſt inda gare motus medios, ſed veros, ideſt, reperire vbinã ſit in Zodiaco ipſum aſtri <lb/>corpus, in hunc enim finem medij motus excogitati ſunt, idcirco neceſſe eſt inueſtigare in quo gradu peri-<lb/>pheriæ ipſius epicly. </s> <s xml:id="echoid-s8980" xml:space="preserve">Luna ipſa verſetur, quod idem eſt, ac Lunæ Anomaliam ad calculum reuocare, ſit igi-<lb/>tur ſecunda propoſitio.</s> <s xml:id="echoid-s8981" xml:space="preserve"/> </p> <div xml:id="echoid-div185" type="float" level="2" n="1"> <note position="right" xlink:label="note-0112-01" xlink:href="note-0112-01a" xml:space="preserve"> <lb/>Anni Rad. # 1600 <lb/>Anni # 15 <lb/>Biſſext. Iunius. <lb/>Dies # 16 <lb/>Hor. # 1 <lb/>Min. # 15 <lb/>Summa longit. # *** <lb/></note> <note position="right" xlink:label="note-0112-02" xlink:href="note-0112-02a" xml:space="preserve"> <lb/>Sig. # Gra. # 1. <lb/>7 # 25 # 9 <lb/>6 # 0 # 17 <lb/>7 # 28 # 6 <lb/>7 # 0 # 49 <lb/>0 # 0 # 33 <lb/>0 # 0 # 8 <lb/>4 # 25 # 2 <lb/></note> </div> </div> <div xml:id="echoid-div187" type="section" level="1" n="121"> <head xml:id="echoid-head133" style="it" xml:space="preserve">Ad datum temporis momentum, Anomaliam Lunæ computare. Propoſ. 11.</head> <p> <s xml:id="echoid-s8982" xml:space="preserve">ADdatum igitur idem tempus, ſit Anomalia ***. </s> <s xml:id="echoid-s8983" xml:space="preserve">inuenienda: </s> <s xml:id="echoid-s8984" xml:space="preserve">eodem igitur tempore vt ſupra diſpoſito, vt <lb/>hic vides per ſingulas temporis ſpecies, accipiendi ſuot motus illi reſpõdentes in ſecunda columna Ta-<lb/>bularum, quæ anomaliæ dicata eſt. </s> <s xml:id="echoid-s8985" xml:space="preserve">primo qui-<lb/> <anchor type="note" xlink:label="note-0112-03a" xlink:href="note-0112-03"/> <anchor type="note" xlink:label="note-0112-04a" xlink:href="note-0112-04"/> dem ex Tabula annorũ accipiatur Radix Ano-<lb/>maliæ, videlicet Sig. </s> <s xml:id="echoid-s8986" xml:space="preserve">o. </s> <s xml:id="echoid-s8987" xml:space="preserve">Gra. </s> <s xml:id="echoid-s8988" xml:space="preserve">6. </s> <s xml:id="echoid-s8989" xml:space="preserve">40′. </s> <s xml:id="echoid-s8990" xml:space="preserve">ſecundo in <lb/>directum annorum 15. </s> <s xml:id="echoid-s8991" xml:space="preserve">ſumatur ex eadem co-<lb/>lumna 9. </s> <s xml:id="echoid-s8992" xml:space="preserve">19. </s> <s xml:id="echoid-s8993" xml:space="preserve">59′. </s> <s xml:id="echoid-s8994" xml:space="preserve">& </s> <s xml:id="echoid-s8995" xml:space="preserve">ſic cum reliquis ſpeciebus <lb/>temporis, ex proprijs Tabulis, ex colũna Ano-<lb/>maliæ, ſumpti motus ſcribantur, vti factum. <lb/></s> <s xml:id="echoid-s8996" xml:space="preserve">vides in formula exempli. </s> <s xml:id="echoid-s8997" xml:space="preserve">tandem in vnam re-<lb/>digantur ſummam, quæ ſit o. </s> <s xml:id="echoid-s8998" xml:space="preserve">4. </s> <s xml:id="echoid-s8999" xml:space="preserve">11′. </s> <s xml:id="echoid-s9000" xml:space="preserve">vnde co-<lb/>gnoſcitur Lunam diſtare ab epic. </s> <s xml:id="echoid-s9001" xml:space="preserve">apogæo, vn-<lb/>de incipit numeratio verſus dextram, nullo ſi-<lb/>gno, ſed grad. </s> <s xml:id="echoid-s9002" xml:space="preserve">tantum 4. </s> <s xml:id="echoid-s9003" xml:space="preserve">11′. </s> <s xml:id="echoid-s9004" xml:space="preserve">talis locus eſſet in <lb/>epic. </s> <s xml:id="echoid-s9005" xml:space="preserve">figuræ inferioris in ſequenti facie. </s> <s xml:id="echoid-s9006" xml:space="preserve">vbi eſt <lb/>littera o. </s> <s xml:id="echoid-s9007" xml:space="preserve">quæ Lunæ poſitio in epicy. </s> <s xml:id="echoid-s9008" xml:space="preserve">facit vt in Zodiaco ſit magis occidentalis, quam epic. </s> <s xml:id="echoid-s9009" xml:space="preserve">centrum; </s> <s xml:id="echoid-s9010" xml:space="preserve">hoc eſt <lb/>motus Lunę verus ſit minor motu medio, quanta vero ſit hæc differẽtia adhuc reſtat inueſtigandũ, hoc enim <lb/>fine Anomaliam hanc computauimus. </s> <s xml:id="echoid-s9011" xml:space="preserve">hanc porrò differentiam Aſtronomi æquat@onem appellãt, quod per <lb/>eam verus Lunæ motus æquetur; </s> <s xml:id="echoid-s9012" xml:space="preserve">quam quationem peripſam Anomaliam venantur, varia enim Anoma-<lb/>lia variam efficit æquationem: </s> <s xml:id="echoid-s9013" xml:space="preserve">quapropter pro ſingulis Anomaliæ gradibus æquationes cõpererunt, eaſq; </s> <s xml:id="echoid-s9014" xml:space="preserve"><lb/>in Tabula æquationum deſcripſerunt, de qua nunc dicendum. </s> <s xml:id="echoid-s9015" xml:space="preserve">eſt autem æquatio arcus Zodiaci inter lineas <lb/>medij, ac veri motus interceptus, qualis in figura citata eſt arcus M N.</s> <s xml:id="echoid-s9016" xml:space="preserve"/> </p> <div xml:id="echoid-div187" type="float" level="2" n="1"> <note position="right" xlink:label="note-0112-03" xlink:href="note-0112-03a" xml:space="preserve"> <lb/>Rad. # 1600 <lb/>Anni # 15 <lb/>Biſſext. Iunius. <lb/>Dies # 16 <lb/>Hor. # 1 <lb/>Min. # 15 <lb/>## Summa Anomaliæ. <lb/></note> <note position="right" xlink:label="note-0112-04" xlink:href="note-0112-04a" xml:space="preserve"> <lb/>Sig. # Gra. # 1. <lb/>0 # 6 # 40 <lb/>9 # 19 # 59 <lb/>7 # 7 # 50 <lb/>6 # 29 # 2 <lb/>0 # 0 # 32 <lb/>0 # 0 # 8 <lb/>0 # 4 # 11 <lb/></note> </div> </div> <div xml:id="echoid-div189" type="section" level="1" n="122"> <head xml:id="echoid-head134" style="it" xml:space="preserve">Aequationum Lunæ, & verameius longitudinem ad datum tempus reperire. <lb/>Propoſ. III.</head> <p> <s xml:id="echoid-s9017" xml:space="preserve">QVoniam vero Anomalia non ſui gratia inueſtigatur, ſed vt per eam æquationem; </s> <s xml:id="echoid-s9018" xml:space="preserve">atque per æquationẽ <lb/>verum motum, ſeu locum Lunæ in Zodiaco reperiamus: </s> <s xml:id="echoid-s9019" xml:space="preserve">idcirco reliquum eſt, vt per Anomaliam ſupe- <pb o="93" file="0113" n="117" rhead="Liber Nonus."/> rius ad datum tempus computatam. </s> <s xml:id="echoid-s9020" xml:space="preserve">æquationem ei debitam, ex præmiſſa æquationis Tabula eruamus, eaq; <lb/></s> <s xml:id="echoid-s9021" xml:space="preserve">ruxta præcepta vtamur. </s> <s xml:id="echoid-s9022" xml:space="preserve">Erat ſuperior Anomalia Sig. </s> <s xml:id="echoid-s9023" xml:space="preserve">o. </s> <s xml:id="echoid-s9024" xml:space="preserve">gr. </s> <s xml:id="echoid-s9025" xml:space="preserve">4. </s> <s xml:id="echoid-s9026" xml:space="preserve">12′. </s> <s xml:id="echoid-s9027" xml:space="preserve">quæ quia nullum ſignum integrum conti-<lb/>net, ſed tantum gr. </s> <s xml:id="echoid-s9028" xml:space="preserve">4. </s> <s xml:id="echoid-s9029" xml:space="preserve">12′. </s> <s xml:id="echoid-s9030" xml:space="preserve">ideo in prima ſerie deſcendente reperio gr. </s> <s xml:id="echoid-s9031" xml:space="preserve">4. </s> <s xml:id="echoid-s9032" xml:space="preserve">in quorum directo ſub prima colum-<lb/>na, cuio. </s> <s xml:id="echoid-s9033" xml:space="preserve">inſcribitur, accipio 20′. </s> <s xml:id="echoid-s9034" xml:space="preserve">æquationem gr. </s> <s xml:id="echoid-s9035" xml:space="preserve">4. </s> <s xml:id="echoid-s9036" xml:space="preserve">competentem. </s> <s xml:id="echoid-s9037" xml:space="preserve">minuta autem 12. </s> <s xml:id="echoid-s9038" xml:space="preserve">poſſunt facilitatis cau-<lb/>ſa negligi, cum erroris ferè nihil ingerant. </s> <s xml:id="echoid-s9039" xml:space="preserve">poteſt autem hæc regula obſeruari; </s> <s xml:id="echoid-s9040" xml:space="preserve">ſi minuta non plura fuerint <lb/>quam 30. </s> <s xml:id="echoid-s9041" xml:space="preserve">ommitti poſlunt: </s> <s xml:id="echoid-s9042" xml:space="preserve">ſi vero plura quam 30. </s> <s xml:id="echoid-s9043" xml:space="preserve">poſſunt pro gradu vno accipi; </s> <s xml:id="echoid-s9044" xml:space="preserve">ſic vt numerus graduũ vna <lb/>vnitate augeatur. </s> <s xml:id="echoid-s9045" xml:space="preserve">Hæc igitur æquatio quia reſpondet Anomaliæ orioris ſemicirculi, ideo auferenda eſt a <lb/>medio motu longitudinis *** ſuperius computato, vt vera <lb/> <anchor type="note" xlink:label="note-0113-01a" xlink:href="note-0113-01"/> Lunæ longitudo relinquatur; </s> <s xml:id="echoid-s9046" xml:space="preserve">erat media longitudo, qua <lb/>lem oſtendit formula exẽpli, a qua ſi dematur æquatio nęc <lb/>relinquitur vera Lunæ diſtantia ab æquinoctio. </s> <s xml:id="echoid-s9047" xml:space="preserve">Sig. </s> <s xml:id="echoid-s9048" xml:space="preserve">4 gr. <lb/></s> <s xml:id="echoid-s9049" xml:space="preserve">24. </s> <s xml:id="echoid-s9050" xml:space="preserve">42′. </s> <s xml:id="echoid-s9051" xml:space="preserve">quamuis hæc æquatio fit paulo iuſto minor, quo-<lb/>niam aliquantulum a nouilunio diſtat datum tempus. </s> <s xml:id="echoid-s9052" xml:space="preserve"><lb/>Illud nunc repetendum, quod ſupra monuimus; </s> <s xml:id="echoid-s9053" xml:space="preserve">datum <lb/>videlicet tempus ex ſuppoſitione referri ad meridianum Venetum, quare in omnibus locis, ſub dicto meri-<lb/>diano, die 16. </s> <s xml:id="echoid-s9054" xml:space="preserve">Iulij hor. </s> <s xml:id="echoid-s9055" xml:space="preserve">1. </s> <s xml:id="echoid-s9056" xml:space="preserve">15′. </s> <s xml:id="echoid-s9057" xml:space="preserve">p. </s> <s xml:id="echoid-s9058" xml:space="preserve">merid. </s> <s xml:id="echoid-s9059" xml:space="preserve">Luna habet prædictam diſtantiam ab æquinoctio, eſtque in gr. </s> <s xml:id="echoid-s9060" xml:space="preserve">24 42′. </s> <s xml:id="echoid-s9061" xml:space="preserve"><lb/>Leonis. </s> <s xml:id="echoid-s9062" xml:space="preserve">nos igitur qui Foronoui, nunc relaxationis cauſa degimus, cuius meridianus occidentalior eſt meri-<lb/>diano Veneto, gradu ferè vno, ideo iuxta noſtrum meridianum, ideſt, iuxta horas, & </s> <s xml:id="echoid-s9063" xml:space="preserve">minuta ad ipſum rela-<lb/>ta, prius hæc Lunæ longitudo abſoluta eſt: </s> <s xml:id="echoid-s9064" xml:space="preserve">vnus autem gradus importat 4′. </s> <s xml:id="echoid-s9065" xml:space="preserve">minuta horarum, vt parte@ex ta-<lb/>bella ſuperius in cap. </s> <s xml:id="echoid-s9066" xml:space="preserve">de æquatore poſita. </s> <s xml:id="echoid-s9067" xml:space="preserve">quare ſecundum noſtrum tempus dicendum eſt. </s> <s xml:id="echoid-s9068" xml:space="preserve">die 16. </s> <s xml:id="echoid-s9069" xml:space="preserve">lulij, hor. </s> <s xml:id="echoid-s9070" xml:space="preserve">1. </s> <s xml:id="echoid-s9071" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s9072" xml:space="preserve">11. </s> <s xml:id="echoid-s9073" xml:space="preserve">tamen minutis, Lunam obtinuiſſe prædictam veram ab æquinoctio diſtantiam. </s> <s xml:id="echoid-s9074" xml:space="preserve">ſimilis, ſed tamen con-<lb/>traria methodus, ſeruanda eſt, cum ad meridianum magis orientalem, transferenda eſt calculatio.</s> <s xml:id="echoid-s9075" xml:space="preserve"/> </p> <div xml:id="echoid-div189" type="float" level="2" n="1"> <note position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve"> <lb/>Sig. # Gra. # 1. <lb/>4 # 25 # 2 # Media longitudo. <lb/>0 # 0 # 20 # Æquatio demenda. <lb/>4 # 24 # 42 # Verus motus ***. <lb/></note> </div> <p> <s xml:id="echoid-s9076" xml:space="preserve">Quod ſi ad tempus ante Radicem 1600. </s> <s xml:id="echoid-s9077" xml:space="preserve">datum, eſſet calculandum, omnia ſimiliter vt in allato exemplo <lb/>ſunt exequenda; </s> <s xml:id="echoid-s9078" xml:space="preserve">præterquam quòd ſummæ motuum mediorum collectæ, nõn ſunt addendæ Radicibus mo-<lb/>tuum, ſed demendæ; </s> <s xml:id="echoid-s9079" xml:space="preserve">addito integro circulo, ſeu ſignis 12. </s> <s xml:id="echoid-s9080" xml:space="preserve">ſi nequeat fieri ſubtractio. </s> <s xml:id="echoid-s9081" xml:space="preserve">ante tamen annum. <lb/></s> <s xml:id="echoid-s9082" xml:space="preserve">Domini 1582. </s> <s xml:id="echoid-s9083" xml:space="preserve">habenda eſſet ratio dierum 10. </s> <s xml:id="echoid-s9084" xml:space="preserve">qui eo anno, ob Calendarij correctonem exempti ſunt: </s> <s xml:id="echoid-s9085" xml:space="preserve">fed <lb/>fortè nimis longum fecimus.</s> <s xml:id="echoid-s9086" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div191" type="section" level="1" n="123"> <head xml:id="echoid-head135" style="it" xml:space="preserve">Aliter, & Practicè.</head> <p> <s xml:id="echoid-s9087" xml:space="preserve">POſſumus autem non iniucunda praxi eandem calculationem abſoluere, ſimulque eius rationem intelli-<lb/>gere. </s> <s xml:id="echoid-s9088" xml:space="preserve">paretur igitur figura qualis eſt præſens, in qua ſemidiam. </s> <s xml:id="echoid-s9089" xml:space="preserve">epicy. </s> <s xml:id="echoid-s9090" xml:space="preserve">C B. </s> <s xml:id="echoid-s9091" xml:space="preserve">ad ſemidiam. </s> <s xml:id="echoid-s9092" xml:space="preserve">A B. </s> <s xml:id="echoid-s9093" xml:space="preserve">habeat ve-<lb/>ram proportionem, quam ſupra <lb/> <anchor type="figure" xlink:label="fig-0113-01a" xlink:href="fig-0113-01"/> poſuimus. </s> <s xml:id="echoid-s9094" xml:space="preserve">in ea, linea A B C. <lb/></s> <s xml:id="echoid-s9095" xml:space="preserve">tranſeat per gr. </s> <s xml:id="echoid-s9096" xml:space="preserve">25. </s> <s xml:id="echoid-s9097" xml:space="preserve">9′. </s> <s xml:id="echoid-s9098" xml:space="preserve">Scorpio-<lb/>nis, vt referat Radice 6600. </s> <s xml:id="echoid-s9099" xml:space="preserve">lon-<lb/>gltudinis mediæ Lunæ. </s> <s xml:id="echoid-s9100" xml:space="preserve">ſic igi-<lb/>tur ſuperius exẽplum dati tem-<lb/>poris in hac figura computabis. </s> <s xml:id="echoid-s9101" xml:space="preserve"><lb/>reliquorũ annorũ 15. </s> <s xml:id="echoid-s9102" xml:space="preserve">motus eſt <lb/>Sig. </s> <s xml:id="echoid-s9103" xml:space="preserve">6. </s> <s xml:id="echoid-s9104" xml:space="preserve">gr. </s> <s xml:id="echoid-s9105" xml:space="preserve">0. </s> <s xml:id="echoid-s9106" xml:space="preserve">17′. </s> <s xml:id="echoid-s9107" xml:space="preserve">@deo lineã A B. </s> <s xml:id="echoid-s9108" xml:space="preserve"><lb/>promoueas ſecundũ conſequen <lb/>tiam Sig. </s> <s xml:id="echoid-s9109" xml:space="preserve">6. </s> <s xml:id="echoid-s9110" xml:space="preserve">gr. </s> <s xml:id="echoid-s9111" xml:space="preserve">0. </s> <s xml:id="echoid-s9112" xml:space="preserve">17′. </s> <s xml:id="echoid-s9113" xml:space="preserve">perueniet-<lb/>que ad Tauri gr. </s> <s xml:id="echoid-s9114" xml:space="preserve">25. </s> <s xml:id="echoid-s9115" xml:space="preserve">29′. </s> <s xml:id="echoid-s9116" xml:space="preserve">quod <lb/>pùctis notabis. </s> <s xml:id="echoid-s9117" xml:space="preserve">deinde quia mo-<lb/>tus longitudinis mẽſis lunij Biſ <lb/>ſext. </s> <s xml:id="echoid-s9118" xml:space="preserve">eſt, Sig. </s> <s xml:id="echoid-s9119" xml:space="preserve">4. </s> <s xml:id="echoid-s9120" xml:space="preserve">gr. </s> <s xml:id="echoid-s9121" xml:space="preserve">28. </s> <s xml:id="echoid-s9122" xml:space="preserve">6′. </s> <s xml:id="echoid-s9123" xml:space="preserve">Ideo <lb/>promoue adhuc lineam per to-<lb/>tidem ſig. </s> <s xml:id="echoid-s9124" xml:space="preserve">gra. </s> <s xml:id="echoid-s9125" xml:space="preserve">′. </s> <s xml:id="echoid-s9126" xml:space="preserve">& </s> <s xml:id="echoid-s9127" xml:space="preserve">perueniet ad <lb/>gr. </s> <s xml:id="echoid-s9128" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s9129" xml:space="preserve">♑. </s> <s xml:id="echoid-s9130" xml:space="preserve">vbi puncta notabis. </s> <s xml:id="echoid-s9131" xml:space="preserve"><lb/>tertio quia motus dierum 16. </s> <s xml:id="echoid-s9132" xml:space="preserve">& </s> <s xml:id="echoid-s9133" xml:space="preserve"><lb/>horæ vnius, ac 15′. </s> <s xml:id="echoid-s9134" xml:space="preserve">eſt ſig. </s> <s xml:id="echoid-s9135" xml:space="preserve">7. </s> <s xml:id="echoid-s9136" xml:space="preserve">gr. </s> <s xml:id="echoid-s9137" xml:space="preserve"><lb/>1.</s> <s xml:id="echoid-s9138" xml:space="preserve">31′. </s> <s xml:id="echoid-s9139" xml:space="preserve">vlterius adhuc lineam tan-<lb/>tundem deducas; </s> <s xml:id="echoid-s9140" xml:space="preserve">peruenietque <lb/>ad gr. </s> <s xml:id="echoid-s9141" xml:space="preserve">25. </s> <s xml:id="echoid-s9142" xml:space="preserve">Leonis cum 2′. </s> <s xml:id="echoid-s9143" xml:space="preserve">vbi vi-<lb/>des puncta notata; </s> <s xml:id="echoid-s9144" xml:space="preserve">in eum ſcili-<lb/>cet locum, in quem etiam calcu-<lb/>lus centrũ epic. </s> <s xml:id="echoid-s9145" xml:space="preserve">coniecit; </s> <s xml:id="echoid-s9146" xml:space="preserve">illucq; </s> <s xml:id="echoid-s9147" xml:space="preserve"><lb/>debes imaginari eſſe translatum <lb/>epicyclum in K. </s> <s xml:id="echoid-s9148" xml:space="preserve">ſimiliter fac cũ <lb/>motibus Anomaliæ, cuius radix <lb/>ad 1600. </s> <s xml:id="echoid-s9149" xml:space="preserve">eſt ſig. </s> <s xml:id="echoid-s9150" xml:space="preserve">0. </s> <s xml:id="echoid-s9151" xml:space="preserve">g. </s> <s xml:id="echoid-s9152" xml:space="preserve">6. </s> <s xml:id="echoid-s9153" xml:space="preserve">40′. </s> <s xml:id="echoid-s9154" xml:space="preserve">nota-<lb/>s<unsure/>urq; </s> <s xml:id="echoid-s9155" xml:space="preserve">linea imaginaria B O. </s> <s xml:id="echoid-s9156" xml:space="preserve">igi- <pb o="94" file="0114" n="118" rhead="De Mundi Fabrica,"/> tur ſecundum reliquos motus annorum 15 menſis Iunij dierum 16. </s> <s xml:id="echoid-s9157" xml:space="preserve">hor. </s> <s xml:id="echoid-s9158" xml:space="preserve">1. </s> <s xml:id="echoid-s9159" xml:space="preserve">15′. </s> <s xml:id="echoid-s9160" xml:space="preserve">circum ſeras lineam B O. </s> <s xml:id="echoid-s9161" xml:space="preserve">gra-<lb/>datim, & </s> <s xml:id="echoid-s9162" xml:space="preserve">tandem quieſcet in R. </s> <s xml:id="echoid-s9163" xml:space="preserve">paulo ante locum o. </s> <s xml:id="echoid-s9164" xml:space="preserve">videlicetin gr. </s> <s xml:id="echoid-s9165" xml:space="preserve">4. </s> <s xml:id="echoid-s9166" xml:space="preserve">12′. </s> <s xml:id="echoid-s9167" xml:space="preserve">ab apogæo; </s> <s xml:id="echoid-s9168" xml:space="preserve">hoc eſt, duos ferè gra-<lb/>dus ante o. </s> <s xml:id="echoid-s9169" xml:space="preserve">debes autem intelligere epic. </s> <s xml:id="echoid-s9170" xml:space="preserve">eſſe translatum ad prædictum gr. </s> <s xml:id="echoid-s9171" xml:space="preserve">Leonis, cum ſuis lineamentis, cir-<lb/>ca centrum K. </s> <s xml:id="echoid-s9172" xml:space="preserve">ſi igitur produxeris lineam A R S. </s> <s xml:id="echoid-s9173" xml:space="preserve">vſque ad Zodiacum, habebis pro æquatione arcum N S. </s> <s xml:id="echoid-s9174" xml:space="preserve">de-<lb/>mendum a loco medio N. </s> <s xml:id="echoid-s9175" xml:space="preserve">vt verus Lunæ motus in longitudine relinquatur, qui ſit in gr. </s> <s xml:id="echoid-s9176" xml:space="preserve">24. </s> <s xml:id="echoid-s9177" xml:space="preserve">42′. </s> <s xml:id="echoid-s9178" xml:space="preserve">Leonis, vt <lb/>pri us per calculum.</s> <s xml:id="echoid-s9179" xml:space="preserve"/> </p> <div xml:id="echoid-div191" type="float" level="2" n="1"> <figure xlink:label="fig-0113-01" xlink:href="fig-0113-01a"> <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/> </figure> </div> </div> <div xml:id="echoid-div193" type="section" level="1" n="124"> <head xml:id="echoid-head136" style="it" xml:space="preserve">Ad datum temporis instans, Nodum ☊. euchentem reperire. Propoſ. IIII.</head> <p> <s xml:id="echoid-s9180" xml:space="preserve">IVcundum, ac pariter vtile eſt præſertim ad diuinandas Eclypſes loca Nodorum præſcire. </s> <s xml:id="echoid-s9181" xml:space="preserve">Primo igitur <lb/>ad idem ſuperioris temporis inſtans, ex Tabula med. </s> <s xml:id="echoid-s9182" xml:space="preserve">motus in annis ex 3. </s> <s xml:id="echoid-s9183" xml:space="preserve">columna, cui inſcribitur, motus, <lb/>♌. </s> <s xml:id="echoid-s9184" xml:space="preserve">accipem Radicem nodi ♌. </s> <s xml:id="echoid-s9185" xml:space="preserve">quæ eſt è regione rad. </s> <s xml:id="echoid-s9186" xml:space="preserve">1600. </s> <s xml:id="echoid-s9187" xml:space="preserve">eſtque ſig. </s> <s xml:id="echoid-s9188" xml:space="preserve">9. </s> <s xml:id="echoid-s9189" xml:space="preserve">gr. </s> <s xml:id="echoid-s9190" xml:space="preserve">12. </s> <s xml:id="echoid-s9191" xml:space="preserve">0′. </s> <s xml:id="echoid-s9192" xml:space="preserve">ſecundo motum eius pro <lb/>annis 15. </s> <s xml:id="echoid-s9193" xml:space="preserve">tandem reliquos motus reliquis temporibus <lb/> <anchor type="note" xlink:label="note-0114-01a" xlink:href="note-0114-01"/> conuenientes ex eadem columna tertia Tabularum. <lb/></s> <s xml:id="echoid-s9194" xml:space="preserve">excipe, eoſque illis adſcribe, vt in formula hac vides. </s> <s xml:id="echoid-s9195" xml:space="preserve"><lb/>hos omnes motus, excepta radice, in vnam ſummam. </s> <s xml:id="echoid-s9196" xml:space="preserve"><lb/>cõpone, vt factũ vides, hanc ſumma à rad. </s> <s xml:id="echoid-s9197" xml:space="preserve">deme quod <lb/>reliquum erit, indicabit locum ☊. </s> <s xml:id="echoid-s9198" xml:space="preserve">è cuius diametro re-<lb/>peritur alter nodus ☊. </s> <s xml:id="echoid-s9199" xml:space="preserve">boreus, ſeu deſcendens. </s> <s xml:id="echoid-s9200" xml:space="preserve">reliquũ <lb/>illud indicat ☊. </s> <s xml:id="echoid-s9201" xml:space="preserve">diſtare ab æquinoctio per ſigna 11. </s> <s xml:id="echoid-s9202" xml:space="preserve">gr. </s> <s xml:id="echoid-s9203" xml:space="preserve"><lb/>10. </s> <s xml:id="echoid-s9204" xml:space="preserve">45′ hoe eſt verſari in 11. </s> <s xml:id="echoid-s9205" xml:space="preserve">graduum Piſcium. </s> <s xml:id="echoid-s9206" xml:space="preserve">Ope-<lb/>ratio autem huius calculi diuerſa eſt ab alijs, quoniam <lb/>motus nodorum in Zodiaco eſt retrogradus, ideſt mo-<lb/>uetur in præcedentia, ſeu contra ordinem ſignorum: </s> <s xml:id="echoid-s9207" xml:space="preserve"><lb/>quia enim alij motus in conſequentia procedebant, <lb/>ideo addendi erant radici, per additionem enim continuatur progreſſus in conſequentia; </s> <s xml:id="echoid-s9208" xml:space="preserve">at vero quoniam <lb/>motus nodorum eſt in præcedentia, ideo motus temporum ſunt ſubtrahendi à ſua radice, per hanc detractio-<lb/>nem fit retroceſſio, ſcu continuatur motus in præcedentia, vt ſpeculanti tibi manifeſtum erit.</s> <s xml:id="echoid-s9209" xml:space="preserve"/> </p> <div xml:id="echoid-div193" type="float" level="2" n="1"> <note position="right" xlink:label="note-0114-01" xlink:href="note-0114-01a" xml:space="preserve"> <lb/># # Sig. # Gra. # 1. <lb/>Radix # 1600 # 9 # 12 # 0 <lb/>Anni # 15 # 9 # 20 # 5 <lb/>Biſſext. Iunius. # # 9 # 9 # 38 <lb/>Dies # 16 # 0 # 0 # 51 <lb/>Hora # 1 # 0 # 0 # 0 <lb/>Min. # 15 # 0 # 0 # 2 <lb/>## Summa detrahenda \\ Rad. # 10 # 0 # 36 <lb/>### # Reliquum. # 11 # 11 # 24 <lb/></note> </div> </div> <div xml:id="echoid-div195" type="section" level="1" n="125"> <head xml:id="echoid-head137" style="it" xml:space="preserve">Idem practicè.</head> <p> <s xml:id="echoid-s9210" xml:space="preserve">EOdem modo, ’quo in alijs præcedentibus motibus, poſſumus practicè in figura ſuperiori hunc calculum <lb/>abſoluere: </s> <s xml:id="echoid-s9211" xml:space="preserve">mouendo tamen lineam A X. </s> <s xml:id="echoid-s9212" xml:space="preserve">quæ eſt radix huius motus, non in conſequentia ſed in præce-<lb/>dentia, ſecundum exigentiam ſingulorum motuum ſingulis temporum ſpeciebus debi<unsure/>torum: </s> <s xml:id="echoid-s9213" xml:space="preserve">hæc enim. <lb/></s> <s xml:id="echoid-s9214" xml:space="preserve">promotio radicis in præcedentia æquiualet fubtractioni ſuperioris calculi: </s> <s xml:id="echoid-s9215" xml:space="preserve">demonſtratq; </s> <s xml:id="echoid-s9216" xml:space="preserve">apertè cur ea ſub-<lb/>ſtractio ſit facienda.</s> <s xml:id="echoid-s9217" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div196" type="section" level="1" n="126"> <head xml:id="echoid-head138" style="it" xml:space="preserve">Motum verum latitudinis Lunæreperire. Propoſ. V.</head> <p> <s xml:id="echoid-s9218" xml:space="preserve">IAm vero cum conſtet ex calculo Lunam occupare gr. </s> <s xml:id="echoid-s9219" xml:space="preserve">25. </s> <s xml:id="echoid-s9220" xml:space="preserve">Leonis, nodum verò boreum 11. </s> <s xml:id="echoid-s9221" xml:space="preserve">X. </s> <s xml:id="echoid-s9222" xml:space="preserve">elicitur hinc <lb/>Lunam diſtare à ☊, gr. </s> <s xml:id="echoid-s9223" xml:space="preserve">164. </s> <s xml:id="echoid-s9224" xml:space="preserve">ſiue ſigna 5. </s> <s xml:id="echoid-s9225" xml:space="preserve">gr. </s> <s xml:id="echoid-s9226" xml:space="preserve">14. </s> <s xml:id="echoid-s9227" xml:space="preserve">quem appellant motum ***, in latitudinem. </s> <s xml:id="echoid-s9228" xml:space="preserve">propinquam <lb/>vero eſſe ☋, per gr. </s> <s xml:id="echoid-s9229" xml:space="preserve">16. </s> <s xml:id="echoid-s9230" xml:space="preserve">ſequitnr præter@a Lunam habere latitudinem borealem, cum adhuc verſetur in ſe-<lb/>micirculo ſuæ orbitæ boreali, ideſt, nondum diſtet a ☊, pluſquam 90. </s> <s xml:id="echoid-s9231" xml:space="preserve">gr. </s> <s xml:id="echoid-s9232" xml:space="preserve">tertio ex hoc motu in latitudinem <lb/>eruitur vera latitudo eius, ideſt, diſtantia eius ab eclyptica, idque auxilio Tabulæ latitudinis Lunæ, quã ſup. <lb/></s> <s xml:id="echoid-s9233" xml:space="preserve">dedimus, nuncq; </s> <s xml:id="echoid-s9234" xml:space="preserve">exemplo dati temporis exponemus.</s> <s xml:id="echoid-s9235" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div197" type="section" level="1" n="127"> <head xml:id="echoid-head139" style="it" xml:space="preserve">Veram Lunæ latitudinem ad datum tempus reperire. Propoſ. VI.</head> <p> <s xml:id="echoid-s9236" xml:space="preserve">PEr præcedentem propoſ. </s> <s xml:id="echoid-s9237" xml:space="preserve">habeas veram ***, diſtãtiam à ☊ quæ eſt ſigna 5. </s> <s xml:id="echoid-s9238" xml:space="preserve">gr. </s> <s xml:id="echoid-s9239" xml:space="preserve">14. </s> <s xml:id="echoid-s9240" xml:space="preserve">cum qua adeas Tabulam <lb/>latitudinis ***, & </s> <s xml:id="echoid-s9241" xml:space="preserve">accipe ſigna 5. </s> <s xml:id="echoid-s9242" xml:space="preserve">in fronte, gradus autem 14. </s> <s xml:id="echoid-s9243" xml:space="preserve">in ſerie prima deſcendente, & </s> <s xml:id="echoid-s9244" xml:space="preserve">in communi <lb/>concurſu verſus 14. </s> <s xml:id="echoid-s9245" xml:space="preserve">cum columna ſigni quinti, inuenies gr. </s> <s xml:id="echoid-s9246" xml:space="preserve">1. </s> <s xml:id="echoid-s9247" xml:space="preserve">23′. </s> <s xml:id="echoid-s9248" xml:space="preserve">pro latitudine ***, quæ borealis eſt, vt etiam <lb/>titulus Tabulæmdicat.</s> <s xml:id="echoid-s9249" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9250" xml:space="preserve">His igitur omnibus computati<unsure/>s habes verum, & </s> <s xml:id="echoid-s9251" xml:space="preserve">abſolutum ***, locum in locum in Zodiaco ad datum tem-<lb/>pus, tam reſpectu longitudinis ab æquinoctio, quam reſpectu diſtantiæ d<unsure/> ☊, necnon eius diſtantię ab eclypti-<lb/>ca, quæ eſt eius latitudo, deſideratur eiusa Sole eiongatio, quæ ſciri nequit ex noſtris Tabul@s, abſque veri <lb/>loci *** calculo, de quo poſtea. </s> <s xml:id="echoid-s9252" xml:space="preserve">poteſt tamen nunc ex anno quem noſtro Zodiaco inſcripſimus in ſphæra ma-<lb/>teria@i, conoſcere plus minus, in quo gradus ſit ***, quem d@e 16. </s> <s xml:id="echoid-s9253" xml:space="preserve">Iulij dato, reperies occupare gr. </s> <s xml:id="echoid-s9254" xml:space="preserve">14 ♋. </s> <s xml:id="echoid-s9255" xml:space="preserve">Luna <lb/>autem eſt in 24 42. </s> <s xml:id="echoid-s9256" xml:space="preserve">☊. </s> <s xml:id="echoid-s9257" xml:space="preserve">quare vera ***, elong@tio erit graduum ferè 25.</s> <s xml:id="echoid-s9258" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9259" xml:space="preserve">Sciat demum lector, auxi@io caleuli Aſtronomos condere ſibi Tabulas verorum motuum, quas Epheme <lb/>rides, ſeu Diar@a appellant, quæperpetua nequeunt eſſe, ſed tamen per plures annos oſtendunt ſingulis dic-<lb/>bus vera loca planetarum, cũ omnibus illorum paſſionibus, ideſt, aſpectibus, latitudinibus, ortus, occaſus, &</s> <s xml:id="echoid-s9260" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s9261" xml:space="preserve">verum in his nihil àdmirabilius, quam per annos complures intueri, ac contemplari poſie futurarum ecly-<lb/>pſ@um vtriulque luminaris, exactas delineationes.</s> <s xml:id="echoid-s9262" xml:space="preserve"/> </p> <pb o="95" file="0115" n="119" rhead="Liber Nonus."/> </div> <div xml:id="echoid-div198" type="section" level="1" n="128"> <head xml:id="echoid-head140" style="it" xml:space="preserve">Nouilunium, atque atatem Lun@ reperire. Propoſ. VII.</head> <p> <s xml:id="echoid-s9263" xml:space="preserve">1 PEraureum numerum currentem, quem hoc modo reperies: </s> <s xml:id="echoid-s9264" xml:space="preserve">Anno Domini propoſito, ideſt, cuius au-<lb/>reus numerus inquirendus eſt, addatur 1. </s> <s xml:id="echoid-s9265" xml:space="preserve">& </s> <s xml:id="echoid-s9266" xml:space="preserve">numerus compoſitus diuidatur per 19. </s> <s xml:id="echoid-s9267" xml:space="preserve">qui eſt integra pe-<lb/>riodus numeri aurei, vti ſupra dixi, numerus enim non quotiens, ſed qui relinquitur ex hac diuiſione, erit au-<lb/>reus numerus anni propoſiti. </s> <s xml:id="echoid-s9268" xml:space="preserve">quod ſi ex diuiſione nil remaneat, erit aureus numerus 19. </s> <s xml:id="echoid-s9269" xml:space="preserve">v. </s> <s xml:id="echoid-s9270" xml:space="preserve">g. </s> <s xml:id="echoid-s9271" xml:space="preserve">quæratur aureus <lb/>numerus huius labentis anni 1616. </s> <s xml:id="echoid-s9272" xml:space="preserve">ei addatur 1. </s> <s xml:id="echoid-s9273" xml:space="preserve">fiunt 1617. </s> <s xml:id="echoid-s9274" xml:space="preserve">hunc diuido per 19. </s> <s xml:id="echoid-s9275" xml:space="preserve">remanent 2. </s> <s xml:id="echoid-s9276" xml:space="preserve">Ergo aureus nu-<lb/>merus huius anni eſt 2. </s> <s xml:id="echoid-s9277" xml:space="preserve">Quotiens aut<unsure/>em eſt 85. </s> <s xml:id="echoid-s9278" xml:space="preserve">cuius nulla habetur ratio, quia tantummodo oſtendit ab anno <lb/>Domini primo hucuſque, elapſas eſſe aurei numeri reuolutiones integras 85. </s> <s xml:id="echoid-s9279" xml:space="preserve">quod nihit refert. </s> <s xml:id="echoid-s9280" xml:space="preserve">Secundus <lb/>autem quæ ſuperſunt indicant ſecundum annum 86. </s> <s xml:id="echoid-s9281" xml:space="preserve">reuolutionis præterire. </s> <s xml:id="echoid-s9282" xml:space="preserve">ſequenti anno 1617. </s> <s xml:id="echoid-s9283" xml:space="preserve">erit aureus <lb/>num. </s> <s xml:id="echoid-s9284" xml:space="preserve">3. </s> <s xml:id="echoid-s9285" xml:space="preserve">& </s> <s xml:id="echoid-s9286" xml:space="preserve">ſic deinceps vſq; </s> <s xml:id="echoid-s9287" xml:space="preserve">ad 19. </s> <s xml:id="echoid-s9288" xml:space="preserve">in gyrum reeurrit.</s> <s xml:id="echoid-s9289" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9290" xml:space="preserve">Aliter idem aſſequeris ex ſequenti Tabella; </s> <s xml:id="echoid-s9291" xml:space="preserve">cuius hic eſt vſus. </s> <s xml:id="echoid-s9292" xml:space="preserve">Primus aureus numerus qui eſt 6. </s> <s xml:id="echoid-s9293" xml:space="preserve">debetur <lb/>anno 1582. </s> <s xml:id="echoid-s9294" xml:space="preserve">correctionis Calendarij à Greg. </s> <s xml:id="echoid-s9295" xml:space="preserve">XIII. </s> <s xml:id="echoid-s9296" xml:space="preserve">Sum. </s> <s xml:id="echoid-s9297" xml:space="preserve">Pont. </s> <s xml:id="echoid-s9298" xml:space="preserve">factæ. <lb/></s> <s xml:id="echoid-s9299" xml:space="preserve"> <anchor type="note" xlink:label="note-0115-01a" xlink:href="note-0115-01"/> incipiendo à die 15. </s> <s xml:id="echoid-s9300" xml:space="preserve">Octobris, qui fuit die correctionis. </s> <s xml:id="echoid-s9301" xml:space="preserve">ſecundus num. </s> <s xml:id="echoid-s9302" xml:space="preserve">7. </s> <s xml:id="echoid-s9303" xml:space="preserve">debetur anno 1583. </s> <s xml:id="echoid-s9304" xml:space="preserve">& </s> <s xml:id="echoid-s9305" xml:space="preserve">ſic deinceps, <lb/>vque ad quemuis datum annum, ad initium Tabulæ recurrendo, cum opus eſt, quo per eã recurſu inuenies <lb/>allatum annum 1616. </s> <s xml:id="echoid-s9306" xml:space="preserve">cadere ſuper numerum 2. </s> <s xml:id="echoid-s9307" xml:space="preserve">quem etiam antea per diuiſionem inuenimus. </s> <s xml:id="echoid-s9308" xml:space="preserve">de prædicta <lb/>correctione agemus in anno ſolari.</s> <s xml:id="echoid-s9309" xml:space="preserve"/> </p> <div xml:id="echoid-div198" type="float" level="2" n="1"> <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve"> <lb/>Aur. nu. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 1 # 2 # 3 # 4 # 5 <lb/>Epactæ. # 26 # 7 # 18 # 29 # 10 # 21 # 2 # 13 # 24 # 5 # 16 # 27 # 8 # 19 # 1 # 12 # 23 # 4 # 15 <lb/></note> </div> <p> <s xml:id="echoid-s9310" xml:space="preserve">Habito igitur vtrouis modo aureo numero currente, adeas Calendarium, cui aureus numerus præſcriba-<lb/>tur; </s> <s xml:id="echoid-s9311" xml:space="preserve">in eo aureum num. </s> <s xml:id="echoid-s9312" xml:space="preserve">iam inuentum repetas; </s> <s xml:id="echoid-s9313" xml:space="preserve">ijs enim diebus nouilunia erunt, quibus ipſe præfigititur; </s> <s xml:id="echoid-s9314" xml:space="preserve">ſic <lb/>anno præſenti 1616. </s> <s xml:id="echoid-s9315" xml:space="preserve">vbicumque in Calendario fuerit 3. </s> <s xml:id="echoid-s9316" xml:space="preserve">ibi Luna renaſeitur. </s> <s xml:id="echoid-s9317" xml:space="preserve">porro Eccleſia Latina vſa eſt au-<lb/>reis in Calendario numeris vſque ad annũ correſctionis Calendarij. </s> <s xml:id="echoid-s9318" xml:space="preserve">deinceps loco eius numeros Epactales <lb/>ſubrogauit. </s> <s xml:id="echoid-s9319" xml:space="preserve">complures tamen adhuc Calendarium vetus cum aureo numero retinent. </s> <s xml:id="echoid-s9320" xml:space="preserve">Iam vero reperto <lb/>die nouiluni ſi ab eo numeraueris vſque ad currentem diem, numerus ille erit numerus dierum Lunæ, quæ <lb/>ætas Lunæ dicitur.</s> <s xml:id="echoid-s9321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9322" xml:space="preserve">2 Per Epactas, quæ in nouo Calendario poſt correctionem, loco aurei numeri ſuffectæ ſunt. </s> <s xml:id="echoid-s9323" xml:space="preserve">Epacta, ſi-<lb/>ue potius epactæ ſunt dies illi 11. </s> <s xml:id="echoid-s9324" xml:space="preserve">quibus annis Lunaris deficit a Solari, vt ſupra diximus, dicuntur epactæ, <lb/>quaſi inditi, aut additi dies; </s> <s xml:id="echoid-s9325" xml:space="preserve">adduntur enim ſequentis anni Lunationi primæ, vt tota habeatur. </s> <s xml:id="echoid-s9326" xml:space="preserve">ſi igitur ini-<lb/>tio alicuius anni Solaris fiat nouil. </s> <s xml:id="echoid-s9327" xml:space="preserve">ideſt Sol, & </s> <s xml:id="echoid-s9328" xml:space="preserve">Luna ſimul annum incipiant, Luna diebus 11. </s> <s xml:id="echoid-s9329" xml:space="preserve">prius ſuum an-<lb/>num abſoluet, qui dies 11. </s> <s xml:id="echoid-s9330" xml:space="preserve">erunt Epacta, non illius anni, ſed ſequẽtis; </s> <s xml:id="echoid-s9331" xml:space="preserve">pertinet enim ad Lunationem primam <lb/>ſequentis anni, ideſt, Luna in principio ſequentis anni habebit dies 11. </s> <s xml:id="echoid-s9332" xml:space="preserve">addendique eruntalijs diebus, quos <lb/>in ſequenti anno habebit. </s> <s xml:id="echoid-s9333" xml:space="preserve">quoniam vero nouilunia anticipant ſequenti anno, ſimiliter diebus 11. </s> <s xml:id="echoid-s9334" xml:space="preserve">fit vt ad fi-<lb/>nem huius ſecundi anni Luna abſoluat annum ſuum diebus 22. </s> <s xml:id="echoid-s9335" xml:space="preserve">priuſquam Sol, qui dies 22. </s> <s xml:id="echoid-s9336" xml:space="preserve">erunt epacta ſe-<lb/>quentis anni tertij. </s> <s xml:id="echoid-s9337" xml:space="preserve">In fine vero huius tertij anni Luna abſoluet annum diebustantum 3. </s> <s xml:id="echoid-s9338" xml:space="preserve">prius quam Sol; </s> <s xml:id="echoid-s9339" xml:space="preserve">quia <lb/>anticipatio dierum 11. </s> <s xml:id="echoid-s9340" xml:space="preserve">ante dies 22. </s> <s xml:id="echoid-s9341" xml:space="preserve">prædictos, fecit vt vlt@ma Luna anticipãt dies 33. </s> <s xml:id="echoid-s9342" xml:space="preserve">qui pluſquam integram <lb/>lunationem conflant. </s> <s xml:id="echoid-s9343" xml:space="preserve">quare Luna abſoluit hoc anno tertio. </s> <s xml:id="echoid-s9344" xml:space="preserve">annum tribus tantum diebus ante Solem. </s> <s xml:id="echoid-s9345" xml:space="preserve">quare <lb/>spacta ſequentis anni quarti erit tantum 3. </s> <s xml:id="echoid-s9346" xml:space="preserve">ſic quoties epacta ſuperat. </s> <s xml:id="echoid-s9347" xml:space="preserve">30. </s> <s xml:id="echoid-s9348" xml:space="preserve">abiectis 30. </s> <s xml:id="echoid-s9349" xml:space="preserve">reliquus num. </s> <s xml:id="echoid-s9350" xml:space="preserve">eſt epacta, <lb/>& </s> <s xml:id="echoid-s9351" xml:space="preserve">lunatio illa dicitur Emboliſmica; </s> <s xml:id="echoid-s9352" xml:space="preserve">& </s> <s xml:id="echoid-s9353" xml:space="preserve">annus Emboliſinicus, qui conſtat ex 13. </s> <s xml:id="echoid-s9354" xml:space="preserve">Lunis, v@ſupra diximus. </s> <s xml:id="echoid-s9355" xml:space="preserve">Ad <lb/>inuenienda igitur nouilunia per epactam neceſſe è præſcire epactam currentem, quam ex modo dictis facile <lb/>eſt inuenire, dummodo tenueris epactam aliquam præcedentis alicuius anni, nam per additionẽ continuam <lb/>@1. </s> <s xml:id="echoid-s9356" xml:space="preserve">dierum conflantur epactæ ſequentium annorum, abiectis 30. </s> <s xml:id="echoid-s9357" xml:space="preserve">quando 30. </s> <s xml:id="echoid-s9358" xml:space="preserve">ſuperant.</s> <s xml:id="echoid-s9359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9360" xml:space="preserve">Aduertendum tamen eſt, quod currente aureo num. </s> <s xml:id="echoid-s9361" xml:space="preserve">19. </s> <s xml:id="echoid-s9362" xml:space="preserve">tunc epactæ præcedenti addendi ſunt dies non <lb/>11. </s> <s xml:id="echoid-s9363" xml:space="preserve">vt ſolet, ſed 12. </s> <s xml:id="echoid-s9364" xml:space="preserve">ad conflandam epactam ſequ<unsure/>entis anni, cuius anreus num. </s> <s xml:id="echoid-s9365" xml:space="preserve">erit 1. </s> <s xml:id="echoid-s9366" xml:space="preserve">Verum ex præcedenti <lb/>Tabella, ex qua aureum numerum accepimus, etiam epactas illis ſubſcriptas in promptu habemus: </s> <s xml:id="echoid-s9367" xml:space="preserve">incipit <lb/>etiam hæc periodus epactarum ab anno 1582. </s> <s xml:id="echoid-s9368" xml:space="preserve">vna cum aureo numero ſic, quia hoc anno 1616. </s> <s xml:id="echoid-s9369" xml:space="preserve">aureus nume-<lb/>rus eſt 2. </s> <s xml:id="echoid-s9370" xml:space="preserve">erit epacta 12. </s> <s xml:id="echoid-s9371" xml:space="preserve">illi ſubſcripta. </s> <s xml:id="echoid-s9372" xml:space="preserve">ſequentis anni additi 11. </s> <s xml:id="echoid-s9373" xml:space="preserve">erit 23. </s> <s xml:id="echoid-s9374" xml:space="preserve">& </s> <s xml:id="echoid-s9375" xml:space="preserve">ſic deinceps. </s> <s xml:id="echoid-s9376" xml:space="preserve">habita gitur epacta, <lb/>adeas Calendarium nouum, in quo diebus menſium præfixi ſunt hi numeri epactal@s; </s> <s xml:id="echoid-s9377" xml:space="preserve">& </s> <s xml:id="echoid-s9378" xml:space="preserve">vbicumque reperies <lb/>epactam currentem, v.</s> <s xml:id="echoid-s9379" xml:space="preserve">g. </s> <s xml:id="echoid-s9380" xml:space="preserve">12. </s> <s xml:id="echoid-s9381" xml:space="preserve">pro hoc anno 1616. </s> <s xml:id="echoid-s9382" xml:space="preserve">ibi erunt nouilunia. </s> <s xml:id="echoid-s9383" xml:space="preserve">ſic, hoc lulio menſe, quia 12. </s> <s xml:id="echoid-s9384" xml:space="preserve">præſcr bi-<lb/>tur diei 15. </s> <s xml:id="echoid-s9385" xml:space="preserve">Ideo cognoſco eo die Lunam renouari; </s> <s xml:id="echoid-s9386" xml:space="preserve">Aetatem autẽ Lunæ hodie quæ eſt 21. </s> <s xml:id="echoid-s9387" xml:space="preserve">lulij, ſic ob ineo; <lb/></s> <s xml:id="echoid-s9388" xml:space="preserve">numero à 15. </s> <s xml:id="echoid-s9389" xml:space="preserve">vſque ad 21. </s> <s xml:id="echoid-s9390" xml:space="preserve">incluſiue vtrinque, ſuntque 7. </s> <s xml:id="echoid-s9391" xml:space="preserve">dies pro ætate Lunæ. </s> <s xml:id="echoid-s9392" xml:space="preserve">plura de hac re videas ſi lubet <lb/>apud P. </s> <s xml:id="echoid-s9393" xml:space="preserve">Clauium in explicatione Romani Calendarij.</s> <s xml:id="echoid-s9394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9395" xml:space="preserve">3. </s> <s xml:id="echoid-s9396" xml:space="preserve">Per regulam quandam popularem, quam Epactam vocant, idem & </s> <s xml:id="echoid-s9397" xml:space="preserve">quidem memoriter, ac promptè <lb/>@btinebis, ſic, ep@ctam currentem, & </s> <s xml:id="echoid-s9398" xml:space="preserve">dies menſis ſimul adduntur, ſumma enim eorum ſi nõ exceſſeri<unsure/>t 30. </s> <s xml:id="echoid-s9399" xml:space="preserve">er@t <lb/>æ<unsure/>tas ***, ſi exceſſerit, exceſſus ille erit quæſita ætas. </s> <s xml:id="echoid-s9400" xml:space="preserve">Et hoc ſolum ſufficit in primis duobus menſibus Ianua-<lb/>rij, & </s> <s xml:id="echoid-s9401" xml:space="preserve">Februarij, v.</s> <s xml:id="echoid-s9402" xml:space="preserve">g. </s> <s xml:id="echoid-s9403" xml:space="preserve">hoc anno 1616. </s> <s xml:id="echoid-s9404" xml:space="preserve">die 18. </s> <s xml:id="echoid-s9405" xml:space="preserve">Ianuarij volebam ſcire ætatem ***, quia ergo epacta eſt 12 & </s> <s xml:id="echoid-s9406" xml:space="preserve">dies <lb/>menſis ſunt 18. </s> <s xml:id="echoid-s9407" xml:space="preserve">qui additi faciunt 30. </s> <s xml:id="echoid-s9408" xml:space="preserve">ideo cognoui Lunam habere 30. </s> <s xml:id="echoid-s9409" xml:space="preserve">dies. </s> <s xml:id="echoid-s9410" xml:space="preserve">ſequenti die qui erat 19. </s> <s xml:id="echoid-s9411" xml:space="preserve">addebam <lb/>illis 13. </s> <s xml:id="echoid-s9412" xml:space="preserve">eratque ſumma 31. </s> <s xml:id="echoid-s9413" xml:space="preserve">exceſſus ſupra 30. </s> <s xml:id="echoid-s9414" xml:space="preserve">erat 1. </s> <s xml:id="echoid-s9415" xml:space="preserve">ideo erat nouil. </s> <s xml:id="echoid-s9416" xml:space="preserve">in reliquis vero 10. </s> <s xml:id="echoid-s9417" xml:space="preserve">menſibus, præter ea, <lb/>adduntur etiam numeri Calendarum, ideſt, pro ſingulis Calendis, ſeu Menſibus, vnuminc@piendo a Mar@io, <lb/>exempli gratia hodie, qui eſt 21. </s> <s xml:id="echoid-s9418" xml:space="preserve">Iulij, tria hęc, dies Menſis 21. </s> <s xml:id="echoid-s9419" xml:space="preserve">Epactam 12. </s> <s xml:id="echoid-s9420" xml:space="preserve">Calendas 5. </s> <s xml:id="echoid-s9421" xml:space="preserve">in vnum colligo, fiunt- <pb o="96" file="0116" n="120" rhead="De Mundi Fabrica,"/> que 38. </s> <s xml:id="echoid-s9422" xml:space="preserve">abiectis 30.</s> <s xml:id="echoid-s9423" xml:space="preserve">′ ſuperſunt 8. </s> <s xml:id="echoid-s9424" xml:space="preserve">dies pro ætate ***, quam ſupra inuenimus eſſe tantum 7. </s> <s xml:id="echoid-s9425" xml:space="preserve">quæ diſcrepantia in-<lb/>de oritur, quia hæ duæ regulæ ſunt ciuiles, & </s> <s xml:id="echoid-s9426" xml:space="preserve">populares, non omnino Aſtronomicæ, & </s> <s xml:id="echoid-s9427" xml:space="preserve">propterea ætatem ***, <lb/>non omnino exactè exhibent: </s> <s xml:id="echoid-s9428" xml:space="preserve">ſequuntur enim medium motum *** non verum.</s> <s xml:id="echoid-s9429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9430" xml:space="preserve">Sciendum etiaminitio anni incipere nouas epactas, ac nouum aureum, numerum; </s> <s xml:id="echoid-s9431" xml:space="preserve">ideſt, ad primam Ia-<lb/>nuarij diem.</s> <s xml:id="echoid-s9432" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9433" xml:space="preserve">Ratio huius vulgaris regulæ, quam ſolum apud Ioan. </s> <s xml:id="echoid-s9434" xml:space="preserve">Lucidum vidi, hæc eſt. </s> <s xml:id="echoid-s9435" xml:space="preserve">Primo in duobus primis <lb/>menſibus Ianuarij, & </s> <s xml:id="echoid-s9436" xml:space="preserve">Februarij computantur tantum dies epactæ currentis, & </s> <s xml:id="echoid-s9437" xml:space="preserve">dies menſis, quia epactæ per-<lb/>tinent ad primam anni lunationem, & </s> <s xml:id="echoid-s9438" xml:space="preserve">dies menſis pariter ſunt dies lunę; </s> <s xml:id="echoid-s9439" xml:space="preserve">vt in allato exemplo ad diem 18. </s> <s xml:id="echoid-s9440" xml:space="preserve">Ia-<lb/>nuarij; </s> <s xml:id="echoid-s9441" xml:space="preserve">computo dies 18. </s> <s xml:id="echoid-s9442" xml:space="preserve">quia eos Luna acquiſciuit a principio anni vſq; </s> <s xml:id="echoid-s9443" xml:space="preserve">ad 18. </s> <s xml:id="echoid-s9444" xml:space="preserve">diem; </s> <s xml:id="echoid-s9445" xml:space="preserve">computo etiam epactam <lb/>12. </s> <s xml:id="echoid-s9446" xml:space="preserve">quia totidem dies habebat Luna in principi<unsure/>o anni. </s> <s xml:id="echoid-s9447" xml:space="preserve">quando ſumma excedit 30. </s> <s xml:id="echoid-s9448" xml:space="preserve">abijcitur 30. </s> <s xml:id="echoid-s9449" xml:space="preserve">quæ eſt inte-<lb/>gra lunatio, & </s> <s xml:id="echoid-s9450" xml:space="preserve">accipitur exceſſus pro ætate ***, quæritur enim ætas Lunæ, omiſſis integris lunationibus. </s> <s xml:id="echoid-s9451" xml:space="preserve">in his <lb/>duobus menſibus non computantur Calendæ, quia hi duo menſes ſimul efficiunt duas integras lunationes, <lb/>ideſt, dies 59. </s> <s xml:id="echoid-s9452" xml:space="preserve">eſt enim prima lunatio dierum 30. </s> <s xml:id="echoid-s9453" xml:space="preserve">ſecunda vero dierum 29. </s> <s xml:id="echoid-s9454" xml:space="preserve">qui ſimul pariter efficiunt 59. </s> <s xml:id="echoid-s9455" xml:space="preserve">in re-<lb/>liquis 10. </s> <s xml:id="echoid-s9456" xml:space="preserve">menſibus, computantur etiam Calendæ eorum, ideſt, pro ſingulis dies 1. </s> <s xml:id="echoid-s9457" xml:space="preserve">quia à Martio inci<unsure/>uſiuè in-<lb/>cipiendo ſinguli mẽſes ſuperant lunationem vnam vno die, qui etiam in ætatem lunationum præteritarum, <lb/>computari debent. </s> <s xml:id="echoid-s9458" xml:space="preserve">Exempli gr. </s> <s xml:id="echoid-s9459" xml:space="preserve">hoc anno 1616. </s> <s xml:id="echoid-s9460" xml:space="preserve">die 13. </s> <s xml:id="echoid-s9461" xml:space="preserve">Martij; </s> <s xml:id="echoid-s9462" xml:space="preserve">pro ætate Lunæ indaganda computabam 31. <lb/></s> <s xml:id="echoid-s9463" xml:space="preserve">dies menſis; </s> <s xml:id="echoid-s9464" xml:space="preserve">item 12. </s> <s xml:id="echoid-s9465" xml:space="preserve">pro epacta, quia pertinent ad lunationes hactenus elapſas. </s> <s xml:id="echoid-s9466" xml:space="preserve">computo tandem 1. </s> <s xml:id="echoid-s9467" xml:space="preserve">pro Ca-<lb/>lendis Martij quia Martius habet dies 31. </s> <s xml:id="echoid-s9468" xml:space="preserve">quibus vno die ſuperat lunationem ſibi reſpondentem, quæ eſt 30. </s> <s xml:id="echoid-s9469" xml:space="preserve"><lb/>dierum. </s> <s xml:id="echoid-s9470" xml:space="preserve">omnibus ſimul computatis fit ſumma dierum 44. </s> <s xml:id="echoid-s9471" xml:space="preserve">abiectis 30. </s> <s xml:id="echoid-s9472" xml:space="preserve">ſuperſunt 14. </s> <s xml:id="echoid-s9473" xml:space="preserve">dies ætatis Lunę. </s> <s xml:id="echoid-s9474" xml:space="preserve">Vbi con-<lb/>ſiderandum eſt, quod tacite omittuntur omnes integræ lunationes a principio anni, vſque ad oblatui<unsure/>n diem<unsure/> <lb/>exactæ; </s> <s xml:id="echoid-s9475" xml:space="preserve">vna ſcilicet pro ſingulis menſibus, ſeu pro quolibet menſe. </s> <s xml:id="echoid-s9476" xml:space="preserve">Computantur tandem Calendæ, quia vl-<lb/>tra integras Lunas, quilibet menſis exhibet dies vnum amplius ad Lunam pertinentem. </s> <s xml:id="echoid-s9477" xml:space="preserve">ſuntque hæ Calen-<lb/>dæ, tanquam epactæ quædam partiales menſium præterit<unsure/>orum; </s> <s xml:id="echoid-s9478" xml:space="preserve">ex quibus paulatim conflatur epacta ſeq. </s> <s xml:id="echoid-s9479" xml:space="preserve">an-<lb/>ni. </s> <s xml:id="echoid-s9480" xml:space="preserve">quamuis autem ſin tantumt 10. </s> <s xml:id="echoid-s9481" xml:space="preserve">mẽſes vſq; </s> <s xml:id="echoid-s9482" xml:space="preserve">ad finem anni, aſtronomi tamen, qui has regulas ciuiles condi-<lb/>derunt, aſſumunt pro epacta 11. </s> <s xml:id="echoid-s9483" xml:space="preserve">ſic enim melius regulæ huius regulas conſeruatur.</s> <s xml:id="echoid-s9484" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9485" xml:space="preserve">Sciendum poſtremo, haſce regulas epactales, non exactè veram Lunæ etatem exhibere, ſed ſemper paulo <lb/>minorem vera, quia tamen exiguus eſt error, ideo in vulgus vtiles ſunt.</s> <s xml:id="echoid-s9486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9487" xml:space="preserve">4 Per Aſtronomicum calculum, & </s> <s xml:id="echoid-s9488" xml:space="preserve">quidem præciſius, quam per præcedentes vulgares regulas. </s> <s xml:id="echoid-s9489" xml:space="preserve">primo <lb/>igitur oportet ſcire, ad datum temporis inſtans, loca luminarium in Zodiaco, & </s> <s xml:id="echoid-s9490" xml:space="preserve">conſequẽtur quanta ſit elon-<lb/>gatio *** a ***, quam propoſ. </s> <s xml:id="echoid-s9491" xml:space="preserve">6. </s> <s xml:id="echoid-s9492" xml:space="preserve">inuenimus fuiſſe gr. </s> <s xml:id="echoid-s9493" xml:space="preserve">30. </s> <s xml:id="echoid-s9494" xml:space="preserve">quoniam vero Luna elongatur a Sole diario motu gr. <lb/></s> <s xml:id="echoid-s9495" xml:space="preserve">12′ 11′. </s> <s xml:id="echoid-s9496" xml:space="preserve">ſi prædicta elongatio diuidatur per hunc motum diarium, quotiens numerus indicabit quot diebus <lb/>anteceſſerit nouilunium, quare cum 12. </s> <s xml:id="echoid-s9497" xml:space="preserve">11′. </s> <s xml:id="echoid-s9498" xml:space="preserve">contineantur bis in 30. </s> <s xml:id="echoid-s9499" xml:space="preserve">neceſſe erit nouilunium præceſſiſſe duo-<lb/>bus diebus momẽtum temporis dati, Iulij die 16. </s> <s xml:id="echoid-s9500" xml:space="preserve">h. </s> <s xml:id="echoid-s9501" xml:space="preserve">1 {1/4}. </s> <s xml:id="echoid-s9502" xml:space="preserve">p. </s> <s xml:id="echoid-s9503" xml:space="preserve">m. </s> <s xml:id="echoid-s9504" xml:space="preserve">rurſus diuiſis 30. </s> <s xml:id="echoid-s9505" xml:space="preserve">per 12. </s> <s xml:id="echoid-s9506" xml:space="preserve">11′ ſuperſunt 338′. </s> <s xml:id="echoid-s9507" xml:space="preserve">min. </s> <s xml:id="echoid-s9508" xml:space="preserve"><lb/>ea diuidenda erant per horariam elongationem Lunæ a Sole: </s> <s xml:id="echoid-s9509" xml:space="preserve">quæ ex diaria 12. </s> <s xml:id="echoid-s9510" xml:space="preserve">11′, facilè habetur, eſt enim. </s> <s xml:id="echoid-s9511" xml:space="preserve"><lb/>illius pars 24. </s> <s xml:id="echoid-s9512" xml:space="preserve">videlicet 30′. </s> <s xml:id="echoid-s9513" xml:space="preserve">27″. </s> <s xml:id="echoid-s9514" xml:space="preserve">diuiſis igiter 338′. </s> <s xml:id="echoid-s9515" xml:space="preserve">per 30′. </s> <s xml:id="echoid-s9516" xml:space="preserve">27'<unsure/>. </s> <s xml:id="echoid-s9517" xml:space="preserve">proueniũt ferè 11. </s> <s xml:id="echoid-s9518" xml:space="preserve">horæ ſcilicet, quibus præter <lb/>duos dies nouilunium anteceſſit tempus datum. </s> <s xml:id="echoid-s9519" xml:space="preserve">præceſſit igitur dies 2. </s> <s xml:id="echoid-s9520" xml:space="preserve">h. </s> <s xml:id="echoid-s9521" xml:space="preserve">11. </s> <s xml:id="echoid-s9522" xml:space="preserve">quibus demptis ex dato tempo-<lb/>re diei 16. </s> <s xml:id="echoid-s9523" xml:space="preserve">h. </s> <s xml:id="echoid-s9524" xml:space="preserve">1 {1/4}. </s> <s xml:id="echoid-s9525" xml:space="preserve">p.</s> <s xml:id="echoid-s9526" xml:space="preserve">m. </s> <s xml:id="echoid-s9527" xml:space="preserve">remanet dies 13. </s> <s xml:id="echoid-s9528" xml:space="preserve">h. </s> <s xml:id="echoid-s9529" xml:space="preserve">14 {1/4}. </s> <s xml:id="echoid-s9530" xml:space="preserve">p.</s> <s xml:id="echoid-s9531" xml:space="preserve">m. </s> <s xml:id="echoid-s9532" xml:space="preserve">ideſt, duabus hor. </s> <s xml:id="echoid-s9533" xml:space="preserve">poſt mediam noctem, quæ interce<unsure/>-<lb/>dit inter diem 13. </s> <s xml:id="echoid-s9534" xml:space="preserve">& </s> <s xml:id="echoid-s9535" xml:space="preserve">14.</s> <s xml:id="echoid-s9536" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div200" type="section" level="1" n="129"> <head xml:id="echoid-head141" style="it" xml:space="preserve">Aliter exactius.</head> <p> <s xml:id="echoid-s9537" xml:space="preserve">EX calculo ***, quem infra habebis, necnon ex calculo ***, habeas ad datum tempus mediam vtriuſq; </s> <s xml:id="echoid-s9538" xml:space="preserve">lon-<lb/>gitudinem ab æquinoctio atque hinc mediam *** a *** elongationem, quam per diurnam elongationem <lb/>mediam 12. </s> <s xml:id="echoid-s9539" xml:space="preserve">11′. </s> <s xml:id="echoid-s9540" xml:space="preserve">diuide, quotiens enim dabit dies, quibus medium nouil. </s> <s xml:id="echoid-s9541" xml:space="preserve">præceſſit datum tempus. </s> <s xml:id="echoid-s9542" xml:space="preserve">medium <lb/>noui<unsure/>l. </s> <s xml:id="echoid-s9543" xml:space="preserve">eſt coniunctio centri epicycli cum loco Solis medio. </s> <s xml:id="echoid-s9544" xml:space="preserve">habito temporis coniunctionis mediæ ☌, ad il-<lb/>lud computa æquationes tam ***, quam ***, ex quibus cognoſces quantum tempus mediæ ☌, diſtent vera lo-<lb/>ca luminarium. </s> <s xml:id="echoid-s9545" xml:space="preserve">ſi Luna Solem præcedit, i<unsure/>deſt ſi habet minorem diſtantiam ab æquinoctio, nondum facta eſt <lb/>vera ☌, ſeu nouil, conſidera igitur veram luminarium diſlantiam, ideſt, quot gradus diſtent, & </s> <s xml:id="echoid-s9546" xml:space="preserve">conijcere po-<lb/>teris quot horis poſt mediam ☌, futurum ſit verum nouilunium: </s> <s xml:id="echoid-s9547" xml:space="preserve">ſi vero Luna Solẽ ſequatur, iam ante mediã<unsure/> <lb/>☌, præceſſit vera; </s> <s xml:id="echoid-s9548" xml:space="preserve">idque tot horis, quot diſtantia luminarium vera importare videris. </s> <s xml:id="echoid-s9549" xml:space="preserve">quia vera in ſuperiori <lb/>exemplo, tempore mediæ ☌, quæ fuit circa meridiem diei 13. </s> <s xml:id="echoid-s9550" xml:space="preserve">Luna ſequebatur per 3. </s> <s xml:id="echoid-s9551" xml:space="preserve">circiter gradus, quibus <lb/>Luna a Sole elongatur per horas ferè 6. </s> <s xml:id="echoid-s9552" xml:space="preserve">ideo verum nouilunium factum eſt die 13. </s> <s xml:id="echoid-s9553" xml:space="preserve">hora poſt merid. </s> <s xml:id="echoid-s9554" xml:space="preserve">18. </s> <s xml:id="echoid-s9555" xml:space="preserve">Præ-<lb/>terea quia Luna erat in ſuperiori parte epicycli propè apogæum, vbi reſpectu motus longitudinis, & </s> <s xml:id="echoid-s9556" xml:space="preserve">elon-<lb/>gationis a ***, propterea tardiſſima euadit, fit vt verum nouilunium adhuc prius acciderit; </s> <s xml:id="echoid-s9557" xml:space="preserve">videlicet circa. <lb/></s> <s xml:id="echoid-s9558" xml:space="preserve">diei 31. </s> <s xml:id="echoid-s9559" xml:space="preserve">mediam noctem. </s> <s xml:id="echoid-s9560" xml:space="preserve">ex quibus etiam ætas *** conſtabit. </s> <s xml:id="echoid-s9561" xml:space="preserve">Verum iſta ſubtilius indagere, extra præfixas no-<lb/>bis metas nimis excurrit.</s> <s xml:id="echoid-s9562" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div201" type="section" level="1" n="130"> <head xml:id="echoid-head142" style="it" xml:space="preserve">Inuenire tempus, ſeu horas, quibus noctu Luna luceat. Propoſ. VIII.</head> <p> <s xml:id="echoid-s9563" xml:space="preserve">HIc Aſtronomi loquuntur de horis inæqualibus, quibus olim Romani vtebantur, & </s> <s xml:id="echoid-s9564" xml:space="preserve">quibus tam æſtate, <lb/>quam hyeme; </s> <s xml:id="echoid-s9565" xml:space="preserve">tam diem, quam noctẽ, in 12. </s> <s xml:id="echoid-s9566" xml:space="preserve">horas diuidebant, quæ propterea dictæ ſunt inæquales, quia <lb/>pro varia diei, ac noct s magnitudine ipſæ quoque variæ erant. </s> <s xml:id="echoid-s9567" xml:space="preserve">Cum enim maximi erant dies, ipſæ quoque <lb/>maximæ erant; </s> <s xml:id="echoid-s9568" xml:space="preserve">cum minimi, minimæ. </s> <s xml:id="echoid-s9569" xml:space="preserve">ſemper tamen ſunt partes diei, vel noctis, duodecimæ de his in Euan- <pb o="97" file="0117" n="121" rhead="Liber Nonus."/> @elio dictum eſt, nonne 12. </s> <s xml:id="echoid-s9570" xml:space="preserve">ſunt horæ diei@ ratio autem cur Aſtronomi hoc loco eas adhibeant, eſt quia ani-<lb/>maduerterunt, ita ſe habere ætatem, ſeu dies Lunę, vi<unsure/>que ad plenitunium, ad horas inæquales, quibus ea no-<lb/>ctu lucet; </s> <s xml:id="echoid-s9571" xml:space="preserve">quemadmodum ſe habent 5. </s> <s xml:id="echoid-s9572" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s9573" xml:space="preserve">Pariter poſt plenilunium reliquum eius ætatis, aut reliquos eius <lb/>dies vſq; </s> <s xml:id="echoid-s9574" xml:space="preserve">ad 30. </s> <s xml:id="echoid-s9575" xml:space="preserve">ita ſe habere ad horas, quibus noctu lucet, vt 5. </s> <s xml:id="echoid-s9576" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s9577" xml:space="preserve">quare vt haſce horas reperiant, ſic agunt: <lb/></s> <s xml:id="echoid-s9578" xml:space="preserve">Aetatem Lunæ per ſuperiores regulas, v. </s> <s xml:id="echoid-s9579" xml:space="preserve">g. </s> <s xml:id="echoid-s9580" xml:space="preserve">per epactam inueniunt, cui addunt vnitatem; </s> <s xml:id="echoid-s9581" xml:space="preserve">quoniam, vti di-<lb/>ximus, ætas Lunæ per regulas aurei numeri aut epactarũ inuenta, eſt aliquanto vera minor. </s> <s xml:id="echoid-s9582" xml:space="preserve">hanc igitur æta-<lb/>tem ſic auctam, multiplicant per 4. </s> <s xml:id="echoid-s9583" xml:space="preserve">numerumq; </s> <s xml:id="echoid-s9584" xml:space="preserve">genitum diuidunt per 5. </s> <s xml:id="echoid-s9585" xml:space="preserve">Quotiens enim indicat horas inæ-<lb/>quales, ſiue partes duodecimas noctis, quibus Luna ſplendet; </s> <s xml:id="echoid-s9586" xml:space="preserve">& </s> <s xml:id="echoid-s9587" xml:space="preserve">ſi ſuperſint aliquot vnitates ex hac diur<unsure/>ſione; </s> <s xml:id="echoid-s9588" xml:space="preserve"><lb/>cæ indicabunt totidem quintas partes vnius horæ, quibus præterea ſplendet. </s> <s xml:id="echoid-s9589" xml:space="preserve">poſt plenilunium vero eædem. </s> <s xml:id="echoid-s9590" xml:space="preserve"><lb/>computãdæ ſunt ante Solis ortum; </s> <s xml:id="echoid-s9591" xml:space="preserve">ratio eſt, quia creſcente Luna, ſiue ante plenil. </s> <s xml:id="echoid-s9592" xml:space="preserve">fulſio ipſius eſt veſpertina, <lb/>occaſo enim Sole ſtatim in cælo apparet: </s> <s xml:id="echoid-s9593" xml:space="preserve">eadem vero decreſcente ſiue poſt plenil. </s> <s xml:id="echoid-s9594" xml:space="preserve">fulſio eius matutina eſt; </s> <s xml:id="echoid-s9595" xml:space="preserve"><lb/>quia ſingulis noctibus, vna ferè hora tardius oritur; </s> <s xml:id="echoid-s9596" xml:space="preserve">ſed vſque mane fulget. </s> <s xml:id="echoid-s9597" xml:space="preserve">ſi vero ſit ipſum plenil. </s> <s xml:id="echoid-s9598" xml:space="preserve">tota nocte <lb/>fulget, quia occidente Sole oritur, & </s> <s xml:id="echoid-s9599" xml:space="preserve">oriente occidit, v.</s> <s xml:id="echoid-s9600" xml:space="preserve">g. </s> <s xml:id="echoid-s9601" xml:space="preserve">hoc anno 1616. </s> <s xml:id="echoid-s9602" xml:space="preserve">die 23. </s> <s xml:id="echoid-s9603" xml:space="preserve">Iulij, reperio per epactas in <lb/>Calẽdario ſcriptas, ætatem Lunæ eſſe 9. </s> <s xml:id="echoid-s9604" xml:space="preserve">dierum, & </s> <s xml:id="echoid-s9605" xml:space="preserve">addita vnitate, eſſe 10. </s> <s xml:id="echoid-s9606" xml:space="preserve">quos in 4. </s> <s xml:id="echoid-s9607" xml:space="preserve">duco, fiunt 40. </s> <s xml:id="echoid-s9608" xml:space="preserve">hos diuido <lb/>per 5. </s> <s xml:id="echoid-s9609" xml:space="preserve">fiunt 8. </s> <s xml:id="echoid-s9610" xml:space="preserve">pro quotiẽte. </s> <s xml:id="echoid-s9611" xml:space="preserve">Luna igitur noctu lucet per horas 8. </s> <s xml:id="echoid-s9612" xml:space="preserve">integras poſt Solis occaſum, quoniã creſcens <lb/>eſt, atq; </s> <s xml:id="echoid-s9613" xml:space="preserve">ante plenil. </s> <s xml:id="echoid-s9614" xml:space="preserve">rurſus eodem anno die 3. </s> <s xml:id="echoid-s9615" xml:space="preserve">Auguſti, reperio ætatẽ Lunæ dierum 20. </s> <s xml:id="echoid-s9616" xml:space="preserve">additaq; </s> <s xml:id="echoid-s9617" xml:space="preserve">vnitate 21. </s> <s xml:id="echoid-s9618" xml:space="preserve">& </s> <s xml:id="echoid-s9619" xml:space="preserve"><lb/>quia tranſactũ eſt plenil. </s> <s xml:id="echoid-s9620" xml:space="preserve">accipio reliquum ætatis Lunę vſque ad 30. </s> <s xml:id="echoid-s9621" xml:space="preserve">qui ſunt dies 9. </s> <s xml:id="echoid-s9622" xml:space="preserve">quibus per 4. </s> <s xml:id="echoid-s9623" xml:space="preserve">multiplicatis <lb/>producitur 36. </s> <s xml:id="echoid-s9624" xml:space="preserve">hunc diuido per 5. </s> <s xml:id="echoid-s9625" xml:space="preserve">fit quotiens 7 {1/5}. </s> <s xml:id="echoid-s9626" xml:space="preserve">qui indicat Lunã, mane ante Soli<unsure/>s ortũ, fulgere per horas 7. </s> <s xml:id="echoid-s9627" xml:space="preserve"><lb/>inæquales, cũ {3/5}. </s> <s xml:id="echoid-s9628" xml:space="preserve">horæ. </s> <s xml:id="echoid-s9629" xml:space="preserve">eſt enim decreſcens. </s> <s xml:id="echoid-s9630" xml:space="preserve">præterea ſit in pleni<unsure/>l. </s> <s xml:id="echoid-s9631" xml:space="preserve">ætas Lunæ dies 15. </s> <s xml:id="echoid-s9632" xml:space="preserve">hancduco in 4. </s> <s xml:id="echoid-s9633" xml:space="preserve">fiunt 60. </s> <s xml:id="echoid-s9634" xml:space="preserve"><lb/>hunc diuido per 5. </s> <s xml:id="echoid-s9635" xml:space="preserve">erit quotiens 12. </s> <s xml:id="echoid-s9636" xml:space="preserve">ideſt, horæ 12. </s> <s xml:id="echoid-s9637" xml:space="preserve">inæquales, quæ totam noctem cõplent. </s> <s xml:id="echoid-s9638" xml:space="preserve">Eadem ratione. </s> <s xml:id="echoid-s9639" xml:space="preserve"><lb/>reperies Lunam in ambabus quadraturis, ideſt vel cum creſcẽs habet dies 7 {1/2}. </s> <s xml:id="echoid-s9640" xml:space="preserve">vel cum ei ſeneſcenti ſuperſunt <lb/>7 {1/2}. </s> <s xml:id="echoid-s9641" xml:space="preserve">ſplendeſcere per 6. </s> <s xml:id="echoid-s9642" xml:space="preserve">horas inæquales; </s> <s xml:id="echoid-s9643" xml:space="preserve">hoc eſt, per dimidiã noctem, quæ tunc erit veſpertina, nunc matutina.</s> <s xml:id="echoid-s9644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9645" xml:space="preserve">Hęc porrò@regula nititur regula aurea, ſeu trium, quoniã enim ita eſt 5. </s> <s xml:id="echoid-s9646" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s9647" xml:space="preserve">ſicut dies Lunę ad horas inæqu. <lb/></s> <s xml:id="echoid-s9648" xml:space="preserve">quibus fulget; </s> <s xml:id="echoid-s9649" xml:space="preserve">ſuntq; </s> <s xml:id="echoid-s9650" xml:space="preserve">ſemper tres termini noti, videlicet 5. </s> <s xml:id="echoid-s9651" xml:space="preserve">4. </s> <s xml:id="echoid-s9652" xml:space="preserve">& </s> <s xml:id="echoid-s9653" xml:space="preserve">10. </s> <s xml:id="echoid-s9654" xml:space="preserve">v. </s> <s xml:id="echoid-s9655" xml:space="preserve">g. </s> <s xml:id="echoid-s9656" xml:space="preserve">dies Lunæ; </s> <s xml:id="echoid-s9657" xml:space="preserve">fit vt ſi 4. </s> <s xml:id="echoid-s9658" xml:space="preserve">in dies Lunæ, v.</s> <s xml:id="echoid-s9659" xml:space="preserve">g. </s> <s xml:id="echoid-s9660" xml:space="preserve"><lb/>10. </s> <s xml:id="echoid-s9661" xml:space="preserve">ducantur, & </s> <s xml:id="echoid-s9662" xml:space="preserve">productus diuidãtur per 5. </s> <s xml:id="echoid-s9663" xml:space="preserve">proueniãt in quotiente horæ inęquales fulſionis nocturnę lunaris.</s> <s xml:id="echoid-s9664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9665" xml:space="preserve">Hac igitur regula vti poſſumus, cum oportuerit nocturnam Lunæ fulſionem indagere; </s> <s xml:id="echoid-s9666" xml:space="preserve">verum, vt nos hoc <lb/>labore leuaremur, condita eſt per præcedentem regulam ſequens Tabella, in qua per ætatem Lunæ præha-<lb/>bitam, ſtatim ſine vllo numerorum labore, nocturnam Lunæ fulſionem reperies.</s> <s xml:id="echoid-s9667" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div202" type="section" level="1" n="131"> <head xml:id="echoid-head143" style="it" xml:space="preserve">Tabella inuentionis temporis quo Luna nocta<unsure/> lucet.</head> <note position="right" xml:space="preserve"> <lb/>## Aetas ***. ante ple- \\ nil.ſeu creſcentis. ## Horæ inæquales \\ quibus lucet. ## Ætas *** poſt p. enil. \\ ideſtſeneſcentis. <lb/>1 # # {4/5} # # 29 <lb/>2 # # 1 {3/5} # # 28 <lb/>3 # # 2 {2/5} # # 27 <lb/>4 # # 3 {1/5} # # 26 <lb/>5 # # 4 # # 25 <lb/>6 # # 4 {4/5} # # 24 <lb/>7 # # 5 {2/5} # # 23 <lb/>8 # # 6 {1/2} # # 22 <lb/>9 # # 7 {1/5} # # 21 <lb/>10 # # 8 # # 20 <lb/>11 # # 8 {4/5} # # 19 <lb/>12 # # 9 {3/5} # # 18 <lb/>13 # # 10 {2/5} # # 17 <lb/>14 # # 11 {1/5} # # 16 <lb/>15 # Pleni- # 12 # Lunium. # 15 <lb/></note> <p> <s xml:id="echoid-s9668" xml:space="preserve">VSus Tabellæ eſt hic: </s> <s xml:id="echoid-s9669" xml:space="preserve">Aetatẽ Lunæ prę-<lb/>habitam accipe in columna ſiniſtra an-<lb/>te plenil. </s> <s xml:id="echoid-s9670" xml:space="preserve">in dextra poſt. </s> <s xml:id="echoid-s9671" xml:space="preserve">Et è regione illius <lb/>in columna media reperies horas inęquales <lb/>nocturn@s fulſionis Lunæ: </s> <s xml:id="echoid-s9672" xml:space="preserve">quæ ante plenil. <lb/></s> <s xml:id="echoid-s9673" xml:space="preserve">poſt Solis occaſum numerandæ ſunt: </s> <s xml:id="echoid-s9674" xml:space="preserve">Poſt <lb/>plenil. </s> <s xml:id="echoid-s9675" xml:space="preserve">ante Solis ortum, v.</s> <s xml:id="echoid-s9676" xml:space="preserve">g. </s> <s xml:id="echoid-s9677" xml:space="preserve">ſuperius ætas <lb/>Lunæ erat 10. </s> <s xml:id="echoid-s9678" xml:space="preserve">di<unsure/>es, quæ in columna ſiniſtra <lb/>reperitur ante, plenil. </s> <s xml:id="echoid-s9679" xml:space="preserve">è cuius directo, in me-<lb/>di<unsure/>a columna reſpondent 8. </s> <s xml:id="echoid-s9680" xml:space="preserve">horæ inæquales <lb/>quibus poſt occaſum Luna fulgebat.</s> <s xml:id="echoid-s9681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9682" xml:space="preserve">Rurſus in altero exemplo ętas Lunæ erat <lb/>dierum 21. </s> <s xml:id="echoid-s9683" xml:space="preserve">poſt plenil. </s> <s xml:id="echoid-s9684" xml:space="preserve">quæ reperitur in co-<lb/>lumna dextra, cui in media relpondent ho-<lb/>ræ 7 {1/5}. </s> <s xml:id="echoid-s9685" xml:space="preserve">inæquales, quibus ante ortum Solis <lb/>ſplendebat.</s> <s xml:id="echoid-s9686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9687" xml:space="preserve">Porrò non difficile erit cognoſcere quot <lb/>horis etiam æqualibus ſplendeat: </s> <s xml:id="echoid-s9688" xml:space="preserve">cogni<unsure/>to <lb/>enim numero horarũ inæqua ium, quæ no-<lb/>ctem oblatam complent, eum diuide in par-<lb/>tes 12. </s> <s xml:id="echoid-s9689" xml:space="preserve">æquales, tot enim ex dictis partibus <lb/>Luna lucebit, quot etiam horas inæquales, <lb/>v.</s> <s xml:id="echoid-s9690" xml:space="preserve">g. </s> <s xml:id="echoid-s9691" xml:space="preserve">quia in ſuperiori exemplo diei 23. </s> <s xml:id="echoid-s9692" xml:space="preserve">lulij <lb/>horæ nocturnæ æquales ſunt 9. </s> <s xml:id="echoid-s9693" xml:space="preserve">in noſtra al-<lb/>titudinc poli gr. </s> <s xml:id="echoid-s9694" xml:space="preserve">45. </s> <s xml:id="echoid-s9695" xml:space="preserve">Luna autem lucet ho-<lb/>ras inæquales 8. </s> <s xml:id="echoid-s9696" xml:space="preserve">ideſt, 8. </s> <s xml:id="echoid-s9697" xml:space="preserve">duodecimas illius <lb/>noctis. </s> <s xml:id="echoid-s9698" xml:space="preserve">diuiſis i<unsure/>gitur hor. </s> <s xml:id="echoid-s9699" xml:space="preserve">ęqualibus 9. </s> <s xml:id="echoid-s9700" xml:space="preserve">per 12. <lb/></s> <s xml:id="echoid-s9701" xml:space="preserve">fit quotiens {3/4}. </s> <s xml:id="echoid-s9702" xml:space="preserve">horæ inæqualis, quæ eſt pars <lb/>duodecima noctis illius. </s> <s xml:id="echoid-s9703" xml:space="preserve">Luna igitur lucet <lb/>per 8. </s> <s xml:id="echoid-s9704" xml:space="preserve">huius duodecimas. </s> <s xml:id="echoid-s9705" xml:space="preserve">ſi igitur {3/4}. </s> <s xml:id="echoid-s9706" xml:space="preserve">ducãtur <lb/>in 8. </s> <s xml:id="echoid-s9707" xml:space="preserve">gignentur {24/@4}. </s> <s xml:id="echoid-s9708" xml:space="preserve">ſine 6. </s> <s xml:id="echoid-s9709" xml:space="preserve">vnde colligitur Lu-<lb/>nam lucere h. </s> <s xml:id="echoid-s9710" xml:space="preserve">6. </s> <s xml:id="echoid-s9711" xml:space="preserve">æqualibus veſpertinis, ſiue <lb/>poſt occaſum Solis.</s> <s xml:id="echoid-s9712" xml:space="preserve"/> </p> <pb o="98" file="0118" n="122" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s9713" xml:space="preserve">Poſtremo Lector aduertat hæc tempora non omnino exactè reperiri; </s> <s xml:id="echoid-s9714" xml:space="preserve">tum quia pendent ab ætate Lunæ <lb/>per epactas, aut aureum numerum inuenta; </s> <s xml:id="echoid-s9715" xml:space="preserve">quæ vti ſupra diximus regulæ populares ſunt; </s> <s xml:id="echoid-s9716" xml:space="preserve">tum etiam ob alias <lb/>Lunæ motus irregularitates: </s> <s xml:id="echoid-s9717" xml:space="preserve">ſatis tamen eſt, ac valde vtile, ea plus minus comperta habere poſſe.</s> <s xml:id="echoid-s9718" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div203" type="section" level="1" n="132"> <head xml:id="echoid-head144" style="it" xml:space="preserve">Eclypſim Lunæ prædicer@. Propoſ. VIII.</head> <p> <s xml:id="echoid-s9719" xml:space="preserve">NEgotium iſtud ſummæ ſubtilitatis eſt, ac proinde multis etiam tricis impeditum. </s> <s xml:id="echoid-s9720" xml:space="preserve">nihil autem in tota. <lb/></s> <s xml:id="echoid-s9721" xml:space="preserve">Aſtronom. </s> <s xml:id="echoid-s9722" xml:space="preserve">vulgo admi<unsure/>rabilius, quam hæc tam exacta eclypſium diuinatio, præſertim ad annos com-<lb/>plures: </s> <s xml:id="echoid-s9723" xml:space="preserve">Annunciate nobis quæ futura ſunt, & </s> <s xml:id="echoid-s9724" xml:space="preserve">eritis ſicut Dij, inquit Sapiens. </s> <s xml:id="echoid-s9725" xml:space="preserve">merito igitur in ſui admiratio-<lb/>nem cunctos morales pertrahit, ac ſimul in ſyderalis ſcientiæ venerationem. </s> <s xml:id="echoid-s9726" xml:space="preserve">merito etiam Anaxagoras Cla-<lb/>zomenius, qui primus lunares defectus prædixit, ſum<unsure/>mo honore habitus eſt, ante Domini aduentum ann. </s> <s xml:id="echoid-s9727" xml:space="preserve">fe-<lb/>rè 550. </s> <s xml:id="echoid-s9728" xml:space="preserve">alius etiam ob id ab rege Syracuſano Talento donatus eſt.</s> <s xml:id="echoid-s9729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9730" xml:space="preserve">Par igitur eſt, cum ad hunc Aſtronomiæ apicem aſcendere nunc nequeamus, ſaltem eum à longe indigi-<lb/>tare. </s> <s xml:id="echoid-s9731" xml:space="preserve">Exempli gratia libeat examinare ſequens plenilunium huius menſis lulij, an ſit eclypticum. </s> <s xml:id="echoid-s9732" xml:space="preserve">oportet <lb/>igitur, primo inuenire mediam luminarium ☍. </s> <s xml:id="echoid-s9733" xml:space="preserve">oppoſitionem, rudi Minerua per regulas traditas, qua rum <lb/>melior eſt ea, quæ calculo nititur. </s> <s xml:id="echoid-s9734" xml:space="preserve">quia igitur ſuperius inuentum eſt nouil. </s> <s xml:id="echoid-s9735" xml:space="preserve">menſis eurrentis contigiſſe circa<unsure/> <lb/>mediam noctem ſequentem poſt dies 13. </s> <s xml:id="echoid-s9736" xml:space="preserve">ideo hinc conijcij plenilunij futuri tempus hoc modo, tempus me. <lb/></s> <s xml:id="echoid-s9737" xml:space="preserve"> <anchor type="note" xlink:label="note-0118-01a" xlink:href="note-0118-01"/> diæ lunationis eſt dies 14 hora 18. </s> <s xml:id="echoid-s9738" xml:space="preserve">22′. </s> <s xml:id="echoid-s9739" xml:space="preserve">hoc tempus addo tẽpore nouilunij, ideſt, diei<unsure/>-<lb/>13. </s> <s xml:id="echoid-s9740" xml:space="preserve">& </s> <s xml:id="echoid-s9741" xml:space="preserve">horis 12. </s> <s xml:id="echoid-s9742" xml:space="preserve">fiuntq; </s> <s xml:id="echoid-s9743" xml:space="preserve">dies 28. </s> <s xml:id="echoid-s9744" xml:space="preserve">horæ 6. </s> <s xml:id="echoid-s9745" xml:space="preserve">22′. </s> <s xml:id="echoid-s9746" xml:space="preserve">lulij, pro tempore plenilunij futuri. </s> <s xml:id="echoid-s9747" xml:space="preserve">Iam <lb/>vero antequam rem exactius expendam inquiro ad hoc tempus plenilunij locũ ☊. <lb/></s> <s xml:id="echoid-s9748" xml:space="preserve">per calculum, inuenioque eum eſſe in 10.</s> <s xml:id="echoid-s9749" xml:space="preserve">′ gr. </s> <s xml:id="echoid-s9750" xml:space="preserve">26′. </s> <s xml:id="echoid-s9751" xml:space="preserve">min. </s> <s xml:id="echoid-s9752" xml:space="preserve">♓. </s> <s xml:id="echoid-s9753" xml:space="preserve">& </s> <s xml:id="echoid-s9754" xml:space="preserve">conſequenter ☊ eſſe in <lb/>gr. </s> <s xml:id="echoid-s9755" xml:space="preserve">10. </s> <s xml:id="echoid-s9756" xml:space="preserve">36. </s> <s xml:id="echoid-s9757" xml:space="preserve">♍. </s> <s xml:id="echoid-s9758" xml:space="preserve">cum autem ***. </s> <s xml:id="echoid-s9759" xml:space="preserve">ſit in 5. </s> <s xml:id="echoid-s9760" xml:space="preserve">gr. </s> <s xml:id="echoid-s9761" xml:space="preserve">12′. </s> <s xml:id="echoid-s9762" xml:space="preserve">♌ erit ***<unsure/>. </s> <s xml:id="echoid-s9763" xml:space="preserve">ei oppoſita in 6. </s> <s xml:id="echoid-s9764" xml:space="preserve">12′. </s> <s xml:id="echoid-s9765" xml:space="preserve">♒ vbi pro-<lb/>citur vmbra terræ. </s> <s xml:id="echoid-s9766" xml:space="preserve">Ergo ***. </s> <s xml:id="echoid-s9767" xml:space="preserve">diſtat a ☊. </s> <s xml:id="echoid-s9768" xml:space="preserve">ideſt a loco, à quo non longè defectus con-<lb/>tingunt per gr. </s> <s xml:id="echoid-s9769" xml:space="preserve">34. </s> <s xml:id="echoid-s9770" xml:space="preserve">ſciendum autem eſt, quod ſi plenilunium verum, ſeu ſi ***. </s> <s xml:id="echoid-s9771" xml:space="preserve">in vera <lb/>oppoſitione, non diſtiterit a nodis, pluſquam gr. </s> <s xml:id="echoid-s9772" xml:space="preserve">12. </s> <s xml:id="echoid-s9773" xml:space="preserve">hinc inde, futuram eſſe aliquam <lb/>eclypſim, atque eo maiorem, quo nodis propius acciderit. </s> <s xml:id="echoid-s9774" xml:space="preserve">hanc diſtantiam vocant <lb/>terminos eclypticos; </s> <s xml:id="echoid-s9775" xml:space="preserve">quod intra eos defectus omnes contingant, extra eos fieri nequeant: </s> <s xml:id="echoid-s9776" xml:space="preserve">Ratio eſt, quia in <lb/>hiſce terminis, Luna habet talem latitudinem, vt ſemidiameter ipſius, & </s> <s xml:id="echoid-s9777" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s9778" xml:space="preserve">vmbrę terræ, occurrentes ſibi <lb/>in anguſtijs illis, nequeant ſibi mutuo de via cedere, ſed ***. </s> <s xml:id="echoid-s9779" xml:space="preserve">cogitur vmbram terræ perſt@ingere, aut in eam <lb/>impingere. </s> <s xml:id="echoid-s9780" xml:space="preserve">cum ergo in hoc plenilunio ***. </s> <s xml:id="echoid-s9781" xml:space="preserve">diſtet à ☊. </s> <s xml:id="echoid-s9782" xml:space="preserve">a gr. </s> <s xml:id="echoid-s9783" xml:space="preserve">34. </s> <s xml:id="echoid-s9784" xml:space="preserve">& </s> <s xml:id="echoid-s9785" xml:space="preserve">a ☊. </s> <s xml:id="echoid-s9786" xml:space="preserve">conſequenter gr. </s> <s xml:id="echoid-s9787" xml:space="preserve">146. </s> <s xml:id="echoid-s9788" xml:space="preserve">certum eſt nullam <lb/>fore eclyp. </s> <s xml:id="echoid-s9789" xml:space="preserve">quare non amplius de eo cogito.</s> <s xml:id="echoid-s9790" xml:space="preserve"/> </p> <div xml:id="echoid-div203" type="float" level="2" n="1"> <note position="right" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve"> <lb/>D. # H. # I <lb/>13. # 22. # 0,. <lb/>14. # 18. # 22,. <lb/>28. # 6. # 22. <lb/></note> </div> <p> <s xml:id="echoid-s9791" xml:space="preserve">Rurſus examino ſequens Auguſti plenil. </s> <s xml:id="echoid-s9792" xml:space="preserve">quod ſic reperio, quia ab vno plenilunio ad alterum ſunt dies 29. <lb/></s> <s xml:id="echoid-s9793" xml:space="preserve">h. </s> <s xml:id="echoid-s9794" xml:space="preserve">12. </s> <s xml:id="echoid-s9795" xml:space="preserve">{3/4}. </s> <s xml:id="echoid-s9796" xml:space="preserve">eos addo diebus 28. </s> <s xml:id="echoid-s9797" xml:space="preserve">h. </s> <s xml:id="echoid-s9798" xml:space="preserve">6. </s> <s xml:id="echoid-s9799" xml:space="preserve">lulij, ideſt, tempori plenilunij; </s> <s xml:id="echoid-s9800" xml:space="preserve">conflanturq; </s> <s xml:id="echoid-s9801" xml:space="preserve">dies 57. </s> <s xml:id="echoid-s9802" xml:space="preserve">h. </s> <s xml:id="echoid-s9803" xml:space="preserve">18 {3/4}. </s> <s xml:id="echoid-s9804" xml:space="preserve">a quibus demo dies <lb/>31. </s> <s xml:id="echoid-s9805" xml:space="preserve">meuſis lulij, remanentq; </s> <s xml:id="echoid-s9806" xml:space="preserve">dies 26. </s> <s xml:id="echoid-s9807" xml:space="preserve">h. </s> <s xml:id="echoid-s9808" xml:space="preserve">18 {3/4}. </s> <s xml:id="echoid-s9809" xml:space="preserve">Auguſti, pro tempore plenilunij (aliter tamen potuiſſet inueniri <lb/>hoc plenilunium ex ſuperioribus præceptis, iuxta lectoris ſolertiam.) </s> <s xml:id="echoid-s9810" xml:space="preserve">hoc autem tẽpore oppoſitus locus ***. </s> <s xml:id="echoid-s9811" xml:space="preserve"><lb/>ſiue locus vmbræ terræ, eſt in gr. </s> <s xml:id="echoid-s9812" xml:space="preserve">4. </s> <s xml:id="echoid-s9813" xml:space="preserve">♓. </s> <s xml:id="echoid-s9814" xml:space="preserve">eodem tempore video ex calculo ☊. </s> <s xml:id="echoid-s9815" xml:space="preserve">eſſe in gr. </s> <s xml:id="echoid-s9816" xml:space="preserve">9. </s> <s xml:id="echoid-s9817" xml:space="preserve">♓. </s> <s xml:id="echoid-s9818" xml:space="preserve">quare plenil. </s> <s xml:id="echoid-s9819" xml:space="preserve">diſtat <lb/>2 ☊. </s> <s xml:id="echoid-s9820" xml:space="preserve">gr. </s> <s xml:id="echoid-s9821" xml:space="preserve">tantum 5. </s> <s xml:id="echoid-s9822" xml:space="preserve">ergo cum ſit intra diſtantiam gr. </s> <s xml:id="echoid-s9823" xml:space="preserve">12. </s> <s xml:id="echoid-s9824" xml:space="preserve">& </s> <s xml:id="echoid-s9825" xml:space="preserve">quidem multum, hinc certo prænuncio futurum lu-<lb/>narem defectum; </s> <s xml:id="echoid-s9826" xml:space="preserve">& </s> <s xml:id="echoid-s9827" xml:space="preserve">quidem ſatis magnum, cum in magnis anguſtijs vmbræ Luna occurrat. </s> <s xml:id="echoid-s9828" xml:space="preserve">in tali enim di-<lb/>ſtantia a ☊. </s> <s xml:id="echoid-s9829" xml:space="preserve">habet latitudinem 26′. </s> <s xml:id="echoid-s9830" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s9831" xml:space="preserve">autem vmbræ occupat min. </s> <s xml:id="echoid-s9832" xml:space="preserve">ferè 50′. </s> <s xml:id="echoid-s9833" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s9834" xml:space="preserve">verò Lunę eſt min. </s> <s xml:id="echoid-s9835" xml:space="preserve">17′.</s> <s xml:id="echoid-s9836" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9837" xml:space="preserve">Sit igitur figura in qua A B. </s> <s xml:id="echoid-s9838" xml:space="preserve">ſit eclyptica C D. </s> <s xml:id="echoid-s9839" xml:space="preserve">fit via lunaris E. </s> <s xml:id="echoid-s9840" xml:space="preserve">ſit ☊. </s> <s xml:id="echoid-s9841" xml:space="preserve">E F. </s> <s xml:id="echoid-s9842" xml:space="preserve">ſit diſtantia gr. </s> <s xml:id="echoid-s9843" xml:space="preserve">5. </s> <s xml:id="echoid-s9844" xml:space="preserve">a ☊. </s> <s xml:id="echoid-s9845" xml:space="preserve">F G. </s> <s xml:id="echoid-s9846" xml:space="preserve">ſit la-<lb/> <anchor type="figure" xlink:label="fig-0118-01a" xlink:href="fig-0118-01"/> titudo ***. </s> <s xml:id="echoid-s9847" xml:space="preserve">26′. </s> <s xml:id="echoid-s9848" xml:space="preserve">circulũ vni<unsure/>bræ ſit circa cen-<lb/>trum F. </s> <s xml:id="echoid-s9849" xml:space="preserve">cuius ſemid. </s> <s xml:id="echoid-s9850" xml:space="preserve">F H. </s> <s xml:id="echoid-s9851" xml:space="preserve">50′. </s> <s xml:id="echoid-s9852" xml:space="preserve">Luna ſit cir-<lb/>ca centrum G. </s> <s xml:id="echoid-s9853" xml:space="preserve">cuius ſemid. </s> <s xml:id="echoid-s9854" xml:space="preserve">G I. </s> <s xml:id="echoid-s9855" xml:space="preserve">17′. </s> <s xml:id="echoid-s9856" xml:space="preserve">quare <lb/>tota Luna ambulabit aliquandi<unsure/>u in tene-<lb/>bris. </s> <s xml:id="echoid-s9857" xml:space="preserve">Erit igitur defectus totalis cum mo-<lb/>ra. </s> <s xml:id="echoid-s9858" xml:space="preserve">Quod ſi ad hoc tempus quæratur Lu-<lb/>næ ęquatio, ea erit 27. </s> <s xml:id="echoid-s9859" xml:space="preserve">adiectiua, ideſt, Lu-<lb/>na in motu diurno, ſequitur centrum vm-<lb/>bræ per 27′. </s> <s xml:id="echoid-s9860" xml:space="preserve">quare adhuc colligo hunc ve-<lb/>rum defectum contingere priuſquam me-<lb/>dium vna fermè hora, propter 27′. </s> <s xml:id="echoid-s9861" xml:space="preserve">Et quia <lb/>videtur duratura horas circiter 4. </s> <s xml:id="echoid-s9862" xml:space="preserve">ideo ini-<lb/>tium eius erit dies 26. </s> <s xml:id="echoid-s9863" xml:space="preserve">Auguſti poſt merid. <lb/></s> <s xml:id="echoid-s9864" xml:space="preserve">h. </s> <s xml:id="echoid-s9865" xml:space="preserve">15. </s> <s xml:id="echoid-s9866" xml:space="preserve">quod erit mane diei 27. </s> <s xml:id="echoid-s9867" xml:space="preserve">ciuilis, ante <lb/>ortum Solis horis ferè duabus. </s> <s xml:id="echoid-s9868" xml:space="preserve">atq; </s> <s xml:id="echoid-s9869" xml:space="preserve">hæc rudi Minerua; </s> <s xml:id="echoid-s9870" xml:space="preserve">reliqua vero eius accidentia exactius inueſtigare, al-<lb/>tiſſimi eſt loci, atque extra noſtros limites nimis euagatur: </s> <s xml:id="echoid-s9871" xml:space="preserve">qua etiam de cauſa, nihil de æquatione temporis <lb/>viſum eſt dicere, cum ea res nimis abſtruſa ſit, calculatoreſq; </s> <s xml:id="echoid-s9872" xml:space="preserve">exactos tantum condeceat.</s> <s xml:id="echoid-s9873" xml:space="preserve"/> </p> <div xml:id="echoid-div204" type="float" level="2" n="2"> <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a"> <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/> </figure> </div> <pb o="99" file="0119" n="123"/> </div> <div xml:id="echoid-div206" type="section" level="1" n="133"> <head xml:id="echoid-head145" xml:space="preserve">LIBER DECIMVS <lb/>DE SOLE.</head> <p> <s xml:id="echoid-s9874" xml:space="preserve">POſt Lunam luminare minus, conueniens eſt ad Solem alterum luminare maius, quod inter <lb/>omnia naturæ opera pulchritudine ac maieſtate antecellit, gradum facere, cum ipſe veluti <lb/>eæterorum planetarum Dominus, medium inter eos locum communi Aſtronomorũ con-<lb/>ſenſu obtineat. </s> <s xml:id="echoid-s9875" xml:space="preserve">præterea quoniam ipſius regio cæleſtis, ſeu cælum, necnon ipſius gyratio-<lb/>nes terræ ac mundi centrum@, non ſecus ac elementa, & </s> <s xml:id="echoid-s9876" xml:space="preserve">Luna reſpiciunt. </s> <s xml:id="echoid-s9877" xml:space="preserve">aliam rationem. <lb/></s> <s xml:id="echoid-s9878" xml:space="preserve">addunt Aſtronomi non adeo veteres, ſed tamen probatiſſimi Copernicus, Tycho, & </s> <s xml:id="echoid-s9879" xml:space="preserve">nunc <lb/>etiam Keplerus, quod videlicet Sol ipſe ſit veluti centrum, circa quod reliqui omnes plane-<lb/>tæ, præter Lunam, ſuos curſus circumducant. </s> <s xml:id="echoid-s9880" xml:space="preserve">quod ipſi proprijs obſeruationibus ſe depræhendiſſe aſſerunt: </s> <s xml:id="echoid-s9881" xml:space="preserve"><lb/>quamuis, quod ad Mercurium, ac Venerem attinet, etiam veteres idem ſenſerint, vt ex Vitruuio, & </s> <s xml:id="echoid-s9882" xml:space="preserve">Martiano <lb/>Capella manifeſtum eſt, quorum verba ſuis locis recitabuntur. </s> <s xml:id="echoid-s9883" xml:space="preserve">tandem quoniam ſupra Lunam in cæleſtium <lb/>corporum ordine primus collocari debeat: </s> <s xml:id="echoid-s9884" xml:space="preserve">quamuis enim Venus, & </s> <s xml:id="echoid-s9885" xml:space="preserve">Mercurius, & </s> <s xml:id="echoid-s9886" xml:space="preserve">ſecundum Tychonem <lb/>atque Keplerum, Mars etiam, aliquando Lunam ac Solem interſint, id tamen non eſt perpetuum; </s> <s xml:id="echoid-s9887" xml:space="preserve">imo ſæpè <lb/>contingit eos ſimul ſupra Solem efferri, nihilque propterea tunc, quod ſciamus inter duo luminaria, præter <lb/>ingens cæli interuallum interponi.</s> <s xml:id="echoid-s9888" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div207" type="section" level="1" n="134"> <head xml:id="echoid-head146" style="it" xml:space="preserve">De loco Solis, ſiue distantia eius à centro Terræ. Cap. I.</head> <p> <s xml:id="echoid-s9889" xml:space="preserve">1 SOlem eſſe Luna altiorem ex ſolaribus eclypſibus perſpicuum eſt, ideo enim Sol priuatur lumine, quòd <lb/>infra ipſum tunc temporis Luna ſubterlabatur; </s> <s xml:id="echoid-s9890" xml:space="preserve">quod quidem ſenſu ipſo percipimus; </s> <s xml:id="echoid-s9891" xml:space="preserve">vt infra patebie<unsure/> <lb/>eum de hac eclypſi, ac modis eam inſpiciendi agemus. </s> <s xml:id="echoid-s9892" xml:space="preserve">Idem patet ex vmbris Solis, & </s> <s xml:id="echoid-s9893" xml:space="preserve">Lunæ, vt in Luna. <lb/></s> <s xml:id="echoid-s9894" xml:space="preserve">diximus.</s> <s xml:id="echoid-s9895" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9896" xml:space="preserve">2 At vero quantum ſupra Lunam eleuetur, ſeu quanta ſit eius à centro mundi diſtantia, hiſce rationibus <lb/>indagare conati ſunt. </s> <s xml:id="echoid-s9897" xml:space="preserve">quarũ ſit ea, quæ à parallaxi deſumitur, quæ vt probè percipiatur repetenda prius ſunt <lb/>ea, quæ ſupra de parallaxi Lunæ diximus. </s> <s xml:id="echoid-s9898" xml:space="preserve">ex ſententia igitur Copernici, ac Tychonis, quorum obſeruationes <lb/>maximè probantur, aliquam Sol exhibet parallaxim, quoniam terræ ſemidiameter non eſt prorſus inſenſibi-<lb/>lis ad diſtantiam Solis à terra. </s> <s xml:id="echoid-s9899" xml:space="preserve">Vtautem hanc aſpectus diuerſitatem aſſequerentur, neceſſe fuit eos prius cer-<lb/>tum habuiſſe Solis centrum ſemper ſub eclyptica progredi, quod Aſtronomi hiſce modis compererunt. </s> <s xml:id="echoid-s9900" xml:space="preserve">pri-<lb/>mo per organicas obſeruationes menſurando quotidie eius ab æquatore declinationem, præſertim cum me-<lb/>ridianum circulum pertranſit; </s> <s xml:id="echoid-s9901" xml:space="preserve">collegerunt enim eum ad æquatorem ſenſim ac proportionaliter, ita accede-<lb/>re, ac recedere, vt eclypticam ipſam deſcribat. </s> <s xml:id="echoid-s9902" xml:space="preserve">ſecundo & </s> <s xml:id="echoid-s9903" xml:space="preserve">quidem certius à Lunæ defectibus idem cognoue-<lb/>runt, in ijs enim luminaria diametraliter, ſaltem ſecundum partem aliquam, opponuntur, & </s> <s xml:id="echoid-s9904" xml:space="preserve">varij Lunæ de-<lb/>fectus, qui modo magni, modo parui, modo boreales, modo auſtrales, modo partiales, modo totales, omnes ſi-<lb/>mul manifeſtè conuincunt vmbram terræ quæ directè in auerſas Soli partes eijcitur, ita ferri in eclyptica, vt <lb/>axis eius, ſiue medium eius ſemper eclypticam obtineat. </s> <s xml:id="echoid-s9905" xml:space="preserve">vnde collegerunt Solis quoque medium in parte dia-<lb/>metraliter oppoſita, eclypticam poſſidere. </s> <s xml:id="echoid-s9906" xml:space="preserve">hoc igitur aſſumpto ſic Solis parallaxim rimat<unsure/>i ſunt, per Aſtrono-<lb/>micum quadrantcm aſtronomice collocatum, obſeruant Solis meridianam ſupra horiyontem altitudiuem, <lb/>præſertim eam, quæ circa gr. </s> <s xml:id="echoid-s9907" xml:space="preserve">45. </s> <s xml:id="echoid-s9908" xml:space="preserve">aut ſupra eleuatur, ibi enim refractiones ceſſant, quę parallaxibus negotium <lb/>faceſſunt. </s> <s xml:id="echoid-s9909" xml:space="preserve">Hæc igitur Solis altitudo organicè depræhenſa minor erit altitudine illius eclypticæ gradus, quẽ <lb/>Sol tunc temporis occupabit, & </s> <s xml:id="echoid-s9910" xml:space="preserve">conſequẽter minor vera Solis altitudine. </s> <s xml:id="echoid-s9911" xml:space="preserve">facile eſt autem cognoſcere veram <lb/>gradus cuiuſuis eclypticæ altitudinem horizontalem, cognita enim poli altitudine datæ regionis, ſequitur <lb/>notas eſſe meridianas omnium eclypticæ punctorum altitudinem; </s> <s xml:id="echoid-s9912" xml:space="preserve">quia notas habent ab æquatore declina-<lb/>@iones; </s> <s xml:id="echoid-s9913" xml:space="preserve">æquator autem notam habet merid. </s> <s xml:id="echoid-s9914" xml:space="preserve">altitudinem, quæ ſemper eſt altitudinis poli complementum, vt <lb/> <anchor type="figure" xlink:label="fig-0119-01a" xlink:href="fig-0119-01"/> ſupra oſtenſum eſt. </s> <s xml:id="echoid-s9915" xml:space="preserve">differentia igitur, inter veram Solis altitudinem, & </s> <s xml:id="echoid-s9916" xml:space="preserve"><lb/>obſeruatam erit quæſita viſus ab erratio, ſeu parallaxis, quæ melius in fi-<lb/>gura percipientur, in qua Sol ſit vbi D. </s> <s xml:id="echoid-s9917" xml:space="preserve">eleuatus ſupra horizontem F E. <lb/></s> <s xml:id="echoid-s9918" xml:space="preserve">quantitate arcus D E. </s> <s xml:id="echoid-s9919" xml:space="preserve">v.</s> <s xml:id="echoid-s9920" xml:space="preserve">g. </s> <s xml:id="echoid-s9921" xml:space="preserve">grad. </s> <s xml:id="echoid-s9922" xml:space="preserve">45. </s> <s xml:id="echoid-s9923" xml:space="preserve">& </s> <s xml:id="echoid-s9924" xml:space="preserve">conſequenter diſtet a@vertice A. </s> <s xml:id="echoid-s9925" xml:space="preserve">to-<lb/>tidem gr. </s> <s xml:id="echoid-s9926" xml:space="preserve">45. </s> <s xml:id="echoid-s9927" xml:space="preserve">ſitque hæc vera eius eleuatio, aut diſtantia ab horizonte co-<lb/>gnita ex eleuatione gr. </s> <s xml:id="echoid-s9928" xml:space="preserve">Solis, in qua Sol tempore obſeruationis moratur, <lb/>vt ſupra indicatum eſt. </s> <s xml:id="echoid-s9929" xml:space="preserve">iam ſi ab oculo in ſuperficie terræ poſito, v.</s> <s xml:id="echoid-s9930" xml:space="preserve">g. </s> <s xml:id="echoid-s9931" xml:space="preserve">in <lb/>B. </s> <s xml:id="echoid-s9932" xml:space="preserve">indagetur per inſtrumentum diſtantia eius à vertice A. </s> <s xml:id="echoid-s9933" xml:space="preserve">apparebit hæc <lb/>diſtãtia maior, quam gr. </s> <s xml:id="echoid-s9934" xml:space="preserve">45. </s> <s xml:id="echoid-s9935" xml:space="preserve">ideſt maior quam vera, ſeu maior quã ſit arcus <lb/>A D. </s> <s xml:id="echoid-s9936" xml:space="preserve">angulus enim A B D. </s> <s xml:id="echoid-s9937" xml:space="preserve">maior eſt angulo B C D. </s> <s xml:id="echoid-s9938" xml:space="preserve">per 16. </s> <s xml:id="echoid-s9939" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s9940" xml:space="preserve"><lb/>quare ſi ex cẽtro B. </s> <s xml:id="echoid-s9941" xml:space="preserve">deſcriptus, intelligatur arcus H I M. </s> <s xml:id="echoid-s9942" xml:space="preserve">is plures gr. </s> <s xml:id="echoid-s9943" xml:space="preserve">con-<lb/>tinebit, quam arcus A D. </s> <s xml:id="echoid-s9944" xml:space="preserve">hunc arcum exhibet inſtrumentum obſeruato-<lb/>ris, veluti quadrans, quia centrum eius ponitur in B. </s> <s xml:id="echoid-s9945" xml:space="preserve">& </s> <s xml:id="echoid-s9946" xml:space="preserve">latus vnum con-<lb/>gruens lineæ A B. </s> <s xml:id="echoid-s9947" xml:space="preserve">linea flducia in dioptra congruit lineæ B D. </s> <s xml:id="echoid-s9948" xml:space="preserve">arcus vero <pb o="100" file="0120" n="124" rhead="De Mundi Fabrica,"/> eius cum vergat ad Solẽ, intercipietur pars eius inter lineas H B. </s> <s xml:id="echoid-s9949" xml:space="preserve">B D. </s> <s xml:id="echoid-s9950" xml:space="preserve">quæ pars cum diuiſa ſit in gr. </s> <s xml:id="echoid-s9951" xml:space="preserve">& </s> <s xml:id="echoid-s9952" xml:space="preserve">in min. <lb/></s> <s xml:id="echoid-s9953" xml:space="preserve">ſtatim oſtendit eius quantitatem, ac proinde exceſſum anguli A B D. </s> <s xml:id="echoid-s9954" xml:space="preserve">ſupra angul. </s> <s xml:id="echoid-s9955" xml:space="preserve">A C D. </s> <s xml:id="echoid-s9956" xml:space="preserve">qui exceſſus vt ſu-<lb/>pra in Luna monuimus, æqualis eſt angulo D. </s> <s xml:id="echoid-s9957" xml:space="preserve">ac propterea ipſe eſt parallaxis ſeu euariatio. </s> <s xml:id="echoid-s9958" xml:space="preserve">cum igitur in tri-<lb/>gono B C D. </s> <s xml:id="echoid-s9959" xml:space="preserve">noti<unsure/> ſint anguli, & </s> <s xml:id="echoid-s9960" xml:space="preserve">etiam latus B C. </s> <s xml:id="echoid-s9961" xml:space="preserve">quippe terrę ſemidiameter, nota etiam euadet laterum pro-<lb/>portio per 6. </s> <s xml:id="echoid-s9962" xml:space="preserve">Appar. </s> <s xml:id="echoid-s9963" xml:space="preserve">ideſt, quoties latus B C. </s> <s xml:id="echoid-s9964" xml:space="preserve">contineatur in latere C D. </s> <s xml:id="echoid-s9965" xml:space="preserve">ideſt, quot terræ ſemidiametris Sol à<unsure/> <lb/>terra, & </s> <s xml:id="echoid-s9966" xml:space="preserve">conſequenter notum erit, quantum ſupra Lunam eleuetur. </s> <s xml:id="echoid-s9967" xml:space="preserve">Porrò ſi ſolus angulus D. </s> <s xml:id="echoid-s9968" xml:space="preserve">qui parallaxis <lb/>Soli<unsure/>s eſt conferatur cum parallaxi Lunæ, manifeſtabit Solem eſſe ipſa altiorem, quia in Sole minor eſt, quam <lb/>in Luna: </s> <s xml:id="echoid-s9969" xml:space="preserve">ſydus autem illud ſublimius eſt, cuius parallaxís (cæteris paribus) minor eſt. </s> <s xml:id="echoid-s9970" xml:space="preserve">debent autem duo ſy-<lb/>dera quò<unsure/>rum parallaxis comparantur, eſſe in eadem vera altitudine ſupra horizontem. </s> <s xml:id="echoid-s9971" xml:space="preserve">poteſt etiam inferius <lb/>ſydus minorem exhibere parallaxim quam ſuperius ſi illud ſit ſupra horizõtem altius, vt ſi Luna ſit in M. </s> <s xml:id="echoid-s9972" xml:space="preserve">ea-<lb/>dem altitudine cum Sol erit angulus B M C. </s> <s xml:id="echoid-s9973" xml:space="preserve">maior angulo D. </s> <s xml:id="echoid-s9974" xml:space="preserve">per 16. </s> <s xml:id="echoid-s9975" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s9976" xml:space="preserve">at vero exiſtete Luna in I. </s> <s xml:id="echoid-s9977" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0120-01a" xlink:href="fig-0120-01"/> altiore ſupra horizõtem, poterit angulus I. </s> <s xml:id="echoid-s9978" xml:space="preserve">qui eſt parallaxis minor eſſe, <lb/>quam angulus D. </s> <s xml:id="echoid-s9979" xml:space="preserve">quamuis Luna ſit terræ propior. </s> <s xml:id="echoid-s9980" xml:space="preserve">cum ergo ſeruata pa-<lb/>ri altitudine ab horizonte, Sol minorem efficiat paral. </s> <s xml:id="echoid-s9981" xml:space="preserve">euidens eſt ipſum <lb/>Lunam eſſe ſuperiorem. </s> <s xml:id="echoid-s9982" xml:space="preserve">parall. </s> <s xml:id="echoid-s9983" xml:space="preserve">autẽ Solis in altitudine gr. </s> <s xml:id="echoid-s9984" xml:space="preserve">45 proditur à <lb/>peritis Aſtronomis eſſe 2′. </s> <s xml:id="echoid-s9985" xml:space="preserve">12″. </s> <s xml:id="echoid-s9986" xml:space="preserve">maxima vero quæ eſſe poſſit apud hori-<lb/>zontem eſt 3′. </s> <s xml:id="echoid-s9987" xml:space="preserve">7″. </s> <s xml:id="echoid-s9988" xml:space="preserve">computatis refractionibus: </s> <s xml:id="echoid-s9989" xml:space="preserve">quæ parallaxes multo mi-<lb/>nores ſunt ijs, quas ſupra Lunæ attribuimus.</s> <s xml:id="echoid-s9990" xml:space="preserve"/> </p> <div xml:id="echoid-div207" type="float" level="2" n="1"> <figure xlink:label="fig-0119-01" xlink:href="fig-0119-01a"> <image file="0119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0119-01"/> </figure> <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a"> <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-01"/> </figure> </div> <p> <s xml:id="echoid-s9991" xml:space="preserve">3 Eandẽ Solis à terra altitudinẽ Ariſtarchus Samius, antiquiſſimus <lb/>Aſtronomus in libello de diſtantijs, ac magnitudinibus Solis, Lunæ & </s> <s xml:id="echoid-s9992" xml:space="preserve"><lb/>terræ; </s> <s xml:id="echoid-s9993" xml:space="preserve">ſic ſubtiliſſime indagauit. </s> <s xml:id="echoid-s9994" xml:space="preserve">primo autem ſupponit (quod facile eſt <lb/>obſeruare) Lunã cum nobis dimidiata ſplendet a Sole per gr. </s> <s xml:id="echoid-s9995" xml:space="preserve">87. </s> <s xml:id="echoid-s9996" xml:space="preserve">diſtare. <lb/></s> <s xml:id="echoid-s9997" xml:space="preserve">ſecundo conſinium i<unsure/>llud, quod in Luna ſplendidum a tenebris diuidit, <lb/>eſſe circuli peripheriam, qui ita in oculum noſtrum vergit, vt ſi planum <lb/>eius extendatur, oculo noſtro occurrat. </s> <s xml:id="echoid-s9998" xml:space="preserve">ſit iam figura in qua terra vbi B. </s> <s xml:id="echoid-s9999" xml:space="preserve"><lb/>dimidiata C I O N. </s> <s xml:id="echoid-s10000" xml:space="preserve">pars illuminata I O N. </s> <s xml:id="echoid-s10001" xml:space="preserve">circulus diuidens opacũ a ſplendido ſit ſub linea I N. </s> <s xml:id="echoid-s10002" xml:space="preserve">quæ ad ocu-<lb/>lum noſtrum in B. </s> <s xml:id="echoid-s10003" xml:space="preserve">dirigatur. </s> <s xml:id="echoid-s10004" xml:space="preserve">quia vero pars ſplendida I O N. </s> <s xml:id="echoid-s10005" xml:space="preserve">ſemper recta Solem aſpicit, ſi<unsure/>t vt ſi producatur <lb/> <anchor type="figure" xlink:label="fig-0120-02a" xlink:href="fig-0120-02"/> linea C O. </s> <s xml:id="echoid-s10006" xml:space="preserve">perpendicularis ipſi lineæ I N. </s> <s xml:id="echoid-s10007" xml:space="preserve">ipſa ad Solis centrum A. </s> <s xml:id="echoid-s10008" xml:space="preserve">pertineat. </s> <s xml:id="echoid-s10009" xml:space="preserve">fit <lb/>præterea angulus D B A. </s> <s xml:id="echoid-s10010" xml:space="preserve">gr. </s> <s xml:id="echoid-s10011" xml:space="preserve">87. </s> <s xml:id="echoid-s10012" xml:space="preserve">quot ſcilicet Luna dimidiata a Sole recedit; </s> <s xml:id="echoid-s10013" xml:space="preserve">erit <lb/>igitur trigonum A B C. </s> <s xml:id="echoid-s10014" xml:space="preserve">notorum angulorum, angulus enim ad C. </s> <s xml:id="echoid-s10015" xml:space="preserve">in centro Lu-<lb/>næ eſt rectus, angulus B eſt gr. </s> <s xml:id="echoid-s10016" xml:space="preserve">87. </s> <s xml:id="echoid-s10017" xml:space="preserve">quare & </s> <s xml:id="echoid-s10018" xml:space="preserve">reliquus A. </s> <s xml:id="echoid-s10019" xml:space="preserve">3. </s> <s xml:id="echoid-s10020" xml:space="preserve">gr. </s> <s xml:id="echoid-s10021" xml:space="preserve">non latebit. </s> <s xml:id="echoid-s10022" xml:space="preserve">conſe-<lb/>quenter per 5. </s> <s xml:id="echoid-s10023" xml:space="preserve">apparatus eſt conſtructione trianguli huic magno ſimilis, non la-<lb/>tebunt proportiones laterum: </s> <s xml:id="echoid-s10024" xml:space="preserve">vnde notum erit quoties B C. </s> <s xml:id="echoid-s10025" xml:space="preserve">contineatur in B A. <lb/></s> <s xml:id="echoid-s10026" xml:space="preserve">ideſt, quoties diſtantia Lunæ a terra ſuperetur a diſtantia Solis.</s> <s xml:id="echoid-s10027" xml:space="preserve"/> </p> <div xml:id="echoid-div208" type="float" level="2" n="2"> <figure xlink:label="fig-0120-02" xlink:href="fig-0120-02a"> <image file="0120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-02"/> </figure> </div> <p> <s xml:id="echoid-s10028" xml:space="preserve">4 Iuxta modum Ptolemæi, qui primo ſupponit diſtantiam Lunæ à terra eſ-<lb/>ſe cognitam, vt ſuperius oſtenſum eſt, ſecundo cognitam eſſe proportionem dia-<lb/>metrorum terræ, & </s> <s xml:id="echoid-s10029" xml:space="preserve">vmbræ eius, in loco tranſitus Lunæ; </s> <s xml:id="echoid-s10030" xml:space="preserve">vti eriam oſtenſum eſt <lb/>ſupra. </s> <s xml:id="echoid-s10031" xml:space="preserve">terti<unsure/>o aliquando Lunam ita Solem eclypſare vt ipſum abſque vlla mora <lb/>totum contegat. </s> <s xml:id="echoid-s10032" xml:space="preserve">fit in figura ſeq. </s> <s xml:id="echoid-s10033" xml:space="preserve">terra G K E. </s> <s xml:id="echoid-s10034" xml:space="preserve">diſtantia Lunæ ab ea K L. </s> <s xml:id="echoid-s10035" xml:space="preserve">quan-<lb/>do Solem totum fine mora obumbrat. </s> <s xml:id="echoid-s10036" xml:space="preserve">diameter vmbræ, in loco tranſitus Lunæ <lb/>ſit Q R. </s> <s xml:id="echoid-s10037" xml:space="preserve">productis ergo lineis G Q. </s> <s xml:id="echoid-s10038" xml:space="preserve">E R. </s> <s xml:id="echoid-s10039" xml:space="preserve">coibunt in S. </s> <s xml:id="echoid-s10040" xml:space="preserve">quare vmbra terræ erit <lb/>G S E. </s> <s xml:id="echoid-s10041" xml:space="preserve">quapropter ſi ædem lineæ in alteram quoq; </s> <s xml:id="echoid-s10042" xml:space="preserve">partem extendantur verſus <lb/>A. </s> <s xml:id="echoid-s10043" xml:space="preserve">& </s> <s xml:id="echoid-s10044" xml:space="preserve">C. </s> <s xml:id="echoid-s10045" xml:space="preserve">ipſæ neceſiario tangent hinc in de ſolare corpus; </s> <s xml:id="echoid-s10046" xml:space="preserve">cum extremi radij So-<lb/>lis ſint vmbrarum finitores, vt ſupra cum de lumine, & </s> <s xml:id="echoid-s10047" xml:space="preserve">vmbra mudi expoſuimus. <lb/></s> <s xml:id="echoid-s10048" xml:space="preserve">producatur etiam linea S K A. </s> <s xml:id="echoid-s10049" xml:space="preserve">per centrum terræ, quæ ſit axis vmbræ, in alteram <lb/>partem verſus D. </s> <s xml:id="echoid-s10050" xml:space="preserve">ſitque ea Luna N L O. </s> <s xml:id="echoid-s10051" xml:space="preserve">ſecundum centrum L. </s> <s xml:id="echoid-s10052" xml:space="preserve">ſintq; </s> <s xml:id="echoid-s10053" xml:space="preserve">L K. </s> <s xml:id="echoid-s10054" xml:space="preserve">K F. </s> <s xml:id="echoid-s10055" xml:space="preserve"><lb/>æquales: </s> <s xml:id="echoid-s10056" xml:space="preserve">ſi igitur ducantur lineæ K N. </s> <s xml:id="echoid-s10057" xml:space="preserve">K O. </s> <s xml:id="echoid-s10058" xml:space="preserve">Lunam tangentes, producanturq; </s> <s xml:id="echoid-s10059" xml:space="preserve"><lb/>verſus Solem, ipſum neceſſario vtrinque contingent; </s> <s xml:id="echoid-s10060" xml:space="preserve">aliter Luna non eſſet in ea <lb/>diſtantia in qua totum Solem ſine mora nobis occultaret. </s> <s xml:id="echoid-s10061" xml:space="preserve">tam igitur duæ lineæ <lb/>S A. </s> <s xml:id="echoid-s10062" xml:space="preserve">S C. </s> <s xml:id="echoid-s10063" xml:space="preserve">quam duæ K A. </s> <s xml:id="echoid-s10064" xml:space="preserve">K C. </s> <s xml:id="echoid-s10065" xml:space="preserve">in ijſdem ferè partibus A, & </s> <s xml:id="echoid-s10066" xml:space="preserve">C. </s> <s xml:id="echoid-s10067" xml:space="preserve">Soli occurrunt; </s> <s xml:id="echoid-s10068" xml:space="preserve"><lb/>imò ſibi mutuo occurrunt propè puncta A C. </s> <s xml:id="echoid-s10069" xml:space="preserve">quare diſtantia ſeu linea A C. </s> <s xml:id="echoid-s10070" xml:space="preserve">erit <lb/>Solis diameter, cuius centrum D. </s> <s xml:id="echoid-s10071" xml:space="preserve">cum itaque nota ſint ea, quæ ſuppoſuimus, po-<lb/>terimus hanc figuram cum ſuis veris proportionibus delineare (quemadmodum <lb/>fecimus in figura pag. </s> <s xml:id="echoid-s10072" xml:space="preserve">78.) </s> <s xml:id="echoid-s10073" xml:space="preserve">ſicque in ea ad ſenſum apparebit, quanta ſit diſtantia <lb/>D K. </s> <s xml:id="echoid-s10074" xml:space="preserve">Solis a terra, ideſt, quot terræ ſemidiametri contineat, quotieſque Luna-<lb/>rem diſtantiam L K. </s> <s xml:id="echoid-s10075" xml:space="preserve">excedat, quod præcipuè intendimus. </s> <s xml:id="echoid-s10076" xml:space="preserve">erit etiam figura hæc <lb/>parua ſimilis omnino illi magnę, quam in mundo concipimus; </s> <s xml:id="echoid-s10077" xml:space="preserve">conſtabunt etiam <lb/>ambæ ex triangulis ſimilibus. </s> <s xml:id="echoid-s10078" xml:space="preserve">Hiſce igitur modis ex accuratis obſeruationibus <lb/>tradunt Aſtronomi minorem ſeu perigæam Solis diſtantiam conſtare ſemidia-<lb/>metris terræ 1101. </s> <s xml:id="echoid-s10079" xml:space="preserve">mediam vero 1′142′. </s> <s xml:id="echoid-s10080" xml:space="preserve">maximam vero 1182.</s> <s xml:id="echoid-s10081" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10082" xml:space="preserve">Ex quibus obiter etiam colligimus craſſitiẽ cęli, aut regionis ſolaris, per quam <lb/>ſcilicet Sol ſuſque deque exſpaciatur eſſe 81. </s> <s xml:id="echoid-s10083" xml:space="preserve">terræ ſemidiametros. </s> <s xml:id="echoid-s10084" xml:space="preserve">Demum me-<lb/>mineris non ſic Solem ſupra Lunam collocaſſe, vt nullus alius planeta aliquan- <pb o="101" file="0121" n="125" rhead="Liber Decimus."/> do interſit, vt etiam initio innuimus, & </s> <s xml:id="echoid-s10085" xml:space="preserve">infra demonſtrabimus Venus & </s> <s xml:id="echoid-s10086" xml:space="preserve">Mercurius directà infra Solem ali <lb/>quando deſcendunt; </s> <s xml:id="echoid-s10087" xml:space="preserve">Mars etiam infra Solis regionem quandoq; </s> <s xml:id="echoid-s10088" xml:space="preserve">defertur.</s> <s xml:id="echoid-s10089" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div210" type="section" level="1" n="135"> <head xml:id="echoid-head147" style="it" xml:space="preserve">De Solis Figura. Cap. II.</head> <p> <s xml:id="echoid-s10090" xml:space="preserve">SOlem eſſe ſphæricumomnes tum Philoſophi@, tum Mathematici conſentiunt, hiſce rationibus perſuaſi <lb/>Prima, quia hæc figura ſola videtur aptiſſima lumini ad omnes partes æquè diffundendo; </s> <s xml:id="echoid-s10091" xml:space="preserve">quod maximè <lb/>Soli, quod totius mundi luminare maius eſt, competit. </s> <s xml:id="echoid-s10092" xml:space="preserve">Secunda, cum Terra, Aqua, Luna, Venus etiam vt <lb/>oftendemus, ſint ſphærica, multo magis eadem Soli figura attribuenda erit. </s> <s xml:id="echoid-s10093" xml:space="preserve">Tertia inidem conſentiunt So-<lb/>lis illuminationes quæ omnes, per quoduis foramen quantumuis irregulare illapſæ, ad perfectam tamen ro-<lb/>@unditatem poſt iuſtum interuallum tandem perueniunt, vt poſtea oſtendemus: </s> <s xml:id="echoid-s10094" xml:space="preserve">quæ ſaltem eius circularem <lb/> <anchor type="figure" xlink:label="fig-0121-01a" xlink:href="fig-0121-01"/> rotunditatem conuincunt. </s> <s xml:id="echoid-s10095" xml:space="preserve">Quarta, eaque noua ratio deſumitur à corporibus il-<lb/>lis, quæ circa Solem tarde, per Teleſcopium moueri depræhenſa ſunt, quæq; </s> <s xml:id="echoid-s10096" xml:space="preserve">ob <lb/>ſimilitudinem, Solis maculæ denominatæ ſunt. </s> <s xml:id="echoid-s10097" xml:space="preserve">ea enim ita circa Solem moueri <lb/>apparent, ac ſi circa corpus globoſum mouerentur, ſit namq; </s> <s xml:id="echoid-s10098" xml:space="preserve">Sol circa centrum <lb/>B. </s> <s xml:id="echoid-s10099" xml:space="preserve">oculus vero noſter in A. </s> <s xml:id="echoid-s10100" xml:space="preserve">macula quæpiam incipiat apparere in extremitate <lb/>Solis vt in C. </s> <s xml:id="echoid-s10101" xml:space="preserve">vbi quia oculo A. </s> <s xml:id="echoid-s10102" xml:space="preserve">obliquè obijcitur, videtur contractior, & </s> <s xml:id="echoid-s10103" xml:space="preserve">minor, <lb/>quam in alijs locis, per quæ mouetur ad D. </s> <s xml:id="echoid-s10104" xml:space="preserve">in qu@bus ſen ſim ſem per augeri vide-<lb/>tur, donec ſit in D. </s> <s xml:id="echoid-s10105" xml:space="preserve">vbi maxima ſpectatur, quoniam oculo rectè, ac ſecundum to-<lb/>tam ſui longitudinem obijcitur; </s> <s xml:id="echoid-s10106" xml:space="preserve">ac propterea latior, & </s> <s xml:id="echoid-s10107" xml:space="preserve">maior cernitur. </s> <s xml:id="echoid-s10108" xml:space="preserve">vnde di-<lb/>ſcedens iterum minor, ac minor videtur donec promota ſit ad alterum extremũ <lb/>E. </s> <s xml:id="echoid-s10109" xml:space="preserve">vbi iterum minima ſicuti etiam apud C. </s> <s xml:id="echoid-s10110" xml:space="preserve">ob ſui obliquitate m conſpicitur. </s> <s xml:id="echoid-s10111" xml:space="preserve">quæ <lb/>apparentia ſatis conuincit Solis ſphæricitatem. </s> <s xml:id="echoid-s10112" xml:space="preserve">Porrò omnes hæ rationes oſten-<lb/>dunt Solem eſſe quidem rotũdum, non autem eſſe integram ſphæram, ſed ſolum <lb/>hemiſphærium; </s> <s xml:id="echoid-s10113" xml:space="preserve">poſito enim Sole hemiſphærico ſaluantur p hænomena, ſicuti <lb/>etiam in Luna monuimus. </s> <s xml:id="echoid-s10114" xml:space="preserve">pariter ex ijs rationibus non aſſeritur perfecta ac geo-<lb/>metrica Solis ſphæricitas, in qua nullæ ſint aſperitates; </s> <s xml:id="echoid-s10115" xml:space="preserve">ſed ſicuti in Luna accidit, <lb/>quam prius omnes perfectè ſphæricam, ac perpolitam arbitrabantur, ita in Sole <lb/>accidere poſſe non omnino abſurdum eſt opinari.</s> <s xml:id="echoid-s10116" xml:space="preserve"/> </p> <div xml:id="echoid-div210" type="float" level="2" n="1"> <figure xlink:label="fig-0121-01" xlink:href="fig-0121-01a"> <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0121-01"/> </figure> </div> </div> <div xml:id="echoid-div212" type="section" level="1" n="136"> <head xml:id="echoid-head148" style="it" xml:space="preserve">Corollarium de Sole Elliptico.</head> <p> <s xml:id="echoid-s10117" xml:space="preserve">QVamuis Sol ſit ſphæricus, diligenti tamen inſpectione per Teleſcopium facta, Sole prope horizontem <lb/>exiſtente: </s> <s xml:id="echoid-s10118" xml:space="preserve">apparebit non rotundus, ſed ellipticus, ſeu oualis; </s> <s xml:id="echoid-s10119" xml:space="preserve">ita vt altera eius diameter, quæ horizontis <lb/>æquidiſtat longior ſit altera, quæ horizonti perpendicularis eſt. </s> <s xml:id="echoid-s10120" xml:space="preserve">quarum exceſſus varius eſt, ſecu ndũ <lb/>variam horizonti propinquitatem, & </s> <s xml:id="echoid-s10121" xml:space="preserve">aeris eonſtitutionem. </s> <s xml:id="echoid-s10122" xml:space="preserve">aliquando tamen quinta ſui parte illa hanc ex-<lb/>cedit. </s> <s xml:id="echoid-s10123" xml:space="preserve">cauſa huius deceptionis eſt, quia tunc Sol per refractionem (vt optici loquuntur) ſpectatur, quam effi-<lb/>cit aer craſſus, & </s> <s xml:id="echoid-s10124" xml:space="preserve">impurus, circa terram conſiſtens, hac de re in dioptrica fusè ab opticis tractatur. </s> <s xml:id="echoid-s10125" xml:space="preserve">hanc Solis <lb/>elliptici obſeruationem primus noſtra tempeſtate habuit P. </s> <s xml:id="echoid-s10126" xml:space="preserve">Chriſtophorus Scheiner noſtræ Soc. </s> <s xml:id="echoid-s10127" xml:space="preserve">ac Mathe-<lb/>ſeos profeſſoris; </s> <s xml:id="echoid-s10128" xml:space="preserve">libellumque pulcherrimum de ea ed@dit, quem Solem ellipticum nun cupauit. </s> <s xml:id="echoid-s10129" xml:space="preserve">eum tu con-<lb/>ſule ſi plura de hac re ſcitu iucunda, ac digna ſcire deſideras. </s> <s xml:id="echoid-s10130" xml:space="preserve">Ego quidem mane aliquando abſque Teleſco-<lb/>pio certo hanc Solis ellipſim animaduerti.</s> <s xml:id="echoid-s10131" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div213" type="section" level="1" n="137"> <head xml:id="echoid-head149" style="it" xml:space="preserve">De Solis Magnitudine. Cap. III.</head> <p> <s xml:id="echoid-s10132" xml:space="preserve">1 SOlem multo maiorem eſſe, quam vt pedalis ſit vti apparet, primi Aſtronomiæ cultores, hoc modo ru-<lb/>di Minerua demonſtrabant. </s> <s xml:id="echoid-s10133" xml:space="preserve">dum Sol incipit ex horizonte ſecundum limbum emicare, ſubito per am-<lb/>plam planitiem equus curſu citatiſſimo excurrere incipiat, emerſo autem toto Sole, ſtet equus; </s> <s xml:id="echoid-s10134" xml:space="preserve">hoc quamuis <lb/>breui temporis ſpatio, equum amplius quam milliare vnum emenſum eſſe neceſſe eſt, igitur neceſſe pariter <lb/>eſt Solis diametrum huic ſaltem decurſo ſpatio æqualem eſſe; </s> <s xml:id="echoid-s10135" xml:space="preserve">dum enim ſpatium illud equus decurrit, hori-<lb/>zon pariter totum Solem pertranſit. </s> <s xml:id="echoid-s10136" xml:space="preserve">Verum enim vero cum Sol ſit equo ſexcenties velocior, erit etiam Sol <lb/>prædicto ſpatio toties maior. </s> <s xml:id="echoid-s10137" xml:space="preserve">Eundem argumentali modum transfesre poſſumus ad auis perniciſſimæ vola-<lb/>@um, quo quidem velociorem eſſe Solem ex velociſſima eius circa totum vniuerſum vnius diei ſpatio reuo-<lb/>lutione conſtat. </s> <s xml:id="echoid-s10138" xml:space="preserve">vnde licebit inferre Solis molem ſuperare ſpatium ab aue tempore ſuæ emerſionis præter-<lb/>uolatum, quod ſpatium pluſquam milliaria 100. </s> <s xml:id="echoid-s10139" xml:space="preserve">continere quis non dixerit? </s> <s xml:id="echoid-s10140" xml:space="preserve">non igitur Sol pedalis erit, vti <lb/>ſpectantibus ſe offert.</s> <s xml:id="echoid-s10141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10142" xml:space="preserve">Alio item modo veteres Aegyptij Hydrologijs, ſic Solis magnitudinem captabant. </s> <s xml:id="echoid-s10143" xml:space="preserve">toto temporis inter-<lb/>@allo, quo Sol è finitore totus exilit, è cler ſydra fluat aqua, eaque menſuretur. </s> <s xml:id="echoid-s10144" xml:space="preserve">iterum per totum diem, ideſt, <lb/>tota Solis circulatione effluat aqua, qua pariter menſurata, atque cum priori comparata, repererunt primam <lb/>aquæ menſuram ad ſecundam eſſe ſicuti 1. </s> <s xml:id="echoid-s10145" xml:space="preserve">ad 750. </s> <s xml:id="echoid-s10146" xml:space="preserve">v.</s> <s xml:id="echoid-s10147" xml:space="preserve">g. </s> <s xml:id="echoid-s10148" xml:space="preserve">ſi prima erat cyathus, ſecunda cyathos 750. </s> <s xml:id="echoid-s10149" xml:space="preserve">efficiebat. <lb/></s> <s xml:id="echoid-s10150" xml:space="preserve">vnde ſi Sol pedalis eſſet, ſequeretur neceſſario ſolaris cæli periphæriam, quam Sol quotidie percurrit conti-<lb/>nere tantummodo pedes 750. </s> <s xml:id="echoid-s10151" xml:space="preserve">quod ſane ridiculum eſt credere.</s> <s xml:id="echoid-s10152" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10153" xml:space="preserve">Poſtremo in locis Zonæ torridę ſubiectis vnus eligatur locus, cui Sol directè ſupra verticem incumbat; </s> <s xml:id="echoid-s10154" xml:space="preserve">vti <pb o="102" file="0122" n="126" rhead="De Mundi Fabrica,"/> ſupra diximus Vrbem eſſe Syenem, cui Sol Cancri tropicum percurrens fit verticalis. </s> <s xml:id="echoid-s10155" xml:space="preserve">in tali enim loco cir-<lb/>cumcirca per 300. </s> <s xml:id="echoid-s10156" xml:space="preserve">ſtadia, quę efficiunt milliaria ferè 37. </s> <s xml:id="echoid-s10157" xml:space="preserve">corpora nullas proijciunt vmbras. </s> <s xml:id="echoid-s10158" xml:space="preserve">quod manifeſtum <lb/>ſignum eſt Solem maiorum eſſe prædicto tractu milliar. </s> <s xml:id="echoid-s10159" xml:space="preserve">37. </s> <s xml:id="echoid-s10160" xml:space="preserve">cum enim Sol vti oſtenſum eſt, valde ſublimis ſit, <lb/>& </s> <s xml:id="echoid-s10161" xml:space="preserve">vnumquodq; </s> <s xml:id="echoid-s10162" xml:space="preserve">illorum corporum vndique adeo colluſtret, vt nulla relinquatur vmbra, neceſſario ſequitur <lb/> <anchor type="figure" xlink:label="fig-0122-01a" xlink:href="fig-0122-01"/> extrema illius tractus corpora, veluti turres, habere ſupra ſuum verticem partẽ aliquam ſola-<lb/>ris corporis: </s> <s xml:id="echoid-s10163" xml:space="preserve">quare neceſtario cogimur aſſerere Solis magnitudinem eſſe ſaltem milliar. </s> <s xml:id="echoid-s10164" xml:space="preserve">37. </s> <s xml:id="echoid-s10165" xml:space="preserve">ſit <lb/>enim figura tractus terræ A B. </s> <s xml:id="echoid-s10166" xml:space="preserve">in quo extremæ turres A D. </s> <s xml:id="echoid-s10167" xml:space="preserve">B E. </s> <s xml:id="echoid-s10168" xml:space="preserve">nullam efficiant vmbram. <lb/></s> <s xml:id="echoid-s10169" xml:space="preserve">ergo ſi intelligamus duo illa corpora recta ſurſum produci, tandem Solem vtrinque contin-<lb/>gent: </s> <s xml:id="echoid-s10170" xml:space="preserve">quod ſi ita producantur vt A D. </s> <s xml:id="echoid-s10171" xml:space="preserve">contineat ſemidiametros terræ 1, 182, quot ſcilicet à <lb/>terra diſtat Sol, quando eſt ſupra Syenem, tunc enim eſt in tropico Cancri, ac propterea apo-<lb/>gæus diſtat ſemid. </s> <s xml:id="echoid-s10172" xml:space="preserve">1, 182,. </s> <s xml:id="echoid-s10173" xml:space="preserve">(vti ſupra demonſtratum eſt:) </s> <s xml:id="echoid-s10174" xml:space="preserve">ijs igitur productis ducatnr linea <lb/>eorum ſummas extremitates coniungens, qualis eſſet linea D E. </s> <s xml:id="echoid-s10175" xml:space="preserve">hæc enim erit diameter So-<lb/>lis, habebitq; </s> <s xml:id="echoid-s10176" xml:space="preserve">veram proportionem ad terrę diametrum A F. </s> <s xml:id="echoid-s10177" xml:space="preserve">quam vera diameter Solis habet <lb/>ad veram terræ diametrum. </s> <s xml:id="echoid-s10178" xml:space="preserve">vnde vera Solis magnitudo non latebit, vt paulo poſt explicabimus.</s> <s xml:id="echoid-s10179" xml:space="preserve"/> </p> <div xml:id="echoid-div213" type="float" level="2" n="1"> <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a"> <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-01"/> </figure> </div> <p> <s xml:id="echoid-s10180" xml:space="preserve">2 Dico olem eſſe Luna maiorem, quod inde patere poteſt, quia vt ſupra oſtenſum eſt, Sol eſt Luna mul <lb/>to ſublimior, & </s> <s xml:id="echoid-s10181" xml:space="preserve">tamen videtur eſſe eiuſdem cum ea magnitudinis; </s> <s xml:id="echoid-s10182" xml:space="preserve">at quæ ſunt remotiora minora ſemper, cę-<lb/>teris paribus apparent, quam propiora, vt opticorum obſeruationes docent, quare ſi Sol deſcenderet a d Lu-<lb/>næ locum multo maior quam Luna appareret. </s> <s xml:id="echoid-s10183" xml:space="preserve">Idem perſpicuè colligitur ex ſolari illa eclypſi, in qua Luna <lb/>totum Solem adæquate nobis occultat; </s> <s xml:id="echoid-s10184" xml:space="preserve">tunc enim videmus Lunam, & </s> <s xml:id="echoid-s10185" xml:space="preserve">Solem ſub eodem angulo, vt ſupra ina <lb/>figura cap. </s> <s xml:id="echoid-s10186" xml:space="preserve">1. </s> <s xml:id="echoid-s10187" xml:space="preserve">videre eſt, in qua ſub eodem angulo A K C. </s> <s xml:id="echoid-s10188" xml:space="preserve">vtruinq; </s> <s xml:id="echoid-s10189" xml:space="preserve">luminare compræhenditur, ac proptere <lb/>Solibi Lunam magnitudine valde ſuperat.</s> <s xml:id="echoid-s10190" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10191" xml:space="preserve">3 Aſſero Solem eſſe terreſtri ſphæra maiorem: </s> <s xml:id="echoid-s10192" xml:space="preserve">quod manifeſte conuincitur ex vmbra terræ, quæ à Sole <lb/>procedit; </s> <s xml:id="echoid-s10193" xml:space="preserve">ea enim, vt ſupra oſtenſum eſt, conica ſeu acuminata eſt, atq; </s> <s xml:id="echoid-s10194" xml:space="preserve">in nihilum deſineſis; </s> <s xml:id="echoid-s10195" xml:space="preserve">quod nullo mo-<lb/>do fieri poſſet, niſi Sol illuminans, tota terra illuminata, amplior eſſet, quæ ratio optimè demonſtrat ſi ea re-<lb/>petantur, quæ de lumine, & </s> <s xml:id="echoid-s10196" xml:space="preserve">vmbra ſuperius in tractatu de mundo præmiſſa ſunt.</s> <s xml:id="echoid-s10197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10198" xml:space="preserve">4 Aio Solem eſſe adeo magnum vt terram centies, & </s> <s xml:id="echoid-s10199" xml:space="preserve">quadragies contineat. </s> <s xml:id="echoid-s10200" xml:space="preserve">quæ propoſitio eſt probatiſ-<lb/>ſimi Aſtronomi Tychonis, quam hiſce rationibus euidenter oſtendemus. </s> <s xml:id="echoid-s10201" xml:space="preserve">Primo quidem ex conſtructione <lb/>figuræ quam cap. </s> <s xml:id="echoid-s10202" xml:space="preserve">1. </s> <s xml:id="echoid-s10203" xml:space="preserve">huius tractatus num. </s> <s xml:id="echoid-s10204" xml:space="preserve">4. </s> <s xml:id="echoid-s10205" xml:space="preserve">pro Solis diſtantia inuenienda adumbrauimus; </s> <s xml:id="echoid-s10206" xml:space="preserve">ſi enim illa figura <lb/>cum ſuis veris proportionibus accuratè conſtruatur, vt factum eſt in figura pag 38. </s> <s xml:id="echoid-s10207" xml:space="preserve">num. </s> <s xml:id="echoid-s10208" xml:space="preserve">6. </s> <s xml:id="echoid-s10209" xml:space="preserve">ſtatim in ea appa-<lb/>rebit, quam rationem habeat dimetiens A C. </s> <s xml:id="echoid-s10210" xml:space="preserve">Solis ad dimetientem G E. </s> <s xml:id="echoid-s10211" xml:space="preserve">terræ; </s> <s xml:id="echoid-s10212" xml:space="preserve">quæ ferè erit vt 5 {1/5}. </s> <s xml:id="echoid-s10213" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s10214" xml:space="preserve">hoc <lb/>eſt diameter Solis continet terræ diametrum quinquies, & </s> <s xml:id="echoid-s10215" xml:space="preserve">præ erea quintam eiuſdem partem qua propor-<lb/>tione habita facilè eſt ſphærarum quoque ipſarum mutuam habitudinam cognoſcere. </s> <s xml:id="echoid-s10216" xml:space="preserve">Primo mechanicè, ſi <lb/>enim fiant duo globi ex eadem materia, vti ex plumbo, habentes ſuos diametros æquales diametris A C. </s> <s xml:id="echoid-s10217" xml:space="preserve">G E. <lb/></s> <s xml:id="echoid-s10218" xml:space="preserve">quos deinde vel pondere, vel menſura expendamus, videbimus maiorcm ad minorem eſſe vt 140. </s> <s xml:id="echoid-s10219" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s10220" xml:space="preserve">idem <lb/>Geometricè aſſequemur, eadem omnino ratione, qua vſi ſumus in Lunæ magnitudine inquirenda, ideſt, <lb/>ex eo, quod ſphæræ habent triplicatam proportionem ſuarum diametrorum. </s> <s xml:id="echoid-s10221" xml:space="preserve">cum igitur diameter Solis ad <lb/>diam. </s> <s xml:id="echoid-s10222" xml:space="preserve">terræ, ſit vt 5 {1/5}. </s> <s xml:id="echoid-s10223" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s10224" xml:space="preserve">ſiue vt 26. </s> <s xml:id="echoid-s10225" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s10226" xml:space="preserve">ſi accipiantur quatuornumeri, ſicuti etiam in Luna, in continua ea-<lb/>rum ratione, quales ſunt hi 303. </s> <s xml:id="echoid-s10227" xml:space="preserve">135 {1/5}. </s> <s xml:id="echoid-s10228" xml:space="preserve">26. </s> <s xml:id="echoid-s10229" xml:space="preserve">5. </s> <s xml:id="echoid-s10230" xml:space="preserve">erit ratio primi 703. </s> <s xml:id="echoid-s10231" xml:space="preserve">ad vltimum 5. </s> <s xml:id="echoid-s10232" xml:space="preserve">eadem quæ Solis ad terram. </s> <s xml:id="echoid-s10233" xml:space="preserve"><lb/>continet autem ille numerus hunc centies, & </s> <s xml:id="echoid-s10234" xml:space="preserve">quadrigies, vt patet diuidendo 703. </s> <s xml:id="echoid-s10235" xml:space="preserve">per 5. </s> <s xml:id="echoid-s10236" xml:space="preserve">quotiens enim eſt <lb/>140 {3/5}. </s> <s xml:id="echoid-s10237" xml:space="preserve">Sol igitur terra maior eſt, ita vt ipſam toties compræhendat, vti propoſuimus.</s> <s xml:id="echoid-s10238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10239" xml:space="preserve">Hinc facilè etiam licet colligere quanto maior ſit quam Luna, cum enim terra Lunam contineat quadra-<lb/>gies; </s> <s xml:id="echoid-s10240" xml:space="preserve">Sol vero terrã centies, & </s> <s xml:id="echoid-s10241" xml:space="preserve">quadragies, ſi numeri 40. </s> <s xml:id="echoid-s10242" xml:space="preserve">& </s> <s xml:id="echoid-s10243" xml:space="preserve">140. </s> <s xml:id="echoid-s10244" xml:space="preserve">inuicem multiplicentur, prodibit num. </s> <s xml:id="echoid-s10245" xml:space="preserve">5, 600. <lb/></s> <s xml:id="echoid-s10246" xml:space="preserve">qui indicat Solem continere Lunam quinquies millies, ac ſexcenties. </s> <s xml:id="echoid-s10247" xml:space="preserve">Rurſus eandem proportionem com-<lb/>probamus ex angulo, ſub quo Sol videtur, ſiue ex diametro eius apparenti, vna cũ diſtantia eius a centro vni-<lb/> <anchor type="figure" xlink:label="fig-0122-02a" xlink:href="fig-0122-02"/> uerſi, quam ſupra indagauimus. </s> <s xml:id="echoid-s10248" xml:space="preserve">diametrum autem eius apparentem ſic olim Hippar-<lb/>chus inquirebat. </s> <s xml:id="echoid-s10249" xml:space="preserve">huius enim rei gratia dioptram quandam excogitauit, cuius imagi-<lb/>nem exhibuimus pag. </s> <s xml:id="echoid-s10250" xml:space="preserve">74. </s> <s xml:id="echoid-s10251" xml:space="preserve">vbi de Lunæ magnitudine egimus; </s> <s xml:id="echoid-s10252" xml:space="preserve">per eam ſic diametrum <lb/>apparentem capiebat; </s> <s xml:id="echoid-s10253" xml:space="preserve">ea namque in ſolem obuerſa alteroque oculo foramini D. </s> <s xml:id="echoid-s10254" xml:space="preserve">ap-<lb/>plicato, ita tabellam E F. </s> <s xml:id="echoid-s10255" xml:space="preserve">vltro citroq; </s> <s xml:id="echoid-s10256" xml:space="preserve">commouebat, vt ocuius per D. </s> <s xml:id="echoid-s10257" xml:space="preserve">ac ſimul per <lb/>duo foramina E F. </s> <s xml:id="echoid-s10258" xml:space="preserve">inſpiciens Solis limbum, ſeu oram, viſus leuiter perſtringeret: <lb/></s> <s xml:id="echoid-s10259" xml:space="preserve">atq; </s> <s xml:id="echoid-s10260" xml:space="preserve">in ea diſtantia obfirmata tabella E F. </s> <s xml:id="echoid-s10261" xml:space="preserve">angul. </s> <s xml:id="echoid-s10262" xml:space="preserve">contipiebat F D E. </s> <s xml:id="echoid-s10263" xml:space="preserve">eumq; </s> <s xml:id="echoid-s10264" xml:space="preserve">quantus eſ-<lb/>ſet expendebat: </s> <s xml:id="echoid-s10265" xml:space="preserve">vt in prop. </s> <s xml:id="echoid-s10266" xml:space="preserve">2. </s> <s xml:id="echoid-s10267" xml:space="preserve">Appar. </s> <s xml:id="echoid-s10268" xml:space="preserve">dictum eſt. </s> <s xml:id="echoid-s10269" xml:space="preserve">reperitq; </s> <s xml:id="echoid-s10270" xml:space="preserve">hic angulum in mediocri <lb/>Solis a terra diſtantia continere min. </s> <s xml:id="echoid-s10271" xml:space="preserve">31. </s> <s xml:id="echoid-s10272" xml:space="preserve">ſiue diametrum Solis apparentem ſub ten-<lb/>dere 31@.</s> <s xml:id="echoid-s10273" xml:space="preserve"/> </p> <div xml:id="echoid-div214" type="float" level="2" n="2"> <figure xlink:label="fig-0122-02" xlink:href="fig-0122-02a"> <image file="0122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-02"/> </figure> </div> <p> <s xml:id="echoid-s10274" xml:space="preserve">Eadem Dioptra alij aliter vtuntur, nam pro viſiuis radijs excipiunt per foramina <lb/>E F. </s> <s xml:id="echoid-s10275" xml:space="preserve">Solis radios tabellamque E F. </s> <s xml:id="echoid-s10276" xml:space="preserve">tandium mouent donec binæ Solis illuminationes <lb/>per foramina E F. </s> <s xml:id="echoid-s10277" xml:space="preserve">illapſæ, atque in oppoſita tabella R D. </s> <s xml:id="echoid-s10278" xml:space="preserve">exceptę, ſe mutuo ad D. </s> <s xml:id="echoid-s10279" xml:space="preserve">con-<lb/>tingant; </s> <s xml:id="echoid-s10280" xml:space="preserve">tunc enim angulus E D F. </s> <s xml:id="echoid-s10281" xml:space="preserve">comprehendit diametrum Solis viſibilem; </s> <s xml:id="echoid-s10282" xml:space="preserve">vt in <lb/>figura binæ illuminationes per foramina E F. </s> <s xml:id="echoid-s10283" xml:space="preserve">ad punctum D. </s> <s xml:id="echoid-s10284" xml:space="preserve">concurant, ita vt duo <lb/>luminoſi circelli ſe mutuo in D. </s> <s xml:id="echoid-s10285" xml:space="preserve">contingant, eritque angulus E D F. </s> <s xml:id="echoid-s10286" xml:space="preserve">angulus ſub quo <lb/>Solis diameter ſpectatur. </s> <s xml:id="echoid-s10287" xml:space="preserve">imo ex vnica illuminatione eundem angulum obtinebimus, <lb/>angulus enim R E D. </s> <s xml:id="echoid-s10288" xml:space="preserve">eſt angulus, ſub quo ſol apparet; </s> <s xml:id="echoid-s10289" xml:space="preserve">ſi enim duo radij R E D. </s> <s xml:id="echoid-s10290" xml:space="preserve">pro-<lb/>ducantur verſus Solem, eum tandem hinc inde attinget, eruntque anguli ad verticem <pb o="103" file="0123" n="127" rhead="Liber Decimus."/> E. </s> <s xml:id="echoid-s10291" xml:space="preserve">æquales, per 15. </s> <s xml:id="echoid-s10292" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s10293" xml:space="preserve">Tandem etiam per duos Quadrantes, duoſque obſeruatores quemadmo-<lb/>dum iu Luna dictum eſt, voti compotes erimus. </s> <s xml:id="echoid-s10294" xml:space="preserve">Habita igitur quouis modo hac apparenti diametro ad cer-<lb/>@am aliquam Solis a centro diſtantiam, v.</s> <s xml:id="echoid-s10295" xml:space="preserve">g. </s> <s xml:id="echoid-s10296" xml:space="preserve">ad mediocrẽ, quam ſtatuimus eſſe ſemediametrorum terræ 1142. <lb/></s> <s xml:id="echoid-s10297" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0123-01a" xlink:href="fig-0123-01"/> in qua diſtantia diameter appa. </s> <s xml:id="echoid-s10298" xml:space="preserve">eſt minutorum 31. </s> <s xml:id="echoid-s10299" xml:space="preserve">con-<lb/>ſtruatur triangulum A B C. </s> <s xml:id="echoid-s10300" xml:space="preserve">Iſoſceles, cuius angulus A. </s> <s xml:id="echoid-s10301" xml:space="preserve">ſit <lb/>31′. </s> <s xml:id="echoid-s10302" xml:space="preserve">latera vero A B. </s> <s xml:id="echoid-s10303" xml:space="preserve">A C. </s> <s xml:id="echoid-s10304" xml:space="preserve">contineant partes æquales 1142. <lb/></s> <s xml:id="echoid-s10305" xml:space="preserve">quæ ſemidiametros terrę referant. </s> <s xml:id="echoid-s10306" xml:space="preserve">hoc|eenim triangulum <lb/>ſimile, ac proportionale erit triangulo illi magno, ſub quo <lb/>Solem cernimus, quare vtſe habet in co baſis B C. </s> <s xml:id="echoid-s10307" xml:space="preserve">ad particulas 1142. </s> <s xml:id="echoid-s10308" xml:space="preserve">lateris A B. </s> <s xml:id="echoid-s10309" xml:space="preserve">ira ſe habet diameter Solis, <lb/>in magno triangulo, ad mediocrem eius diſtantiam: </s> <s xml:id="echoid-s10310" xml:space="preserve">quot igitur particulas ex illis 1142. </s> <s xml:id="echoid-s10311" xml:space="preserve">continebit biſis <lb/>B C. </s> <s xml:id="echoid-s10312" xml:space="preserve">totidem etiam terræ ſemidiametros continebit Solis dimetiens. </s> <s xml:id="echoid-s10313" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s10314" xml:space="preserve">ipſa Solis dimetiens cogni-<lb/>ta erit, & </s> <s xml:id="echoid-s10315" xml:space="preserve">conſequenter Solis ſphæræ magnitudo ad terram.</s> <s xml:id="echoid-s10316" xml:space="preserve"/> </p> <div xml:id="echoid-div215" type="float" level="2" n="3"> <figure xlink:label="fig-0123-01" xlink:href="fig-0123-01a"> <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01"/> </figure> </div> </div> <div xml:id="echoid-div217" type="section" level="1" n="138"> <head xml:id="echoid-head150" style="it" xml:space="preserve">De Solis motibus. Cap. IIII.</head> <p> <s xml:id="echoid-s10317" xml:space="preserve">PRimi cęleſtium rerum exploratores, vt penitus Solis motum perſpectum haberent, primo obſeruarunt <lb/>eum moueri ab ortu in occaſum, non ſemper per eamdem viam, ſeu circulationem; </s> <s xml:id="echoid-s10318" xml:space="preserve">neque oriri, aut oc-<lb/>cidere in ijſdem ſemper horizontis punctis; </s> <s xml:id="echoid-s10319" xml:space="preserve">ſed quotidie hæc omnia variari: </s> <s xml:id="echoid-s10320" xml:space="preserve">ſic eum in ſumma æſtate, præ-<lb/>ſertim extra Zonam torridam, incedere videbant propè verticem. </s> <s xml:id="echoid-s10321" xml:space="preserve">dein paulatim quotidie per alias circula-<lb/>tiones a vertice remotiores; </s> <s xml:id="echoid-s10322" xml:space="preserve">& </s> <s xml:id="echoid-s10323" xml:space="preserve">pariter eum oriri, & </s> <s xml:id="echoid-s10324" xml:space="preserve">occidere in punctis horizontis auſtralioribus; </s> <s xml:id="echoid-s10325" xml:space="preserve">atque <lb/>in meridiano humilius pertranſire, donec tandem in ſumma hyeme, brunali tempore, humillime per meri-<lb/>diem incedat. </s> <s xml:id="echoid-s10326" xml:space="preserve">vnde poſtea iterum ſupra horizontem ſubleuari incipiat, ac verſus vert cem noſtrum reuerti. <lb/></s> <s xml:id="echoid-s10327" xml:space="preserve">hiſce præhabitis, poſtea per inſtrumenta huius ſolaris euagationis a borea in auſtrum, & </s> <s xml:id="echoid-s10328" xml:space="preserve">è contra, latitudi-<lb/>nem, ac metas ſeu tropicos compererunt, idque eo modo, quem ſup. </s> <s xml:id="echoid-s10329" xml:space="preserve">in tractatu de Tropicis explicauimus. </s> <s xml:id="echoid-s10330" xml:space="preserve"><lb/>hanc autem Tropicorum, diſtantiã inuenerunt eſſe gr. </s> <s xml:id="echoid-s10331" xml:space="preserve">ferè 47. </s> <s xml:id="echoid-s10332" xml:space="preserve">qui numerantur in merid ano circulo. </s> <s xml:id="echoid-s10333" xml:space="preserve">quem <lb/>arcum ſi bifariam diuiſeris, habebis locum æquatoris circuli, ab vtroque tropico æque diſtantis per gradus <lb/>23 {1/2}. </s> <s xml:id="echoid-s10334" xml:space="preserve">ferè. </s> <s xml:id="echoid-s10335" xml:space="preserve">His conſtructis qua via Sol ab vno tropico ad alterum remearet inquirebant. </s> <s xml:id="echoid-s10336" xml:space="preserve">ac tandem eodem <lb/>modo, quem ſupra cap. </s> <s xml:id="echoid-s10337" xml:space="preserve">primo huis tract. </s> <s xml:id="echoid-s10338" xml:space="preserve">expoſui, obſeruarunt eum per viam, ſeu ſub via, quam eclypticam <lb/>iam nominauimus perpetuo à borea in auſtrum, & </s> <s xml:id="echoid-s10339" xml:space="preserve">viciſſim accedere, & </s> <s xml:id="echoid-s10340" xml:space="preserve">reuerti. </s> <s xml:id="echoid-s10341" xml:space="preserve">quanta autem ſit maxima. </s> <s xml:id="echoid-s10342" xml:space="preserve"><lb/>eclypticæ diſtantia, & </s> <s xml:id="echoid-s10343" xml:space="preserve">quam variationem ſubeat, quanraque ſit ſingulorum punctorum eius declinatio, di-<lb/>ctum eſt in cap. </s> <s xml:id="echoid-s10344" xml:space="preserve">de Zodiaco, & </s> <s xml:id="echoid-s10345" xml:space="preserve">eclyptica. </s> <s xml:id="echoid-s10346" xml:space="preserve">cuius in ea progreſſum cum attentius obſeruarent, cognouerunt <lb/>tandem Solem percurrere totam eclypticam, & </s> <s xml:id="echoid-s10347" xml:space="preserve">conſequenter totum Zodiacum abſoluere diebus 365. </s> <s xml:id="echoid-s10348" xml:space="preserve">horis <lb/>5. </s> <s xml:id="echoid-s10349" xml:space="preserve">minutis horarum 49′. </s> <s xml:id="echoid-s10350" xml:space="preserve">quod tempus, aſtronomicus annus, tropicus ſi ad tropicos, æquinoctialis ſi ad æqui-<lb/>noctialem referatur, vertens, actemporalis, naturaliſque appellatus eſt. </s> <s xml:id="echoid-s10351" xml:space="preserve">initiumq; </s> <s xml:id="echoid-s10352" xml:space="preserve">ac finem huius annuæ reuo-<lb/>lutionis ſtatuerunt eſſe vel punctum vnum ſolſtitiale, ſeu tropicale, aut æquinoctiale alterum. </s> <s xml:id="echoid-s10353" xml:space="preserve">vnde ſequitur <lb/>Solem ſingulis diebus in vniuerſum progredi in eclyptica m. </s> <s xml:id="echoid-s10354" xml:space="preserve">59′ 8. </s> <s xml:id="echoid-s10355" xml:space="preserve">19 1′1. </s> <s xml:id="echoid-s10356" xml:space="preserve">& </s> <s xml:id="echoid-s10357" xml:space="preserve">c. </s> <s xml:id="echoid-s10358" xml:space="preserve">hunc autem in eclyptica pro-<lb/>greſſum animaduerterunt fieri ab occaſu in ortum, ſeu ſecundum ſignorum ordinem ac ſequelam. </s> <s xml:id="echoid-s10359" xml:space="preserve">Huncq; </s> <s xml:id="echoid-s10360" xml:space="preserve"><lb/>etiam proprium Solis motum ſtatuernnt, motumque in longitudinem appellarunt. </s> <s xml:id="echoid-s10361" xml:space="preserve">quem ſic facile cogno-<lb/>uerunt; </s> <s xml:id="echoid-s10362" xml:space="preserve">viderunt enim ſtellas, quæ mane ante Solem oriuntur quo idie c tius oriri, ac Solem magis præue-<lb/>ni re; </s> <s xml:id="echoid-s10363" xml:space="preserve">quod inde neceſſe oritur quia Sol ab eis paulatim verſus orientem recedit. </s> <s xml:id="echoid-s10364" xml:space="preserve">idem ex ſtellis veſpertinis <lb/>aſſequi licuit, quibus Sol quotidie veſperi fit propior, donec eas aſſequatur, ac ſuo lumine occultet.</s> <s xml:id="echoid-s10365" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10366" xml:space="preserve">Hinc etiam diligenter annotarunt Solem ad eandem affixam ſtellam reuerti diebus 365. </s> <s xml:id="echoid-s10367" xml:space="preserve">horis 6 min. </s> <s xml:id="echoid-s10368" xml:space="preserve">9@ <lb/>huncque circuirum, annum ſydereum, appellarunt; </s> <s xml:id="echoid-s10369" xml:space="preserve">qui paulo maior eſt anno tropico quoniam ſtellæ motu <lb/>proprio tardiſſimo mouentur verſus ortum, quapropter ad eas Sol tardius reuertitur, quam ad ſtabile æqui-<lb/>noctij punctum.</s> <s xml:id="echoid-s10370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10371" xml:space="preserve">Vt autem prædictas motuum, atq; </s> <s xml:id="echoid-s10372" xml:space="preserve">annorum quantitates quam exactiſſime definirent, hanc methodum <lb/>inierunt. </s> <s xml:id="echoid-s10373" xml:space="preserve">primo omnium tempus ſeu momentum, quo Sol in aliquod quatuor punctorum cardinalium Zo-<lb/>diaci ingreditur, accuratiſſime obſeruarunt. </s> <s xml:id="echoid-s10374" xml:space="preserve">quoniam vero ingreſſus in duo puncta ſolſtitialia difficilior ſit, <lb/>quam in puncta ęquinoctialia (quia hic Solis declinatio magis ſenſibiliter ad ſingulos dies variatur) propte-<lb/>rea de eo, hoc eſt, qua ratione momentum æquinoctij deprehendatur, nunc dicemus.</s> <s xml:id="echoid-s10375" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div218" type="section" level="1" n="139"> <head xml:id="echoid-head151" style="it" xml:space="preserve">Momentum ingreſſus Solis in puncta Aequinoctia determinare. Cap. V.</head> <p> <s xml:id="echoid-s10376" xml:space="preserve">ANte omnia neceſſe eſt exactè altititudinem poli, ac proinde altitudinem æquatoris meridianam loci il-<lb/>lius, vbi fit obſeruatio, & </s> <s xml:id="echoid-s10377" xml:space="preserve">præterea declinationes punctorum eclypticæ ab æquatore, de qu bus iam egi-<lb/>mus, prænouiſſe. </s> <s xml:id="echoid-s10378" xml:space="preserve">poſtea per noſtrum Quadrantem, circa tempus æquinoctij obſeruandi, obſerua diligenter <lb/>meridianas Solis altitudines eo modo, quo ſupra Tropicorum diſtantiam, & </s> <s xml:id="echoid-s10379" xml:space="preserve">æquatoris altitudinem obſerua-<lb/>re docuim 28. </s> <s xml:id="echoid-s10380" xml:space="preserve">ſi enim altitudo Solis meridiana fuerit omnino æqualis altitudini æquatoris, erit tunc tempo-<lb/>ris in meridie ipſum Æquinoctij momentum, ideſt, in puncto meridiei Sol Arietem vel Lib am vna cum <lb/>æquatore attinget. </s> <s xml:id="echoid-s10381" xml:space="preserve">Si iuxta vernale æquinoctlum altitudo Solis meridiana fuerit proximè minor altitudine <lb/>æquatoris, erit is defectus aliquot minutorum. </s> <s xml:id="echoid-s10382" xml:space="preserve">pro ſingulis igitur minutis vnam horam accipe, tot enim ho-<lb/>ris poſt illius diei meridiem erit æquinoctij inſtans quot minutis deficit illa altitudo. </s> <s xml:id="echoid-s10383" xml:space="preserve">Idem proportionaliter <lb/>fiat ad autumni æquinoctium explorãdum, notetur enim altitudo meridiana Solis proximè maior altitudi- <pb o="104" file="0124" n="128" rhead="De Mundi Fabrica,"/> ne æquatoris, quot enim minutis eam excedit, tot horis, poſt illum meridiem, eontinget æquinoctium.</s> <s xml:id="echoid-s10384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10385" xml:space="preserve">Vel ſic, obſerua duas altitudines Solis meridianas, vnam ante æquinoctium, alteram poſt. </s> <s xml:id="echoid-s10386" xml:space="preserve">vna erit proxi-<lb/>mè minor, altera proximè maior altitudine æquatoris, & </s> <s xml:id="echoid-s10387" xml:space="preserve">quia minuta exceſſus, & </s> <s xml:id="echoid-s10388" xml:space="preserve">defectus ſunt declinatio-<lb/>nes punctorum eclypticę, ideo ex Tabula declinat. </s> <s xml:id="echoid-s10389" xml:space="preserve">iam cap de Zodiaco præmiſſa; </s> <s xml:id="echoid-s10390" xml:space="preserve">accipe duo puncta eclypti-<lb/>cæ quibus tales conueniant declinationes. </s> <s xml:id="echoid-s10391" xml:space="preserve">quibus cognitis accipe eorum diſtantias ab æquinoctiali puncto, <lb/>quarum vna præcedit, altera ſequitur æquinoctium; </s> <s xml:id="echoid-s10392" xml:space="preserve">eæ ſimul additæ componunt motum Solis diurnum, <lb/>ideſt, eas Sol horis 24. </s> <s xml:id="echoid-s10393" xml:space="preserve">percurrit in priori enim puncto Sol erat in antecedente meridie, in poſteriori vero in <lb/>ſubſequenti meridie. </s> <s xml:id="echoid-s10394" xml:space="preserve">hunc igitur motum diurnum diuide in 24. </s> <s xml:id="echoid-s10395" xml:space="preserve">partes, quarũ ſingulæ ſingulis horis deben-<lb/>tur: </s> <s xml:id="echoid-s10396" xml:space="preserve">quot igitur ex dictis partibus ab vtrouis puncto obſeruationis diſtiterit Arietis initium; </s> <s xml:id="echoid-s10397" xml:space="preserve">tot etiam horis. <lb/></s> <s xml:id="echoid-s10398" xml:space="preserve">vel poſt primum meridiem, vel ante ſecundum, continget æquinoctium.</s> <s xml:id="echoid-s10399" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10400" xml:space="preserve">2 Ex Ptolomæi Armilla æquatoria. </s> <s xml:id="echoid-s10401" xml:space="preserve">Erat hæc magnus æquatoris circulus, cuidam parieti firmiter affi-<lb/>@us, ibique Aſtronomicè ita collocatus, vt æquatoris poſitionem omnino imitaretur. </s> <s xml:id="echoid-s10402" xml:space="preserve">igitur circa æquinoctij <lb/>tempus ruditer cognitum, obſeruabat vmbram, ac illuminationem illius; </s> <s xml:id="echoid-s10403" xml:space="preserve">nam ſi pars ſuperior Soli obuerſa <lb/>totam alteram partem inferiorem, & </s> <s xml:id="echoid-s10404" xml:space="preserve">cauam præcisè, & </s> <s xml:id="echoid-s10405" xml:space="preserve">adæquatè obumbraſſet, tunc temporis æquinoctium <lb/>contingebat. </s> <s xml:id="echoid-s10406" xml:space="preserve">quoniam vero in æquinoctijs Sol moratur ſupra horizontem h. </s> <s xml:id="echoid-s10407" xml:space="preserve">12. </s> <s xml:id="echoid-s10408" xml:space="preserve">facilè accidere poteſt, vt in-<lb/>terdiu æquinoctium contingat, ac proinde momentum ipſius ex tali obumbratione dignoſcatur. </s> <s xml:id="echoid-s10409" xml:space="preserve">non enim <lb/>in meridie tantum, ſed qualibet diei hora id fieri poteſt. </s> <s xml:id="echoid-s10410" xml:space="preserve">Pariter ex ſphæra materiali rectè conſtructa atque <lb/>Aſtronomicè collocata id aſſequemur, quamuis non æquè tuto ac per affixam Armillam; </s> <s xml:id="echoid-s10411" xml:space="preserve">Quamuis nec per <lb/>Armillam, nec aliud quoduis inſtrumentum, fieri queat, vt exactè, ſed tantummodo quam proximè ipſum <lb/>æquinoctij momentum difiniatur.</s> <s xml:id="echoid-s10412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10413" xml:space="preserve">3 Ex calculo Solis Aſtronomi tempus æquinoctij explorant, vbi motum Solis cognitum iam ſupponũt, <lb/>quem vt cognoſcerent neceſſe fuit prius æquinoctium ex obſeruatione o ganica determinare; </s> <s xml:id="echoid-s10414" xml:space="preserve">vti modo do-<lb/>cuimus. </s> <s xml:id="echoid-s10415" xml:space="preserve">ideo nunc nobis minimè licet docere qua via ex calculo, ac proinde ex motu Solis cognito æquino-<lb/>ctium inueniamus: </s> <s xml:id="echoid-s10416" xml:space="preserve">hoc enim modo in Logicam peccaremus petentes principium, ſupponeremus etiam mo. <lb/></s> <s xml:id="echoid-s10417" xml:space="preserve">tum Solis eſſe nobis cognitum, quem ex æquinoctijs indagare volumus.</s> <s xml:id="echoid-s10418" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div219" type="section" level="1" n="140"> <head xml:id="echoid-head152" style="it" xml:space="preserve">Anni æquinoct. ac ſyderei quantitatem Astronomicè definire. Cap. V I.</head> <p> <s xml:id="echoid-s10419" xml:space="preserve">QVoniam verus annus temporalis, qui nobis quatuor temporum viciſſitudines affert, oritur ex Solis per <lb/>Zodiacum integra reuolutione, fit vt tempus ab vno eodemque æquinoctio ad idem, ſit æquinoctiale <lb/>tempus annuum. </s> <s xml:id="echoid-s10420" xml:space="preserve">Vetuſtiores igitur Aſtronomi Calippus, Ariſtarchus, Archimedes, Hipparchus, <lb/>inter duo æquinoctia ritè, quantum fieri potuit obſeruata, vt inter duo verna, aut duo autumnalia, compere-<lb/>runt contineri dies 365. </s> <s xml:id="echoid-s10421" xml:space="preserve">& </s> <s xml:id="echoid-s10422" xml:space="preserve">horas 6. </s> <s xml:id="echoid-s10423" xml:space="preserve">Verum aliquam obſeruationum imperfectionem exactam anni quanti-<lb/>catem tam breui tempore, neutiquam attigerunt. </s> <s xml:id="echoid-s10424" xml:space="preserve">Verior enim anni magnitudo, non niſi per multos annos, <lb/>inter duo æquinoctia eiuſdem generis, præteritos indagari poteſt. </s> <s xml:id="echoid-s10425" xml:space="preserve">Quamobrem Ptolemæus prædictam an-<lb/>ni quantitatem examinaturus bina aſſumpſit æquinoctia, quæ plurimis ab inuicem annis diſtarent. </s> <s xml:id="echoid-s10426" xml:space="preserve">quorum <lb/>prius denotatum fuerat ab Hipparcho, alterum vero a ſeipſo. </s> <s xml:id="echoid-s10427" xml:space="preserve">in quo annorum interuallo reperit non potuiſ-<lb/>ſe contineri annos integros conſtantes ex diebus 365 {1/4}. </s> <s xml:id="echoid-s10428" xml:space="preserve">verum in annis trecentis vnum diem interire. </s> <s xml:id="echoid-s10429" xml:space="preserve">vnde <lb/>collegitur annum cõ@inere dies 365′. </s> <s xml:id="echoid-s10430" xml:space="preserve">minus parte 300. </s> <s xml:id="echoid-s10431" xml:space="preserve">diei. </s> <s xml:id="echoid-s10432" xml:space="preserve">quæ efficit 12″. </s> <s xml:id="echoid-s10433" xml:space="preserve">ſecunda diei. </s> <s xml:id="echoid-s10434" xml:space="preserve">quare annus illi fuit <lb/>dierum 365. </s> <s xml:id="echoid-s10435" xml:space="preserve">14′. </s> <s xml:id="echoid-s10436" xml:space="preserve">48′. </s> <s xml:id="echoid-s10437" xml:space="preserve">ſeu dierum 365. </s> <s xml:id="echoid-s10438" xml:space="preserve">horarum 5. </s> <s xml:id="echoid-s10439" xml:space="preserve">55′. </s> <s xml:id="echoid-s10440" xml:space="preserve">12″. </s> <s xml:id="echoid-s10441" xml:space="preserve">Eodem modo Albategnius Arabs, poſt Ptolemæũ <lb/>annis 743. </s> <s xml:id="echoid-s10442" xml:space="preserve">conterens ſuas obſeruationes cum Ptolemaicis, annum ſtatuit eſſe dies 365. </s> <s xml:id="echoid-s10443" xml:space="preserve">horas 5. </s> <s xml:id="echoid-s10444" xml:space="preserve">46′. </s> <s xml:id="echoid-s10445" xml:space="preserve">Alij de-<lb/>inceps Aſtronomi in idẽ ſtudium incubuerunt; </s> <s xml:id="echoid-s10446" xml:space="preserve">donec vltimus omnium Tycho exactiſſimus obſeruator anti-<lb/>quorum veſtigijs inſiſtens, prodidit annum naturalem, ſeu ęquinoctialem conſtare ex diebus 365. </s> <s xml:id="echoid-s10447" xml:space="preserve">hor. </s> <s xml:id="echoid-s10448" xml:space="preserve">5. </s> <s xml:id="echoid-s10449" xml:space="preserve">48′. <lb/></s> <s xml:id="echoid-s10450" xml:space="preserve">45″. </s> <s xml:id="echoid-s10451" xml:space="preserve">ſeu ex diebus 365. </s> <s xml:id="echoid-s10452" xml:space="preserve">14′. </s> <s xml:id="echoid-s10453" xml:space="preserve">31″. </s> <s xml:id="echoid-s10454" xml:space="preserve">52″′. </s> <s xml:id="echoid-s10455" xml:space="preserve">dierum. </s> <s xml:id="echoid-s10456" xml:space="preserve">Similiter labore ac methodo circa annum ſydereum tradiderũt <lb/>recentiores eum conſtare ex diebus 365. </s> <s xml:id="echoid-s10457" xml:space="preserve">hor. </s> <s xml:id="echoid-s10458" xml:space="preserve">6.</s> <s xml:id="echoid-s10459" xml:space="preserve">9′. </s> <s xml:id="echoid-s10460" xml:space="preserve">26″. </s> <s xml:id="echoid-s10461" xml:space="preserve">Hos porrò annos cõ tantes ex fractionibus horarum, <lb/>minutis, ac ſecundis, appellant Aſtronomicos, qui differunt ab anno ciuili de quo poſtea.</s> <s xml:id="echoid-s10462" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div220" type="section" level="1" n="141"> <head xml:id="echoid-head153" style="it" xml:space="preserve">Motus Solis medios inuestigare. Cap. VII.</head> <p> <s xml:id="echoid-s10463" xml:space="preserve">CVm igitur Sol totum Zodiacũ emetiatur anno æquinoctiali, hoc eſt diebus 365. </s> <s xml:id="echoid-s10464" xml:space="preserve">hor. </s> <s xml:id="echoid-s10465" xml:space="preserve">5. </s> <s xml:id="echoid-s10466" xml:space="preserve">48′. </s> <s xml:id="echoid-s10467" xml:space="preserve">45″. </s> <s xml:id="echoid-s10468" xml:space="preserve">ſi totum <lb/>Zodiacum, ſeu ſi gradus 360. </s> <s xml:id="echoid-s10469" xml:space="preserve">diuiſerimus pertot dies, horas, & </s> <s xml:id="echoid-s10470" xml:space="preserve">c. </s> <s xml:id="echoid-s10471" xml:space="preserve">prodibit in quotiente motus Solis me-<lb/>dius diurnus gr. </s> <s xml:id="echoid-s10472" xml:space="preserve">0. </s> <s xml:id="echoid-s10473" xml:space="preserve">59′. </s> <s xml:id="echoid-s10474" xml:space="preserve">8′. </s> <s xml:id="echoid-s10475" xml:space="preserve">20″′. </s> <s xml:id="echoid-s10476" xml:space="preserve">& </s> <s xml:id="echoid-s10477" xml:space="preserve">c. </s> <s xml:id="echoid-s10478" xml:space="preserve">qui numeratur ab Arietis initio, diciturq; </s> <s xml:id="echoid-s10479" xml:space="preserve">motus longitudinis. </s> <s xml:id="echoid-s10480" xml:space="preserve">diuiſionẽ <lb/>hanc iſi Luna docuimus. </s> <s xml:id="echoid-s10481" xml:space="preserve">Soligitur ſinguli diebus mediocri motu, ideſt, ſi æqualiter in Zodiaco moueatur, <lb/>perficit 59′. </s> <s xml:id="echoid-s10482" xml:space="preserve">8″. </s> <s xml:id="echoid-s10483" xml:space="preserve">& </s> <s xml:id="echoid-s10484" xml:space="preserve">c. </s> <s xml:id="echoid-s10485" xml:space="preserve">huius pars 24. </s> <s xml:id="echoid-s10486" xml:space="preserve">erit motus medius horarius. </s> <s xml:id="echoid-s10487" xml:space="preserve">ſi vero eum multiplicaucrimus per aliquem <lb/>dierum numerum, habebimns motus illi correſpondentes, ſic motus annuos, meſtruos, diarios, & </s> <s xml:id="echoid-s10488" xml:space="preserve">horarios, <lb/>facilè obtinebimus. </s> <s xml:id="echoid-s10489" xml:space="preserve">ex quibus ſicuti etiam in Luna, Tabulas mediorum motuum conſtruemus. </s> <s xml:id="echoid-s10490" xml:space="preserve">Supradi@tam <lb/>diuiſionem ſic peregi. </s> <s xml:id="echoid-s10491" xml:space="preserve">reſolui totum circulum, ideſt, gr. </s> <s xml:id="echoid-s10492" xml:space="preserve">360. </s> <s xml:id="echoid-s10493" xml:space="preserve">io tertia 77, 760, 000″. </s> <s xml:id="echoid-s10494" xml:space="preserve">ſimiliter reduxi totum an-<lb/>num, ideſt, dies 365. </s> <s xml:id="echoid-s10495" xml:space="preserve">hor. </s> <s xml:id="echoid-s10496" xml:space="preserve">548′. </s> <s xml:id="echoid-s10497" xml:space="preserve">45″. </s> <s xml:id="echoid-s10498" xml:space="preserve">in ſecunda 1,314,872, poſtea diuiſi illa tertia, per hanc ſecunda, & </s> <s xml:id="echoid-s10499" xml:space="preserve">proue-<lb/>neiunt 59′. </s> <s xml:id="echoid-s10500" xml:space="preserve">prima. </s> <s xml:id="echoid-s10501" xml:space="preserve">ſuperfuerunt in diuiſione tertia 182,561″′. </s> <s xml:id="echoid-s10502" xml:space="preserve">quæ duxi in 60. </s> <s xml:id="echoid-s10503" xml:space="preserve">produxique 10,953,650. </s> <s xml:id="echoid-s10504" xml:space="preserve">quarta <lb/>hæc iterum partitus ſum per eadem ſecunda, & </s> <s xml:id="echoid-s10505" xml:space="preserve">c. </s> <s xml:id="echoid-s10506" xml:space="preserve">ideſt, per eumdem diuiſorem, & </s> <s xml:id="echoid-s10507" xml:space="preserve">prodijt quotiens 8 @ @. </s> <s xml:id="echoid-s10508" xml:space="preserve">ſe-<lb/>cunda, & </s> <s xml:id="echoid-s10509" xml:space="preserve">ſic deinceps iuxta regulam ſuperius de diuiſione traditam. </s> <s xml:id="echoid-s10510" xml:space="preserve">reperique motum Solis diarium in lon-<lb/>gitudinem 59′. </s> <s xml:id="echoid-s10511" xml:space="preserve">8″. </s> <s xml:id="echoid-s10512" xml:space="preserve">20″′. </s> <s xml:id="echoid-s10513" xml:space="preserve">& </s> <s xml:id="echoid-s10514" xml:space="preserve">c.</s> <s xml:id="echoid-s10515" xml:space="preserve"/> </p> <pb o="105" file="0125" n="129" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div221" type="section" level="1" n="142"> <head xml:id="echoid-head154" style="it" xml:space="preserve">De irregularitate ſeu Anomaliamotus Solis. Cap. VIII.</head> <p> <s xml:id="echoid-s10516" xml:space="preserve">POſt hæc Solem annotarunt non æqualiter, ac vniformiter ſub Zodiaco ferri; </s> <s xml:id="echoid-s10517" xml:space="preserve">depræhẽderunt enim eum <lb/>in ſemicirculo Zodiaci Boreali immorari dies ferè 8 {1/2}. </s> <s xml:id="echoid-s10518" xml:space="preserve">amplius, quam in ſemicirculo auſtrali nã ab æqui-<lb/>noctio verno ad autumnale interſunt dies 186. </s> <s xml:id="echoid-s10519" xml:space="preserve">cum h. </s> <s xml:id="echoid-s10520" xml:space="preserve">18 {1/2}. </s> <s xml:id="echoid-s10521" xml:space="preserve">ab autumnali vero rurſus ad vernum inſunt dies <lb/>tantum 178. </s> <s xml:id="echoid-s10522" xml:space="preserve">cum horis 11 {1/2}. </s> <s xml:id="echoid-s10523" xml:space="preserve">quod maniſeſtè apparet ſi in Calẽdario numeres dies à 21. </s> <s xml:id="echoid-s10524" xml:space="preserve">Martij, in quo fit æqui-<lb/>noctium vernum, vſque ad 23. </s> <s xml:id="echoid-s10525" xml:space="preserve">Septembris, in quem autumnale æquinoctium incidit. </s> <s xml:id="echoid-s10526" xml:space="preserve">ad hæc cognouerunt <lb/>eum inæqualiter etiam moueri in quadrantibus Zodiaci, nam Hippatchi, & </s> <s xml:id="echoid-s10527" xml:space="preserve">Ptolemæi ſæculi plures dies in-<lb/>ſumebat in primo quadrante, ideſt, ab æquinoctio verno ad ſolſtitium æſtiuum, quam in ſecundo illinc ad <lb/>Libram vſque. </s> <s xml:id="echoid-s10528" xml:space="preserve">noſtra@autem tempeſtate ſegnior@eſt in ſecundo, quam in primo, tardiſſimus autem circa gr. </s> <s xml:id="echoid-s10529" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s10530" xml:space="preserve">Cancri. </s> <s xml:id="echoid-s10531" xml:space="preserve">Præterea obſeruarunt, quod cæteris paribus, quanto Sol tardior eſt, tanto etiã maior apparet; </s> <s xml:id="echoid-s10532" xml:space="preserve">quan-<lb/>to vero velocior tanto maior. </s> <s xml:id="echoid-s10533" xml:space="preserve">nam circa æſtiuam tropem vbi ſegnior eſt, minor etiam apparet, eiuſq; </s> <s xml:id="echoid-s10534" xml:space="preserve">appa-<lb/>rens diameter eſt@min. </s> <s xml:id="echoid-s10535" xml:space="preserve">quaſi 30′. </s> <s xml:id="echoid-s10536" xml:space="preserve">ad alteram vero tropem, vbi velocior apparet. </s> <s xml:id="echoid-s10537" xml:space="preserve">ibi etiam maior cernitur, eius <lb/>@nim apparens diameter aliquantum excedit min. </s> <s xml:id="echoid-s10538" xml:space="preserve">32′,</s> </p> <p> <s xml:id="echoid-s10539" xml:space="preserve">His igitur accurate perſpectis conſiderare cæperunt quibus circulis neceſſe eſſet Solem moueri, ad hoc, vt <lb/>prædictæ apparentiæ, & </s> <s xml:id="echoid-s10540" xml:space="preserve">obſeruationes ſaluarentur, & </s> <s xml:id="echoid-s10541" xml:space="preserve">quamuis per epicyclum ſicut in Luna, id effici poſſet, <lb/>fimplicior tamen viſus eſt eccentrici circuli modus. </s> <s xml:id="echoid-s10542" xml:space="preserve">Quapropter imaginati ſunt circulum quendam eccen-<lb/>tricum, ideſt, cuius centrum eſſet aliud a centro vniuerſi, in ea diſtantia a terra quam ſupra Soli attribuimus, <lb/>quique eſſet directè ſub eclyptica conſtitutus. </s> <s xml:id="echoid-s10543" xml:space="preserve">in cuius peripheria Sol circumferretur; </s> <s xml:id="echoid-s10544" xml:space="preserve">vel potius cuius peri-<lb/>pheriam motu proprio, & </s> <s xml:id="echoid-s10545" xml:space="preserve">æquali ab occaſu in ortum, ſeu in conſequentia deſcriberet, eumque annuo ſpatio <lb/>abſolueret. </s> <s xml:id="echoid-s10546" xml:space="preserve">ſed vt omnia faeile percipiantur opus eſt figura in qua A. </s> <s xml:id="echoid-s10547" xml:space="preserve">ſit centrum terræ, & </s> <s xml:id="echoid-s10548" xml:space="preserve">vniuerſi, ac pro-<lb/> <anchor type="figure" xlink:label="fig-0125-01a" xlink:href="fig-0125-01"/> inde Zodiaci, & </s> <s xml:id="echoid-s10549" xml:space="preserve">eclypticæ, quæ ſit G M H L. </s> <s xml:id="echoid-s10550" xml:space="preserve">circa vero <lb/>aliud centrum B. </s> <s xml:id="echoid-s10551" xml:space="preserve">ſit circulus eccentricus C Q E P. </s> <s xml:id="echoid-s10552" xml:space="preserve">linea <lb/>linea D B F. </s> <s xml:id="echoid-s10553" xml:space="preserve">incedens per vtrumque centrum oſtendit iu <lb/>puncto C. </s> <s xml:id="echoid-s10554" xml:space="preserve">punctum eccentrici aterra remotiſſimum, quod <lb/>propterea Græcè Apogæum dicitur, Arabicè autem Aux. <lb/></s> <s xml:id="echoid-s10555" xml:space="preserve">in E. </s> <s xml:id="echoid-s10556" xml:space="preserve">vero puncto oppoſito, deſignat punctum terræ pro-<lb/>ximum, ideoque Perigæum Græcè dictum, Arabicè oppo-<lb/>ſitum Augis. </s> <s xml:id="echoid-s10557" xml:space="preserve">puncta autem D F. </s> <s xml:id="echoid-s10558" xml:space="preserve">ſunt loca Zodiaci in qui-<lb/>bus Apogæum, & </s> <s xml:id="echoid-s10559" xml:space="preserve">Perigæum eſſe dicuntur. </s> <s xml:id="echoid-s10560" xml:space="preserve">ipſa vero linea <lb/>dicitur linea Apogæi. </s> <s xml:id="echoid-s10561" xml:space="preserve">altera linea G H. </s> <s xml:id="echoid-s10562" xml:space="preserve">per vtrumque ſol-<lb/>ſtitium incedens, ſolſtitialis appellatur. </s> <s xml:id="echoid-s10563" xml:space="preserve">linea M A L. </s> <s xml:id="echoid-s10564" xml:space="preserve">eſt <lb/>æquinoctialis, ideſt, ſectio æquatoris cum plano eclypticæ <lb/>hæc eclypticam bifariam ſecat in duobus æquinoctiorum. </s> <s xml:id="echoid-s10565" xml:space="preserve"><lb/>punctis ♈. </s> <s xml:id="echoid-s10566" xml:space="preserve">♎. </s> <s xml:id="echoid-s10567" xml:space="preserve">linea Q B P. </s> <s xml:id="echoid-s10568" xml:space="preserve">eccentrici diameter, eumq; </s> <s xml:id="echoid-s10569" xml:space="preserve">bi-<lb/>fariam ſecans, ſic prædictę paralella. </s> <s xml:id="echoid-s10570" xml:space="preserve">diſtantia vtriuſq; </s> <s xml:id="echoid-s10571" xml:space="preserve">cen-<lb/>tri B A. </s> <s xml:id="echoid-s10572" xml:space="preserve">dicitur eccentricitas. </s> <s xml:id="echoid-s10573" xml:space="preserve">huius igitur eccentrici peri-<lb/>pheriam Sol æquali motu, & </s> <s xml:id="echoid-s10574" xml:space="preserve">annuo deſcribit, ſit v.</s> <s xml:id="echoid-s10575" xml:space="preserve">g. </s> <s xml:id="echoid-s10576" xml:space="preserve">in O. </s> <s xml:id="echoid-s10577" xml:space="preserve"><lb/>intelligantur linea B O. </s> <s xml:id="echoid-s10578" xml:space="preserve">A O. </s> <s xml:id="echoid-s10579" xml:space="preserve">& </s> <s xml:id="echoid-s10580" xml:space="preserve">A X. </s> <s xml:id="echoid-s10581" xml:space="preserve">paralelia ipſi B O. </s> <s xml:id="echoid-s10582" xml:space="preserve">ha-<lb/>rum linearum ipſæ B O. </s> <s xml:id="echoid-s10583" xml:space="preserve">& </s> <s xml:id="echoid-s10584" xml:space="preserve">A X. </s> <s xml:id="echoid-s10585" xml:space="preserve">paralellæ, dicuntur lineæ <lb/>medij ſeu æqualis motus Solis, illa in eccentrico, hæc in Zod@aco, ambę enim æqualiter mouentur, ſemperq; </s> <s xml:id="echoid-s10586" xml:space="preserve"><lb/>@quales angulos faciunt cum linea Apogæi D F. </s> <s xml:id="echoid-s10587" xml:space="preserve">vnde tantus ſemper ect arcus Zodiaci X D. </s> <s xml:id="echoid-s10588" xml:space="preserve">quantus eſt ar-<lb/>cus eccentricus C O. </s> <s xml:id="echoid-s10589" xml:space="preserve">cum autem Sol in Apogæo, aut Perigæo fuerit, prædictæ lineæ ſimul vniuntur; </s> <s xml:id="echoid-s10590" xml:space="preserve">alibi ſc-<lb/>parantur, & </s> <s xml:id="echoid-s10591" xml:space="preserve">æquidiſtant. </s> <s xml:id="echoid-s10592" xml:space="preserve">linea A O. </s> <s xml:id="echoid-s10593" xml:space="preserve">dicitur veri, & </s> <s xml:id="echoid-s10594" xml:space="preserve">apparentis motus Solis, quæ non mouetur regulariter, <lb/>oſtenditque propterea verum Solis locum in Zodiaco, in puncto Z. </s> <s xml:id="echoid-s10595" xml:space="preserve">ex hac hypotheſi ſaluari poſſunt omnes <lb/>apparentiæ, & </s> <s xml:id="echoid-s10596" xml:space="preserve">obſeruationes. </s> <s xml:id="echoid-s10597" xml:space="preserve">& </s> <s xml:id="echoid-s10598" xml:space="preserve">prima quidem cauſa reddi poteſt, cur motus Solis in Zodiaco anomalus, ſeu <lb/>inæqualis apparea: </s> <s xml:id="echoid-s10599" xml:space="preserve">oculus enim noſter cum ſit in centro mundi A. </s> <s xml:id="echoid-s10600" xml:space="preserve">Solq; </s> <s xml:id="echoid-s10601" xml:space="preserve">moueatur æqualiter in eccentr. </s> <s xml:id="echoid-s10602" xml:space="preserve">ſe-<lb/>quitur Solem exiſtentem in I. </s> <s xml:id="echoid-s10603" xml:space="preserve">nobis apparere in L. </s> <s xml:id="echoid-s10604" xml:space="preserve">ſic quando eſt in Y. </s> <s xml:id="echoid-s10605" xml:space="preserve">videri in G. </s> <s xml:id="echoid-s10606" xml:space="preserve">quando in K. </s> <s xml:id="echoid-s10607" xml:space="preserve">ſpectatur in <lb/>M. </s> <s xml:id="echoid-s10608" xml:space="preserve">quando tandem in T. </s> <s xml:id="echoid-s10609" xml:space="preserve">cernitur in H. </s> <s xml:id="echoid-s10610" xml:space="preserve">dum igitur Sol perambulat eccentr. </s> <s xml:id="echoid-s10611" xml:space="preserve">portionem I Y K. </s> <s xml:id="echoid-s10612" xml:space="preserve">quæ multo <lb/>maior eſt ſemicirculo P Y Q. </s> <s xml:id="echoid-s10613" xml:space="preserve">apparet ſemper eſſe in ſemicirculo Zodiaci boreali L G M. </s> <s xml:id="echoid-s10614" xml:space="preserve">maior igitur por-<lb/>tio eccentr@ reſpondet ſemicirculo Zodiaci, & </s> <s xml:id="echoid-s10615" xml:space="preserve">conſeequenter reliqua cccentr. </s> <s xml:id="echoid-s10616" xml:space="preserve">minor portio K T I. </s> <s xml:id="echoid-s10617" xml:space="preserve">reſpon-<lb/>debit alteri ſemicirculo Zodiaci M K L. </s> <s xml:id="echoid-s10618" xml:space="preserve">quoniã vero Sol vniformiter in eccentr. </s> <s xml:id="echoid-s10619" xml:space="preserve">mouetur, ideo plures dies <lb/>inſumet in maiori parte I Y K. </s> <s xml:id="echoid-s10620" xml:space="preserve">quam in minori K T I. </s> <s xml:id="echoid-s10621" xml:space="preserve">& </s> <s xml:id="echoid-s10622" xml:space="preserve">conſequenter nos putabimus eũ irregulariter mo-<lb/>ueri in Zodiaco, quia maior pars motus, in minori portione eccentr. </s> <s xml:id="echoid-s10623" xml:space="preserve">reſpondet alteri ſemicirculo Zodiaci: </s> <s xml:id="echoid-s10624" xml:space="preserve"><lb/>quare plus motus æqualis, ac conſequenter temporis, inſumet in eo Zodiaci ſemicirculo, cui maior pars ſu-<lb/>bijcitur; </s> <s xml:id="echoid-s10625" xml:space="preserve">ac pręterea ibi tardior apparebit, quam in altero ſemicirculo, cui minor pars eccentr. </s> <s xml:id="echoid-s10626" xml:space="preserve">motus, actem-<lb/>poris, ſubijci nobis apparet. </s> <s xml:id="echoid-s10627" xml:space="preserve">hæc autem Solis inæqualitas, ita per totum Zodiacũ diſtribuitur, vt propè Apo-<lb/>gæum ſit tardiſſimus, propè Perigæum velociſſimus, in cæteris locis prout fuerit Apogæo aut Perigæo pro-<lb/>pior, tanto ſegnior, vel velocior apparebit. </s> <s xml:id="echoid-s10628" xml:space="preserve">in medijs tamen locis K I. </s> <s xml:id="echoid-s10629" xml:space="preserve">præcedentis figuræ, in quibus a terra <lb/>mediocriter remouetur, motum exhibet æqualem medio motui. </s> <s xml:id="echoid-s10630" xml:space="preserve">nam diatius eius motus ibi eſt 59′. </s> <s xml:id="echoid-s10631" xml:space="preserve">8″. </s> <s xml:id="echoid-s10632" xml:space="preserve">in <lb/>Apogæo eſt tantum 57′. </s> <s xml:id="echoid-s10633" xml:space="preserve">5″. </s> <s xml:id="echoid-s10634" xml:space="preserve">in Perigæo 71′. </s> <s xml:id="echoid-s10635" xml:space="preserve">21″. </s> <s xml:id="echoid-s10636" xml:space="preserve">ſic igitur Anomalia Solis excuſari poteſt.</s> <s xml:id="echoid-s10637" xml:space="preserve"/> </p> <div xml:id="echoid-div221" type="float" level="2" n="1"> <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a"> <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-01"/> </figure> </div> <p> <s xml:id="echoid-s10638" xml:space="preserve">Ex eadem paritereccentr. </s> <s xml:id="echoid-s10639" xml:space="preserve">ſuppoſitione cauſa redditur, cur Sol propè Apogæum minor appareat, quam <pb o="106" file="0126" n="130" rhead="De Mundi Fabrica,"/> propè Perigæum, quia ſcilicet ibi remotior, quam hic, quæ enim propriora ſunt maiora apparent.</s> <s xml:id="echoid-s10640" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10641" xml:space="preserve">Porrò Hipparchus, ac poſtea Ptolemæus exiſtimarunt loci Apogæi in Zodiaco eſſe ſtabilem, eſſeq; </s> <s xml:id="echoid-s10642" xml:space="preserve">in par-<lb/>te 5 {1/2}. </s> <s xml:id="echoid-s10643" xml:space="preserve">Geminorum, ſed aliter a ſuccedentibus Aſtronomis Albategnio, Arzahele, Copernico, ac Tychone <lb/>depræhenſum eſt; </s> <s xml:id="echoid-s10644" xml:space="preserve">illud ſcilicet in ſignorum conſequentia tardè promoueri: </s> <s xml:id="echoid-s10645" xml:space="preserve">ita vt hac tempeſtate 6. </s> <s xml:id="echoid-s10646" xml:space="preserve">Cancri <lb/>gradui ſupponatur, ſinguliſq; </s> <s xml:id="echoid-s10647" xml:space="preserve">annis 45″. </s> <s xml:id="echoid-s10648" xml:space="preserve">tantum ſecundis promoueatnr. </s> <s xml:id="echoid-s10649" xml:space="preserve">vnde facilè eſt cognoſcere, quan to <lb/>annorum interuallo, totum Zodiacũ recurrat<unsure/>. </s> <s xml:id="echoid-s10650" xml:space="preserve">ſi enim omnia eclypticæ ſecũdę ſecunda, quę ſunt 1,296,000, ″. <lb/></s> <s xml:id="echoid-s10651" xml:space="preserve">diuiſerimus per 45″. </s> <s xml:id="echoid-s10652" xml:space="preserve">motum, ſcilicet annuum, prodibit in quotiente numerus annorum quæſitus; </s> <s xml:id="echoid-s10653" xml:space="preserve">videlicet <lb/>28′800′. </s> <s xml:id="echoid-s10654" xml:space="preserve">quibus Apogæum totum Zodiacum abſoluat.</s> <s xml:id="echoid-s10655" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div223" type="section" level="1" n="143"> <head xml:id="echoid-head155" style="it" xml:space="preserve">De Apogæiloco, & Eccentricitate inuenienda. Cap. IX.</head> <p> <s xml:id="echoid-s10656" xml:space="preserve">QVoniam Solis motus, quamuis ſit inæqualis, nõ tamen ſenſu ea inæqualitas percipitur, ac proinde neq; <lb/></s> <s xml:id="echoid-s10657" xml:space="preserve">in quo Zodiaci loco ſit tardiſſimus, & </s> <s xml:id="echoid-s10658" xml:space="preserve">conſequenter non patet ſenſu vbinam ſit Apogæum; </s> <s xml:id="echoid-s10659" xml:space="preserve">ideo Ptole-<lb/>mæus vt illud perſcrutaretur, ſic ex ſuis obſeruationibus ratiocinatus eſt. </s> <s xml:id="echoid-s10660" xml:space="preserve">Primo, quia tempus ab Ariete ad <lb/>Libram, maius eſt reliquo tempore, ideo neceſſe fuit Apogæum eſſe in ſemicirculo boreali Zodiaci; </s> <s xml:id="echoid-s10661" xml:space="preserve">pariter <lb/>quia in primo eius quadrante, ideſt, ab Ariete ad Cancrum, tardior erat Sol, quam in altero à Cancro ad Li-<lb/>bram, ibi enim inſumebat dies 94 {1/2}. </s> <s xml:id="echoid-s10662" xml:space="preserve">hic vero 92 {1/2}. </s> <s xml:id="echoid-s10663" xml:space="preserve">ideo concluſit Apogæum neceſſario verſari in primo qua-<lb/>drante. </s> <s xml:id="echoid-s10664" xml:space="preserve">ex his cæpit figura conſtruere, cuius auxilio reliqua exactè conſecutus eſt. </s> <s xml:id="echoid-s10665" xml:space="preserve">ſit eclyptica circa centrum <lb/> <anchor type="figure" xlink:label="fig-0126-01a" xlink:href="fig-0126-01"/> E. </s> <s xml:id="echoid-s10666" xml:space="preserve">in qua puncta quatuor Cardinalia ſint A B G D A. </s> <s xml:id="echoid-s10667" xml:space="preserve">punctum <lb/>vernale. </s> <s xml:id="echoid-s10668" xml:space="preserve">B. </s> <s xml:id="echoid-s10669" xml:space="preserve">ſolſtitiale. </s> <s xml:id="echoid-s10670" xml:space="preserve">G. </s> <s xml:id="echoid-s10671" xml:space="preserve">Autumnale. </s> <s xml:id="echoid-s10672" xml:space="preserve">D. </s> <s xml:id="echoid-s10673" xml:space="preserve">hyemale. </s> <s xml:id="echoid-s10674" xml:space="preserve">primus qua-<lb/>drans eſt A B. </s> <s xml:id="echoid-s10675" xml:space="preserve">in quo concluſit eſſe Apogæum, & </s> <s xml:id="echoid-s10676" xml:space="preserve">conſequenter <lb/>centrum eccentrici, in hac parte, v.</s> <s xml:id="echoid-s10677" xml:space="preserve">g.</s> <s xml:id="echoid-s10678" xml:space="preserve">vbi F. </s> <s xml:id="echoid-s10679" xml:space="preserve">ex quo deſcriptus ſit <lb/>eccentricus T K Q R. </s> <s xml:id="echoid-s10680" xml:space="preserve">duabus ecly pticæ diametris A G. </s> <s xml:id="echoid-s10681" xml:space="preserve">B D. </s> <s xml:id="echoid-s10682" xml:space="preserve">pa-<lb/>ralellæ ducantur duæ eccẽtrici diametri N Q. </s> <s xml:id="echoid-s10683" xml:space="preserve">X R. </s> <s xml:id="echoid-s10684" xml:space="preserve">tandem du-<lb/>cta per vtrumq; </s> <s xml:id="echoid-s10685" xml:space="preserve">centrum linea E F H. </s> <s xml:id="echoid-s10686" xml:space="preserve">erit Apogæi linea; </s> <s xml:id="echoid-s10687" xml:space="preserve">eritq; <lb/></s> <s xml:id="echoid-s10688" xml:space="preserve">H. </s> <s xml:id="echoid-s10689" xml:space="preserve">locus Apogæi in Zodiaco. </s> <s xml:id="echoid-s10690" xml:space="preserve">quem vt vna cum E F. </s> <s xml:id="echoid-s10691" xml:space="preserve">eccentrici-<lb/>tate cognoſceret, ſic perrexit rationari. </s> <s xml:id="echoid-s10692" xml:space="preserve">cum conſtet Solem obi-<lb/>re quadrantem A B. </s> <s xml:id="echoid-s10693" xml:space="preserve">d ebus 94 {1/2}. </s> <s xml:id="echoid-s10694" xml:space="preserve">eodemq; </s> <s xml:id="echoid-s10695" xml:space="preserve">etiam tempore nam-<lb/>bulet arcum eccentric T K. </s> <s xml:id="echoid-s10696" xml:space="preserve">æquali, ac medio motu, conſtetque <lb/>quantum ſingulis diebus motu æquali proficiat, conſtabit etiam <lb/>quantum diebus 94 {1/2}. </s> <s xml:id="echoid-s10697" xml:space="preserve">proficiat in eccentrico, hoc eſt, quantus ſit <lb/>arcus T K. </s> <s xml:id="echoid-s10698" xml:space="preserve">fuitq; </s> <s xml:id="echoid-s10699" xml:space="preserve">graduum 93.</s> <s xml:id="echoid-s10700" xml:space="preserve">9′. </s> <s xml:id="echoid-s10701" xml:space="preserve">ſimili modo reperit arcum ec-<lb/>centrici K L. </s> <s xml:id="echoid-s10702" xml:space="preserve">eſſe gradus 91.</s> <s xml:id="echoid-s10703" xml:space="preserve">11″. </s> <s xml:id="echoid-s10704" xml:space="preserve">ergo totus arcus T K L. </s> <s xml:id="echoid-s10705" xml:space="preserve">notus <lb/>fuit; </s> <s xml:id="echoid-s10706" xml:space="preserve">vnde & </s> <s xml:id="echoid-s10707" xml:space="preserve">T X. </s> <s xml:id="echoid-s10708" xml:space="preserve">dimidium eius cognitum. </s> <s xml:id="echoid-s10709" xml:space="preserve">quia vero X N. </s> <s xml:id="echoid-s10710" xml:space="preserve">eſt <lb/>quadrans eccentrici notus, ideo ſi auferatur ab arcu T X. </s> <s xml:id="echoid-s10711" xml:space="preserve">noto, <lb/>notus relinquetur arcus T N. </s> <s xml:id="echoid-s10712" xml:space="preserve">gr.</s> <s xml:id="echoid-s10713" xml:space="preserve">2.</s> <s xml:id="echoid-s10714" xml:space="preserve">10′. </s> <s xml:id="echoid-s10715" xml:space="preserve">ſimiliter ex arcu T K.</s> <s xml:id="echoid-s10716" xml:space="preserve">iam <lb/>noto, ablato T X. </s> <s xml:id="echoid-s10717" xml:space="preserve">pariter noto, notus relinquitur K X. </s> <s xml:id="echoid-s10718" xml:space="preserve">59. </s> <s xml:id="echoid-s10719" xml:space="preserve">min-<lb/>hinc Ptolemæus ex doctrina chordarum, vel ſinuum, propoſitum aſſequutus eſt, nos autem facilitatis cauſa <lb/>idem practicè ſic obtinebimus. </s> <s xml:id="echoid-s10720" xml:space="preserve">primo deſcribatur eccentricus vt in præcedenti figuræ, ex centro F. </s> <s xml:id="echoid-s10721" xml:space="preserve">ductiſq; </s> <s xml:id="echoid-s10722" xml:space="preserve"><lb/>diametris Q N. </s> <s xml:id="echoid-s10723" xml:space="preserve">X R. </s> <s xml:id="echoid-s10724" xml:space="preserve">ad angulos rectos, diuiſus erit in quatuor quadrantes. </s> <s xml:id="echoid-s10725" xml:space="preserve">deinde ſumatur arcus N T. </s> <s xml:id="echoid-s10726" xml:space="preserve">gr.</s> <s xml:id="echoid-s10727" xml:space="preserve">2. </s> <s xml:id="echoid-s10728" xml:space="preserve"><lb/>10′. </s> <s xml:id="echoid-s10729" xml:space="preserve">arcus vero X K. </s> <s xml:id="echoid-s10730" xml:space="preserve">min.</s> <s xml:id="echoid-s10731" xml:space="preserve">59′. </s> <s xml:id="echoid-s10732" xml:space="preserve">& </s> <s xml:id="echoid-s10733" xml:space="preserve">per puncta T K. </s> <s xml:id="echoid-s10734" xml:space="preserve">ducantur duæ A T G. </s> <s xml:id="echoid-s10735" xml:space="preserve">B K D. </s> <s xml:id="echoid-s10736" xml:space="preserve">diametris eccentrici paralel-<lb/>læ; </s> <s xml:id="echoid-s10737" xml:space="preserve">atq; </s> <s xml:id="echoid-s10738" xml:space="preserve">ex earum communi puncto E. </s> <s xml:id="echoid-s10739" xml:space="preserve">deſcribatur eclyptica A B G D. </s> <s xml:id="echoid-s10740" xml:space="preserve">tandem per vtrumque centrum E F. </s> <s xml:id="echoid-s10741" xml:space="preserve"><lb/>ducatur linea E F H. </s> <s xml:id="echoid-s10742" xml:space="preserve">quæ erit Apogæi linea, tranſibit enim per eccentrici Apogæum 1. </s> <s xml:id="echoid-s10743" xml:space="preserve">indicabitq; </s> <s xml:id="echoid-s10744" xml:space="preserve">in ecly-<lb/>ptica eius locũ in K. </s> <s xml:id="echoid-s10745" xml:space="preserve">hæc figura ſic conſtructa habebit veras proportiones, atq; </s> <s xml:id="echoid-s10746" xml:space="preserve">eaſdem quas haberet magna <lb/>figura quam in mundo concipimus. </s> <s xml:id="echoid-s10747" xml:space="preserve">diuiſa itaq; </s> <s xml:id="echoid-s10748" xml:space="preserve">eccentrici ſemid. </s> <s xml:id="echoid-s10749" xml:space="preserve">F I<unsure/>. </s> <s xml:id="echoid-s10750" xml:space="preserve">in partes 60. </s> <s xml:id="echoid-s10751" xml:space="preserve">æquales, apparebit auxilio <lb/>circini eccentricitatem E F. </s> <s xml:id="echoid-s10752" xml:space="preserve">conſtare ex duabus ex illis ſexageſimis ac medietate ferè. </s> <s xml:id="echoid-s10753" xml:space="preserve">quare proportio ſemi-<lb/>diametri ad eccentricitatem eſt ſicuti 24. </s> <s xml:id="echoid-s10754" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s10755" xml:space="preserve">ferè. </s> <s xml:id="echoid-s10756" xml:space="preserve">ſimiliter circini beneficio cognoſcemus arcum A H. </s> <s xml:id="echoid-s10757" xml:space="preserve">eſſe <lb/>gr.</s> <s xml:id="echoid-s10758" xml:space="preserve">65 {1/2}.</s> <s xml:id="echoid-s10759" xml:space="preserve">ideſt, Apogæum eſſe in gr.</s> <s xml:id="echoid-s10760" xml:space="preserve">5 {1/2}. </s> <s xml:id="echoid-s10761" xml:space="preserve">Geminorum, Perigæum autem in oppoſito loco. </s> <s xml:id="echoid-s10762" xml:space="preserve">Atque hæc perſcru-<lb/>tanda erant.</s> <s xml:id="echoid-s10763" xml:space="preserve"/> </p> <div xml:id="echoid-div223" type="float" level="2" n="1"> <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a"> <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01"/> </figure> </div> <p> <s xml:id="echoid-s10764" xml:space="preserve">Simili methodo idem Apogæum, noſtro æuo, ſtatuerunt in 6. </s> <s xml:id="echoid-s10765" xml:space="preserve">Cancri eccentricitatem vero partium 2. </s> <s xml:id="echoid-s10766" xml:space="preserve">9′. <lb/></s> <s xml:id="echoid-s10767" xml:space="preserve">qualium ſemidiameter eſt 60.</s> <s xml:id="echoid-s10768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10769" xml:space="preserve">Porrò ſciendum eſt eccentricitatem eſſe dimidium craſſitiei cæli Solis, quod patebit deſcriptis ex centro <lb/>mundi E. </s> <s xml:id="echoid-s10770" xml:space="preserve">duobus circulis, vno per Apogæum, altero per Perigæum tranſeunte, inter eos enim claudetur cæ-<lb/>li craſſities, quam duplam eſſe eccentricitatis circino comperies. </s> <s xml:id="echoid-s10771" xml:space="preserve">cum igitur nos ſuperius ſtatuerimus craſſi-<lb/>tiem illam eſſe ſemidiametros terræ 81. </s> <s xml:id="echoid-s10772" xml:space="preserve">erit eius ſemiſſis 40 {1/2}. </s> <s xml:id="echoid-s10773" xml:space="preserve">eccentricitas, ideſt, tantum diſtabit a terræ cen-<lb/>tro eccentrici centrum.</s> <s xml:id="echoid-s10774" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10775" xml:space="preserve">His igitur ſic conſtitutis, rurſus ad ſolarem motum redeamus. </s> <s xml:id="echoid-s10776" xml:space="preserve">primoq; </s> <s xml:id="echoid-s10777" xml:space="preserve">illud annotandum, diſtantiam lineę <lb/>medij motus in Zodiaco ab Apogeo dici Anomaliam Solis mediam, vt in priori ſigura pag. </s> <s xml:id="echoid-s10778" xml:space="preserve">105. </s> <s xml:id="echoid-s10779" xml:space="preserve">arcus Zodia-<lb/>ci D X. </s> <s xml:id="echoid-s10780" xml:space="preserve">erit Anomalia media. </s> <s xml:id="echoid-s10781" xml:space="preserve">Sol autem ab Apogæo in conſequentia recedit annuo tempore paulo minus, <lb/>quam ab æquinoctio, quia illud mobile eſt pariter in conſequentia; </s> <s xml:id="echoid-s10782" xml:space="preserve">quare tanto minus Sol annuatim reccdit <lb/>ab eo, quanto eſt ipſius Apogæi motus, nempe 45″. </s> <s xml:id="echoid-s10783" xml:space="preserve">Diſtantia vero inter lineam medij, & </s> <s xml:id="echoid-s10784" xml:space="preserve">veri motus, dicitur <lb/>æquatio, qualis eſt in eadem figura arcus X Z. </s> <s xml:id="echoid-s10785" xml:space="preserve">de qua poſtea fuſius. </s> <s xml:id="echoid-s10786" xml:space="preserve">Poſtremo illud quoq; </s> <s xml:id="echoid-s10787" xml:space="preserve">animaduerſione di-<lb/>gnum eſt, quod ſi Sol, hoc ſolo proprio motu in eccentrico moueretur, ideſt, ſi motu d<unsure/>iurno, ſeu primi mobi- <pb o="107" file="0127" n="131" rhead="Liber Decimus."/> lis ad occaſum non reperiretur, fore vt in Occidente oriretur, tendenſq; </s> <s xml:id="echoid-s10788" xml:space="preserve">ad Orientem, ſpatio ſex menſium, ſu-<lb/>pra noſtrũ Horizontem moraretur, donectandem in Oriente occideret:</s> <s xml:id="echoid-s10789" xml:space="preserve">ij tamen qui ſub polis eclyp@cæ de-<lb/>gunt, eum perpetuò horizontis ſui limbum circuire circumſpicerent.</s> <s xml:id="echoid-s10790" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10791" xml:space="preserve">His de motu Solis in eccentrico explicatis, reſtat ad planam motuum c<unsure/>ius intelligentiam, vt hunc cum a@ <lb/>motibus implicemus, vt ex eorum mixtione, vltimus ipſius motus reſultet. </s> <s xml:id="echoid-s10792" xml:space="preserve">debemus igitur nobis ob @ <lb/>ſphæram materialem aſtronomice collocatam ſt<unsure/>atuere, eccentricumque prædi<unsure/>ctum imaginari ſub ec@yptica <lb/>ſitum, Apogæo ſub gr. </s> <s xml:id="echoid-s10793" xml:space="preserve">6. </s> <s xml:id="echoid-s10794" xml:space="preserve">Cancri ſuppoſito. </s> <s xml:id="echoid-s10795" xml:space="preserve">deinde aſſumendus eſt Sol materialis, qui circulo ſecundorum <lb/>mobilium affixus eſt atque in eo directè ſub eclyptica mouetur. </s> <s xml:id="echoid-s10796" xml:space="preserve">Sol igitur hic materialis auxilio illius circuli <lb/>tardè promoueatur in conſequentia, ſic enim repręſentabit motum Solis in eccentrico: </s> <s xml:id="echoid-s10797" xml:space="preserve">dum autem hoc mo-<lb/>do tardè mouetur, interim ei ſuperueniat motus primi mobilis qui totam illam ſphæræ partẽ, quam primum <lb/>mobile appellauimus, vna cum Sole materiali ſecum ab ortu in occaſum velociter, ſpatio 24. </s> <s xml:id="echoid-s10798" xml:space="preserve">horarum, reuol-<lb/>uat, minimè interim ceſſante Sole materiali a proprio motu in conſequentia; </s> <s xml:id="echoid-s10799" xml:space="preserve">ita vt pro ſingulis primi mobi-<lb/>lis reuoluntionibus integris, gra. </s> <s xml:id="echoid-s10800" xml:space="preserve">vnum ille è contra proficiat in conſequentia. </s> <s xml:id="echoid-s10801" xml:space="preserve">idque continenter ſiat, dones<unsure/> <lb/>Sol ille totum Zodiacum graduatim peragrauerit. </s> <s xml:id="echoid-s10802" xml:space="preserve">ex his duab. </s> <s xml:id="echoid-s10803" xml:space="preserve">motionibus, tertia, & </s> <s xml:id="echoid-s10804" xml:space="preserve">vltima neceſſario orie<unsure/>-<lb/>tur, quæ ſpiralis erit, Sol enim hac ratione deſcribet, pergendo per Zodiacum ab vno tropico ad alterum, li-<lb/>neam ſpiralem, ſicuti etiam Luna, quæ ſpira conſtabit ex 182. </s> <s xml:id="echoid-s10805" xml:space="preserve">quaſi glomerationibus diurnis. </s> <s xml:id="echoid-s10806" xml:space="preserve">Hæc autem ſpi-<lb/>ra la xior erit ad Apogæum, quam ad Perigæum, quia ibi Sol remotior, quæ hic circunferatur. </s> <s xml:id="echoid-s10807" xml:space="preserve">porrò ex hu-<lb/>ius ſpiræ conſideratione apparebit cur Sol accedat, & </s> <s xml:id="echoid-s10808" xml:space="preserve">recedat a vertice; </s> <s xml:id="echoid-s10809" xml:space="preserve">cur in varijs horizontis punctis oria-<lb/>tur, & </s> <s xml:id="echoid-s10810" xml:space="preserve">occidat; </s> <s xml:id="echoid-s10811" xml:space="preserve">qua ratiop<unsure/>e quatuor anni tempora nobis attemperet, cur dies, ac noctes alternatim creſcant, <lb/>& </s> <s xml:id="echoid-s10812" xml:space="preserve">decreſcant: </s> <s xml:id="echoid-s10813" xml:space="preserve">vnde æquinoctia, ac ſolſtitia oriantur, & </s> <s xml:id="echoid-s10814" xml:space="preserve">alia plura.</s> <s xml:id="echoid-s10815" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10816" xml:space="preserve">Tandem ex hac contemplatione percipies cur dicatur Sol moueri duobus contrá<unsure/>rijs motibus ideſt, vno ſpi-<lb/>rali, qui conflatur ex duobus, ſcilicet ex motu proprio in eccentrico, & </s> <s xml:id="echoid-s10817" xml:space="preserve">diurno primi mobilis; </s> <s xml:id="echoid-s10818" xml:space="preserve">ſemper tame@ <lb/>Sol occaſui fit propior, quia motus primi mobilis altero velocior eſt.</s> <s xml:id="echoid-s10819" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div225" type="section" level="1" n="144"> <head xml:id="echoid-head156" style="it" xml:space="preserve">COROLLARIVM.</head> <p> <s xml:id="echoid-s10820" xml:space="preserve">QVot milliaria diurno motu Sol conficit? </s> <s xml:id="echoid-s10821" xml:space="preserve">Reſpon. </s> <s xml:id="echoid-s10822" xml:space="preserve">Solem in diſtantia à terra mediocri, quam ſtatuimus <lb/>ſemid. </s> <s xml:id="echoid-s10823" xml:space="preserve">terræ 1142. </s> <s xml:id="echoid-s10824" xml:space="preserve">peragere milliaria 1,027,800. </s> <s xml:id="echoid-s10825" xml:space="preserve">nam cum hæc diſtantia contineat ſemidiametros ter-<lb/>ræ 142. </s> <s xml:id="echoid-s10826" xml:space="preserve">continebit pariter ille Solis circuitus terræ circunferentiam 1142. </s> <s xml:id="echoid-s10827" xml:space="preserve">vicibus nam vti eſt diame-<lb/>ter ad diametrum, ita circunferentiam, ad circunferentiam, cum igitur in terreſtri peripheria contineantur <lb/>milliaria Aſtronomica 21600, ſi ea multiplicentur per 1142, prodibit 24,667,200, milliariorum ſolaris cir-<lb/>cuitus, qui diuiſus per 24. </s> <s xml:id="echoid-s10828" xml:space="preserve">horas, exhibet milliaria 1,027,800, quæ ſingulis horis Sol percurrit. </s> <s xml:id="echoid-s10829" xml:space="preserve">Vtrum Sol as<unsure/> <lb/>Luna ſæpius diurno motu reuoluatur? </s> <s xml:id="echoid-s10830" xml:space="preserve">Hactenus de solis motibus.</s> <s xml:id="echoid-s10831" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div226" type="section" level="1" n="145"> <head xml:id="echoid-head157" style="it" xml:space="preserve">De Solaribus Temporibus. Cap. X.</head> <p> <s xml:id="echoid-s10832" xml:space="preserve">POſt tractationem de Solis motu, proxime ſequitur tractatio de eiuſdem temporibus; </s> <s xml:id="echoid-s10833" xml:space="preserve">tempora enim nihil<unsure/> <lb/>aliud ſunt, quam motus quidam, qui ob aliqua accidentia tempeſtatum, aut lucis, & </s> <s xml:id="echoid-s10834" xml:space="preserve">tenebrarum, ab alija <lb/>motibus diſtinguuntur, ob idque euadunt tempora, ideſt, aſſumuntur ad rerum durationes menſuradas, a <lb/>motu Solis hæc oriuntur tempora, annus, menſis, dies, &</s> <s xml:id="echoid-s10835" xml:space="preserve">c.</s> <s xml:id="echoid-s10836" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10837" xml:space="preserve">Annus igitur ſicuti in Luna quoque dictum eſt, duplex eſt, Aſtronomicus, & </s> <s xml:id="echoid-s10838" xml:space="preserve">Ciuilis. </s> <s xml:id="echoid-s10839" xml:space="preserve">de Aſtronomico ſatis <lb/>dictum ſit in præcedenti cap. </s> <s xml:id="echoid-s10840" xml:space="preserve">qui conſtat ex diebus, & </s> <s xml:id="echoid-s10841" xml:space="preserve">dierum fractionibus, quæ minimè populis vſui eſſe poſ-<lb/>ſunt. </s> <s xml:id="echoid-s10842" xml:space="preserve">Ciuilis igitur commoditatis cauſa, ex diebus tantummodo integris ab hominibus aſſumptus eſt, fuerunt-<lb/>que pro diuerſitate gentium, diuerſi quoque anni. </s> <s xml:id="echoid-s10843" xml:space="preserve">apud Aſtronomos frequens eſt mentio, & </s> <s xml:id="echoid-s10844" xml:space="preserve">vſus annorum <lb/>Ægyptiorum, qui conſtabant ex diebus 365. </s> <s xml:id="echoid-s10845" xml:space="preserve">integris. </s> <s xml:id="echoid-s10846" xml:space="preserve">Annus hic diuiſus continebat menſes 12. </s> <s xml:id="echoid-s10847" xml:space="preserve">conſtantes <lb/>ſingulos ex 30. </s> <s xml:id="echoid-s10848" xml:space="preserve">diebus, præterea dies quinque; </s> <s xml:id="echoid-s10849" xml:space="preserve">qui vltimo menſi, in ſine anni addebantur; </s> <s xml:id="echoid-s10850" xml:space="preserve">Additique dice-<lb/>bantur. </s> <s xml:id="echoid-s10851" xml:space="preserve">At nobis de anno Romano, ſeu luliano fuſius dicendum eſt; </s> <s xml:id="echoid-s10852" xml:space="preserve">hoc enim Romana quoque Eccleſia, & </s> <s xml:id="echoid-s10853" xml:space="preserve"><lb/>vniuerſus ferè Chriſtianus orbis etiamnum vtitur. </s> <s xml:id="echoid-s10854" xml:space="preserve">lulius igitur Cæſar Soſigenijs Aſtronomi opera, annum <lb/>hunc ordinauit eumque duplicem fecit, alterum communem appellauit, quæ ex diebus tamen 365. </s> <s xml:id="echoid-s10855" xml:space="preserve">alterum <lb/>biſſextilem, qui ex diebus 366. </s> <s xml:id="echoid-s10856" xml:space="preserve">conſtaret: </s> <s xml:id="echoid-s10857" xml:space="preserve">hoc tamen ordine vt tres anni eſſent continuo communes, quartus <lb/>vero eſſet biſſextilis, ſeu intercalaris. </s> <s xml:id="echoid-s10858" xml:space="preserve">Ratio huius eſt, quia ſecundum rei veritatem, anni ſinguli conſtare de-<lb/>berent ex diebus 365. </s> <s xml:id="echoid-s10859" xml:space="preserve">& </s> <s xml:id="echoid-s10860" xml:space="preserve">horis 6. </s> <s xml:id="echoid-s10861" xml:space="preserve">ſed quia horæ illæ negotium populo faceſſerent, neque certum anni princi-<lb/>pium conſtaret, ideo omitti voluit ſex horas ſingulorum trium annorum communium, quæ efficiunt hora@ <lb/>18. </s> <s xml:id="echoid-s10862" xml:space="preserve">quas cum 6. </s> <s xml:id="echoid-s10863" xml:space="preserve">horis anni quarti biſſextilis componi voluit; </s> <s xml:id="echoid-s10864" xml:space="preserve">vt ex illis horis 24. </s> <s xml:id="echoid-s10865" xml:space="preserve">dies vnus conflaretur; </s> <s xml:id="echoid-s10866" xml:space="preserve">ac quar-<lb/>to cuique anno adderetur, leu intercalaretur poſt 24. </s> <s xml:id="echoid-s10867" xml:space="preserve">diem Februarij. </s> <s xml:id="echoid-s10868" xml:space="preserve">quoniam verò hæc dies intercalatis non <lb/>crat in Calendario ſcripta, ſed mente tantum addebatur, ideo 24. </s> <s xml:id="echoid-s10869" xml:space="preserve">dies bis repetebatur ſeu vt tunc moris erat <lb/>dicebatur bis, ſexto Calendas Martij, vnde annus, & </s> <s xml:id="echoid-s10870" xml:space="preserve">biſſextum denominatum eſt. </s> <s xml:id="echoid-s10871" xml:space="preserve">Ita autem horum anno-<lb/>rum ſeries cum annis Chriſti incidit, vt tres primi anni a Chriſti natiuitate eſſent communes, quartus autem <lb/>eſſet biſſextilis; </s> <s xml:id="echoid-s10872" xml:space="preserve">ſicque quartus quiſque annus a Chriſt<unsure/>i natiuitate ſemper adhuc eſt biſſextilis@. </s> <s xml:id="echoid-s10873" xml:space="preserve">pręter nonnul-<lb/>los à correctione Calendarij exceptos, de quare poſtea dicendum erit.</s> <s xml:id="echoid-s10874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10875" xml:space="preserve">Porrò Iulianus hic annus ita in Calendario in menſes diſtributus eſt, vt æquinoctia, & </s> <s xml:id="echoid-s10876" xml:space="preserve">ſolſtitia certis men-<lb/>ſium diebus perpetuo aſ<unsure/>ſ<unsure/>ixa eſſe deberent v. </s> <s xml:id="echoid-s10877" xml:space="preserve">g. </s> <s xml:id="echoid-s10878" xml:space="preserve">æquinectium vernum 21. </s> <s xml:id="echoid-s10879" xml:space="preserve">di<unsure/>ei Martij. </s> <s xml:id="echoid-s10880" xml:space="preserve">affixum erat; </s> <s xml:id="echoid-s10881" xml:space="preserve">cui diei <lb/>etiam à Nicęno Concilio (quod anno Chriſti 325. </s> <s xml:id="echoid-s10882" xml:space="preserve">celebratum eſt) affixum fuerat. </s> <s xml:id="echoid-s10883" xml:space="preserve">quod fieret, vt varia anni <pb o="108" file="0128" n="132" rhead="De Mundi Fabrica,"/> tempora, ſuis perpetuo menſibus reſponderent. </s> <s xml:id="echoid-s10884" xml:space="preserve">ſic æſtas ſuos menſes, ſic autumnus, & </s> <s xml:id="echoid-s10885" xml:space="preserve">reliqua anni tempora, <lb/>proprios menſes ſtatos, ac determinatos magno gentium commodo retinerent. </s> <s xml:id="echoid-s10886" xml:space="preserve">Verum ſenſim, & </s> <s xml:id="echoid-s10887" xml:space="preserve">inſenſibi-<lb/>liter, ſuccedenti tempore, ęquinoctium anticipabat, ideſt, ante 21. </s> <s xml:id="echoid-s10888" xml:space="preserve">diem Martij ſemper magis contingebat, vt <lb/>à Concilio Nicæno vſq; </s> <s xml:id="echoid-s10889" xml:space="preserve">ad Greg. </s> <s xml:id="echoid-s10890" xml:space="preserve">XIII. </s> <s xml:id="echoid-s10891" xml:space="preserve">Pont. </s> <s xml:id="echoid-s10892" xml:space="preserve">Max. </s> <s xml:id="echoid-s10893" xml:space="preserve">anticiparet per 10. </s> <s xml:id="echoid-s10894" xml:space="preserve">dies; </s> <s xml:id="echoid-s10895" xml:space="preserve">contingebat enim die Martij <lb/>vndecima: </s> <s xml:id="echoid-s10896" xml:space="preserve">ſic reliqua ſolſtitia, & </s> <s xml:id="echoid-s10897" xml:space="preserve">æquinoctia veteres ſuos dies præueniebant. </s> <s xml:id="echoid-s10898" xml:space="preserve">vnde niſi correctio adhibita <lb/>eſſet paulatim æſtas ſub menſibus hyemis; </s> <s xml:id="echoid-s10899" xml:space="preserve">& </s> <s xml:id="echoid-s10900" xml:space="preserve">hyems ſub menſibus æſtatis, magno populi incommodo, ac tem-<lb/>porum perturbatione, longo poſt tempore, traſcurriſſent. </s> <s xml:id="echoid-s10901" xml:space="preserve">Cauſa autem huius anticipationis eſt, quia annus <lb/>lulianus ciuilis, paulo maior eſt iuſto, & </s> <s xml:id="echoid-s10902" xml:space="preserve">vero anno, qui eſt Aſtronomicus; </s> <s xml:id="echoid-s10903" xml:space="preserve">vt enim dixi, ille præter dies inte-<lb/>gros conſtat 6. </s> <s xml:id="echoid-s10904" xml:space="preserve">horis; </s> <s xml:id="echoid-s10905" xml:space="preserve">hic vero horis tantum quinque cum min. </s> <s xml:id="echoid-s10906" xml:space="preserve">48′. </s> <s xml:id="echoid-s10907" xml:space="preserve">quia igitur annus ciuilis paulo maior eſt <lb/>anno naturali, & </s> <s xml:id="echoid-s10908" xml:space="preserve">vero, fit vt aliquanto prius abſoluatur annus verus, quam ciuilis, hoc eſt paulo prius æquino-<lb/>ctium contingat, quam per ciuilem annum denotatur; </s> <s xml:id="echoid-s10909" xml:space="preserve">quę anticipatio quamuis ſingulis annis exigua ſit, ſue-<lb/>cedente tamen tempore, excreſcit in diem vnum; </s> <s xml:id="echoid-s10910" xml:space="preserve">quod fit in annis circiter 134. </s> <s xml:id="echoid-s10911" xml:space="preserve">qua ratione à Concilio Nicę-<lb/>no ad noſtra tempora, ideſt, in annis ferè 1265. </s> <s xml:id="echoid-s10912" xml:space="preserve">excreuerat ad dies 10. </s> <s xml:id="echoid-s10913" xml:space="preserve">atq; </s> <s xml:id="echoid-s10914" xml:space="preserve">ad plures dies in poſterum excre-<lb/>uiſſet. </s> <s xml:id="echoid-s10915" xml:space="preserve">Quapropter Greg. </s> <s xml:id="echoid-s10916" xml:space="preserve">Pont. </s> <s xml:id="echoid-s10917" xml:space="preserve">Max. </s> <s xml:id="echoid-s10918" xml:space="preserve">Aſtronomorum conſilio anni, ſeu Calendarij correctionem ſic inſti-<lb/>t<unsure/>uit, vt æquinoctia, ac ſolſtitia ad veteres, ac priſtinas ſedes reuerterentur, eiſque perpetuo inhærerent. </s> <s xml:id="echoid-s10919" xml:space="preserve">quod <lb/>effeci t ex imendo ab anno 1582. </s> <s xml:id="echoid-s10920" xml:space="preserve">dies 10. </s> <s xml:id="echoid-s10921" xml:space="preserve">quibus fiebat anticipatio. </s> <s xml:id="echoid-s10922" xml:space="preserve">exemptio autẽ hæc facta eſt reticendo dies <lb/>10. </s> <s xml:id="echoid-s10923" xml:space="preserve">qui ſunt inter diem 5. </s> <s xml:id="echoid-s10924" xml:space="preserve">& </s> <s xml:id="echoid-s10925" xml:space="preserve">15. </s> <s xml:id="echoid-s10926" xml:space="preserve">Octobris; </s> <s xml:id="echoid-s10927" xml:space="preserve">loco enim diei 5. </s> <s xml:id="echoid-s10928" xml:space="preserve">vbiq; </s> <s xml:id="echoid-s10929" xml:space="preserve">dictum eſt die 15. </s> <s xml:id="echoid-s10930" xml:space="preserve">ſeu poſt quartam diem pro <lb/>die quinta omiſſis to. </s> <s xml:id="echoid-s10931" xml:space="preserve">diebus aſsũpta eſt ab omnibus dies 15. </s> <s xml:id="echoid-s10932" xml:space="preserve">hac enim ratione æquinoctia, & </s> <s xml:id="echoid-s10933" xml:space="preserve">ſolſtitia ſequen-<lb/>tis anni 1583. </s> <s xml:id="echoid-s10934" xml:space="preserve">ad priſtinos ſuos dies redierunt. </s> <s xml:id="echoid-s10935" xml:space="preserve">nam dies vndecima in qua perperam ſiebat æquinoctium, eua-<lb/>ſit atq; </s> <s xml:id="echoid-s10936" xml:space="preserve">appellata eſt 21. </s> <s xml:id="echoid-s10937" xml:space="preserve">& </s> <s xml:id="echoid-s10938" xml:space="preserve">ſic de reliquis.</s> <s xml:id="echoid-s10939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10940" xml:space="preserve">Annus autem 1582. </s> <s xml:id="echoid-s10941" xml:space="preserve">fuit annus correctionis, & </s> <s xml:id="echoid-s10942" xml:space="preserve">reliqui anni ſubſequentes dicitur aliquando anni Gre-<lb/>goriani.</s> <s xml:id="echoid-s10943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10944" xml:space="preserve">Vt autem Calendarium ſic correctum perpetuum ſit, neq; </s> <s xml:id="echoid-s10945" xml:space="preserve">vlla amplius eontingat temporum perturba-<lb/>tio, ſic ſtatuit, vt ſcilicet poſt annum 1600. </s> <s xml:id="echoid-s10946" xml:space="preserve">tres anni centeſimi 1700. </s> <s xml:id="echoid-s10947" xml:space="preserve">1800. </s> <s xml:id="echoid-s10948" xml:space="preserve">1900. </s> <s xml:id="echoid-s10949" xml:space="preserve">qui deberent eſſe biſſextiles, <lb/>non ſint in poſterum, annus vero 2000. </s> <s xml:id="echoid-s10950" xml:space="preserve">ſit biſſextilis. </s> <s xml:id="echoid-s10951" xml:space="preserve">hac enim ratione tres dies ſpatio 400. </s> <s xml:id="echoid-s10952" xml:space="preserve">annorum ab an-<lb/>no eximuntur. </s> <s xml:id="echoid-s10953" xml:space="preserve">nam ſingulis quibuſq; </s> <s xml:id="echoid-s10954" xml:space="preserve">annis 134. </s> <s xml:id="echoid-s10955" xml:space="preserve">vt dixi, fit error vnius diei; </s> <s xml:id="echoid-s10956" xml:space="preserve">quare in annis 400. </s> <s xml:id="echoid-s10957" xml:space="preserve">error creſci@ <lb/>ad 3. </s> <s xml:id="echoid-s10958" xml:space="preserve">dies; </s> <s xml:id="echoid-s10959" xml:space="preserve">qui omittendo intercalationem auferuntur. </s> <s xml:id="echoid-s10960" xml:space="preserve">atq; </s> <s xml:id="echoid-s10961" xml:space="preserve">hoc modo in alijs ſequentibus ſæculis, hæc tacita <lb/>correctio adhibenda eſt, eritq; </s> <s xml:id="echoid-s10962" xml:space="preserve">Calendarium ex hac parte perpetuum: </s> <s xml:id="echoid-s10963" xml:space="preserve">ſicque annis 2100. </s> <s xml:id="echoid-s10964" xml:space="preserve">2200. </s> <s xml:id="echoid-s10965" xml:space="preserve">2300. </s> <s xml:id="echoid-s10966" xml:space="preserve">non fiet <lb/>intercalatio, &</s> <s xml:id="echoid-s10967" xml:space="preserve">c.</s> <s xml:id="echoid-s10968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10969" xml:space="preserve">Vbi Lectorem monitum volo ad rectam Calendarij correctionem nihil referre, aſſnmatur ne annus æqui-<lb/>noctialis Tychonis, qui hodie communis ab Aſtronomis recepitur; </s> <s xml:id="echoid-s10970" xml:space="preserve">an vero Alfonſinus, qui a correctoribus <lb/>Calendarij aſſumptus eſt, cum horum annorum differentia ſit ferè vnius tantum horæ minuti, quæ proinde <lb/>numquam poſſit Gregorianæ correctionis officere. </s> <s xml:id="echoid-s10971" xml:space="preserve">Quinimo, cum annus tychonis ſit tantummodo noſtris <lb/>ſæculis accõ<unsure/>modatus, contra vero Alphonſinus magis perpetuus, ac proinde ad Calẽdarij correcti perpetui-<lb/>tatem aptior; </s> <s xml:id="echoid-s10972" xml:space="preserve">ſequitur apte vtroſque faceſſe, ideſt, correctores aptius annũ Alphonſinũ ſuæ correctioni, me <lb/>autem Tychonicum meæ introductioni cooptaſſe. </s> <s xml:id="echoid-s10973" xml:space="preserve">quod dixerim propter huius correctionis impugnatores, <lb/>ne videlicet exiſtiment ſe poſſe ex hac parte vllo modo huic correctioni detrahere.</s> <s xml:id="echoid-s10974" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10975" xml:space="preserve">Principium anni Iuliani, alij ſumunt a meridie vltimi diei Decembris, qui eſt pridie Calen. </s> <s xml:id="echoid-s10976" xml:space="preserve">Ian. </s> <s xml:id="echoid-s10977" xml:space="preserve">ſic Magi-<lb/>nus in ſupplemento Ephem. </s> <s xml:id="echoid-s10978" xml:space="preserve">& </s> <s xml:id="echoid-s10979" xml:space="preserve">nos in Tabulis noſtris huius ſphæræ. </s> <s xml:id="echoid-s10980" xml:space="preserve">Alij a media nocte ſequenti, ſic Tabulæ <lb/>Prutenicæ. </s> <s xml:id="echoid-s10981" xml:space="preserve">Alij a meridie Calen. </s> <s xml:id="echoid-s10982" xml:space="preserve">Ian. </s> <s xml:id="echoid-s10983" xml:space="preserve">ſic Tycho, in ſuis Tabulis.</s> <s xml:id="echoid-s10984" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10985" xml:space="preserve">De menſibus nihil dicendum occurrit.</s> <s xml:id="echoid-s10986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10987" xml:space="preserve">De diebus illud ſcitu dignum, quod quamuis dies ciuiles aſſumantur omnes lnuicem ęquales, Aſtronomi-<lb/>ci tamen, & </s> <s xml:id="echoid-s10988" xml:space="preserve">veri dies ſunt inuicem inæquales, vt infra in eap. </s> <s xml:id="echoid-s10989" xml:space="preserve">de illuminatione dicetur.</s> <s xml:id="echoid-s10990" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div227" type="section" level="1" n="146"> <head xml:id="echoid-head158" style="it" xml:space="preserve">Propoſitus Annus, an Biſſextilis ſit. Cap. X V.</head> <p> <s xml:id="echoid-s10991" xml:space="preserve">ANnus biſſextilis eſt cum numerus annorũ Chriſti oblatus, per 4. </s> <s xml:id="echoid-s10992" xml:space="preserve">diuiſus, nihil relinquit, vt hic annus 1616 <lb/>diuiſus per 4. </s> <s xml:id="echoid-s10993" xml:space="preserve">nihil relinquitur, lergo intercalaris eſt. </s> <s xml:id="echoid-s10994" xml:space="preserve">vt autem hęc diuiſio com node fiat, omitte omnes <lb/>annos milleſimos, centeſimos, ac vigeſimos, quoties potes, reliquum diuide per 4. </s> <s xml:id="echoid-s10995" xml:space="preserve">vt hoc anno, omiſſis omni-<lb/>bus milleſimis, centeſimis, relinquuntur 16. </s> <s xml:id="echoid-s10996" xml:space="preserve">qui diuiſi per 4. </s> <s xml:id="echoid-s10997" xml:space="preserve">nihil relinquunt, ergo annus eſt biſſexti. </s> <s xml:id="echoid-s10998" xml:space="preserve">quod ſi <lb/>vnus, aut duo, aut tres relinquãtur, annus etiam oblatus erit primus aut ſecundus, autt<unsure/>ertius communis poſt <lb/>biſſextum. </s> <s xml:id="echoid-s10999" xml:space="preserve">Ratio huius pendet ex eo, quod quartus quiſque Chriſti annus ſit cum biſſexto. </s> <s xml:id="echoid-s11000" xml:space="preserve">ſed meminiſſe <lb/>oportet poſt annum 1600. </s> <s xml:id="echoid-s11001" xml:space="preserve">centeſimos omnes non eſſe biſſextiles, vt olim; </s> <s xml:id="echoid-s11002" xml:space="preserve">quartus tantum, co<unsure/>nteſimus, vt ſu-<lb/>pra dictum eſt, biſſextilis erit.</s> <s xml:id="echoid-s11003" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div228" type="section" level="1" n="147"> <head xml:id="echoid-head159" style="it" xml:space="preserve">De Solis illuminatione. Cap. X V I.</head> <p> <s xml:id="echoid-s11004" xml:space="preserve">RErum omnium pulcherrima res eſt lumen Solis, atq; </s> <s xml:id="echoid-s11005" xml:space="preserve">adeo rerum omnium Deo ſimillima; </s> <s xml:id="echoid-s11006" xml:space="preserve">vnde in ſacris <lb/>literis Sol appellatur Vas admirabile opus excelſi, ac maius luminare, quod diei pręfidet. </s> <s xml:id="echoid-s11007" xml:space="preserve">a Cicerone au-<lb/>tem Princeps, & </s> <s xml:id="echoid-s11008" xml:space="preserve">auctor lnminum; </s> <s xml:id="echoid-s11009" xml:space="preserve">à Poetis tandem, oculus mundi. </s> <s xml:id="echoid-s11010" xml:space="preserve">Quamobrem in tam illuſtri lumine mi-<lb/>nimè decet nos cæcutire, ſed breuiter pro inſtituto, nonnulla in lucem proferre. </s> <s xml:id="echoid-s11011" xml:space="preserve">Primo igitur loco, in So-<lb/>lem ipſum tocius lucis fontem obtu@um intendamus, quamuis enim Aquilina oculorum acie minime præditi <lb/>f@mus, auxilio tamen Teleſcopij nuper adinuenti, inſtar Aquilarum oculos in Solem, inuito ipſius iubare, de- <pb o="109" file="0129" n="133" rhead="Liber Decimnus."/> figere non dubitabimus. </s> <s xml:id="echoid-s11012" xml:space="preserve">quod vt innoxijs oculis efficiamus, neceſſe eſt vitrum aliquod coloratum, ac ſatis <lb/>opacum priori lenti, ſeu vitro præponere; </s> <s xml:id="echoid-s11013" xml:space="preserve">hac enim ratione nimius Solis fulgor, alioquin pupillas læſurus, <lb/>retunditur. </s> <s xml:id="echoid-s11014" xml:space="preserve">obfirmato deinde atq; </s> <s xml:id="echoid-s11015" xml:space="preserve">in Solem directo Teleſcopio, ſi per ipſum intuentes ſolarem diſcum per-<lb/>ſcrutati fuerimus, mirum viſu, ac dictu, atq; </s> <s xml:id="echoid-s11016" xml:space="preserve">exactis ætatibus ignotum, ac paradoxum, faciem ipſius Solis ma-<lb/>culoſam videbimus. </s> <s xml:id="echoid-s11017" xml:space="preserve">Verum de hiſce maculis ſeorſim ex inſtituto, pluribus diſſeremus. </s> <s xml:id="echoid-s11018" xml:space="preserve">Spectabimus præ-<lb/>terea eandem Solis faciem, non codem modo, vbiq; </s> <s xml:id="echoid-s11019" xml:space="preserve">lucidam, ſed areolas quaſdam frequentes, reliquis parti-<lb/>bus lucidiores; </s> <s xml:id="echoid-s11020" xml:space="preserve">quæ Solis faculæ à nonnullis appellantur. </s> <s xml:id="echoid-s11021" xml:space="preserve">hæc de ipſo luminis fonte.</s> <s xml:id="echoid-s11022" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11023" xml:space="preserve">Nunc de luminis ab eo profuſione dicendum. </s> <s xml:id="echoid-s11024" xml:space="preserve">Obſeruãt igitur optici lumen a Sole per lineas rectas propa-<lb/>gari, quæ lineæ radij dicuntur; </s> <s xml:id="echoid-s11025" xml:space="preserve">quotidiana enim experientia videmus Solis radios per varia foramina illa-<lb/>pſos ſemper, ac ſolum recta tendere, ac propagari, numquam autem ad latera. </s> <s xml:id="echoid-s11026" xml:space="preserve">præterea conſtat à<unsure/> quolibet <lb/>Solis puncto radios quoquouerſus diffundi, videmus enim quamlibet ſolaris corporis partem, vel minimam <lb/>ad quamlibet partem omnia circumquaque colluſtrare. </s> <s xml:id="echoid-s11027" xml:space="preserve">ſic oriente Sole primus ipſius emergens limbus to-<lb/>tum@illico horizontem lumine perfundit. </s> <s xml:id="echoid-s11028" xml:space="preserve">verum quidem eſt Aſtronomos præſertim Gnomonicos, qui de <lb/>ſolaribus Horologijs tractant, ſolere præcipuam habere rationem centralium radiorum, eorum videlicet, <lb/>qui à Sole ita emicant, ac ſi à centro ipſius effunderentur; </s> <s xml:id="echoid-s11029" xml:space="preserve">hi enim cæteris validiores ac fortiores ſe produnt.</s> <s xml:id="echoid-s11030" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11031" xml:space="preserve">Quod autem, vt ait Cic. </s> <s xml:id="echoid-s11032" xml:space="preserve">Sol ſit princeps, & </s> <s xml:id="echoid-s11033" xml:space="preserve">auctor luminum, a quo ſcilicet reliqua ſydera, & </s> <s xml:id="echoid-s11034" xml:space="preserve">elementa per <lb/>ſeſe lumina caſſa, & </s> <s xml:id="echoid-s11035" xml:space="preserve">obſcura, lumine perfundantur, ſic patere poteſt. </s> <s xml:id="echoid-s11036" xml:space="preserve">Primo quia certũ eſt Lunam, vti oſten-<lb/>dimus ſolari luce ſplendeſcere. </s> <s xml:id="echoid-s11037" xml:space="preserve">Secundo in Venerem idem palam faciemus, cum ipſa non ſecus, ae Luna, cir-<lb/>@a Solem recurrens, corniculata, dimidiata, & </s> <s xml:id="echoid-s11038" xml:space="preserve">plena, per Teleſcopium ſpectetur. </s> <s xml:id="echoid-s11039" xml:space="preserve">Tertio, tandem ex Iouis <lb/>aſtro, quod vt ſuo loco oſtendemus, vmbram a Sole auerſam proijcit. </s> <s xml:id="echoid-s11040" xml:space="preserve">ex quibus inferre licet reliquas quo<unsure/>que <lb/>ſtellas eodem modo lumen a Sole mutuare. </s> <s xml:id="echoid-s11041" xml:space="preserve">quod tandem elementa, reliquaque opaciora corpora indidem. <lb/></s> <s xml:id="echoid-s11042" xml:space="preserve">colluſtrentur, ipſorum vmbræ teſtimonio ſunt, cum videamus ea omnia ſolarem vmbram emitterre. </s> <s xml:id="echoid-s11043" xml:space="preserve">Terra <lb/>in primis vti oſtenſum eſt, vmbram efficit, quæ circa ipſam circumlata diei, ac noctis viciſſitudinem vbique <lb/>terrarum efficit: </s> <s xml:id="echoid-s11044" xml:space="preserve">nihil enim aliud nox eſt, quam vmbra terræ.</s> <s xml:id="echoid-s11045" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11046" xml:space="preserve">Sol igitur terram in orbem colluſtrans dierum, ac noctium, item crepuſculorum diſcrimina efficit. </s> <s xml:id="echoid-s11047" xml:space="preserve">vna ip-<lb/>ſius integra gyratio dies naturalis eſt, mora vero ipſius ſupra horizontem, dies artificialis; </s> <s xml:id="echoid-s11048" xml:space="preserve">ſicuti latebra eius <lb/>infra horizontem, nox artificialis eſt. </s> <s xml:id="echoid-s11049" xml:space="preserve">Lux autem illa crepera, ſiue inter diem ac noctem dubia, crepuſculum <lb/>appellatur: </s> <s xml:id="echoid-s11050" xml:space="preserve">vulgus tamen crepuſculum vtrumq; </s> <s xml:id="echoid-s11051" xml:space="preserve">matutinum, ac veſpertinum, in diem computat. </s> <s xml:id="echoid-s11052" xml:space="preserve">Sequitur <lb/>nunc vt de quantitate dierum naturalium, ac artificialium, necnon crepuſculorum diſſeramus.</s> <s xml:id="echoid-s11053" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div229" type="section" level="1" n="148"> <head xml:id="echoid-head160" style="it" xml:space="preserve">Quantitas dierum natur alium. Cap. X I V.</head> <p> <s xml:id="echoid-s11054" xml:space="preserve">SCiendum igitur primo illud quod vulgo paradoxum putatur, dies ſcilicet naturales non omnes eſſe inui-<lb/>cem æquales, ideſt, tempus quod eſt ab vno meridie ad alterum meridiem, non eſſe æquale cuilibet alteri <lb/>tempori, a meridie in meridiem intercepto; </s> <s xml:id="echoid-s11055" xml:space="preserve">quamuis eorum differentia ſit adeo parua, vt inſenſibilis euadat. <lb/></s> <s xml:id="echoid-s11056" xml:space="preserve">quoniam vero Aſtronomi vtuntur diebus tanquam motuum menſuris; </s> <s xml:id="echoid-s11057" xml:space="preserve">menſurę autem æquales eſſe oportet, <lb/>hinc factum eſt, vt ipſi aſſumant omnes dies tanquam æquales, ſeu mediocres, ortaq; </s> <s xml:id="echoid-s11058" xml:space="preserve">hinc ſint duo genera die-<lb/>rum, æqualium ſcilicet, & </s> <s xml:id="echoid-s11059" xml:space="preserve">inæqualium, ſeu differentium. </s> <s xml:id="echoid-s11060" xml:space="preserve">Dies autem naturalis mediocris ſeu æqualis, eſt in-<lb/>tegra æquatoris reuolutio, & </s> <s xml:id="echoid-s11061" xml:space="preserve">præterea 59′.</s> <s xml:id="echoid-s11062" xml:space="preserve">8″. </s> <s xml:id="echoid-s11063" xml:space="preserve">quotidie enim totus æquator, cum aliqua parte ipſius reuolui-<lb/>tur, quæ reſpondet illi parti Zodiaci, quam Sol ſingulis diebus percurrit. </s> <s xml:id="echoid-s11064" xml:space="preserve">quæ pars Zodiaci diaria, non ſem-<lb/>per eſt ſibi æqualis; </s> <s xml:id="echoid-s11065" xml:space="preserve">& </s> <s xml:id="echoid-s11066" xml:space="preserve">conſequenter neq; </s> <s xml:id="echoid-s11067" xml:space="preserve">partes æquatoris illi correſpondentes; </s> <s xml:id="echoid-s11068" xml:space="preserve">ſed aliquando ſunt maiores, <lb/>aliquando minores quam 59′. </s> <s xml:id="echoid-s11069" xml:space="preserve">& </s> <s xml:id="echoid-s11070" xml:space="preserve">8″. </s> <s xml:id="echoid-s11071" xml:space="preserve">ita vt 59′.</s> <s xml:id="echoid-s11072" xml:space="preserve">8″. </s> <s xml:id="echoid-s11073" xml:space="preserve">medium ſit inter vtrum que exeſſum. </s> <s xml:id="echoid-s11074" xml:space="preserve">hanc autem æqua-<lb/>litatem ſic reperiunt; </s> <s xml:id="echoid-s11075" xml:space="preserve">quoniam ſingulis diebus totus æquator cum additamento illo reuoluitur, fit vt in anno <lb/>vno omnia illa additamenta totum æquatorem inſumant, quare diuidunt totum æquatorem, ſeu aggregatũ <lb/>ex illis additamentis, in tot partes æquales, quot dies in anno continentur, quarũ quælibet continet ferè 59′. </s> <s xml:id="echoid-s11076" xml:space="preserve"><lb/>8″. </s> <s xml:id="echoid-s11077" xml:space="preserve">& </s> <s xml:id="echoid-s11078" xml:space="preserve">ſingulas ſingulis æquatoris reuolutionibus adijciunt, atq; </s> <s xml:id="echoid-s11079" xml:space="preserve">ita conſtituunt dies mediocres, quibus in Ta-<lb/>bulis Aſtronomicis, & </s> <s xml:id="echoid-s11080" xml:space="preserve">in calculis vtuntur. </s> <s xml:id="echoid-s11081" xml:space="preserve">propterea ſolent tempus oblatum ſeu dies oblatos vulgares, ſeu ci-<lb/>uiles, qui differentes ſunt, ad quos motus cæleſtes calculare volunt, prius ad æqualitatem reuocare, ſeu in dies <lb/>æquales conuertere; </s> <s xml:id="echoid-s11082" xml:space="preserve">cuius rei gratia compoſuerunt Tabulam æquationis dierum; </s> <s xml:id="echoid-s11083" xml:space="preserve">quam nos breuitatis cauſa <lb/>omittimus; </s> <s xml:id="echoid-s11084" xml:space="preserve">præſertim cum res hæc aliquid diſcriminis lunari tantum calculo ingerat; </s> <s xml:id="echoid-s11085" xml:space="preserve">dies enim vnus diffe-<lb/>rens, ab vno die æquali inſenſibiliter differt; </s> <s xml:id="echoid-s11086" xml:space="preserve">quamuis omnes dies differẽtes maiores, aut minores æqualibus, <lb/>comparati cum æqualibus eos ſuperent paulo pluſquam dimidia hora oritur autem inæqualitas dierum, pri-<lb/>mo ex Solis circulo eccentrico, eo enim poſito, vt vidimus ſequitur Solem in vna Zodiaci parte tardius mo-<lb/>meri, quam in altera, & </s> <s xml:id="echoid-s11087" xml:space="preserve">conſequenter minus quotidie de Zodiaco, motu proprio, conficere, quam in altera <lb/>parte, quare etiam partes æquatoris illis reſpondentes eſſe minores, & </s> <s xml:id="echoid-s11088" xml:space="preserve">conſequenter ibi facere dies minores; </s> <s xml:id="echoid-s11089" xml:space="preserve"><lb/>hic autem maiores æqualibus: </s> <s xml:id="echoid-s11090" xml:space="preserve">bis tamen in anno cum æqualibus congruunt. </s> <s xml:id="echoid-s11091" xml:space="preserve">quod accidit cum fit tranſitus a <lb/>minoribus ad maiores; </s> <s xml:id="echoid-s11092" xml:space="preserve">& </s> <s xml:id="echoid-s11093" xml:space="preserve">è contra. </s> <s xml:id="echoid-s11094" xml:space="preserve">ſecunda cauſa eſt, quia partibus Zodiaci etiam æqualibus, non reſpondent <lb/>partes æquatoris æquales in motu diurno; </s> <s xml:id="echoid-s11095" xml:space="preserve">ſicuti in Aſcenſionibus explicabitur: </s> <s xml:id="echoid-s11096" xml:space="preserve">cum autem illæ partes æqua-<lb/>toris concurrant ad complendos dies, erunt neceſſario dies inæquales. </s> <s xml:id="echoid-s11097" xml:space="preserve">eadem inæqualitas etiam in horas ne-<lb/>ceſſario transfunditur. </s> <s xml:id="echoid-s11098" xml:space="preserve">Hæc de diebus naturalibus.</s> <s xml:id="echoid-s11099" xml:space="preserve"/> </p> <pb o="110" file="0130" n="134" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div230" type="section" level="1" n="149"> <head xml:id="echoid-head161" style="it" xml:space="preserve">Quantitas dierum artificialium. Cap. XV.</head> <p> <s xml:id="echoid-s11100" xml:space="preserve">PRimo conſiderandum eſt cur dies artificiales varij ſint in varijs terræ locis; </s> <s xml:id="echoid-s11101" xml:space="preserve">ſub æquatore enim vbi nihil <lb/>eleuatur polus perpetuum eſt æquinoctium; </s> <s xml:id="echoid-s11102" xml:space="preserve">in alijs vero locis vbi polus eleuatur magnam ſubeunt va-<lb/>rietatem, tum ſi inuicem comparentur dies eiuſdem eleuationis, tum etiam ſi cum diebus alterius eleuationis <lb/>conferantur. </s> <s xml:id="echoid-s11103" xml:space="preserve">in eadem enim eleuatione boreali dies lõgiſſimus eſt in tropico Cancri, poſtea decreſcunt vſq; <lb/></s> <s xml:id="echoid-s11104" xml:space="preserve">ad tropicum Capricorni, vbi nox lõgiſſima efficitur; </s> <s xml:id="echoid-s11105" xml:space="preserve">vt vulgo notum eſt. </s> <s xml:id="echoid-s11106" xml:space="preserve">in diuerſis autem eleuationibus hic <lb/>ordo ſeruatur, vt quanto maior eſt eleuatio poli. </s> <s xml:id="echoid-s11107" xml:space="preserve">tanto maior ſit dies longiſſima æſtiualis; </s> <s xml:id="echoid-s11108" xml:space="preserve">tantoq; </s> <s xml:id="echoid-s11109" xml:space="preserve">minor nox. </s> <s xml:id="echoid-s11110" xml:space="preserve"><lb/>hyemalis verò maxima. </s> <s xml:id="echoid-s11111" xml:space="preserve">cur autem hæc contingant, vt intelligas, conſiderandum eſt, Solem dum ab vno tro-<lb/>pico ad alterum accedit, deſcribere motu diurno circulos ferè 182. </s> <s xml:id="echoid-s11112" xml:space="preserve">inuicem paralellos: </s> <s xml:id="echoid-s11113" xml:space="preserve">quotidie videlices <lb/>vnum, quamuis reuera Sol non circulos, ſed ſpiras efficiat, vt alias diximus: </s> <s xml:id="echoid-s11114" xml:space="preserve">attamen ſine vllo errore, imò fa-<lb/>cilioris intelligentiæ cauſa, conſiderantur vt circuli. </s> <s xml:id="echoid-s11115" xml:space="preserve">hi igitur dicuntur circuli dierum naturalium, arcus ve-<lb/>ro ſiue portiones ipſorum ſupra horizontem extantes dicuntur arcus diurni dierum artificialium; </s> <s xml:id="echoid-s11116" xml:space="preserve">qui vero <lb/>infra horizontem arcus nocturni noctium artificialium. </s> <s xml:id="echoid-s11117" xml:space="preserve">in ſphæra autem materiali tres tantum horum cir-<lb/>culorum, ad vitandam confuſionem, ponuntur: </s> <s xml:id="echoid-s11118" xml:space="preserve">duo videlicet tropici, & </s> <s xml:id="echoid-s11119" xml:space="preserve">æquator. </s> <s xml:id="echoid-s11120" xml:space="preserve">cum igitur Sol motu diur-<lb/>no vniformiter moueatur, ſequitur vbi arcus diurni fuerint æquales nocturnis, dies noctibus pariter adæqua-<lb/>ri. </s> <s xml:id="echoid-s11121" xml:space="preserve">vbi vero maiores, vel minores fuerint, maiores pariter, ac minores fore dies noctibus. </s> <s xml:id="echoid-s11122" xml:space="preserve">Hinc ſequitur in <lb/>ſphæra recta perpetuum eſſe æquinoctium, quod ex materiali ſphæra ita conſtituta, vt poli mundi ſint in ho-<lb/>rizonte (quæ eſt ſphæræ rectæ conſtitutio) facile intelligi poteſt. </s> <s xml:id="echoid-s11123" xml:space="preserve">ex tali enim cõſtitutione apparet vtrum-<lb/>que tropicum, æquatorem, ac proinde reliquos omnes Solis paralellos ibi conceptos, bifariam ab horizonte <lb/>diuidi, ac propterea arcus diurnos, ac nocturnos eſſe æquales. </s> <s xml:id="echoid-s11124" xml:space="preserve">in ſphæris vero obliquis vſq; </s> <s xml:id="echoid-s11125" xml:space="preserve">ad poli eleuatio-<lb/>nem gr. </s> <s xml:id="echoid-s11126" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s11127" xml:space="preserve">quoniã horizon ſecat omnes paralellos, excepto æquatore, inæqualiter, ita vt omnes arcus diur-<lb/>ni, qui ſunt ab æquatore ad polum eleuatum, maiores ſint nocturnis: </s> <s xml:id="echoid-s11128" xml:space="preserve">reliqui vero ad polum occultum vltra <lb/>æquatorem, ſint minores nocturnis (quod in materiali ſphæra obliquè conſtituta apparebit) ſequitur maio-<lb/>res eſſe dies verſus polum eleuatum quam verſus depreſſum. </s> <s xml:id="echoid-s11129" xml:space="preserve">quorum cauſa eſt polorum infra aut ſupra ho-<lb/>rizontem eleuatio, ac depreſſio. </s> <s xml:id="echoid-s11130" xml:space="preserve">hinc ſequitur in noſtra ſphæra, cui boreus polus eleuatur, dies æſtiuos hyber-<lb/>nis maiores eſſe; </s> <s xml:id="echoid-s11131" xml:space="preserve">atq; </s> <s xml:id="echoid-s11132" xml:space="preserve">inter æſtiuos, eos cæteris maiores eſſe, qui tropico Cancri, vbi dies fit maximus, propio-<lb/>res fuerint. </s> <s xml:id="echoid-s11133" xml:space="preserve">cuius contrarium accidit in parte auſtrali. </s> <s xml:id="echoid-s11134" xml:space="preserve">notandum etiam arcus diurnos boreales eſſe æquales <lb/>arcubus nocturnis auſtralibus; </s> <s xml:id="echoid-s11135" xml:space="preserve">& </s> <s xml:id="echoid-s11136" xml:space="preserve">è contra. </s> <s xml:id="echoid-s11137" xml:space="preserve">lam vero vbi polus eleuatur præcisè gr. </s> <s xml:id="echoid-s11138" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s11139" xml:space="preserve">ac propterea tropi-<lb/>cus vnus totus ſupra horizontem emergit: </s> <s xml:id="echoid-s11140" xml:space="preserve">alter vero totus deprimitur, ita tamen vt horizontẽ in vnico pun-<lb/>cto tangant, ſequetur tam diem, quam noctem maximam conſtare hor. </s> <s xml:id="echoid-s11141" xml:space="preserve">24. </s> <s xml:id="echoid-s11142" xml:space="preserve">percurrente videlicet Sole tropi-<lb/>cos. </s> <s xml:id="echoid-s11143" xml:space="preserve">In eleuatiori vero ſphæra, quam gr. </s> <s xml:id="echoid-s11144" xml:space="preserve">66 {1/2} tam dies quam noctes conſtabunt hor. </s> <s xml:id="echoid-s11145" xml:space="preserve">pluſquam 24. </s> <s xml:id="echoid-s11146" xml:space="preserve">Demum <lb/>in ſphæra paralella, ſiue præcisè ſub polo, e@ it tam dies, quam nox, ſex menſium. </s> <s xml:id="echoid-s11147" xml:space="preserve">Porrò & </s> <s xml:id="echoid-s11148" xml:space="preserve">hoc non præter-<lb/>eundum, quod eodem tempore æquinoctium fit omnibus habitatoribus vbique terrarum; </s> <s xml:id="echoid-s11149" xml:space="preserve">quoniam in omni <lb/>ſphæræ conſtitutione excepta paralella, æquator ſecatur bifariam ab horizonte, vnde ai<unsure/>cus ipſius diurnus <lb/>æqualis ſemper eſt nocturno. </s> <s xml:id="echoid-s11150" xml:space="preserve">Extremo in ſphęra obliqua bini dies artificiales ab alterutro ſolſtitiorum æquè <lb/>remoti æquales ſunt. </s> <s xml:id="echoid-s11151" xml:space="preserve">quæ omnia inſpecta materiali ſphæra, eaq; </s> <s xml:id="echoid-s11152" xml:space="preserve">varijs habitatoribus accommodata, perſpi-<lb/>cua fiunt.</s> <s xml:id="echoid-s11153" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11154" xml:space="preserve">Reliquum eſt docere qua ratione inueſtigetur quãtitas diei, ac noctis artificialis in quauis poli eleuatione-<lb/>Primo igitur ex materiali ſphæra accurate cõſtructa, quales eſſe ſolent æneæ, ſic; </s> <s xml:id="echoid-s11155" xml:space="preserve">vbi eleuatio poli non tran-<lb/>ſcendit gr. </s> <s xml:id="echoid-s11156" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s11157" xml:space="preserve">ſiue vbi horizon ſecat omnes Solis paralellos, hanc quantitatem reperies. </s> <s xml:id="echoid-s11158" xml:space="preserve">Eleuato ſupra ho-<lb/>rizontem polo iuxta loci exigentiam, pone gradum Zodiaci quem Sol occupat, eo die, cuius quantitatem <lb/>quæris in horizonte orientali. </s> <s xml:id="echoid-s11159" xml:space="preserve">quo ibi manente nota illum æquatoris gradum, qui pariter orientalem hori-<lb/>zontem tangit; </s> <s xml:id="echoid-s11160" xml:space="preserve">poſtea primum mobile motu diurno reuolue, donec grad. </s> <s xml:id="echoid-s11161" xml:space="preserve">ille Solis ad occiduum horizontem <lb/>perueniat; </s> <s xml:id="echoid-s11162" xml:space="preserve">tandem numera gradus æquatoris ab illa nota ſupra horizontem exortos, nam ſingulæ graduum <lb/>quindenæ ſingulas horas effici<unsure/>unt. </s> <s xml:id="echoid-s11163" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s11164" xml:space="preserve">ſemiſſes, & </s> <s xml:id="echoid-s11165" xml:space="preserve">quadrantes horarũ facile dignoſces. </s> <s xml:id="echoid-s11166" xml:space="preserve">idem circa quan-<lb/>titatem noctium obſeruandum eſt. </s> <s xml:id="echoid-s11167" xml:space="preserve">ſit exempli gr. </s> <s xml:id="echoid-s11168" xml:space="preserve">in noſtra poli eleuatione gr. </s> <s xml:id="echoid-s11169" xml:space="preserve">45. </s> <s xml:id="echoid-s11170" xml:space="preserve">inueſtiganda qnantitas diei <lb/>maximi, quando ſcilicet Sol eſt in primo gra. </s> <s xml:id="echoid-s11171" xml:space="preserve">Cancri, ad diem 22. </s> <s xml:id="echoid-s11172" xml:space="preserve">Iunij. </s> <s xml:id="echoid-s11173" xml:space="preserve">pono igitur primum Cancri gradum <lb/>in horizonte ortiuo, notoq; </s> <s xml:id="echoid-s11174" xml:space="preserve">ſimul æquatoris punctum ſimul cooriens; </s> <s xml:id="echoid-s11175" xml:space="preserve">poſtea ſphæræ primum mobile iuxta <lb/>diurnam conuerſionem conuerto, donec idem primus gradus Cancri horizontem occiduum attingat; </s> <s xml:id="echoid-s11176" xml:space="preserve">de-<lb/>mum manente ſic ſphæra numero grad. </s> <s xml:id="echoid-s11177" xml:space="preserve">omnes æquatoris in hac motione exortos, interceptos ſcilicet inter <lb/>notam in æquatore factam, & </s> <s xml:id="echoid-s11178" xml:space="preserve">horizontẽ orientalem. </s> <s xml:id="echoid-s11179" xml:space="preserve">reperioq; </s> <s xml:id="echoid-s11180" xml:space="preserve">gradus f rè 232 {1/2}. </s> <s xml:id="echoid-s11181" xml:space="preserve">quos diuido per 15. </s> <s xml:id="echoid-s11182" xml:space="preserve">& </s> <s xml:id="echoid-s11183" xml:space="preserve">pro-<lb/>uenit quotiens pariter 15. </s> <s xml:id="echoid-s11184" xml:space="preserve">reſiduiq; </s> <s xml:id="echoid-s11185" xml:space="preserve">ſunt gr. </s> <s xml:id="echoid-s11186" xml:space="preserve">ferè 7 {1/2}. </s> <s xml:id="echoid-s11187" xml:space="preserve">quare pronuncio diem hunc maximam conſtare ex horis <lb/>15 {1/2}. </s> <s xml:id="echoid-s11188" xml:space="preserve">quia quotiens eſt 15. </s> <s xml:id="echoid-s11189" xml:space="preserve">quæ efficiunt hor. </s> <s xml:id="echoid-s11190" xml:space="preserve">15. </s> <s xml:id="echoid-s11191" xml:space="preserve">& </s> <s xml:id="echoid-s11192" xml:space="preserve">ſuperſunt gr. </s> <s xml:id="echoid-s11193" xml:space="preserve">7 {1/2}. </s> <s xml:id="echoid-s11194" xml:space="preserve">qui dimidiam dant hor. </s> <s xml:id="echoid-s11195" xml:space="preserve">vel ex Tabula con-<lb/>uerſionis graduum, &</s> <s xml:id="echoid-s11196" xml:space="preserve">c. </s> <s xml:id="echoid-s11197" xml:space="preserve">æquatoris in horas, &</s> <s xml:id="echoid-s11198" xml:space="preserve">c. </s> <s xml:id="echoid-s11199" xml:space="preserve">reperio primo è regione gr. </s> <s xml:id="echoid-s11200" xml:space="preserve">230. </s> <s xml:id="echoid-s11201" xml:space="preserve">hor. </s> <s xml:id="echoid-s11202" xml:space="preserve">15. </s> <s xml:id="echoid-s11203" xml:space="preserve">min. </s> <s xml:id="echoid-s11204" xml:space="preserve">20′. </s> <s xml:id="echoid-s11205" xml:space="preserve">deinde è re-<lb/>gione gr. </s> <s xml:id="echoid-s11206" xml:space="preserve">2. </s> <s xml:id="echoid-s11207" xml:space="preserve">reperio hor.</s> <s xml:id="echoid-s11208" xml:space="preserve">0<unsure/>@3′. </s> <s xml:id="echoid-s11209" xml:space="preserve">Tandem è regione gr. </s> <s xml:id="echoid-s11210" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s11211" xml:space="preserve">ideſt, 30. </s> <s xml:id="echoid-s11212" xml:space="preserve">min. </s> <s xml:id="echoid-s11213" xml:space="preserve">reperio c--;</s> <s xml:id="echoid-s11214" xml:space="preserve">2′. </s> <s xml:id="echoid-s11215" xml:space="preserve">Quorum ſumma efficiunt <lb/>h. </s> <s xml:id="echoid-s11216" xml:space="preserve">15 30′. </s> <s xml:id="echoid-s11217" xml:space="preserve">ſiue h. </s> <s xml:id="echoid-s11218" xml:space="preserve">15 {1/2}. </s> <s xml:id="echoid-s11219" xml:space="preserve">vt prius.</s> <s xml:id="echoid-s11220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11221" xml:space="preserve">Vbi vero polus eleuatur gr. </s> <s xml:id="echoid-s11222" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s11223" xml:space="preserve">vbi ſcilicet tropicus vnus tangit horizontem, totuſq; </s> <s xml:id="echoid-s11224" xml:space="preserve">ſupra eum emergit; <lb/></s> <s xml:id="echoid-s11225" xml:space="preserve">alter è contrario tangens horizontem totus deprimitur, in tali inquam habitatione dies maximus, & </s> <s xml:id="echoid-s11226" xml:space="preserve">nox ma-<lb/>xima erunt 24. </s> <s xml:id="echoid-s11227" xml:space="preserve">horarum. </s> <s xml:id="echoid-s11228" xml:space="preserve">In maiore poſtea<unsure/> e<unsure/>le<unsure/>uatione vbi tropici non tangunt horizontem, dies maiores <lb/>ſunt hor. </s> <s xml:id="echoid-s11229" xml:space="preserve">24. </s> <s xml:id="echoid-s11230" xml:space="preserve">& </s> <s xml:id="echoid-s11231" xml:space="preserve">alicubi continent etiam menſes totos; </s> <s xml:id="echoid-s11232" xml:space="preserve">vt igitur ibi quantitas horum dierum continuorum re-<lb/>periatur ex ſphæra materiali, eleuato polo ad datam altitudinem, oportet diligenter notare arcum eclypti- <pb o="111" file="0131" n="135" rhead="Liber Decimus."/> cæ, qui numquam occidit, quot enim gr. </s> <s xml:id="echoid-s11233" xml:space="preserve">ille arcus continebit, tot ferè dies naturales continebit dies ille con-<lb/>tinuus. </s> <s xml:id="echoid-s11234" xml:space="preserve">idem intellige proportionaliter de nocte continua. </s> <s xml:id="echoid-s11235" xml:space="preserve">Sicigitur quantitates omnium dierum poſſunt <lb/>inueniri. </s> <s xml:id="echoid-s11236" xml:space="preserve">& </s> <s xml:id="echoid-s11237" xml:space="preserve">quoniam dies omnes ſemicirculo Zodiaci deſcendentis, ideſt, à Cancro ad Capricornum, ſunt <lb/>æquales ſingulis diebus alterius ſemicirculi aſcendentis a Capricorno ad Cancrum; </s> <s xml:id="echoid-s11238" xml:space="preserve">ideo ſatis eſt vnius tan-<lb/>tum ſemicirculi quantitates explorare. </s> <s xml:id="echoid-s11239" xml:space="preserve">vnde & </s> <s xml:id="echoid-s11240" xml:space="preserve">Tabulæ quantitatis dierum conſtrui poſſunt. </s> <s xml:id="echoid-s11241" xml:space="preserve">Verum infra ali-<lb/>ter hanc quantitatum ſimul cum quantitate crepuſculi explorabimus.</s> <s xml:id="echoid-s11242" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div231" type="section" level="1" n="150"> <head xml:id="echoid-head162" style="it" xml:space="preserve">De crepuſculorum quantitate. Cap. XVI.</head> <p> <s xml:id="echoid-s11243" xml:space="preserve">SVpra in tractatu de aere dictum eſt, quid ſit crepuſculum, & </s> <s xml:id="echoid-s11244" xml:space="preserve">quomodo fiat. </s> <s xml:id="echoid-s11245" xml:space="preserve">quod vero ad eius quãtitatem, <lb/>ſciendum eſt eam eſſe variam, non ſolum in eodem loco, ſed etiam in diuerſis poli eleuationibus. </s> <s xml:id="echoid-s11246" xml:space="preserve">neq; </s> <s xml:id="echoid-s11247" xml:space="preserve">va-<lb/>riatur ſecundum dierum varietatem, ſed peculiari modo, in æſtate enim quando dies ſunt longiſſimi, longiſ-<lb/>ſima pariter ſunt crepu<unsure/>ſcula; </s> <s xml:id="echoid-s11248" xml:space="preserve">at vero in ſumma hyeme cum breuiſſimi dies ſunt, non itidem breuiſſima ſunt <lb/>crepuſcula, quam<unsure/>uis breuiora fiant, quam in æſtate. </s> <s xml:id="echoid-s11249" xml:space="preserve">breuiſſima tandem (quod mirum videtur) circum dimi-<lb/>diam Libiã, ac dimidios Piſces contingunt; </s> <s xml:id="echoid-s11250" xml:space="preserve">etiam ſi dies tunc non ſint breuiſſimi. </s> <s xml:id="echoid-s11251" xml:space="preserve">quare crepuſculorum quan-<lb/>titas non ſequetur dierum quantitatem, dies enim decreſcunt à Cancro ad Capricornum, crepuſcula vero à <lb/>Cancro ad dimidium ferè Libræ. </s> <s xml:id="echoid-s11252" xml:space="preserve">vnde iterum vſq; </s> <s xml:id="echoid-s11253" xml:space="preserve">ad Capricornum augentur. </s> <s xml:id="echoid-s11254" xml:space="preserve">idem fit in altero Zodiaci ſe-<lb/>micirculo aſcendente à Capricorno ad Cancrum. </s> <s xml:id="echoid-s11255" xml:space="preserve">Porro crepuſculum duplex eſt, matutinum, & </s> <s xml:id="echoid-s11256" xml:space="preserve">veſperti-<lb/>num. </s> <s xml:id="echoid-s11257" xml:space="preserve">quorum quantitas indagari poterit ex ſphæra materiali, cui additus ſit circulus crepuſculinus; </s> <s xml:id="echoid-s11258" xml:space="preserve">de <lb/>quo lib. </s> <s xml:id="echoid-s11259" xml:space="preserve">1. </s> <s xml:id="echoid-s11260" xml:space="preserve">cap. </s> <s xml:id="echoid-s11261" xml:space="preserve">11. </s> <s xml:id="echoid-s11262" xml:space="preserve">dictum eſt, eum infra horizontem deprimi gr. </s> <s xml:id="echoid-s11263" xml:space="preserve">18. </s> <s xml:id="echoid-s11264" xml:space="preserve">eique æquidiſtare. </s> <s xml:id="echoid-s11265" xml:space="preserve">poſito enim Solis <lb/>gradu diei propoſito in circulo crepuſculino, ſiue orientali, ſiue occidentali, numerentur æquatoris gradus, <lb/>qui aſcendunt ſupra horizontem, dum Sol a circulo crepuſculi ad horizontem aſcendit. </s> <s xml:id="echoid-s11266" xml:space="preserve">ij enim dabunt ho-<lb/>ras, necnon ſemiſſes, & </s> <s xml:id="echoid-s11267" xml:space="preserve">quadrantes earum, quibus duratio, ſeu quantitas crepuſculi computatur, eo videlicet <lb/>modo quo antea dierum quantitatem computare docuimus, v.</s> <s xml:id="echoid-s11268" xml:space="preserve">g. </s> <s xml:id="echoid-s11269" xml:space="preserve">in eleuatione poli gr. </s> <s xml:id="echoid-s11270" xml:space="preserve">45. </s> <s xml:id="echoid-s11271" xml:space="preserve">Sole in primo gra-<lb/>du Cancri exiſtente, pono hunc grad. </s> <s xml:id="echoid-s11272" xml:space="preserve">in circulo crepuſculi, eumq; </s> <s xml:id="echoid-s11273" xml:space="preserve">vſque ad horizontem promoueo, nume-<lb/>roq; </s> <s xml:id="echoid-s11274" xml:space="preserve">grad. </s> <s xml:id="echoid-s11275" xml:space="preserve">æquatoris interim ſupra horizontem emergentes, ideſt, quia aſcendunt ſupra horizontem, dum <lb/>Sol a circulo crepuſculi ad horizontẽ aſcendit; </s> <s xml:id="echoid-s11276" xml:space="preserve">quos reperio eſſe ferè gr. </s> <s xml:id="echoid-s11277" xml:space="preserve">40. </s> <s xml:id="echoid-s11278" xml:space="preserve">eos diuido per 15. </s> <s xml:id="echoid-s11279" xml:space="preserve">prouenit quo-<lb/>tiens 2. </s> <s xml:id="echoid-s11280" xml:space="preserve">& </s> <s xml:id="echoid-s11281" xml:space="preserve">remanent 10. </s> <s xml:id="echoid-s11282" xml:space="preserve">gradus, ex quibus infero crepuſculum illius diei, in ea eleuatione, durare hor. </s> <s xml:id="echoid-s11283" xml:space="preserve">duas, cũ <lb/>duabus tertijs horarum, gradus enim 10. </s> <s xml:id="echoid-s11284" xml:space="preserve">in motu diurno efficiunt {2/3}. </s> <s xml:id="echoid-s11285" xml:space="preserve">horæ, vel ſic, quotiens eſt 2 {10/15}. </s> <s xml:id="echoid-s11286" xml:space="preserve">ſiue 2 {2/3}. </s> <s xml:id="echoid-s11287" xml:space="preserve">er-<lb/>go crepuſculi quantitas eſt horarum 2 {2/3}. </s> <s xml:id="echoid-s11288" xml:space="preserve">vel ſic, ex Tabula conuerſionis grad. </s> <s xml:id="echoid-s11289" xml:space="preserve">æquatoris in horas, &</s> <s xml:id="echoid-s11290" xml:space="preserve">c. </s> <s xml:id="echoid-s11291" xml:space="preserve">quam <lb/>in cap. </s> <s xml:id="echoid-s11292" xml:space="preserve">de æquatore dedimus, è regione grad. </s> <s xml:id="echoid-s11293" xml:space="preserve">40. </s> <s xml:id="echoid-s11294" xml:space="preserve">reperio horas 2. </s> <s xml:id="echoid-s11295" xml:space="preserve">cum 40′. </s> <s xml:id="echoid-s11296" xml:space="preserve">min. </s> <s xml:id="echoid-s11297" xml:space="preserve">minuta autem 40. </s> <s xml:id="echoid-s11298" xml:space="preserve">efficiunt <lb/>{2/3}. </s> <s xml:id="echoid-s11299" xml:space="preserve">horæ.</s> <s xml:id="echoid-s11300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11301" xml:space="preserve">Porrò hi gradus æquatoris coaſcendentes, ideo crepuſculi magnitudinem oſtendunt, quia ij ſimul cum <lb/>gr. </s> <s xml:id="echoid-s11302" xml:space="preserve">Solis oriuntur, & </s> <s xml:id="echoid-s11303" xml:space="preserve">occidunt, dum Sol crepuſculum tam matutinum quam veſpertinum, quę æqualia ſunt, <lb/>abſoluit.</s> <s xml:id="echoid-s11304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11305" xml:space="preserve">Nunc vero conſiderandum eſt varias reperiri crepuſculorum differentias, nam vbi paralellus Solis ſecat <lb/>& </s> <s xml:id="echoid-s11306" xml:space="preserve">horizontem, & </s> <s xml:id="echoid-s11307" xml:space="preserve">crepuſculinum, @bi fit crepuſculum, ſed nõ per totam noctem, vt in allato exemplo patuit, <lb/>vbi vero Solis paralellus ſecat tantum horizontem non autem crepuſculinum, ibi fit crepuſculum per totam <lb/>noctem. </s> <s xml:id="echoid-s11308" xml:space="preserve">Tertio vbi paralellus Solis neutrum ſecat ibi nullum accidit crepuſculũ ſed vel dies puros, vel nox <lb/>pura. </s> <s xml:id="echoid-s11309" xml:space="preserve">quod manifeſtè patebit ſi materialis ſphęra conſtituatur ad eleuationem poli gr. </s> <s xml:id="echoid-s11310" xml:space="preserve">66. </s> <s xml:id="echoid-s11311" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s11312" xml:space="preserve">atq; </s> <s xml:id="echoid-s11313" xml:space="preserve">etiam ad ma-<lb/>i<unsure/>orem, v.</s> <s xml:id="echoid-s11314" xml:space="preserve">g. </s> <s xml:id="echoid-s11315" xml:space="preserve">grad. </s> <s xml:id="echoid-s11316" xml:space="preserve">70. </s> <s xml:id="echoid-s11317" xml:space="preserve">ibi enim erunt paralelli Solis, qui toti ſupra horizontem extabunt, ijque nullum dabunt <lb/>crepuſculum; </s> <s xml:id="echoid-s11318" xml:space="preserve">vnus vero ipſum tanget, qui nullum quoq; </s> <s xml:id="echoid-s11319" xml:space="preserve">crepuſculum dabit. </s> <s xml:id="echoid-s11320" xml:space="preserve">alij ſecabunt horizontem, ſed <lb/>non crepuſculinum, ijque exhibebunt crepuſculum per totam noctem. </s> <s xml:id="echoid-s11321" xml:space="preserve">alij tãdem vtrum<unsure/>q; </s> <s xml:id="echoid-s11322" xml:space="preserve">ſecabunt, qui cre-<lb/>puſculum partem noctis efficient. </s> <s xml:id="echoid-s11323" xml:space="preserve">In ſphæra tandem obliquiſſima eleuationis gr. </s> <s xml:id="echoid-s11324" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s11325" xml:space="preserve">vſq; </s> <s xml:id="echoid-s11326" xml:space="preserve">ad ſphæram para-<lb/>lellam circulus, crepuſculi non ſecat omnes paralellos, quia plures infra ipſum exiſtunt, quos Sole percurren <lb/>te nox intempeſta orbi incumbit, &</s> <s xml:id="echoid-s11327" xml:space="preserve">c.</s> <s xml:id="echoid-s11328" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div232" type="section" level="1" n="151"> <head xml:id="echoid-head163" style="it" xml:space="preserve">Aliter dierum, ac crepuſculorum quantitatem computare.</head> <p> <s xml:id="echoid-s11329" xml:space="preserve">ALiter poſſumus vna eademque opera dierum, noctium, & </s> <s xml:id="echoid-s11330" xml:space="preserve">crepuſculorum, quantitatem ex Analem-<lb/>mate reperire. </s> <s xml:id="echoid-s11331" xml:space="preserve">Eſt autem Analemma figura plana ex circulis, rectiſque lineis conſtans, referens ſphæ-<lb/>ræ circulos, axes, diametros, centra, &</s> <s xml:id="echoid-s11332" xml:space="preserve">c. </s> <s xml:id="echoid-s11333" xml:space="preserve">vti eſt præſens, in qua circulus A E B H. </s> <s xml:id="echoid-s11334" xml:space="preserve">refert circulum meridia-<lb/>num, & </s> <s xml:id="echoid-s11335" xml:space="preserve">f<unsure/>aciem eius orientalem. </s> <s xml:id="echoid-s11336" xml:space="preserve">C, eſt centrum mundi. </s> <s xml:id="echoid-s11337" xml:space="preserve">A B, diameter horizontis. </s> <s xml:id="echoid-s11338" xml:space="preserve">I K, diameter circuli <lb/>crepuſculorum, qui debet eſſe infra horizontem grad. </s> <s xml:id="echoid-s11339" xml:space="preserve">18. </s> <s xml:id="echoid-s11340" xml:space="preserve">duo enim arcus A I, B K, per prima propoſ. </s> <s xml:id="echoid-s11341" xml:space="preserve">Ap-<lb/>par. </s> <s xml:id="echoid-s11342" xml:space="preserve">continent grad. </s> <s xml:id="echoid-s11343" xml:space="preserve">18. </s> <s xml:id="echoid-s11344" xml:space="preserve">quanta videlicet eſt Solis depreſſio ſub horizonte ini@io crepuſculi matutini, & </s> <s xml:id="echoid-s11345" xml:space="preserve">fine <lb/>veſpert<unsure/>ini. </s> <s xml:id="echoid-s11346" xml:space="preserve">Arcus B P, eſt poli eleuatio pro data regione, v. </s> <s xml:id="echoid-s11347" xml:space="preserve">gr. </s> <s xml:id="echoid-s11348" xml:space="preserve">grad. </s> <s xml:id="echoid-s11349" xml:space="preserve">45. </s> <s xml:id="echoid-s11350" xml:space="preserve">totus eſt oppoſitus arcus A π. </s> <s xml:id="echoid-s11351" xml:space="preserve">linea <lb/>ergo π C P, eſt axis mundi. </s> <s xml:id="echoid-s11352" xml:space="preserve">P, polus nobis arcticus. </s> <s xml:id="echoid-s11353" xml:space="preserve">π, antarcticus. </s> <s xml:id="echoid-s11354" xml:space="preserve">linea C D, perpendicularis ipſi axi, erit <lb/>æquatoris diameter. </s> <s xml:id="echoid-s11355" xml:space="preserve">accipiatur deinde hinc inde ab æquatore maxima eclypticæ declinatio, ideſt, arcus con-<lb/>@inens gr. </s> <s xml:id="echoid-s11356" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s11357" xml:space="preserve">& </s> <s xml:id="echoid-s11358" xml:space="preserve">notentur punctis E G F H, quare duæ lineæ E F, G H. </s> <s xml:id="echoid-s11359" xml:space="preserve">erunt diametri tropicorum. </s> <s xml:id="echoid-s11360" xml:space="preserve">ſint igi-<lb/>tur, exempli gratia, in hac noſtra eleuatione poli gr. </s> <s xml:id="echoid-s11361" xml:space="preserve">45. </s> <s xml:id="echoid-s11362" xml:space="preserve">ad quam Alemma conſtruximus, inquirenda tria <lb/>prædicta, quando Soloccupat initium Cancri, ſiue quando Cancri tropicum percurrit; </s> <s xml:id="echoid-s11363" xml:space="preserve">quod ad 22. </s> <s xml:id="echoid-s11364" xml:space="preserve">Iunij <pb o="112" file="0132" n="136" rhead="De Mundi Fabrica,"/> diem accidit. </s> <s xml:id="echoid-s11365" xml:space="preserve">quoniam vero E F, eſt diameter prædicti <lb/> <anchor type="figure" xlink:label="fig-0132-01a" xlink:href="fig-0132-01"/> tropici, erit L, medium ipſius punctum, centrum eiuſdem <lb/>tropici: </s> <s xml:id="echoid-s11366" xml:space="preserve">axis enim π P, tranſit per centrum omnium pa-<lb/>ralellorum æquatoris. </s> <s xml:id="echoid-s11367" xml:space="preserve">ex centro igitur L. </s> <s xml:id="echoid-s11368" xml:space="preserve">deſcribatur cir-<lb/>culus E o p F. </s> <s xml:id="echoid-s11369" xml:space="preserve">& </s> <s xml:id="echoid-s11370" xml:space="preserve">à punctis M N. </s> <s xml:id="echoid-s11371" xml:space="preserve">in quibus diameter tropi-<lb/>ci ſecat diametros horizontis, & </s> <s xml:id="echoid-s11372" xml:space="preserve">circuli crepuſculorum, <lb/>e<unsure/>ducantur duæ perpendiculares M O. </s> <s xml:id="echoid-s11373" xml:space="preserve">N p. </s> <s xml:id="echoid-s11374" xml:space="preserve">Iam debemus <lb/>concipere hunc ſemicirculum eſſe perpendiculariter ele-<lb/>uatum ſupra planum meridiani ad partem orientalem, <lb/>in quo ſitu M o, apparebit iacere in plano horizõtis. </s> <s xml:id="echoid-s11375" xml:space="preserve">N p, <lb/>vero in plano crepuſculini circuli. </s> <s xml:id="echoid-s11376" xml:space="preserve">nunc conſiderandum <lb/>eſt, punctum F, eſſe punctum mediæ noctis. </s> <s xml:id="echoid-s11377" xml:space="preserve">quare dum <lb/>Soleo die aſcendit ab F, ad p, ſcandens arcum F p. </s> <s xml:id="echoid-s11378" xml:space="preserve">efficis <lb/>tenebras ac intempeſtam noctem. </s> <s xml:id="echoid-s11379" xml:space="preserve">in p, vero auroram ſeu <lb/>crepuſculi initiũ efficit. </s> <s xml:id="echoid-s11380" xml:space="preserve">a p, deinde vſq; </s> <s xml:id="echoid-s11381" xml:space="preserve">ad o, Sole aſcen-<lb/>dente abſoluitur crepuſculum. </s> <s xml:id="echoid-s11382" xml:space="preserve">& </s> <s xml:id="echoid-s11383" xml:space="preserve">quoniam o@ eſt in hori-<lb/>zonte, in eo Sol diem artificialem incipit. </s> <s xml:id="echoid-s11384" xml:space="preserve">abo, vero vſq; <lb/></s> <s xml:id="echoid-s11385" xml:space="preserve">ad E, quod eſt in meridiano, dimidium abſoluet diem. </s> <s xml:id="echoid-s11386" xml:space="preserve"><lb/>atque in ipſo E, meridiem efficiet. </s> <s xml:id="echoid-s11387" xml:space="preserve">erit igltur arcus F O, <lb/>arcus ſeminocturnus. </s> <s xml:id="echoid-s11388" xml:space="preserve">p O, arcus crepuſculi. </s> <s xml:id="echoid-s11389" xml:space="preserve">O E, arcus <lb/>ſemidiurnus. </s> <s xml:id="echoid-s11390" xml:space="preserve">ſi igitur hi arcus iuxta priores Appar. </s> <s xml:id="echoid-s11391" xml:space="preserve">propo-<lb/>@@tiones, diuidantur in grad. </s> <s xml:id="echoid-s11392" xml:space="preserve">& </s> <s xml:id="echoid-s11393" xml:space="preserve">diligenter expendantur, innoteſcent grad. </s> <s xml:id="echoid-s11394" xml:space="preserve">ſingulorum, & </s> <s xml:id="echoid-s11395" xml:space="preserve">conſequenter du-<lb/>rationes, tempora, ſeu quantitates temporis ſeminocturni, crepuſculi, & </s> <s xml:id="echoid-s11396" xml:space="preserve">ſemidiurni temporis, ijs modis qui-<lb/>bus antea in dierum quantitatem vſi ſumus.</s> <s xml:id="echoid-s11397" xml:space="preserve"/> </p> <div xml:id="echoid-div232" type="float" level="2" n="1"> <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a"> <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0132-01"/> </figure> </div> <p> <s xml:id="echoid-s11398" xml:space="preserve">Eodem modo exiſtente Sole in quouis alio grad. </s> <s xml:id="echoid-s11399" xml:space="preserve">agendum eſt, ſed quando percurrit æquatorem, non eſt <lb/>nouus ſemicirculus pro eo deſcribendus, quoniam vteruis meridiani ſemicirculus fungi poteſt officio ipſius, <lb/>ſi nimirum cogitetur eleuatus perpendiculariter orientem verſus. </s> <s xml:id="echoid-s11400" xml:space="preserve">& </s> <s xml:id="echoid-s11401" xml:space="preserve">à puncto R, ducta ſit paralella ipſi C P, <lb/>vſque ad peripheriam in S, arcus enim S P, indicaret crepuſculi quantitatem, &</s> <s xml:id="echoid-s11402" xml:space="preserve">c. </s> <s xml:id="echoid-s11403" xml:space="preserve">circa tropicum Capricor-<lb/>ni ſimiliter agendum eſt, vti factum in tropico Cancri. </s> <s xml:id="echoid-s11404" xml:space="preserve">verum afferamus aliud exemplum, Sole nec tropicos, <lb/>nec æquatorem percurrente. </s> <s xml:id="echoid-s11405" xml:space="preserve">igitur ſint illa eadem tria inquirenda, quando Sol eſt in principio Scorpij. </s> <s xml:id="echoid-s11406" xml:space="preserve">Ex <lb/>tabella igitur declinationum eclypticæ accipio declinationem initij Scorpionis, quæ eſt gr. </s> <s xml:id="echoid-s11407" xml:space="preserve">11. </s> <s xml:id="echoid-s11408" xml:space="preserve">30′. </s> <s xml:id="echoid-s11409" xml:space="preserve">auſtra-<lb/>lis, & </s> <s xml:id="echoid-s11410" xml:space="preserve">à puncto c, minuſculo, quod eſt in circumferentia, verſus G, ideſt, in auſtrum, ſumatur arcus C T. </s> <s xml:id="echoid-s11411" xml:space="preserve">gr. <lb/></s> <s xml:id="echoid-s11412" xml:space="preserve">11. </s> <s xml:id="echoid-s11413" xml:space="preserve">30′. </s> <s xml:id="echoid-s11414" xml:space="preserve">ductaq; </s> <s xml:id="echoid-s11415" xml:space="preserve">T V, erit diameter paralelli Solis exiſtentis in principio Scorpij. </s> <s xml:id="echoid-s11416" xml:space="preserve">X, vero erit eius centrum, <lb/>ex quo deſcribatur ſemicirculus T γ V, & </s> <s xml:id="echoid-s11417" xml:space="preserve">ex punctis Z α, ducantur duæ lineæ z β, α γ, perpendiculares ipſi <lb/>TV; </s> <s xml:id="echoid-s11418" xml:space="preserve">ac proinde inuicem paralellæ. </s> <s xml:id="echoid-s11419" xml:space="preserve">Iam ſi vt prius cogitetur ſemicirculus T γ V, in proprio ſitus eleuatus <lb/>perpendiculariter ad meridiem erunt prædictæ duæ paralellæ, vna in plano horizontis, altera in plano cir-<lb/>culi crepuſculorum, eritque vt antea arcus V γ, arcus dimidiæ noctis puræ, ac intempeſtæ. </s> <s xml:id="echoid-s11420" xml:space="preserve">γ β, arcus cre-<lb/>puſculi. </s> <s xml:id="echoid-s11421" xml:space="preserve">V β, arcus ſeminocturnus. </s> <s xml:id="echoid-s11422" xml:space="preserve">arcus β T, arcus ſemidiurnus. </s> <s xml:id="echoid-s11423" xml:space="preserve">eodem modo procedendum eſt in quolibet <lb/>gradu, & </s> <s xml:id="echoid-s11424" xml:space="preserve">qualibet poli altitudine. </s> <s xml:id="echoid-s11425" xml:space="preserve">vbi notandum eſt arcum nocturnum haberi poſſe ex præhabito areu diur-<lb/>no; </s> <s xml:id="echoid-s11426" xml:space="preserve">ſi enim arcus diurnus detrahatur ex integro circulo, reliquus arcus, nocturnus erit: </s> <s xml:id="echoid-s11427" xml:space="preserve">viciſſim ex arcu no-<lb/>cturno diurnus elici poteſt.</s> <s xml:id="echoid-s11428" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11429" xml:space="preserve">Hoc loco habenda eſt ratio trium locorum differentiarum, quas ſupra attullimus; </s> <s xml:id="echoid-s11430" xml:space="preserve">loca ſcilicet quædam <lb/>eſſe vbi fit crepuſculum, quod eſt pars noctis: </s> <s xml:id="echoid-s11431" xml:space="preserve">quædam vero vbi crepuſculum totam noctem occupat: </s> <s xml:id="echoid-s11432" xml:space="preserve">quæ-<lb/>dam tantum nullum habent crepuſculum. </s> <s xml:id="echoid-s11433" xml:space="preserve">qu omnia rectè intelligentur, ſi Analemma conſtruatur ad poli <lb/>eleuationem maiorem, quam 66 {1/2}. </s> <s xml:id="echoid-s11434" xml:space="preserve">v. </s> <s xml:id="echoid-s11435" xml:space="preserve">g. </s> <s xml:id="echoid-s11436" xml:space="preserve">grad. </s> <s xml:id="echoid-s11437" xml:space="preserve">70. </s> <s xml:id="echoid-s11438" xml:space="preserve">in hac enim ſphæra videbis tria paralellorum Solis genera; <lb/></s> <s xml:id="echoid-s11439" xml:space="preserve">alij enim toti ſupra horizontem extabunt; </s> <s xml:id="echoid-s11440" xml:space="preserve">vnus tantum ipſum tanget; </s> <s xml:id="echoid-s11441" xml:space="preserve">hique nullum dant crepuſculum. </s> <s xml:id="echoid-s11442" xml:space="preserve">alij <lb/>horizontem tantum ſecabunt, non autem crepuſculinum, hique noctem totam conuertunt in crepuſculum. </s> <s xml:id="echoid-s11443" xml:space="preserve"><lb/>alij demum vtrumque ſecabunt, hique partem noctis tantum crepuſculum eſſiciens his itaque modis com-<lb/>poni poſſunt duæ Tabulæ per totum annum, ſiue per omnes Zodiaci grad. </s> <s xml:id="echoid-s11444" xml:space="preserve">necnon ad omnes poli altitudi-<lb/>nes. </s> <s xml:id="echoid-s11445" xml:space="preserve">quarum prima contineat tempus diurnum. </s> <s xml:id="echoid-s11446" xml:space="preserve">ac nocturnum. </s> <s xml:id="echoid-s11447" xml:space="preserve">Altera vero quantitatem crepuſculorum <lb/>quales infra dabimus.</s> <s xml:id="echoid-s11448" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div234" type="section" level="1" n="152"> <head xml:id="echoid-head164" style="it" xml:space="preserve">Eadem reperire ex Analemmate Vniuerſali</head> <p> <s xml:id="echoid-s11449" xml:space="preserve">TVm ex paulo ante dictis, tum ex declaratione præſentis figuræ, quæ ipſum Analemma eſt vniuerſale, <lb/>manifeſta fient, quæ propoſuimus. </s> <s xml:id="echoid-s11450" xml:space="preserve">Analemma igitur vniuerſale eſt figura in plano deſcripta, quæ ta-<lb/>men ſolidam, ideſt, ſphæram Armillarem repræſentat; </s> <s xml:id="echoid-s11451" xml:space="preserve">cuius vna pars eſt mobilis circa centrum, po@ietqu@ <lb/>appellari Planiſphærium. </s> <s xml:id="echoid-s11452" xml:space="preserve">talis eſt figura præſens, quæ conſtans ex duabus partibus, altera ſtabili, altera mo-<lb/>bili ſtabilis eſt inferior, in qua circulus A B C D, refert circulum meridianum. </s> <s xml:id="echoid-s11453" xml:space="preserve">A C, diametrum horizontis. <lb/></s> <s xml:id="echoid-s11454" xml:space="preserve">E F, diametrum circuli crepuſculini, quæ eſt infra horizontem gr. </s> <s xml:id="echoid-s11455" xml:space="preserve">18. </s> <s xml:id="echoid-s11456" xml:space="preserve">qui gr. </s> <s xml:id="echoid-s11457" xml:space="preserve">18. </s> <s xml:id="echoid-s11458" xml:space="preserve">accipiendi ſunt in interiori <lb/>circulo, ita vt arcus G H, K I, vterque ſit gr. </s> <s xml:id="echoid-s11459" xml:space="preserve">18. </s> <s xml:id="echoid-s11460" xml:space="preserve">quadrans C B. </s> <s xml:id="echoid-s11461" xml:space="preserve">diuidatur in gr. </s> <s xml:id="echoid-s11462" xml:space="preserve">90. </s> <s xml:id="echoid-s11463" xml:space="preserve">vt ad omnes poli altitudi-<lb/>nes accommodari poſſit par<unsure/>s mobilis. </s> <s xml:id="echoid-s11464" xml:space="preserve">loco autem duarum linearum A C, E F. </s> <s xml:id="echoid-s11465" xml:space="preserve">tendenda ſunt duo fila ſubti-<lb/>liſſima. </s> <s xml:id="echoid-s11466" xml:space="preserve">quod vt recte fieri poſſit, deſcribenda eſt hæc pars ſtabilis in charta ſolidiori, aut in tabula quapiam <pb file="0132b" n="137"/> <pb file="0133" n="138"/> <anchor type="figure" xlink:label="fig-0133-01a" xlink:href="fig-0133-01"/> <pb file="0134" n="139"/> <anchor type="figure" xlink:label="fig-0134-01a" xlink:href="fig-0134-01"/> <pb o="113" file="0135" n="140" rhead="Liber Decimus."/> bene complanata. </s> <s xml:id="echoid-s11467" xml:space="preserve">Pars vero mobilis ſic conſtructa eſt. </s> <s xml:id="echoid-s11468" xml:space="preserve">ex centro A. </s> <s xml:id="echoid-s11469" xml:space="preserve">deſcriptus eſt circulus B C D E, æqua-<lb/>lis circulo G H I K, prioris partis, qui æquatorem refert. </s> <s xml:id="echoid-s11470" xml:space="preserve">cuius diameter eſt B A D, E A C, eſt axis mundi, <lb/>C, indicat polum arcticum. </s> <s xml:id="echoid-s11471" xml:space="preserve">E, antarcticum. </s> <s xml:id="echoid-s11472" xml:space="preserve">diuiſus eſt vterque eius ſemicirculus in partes 12. </s> <s xml:id="echoid-s11473" xml:space="preserve">æquales, quæ <lb/>horas 12. </s> <s xml:id="echoid-s11474" xml:space="preserve">ſignifi ant. </s> <s xml:id="echoid-s11475" xml:space="preserve">ſed notandum hunc circulum accipi etiam poſſe pro meridiano quatenus concipitur in <lb/>plano meridiani; </s> <s xml:id="echoid-s11476" xml:space="preserve">quando enim pro æquatore ſumitur tunc accipiendus eſt perpendiculariter meridiano ad-<lb/>hærere. </s> <s xml:id="echoid-s11477" xml:space="preserve">quatenus ergo refert meridianum in eo inſcriptæ ſunt diametri reliquorum paralellorum æquato-<lb/>ris tranſeuntium per initia 12. </s> <s xml:id="echoid-s11478" xml:space="preserve">ſignorum Zodiaci, ſic duæ lineæ G E, H I, ſunt diametri ſemicirculorum <lb/>G X F, H V I; </s> <s xml:id="echoid-s11479" xml:space="preserve">illa tranſit per initia Tauri, & </s> <s xml:id="echoid-s11480" xml:space="preserve">Virginis. </s> <s xml:id="echoid-s11481" xml:space="preserve">hic per initia Scorpij, & </s> <s xml:id="echoid-s11482" xml:space="preserve">Piſcium. </s> <s xml:id="echoid-s11483" xml:space="preserve">diſtant etiam dia-<lb/>metri eorum a diametro æquatoris gr. </s> <s xml:id="echoid-s11484" xml:space="preserve">11. </s> <s xml:id="echoid-s11485" xml:space="preserve">30′. </s> <s xml:id="echoid-s11486" xml:space="preserve">iuxta eorum declinationes. </s> <s xml:id="echoid-s11487" xml:space="preserve">quare vterque arcus H D, G D <lb/> <anchor type="figure" xlink:label="fig-0135-01a" xlink:href="fig-0135-01"/> ſunt gr. </s> <s xml:id="echoid-s11488" xml:space="preserve">11. </s> <s xml:id="echoid-s11489" xml:space="preserve">30′. </s> <s xml:id="echoid-s11490" xml:space="preserve">lineæ O P, K L, diametri ſunt paralellorum tranſeuntium per initia Geminorum, & </s> <s xml:id="echoid-s11491" xml:space="preserve">Leo-<lb/>nis: </s> <s xml:id="echoid-s11492" xml:space="preserve">quorum declinationes ſiue arcus D O, D K, ſunt gr. </s> <s xml:id="echoid-s11493" xml:space="preserve">20. </s> <s xml:id="echoid-s11494" xml:space="preserve">12′. </s> <s xml:id="echoid-s11495" xml:space="preserve">eorum tamen ſemicircu i non ſunt deſcri-<lb/>pti ad vitandam confuſionem, quæ confuſio vitari poterit vario colore adhibito, diametri tandem tropico-<lb/>rum ſunt Q R, M N, cum ſuis ſemicirculis, qui omnes concipiendi ſunt perpendiculariter erecti ad meri-<lb/>dianum iuxta eorum naturalem ſitum. </s> <s xml:id="echoid-s11496" xml:space="preserve">eodem modo per quemuis alium celypticæ gradum deſcribi poterũt <lb/>quotuis paralelli. </s> <s xml:id="echoid-s11497" xml:space="preserve">linea Q A N, eſt diameter eclypticæ, quæ à diametris prædictis diuiditur in ſex partes, <lb/>quarum quælibet duobus ſignis reſpondet, vt apparet ex notis ei adſcriptis. </s> <s xml:id="echoid-s11498" xml:space="preserve">ſemicirculus autem Q E N, vel <lb/>N C Q, ipſam ei eclypticam referre poteſt. </s> <s xml:id="echoid-s11499" xml:space="preserve">Lineæ tandem plurimæ quæ ſunt paralellæ axi mundi, & </s> <s xml:id="echoid-s11500" xml:space="preserve">con-<lb/>ſequenter perpendiculares diametris ſemicirculorum prædictis, ductæ ſunt ad incertum numerun que quo <lb/>tamen plures fuerint, eo melius inſeruient, vt mox patebit. </s> <s xml:id="echoid-s11501" xml:space="preserve">Hæc igitur pars ſic conſtructa applicanda eſt al-<lb/>teri parte ſtabili, ſeu meridiano, ita vt centrum A, reſpondeat centro L, illius. </s> <s xml:id="echoid-s11502" xml:space="preserve">imo ei aliquo axiculo, i@a affi-<lb/>gatur, vt circa eum poſſit conuerti, inſeraturque intra duo fila A C, E F, ita vt ſub ipſs circa centra A L. </s> <s xml:id="echoid-s11503" xml:space="preserve">gy- <pb o="114" file="0136" n="141" rhead="De Mundi Fabrica,"/> rati quæat. </s> <s xml:id="echoid-s11504" xml:space="preserve">ſic enim paratum erit inſtrumentum, quo ad omnes poli eleuationes, necnon ad omnes Zodiaci <lb/>gradus, ſeu ad quodlibet anni tempus, magna facilitate æque, aciucunditate inuenire poterimus tria hæc, <lb/>a cum ſemidiurnum, arcum ſeminocturnum, & </s> <s xml:id="echoid-s11505" xml:space="preserve">crepuſculi quantitatem, vt exemplo patebit. </s> <s xml:id="echoid-s11506" xml:space="preserve">vtautem faci-<lb/>lius intelligamus horum rationem debemus concipere totum hoc inſtrumentum collocatum eſſe aſtronomi-<lb/>cè, hoc videlicet modo; </s> <s xml:id="echoid-s11507" xml:space="preserve">ipſe meridianus debet meridiano mundi congruere, acproinde erigi perpendicu-<lb/>lariter ad horizontem; </s> <s xml:id="echoid-s11508" xml:space="preserve">& </s> <s xml:id="echoid-s11509" xml:space="preserve">linea A C, ipſi horizonti æquidiſtare, & </s> <s xml:id="echoid-s11510" xml:space="preserve">quadrans diuiſus in gr. </s> <s xml:id="echoid-s11511" xml:space="preserve">90. </s> <s xml:id="echoid-s11512" xml:space="preserve">vergere ad po-<lb/>lum noſtrum arcticum. </s> <s xml:id="echoid-s11513" xml:space="preserve">poſtea polus Z, partis mobilis eleuetur ad quamuis propoſitam poli eleuationem; <lb/></s> <s xml:id="echoid-s11514" xml:space="preserve">in qua poſitione erit inſtrumentum iſtud aſtronomicè collocatum. </s> <s xml:id="echoid-s11515" xml:space="preserve">vnde melius eius rationem intelligere <lb/>poterimus; </s> <s xml:id="echoid-s11516" xml:space="preserve">præſer@im ſi concipiamus eius ſemicirculos erectos perpendiculariter ad meridianum; </s> <s xml:id="echoid-s11517" xml:space="preserve">ex qua <lb/>poſitione ſequitur eos eſſe ſemicirculos orientales, cum in parte orientali conſtituantur. </s> <s xml:id="echoid-s11518" xml:space="preserve">ſed vt eius vſus pa-<lb/>teſcat, demus exemplum. </s> <s xml:id="echoid-s11519" xml:space="preserve">ſint in ſphæra recta inuenienda prædicta tria, ad initia Cancri, Capricorni, Arie-<lb/>tis, & </s> <s xml:id="echoid-s11520" xml:space="preserve">Libræ. </s> <s xml:id="echoid-s11521" xml:space="preserve">applico igitur polum vtrumque T Z, horizonti, in quo ſitu obfirmata parte mobili, accipio <lb/>duo puncta S y, in quibus duo ſila ſecant diametrum Q R, Capricorni. </s> <s xml:id="echoid-s11522" xml:space="preserve">atq; </s> <s xml:id="echoid-s11523" xml:space="preserve">ex his duobus punctis duco duas <lb/>perpendiculares S T, γ λ, vſque ad ſemicirculum eiuſdem Capricorni in punctis T λ. </s> <s xml:id="echoid-s11524" xml:space="preserve">aſſumo itaque arcum <lb/>T λ, ab eis interceptum eumque quot horas ac minuta contineat expendo; </s> <s xml:id="echoid-s11525" xml:space="preserve">ſunt enim hi ſemicirculi diuiſi in <lb/>horas, & </s> <s xml:id="echoid-s11526" xml:space="preserve">hora vna ſaltem oportet ſit diuiſa in quatuor partes æquales; </s> <s xml:id="echoid-s11527" xml:space="preserve">quæ erunt horæ quadrantes, quarum <lb/>ſingulæ continent horæ minuta 15′. </s> <s xml:id="echoid-s11528" xml:space="preserve">arcus enim T ω, eſt hora vna. </s> <s xml:id="echoid-s11529" xml:space="preserve">arcus ω λ, ſuperat quartam horæ partem, <lb/>ita vt ſit vna ferè tertia pars horæ; </s> <s xml:id="echoid-s11530" xml:space="preserve">quare in ſphæra recta crepuſculum tempore ſolſtitij erit hora 1. </s> <s xml:id="echoid-s11531" xml:space="preserve">min. </s> <s xml:id="echoid-s11532" xml:space="preserve">19′. </s> <s xml:id="echoid-s11533" xml:space="preserve"><lb/>tantundem erit in altero tropico. </s> <s xml:id="echoid-s11534" xml:space="preserve">ſic ſemper faciendum eſt, ideſt, accipiendæ ſunt ſemper duæ perpendicu-<lb/>lares à punctis, in quibus diameter paralelli propoſiti, ſecatur a filis horizontis, & </s> <s xml:id="echoid-s11535" xml:space="preserve">crepuſculi, quæ lineæ pro-<lb/>ducantur vſque ad ſemicirculum eiuſdem paralelli, arcus enim inter ipſas interceptus dabit quantitatem <lb/>crepuſculi; </s> <s xml:id="echoid-s11536" xml:space="preserve">quod ſi perpendiculares ibi deſcriptæ, non præcisè per dicta puncta ſectionum tranſierint, aliæ <lb/>iuxta eas concipiendæ ſunt. </s> <s xml:id="echoid-s11537" xml:space="preserve">rurſus in eodem paralello, & </s> <s xml:id="echoid-s11538" xml:space="preserve">in eadem ſphæra recta arcus T Q, erit arcus diur-<lb/>nus, arcus vero λ R, erit nocturnus puræ, ſeu intempeſtæ noctis. </s> <s xml:id="echoid-s11539" xml:space="preserve">eodem modo in æquatore agendum eſt, <lb/>puncta ſectionum in diametro erunt A β, perpendiculares erunt A E, β δ, vſque ad ſemicirculum eiuſdem <lb/>æquatoris, intercipientes arcum E δ, qui continet horam vnam, & </s> <s xml:id="echoid-s11540" xml:space="preserve">quantam horæ partem, ideſt, min. </s> <s xml:id="echoid-s11541" xml:space="preserve">12′. </s> <s xml:id="echoid-s11542" xml:space="preserve"><lb/>Alterum exemplum, ſit in ſphæra paralella quærendum crepuſculum, &</s> <s xml:id="echoid-s11543" xml:space="preserve">c. </s> <s xml:id="echoid-s11544" xml:space="preserve">pono igitur polum Z, in vertice, <lb/>ſeu in fine gr. </s> <s xml:id="echoid-s11545" xml:space="preserve">90. </s> <s xml:id="echoid-s11546" xml:space="preserve">ibique eo obfirmato, noto punctum in diametro eclypticæ, quod ſecatur à filo crepuſculo-<lb/>rum, à quo duco perpendicularem ipſi eclypticæ diametro, vſque ad ſemicirculum ipſius eclypticæ Q E N, <lb/>alteram perpendicularem duco a centro A, vbi ſecatur à linea ſeu filo horizontali, vſque ad eundem ſemi-<lb/>circulum eclypticæ; </s> <s xml:id="echoid-s11547" xml:space="preserve">arcus en im interceptus dabit quantitatem crepuſculi. </s> <s xml:id="echoid-s11548" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s11549" xml:space="preserve">ferè 48. </s> <s xml:id="echoid-s11550" xml:space="preserve">quos eclypticæ <lb/>gradus motu propri<unsure/>o Sol percurrit totidem ferè diebus, quare huic habitationi primũ crepuſculum erit die-<lb/>rum 48. </s> <s xml:id="echoid-s11551" xml:space="preserve">ab initio Lib æ vſq; </s> <s xml:id="echoid-s11552" xml:space="preserve">ad gr. </s> <s xml:id="echoid-s11553" xml:space="preserve">18. </s> <s xml:id="echoid-s11554" xml:space="preserve">Scorpij. </s> <s xml:id="echoid-s11555" xml:space="preserve">Rurſus a gr. </s> <s xml:id="echoid-s11556" xml:space="preserve">12. </s> <s xml:id="echoid-s11557" xml:space="preserve">Aquarij vſq; </s> <s xml:id="echoid-s11558" xml:space="preserve">ad Arietem, erit alterum crepu-<lb/>ſcuium dierum totidem 48. </s> <s xml:id="echoid-s11559" xml:space="preserve">quare in vniuerſum tempus crcpuſculi erit trium menſiũ, dierum ſex conſequen-<lb/>ter, nox pura erit reliquum ſex menſium, nimirum duorum menſium, dierum 24.</s> <s xml:id="echoid-s11560" xml:space="preserve"/> </p> <div xml:id="echoid-div234" type="float" level="2" n="1"> <figure xlink:label="fig-0133-01" xlink:href="fig-0133-01a"> <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0133-01"/> </figure> <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a"> <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0134-01"/> </figure> <figure xlink:label="fig-0135-01" xlink:href="fig-0135-01a"> <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01"/> </figure> </div> <p> <s xml:id="echoid-s11561" xml:space="preserve">In eadem ſphæra paralella, licebit videre vnicum eſſe diem ſex menſium continuum, & </s> <s xml:id="echoid-s11562" xml:space="preserve">noctem pariter <lb/>vnam intempeſtam dnorum menſium, ac dierum 24. </s> <s xml:id="echoid-s11563" xml:space="preserve">duo vero crepuſcula ſingula dierum 48. </s> <s xml:id="echoid-s11564" xml:space="preserve">vnde ſequitur <lb/>eos habere diem artificialem, computatis crepuſculis, menſium 9. </s> <s xml:id="echoid-s11565" xml:space="preserve">dierum 6. </s> <s xml:id="echoid-s11566" xml:space="preserve">& </s> <s xml:id="echoid-s11567" xml:space="preserve">amplius. </s> <s xml:id="echoid-s11568" xml:space="preserve">pro exemplo autem <lb/>eleuationis polaris inter ſphæram rectam, & </s> <s xml:id="echoid-s11569" xml:space="preserve">paralellam, ſufficiat illud quod allatum eſt ſuperius in Ana-<lb/>lemmate particular.</s> <s xml:id="echoid-s11570" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11571" xml:space="preserve">Cæterum ex varia poſitione Analemmatis, ad varias poli eleuationes licebit magna cũ voluptate, quo di-<lb/>ximus modo, @@atim reperire non ſolum quantitatem dierum, noctium. </s> <s xml:id="echoid-s11572" xml:space="preserve">& </s> <s xml:id="echoid-s11573" xml:space="preserve">crepuſculorum; </s> <s xml:id="echoid-s11574" xml:space="preserve">ſed etiam diuerſi-<lb/>tat@m inter vnam habitationem, & </s> <s xml:id="echoid-s11575" xml:space="preserve">alteram; </s> <s xml:id="echoid-s11576" xml:space="preserve">nec non diuerſitatem currentem pertotum annum in eadem <lb/>ſphæra. </s> <s xml:id="echoid-s11577" xml:space="preserve">Apparebit primo in tropico Cãcri, ſemper maiora eſſe crepuſcula, quam in altero: </s> <s xml:id="echoid-s11578" xml:space="preserve">minima vero con-<lb/>tingere ci<unsure/>rca dimidiam L bram, & </s> <s xml:id="echoid-s11579" xml:space="preserve">Piſces; </s> <s xml:id="echoid-s11580" xml:space="preserve">dummodo eleuatio poli non tranſcendat gra. </s> <s xml:id="echoid-s11581" xml:space="preserve">66 {1/2}; </s> <s xml:id="echoid-s11582" xml:space="preserve">nam in maiori <lb/>eleuatione crepuſcula Capricorni decreſcunt, ac non ſolum mi<unsure/>nora euadunt, quam circa dimidiam Libram. <lb/></s> <s xml:id="echoid-s11583" xml:space="preserve">& </s> <s xml:id="echoid-s11584" xml:space="preserve">Piſces; </s> <s xml:id="echoid-s11585" xml:space="preserve">ſed omnium breuiſſima eſſe poſſunt. </s> <s xml:id="echoid-s11586" xml:space="preserve">quod alij non videntur ammaduertiſi<unsure/>e, cum abſolute dicant <lb/>minima eſſe ad dimidiam Libram, & </s> <s xml:id="echoid-s11587" xml:space="preserve">Piſces quod præterea falſum eſt in ſphæra recta, in ea enim crepuſcu-<lb/>lum æquatoris minimum eſt omnium. </s> <s xml:id="echoid-s11588" xml:space="preserve">apparebit etiam falſum eſſe, quod dicunt crepuſculum Capricorni eſſe <lb/>ſemper maius crepuſculo æquatoris; </s> <s xml:id="echoid-s11589" xml:space="preserve">nam in ſphęris obliquiſſimis, vt modo diximus, eſt omnium minimum. </s> <s xml:id="echoid-s11590" xml:space="preserve"><lb/>Secundo apparebit, quanto magis eleuatur polus, tanto maiora euadere crepuſcula, quæ omni patebunt ex<unsure/> <lb/>conſideratione @patiorum, quæ includuntur inter lineam horizontis, & </s> <s xml:id="echoid-s11591" xml:space="preserve">lineam crepuſculi, & </s> <s xml:id="echoid-s11592" xml:space="preserve">duos diame-<lb/>tro tropicorum; </s> <s xml:id="echoid-s11593" xml:space="preserve">in toto enim eo ſpatio fit crepuſculum. </s> <s xml:id="echoid-s11594" xml:space="preserve">hoc autem ſpatium ſemper maius eſt in eleuator@ <lb/>ſphæra, adeo vt maximum ſit in paralella. </s> <s xml:id="echoid-s11595" xml:space="preserve">qua in re conſideranda eſt diuina prouidentia, quæ vt incommo-<lb/>da ſphærarum borealiorum, aliquo bono, compenſaret, maiora eis crepuſcula, ideſt, maiorem lucis copiam <lb/>attribuit, quam reliquis auſtralioribus; </s> <s xml:id="echoid-s11596" xml:space="preserve">quod paradoxum vulgo putatur. </s> <s xml:id="echoid-s11597" xml:space="preserve">fic crepuſcula ſphæræ borealiſ@imæ, <lb/>ideſt, paralellæ, conſtant menſibus tribus, diebus 7. </s> <s xml:id="echoid-s11598" xml:space="preserve">& </s> <s xml:id="echoid-s11599" xml:space="preserve">amplius; </s> <s xml:id="echoid-s11600" xml:space="preserve">at crepuſcula ſphæræ rectæ ſimul ſumpta dies<unsure/> <lb/>tantum 39. </s> <s xml:id="echoid-s11601" xml:space="preserve">circiter continet. </s> <s xml:id="echoid-s11602" xml:space="preserve">Tertio conſtabit in nonnullis ſphæris aliquando eſſe diem continuum ſine cre-<lb/>puſcui<unsure/>o, & </s> <s xml:id="echoid-s11603" xml:space="preserve">nocte: </s> <s xml:id="echoid-s11604" xml:space="preserve">aliquando diem cum crepuſculo tantum, quia ibi crepuſculum durat tota nocte: </s> <s xml:id="echoid-s11605" xml:space="preserve">aliquan-<lb/>do diem, crepuſculum, & </s> <s xml:id="echoid-s11606" xml:space="preserve">noctem. </s> <s xml:id="echoid-s11607" xml:space="preserve">aliquando crepuſculum cõtinuum; </s> <s xml:id="echoid-s11608" xml:space="preserve">aliquando noctem puram continuam; </s> <s xml:id="echoid-s11609" xml:space="preserve"><lb/>aliquando crepuſculum, & </s> <s xml:id="echoid-s11610" xml:space="preserve">noctem ſimul. </s> <s xml:id="echoid-s11611" xml:space="preserve">exempli cauſa; </s> <s xml:id="echoid-s11612" xml:space="preserve">conſtituto Analemmate ad eleuationem gr. </s> <s xml:id="echoid-s11613" xml:space="preserve">86. </s> <s xml:id="echoid-s11614" xml:space="preserve">quiæ <lb/>video diametrum Cancri totum ſupra horizontem, agnoſco Sole cancrum percurrente eſſe diem cõtinuum <lb/>purum, abſque crepuſculo, ibidem quia diameter æquatoris partim ſupra horizontem, partim infra exiſtens <pb o="115" file="0137" n="142" rhead="Liber Decimus."/> non attingit lineam crepuſculi, agnoſco ſole æquatorem deſcribente effici diem cum crepuſeulo ſolo, quod <lb/>per totam noctem durat. </s> <s xml:id="echoid-s11615" xml:space="preserve">ibidem quia diameter Scorpij tota infra horizontem, ſed tota etiam ſupra lineam <lb/>crepuſculi, ideo infero tunc temporis Solem efficere ſolum. </s> <s xml:id="echoid-s11616" xml:space="preserve">crepuſculum continuum. </s> <s xml:id="echoid-s11617" xml:space="preserve">pręterea quoniam dia-<lb/>meter Sagittarij tota eſt infra horizontem, ſed pars etiam upra lineam crepuſculi, & </s> <s xml:id="echoid-s11618" xml:space="preserve">pars infra, ideo Sole <lb/>eum obeunte effici ibidem ſolius crepuſculi, & </s> <s xml:id="echoid-s11619" xml:space="preserve">noctis intempeſtæ viciſſitudinem. </s> <s xml:id="echoid-s11620" xml:space="preserve">tandem quia tota diameter <lb/>Capricorni, eſt infra lineam crepuſculi, ideo Sole brunam efficiente, effici etiam noctem meram, & </s> <s xml:id="echoid-s11621" xml:space="preserve">intem-<lb/>peſtam. </s> <s xml:id="echoid-s11622" xml:space="preserve">diem continuum, noctem continuam, crepuſculum continuum appello illud, quod ſpatium vnius <lb/>diurnæ reuolutionis tranſcendit. </s> <s xml:id="echoid-s11623" xml:space="preserve">eadem ratione alias aliarũ habitationum varietates in Alemmate hoc vni-<lb/>uerſali contemplari poteris. </s> <s xml:id="echoid-s11624" xml:space="preserve">Illud etiam non omittendum, ex his patere in omnibus ſphæræ eleuationibus, <lb/>vſque ad gr. </s> <s xml:id="echoid-s11625" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s11626" xml:space="preserve">à Capricorno verſus Arietem crepuſcula minui, dies vero augeri ex qua contrarietate ori-<lb/>tur ſolſtitium longius, ideſt, dies artificiales vulgares tardiſſimè creſcunt. </s> <s xml:id="echoid-s11627" xml:space="preserve">Quarto tandem quod præcipuum <lb/>eſt; </s> <s xml:id="echoid-s11628" xml:space="preserve">poterimus nullo negotio computare ex hoc Analemmate duas Tabulas; </s> <s xml:id="echoid-s11629" xml:space="preserve">vnã temporis diurni ac noctur-<lb/>ni: </s> <s xml:id="echoid-s11630" xml:space="preserve">alteram crepuſculorum. </s> <s xml:id="echoid-s11631" xml:space="preserve">eaſque ad omnes poli eleuationes, nec non ad ſingulos anni dies in quauis eleua-<lb/>tione. </s> <s xml:id="echoid-s11632" xml:space="preserve">huiuſmodi ſunt duæ ſequentes, quarum quæ crepuſculorum eſt, ego ex Analemmate accurate con-<lb/>ſtructo computaui. </s> <s xml:id="echoid-s11633" xml:space="preserve">ne autem nimis excreſceret, ad eas tantum habitationes computaui, quorum crepuſculo-<lb/>rum differentiæ quadrantem vix horæ excederent. </s> <s xml:id="echoid-s11634" xml:space="preserve">eadem de cauſa eam. </s> <s xml:id="echoid-s11635" xml:space="preserve">non per ſingulos dies, ſed tantum ad <lb/>initia ſignorum 12. </s> <s xml:id="echoid-s11636" xml:space="preserve">calculaui, quod ſufficere ciuili vſui exiſtimauerim. </s> <s xml:id="echoid-s11637" xml:space="preserve">Similitertabulam temporis ſemidiur-<lb/>ni, vt ad breuitatem redigerem, non ad ſingulas eleuationes, nec ad ſingulos gradus Zodiaci, ſed per inter-<lb/>ualla, quæ parum ſe excederent eam deduxi, vtramque accipe.</s> <s xml:id="echoid-s11638" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11639" xml:space="preserve">Porro ſequẽs Tabella ſeruit populis Borealibus, ſed vt ſeruiat Auſtralibus commutanda ſunt ſex ſigna Bo-<lb/>realia in Auſtralia,|& </s> <s xml:id="echoid-s11640" xml:space="preserve">ſex Auſtralia in Borealia exempli gratia in altitud. </s> <s xml:id="echoid-s11641" xml:space="preserve">pol. </s> <s xml:id="echoid-s11642" xml:space="preserve">gr. </s> <s xml:id="echoid-s11643" xml:space="preserve">8. </s> <s xml:id="echoid-s11644" xml:space="preserve">cum Sol eſt initio ♋. </s> <s xml:id="echoid-s11645" xml:space="preserve">Au-<lb/>ſtralibus ſemidiurnum tempus eſt tantum, quantum, ſi Sol eſſet in initio ♑. </s> <s xml:id="echoid-s11646" xml:space="preserve">eſiet Borealibus, hoc eſt hora-<lb/>rum 5. </s> <s xml:id="echoid-s11647" xml:space="preserve">min. </s> <s xml:id="echoid-s11648" xml:space="preserve">46.</s> <s xml:id="echoid-s11649" xml:space="preserve"/> </p> <figure> <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/> </figure> <pb o="116" file="0138" n="143" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div236" type="section" level="1" n="153"> <head xml:id="echoid-head165" style="it" xml:space="preserve">TABVLA TEMPORIS SEMIDIVRNA <lb/>ad initia Signorum, & ad eleuationes Poli Arctici.</head> <note position="right" xml:space="preserve"> <lb/>## Alt. poli. ## 0 ## 8 ## 16 ## 23 ## 30 ## 36 ## 40 ## 45 <lb/># H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. <lb/>## ♋ # 6 # 0 # 6 # 14 # 6 # 29 # 6 # 43 # 6 # 58 # 7 # 14 # 7 # 26 # 7 # 43 <lb/>♊ # ♌ # 6 # 0 # 6 # 12 # 6 # 24 # 6 # 36 # 6 # 49 # 7 # 2 # 7 # 12 # 7 # 26 <lb/>♉ # ♍ # 6 # 0 # 6 # 7 # 6 # 13 # 6 # 20 # 6 # 27 # 6 # 34 # 6 # 39 # 6 # 47 <lb/>*** # ♎ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # 6 # 0 # 5 # 53 # 5 # 47 # 5 # 40 # 5 # 33 # 5 # 26 # 5 # 21 # 5 # 13 <lb/>♒ # ♐ # 6 # 0 # 5 # 48 # 5 # 36 # 5 # 24 # 5 # 11 # 4 # 58 # 4 # 48 # 4 # 34 <lb/>## ♑ # 6 # 0 # 5 # 46 # 5 # 31 # 5 # 17 # 5 # 2 # 4 # 46 # 4 # 34 # 4 # 17 <lb/>## Alt. poli. ## 63 ## 64 ## 65 ## 66 ## 66 {1/2} ## 67 ## 68 ## 69 <lb/>## ♋ # 9 # 44 # 10 # 12 # 10 # 35 # 11 # 10 # 12 # 0 # d. # c. # d. # c. # d. # c. <lb/>♊ # ♌ # 9 # 5 # 9 # 16 # 9 # 28 # 9 # 43 # 9 # 51 # 10 # 0 # 10 # 22 # 10 # 54 <lb/>♉ # ♍ # 7 # 34 # 7 # 39 # 7 # 43 # 7 # 49 # 7 # 52 # 7 # 55 # 8 # 1 # 8 # 5 <lb/>♈ # ♎ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # 4 # 26 # 4 # 21 # 4 # 17 # 4 # 11 # 4 # 8 # 4 # 5 # 3 # 59 # 3 # 52 <lb/>♒ # ♐ # 2 # 25 # 2 # 44 # 2 # 32 # 2 # 17 # 2 # 9 # 2 # 0 # 1 # 38 # 1 # 16 <lb/>## ♑ # 2 # 6 # 1 # 48 # 1 # 25 # 0 # 50 # n. # c. # n. # c. # n. # c. # n. # c. <lb/>## Alt. poli. ## 77 ## 78 ## 79 ## 80 ## 81 ## 82 ## 83 ## 84 <lb/>## ♋ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♊ # ♌ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♉ # ♍ # 10 # 7 # 10 # 53 # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♈ # ♎ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # 1 # 53 # 1 # 7 # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>♒ # ♐ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>## ♑ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/></note> <pb o="117" file="0139" n="144" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div237" type="section" level="1" n="154"> <head xml:id="echoid-head166" style="it" xml:space="preserve">TABVLA TEMPORIS SEMIDIVRNA <lb/>ad initia Signorum, & ad eleuationes Polis Arctici.</head> <note position="right" xml:space="preserve"> <lb/>## Alt. poli. ## 48 ## 51 ## 54 ## 56 ## 58 ## 60 ## 62 <lb/># # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. <lb/>## ♋ # 7 # 56 # 8 # 10 # 8 # 27 # 8 # 40 # 8 # 56 # 9 # 16 # 9 # 39 <lb/>♊ # ♌ # 7 # 36 # 7 # 48 # 8 # 2 # 8 # 12 # 8 # 24 # 8 # 38 # 8 # 55 <lb/>♉ # ♍ # 6 # 57 # 6 # 58 # 7 # 5 # 7 # 10 # 7 # 16 # 7 # 23 # 7 # 30 <lb/>♈ # ♌ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # 5 # 8 # 5 # 2 # 4 # 55 # 4 # 50 # 4 # 44 # 4 # 37 # 4 # 30 <lb/>♒ # ♐ # 4 # 24 # 4 # 12 # 3 # 58 # 3 # 48 # 3 # 36 # 3 # 22 # 3 # 5 <lb/>## ♑ # 4 # 4 # 3 # 50 # 3 # 33 # 3 # 20 # 3 # 4 # 2 # 44 # 2 # 21 <lb/>## Alt. poli. ## 70 ## 71 ## 72 ## 73 ## 74 ## 75 ## 76 <lb/>## ♋ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♊ # ♌ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♉ # ♍ # 8 # 16 # 8 # 25 # 8 # 35 # 8 # 47 # 9 # 1 # 9 # 18 # 9 # 39 <lb/>♈ # ♎ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # 3 # 44 # 3 # 35 # 3 # 25 # 3 # 13 # 2 # 59 # 2 # 42 # 2 # 21 <lb/>♒ # ♐ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>## ♑ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>## Alt. poli. ## 85 ## 86 ## 87 ## 88 ## 89 ## 90 <lb/>## ♋ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. ## 6. menſ. <lb/>♊ # ♌ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♉ # ♍ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♈ # ♎ # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 # 6 # 0 <lb/>♓ # ♏ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>♒ # ♐ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. <lb/>## ♑ # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. # n. # c. ## 6. menſ. <lb/></note> <pb o="118" file="0140" n="145" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div238" type="section" level="1" n="155"> <head xml:id="echoid-head167" style="it" xml:space="preserve">TAULA CREPVSCVLORVM <lb/>ad initia Signorum, & ad altitudines Poli Arcti<unsure/>ci<unsure/>.</head> <note position="right" xml:space="preserve"> <lb/>## Alt. poli. ## 0 ## 5 ## 10 ## 15 ## 20 ## 25 ## 30 ## 35 <lb/># H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. # H. # ′. <lb/>## ♋ # 1 # 19 # 1 # 19 # 1 # 20 # 1 # 23 # 1 # 26 # 1 # 29 # 1 # 36 # 1 # 49 <lb/>♊ # ♌ # 1 # 14 # 1 # 14 # 1 # 15 # 1 # 18 # 1 # 21 # 1 # 25 # 1 # 31 # 1 # 41 <lb/>*** # ♍ # 1 # 13 # 1 # 13 # 1 # 14 # 1 # 16 # 1 # 20 # 1 # 23 # 1 # 28 # 1 # 35 <lb/>*** # ♎ # 1 # 12 # 1 # 12 # 1 # 13 # 1 # 15 # 1 # 18 # 1 # 22 # 1 # 25 # 1 # 29 <lb/>♓ # ♏ # 1 # 13 # 1 # 13 # 1 # 14 # 1 # 14 # 1 # 15 # 1 # 17 # 1 # 20 # 1 # 26 <lb/>♒ # ♐ # 1 # 14 # 1 # 14 # 1 # 15 # 1 # 16 # 1 # 17 # 1 # 20 # 1 # 26 # 1 # 34 <lb/>## ♑ # 1 # 19 # 1 # 19 # 1 # 19 # 1 # 20 # 1 # 22 # 1 # 25 # 1 # 29 # 1 # 37 <lb/>## Alt. poli. ## 59 ## 60 {1/2} ## 61 ## 62 ## 63 ## 64 ## 65 ## 66 {1/2} <lb/>## ♋ # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. ## di c. pur. <lb/>♊ # ♌ # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. <lb/>♉ # ♍ # 3 # 54 # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. <lb/>♈ # ♎ # 2 # 27 # 2 # 35 # 2 # 36 # 2 # 37 # 2 # 42 # 2 # 50 # 3 # 1 # 3 # 18 <lb/>♓ # ♏ # 2 # 24 # 2 # 30 # 2 # 33 # 2 # 36 # 2 # 42 # 2 # 50 # 2 # 54 # 3 # 9 <lb/>♒ # ♐ # 2 # 39 # 2 # 45 # 2 # 50 # 5 # 56 # 3 # 0 # 3 # 7 # 3 # 20 # 3 # 31 <lb/>## ♑ # 2 # 49 # 3 # 0 # 3 # 4 # 3 # 9 # 3 # 26 # 3 # 40 # 4 # 9 # 5 # 25 <lb/>## Alt. poli. ## 77 ## 78 {1/2} ## 79 ## 80 ## 81 ## 82 ## 83 {1/2} ## 84 {1/2} <lb/>## ♋ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♊ # ♌ # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♉ # ♍ # t. # n. ## di c. pur. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. # d. # c. <lb/>♈ # ♎ # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. # t. # n. <lb/>♓ # ♏ # 6 # 15 # 8 # 9 # 8 # 14 # 8 # 32 # 8 # 42 # 9 # 17 # t. # n. # t. # n. <lb/>♒ # ♐ # 5 # 25 # 5 # 18 # 5 # 15 # 5 # 10 # 5 # 5 # 5 # 0 # 4 # 40 # 4 # 10 <lb/>## ♑ # 4 # 25 # 4 # 12 # 4 # 3 # 3 # 56 # 3 # 36 # 2 # 15 # 2 # 10 ## Inſtans. <lb/></note> <pb o="117" file="0141" n="146" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div239" type="section" level="1" n="156"> <head xml:id="echoid-head168" style="it" xml:space="preserve">TABVLA CREPVSCVLORVM <lb/>adinitia Signorum, & ad altitudines Pelis Arctici.</head> <note position="right" xml:space="preserve"> <lb/>38 # 40 # 43 # 45 # 48 {1/2} # 52 # 54 # 55 # 58 <lb/>H. ′. # H. ′. # H. ′. # H. ′. # H. ′. # H. ′. # H. ′. # H. ′. # H. ′. <lb/>2 1 # 2 9 # 2 25 # 3 39 # t. n. # t. n. # t. n. # t. n. # t. n. <lb/>1 46 # 1 50 # 2 9 # 2 19 # 2 40 # t. n. # t. n. # t. n. # t. n. <lb/>1 39 # 1 43 # 1 48 # 1 55 # 2 4 # 2 22 # 2 39 # 2 56 # 3 25 <lb/>1 32 # 1 35 # 1 40 # 1 45 # 1 50 # 2 1 # 2 5 # 2 10 # 2 23 <lb/>1 31 # 1 35 # 1 37 # 1 43 # 1 49 # 1 59 # 2 4 # 2 9 # 2 10 <lb/>1 37 # 1 40 # 1 45 # 1 49 # 1 56 # 2 8 # 2 15 # 2 20 # 2 30 <lb/>1 40 # 1 43 # 1 48 # 1 53 # 2 2 # 2 14 # 2 19 # 2 26 # 2 41 <lb/>67 # 68 # 69.48′ # 71 # 72 # 73 # 74 # 75 # 76 <lb/>d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. <lb/>t. n. # t. n. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. <lb/>t. n. # t. n. # t. n. # t. n. # t. n. # t. n. # t. n. # t. n. # t. n. <lb/>3 22 # 3 27 # 4 8 # 4 20 # t. n. # t. n. # t. n. # t. n. # t. n. <lb/>3 19 # 3 30 # 3 36 # 3 45 # 3 56 # 2 25 # 3 49 # 5 2 # 5 26 <lb/>3 35 # 4 10 # 5 48 # 5 46 # 5 40 # 3 35 # 5 31 # 5 29 # 5 27 <lb/>5 23 # 5 18 # 5 9 # 5 5 # 5 2 # 4 51 # 4 45 # 4 41 # 4 12 <lb/>85 # 86| # 87 # 88 # 88.48′ # 89 # 90 <lb/>d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. ## Hæe Tabula inſer- \\ uire et@ã poteſt pro \\ Hemiſphærio Au- \\ ſtrali, commutatis \\ ſex ſignis Boreali- \\ bus in Auſt ralia. <lb/>d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. <lb/>d. c. # d. c. # d. c. # d. c. # d. c. # d. c. # d. c. <lb/>t. n. # t. n. # t. n. # t. n. # t. n. # t. n. # t. n. <lb/>t. n. # t. n. # t. n. # t. n. # t. n. # t. n. # t. n. <lb/>4 15 # 3 40 # 2 38 # 2 0 # Inſtans. # n. p. # n. p. <lb/>nox pur. # n. p. # n. p. # n. p. # n p. # n. p. # n. p. <lb/></note> <pb o="120" file="0142" n="147" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div240" type="section" level="1" n="157"> <head xml:id="echoid-head169" style="it" xml:space="preserve">Declaratio, & vſus Tabulæ primæ.</head> <p> <s xml:id="echoid-s11650" xml:space="preserve">IN prima linea continentur numeri elcuationum Poli Arcticiad quas Tabula eſt computata. </s> <s xml:id="echoid-s11651" xml:space="preserve">prima autem <lb/>nota quæ eſt o. </s> <s xml:id="echoid-s11652" xml:space="preserve">ſeu cifra, ſignificat nullum gradum eleuationis, ideſt, ſignificat ſphæram rectam, in qua po-<lb/>li ſupra horizontem non eleuantur. </s> <s xml:id="echoid-s11653" xml:space="preserve">In ſecunda linea ſignificat H. </s> <s xml:id="echoid-s11654" xml:space="preserve">Horam. </s> <s xml:id="echoid-s11655" xml:space="preserve">¹, vero ſignificat minuta. </s> <s xml:id="echoid-s11656" xml:space="preserve">In ter-<lb/>tia linea ſunt numeri horarum ac minuta, quæ competunt eleuationibus poli ſibi directè ſuperpoſitis, quę ho-<lb/>ræ ac minuta dant quantitatem temporis ſemidiurni Sole Cancrum adeunte, ſiue temporis ſolſtitij æſtiui ad <lb/>21. </s> <s xml:id="echoid-s11657" xml:space="preserve">Iunij, vt character hic ♋ Cancri lineæ ad ſiniſtram præpoſitns indicat. </s> <s xml:id="echoid-s11658" xml:space="preserve">Eadem de rel quis lineis propor-<lb/>tionaliter ſunt intelligenda. </s> <s xml:id="echoid-s11659" xml:space="preserve">literæ d c, quæ loco numerorum ponuntur, ſignificant diem continuum. </s> <s xml:id="echoid-s11660" xml:space="preserve">n c, no-<lb/>ctem continuam, quæ contineat etiam crepi ſculum. </s> <s xml:id="echoid-s11661" xml:space="preserve">Vſus autem eius eſt. </s> <s xml:id="echoid-s11662" xml:space="preserve">primo vt in ea omnium dierum, a@ <lb/>noctium varietatem peromnes mundi habitationes contemplari facilè poſſimus.</s> <s xml:id="echoid-s11663" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11664" xml:space="preserve">Secundo vt ex ea eliciamus ad quoduis tempus, & </s> <s xml:id="echoid-s11665" xml:space="preserve">in quauis habitatione quantitatem diei ac noctis, atq; </s> <s xml:id="echoid-s11666" xml:space="preserve">ho-<lb/>ram ortus, & </s> <s xml:id="echoid-s11667" xml:space="preserve">occaſus Solis, horam meridiei, & </s> <s xml:id="echoid-s11668" xml:space="preserve">mediæ noctis. </s> <s xml:id="echoid-s11669" xml:space="preserve">quod vno aut altero exemplo patebit, ſint v.</s> <s xml:id="echoid-s11670" xml:space="preserve">g. </s> <s xml:id="echoid-s11671" xml:space="preserve">in <lb/>eleuatione poli Parmenſi gr. </s> <s xml:id="echoid-s11672" xml:space="preserve">45. </s> <s xml:id="echoid-s11673" xml:space="preserve">ferè, quærẽda ea quæ dicta ſuntad diem 21. </s> <s xml:id="echoid-s11674" xml:space="preserve">Ianuarij, quo tempore Sol Aqua-<lb/>rij ſignum ingreditur. </s> <s xml:id="echoid-s11675" xml:space="preserve">quæro igitur in linea eleuationum polarium gr. </s> <s xml:id="echoid-s11676" xml:space="preserve">45. </s> <s xml:id="echoid-s11677" xml:space="preserve">deinde in latere ſiniſtro ſignum ♒, <lb/>in cuius linea fub gr. </s> <s xml:id="echoid-s11678" xml:space="preserve">45. </s> <s xml:id="echoid-s11679" xml:space="preserve">reperio 4. </s> <s xml:id="echoid-s11680" xml:space="preserve">34. </s> <s xml:id="echoid-s11681" xml:space="preserve">ideſt, hor. </s> <s xml:id="echoid-s11682" xml:space="preserve">4. </s> <s xml:id="echoid-s11683" xml:space="preserve">min. </s> <s xml:id="echoid-s11684" xml:space="preserve">34. </s> <s xml:id="echoid-s11685" xml:space="preserve">quod eſt tempus ſemidiurnum, quo duplicato ha-<lb/>beo tempus diurnum ſiue quantitatem diei hor. </s> <s xml:id="echoid-s11686" xml:space="preserve">9,. </s> <s xml:id="echoid-s11687" xml:space="preserve">min. </s> <s xml:id="echoid-s11688" xml:space="preserve">8. </s> <s xml:id="echoid-s11689" xml:space="preserve">quibus demptis a 24. </s> <s xml:id="echoid-s11690" xml:space="preserve">habeo quantitatem noctis hor. <lb/></s> <s xml:id="echoid-s11691" xml:space="preserve">14. </s> <s xml:id="echoid-s11692" xml:space="preserve">min. </s> <s xml:id="echoid-s11693" xml:space="preserve">52′. </s> <s xml:id="echoid-s11694" xml:space="preserve">quare iuxta Italicas hora Soloritur hora 14. </s> <s xml:id="echoid-s11695" xml:space="preserve">52′. </s> <s xml:id="echoid-s11696" xml:space="preserve">prędictus autem tempus ſemidiurnum detractum <lb/>à 24. </s> <s xml:id="echoid-s11697" xml:space="preserve">dabit tempus meridiei hora 19. </s> <s xml:id="echoid-s11698" xml:space="preserve">26′. </s> <s xml:id="echoid-s11699" xml:space="preserve">tempus mediæ noctis habetur diuidendo tempus nocturnum bifarif<unsure/>, <lb/>eritq; </s> <s xml:id="echoid-s11700" xml:space="preserve">hora 7. </s> <s xml:id="echoid-s11701" xml:space="preserve">26′.</s> <s xml:id="echoid-s11702" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11703" xml:space="preserve">Quod ſi eleuatio poli oblata non reperiatur in Tabula, accipe propinquiorem, eique adde quantũm iudica-<lb/>ueris addendum eſſe, parum enim a vero aberrabis. </s> <s xml:id="echoid-s11704" xml:space="preserve">pariter ſi tempus oblatum ſeu ſi gradus Solis non reperies. <lb/></s> <s xml:id="echoid-s11705" xml:space="preserve">à vicinioribus ſupplementum petes, addendo aliquid iuxta earum differentiam, v.</s> <s xml:id="echoid-s11706" xml:space="preserve">g. </s> <s xml:id="echoid-s11707" xml:space="preserve">ſi ad 20. </s> <s xml:id="echoid-s11708" xml:space="preserve">gr. </s> <s xml:id="echoid-s11709" xml:space="preserve">Capricorni, <lb/>qui non eſtin Tabula, eſſet quantitas diei ex Tabula hac eruenda, in eadem Parmenſi habitatione, video in <lb/>Tabula ad initium Capricorni quantitatem temporis ſemidiurni eſſe hor. </s> <s xml:id="echoid-s11710" xml:space="preserve">4. </s> <s xml:id="echoid-s11711" xml:space="preserve">17′. </s> <s xml:id="echoid-s11712" xml:space="preserve">in principio vero ſequenti ſi-<lb/>gni Aquarij eſſe horarum 4. </s> <s xml:id="echoid-s11713" xml:space="preserve">34′. </s> <s xml:id="echoid-s11714" xml:space="preserve">horum differẽtia eſt min. </s> <s xml:id="echoid-s11715" xml:space="preserve">27. </s> <s xml:id="echoid-s11716" xml:space="preserve">quia igitur gr. </s> <s xml:id="echoid-s11717" xml:space="preserve">20. </s> <s xml:id="echoid-s11718" xml:space="preserve">Capricorni eſt ferè medius in-<lb/>ter v@rumque, ideo minori tempori 4. </s> <s xml:id="echoid-s11719" xml:space="preserve">17′. </s> <s xml:id="echoid-s11720" xml:space="preserve">addo pluſculũ dimij differentię, conficioq; </s> <s xml:id="echoid-s11721" xml:space="preserve">hor. </s> <s xml:id="echoid-s11722" xml:space="preserve">4 min. </s> <s xml:id="echoid-s11723" xml:space="preserve">26 pro quan-<lb/>titate temporis ſemidiurni gr. </s> <s xml:id="echoid-s11724" xml:space="preserve">20. </s> <s xml:id="echoid-s11725" xml:space="preserve">Capricorni, tempore igitur ſemidiurno habito, reliqua vt ſupra ex ipſo col-<lb/>liguntur.</s> <s xml:id="echoid-s11726" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11727" xml:space="preserve">Cæterum hæc eadem Tabula inſeruire poteſt exiſtentibus in hemiſphærio Auſtrali, ſi ſigna, & </s> <s xml:id="echoid-s11728" xml:space="preserve">characteres <lb/>ſignorum loca inuicem permutent, vt cuique facilè eſt intelligere, v.</s> <s xml:id="echoid-s11729" xml:space="preserve">g. </s> <s xml:id="echoid-s11730" xml:space="preserve">vbi eſt ♋, ponatur ♑, & </s> <s xml:id="echoid-s11731" xml:space="preserve">è contra.</s> <s xml:id="echoid-s11732" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div241" type="section" level="1" n="158"> <head xml:id="echoid-head170" style="it" xml:space="preserve">Declaratio, & vſus Tabulæ ſecundæ crepuſ culorum.</head> <p> <s xml:id="echoid-s11733" xml:space="preserve">IN hac pariter Tabula altitudines poli ſunt in ſuprema linea, ibiq; </s> <s xml:id="echoid-s11734" xml:space="preserve">notao, ſignificat ſphæram rectam. </s> <s xml:id="echoid-s11735" xml:space="preserve">reli-<lb/>quæ etiam lineæ debentur ſignis ſibi ad ſiniſtram adſcriptis, numeriq; </s> <s xml:id="echoid-s11736" xml:space="preserve">earum ſignificant quantitatem crepu-<lb/>ſculi, ſiue matutini, ſiue veſpertini, ſiue continui. </s> <s xml:id="echoid-s11737" xml:space="preserve">quando loco numerorum occurrunt literætn, eæ denotant <lb/>crepuſculum tota nocte durare literę d c, denotantibi nullum eſſe crepuſculum, ſed diem purum ac continuũ. <lb/></s> <s xml:id="echoid-s11738" xml:space="preserve">literæ tandem n p, indicant ibi eſſe noctem puram ſine crepuſculo. </s> <s xml:id="echoid-s11739" xml:space="preserve">vſus eius exemplo patebit, ſit accipienda <lb/>quantitas crepuſculi ad eundem diem 21. </s> <s xml:id="echoid-s11740" xml:space="preserve">Ianuarij in eleuatione 45. </s> <s xml:id="echoid-s11741" xml:space="preserve">ſcilicet cum Sól circa initium Aquarij ver-<lb/>ſatur. </s> <s xml:id="echoid-s11742" xml:space="preserve">igitur ſub eleuatione 45. </s> <s xml:id="echoid-s11743" xml:space="preserve">reperta in Tabula è regione ſigni ♒ Aquarij, ſeu in linea cui adſcriptus eſt <lb/>character hic ♒, accipio numerum hor. </s> <s xml:id="echoid-s11744" xml:space="preserve">1. </s> <s xml:id="echoid-s11745" xml:space="preserve">min. </s> <s xml:id="echoid-s11746" xml:space="preserve">49 pro quantitate crepuſculi. </s> <s xml:id="echoid-s11747" xml:space="preserve">& </s> <s xml:id="echoid-s11748" xml:space="preserve">quia quotid efiunt duo crepu-<lb/>ſcula matutinum, & </s> <s xml:id="echoid-s11749" xml:space="preserve">veſpertinum, ideo tantum illius temporis crepuſculum erit hor. </s> <s xml:id="echoid-s11750" xml:space="preserve">3. </s> <s xml:id="echoid-s11751" xml:space="preserve">min. </s> <s xml:id="echoid-s11752" xml:space="preserve">38′. </s> <s xml:id="echoid-s11753" xml:space="preserve">quod tempus <lb/>ſi addatur quantitati diei ſuperius ad idemtempus inuentæ quæ fuit hor. </s> <s xml:id="echoid-s11754" xml:space="preserve">9.</s> <s xml:id="echoid-s11755" xml:space="preserve">8′. </s> <s xml:id="echoid-s11756" xml:space="preserve">conflabitur tota dies artificialis <lb/>vulgaris, eritq; </s> <s xml:id="echoid-s11757" xml:space="preserve">hor. </s> <s xml:id="echoid-s11758" xml:space="preserve">12. </s> <s xml:id="echoid-s11759" xml:space="preserve">min. </s> <s xml:id="echoid-s11760" xml:space="preserve">46′. </s> <s xml:id="echoid-s11761" xml:space="preserve">quo toto tempore artifices lumen vident atq; </s> <s xml:id="echoid-s11762" xml:space="preserve">operari poſſunt quare nox pu-<lb/>ra, & </s> <s xml:id="echoid-s11763" xml:space="preserve">mera erit hor. </s> <s xml:id="echoid-s11764" xml:space="preserve">11. </s> <s xml:id="echoid-s11765" xml:space="preserve">16′. </s> <s xml:id="echoid-s11766" xml:space="preserve">quæ omnia ita ſe habent dummodo tempora nubila non obſtent. </s> <s xml:id="echoid-s11767" xml:space="preserve">atq; </s> <s xml:id="echoid-s11768" xml:space="preserve">hęc eſt præ-<lb/>cipua huius Tabulæ vtilitas, vt ſcilicet quantitastotius diei artificialis vulgaris, ideſt, quantum temporis ab ini-<lb/>tio Auroræ vſq; </s> <s xml:id="echoid-s11769" xml:space="preserve">ad intempeſtam noctem intercedat.</s> <s xml:id="echoid-s11770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11771" xml:space="preserve">Quod ſi gradus Zodiaci oblatus, aut eleuatio poli oblata non reperiatur in Tabula, ex vicinioribus gradi-<lb/>bus, & </s> <s xml:id="echoid-s11772" xml:space="preserve">eleuationibus iudicio cuiuſque ſupplendum erit, vt plurimum enim differentiæ ſunt modicæ, ex qui-<lb/>bus ſi pars conueniens accipiatur, nullus error ſenſibilis contingit. </s> <s xml:id="echoid-s11773" xml:space="preserve">Ex eadem Tabula liquet falſum videri <lb/>quod alij dicunt, nimirum crepuſcula in Capricorno ſemper eſſe maiora crepuſculis ad dimidiam Libram, <lb/>& </s> <s xml:id="echoid-s11774" xml:space="preserve">Piſces, nam ſub altitudine poli grad. </s> <s xml:id="echoid-s11775" xml:space="preserve">83 {1/2}. </s> <s xml:id="echoid-s11776" xml:space="preserve">Tabula exhibet Capricorni crepuſcu lum hor. </s> <s xml:id="echoid-s11777" xml:space="preserve">2. </s> <s xml:id="echoid-s11778" xml:space="preserve">10′. </s> <s xml:id="echoid-s11779" xml:space="preserve">at per totam <lb/>Libram, & </s> <s xml:id="echoid-s11780" xml:space="preserve">Piſces exhibet crepuſculum per totam noctem. </s> <s xml:id="echoid-s11781" xml:space="preserve">(quod etiam ab horis 12. </s> <s xml:id="echoid-s11782" xml:space="preserve">vſque ad hor. </s> <s xml:id="echoid-s11783" xml:space="preserve">fermè 20.) <lb/></s> <s xml:id="echoid-s11784" xml:space="preserve">excreſcit. </s> <s xml:id="echoid-s11785" xml:space="preserve">idem accidit in alijs eleuationibus ſupra eleuationem gr. </s> <s xml:id="echoid-s11786" xml:space="preserve">74. </s> <s xml:id="echoid-s11787" xml:space="preserve">vt in Tabula videre eſt.</s> <s xml:id="echoid-s11788" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11789" xml:space="preserve">Notandum vltimo in omnibus eleuationibus, vbi ſunt appoſiti numeri indicantes quantitatem crepuſculi, <lb/>eos indicare dimidium tantum crepuſculum, quod vni diei debetur, quia ſunt in quolibet die bina crepuſcula, <lb/>quorum alterum Tabula exhibet. </s> <s xml:id="echoid-s11790" xml:space="preserve">quod etiam ſeruatur vbi dimidium crepuſculi alteri dimidio continuatur, <lb/>vt accidit in ijs paralellis, quorum diametri pars eſt infra horizontem, ſed ſupra lineam crepuſculi, ea enim <lb/>pars efficit crepuſculum, cuius tantum dimidium in Tabula ponitur, ſecus eſt vbi ſunt lineætn &</s> <s xml:id="echoid-s11791" xml:space="preserve">c.</s> <s xml:id="echoid-s11792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11793" xml:space="preserve">Hæc pariter Tabuia inſeruiet pro hemiſphærio Auftrali commutatis ſex ſignis Borealibus in Auſtralia, vt<unsure/> <lb/>@onſideranti manifeſtum eſt.</s> <s xml:id="echoid-s11794" xml:space="preserve"/> </p> <pb o="121" file="0143" n="148" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div242" type="section" level="1" n="159"> <head xml:id="echoid-head171" style="it" xml:space="preserve">De Horis. Cap. XVII.</head> <p> <s xml:id="echoid-s11795" xml:space="preserve">CVm iam de annis, de diebus, de crepuſculis ſatis dictum ſit, ſupereſt vt de horis etiam nonnulla adiunga-<lb/>mus, nam ex profeſſo de horis tractare pertinet ad tractatum de Horologijs: </s> <s xml:id="echoid-s11796" xml:space="preserve">hora enim eſt pars vigeſi-<lb/>ma quarta diei naturalis. </s> <s xml:id="echoid-s11797" xml:space="preserve">Horæ Aſtronomicæ ſunt partes diei Aſtronomici, qui incipit a meridie, atque in <lb/>meridiem deſinit. </s> <s xml:id="echoid-s11798" xml:space="preserve">Horæ Babylonicæ, ſiue ab ortu, ſunt partes diei Babylonici incipientis ab ortu Solis, at-<lb/>que in eundem ortum deſinentis. </s> <s xml:id="echoid-s11799" xml:space="preserve">Horæ Italicæ ſiue ab occaſu, ſunt partes diei more Italorum, incipientis ab <lb/>occaſu Solis, vſque ad alterum occaſum perdurantis. </s> <s xml:id="echoid-s11800" xml:space="preserve">Horæ antiquæ erant partes duodecimæ tam diei quam <lb/>noctis artificialis, de quibus ſcriptum eſt in Euangelio, nonne 12. </s> <s xml:id="echoid-s11801" xml:space="preserve">ſunt horæ diei. </s> <s xml:id="echoid-s11802" xml:space="preserve">ſit ergo problema primum <lb/>de horis Italicis.</s> <s xml:id="echoid-s11803" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div243" type="section" level="1" n="160"> <head xml:id="echoid-head172" style="it" xml:space="preserve">Quota ſit hora Italica interdiu ex Sphæra materiali indagare.</head> <p> <s xml:id="echoid-s11804" xml:space="preserve">HAbeas primo gradum Solis in eclyptica pro oblata die; </s> <s xml:id="echoid-s11805" xml:space="preserve">deinde ſphæra Aſtronomicè conſtituta, pri-<lb/>mum mobile ſic motu diurno conuerte, vt gradus Solis ad Solem ipſum collucentem directè aſpiciat; <lb/></s> <s xml:id="echoid-s11806" xml:space="preserve">quod exactè fiet ſi vmbra Zodiaci tota ceciderit in concauum partis Zodiaci oppoſitæ, ita vt torum illud con-<lb/>cauum exactè obumbretur. </s> <s xml:id="echoid-s11807" xml:space="preserve">tunc nota gradum æquatoris tangentem horizontem occiduum. </s> <s xml:id="echoid-s11808" xml:space="preserve">dein verte pri-<lb/>mum mobile donec gradus Solis horizontem occiduum attingat, atque iterum nota gradum æquatoris, qui <lb/>eundem horizontem tangi. </s> <s xml:id="echoid-s11809" xml:space="preserve">numera iam gradus æquatoris inter hos duos gradus interceptos, eoſq; </s> <s xml:id="echoid-s11810" xml:space="preserve">in tẽpus, <lb/>ſeu horas conuerte, numerumque horarum inuentum deme à 24. </s> <s xml:id="echoid-s11811" xml:space="preserve">ſic enim relinquitur numerus horarum ab <lb/>occaſu, ſeu Italicarum tunc temporis elapſarum.</s> <s xml:id="echoid-s11812" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div244" type="section" level="1" n="161"> <head xml:id="echoid-head173" style="it" xml:space="preserve">Qua hora Italica Sol oriatur, ſit meridies, & medianox.</head> <p> <s xml:id="echoid-s11813" xml:space="preserve">1 TEmpus diurnum, vti diximus ſupra in tractatu de quantitate dierum artificialium, prius inuentum <lb/>de me à 24. </s> <s xml:id="echoid-s11814" xml:space="preserve">ſic enim relinquetur tempus nocturnum, ideſt, numerus horarum noctis, quibus elapſis <lb/>Soloritur.</s> <s xml:id="echoid-s11815" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11816" xml:space="preserve">2 Deme tempus ſemidiurnum à 24. </s> <s xml:id="echoid-s11817" xml:space="preserve">reſiduus enim numerus eſt numerus horarum, quibus exactis meri-<lb/>dies eſt.</s> <s xml:id="echoid-s11818" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11819" xml:space="preserve">3 lam dimidium temporis nocturni, ideſt, dimidium numeri horarum nocturnarum exhibebit horam <lb/>mediæ noctis.</s> <s xml:id="echoid-s11820" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11821" xml:space="preserve">Cæterum quod ad alia horarum genera attinet, ne ſim longior, facilè fuerit cuique ſtudioſo eadem inda-<lb/>gare, quæ de Italicis modo ſunt indagata.</s> <s xml:id="echoid-s11822" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div245" type="section" level="1" n="162"> <head xml:id="echoid-head174" style="it" xml:space="preserve">Cur Solis illuminationes per quæuis foramina ingredientes rotunda <lb/>appareant. Cap. X V III.</head> <p> <s xml:id="echoid-s11823" xml:space="preserve">SEquitur iam, vt admirabile quiddam de Solis illuminatione elucidemus, qua ratione videlicet fieri poſ-<lb/>ſit, vt Solis illuminationes quæ per foramina tectorum, aut feneſtrarum anguloſa, ac valdè irregularia il-<lb/>labuntur, perpetuo inuita foraminis figura, in oppoſitis planis, aut ouales, aut rotundæ appareant. </s> <s xml:id="echoid-s11824" xml:space="preserve">huic pul-<lb/>cherrimæ quæſtioni, quæ ſuperiorum philoſophantiũ ingenia mirè vexauit, alias in opere de locis Mathem. <lb/></s> <s xml:id="echoid-s11825" xml:space="preserve">Ariſtotelis Geometricè reſpondimus; </s> <s xml:id="echoid-s11826" xml:space="preserve">nunc aliter, ſed facilius ex 10. </s> <s xml:id="echoid-s11827" xml:space="preserve">Keplero hac experientia ſatisfaciemus. </s> <s xml:id="echoid-s11828" xml:space="preserve"><lb/>Summo igitur laqueari affige corpus aliquod, verbi gratia, rotundam Tabellam, quæ Solem referat; </s> <s xml:id="echoid-s11829" xml:space="preserve">infra <lb/>quam in medio inter ipſam, & </s> <s xml:id="echoid-s11830" xml:space="preserve">pauimentum, ſit foramen aliquod, verbi gratia triangulare, iam ex aliquo <lb/>puncto peripheriæ rotundæ deſcendat filum, quod ſit ſolaris radij inſtar, per foramen illud tri<unsure/>angulare ad <lb/>pauimentum filum iſtud ſecus trianguli latera ab aliquo circumlatum, altero extremo inferiori ſignet in pa-<lb/>nimento veſtigium. </s> <s xml:id="echoid-s11831" xml:space="preserve">idemque fiat ex quatuor, aut quinque punctis eiuſdem peripheriæ, & </s> <s xml:id="echoid-s11832" xml:space="preserve">illico in pauimento <lb/>apparebunt quatuor, aut quinque triangula in orbem conſtituta. </s> <s xml:id="echoid-s11833" xml:space="preserve">ſicque ex omnibus illius pũctis omnia trian-<lb/>gula in pauimento delineata in gyrum conſtituta apparebunt; </s> <s xml:id="echoid-s11834" xml:space="preserve">ac propterea omnes ſimui rotundam quãdam <lb/>figuram efficiunt. </s> <s xml:id="echoid-s11835" xml:space="preserve">quanto autem foramen illud fuerit ſublimius, tanto citius triangula illa in rotundiorem <lb/>orbem ſeſe accommodabunt. </s> <s xml:id="echoid-s11836" xml:space="preserve">quod ſi foramen illud non ſit perpendiculariter ſub Tabella, ſed ad partem <lb/>vnam, ita vt filum per illud recta intrans obliquè pauimento accidat, tunc triangula illa ſeſe in oualem figurã <lb/>componunt. </s> <s xml:id="echoid-s11837" xml:space="preserve">ex hac igitur obſeruatione diligenter facta, & </s> <s xml:id="echoid-s11838" xml:space="preserve">conſiderata, variatiſq; </s> <s xml:id="echoid-s11839" xml:space="preserve">foraminibus ac Tabellæ <lb/>@guris, manifeſtè apparebit qua ratione ſua Sol illuminationes ſemper, aut rotundas efficiat, aut ouales, aut <lb/>cclypſis tempore eclypſatas.</s> <s xml:id="echoid-s11840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11841" xml:space="preserve">Hæc porro conſideratio, vt rectè perficiatur eo indiget principio, quod ſupra poſuimus, à quolibet vi-<lb/>delicet Solis puncto, lucem per lineas rectas quoquo verſus emicare; </s> <s xml:id="echoid-s11842" xml:space="preserve">ſic enim non ſolum à punctis periphe-<lb/>riæ, ſed a quolibet etiam ſolaris diſci puncto, radij per foramina ad rotundas illuminationes efficiendas<unsure/> <lb/>prodibunt.</s> <s xml:id="echoid-s11843" xml:space="preserve"/> </p> <pb o="122" file="0144" n="149" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div246" type="section" level="1" n="163"> <head xml:id="echoid-head175" style="it" xml:space="preserve">Aliud mirabile de luce Solis.</head> <p> <s xml:id="echoid-s11844" xml:space="preserve">NOn ſolum autem Solis lumen iſtud in ſe ipſo efficit, ſed rebus etiam ab ſe aliquo modo illuminatis ean-<lb/>dem virtutem communicat: </s> <s xml:id="echoid-s11845" xml:space="preserve">quod hac pulcherrima experientia patebit. </s> <s xml:id="echoid-s11846" xml:space="preserve">in ali<unsure/>quo igitur conclaui, por-<lb/>tis ac feneſtris omnino obſeratis, per ſolum paruum foramen luci pateat aditus: </s> <s xml:id="echoid-s11847" xml:space="preserve">tunc formæ externarum re-<lb/>rum, quas Solis ſplendor foris illuſtrat, in obſcurum conclaue per anguſtum illud foramen, vna cum lumine <lb/>ſubeunt; </s> <s xml:id="echoid-s11848" xml:space="preserve">obiectaq; </s> <s xml:id="echoid-s11849" xml:space="preserve">charta, in ea velut proprijs lineamentis expreſſæ conſpiciuntur, ſubobſcurius tamen quam <lb/>resipſæ ſint propter luminis trãslapſi imbecillitatem: </s> <s xml:id="echoid-s11850" xml:space="preserve">atq; </s> <s xml:id="echoid-s11851" xml:space="preserve">inuerſo ſitu; </s> <s xml:id="echoid-s11852" xml:space="preserve">cuius cauſa eſt radiorum ab ipſorum <lb/>lumine procedentium, in foramine illo mutua decuſſatio, ex qua formæ radijs illis delatæ, poſt foramen fitũ <lb/>commutant, atq; </s> <s xml:id="echoid-s11853" xml:space="preserve">inuertunt, verum iſta exactius explicare opticorum eſt.</s> <s xml:id="echoid-s11854" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div247" type="section" level="1" n="164"> <head xml:id="echoid-head176" style="it" xml:space="preserve">De Eclypſi Solis. Cap. XIX.</head> <p> <s xml:id="echoid-s11855" xml:space="preserve">VLtimo loco videndum eſt, quanam ratione Sol ipſe omnis parens luminis, aliquando lumine priuetur, <lb/>terrificamq; </s> <s xml:id="echoid-s11856" xml:space="preserve">eclypſim patiatur. </s> <s xml:id="echoid-s11857" xml:space="preserve">Verum iſthæc ſolaris eclypſis, nequaquam Solis, ſed noſtra priuatio di-<lb/>cẽda eſt. </s> <s xml:id="echoid-s11858" xml:space="preserve">nos enim ipſi ſumus, qui dum putamus Solem defectu luminis laborare, ipſius luminis ob ſuppoſitam <lb/>illi Lunam damno afficimur. </s> <s xml:id="echoid-s11859" xml:space="preserve">Dico igitur ſolarem obſcurationem effici ob Lunæ inter nos, & </s> <s xml:id="echoid-s11860" xml:space="preserve">Solem, inter-<lb/>poſitionem, quod qua ratione contingat vt intelligamus, meminiſſe debemus lunarẽ viam, ſeu circuitum, di-<lb/>uaricari ab eclyptica, ſeu via ſolari, ac propterea ſe mutuo ſecare in duobus oppoſitis punctis. </s> <s xml:id="echoid-s11861" xml:space="preserve">quorũ alterum <lb/>dicitur nodus euehens, & </s> <s xml:id="echoid-s11862" xml:space="preserve">boreus; </s> <s xml:id="echoid-s11863" xml:space="preserve">alter vero nodus deuehens, & </s> <s xml:id="echoid-s11864" xml:space="preserve">auſtrinus. </s> <s xml:id="echoid-s11865" xml:space="preserve">ſumma autem harum viarum di-<lb/>uaricatio ad gr. </s> <s xml:id="echoid-s11866" xml:space="preserve">5. </s> <s xml:id="echoid-s11867" xml:space="preserve">aſcendit, tam in boream, quam in auſtrum. </s> <s xml:id="echoid-s11868" xml:space="preserve">quæ duo loca dicuntur limites, ille boreus, hic <lb/>auſtrinus, vt alias explicauimus. </s> <s xml:id="echoid-s11869" xml:space="preserve">Cum igitur in nouilunijs accidit Lunam propè alterum nodorum, aut in <lb/>ipſo nodo, ita ſoli coniungi, vt vel corporis lunaris pars, vel totum, inter nos, & </s> <s xml:id="echoid-s11870" xml:space="preserve">Solem interponatur, ſequi-<lb/>tur neceſſario, vt Luna lumen Solis a nobis ſurſum auertat, vmbraq; </s> <s xml:id="echoid-s11871" xml:space="preserve">ſua nos contingat. </s> <s xml:id="echoid-s11872" xml:space="preserve">Quapropter cum no@ <lb/>ſolarem hunc defectum patimur, in vmbra lunari verſamur; </s> <s xml:id="echoid-s11873" xml:space="preserve">quæ vmbra, ſicuti ſupra <lb/> <anchor type="figure" xlink:label="fig-0144-01a" xlink:href="fig-0144-01"/> oſtendimus, atq; </s> <s xml:id="echoid-s11874" xml:space="preserve">depinximus, ad terram deſcendit, eamq; </s> <s xml:id="echoid-s11875" xml:space="preserve">non multum tranſcendit. <lb/></s> <s xml:id="echoid-s11876" xml:space="preserve">quoniam vero Luna minor eſt quam terra, vmbraq; </s> <s xml:id="echoid-s11877" xml:space="preserve">lunaris turbinata eſt, parumque <lb/>terram tranſcendit, fit vt propè vmbræ verticem terram inuadat; </s> <s xml:id="echoid-s11878" xml:space="preserve">ac proinde in parte <lb/>vmbræ multo, quam terra graciliori. </s> <s xml:id="echoid-s11879" xml:space="preserve">ex quo ſequitur totam terram interiectu Lunæ, <lb/>nunquam obſcurari poſſe. </s> <s xml:id="echoid-s11880" xml:space="preserve">quare alicubi terrarum defectus ſolaris apparebit, alicubi <lb/>non. </s> <s xml:id="echoid-s11881" xml:space="preserve">ſimiliter aliquando totus Sol obſcurabitur, aliquando pars, quæ omnia in hac <lb/>figura contemplari potes in qua Sol vbi A, Luna vbi B C, Terra E F, vmbra Lunæ <lb/>B D C, quæ terram partim obumbrat, partim non, quare ſi quis eſſet ad partes F, to-<lb/>tum Solem videre videretur obſcuratum: </s> <s xml:id="echoid-s11882" xml:space="preserve">ſi vero eſſet ad partes E, non totum, ſed par <lb/>tem tantum H G, eam vero partem, quæ inter duas lineas E G, E H, interciperetur <lb/>videret colluſcentem; </s> <s xml:id="echoid-s11883" xml:space="preserve">quæ quidem concipi debet pars corporis ſphærici defectiua ob <lb/>Lunæ interpoſitionem. </s> <s xml:id="echoid-s11884" xml:space="preserve">quæ quoniam pariter ſphærica eſt, ideo pars hæc ſolaris cor-<lb/>poris exiſtentibus in E, corniculata apparebit; </s> <s xml:id="echoid-s11885" xml:space="preserve">cornua obuertens ad partes H G, ſub <lb/>quibus Luna exiſtens Solem deficientem efficit.</s> <s xml:id="echoid-s11886" xml:space="preserve"/> </p> <div xml:id="echoid-div247" type="float" level="2" n="1"> <figure xlink:label="fig-0144-01" xlink:href="fig-0144-01a"> <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0144-01"/> </figure> </div> <p> <s xml:id="echoid-s11887" xml:space="preserve">Cæterum ex dictis de eclypſi, tam Lunæ quam Solis, conſideratione dignum vide-<lb/>tur, quod quemadmodum Luna obiectu, & </s> <s xml:id="echoid-s11888" xml:space="preserve">vmbra terrę, ſolari lumine priuatur: </s> <s xml:id="echoid-s11889" xml:space="preserve">ita vi-<lb/>ciſſim terra obiectu, & </s> <s xml:id="echoid-s11890" xml:space="preserve">vmbra Lunæ eodem ſolari ſplendore deſtituitur.</s> <s xml:id="echoid-s11891" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11892" xml:space="preserve">Quod autem ob Lunæ ſuppoſitionem Sol deficiat; </s> <s xml:id="echoid-s11893" xml:space="preserve">ſic patere poteſt; </s> <s xml:id="echoid-s11894" xml:space="preserve">tempore enim <lb/>huius defectus, adhibita diligenti induſtria, oculis ipſis teſ@ãtibus Lunam Soli ſubie-<lb/>ctam cernimus; </s> <s xml:id="echoid-s11895" xml:space="preserve">his modis, aſſumpto vitro, colore quopiam, opacato, vt lumen Solis, ſi <lb/>quod remanet, infringatur, ſi per ipſum deficientem Solem inſpexerimus, Lunam <lb/>illico ſub ipſo latentem, eumq; </s> <s xml:id="echoid-s11896" xml:space="preserve">nobis abſcondentem intuebimur. </s> <s xml:id="echoid-s11897" xml:space="preserve">Secundo ope Tele-<lb/>ſcopij, cui præpoſitum ſit vitrum ſatis opacum, tunc temporis perſpicue Lunam So-<lb/>lem nobis occultantem, videbimus. </s> <s xml:id="echoid-s11898" xml:space="preserve">Certum eſt, eclypſim hanc non niſi nouilunij tem <lb/>pore accidere, quo etiam tempore certum eſt, Lunam Soli coniungi, vnde manifeſtũ <lb/>euadit, huius rei cauſam eſſe Lunam. </s> <s xml:id="echoid-s11899" xml:space="preserve">Quarto ſuppoſito quod Luna ſit cauſa huius de-<lb/>fectus, laluantur omnes apparentiæ, videlicet, cur Solincipiat eclypſari in parte ſui <lb/>occidentali, & </s> <s xml:id="echoid-s11900" xml:space="preserve">in orientali deſinat. </s> <s xml:id="echoid-s11901" xml:space="preserve">cur in principio eclypſis Solappareat inſtar Lu-<lb/>næ corniculatæ, quæ cornua in occidẽtem obuertat; </s> <s xml:id="echoid-s11902" xml:space="preserve">in fine vero ſit pariter inſtar no-<lb/>uæ Lunæ, quæ cornua in orientem dirigat: </s> <s xml:id="echoid-s11903" xml:space="preserve">ratio eſt, quia Luna tunc mouetur ſub So-<lb/>le, ab occidente verſus orientem, eumq; </s> <s xml:id="echoid-s11904" xml:space="preserve">motu proprio ſuperat. </s> <s xml:id="echoid-s11905" xml:space="preserve">Hinc etiam patet cur <lb/>hæc eclypſis ſit modo partialis; </s> <s xml:id="echoid-s11906" xml:space="preserve">modo totalis, nunquam tamen cum mora, ideſt, nun-<lb/>quam Soltotus obumbratus maneat; </s> <s xml:id="echoid-s11907" xml:space="preserve">ſed ſtatim poſt totalem obſcurationem incipiat <lb/>ex parte occidentis ſplendeſcere. </s> <s xml:id="echoid-s11908" xml:space="preserve">pariter cur tantum duret, & </s> <s xml:id="echoid-s11909" xml:space="preserve">non amplius. </s> <s xml:id="echoid-s11910" xml:space="preserve">Quin-<lb/>to indicat idem calculus eclypſium, Aſtronomi enim ex motu Lunæ, & </s> <s xml:id="echoid-s11911" xml:space="preserve">Solis computato, Solem oblcu-<lb/>randum infallibiliter prænunciant. </s> <s xml:id="echoid-s11912" xml:space="preserve">Sexto tandem nulla alia occurrit cauſa; </s> <s xml:id="echoid-s11913" xml:space="preserve">Luna igitur cauſa eſt ſolaris <lb/>defectus.</s> <s xml:id="echoid-s11914" xml:space="preserve"/> </p> <pb o="123" file="0145" n="150" rhead="Liber Decimus."/> <p> <s xml:id="echoid-s11915" xml:space="preserve">Sed quæritur, cur in omni nouilunio, Solẽ Luna nobis non adimat? </s> <s xml:id="echoid-s11916" xml:space="preserve">Cauſa eſt inclinatio viæ Lunaris a via <lb/>Solis, quæ eſt eclyptica; </s> <s xml:id="echoid-s11917" xml:space="preserve">ſæpè enim nouiluniun accidit adeo longè ab interſectionibus harum viarum, ſeua <lb/>nodis, vt diſtantia luminarium tanta ſit quæ luminaria ipſa ſibi viſibiliter copultari non permitat. </s> <s xml:id="echoid-s11918" xml:space="preserve">in nodis <lb/>viæ vniuntur, poſtea deinceps ſemper magis vſque ad gra. </s> <s xml:id="echoid-s11919" xml:space="preserve">5. </s> <s xml:id="echoid-s11920" xml:space="preserve">dilatantur; </s> <s xml:id="echoid-s11921" xml:space="preserve">quare aliquando tanta eſt dilatatio <lb/>hæc vt diſtantiam prædictam importet. </s> <s xml:id="echoid-s11922" xml:space="preserve">deſinierunt autem Aſtronomi diſfantias quaſdam a nodis, quas ter-<lb/>minos eclipticos vocarunt, eo quod intra illos terminos, eclypſes contingant. </s> <s xml:id="echoid-s11923" xml:space="preserve">ſuntautem alij termini poſ-<lb/>ſibiles, intra quos ſcilicet eclypſis poteſt quidem fieri, ſed non neceſſario fit alij ſunt termini neceſſarij, intra <lb/>quos exiſtente nouilunio, neceſſario ſequitur Solis defectus. </s> <s xml:id="echoid-s11924" xml:space="preserve">& </s> <s xml:id="echoid-s11925" xml:space="preserve">quoniam duplex faciunt nouilunium, mediũ <lb/>ſcilicet, & </s> <s xml:id="echoid-s11926" xml:space="preserve">verum, ponam Solum neceſſarios terminos veri nouilunij. </s> <s xml:id="echoid-s11927" xml:space="preserve">quando igitur in nouilunijs veris, <lb/>Luna exiſtens borealis, non diſtiterit a nodis pluſquam gra. </s> <s xml:id="echoid-s11928" xml:space="preserve">15.</s> <s xml:id="echoid-s11929" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s11930" xml:space="preserve">exiſtens vero auſtralis, non aberit pluſquam <lb/>gra. </s> <s xml:id="echoid-s11931" xml:space="preserve">7. </s> <s xml:id="echoid-s11932" xml:space="preserve">neceſſario Solem obſcurabit; </s> <s xml:id="echoid-s11933" xml:space="preserve">tantoque maior erit obſcuratio, quanto nodis proprior fuerit. </s> <s xml:id="echoid-s11934" xml:space="preserve">maxima <lb/>vero in ipſis nodis. </s> <s xml:id="echoid-s11935" xml:space="preserve">cur autem in boreali latitudine Lunæ, maiores ſint termini, quam in auſtrali, cauſa eſt <lb/>Lunæ parallaxis, quæ in latitudine boreali, eam deprimit verſus Solem, ideſt, facit latitudinem Lunæ appa-<lb/>rere minorem, quam ſit. </s> <s xml:id="echoid-s11936" xml:space="preserve">è contra in auſtrali parallaxis eam deprimit a Sole, ideſt, maiorem facit Lunæ lati-<lb/>tudinem apparere quam ſit; </s> <s xml:id="echoid-s11937" xml:space="preserve">quare in hac parte niſi Luna vere parum diſtet a via Solis, quod non niſi apud <lb/>nodos accidit, nimirum ob parallaxim detrahitur a Sole, ita vteum occultare nequeat. </s> <s xml:id="echoid-s11938" xml:space="preserve">in parte boreali <lb/>quamuis Luna habeat magnam latitudinem, & </s> <s xml:id="echoid-s11939" xml:space="preserve">conſequenter plus diſtet a nodis, quia tamen parallax@s eam <lb/>verſus Solem deprimit, ideo poteſt Soli opponi, ſicque eclypſim eſſicere. </s> <s xml:id="echoid-s11940" xml:space="preserve">fateor tamen hanc ſpeculatio-<lb/>nem eſſe ſatis difficilem, adhibita tamen ſphæra materiali, in qua lunarem viam ritè capi<unsure/>amus oculumque <lb/>noſtrum in terra poſitum ad Lunam aſpicere, ac parallaxim efficere imaginemur, non difficile erit totam <lb/>hanc rem percipere.</s> <s xml:id="echoid-s11941" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div249" type="section" level="1" n="165"> <head xml:id="echoid-head177" style="it" xml:space="preserve">Qua ratione ſolaris eclypſis magnitudo facillimè obſeruetur.</head> <p> <s xml:id="echoid-s11942" xml:space="preserve">DE hac re fuſius ſcripſi in opere de locis Mathem. </s> <s xml:id="echoid-s11943" xml:space="preserve">Ariſt. </s> <s xml:id="echoid-s11944" xml:space="preserve">ad Problem. </s> <s xml:id="echoid-s11945" xml:space="preserve">10. </s> <s xml:id="echoid-s11946" xml:space="preserve">ſect. </s> <s xml:id="echoid-s11947" xml:space="preserve">15. </s> <s xml:id="echoid-s11948" xml:space="preserve">nunc rem paucis perſtrin-<lb/>gam: </s> <s xml:id="echoid-s11949" xml:space="preserve">tempore igitur ſolaris defectus, intra parietes vſpiam clauſis omnibus feneſtris, ad mittatur ſo laris <lb/>radius per anguſtum foramen rotundum, excipiaturq; </s> <s xml:id="echoid-s11950" xml:space="preserve">radius hic perpendiculari-<lb/> <anchor type="figure" xlink:label="fig-0145-01a" xlink:href="fig-0145-01"/> ter in plana Tabella: </s> <s xml:id="echoid-s11951" xml:space="preserve">vbi certo quantum Sol defecerit, ad vnguem licet videre, <lb/>abſque vlla intuitus moleſtia, ac tam perfectè, ac ſi in cœlo coram adeſſes. </s> <s xml:id="echoid-s11952" xml:space="preserve">illumi-<lb/>natio enim Solis, quæ alias rotunda eſſet, erit temporis eclypſis pariter defectiua, <lb/>totamq; </s> <s xml:id="echoid-s11953" xml:space="preserve">defectus varietatem repræſentabit: </s> <s xml:id="echoid-s11954" xml:space="preserve">quamuis inuerſo ſitu, ob cauſam ſupe-<lb/>rius tactam. </s> <s xml:id="echoid-s11955" xml:space="preserve">initio enim eclypſis, hæc illuminatio defectiua apparebit ex parte oc-<lb/>cidentis, contrario ſitu, quam in Sole ipſo, conſimili tamen magnitudine, & </s> <s xml:id="echoid-s11956" xml:space="preserve">dura-<lb/>tione. </s> <s xml:id="echoid-s11957" xml:space="preserve">quantaigitur pars illius illuminationis defecerit, præſertim circa medium <lb/>eclypſis, tanta quoque pars ſolaris diſci obſcurabitur. </s> <s xml:id="echoid-s11958" xml:space="preserve">oportet igitur imaginem il-<lb/>lius illuminationis in Tabella delineare, totamq; </s> <s xml:id="echoid-s11959" xml:space="preserve">eius diametrum in partes 12. </s> <s xml:id="echoid-s11960" xml:space="preserve">di-<lb/>uidere; </s> <s xml:id="echoid-s11961" xml:space="preserve">quas Aſtronomi digitos eclypticos vocant. </s> <s xml:id="echoid-s11962" xml:space="preserve">tandemq; </s> <s xml:id="echoid-s11963" xml:space="preserve">obſeruare quot di-<lb/>giti obſcurentur, magnitudo enim ex numero digitorum deficientium deſumi-<lb/>tur, vt in hac figura, vides quatuor tantum digitos, ſeu tertiam partem diametri illuminationis, ac pro-<lb/>inde Solis, defeciſſe.</s> <s xml:id="echoid-s11964" xml:space="preserve"/> </p> <div xml:id="echoid-div249" type="float" level="2" n="1"> <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a"> <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-01"/> </figure> </div> </div> <div xml:id="echoid-div251" type="section" level="1" n="166"> <head xml:id="echoid-head178" style="it" xml:space="preserve">Corollarium de miraculoſa eclypſi Solis in paſſione Domini.</head> <p> <s xml:id="echoid-s11965" xml:space="preserve">EX prædictis de ſolari defectu, manifeſtum fit quam miraculoſum, quamque contra naturæ leges, exti-<lb/>terit ſolare illud deliquium, quod paſſionis Domini Noſtri tempore factum eſt. </s> <s xml:id="echoid-s11966" xml:space="preserve">primo quia tempore <lb/>plenilunij contigit, quando Luna Soli diametraliter oppoſita, nnllo modo eum occultare poteſt. </s> <s xml:id="echoid-s11967" xml:space="preserve">Secun-<lb/>do quia non ſolum fuit totale, quo ſcilicet totus Sol obſcuraretur, ſed etiam vniuerſale, ideſt, per vniuer-<lb/>ſam terram, quod non ſolet. </s> <s xml:id="echoid-s11968" xml:space="preserve">Tertio quoniam Sol obſcurari cæpit ex parte orientis, ex parte vero occiden-<lb/>tis deſijt, contra ordinem naturæ: </s> <s xml:id="echoid-s11969" xml:space="preserve">quemadmodum ſe obſeruaſſe narrat Beatus Dionyſius Areopagita, & </s> <s xml:id="echoid-s11970" xml:space="preserve">in <lb/>Epiſt. </s> <s xml:id="echoid-s11971" xml:space="preserve">7. </s> <s xml:id="echoid-s11972" xml:space="preserve">ad Polycarpum, & </s> <s xml:id="echoid-s11973" xml:space="preserve">in 11. </s> <s xml:id="echoid-s11974" xml:space="preserve">ad Apollophanem philoſophum, cum quo apud Heliopolim in Aegy-<lb/>pto, hanc ſimul eclypſim obſeruarunt, atque admirati ſunt vehementer, adeo vt Apollophanes dixerit; </s> <s xml:id="echoid-s11975" xml:space="preserve">hæ <lb/>ſunt, ò bone Dionyſi, rerum viciſſitudines diuinarum. </s> <s xml:id="echoid-s11976" xml:space="preserve">alij etiam tradunt ipſum Beatum Dionyſium excla-<lb/>maſſe, aut Deus naturæ patitur, aut mundi machina diſſoluetur. </s> <s xml:id="echoid-s11977" xml:space="preserve">Quarto quoniam vt ſe vidiſſe, ibidem te-<lb/>ſtatur Beatus Dionyſius, Luna ex oppoſito Solis, progreſſa eſt ad coniunctionem, contra ordinem proprij <lb/>motus: </s> <s xml:id="echoid-s11978" xml:space="preserve">mouebatur enim ab oriente in occidentem. </s> <s xml:id="echoid-s11979" xml:space="preserve">vnde factum eſt, vt ex parte orientis primo Solem in-<lb/>uaſerit. </s> <s xml:id="echoid-s11980" xml:space="preserve">Quinto neceſſe etiam eſt Lunam humilius ſolito, atque infra ſuum cælum inceſſiſſe, vt toti terræ <lb/>@otum Solem occultaret. </s> <s xml:id="echoid-s11981" xml:space="preserve">ſicque tenebræ per vniuerſam terram effunderentur. </s> <s xml:id="echoid-s11982" xml:space="preserve">quanto enim oculis noſtris <lb/>opacum quodpiam propius fit. </s> <s xml:id="echoid-s11983" xml:space="preserve">tanto maius ſpatium nobis occultat. </s> <s xml:id="echoid-s11984" xml:space="preserve">Sed maximè duæ citatæ Beati Diony-<lb/>ſij Epiſt. </s> <s xml:id="echoid-s11985" xml:space="preserve">dignæ ſunt quæ legantur.</s> <s xml:id="echoid-s11986" xml:space="preserve"/> </p> <pb o="124" file="0146" n="151" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div252" type="section" level="1" n="167"> <head xml:id="echoid-head179" style="it" xml:space="preserve">De calculatione Solis. Cap. X X.</head> <p> <s xml:id="echoid-s11987" xml:space="preserve">QViappendicem de Aſtronomico calculo, quam in Luna dedimus, perceperit, is nullo negotio hanc <lb/>quoque intelliget. </s> <s xml:id="echoid-s11988" xml:space="preserve">quippe quod calculus hic ſit multo expeditior. </s> <s xml:id="echoid-s11989" xml:space="preserve">Oporter autem in primis, ea ferè <lb/>omnia, quæ de Aſtronomicis Lunæ Tabulis dicta ſunt, ſequentibus Tabulis etiam ſolaribus appli-<lb/>care; </s> <s xml:id="echoid-s11990" xml:space="preserve">ſunt enim hæ illis perſimiles, ſunt enim eodem modo conſtructæ ad eiuſdem anni 1600. </s> <s xml:id="echoid-s11991" xml:space="preserve">Radicem & </s> <s xml:id="echoid-s11992" xml:space="preserve"><lb/>ad eundem meridianum Venetum, &</s> <s xml:id="echoid-s11993" xml:space="preserve">c.</s> <s xml:id="echoid-s11994" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11995" xml:space="preserve">Sunt autem hæ tantummodo tres. </s> <s xml:id="echoid-s11996" xml:space="preserve">in quarũ prima deſcribuntur duo medij, motus alter Apogæi ſolaris, al-<lb/>ter longitudinis Solis ab æquinoctio, qui motus reſpondent annis Romanis, & </s> <s xml:id="echoid-s11997" xml:space="preserve">Gregorianis, ſimili ordine a@ <lb/>in Luna. </s> <s xml:id="echoid-s11998" xml:space="preserve">in eadem Tabula compræhenduntur anni, & </s> <s xml:id="echoid-s11999" xml:space="preserve">menſes. </s> <s xml:id="echoid-s12000" xml:space="preserve">In ſecunda Tabula quæ eſt dierum, hora-<lb/>rum, & </s> <s xml:id="echoid-s12001" xml:space="preserve">minutorum, omiſſus eſt Apogæi motus; </s> <s xml:id="echoid-s12002" xml:space="preserve">is enim cum tardiſſimus ſit, ſatis eſt annuum eius motum <lb/>computare. </s> <s xml:id="echoid-s12003" xml:space="preserve">Hic verò conſiderandum eſt, qua ratione in eadem columna continuantur motus medij, qui <lb/>idem inſeruiunt horis, & </s> <s xml:id="echoid-s12004" xml:space="preserve">minutis, quod in Luna ſatis expiicatum eſt. </s> <s xml:id="echoid-s12005" xml:space="preserve">Tertia Tabula eſt æquationum Solis, <lb/>quæ ſolum differt ab æquationibus Lunæ, quod illæ proueniant ob eccentricum, hæ autem ob epicyclum, <lb/>cæterum ſimiles ſunt.</s> <s xml:id="echoid-s12006" xml:space="preserve"/> </p> <figure> <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-01"/> </figure> <pb o="125" file="0147" n="152" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div253" type="section" level="1" n="168"> <head xml:id="echoid-head180" style="it" xml:space="preserve">Tabula prima mediorum motuum Solis.</head> <note position="right" xml:space="preserve"> <lb/>####### In Annis ſingulis. # #### In menſibus An. communis. <lb/># ### Apogæi. ### Longitudinis ab ♈. # #### Longitudinis ab ♈. <lb/># Anni. # ′. # ″. # Sig. # Gra. # ′. # # Sig. # Gra. <lb/># 1 # 0 # 45 # 11 # 29 # 46 <lb/># 2 # 1 # 30 # 11 # 29 # 31 <lb/>B # 3 # 2 # 15 # 11 # 29 # 17 # # Ian. # 1 # 0 # 33 <lb/># 4 # 3 # 0 # 0 # 0 # 1 # # Febr. # 1 # 28 # 9 <lb/># 5 # 3 # 45 # 11 # 29 # 47 # # Mart. # 2 # 28 # 42 <lb/># 6 # 4 # 30 # 11 # 29 # 43 # # Apr. # 3 # 28 # 16 <lb/>B # 7 # 5 # 15 # 11 # 29 # 18 <lb/># 8 # 6 # 0 # 0 # 0 # 3 # # Mai. # 4 # 25 # 50 <lb/># # # # # # # # Iun. # 5 # 28 # 24 <lb/># 9 # 6 # 45 # 11 # 29 # 49 <lb/># 10 # 7 # 30 # 11 # 29 # 35 # # Iul. # 6 # 28 # 57 <lb/>B # 11 # 8 # 15 # 11 # 29 # 20 # # Aug. # 7 # 29 # 31 <lb/># 12 # 9 # 0 # 0 # 0 # 5 <lb/># # # # # # # # Sept. # 8 # 29 # 5 <lb/># 13 # 9 # 45 # 11 # 29 # 51 # # Oct. # 9 # 29 # 38 <lb/># 14 # 10 # 30 # 11 # 29 # 36 <lb/>B # 15 # 11 # 15 # 11 # 29 # 22 # # Nou. # 10 # 29 # 12 <lb/># 16 # 12 # 0 # 0 # 0 # 7 # # Dec. # 11 # 29 # 46 <lb/># 17 # 12 # 45 # 11 # 29 # 53 <lb/># 18 # 13 # 30 # 11 # 29 # 39 <lb/>B # 19 # 14 # 15 # 11 # 29 # 24 <lb/># 20 # 15 # 0 # 0 # 0 # 9 # 15″. <lb/># # Gra. # ′. # Sig. # Gra. # ′. # #### In menſibus Ann. Biſſext. <lb/># 40 # 0 # 30 # 0 # 0 # 18 # # # Sig. # Gra. # ′. <lb/>In # 60 # 0 # 45 # 0 # 0 # 28 <lb/># 80 # 1 # 0 # 0 # 0 # 37 # # Ian. # 1 # 0 # 33 <lb/># 100 # 1 # 15 # 0 # 0 # 46 # # Febr. # 1 # 29 # 8 <lb/># # # # # # # # Mart. # 2 # 29 # 42 <lb/># 200 # 2 # 30 # 0 # 1 # 32 # # Apr. # 3 # 29 # 16 <lb/>Annis # 300 # 3 # 45 # 0 # 2 # 19 <lb/># 400 # 5 # 0 # 0 # 3 # 5 # # Maius # 4 # 29 # 49 <lb/># 500 # 6 # 15 # 0 # 3 # 51 # # Iun. # 5 # 29 # 23 <lb/># # # # # # # # Iulius # 6 # 29 # 57 <lb/>aggregatis. # 600 # 7 # 30 # 0 # 4 # 37 # # Aug. # 8 # 0 # 30 <lb/># 700 # 8 # 45 # 0 # 5 # 27 <lb/># 800 # 10 # 0 # 0 # 6 # 10 # # Sept. # 9 # 0 # 4 <lb/># # # # # # # # Octo. # 10 # 0 # 37 <lb/># 900 # 11 # 15 # 0 # 6 # 56 # # Nou. # 11 # 0 # 12 <lb/># 1000 # 12 # 30 # 0 # 7 # 42 # # Dec. # 0 # 0 # 45 <lb/></note> <head xml:id="echoid-head181" xml:space="preserve">Radices æqualium motuum ***, an Ann. 1600. abſolutum in meridie vltimi diei Decembris, \\ idest, Pridie Kaleud. Ianuarij Ano. 3601.</head> <note position="right" xml:space="preserve">## Radix # Sig. # Gra. # ′. # Rad. # Sig. # Gra. # 1<lb/>B # 1600 # 3 # 5 # 40 # # 9 # 10 # 4<lb/></note> <pb o="126" file="0148" n="153" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div254" type="section" level="1" n="169"> <head xml:id="echoid-head182" style="it" xml:space="preserve">Tabula ſecunda Aequalis motus longitudinis Solis.</head> <note position="right" xml:space="preserve"> <lb/>### In diebus. # #### In horis, & minutis. <lb/>Dic<unsure/>s # Gra. # ′. # Horæ. # 0 # Gra. # ′. <lb/># # # # Min. # Gra. # ′. # ″. <lb/>1 # 0 # 59 <lb/>2 # 1 # 58 # 1 # 0 # 0 # 2 <lb/># # # # 2 # 0 # 0 # 5 <lb/>3 # 2 # 57 <lb/>4 # 3 # 57 # 3 # 0 # 0 # 7 <lb/># # # # 4 # 0 # 0 # 10 <lb/>5 # 4 # 56 <lb/>6 # 5 # 55 # 5 # 0 # 0 # 12 <lb/># # # # 6 # 0 # 0 # 15 <lb/>7 # 6 # 54 <lb/>8 # 7 # 53 # 7 # 0 # 0 # 17 <lb/># # # # 8 # 0 # 0 # 20 <lb/>9 # 8 # 52 <lb/>10 # 9 # 51 # 9 # 0 # 0 # 22 <lb/># # # # 10 # 0 # 0 # 25 <lb/>11 # 10 # 51 <lb/>12 # 11 # 50 # 11 # 0 # 0 # 30 <lb/># # # # 12 # 0 # 0 # 29 <lb/>13 # 12 # 49 <lb/>14 # 13 # 48 # 13 # 0 # 0 # 32 <lb/># # # # 14 # 0 # 0 # 34 <lb/>15 # 14 # 47 <lb/>16 # 15 # 46 # 15 # 0 # 0 # 37 <lb/># # # # 16 # 0 # 0 # 39 <lb/>17 # 16 # 45 <lb/>18 # 17 # 44 # 17 # 0 # 0 # 42 <lb/># # # # 18 # 0 # 0 # 44 <lb/>19 # 18 # 44 <lb/>20 # 19 # 43 # 19 # 0 # 0 # 47 <lb/># # # # 20 # 0 # 0 # 49 <lb/>21 # 20 # 42 <lb/>22 # 21 # 41 # 21 # 0 # 0 # 52 <lb/># # # # 22 # 0 # 0 # 54 <lb/>23 # 22 # 40 <lb/>24 # 23 # 39 # 23 # 0 # 0 # 57 <lb/># # # # 24 # 0 # 0 # 59 <lb/>25 # 24 # 38 <lb/>26 # 25 # 38 # 25 # 0 # 1 # 2 <lb/># # # # 26 # 0 # 1 # 4 <lb/>27 # 26 # 37 <lb/>28 # 27 # 36 # 27 # 0 # 1 # 7 <lb/># # # # 26 # 0 # 1 # 9 <lb/>29 # 28 # 35 <lb/>30 # 29 # 34 # 29 # 0 # 1 # 11 <lb/>31 # 30 # 33 # 30 # 0 # 1 # 14 <lb/></note> <pb o="127" file="0149" n="154" rhead="Liber Decimus."/> </div> <div xml:id="echoid-div255" type="section" level="1" n="170"> <head xml:id="echoid-head183" style="it" xml:space="preserve">TABVLA TERTIA AEQVATIONVM SOLIS.</head> <note position="right" xml:space="preserve"> <lb/> Priora ſ<unsure/>ex ſigna Anomaliæ in quibus æquatio demitur. # ## 0 ## 1 ## 2 ## 3 ## 4 ## 5 # Gr. # ′. # Gr. # ′. # Gr. # ′. # Gr. # ′. # Gr. # ′. # Gr. # ′. 1 # 0 # 2 # 1 # 2 # 1 # 46 # 2 # 3 # 1 # 48 # 1 # 1 # 29 2 # 2 # 4 # 1 # 4 # 1 # 47 # 2 # 3 # 1 # 46 # 1 # 0 # 28 3 # 0 # 6 # 1 # 5 # 1 # 48 # 2 # 3 # 1 # 45 # 0 # 58 # 27 4 # 0 # 8 # 1 # 7 # 1 # 49 # 2 # 3 # 1 # 44 # 0 # 56 # 26 5 # 0 # 10 # 1 # 9 # 1 # 50 # 2 # 3 # 1 # 43 # 0 # 54 # 25 6 # 0 # 12 # 1 # 10 # 1 # 51 # 2 # 3 # 1 # 42 # 0 # 52 # 24 7 # 0 # 14 # 1 # 12 # 1 # 52 # 2 # 3 # 1 # 41 # 0 # 50 # 23 8 # 0 # 17 # 1 # 14 # 1 # 53 # 2 # 3 # 1 # 39 # 0 # 48 # 22 9 # 0 # 19 # 1 # 15 # 1 # 53 # 2 # 2 # 1 # 38 # 0 # 46 # 21 10 # 0 # 21 # 1 # 17 # 1 # 54 # 2 # 2 # 1 # 37 # 0 # 44 # 20 11 # 0 # 23 # 1 # 19 # 1 # 55 # 2 # 2 # 1 # 35 # 0 # 42 # 19 12 # 0 # 25 # 1 # 21 # 1 # 56 # 2 # 1 # 1 # 34 # 0 # 39 # 18 13 # 0 # 27 # 1 # 22 # 1 # 57 # 2 # 1 # 1 # 32 # 0 # 37 # 17 14 # 0 # 29 # 1 # 23 # 1 # 57 # 2 # 1 # 1 # 31 # 0 # 35 # 16 15 # 0 # 31 # 1 # 25 # 1 # 58 # 2 # 0 # 1 # 29 # 0 # 33 # 15 16 # 0 # 33 # 1 # 26 # 1 # 58 # 2 # 0 # 1 # 28 # 0 # 30 # 14 17 # 0 # 35 # 1 # 28 # 1 # 59 # 2 # 0 # 1 # 26 # 0 # 29 # 13 18 # 0 # 37 # 1 # 29 # 2 # 0 # 2 # 0 # 1 # 23 # 0 # 27 # 12 19 # 0 # 39 # 1 # 30 # 2 # 0 # 2 # 0 # 1 # 23 # 0 # 24 # 11 20 # 0 # 41 # 1 # 33 # 3 # 0 # 1 # 57 # 1 # 21 # 0 # 22 # 10 21 # 0 # 43 # 1 # 34 # 2 # 1 # 1 # 56 # 1 # 20 # 0 # 20 # 9 22 # 0 # 45 # 1 # 35 # 2 # 1 # 1 # 56 # 1 # 18 # 0 # 18 # 8 23 # 0 # 47 # 1 # 36 # 2 # 2 # 1 # 55 # 1 # 16 # 0 # 16 # 7 24 # 0 # 49 # 1 # 38 # 2 # 2 # 1 # 54 # 1 # 14 # 0 # 13 # 6 25 # 0 # 50 # 1 # 39 # 2 # 2 # 1 # 53 # 1 # 12 # 0 # 11 # 5 26 # 0 # 53 # 1 # 40 # 2 # 3 # 1 # 52 # 1 # 10 # 0 # 9 # 4 27 # 0 # 54 # 1 # 42 # 2 # 3 # 1 # 52 # 1 # 9 # 9 # 7 # 3 28 # 0 # 56 # 1 # 42 # 2 # 3 # 1 # 51 # 1 # 4 # 0 # 4 # 2 29 # 0 # 58 # 1 # 44 # 2 # 3 # 1 # 50 # 1 # 5 # 0 # 2 # 1 30 # 1 # 0 # 1 # 45 # 2 # 3 # 1 # 49 # 1 # 4 # 0 # 0 # 0 # ## 11 ## 10 ## 9 ## 8 ## 7 ## 6 </note> </div> <div xml:id="echoid-div256" type="section" level="1" n="171"> <head xml:id="echoid-head184" xml:space="preserve">Poſteriora ſex ſigna Anomaliæ in quibus æquatio additur.</head> <pb o="128" file="0150" n="155" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div257" type="section" level="1" n="172"> <head xml:id="echoid-head185" style="it" xml:space="preserve">Vſus Tabularum præcedentium.</head> <p> <s xml:id="echoid-s12007" xml:space="preserve">SEd reliquum eſt, vt exemplis harum Tabularum vſum, & </s> <s xml:id="echoid-s12008" xml:space="preserve">finem explicemus. </s> <s xml:id="echoid-s12009" xml:space="preserve">Sitigitur oblatum vulgare <lb/>tempus iſtud quo hæc ſcribimus, Anni Chriſti 1616. </s> <s xml:id="echoid-s12010" xml:space="preserve">die 6. </s> <s xml:id="echoid-s12011" xml:space="preserve">Septembris, horis duabus, cũ tribus quadran-<lb/>tibus horæ poſt meridiem. </s> <s xml:id="echoid-s12012" xml:space="preserve">ad hoc inſtans quæritur verus Solis locus in Zodiaco, ſiue verus etiam motus ab <lb/>æquinoctio ſeu diſtantia, & </s> <s xml:id="echoid-s12013" xml:space="preserve">longitudo vera ab initio ♈. </s> <s xml:id="echoid-s12014" xml:space="preserve">quæ inueſtiganda eſt auxilio medij Solis motus, & </s> <s xml:id="echoid-s12015" xml:space="preserve"><lb/>Apogæi, & </s> <s xml:id="echoid-s12016" xml:space="preserve">tandem æquationis. </s> <s xml:id="echoid-s12017" xml:space="preserve">tempus igitur datum ciuile, ac vulgare, ad vſum Aſtronomicum præparari <lb/>debet, fignificabitq; </s> <s xml:id="echoid-s12018" xml:space="preserve">annos Chriſti completos 1615. </s> <s xml:id="echoid-s12019" xml:space="preserve">menſem Auguſti completum, & </s> <s xml:id="echoid-s12020" xml:space="preserve">præterea dies 6. </s> <s xml:id="echoid-s12021" xml:space="preserve">hota@ <lb/>que 2 {3/4}. </s> <s xml:id="echoid-s12022" xml:space="preserve">abſolutas poſt meridiem ciuilis diei 6. </s> <s xml:id="echoid-s12023" xml:space="preserve">Septembris ficigitur ſtabit formula.</s> <s xml:id="echoid-s12024" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Sig. # Gra. <lb/>Anni 1600. # 3 # 5 # 40 # Radix Apogæi. <lb/>Anni 15. # 0 # 0 # 11 # Apogæum ***. <lb/>Summa # 3 # 5 # 51 # Rad. mot. Solis in long. <lb/>Anni 1600. # 9 # 10 # 4 <lb/>Anni 15. # 11 # 29 # 22 <lb/>Auguſtus. # 8 # 0 # 30 <lb/>Dies. # 0 # 5 # 55 <lb/>Horæ 2. # 0 # 0 # 5 <lb/>Min. 30. # 0 # 0 # 1 <lb/>Min. 15. # 0 # 0 # 1 <lb/>Summa. # 5 # 15 # 58 # Longitudine ***. media à \\ qua detrahitur Apogæum, \\ & relinquitur Anomalia ***. \\ æquatio aufertur à longi- \\ tudine media. <lb/>Apogæum. ſubtr. # 3 # 5 # 51 <lb/>Anomali<unsure/>a. demen. # 2 # 10 # 7 <lb/># 0 # 1 # 54 <lb/># 5 # 14 # 4 # Verus locus ***. quirelin \\ quitur detracta æquatione \\ à longitudine ***. media. <lb/></note> <p> <s xml:id="echoid-s12025" xml:space="preserve">Primo igitur inuenies apogæum accipiendo ex prima Tabula in calce columnæ apogæi Radicem anno-<lb/>rum 1600. </s> <s xml:id="echoid-s12026" xml:space="preserve">quæ eſt ſigno 3. </s> <s xml:id="echoid-s12027" xml:space="preserve">grad. </s> <s xml:id="echoid-s12028" xml:space="preserve">5. </s> <s xml:id="echoid-s12029" xml:space="preserve">min. </s> <s xml:id="echoid-s12030" xml:space="preserve">40′. </s> <s xml:id="echoid-s12031" xml:space="preserve">quam ſcribe è regione annorum 1600. </s> <s xml:id="echoid-s12032" xml:space="preserve">deinde in eadem Tabula <lb/>è regione annorum 15. </s> <s xml:id="echoid-s12033" xml:space="preserve">in eadem columna apogæi, accipe motum 11′. </s> <s xml:id="echoid-s12034" xml:space="preserve">quem referas in directum annorum 15. <lb/></s> <s xml:id="echoid-s12035" xml:space="preserve">poſtea due in vnam ſummam prædictos motus, & </s> <s xml:id="echoid-s12036" xml:space="preserve">confi<unsure/>abunt ſigna 3. </s> <s xml:id="echoid-s12037" xml:space="preserve">gr. </s> <s xml:id="echoid-s12038" xml:space="preserve">5. </s> <s xml:id="echoid-s12039" xml:space="preserve">min. </s> <s xml:id="echoid-s12040" xml:space="preserve">51. </s> <s xml:id="echoid-s12041" xml:space="preserve">quæ eſt diſtantia apogæi <lb/>ab æquinoctio; </s> <s xml:id="echoid-s12042" xml:space="preserve">quare erit apogæum Solis circa finem gradus 6. </s> <s xml:id="echoid-s12043" xml:space="preserve">Cancri. </s> <s xml:id="echoid-s12044" xml:space="preserve">pro reliquis autem temporis ipecie-<lb/>bus, non eſt cur apogæi motus inquiratur, ſed ſatis eſt illud ad annos inquirere. </s> <s xml:id="echoid-s12045" xml:space="preserve">Iam igitur longit. </s> <s xml:id="echoid-s12046" xml:space="preserve">***, mediam <lb/>computemus. </s> <s xml:id="echoid-s12047" xml:space="preserve">Primo ad annos 1600. </s> <s xml:id="echoid-s12048" xml:space="preserve">ſumo Radicem in columnæ longitudinis calce, quam in formula annis <lb/>1600. </s> <s xml:id="echoid-s12049" xml:space="preserve">adſcribe, vti vides factum eſſe. </s> <s xml:id="echoid-s12050" xml:space="preserve">Secundo in eadem columna ad annos 15. </s> <s xml:id="echoid-s12051" xml:space="preserve">accipio motum long itudinis <pb o="129" file="0151" n="156" rhead="Liber Decimus."/> quem pariter annis 15. </s> <s xml:id="echoid-s12052" xml:space="preserve">formulæ aſeribo. </s> <s xml:id="echoid-s12053" xml:space="preserve">Tertio ex columna menſium anni bif<unsure/>ſextilis (annus enim 1616. </s> <s xml:id="echoid-s12054" xml:space="preserve">cur-<lb/>rens eſt biſſextilis) acceptum motum aſcribo in formula menſi Auguſto. </s> <s xml:id="echoid-s12055" xml:space="preserve">Quarto ex ſecunda Tabula, quæ eſt <lb/>dierum, horarum, ac minutorum, ſimiliter acceptos motus ex proprijs columnis dierum, & </s> <s xml:id="echoid-s12056" xml:space="preserve">horarum, ac <lb/>minut. </s> <s xml:id="echoid-s12057" xml:space="preserve">eos in formula ſuis temporibus reſpondentes tranſcribo; </s> <s xml:id="echoid-s12058" xml:space="preserve">vti videre eſt quoniam vero minuta horarum <lb/>45. </s> <s xml:id="echoid-s12059" xml:space="preserve">in columna horarum, ac minutorum non reperiuntur, ideo primo cum min. </s> <s xml:id="echoid-s12060" xml:space="preserve">30′. </s> <s xml:id="echoid-s12061" xml:space="preserve">deinde cum min. </s> <s xml:id="echoid-s12062" xml:space="preserve">15′. <lb/></s> <s xml:id="echoid-s12063" xml:space="preserve">ingredior Tabulam, ex qua motus proprios, omiſſis tamen ſecundis, trãſcribo in formulam tandem hoſce om <lb/>nes medios longitudinis motus, in ſummam vnam confero, à<unsure/> qua ſumma detrahitur motus apogæi, & </s> <s xml:id="echoid-s12064" xml:space="preserve">quod <lb/>remanet, videlicet, ſig. </s> <s xml:id="echoid-s12065" xml:space="preserve">2. </s> <s xml:id="echoid-s12066" xml:space="preserve">gra. </s> <s xml:id="echoid-s12067" xml:space="preserve">10. </s> <s xml:id="echoid-s12068" xml:space="preserve">min. </s> <s xml:id="echoid-s12069" xml:space="preserve">′. </s> <s xml:id="echoid-s12070" xml:space="preserve">eſt Solis diſtantia ab apogæo, quæ dicitur anomalia Solis. </s> <s xml:id="echoid-s12071" xml:space="preserve">cum hac <lb/>anomalia ingredior tertiam Tabulam æquationum, in qua reperio ſigna 2. </s> <s xml:id="echoid-s12072" xml:space="preserve">in fronte Tabule, gradus autem 10. </s> <s xml:id="echoid-s12073" xml:space="preserve"><lb/>accipio in latere ſiniſtro, quia illi ſunt gradus ſuperiorum ſex ſignorum, quæ ſunt in fronte Tabulæ igitur in <lb/>directum gra. </s> <s xml:id="echoid-s12074" xml:space="preserve">10. </s> <s xml:id="echoid-s12075" xml:space="preserve">reperio ſub ſigno 2. </s> <s xml:id="echoid-s12076" xml:space="preserve">æquationem gr. </s> <s xml:id="echoid-s12077" xml:space="preserve">1. </s> <s xml:id="echoid-s12078" xml:space="preserve">54. </s> <s xml:id="echoid-s12079" xml:space="preserve">hanc æquationum demo ex motu longitudinis ***, <lb/>iuxta titulum Tabulæ, qui iubet æquationem demendam eſſe in primis 6. </s> <s xml:id="echoid-s12080" xml:space="preserve">ſignis, & </s> <s xml:id="echoid-s12081" xml:space="preserve">relinquitur ſig. </s> <s xml:id="echoid-s12082" xml:space="preserve">5. </s> <s xml:id="echoid-s12083" xml:space="preserve">gr. </s> <s xml:id="echoid-s12084" xml:space="preserve">14. </s> <s xml:id="echoid-s12085" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s12086" xml:space="preserve">54′. </s> <s xml:id="echoid-s12087" xml:space="preserve">pro vera ***, longitudine ab æquinoctio, quæ pertinet ad gr. </s> <s xml:id="echoid-s12088" xml:space="preserve">ferè 15. </s> <s xml:id="echoid-s12089" xml:space="preserve">Virginis. </s> <s xml:id="echoid-s12090" xml:space="preserve">vt autem intelligas <lb/>huius rei rationem inſpice figuram lib. </s> <s xml:id="echoid-s12091" xml:space="preserve">10. </s> <s xml:id="echoid-s12092" xml:space="preserve">cap. </s> <s xml:id="echoid-s12093" xml:space="preserve">8. </s> <s xml:id="echoid-s12094" xml:space="preserve">Sol eſt in O. </s> <s xml:id="echoid-s12095" xml:space="preserve">linea medij motus A X. </s> <s xml:id="echoid-s12096" xml:space="preserve">veri A O Z. </s> <s xml:id="echoid-s12097" xml:space="preserve">apogæum <lb/>erit arcus L G D. </s> <s xml:id="echoid-s12098" xml:space="preserve">motus medius longitudinis L D X. </s> <s xml:id="echoid-s12099" xml:space="preserve">Anomalia D Z X. </s> <s xml:id="echoid-s12100" xml:space="preserve">æquatio X Z. </s> <s xml:id="echoid-s12101" xml:space="preserve">quæ detracta ab arcu <lb/>L D X, relinquit arcum L D Z. </s> <s xml:id="echoid-s12102" xml:space="preserve">quæ eſt vera diſtantia ab æquinoctio, atque verus Solis locus. </s> <s xml:id="echoid-s12103" xml:space="preserve">qui huius cal-<lb/>culi ſcopus erat.</s> <s xml:id="echoid-s12104" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div258" type="section" level="1" n="173"> <head xml:id="echoid-head186" style="it" xml:space="preserve">ALTERVM EXEMPLVM. <lb/>Quæratur locus ***, verus ad annum Domini 1641. die vltima Martij in meridie.</head> <p> <s xml:id="echoid-s12105" xml:space="preserve">TEmpus vulgare ſic oblatum accomo dandum eſt calculo, vti vides in formula. </s> <s xml:id="echoid-s12106" xml:space="preserve">ſatis eſt autem habere mo-<lb/>tum apogæi ad annos 1640. </s> <s xml:id="echoid-s12107" xml:space="preserve">omiſſo Auguſto, qui apogæi motus detrahendus eſt ex longitudine media, <lb/>vti indicat formula. </s> <s xml:id="echoid-s12108" xml:space="preserve">in qua ſubtractione quia maior eſt numerus detrahendus, quam numerus à quo demen-<lb/>dus eſt, ideo illi addendus eſt circulus, ideſt, ſigna 12. </s> <s xml:id="echoid-s12109" xml:space="preserve">vt fieri poſſit ſubtractio. </s> <s xml:id="echoid-s12110" xml:space="preserve">ex qua ſubtractione anomalia <lb/>relinquitur quæ eſt ſig. </s> <s xml:id="echoid-s12111" xml:space="preserve">9. </s> <s xml:id="echoid-s12112" xml:space="preserve">gra. </s> <s xml:id="echoid-s12113" xml:space="preserve">2. </s> <s xml:id="echoid-s12114" xml:space="preserve">54′. </s> <s xml:id="echoid-s12115" xml:space="preserve">cum qua ex Tabula æquationum elicio æquationem gr. </s> <s xml:id="echoid-s12116" xml:space="preserve">2. </s> <s xml:id="echoid-s12117" xml:space="preserve">3′. </s> <s xml:id="echoid-s12118" xml:space="preserve">accipio au-<lb/>r<unsure/>em ſigna 9. </s> <s xml:id="echoid-s12119" xml:space="preserve">in calce Tabulæ, & </s> <s xml:id="echoid-s12120" xml:space="preserve">gr. </s> <s xml:id="echoid-s12121" xml:space="preserve">2. </s> <s xml:id="echoid-s12122" xml:space="preserve">in latere dextero, vel potius gra. </s> <s xml:id="echoid-s12123" xml:space="preserve">3. </s> <s xml:id="echoid-s12124" xml:space="preserve">computando 54′. </s> <s xml:id="echoid-s12125" xml:space="preserve">pro gra. </s> <s xml:id="echoid-s12126" xml:space="preserve">vno iuxta <lb/>regulam in Lunatraditam: </s> <s xml:id="echoid-s12127" xml:space="preserve">nam in communi eorum concurſu, reperitur prædicta æquatio, quæ addenda eſt <lb/>longitudini iuxta inferiorem Tabulę titulum.</s> <s xml:id="echoid-s12128" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. # ′. <lb/>1600. # 3 # 5 # 40 # Radix. <lb/>40. # 0 # 0 # 30 <lb/># # 3 # 6 # 10 # Apogæum. <lb/>1600. # 9 # 10 # 4 # Radix. <lb/>40. # 0 # 0 # 18 <lb/>Completo Martio. # 2 # 28 # 42 <lb/># # 0 # 9 # 4 # Summam longit. mediæ ***. <lb/># # 3 # 6 # 10 # Apogæum detrahendum ab ea. <lb/># # 9 # 2 # 54 # Reliqua Anomalia. <lb/># # 0 # 2 # 3 # Aequatio addenda longit. vnde. <lb/># # 0 # 11 # 7 # Verus *** locus in gr. 11. Arietis qui \\ cõponitur ex æquat. & long. media. <lb/></note> <pb o="130" file="0152" n="157" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s12129" xml:space="preserve">Horum rationem contemplari poteris in eadem figura, quam in præcedenti exemplo citauimus; </s> <s xml:id="echoid-s12130" xml:space="preserve">in qua <lb/>iuxta præſens exemplum, Sol ſit in R. </s> <s xml:id="echoid-s12131" xml:space="preserve">linea medij motus A N. </s> <s xml:id="echoid-s12132" xml:space="preserve">linea veri motus A S. </s> <s xml:id="echoid-s12133" xml:space="preserve">Æquatio N S. </s> <s xml:id="echoid-s12134" xml:space="preserve">Apogęi <lb/>motus L D. </s> <s xml:id="echoid-s12135" xml:space="preserve">detrahendus a longitudine media L N. </s> <s xml:id="echoid-s12136" xml:space="preserve">vt relinquatur anomalia D M N. </s> <s xml:id="echoid-s12137" xml:space="preserve">cum qua elicitur æqua-<lb/>tio N S. </s> <s xml:id="echoid-s12138" xml:space="preserve">quæ addenda eſt logitudini L N. </s> <s xml:id="echoid-s12139" xml:space="preserve">vt componatur vera longitudo L S. </s> <s xml:id="echoid-s12140" xml:space="preserve">ſeu verus Solis locus S. </s> <s xml:id="echoid-s12141" xml:space="preserve">ad me-<lb/>ridianum Venetum ad meridianum autem Foronoui, vbi hæc computo, reducendus eſt, eo modo quo Lu<unsure/>-<lb/>na vbi ſumus.</s> <s xml:id="echoid-s12142" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div259" type="section" level="1" n="174"> <head xml:id="echoid-head187" style="it" xml:space="preserve">Solaris Eclypſis prædictionem attentare.</head> <p> <s xml:id="echoid-s12143" xml:space="preserve">EClypſium Solariũ prædictio pluribus tricis; </s> <s xml:id="echoid-s12144" xml:space="preserve">quam lunariũ, impedita eſt, quod accidit ob luminaris paral-<lb/>laxes, ſeſe in hoſce defectus ingerentes. </s> <s xml:id="echoid-s12145" xml:space="preserve">ob parallaxim enim vtrumque luminare horizonti propius ap-<lb/>paret, quam re vera ſit. </s> <s xml:id="echoid-s12146" xml:space="preserve">idque variè admodum pro varia eorum altitudine tum a terra, tum ab horizonte. </s> <s xml:id="echoid-s12147" xml:space="preserve">quæ <lb/>varietas aliam ſubit a diuerſis climatibus diuerſitatem. </s> <s xml:id="echoid-s12148" xml:space="preserve">quapropter admirationi ſemper fuere ij, qui hoſce <lb/>Solis labores prædixere, inter quos admirabilis olim habitus eſt Thales Mileſius, quippe qui omniũ primus <lb/>auſus eſt ſolares haſce defectiones prænuntiare. </s> <s xml:id="echoid-s12149" xml:space="preserve">quarũ prima teſte Plinio contingit anno ab Vrbe cond. </s> <s xml:id="echoid-s12150" xml:space="preserve">170.</s> <s xml:id="echoid-s12151" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12152" xml:space="preserve">Qua propter ſatis nobis erit, ſi eas, rudi tantum Minerua, ideſt, abſque præciſa temporis, aut durationis, aut <lb/>quantitatis denotatione prænoſcere poterimus. </s> <s xml:id="echoid-s12153" xml:space="preserve">Primo gitur quoniam eclypſes iſtæ contingunt tantum in <lb/>nouilunijs, oportet nouilunij illius, quod an eclypticum, ſit, explorandum eſt, tempus ex Lunari calculo di-<lb/>ligenter inueſtigare: </s> <s xml:id="echoid-s12154" xml:space="preserve">deinde ad illud tempus, cognoſcendus eſt pariter ex calculo locus nouilunij in Zodiaco, <lb/>necnon loca, ☊, & </s> <s xml:id="echoid-s12155" xml:space="preserve">☋, in Zodiaco, vti in Luna docuimus. </s> <s xml:id="echoid-s12156" xml:space="preserve">quibus habitis reminiſci oportet ea, quæ de termi-<lb/>nis eclyptis cap. </s> <s xml:id="echoid-s12157" xml:space="preserve">præcedenti diximus: </s> <s xml:id="echoid-s12158" xml:space="preserve">videlicet ſi tempore nouilunij veri, Luna fuerit borealis, diſtiteritque <lb/>ab alterutro nodorum intra gradus 15. </s> <s xml:id="echoid-s12159" xml:space="preserve">38. </s> <s xml:id="echoid-s12160" xml:space="preserve">neceſſario continget aliqua alicubi Solis obſcuratio; </s> <s xml:id="echoid-s12161" xml:space="preserve">eaque tanto <lb/>maior, quanto nodo propior acceſſerit: </s> <s xml:id="echoid-s12162" xml:space="preserve">ſi vero auſtralis Luna ſit, diſtiteritque ab alterutro nodorum intra gr. <lb/></s> <s xml:id="echoid-s12163" xml:space="preserve">7. </s> <s xml:id="echoid-s12164" xml:space="preserve">neceſſario pariter ſequitur obſcuratio Solis, vti modo dictum eſt. </s> <s xml:id="echoid-s12165" xml:space="preserve">Quod ſi Luna in vero nouilunio prædi-<lb/>ctos terminos exceſſerit, ita vt in parte quidem boreali pertingat vſque ad gr. </s> <s xml:id="echoid-s12166" xml:space="preserve">17. </s> <s xml:id="echoid-s12167" xml:space="preserve">41′. </s> <s xml:id="echoid-s12168" xml:space="preserve">in auſtrali vero v ſque <lb/>ad gr. </s> <s xml:id="echoid-s12169" xml:space="preserve">11. </s> <s xml:id="echoid-s12170" xml:space="preserve">22′. </s> <s xml:id="echoid-s12171" xml:space="preserve">poſſibilis tantum, ſed non neceſſaria erit Eclypſis. </s> <s xml:id="echoid-s12172" xml:space="preserve">Extra autem hos terminos nulla continge-<lb/>re poterit obſcuratio. </s> <s xml:id="echoid-s12173" xml:space="preserve">Exemplum.</s> <s xml:id="echoid-s12174" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12175" xml:space="preserve">Libet videre num ſequens nouilunium, quod ſiet Septembris die 10. </s> <s xml:id="echoid-s12176" xml:space="preserve">horis 15. </s> <s xml:id="echoid-s12177" xml:space="preserve">poſt mer. </s> <s xml:id="echoid-s12178" xml:space="preserve">huius anni 1616. <lb/></s> <s xml:id="echoid-s12179" xml:space="preserve">ſit eclypticum. </s> <s xml:id="echoid-s12180" xml:space="preserve">Inuenio igitur ex calculo ad illud tempus luminaria eſſe in gr. </s> <s xml:id="echoid-s12181" xml:space="preserve">18. </s> <s xml:id="echoid-s12182" xml:space="preserve">♍, nodum autem ☋, auſtra<unsure/>-<lb/>lem eſſe in gr. </s> <s xml:id="echoid-s12183" xml:space="preserve">8. </s> <s xml:id="echoid-s12184" xml:space="preserve">eiuſdem ♍, Luna igitur diſtat ab hoc nodo, in auſtrum gr. </s> <s xml:id="echoid-s12185" xml:space="preserve">10. </s> <s xml:id="echoid-s12186" xml:space="preserve">quare auſtralis eſt; </s> <s xml:id="echoid-s12187" xml:space="preserve">vnde ex <lb/>præcedentibus regulis, pronuntio eclypſium non eſſe neceſſariam. </s> <s xml:id="echoid-s12188" xml:space="preserve">quia in parte auſtrali, termini neceſſari@ <lb/>ſunt gra. </s> <s xml:id="echoid-s12189" xml:space="preserve">7. </s> <s xml:id="echoid-s12190" xml:space="preserve">dico tamen aliquantulam defectionem eſſe poſſibilem, cum Luna vltra gradi 11. </s> <s xml:id="echoid-s12191" xml:space="preserve">qui ſunt auſtra-<lb/>les termini poſſibiles, non recedat a nodo.</s> <s xml:id="echoid-s12192" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12193" xml:space="preserve">Alterum exemplum. </s> <s xml:id="echoid-s12194" xml:space="preserve">anno Domini 1618. </s> <s xml:id="echoid-s12195" xml:space="preserve">erit nouilunium die 21. </s> <s xml:id="echoid-s12196" xml:space="preserve">Iulij, horis octo poſt meridiem. </s> <s xml:id="echoid-s12197" xml:space="preserve">exploro <lb/>an ſit eclypticum, hoc modo; </s> <s xml:id="echoid-s12198" xml:space="preserve">reperio ex calculo luminaria tunc in parte Cancri 29. </s> <s xml:id="echoid-s12199" xml:space="preserve">verſari: </s> <s xml:id="echoid-s12200" xml:space="preserve">☊. </s> <s xml:id="echoid-s12201" xml:space="preserve">autem eſſe in <lb/>parte ſecunda Aquarij. </s> <s xml:id="echoid-s12202" xml:space="preserve">quare ☋. </s> <s xml:id="echoid-s12203" xml:space="preserve">erit in parte ſecunda Leonis. </s> <s xml:id="echoid-s12204" xml:space="preserve">Luna igitur præcedit ☋, tribus tantum modo <lb/>partibus, eſtque borealis tempore huius coniunctionis. </s> <s xml:id="echoid-s12205" xml:space="preserve">at in parte boreali, termini eclyptici neceſſarij ſunt <lb/>gra. </s> <s xml:id="echoid-s12206" xml:space="preserve">15. </s> <s xml:id="echoid-s12207" xml:space="preserve">quare Luna multum intra neceſſarios terminos reperitur; </s> <s xml:id="echoid-s12208" xml:space="preserve">atque admodum nodo vicina; </s> <s xml:id="echoid-s12209" xml:space="preserve">quare certo <lb/>prædico Solem fore magnum lucis deliquium, & </s> <s xml:id="echoid-s12210" xml:space="preserve">quoniam reſpectu Veneti meridiani, nouilunium iſtud fit <lb/>8. </s> <s xml:id="echoid-s12211" xml:space="preserve">circiter horis poſt meridiem die 21. </s> <s xml:id="echoid-s12212" xml:space="preserve">Iulij, quo in noſtra eleuatione gra. </s> <s xml:id="echoid-s12213" xml:space="preserve">45. </s> <s xml:id="echoid-s12214" xml:space="preserve">arcus ſemidiurnus eſt horarum <lb/>7 {1/2}. </s> <s xml:id="echoid-s12215" xml:space="preserve">ferè fit vt poſt occaſum Solis à noſtro horizonte Veneto, ſeu Parmenſi, obſeruatio hæc contingat: </s> <s xml:id="echoid-s12216" xml:space="preserve">qua-<lb/>re nos eam, niſi fortè principij quidpiam, neutique videbimus. </s> <s xml:id="echoid-s12217" xml:space="preserve">populi tamen occidentaliores, vt Galli <lb/>vltimi, & </s> <s xml:id="echoid-s12218" xml:space="preserve">Hiſpani, eam videbunt ante ſolis occaſum. </s> <s xml:id="echoid-s12219" xml:space="preserve">Noui orbis habitatores eam circa meridiem admi-<lb/>rabuntur. </s> <s xml:id="echoid-s12220" xml:space="preserve">Hactenus de Solis defectu.</s> <s xml:id="echoid-s12221" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div260" type="section" level="1" n="175"> <head xml:id="echoid-head188" style="it" xml:space="preserve">De Maculis Solis. Cap. XXI.</head> <p> <s xml:id="echoid-s12222" xml:space="preserve">HIſce circa Solem explicatis, reliquum eſt ea perſequi, quæ circa ipſum tanquam centrum, ſuas circinan@ <lb/>reuolutiones. </s> <s xml:id="echoid-s12223" xml:space="preserve">probatiffimi enim Aſtronomi, docent in hac Mundi Fabrica, duo præcipua eſſe centra, <lb/>ad quæ omnes mundi partes referuntur; </s> <s xml:id="echoid-s12224" xml:space="preserve">centrum videlicet Vniuerſi, circa quod Elementa, Lunaris, ac So-<lb/>laris regio, necnon octaua Sphæra conſiſtunt. </s> <s xml:id="echoid-s12225" xml:space="preserve">Et centrum Solis, circa quod Maculæ, Mercurius, Venus, <lb/>Mars, lupiter, & </s> <s xml:id="echoid-s12226" xml:space="preserve">Saturnus circumferuntur. </s> <s xml:id="echoid-s12227" xml:space="preserve">porrò quod ad Maculas, Mercurium, ac Venerem attinet, idem <lb/>ſentiu nt P. </s> <s xml:id="echoid-s12228" xml:space="preserve">Chriſtophorus Scheiner in Diſquiſ. </s> <s xml:id="echoid-s12229" xml:space="preserve">Mathem. </s> <s xml:id="echoid-s12230" xml:space="preserve">quod ad ſolas maculas etiã P. </s> <s xml:id="echoid-s12231" xml:space="preserve">Aguillonius in Optic. <lb/></s> <s xml:id="echoid-s12232" xml:space="preserve">lib. </s> <s xml:id="echoid-s12233" xml:space="preserve">penult. </s> <s xml:id="echoid-s12234" xml:space="preserve">& </s> <s xml:id="echoid-s12235" xml:space="preserve">quod ad Venerem, etiam P. </s> <s xml:id="echoid-s12236" xml:space="preserve">Clauius, eſſe enim talẽipſe in vltima ſphæræ editione Veneris illu-<lb/>minationem, vnde euincitur ipſam circa Solem circumferri. </s> <s xml:id="echoid-s12237" xml:space="preserve">Cumq; </s> <s xml:id="echoid-s12238" xml:space="preserve">ſatis de Sole ip@o tractatum ſit, ordo po-<lb/>ſtulat, vt hæc quaſi circumſolaria corpora aggrediamur. </s> <s xml:id="echoid-s12239" xml:space="preserve">ac primo maculas, quippe quæ ipſi propriores ſunt.</s> <s xml:id="echoid-s12240" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div261" type="section" level="1" n="176"> <head xml:id="echoid-head189" style="it" xml:space="preserve">Quibus modis Solis maculas videre liceat.</head> <p> <s xml:id="echoid-s12241" xml:space="preserve">TEleſcopij adinuentionem, admiranda conſequuta ſunt inuenta. </s> <s xml:id="echoid-s12242" xml:space="preserve">è quibus illud maximè mirum, atq; </s> <s xml:id="echoid-s12243" xml:space="preserve">ha-<lb/>ctenus incredibile, Solem totius luminis parẽtem teterrimis maculis apparere ſœdatum. </s> <s xml:id="echoid-s12244" xml:space="preserve">has igitur ma-<lb/>culas hic certo intueri licebit. </s> <s xml:id="echoid-s12245" xml:space="preserve">Primo mane, & </s> <s xml:id="echoid-s12246" xml:space="preserve">veſperi, cum Sol propè horizontem exiſtens vaporibus ob-<lb/>ſidetur, ſi ipſum per Teleſcopium inſpiciens perſcrutatus fueris, varias in eo nigricantes maculas conſpicies.</s> <s xml:id="echoid-s12247" xml:space="preserve"> <pb o="131" file="0153" n="158" rhead="Liber Decimus."/> idem accidit, vteumq; </s> <s xml:id="echoid-s12248" xml:space="preserve">eleuatus ſit ſuper horizontem, ſi tamen nube adeo tenui tegatur, vt per eam ſatis tran-<lb/>ſpareat. </s> <s xml:id="echoid-s12249" xml:space="preserve">Se cundo quando Sol clariſſimus eſt, præponatur vitrum colore aliquo opacum, ille Teleſcopij vi-<lb/>tro, cui oculus apponi ſolet, ſic enim nimius fulgor retunditur, vnde tuto Solem, quamuis fulgidiſſimum, in-<lb/>ſtar Aquilarum intueri poſſumus, atq; </s> <s xml:id="echoid-s12250" xml:space="preserve">ipſius maculas detegere. </s> <s xml:id="echoid-s12251" xml:space="preserve">Tertio item per Teleſcopium abſq; </s> <s xml:id="echoid-s12252" xml:space="preserve">illo opa-<lb/>cato vitro, nec inſpicientes per ipſum, ſed hoc modo; </s> <s xml:id="echoid-s12253" xml:space="preserve">Teleſcopium in Solem dirigatur, & </s> <s xml:id="echoid-s12254" xml:space="preserve">obfirmetur, ita vt <lb/>Solis radius per ſuperius vitrum I<unsure/>nferius ingrediens, & </s> <s xml:id="echoid-s12255" xml:space="preserve">per inferius egrediens, in albam chartam excipia-<lb/>tur. </s> <s xml:id="echoid-s12256" xml:space="preserve">in illa enim ro unda illuminatione ſolares maculæ perſpicuè apparebunt. </s> <s xml:id="echoid-s12257" xml:space="preserve">idque tanto perfectius, quanto <lb/>in opaciori loco fuerit charta: </s> <s xml:id="echoid-s12258" xml:space="preserve">quapropter ſolent circa inferius Teleſcopij extremum aliam ſolidiorem char <lb/>tam circumponere, quæ inſtar vmbellæ, prædictam chartam inumbret. </s> <s xml:id="echoid-s12259" xml:space="preserve">perfectius quoque id aſſequemur, ſi <lb/>Teleſcopij pars ſuperior extra foramen alicuius feneſtræ, pars vero inferior intra obſcurum conclaue, emi-<lb/>neat, in illis enim tenebris, omnes vel minimæ conſpiciuntur. </s> <s xml:id="echoid-s12260" xml:space="preserve">quo autem longius charta ab inſtrumento re-<lb/>ceſſerit, eo maiores ac euidentiores euadunt. </s> <s xml:id="echoid-s12261" xml:space="preserve">Hic porrò modus per commodus eſt, cum ſine vlla oculi mo-<lb/>leſtia, aut labore, imo magna cnm delectatione cernantur. </s> <s xml:id="echoid-s12262" xml:space="preserve">Quarto abſque Teleſcopio, ſic in lignea feneſtra <lb/>cubiculi cuiuſpiam, fiat exiguum foramen, deinde feneſtris ac ianuis clauſis, tenebroſum reddatur conclaue, <lb/>ita vt per ſolum illud foramen Solis radius illabatur, qui in obiectam chartam appulſus, omnes maculas cla-<lb/>riſſimè manifeſtabit. </s> <s xml:id="echoid-s12263" xml:space="preserve">atq; </s> <s xml:id="echoid-s12264" xml:space="preserve">hic modus certiſſimus eſt, cum omni inſtrumentorum ſuſpitione vacet. </s> <s xml:id="echoid-s12265" xml:space="preserve">Illud an-<lb/>dem aduertendum duobus hiſce vltimis modis, maculas apparere inuerſo ſitu, ab eo quem in ſolari diſco ob-<lb/>tinent; </s> <s xml:id="echoid-s12266" xml:space="preserve">dextræ enim fiunt ſiniſtræ, & </s> <s xml:id="echoid-s12267" xml:space="preserve">ſuperiores fiunt inferiores; </s> <s xml:id="echoid-s12268" xml:space="preserve">cuius cauſa eſt rad orum Solis decuſſatio <lb/>propè foramen, vti ſuperius tactum eſt. </s> <s xml:id="echoid-s12269" xml:space="preserve">cum igitur hi modi in macularum reuelatione couſentiant, nullus <lb/>reſtat dubitandi locus, quo minus eas concedamus.</s> <s xml:id="echoid-s12270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12271" xml:space="preserve">Illud autem non ignorandum, numerum ac diſpoſitionem macularum quotidie variari, ita vt aliquando <lb/>plures, aliquando pauciores; </s> <s xml:id="echoid-s12272" xml:space="preserve">quandoque conſtipatiores, quandoque laxiores appareant. </s> <s xml:id="echoid-s12273" xml:space="preserve">nonnullæ primo <lb/>apparere incipiunt in medio Solis; </s> <s xml:id="echoid-s12274" xml:space="preserve">aliæ vero quæ primo ex vna parte apparuerunt, poſtea circa Solis me-<lb/>dium euanuerunt. </s> <s xml:id="echoid-s12275" xml:space="preserve">apponam tamen vnam ſaltem figuram, qua conſpectæ ſunt a Galilæo die 9. </s> <s xml:id="echoid-s12276" xml:space="preserve">Iunij, Anni <lb/>2612. </s> <s xml:id="echoid-s12277" xml:space="preserve">ex eius Italico libro de maculis.</s> <s xml:id="echoid-s12278" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div262" type="section" level="1" n="177"> <head xml:id="echoid-head190" style="it" xml:space="preserve">Motus macularum.</head> <p> <s xml:id="echoid-s12279" xml:space="preserve">PRimo ſe dant in conſpectum in parte Solis orientali, & </s> <s xml:id="echoid-s12280" xml:space="preserve">in de per ſolarem diſcum incedunt paulatim ver-<lb/>ſus partem occidentalem, quouſque euaneſcant. </s> <s xml:id="echoid-s12281" xml:space="preserve">viæ autem earum ſunt eclypticæ pararellæ. </s> <s xml:id="echoid-s12282" xml:space="preserve">vt in figura <lb/>ſequenti macula C. </s> <s xml:id="echoid-s12283" xml:space="preserve">apparuit primo in D, orientali Solis lim-<lb/> <anchor type="figure" xlink:label="fig-0153-01a" xlink:href="fig-0153-01"/> bo, deinde perlineam punctualem D E. </s> <s xml:id="echoid-s12284" xml:space="preserve">eclypticæ A B. </s> <s xml:id="echoid-s12285" xml:space="preserve">pa-<lb/>ralellam, inceſſit paulatim ad E. </s> <s xml:id="echoid-s12286" xml:space="preserve">occidentis limbum, vbique <lb/>viſui ſe ſubtraxit. </s> <s xml:id="echoid-s12287" xml:space="preserve">Has porrò vias, ſeu totam Solis faciem <lb/>tranſigunt diebus circiter 15. </s> <s xml:id="echoid-s12288" xml:space="preserve">eſtque earum motus in princi-<lb/>pio ac fine ſignior, quam circa medium. </s> <s xml:id="echoid-s12289" xml:space="preserve">Ipſæ vero in prin-<lb/>cipio ac fine apparent breuiores, & </s> <s xml:id="echoid-s12290" xml:space="preserve">graciliores, quam circa <lb/>medium. </s> <s xml:id="echoid-s12291" xml:space="preserve">Præterea apud Solis limbos, ſeu margines magis <lb/>nigricant, quam propè medium; </s> <s xml:id="echoid-s12292" xml:space="preserve">quia ſcilicet ibi obliquè, ac <lb/>ſecundum latus ſpectantur; </s> <s xml:id="echoid-s12293" xml:space="preserve">ita vt priores partes, poſteriores <lb/>occultent: </s> <s xml:id="echoid-s12294" xml:space="preserve">ſicque totæ denſiores, & </s> <s xml:id="echoid-s12295" xml:space="preserve">opaciores euadant quam <lb/>in medio, vbi directè, ac ſecundum latitudinem, quæ tenu-<lb/>uior eſt, viſuntur; </s> <s xml:id="echoid-s12296" xml:space="preserve">ſicque magis lumen Solic eas peruadens <lb/>conſpicuum fit, vnde & </s> <s xml:id="echoid-s12297" xml:space="preserve">ipſæ<unsure/> magis clareſcunt. </s> <s xml:id="echoid-s12298" xml:space="preserve">vnde colligi-<lb/>tur eas non omnino opacas eſſe, ſed aliquatenus inſtar nu-<lb/>bium, tranſparentes. </s> <s xml:id="echoid-s12299" xml:space="preserve">Quæ omnia innuunt ea circulari-<lb/>ter circa Solem reuolui; </s> <s xml:id="echoid-s12300" xml:space="preserve">vel cum ipſo Sole ſpatio menſtruæ <lb/>conuerſionis circumuerti: </s> <s xml:id="echoid-s12301" xml:space="preserve">quam ſententiam Galilæus pu-<lb/>tat probabilem.</s> <s xml:id="echoid-s12302" xml:space="preserve"/> </p> <div xml:id="echoid-div262" type="float" level="2" n="1"> <figure xlink:label="fig-0153-01" xlink:href="fig-0153-01a"> <image file="0153-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0153-01"/> </figure> </div> </div> <div xml:id="echoid-div264" type="section" level="1" n="178"> <head xml:id="echoid-head191" style="it" xml:space="preserve">Figura macularum.</head> <p> <s xml:id="echoid-s12303" xml:space="preserve">OMnes ſunt figura admodum irregulari, & </s> <s xml:id="echoid-s12304" xml:space="preserve">varia, eamq; </s> <s xml:id="echoid-s12305" xml:space="preserve">ſubinde variant. </s> <s xml:id="echoid-s12306" xml:space="preserve">Primo enim contractiores, & </s> <s xml:id="echoid-s12307" xml:space="preserve"><lb/>graciliores ſe præbent, poſtea latiores, ac tandem latiſſimæ circa medium iter, poſtea iterum gracile-<lb/>ſcunt. </s> <s xml:id="echoid-s12308" xml:space="preserve">ſæpe etiam quæ vna initio videbatur, poſtea in plures diuiditur. </s> <s xml:id="echoid-s12309" xml:space="preserve">Ex quibus earum figura ali<unsure/>quate-<lb/>nus plana eſſe conuincitur: </s> <s xml:id="echoid-s12310" xml:space="preserve">cum enim Sol ſit ſphæricus, & </s> <s xml:id="echoid-s12311" xml:space="preserve">maculæ vel cum ipſo, vel circa ipſum moueantur, <lb/>neceſſario in ipſius extremitatibus obliquè, & </s> <s xml:id="echoid-s12312" xml:space="preserve">in latera cernentur, vnde & </s> <s xml:id="echoid-s12313" xml:space="preserve">contractiores. </s> <s xml:id="echoid-s12314" xml:space="preserve">circa medium ve-<lb/>ro directè, ſiue ſecundum planitiem, & </s> <s xml:id="echoid-s12315" xml:space="preserve">frontem, quam nobis obuerrunt, ſpectantur; </s> <s xml:id="echoid-s12316" xml:space="preserve">quapropter eti<unsure/>am la-<lb/>tiores, & </s> <s xml:id="echoid-s12317" xml:space="preserve">ampliores ſe præbent. </s> <s xml:id="echoid-s12318" xml:space="preserve">Eadem de cauſa, vna plures aliquando euadit; </s> <s xml:id="echoid-s12319" xml:space="preserve">quia nimirum in principio, <lb/>fiue in margine Solis vna poſt alteram latebat; </s> <s xml:id="echoid-s12320" xml:space="preserve">quæ poſtea Solis medio appropinquantes, paulatim emer-<lb/>gunt, atque ab inuicem ſeparari videntur. </s> <s xml:id="echoid-s12321" xml:space="preserve">quia videlicet vna non amplius eſt ante altera, vt ipſam occul-<lb/>tare queat.</s> <s xml:id="echoid-s12322" xml:space="preserve"/> </p> <pb o="132" file="0154" n="159" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div265" type="section" level="1" n="179"> <head xml:id="echoid-head192" style="it" xml:space="preserve">Locus macularum.</head> <p> <s xml:id="echoid-s12323" xml:space="preserve">EAs aut propè Solem, aut Soli contiguas cum eo reuolui, hæ rationes videntur conuincere. </s> <s xml:id="echoid-s12324" xml:space="preserve">Primo quia <lb/>nullam reſpectu Solis patiuntur parallaxim; </s> <s xml:id="echoid-s12325" xml:space="preserve">vbiq; </s> <s xml:id="echoid-s12326" xml:space="preserve">enim terrarum eadem macula ſpectatur in eodem ſo-<lb/>laris diſci loco, nam Romæ, Ingolſtadij, Bruxellæ, loco adeo diſſitis, eadem macula viſa eſt in medio, v.</s> <s xml:id="echoid-s12327" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s12328" xml:space="preserve">ſolaris diſci, vt teſtantur obſeruationes Galilæi, Apellis, & </s> <s xml:id="echoid-s12329" xml:space="preserve">aliorum. </s> <s xml:id="echoid-s12330" xml:space="preserve">quod ſi a Sole ſatis diſtarent, in locis <lb/>borealioribus, vti ſunt Ingoiſtadium, & </s> <s xml:id="echoid-s12331" xml:space="preserve">Bruxella, videretur eadem macula infra ſolaris diſci medium, quæ <lb/>Romæ in medio viſa eſt, vt naturam parallaxis intelligenti manifeſtum eſt. </s> <s xml:id="echoid-s12332" xml:space="preserve">Secundo ſi à<unsure/> Sole multum di-<lb/>ſtarent, vlderentur etiam quando ſunt ad Solis latera, ideſt, antequam inter Solem, & </s> <s xml:id="echoid-s12333" xml:space="preserve">nos, interpone ren-<lb/>tur, ſeu antequam eſſet ſub Sole; </s> <s xml:id="echoid-s12334" xml:space="preserve">quia ibi eſſent illuminatæ, quate non ſecus, ac Mercurius & </s> <s xml:id="echoid-s12335" xml:space="preserve">Venus, ſeſe <lb/>ibi in conſpectum darent.</s> <s xml:id="echoid-s12336" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div266" type="section" level="1" n="180"> <head xml:id="echoid-head193" style="it" xml:space="preserve">Numerus, & magnitudo macularum.</head> <p> <s xml:id="echoid-s12337" xml:space="preserve">NVmerus earum incertus ac varius eſt. </s> <s xml:id="echoid-s12338" xml:space="preserve">plurimas aliquando conſpexi, ac numeraui 33. </s> <s xml:id="echoid-s12339" xml:space="preserve">aliquando tres tan-<lb/>tum, vel quatuor.</s> <s xml:id="echoid-s12340" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12341" xml:space="preserve">Magnitudo quoq; </s> <s xml:id="echoid-s12342" xml:space="preserve">varia eſt. </s> <s xml:id="echoid-s12343" xml:space="preserve">maximas puto æquales ferè toti terræ, mediocres æquales ſaltem toti Euro-<lb/>pæ, aut Africæ. </s> <s xml:id="echoid-s12344" xml:space="preserve">minimas Corſicæ aut Sardiniæ. </s> <s xml:id="echoid-s12345" xml:space="preserve">nam diameter Solis apparens maior eſt diametro terræ 5 {1/2}. <lb/></s> <s xml:id="echoid-s12346" xml:space="preserve">in figuris autem obſeruationum Galilæi, quædam macula occupat partem ſeptimam diametri Solaris; </s> <s xml:id="echoid-s12347" xml:space="preserve">terre<unsure/> <lb/>vero occuparet quintam circiter partem, vnde conuincitur eam fuiſſe paulò terram minorem.</s> <s xml:id="echoid-s12348" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div267" type="section" level="1" n="181"> <head xml:id="echoid-head194" style="it" xml:space="preserve">Corollarium, an ſint Stellæ<unsure/>.</head> <p> <s xml:id="echoid-s12349" xml:space="preserve">QVæri ſolet ſint ne in ſtellarum numerum recenſendæ. </s> <s xml:id="echoid-s12350" xml:space="preserve">verùm communiter negant: </s> <s xml:id="echoid-s12351" xml:space="preserve">primo quia ſunt ſi-<lb/>guræ irregularis, ſtellæ vero rotundæ. </s> <s xml:id="echoid-s12352" xml:space="preserve">Secundo quia propriam non ſeruant figuram, ſtellæ vero maxi-<lb/>mè. </s> <s xml:id="echoid-s12353" xml:space="preserve">Tertio quia eædem nunquam reuertuntur, contra vero ſtellæ. </s> <s xml:id="echoid-s12354" xml:space="preserve">Quarto quia aliæ ncuæ in facie <lb/>Solis oriuntur, aliæ vero inibi extinguuntur; </s> <s xml:id="echoid-s12355" xml:space="preserve">aliter vero ſtellæ. </s> <s xml:id="echoid-s12356" xml:space="preserve">Quinto tandem, ſtellæ ſunt lucidæ, hæ ve-<lb/>ro nigricantes, & </s> <s xml:id="echoid-s12357" xml:space="preserve">obſcuræ.</s> <s xml:id="echoid-s12358" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12359" xml:space="preserve">Plura de hiſce maculis, & </s> <s xml:id="echoid-s12360" xml:space="preserve">quidem ſcitu digna apud P. </s> <s xml:id="echoid-s12361" xml:space="preserve">Chriſtophorum Scheiner Societate noſtræ in ſuo <lb/>Apelle poſt Tabulam latente, & </s> <s xml:id="echoid-s12362" xml:space="preserve">in Epiſt. </s> <s xml:id="echoid-s12363" xml:space="preserve">Galilæi Italicis de hiſce maculis ſolaribus: </s> <s xml:id="echoid-s12364" xml:space="preserve">necnon in Opticis P <lb/>Aguillonij pariter noſtræ Societatis. </s> <s xml:id="echoid-s12365" xml:space="preserve">Et nouiſſimè in magno lib. </s> <s xml:id="echoid-s12366" xml:space="preserve">Scheineri eiuſdem de Maculis ſeu in roſa V@ſina.</s> <s xml:id="echoid-s12367" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div268" type="section" level="1" n="182"> <head xml:id="echoid-head195" xml:space="preserve">LIBER VNDECIMVS <lb/>DE MERCVRIO.</head> <head xml:id="echoid-head196" style="it" xml:space="preserve">De loco Mercurij. Cap. I.</head> <p> <s xml:id="echoid-s12368" xml:space="preserve">CIrca Solem tanquam centrum, cæteris quinque Planetis propius Mercurij ſtella cir-<lb/>cuit, cuius Hieroglyphicum, quo ſæpe Aſtronomi breuitatis cauſa vtuntur, eſt Ca-<lb/>duceum, erat enim Caduceum Mercurij virga, quam Ægyptij in ſpeciem duorum <lb/>draconum figurauerunt, qui parte media ſui voluminis ſibi colligantur, ſummiſque <lb/>partibus in modum circuli reflexi oſcula iungunt, vti ſuperior nota vtcumque re-<lb/>fert. </s> <s xml:id="echoid-s12369" xml:space="preserve">Non ſolum autẽ recentiores Aſtronomi Mercurium, & </s> <s xml:id="echoid-s12370" xml:space="preserve">Venerem circa Solem <lb/>circuire depręhenderunt; </s> <s xml:id="echoid-s12371" xml:space="preserve">verum etiam vetuſtiſſimi, vti Vitruuius, & </s> <s xml:id="echoid-s12372" xml:space="preserve">Martianus Ca-<lb/>pella tradunt. </s> <s xml:id="echoid-s12373" xml:space="preserve">ille enim lib. </s> <s xml:id="echoid-s12374" xml:space="preserve">9. </s> <s xml:id="echoid-s12375" xml:space="preserve">cap. </s> <s xml:id="echoid-s12376" xml:space="preserve">4. </s> <s xml:id="echoid-s12377" xml:space="preserve">ſic ſcribit; </s> <s xml:id="echoid-s12378" xml:space="preserve">Mercurij autem, & </s> <s xml:id="echoid-s12379" xml:space="preserve">Veneris ſtellæ <lb/>circa ſolis, Solem ipſum, vti centrum itineribus coronantes, regreſſus faciunt, &</s> <s xml:id="echoid-s12380" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s12381" xml:space="preserve">Alter vero lib. </s> <s xml:id="echoid-s12382" xml:space="preserve">8. </s> <s xml:id="echoid-s12383" xml:space="preserve">Philologiæ hæc habet, Venus, & </s> <s xml:id="echoid-s12384" xml:space="preserve">Mercurius, licet ortus & </s> <s xml:id="echoid-s12385" xml:space="preserve">occaſus <lb/>quotidianos oſtendant, corum, tamen circuli terras omnino non anibiunt, ſed circa Solem, laxio<unsure/>re ambitu, <lb/>circulantur: </s> <s xml:id="echoid-s12386" xml:space="preserve">denique ſuorum circulorum centrum in Sole conſtituunt, ita vt ſupra ipſum aliquando, infra <lb/>plerumque propinquiores terris ferantur. </s> <s xml:id="echoid-s12387" xml:space="preserve">Recentiores etiam omnes accuratiffimis obſeruationibus, eius pa-<lb/>rall. </s> <s xml:id="echoid-s12388" xml:space="preserve">xim explorantes, eum planetarum omnium Soli proximnm, Solemque ſuo gyro complectem aſſerunt. </s> <s xml:id="echoid-s12389" xml:space="preserve"><lb/>Præterea cum ſtatuant planetas quinque circa Solem circuncuſare, ſequitur eos cæteris illi viciniores, eſſe <lb/>qui minus ab eo digrediuntur; </s> <s xml:id="echoid-s12390" xml:space="preserve">atqui Mercurius minus omnium ab eo recedit, minoremque circulum deſcri-<lb/>bit, ergo omnium Soli proximus. </s> <s xml:id="echoid-s12391" xml:space="preserve">Tandem, cum maculæ, vt vidimus; </s> <s xml:id="echoid-s12392" xml:space="preserve">& </s> <s xml:id="echoid-s12393" xml:space="preserve">Venus, vt videbimus, Solem circum-<lb/>dent, conueniens admodum eſt idem de Mercurio exiſtimare; </s> <s xml:id="echoid-s12394" xml:space="preserve">cum vero a Sole pluſquam maculæ, minus vero <lb/>quam Venus digrediatur, ideo rectè inter vtraſque collocari debet. </s> <s xml:id="echoid-s12395" xml:space="preserve">Porrò cum eum circa Solem, vti centrum <lb/>circumire ſtatuamus, deſcribet neceſſario circa Solem epicyclum, in quo modo ſupra, modo infra Solem exi-<lb/>ſtet, ac propterea varia erit eius a terra diſtantia. </s> <s xml:id="echoid-s12396" xml:space="preserve">centrum epicycli eius erit in Sole, quare epicyclus eamdem <pb o="133" file="0155" n="160" rhead="Liber Vndecimus."/> c<unsure/>um Sole ſorti etur à terra diſtantiam. </s> <s xml:id="echoid-s12397" xml:space="preserve">ſtella vero Mercurij aliquando maiorem, aliquando minorem, quam <lb/>Sol a terra rem otionem obtinebit, prout in Apogæo vel Perigæo epicycli fuerit.</s> <s xml:id="echoid-s12398" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div269" type="section" level="1" n="183"> <head xml:id="echoid-head197" style="it" xml:space="preserve">Motus Mercurij. Cap. II.</head> <p> <s xml:id="echoid-s12399" xml:space="preserve">QVæ ab Aſtronomis de Mercurij motibus traduntur, multis ſunt tricis perplexa, ac minus quam in cæ-<lb/>teris planetis certa: </s> <s xml:id="echoid-s12400" xml:space="preserve">cum enim parum a Sole digrediatur, rarò commode videri poteſt; </s> <s xml:id="echoid-s12401" xml:space="preserve">quia cum appa-<lb/>ret, aut nimia Solis vicinitate, aut ob vapores qui <lb/> <anchor type="figure" xlink:label="fig-0155-01a" xlink:href="fig-0155-01"/> horizontem obſident (nonniſi enim apud hori-<lb/>zontem manè aut veſperi ſpectari poteſt incertè <lb/>ac difficilè admodum obſeruari poteſt: </s> <s xml:id="echoid-s12402" xml:space="preserve">propte-<lb/>rea ea tantummodo proferam, quæ certiora ac <lb/>maioris momenti videbuntur.</s> <s xml:id="echoid-s12403" xml:space="preserve"/> </p> <div xml:id="echoid-div269" type="float" level="2" n="1"> <figure xlink:label="fig-0155-01" xlink:href="fig-0155-01a"> <image file="0155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0155-01"/> </figure> </div> <p> <s xml:id="echoid-s12404" xml:space="preserve">Obſeruationes igitur docent Mercurium circa <lb/>Solem, & </s> <s xml:id="echoid-s12405" xml:space="preserve">cum Sole, hoc pacto, moueri, vt in prę-<lb/>ſenti figura melius explicabitur, in qua terra vbi <lb/>T. </s> <s xml:id="echoid-s12406" xml:space="preserve">Sol vbi S. </s> <s xml:id="echoid-s12407" xml:space="preserve">& </s> <s xml:id="echoid-s12408" xml:space="preserve">Solis circuitus S O P Q. </s> <s xml:id="echoid-s12409" xml:space="preserve">circa So-<lb/>lem deſcriptus ſit epicyclus ſpiralis, ſeu linea ſpi-<lb/>ralis, A B C D E F G H I K L M N. </s> <s xml:id="echoid-s12410" xml:space="preserve">cuius ma-<lb/>ior ſpira ſeu gyrus ſit A B C D. </s> <s xml:id="echoid-s12411" xml:space="preserve">quæ diſtet à Sole <lb/>vtrinque per gra. </s> <s xml:id="echoid-s12412" xml:space="preserve">28. </s> <s xml:id="echoid-s12413" xml:space="preserve">minor vero F G H I, quæ <lb/>diſtet à<unsure/> Sole vtrinque gr. </s> <s xml:id="echoid-s12414" xml:space="preserve">20. </s> <s xml:id="echoid-s12415" xml:space="preserve">& </s> <s xml:id="echoid-s12416" xml:space="preserve">in hac linea ſit ali-<lb/>cubi ſydus Mercurij. </s> <s xml:id="echoid-s12417" xml:space="preserve">dum igitur Sol motu ſuo <lb/>mouetur ſub Zodiaco ab S. </s> <s xml:id="echoid-s12418" xml:space="preserve">in O. </s> <s xml:id="echoid-s12419" xml:space="preserve">cum eo pariter <lb/>mouetur epicyclus, & </s> <s xml:id="echoid-s12420" xml:space="preserve">conſequem<unsure/>er planeta. </s> <s xml:id="echoid-s12421" xml:space="preserve">Epi-<lb/>cyclus igitur hic mouetur eadem velocitate cum <lb/>Sole in longitudem ſeu in conſequentia ſigno-<lb/>rum, & </s> <s xml:id="echoid-s12422" xml:space="preserve">pariter etiam cum Sole diurna motione <lb/>ſpatio 24. </s> <s xml:id="echoid-s12423" xml:space="preserve">horarum: </s> <s xml:id="echoid-s12424" xml:space="preserve">dum igitur hoc modo epicy-<lb/>clus hic imaginarius Solem comitatur, in eo pla-<lb/>neta continuo circa Solem circuit, atque hoc mo-<lb/>do, in ſuperiori parte, verbi gratia D A B. </s> <s xml:id="echoid-s12425" xml:space="preserve">proce-<lb/>ditab occaſu in ortum, ideſt, a D. </s> <s xml:id="echoid-s12426" xml:space="preserve">ad A. </s> <s xml:id="echoid-s12427" xml:space="preserve">& </s> <s xml:id="echoid-s12428" xml:space="preserve">a ab A. <lb/></s> <s xml:id="echoid-s12429" xml:space="preserve">ad B. </s> <s xml:id="echoid-s12430" xml:space="preserve">hinc conſequenter pergit ad C. </s> <s xml:id="echoid-s12431" xml:space="preserve">hinc verſus D. </s> <s xml:id="echoid-s12432" xml:space="preserve">& </s> <s xml:id="echoid-s12433" xml:space="preserve">propterea in inferiori parte tendit ab ortu in occaſum. </s> <s xml:id="echoid-s12434" xml:space="preserve"><lb/>hic motus epicyclaris dicitur motus Anomaliæ, & </s> <s xml:id="echoid-s12435" xml:space="preserve">irregularitatis; </s> <s xml:id="echoid-s12436" xml:space="preserve">ex eo enim fit, vt Mercurius videatur <lb/>irregulariter in Zodiaco moueri; </s> <s xml:id="echoid-s12437" xml:space="preserve">quando enim eſt in ſuperiori parte ſpiralis lineæ velocior apparet, quia <lb/>t<unsure/>unc motus eius conſentit cum motu centri epicycli in longitudinem: </s> <s xml:id="echoid-s12438" xml:space="preserve">quando vero eſt in parte inferiori, mo-<lb/>uetur contra motum centri epicycli, ac propterea tardior apparet. </s> <s xml:id="echoid-s12439" xml:space="preserve">hunc epicycli gyrum ſiue ſpiram vnam, <lb/>v.</s> <s xml:id="echoid-s12440" xml:space="preserve">g. </s> <s xml:id="echoid-s12441" xml:space="preserve">a b c d e. </s> <s xml:id="echoid-s12442" xml:space="preserve">abſoluit diebus 115. </s> <s xml:id="echoid-s12443" xml:space="preserve">horis 21. </s> <s xml:id="echoid-s12444" xml:space="preserve">min. </s> <s xml:id="echoid-s12445" xml:space="preserve">5. </s> <s xml:id="echoid-s12446" xml:space="preserve">vnde ſingulis diebus peragrat de eius peripheria gr. </s> <s xml:id="echoid-s12447" xml:space="preserve">3. </s> <s xml:id="echoid-s12448" xml:space="preserve">6′. </s> <s xml:id="echoid-s12449" xml:space="preserve"><lb/>24″. </s> <s xml:id="echoid-s12450" xml:space="preserve">quare totam v.</s> <s xml:id="echoid-s12451" xml:space="preserve">g. </s> <s xml:id="echoid-s12452" xml:space="preserve">ab A. </s> <s xml:id="echoid-s12453" xml:space="preserve">ad E. </s> <s xml:id="echoid-s12454" xml:space="preserve">reuolutionem abſoluit non integris 4. </s> <s xml:id="echoid-s12455" xml:space="preserve">menſibus ſolaribus, ſed deſunt dies <lb/>ferè 6. </s> <s xml:id="echoid-s12456" xml:space="preserve">Præterea non abſoluit ſpiram in e, ſub a, paulo vltra ſub N. </s> <s xml:id="echoid-s12457" xml:space="preserve">quia ob motum apogæi A. </s> <s xml:id="echoid-s12458" xml:space="preserve">ſecundum ſi-<lb/>gnorum ordinem, ipſum A, transfertur ad n. </s> <s xml:id="echoid-s12459" xml:space="preserve">pręterea ſciendum eſt huius anomaliæ principium ab Aſtrono-<lb/>mis poni in punctis ſupremis A. </s> <s xml:id="echoid-s12460" xml:space="preserve">E. </s> <s xml:id="echoid-s12461" xml:space="preserve">I. </s> <s xml:id="echoid-s12462" xml:space="preserve">ab his enim locis hunc motum computant, ſeu numerant.</s> <s xml:id="echoid-s12463" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12464" xml:space="preserve">Oſeruarunt præterea non ſemper Mercurium in eadem diſtãtia a Sole circumire; </s> <s xml:id="echoid-s12465" xml:space="preserve">ſicut non ſemper æqua-<lb/>lem circa Solem deſcribere circulationem; </s> <s xml:id="echoid-s12466" xml:space="preserve">in vna enim parte Zodiaci magis à Sole hinc inde digrediebatur, <lb/>quam in altera; </s> <s xml:id="echoid-s12467" xml:space="preserve">ſemel enim in anno digredietur à Sole gradibus 28. </s> <s xml:id="echoid-s12468" xml:space="preserve">circiter; </s> <s xml:id="echoid-s12469" xml:space="preserve">alias verò gra. </s> <s xml:id="echoid-s12470" xml:space="preserve">20. </s> <s xml:id="echoid-s12471" xml:space="preserve">tantum: </s> <s xml:id="echoid-s12472" xml:space="preserve">hunc <lb/>motum non ineptè ſaluare poſſumus poſita ſpirali linea, in qua Mercurius moueatur ab exteriori, & </s> <s xml:id="echoid-s12473" xml:space="preserve">amplio-<lb/>ri circuitu A B D. </s> <s xml:id="echoid-s12474" xml:space="preserve">paulatim, & </s> <s xml:id="echoid-s12475" xml:space="preserve">ſpiratim per loca E F G H I K L M N. </s> <s xml:id="echoid-s12476" xml:space="preserve">ad interiorem, ac minorem F G H I. <lb/></s> <s xml:id="echoid-s12477" xml:space="preserve">locus autem ille Zodiaci, in quo Mercurius ſemper eſt in minori gyro F G H. </s> <s xml:id="echoid-s12478" xml:space="preserve">appellatur apogæum primum <lb/>Mercurij; </s> <s xml:id="echoid-s12479" xml:space="preserve">fit enim ibi a terra remotior. </s> <s xml:id="echoid-s12480" xml:space="preserve">nec ſemper in eodem Zodiaci loco apogæum iſtud manet, ſed moue-<lb/>tur tardiſſimè in conſequentia; </s> <s xml:id="echoid-s12481" xml:space="preserve">nam annuus eius motus eſt tantum, min. </s> <s xml:id="echoid-s12482" xml:space="preserve">1′<unsure/>. </s> <s xml:id="echoid-s12483" xml:space="preserve">ſecundorum 49″. </s> <s xml:id="echoid-s12484" xml:space="preserve">quare gradum <lb/>vnum peragit annis 33. </s> <s xml:id="echoid-s12485" xml:space="preserve">& </s> <s xml:id="echoid-s12486" xml:space="preserve">totum Zodiacum in annis circiter 11′ 880′. </s> <s xml:id="echoid-s12487" xml:space="preserve">Oppoſitus autem Zodiaci locus eſt pe-<lb/>rigæum, in quo percurrit ampliorem lineam, fitq; </s> <s xml:id="echoid-s12488" xml:space="preserve">terræ vicin or. </s> <s xml:id="echoid-s12489" xml:space="preserve">in medijs vero locis per medias ſpiras re-<lb/>uoluitur. </s> <s xml:id="echoid-s12490" xml:space="preserve">noſtra autem tempeſtate apogæum iſtud verſatur in principio Sagittarij, ibi enim Mercurius mi-<lb/>nus a Sole digreditur. </s> <s xml:id="echoid-s12491" xml:space="preserve">Perigæum verò in oppoſito loco, nimirum in principio Geminorum, vbi latius cir-<lb/>c<unsure/>a Solem euagatur. </s> <s xml:id="echoid-s12492" xml:space="preserve">Porrò hoſce medios motus ac tempora ijſdem modis, ac in Luna, & </s> <s xml:id="echoid-s12493" xml:space="preserve">Sole compererunt.</s> <s xml:id="echoid-s12494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12495" xml:space="preserve">Prædicti igitur motus ſiunt ſecundum Zodiaci longitudinem, verum præter eos alium habet, quo moue <lb/>tur ſecundum latitudinem Zodiaci, hoc eſt, modo in Auſtrum, modo in Boream ab eclypti a exorbitat, vſq; <lb/></s> <s xml:id="echoid-s12496" xml:space="preserve">aliquando ad gr. </s> <s xml:id="echoid-s12497" xml:space="preserve">4. </s> <s xml:id="echoid-s12498" xml:space="preserve">10′. </s> <s xml:id="echoid-s12499" xml:space="preserve">vnde modo Borealis, modo Auſtralis denominatur; </s> <s xml:id="echoid-s12500" xml:space="preserve">quod inde<unsure/> ori<unsure/>tur quia ſpiralem <lb/>hanc epicyclicam non deſcribit ſemper ſub eclyptica, ſed aliquando citra, aliquando v tra eam.</s> <s xml:id="echoid-s12501" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12502" xml:space="preserve">Poſtremo ex hiſce omnibus motibus, exurgit tandem vltimus, & </s> <s xml:id="echoid-s12503" xml:space="preserve">compoſitus Mercurij motus; </s> <s xml:id="echoid-s12504" xml:space="preserve">qui ab vno <lb/>tropico ad alterum ſpiralis erit, ſicuti in Sole, & </s> <s xml:id="echoid-s12505" xml:space="preserve">Luna.</s> <s xml:id="echoid-s12506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12507" xml:space="preserve">Lam vero, vt quæ reliqua ſunt abſoluamus, ſit in figura ductæ duæ lineæ T B. </s> <s xml:id="echoid-s12508" xml:space="preserve">T D. </s> <s xml:id="echoid-s12509" xml:space="preserve">à centro mundi T. </s> <s xml:id="echoid-s12510" xml:space="preserve">tan- <pb o="134" file="0156" n="161" rhead="De Mundi Fabrica,"/> gentes vtrimq; </s> <s xml:id="echoid-s12511" xml:space="preserve">in punctis B D. </s> <s xml:id="echoid-s12512" xml:space="preserve">epicyclum; </s> <s xml:id="echoid-s12513" xml:space="preserve">quibus aliæ ſimiles intelligantur tangentes alias minores ſpiras.</s> <s xml:id="echoid-s12514" xml:space="preserve"><unsure/> ſit <lb/>etiam ducta T S A. </s> <s xml:id="echoid-s12515" xml:space="preserve">ſecans bifariam epicyclum, & </s> <s xml:id="echoid-s12516" xml:space="preserve">ſpiras eius in punctis C L G I E A. </s> <s xml:id="echoid-s12517" xml:space="preserve">puncta igitur ſuperiora <lb/>A E I. </s> <s xml:id="echoid-s12518" xml:space="preserve">ſunt ea à<unsure/> quibus numeratio Anomaliæ incipit, & </s> <s xml:id="echoid-s12519" xml:space="preserve">quæ apogęa ſpirarum dici poſſunt: </s> <s xml:id="echoid-s12520" xml:space="preserve">reliqua inferio-<lb/>ra G L C. </s> <s xml:id="echoid-s12521" xml:space="preserve">dici poſſunt perigæa ſpirarum, quod in illis planeta maximè a<unsure/> terra recedat, in his vero maximè ad <lb/>@erram accedat: </s> <s xml:id="echoid-s12522" xml:space="preserve">pars ſuperior D A B. </s> <s xml:id="echoid-s12523" xml:space="preserve">definitur à lineis tangentibus in punctis D B. </s> <s xml:id="echoid-s12524" xml:space="preserve">& </s> <s xml:id="echoid-s12525" xml:space="preserve">diuiditur pariter ab in-<lb/>feriori B O D. </s> <s xml:id="echoid-s12526" xml:space="preserve">idem intelligas in alijs ſpiris. </s> <s xml:id="echoid-s12527" xml:space="preserve">quoniam igitur planeta pergit in ſuperiori arcu verſus orien-<lb/>tem à<unsure/> D. </s> <s xml:id="echoid-s12528" xml:space="preserve">ad A. </s> <s xml:id="echoid-s12529" xml:space="preserve">& </s> <s xml:id="echoid-s12530" xml:space="preserve">hinc ad B. </s> <s xml:id="echoid-s12531" xml:space="preserve">in inferiori vero contra, ſequitur eum ibi eſſe velociorem<unsure/> in Zodiaco, quam in <lb/>inferiori, quia ibi tam motus centri epicycli, quam motus ipſius planetæ tendunt ad eaſdem partes orienta@ <lb/>les: </s> <s xml:id="echoid-s12532" xml:space="preserve">in inferiori vero tardiorem, quia hic motus planetæ contrarius eſt motui epicycli, adeo vt etiam retro-<lb/>gredi in Zodiaco videatur. </s> <s xml:id="echoid-s12533" xml:space="preserve">Hinc ſequitur planetam directum dici, quando adeo velox eſt, vt in Zodiaco pro-<lb/>grediatur: </s> <s xml:id="echoid-s12534" xml:space="preserve">Retrogradum vero quando in inferiori arcu ſpiræ, plus retrocedit in Zodiaco, quam progredia-<lb/>tur epicycli centrum, ſic enim videtur in Zo diaco repedare: </s> <s xml:id="echoid-s12535" xml:space="preserve">Stationarium tandem quando in eodem Zu<unsure/>-<lb/>diaci loco perſiſtit, quod accidit parum infra puncta contactuum B D. </s> <s xml:id="echoid-s12536" xml:space="preserve">v. </s> <s xml:id="echoid-s12537" xml:space="preserve">g. </s> <s xml:id="echoid-s12538" xml:space="preserve">in R V. </s> <s xml:id="echoid-s12539" xml:space="preserve">ſtatio prima eſt in R. </s> <s xml:id="echoid-s12540" xml:space="preserve">ſe-<lb/>@unda in V.</s> <s xml:id="echoid-s12541" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12542" xml:space="preserve">Arcus V A R. </s> <s xml:id="echoid-s12543" xml:space="preserve">dicitur arcus directionis, quod planeta eum percurrens in Zodiaco proficiat, vnde & </s> <s xml:id="echoid-s12544" xml:space="preserve">dire-<lb/>@tus fit: </s> <s xml:id="echoid-s12545" xml:space="preserve">reliquus arcus R C V. </s> <s xml:id="echoid-s12546" xml:space="preserve">arcus eſt regreſſus, in quo ſcilicet planeta retrogradus apparet.</s> <s xml:id="echoid-s12547" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12548" xml:space="preserve">Velox præterea planeta dicitur, cùm velocior eſt quàm epicycli centrum: </s> <s xml:id="echoid-s12549" xml:space="preserve">Tardus vero cũ eodem ſegnior <lb/>eſt: </s> <s xml:id="echoid-s12550" xml:space="preserve">Mediocris, & </s> <s xml:id="echoid-s12551" xml:space="preserve">æqualis quando cum eodem æqualiter incedit, qui motus medius appellatur. </s> <s xml:id="echoid-s12552" xml:space="preserve">Orientalis, <lb/>& </s> <s xml:id="echoid-s12553" xml:space="preserve">matutinus dicitur cum manè ante Solem oritur, quod accidit in ſemicirculo occidentali C D A. </s> <s xml:id="echoid-s12554" xml:space="preserve">dum vi-<lb/>delicet planeta ſcandit à<unsure/> perigæis ſpirarum ab apogæa, quia ibi præcedit Solem in motu diurno, vt conſide-<lb/>ranti patere poteſt. </s> <s xml:id="echoid-s12555" xml:space="preserve">Occidentalis, & </s> <s xml:id="echoid-s12556" xml:space="preserve">veſpertinus, cum poſt Solem occumbit; </s> <s xml:id="echoid-s12557" xml:space="preserve">quod accidit dum planeta de-<lb/>ſcendit in ſemicirculo orientali A B C. </s> <s xml:id="echoid-s12558" xml:space="preserve">quia ibi ſequitur Solem in motu diurno.</s> <s xml:id="echoid-s12559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12560" xml:space="preserve">Ortus heliacus ſeu ſolaris matutinus planetæ, fit quando planeta mane ante Solem incipit extra ſolares ra-<lb/>dios tranſactis perigæis C L G, apparere.</s> <s xml:id="echoid-s12561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12562" xml:space="preserve">Occaſus heliacus@eu ſolaris matutinus, fit cũ oriente Sole, planeta qui prius apparebat Soli appropinquans <lb/>apud apogæa ſpirarum A E I, Solis fulgorem ſubiens, occultatur.</s> <s xml:id="echoid-s12563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12564" xml:space="preserve">Ortus heliacus veſpertinus fit, cum planeta tranſacto ſpiræ apogæo iam verſatur in ſemicirculo orien tali <lb/>A B C. </s> <s xml:id="echoid-s12565" xml:space="preserve">in quo Solẽ<unsure/> ſequitur, & </s> <s xml:id="echoid-s12566" xml:space="preserve">propterea poſt Solis occaſum veſperi in occidente è fulgore Solis emergens, <lb/>apparere incipit.</s> <s xml:id="echoid-s12567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12568" xml:space="preserve">Occaſus heliacus veſpertinus fit, quando planeta ita ad perigæum ſpirarum acceſſerit, vt cum antea vide-<lb/>retur, non amplius ob Solis fulgorem, quem iam ſubijt, appareat.</s> <s xml:id="echoid-s12569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12570" xml:space="preserve">In hoc autem ſpirarum epicycli ambitu, bis Soli, reſpectu noſtri, qui ſumus in centro mundi, videtur con-<lb/>iungi, ideſt, in perigæis, & </s> <s xml:id="echoid-s12571" xml:space="preserve">apogęis ſpirarum, quando directè ſub Sole, & </s> <s xml:id="echoid-s12572" xml:space="preserve">ſupra Solem reperitur in linea T A. <lb/></s> <s xml:id="echoid-s12573" xml:space="preserve">in punctis vero linearum tangentium B D. </s> <s xml:id="echoid-s12574" xml:space="preserve">maximos a Sole receſius patitur, in maiori ambitu grad. </s> <s xml:id="echoid-s12575" xml:space="preserve">ferè 28. </s> <s xml:id="echoid-s12576" xml:space="preserve">in <lb/>minori gr. </s> <s xml:id="echoid-s12577" xml:space="preserve">20. </s> <s xml:id="echoid-s12578" xml:space="preserve">quapropter nunquam Soli opponi poteſt, ſed veluti ſeruus eius, parum ab eius latere diicedit: </s> <s xml:id="echoid-s12579" xml:space="preserve"><lb/>quæ cauſa eſt cur propè horizontem tantum in vaporoſo, ac condenſo aere ægrè conſpici ac obſeruari poſſit: </s> <s xml:id="echoid-s12580" xml:space="preserve"><lb/>ſimul enim ab aere craſſo, atq; </s> <s xml:id="echoid-s12581" xml:space="preserve">a Solis fulgo@e aſpectus eius offuſcatur. </s> <s xml:id="echoid-s12582" xml:space="preserve">Prædicta verò omnia ſunt etiam com-<lb/>munia Veneri, partim etiam alijs planetis, vt poſtea patebit.</s> <s xml:id="echoid-s12583" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div271" type="section" level="1" n="184"> <head xml:id="echoid-head198" style="it" xml:space="preserve">Figura Mercurij. Cap. III.</head> <p> <s xml:id="echoid-s12584" xml:space="preserve">EXiſtimandum eſt eſſe ſphęricum, non tamen Geometricè, ſed ſicuti Luna aſperitatibus refertum; </s> <s xml:id="echoid-s12585" xml:space="preserve">ſi enim <lb/>perfectè ſphæricus eſſ<unsure/>et, vnicus vix ab ipſo Solis radius nobis reflecteretur, qui diſperderetur, ac propte-<lb/>rea ipſum Mercuriũ neutiquam videremus: </s> <s xml:id="echoid-s12586" xml:space="preserve">ſigura namq; </s> <s xml:id="echoid-s12587" xml:space="preserve">perfectè ſphærica & </s> <s xml:id="echoid-s12588" xml:space="preserve">terſa lumen occurrens vndiq; <lb/></s> <s xml:id="echoid-s12589" xml:space="preserve">diſpergit, vt ex perientia, & </s> <s xml:id="echoid-s12590" xml:space="preserve">ratio Optica docet. </s> <s xml:id="echoid-s12591" xml:space="preserve">Enimuero Elementa quatuor ſphærica figura prædita ſunt; </s> <s xml:id="echoid-s12592" xml:space="preserve"><lb/>Luna pariter, & </s> <s xml:id="echoid-s12593" xml:space="preserve">Sol, Venus etiam perſpicue rotunda apparet; </s> <s xml:id="echoid-s12594" xml:space="preserve">quidni igitur Mercurius rotundus erit?</s> <s xml:id="echoid-s12595" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div272" type="section" level="1" n="185"> <head xml:id="echoid-head199" style="it" xml:space="preserve">Illuminatio Mercurij, & vmbra. Cap. IV.</head> <p> <s xml:id="echoid-s12596" xml:space="preserve">CVm fit ſphæricus, atq; </s> <s xml:id="echoid-s12597" xml:space="preserve">à Sole illuſtretur, puto ipſum inſtar Lune, ſeu potius inſtar Veneris corniculatim, <lb/>& </s> <s xml:id="echoid-s12598" xml:space="preserve">dimidiatum, & </s> <s xml:id="echoid-s12599" xml:space="preserve">plenè illuminari, &</s> <s xml:id="echoid-s12600" xml:space="preserve">c. </s> <s xml:id="echoid-s12601" xml:space="preserve">vt poſtea in Venere videbimus; </s> <s xml:id="echoid-s12602" xml:space="preserve">hos enim ambos planetas eodẽ <lb/>prorſus modo colluſtrari a Sole exiſtimo.</s> <s xml:id="echoid-s12603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12604" xml:space="preserve">Sed quæritur quanta ſit vmbra Mercurij, & </s> <s xml:id="echoid-s12605" xml:space="preserve">an ad Venerem pertingat, eamq; </s> <s xml:id="echoid-s12606" xml:space="preserve">eclypſet. </s> <s xml:id="echoid-s12607" xml:space="preserve">Reſpondeo longi-<lb/>tudinem vmbræ eius eſſe ſemidiametros terræ circiter 43. </s> <s xml:id="echoid-s12608" xml:space="preserve">quod eodẽ modo, ac ſiguratione reperi, qua etiam <lb/>quantitatem vmbræ terreſtris, quæ ab eo multo pluſquam ducentis terræ ſemidiametris ſemper recedit.</s> <s xml:id="echoid-s12609" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div273" type="section" level="1" n="186"> <head xml:id="echoid-head200" style="it" xml:space="preserve">Magnitudo Mercurij, & Epicycli eius. Cap. V.</head> <p> <s xml:id="echoid-s12610" xml:space="preserve">VT antea vidimus, duo neceſſaria ſunt ad magnitudinem planetarum inquirẽdam. </s> <s xml:id="echoid-s12611" xml:space="preserve">primum eſt corum di-<lb/>ſtantia a mundi medio; </s> <s xml:id="echoid-s12612" xml:space="preserve">ſecundum eſt eorumdem apparens diameter in eadẽ diſtantia: </s> <s xml:id="echoid-s12613" xml:space="preserve">quæ duo ſic in Mer<unsure/> <lb/>ourio obtinebis; </s> <s xml:id="echoid-s12614" xml:space="preserve">Eum obſerua quando maximè à Sole recedit; </s> <s xml:id="echoid-s12615" xml:space="preserve">præſertim in maiori epicycli ſpira, vbi minus <lb/>a Solis iubare, offuſcatur; </s> <s xml:id="echoid-s12616" xml:space="preserve">ibi enim ſortitur eandem cum Sole a terra diſtantiam, quæ quando mediocris eſt, <lb/>continet<unsure/> terræ ſemidiametros 1142. </s> <s xml:id="echoid-s12617" xml:space="preserve">tunc igitur obſerua apparentem eius diame<unsure/>trum per quadrantem, quam <pb o="135" file="0157" n="162" rhead="Liber Vndecimus."/> attenta inſpectione reperies minutorum 2 {1/6}. </s> <s xml:id="echoid-s12618" xml:space="preserve">iuxta Tychonicas obſeruationes. </s> <s xml:id="echoid-s12619" xml:space="preserve">iam ex apparatu noſtræ ſphæ-<lb/>ræ, conſtrue triangulum Iſoſceles, cuius duo latera æqualia efficiant angulum min. </s> <s xml:id="echoid-s12620" xml:space="preserve">2 {6/1}. </s> <s xml:id="echoid-s12621" xml:space="preserve">eorumque longitudo <lb/>c<unsure/>ontinear particulas 1142. </s> <s xml:id="echoid-s12622" xml:space="preserve">quæ referunt terræ diametros conflantes eius diſtantiam, vt in ſ<unsure/>igura vides. </s> <s xml:id="echoid-s12623" xml:space="preserve">baſis <lb/>eius B C. </s> <s xml:id="echoid-s12624" xml:space="preserve">refert diametrũ Mercurij min. </s> <s xml:id="echoid-s12625" xml:space="preserve">2 {1/6}. <lb/></s> <s xml:id="echoid-s12626" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0157-01a" xlink:href="fig-0157-01"/> practicè igitur per circinum, & </s> <s xml:id="echoid-s12627" xml:space="preserve">accuratè ex-<lb/>perire quam rationem habeat baſis B C. </s> <s xml:id="echoid-s12628" xml:space="preserve">ad <lb/>ad vnam ex particulis laterũ, quæ refert dia-<lb/>metrum terræ: </s> <s xml:id="echoid-s12629" xml:space="preserve">quam rationem reperies eſſe <lb/>vti 3. </s> <s xml:id="echoid-s12630" xml:space="preserve">ad 8. </s> <s xml:id="echoid-s12631" xml:space="preserve">hæc antem ratio triplicata, vt alias <lb/>docuimus, dabit etiam ſphærarum proportionem, quæ erit vt 1. </s> <s xml:id="echoid-s12632" xml:space="preserve">ad 19. </s> <s xml:id="echoid-s12633" xml:space="preserve">ferè; </s> <s xml:id="echoid-s12634" xml:space="preserve">Quare Mercurius vnde<unsure/>uicies a<unsure/> <lb/>terra continetur. </s> <s xml:id="echoid-s12635" xml:space="preserve">ſic<unsure/> autem facilè habebimus triplicatam rationem quorumlibet duorum numerorum, multi-<lb/>plicando videlicet vtrumq; </s> <s xml:id="echoid-s12636" xml:space="preserve">cubicè, cubi enim numeri ſunt in triplicata proportione ſuorum laterum per 12. <lb/></s> <s xml:id="echoid-s12637" xml:space="preserve">octaui elementorum: </s> <s xml:id="echoid-s12638" xml:space="preserve">multiplicare autem numerum cubicè fit multiplicando ipſum per ſeipſum, & </s> <s xml:id="echoid-s12639" xml:space="preserve">produ-<lb/>ctum rurſus per eundem datum numerum, v.</s> <s xml:id="echoid-s12640" xml:space="preserve">g. </s> <s xml:id="echoid-s12641" xml:space="preserve">duco 3. </s> <s xml:id="echoid-s12642" xml:space="preserve">in 3. </s> <s xml:id="echoid-s12643" xml:space="preserve">& </s> <s xml:id="echoid-s12644" xml:space="preserve">producuntur 9. </s> <s xml:id="echoid-s12645" xml:space="preserve">rurſum multiplico 9. </s> <s xml:id="echoid-s12646" xml:space="preserve">per 3. </s> <s xml:id="echoid-s12647" xml:space="preserve">& </s> <s xml:id="echoid-s12648" xml:space="preserve"><lb/>fiunt 27. </s> <s xml:id="echoid-s12649" xml:space="preserve">qui numerus eſt cubus, euius latus eſt 3. </s> <s xml:id="echoid-s12650" xml:space="preserve">eodem modo numeri 8. </s> <s xml:id="echoid-s12651" xml:space="preserve">cubus eſt 512. </s> <s xml:id="echoid-s12652" xml:space="preserve">ratio igitur 27. </s> <s xml:id="echoid-s12653" xml:space="preserve">ad 512. </s> <s xml:id="echoid-s12654" xml:space="preserve"><lb/>eſt triplicata laterum 3. </s> <s xml:id="echoid-s12655" xml:space="preserve">8. </s> <s xml:id="echoid-s12656" xml:space="preserve">ratio autem cuborum habetur diuidendo maiorem 512. </s> <s xml:id="echoid-s12657" xml:space="preserve">per minorem 27. </s> <s xml:id="echoid-s12658" xml:space="preserve">quotiens <lb/>enim eſt ferè 19. </s> <s xml:id="echoid-s12659" xml:space="preserve">vnde patet numerum maiorem continere minorem vndeuicies.</s> <s xml:id="echoid-s12660" xml:space="preserve"/> </p> <div xml:id="echoid-div273" type="float" level="2" n="1"> <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a"> <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0157-01"/> </figure> </div> <p> <s xml:id="echoid-s12661" xml:space="preserve">Secundò in eadem diſtantia Sol exhibet diametrum apparentem min. </s> <s xml:id="echoid-s12662" xml:space="preserve">31<emph style="super">1</emph>. </s> <s xml:id="echoid-s12663" xml:space="preserve">Mercurius vero min. </s> <s xml:id="echoid-s12664" xml:space="preserve">2 {1/6}. </s> <s xml:id="echoid-s12665" xml:space="preserve">nota <lb/>igitur erit horum diametrorum proportio, eritq; </s> <s xml:id="echoid-s12666" xml:space="preserve">ſicut 13. </s> <s xml:id="echoid-s12667" xml:space="preserve">ad 186. </s> <s xml:id="echoid-s12668" xml:space="preserve">vnde & </s> <s xml:id="echoid-s12669" xml:space="preserve">ſphęrarum Solis, & </s> <s xml:id="echoid-s12670" xml:space="preserve">Mercurij ratio <lb/>non latebit, eritq; </s> <s xml:id="echoid-s12671" xml:space="preserve">vt ferè 2928. </s> <s xml:id="echoid-s12672" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s12673" xml:space="preserve">cum autem ratio terræ ad Solem manifeſta ſit, manif<unsure/>eſta quoque erit ad <lb/>Mercurium, nam cum in Sole contineantur Mercurij 2918. </s> <s xml:id="echoid-s12674" xml:space="preserve">terræ autem 40. </s> <s xml:id="echoid-s12675" xml:space="preserve">ſi ille numerus per hunc diui da-<lb/>tur, quotiens indicabit eum a terra compræhendi vndeuicies. </s> <s xml:id="echoid-s12676" xml:space="preserve">Tertio. </s> <s xml:id="echoid-s12677" xml:space="preserve">Terra continet 19. </s> <s xml:id="echoid-s12678" xml:space="preserve">Mercurius, Lunas <lb/>autem 40. </s> <s xml:id="echoid-s12679" xml:space="preserve">ergo Mercurius ferè duplo maior eſt Luna.</s> <s xml:id="echoid-s12680" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div275" type="section" level="1" n="187"> <head xml:id="echoid-head201" style="it" xml:space="preserve">Quantitas Epicycli.</head> <p> <s xml:id="echoid-s12681" xml:space="preserve">CVm maxima Mercurij à Sole remotio fit gra. </s> <s xml:id="echoid-s12682" xml:space="preserve">28. </s> <s xml:id="echoid-s12683" xml:space="preserve">epicycli magnitudo facilè conſtabit, deſcripto ad di-<lb/>ctam diſtantiam circulo circa Solem tanquam centrum, is enim circulus habebit veram rationem ad <lb/>circuitum Solis, deſcendetq; </s> <s xml:id="echoid-s12684" xml:space="preserve">infra Solem medio ferè loco inter Solem, & </s> <s xml:id="echoid-s12685" xml:space="preserve">terram: </s> <s xml:id="echoid-s12686" xml:space="preserve">cum præterea minima eius <lb/>à Sole elongatio ſit gr. </s> <s xml:id="echoid-s12687" xml:space="preserve">20. </s> <s xml:id="echoid-s12688" xml:space="preserve">manifeſta erit ex deſcriptione ſpira is epicycli circa Solem, eius quantitas; </s> <s xml:id="echoid-s12689" xml:space="preserve">latitu-<lb/>do enim totius euagationis in epicyclo erit gr. </s> <s xml:id="echoid-s12690" xml:space="preserve">8. </s> <s xml:id="echoid-s12691" xml:space="preserve">circiter vti ſuperior figura indicat. </s> <s xml:id="echoid-s12692" xml:space="preserve">maxima diſtantia Mer-<lb/>curij a Sole eſt diametrorum terræ 581.</s> <s xml:id="echoid-s12693" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div276" type="section" level="1" n="188"> <head xml:id="echoid-head202" style="it" xml:space="preserve">Appendix de calculo Mercurij. Cap. V I.</head> <p> <s xml:id="echoid-s12694" xml:space="preserve">TRes Mercurij motus ad calculum redigemus, quorum primus ſit motus in longitudinem, ſeu motus <lb/>centri epicycli in longitudinem. </s> <s xml:id="echoid-s12695" xml:space="preserve">qui, vt diximus, eſt idem cum motu Solis in longitudinem; </s> <s xml:id="echoid-s12696" xml:space="preserve">habito igi-<lb/>tur Solis motu, habetur locus centri epicycli Mercurij in Zodiaco. </s> <s xml:id="echoid-s12697" xml:space="preserve">Secundus motus eſt motus apogæi pri-<lb/>mi, qui quoniam tardiſſimus eſt, annis enim 33. </s> <s xml:id="echoid-s12698" xml:space="preserve">vnum tantum gradum peragrat, ideo nullam ei conſtrue-<lb/>mus Tabulam, ſed tantummodo radices nonnullas, ex quibus reliquorum annorum apogæa eliciantur: </s> <s xml:id="echoid-s12699" xml:space="preserve">ſunt <lb/>au@em ſequentes.</s> <s xml:id="echoid-s12700" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div277" type="section" level="1" n="189"> <head xml:id="echoid-head203" style="it" xml:space="preserve">Radices Apogæi Mercurij, ad annos ſequentes.</head> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. # ´. # # in primo. <lb/>2600 # 8 # 0 # 34 # ideſt # in ſecundo. # gr.♐ <lb/>1633 # 8 # 1 # 34 # # in tertio. <lb/>3666 # 8 # 2 # 34 # # in quarto. <lb/>1699 # 8 # 3 # 34 <lb/></note> <p> <s xml:id="echoid-s12701" xml:space="preserve">Tertius motus eſt auomaliæ Mercurij, qui indicat eius poſitionem in epicyclo, pro qno damus Tabu-<lb/>@@@ ſequentem.</s> <s xml:id="echoid-s12702" xml:space="preserve"/> </p> <pb o="136" file="0158" n="163" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div278" type="section" level="1" n="190"> <head xml:id="echoid-head204" style="it" xml:space="preserve">TABVLA MOTVS ANOMALIÆ MERCVR.</head> <note position="right" xml:space="preserve"> <lb/>##### In Annis ſingu lis. #### In menſib. compl. An. cõis. ### In diebus. <lb/># Anni. # Sig. # G@a. # ´. # # Sig. # Gra. # ´. # Dies # Sig. # Gra. <lb/># 1 # 1 # 23 # 57 # Ian. # 3 # 6 # 19 # 1 # 0 # 3 <lb/># 2 # 3 # 17 # 54 # Febr. # 6 # 3 # 18 # 2 # 0 # 0 <lb/>B # 3 # 5 # 11 # 51 # Mart. # 9 # 9 # 36 # 3 # 0 # 9 <lb/># 4 # 7 # 8 # 56 # Apr. # 0 # 12 # 48 <lb/># # # # # # # # # 4 # 0 # 12 <lb/># 5 # 9 # 2 # 53 # Mai. # 3 # 19 # 7 # 5 # 0 # 16 <lb/># 6 # 10 # 26 # 47 # Iun. # 6 # 22 # 19 # 6 # 0 # 19 <lb/>B # 7 # 0 # 20 # 45 # lul. # 9 # 28 # 38 <lb/># 8 # 2 # 17 # 48 # Aug. # 1 # 4 # 56 # 7 # 0 # 21 <lb/># # # # # # # # # 8 # 0 # 25 <lb/># 9 # 4 # 11 # 45 # Sept. # 4 # 8 # 8 # 9 # 0 # 28 <lb/># 10 # 0 # 5 # 43 # Oct. # 7 # 14 # 27 # 10 # 1 # 1 <lb/>B # 11 # 7 # 29 # 40 # Nou. # 10 # 17 # 39 <lb/># 12 # 9 # 26 # 44 # Dec. # 1 # 23 # 57 # 11 # 1 # 4 <lb/># # # # # # # # # 12 # 1 # 7 <lb/># 13 # 11 # 20 # 41 # # # # # 13 # 1 # 10 <lb/># 14 # 1 # 14 # 38 #### In menſibus Ann. Biſſext. # 13 # 1 # 13 <lb/>B # 15 # 3 # 8 # 35 <lb/># 16 # 5 # 5 # 39 # Ian. # 3 # 6 # 19 # 15 # 1 # 17 <lb/># # # # # Febr. # 6 # 6 # 24 # 16 # 1 # 20 <lb/># 17 # 6 # 29 # 36 # Mart. # 9 # 12 # 43 # 17 # 1 # 23 <lb/># 18 # 8 # 23 # 33 # Apri. # 0 # 15 # 55 # 18 # 1 # 26 <lb/>B # 19 # 10 # 17 # 30 <lb/># 20 # 0 # 14 # 40 # Mai. # 3 # 22 # 13 # 19 # 1 # 29 <lb/># # # # # Iun. # 6 # 25 # 26 # 20 # 2 # 2 <lb/># # # # # Iulius # 10 # 1 # 44 # 21 # 2 # 5 <lb/># # # # # Aug. # 1 # 8 # 3 # 22 # 2 # 8 <lb/># 40 # 0 # 29 # 21 <lb/>In # 60 # 1 # 14 # 2 # Sept. # 4 # 11 # 15 # 23 # 2 # 11 <lb/># 80 # 1 # 28 # 42 # Octo. # 7 # 17 # 33 # 24 # 2 # 15 <lb/># 100 # 2 # 13 # 23 # Nou. # 10 # 20 # 45 # 25 # 2 # 18 <lb/># # # # # Dec. # 1 # 27 # 4 # 26 # 2 # 21 <lb/># 200 # 4 # 26 # 45 <lb/>Annis # 300 # 7 # 10 # 9 # # # # # 27 # 2 # 24 <lb/># 400 # 9 # 23 # 31 # # # # # 28 # 2 # 27 <lb/># 500 # 0 # 6 # 55 # # # # # 29 # 3 # 0 <lb/># # # # # # # # # 30 # 3 # 3 <lb/># 600 # 2 # 20 # 17 # # # # # 31 # 3 # 6 <lb/>aggregatis. # 700 # 5 # 3 # 40 <lb/># 800 # 7 # 17 # 4 # # # # # ### In horis aliquot. <lb/># 900 # 10 # 0 # 26 # # # # # ### Horæ Gra. <lb/># 1000 # 0 # 13 # 50 <lb/># # # # # # # # # 8 # # 1 <lb/># #### Radix ad Ann. 1600. ab- \\ ſo@utum. # # # # # 16 # # 2 <lb/># 1600 # 3 # 18 # 30 # Radix. # # # # 24 # # 3 <lb/></note> <pb o="137" file="0159" n="164" rhead="Liber Vndecimus."/> </div> <div xml:id="echoid-div279" type="section" level="1" n="191"> <head xml:id="echoid-head205" style="it" xml:space="preserve">Constructio, & vſus Tabulæ præcedentis.</head> <p> <s xml:id="echoid-s12703" xml:space="preserve">EIus conſtructio, expoſitio, & </s> <s xml:id="echoid-s12704" xml:space="preserve">vſus perſpicua erunt intelligenti ſuperiores Tabulas Lunæ, & </s> <s xml:id="echoid-s12705" xml:space="preserve">Solis: </s> <s xml:id="echoid-s12706" xml:space="preserve">ſatis <lb/>igitur ſit afferre exemplum. </s> <s xml:id="echoid-s12707" xml:space="preserve">Libet igitur ad tempus præſcns, quo hæc ſcribo inquirere tres prædictos <lb/>motus Mercurij, videlicet ad ann. </s> <s xml:id="echoid-s12708" xml:space="preserve">1616. </s> <s xml:id="echoid-s12709" xml:space="preserve">die 6. </s> <s xml:id="echoid-s12710" xml:space="preserve">hora 14 {3/4}. </s> <s xml:id="echoid-s12711" xml:space="preserve">ſecundum Italos, ſeu vigeſimam poſt meridi<unsure/>em diei <lb/>quintæ Octobris. </s> <s xml:id="echoid-s12712" xml:space="preserve">quod tempus ſic ad calculum accommodari debet.</s> <s xml:id="echoid-s12713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12714" xml:space="preserve">Quod igitur ad motum centri <lb/> <anchor type="note" xlink:label="note-0159-01a" xlink:href="note-0159-01"/> epicycli attinet, is cum ſit idem <lb/>cum motu, ſeu loco Solis, ex cal-<lb/>culo loci Solis ex proprijs Tabu-<lb/>lis ad datum tempus reperies eu n <lb/>eſſe in gr. </s> <s xml:id="echoid-s12715" xml:space="preserve">13. </s> <s xml:id="echoid-s12716" xml:space="preserve">♎, quare & </s> <s xml:id="echoid-s12717" xml:space="preserve">ibidem <lb/>erit epicyclus Merc.</s> <s xml:id="echoid-s12718" xml:space="preserve"/> </p> <div xml:id="echoid-div279" type="float" level="2" n="1"> <note position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve"> <lb/># Sig. # Gra. # ´. <lb/>Rad. 1600. # 3 # 18 # 30 <lb/>Anni 15. # 3 # 18 # 35 <lb/>Biſſex. Sept. # 4 # 11 # 15 <lb/>Dies 9. # 0 # 28 # 30 <lb/>Summa Anomaliæ Mercurij # 12 # 18 # 50 <lb/></note> </div> <p> <s xml:id="echoid-s12719" xml:space="preserve">Circa locum apogæi, vides il-<lb/>lud ex ſuperioribus eius Radici-<lb/>bus abſoluiſſe ſigna 8. </s> <s xml:id="echoid-s12720" xml:space="preserve">& </s> <s xml:id="echoid-s12721" xml:space="preserve">occupare <lb/>partem primam noni ſigni, ideſt, <lb/>gr. </s> <s xml:id="echoid-s12722" xml:space="preserve">1. </s> <s xml:id="echoid-s12723" xml:space="preserve">Sagittarij. </s> <s xml:id="echoid-s12724" xml:space="preserve">Quapropter re-<lb/>ſtat, vt ex propria Mercurij Ta-<lb/>bula computemus eius anomaliã. <lb/></s> <s xml:id="echoid-s12725" xml:space="preserve">ex Tabula igitur anomaliæ in cal-<lb/>@e columnæ annorum, accipio radicem, ideſt, motum debitum anno 1600. </s> <s xml:id="echoid-s12726" xml:space="preserve">exacto, eumq; </s> <s xml:id="echoid-s12727" xml:space="preserve">in formula exem-<lb/>pli adſcribo anno 1600. </s> <s xml:id="echoid-s12728" xml:space="preserve">vt vides: </s> <s xml:id="echoid-s12729" xml:space="preserve">poſtea cum annis quindecim ex eadem columna e@icio motum eis debitum, <lb/>quem in formula ijſdem adſcribo. </s> <s xml:id="echoid-s12730" xml:space="preserve">idem facio cum menſe Septembri ex columna menſium anni biſſextilis, <lb/>quia annus 1616. </s> <s xml:id="echoid-s12731" xml:space="preserve">labens, ad quem pertinet hic menſis eſt biſſextilis: </s> <s xml:id="echoid-s12732" xml:space="preserve">ſimiliter in diebus 9. </s> <s xml:id="echoid-s12733" xml:space="preserve">necnon cum hor. </s> <s xml:id="echoid-s12734" xml:space="preserve">20. </s> <s xml:id="echoid-s12735" xml:space="preserve"><lb/>quæ quamuis non reperiantur in Tabula, conijcio tamen eis deberi gr. </s> <s xml:id="echoid-s12736" xml:space="preserve">2 {1/2}. </s> <s xml:id="echoid-s12737" xml:space="preserve">hos igitur omnes motus in ſum-<lb/>mam redigo, quæ eſt ſign. </s> <s xml:id="echoid-s12738" xml:space="preserve">12. </s> <s xml:id="echoid-s12739" xml:space="preserve">gr. </s> <s xml:id="echoid-s12740" xml:space="preserve">18. </s> <s xml:id="echoid-s12741" xml:space="preserve">50′. </s> <s xml:id="echoid-s12742" xml:space="preserve">ſed quia 12. </s> <s xml:id="echoid-s12743" xml:space="preserve">ſigna efficiunt integrum circulum, ijſdem abiectis, erit <lb/>locus Merc. </s> <s xml:id="echoid-s12744" xml:space="preserve">in epicyclo infra apogæum ſpiræ gr. </s> <s xml:id="echoid-s12745" xml:space="preserve">9. </s> <s xml:id="echoid-s12746" xml:space="preserve">ferè. </s> <s xml:id="echoid-s12747" xml:space="preserve">& </s> <s xml:id="echoid-s12748" xml:space="preserve">quoniam locus epicycli eſt fere in medio inter <lb/>perigæum, & </s> <s xml:id="echoid-s12749" xml:space="preserve">apogæum primum, ideo Merc. </s> <s xml:id="echoid-s12750" xml:space="preserve">non percurret nec maiorem ſpiram, nec minorem, ſed me-<lb/>diam, quare erit hodie infra punctum E, ſuperioris figuræ in media ſpira, gr. </s> <s xml:id="echoid-s12751" xml:space="preserve">ferè 9. </s> <s xml:id="echoid-s12752" xml:space="preserve">ſicuti eum ibi depinxi-<lb/>mus. </s> <s xml:id="echoid-s12753" xml:space="preserve">Vnde infero eum eſſe directum, ac velocem. </s> <s xml:id="echoid-s12754" xml:space="preserve">cumque ſit in parte orientali epicycli erit veſpertinis, ſed <lb/>ſoli propior, quam vt videri poſſit; </s> <s xml:id="echoid-s12755" xml:space="preserve">quare poſt aliquos dies orietur ortu heliaco veſpertino. </s> <s xml:id="echoid-s12756" xml:space="preserve">ſi eius locum in <lb/>Zodiaco habere vis, duc lineam T Merc. </s> <s xml:id="echoid-s12757" xml:space="preserve">quæ in puncto K, ſecans gyrum Solis, arcus S X, indicabit gradus <lb/>ferè 7. </s> <s xml:id="echoid-s12758" xml:space="preserve">quibus Merc. </s> <s xml:id="echoid-s12759" xml:space="preserve">Solem in Zodiaco quidem præcedit, at in latione diurna ſubſequitur.</s> <s xml:id="echoid-s12760" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12761" xml:space="preserve">Porrò ſi quis Merc. </s> <s xml:id="echoid-s12762" xml:space="preserve">videre aut obſeruare velit, id menſe Maio, quando nimirum maiorem ſpiram ducens, <lb/>magis à Sole recedit, melius perficiet: </s> <s xml:id="echoid-s12763" xml:space="preserve">tunc enim tẽporis verſatur in principio Geminorum, vbi eſt perigæus.</s> <s xml:id="echoid-s12764" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div281" type="section" level="1" n="192"> <head xml:id="echoid-head206" xml:space="preserve">LIBER DECIMVSSECVNDVS <lb/>DE VENERE.</head> <p> <s xml:id="echoid-s12765" xml:space="preserve">SPeculum rotundum cum capulo fuit apud Aegyptios Veneris Hieroglyphicum, & </s> <s xml:id="echoid-s12766" xml:space="preserve">quidem illis <lb/>conueniens, cum referat ſpeculum geſtatorium, cuius manubrium inferius eſt, impudicæ <lb/>Deæ ſatis aptum inſigne: </s> <s xml:id="echoid-s12767" xml:space="preserve">ea nota breuitatis cauſa vtuntur Aſtronomi præcipuè in calculatio-<lb/>nibus. </s> <s xml:id="echoid-s12768" xml:space="preserve">ſuntalij, quæ velint eandem notam potius referre pomum illud, quod Veneri tanquam <lb/>pulchriori dono datum fuit.</s> <s xml:id="echoid-s12769" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div282" type="section" level="1" n="193"> <head xml:id="echoid-head207" style="it" xml:space="preserve">Locus Veneris. Cap. I.</head> <p> <s xml:id="echoid-s12770" xml:space="preserve">VT iam de Veneris planeta agamus, naturalis planetarum ordo poſtulat. </s> <s xml:id="echoid-s12771" xml:space="preserve">ea enim poſt Mercurium, am-<lb/>pliorem circa Solem circunducit, orbem, ita vt ipſius Mercurij gyrum, gyrus Veneris compręhendat: <lb/></s> <s xml:id="echoid-s12772" xml:space="preserve">contra vero aliorum planetarum circitibus compręhendatur; </s> <s xml:id="echoid-s12773" xml:space="preserve">quod primo authoritate, non ſolum antiquo-<lb/>rum aſtronomorum confirmatur, quos ſupra in Mercurio, ex Vitruuio, ac Martiano Capella citauimus; </s> <s xml:id="echoid-s12774" xml:space="preserve">ve-<lb/>rum etiam recentiorum omnium etiam noſtræ Soc. </s> <s xml:id="echoid-s12775" xml:space="preserve">ſcriptorum, obſeruationes atteſtantur. </s> <s xml:id="echoid-s12776" xml:space="preserve">è quibus iucunda <lb/>æquè, admiranda illa eſt, quæ per Teleſcopium perficitur; </s> <s xml:id="echoid-s12777" xml:space="preserve">ſi enim in Veneris ſydus Teleſcopij auxilio accu-<lb/>rata inſpectione inquiramus, eam ita illuminari a Sole conſpiciemus, vt neceſlario ſequatur eam circa Solem <lb/>tanquam centrum circuire, ita vt modo infra ipſum feratur; </s> <s xml:id="echoid-s12778" xml:space="preserve">vti ſequenti capite explicabimus. </s> <s xml:id="echoid-s12779" xml:space="preserve">Infra etiam <lb/>cap. </s> <s xml:id="echoid-s12780" xml:space="preserve">6. </s> <s xml:id="echoid-s12781" xml:space="preserve">nouum modum habebis menſurandæ eius diſtantiæ à terra, & </s> <s xml:id="echoid-s12782" xml:space="preserve">à Sole.</s> <s xml:id="echoid-s12783" xml:space="preserve"/> </p> <pb o="138" file="0160" n="165" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div283" type="section" level="1" n="194"> <head xml:id="echoid-head208" style="it" xml:space="preserve">Illuminatie<unsure/>, & Vmbra Veneris. Cap. II.</head> <p> <s xml:id="echoid-s12784" xml:space="preserve">IInter admiranda, quæ nuper ope Teleſcopij cælitus innotuerunt, illud ſane pulcherrimũ de Veneris illu-<lb/>minatione; </s> <s xml:id="echoid-s12785" xml:space="preserve">qua non vnicam in cælo Lunam, ſed duas in cælo Lunas rimatus, atque miratus eſt mundus: <lb/></s> <s xml:id="echoid-s12786" xml:space="preserve">illuminatur enim à Sole, ita vt modo falcata, modo ſemiplena, modo plena lumine conſpiciatur, non aliter ac <lb/>Luna, quamuis alio @rdine; </s> <s xml:id="echoid-s12787" xml:space="preserve">quæ illuminationum ſeries, & </s> <s xml:id="echoid-s12788" xml:space="preserve">modus in apoſita figura clarior euadet. </s> <s xml:id="echoid-s12789" xml:space="preserve">in qua ocu-<lb/>lus noſter aſpiciens haſce illuminationes ſit vbi O, Sol ſit vbi S. </s> <s xml:id="echoid-s12790" xml:space="preserve">gyruſ-<lb/> <anchor type="figure" xlink:label="fig-0160-01a" xlink:href="fig-0160-01"/> que Solis proprius ſit X S Y. </s> <s xml:id="echoid-s12791" xml:space="preserve">Epicyclus ſiue gyrus Veneris circa Solem, <lb/>ſit quem vides; </s> <s xml:id="echoid-s12792" xml:space="preserve">in cuius varijs locis depicta eſt Veneris ſphæra, eodem <lb/>modo ſemper illuminata; </s> <s xml:id="echoid-s12793" xml:space="preserve">verum non eodem modo ſe oculo in O, ſito <lb/>apparens. </s> <s xml:id="echoid-s12794" xml:space="preserve">duæ lineæ O X. </s> <s xml:id="echoid-s12795" xml:space="preserve">O Y. </s> <s xml:id="echoid-s12796" xml:space="preserve">tangentes epicyclum diſtant à linea <lb/>O S A. </s> <s xml:id="echoid-s12797" xml:space="preserve">ipſum bifariam ſecante, hinc inde per gr. </s> <s xml:id="echoid-s12798" xml:space="preserve">48. </s> <s xml:id="echoid-s12799" xml:space="preserve">ideſt, arcus S X, <lb/>S Y. </s> <s xml:id="echoid-s12800" xml:space="preserve">ſunt gra. </s> <s xml:id="echoid-s12801" xml:space="preserve">48. </s> <s xml:id="echoid-s12802" xml:space="preserve">ſinguli, iuxta maximam Veneris à Sole digreſſionem. <lb/></s> <s xml:id="echoid-s12803" xml:space="preserve">quando igitur Venus incipit eſſe Veſpertinus Heſperus, quando ſcili-<lb/>cet poſt Solis occaſum primo apparet, tunc per Teleſcopium viſa, rotun <lb/>da ſeu plena apparet, quia eſt in B. </s> <s xml:id="echoid-s12804" xml:space="preserve">in quo ſitu totam ſui illuminationem <lb/>oculo in O. </s> <s xml:id="echoid-s12805" xml:space="preserve">ſito. </s> <s xml:id="echoid-s12806" xml:space="preserve">videndam obuertit. </s> <s xml:id="echoid-s12807" xml:space="preserve">poſtea recedens à Sole rotundita-<lb/>tem paulatim amittit, quia deſcendit ad C. </s> <s xml:id="echoid-s12808" xml:space="preserve">vbi amplius tota illuminatio <lb/>ab oculo videri nequit, & </s> <s xml:id="echoid-s12809" xml:space="preserve">propterea gibboſa apparet. </s> <s xml:id="echoid-s12810" xml:space="preserve">deinde dimidia <lb/>ſeu ſemiplena apparet, quoniam ad D. </s> <s xml:id="echoid-s12811" xml:space="preserve">deuoluta eſt, vbi dimidiam ſui <lb/>illuminationem oculo exhibet. </s> <s xml:id="echoid-s12812" xml:space="preserve">dehinc in E. </s> <s xml:id="echoid-s12813" xml:space="preserve">delapſa corniculata cerni-<lb/>tur, quia oculus O. </s> <s xml:id="echoid-s12814" xml:space="preserve">paruam illuminationis partem, eamque falcatam vi-<lb/>dere poteſt, ſicuti etiam in Luna explicatum eſt. </s> <s xml:id="echoid-s12815" xml:space="preserve">In A. </s> <s xml:id="echoid-s12816" xml:space="preserve">& </s> <s xml:id="echoid-s12817" xml:space="preserve">F. </s> <s xml:id="echoid-s12818" xml:space="preserve">videri ne-<lb/>quit ob nimium Solis fulgorem, eaſdem apparentias alterum epicycli <lb/>ſemicirculum ingrediens, vbi ex Heſpero euaſit Lucifer, & </s> <s xml:id="echoid-s12819" xml:space="preserve">manè præ-<lb/>fulget, reſtituit; </s> <s xml:id="echoid-s12820" xml:space="preserve">ſed inuerſo ordine, nam in G. </s> <s xml:id="echoid-s12821" xml:space="preserve">corniculata, in H. </s> <s xml:id="echoid-s12822" xml:space="preserve">dimi-<lb/>diaca, in I. </s> <s xml:id="echoid-s12823" xml:space="preserve">gibboſa, in K. </s> <s xml:id="echoid-s12824" xml:space="preserve">plena conſpicitur: </s> <s xml:id="echoid-s12825" xml:space="preserve">vt conſideranti patere poteſt; </s> <s xml:id="echoid-s12826" xml:space="preserve">oculus enim videt eam ſolam par-<lb/>tem illuminationis, quæ continetur literis e r p. </s> <s xml:id="echoid-s12827" xml:space="preserve">quæ falcata apparet, quia eſt in ſuperficie ſphærica, eamq; </s> <s xml:id="echoid-s12828" xml:space="preserve"><lb/>præcingit. </s> <s xml:id="echoid-s12829" xml:space="preserve">quæ omnia ſaluantur perfectè, ſi dicamus Venerem circa Solem circumcurſare, vt in figura oſten-<lb/>ditur. </s> <s xml:id="echoid-s12830" xml:space="preserve">Idem hac iucunda experientia confirmari, ac ritè percipi poteſt. </s> <s xml:id="echoid-s12831" xml:space="preserve">Cape ſphæram aliquam terſam, eam-<lb/>que circa lumen aliquod paulatim circunducas, ita vt oculus tuus extra gyrum ſit, gyrus porrò hic debet eſſe <lb/>in plano imaginario per oculum tuum tranſeunte. </s> <s xml:id="echoid-s12832" xml:space="preserve">in hac igitur ſphæræ gyratione iucundè contemplaberis <lb/>has omnes Veneris illuminationes: </s> <s xml:id="echoid-s12833" xml:space="preserve">hoc eodem modo Mercurium illuminari exiſtimo. </s> <s xml:id="echoid-s12834" xml:space="preserve">Hac Veneris illumi-<lb/>natione ſic proſpecta @ſatisfacere poſſumus cuidam quæſtioni, quæ priores Aſtronomos vrgebat; </s> <s xml:id="echoid-s12835" xml:space="preserve">cur nimi-<lb/>rum Vcnus quando circa ima epicycli verſatur, nobiſque propior eſt, minor appareat, quam cum ſublimior <lb/>fertur, contrarium enim accidere deberet, quæ enim propria ſunt, maiora videntur. </s> <s xml:id="echoid-s12836" xml:space="preserve">Reſpondemus igitur <lb/>ideo minorem videri, quia non tota videtur, ſed minor eius pars illuminata, vti modo explicatum eſt; </s> <s xml:id="echoid-s12837" xml:space="preserve">& </s> <s xml:id="echoid-s12838" xml:space="preserve">ap-<lb/>paret inſpicientibus etiam per Teleſcopium. </s> <s xml:id="echoid-s12839" xml:space="preserve">quod ſcilicet quando eſt infra Solem, parum illuminationis eius <lb/>cernitur.</s> <s xml:id="echoid-s12840" xml:space="preserve"/> </p> <div xml:id="echoid-div283" type="float" level="2" n="1"> <figure xlink:label="fig-0160-01" xlink:href="fig-0160-01a"> <image file="0160-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0160-01"/> </figure> </div> <p> <s xml:id="echoid-s12841" xml:space="preserve">Notandum præterea ſolam Venerem inter omnes planetas, luminaria, interdiu non raro percommodè <lb/>videri, quod ei accidit, cum plenam ſui illuminationem nobis exhibet, ac ſimul extra Solis fulgorem euaſit: <lb/></s> <s xml:id="echoid-s12842" xml:space="preserve">adeo enim magna aliquando conſpicitur, vt vulgus eam, aut cometam, aut, nouam aliquam ſtellam exiſtimet <lb/>illud tandem ei proprium ex quinque planetis, vt noctu cum pleno iubare fulget, corpora ab ipſa colluſtra-<lb/>ta, vmbras efficiant: </s> <s xml:id="echoid-s12843" xml:space="preserve">Porrò locus Plinij ex lib. </s> <s xml:id="echoid-s12844" xml:space="preserve">2. </s> <s xml:id="echoid-s12845" xml:space="preserve">cap. </s> <s xml:id="echoid-s12846" xml:space="preserve">7. </s> <s xml:id="echoid-s12847" xml:space="preserve">dignus eſt qui hunc referatur; </s> <s xml:id="echoid-s12848" xml:space="preserve">Solem, inquit, ambit <lb/>ingens ſydus appellatum Veneris, alterno motu vagum, ipſis cognominibus æmulum Solis, & </s> <s xml:id="echoid-s12849" xml:space="preserve">Lunæ; </s> <s xml:id="echoid-s12850" xml:space="preserve">præ-<lb/>ueniens quippe, & </s> <s xml:id="echoid-s12851" xml:space="preserve">ante matutinum exoriens, Luciferi nomen accepit, vt Sol alter diem maturans: </s> <s xml:id="echoid-s12852" xml:space="preserve">contra <lb/>ab occaſu refulgens nuncupatur Veſper, aut prorogans lucem, vicemque Lunæ reddens. </s> <s xml:id="echoid-s12853" xml:space="preserve">quam eius natu-<lb/>ram Pythagoras Samius primus depræhendit Olympiade circiter 42. </s> <s xml:id="echoid-s12854" xml:space="preserve">qui fuit Vrbis Romæ 142. </s> <s xml:id="echoid-s12855" xml:space="preserve">Iam ma-<lb/>gnitudine extra cuncta alia ſydera eſt claritas quidem tantæ, vt vnius huius ſtellæ radijs vmbræ reddantur. </s> <s xml:id="echoid-s12856" xml:space="preserve"><lb/>hæc ille.</s> <s xml:id="echoid-s12857" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12858" xml:space="preserve">Poſtremo non eſt prætereunda cõſideratio vmbræ ipſius Veneris quanta videlicet ſit; </s> <s xml:id="echoid-s12859" xml:space="preserve">eam ſic habebimus, <lb/>conſtructa figura in qua veræ ſint corporum Solis, & </s> <s xml:id="echoid-s12860" xml:space="preserve">Veneris necnon diſtantiæ proportiones, ductis duabus <lb/>lineis tangentibus vtrumque, exurget vmbra conica Veneris, ex parte concurſus linearum tangentium, <lb/>quemadmodum in Luna factum eſt: </s> <s xml:id="echoid-s12861" xml:space="preserve">ſed, & </s> <s xml:id="echoid-s12862" xml:space="preserve">alio modo, quo vſi ſumus in inueſtiganda vmbra terræ, & </s> <s xml:id="echoid-s12863" xml:space="preserve">Mer-<lb/>curij, cuius demonſtrationem, & </s> <s xml:id="echoid-s12864" xml:space="preserve">figuram habes pag. </s> <s xml:id="echoid-s12865" xml:space="preserve">78. </s> <s xml:id="echoid-s12866" xml:space="preserve">duo tamen ſupponenda ſunt, quæ paulò poſt pro-<lb/>babimus: </s> <s xml:id="echoid-s12867" xml:space="preserve">diſtantia nimirum Solis, & </s> <s xml:id="echoid-s12868" xml:space="preserve">Veneris; </s> <s xml:id="echoid-s12869" xml:space="preserve">necnon vtriuſque diametrorum proportio, diſtant erit ſemi-<lb/>diam. </s> <s xml:id="echoid-s12870" xml:space="preserve">terræ 855. </s> <s xml:id="echoid-s12871" xml:space="preserve">diameter Solis ad diametrum Veneris eſt, ſicuti 26. </s> <s xml:id="echoid-s12872" xml:space="preserve">ad {30/11}. </s> <s xml:id="echoid-s12873" xml:space="preserve">vt igitur eſt 23 {3/11} ad 2 {8/11}. </s> <s xml:id="echoid-s12874" xml:space="preserve">ſic fiat <lb/>855. </s> <s xml:id="echoid-s12875" xml:space="preserve">ad aliud per auream regulam, reperieſque 102. </s> <s xml:id="echoid-s12876" xml:space="preserve">fere; </s> <s xml:id="echoid-s12877" xml:space="preserve">quare Veneris vmbra totidem terræ ſemidiam. </s> <s xml:id="echoid-s12878" xml:space="preserve">pro-<lb/>te<unsure/>nditur: </s> <s xml:id="echoid-s12879" xml:space="preserve">qua propter nullo pacto Lunam obumbrare poterit, quæ infra ipſam pluſquam ducentis ſemidia-<lb/>metris a<unsure/> Sole gyrat.</s> <s xml:id="echoid-s12880" xml:space="preserve"/> </p> <pb o="139" file="0161" n="166" rhead="Liber decimusſeptimus."/> </div> <div xml:id="echoid-div285" type="section" level="1" n="195"> <head xml:id="echoid-head209" style="it" xml:space="preserve">Figura Veneris. Cap. III.</head> <p> <s xml:id="echoid-s12881" xml:space="preserve">CVm, vt vidimus, ſphæricè ſeu in modum ſphæræ illuminetur, neceſſario ſphærica erit, ſi enim ſphæri-<lb/>ca non ſit, numquam prædicto modo illuminabitur: </s> <s xml:id="echoid-s12882" xml:space="preserve">credideri@ tamen non Geometricè, ſed ruditer <lb/>eſſe ſphæricam, ob cauſam in Luna, & </s> <s xml:id="echoid-s12883" xml:space="preserve">Mercurio allatam.</s> <s xml:id="echoid-s12884" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div286" type="section" level="1" n="196"> <head xml:id="echoid-head210" style="it" xml:space="preserve">Motus Veneris. Cap. IV.</head> <p> <s xml:id="echoid-s12885" xml:space="preserve">SI cuti in Mercurio, quatuor motus recenſebimus. </s> <s xml:id="echoid-s12886" xml:space="preserve">Primò motum apogęi primi, quod eſt locus in Zodiaco, <lb/>vbi Venusa terris magis diſtare videtur, quod ibi minorem aliquanto epicyclum deſcribat: </s> <s xml:id="echoid-s12887" xml:space="preserve">hic igitur lo-<lb/>cus, ſeu apogæum mouetur ſingulis annis ſecundis tantum. </s> <s xml:id="echoid-s12888" xml:space="preserve">51″. </s> <s xml:id="echoid-s12889" xml:space="preserve">qui eſt idem cum motu ſtellarum fixarum, <lb/>vt poſtea patebit|. </s> <s xml:id="echoid-s12890" xml:space="preserve">noſtro autem ſæculo apogæum iſtud verſatur circa gra. </s> <s xml:id="echoid-s12891" xml:space="preserve">7. </s> <s xml:id="echoid-s12892" xml:space="preserve">Geminorum; </s> <s xml:id="echoid-s12893" xml:space="preserve">diſtat enim ab <lb/>æquinoctio ſig. </s> <s xml:id="echoid-s12894" xml:space="preserve">2. </s> <s xml:id="echoid-s12895" xml:space="preserve">& </s> <s xml:id="echoid-s12896" xml:space="preserve">gra. </s> <s xml:id="echoid-s12897" xml:space="preserve">ferè 17.</s> <s xml:id="echoid-s12898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12899" xml:space="preserve">Secundò. </s> <s xml:id="echoid-s12900" xml:space="preserve">Motum Veneris in longitudinem, quo motu centrum epicycli mouetur in conſequentia ſigno-<lb/>rum, & </s> <s xml:id="echoid-s12901" xml:space="preserve">quoniam epicyclus ſemper Solem circumambiens, eum comitatur, ſequitur motum centri epicycli <lb/>eſſe idem cum motu Solis.</s> <s xml:id="echoid-s12902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12903" xml:space="preserve">Tertiò Motum anomaliæ; </s> <s xml:id="echoid-s12904" xml:space="preserve">quo planeta ipſe peripheriam epicycli circuncurrit; </s> <s xml:id="echoid-s12905" xml:space="preserve">in ſuperiori quidem par-<lb/>te, ſicut etiam Mercurius, ſecundum ord nem ſignorum; </s> <s xml:id="echoid-s12906" xml:space="preserve">in inferiori vero contra ordinem ſignorum, ſeu ad <lb/>occidentem: </s> <s xml:id="echoid-s12907" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s12908" xml:space="preserve">Directa, & </s> <s xml:id="echoid-s12909" xml:space="preserve">Retrograda, & </s> <s xml:id="echoid-s12910" xml:space="preserve">Stationaria euadit; </s> <s xml:id="echoid-s12911" xml:space="preserve">quapropter motus eius in longitudinem <lb/>e<unsure/>ſt anomalus: </s> <s xml:id="echoid-s12912" xml:space="preserve">hanc anomaliam in epicyclo Aſtronomi numerant ab A. </s> <s xml:id="echoid-s12913" xml:space="preserve">apogæo epicycli, à quo diario motu <lb/>recedit min. </s> <s xml:id="echoid-s12914" xml:space="preserve">37′. </s> <s xml:id="echoid-s12915" xml:space="preserve">annuo vero ſignis 7. </s> <s xml:id="echoid-s12916" xml:space="preserve">gra. </s> <s xml:id="echoid-s12917" xml:space="preserve">15. </s> <s xml:id="echoid-s12918" xml:space="preserve">1′. </s> <s xml:id="echoid-s12919" xml:space="preserve">eiuſque integrã periodum abſoluit anno vno ſimplici, cum <lb/>diebus 218. </s> <s xml:id="echoid-s12920" xml:space="preserve">& </s> <s xml:id="echoid-s12921" xml:space="preserve">horis 21 {1/4}. </s> <s xml:id="echoid-s12922" xml:space="preserve">ſeu menſibus 19. </s> <s xml:id="echoid-s12923" xml:space="preserve">& </s> <s xml:id="echoid-s12924" xml:space="preserve">præterea diebus ferè 8.</s> <s xml:id="echoid-s12925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12926" xml:space="preserve">Venus quando oritur veſperi heliace, tuncincipit deſcendere ab A. </s> <s xml:id="echoid-s12927" xml:space="preserve">apogæo epicycli, appellaturque He-<lb/>ſperus, & </s> <s xml:id="echoid-s12928" xml:space="preserve">Veſperugo in toto ſemicirculo orientali A C F. </s> <s xml:id="echoid-s12929" xml:space="preserve">inde a perigæo F. </s> <s xml:id="echoid-s12930" xml:space="preserve">pergens manè oritur heliacè, <lb/>tranſmutaturque in Luciferum, Solem manè præueniens, ac præfulgens: </s> <s xml:id="echoid-s12931" xml:space="preserve">ſicque in altero ſemicirculo F I A. <lb/></s> <s xml:id="echoid-s12932" xml:space="preserve">perſeuerat. </s> <s xml:id="echoid-s12933" xml:space="preserve">Sciendum porrò priores mundi habitatores exiſtimaſſe Luciferum ac Heſperum duas eſſe ſtellas <lb/>ab inuicem diſtinctas, quem errorem primus Pythagoras abſtulit; </s> <s xml:id="echoid-s12934" xml:space="preserve">Plinius enim lib. </s> <s xml:id="echoid-s12935" xml:space="preserve">2. </s> <s xml:id="echoid-s12936" xml:space="preserve">cap. </s> <s xml:id="echoid-s12937" xml:space="preserve">7. </s> <s xml:id="echoid-s12938" xml:space="preserve">hæc habet anti-<lb/>quitas illa, quæ Pythagoram præceſſit, eam binas eſſe ſtellas exiſtimauit, ſed ſolertiſſimus ille Philoſophus <lb/>Pythagoras primus deceptionem hanc mortales dedocuit, oſtenditque Luciferum atque Heſperum vnam <lb/>eamdemque eſſe ſtellam.</s> <s xml:id="echoid-s12939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12940" xml:space="preserve">Quartò. </s> <s xml:id="echoid-s12941" xml:space="preserve">Motum in latitudinem, qui inde oritur, quia epicyclus Veneris non iacet ſemper in plano ecly-<lb/>pticæ, ſed ab eo nunc in Auſtrum, nunc in Boream obliquatur: </s> <s xml:id="echoid-s12942" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s12943" xml:space="preserve">planeta eum percutrens auſtralis, & </s> <s xml:id="echoid-s12944" xml:space="preserve"><lb/>borealis euadit, & </s> <s xml:id="echoid-s12945" xml:space="preserve">reſpectu eclypticæ ſortitur latitudinem vtrinque ab ea, quæ ad ſummum gradus ſeptem <lb/>excedit; </s> <s xml:id="echoid-s12946" xml:space="preserve">quare ſola ex omnibus planetis extra Zodiacum euagatur aliquando, latitudo enim ordinaria Zodia-<lb/>ci eſt gra. </s> <s xml:id="echoid-s12947" xml:space="preserve">12. </s> <s xml:id="echoid-s12948" xml:space="preserve">ſecundum communem ſententiam; </s> <s xml:id="echoid-s12949" xml:space="preserve">nonnuli tamen vt Venerem quoque intra Zodiacum conti-<lb/>neant, eum ad gra. </s> <s xml:id="echoid-s12950" xml:space="preserve">14. </s> <s xml:id="echoid-s12951" xml:space="preserve">dilatant. </s> <s xml:id="echoid-s12952" xml:space="preserve">hic igitur eſt motus in latitudinem.</s> <s xml:id="echoid-s12953" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12954" xml:space="preserve">Quintò. </s> <s xml:id="echoid-s12955" xml:space="preserve">Dum igitur Venus hiſce motibus agitatur, interim cum Sole d@urnam conuerſionem, ac conſe-<lb/>quenter annuum cum eo motum, quare ab vno tropico ad alterum remeando vltimum tandem ac ſpiralem <lb/>motum deſcribit.</s> <s xml:id="echoid-s12956" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div287" type="section" level="1" n="197"> <head xml:id="echoid-head211" style="it" xml:space="preserve">Magnitudo Epicycli, atque ipſius Stellæ Veneris. Cap. V.</head> <p> <s xml:id="echoid-s12957" xml:space="preserve">QVoniam Venus interdiu aliquando commodè ſpectatur, ideo per Quadrantem facilè poteris eius à So-<lb/>le digreſſionem per aliquot dies obſeruare, quouſque maxima ſit, quæ ſcilicet amplius non creſcat, ea <lb/>autem eritad ſummum gra. </s> <s xml:id="echoid-s12958" xml:space="preserve">48. </s> <s xml:id="echoid-s12959" xml:space="preserve">igitur ſi hinc inde à Sole, duo arcus graduum ſinguli 48. </s> <s xml:id="echoid-s12960" xml:space="preserve">aſſumpti <lb/>ſint, ducanturque duæ rectæ O X. </s> <s xml:id="echoid-s12961" xml:space="preserve">O Y. </s> <s xml:id="echoid-s12962" xml:space="preserve">illos arcus terminantes, deſcripuſque fuerit epicyclus ex centro So-<lb/>lis eas tangens, eius epicycli magnitudo apparebit, quæ ad gradus tantum 45. </s> <s xml:id="echoid-s12963" xml:space="preserve">vtrinque à Sole perueniet. </s> <s xml:id="echoid-s12964" xml:space="preserve">erit-<lb/>que ſemidiameter epicycli S F. </s> <s xml:id="echoid-s12965" xml:space="preserve">tres quartæ partes totius diſtantiæ S O. </s> <s xml:id="echoid-s12966" xml:space="preserve">erit, O F. </s> <s xml:id="echoid-s12967" xml:space="preserve">ſemidiametri terræ 287. </s> <s xml:id="echoid-s12968" xml:space="preserve">re-<lb/>liqua vero F S. </s> <s xml:id="echoid-s12969" xml:space="preserve">855.</s> <s xml:id="echoid-s12970" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12971" xml:space="preserve">Arcus præ@erea epicycli inferior D F H. </s> <s xml:id="echoid-s12972" xml:space="preserve">ſic innoteſcer, angulus enim D O H. </s> <s xml:id="echoid-s12973" xml:space="preserve">notus eſt, gra. </s> <s xml:id="echoid-s12974" xml:space="preserve">96. </s> <s xml:id="echoid-s12975" xml:space="preserve">ergo in <lb/>quadrilatero D S H O. </s> <s xml:id="echoid-s12976" xml:space="preserve">angulus ei oppoſitus D S H. </s> <s xml:id="echoid-s12977" xml:space="preserve">erit eius complementum ad duos rectos, ſeu ad gra 180. <lb/></s> <s xml:id="echoid-s12978" xml:space="preserve">angulus igitur D S H. </s> <s xml:id="echoid-s12979" xml:space="preserve">erit gr. </s> <s xml:id="echoid-s12980" xml:space="preserve">84. </s> <s xml:id="echoid-s12981" xml:space="preserve">quia cum gr. </s> <s xml:id="echoid-s12982" xml:space="preserve">96. </s> <s xml:id="echoid-s12983" xml:space="preserve">complet. </s> <s xml:id="echoid-s12984" xml:space="preserve">gr. </s> <s xml:id="echoid-s12985" xml:space="preserve">180. </s> <s xml:id="echoid-s12986" xml:space="preserve">ratio eſt, quia in hoc quadrilatero, qua-<lb/>tuor angulis rectis per coroll. </s> <s xml:id="echoid-s12987" xml:space="preserve">32. </s> <s xml:id="echoid-s12988" xml:space="preserve">primi ſed duo anguli ad D. </s> <s xml:id="echoid-s12989" xml:space="preserve">& </s> <s xml:id="echoid-s12990" xml:space="preserve">H. </s> <s xml:id="echoid-s12991" xml:space="preserve">ſunt recti per 18. </s> <s xml:id="echoid-s12992" xml:space="preserve">tertij Elem. </s> <s xml:id="echoid-s12993" xml:space="preserve">ergo duo an-<lb/>guli ad O, & </s> <s xml:id="echoid-s12994" xml:space="preserve">S. </s> <s xml:id="echoid-s12995" xml:space="preserve">ſimul ſunt æquales duob. </s> <s xml:id="echoid-s12996" xml:space="preserve">rectis; </s> <s xml:id="echoid-s12997" xml:space="preserve">ergo alter alterius ad duos rectos complementum erit tandem <lb/>detracto arcu inferiori D F H. </s> <s xml:id="echoid-s12998" xml:space="preserve">ex toto circulo, remanet pars epicycli ſuperior cognita gr. </s> <s xml:id="echoid-s12999" xml:space="preserve">276.</s> <s xml:id="echoid-s13000" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div288" type="section" level="1" n="198"> <head xml:id="echoid-head212" style="it" xml:space="preserve">Magnitudo Stellæ Veneris.</head> <p> <s xml:id="echoid-s13001" xml:space="preserve">PRimò indagabimus diſtantiam Veneris tum à Sole, tum à terra, eodem prorſus modo, quo ſupra ex Ari-<lb/>ſtarcho Samio diſtantias Lunæ, Te<unsure/>rræ, & </s> <s xml:id="echoid-s13002" xml:space="preserve">Sole indagauimus. </s> <s xml:id="echoid-s13003" xml:space="preserve">nam quando nobis per Teleſcopium dimi- <pb o="140" file="0162" n="167" rhead="De Mundi Fabrica,"/> diata præcisè apparet, ſiue veſperi in D, ſiue manè in H, figuræ præcedentis; </s> <s xml:id="echoid-s13004" xml:space="preserve">debemus concípere triangu-<lb/>lum rectangulum O D S, vel O H S, in quo latus O S, notum eſt, diſtantia Sólis a terra; </s> <s xml:id="echoid-s13005" xml:space="preserve">præterea angulus <lb/>ad D, vel ad H, eſt rectus, vtantea oſtendit: </s> <s xml:id="echoid-s13006" xml:space="preserve">angulus etiam D O S, vel S O H, notus erit, dimidium quippè <lb/>totius anguli noti D O H, ergo per 9. </s> <s xml:id="echoid-s13007" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s13008" xml:space="preserve">noſtri Apparat. </s> <s xml:id="echoid-s13009" xml:space="preserve">nota euadet O H, diſtantia Venerisa nob is; <lb/></s> <s xml:id="echoid-s13010" xml:space="preserve">necnon H S, diſtantia eius a Sole. </s> <s xml:id="echoid-s13011" xml:space="preserve">depræhenditur autem in figura O D, vel O H, continere duas tertiasto-<lb/>tius O S, ſiue diametros terræ 762. </s> <s xml:id="echoid-s13012" xml:space="preserve">circiter. </s> <s xml:id="echoid-s13013" xml:space="preserve">Iam ad eandem diſtantiam, diameter eius apparens obſeruetur <lb/>accuratè, depræhendeturque eſſe min. </s> <s xml:id="echoid-s13014" xml:space="preserve">ferè 3′. </s> <s xml:id="echoid-s13015" xml:space="preserve">quibus habitis, ijſdem modis, quibus in Mercurio proportio-<lb/>nem diametri Veneris ad diametrum terræ inueniemus eſſe vt 6. </s> <s xml:id="echoid-s13016" xml:space="preserve">ad 11. </s> <s xml:id="echoid-s13017" xml:space="preserve">atque hinc proportio quoque ſphæ-<lb/>rarum innoteſcet, eritque ficuti 1. </s> <s xml:id="echoid-s13018" xml:space="preserve">ad 6. </s> <s xml:id="echoid-s13019" xml:space="preserve">propè. </s> <s xml:id="echoid-s13020" xml:space="preserve">Quare terra ſexies Venerem compræhendit. </s> <s xml:id="echoid-s13021" xml:space="preserve">Hinc etiam <lb/>ſequetur Venerem ad Lunam eſſe ſicuti 7. </s> <s xml:id="echoid-s13022" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13023" xml:space="preserve">propè: </s> <s xml:id="echoid-s13024" xml:space="preserve">ad Mercurium vero v@i 3 {1/2}. </s> <s xml:id="echoid-s13025" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13026" xml:space="preserve">ad Solem tandem. </s> <s xml:id="echoid-s13027" xml:space="preserve"><lb/>vti 1. </s> <s xml:id="echoid-s13028" xml:space="preserve">ad 840. </s> <s xml:id="echoid-s13029" xml:space="preserve">quaſi. </s> <s xml:id="echoid-s13030" xml:space="preserve">ijs modis quibus in Mercurio.</s> <s xml:id="echoid-s13031" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div289" type="section" level="1" n="199"> <head xml:id="echoid-head213" style="it" xml:space="preserve">Appendix de calculo Veneris. Cap. VI.</head> <p> <s xml:id="echoid-s13032" xml:space="preserve">CAleulus Veneris perſimilis eſt calculo Mercurij: </s> <s xml:id="echoid-s13033" xml:space="preserve">nam motus apogæi primi Veneris tardiſſimus eſt, an-<lb/>nuo enim motu procedit in conſequentia ſecundis tantum 51″: </s> <s xml:id="echoid-s13034" xml:space="preserve">Vnde gradum vnum ſuperat annis fe-<lb/>rè 70. </s> <s xml:id="echoid-s13035" xml:space="preserve">quare pro calculo eius ſufliciant ſequentes annorum Radices.</s> <s xml:id="echoid-s13036" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div290" type="section" level="1" n="200"> <head xml:id="echoid-head214" style="it" xml:space="preserve">Motus Apogai Vener. Radices.</head> <note position="right" xml:space="preserve"> <lb/># # Sig. # Gra. # ′. <lb/># 1600 # 2 # 16 # 36 <lb/>Annis # 1670 # 2 # 17 # 36. <lb/># 1700 # 2 # 18 # 2 <lb/></note> <p> <s xml:id="echoid-s13037" xml:space="preserve">Motus verò Veueris in <lb/>longitudinem eſt idem cum <lb/>Solis, ac Mercurij motibus <lb/>in longitudinem: </s> <s xml:id="echoid-s13038" xml:space="preserve">quare ha-<lb/>bito, ex calculo, loco Solis in <lb/>Zodiaco, habemus ſimul lo-<lb/>cus centri epicycli Veneris, <lb/>& </s> <s xml:id="echoid-s13039" xml:space="preserve">Mercurij.</s> <s xml:id="echoid-s13040" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13041" xml:space="preserve">Reſtat igitur motus Ano-<lb/>maliæ, quo Venus in epicy@ <lb/>clo reuoluitur: </s> <s xml:id="echoid-s13042" xml:space="preserve">pro cnius calculatione damus ſequentem Tabuiam.</s> <s xml:id="echoid-s13043" xml:space="preserve"/> </p> <figure> <image file="0162-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0162-01"/> </figure> <pb o="141" file="0163" n="168" rhead="Liber Decimusſectimus."/> </div> <div xml:id="echoid-div291" type="section" level="1" n="201"> <head xml:id="echoid-head215" style="it" xml:space="preserve">TABVLA MOTVS ANOMALIAE VENER.</head> <note position="right" xml:space="preserve"> <lb/>##### In Annis ſingulis. #### In m@nſibus An. communis. ### In diebus. <lb/># Anni. # Sig. # Gra. # ′. # @ # Sig. # Gra. # ′. # Dies # Gra. # ′. <lb/># 1 # 7 # 45 # 2 # Ian. # 0 # 19 # 7 # 1 # 0 # 37 <lb/># 2 # 3 # 0 # 4 # Febr. # 1 # 0 # 22 # 2 # 1 # 14 <lb/>B # 3 # 10 # 15 # 5 # Marc. # 1 # 25 # 29 # 3 # 1 # 51 <lb/># 4 # 6 # 0 # 44 # Apr. # 2 # 13 # 59 <lb/># # # # # # # # # 4 # 1 # 28 <lb/># 5 # 1 # 15 # 46 # Mai. # 3 # 3 # 6 # 5 # 3 # 5 <lb/># 6 # 9 # 0 # 48 # Iun. # 3 # 21 # 35 # 6 # 3 # 42 <lb/>B # 7 # 4 # 45 # 49 # Iul. # 4 # 10 # 42 <lb/># 8 # 0 # 1 # 23 # Aug. # 5 # 29 # 49 # 7 # 4 # 19 <lb/># # # # # # # # # 8 # 4 # 56 <lb/># 9 # 7 # 16 # 30 # ept. # 5 # 18 # 9 # 9 # 9 # 33 <lb/># 10 # 4 # 1 # 32 # Oct. # 6 # 7 # 25 # 10 # 6 # 10 <lb/>B # 11 # 10 # 16 # 33 # Nou. # 6 # 25 # 55 <lb/># 12 # 6 # 2 # 12 # Dec. # 7 # 15 # 2 # 11 # 6 # 47 <lb/># # # # # # # # # 12 # 7 # 24 <lb/># 13 # 1 # 17 # 14 #### In menſibus Ann. Biſſext. # 13 # 8 # 1 <lb/># 14 # 9 # 2 # 16 # # # # # 14 # 8 # 38 <lb/>B # 15 # 4 # 17 # 17 # # Sig. # Gra. # ′. <lb/># 16 # 0 # 2 # 56 # # # # # 51 # 9 # 15 <lb/># # # # # Ian. # 0 # 19 # 7 # 16 # 9 # 52 <lb/># 17 # 7 # 17 # 58 # Febr. # 1 # 6 # 59 # 17 # 10 # 26 <lb/># 18 # 3 # 3 # 0 # Mart. # 1 # 26 # 6 # 18 # 11 # 6 <lb/>B # 19 # 10 # 18 # 1 # Apr. # 2 # 14 # 36 <lb/># 20 # 6 # 3 # 40 # # # # # 19 # 11 # 43 <lb/># # # # # Maius # 3 # 3 # 43 # 20 # 12 # 20 <lb/># # # # # Iun. # 3 # 22 # 12 # 21 # 12 # 57 <lb/># 40 # 0 # 7 # 20 # Iulius # 4 # 11 # 19 # 22 # 13 # 34 <lb/>In # 60 # 6 # 11 # 0 # Aug. # 5 # 0 # 26 <lb/># 80 # 0 # 14 # 40 # # # # # 23 # 14 # 11 <lb/># 100 # 6 # 18 # 20 # Sept. # 5 # 18 # 56 # 24 # 14 # 48 <lb/># # # # # Octo. # 6 # 8 # 2 # 25 # 15 # 25 <lb/># 200 # 1 # 6 # 41 # Nou. # 6 # 26 # 32 # 26 # 16 # 2 <lb/>Annis # 300 # 7 # 25 # 1 # Dec. # 7 # 15 # 39 <lb/># 400 # 2 # 13 # 21 # # # # # 27 # 16 # 39 <lb/># 500 # 9 # 1 # 42 # # # # # 28 # 17 # 16 <lb/># # # # # # # # # 29 # 17 # 53 <lb/># 600 # 3 # 20 # 2 # # # # # 30 # 18 # 30 <lb/>aggregatis. # 700 # 10 # 8 # 22 # # # # # 31 # 19 # 7 <lb/># 800 # 4 # 26 # 43 # # # # ### In horis aliquor. <lb/># 900 # 11 # 15 # 3 <lb/># 1000 # 6 # 3 # 24 # # # # Hor. # 0 # 12 <lb/>##### Radix ad Ann. 1600 ab- \\ ſolutum. # # # # # 16 # 0 # 25 <lb/># # # # # # # # # # 24 # 0 # 37 <lb/># 1600 # 1 # 23 # 45 # Radix. # # # # 24 # 0 # 37 <lb/></note> <pb o="142" file="0164" n="169" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div292" type="section" level="1" n="202"> <head xml:id="echoid-head216" style="it" xml:space="preserve">Constructio, & vſus Tabulæ præcedentis.</head> <p> <s xml:id="echoid-s13044" xml:space="preserve">CVius conſtructio patet ex ſuperioribus, vſus vero ex ſequenti exemplo. </s> <s xml:id="echoid-s13045" xml:space="preserve">Quæramus ergo admeridiem <lb/>præſentis diei, quo hæcſcribo, prædictos Vener. </s> <s xml:id="echoid-s13046" xml:space="preserve">motus, nimirum diei 12. </s> <s xml:id="echoid-s13047" xml:space="preserve">Octobris, anni biſſextilis <lb/>1616. </s> <s xml:id="echoid-s13048" xml:space="preserve">accommodato igitur tempora dato ad v@um Aſtronomicum, vt in formula vides accip o ex Tabula, <lb/> <anchor type="note" xlink:label="note-0164-01a" xlink:href="note-0164-01"/> & </s> <s xml:id="echoid-s13049" xml:space="preserve">ex proprijs columnis omnes motus tem-<lb/>poribus correſpondentes, quorum ſumma <lb/>indicat aſtrum Vener. </s> <s xml:id="echoid-s13050" xml:space="preserve">diſtare ab apogęo epi-<lb/>cycli A, gr. </s> <s xml:id="echoid-s13051" xml:space="preserve">7. </s> <s xml:id="echoid-s13052" xml:space="preserve">numerãdo ab A, verſus B, vſq; <lb/></s> <s xml:id="echoid-s13053" xml:space="preserve">Veneris characterem. </s> <s xml:id="echoid-s13054" xml:space="preserve">Eſt igitur Venusin <lb/>ſemicirculo epicyclo orientali, quare in mo-<lb/>tu diurno, veſperi poſt Solem occumbet, He-<lb/>ſperuſq; </s> <s xml:id="echoid-s13055" xml:space="preserve">dicetur; </s> <s xml:id="echoid-s13056" xml:space="preserve">non tamen videri poterit, <lb/>quia non ſatis a Sole diſtat, nam paulo ante <lb/>in A, Soli coniungebatur. </s> <s xml:id="echoid-s13057" xml:space="preserve">ſi videri poſſet per <lb/>Teleſcopium plena videretur ob rationem <lb/>ſupra allatam. </s> <s xml:id="echoid-s13058" xml:space="preserve">ſi in figura rectè conſtructa du-<lb/>catur linea O, Vener. </s> <s xml:id="echoid-s13059" xml:space="preserve">tranſiens per M. </s> <s xml:id="echoid-s13060" xml:space="preserve">in gy-<lb/>ro Solis, erit arcus M S, quantitas, qua Venus <lb/>Solem in Zodiaco præcedit ſecundum ordi-<lb/>nem ſignorum; </s> <s xml:id="echoid-s13061" xml:space="preserve">hodie etiam Sol occupat 20. </s> <s xml:id="echoid-s13062" xml:space="preserve">grad. </s> <s xml:id="echoid-s13063" xml:space="preserve">♎, quare ibidem eſt centrum epicycli S; </s> <s xml:id="echoid-s13064" xml:space="preserve">arcus vero M S, <lb/>videtur eſſe quaſi graduum trium: </s> <s xml:id="echoid-s13065" xml:space="preserve">Quare Venus occupabit 23. </s> <s xml:id="echoid-s13066" xml:space="preserve">gradum ♎. </s> <s xml:id="echoid-s13067" xml:space="preserve">De motu eius in latitudinem <lb/>conſulto taceo: </s> <s xml:id="echoid-s13068" xml:space="preserve">hæc enim nobis ſufficiunt.</s> <s xml:id="echoid-s13069" xml:space="preserve"/> </p> <div xml:id="echoid-div292" type="float" level="2" n="1"> <note position="right" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve"> <lb/># Sig. # Gra. # ′. <lb/>Rad. 1606. # 1 # 23 # 45 <lb/>Annis 51. # 4 # 17 # 17 <lb/>Biſſext. menſ. Sept. # 5 # 18 # 56 <lb/>Dies 12. # 0 # 7 # 24 <lb/>Summa Anom. # 0 # 7 # 22 <lb/></note> </div> </div> <div xml:id="echoid-div294" type="section" level="1" n="203"> <head xml:id="echoid-head217" xml:space="preserve">LIBER DECIMVSTERTIVS <lb/>DE MARTE.</head> <p> <s xml:id="echoid-s13070" xml:space="preserve">MArtis nota Telum refert, quam Aegyptij ad Martem belli Deum denotandum, veluti ipſius inſign@ <lb/>adhibebant; </s> <s xml:id="echoid-s13071" xml:space="preserve">eam igitur Aſtronomi pro Marte aliquando vſurpant.</s> <s xml:id="echoid-s13072" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div295" type="section" level="1" n="204"> <head xml:id="echoid-head218" style="it" xml:space="preserve">Locus Martis. Cap. I.</head> <p> <s xml:id="echoid-s13073" xml:space="preserve">COmmunis Aſtronomorum ſententia reliquos tres planetas Martem, Iouem, Saturnum, quos ſuperio-<lb/>res appellant, ſic collocat, vt intra eos prædicta iam omnia videlicet Elementa, Luna, Sol, Mercurius, <lb/>ac Venus contineatur: </s> <s xml:id="echoid-s13074" xml:space="preserve">non deſunt tamen, qui ab hac ſententia recedentes, ſed magnæ auctoritatis Aſtrono-<lb/>mi, Copernicus, Tycho, Keplerus, eos ita moueri tradunt, vt ad centrum vniu<unsure/>erſi non referantur, ſed po-<lb/>tius vna cũ cæteris planetis Solem tanquam medium reſpiciant, ideſt, reſpectu vniuerſi ſint eccentrici, quo-<lb/>rum tamen centrum ſit in Sole: </s> <s xml:id="echoid-s13075" xml:space="preserve">quam totam poſitionem melius concipies ex inſpectione figuræ vniuerſalis <lb/>totius mundi, quam initio huius tertiæ partis exhibuimus.</s> <s xml:id="echoid-s13076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13077" xml:space="preserve">Id autem primo probant ex parallaxibus Martis, quæ ſumma diligentia, & </s> <s xml:id="echoid-s13078" xml:space="preserve">optimis organis depręhenſæ, <lb/>aliquando ſunt multo minores, quam Solis; </s> <s xml:id="echoid-s13079" xml:space="preserve">aliquando etiam maiores: </s> <s xml:id="echoid-s13080" xml:space="preserve">attingunt enim ferè min. </s> <s xml:id="echoid-s13081" xml:space="preserve">4′. </s> <s xml:id="echoid-s13082" xml:space="preserve">Solis ve-<lb/>rò parallaxis eſt min. </s> <s xml:id="echoid-s13083" xml:space="preserve">3′. </s> <s xml:id="echoid-s13084" xml:space="preserve">illæ quidem euincuot Martem ſupra Solem altiſſimè attolli; </s> <s xml:id="echoid-s13085" xml:space="preserve">hæ vero aliquando in-<lb/>fra eiuſdem orb tam deſcendere. </s> <s xml:id="echoid-s13086" xml:space="preserve">Iuxta Tychonis obſeruationes, minima diſtantia Marti a terra continet <lb/>ſemid. </s> <s xml:id="echoid-s13087" xml:space="preserve">terræ 761. </s> <s xml:id="echoid-s13088" xml:space="preserve">circiter: </s> <s xml:id="echoid-s13089" xml:space="preserve">quæ ſunt duæ tertiæ partes ſolaris à terra diſtantiæ: </s> <s xml:id="echoid-s13090" xml:space="preserve">Mediocris vero diſtantia ſemi-<lb/>diam. </s> <s xml:id="echoid-s13091" xml:space="preserve">terræ 1745. </s> <s xml:id="echoid-s13092" xml:space="preserve">De maxima verò quamuis nihil afferat ſequitur tamen eam continere ſaltem ſemid. </s> <s xml:id="echoid-s13093" xml:space="preserve">terræ <lb/>2729. </s> <s xml:id="echoid-s13094" xml:space="preserve">ſic enim mediocris diſtantia tanto ſuperabit minimam, quanto eadem à maxima ſuperabitur. </s> <s xml:id="echoid-s13095" xml:space="preserve">Secundò, <lb/>ſi@@@ Maculæ, Mercurius, Venus, Solem circumeunt; </s> <s xml:id="echoid-s13096" xml:space="preserve">quidni etiam Mars? </s> <s xml:id="echoid-s13097" xml:space="preserve">Tertiò<unsure/>, Mars reliquos duos Io-<lb/>uem, & </s> <s xml:id="echoid-s13098" xml:space="preserve">Satutnum aliquando occultat, igitur infra eos incedit, occultatur autem à Sole Mercurio, Venere, <lb/>ergo, ſuperior illis eſt. </s> <s xml:id="echoid-s13099" xml:space="preserve">Quarto videmus eum ſingulis annis Soli coniungi, idemque diametraliter poſtea <lb/>opponi ita vt intereos, nosmedij interponamur: </s> <s xml:id="echoid-s13100" xml:space="preserve">ergo Mars ſua gyratione ſaltem amplectitur Lunarem re-<lb/>gionem. </s> <s xml:id="echoid-s13101" xml:space="preserve">Quintò ex velocitate motuum; </s> <s xml:id="echoid-s13102" xml:space="preserve">Mars enim citius ſuum curſum in longitudinem abſoluit quam <lb/>l<unsure/>upiter, & </s> <s xml:id="echoid-s13103" xml:space="preserve">Saturnus; </s> <s xml:id="echoid-s13104" xml:space="preserve">ergo vt alias diximus infra eos<unsure/> collocari debet.</s> <s xml:id="echoid-s13105" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div296" type="section" level="1" n="205"> <head xml:id="echoid-head219" style="it" xml:space="preserve">Motus Martis. Cap. II.</head> <p> <s xml:id="echoid-s13106" xml:space="preserve">QVamuis Martis motus pænè ſint inextricabiles, adeò vt merito Plinius quæratur Martis ſydus inobſer-<lb/>uabile eſſe nos tamen n<unsure/>õnulla pro inſtituto faciliora ſimul, & </s> <s xml:id="echoid-s13107" xml:space="preserve">certiora proponemus. </s> <s xml:id="echoid-s13108" xml:space="preserve">Ad ſaluanda igitur <lb/>ipſius præcipua phænomena, & </s> <s xml:id="echoid-s13109" xml:space="preserve">obſeruationes, debemus, primò concipere circulum reſpectu tocius <lb/>mundi eccentricum, tame@ centrum ſit in Sole, quem in ſequenti figura notauimus literis N. </s> <s xml:id="echoid-s13110" xml:space="preserve">O. </s> <s xml:id="echoid-s13111" xml:space="preserve">G. </s> <s xml:id="echoid-s13112" xml:space="preserve">hunc <pb o="143" file="0165" n="170" rhead="Liber Decimusſextus."/> <anchor type="figure" xlink:label="fig-0165-01a" xlink:href="fig-0165-01"/> circulum vocant deferente@ epicycli, quoniam adhuc <lb/>conueniens eſt ei ſuperaddere epicyclum A E M. </s> <s xml:id="echoid-s13113" xml:space="preserve">cuius <lb/>centrum E. </s> <s xml:id="echoid-s13114" xml:space="preserve">ſit in ipſo deferente, & </s> <s xml:id="echoid-s13115" xml:space="preserve">in cuius ambitu re-<lb/>uoluatur ſydus Martis, vt in figura apparet. </s> <s xml:id="echoid-s13116" xml:space="preserve">hanc porrò <lb/>figuram hac ratione conſtruximus; </s> <s xml:id="echoid-s13117" xml:space="preserve">circaterram T. </s> <s xml:id="echoid-s13118" xml:space="preserve">d@-<lb/>ſcriptus eſt primò gy<unsure/>rus Solis S T. </s> <s xml:id="echoid-s13119" xml:space="preserve">i@mediorum diſtan <lb/>tia T S. </s> <s xml:id="echoid-s13120" xml:space="preserve">Solis à terra, quæ eſt ſemid. </s> <s xml:id="echoid-s13121" xml:space="preserve">terræ 1142. </s> <s xml:id="echoid-s13122" xml:space="preserve">T P@ve-<lb/>rò ſit minima Martis a terra remotio cõtinen duaster <lb/>tias totius T V. </s> <s xml:id="echoid-s13123" xml:space="preserve">quę ſunt ſemid. </s> <s xml:id="echoid-s13124" xml:space="preserve">761. </s> <s xml:id="echoid-s13125" xml:space="preserve">vt antea dictum eſt. <lb/></s> <s xml:id="echoid-s13126" xml:space="preserve">T M. </s> <s xml:id="echoid-s13127" xml:space="preserve">ſit mediocris Martis à terra diſtantia 1745. </s> <s xml:id="echoid-s13128" xml:space="preserve">T A. </s> <s xml:id="echoid-s13129" xml:space="preserve"><lb/>maxima, & </s> <s xml:id="echoid-s13130" xml:space="preserve">altiſſima Martis à terra ſublimitas 2729 ad <lb/>quas tres diſtantias deſcripti ſunt circa Solem trescir-<lb/>cuitus, quorum minimus M P. </s> <s xml:id="echoid-s13131" xml:space="preserve">in quo Mars ſemper eſt <lb/>perigæus, ſed maximè in P. </s> <s xml:id="echoid-s13132" xml:space="preserve">vbi eriam eſt terrę propior, <lb/>quam Sol. </s> <s xml:id="echoid-s13133" xml:space="preserve">Secundus gyrus E N. </s> <s xml:id="echoid-s13134" xml:space="preserve">G O. </s> <s xml:id="echoid-s13135" xml:space="preserve">qui deferens di@ <lb/>citur, quod deferat centrum E. </s> <s xml:id="echoid-s13136" xml:space="preserve">vel G. </s> <s xml:id="echoid-s13137" xml:space="preserve">epicycli, ac pro-<lb/>inde epicyclum ſecundum ordinem ſignorum, ſinè in <lb/>longitudinem. </s> <s xml:id="echoid-s13138" xml:space="preserve">In hoc gyro circa puncta N O. </s> <s xml:id="echoid-s13139" xml:space="preserve">contrum <lb/>epicycli ſortitur mediam à terra diſtantiam. </s> <s xml:id="echoid-s13140" xml:space="preserve">Tertius, <lb/>& </s> <s xml:id="echoid-s13141" xml:space="preserve">vltimus Martis gyrus circa Solem eſt A B. </s> <s xml:id="echoid-s13142" xml:space="preserve">in quo <lb/>Mars eſt apogæus, ſed maximè ad punctum A. </s> <s xml:id="echoid-s13143" xml:space="preserve">ſupra <lb/>Solem directè poſitũ. </s> <s xml:id="echoid-s13144" xml:space="preserve">hac porrò ratione diameter epi-<lb/>@ycli, ac proinde craſſities cæli, ſeu regionis Martialis, erit ſemid. </s> <s xml:id="echoid-s13145" xml:space="preserve">terræ 984. </s> <s xml:id="echoid-s13146" xml:space="preserve">ſeu 1000. </s> <s xml:id="echoid-s13147" xml:space="preserve">nihil tamen certi in re <lb/>adeò à nobis ſemota affirmarim. </s> <s xml:id="echoid-s13148" xml:space="preserve">debemus præterea hoſce circuitus concipere ſub Zodiaco, eoſque eſſe orbi-<lb/>tam, per quam centrum epicycli E. </s> <s xml:id="echoid-s13149" xml:space="preserve">vel G. </s> <s xml:id="echoid-s13150" xml:space="preserve">pergat ſub Zodiaco, ſecundum ſignorum ordinem, medio motu <lb/>quotidie min. </s> <s xml:id="echoid-s13151" xml:space="preserve">31′. </s> <s xml:id="echoid-s13152" xml:space="preserve">ſec. </s> <s xml:id="echoid-s13153" xml:space="preserve">26″. </s> <s xml:id="echoid-s13154" xml:space="preserve">annuatim vero ſigna 6. </s> <s xml:id="echoid-s13155" xml:space="preserve">gr. </s> <s xml:id="echoid-s13156" xml:space="preserve">11. </s> <s xml:id="echoid-s13157" xml:space="preserve">15′. </s> <s xml:id="echoid-s13158" xml:space="preserve">totumq; </s> <s xml:id="echoid-s13159" xml:space="preserve">Zodiacũ hoc proprio motu, peragrat <lb/>anno vno ſimplici, cum diebus præterea ferè 322. </s> <s xml:id="echoid-s13160" xml:space="preserve">Hic dicitur motus Martis in longitudinem, & </s> <s xml:id="echoid-s13161" xml:space="preserve">numeratur <lb/>vtinalijs planetis à principio Zodiaci, ſeu ſigni Arietis.</s> <s xml:id="echoid-s13162" xml:space="preserve"/> </p> <div xml:id="echoid-div296" type="float" level="2" n="1"> <figure xlink:label="fig-0165-01" xlink:href="fig-0165-01a"> <image file="0165-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0165-01"/> </figure> </div> <p> <s xml:id="echoid-s13163" xml:space="preserve">Notanda præterea ſunt in hoc eccentrico apogæum, & </s> <s xml:id="echoid-s13164" xml:space="preserve">perigæum: </s> <s xml:id="echoid-s13165" xml:space="preserve">apogæum ſemper eſt directè ſupra So-<lb/>lem, quale eſt in figura punctum E. </s> <s xml:id="echoid-s13166" xml:space="preserve">quod tamen non ſemper erit centrum epicycli, vt eſt in hac figura. </s> <s xml:id="echoid-s13167" xml:space="preserve">Peri-<lb/>gæum eſt ei oppoſitum, quale eſt G. </s> <s xml:id="echoid-s13168" xml:space="preserve">terræ propius, ſoliq; </s> <s xml:id="echoid-s13169" xml:space="preserve">diametraliter oppoſitum, in quo ſydus Martis ma-<lb/>ximum ſpectatur: </s> <s xml:id="echoid-s13170" xml:space="preserve">hæc duo ſunt apogæum, & </s> <s xml:id="echoid-s13171" xml:space="preserve">perigæum eccentrici.</s> <s xml:id="echoid-s13172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13173" xml:space="preserve">Dum igitur centrum epicycli hoc motus Zodiacum verſus orientem percurrit, interim planeta ipſe in <lb/>ambitu ipſius epicycli girat, in ſuperiori quidem parte ſecundum ſignorum ordinem, in inferiori vero con-<lb/>tra, ſicuti etiam reliqui quinque planetæ; </s> <s xml:id="echoid-s13174" xml:space="preserve">fitque in hac circulatione Directus, Stationarius, & </s> <s xml:id="echoid-s13175" xml:space="preserve">Retrogradus, <lb/>non ſecus ac illi. </s> <s xml:id="echoid-s13176" xml:space="preserve">hic dicitur motus anomaliæ ſicut in alijs, quod ſit cauſa irregularis progreſius Martis per <lb/>Zodiacum. </s> <s xml:id="echoid-s13177" xml:space="preserve">Diarius porrò motus æqualis anomaliæ ſiue planetæ in peripheria epicycli eſt min. </s> <s xml:id="echoid-s13178" xml:space="preserve">27′ 41″. </s> <s xml:id="echoid-s13179" xml:space="preserve">An-<lb/>nuus vero eſt ſig. </s> <s xml:id="echoid-s13180" xml:space="preserve">5. </s> <s xml:id="echoid-s13181" xml:space="preserve">gr. </s> <s xml:id="echoid-s13182" xml:space="preserve">8. </s> <s xml:id="echoid-s13183" xml:space="preserve">28′. </s> <s xml:id="echoid-s13184" xml:space="preserve">totumq; </s> <s xml:id="echoid-s13185" xml:space="preserve">recurritannis duobus, diebus 49. </s> <s xml:id="echoid-s13186" xml:space="preserve">horis fere 20. </s> <s xml:id="echoid-s13187" xml:space="preserve">& </s> <s xml:id="echoid-s13188" xml:space="preserve">vt in alijs numeratur <lb/>ab apogæo A. </s> <s xml:id="echoid-s13189" xml:space="preserve">epicycli, eſt enim vt in alijs hic quoq; </s> <s xml:id="echoid-s13190" xml:space="preserve">apogęum, & </s> <s xml:id="echoid-s13191" xml:space="preserve">perigæum epicycli. </s> <s xml:id="echoid-s13192" xml:space="preserve">quando autem planeta <lb/>fuerit in perigæo tam eccentrici, quam epicycli maximum ac fulgidiflimum ſpectatur, videlicet in puncto P. <lb/></s> <s xml:id="echoid-s13193" xml:space="preserve">ita vt magnitudinem Venerem adæquet, quo etiam tempore eſt quam Sol terræ propior.</s> <s xml:id="echoid-s13194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13195" xml:space="preserve">Porrò hæc Martis, ac reliquorum duorum ſuperiorum Iouis, & </s> <s xml:id="echoid-s13196" xml:space="preserve">Saturni in ſuis epicyclis reuolutio, mira-<lb/>bili habitudini ad Solis motum comparata eſt. </s> <s xml:id="echoid-s13197" xml:space="preserve">nam quotieſcunque Sol alicui horum tr@um planerarum con-<lb/>iungitur, vel eum aſſequitur, ſemper planeta ille apogæum epicycli occupat, ac proinde exiſtit apogæus in <lb/>extremo gvro A B. </s> <s xml:id="echoid-s13198" xml:space="preserve">Sole poſtea illum prætereunte, quippe eo velocior, planeta ab apogęo epicycli delabi in-<lb/>@ipit, quaſi Solem inſequi vellet, tantumq; </s> <s xml:id="echoid-s13199" xml:space="preserve">in epicyclo deſcendit, quantum Sol ab epicycli centro recedit: <lb/></s> <s xml:id="echoid-s13200" xml:space="preserve">Quare cum Sol per ſemicirculum, ſeu per diametrum a centro epicycli receſſerit, ſiue ei diametraliter op-<lb/>poſi us fuerit; </s> <s xml:id="echoid-s13201" xml:space="preserve">tunc pariter planeta ſemicirculum epicycli orientalem cõfecerit, eritq; </s> <s xml:id="echoid-s13202" xml:space="preserve">propterea in perigæo <lb/>epicycli, & </s> <s xml:id="echoid-s13203" xml:space="preserve">ſimul minimo gyro M P. </s> <s xml:id="echoid-s13204" xml:space="preserve">Poſtea Sole hinc ei appropinquante, planeta ab hoc perigæo paulatim <lb/>ſcandit alterum epicycli ſemicirculum; </s> <s xml:id="echoid-s13205" xml:space="preserve">atq; </s> <s xml:id="echoid-s13206" xml:space="preserve">iterum in noua Solis coniunctione cum epicyclo, apogæum epi-<lb/>cycli obtinet, ac Soli coniungitur, ideſt, in eodem cum eo gradu Zodiaci reperitur. </s> <s xml:id="echoid-s13207" xml:space="preserve">quare ſequitur in con-<lb/>iuctione cum Sole eſſe directos, in oppoſitione eſſe retrogrados, in quadratis eſſe ſtationarios; </s> <s xml:id="echoid-s13208" xml:space="preserve">ſic ſuperiores <lb/>hi tres planetæ mira ad Solem alluſione, perpetuas circa cum choreas exercent.</s> <s xml:id="echoid-s13209" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13210" xml:space="preserve">Hinc ſequitur quod hi planetæ, dum deſcendũt in ſemicirculo orientali ſuorum epicyclorum, ſint orien-<lb/>tales, & </s> <s xml:id="echoid-s13211" xml:space="preserve">matutini, ideſt, manè ante Solem oriantur: </s> <s xml:id="echoid-s13212" xml:space="preserve">& </s> <s xml:id="echoid-s13213" xml:space="preserve">quidem heliacè cum primum è radij Solis emerſe-<lb/>rint, atq; </s> <s xml:id="echoid-s13214" xml:space="preserve">effulſerint; </s> <s xml:id="echoid-s13215" xml:space="preserve">quod illis accidit a coniunctione cum Sole vſque ad oppoſitionem. </s> <s xml:id="echoid-s13216" xml:space="preserve">quando vero ſcan-<lb/>dunt ſemicirculum@occidentalem, ſint occidentales, & </s> <s xml:id="echoid-s13217" xml:space="preserve">veſpertini, ideſt, veſperi in oriente oriantur, quod <lb/>illis accidit ab oppoſit: </s> <s xml:id="echoid-s13218" xml:space="preserve">one ad coniunctionem. </s> <s xml:id="echoid-s13219" xml:space="preserve">Præterea quando planeta eſt Soli oppoſitus, quod eſt quan-<lb/>do eſt in epicyclo perigæus, dicitur Acronycus, quod idem valet, ac veſpertinus; </s> <s xml:id="echoid-s13220" xml:space="preserve">nam ακρονυξ, ſeu ακρονυχ@@, <lb/>e<unsure/>ſt principiun noctis.</s> <s xml:id="echoid-s13221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13222" xml:space="preserve">Hinc conſiderandæ ſunt variæ habitudines, ſeu aſpectus, quos cum Sole, & </s> <s xml:id="echoid-s13223" xml:space="preserve">cæteris planetis, hi ſupcrio-<lb/>res tres planetæ in Zodiaco ſortiuntur: </s> <s xml:id="echoid-s13224" xml:space="preserve">Sortiuntur primo coniunctionem, quando in eodem gradu Zodia-<lb/>c<unsure/>i cum eis fuerint, cuius cbaracter eſt hic ☿. </s> <s xml:id="echoid-s13225" xml:space="preserve">Sortiuntur oppoſitionem, quando in oppoſito eis Zodiaci gra- <pb o="144" file="0166" n="171" rhead="De Mundi Fabrica,"/> du exiſtent, cuius nota eſt hæc ☍. </s> <s xml:id="echoid-s13226" xml:space="preserve">hi autem duo aſpectus communi nomine dicuntur Sygyziæ, ideſt, coniu-<lb/>gationes. </s> <s xml:id="echoid-s13227" xml:space="preserve">Sextilem aſpectum habent, quando diſtant ab vno eorum per ſextantem, ideſt, ſextam circuli par-<lb/>tem, ſeu per gr. </s> <s xml:id="echoid-s13228" xml:space="preserve">60. </s> <s xml:id="echoid-s13229" xml:space="preserve">eius ſignum eſt hoc *.</s> <s xml:id="echoid-s13230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13231" xml:space="preserve">Quadrato aſ<unsure/>pectu ad alios referuntur, cum ab eorum quopiam per quadrantem, ideſt, quartam circuli par-<lb/>tem, ſeu gr. </s> <s xml:id="echoid-s13232" xml:space="preserve">60. </s> <s xml:id="echoid-s13233" xml:space="preserve">diſtant, cuius nota eſt ♊.</s> <s xml:id="echoid-s13234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13235" xml:space="preserve">Trino aſpectu aliquem planetarum intuentur, cum ab eo per trientem, ſeu tertiam partem, ſeu gr. </s> <s xml:id="echoid-s13236" xml:space="preserve">120. </s> <s xml:id="echoid-s13237" xml:space="preserve">re-<lb/>cedunt, eius nota eſt Δ.</s> <s xml:id="echoid-s13238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13239" xml:space="preserve">Hæ ſunt præ ipuè habitudines quas Aſtrologi, ideſt, iudiciarij conſiderant, reliquas vero intermedias, <lb/>tanquam minus validas miſſas faciunt. </s> <s xml:id="echoid-s13240" xml:space="preserve">Mouetur adhuc Mars motu latitudinis, ſeu in latitudinem, ideſt, <lb/>modo ad vnam eclypticæ partem, modo ad alteram exorbitat, vnde reſpectu eclipticæ fit modo Auſtralis, <lb/>modo Borealis: </s> <s xml:id="echoid-s13241" xml:space="preserve">maximaque eius latitudo ad ſex graduum excreſcit, quare tunc extremam Zodiaci margi-<lb/>nem radit.</s> <s xml:id="echoid-s13242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13243" xml:space="preserve">Poſtremo dum prædictis motibus agitatur, etiam diurna conuerſione in occidentem rapitur, quo mo-<lb/>tu apogæum eccentrici E. </s> <s xml:id="echoid-s13244" xml:space="preserve">ſpatio horarum 24. </s> <s xml:id="echoid-s13245" xml:space="preserve">per totum mundi gyrum ab oriente in occidentem reuolui-<lb/>tur: </s> <s xml:id="echoid-s13246" xml:space="preserve">vnde hic quoque vt in alijs vltimus ac finalis planetæ motus exurgit, qui ſpiralis eſt, quo videlicet a tro-<lb/>pico ad tropicum ſpiratim remeat. </s> <s xml:id="echoid-s13247" xml:space="preserve">Quod ſi motus diurnus in eo ceſſaret, mouereturque tantum ſecun-<lb/>dum longitudinem, fimulque in epicyclo motu anomaliæ reuolueretur, deſcriberet ex ſententiam Keple-<lb/>ri intricatam illam ac perplexam figuram, quam ipſe Keplerus initio operis de Marte depingit, vti eſt ſe-<lb/>quens.</s> <s xml:id="echoid-s13248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13249" xml:space="preserve">In qua A, eſt centrum mundi, circellus autem B, includit ſphæras Solis, Lunæ, & </s> <s xml:id="echoid-s13250" xml:space="preserve">elementorum. </s> <s xml:id="echoid-s13251" xml:space="preserve">Mars<unsure/> <lb/> <anchor type="figure" xlink:label="fig-0166-01a" xlink:href="fig-0166-01"/> igitur initium fecit in C. </s> <s xml:id="echoid-s13252" xml:space="preserve">perrexis<unsure/> <lb/>in D. </s> <s xml:id="echoid-s13253" xml:space="preserve">perigæum epicycli verſus <lb/>terram; </s> <s xml:id="echoid-s13254" xml:space="preserve">poſtea retrogradus fa-<lb/>ctus per epicyclum reflexit iter <lb/>per E F. </s> <s xml:id="echoid-s13255" xml:space="preserve">quouſque peruenit in <lb/>G. </s> <s xml:id="echoid-s13256" xml:space="preserve">apogæum epicycli, vnde ite-<lb/>rum ad terras deſcendens alias <lb/>ſpiras agglomerauit, deſiijtque <lb/>in H. </s> <s xml:id="echoid-s13257" xml:space="preserve">ſunt autem 8. </s> <s xml:id="echoid-s13258" xml:space="preserve">recurſus in <lb/>16. </s> <s xml:id="echoid-s13259" xml:space="preserve">iuxta proportionem motus <lb/>So is ad motum Martis, quæ ferè <lb/>dupla eſt. </s> <s xml:id="echoid-s13260" xml:space="preserve">reliquum autem Mar-<lb/>tis progreſſum deſcribere, ob li-<lb/>nearum confuſionem, non ex-<lb/>pedit. </s> <s xml:id="echoid-s13261" xml:space="preserve">porrò dum hanc figuram <lb/>in ſuo circulo deducit, interim <lb/>motu diurno pariter ſpirali, vti <lb/>diximus, rapitur.</s> <s xml:id="echoid-s13262" xml:space="preserve"/> </p> <div xml:id="echoid-div297" type="float" level="2" n="2"> <figure xlink:label="fig-0166-01" xlink:href="fig-0166-01a"> <image file="0166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0166-01"/> </figure> </div> <p> <s xml:id="echoid-s13263" xml:space="preserve">Sed dubitabit quis, qua ratio-<lb/>ne poſſit Mars eſſe retrogradus, <lb/>cum enim tardius ipſe moueatur <lb/>in peripher a epicycli, quam ip-<lb/>ſe epicycli in peripheria eccen-<lb/>trici, ſeu in longitudinem, ſe-<lb/>quitur plus ſemper epicyclum <lb/>in Zodiaco progredi, quam pla-<lb/>neta in epicyclo, & </s> <s xml:id="echoid-s13264" xml:space="preserve">conſequen-<lb/>ter etiam quando erit in parte <lb/>epicycli inferiori, in qua aduer-<lb/>ſo illi motu fertur, ſegnius in eo <lb/>retrocedat, quam progrediatur <lb/>in eccentrico, ideſt, motus ano-<lb/>maliæ nunquam ſuperabit motum in longitudinem, quare ſemper in Zodiaco progredietur. </s> <s xml:id="echoid-s13265" xml:space="preserve">Huic ſubti-<lb/>liſſimæ quæſtioni ſic reſpondendum eſt: </s> <s xml:id="echoid-s13266" xml:space="preserve">ob amplitudinem epicycli accidere poſſe, vt gradus qui ſunt iux-<lb/>ta eius perigæum, eo quod ſint nobis propiores multo quam gradus eccentrici, maiorem arcum ſubten-<lb/>dant in Zodiaco, quam ſudtendant gradus eccentrici, quos centrum epicycli percurrit; </s> <s xml:id="echoid-s13267" xml:space="preserve">quare quamuis <lb/>planeta in perigæo epicycli tardius in epicyclo moueatur, quam centrum epicycli in conſequentia, ob vi-<lb/>cinitatem tamen ad terram, poterit motus eius in perigæo velocior videri, quam motus centri epicycli <lb/>in conſequentia, hacque ratione repedare videbit<unsure/>ur. </s> <s xml:id="echoid-s13268" xml:space="preserve">quod experientia confirmatur, videmus enim ea <lb/>quæ mouentur in aere, quamuis ſegnius multo ferantur, quam Sol, eum tamen longo ſpatio ſuperare, <lb/>quod illis accidit ob propinquitatem ad oculum noſtrum: </s> <s xml:id="echoid-s13269" xml:space="preserve">ſic Sol tardus videtur ob maximam diſtantiam, <lb/>quamuis velociſſimè circumferatur.</s> <s xml:id="echoid-s13270" xml:space="preserve"/> </p> <pb o="145" file="0167" n="172" rhead="Liber Decimustertius."/> </div> <div xml:id="echoid-div299" type="section" level="1" n="206"> <head xml:id="echoid-head220" style="it" xml:space="preserve">Figura Martis. Cap. III.</head> <p> <s xml:id="echoid-s13271" xml:space="preserve">QVemadmodum Terra, Luna, Sol, Mercurius, & </s> <s xml:id="echoid-s13272" xml:space="preserve">Venus, ſphærica exiſtunt, idem de Marte conue-<lb/>niens eſt exiſtimare.</s> <s xml:id="echoid-s13273" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div300" type="section" level="1" n="207"> <head xml:id="echoid-head221" style="it" xml:space="preserve">Illuminatio, & Vmbra Martis. Cap. IV.</head> <p> <s xml:id="echoid-s13274" xml:space="preserve">SVperius oſtenſum eſt Lunam, & </s> <s xml:id="echoid-s13275" xml:space="preserve">Venerem, inferius vero oſtendetur Iouem quoque, ex vna parte, à So-<lb/>le illuminari, ex altera verò vmbram proijcere. </s> <s xml:id="echoid-s13276" xml:space="preserve">quare probabile eſt Martem quoque ex vna parte collu-<lb/>ſtrari, ex altera vero vmbram emittere. </s> <s xml:id="echoid-s13277" xml:space="preserve">Porrò lux huius planetæ ignea, ac rubicunda eſt, vnde Græcè Pyrois <lb/>dicitur, quantitatem autem vmbræ indagamus eo modo quo in præcedentibus planetis. </s> <s xml:id="echoid-s13278" xml:space="preserve">nam diameter Solis <lb/>ad diametrum Marti eſt ſicuti 26. </s> <s xml:id="echoid-s13279" xml:space="preserve">ad 2 {1/12}. </s> <s xml:id="echoid-s13280" xml:space="preserve">diſtantia vero eius à Sole maxima, colligitur ex prædictis, eſſe ſe-<lb/>mid. </s> <s xml:id="echoid-s13281" xml:space="preserve">terræ 2729. </s> <s xml:id="echoid-s13282" xml:space="preserve">quare eadem demonſtratione, & </s> <s xml:id="echoid-s13283" xml:space="preserve">figuratione, qua in vmbra terræ vſi ſumus, hunc accom-<lb/>modata, erit vmbra Martis maximè diſtantis à Sole, longa ſemid. </s> <s xml:id="echoid-s13284" xml:space="preserve">terræ 147. </s> <s xml:id="echoid-s13285" xml:space="preserve">vnde licebit cognoſcere an poſ-<lb/>ſit eclypſ are quempiam planetarum, cum planetarum diſtantiæ à Sole, pariter ſint cognitæ. </s> <s xml:id="echoid-s13286" xml:space="preserve">quod ad ſenſum <lb/>in figura magna, & </s> <s xml:id="echoid-s13287" xml:space="preserve">vera apparebit. </s> <s xml:id="echoid-s13288" xml:space="preserve">Mercurium, & </s> <s xml:id="echoid-s13289" xml:space="preserve">Venerem nequit eclypſare quia ipſi ſunt Soli viciniores, <lb/>quam Mars, vmbra autem Martis proijcitur ad partes Solis auerſas. </s> <s xml:id="echoid-s13290" xml:space="preserve">Neque eclipſare Iouem poterit, quia <lb/>minima diſtantia Iouis à Sole eſt ferè 2046. </s> <s xml:id="echoid-s13291" xml:space="preserve">at vero apex vmbrę Martis non protenditur à Sole pluſquã 1775.</s> <s xml:id="echoid-s13292" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div301" type="section" level="1" n="208"> <head xml:id="echoid-head222" style="it" xml:space="preserve">Magnitudo Stellæ Martis. Cap. V.</head> <p> <s xml:id="echoid-s13293" xml:space="preserve">MEdio cris eius à terra remotio eſt ex Tychone 1745. </s> <s xml:id="echoid-s13294" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s13295" xml:space="preserve">terræ. </s> <s xml:id="echoid-s13296" xml:space="preserve">in qua remotione exhibet apparen-<lb/>tem diametrum quaſi 2′. </s> <s xml:id="echoid-s13297" xml:space="preserve">min. </s> <s xml:id="echoid-s13298" xml:space="preserve">Quemadmodum igitur in alijs factum eſt, ſiue practicè per triangulum <lb/>Iſoſceles, cuius baſis ſubtedat angulum 2′. </s> <s xml:id="echoid-s13299" xml:space="preserve">min. </s> <s xml:id="echoid-s13300" xml:space="preserve">ſiue alijs modis ſupra adhibitis, inueniemus proportionem <lb/>eius diametri ad diametrum terræ, eſſe ferè eandem, quæ eſt inter 25. </s> <s xml:id="echoid-s13301" xml:space="preserve">& </s> <s xml:id="echoid-s13302" xml:space="preserve">60. </s> <s xml:id="echoid-s13303" xml:space="preserve">vnde, diameter Martis conti-<lb/>netur in diametro terræ bis cum duabus Quintis. </s> <s xml:id="echoid-s13304" xml:space="preserve">Hinc ſphærarum quoque proportio emerget, eritque vt 1. <lb/></s> <s xml:id="echoid-s13305" xml:space="preserve">ad 13. </s> <s xml:id="echoid-s13306" xml:space="preserve">circiter. </s> <s xml:id="echoid-s13307" xml:space="preserve">tredecies igitur Mars à tetra continetur. </s> <s xml:id="echoid-s13308" xml:space="preserve">Porrò quoniam Luna quadragies, Mercurus vicies, <lb/>Venus ſex ies, Mars vero tredicies in terra continetur: </s> <s xml:id="echoid-s13309" xml:space="preserve">Terra vero a Sole centies, & </s> <s xml:id="echoid-s13310" xml:space="preserve">quadragies: </s> <s xml:id="echoid-s13311" xml:space="preserve">erit Mars <lb/>paulo plus quaum triplus ad Lunam, & </s> <s xml:id="echoid-s13312" xml:space="preserve">pluſquam duplus ad Mercurium, & </s> <s xml:id="echoid-s13313" xml:space="preserve">paulo minus quam ſubduplus ad <lb/>Venerem: </s> <s xml:id="echoid-s13314" xml:space="preserve">ad Solem tandem vt 1. </s> <s xml:id="echoid-s13315" xml:space="preserve">ad 1820.</s> <s xml:id="echoid-s13316" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div302" type="section" level="1" n="209"> <head xml:id="echoid-head223" style="it" xml:space="preserve">Appendix de calculo Martis. Cap. VI.</head> <p> <s xml:id="echoid-s13317" xml:space="preserve">DVos tantummodo motus Martis ad calculum redigemus: </s> <s xml:id="echoid-s13318" xml:space="preserve">quorum primus erit medius eius motus in <lb/>long itudinem, ſeu motus centri epicycli in longitudinem, ſeu in conſenſequentia ſignorum; </s> <s xml:id="echoid-s13319" xml:space="preserve">qui mo-<lb/>tus nobis numeratur ſeu incipit ab æquinoctio veino: </s> <s xml:id="echoid-s13320" xml:space="preserve">pro quo damus ſequentem tabulam, quæ facilè ex ta-<lb/>bulis iam præmiſſis intelligi poteſt.</s> <s xml:id="echoid-s13321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13322" xml:space="preserve">Alter motus, quem calculo ſubijciemus, eſt motus anomaliæ, ſiue aſtri ipſius in epicyclo, cuius numeratio <lb/>iucipit ab apogæo epicycli vt in alijs pro quo nulla indigemus tabula, eam enim ſupplet admirabilis huius <lb/>motus ad motum Solis connexio, & </s> <s xml:id="echoid-s13323" xml:space="preserve">dependentia, quam ſupra explicauimus. </s> <s xml:id="echoid-s13324" xml:space="preserve">Ex calculo autem horum duo-<lb/>rum motuum habebimus ad datum tempus locum Aſtri Martialis in Zodiaco, qui eſt calculi finis.</s> <s xml:id="echoid-s13325" xml:space="preserve"/> </p> <figure> <image file="0167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0167-01"/> </figure> <pb o="146" file="0168" n="173" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div303" type="section" level="1" n="210"> <head xml:id="echoid-head224" style="it" xml:space="preserve">Tabula medij<unsure/> motus Mart. in longitudinem.</head> <note position="right" xml:space="preserve"> <lb/>##### In Annis ſingu@@s. #### In menſib. compl. An. cõis. ### In die@@s. <lb/># Anni. # Sig. # Gr<unsure/>a. # # # Sig. # Gra. # # Dies # Sig. # Gra. <lb/># 1 # 6 # 11 # # Ian. # 0 # 16 # # 1 # 0 # 31 <lb/># 2 # 0 # 22 # # Febr. # 1 # 1 # # 2 # 1 # 3 <lb/>B # 3 # 7 # 4 # # Mart. # 1 # 17 # # 3 # 1 # 34 <lb/># 4 # 1 # 16 # # Apr. # 2 # 3 <lb/># # # # # # # # # 4 # 2 # 6 <lb/># 5 # 7 # 27 # # Mai. # 2 # 19 # # 5 # 1 # 37 <lb/># 6 # 2 # 8 # # Iun. # 3 # 5 # # 6 # 3 # 9 <lb/>B # 7 # 8 # 19 # # Iul. # 3 # 21 <lb/># 8 # 3 # 1 # # Aug. # 4 # 7 # # 7 # 3 # 40 <lb/># # # # # # # # # 8 # 4 # 21 <lb/># 9 # 9 # 12 # # Sept. # 4 # 23 # # 9 # 4 # 43 <lb/># 10 # 3 # 24 # # Oct. # 5 # 9 # # 10 # 5 # 14 <lb/>B. # 11 # 10 # 5 # # Nou. # 5 # 25 <lb/># 12 # 4 # 17 # # Dec. # 6 # 11 # # 11 # 5 # 46 <lb/># # # # # # # # # 12 # 6 # 17 <lb/># 13 # 10 # 28 # # # # # # 13 # 6 # 49 <lb/># 14 # 5 # 9 # #### In menſibus An@. Biſſext. # 13 # 7 # 20 <lb/>B # 15 # 11 # 21 <lb/># 16 # 6 # 2 # # Ian. # 0 # 16 # # 15 # 7 # 52 <lb/># # # # # Febr. # 0 # 1 # # 110 # 8 # 23 <lb/># 17 # 0 # 14 # # Mart. # 0 # 18 # # 17 # 8 # 50 <lb/># 18 # 6 # 25 # # Apri. # 1 # 3 # # 18 # 9 # 26 <lb/>B # 19 # 1 # 6 <lb/># 20 # 7 # 18 # # Mai. # 2 # 20 # # 19 # 9 # 75 <lb/># # # # # Iun. # 3 # 5 # # 20 # 10 # 29 <lb/># # # # # Iulius # 3 # 22 # # 21 # 11 # 0 <lb/># 40 # 3 # 6 # # Ang. # 4 # 8 # # 22 # 11 # 32 <lb/>In # 60 # 10 # 24 <lb/># 80 # 6 # 12 # # Sept. # 4 # 24 # # 23 # 12 # 3 <lb/># 100 # 2 # 0 # # Octo. # 5 # 10 # # 24 # 12 # 35 <lb/># # # # # Nou. # 5 # 26 # # 25 # 13 # 6 <lb/># 200 # 4 # 1 # # Dec. # 6 # 12 # # 26 # 13 # 37 <lb/>Annis # 300 # 6 # 1 <lb/># 400 # 8 # 1 # # # # # # 27 # 14 # 9 <lb/># 500 # 10 # 1 # # # # # # 28 # 14 # 40 <lb/># # # # # # # # # 29 # 15 # 12 <lb/>aggregatis. # 600 # 0 # 2 # # # # # # 30 # 15 # 43 <lb/># 700 # 2 # 2 # # # # # # 31 # 16 # 15 <lb/># 800 # 4 # 2 <lb/># 900 # 6 # 3 <lb/># 1000 # 8 # 3 <lb/># Rad x # Sig. # Gra. <lb/>Rad. # 1600 # 10 # 1 <lb/></note> <pb o="147" file="0169" n="174" rhead="Liber Decimustertius."/> </div> <div xml:id="echoid-div304" type="section" level="1" n="211"> <head xml:id="echoid-head225" style="it" xml:space="preserve">Constructio, & vſus Tabulæ præcedentis.</head> <p> <s xml:id="echoid-s13326" xml:space="preserve">CVm igitur ad datum tempus, quærendus eſt locus Martis in Zodiaco debemus, accommodato prius <lb/>tempore vulgari ad vſum Aſtronomicum, vt alias docuimus; </s> <s xml:id="echoid-s13327" xml:space="preserve">accipere per ſingulas temporis ſpecies <lb/>motus medios eis reſpondentes ex præſenti Tabula; </s> <s xml:id="echoid-s13328" xml:space="preserve">necnon motum Radicis, eoſque motus in ſummam <lb/>vnam colligere. </s> <s xml:id="echoid-s13329" xml:space="preserve">Hæc enim dabit motum longitudinis Martis, ideſt, diſtantiam centri epicycl<unsure/>i ab æquino-<lb/>ctio, ſeu locum eius in Zodiaco qui etiam dicitur medius motus Martis. </s> <s xml:id="echoid-s13330" xml:space="preserve">Secundo oportet habere Solis lo-<lb/>cum in Zodiaco ad idem tempus datum, ſiue ex calculo, ſiue aliunde. </s> <s xml:id="echoid-s13331" xml:space="preserve">Tertio detra r<unsure/>endus eſt motus Mar-<lb/>tis iam inuentus, ex motu Solis inuento, reſiduus enim motus, cui eſt diſtantia Solis a centro epicycli, eſt <lb/>etiam ſimul diſtantia Martis ab apogæo epicycli. </s> <s xml:id="echoid-s13332" xml:space="preserve">vti ſuperius dictunr<unsure/> eſt; </s> <s xml:id="echoid-s13333" xml:space="preserve">quare abſque alio calculo ſic ha-<lb/>bebimus motum anomaliæ Martis. </s> <s xml:id="echoid-s13334" xml:space="preserve">vnde cognoſcitur locus eius in peripheria epicycli. </s> <s xml:id="echoid-s13335" xml:space="preserve">ex quo locum eius <lb/>in Zodiaco plus minus conijcere licebit. </s> <s xml:id="echoid-s13336" xml:space="preserve">non enim hic exactum calculum intendimus, ſed eum, qui nobis <lb/>tantummodo locum Martis in cælo aliquo modo demonſtret, vnde ſydus ipſum noctu cognoſcere valea-<lb/>mus. </s> <s xml:id="echoid-s13337" xml:space="preserve">Exemplo res fiet illuſtrior: </s> <s xml:id="echoid-s13338" xml:space="preserve">ſit ad Meridianum Venetum, data hora prima noctis diei 23. </s> <s xml:id="echoid-s13339" xml:space="preserve">Decem-<lb/>bris anni 1616. </s> <s xml:id="echoid-s13340" xml:space="preserve">qua hæc ſcribo, quæ eſt hora prima noctis quæ præcedit vigiliam Natiuitatis Domini. </s> <s xml:id="echoid-s13341" xml:space="preserve">hac <lb/>igitur hora abſoluta ſcire libeat locum Martis in Zodiaco. </s> <s xml:id="echoid-s13342" xml:space="preserve">tempus datum Aſtronomicè accommodatum <lb/>fic ſe habet.</s> <s xml:id="echoid-s13343" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. <lb/>Anni radicis 1600. # 10 # 1 <lb/>Anni completi 15. # 11 # 21 <lb/>Menſis Nouembris Biſſext. # 5 # 26 <lb/>Dies 23. completi in me- # 0 # 12 # ridie diei 23. ciuilis. <lb/>Horæ 5 {1/2} # 0 # 0. <lb/>Summa # 4 # 0 # in fine Cancri ♋. <lb/></note> <p> <s xml:id="echoid-s13344" xml:space="preserve">Primo igitur pro annis 1600. </s> <s xml:id="echoid-s13345" xml:space="preserve">accipio ex Tabula. </s> <s xml:id="echoid-s13346" xml:space="preserve">Radicem ſigna 10. </s> <s xml:id="echoid-s13347" xml:space="preserve">grad. </s> <s xml:id="echoid-s13348" xml:space="preserve">1. </s> <s xml:id="echoid-s13349" xml:space="preserve">quam eis in directum ſcribo. <lb/></s> <s xml:id="echoid-s13350" xml:space="preserve">idem racio pro annis 15. </s> <s xml:id="echoid-s13351" xml:space="preserve">compietis, &</s> <s xml:id="echoid-s13352" xml:space="preserve">c. </s> <s xml:id="echoid-s13353" xml:space="preserve">vt apparet in ſormul<unsure/>a: </s> <s xml:id="echoid-s13354" xml:space="preserve">quorum motuum ſumma eſt ſigna 4. </s> <s xml:id="echoid-s13355" xml:space="preserve">tantum. </s> <s xml:id="echoid-s13356" xml:space="preserve"><lb/>vnde colligitur centrum epicycli nunc diſtare ſignis 4. </s> <s xml:id="echoid-s13357" xml:space="preserve">ab æquinoctio verno, ideſt, eſſe in principio Leonis. </s> <s xml:id="echoid-s13358" xml:space="preserve"><lb/>omiſiæ ſunt horæ in hac calculatione, quod parum diſ<unsure/>criminis i<unsure/>nferant. </s> <s xml:id="echoid-s13359" xml:space="preserve">Secundo habeatur locus Solis in <lb/>Zodiaco, eſt autem nunc in primo gradu Capricorni: </s> <s xml:id="echoid-s13360" xml:space="preserve">quare motus ei<unsure/>us eſt ſig. </s> <s xml:id="echoid-s13361" xml:space="preserve">9. </s> <s xml:id="echoid-s13362" xml:space="preserve">grad. </s> <s xml:id="echoid-s13363" xml:space="preserve">1. </s> <s xml:id="echoid-s13364" xml:space="preserve">a quo fi dematur <lb/>motus Martis præd ctus, remanet eorum diſtantia ſignorum 5. </s> <s xml:id="echoid-s13365" xml:space="preserve">grad. </s> <s xml:id="echoid-s13366" xml:space="preserve">1. </s> <s xml:id="echoid-s13367" xml:space="preserve">quæ diſtantia æqualis eſt anomaliæ, <lb/>ideſt, totidem ſignis, & </s> <s xml:id="echoid-s13368" xml:space="preserve">grad. </s> <s xml:id="echoid-s13369" xml:space="preserve">diſtat ſtella Martis ab apogæo ſui epicycli. </s> <s xml:id="echoid-s13370" xml:space="preserve">vnde colligitur Martem eſſe in <lb/>ſemicirculo orie@tali epicycli: </s> <s xml:id="echoid-s13371" xml:space="preserve">diſtareque ab apogæo ſignis 5. </s> <s xml:id="echoid-s13372" xml:space="preserve">Ex quious locum eius in Zodiaco ſic abſque <lb/>Tabula æquati<unsure/>onum venabimur. </s> <s xml:id="echoid-s13373" xml:space="preserve">Sciendum enim eſt, tantam eſſe epicycli Martis amplitudinem, vt quan-<lb/>do terris fit propinquior, eius ſemidiameter ſubtendat in cælo grad. </s> <s xml:id="echoid-s13374" xml:space="preserve">rerè 47. </s> <s xml:id="echoid-s13375" xml:space="preserve">quando autem remotior eſt <lb/>ſubtendat grad. </s> <s xml:id="echoid-s13376" xml:space="preserve">37 tunc autem terris propior eſt, cum Sol<unsure/>i magis opponitur; </s> <s xml:id="echoid-s13377" xml:space="preserve">tunc ſubdimior, cum Solem <lb/>magis accedit. </s> <s xml:id="echoid-s13378" xml:space="preserve">nunc autem cum diſtet a Sole ſignis 5. </s> <s xml:id="echoid-s13379" xml:space="preserve">grad. </s> <s xml:id="echoid-s13380" xml:space="preserve">1. </s> <s xml:id="echoid-s13381" xml:space="preserve">ſequitur ei ferè opponi, ac proinde ſubtende-<lb/>re in cælo gradus paulo pauciores, quam<unsure/> 47. </s> <s xml:id="echoid-s13382" xml:space="preserve">præterea notandum Martem tunc maximè diſtare a centro epi-<lb/>cycli, ſecundum longitudinem Zodiaci, quando diſtat ab apogæo epicycli ſignis 4. </s> <s xml:id="echoid-s13383" xml:space="preserve">cum partibus 17. </s> <s xml:id="echoid-s13384" xml:space="preserve">cum <lb/>igitur nunc anomalia ſit ſig. </s> <s xml:id="echoid-s13385" xml:space="preserve">5. </s> <s xml:id="echoid-s13386" xml:space="preserve">ſequi<unsure/>tur Martem minus diſtare a centro epicycli<unsure/> quam grad<unsure/>. </s> <s xml:id="echoid-s13387" xml:space="preserve">47. </s> <s xml:id="echoid-s13388" xml:space="preserve">conſideran-<lb/>dum etiam Martem in apogæo, & </s> <s xml:id="echoid-s13389" xml:space="preserve">perigæo epicycli nihil diſtare a centro epicycli, quare cum maxim<unsure/> è di-<lb/>ſtet, quando diſtatab apogæo vtrinque ſigni<unsure/>s 4. </s> <s xml:id="echoid-s13390" xml:space="preserve">grad. </s> <s xml:id="echoid-s13391" xml:space="preserve">17. </s> <s xml:id="echoid-s13392" xml:space="preserve">nunc autem diſtat a perigæo vnico ſigno licet exi-<lb/>ſtimare eum diſtare a centro epicycli veri<unsure/>us orientem circit<unsure/>er grad. </s> <s xml:id="echoid-s13393" xml:space="preserve">38. </s> <s xml:id="echoid-s13394" xml:space="preserve">centrum autem epicycli erat in prin-<lb/>cipio Leonis; </s> <s xml:id="echoid-s13395" xml:space="preserve">quare Mars ipſe erit circa grad. </s> <s xml:id="echoid-s13396" xml:space="preserve">8. </s> <s xml:id="echoid-s13397" xml:space="preserve">Virginis. </s> <s xml:id="echoid-s13398" xml:space="preserve">eadem intelligas de altero ſemicirculo epicy-<lb/>cli occi<unsure/>dentali, in quo planeta diſtat a centro epicycli verſus occidentem. </s> <s xml:id="echoid-s13399" xml:space="preserve">eſt autem ſtella Martis rubi<unsure/>cun-<lb/>da, magnaque apparebat, cum eſſet perigæa in epicyclo, & </s> <s xml:id="echoid-s13400" xml:space="preserve">oppoſita Soli, quare eam facile dignoſcebam.</s> <s xml:id="echoid-s13401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13402" xml:space="preserve">Verum hoc loco mouendus eſt mini Lector, pro exactiori, ac facillimo Solis, ac Martis calculo, D. </s> <s xml:id="echoid-s13403" xml:space="preserve">Cæ-<lb/>ſarem Marſilium patricium Bononienſem, nobiliſſimum æquè, ac doctiſſimum, rerumq; </s> <s xml:id="echoid-s13404" xml:space="preserve">præci<unsure/>puè Aſtro-<lb/>non@icarum peritiſ<unsure/>ſ<unsure/>i<unsure/>mum; </s> <s xml:id="echoid-s13405" xml:space="preserve">propediem nouas, quæ iam ſub prælo ſunt, labulas editurum.</s> <s xml:id="echoid-s13406" xml:space="preserve"/> </p> <pb o="148" file="0170" n="175" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div305" type="section" level="1" n="212"> <head xml:id="echoid-head226" xml:space="preserve">LIBER DECIMVSQVARTVS <lb/>DE IOVE.</head> <head xml:id="echoid-head227" style="it" xml:space="preserve">Locus, ſeu diſtantia Iouis à terra. Cap. I.</head> <p> <s xml:id="echoid-s13407" xml:space="preserve">SVpra Martis reuolutiones, communis Aſtronomorũ ſententia, Iouis circulationes ſtatuit. </s> <s xml:id="echoid-s13408" xml:space="preserve">Primo quia in <lb/>mutuis eorum Synodis ſydus Martis occultat ſydus Iouis; </s> <s xml:id="echoid-s13409" xml:space="preserve">quod euincit Ioue<unsure/>m ſupra Martem incedere. <lb/></s> <s xml:id="echoid-s13410" xml:space="preserve">Eadem ratione ipſe Iupiter infra Saturnum collocatur. </s> <s xml:id="echoid-s13411" xml:space="preserve">Secundo Iupiter minorem exhibet parallaxim, <lb/>quam Mars; </s> <s xml:id="echoid-s13412" xml:space="preserve">maiorem vero quam Saturnus, ex Tychone: </s> <s xml:id="echoid-s13413" xml:space="preserve">igitur medius intra eos reſidebit. </s> <s xml:id="echoid-s13414" xml:space="preserve">Tertio ex motuũ <lb/>velocitate idem conijcitur, eſt enim Marte velocior, Saturno vero tardior; </s> <s xml:id="echoid-s13415" xml:space="preserve">medius igitur ei locus conceda-<lb/>tur. </s> <s xml:id="echoid-s13416" xml:space="preserve">diſtantiam vero Iouis a terra mediocrem, ex Tychone, pono eſſe ſemid. </s> <s xml:id="echoid-s13417" xml:space="preserve">terrę 3990. </s> <s xml:id="echoid-s13418" xml:space="preserve">quam ipſe ex deprę-<lb/>henſa accuratè eius parallaxi, deduxit. </s> <s xml:id="echoid-s13419" xml:space="preserve">ſed alio modo, & </s> <s xml:id="echoid-s13420" xml:space="preserve">quidem peracuto, quem nuper Pater Chriſtophorus <lb/>Scheiner in ſuis Mathem. </s> <s xml:id="echoid-s13421" xml:space="preserve">diſquiſitionibus expoſuit, diſtantia huius planetæ à terra inueſtigari poteſt: </s> <s xml:id="echoid-s13422" xml:space="preserve">qui <lb/>modus nititur motibus ſatellitum Iouis, quos ope Teleſcopij acutiſſimus Galilæus omnium primus mundo <lb/>reuelauit, vt ſuo loco dicetur. </s> <s xml:id="echoid-s13423" xml:space="preserve">ſunt autem quatuor paruæ ſtellulæ, quæ perpetuo circa Iouem circumferun-<lb/>tur, eo modo quo Mercurius, & </s> <s xml:id="echoid-s13424" xml:space="preserve">Venus circa Solem. </s> <s xml:id="echoid-s13425" xml:space="preserve">Verum præſens figura inſpiciatur, in qua ſidus A. </s> <s xml:id="echoid-s13426" xml:space="preserve">ſit <lb/> <anchor type="figure" xlink:label="fig-0170-01a" xlink:href="fig-0170-01"/> Iupiter. </s> <s xml:id="echoid-s13427" xml:space="preserve">B, Terra. </s> <s xml:id="echoid-s13428" xml:space="preserve">C, Sol iam demerſus: </s> <s xml:id="echoid-s13429" xml:space="preserve">fiat igitur trigonum <lb/>A B C, cuius latus A B, referat diſtantiam Iouis a terra, cuius <lb/>quantitas indaganda proponitur. </s> <s xml:id="echoid-s13430" xml:space="preserve">circelli 4. </s> <s xml:id="echoid-s13431" xml:space="preserve">circa Iouem de-<lb/>ſcripti, ſunt ij, quos eius comites N G D K. </s> <s xml:id="echoid-s13432" xml:space="preserve">circa eum deſcri-<lb/>bunt, quorum Ioui propinquior D S L F. </s> <s xml:id="echoid-s13433" xml:space="preserve">percurritur a ſtella <lb/>D, quam nunc aſſumimus. </s> <s xml:id="echoid-s13434" xml:space="preserve">conus A Y, niger, eſt vmbra Iouis <lb/>quam ipſius hi comites manifeſtam reddiderunt, dum in ea <lb/>(non ſecus ac Luna in vmbra terræ) latitantes, ſuos quandoq; <lb/></s> <s xml:id="echoid-s13435" xml:space="preserve">inſpectores deludunt. </s> <s xml:id="echoid-s13436" xml:space="preserve">Prænotandũ etiam eſt ſtellam ſeu pla-<lb/>netam D, ſuam circa louẽ reuolutionem abſoluere hor. </s> <s xml:id="echoid-s13437" xml:space="preserve">42 {1/2}. </s> <s xml:id="echoid-s13438" xml:space="preserve"><lb/>eundemq; </s> <s xml:id="echoid-s13439" xml:space="preserve">bis ſupra Iouem latere; </s> <s xml:id="echoid-s13440" xml:space="preserve">latet enim primo directè <lb/>ſupra Iouem apud S, ob Iouis interpoſitionem, & </s> <s xml:id="echoid-s13441" xml:space="preserve">fulgorem. </s> <s xml:id="echoid-s13442" xml:space="preserve"><lb/>ſecũdo quando in vmbram propè V, incurrit. </s> <s xml:id="echoid-s13443" xml:space="preserve">oportet igitur <lb/>diligenter obſeruare tẽpus quod à prima latebra S, ad ſecun-<lb/>dam V, intercedit. </s> <s xml:id="echoid-s13444" xml:space="preserve">quo tempore conficit arcum S V, ex noti-<lb/>tia enim huius temporis innoteſcet arcus S V, & </s> <s xml:id="echoid-s13445" xml:space="preserve">conſequen-<lb/>ter angulus S A V, ei inſiſtens; </s> <s xml:id="echoid-s13446" xml:space="preserve">hoc modo; </s> <s xml:id="echoid-s13447" xml:space="preserve">ponamus tempus <lb/>illud ex obſeruatione depræhenſum, duarum eſſe horarum; </s> <s xml:id="echoid-s13448" xml:space="preserve"><lb/>iam ſic per auream Arithm. </s> <s xml:id="echoid-s13449" xml:space="preserve">regulam ratiocinandũ eſt; </s> <s xml:id="echoid-s13450" xml:space="preserve">ſi hor. </s> <s xml:id="echoid-s13451" xml:space="preserve"><lb/>42 {1/2}. </s> <s xml:id="echoid-s13452" xml:space="preserve">ſtella D, perficit totum gyrum, ſeu gr. </s> <s xml:id="echoid-s13453" xml:space="preserve">360. </s> <s xml:id="echoid-s13454" xml:space="preserve">duabus horis <lb/>quot gradus percurret, inueniemus gr. </s> <s xml:id="echoid-s13455" xml:space="preserve">17 {1/7}. </s> <s xml:id="echoid-s13456" xml:space="preserve">ergo arcus S V, & </s> <s xml:id="echoid-s13457" xml:space="preserve"><lb/>proinde angulus S A V, erit totidem graduum; </s> <s xml:id="echoid-s13458" xml:space="preserve">quare & </s> <s xml:id="echoid-s13459" xml:space="preserve">an-<lb/>gulus B A C, ei ad verticem, & </s> <s xml:id="echoid-s13460" xml:space="preserve">æqualis per 15. </s> <s xml:id="echoid-s13461" xml:space="preserve">primi, erit pa-<lb/>riter gr. </s> <s xml:id="echoid-s13462" xml:space="preserve">17 {1/7}. </s> <s xml:id="echoid-s13463" xml:space="preserve">eſt autem angulus trianguli B A B, ſed angulus <lb/>quoque B, cognoſcitur, continet enim diſtantiam inter Io-<lb/>uem, & </s> <s xml:id="echoid-s13464" xml:space="preserve">Solem in Zodiaco, quã refert arcus R Q C, ex B, de-<lb/>ſcriptus; </s> <s xml:id="echoid-s13465" xml:space="preserve">quem Aſtronomos tum ex obſeruatione, tum ex cal-<lb/>culo cognoſcere poſſe certum eſt. </s> <s xml:id="echoid-s13466" xml:space="preserve">Latus præterea B C, cum <lb/>ſit diſtantia Solis à terra, notum eſt. </s> <s xml:id="echoid-s13467" xml:space="preserve">Cum igitur in hoc triangulo A B C, noti ſunt duo anguli cum vno late-<lb/>re, patet ex Apparatu noſtro, nos poſſe cognoſcere laterũ proportiones. </s> <s xml:id="echoid-s13468" xml:space="preserve">quare non latebit quoties latus B C, <lb/>notum, contineatur in B A, vnde nota euadet B A, diſtantia Iouis a terra, quod erat inquirendum. </s> <s xml:id="echoid-s13469" xml:space="preserve">Verum <lb/>opus eſt pluribus accuratiſq; </s> <s xml:id="echoid-s13470" xml:space="preserve">obſeruationibus, ijſque optimo Teleſcopio peractis.</s> <s xml:id="echoid-s13471" xml:space="preserve"/> </p> <div xml:id="echoid-div305" type="float" level="2" n="1"> <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a"> <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-01"/> </figure> </div> </div> <div xml:id="echoid-div307" type="section" level="1" n="213"> <head xml:id="echoid-head228" style="it" xml:space="preserve">Motus Iouis. Cap. II.</head> <p> <s xml:id="echoid-s13472" xml:space="preserve">VT Aſtronomi obſeruationes, quam in motibus Iouis habuerunt, ſaluare poſſent, ſuppoſuerunt gyrum, <lb/>ſiue regionem eius, eſſe centro mundi eccentricam; </s> <s xml:id="echoid-s13473" xml:space="preserve">ſed habere pro centro Solem, quemadmodũ etiam <lb/>Mars; </s> <s xml:id="echoid-s13474" xml:space="preserve">quare eandem figuram, quam pro Marte conſtruximus, nũc Ioui applicare poſſumus, variatis tantum-<lb/>modo diſtantijs, & </s> <s xml:id="echoid-s13475" xml:space="preserve">magnitudinibus. </s> <s xml:id="echoid-s13476" xml:space="preserve">Ea igitur nunc repetatur, in qua epicyclus, & </s> <s xml:id="echoid-s13477" xml:space="preserve">eccentricus modi Ioui in-<lb/>ſeruiant. </s> <s xml:id="echoid-s13478" xml:space="preserve">linea igitur T M, quæ refert mediocrem planetæ diſtantiam a terra, continebit nunc ſemid. </s> <s xml:id="echoid-s13479" xml:space="preserve">terræ <lb/>3990. </s> <s xml:id="echoid-s13480" xml:space="preserve">linea vero T P, multo longior quã in Marte erit; </s> <s xml:id="echoid-s13481" xml:space="preserve">quippe quod Iupiter non deſcendat intra Solis regio-<lb/>nem, quanta autem ſit, non definio. </s> <s xml:id="echoid-s13482" xml:space="preserve">debet tamen eſſe breuior, quam T M, ideſt, cont@nere pauciores ſemid. <lb/></s> <s xml:id="echoid-s13483" xml:space="preserve">quam 3990. </s> <s xml:id="echoid-s13484" xml:space="preserve">linea autem T E A, quæ maximam, & </s> <s xml:id="echoid-s13485" xml:space="preserve">apogæam remotionem planetę refert, maior quidem erit <pb o="149" file="0171" n="176" rhead="Liber Decimusquartus."/> quam ſemid. </s> <s xml:id="echoid-s13486" xml:space="preserve">terræ 3990. </s> <s xml:id="echoid-s13487" xml:space="preserve">veruntamen quanta ſit nihil certi aſſero. </s> <s xml:id="echoid-s13488" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s13489" xml:space="preserve">vero epicycli in minima diſtantia. <lb/></s> <s xml:id="echoid-s13490" xml:space="preserve">ubtendit arcum gr. </s> <s xml:id="echoid-s13491" xml:space="preserve">11 {1/2}. </s> <s xml:id="echoid-s13492" xml:space="preserve">in Zodiaco, dum a nobis è terra obſeruatur; </s> <s xml:id="echoid-s13493" xml:space="preserve">in maxima autem ſubtendit gr. </s> <s xml:id="echoid-s13494" xml:space="preserve">10 {1/2}. </s> <s xml:id="echoid-s13495" xml:space="preserve">qui-<lb/>bus ſic poſitis eius circulationes concipiendæ ſunt, hoc ordine primo ipſum Iouis aſtrum in peripheria epi-<lb/>cycli circa centrum epicycli eodem modo ac Martis aſtrum reuoluitur: </s> <s xml:id="echoid-s13496" xml:space="preserve">nam mirabili ad Solem analogia ita <lb/>circumcurrit, vt cum ei Sol coniungitur, ſeu cum Sol eum in Zodiaco aſſequitur, tunc planeta epicycli apo-<lb/>gæum A, obſideat; </s> <s xml:id="echoid-s13497" xml:space="preserve">poſtea Sole eum prætereunte planeta proportionaliter in epicyclo deſcendit verſus C, <lb/>cumq; </s> <s xml:id="echoid-s13498" xml:space="preserve">Sol ei è diametro aduerſatur, ipſe iam in perigæum epicycli M, delapſus fuerit. </s> <s xml:id="echoid-s13499" xml:space="preserve">inde ſcandens alterũ <lb/>epicycli ſemicirculum, erit iterum in noua cũ ſole coniunctione in apogæo A. </s> <s xml:id="echoid-s13500" xml:space="preserve">hic pariter motus dicitur ano-<lb/>malia, eadem de cauſa qua in alijs. </s> <s xml:id="echoid-s13501" xml:space="preserve">eiuſq; </s> <s xml:id="echoid-s13502" xml:space="preserve">numeratio incipit ab apogæo A, diarius eius motus eſt min. </s> <s xml:id="echoid-s13503" xml:space="preserve">54′. </s> <s xml:id="echoid-s13504" xml:space="preserve">an-<lb/>nuus ſig. </s> <s xml:id="echoid-s13505" xml:space="preserve">10. </s> <s xml:id="echoid-s13506" xml:space="preserve">gr. </s> <s xml:id="echoid-s13507" xml:space="preserve">20. </s> <s xml:id="echoid-s13508" xml:space="preserve">quare totum epicyclum percurrit anno vno ſimplici, cum diebus 33. </s> <s xml:id="echoid-s13509" xml:space="preserve">hor. </s> <s xml:id="echoid-s13510" xml:space="preserve">21. </s> <s xml:id="echoid-s13511" xml:space="preserve">Porrò du<unsure/> pla-<lb/>neta hunc epicycli gyrum terit, interim centrum E, epicycli transfertur ſecundum Zodiaci longitudinem <lb/>ſeu in conſequentia, qui dicitur motus longitudinis, incipitq; </s> <s xml:id="echoid-s13512" xml:space="preserve">eius numeratio ab initio Arietis, ſeu ab æqui-<lb/>noctio verno. </s> <s xml:id="echoid-s13513" xml:space="preserve">moueturq; </s> <s xml:id="echoid-s13514" xml:space="preserve">in eo quotidie motu medio min′<unsure/>. </s> <s xml:id="echoid-s13515" xml:space="preserve">59″. </s> <s xml:id="echoid-s13516" xml:space="preserve">in anno vero gr. </s> <s xml:id="echoid-s13517" xml:space="preserve">30. </s> <s xml:id="echoid-s13518" xml:space="preserve">19′. </s> <s xml:id="echoid-s13519" xml:space="preserve">41″. </s> <s xml:id="echoid-s13520" xml:space="preserve">quaretotũ Zo-<lb/>diacum recurritannis vndecim Aegyptijs, diebus 214. </s> <s xml:id="echoid-s13521" xml:space="preserve">hor. </s> <s xml:id="echoid-s13522" xml:space="preserve">21. </s> <s xml:id="echoid-s13523" xml:space="preserve">hic autem planetæ motus in longitudinem, re <lb/>ipſa inæqualis eſt, ob motum anomaliæ; </s> <s xml:id="echoid-s13524" xml:space="preserve">quia vt in alijs, ob hanc anomaliam planeta ſit directus, ſtationarius, <lb/>retrogradus; </s> <s xml:id="echoid-s13525" xml:space="preserve">vnde neceſſe eſt eum in Zodlaco inęqualiter progredi. </s> <s xml:id="echoid-s13526" xml:space="preserve">imo reliquas Martis affectiones recipit, <lb/>ideſt, eoſdem aſpectus, tum ad ſolem, tum ad alia ſydera. </s> <s xml:id="echoid-s13527" xml:space="preserve">item eoſdem ortus, & </s> <s xml:id="echoid-s13528" xml:space="preserve">occaſus: </s> <s xml:id="echoid-s13529" xml:space="preserve">ſunt enm hi tres ſu-<lb/>periores planetæ inuicem perſimiles. </s> <s xml:id="echoid-s13530" xml:space="preserve">tandem ex motus anomaliæ cum motu longitudinis connexione, fit vt <lb/>lupiter deſcribat aliam figuram ſpiralem ſimilem, ei quam pro Marte deſcripſimus cap. </s> <s xml:id="echoid-s13531" xml:space="preserve">de Motu, eodemq; </s> <s xml:id="echoid-s13532" xml:space="preserve"><lb/>modo explicari debet: </s> <s xml:id="echoid-s13533" xml:space="preserve">quamuis autem ei ſit ſimilis, ab ea tamen differt hæc, quia lineas ſpirales plures habe-<lb/>bit; </s> <s xml:id="echoid-s13534" xml:space="preserve">citius enim in anno ſupiter anomaliam abſoluit, quam Mars.</s> <s xml:id="echoid-s13535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13536" xml:space="preserve">Amplius planeta in latitudinem mouetur; </s> <s xml:id="echoid-s13537" xml:space="preserve">non enim ſub ecliptica alij planetæ præter ſolem incedunt, ſed <lb/>huc illuc in Boream, & </s> <s xml:id="echoid-s13538" xml:space="preserve">Auſtrum ab ea ex currunt: </s> <s xml:id="echoid-s13539" xml:space="preserve">quæ excurſio in Ioue continet ad fummum gr. </s> <s xml:id="echoid-s13540" xml:space="preserve">2. </s> <s xml:id="echoid-s13541" xml:space="preserve">7′<unsure/>. </s> <s xml:id="echoid-s13542" xml:space="preserve">hic igi-<lb/>tur dicetur motus latitudinis. </s> <s xml:id="echoid-s13543" xml:space="preserve">Poſtremo dum planeta ſuos hoſce circuitus in ſua regione peragit, non im-<lb/>munis eſt à diurna totius mundi conuerſione, ob quam ſpiralem lineam ab vno tropico ad alterum agglo-<lb/>merare<unsure/>, quodammodo cogitur; </s> <s xml:id="echoid-s13544" xml:space="preserve">quæ non vniformis erit, ſed alibi laxior, alibi anguſtior, prout ſydus apo-<lb/>gæum, vel perigæum occupauerit.</s> <s xml:id="echoid-s13545" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div308" type="section" level="1" n="214"> <head xml:id="echoid-head229" style="it" xml:space="preserve">Illuminati<unsure/>o, & vmbra Iouis. Cap. III.</head> <p> <s xml:id="echoid-s13546" xml:space="preserve">NOn ſecus ac Lunam, & </s> <s xml:id="echoid-s13547" xml:space="preserve">Venerem à Sole illuſtrari erediderim; </s> <s xml:id="echoid-s13548" xml:space="preserve">præſertim cum vti ſupra dictum eſt, vm-<lb/>bram à ſole efficiat, eam namq; </s> <s xml:id="echoid-s13549" xml:space="preserve">in auerſam a ſole partem proijcit; </s> <s xml:id="echoid-s13550" xml:space="preserve">nam nobis manifeſtam ipſius quatuor <lb/>comites reddiderunt, dum ea ipſos nobis occultare ſolet, ſicu@ infra oſtendetur. </s> <s xml:id="echoid-s13551" xml:space="preserve">Eſt igitur corpus opacum, <lb/>lumenq; </s> <s xml:id="echoid-s13552" xml:space="preserve">à ſole recipit, quod flauo colore refulget. </s> <s xml:id="echoid-s13553" xml:space="preserve">Longitudinem vmbræ Iouis ſic inueſtigabis, vt in præ-<lb/>cedentibus, detrahe minimam diſtantiam ſolis 1101. </s> <s xml:id="echoid-s13554" xml:space="preserve">a maxima Iouis 4753. </s> <s xml:id="echoid-s13555" xml:space="preserve">relinqueturque diſtantia maxima <lb/>Iouis à Sole 3952. </s> <s xml:id="echoid-s13556" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s13557" xml:space="preserve">terræ. </s> <s xml:id="echoid-s13558" xml:space="preserve">præterea quia diameter Solis ad diameter Iouis eſt ſicuti 26. </s> <s xml:id="echoid-s13559" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s13560" xml:space="preserve">vt igitur <lb/>exceſlus illius, qui eſt 21. </s> <s xml:id="echoid-s13561" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s13562" xml:space="preserve">ita diſtantia eorum 3652. </s> <s xml:id="echoid-s13563" xml:space="preserve">ad aliud; </s> <s xml:id="echoid-s13564" xml:space="preserve">& </s> <s xml:id="echoid-s13565" xml:space="preserve">inuenies 859. </s> <s xml:id="echoid-s13566" xml:space="preserve">propè ſemid. </s> <s xml:id="echoid-s13567" xml:space="preserve">terræ. </s> <s xml:id="echoid-s13568" xml:space="preserve">tanta. <lb/></s> <s xml:id="echoid-s13569" xml:space="preserve">igitur eſt ad hanc diſtantiam Iouialis vmbra; </s> <s xml:id="echoid-s13570" xml:space="preserve">cuius operationis ratio demonſtrata eſt in inuentione terreſtris <lb/>vmbræ. </s> <s xml:id="echoid-s13571" xml:space="preserve">vmbra igitur Iouis non eclipſabit Saturnum, quia ipſe diſtat à Sole, minimum 8365. </s> <s xml:id="echoid-s13572" xml:space="preserve">vmbra autem. </s> <s xml:id="echoid-s13573" xml:space="preserve"><lb/>Iouis vna cum diſtantia eius à Sole, extenditur tantummodo 4521.</s> <s xml:id="echoid-s13574" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div309" type="section" level="1" n="215"> <head xml:id="echoid-head230" style="it" xml:space="preserve">Figura Iouis. Cap. IV.</head> <p> <s xml:id="echoid-s13575" xml:space="preserve">FIguram eius eſſe ſphæricam exiſtimo, non tamen, vt in alijs, omnino perfectam; </s> <s xml:id="echoid-s13576" xml:space="preserve">ſed aſperam, vt melius <lb/>lumen ad terras depellat. </s> <s xml:id="echoid-s13577" xml:space="preserve">ſi enim perfectè rotunda eſſet, imperfectè admodum, vel potius minimè vide-<lb/>ri, contingeret, vnus quippe eius tantum radiolus ad oculos noſtros tenderet.</s> <s xml:id="echoid-s13578" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div310" type="section" level="1" n="216"> <head xml:id="echoid-head231" style="it" xml:space="preserve">Magnitudo Iouis. Cap. V.</head> <p> <s xml:id="echoid-s13579" xml:space="preserve">MAgnitudo Iouis eodem modo ac cæterorum reſciri poteſt, videlicet ex cognita eius diſtantia necnon <lb/>ſemidiametro eius apparente, ad eandem diſtantiam. </s> <s xml:id="echoid-s13580" xml:space="preserve">vt quoniam eius mediocris diſtantia poſita eſt <lb/>ſemid. </s> <s xml:id="echoid-s13581" xml:space="preserve">3990. </s> <s xml:id="echoid-s13582" xml:space="preserve">in qua eius diameter apparens ſubtendit angulum min. </s> <s xml:id="echoid-s13583" xml:space="preserve">2 {3/4}. </s> <s xml:id="echoid-s13584" xml:space="preserve">ſi igitur conſtruatur triangulum Iſo-<lb/>ſceles, cuius crura referant diſtantiam, angulus autem contineat min. </s> <s xml:id="echoid-s13585" xml:space="preserve">2 {3/4}. </s> <s xml:id="echoid-s13586" xml:space="preserve">in eo apparebit baſim habere eam-<lb/>proportionem ad diametrum terrę, quam habeat 12. </s> <s xml:id="echoid-s13587" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s13588" xml:space="preserve">vnde ſphærarũ ratio eritſicuti 14. </s> <s xml:id="echoid-s13589" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13590" xml:space="preserve">Iupiter igi-<lb/>tur quaterdecies Tellurem adæquabit. </s> <s xml:id="echoid-s13591" xml:space="preserve">cum autem conſtent rationes terræ ad ***, ***, Merc. </s> <s xml:id="echoid-s13592" xml:space="preserve">Vener. </s> <s xml:id="echoid-s13593" xml:space="preserve">Mart. </s> <s xml:id="echoid-s13594" xml:space="preserve">ex <lb/>ijs deducemus Iou. </s> <s xml:id="echoid-s13595" xml:space="preserve">ad ***, eſſe vt 560. </s> <s xml:id="echoid-s13596" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13597" xml:space="preserve">ad Mercur. </s> <s xml:id="echoid-s13598" xml:space="preserve">vt 280. </s> <s xml:id="echoid-s13599" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13600" xml:space="preserve">ad Vener. </s> <s xml:id="echoid-s13601" xml:space="preserve">vt 84. </s> <s xml:id="echoid-s13602" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13603" xml:space="preserve">ad Mart. </s> <s xml:id="echoid-s13604" xml:space="preserve">vt 182. </s> <s xml:id="echoid-s13605" xml:space="preserve">ad 1. <lb/></s> <s xml:id="echoid-s13606" xml:space="preserve">ad ***, vero vt 1. </s> <s xml:id="echoid-s13607" xml:space="preserve">ad 10.</s> <s xml:id="echoid-s13608" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div311" type="section" level="1" n="217"> <head xml:id="echoid-head232" style="it" xml:space="preserve">Appendix de calculo Iouis. Cap. VI.</head> <p> <s xml:id="echoid-s13609" xml:space="preserve">EOdem modo abſoluemus calculum Iouis, & </s> <s xml:id="echoid-s13610" xml:space="preserve">Saturni, quo antea Martis abſoluimus; </s> <s xml:id="echoid-s13611" xml:space="preserve">ſunt enim tres ſu-<lb/>periores planetæ perſimiles: </s> <s xml:id="echoid-s13612" xml:space="preserve">pro quo ſit Tabula ſequens.</s> <s xml:id="echoid-s13613" xml:space="preserve"/> </p> <pb o="150" file="0172" n="177" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div312" type="section" level="1" n="218"> <head xml:id="echoid-head233" style="it" xml:space="preserve">Tabula medij motus Iou. in longitudinem.</head> <note position="right" xml:space="preserve"> <lb/>##### In Annis ſingulis. #### ſn mẽſibus Ann. communis. #### In diebus. <lb/># Anni. # Sig. # Gra. # # # Sig. # Gra. # Dies # Sig. # Gra. # ′. <lb/># 1 # 1 # 0 # # Ian. # 0 # 3 # 1 # 0 # 0 # 5 <lb/># 2 # 2 # 1 # # Febr. # 0 # 5 # # 2 # 0 # 0 # 10 <lb/>B # 3 # 3 # 1 # # Mart. # 0 # 7 # # 3 # 0 # 0 # 15 <lb/># 4 # 4 # 1 # # Apr. # 8 # 10 <lb/># # # # # # # # # 4 # 0 # 0 # 20 <lb/># 5 # 5 # 2 # # Mai. # 0 # 13 # # 5 # 0 # 0 # 25 <lb/># 6 # 6 # 2 # # Iun. # 0 # 15 # # 6 # 0 # 0 # 30 <lb/>B # 7 # 7 # 2 # # Iul. # 0 # 18 <lb/># 8 # 8 # 3 # # Aug. # 0 # 20 # # 7 # 0 # 0 # 35 <lb/># # # # # # # # # 8 # 0 # 0 # 40 <lb/># 9 # 9 # 3 # # ept. # 0 # 23 # # 9 # 0 # 0 # 45 <lb/># 10 # 10 # 3 # # Oct, # 0 # 25 # # 10 # 0 # 0 # 50 <lb/>B # 11 # 11 # 3 # # Nou. # 0 # 28 <lb/># 12 # 0 # 4 # # Dec. # 1 # 0 # # 11 # 0 # 0 # 55 <lb/># # # # # # # # # 12 # 0 # 1 # 0 <lb/># 13 # 1 # 4 # # # # # # 13 # 0 # 1 # 0 <lb/># 14 # 2 # 5 # #### In menſibus Ann. Biſſext. # 14 # 0 # 1 # 0 <lb/>B # 15 # 3 # 5 <lb/># 16 # 4 # 6 # # # Sig. # Gra. # # 51 # 0 # 1 # 0 <lb/># # # # # # # # # 16 # 0 # 1 # 0 <lb/># 17 # 5 # 6 # # lan. # 0 # 3 # # 17 # 0 # 1 # 0 <lb/># 18 # 6 # 6 # # Febr. # 0 # 5 # # 18 # 0 # 1 # 0 <lb/>B # 19 # 7 # 7 # # Mart. # 0 # 8 <lb/># 20 # 8 # 7 # # Apr. # 0 # 10 # # 19 # 0 # 2 # 0 <lb/># # # # # # # # # 20 # 0 # 2 # 0 <lb/># # # # # Maius # 0 # 13 # # 21 # 0 # 2 # 0 <lb/># 40 # 4 # 14 # # Iun. # 0 # 15 # # 22 # 0 # 2 # 0 <lb/>In # 60 # 0 # 21 # # lulius # 0 # 18 <lb/># 80 # 8 # 28 # # Aug. # 0 # 20 # # 23 # 0 # 2 # 0 <lb/># 100 # 5 # 5 # # # # # # 24 # 0 # 2 # 0 <lb/># # # # # Sept. # 0 # 23 # # 25 # 0 # 2 # 0 <lb/># 200 # 10 # 10 # # Octo. # 0 # 25 # # 26 # 0 # 2 # 0 <lb/>Annis # 300 # 3 # 15 # # Noũ. # 0 # 28 <lb/># 400 # 8 # 20 # # Dec. # 0 # 0 # # 27 # 0 # 2 # 0 <lb/># 500 # 1 # 24 # # # # # # 28 # 0 # 2 # 0 <lb/># # # # # # # # # 29 # 0 # 2 # 0 <lb/>aggregatis. # 600 # 6 # 29 # # # # # # 30 # 0 # 2 # 0 <lb/># 700 # 0 # 4 # # # # # # 31 # 0 # 3 # 0 <lb/># 800 # 5 # 9 <lb/># 900 # 10 # 14 <lb/># 1000 # 3 # 19 <lb/># Radix # Sig. # Gra. # ′. <lb/>## Rad. 1600 # 5 # 9 # 48 <lb/></note> <pb o="151" file="0173" n="178" rhead="Liber Decimusquartus."/> </div> <div xml:id="echoid-div313" type="section" level="1" n="219"> <head xml:id="echoid-head234" style="it" xml:space="preserve">Vſus Tabulæ præcedentis.</head> <p> <s xml:id="echoid-s13614" xml:space="preserve">AD datum igitur tempus, ex præcedenti Tabula motus Iouis, inuenias motum eius in longitudine quem <lb/>detrahes à motu ſolis; </s> <s xml:id="echoid-s13615" xml:space="preserve">reſiduum enim erit motus anomaliæ, vt in Marte. </s> <s xml:id="echoid-s13616" xml:space="preserve">Exemplum. </s> <s xml:id="echoid-s13617" xml:space="preserve">Hodie quæ hæc <lb/>ſcribo, ideſt, anno 1615. </s> <s xml:id="echoid-s13618" xml:space="preserve">die 26. </s> <s xml:id="echoid-s13619" xml:space="preserve">Decembris exacto in meridie, ad meridianum Venetum, qui dies S. </s> <s xml:id="echoid-s13620" xml:space="preserve">Stephani <lb/>eſt; </s> <s xml:id="echoid-s13621" xml:space="preserve">ſic Iouis locum reperio. </s> <s xml:id="echoid-s13622" xml:space="preserve">tempus Aſtronomicum ſe habet, cum motibus ſibi debitis ex Tabula acceptis, <lb/>vt oſtendit ſequens formula.</s> <s xml:id="echoid-s13623" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. <lb/>Radix 1600. # 5 # 10 <lb/>Anni 15. # 3 # 5 <lb/>Nouem. Biſſext. # 0 # 28 <lb/>Dies 26. # 0 # 2 <lb/>Summa # 9 # 15 # in gr. 15. Capric. erit centrum epic. <lb/></note> <p> <s xml:id="echoid-s13624" xml:space="preserve">Motus autem Solis eſt 9. </s> <s xml:id="echoid-s13625" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s13626" xml:space="preserve">cui addo ſig. </s> <s xml:id="echoid-s13627" xml:space="preserve">12. </s> <s xml:id="echoid-s13628" xml:space="preserve">vt demere ab <lb/>eo poſſim motus Iouis 9. </s> <s xml:id="echoid-s13629" xml:space="preserve">15. </s> <s xml:id="echoid-s13630" xml:space="preserve"><lb/>facta detractione remanent <lb/>reſiduum ſig. </s> <s xml:id="echoid-s13631" xml:space="preserve">11. </s> <s xml:id="echoid-s13632" xml:space="preserve">gr. </s> <s xml:id="echoid-s13633" xml:space="preserve">19. </s> <s xml:id="echoid-s13634" xml:space="preserve">tanta <lb/>igitur eſt Iouis anomalia, id-<lb/>eſt, tantum diſtat ab apogæo <lb/>ſui epicycli, numerando ver<unsure/>-<lb/>ſus orientem per perigæum; </s> <s xml:id="echoid-s13635" xml:space="preserve"><lb/>quare diſtabit tantũmodo gr. </s> <s xml:id="echoid-s13636" xml:space="preserve"><lb/>11. </s> <s xml:id="echoid-s13637" xml:space="preserve">ab eodem apogęo in ſemi-<lb/>circulo occidentali, ideſt, ex <lb/>parte occidentis. </s> <s xml:id="echoid-s13638" xml:space="preserve">quare ſtella <lb/>Iouis erit in Zodiaco ante lo-<lb/>cum epicycli aliquot gradibus. </s> <s xml:id="echoid-s13639" xml:space="preserve">quos vt conijciamus, ſciendum eſt, tanta eſſe epicycli ſemidiametrum vt ſub-<lb/>tendat in Zodiaco gr. </s> <s xml:id="echoid-s13640" xml:space="preserve">ferè 11. </s> <s xml:id="echoid-s13641" xml:space="preserve">quare planeta maximè ab eo recedere poteſt vtrinque gr. </s> <s xml:id="echoid-s13642" xml:space="preserve">11. </s> <s xml:id="echoid-s13643" xml:space="preserve">ferè, idq; </s> <s xml:id="echoid-s13644" xml:space="preserve">quando <lb/>diſtat ab apogæo epicycli ſig. </s> <s xml:id="echoid-s13645" xml:space="preserve">3. </s> <s xml:id="echoid-s13646" xml:space="preserve">gr. </s> <s xml:id="echoid-s13647" xml:space="preserve">11. </s> <s xml:id="echoid-s13648" xml:space="preserve">ferè, nunc autem cum diſtet tantum gr. </s> <s xml:id="echoid-s13649" xml:space="preserve">11. </s> <s xml:id="echoid-s13650" xml:space="preserve">licet conijcere parum ab eo <lb/>diſtare; </s> <s xml:id="echoid-s13651" xml:space="preserve">præſertim quia in apogæo, & </s> <s xml:id="echoid-s13652" xml:space="preserve">perigæo epicycli nihil diſtat à loco centri eius in Zodiaco, recedet igi-<lb/>tur nunc grad. </s> <s xml:id="echoid-s13653" xml:space="preserve">circiter 6. </s> <s xml:id="echoid-s13654" xml:space="preserve">in præcedentia. </s> <s xml:id="echoid-s13655" xml:space="preserve">quare verſabitur circa gr. </s> <s xml:id="echoid-s13656" xml:space="preserve">9. </s> <s xml:id="echoid-s13657" xml:space="preserve">Capricorni; </s> <s xml:id="echoid-s13658" xml:space="preserve">eritq; </s> <s xml:id="echoid-s13659" xml:space="preserve">ſoli vicinus gr. </s> <s xml:id="echoid-s13660" xml:space="preserve">5. </s> <s xml:id="echoid-s13661" xml:space="preserve">eum <lb/>ſequens. </s> <s xml:id="echoid-s13662" xml:space="preserve">quare videri non poterit ob ſolis vicinitatem.</s> <s xml:id="echoid-s13663" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div314" type="section" level="1" n="220"> <head xml:id="echoid-head235" style="it" xml:space="preserve">De quatuor nouis planetis Iouis Comitibus. Cap. VII.</head> <p> <s xml:id="echoid-s13664" xml:space="preserve">LOcus inter ea, quæ ope Teleſcopij in cælo ſunt patefacta, mirus æque, ac iucundus eſt hic Iouis Comita-<lb/>tus, eum enim perpetuo quatuor ſtellulæ ſeu exigui quatuor planetæ comitantur, circa eum circumcurſan <lb/>tes, de quibus ſupra nonnulla tetigimus, figuramq; </s> <s xml:id="echoid-s13665" xml:space="preserve">nunc repetendam exhibuimus, in qua Iouis ſydus A, reſi-<lb/>det in centro quatuor circellorũ, quos quatuor ſtellulæ D G K N, circinant. </s> <s xml:id="echoid-s13666" xml:space="preserve">quas vt videamus opus eſt opti-<lb/>mo Teleſcopio, nocte ſereniſſima in Iouem directo, & </s> <s xml:id="echoid-s13667" xml:space="preserve">obfirmato. </s> <s xml:id="echoid-s13668" xml:space="preserve">per quod intuentes, inſpiciemus propè Io-<lb/>uem vnam, aut duas, aut tres, aliquando etiam quatuor, huiuſinodi ſtellas eum comitari; </s> <s xml:id="echoid-s13669" xml:space="preserve">quod non facerent ſi <lb/>affixa, & </s> <s xml:id="echoid-s13670" xml:space="preserve">non errantia eſſent ſydera. </s> <s xml:id="echoid-s13671" xml:space="preserve">ſeruant autem inuicem, & </s> <s xml:id="echoid-s13672" xml:space="preserve">ad Iouem hunc ſitum, vt ſemper ſint ferè in <lb/>ecliptica N A K, aut in linea eclypticæ paralella. </s> <s xml:id="echoid-s13673" xml:space="preserve">neq; </s> <s xml:id="echoid-s13674" xml:space="preserve">eaſdem ſeruant adinuicem, nec ad Iouem apparentes <lb/>diſtantias; </s> <s xml:id="echoid-s13675" xml:space="preserve">ſed modo remotiores, modo propiores ei fiunt: </s> <s xml:id="echoid-s13676" xml:space="preserve">quod eis accidere poteſt, ſi ponamus eos circa Iouẽ <lb/>circulos ducere, non aliter ac circa Solem Mercurius, & </s> <s xml:id="echoid-s13677" xml:space="preserve">Venus reuoluuntur Atq; </s> <s xml:id="echoid-s13678" xml:space="preserve">hæc de loco.</s> <s xml:id="echoid-s13679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13680" xml:space="preserve">Motus. </s> <s xml:id="echoid-s13681" xml:space="preserve">eorum autem motus ſic peragitur, vt in ſuperiori parte ſuorum epicyclorum verſus orientem; </s> <s xml:id="echoid-s13682" xml:space="preserve">in <lb/>inferiori verſus occidentem ferantur. </s> <s xml:id="echoid-s13683" xml:space="preserve">quod manifeſ@e hinc colligitur quia cum tendũt ad orientem, ſæpè bis <lb/>occultantur, ſemel quidem in S, ſupra louem; </s> <s xml:id="echoid-s13684" xml:space="preserve">& </s> <s xml:id="echoid-s13685" xml:space="preserve">iterum in vmbra; </s> <s xml:id="echoid-s13686" xml:space="preserve">quæ occultatio propriè eorum eclipſis eſt <lb/>appellanda: </s> <s xml:id="echoid-s13687" xml:space="preserve">cuius rei manifeſtum ſignum eſt, quod ibi ſemper eclipſantur, vbi hæc vmbra porrigitur. </s> <s xml:id="echoid-s13688" xml:space="preserve">nam <lb/>quando Iupiter veſpertinus apparet, prius latent ob coniunctione cum Ioue. </s> <s xml:id="echoid-s13689" xml:space="preserve">deinde iterum eclipſantur in <lb/>parte orientali, ad quam vmbra extenditur. </s> <s xml:id="echoid-s13690" xml:space="preserve">quando autem mane apparent elipſantur prius in parte Iouis <lb/>occidentali, ad quam videlicet vmbra extenditur, & </s> <s xml:id="echoid-s13691" xml:space="preserve">poſtea ob Iouis coniũctionem in S, quod neutiquam ac-<lb/>cideret niſi in ſuperiori parte mouerentur ad orientem: </s> <s xml:id="echoid-s13692" xml:space="preserve">cum autem retrogradi ſunt, ideſt, tendunt ad occi-<lb/>dentem, tunc ſemel tantum, & </s> <s xml:id="echoid-s13693" xml:space="preserve">quidem ſub Ioue, v.</s> <s xml:id="echoid-s13694" xml:space="preserve">g. </s> <s xml:id="echoid-s13695" xml:space="preserve">in F, abſconduntur: </s> <s xml:id="echoid-s13696" xml:space="preserve">quod iudicium eſt, eos infra Iouem <lb/>repedare, vti diximus. </s> <s xml:id="echoid-s13697" xml:space="preserve">Neq; </s> <s xml:id="echoid-s13698" xml:space="preserve">vero eadem velocitate omnes feruntur, ſed remotior quiſq; </s> <s xml:id="echoid-s13699" xml:space="preserve">propiore tardior <lb/>eſt; </s> <s xml:id="echoid-s13700" xml:space="preserve">nam D, Ioui proximus ſuum gyrum abſoluit die vno, & </s> <s xml:id="echoid-s13701" xml:space="preserve">hor. </s> <s xml:id="echoid-s13702" xml:space="preserve">18 {1/2}. </s> <s xml:id="echoid-s13703" xml:space="preserve">ſecundus G, diebus tribus horiſq; </s> <s xml:id="echoid-s13704" xml:space="preserve">13 {1/3}. <lb/></s> <s xml:id="echoid-s13705" xml:space="preserve">Tertius K, diebus 7. </s> <s xml:id="echoid-s13706" xml:space="preserve">cum hor. </s> <s xml:id="echoid-s13707" xml:space="preserve">4. </s> <s xml:id="echoid-s13708" xml:space="preserve">quartus N, diebus 16. </s> <s xml:id="echoid-s13709" xml:space="preserve">hor. </s> <s xml:id="echoid-s13710" xml:space="preserve">18.</s> <s xml:id="echoid-s13711" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13712" xml:space="preserve">Illuminatio. </s> <s xml:id="echoid-s13713" xml:space="preserve">Quod attinet ad illuminationem, manifeſtum eſt eos à Sole illuminari, cuius ſignum euidens <lb/>eſt, eorum eclipſes non contingere niſi quando inter eos, & </s> <s xml:id="echoid-s13714" xml:space="preserve">Solem Iupiter interponitur, vti diximus, ex qua <lb/>interpoſitione Solis lumine priuantur; </s> <s xml:id="echoid-s13715" xml:space="preserve">ſicuti Luna ex terræ interpoſitione eodem lumine priuatur.</s> <s xml:id="echoid-s13716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13717" xml:space="preserve">Figura. </s> <s xml:id="echoid-s13718" xml:space="preserve">Tandem figuras eorum eſſe ſphæricas putandum eſt.</s> <s xml:id="echoid-s13719" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13720" xml:space="preserve">Magnitudo difficilis eſt cognitu: </s> <s xml:id="echoid-s13721" xml:space="preserve">apparentes tamen eorum magnitudo exiguæ admodum ſunt. </s> <s xml:id="echoid-s13722" xml:space="preserve">Vide nun-<lb/>cium ſydereum, & </s> <s xml:id="echoid-s13723" xml:space="preserve">hiſtoriam Galilæi de maculis ſolaribus, necnon Diſquiſitiones Mathem. </s> <s xml:id="echoid-s13724" xml:space="preserve">P. </s> <s xml:id="echoid-s13725" xml:space="preserve">Chriſtophori <lb/>Sheiner noſtræ Soc. </s> <s xml:id="echoid-s13726" xml:space="preserve">vbi plura ſcitu iucundiſſima fusè pertractant, quippe qui primi hæc omnia mundo ma-<lb/>nifeſtarunt. </s> <s xml:id="echoid-s13727" xml:space="preserve">has quatuor ſtellulas Galilæus iure inuentionis medica ſydera nuncupauit.</s> <s xml:id="echoid-s13728" xml:space="preserve"/> </p> <pb o="152" file="0174" n="179" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div315" type="section" level="1" n="221"> <head xml:id="echoid-head236" xml:space="preserve">LIBER DECIMVS QVINTVS <lb/>DE SATVRNO.</head> <p> <s xml:id="echoid-s13729" xml:space="preserve">SAturni Hierogliphicum falx eſt, qua carnes lanius ſecat, quod poetæ Saturnum omnium rerum lanium <lb/>ſaciant. </s> <s xml:id="echoid-s13730" xml:space="preserve">huius notæ manubrium ſuperius eſt; </s> <s xml:id="echoid-s13731" xml:space="preserve">planetarum notas habes in Pierio Valeriano.</s> <s xml:id="echoid-s13732" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div316" type="section" level="1" n="222"> <head xml:id="echoid-head237" style="it" xml:space="preserve">Locus, & distantia Saturni. Cap. I.</head> <p> <s xml:id="echoid-s13733" xml:space="preserve">SAturnum ſuos circuitus ſupra Iouis regionem exercere, qui Solem vti centrum reſpiciant, vſitatis ra-<lb/>tionibus Aſtronomi confirmant, videlicet primo ab occultationibus, quod a Ioue quandoque occulte-<lb/>tur, vnde ſupra eum neceſſe eſt incedat. </s> <s xml:id="echoid-s13734" xml:space="preserve">Secundo a parallaxi, quam Tycho minorẽ aſſerit, quam louis, eam-<lb/>que quartam partem minuti facit. </s> <s xml:id="echoid-s13735" xml:space="preserve">Tertio à motuum comparatione: </s> <s xml:id="echoid-s13736" xml:space="preserve">nam cum ſit tardiſſimus omnium pla-<lb/>netarum, ei etiam competit amplior gyrus, g<unsure/>ui videlicet maiori tempore, ſiue tardius perambuletur. </s> <s xml:id="echoid-s13737" xml:space="preserve">Di-<lb/>ſtantiam vero eius à terra mediocrem eſſe 10′550′. </s> <s xml:id="echoid-s13738" xml:space="preserve">ſemidiameter terræ idem Tycho tradit. </s> <s xml:id="echoid-s13739" xml:space="preserve">de minima, & </s> <s xml:id="echoid-s13740" xml:space="preserve"><lb/>maxima nihil nunc certi habeo. </s> <s xml:id="echoid-s13741" xml:space="preserve">qua propter eadem figura, quæ pro Marte, ac Ioue inſeruit commodari <lb/>ctiam Saturno poteſt; </s> <s xml:id="echoid-s13742" xml:space="preserve">ſi linea T M, quæ mediocrem diſtantiam refert, ponamus continere ſemidiameter <lb/>terræ 10′550. </s> <s xml:id="echoid-s13743" xml:space="preserve">ea igitur nunc reuiſatur.</s> <s xml:id="echoid-s13744" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div317" type="section" level="1" n="223"> <head xml:id="echoid-head238" style="it" xml:space="preserve">Illuminatio, & vmbra Saturni. Cap. II.</head> <p> <s xml:id="echoid-s13745" xml:space="preserve">ILluminari à Sole vti cæteros pars eſt credere. </s> <s xml:id="echoid-s13746" xml:space="preserve">eſt autem lux eius plumbea. </s> <s xml:id="echoid-s13747" xml:space="preserve">quantitas eius vmbræ in maxi-<lb/>ma eius diſtantia à Sole, indagata eſt eadem ratione vt in ſuperioribus, inuentaque eſt extendi penè ſemi-<lb/>diam. </s> <s xml:id="echoid-s13748" xml:space="preserve">terræ 12′527′. </s> <s xml:id="echoid-s13749" xml:space="preserve">quæ cum maxima eius diſtantia a Sole 10592. </s> <s xml:id="echoid-s13750" xml:space="preserve">efficit 23′124. </s> <s xml:id="echoid-s13751" xml:space="preserve">quare ſi ſtellæ ponantur di-<lb/>ſtare à Sole tantu@modo 13′000. </s> <s xml:id="echoid-s13752" xml:space="preserve">poterunt eclipſari a Saturno. </s> <s xml:id="echoid-s13753" xml:space="preserve">quapropter vaide dignum eſt obſeruatione <lb/>an ſtell@ fixæ ab hac Saturni vmbra obſcurentur. </s> <s xml:id="echoid-s13754" xml:space="preserve">hinc enim plura ſcitu admodũ iucunda poſſunt inueſtigari.</s> <s xml:id="echoid-s13755" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div318" type="section" level="1" n="224"> <head xml:id="echoid-head239" style="it" xml:space="preserve">Figura Saturni. Cap. III.</head> <p> <s xml:id="echoid-s13756" xml:space="preserve">FIguram eius vti in alijs eſſe ſphæricam par eſt exiſtimare. </s> <s xml:id="echoid-s13757" xml:space="preserve">veruntamen ſi per Teleſcopium inſpicia-<lb/>tur non ſemper rotunda apparot, ſed aliquando oualis, aliquando etiam tricorporeus ſpectatur. </s> <s xml:id="echoid-s13758" xml:space="preserve">qua de <lb/>re ſeorſim poſtea agemus.</s> <s xml:id="echoid-s13759" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div319" type="section" level="1" n="225"> <head xml:id="echoid-head240" style="it" xml:space="preserve">Magnitudo Saturni. Cap. IV.</head> <p> <s xml:id="echoid-s13760" xml:space="preserve">IN mediocri diſtantia ſemidiametrorum terræ 10′550. </s> <s xml:id="echoid-s13761" xml:space="preserve">exhibet diametrum apparentem min. </s> <s xml:id="echoid-s13762" xml:space="preserve">propè 19′. <lb/></s> <s xml:id="echoid-s13763" xml:space="preserve">vnde conſtructo de more triangulo, eliciemus rationem diamet. </s> <s xml:id="echoid-s13764" xml:space="preserve">Saturni ad diametrum terræ, & </s> <s xml:id="echoid-s13765" xml:space="preserve">conſe-<lb/>quenter ſphærarum rationes. </s> <s xml:id="echoid-s13766" xml:space="preserve">diameter eius continet diametrum terræ bis, cum {9/11}. </s> <s xml:id="echoid-s13767" xml:space="preserve">in ratione videlicet 31. </s> <s xml:id="echoid-s13768" xml:space="preserve"><lb/>ad 11. </s> <s xml:id="echoid-s13769" xml:space="preserve">vnde ſphærarum proportio erit vt 22. </s> <s xml:id="echoid-s13770" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13771" xml:space="preserve">quare Saturnus terram adæquabit vicies, & </s> <s xml:id="echoid-s13772" xml:space="preserve">bis: </s> <s xml:id="echoid-s13773" xml:space="preserve">cum au-<lb/>tem notæ ſint cæterorum planetarum magnitudines ad eandem terram, notæ quoque euadent ad Satur-<lb/>num; </s> <s xml:id="echoid-s13774" xml:space="preserve">eritque Saturnus ad Iouem vt 1 {4/7}. </s> <s xml:id="echoid-s13775" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13776" xml:space="preserve">ad Solem vti 1. </s> <s xml:id="echoid-s13777" xml:space="preserve">ad 6 {4/11}. </s> <s xml:id="echoid-s13778" xml:space="preserve">ad Martem vti 286. </s> <s xml:id="echoid-s13779" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13780" xml:space="preserve">ad Lunam <lb/>vti 180. </s> <s xml:id="echoid-s13781" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s13782" xml:space="preserve">ad Venerem ſicuti 133. </s> <s xml:id="echoid-s13783" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s13784" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div320" type="section" level="1" n="226"> <head xml:id="echoid-head241" style="it" xml:space="preserve">Motus Saturni. Cap. V.</head> <p> <s xml:id="echoid-s13785" xml:space="preserve">MOtus Sa urni perſimiles ſunt motibus Iouis, & </s> <s xml:id="echoid-s13786" xml:space="preserve">Martis; </s> <s xml:id="echoid-s13787" xml:space="preserve">nam & </s> <s xml:id="echoid-s13788" xml:space="preserve">eodem modo epicyclus mouetur in <lb/>longitudinem; </s> <s xml:id="echoid-s13789" xml:space="preserve">& </s> <s xml:id="echoid-s13790" xml:space="preserve">eodem modo planeta hic motu anomaliæ cietur in peripheria epicycli, vt mirabili <lb/>illo ad Solem reſpectu reuoluatur: </s> <s xml:id="echoid-s13791" xml:space="preserve">pariter etiam in latitudinem exorbitet: </s> <s xml:id="echoid-s13792" xml:space="preserve">& </s> <s xml:id="echoid-s13793" xml:space="preserve">ab ijſdem principijs numere-<lb/>tur. </s> <s xml:id="echoid-s13794" xml:space="preserve">Solummodo differunt in quantitate, nam motus Saturni diarius eſt longitudine min. </s> <s xml:id="echoid-s13795" xml:space="preserve">2′. </s> <s xml:id="echoid-s13796" xml:space="preserve">1″. </s> <s xml:id="echoid-s13797" xml:space="preserve">annuus <lb/>gr. </s> <s xml:id="echoid-s13798" xml:space="preserve">12. </s> <s xml:id="echoid-s13799" xml:space="preserve">13′. </s> <s xml:id="echoid-s13800" xml:space="preserve">quare totum Zodiacum abſoluitannis Aegyptijs 29. </s> <s xml:id="echoid-s13801" xml:space="preserve">diebus 184. </s> <s xml:id="echoid-s13802" xml:space="preserve">hor. </s> <s xml:id="echoid-s13803" xml:space="preserve">8. </s> <s xml:id="echoid-s13804" xml:space="preserve">motus anomaliæ quoti-<lb/>dianus eſt 57′. </s> <s xml:id="echoid-s13805" xml:space="preserve">8′. </s> <s xml:id="echoid-s13806" xml:space="preserve">annuus ſign. </s> <s xml:id="echoid-s13807" xml:space="preserve">11. </s> <s xml:id="echoid-s13808" xml:space="preserve">gr. </s> <s xml:id="echoid-s13809" xml:space="preserve">17. </s> <s xml:id="echoid-s13810" xml:space="preserve">min. </s> <s xml:id="echoid-s13811" xml:space="preserve">32′. </s> <s xml:id="echoid-s13812" xml:space="preserve">totaq; </s> <s xml:id="echoid-s13813" xml:space="preserve">abſoluitur anno vno ſimplici, diebus 12. </s> <s xml:id="echoid-s13814" xml:space="preserve">hor. </s> <s xml:id="echoid-s13815" xml:space="preserve">21. </s> <s xml:id="echoid-s13816" xml:space="preserve">mo-<lb/>tus deniq; </s> <s xml:id="echoid-s13817" xml:space="preserve">in latitudinem tam in Boream, quam in Auſtrum ab ecliptica excurrit pluſquam tres gradus. </s> <s xml:id="echoid-s13818" xml:space="preserve">in-<lb/>terim motu diurno reuoluitur, vnde ab vno tropico ad alterum ſpiratim procedit. </s> <s xml:id="echoid-s13819" xml:space="preserve">quod ſi ab eo immunis eſ-<lb/>ſet, deſcriberet ſpiralem implexam ſimilem martiali; </s> <s xml:id="echoid-s13820" xml:space="preserve">ſed quæ frequentiores haberet lineas; </s> <s xml:id="echoid-s13821" xml:space="preserve">ſæpius enim <lb/>Saturnum Solaſſequitur, quam Martem, & </s> <s xml:id="echoid-s13822" xml:space="preserve">Iouem.</s> <s xml:id="echoid-s13823" xml:space="preserve"/> </p> <pb o="153" file="0175" n="180" rhead="Liber Decimusquintus."/> </div> <div xml:id="echoid-div321" type="section" level="1" n="227"> <head xml:id="echoid-head242" style="it" xml:space="preserve">Appendix de calculo Saturnl. Cap. VI.</head> <p> <s xml:id="echoid-s13824" xml:space="preserve">EOdem prorſus modo hic calculus peragitur, quo in duobus præcedentibus, pro quo ſit Tabula ſequens <lb/>vna cum exemplo. </s> <s xml:id="echoid-s13825" xml:space="preserve">Hodie igitur, ideſt, 26. </s> <s xml:id="echoid-s13826" xml:space="preserve">Decembris exacta ad meridiem Venetum anni 1616. </s> <s xml:id="echoid-s13827" xml:space="preserve">Biſſext. <lb/></s> <s xml:id="echoid-s13828" xml:space="preserve">quæratur ex ſequenti Tabula medij motus Saturni, locus eius in Zodlaco.</s> <s xml:id="echoid-s13829" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Sig. # Gra. # ′. <lb/>Rad. 1606. # 6 # 28 # 28 <lb/>Anni 15. # 6 # 3 # 0 <lb/>Menſis Nouemb. Biſſext. # 0 # 11 # 0 <lb/>Dies 26. # 0 # 0 # 0 <lb/>Summa in gr. 12. # 1 # 12 # 28 # à quo dempto motu epicycli. <lb/>Motus vero Solis eſt # 9 # 4 # 0 # Tauri eſt centrum epicycli. <lb/>Motus epicycli # 1 # 12 # 28 <lb/>Remanet # 7 # 11 # 32 # pro Anom. Saturni. <lb/></note> <p> <s xml:id="echoid-s13830" xml:space="preserve">Stella igitur Saturni transgreſſa eſt perigæum epicycli ſig. </s> <s xml:id="echoid-s13831" xml:space="preserve">1. </s> <s xml:id="echoid-s13832" xml:space="preserve">gr. </s> <s xml:id="echoid-s13833" xml:space="preserve">22. </s> <s xml:id="echoid-s13834" xml:space="preserve">eſtque in ſemicirculo epicycli occiden-<lb/>tali; </s> <s xml:id="echoid-s13835" xml:space="preserve">ac proinde in motu diurno præcedit locum epicycli aliquot gradibus, quos rudi Minerua ſic diuinabe-<lb/>ris: </s> <s xml:id="echoid-s13836" xml:space="preserve">conſidera tantum eſſe ſemidiametrum huius epicycli, vt ad ſummum ſubtendat gradus circiter 6. </s> <s xml:id="echoid-s13837" xml:space="preserve">de Zo. <lb/></s> <s xml:id="echoid-s13838" xml:space="preserve">diaco; </s> <s xml:id="echoid-s13839" xml:space="preserve">quapropter planeta ipſe totidem gradus præcedere, aut ſequi poterit centrum epicycli, idque cum <lb/>deſtiterit vtrinque ab epicycli apogæo ſig. </s> <s xml:id="echoid-s13840" xml:space="preserve">3. </s> <s xml:id="echoid-s13841" xml:space="preserve">gr. </s> <s xml:id="echoid-s13842" xml:space="preserve">7. </s> <s xml:id="echoid-s13843" xml:space="preserve">ferè. </s> <s xml:id="echoid-s13844" xml:space="preserve">quando autem eſt in epicycli perigæo, vel apogæo′, <lb/>cundem ſortitur cum centro locum: </s> <s xml:id="echoid-s13845" xml:space="preserve">nunc autem diſtat ab apogæo in ſemicirculo occiduo ſign. </s> <s xml:id="echoid-s13846" xml:space="preserve">4. </s> <s xml:id="echoid-s13847" xml:space="preserve">gr. </s> <s xml:id="echoid-s13848" xml:space="preserve">8. </s> <s xml:id="echoid-s13849" xml:space="preserve">qua-<lb/>propter non recedet à centro epicycli totos gr. </s> <s xml:id="echoid-s13850" xml:space="preserve">7. </s> <s xml:id="echoid-s13851" xml:space="preserve">ſed circiter 6. </s> <s xml:id="echoid-s13852" xml:space="preserve">vel 5. </s> <s xml:id="echoid-s13853" xml:space="preserve">erit igitur circa gr. </s> <s xml:id="echoid-s13854" xml:space="preserve">Tauri 7. </s> <s xml:id="echoid-s13855" xml:space="preserve">vel 6.</s> <s xml:id="echoid-s13856" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13857" xml:space="preserve">Motum in latitudinem horum trium ſuperiorum planetarum breuitatis cauſa ommittimus.</s> <s xml:id="echoid-s13858" xml:space="preserve"/> </p> <pb o="154" file="0176" n="181" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div322" type="section" level="1" n="228"> <head xml:id="echoid-head243" style="it" xml:space="preserve">Tabula medij motus Satur. in longitudinem.</head> <note position="right" xml:space="preserve"> <lb/>##### In Annis ſingulis. <lb/># Anni. # Sig. # Gra. <lb/># 1 # 0 # 12 <lb/># 2 # 0 # 24 <lb/>B # 3 # 1 # 7 <lb/># 4 # 1 # 19 <lb/># 5 # 2 # 1 <lb/># 6 # 2 # 13 <lb/>B # 7 # 2 # 26 <lb/># 8 # 3 # 8 <lb/># 9 # 3 # 20 <lb/># 10 # 4 # 2 <lb/>B # 11 # 4 # 14 <lb/># 12 # 4 # 27 <lb/># 13 # 5 # 9 <lb/># 14 # 5 # 21 <lb/>B # 15 # 6 # 3 <lb/># 10 # 6 # 15 <lb/># 17 # 6 # 28 <lb/># 18 # 7 # 10 <lb/>B # 19 # 7 # 22 <lb/># 20 # 8 # 4 <lb/># 40 # 4 # 9 <lb/>In # 60 # 0 # 13 <lb/># 80 # 8 # 18 <lb/># 100 # 4 # 22 <lb/># 200 # 9 # 14 <lb/>Annis # 300 # 2 # 0 <lb/># 400 # 6 # 28 <lb/># 500 # 11 # 21 <lb/>aggregatis. # 600 # 4 # 13 <lb/># 700 # 9 # 5 <lb/># 800 # 1 # 27 <lb/># 900 # 6 # 19 <lb/># 1000 # 11 # 11 <lb/># Radix # Sig. # Gra. # @ <lb/>Rad. # 1600 # 6 # 28 # 28 <lb/></note> <note position="right" xml:space="preserve"> <lb/>#### @meſibus Ann. communis. <lb/># Sig. # Gra. <lb/>Ian. # 1 # 0 <lb/>Febr. # 2 # 0 <lb/>Mart. # 3 # 0 <lb/>Apr. # 4 # 0 <lb/>Mai. # 5 # 0 <lb/>Iun. # 6 # 0 <lb/>Iul. # 7 # 0 <lb/>Aug. # 8 # 0 <lb/>Sept. # 9 # 0 <lb/>Oct. # 10 # 0 <lb/>Nou. # 11 # 0 <lb/>Dec. # 12 # 13 <lb/>#### In menſibus Ann. Biſſext. <lb/># Gra. # @. <lb/>Ian. # 1 # 0 <lb/>Febr. # 2 # 0 <lb/>Mart. # 3 # 0 <lb/>Apr. # 4 # 0 <lb/>Ma@us # 5 # 0 <lb/>Iu@ # 6 # 0 <lb/>Iul@us # 7 # 0 <lb/>Aug. # 8 # 0 <lb/>Sept. # 9 # 0 <lb/>Octo. # 10 # 0 <lb/>Nou. # 11 # 0 <lb/>Dec. # 12 # 15 <lb/></note> <note position="right" xml:space="preserve"> <lb/>#### In diebus. <lb/>Dies # Sig. # Gra. <lb/>1 # 0 # 0 <lb/>2 # 0 # 0 <lb/>3 # 0 # 0 <lb/>4 # 0 # 0 <lb/>5 # 0 # 0 <lb/>6 # 0 # 0 <lb/>7 # 0 # 0 <lb/>8 # 0 # 0 <lb/>9 # 0 # 0 <lb/>10 # 0 # 0 <lb/>11 # 0 # 0 <lb/>12 # 0 # 0 <lb/>13 # 0 # 0 <lb/>14 # 0 # 0 <lb/>51 # 0 # 0 <lb/>16 # 0 # 0 <lb/>17 # 0 # 0 <lb/>18 # 0 # 0 <lb/>19 # 0 # 0 <lb/>20 # 0 # 0 <lb/>21 # 0 # 0 <lb/>22 # 0 # 0 <lb/>23 # 0 # 0 <lb/>24 # 0 # 0 <lb/>25 # 0 # 0 <lb/>26 # 0 # 0 <lb/>27 # 0 # 0 <lb/>28 # 0 # 0 <lb/>29 # 0 # 0 <lb/>30 # 1 # 0 <lb/>31 # 1 # 2 <lb/></note> <pb o="155" file="0177" n="182" rhead="Liber Decimusquintus."/> </div> <div xml:id="echoid-div323" type="section" level="1" n="229"> <head xml:id="echoid-head244" style="it" xml:space="preserve">De duobus Saturni Comitibus. Cap. VII.</head> <p> <s xml:id="echoid-s13859" xml:space="preserve">MIrabile eſt illud quoque, quod circa Saturnũ mirabili Teleſcopio noſtræ tempeſtati Aſtronomi rimati, <lb/>ac parirer mirati ſunt; </s> <s xml:id="echoid-s13860" xml:space="preserve">ipſum videlicet duobus paruis ſtipari comitibus, ſicuti Iouem quatuor. </s> <s xml:id="echoid-s13861" xml:space="preserve">qui cum <lb/>Saturno in linea æquatori paralella conſtituuntur, quemadmodum comites Iouis cum eo in linea eclipticæ <lb/>paralella. </s> <s xml:id="echoid-s13862" xml:space="preserve">ſuntque aliquando adeo Saturno proximi, vt non diſtinguan-<lb/> <anchor type="figure" xlink:label="fig-0177-01a" xlink:href="fig-0177-01"/> tur ab eo, ſed eum oualem apparere efficiant, vt in figura B. </s> <s xml:id="echoid-s13863" xml:space="preserve">aliquando <lb/>ab eo plane diſtinguuntur, vt in figura C. </s> <s xml:id="echoid-s13864" xml:space="preserve">ſed illud omnino mirum, quod <lb/>eum Galilæus, & </s> <s xml:id="echoid-s13865" xml:space="preserve">alijs duobus totis annis, & </s> <s xml:id="echoid-s13866" xml:space="preserve">amplius, eos continuo Sa-<lb/>turno aſſiſtere conſpexiſſent, poſtea euanuerunt, nec quid de illis factum <lb/>ſit audio quidquam, quod inopinatum ſpectaculum obſeruatores ſtupi-<lb/>dos tenet ac mirabundos. </s> <s xml:id="echoid-s13867" xml:space="preserve">ego ad finem huius Octobris anni 1616. </s> <s xml:id="echoid-s13868" xml:space="preserve">oualem ac cum duabus maculis rotundis <lb/>ad vtrumque vertice conſpicio, qualem prima figura A. </s> <s xml:id="echoid-s13869" xml:space="preserve">oſtendit in quo ſtatu adhuc perſeuerat hoc menſe. <lb/></s> <s xml:id="echoid-s13870" xml:space="preserve">Nouembri 1619. </s> <s xml:id="echoid-s13871" xml:space="preserve">quo hæc imprimuntur. </s> <s xml:id="echoid-s13872" xml:space="preserve">vide Galilæum in lib. </s> <s xml:id="echoid-s13873" xml:space="preserve">de maculis circa finem; </s> <s xml:id="echoid-s13874" xml:space="preserve">necnon Diſquiſitio-<lb/>nes Mathematicas Pater Chriſtophori Scheiner noſtræ Soc.</s> <s xml:id="echoid-s13875" xml:space="preserve"/> </p> <div xml:id="echoid-div323" type="float" level="2" n="1"> <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a"> <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01"/> </figure> </div> </div> <div xml:id="echoid-div325" type="section" level="1" n="230"> <head xml:id="echoid-head245" xml:space="preserve">LIBER DECIMVSSEXTVS <lb/>DE COMETIS.</head> <p> <s xml:id="echoid-s13876" xml:space="preserve">PLacet hoc loco poſt tractatum de perpetuis, & </s> <s xml:id="echoid-s13877" xml:space="preserve">ordinarijs planetis ſubijcere tractatũ de Co-<lb/>metis, quandoquidem multi ex recentioribus Aſtronomis pleroſq; </s> <s xml:id="echoid-s13878" xml:space="preserve">omnes Cometas, quot-<lb/>quot ipſi videlicet obſeruarũt, eos in planetaria cæli regione depræhenderunt, vnde etiam <lb/>ijſdem placuit planetas extraordinarios, ac temporaneos appellare Cometas. </s> <s xml:id="echoid-s13879" xml:space="preserve">Neque vero <lb/>hæc, de cæleſtibus Cometis ſententia (vt parum eruditi exiſtimant) noua eſt, ſed omnibus <lb/>ſæculis quibus philoſophatum eſt coæua; </s> <s xml:id="echoid-s13880" xml:space="preserve">nam teſtibus Ariſtotile, Seneca, & </s> <s xml:id="echoid-s13881" xml:space="preserve">alijs Py@hago-<lb/>rici, & </s> <s xml:id="echoid-s13882" xml:space="preserve">Italica ſecta, aſſerebant Cometam eſſe vnã ex ſtellis errantibus, ſed longis poſt tem-<lb/>porum interuallis apparere; </s> <s xml:id="echoid-s13883" xml:space="preserve">idem ſenſerunt Hippocrates Chius ex eodem Ariſtotile, necnon Diogenes ex <lb/>Plutarcho de placitis Philos. </s> <s xml:id="echoid-s13884" xml:space="preserve">Chaldæi etiam Aſtronomorum antiquiſſimi, vt refert Apollonius Mindius <lb/>apud Plutarchus Cometas in planetarum numero ponebant. </s> <s xml:id="echoid-s13885" xml:space="preserve">quibus aſſentitur ipſe Apollonius Mindius. </s> <s xml:id="echoid-s13886" xml:space="preserve">Se-<lb/>neca poſtea ſæculo non tam vetuſto, pluribus enixè contendit Cometas non tantum cæleſtes eſſe, verum. <lb/></s> <s xml:id="echoid-s13887" xml:space="preserve">etiam inter æterna naturæ opera ponit. </s> <s xml:id="echoid-s13888" xml:space="preserve">vide eius lib. </s> <s xml:id="echoid-s13889" xml:space="preserve">7. </s> <s xml:id="echoid-s13890" xml:space="preserve">nat. </s> <s xml:id="echoid-s13891" xml:space="preserve">qu. </s> <s xml:id="echoid-s13892" xml:space="preserve">cap. </s> <s xml:id="echoid-s13893" xml:space="preserve">22. </s> <s xml:id="echoid-s13894" xml:space="preserve">& </s> <s xml:id="echoid-s13895" xml:space="preserve">23. </s> <s xml:id="echoid-s13896" xml:space="preserve">propinquiori poſtea æuo, in ea-<lb/>dem ſententia perſeuerauit Albumazar magni inter Arabes nominis; </s> <s xml:id="echoid-s13897" xml:space="preserve">vt tradit Cardanus de ſubtilitate. </s> <s xml:id="echoid-s13898" xml:space="preserve">& </s> <s xml:id="echoid-s13899" xml:space="preserve"><lb/>ſuperiori nobis ſæculo, idem Cardanus citato lib. </s> <s xml:id="echoid-s13900" xml:space="preserve">de ſubtilitat<unsure/>e idem demonſtrare conatus eſt. </s> <s xml:id="echoid-s13901" xml:space="preserve">noſtra deniq; </s> <s xml:id="echoid-s13902" xml:space="preserve"><lb/>ætate, qua Aſtrologicę obſeruationes, magnis ac fabrefactis organis etiam circa Cometas habentur, hanc per <lb/>omnes ætates deductam opinionem veram eſſe, conſultiſſimi Aſtronomiæ luculentiſſimè comprobare ni-<lb/>tuntur. </s> <s xml:id="echoid-s13903" xml:space="preserve">Verum antequam eorum argumenta afferamus, præſtat de Cometarum accidentibus, per apparen-<lb/>tias, & </s> <s xml:id="echoid-s13904" xml:space="preserve">obſeruationes depræhenſis, pertractare.</s> <s xml:id="echoid-s13905" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div326" type="section" level="1" n="231"> <head xml:id="echoid-head246" style="it" xml:space="preserve">Figura Cometarum. Cap. I.</head> <p> <s xml:id="echoid-s13906" xml:space="preserve">VAriæ ſunt Cometarum figuræ, quarum duæ ſunt præcipuæ: </s> <s xml:id="echoid-s13907" xml:space="preserve">Alij enim crines vndique in orbem vi-<lb/>brant, qui criniti, cincinnati, & </s> <s xml:id="echoid-s13908" xml:space="preserve">Cometæ propriæ appellantur: </s> <s xml:id="echoid-s13909" xml:space="preserve">Alij vero ad vnam tantum partem. <lb/></s> <s xml:id="echoid-s13910" xml:space="preserve">barbam, aut caudam radioſam demittunt, hique barbati, caudatique dicuntur. </s> <s xml:id="echoid-s13911" xml:space="preserve">Porro Cometa græca vox <lb/>eſt, nam Kομητης, comatum, ſeu crinitum ſignificat: </s> <s xml:id="echoid-s13912" xml:space="preserve">à Kομη, qua coma latinè dicitur.</s> <s xml:id="echoid-s13913" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div327" type="section" level="1" n="232"> <head xml:id="echoid-head247" style="it" xml:space="preserve">Magnitudo apparens Cometarum.</head> <p> <s xml:id="echoid-s13914" xml:space="preserve">MInimi ſunt inſtar vnius maximæ ſtellæ fixæ; </s> <s xml:id="echoid-s13915" xml:space="preserve">maximi inſtar Solis; </s> <s xml:id="echoid-s13916" xml:space="preserve">nam teſte Seneca, Neronis tempore, <lb/>Cometas vnus Solem magnitudine adæquauit. </s> <s xml:id="echoid-s13917" xml:space="preserve">alij ſuas magnitudines inter haſce extremas multipli-<lb/>ci varietate medias continent. </s> <s xml:id="echoid-s13918" xml:space="preserve">vbi illud maximè notandum, eundem Cometam non ſeruare eandem figuræ <lb/>magnitudinem, ſed eam iuxta motum quem habet proprium, variare, non enim vt videbimus, æquabiliter <lb/>incedunt; </s> <s xml:id="echoid-s13919" xml:space="preserve">quare figuram imminuunt, vel augent, pro vt eorum etiam motus remittitur vel intenditur: </s> <s xml:id="echoid-s13920" xml:space="preserve">quod <lb/>exactè olim Seneca, nunc vero Tycho obſeruarunt, vt ille cap. </s> <s xml:id="echoid-s13921" xml:space="preserve">8. </s> <s xml:id="echoid-s13922" xml:space="preserve">de Cometis: </s> <s xml:id="echoid-s13923" xml:space="preserve">hic vero in Cometa anni 1577. <lb/></s> <s xml:id="echoid-s13924" xml:space="preserve">enarrat. </s> <s xml:id="echoid-s13925" xml:space="preserve">nonnulli initio magni apparent, poſtea paulatim minuuntur, vt amplius diſcerni nequeant; </s> <s xml:id="echoid-s13926" xml:space="preserve">alij <lb/>eontra initio ſunt parui, demum decreſcunt vſq; </s> <s xml:id="echoid-s13927" xml:space="preserve">ad apparentem interitum.</s> <s xml:id="echoid-s13928" xml:space="preserve"/> </p> <pb o="156" file="0178" n="183" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div328" type="section" level="1" n="233"> <head xml:id="echoid-head248" style="it" xml:space="preserve">Apparens duratio Cometarum.</head> <p> <s xml:id="echoid-s13929" xml:space="preserve">MInimum quidam octo dies affulgent: </s> <s xml:id="echoid-s13930" xml:space="preserve">alij ſuas augent ætates, vſq; </s> <s xml:id="echoid-s13931" xml:space="preserve">ad ſemeſtre ſpatium; </s> <s xml:id="echoid-s13932" xml:space="preserve">nam magnus il-<lb/>le Neronis Cometa ſex totis eft<unsure/>ulſit menſibus: </s> <s xml:id="echoid-s13933" xml:space="preserve">alius anno Chriſti 1240. </s> <s xml:id="echoid-s13934" xml:space="preserve">qui crines in medium vſq; </s> <s xml:id="echoid-s13935" xml:space="preserve">cæli <lb/>ab horizonte c<unsure/>uibrabat, vix intra ſex menſes, vt ſcribit Daniel Santbechius, extinctus eſt.</s> <s xml:id="echoid-s13936" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div329" type="section" level="1" n="234"> <head xml:id="echoid-head249" style="it" xml:space="preserve">Motus Cometarum. Cap. II.</head> <p> <s xml:id="echoid-s13937" xml:space="preserve">DVplici motu perinde ac veri, & </s> <s xml:id="echoid-s13938" xml:space="preserve">perpetui planetæ; </s> <s xml:id="echoid-s13939" xml:space="preserve">Cometæ, qui ſpurij, & </s> <s xml:id="echoid-s13940" xml:space="preserve">euanidi pariter ſunt planetæ, <lb/>aguntur: </s> <s xml:id="echoid-s13941" xml:space="preserve">motu videlicet diurno, quo circa mundi centrum integras quotidie conuerſiones abſoluunt, <lb/>ac proinde non aliter, ac cætera ſydera quotidie oriuntur, & </s> <s xml:id="echoid-s13942" xml:space="preserve">occidunt, dummodo in ea cæli parte exiſtant, <lb/>quæ ortum, & </s> <s xml:id="echoid-s13943" xml:space="preserve">occaſum patiatur, ſeu quæ in diurna conuerſione noſtrum horizontem prætereant. </s> <s xml:id="echoid-s13944" xml:space="preserve">præterea <lb/>motu proprio meant, quo non in eodem cæli loco hærent, ſed ab eo, in quo primum affulſerunt, quotidie. <lb/></s> <s xml:id="echoid-s13945" xml:space="preserve">abeunt. </s> <s xml:id="echoid-s13946" xml:space="preserve">qui motus antiquis etiam compertus fuit; </s> <s xml:id="echoid-s13947" xml:space="preserve">nequaquam enim eos inter errantia ſydera computaſſent, <lb/>niſi eo@ planetarum inſtar, peculiari curſu in cælo errabundos eſſe cognouiſſent. </s> <s xml:id="echoid-s13948" xml:space="preserve">Ariſtotiles apertè de quo-<lb/>dam magno Cometa id aſſerit; </s> <s xml:id="echoid-s13949" xml:space="preserve">qui cum primum viſus fit veſperi in occaſu æquinoctiali, Sole in principio <lb/>Capricorni brumam efficiente, neceſſe eſt eum extitiſſe propè æquatorem, è regione primi gradus Sagitta-<lb/>rij, vt in ſphæra materiali videre eſt, ea Aſtronomicè collocata, poſitoq; </s> <s xml:id="echoid-s13950" xml:space="preserve">Sole in principio Capricorni, eoq; </s> <s xml:id="echoid-s13951" xml:space="preserve"><lb/>iam demerſo, ſic enim videbis gradum æquinoctialis occidentem, in quo Cometa erat, eſſe è regione primi <lb/>gradus Sagittarij. </s> <s xml:id="echoid-s13952" xml:space="preserve">poſtea paulatim ad orientem in conſequentia perrexit, vnde & </s> <s xml:id="echoid-s13953" xml:space="preserve">à Sole remotior, & </s> <s xml:id="echoid-s13954" xml:space="preserve">ſupra <lb/>horizontẽ altior ex parte occidentis apparebat; </s> <s xml:id="echoid-s13955" xml:space="preserve">donec ad Orionis zonam aſcendit, vbi extinctus eſt. </s> <s xml:id="echoid-s13956" xml:space="preserve">Orion <lb/>autem tunc temporis erat circa finem ſigni Tauri, quare proprio curſu ad orientem peregit hæc ſigna, Sa-<lb/>gittarium, Capricornum, Aquarium, Piſces, Arietem, & </s> <s xml:id="echoid-s13957" xml:space="preserve">Taurum. </s> <s xml:id="echoid-s13958" xml:space="preserve">qui ſemicirculum, ſeu gr. </s> <s xml:id="echoid-s13959" xml:space="preserve">90. </s> <s xml:id="echoid-s13960" xml:space="preserve">efficiunt. </s> <s xml:id="echoid-s13961" xml:space="preserve">Se-<lb/>neca ipſe motum hunc non ſolum agnouit, ſed præterea obſeruauit per lineam in cælo rectam fieri; </s> <s xml:id="echoid-s13962" xml:space="preserve">ſeu vt <lb/>aiunt Aſtronomi, per circuli maximi portionem, cap. </s> <s xml:id="echoid-s13963" xml:space="preserve">enim 8. </s> <s xml:id="echoid-s13964" xml:space="preserve">ait, Cometarum curſus lenis, & </s> <s xml:id="echoid-s13965" xml:space="preserve">per diem, ac <lb/>noctem quantum tranſierit abſcondit. </s> <s xml:id="echoid-s13966" xml:space="preserve">& </s> <s xml:id="echoid-s13967" xml:space="preserve">paulo poſt ſubdit, Cometarum curſus compoſitus, & </s> <s xml:id="echoid-s13968" xml:space="preserve">deſtinatũ iter <lb/>carpens, nõ confusè, nec tumultuoſe eunt, ceu cauſis turbulentis, & </s> <s xml:id="echoid-s13969" xml:space="preserve">inconſtantibus appellantur. </s> <s xml:id="echoid-s13970" xml:space="preserve">cap. </s> <s xml:id="echoid-s13971" xml:space="preserve">vero 29. </s> <s xml:id="echoid-s13972" xml:space="preserve"><lb/>ſic, alter ille Cometa à Septentrione primum viſus, non deſijt in rectum aſſiduè celſior fieri, donec exceſſit: </s> <s xml:id="echoid-s13973" xml:space="preserve"><lb/>alter intra ſextum menſem dimidiam cæli partem tranſcurrit. </s> <s xml:id="echoid-s13974" xml:space="preserve">Recentiores vero idem exactius, ex accuratis <lb/>obſeruationibus comprobarunt. </s> <s xml:id="echoid-s13975" xml:space="preserve">quorum primus fuit eximius ille I<unsure/>oannes Regiomontanus, qui poſſ<unsure/>ea au-<lb/>reum libellum de Cometis elucubrauit. </s> <s xml:id="echoid-s13976" xml:space="preserve">ſuperiori vero ætate Tycho, cum alijs pluribus Aſtronomis, eũdem <lb/>maximum circulum exactiſſimè ſæpius obſeruarunt, idque hoc ferè modo; </s> <s xml:id="echoid-s13977" xml:space="preserve">curſum, ſeu viam Cometæ pro-<lb/>priam comparant ad viciniores ſtellas ſixas, ſecus quas quotidie progrediuntur, notando ſcilicet eius ab illis <lb/>diſtantias, ideſt, diſtantias locorum Cometæ ab illis, quæ loca poſtea in aſtronomico globo in quo ſtellæ ritè <lb/>ſint collocatæ, depingũt; </s> <s xml:id="echoid-s13978" xml:space="preserve">vnde manifeſtè apparet ea omnia loca in portione circuli maximi exactè, eſſe con-<lb/>ſtituta. </s> <s xml:id="echoid-s13979" xml:space="preserve">Diſtantiæ autem Cometæ à vicinis ſtellis accipi poſſunt per noſtrum quadrantem, ita ſitum, vt ſimul <lb/>per Cometam, & </s> <s xml:id="echoid-s13980" xml:space="preserve">Stellam, eius circumferentia tranſiens, & </s> <s xml:id="echoid-s13981" xml:space="preserve">dioptra nunc ſtellam, nunc Cometam aſpiciens, <lb/>gradus in circumferentia inter vtramq; </s> <s xml:id="echoid-s13982" xml:space="preserve">inſpectionem interceptos manifeſtet.</s> <s xml:id="echoid-s13983" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13984" xml:space="preserve">Cæterum hæc loca cometæ quotidiana, ſic Gemma Friſius in aſtronomico Globo depingit: </s> <s xml:id="echoid-s13985" xml:space="preserve">aſſumit quo-<lb/>cidie ſtellas quatuor cometæ circunſtantes, ita vt cometa ſit in concurſu earum linearum, quæ oppoſitas ſtel-<lb/>las iungant; </s> <s xml:id="echoid-s13986" xml:space="preserve">quod per filum oculis prætenſum, atque aſſumptis ſtellis, & </s> <s xml:id="echoid-s13987" xml:space="preserve">come-<lb/> <anchor type="figure" xlink:label="fig-0178-01a" xlink:href="fig-0178-01"/> tæ obiectum examinat, v.</s> <s xml:id="echoid-s13988" xml:space="preserve">g. </s> <s xml:id="echoid-s13989" xml:space="preserve">ſit cometa A. </s> <s xml:id="echoid-s13990" xml:space="preserve">in medio quatuor ſtellarum B C D E. <lb/></s> <s xml:id="echoid-s13991" xml:space="preserve">ita vt filum per duas E C. </s> <s xml:id="echoid-s13992" xml:space="preserve">& </s> <s xml:id="echoid-s13993" xml:space="preserve">cometam ſimul trãſeat: </s> <s xml:id="echoid-s13994" xml:space="preserve">ſimiliter filum tranſeat per <lb/>duas B D. </s> <s xml:id="echoid-s13995" xml:space="preserve">atque iterum per cometam in globo igitur in quo hæ quatuor ſtellæ <lb/>ſint ſuis locis depictæ, ex tendatur duo fila per binas, ac binas ſtella, & </s> <s xml:id="echoid-s13996" xml:space="preserve">in com-<lb/>muni filorum concurſu erit cometæ locus ſic quotidie fiat, ſingulorumque die-<lb/>rum loca notentur, atque hinc manifeſte eius via, ſeu curſus apparebit eſſe re-<lb/>cta, ſeu portio circuli maximi, omnia enim illa loca erunt in directũ conſtituta.</s> <s xml:id="echoid-s13997" xml:space="preserve"/> </p> <div xml:id="echoid-div329" type="float" level="2" n="1"> <figure xlink:label="fig-0178-01" xlink:href="fig-0178-01a"> <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-01"/> </figure> </div> <p> <s xml:id="echoid-s13998" xml:space="preserve">Porrò<unsure/> hic proprius eorum motus non eſt idem in omnibus, ſed varius; </s> <s xml:id="echoid-s13999" xml:space="preserve">nam <lb/>alij ab occidente in orientem tendunt; </s> <s xml:id="echoid-s14000" xml:space="preserve">alij è contra. </s> <s xml:id="echoid-s14001" xml:space="preserve">omnes diligenter obſeruati deflectunt ad boream, vel <lb/>ad auſtrum, idque variè. </s> <s xml:id="echoid-s14002" xml:space="preserve">alij celerius, alij tardius mouentur. </s> <s xml:id="echoid-s14003" xml:space="preserve">Summa velocitas obſeruata ex Regiomontano <lb/>vno die peregit grad. </s> <s xml:id="echoid-s14004" xml:space="preserve">40. </s> <s xml:id="echoid-s14005" xml:space="preserve">nonnulli initio velociores, quam in fine. </s> <s xml:id="echoid-s14006" xml:space="preserve">alij in principio, & </s> <s xml:id="echoid-s14007" xml:space="preserve">in fine apparitionis <lb/>tarde mouentur: </s> <s xml:id="echoid-s14008" xml:space="preserve">in medio vero velociſſime perinde ac fi in aliquo epicyclo deuoluti prius deſcendentes tar-<lb/>di eſſent, poſ@ea circa epicycli perigæum veloces, tandem epicyclum ſcandentes tardi apparent.</s> <s xml:id="echoid-s14009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14010" xml:space="preserve">Quantitas autem eorum curſum, ſeu viæ, varia etiam eſt; </s> <s xml:id="echoid-s14011" xml:space="preserve">qui maximam peregerunt diſcurrerunt gr. </s> <s xml:id="echoid-s14012" xml:space="preserve">180. <lb/></s> <s xml:id="echoid-s14013" xml:space="preserve">vti ille quem ſupra ex Ariſtotile memorauimus; </s> <s xml:id="echoid-s14014" xml:space="preserve">& </s> <s xml:id="echoid-s14015" xml:space="preserve">alius de quo Regiomontanus, qui a Libra in Arietẽ con-<lb/>tra ſignorum ordinem grad. </s> <s xml:id="echoid-s14016" xml:space="preserve">180. </s> <s xml:id="echoid-s14017" xml:space="preserve">permeauit, alij grad. </s> <s xml:id="echoid-s14018" xml:space="preserve">90. </s> <s xml:id="echoid-s14019" xml:space="preserve">alij 44. </s> <s xml:id="echoid-s14020" xml:space="preserve">adhuc pauciores pro varia eorum natura. </s> <s xml:id="echoid-s14021" xml:space="preserve"><lb/>quamobrem ſicuti perpetui ac ordinarij pl<unsure/>anetæ motibus, velocitate, ac via, inuicem diſſerunt; </s> <s xml:id="echoid-s14022" xml:space="preserve">ita hi eua-<lb/>midi, & </s> <s xml:id="echoid-s14023" xml:space="preserve">extraordinarij ijſdem diſcrepant.</s> <s xml:id="echoid-s14024" xml:space="preserve"/> </p> <pb o="157" file="0179" n="184" rhead="Liber Decimnsſextus."/> </div> <div xml:id="echoid-div331" type="section" level="1" n="235"> <head xml:id="echoid-head250" style="it" xml:space="preserve">COROLLARIVM.</head> <p> <s xml:id="echoid-s14025" xml:space="preserve">EX dictis de motu cometarum videtur non omnino incongruum eſſe exiſtimare cometas deſcribere ſuo <lb/>proprio motu magnum quempiam epicyclum, hoc enim poſito ſaluantur eorum phænomena; </s> <s xml:id="echoid-s14026" xml:space="preserve">ſic enim <lb/>initio tardi, in medio veloces, in fine iterum ſegnes eſſent, hinc etiam maiores, & </s> <s xml:id="echoid-s14027" xml:space="preserve">minores apparebunt, ſi-<lb/>cuti etiam veri planetæ. </s> <s xml:id="echoid-s14028" xml:space="preserve">ſed cur plures initio apparent celeriores? </s> <s xml:id="echoid-s14029" xml:space="preserve">ſi in epicyclo reuoluerentur, omnes eſſent <lb/>initio tardiores, quia in deſcenſu primo apparerent. </s> <s xml:id="echoid-s14030" xml:space="preserve">Reſpondere poſſumus plurimos initio non aparere, ſeu <lb/>non conſpici, propter eorum paruitatem, niſi enim magni ſint, in ſe hominum oculos non conuertunt. </s> <s xml:id="echoid-s14031" xml:space="preserve">opi-<lb/>nior igitur eos quidem in cælo diu viſibiles eſſe, quamuis non animaduertantur; </s> <s xml:id="echoid-s14032" xml:space="preserve">quod ſi tunc, cum poſſunt, <lb/>cernerentur, tardi, ac minores apparent, quam poſtea. </s> <s xml:id="echoid-s14033" xml:space="preserve">Præterea nonnulli diu latent ob Solis vicinitatem; <lb/></s> <s xml:id="echoid-s14034" xml:space="preserve">qua propter cum poſtea heliacè oriuntur, iam circa epicycli perigæum mouemur, ac propterea velociores, <lb/>ac maiores, quam poſtea huius rei exemplum habemus in noua ſtella anni 1572. </s> <s xml:id="echoid-s14035" xml:space="preserve">quam Tycho pag. </s> <s xml:id="echoid-s14036" xml:space="preserve">304. </s> <s xml:id="echoid-s14037" xml:space="preserve">ſcri-<lb/>bit multo prius conſpectam eſſe ab Aurigis, Nautis, & </s> <s xml:id="echoid-s14038" xml:space="preserve">Ruſticis, quam a Philoſophi, aut Aſtronom is, quare <lb/>idem cometis ferè omnibus accidere opinior.</s> <s xml:id="echoid-s14039" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div332" type="section" level="1" n="236"> <head xml:id="echoid-head251" style="it" xml:space="preserve">Barba ſeu cauda Cometarum.</head> <p> <s xml:id="echoid-s14040" xml:space="preserve">ILlud maximè notandum in omnibus cometis barbatis, ſeu caudatis, barbam hanc extendi ad partes Soli@ <lb/>auerſas, ideſt, ſi Sol ſit in occidente, cometa directè barbam proijciet in orientem; </s> <s xml:id="echoid-s14041" xml:space="preserve">è contra ſi Sol fuerit in <lb/>oriente, cauda in occidentem recta dirigetur. </s> <s xml:id="echoid-s14042" xml:space="preserve">in quo recentiores omnes conſentiunt. </s> <s xml:id="echoid-s14043" xml:space="preserve">Petrus Appia@us id <lb/>diligentiſſimè in 8. </s> <s xml:id="echoid-s14044" xml:space="preserve">cometis; </s> <s xml:id="echoid-s14045" xml:space="preserve">Gemma Friſius in alijs, Tycho tandem in quinque barbatis idem exactè admo-<lb/>dum obſeruauit, in vno ſolum dubitat, qui videbatur caudam non a Sole, ſed a Venere directè auertere; </s> <s xml:id="echoid-s14046" xml:space="preserve">quod <lb/>tamen alicui viſus fallaciæ tribuendum putat. </s> <s xml:id="echoid-s14047" xml:space="preserve">Cauſam huius reiputant eſſe Solis fulgorem, corous cometæ <lb/>percadentem, & </s> <s xml:id="echoid-s14048" xml:space="preserve">inde in oppoſitam partem emicantem: </s> <s xml:id="echoid-s14049" xml:space="preserve">ſicuti etiam videmus vitream pilam Soli, expoſitam, <lb/>in partem Soli auerſam lumen Solis ſe peruadens, ita vnire ac tranſmittere, vt non ſolum appareat, ſed com-<lb/>burat etiam. </s> <s xml:id="echoid-s14050" xml:space="preserve">Veruntamen caudæ curuitas, & </s> <s xml:id="echoid-s14051" xml:space="preserve">figura non accuta, ſed lata, difficultatem aliquam ingerit. </s> <s xml:id="echoid-s14052" xml:space="preserve">Cæ-<lb/>terum ſicuti lumen Solis in aere, vel æthere puro neutiquam apparet ſic etiam cauda cometæ in puro ac om-<lb/>nino diaphano cælo ſpectari minimè poterit, quare putandum eſt huic caudo opacam aliquam ſubeſſe mate-<lb/>riam. </s> <s xml:id="echoid-s14053" xml:space="preserve">Maxima autem caudæ longitudo ex obſeruatione d<unsure/>eprehenſa eſt grad. </s> <s xml:id="echoid-s14054" xml:space="preserve">22.</s> <s xml:id="echoid-s14055" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div333" type="section" level="1" n="237"> <head xml:id="echoid-head252" style="it" xml:space="preserve">Parallaxes Cometarum. Cap. III.</head> <p> <s xml:id="echoid-s14056" xml:space="preserve">INgenioſa acſubtilitate plena res eſt parallaxis, per eam enim totius mundanæ fabricæ ordinem ac ſitum <lb/>perſcrutamur. </s> <s xml:id="echoid-s14057" xml:space="preserve">quod ſi in cæteris, ordinarijſque ſyderibus vſum habet præclariſſimum, in cometis certè <lb/>omnem ſuperat admirationem, qui enim fieri poteſt, in re adeo vaga, noua, & </s> <s xml:id="echoid-s14058" xml:space="preserve">inconſtanti, vt parallaxis in-<lb/>dagetur? </s> <s xml:id="echoid-s14059" xml:space="preserve">veteres tamen Aſtronomi hanc in cometis curam omittentes, proinde nihil certi de eorum a terris <lb/>diſtantia tradiderunt. </s> <s xml:id="echoid-s14060" xml:space="preserve">recentiores igitur latini hanc gloriæ palmam ſibi oblatam minimè neglexerunt. </s> <s xml:id="echoid-s14061" xml:space="preserve">Pa-<lb/>rallaxim igitur cometarum dupliciter indagant. </s> <s xml:id="echoid-s14062" xml:space="preserve">Primo ex diuerſis, & </s> <s xml:id="echoid-s14063" xml:space="preserve">valde diffiſis locis, ſecundum terræ la-<lb/>titudinem, quorum ſcilicet poli altitudines valde differant. </s> <s xml:id="echoid-s14064" xml:space="preserve">exemplo ſit illa, quam Tycho Vraniburgi in Da-<lb/>nia, & </s> <s xml:id="echoid-s14065" xml:space="preserve">Tadæus Hagecius Pragæ in Boemia obſeruarunt; </s> <s xml:id="echoid-s14066" xml:space="preserve">quæ duo loca d@fferunt in altitudine poli, nam Vra-<lb/>niburgum altiorem habet polum 6. </s> <s xml:id="echoid-s14067" xml:space="preserve">gradibus, quam Praga: </s> <s xml:id="echoid-s14068" xml:space="preserve">& </s> <s xml:id="echoid-s14069" xml:space="preserve">præterea ſunt ſub eodem ferè meridiano, quod <lb/>negotium illud multum iuuat. </s> <s xml:id="echoid-s14070" xml:space="preserve">vterque pręterea eodem die, eademque hora, & </s> <s xml:id="echoid-s14071" xml:space="preserve">conſequenter in eodem cir-<lb/>culo verticali cometam obſeruauit. </s> <s xml:id="echoid-s14072" xml:space="preserve">Obſeruauit autem vterque quantum d@ſtaret a ſtella, quæ Vultur appel-<lb/>latur, ideſt, quot gradibus eſſet infra eam, erat enim in eodem verticuli cum ea: </s> <s xml:id="echoid-s14073" xml:space="preserve">vterque autem reperit ean-<lb/>dem diſtantiam; </s> <s xml:id="echoid-s14074" xml:space="preserve">& </s> <s xml:id="echoid-s14075" xml:space="preserve">conſequenter vterq; </s> <s xml:id="echoid-s14076" xml:space="preserve">aſpexit eum eſſe in eodem cæli <lb/> <anchor type="figure" xlink:label="fig-0179-01a" xlink:href="fig-0179-01"/> puncto, ac proinde nullam pati parallaxim, ideſt, nullam exhibere va-<lb/>rietatem aſpectus ex locis adeo ſeiunctis. </s> <s xml:id="echoid-s14077" xml:space="preserve">ſit in præſenti figura A. </s> <s xml:id="echoid-s14078" xml:space="preserve">Vra-<lb/>niburgum, B. </s> <s xml:id="echoid-s14079" xml:space="preserve">Praga, F. </s> <s xml:id="echoid-s14080" xml:space="preserve">Stella Vulturis, C. </s> <s xml:id="echoid-s14081" xml:space="preserve">Cometa, in eodem vertica-<lb/>li F C E. </s> <s xml:id="echoid-s14082" xml:space="preserve">iam diſtantia C F. </s> <s xml:id="echoid-s14083" xml:space="preserve">vtriq; </s> <s xml:id="echoid-s14084" xml:space="preserve">viſa eſt gr. </s> <s xml:id="echoid-s14085" xml:space="preserve">17. </s> <s xml:id="echoid-s14086" xml:space="preserve">min. </s> <s xml:id="echoid-s14087" xml:space="preserve">52. </s> <s xml:id="echoid-s14088" xml:space="preserve">quare vterque <lb/>eam in eodem cæli loco conſpexit. </s> <s xml:id="echoid-s14089" xml:space="preserve">quod ſignum euidens eſt Cometam <lb/>ſublimius fuiſſe Luna, & </s> <s xml:id="echoid-s14090" xml:space="preserve">alijs planetis, qui ſenſibilem exhibent paralla-<lb/>xim; </s> <s xml:id="echoid-s14091" xml:space="preserve">ſi enim fuiſ@et in eadem diſtantia cum Luna a terris, v.</s> <s xml:id="echoid-s14092" xml:space="preserve">g. </s> <s xml:id="echoid-s14093" xml:space="preserve">in D. </s> <s xml:id="echoid-s14094" xml:space="preserve">tũc <lb/>Vraniburgi conſpecta fuiſſet in E. </s> <s xml:id="echoid-s14095" xml:space="preserve">humilior, & </s> <s xml:id="echoid-s14096" xml:space="preserve">remotior a Stella F. </s> <s xml:id="echoid-s14097" xml:space="preserve">vt <lb/>oſtendit linea viſiua A D E. </s> <s xml:id="echoid-s14098" xml:space="preserve">ſi fuiſſet in cõcauitate regionis lunaris, quę <lb/>a terra diſtat ſemid. </s> <s xml:id="echoid-s14099" xml:space="preserve">terræ 52. </s> <s xml:id="echoid-s14100" xml:space="preserve">exhibuiſſet parallaxim min. </s> <s xml:id="echoid-s14101" xml:space="preserve">7. </s> <s xml:id="echoid-s14102" xml:space="preserve">ferè, vt pa-<lb/>tebit ex conſtructione figuræ, quæ habeat poli altitudines, quas habet <lb/>Vraniburgum, & </s> <s xml:id="echoid-s14103" xml:space="preserve">Praga, & </s> <s xml:id="echoid-s14104" xml:space="preserve">c. </s> <s xml:id="echoid-s14105" xml:space="preserve">(quas videas apud Tychonem pag. </s> <s xml:id="echoid-s14106" xml:space="preserve">125. <lb/></s> <s xml:id="echoid-s14107" xml:space="preserve">in lib. </s> <s xml:id="echoid-s14108" xml:space="preserve">de Cometis) & </s> <s xml:id="echoid-s14109" xml:space="preserve">præterea Cometa diſtet à terra ſemid. </s> <s xml:id="echoid-s14110" xml:space="preserve">52. </s> <s xml:id="echoid-s14111" xml:space="preserve">in hu@ <lb/>iuſmodi enim figura, non vterque inſpector eundem cæli locum Co-<lb/>metæ conſpiciet, ſed diuerſitas aſpectus prædicta apparebit, hoc igitur modo, ex diuerſis locis parallaxi@ <lb/>depræbenditur.</s> <s xml:id="echoid-s14112" xml:space="preserve"/> </p> <div xml:id="echoid-div333" type="float" level="2" n="1"> <figure xlink:label="fig-0179-01" xlink:href="fig-0179-01a"> <image file="0179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179-01"/> </figure> </div> <pb o="158" file="0180" n="185" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s14113" xml:space="preserve">Sed ex eodem loco, eleganter admodum, vnico filo, in tantæ ſubtilitatis negotium, aduocato, parallaxis <lb/>depræhenditur. </s> <s xml:id="echoid-s14114" xml:space="preserve">Cum igitur Cometa in fine durationis proprio motu adeo lenteſcit, vt vix incedat, bis ob-<lb/>ſeruandus eſt per filum hoc modo. </s> <s xml:id="echoid-s14115" xml:space="preserve">Primo cum valde ab horizonte ſublimis fuerit, notentur binæ ſtellæ ei <lb/>viciniores, inter quas ipſe collocatus ſit in recta linea, quæ ſit horizonti paralella; </s> <s xml:id="echoid-s14116" xml:space="preserve">quod per filum in directum <lb/>ſtellis aſſumptis expoſitum, atq; </s> <s xml:id="echoid-s14117" xml:space="preserve">oculis prætenſum experiri oportet. </s> <s xml:id="echoid-s14118" xml:space="preserve">poſtea cum occaſurus propè horizontẽ <lb/>fueri; </s> <s xml:id="echoid-s14119" xml:space="preserve">iterum prætenſo ſilo expendendum eſt, an in eadem recta linea cum ijſdem ſtellis exiſtat: </s> <s xml:id="echoid-s14120" xml:space="preserve">ſi enim exi-<lb/>ſtit nullam exhibet parallaxim, ac proinde alto cælo ſpatiatur: </s> <s xml:id="echoid-s14121" xml:space="preserve">ſi vero fuerit humilior, quam vt ſit in ea recta. <lb/></s> <s xml:id="echoid-s14122" xml:space="preserve">linea cum ijſdem ſtellis, aliquam ſubibit parallaxim; </s> <s xml:id="echoid-s14123" xml:space="preserve">quæ quanta ſit ſi exactè lubeat ſcire, noſtro quadrante <lb/>obſeruandum eſt, quot minutis, vel gradibus à prædiæa rectitudine diſcedat; </s> <s xml:id="echoid-s14124" xml:space="preserve">tanta enim erit aſpectus euaria-<lb/>tio. </s> <s xml:id="echoid-s14125" xml:space="preserve">Neq; </s> <s xml:id="echoid-s14126" xml:space="preserve">vero quidquam à refractione timendum eſt, quæ propè horizontem ob aeris craſſitiem, ſolet ſyde-<lb/>ra ſupra verum eorum locum efferre; </s> <s xml:id="echoid-s14127" xml:space="preserve">quia hæc ipſius hallucinatio tam Cometam, quam Stellas aſſumptas pa-<lb/>riter eleuabit, ac proinde eadem eorum mutua diſtantia, ac poſitio remanebit, ac ſi nulla eſſet refractio. </s> <s xml:id="echoid-s14128" xml:space="preserve">Ob-<lb/>ſeruari etiam poteſt apud horizontem ortiuum intra binas ſtellas in recta linea horizonti paralella, ſi enim. </s> <s xml:id="echoid-s14129" xml:space="preserve"><lb/>cum poſtea valde ſublimis fuerit, apparuerit in eadem rectitudine nullam patietur parallaxim, ſi vero aſſum-<lb/>ptis ſtellis fuerit altior, quam in recta linea, parallaxim patietur: </s> <s xml:id="echoid-s14130" xml:space="preserve">quod ſi adſit motus proprius, is detrahendus <lb/>eſt pro ratione temporis elapſi à prima obſeruatione vſq; </s> <s xml:id="echoid-s14131" xml:space="preserve">ad ſecundam.</s> <s xml:id="echoid-s14132" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14133" xml:space="preserve">Aliter per quadrantem, hoc modo, obſeruetur diligenter in maxima Cometæ altitud ne diſtantia ipſius <lb/>ab aliqua vicina ſtella fixa, quæ ei ſupra, aut infra directè ſit, ſeu in eodem verticali, atq; </s> <s xml:id="echoid-s14134" xml:space="preserve">eis proxima; </s> <s xml:id="echoid-s14135" xml:space="preserve">idq; </s> <s xml:id="echoid-s14136" xml:space="preserve">fiat <lb/>quando Cometa, aut n<unsure/>ihil, aut vix proprio motu mouetur: </s> <s xml:id="echoid-s14137" xml:space="preserve">poſtea cum prope horizontem deſcenderit, note-<lb/>tur iterum earundem diſtantia, habita etiam ratione motus proprij, ſi quis affuerit; </s> <s xml:id="echoid-s14138" xml:space="preserve">nam ſi eadem diſtantia re-<lb/>manſerit, nulla aderit parallaxis, & </s> <s xml:id="echoid-s14139" xml:space="preserve">Cometa altiſſimus ſupra Lu <lb/> <anchor type="figure" xlink:label="fig-0180-01a" xlink:href="fig-0180-01"/> nam attolletur. </s> <s xml:id="echoid-s14140" xml:space="preserve">ſi vero diſtantia erit mutata, ita vt Cometa in-<lb/>ferior euaſerit, quam oporteret, tãta erit parallaxis, quanta hæc <lb/>diſtantiæ variatio, ſeu differentia a priori, ſiue ea maior, ſiue <lb/>minor apparuerit. </s> <s xml:id="echoid-s14141" xml:space="preserve">vt autem ſciamus quam altè in mundi diame-<lb/>tro hæc parallaxis eum euehat, conſtituẽda erit vera figura quæ <lb/>eandem parallaxim efficiat in eadem alt@tudine ab horizonte in <lb/>qua erat Cometa in vltima obſeruatione; </s> <s xml:id="echoid-s14142" xml:space="preserve">hęc enim diſtantia pa-<lb/>riter tunc notanda eſt; </s> <s xml:id="echoid-s14143" xml:space="preserve">ex tali enim figura apparebit, quot terræ <lb/>ſemidiametris attollatur: </s> <s xml:id="echoid-s14144" xml:space="preserve">vt in præſenti figura, vbi altitudo C E. <lb/></s> <s xml:id="echoid-s14145" xml:space="preserve">ſupra horizontem A C. </s> <s xml:id="echoid-s14146" xml:space="preserve">ponitur æqualis altitudini Cometæ in <lb/>vltima obſeruatione. </s> <s xml:id="echoid-s14147" xml:space="preserve">angulus deinde T E A. </s> <s xml:id="echoid-s14148" xml:space="preserve">debet eſſe æqualis <lb/>parallaxi, ideſt, continere tot grad. </s> <s xml:id="echoid-s14149" xml:space="preserve">aut min. </s> <s xml:id="echoid-s14150" xml:space="preserve">quot erant in dif-<lb/>ferentia diſtantiarum. </s> <s xml:id="echoid-s14151" xml:space="preserve">vltimo trianguli baſis ſit linea T A. </s> <s xml:id="echoid-s14152" xml:space="preserve">quæ <lb/>ſemidiametrum terræ referat. </s> <s xml:id="echoid-s14153" xml:space="preserve">poſtea per circinum diligenter <lb/>examinetur quoties ſemidiameter A T. </s> <s xml:id="echoid-s14154" xml:space="preserve">ingrediatur in lineam. </s> <s xml:id="echoid-s14155" xml:space="preserve"><lb/>A E. </s> <s xml:id="echoid-s14156" xml:space="preserve">nam totidem ſemidiameter diſtabit à terræ centro Cometa.</s> <s xml:id="echoid-s14157" xml:space="preserve"/> </p> <div xml:id="echoid-div334" type="float" level="2" n="2"> <figure xlink:label="fig-0180-01" xlink:href="fig-0180-01a"> <image file="0180-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0180-01"/> </figure> </div> </div> <div xml:id="echoid-div336" type="section" level="1" n="238"> <head xml:id="echoid-head253" style="it" xml:space="preserve">Locus ſiue altitudo Cometarum. Cap. IV.</head> <p> <s xml:id="echoid-s14158" xml:space="preserve">EX præmiſſis de figura, duratione, motu, ſitu, ac parallaxi Cometarum ijdem Aſtronomi non difficile<unsure/> eis <lb/>quoq; </s> <s xml:id="echoid-s14159" xml:space="preserve">locum in hac in<unsure/>undi fabrica tribuere. </s> <s xml:id="echoid-s14160" xml:space="preserve">aſſerunt igitur Cometas eos, qui nullam aut minorem, quam <lb/>Luna exhibent parallaxim, ſupra Lunam in cæleſti regione ſpatiari, quod quidem ipſius parallaxeos natura <lb/>euidenter conuincit, vti ſupra ſæpè oſtenſum eſt: </s> <s xml:id="echoid-s14161" xml:space="preserve">vbi ſciendum eſt recentiores Aſtronomos, qui in hanc curã <lb/>diligenter incubuerunt, comperiſſe Cometas quotquot obſeruarunt aut nullam, aut minorem quam Luna, <lb/>ſubijſſe parallaxim. </s> <s xml:id="echoid-s14162" xml:space="preserve">id luculenter Tycho explicat in quinque a ſe magna diligentia obſeruatis; </s> <s xml:id="echoid-s14163" xml:space="preserve">partim in lib. <lb/></s> <s xml:id="echoid-s14164" xml:space="preserve">integro de Cometa, partim in primo epiſtolarũ tomo. </s> <s xml:id="echoid-s14165" xml:space="preserve">cui alij complures doctiſſimi viri adſtipulantur. </s> <s xml:id="echoid-s14166" xml:space="preserve">qua-<lb/>re non ſolum illos quinque inter cæleſtia corpora annumerant, ſed etiam omnes alios eiuſdem eſſe conditio-<lb/>nis probare conati ſunt, ſequentibus rationibus. </s> <s xml:id="echoid-s14167" xml:space="preserve">Primo ex eorum motu, non proprio, ſed diurno, & </s> <s xml:id="echoid-s14168" xml:space="preserve">commu-<lb/>ni omnibus aſtris; </s> <s xml:id="echoid-s14169" xml:space="preserve">nam Cometæ-hor. </s> <s xml:id="echoid-s14170" xml:space="preserve">24. </s> <s xml:id="echoid-s14171" xml:space="preserve">cum cæteris aſtris circa totam terram reuoluuntur; </s> <s xml:id="echoid-s14172" xml:space="preserve">ac tanto tempore <lb/>ſupra horizontem manent, ſeu apparent, quanto affixa ſydera, aut ordinar j planetæ. </s> <s xml:id="echoid-s14173" xml:space="preserve">quod euidens ſignum <lb/>eſt, eos ſi non ſupra Lunam, ſaltem infra non longè ab ea circumferri; </s> <s xml:id="echoid-s14174" xml:space="preserve">ſi enim ferrentur circa terram ſpatio <lb/>24. </s> <s xml:id="echoid-s14175" xml:space="preserve">hor. </s> <s xml:id="echoid-s14176" xml:space="preserve">in circulo humili propè terram, v.</s> <s xml:id="echoid-s14177" xml:space="preserve">g. </s> <s xml:id="echoid-s14178" xml:space="preserve">in ſupremam aeris regione, aut parum ſupra, ſequeretur neceſſa-<lb/>rio eos breuiſſimo tempore ab ortu ad occaſum præteruolare, ideſt, modicum ſupra horizontem ſenſibilem <lb/>permanere; </s> <s xml:id="echoid-s14179" xml:space="preserve">ſed ſupra e@m, inſtar citiſſimi fulguris, præterlabi. </s> <s xml:id="echoid-s14180" xml:space="preserve">quod hac figuratione explico, atq; </s> <s xml:id="echoid-s14181" xml:space="preserve">demõſtro. </s> <s xml:id="echoid-s14182" xml:space="preserve"><lb/>ſit igitur in ea terræ circulus omniũ minimus, cuius ſemidiameter A C. </s> <s xml:id="echoid-s14183" xml:space="preserve">& </s> <s xml:id="echoid-s14184" xml:space="preserve">in linea A B. </s> <s xml:id="echoid-s14185" xml:space="preserve">contineantur ſemid. </s> <s xml:id="echoid-s14186" xml:space="preserve"><lb/>52. </s> <s xml:id="echoid-s14187" xml:space="preserve">hæc enim erit ſemid. </s> <s xml:id="echoid-s14188" xml:space="preserve">cõcaui lunaris regionis. </s> <s xml:id="echoid-s14189" xml:space="preserve">deſcribantur plures ſemicirculi circa terram, qui variorum <lb/>Cometarum diurnas conuerſiones reſerant, diuiſique ſint in partes 12. </s> <s xml:id="echoid-s14190" xml:space="preserve">æquales quæ correſpondeant hor. </s> <s xml:id="echoid-s14191" xml:space="preserve">12. </s> <s xml:id="echoid-s14192" xml:space="preserve"><lb/>quibus Cometa ſ@pra ſenſibilem horizontem D C E. </s> <s xml:id="echoid-s14193" xml:space="preserve">maneret, ſi eſ@emus in ſphæra recta; </s> <s xml:id="echoid-s14194" xml:space="preserve">ſuppono enim fa-<lb/>cilitatis cauſa, hanc d@monſtrationem fie@i, vel in ſphæra recta, vel ſaltem Cometam aſ@umptum ſub ęquino-<lb/>ctiali, mot@ primi mobilis conuerti. </s> <s xml:id="echoid-s14195" xml:space="preserve">hic proculdubio ex allatis ſuperius apparentijs, hor. </s> <s xml:id="echoid-s14196" xml:space="preserve">12. </s> <s xml:id="echoid-s14197" xml:space="preserve">totas ſub ſenſibi-<lb/>lem horizontem D E. </s> <s xml:id="echoid-s14198" xml:space="preserve">ſpectabitur. </s> <s xml:id="echoid-s14199" xml:space="preserve">ſi igitur Cometa gyraret per ſecundum circulum F G. </s> <s xml:id="echoid-s14200" xml:space="preserve">maneret ſupra ho- <pb o="159" file="0181" n="186" rhead="Liber Decimusſextus."/> @izontem prædictum horis tantum 8. </s> <s xml:id="echoid-s14201" xml:space="preserve">octo enim tantum partes illius, quæ horas octo repræſentant, ſupra ho-<lb/>rizontem extant, vt ipſa figura indicat, in arcu R S. </s> <s xml:id="echoid-s14202" xml:space="preserve">qui 8. </s> <s xml:id="echoid-s14203" xml:space="preserve">tantum partes continet; </s> <s xml:id="echoid-s14204" xml:space="preserve">hic vero gyrus diſtat a ſu-<lb/>perficie terræ vna tantum ſemidiametro, ideſt, milliarijs 3500. </s> <s xml:id="echoid-s14205" xml:space="preserve">atqui re ipſa talis Cometa 12. </s> <s xml:id="echoid-s14206" xml:space="preserve">hor. </s> <s xml:id="echoid-s14207" xml:space="preserve">apparet: <lb/></s> <s xml:id="echoid-s14208" xml:space="preserve">impoſſibile igitur eſt, eum in tam humili gyro reuolui; </s> <s xml:id="echoid-s14209" xml:space="preserve">quare multo minus in ſuprema aeris regione ferre-<lb/>tur, quæ milliaris tantum 50. </s> <s xml:id="echoid-s14210" xml:space="preserve">eleuatur, ibi enim pro apparenti celeritate, ac gyri paruitate ſupra horizõtem <lb/>vixappareret; </s> <s xml:id="echoid-s14211" xml:space="preserve">ſed citiſſimè decurreret ad occaſum. </s> <s xml:id="echoid-s14212" xml:space="preserve">præterea ſi Cometa eſſet in ſupremo aere, altitudinis 50. </s> <s xml:id="echoid-s14213" xml:space="preserve"><lb/>milliar. </s> <s xml:id="echoid-s14214" xml:space="preserve">tunc mutato vel modicè horizonte, aut ad Boream, aut ad Auſtrum occultaretur omnino: </s> <s xml:id="echoid-s14215" xml:space="preserve">verum <lb/> <anchor type="figure" xlink:label="fig-0181-01a" xlink:href="fig-0181-01"/> contra accidit, nam Cometæ vi-<lb/>dentur ab ijs omnibus terræ ha-<lb/>bitatoribus, a quibus etiam ſtellæ <lb/>ei propiores ſpectantur. </s> <s xml:id="echoid-s14216" xml:space="preserve">ſed reuer <lb/>tamur ad figuram, ſi percurreret <lb/>tertium ſemicirculum cuius ſemi-<lb/>diameter cõtinet 10. </s> <s xml:id="echoid-s14217" xml:space="preserve">ſemidiame-<lb/>ter terræ, Cometæ deeſſent {2/3}. </s> <s xml:id="echoid-s14218" xml:space="preserve">ho-<lb/>ræ ex hor. </s> <s xml:id="echoid-s14219" xml:space="preserve">12. </s> <s xml:id="echoid-s14220" xml:space="preserve">vna enim pars tertia <lb/>I L. </s> <s xml:id="echoid-s14221" xml:space="preserve">horę, latet infra horizontem <lb/>ex vna parte, altera I L. </s> <s xml:id="echoid-s14222" xml:space="preserve">ex altera. <lb/></s> <s xml:id="echoid-s14223" xml:space="preserve">in quarto ſemicirculo deeſſent {2/5}. </s> <s xml:id="echoid-s14224" xml:space="preserve"><lb/>horæ M N. </s> <s xml:id="echoid-s14225" xml:space="preserve">tandem in ſemicircu-<lb/>10 D E. </s> <s xml:id="echoid-s14226" xml:space="preserve">cuius ſemid. </s> <s xml:id="echoid-s14227" xml:space="preserve">continet 30. </s> <s xml:id="echoid-s14228" xml:space="preserve"><lb/>ſemid. </s> <s xml:id="echoid-s14229" xml:space="preserve">deeſſent {2/7}. </s> <s xml:id="echoid-s14230" xml:space="preserve">horæ E O. </s> <s xml:id="echoid-s14231" xml:space="preserve">vt fi-<lb/>gura oſtẽdit ad hor. </s> <s xml:id="echoid-s14232" xml:space="preserve">12. </s> <s xml:id="echoid-s14233" xml:space="preserve">ſupra ho-<lb/>rizontem complendas, quas Co-<lb/>meta explet: </s> <s xml:id="echoid-s14234" xml:space="preserve">quod ſi figura am-<lb/>plietur vſque ad ſemid. </s> <s xml:id="echoid-s14235" xml:space="preserve">43. </s> <s xml:id="echoid-s14236" xml:space="preserve">deſunt <lb/>{10/2}. </s> <s xml:id="echoid-s14237" xml:space="preserve">ad hor. </s> <s xml:id="echoid-s14238" xml:space="preserve">12. </s> <s xml:id="echoid-s14239" xml:space="preserve">qua propter adhuc <lb/>ſublimius fertur. </s> <s xml:id="echoid-s14240" xml:space="preserve">certo igitur ex <lb/>hac figura conuincitur Cometas <lb/>ſaltem propè lunarẽ regionẽ re-<lb/>uolui, vbi mora eorũ ſupra hori-<lb/>zontem inſenſibiliter minor eua-<lb/>deret horis 12. </s> <s xml:id="echoid-s14241" xml:space="preserve">verum cum pluri-<lb/>mi, omnem effugi<unsure/>ãt parallaxim, <lb/>ij altiffimo cælo, vel ſupra Solem <lb/>ad Iouis, & </s> <s xml:id="echoid-s14242" xml:space="preserve">Saturni prouincias <lb/>ſunt euehendi.</s> <s xml:id="echoid-s14243" xml:space="preserve"/> </p> <div xml:id="echoid-div336" type="float" level="2" n="1"> <figure xlink:label="fig-0181-01" xlink:href="fig-0181-01a"> <image file="0181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0181-01"/> </figure> </div> <p> <s xml:id="echoid-s14244" xml:space="preserve">2 Præterea aut elementares, <lb/>aut cæleſtes ſunt Cometæ, nõ ele-<lb/>mentares inquiunt, igitur cęleſtes <lb/>erunt. </s> <s xml:id="echoid-s14245" xml:space="preserve">quod minimè elementares <lb/>fint hinc probant. </s> <s xml:id="echoid-s14246" xml:space="preserve">Primo quia ex <lb/>prædictis patuit, eos in cælo fpa-<lb/>tiari, qua igitur ratione elemen-<lb/>tare quiddam in alienã ſibi mun-<lb/>di partem conſcendit, ibiq; </s> <s xml:id="echoid-s14247" xml:space="preserve">tam-<lb/>diu, tam regulariter mouetur, at-<lb/>que affulget? </s> <s xml:id="echoid-s14248" xml:space="preserve">Vnde Seneca, hoc <lb/>loco, ſyderis propriũ eſt, inquit, <lb/>ducere orbem, atq; </s> <s xml:id="echoid-s14249" xml:space="preserve">hoc Cometæ <lb/>omnes efficiunt. </s> <s xml:id="echoid-s14250" xml:space="preserve">deinde omne <lb/>quod cauſa temporalis accendit, <lb/>cito intercidit; </s> <s xml:id="echoid-s14251" xml:space="preserve">ſic faces ardent, ſic <lb/>fulmina in vnum valent ictum, <lb/>fic quæ tranſuerſæ dicuntur ſtel-<lb/>læ, & </s> <s xml:id="echoid-s14252" xml:space="preserve">cadentes præteruoiant, & </s> <s xml:id="echoid-s14253" xml:space="preserve"><lb/>fecantaera. </s> <s xml:id="echoid-s14254" xml:space="preserve">nullis ignibus, niſi in <lb/>ſuo mora eſt. </s> <s xml:id="echoid-s14255" xml:space="preserve">ſi ignis eſſet colle-<lb/>ctitius, & </s> <s xml:id="echoid-s14256" xml:space="preserve">repentinus, alternis die-<lb/>bus maiores, minoreſue fierent. </s> <s xml:id="echoid-s14257" xml:space="preserve">quiſquis eſtignis aere expreffus, in fuga, nec apparet niſi cum cadit. </s> <s xml:id="echoid-s14258" xml:space="preserve">Co-<lb/>metes habet ſuam ſedem, & </s> <s xml:id="echoid-s14259" xml:space="preserve">ideo non cito expellitur, ſed emetitur ſpatium ſuum; </s> <s xml:id="echoid-s14260" xml:space="preserve">nec extinguitur, ſed ex-<lb/>cedit. </s> <s xml:id="echoid-s14261" xml:space="preserve">hæc doctiffimus Latinorum Seneca. </s> <s xml:id="echoid-s14262" xml:space="preserve">quibus à tumultuaria, ac euanida Meteororum turba, Come-<lb/>@as excipit.</s> <s xml:id="echoid-s14263" xml:space="preserve"/> </p> <pb o="160" file="0182" n="187" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s14264" xml:space="preserve">3 Qua ratione motum proprium, quem initio celeriorem oſtendit, pedetentim ordinatè, & </s> <s xml:id="echoid-s14265" xml:space="preserve">proportio-<lb/>nabiliter inhibet?</s> <s xml:id="echoid-s14266" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14267" xml:space="preserve">4 Qua ratione ſublunare meteoron circulum maximum adeo exactè in cælo proprio motu deſcriberet, <lb/>ideſt, perpetuo, vt ait Seneca, tendens in directum.</s> <s xml:id="echoid-s14268" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14269" xml:space="preserve">5 Hic proprius eorum motus erat lunari proprio tardior, ergo ſecũdum vſitatas rationes, ſupra Lunam, <lb/>maiorem ducit orbem.</s> <s xml:id="echoid-s14270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14271" xml:space="preserve">6 Qua ratione elementare ſpectaculum tam longæuum foret, vt vel ad ſex menſes (teſte Seneca, & </s> <s xml:id="echoid-s14272" xml:space="preserve">qui-<lb/>dem oculato) aliquando Cometa appareat?</s> <s xml:id="echoid-s14273" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14274" xml:space="preserve">7 Eorum quoque vera magnitudo celeſtem eorum patria teſtatut; </s> <s xml:id="echoid-s14275" xml:space="preserve">mox enim probabitur nonnullos tota <lb/>terra maiores extitiffe.</s> <s xml:id="echoid-s14276" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14277" xml:space="preserve">8 Tandem eorum caudam quæ ſemper in partes Soli auerſas proijcitur, quid innuit? </s> <s xml:id="echoid-s14278" xml:space="preserve">ſi eſſet ignitum me-<lb/>teoron, flamma hæc potius ſurſum, vel hucilluc agitaretur: </s> <s xml:id="echoid-s14279" xml:space="preserve">ex quibus omnibus concludunt eos in cælo tan-<lb/>quam planetas temporaneos aſciſcendos eſſe: </s> <s xml:id="echoid-s14280" xml:space="preserve">Quod ſi quis vereatur aliquid noui cælo inuehere, ei cum an-<lb/>tiquis Italicis, Pythagoricis A, pollonio Mindio, & </s> <s xml:id="echoid-s14281" xml:space="preserve">Seneca, liceat Cometas inter æterna naturæ opera cenſe-<lb/>re, ita vt non de nouo in cælo generentur ſed de nouo appareant; </s> <s xml:id="echoid-s14282" xml:space="preserve">neq; </s> <s xml:id="echoid-s14283" xml:space="preserve">deſinant eſſe, ſed apparere: </s> <s xml:id="echoid-s14284" xml:space="preserve">forte enim <lb/>deſinunt, quod nimis in cæleſtes ſublimitates euehantur; </s> <s xml:id="echoid-s14285" xml:space="preserve">ſicq; </s> <s xml:id="echoid-s14286" xml:space="preserve">paulatim à noſtris viſibus ſe ſubducant: </s> <s xml:id="echoid-s14287" xml:space="preserve">paula-<lb/>timq; </s> <s xml:id="echoid-s14288" xml:space="preserve">proprium motum remittunt, quia inſtar planetarum in magno quopiam epicyclo ſurſum aſcendunt; <lb/></s> <s xml:id="echoid-s14289" xml:space="preserve">in quo aſcenſu tardi primum, mox ſtationarij euadunt: </s> <s xml:id="echoid-s14290" xml:space="preserve">deinde poſt longa tempora; </s> <s xml:id="echoid-s14291" xml:space="preserve">poſtquam per imagina-<lb/>ria illa ſpatia, quæ etiam extra mundum, nonnulli imaginantur, ſpatiati in ſuperiori parte epicycli fuerunt, <lb/>iterum ad nos deſcendere incipiant, iterumq; </s> <s xml:id="echoid-s14292" xml:space="preserve">in noſtros ſe dimittant aſpectus. </s> <s xml:id="echoid-s14293" xml:space="preserve">Enimuero nonne hac ratio-<lb/>ne Venus, & </s> <s xml:id="echoid-s14294" xml:space="preserve">Mercurius fuas apparitiones, & </s> <s xml:id="echoid-s14295" xml:space="preserve">occultationes alternant? </s> <s xml:id="echoid-s14296" xml:space="preserve">Vide tractatum noſtrum de Cometa <lb/>in opere de locis Mathem. </s> <s xml:id="echoid-s14297" xml:space="preserve">apud Ariſtotelem; </s> <s xml:id="echoid-s14298" xml:space="preserve">vbi plura huc ſpectantia reperies.</s> <s xml:id="echoid-s14299" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14300" xml:space="preserve">Vides igitur Lector, quam verum illud fit, non eſſe ad pauca reſpiciendum ei, qui velit in quauis materia <lb/>pro dignitate quidquam determinare. </s> <s xml:id="echoid-s14301" xml:space="preserve">Lege tamen quæ Claramontius lib. </s> <s xml:id="echoid-s14302" xml:space="preserve">de Stellis & </s> <s xml:id="echoid-s14303" xml:space="preserve">in ſuo Antitychone, <lb/>eiuſq; </s> <s xml:id="echoid-s14304" xml:space="preserve">Apologia contra Keplerum, quæ poſt obitum P. </s> <s xml:id="echoid-s14305" xml:space="preserve">Blancani prodijt in lucem.</s> <s xml:id="echoid-s14306" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div338" type="section" level="1" n="239"> <head xml:id="echoid-head254" style="it" xml:space="preserve">Vera Cometarum magnitudo. Cap. IV.</head> <p> <s xml:id="echoid-s14307" xml:space="preserve">APparens diameter capitis illius Cometę, quam anno 1577. </s> <s xml:id="echoid-s14308" xml:space="preserve">Tycho, & </s> <s xml:id="echoid-s14309" xml:space="preserve">alij plures obſeruarunt, erat min. </s> <s xml:id="echoid-s14310" xml:space="preserve">7. <lb/></s> <s xml:id="echoid-s14311" xml:space="preserve">diſtantia vero eius à terra erat ſemid. </s> <s xml:id="echoid-s14312" xml:space="preserve">terræ 210. </s> <s xml:id="echoid-s14313" xml:space="preserve">ſeu diam. </s> <s xml:id="echoid-s14314" xml:space="preserve">105. </s> <s xml:id="echoid-s14315" xml:space="preserve">fi ergo vt in alijs fiat Iſoſceles, cuius latera <lb/>contineant partes 105. </s> <s xml:id="echoid-s14316" xml:space="preserve">angulus vero min. </s> <s xml:id="echoid-s14317" xml:space="preserve">7. </s> <s xml:id="echoid-s14318" xml:space="preserve">collata baſi cum vna ex illis partibus, ideſt, cum vna diam. </s> <s xml:id="echoid-s14319" xml:space="preserve">terræ, <lb/>baſis continebitur in ea quater cum duabus tertijs, quare earum proportio erit ſicuti 3. </s> <s xml:id="echoid-s14320" xml:space="preserve">ad 14. </s> <s xml:id="echoid-s14321" xml:space="preserve">vnde & </s> <s xml:id="echoid-s14322" xml:space="preserve">ſphæra-<lb/>rum ratio conſtabit ex cubis horum nu nerorum, qui ſunt 27. </s> <s xml:id="echoid-s14323" xml:space="preserve">& </s> <s xml:id="echoid-s14324" xml:space="preserve">2744. </s> <s xml:id="echoid-s14325" xml:space="preserve">habent enim eandem rationem quam <lb/>ſphæræ: </s> <s xml:id="echoid-s14326" xml:space="preserve">quæ cognoſcitur diuiſo 2744. </s> <s xml:id="echoid-s14327" xml:space="preserve">per 27. </s> <s xml:id="echoid-s14328" xml:space="preserve">prouenit enim quotiens quaſi 101. </s> <s xml:id="echoid-s14329" xml:space="preserve">qui indicat Cometam a terra <lb/>contineri, & </s> <s xml:id="echoid-s14330" xml:space="preserve">adæquari centies, & </s> <s xml:id="echoid-s14331" xml:space="preserve">ſemel.</s> <s xml:id="echoid-s14332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14333" xml:space="preserve">Eodem modo longitudo caudæ eius inueſtigatur; </s> <s xml:id="echoid-s14334" xml:space="preserve">nam apparens longitudo ſubtendebat gr. </s> <s xml:id="echoid-s14335" xml:space="preserve">22. </s> <s xml:id="echoid-s14336" xml:space="preserve">diſtantia <lb/>vero a terra erat diam. </s> <s xml:id="echoid-s14337" xml:space="preserve">terrę 105. </s> <s xml:id="echoid-s14338" xml:space="preserve">igitur per Iſoſceles vſitatum, compererunt longitudinem veram huius Co-<lb/>metes continere diam. </s> <s xml:id="echoid-s14339" xml:space="preserve">terræ 48. </s> <s xml:id="echoid-s14340" xml:space="preserve">craſſitudo autem fuerit diam. </s> <s xml:id="echoid-s14341" xml:space="preserve">11.</s> <s xml:id="echoid-s14342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14343" xml:space="preserve">Similiter agendum eſt in alijs Cometis, quia variæ ſunt eorum apparentes magnitudines necnon variæ <lb/>eorum a terra diſtantiæ. </s> <s xml:id="echoid-s14344" xml:space="preserve">Cometa ille Neronianus, qui ex Seneca, magnitudine ſua apparente Solem adæ-<lb/>quabat, proculdubio vera magnitudine Lunam ſuperauit, quandoquidem ſupra eam effulſiue cenſendu@ <lb/>eſt: </s> <s xml:id="echoid-s14345" xml:space="preserve">vt ex ſuperioribus oſtenſum eſt.</s> <s xml:id="echoid-s14346" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div339" type="section" level="1" n="240"> <head xml:id="echoid-head255" style="it" xml:space="preserve">Corollarium de materia Cometarum.</head> <p> <s xml:id="echoid-s14347" xml:space="preserve">SOlent nonnulli Phyſiologi cum Aſtronomis de Cometarum materia contendere, affirmant enim aliqui <lb/>ex illi Cometas ex elementari materia conſtare, atq; </s> <s xml:id="echoid-s14348" xml:space="preserve">etiam in elementari regione verſari, quippe quę Co-<lb/>metas tantum de facie norunt; </s> <s xml:id="echoid-s14349" xml:space="preserve">cum enim eorum circuitus, vias, motus, parallaxes, ne queant perſcrutari, de ijs <lb/>tamen ſecundum vulgarem apparentiam iudicant. </s> <s xml:id="echoid-s14350" xml:space="preserve">verentur præterea ne quam nouitatis notam cælo inurãt. <lb/></s> <s xml:id="echoid-s14351" xml:space="preserve">Ex oppoſito Aſtronomi qui prædicta Cometarum accidentia ſagaciter rimati ſunt, eaque omnino rebus tan <lb/>tum cæleſtibus competere vident, eos non elementares, ſed cæleſtes eſſe autumant. </s> <s xml:id="echoid-s14352" xml:space="preserve">Verum enimuero me ab <lb/>vtriſque gratiam initurum confido, ſi qua ratione lis hæo componi poſſit, oſtendero: </s> <s xml:id="echoid-s14353" xml:space="preserve">ratio igitur eſt, ſi eorũ <lb/>opinionem ſequamur, qui putant Cometas cæleſtes eſſe, ac continuo inter æterna mundi corpora perſeuera-<lb/>re, quamuis raro conſpicua euadant. </s> <s xml:id="echoid-s14354" xml:space="preserve">in qua ſententia fuere olim Pythagorici, & </s> <s xml:id="echoid-s14355" xml:space="preserve">Italorum ſecta: </s> <s xml:id="echoid-s14356" xml:space="preserve">ſed & </s> <s xml:id="echoid-s14357" xml:space="preserve">recen-<lb/>tiores ſuas hypotheſes ita Cometæ accommodant, vt cum antiquis conſentire poſſint; </s> <s xml:id="echoid-s14358" xml:space="preserve">dum enim cos in ma-<lb/>gno epicyclo reuoluunt, omnes ſaluant apparentias, & </s> <s xml:id="echoid-s14359" xml:space="preserve">præterea eos in ſublime cælum ita attollunt, vt pau-<lb/>latim ad viſum minuantur, actandem non pereant, ſed non apparent. </s> <s xml:id="echoid-s14360" xml:space="preserve">hac enim ratione nihil noui cælo infe-<lb/>runt, quod Phyſicis, ne contingat, præcipue curæ eſt. </s> <s xml:id="echoid-s14361" xml:space="preserve">nec eos elementares faciunt, quod Aſtronomi magno-<lb/>pere auerſantur. </s> <s xml:id="echoid-s14362" xml:space="preserve">hæc ſit conciliatio, vero exiſtimo pro materiam Cometarum, magna conſideratione dignũ <lb/>eſle illud, quod P. </s> <s xml:id="echoid-s14363" xml:space="preserve">Horatius Graſſus in Libra Aſtron. </s> <s xml:id="echoid-s14364" xml:space="preserve">refert, ſcilicet toto tẽpore, & </s> <s xml:id="echoid-s14365" xml:space="preserve">antea etiam, quo Trabs, & </s> <s xml:id="echoid-s14366" xml:space="preserve"><lb/>Cometa anni ſuperioris 1618. </s> <s xml:id="echoid-s14367" xml:space="preserve">apparuerunt, nullas in Sole maculas conſpectas eſſe.</s> <s xml:id="echoid-s14368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14369" xml:space="preserve">Ex dictis de planetis tamen ordinarijs, quam extraordinarijs, ſcilicet Venerem, & </s> <s xml:id="echoid-s14370" xml:space="preserve">Mercurium, circa Solẽ <lb/>@ta moueri, vt aliquando infra, aliquãdo ſupra ipſum exiſtant: </s> <s xml:id="echoid-s14371" xml:space="preserve">Martis ſtellam etiam aliquando infra ſolaren@ <pb o="161" file="0183" n="188" rhead="Liber Decimusſextus."/> regionem deſcendere: </s> <s xml:id="echoid-s14372" xml:space="preserve">Cometas per omnes cæli partes proprijs motibus diſcurrere: </s> <s xml:id="echoid-s14373" xml:space="preserve">ſolent nonnuili recen-<lb/>tiores de cæli duritiæ, vel fluiditate nonnulla conijcere; </s> <s xml:id="echoid-s14374" xml:space="preserve">quod eis videatur ſine cæli liquid@tate nõ poſie præ-<lb/>dicta ſaluari, poſito enim cælo duro non vident qua ratione Mercurius, Venus, & </s> <s xml:id="echoid-s14375" xml:space="preserve">Mars, per cælum Solis ſuſ-<lb/>que deque vagari poſſint. </s> <s xml:id="echoid-s14376" xml:space="preserve">neq; </s> <s xml:id="echoid-s14377" xml:space="preserve">qua ratione Cometæ poſſint ipſos quoquo verſus perforare addunt præterea <lb/>nullum vnquam probaſſe cælum planetarum eſſe durum. </s> <s xml:id="echoid-s14378" xml:space="preserve">hinc præterea deduci poſſe putant, cælos planeta-<lb/>rum non eſſe realiter ab inuicem diſtinctos, ſed planetariam regionem eſſe purum cælum indiſtinctũ, in quo <lb/>errantia ſydera certis legibus, ac metis errent. </s> <s xml:id="echoid-s14379" xml:space="preserve">diſtinctionem vero illam in eccentricos, & </s> <s xml:id="echoid-s14380" xml:space="preserve">epicyclos reales <lb/>putant eſſe quandam ſubtilem ad ſaluandos motus excogitatam hypotheſim, quando quidẽ Ptolemæus, Co-<lb/>pernicus, Tycho, ſolas circulares lineas, & </s> <s xml:id="echoid-s14381" xml:space="preserve">quidem imaginarias in cælo deſignarunt.</s> <s xml:id="echoid-s14382" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div340" type="section" level="1" n="241"> <head xml:id="echoid-head256" style="it" xml:space="preserve">Alterum Corollarium ex Senecæ diuinatione.</head> <p> <s xml:id="echoid-s14383" xml:space="preserve">CAp. </s> <s xml:id="echoid-s14384" xml:space="preserve">25. </s> <s xml:id="echoid-s14385" xml:space="preserve">de Cometis; </s> <s xml:id="echoid-s14386" xml:space="preserve">quid miramur, inquit, Cometas, tam rarum mundi ſpectaculum, nondum teneri, cer-<lb/>tis legibus. </s> <s xml:id="echoid-s14387" xml:space="preserve">multæ ſunt gentes, quæ tantum facie nouerint cælum, quę nondum ſciant cur Luna deficiat, <lb/>veniet tempus quo iſta, quę nunc latent, in lucem dies extrahet; </s> <s xml:id="echoid-s14388" xml:space="preserve">& </s> <s xml:id="echoid-s14389" xml:space="preserve">longioris æui diligentia. </s> <s xml:id="echoid-s14390" xml:space="preserve">ad inquiſitionem <lb/>tantorum ætas vna non ſufficit. </s> <s xml:id="echoid-s14391" xml:space="preserve">poſteri noſtri tam aperta nos neſciſſe mirabuntur. </s> <s xml:id="echoid-s14392" xml:space="preserve">& </s> <s xml:id="echoid-s14393" xml:space="preserve">cap. </s> <s xml:id="echoid-s14394" xml:space="preserve">6. </s> <s xml:id="echoid-s14395" xml:space="preserve">erit qui demon-<lb/>ſtret aliquando in quibus Cometæ partibus errent; </s> <s xml:id="echoid-s14396" xml:space="preserve">cur tam ſeducti a cæteris eant; </s> <s xml:id="echoid-s14397" xml:space="preserve">quanti qualeſq; </s> <s xml:id="echoid-s14398" xml:space="preserve">ſint: </s> <s xml:id="echoid-s14399" xml:space="preserve">con-<lb/>tenti fimus inuentis; </s> <s xml:id="echoid-s14400" xml:space="preserve">aliquid veritati, & </s> <s xml:id="echoid-s14401" xml:space="preserve">poſteri conferant: </s> <s xml:id="echoid-s14402" xml:space="preserve">& </s> <s xml:id="echoid-s14403" xml:space="preserve">cap. </s> <s xml:id="echoid-s14404" xml:space="preserve">31. </s> <s xml:id="echoid-s14405" xml:space="preserve">puſilla res eſt mundus, niſi in illo, quod <lb/>quærat omnis mundus habeat. </s> <s xml:id="echoid-s14406" xml:space="preserve">hæc prudentiſſimi Senecæ egregia diuinatio. </s> <s xml:id="echoid-s14407" xml:space="preserve">quæ quantum veritati fuerit <lb/>conformis apparet, ſi in prædictis à nobis ſuperius, conferantur ſuccedentium ætatum inuenta cum præce-<lb/>dentibus. </s> <s xml:id="echoid-s14408" xml:space="preserve">ſed adhuc melius tunc apparebit, cum iam inuento Teleſcopio, Cometam quiſpiam primus illu-<lb/>xerit, ſpero enim auxilio admirandi huius inſtrumenti, ſæculum tandem noſtrum de Cometis triumphatu-<lb/>rum, ſed & </s> <s xml:id="echoid-s14409" xml:space="preserve">Pater Ioanne Baptiſta Cyſſatus in Cometa anni 1618. </s> <s xml:id="echoid-s14410" xml:space="preserve">notauit aggregatum ſtellularum; </s> <s xml:id="echoid-s14411" xml:space="preserve">vide <lb/>eius lib. </s> <s xml:id="echoid-s14412" xml:space="preserve">de Cometa.</s> <s xml:id="echoid-s14413" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div341" type="section" level="1" n="242"> <head xml:id="echoid-head257" style="it" xml:space="preserve">Appendix de Trabe, & Cometa anni 1618. Cap. V.</head> <p> <s xml:id="echoid-s14414" xml:space="preserve">QVod magnopere exoptabam, vt ſcilicet ante huius ſphæræ editionem, Cometa quiſpiam appareret, ex <lb/>cuius obſeruationibus præcipuè per Teleſcopium habitis, de natura, & </s> <s xml:id="echoid-s14415" xml:space="preserve">loco eius aliquid certi conſta-<lb/>ret, ſicq; </s> <s xml:id="echoid-s14416" xml:space="preserve">tractatio hæc abſolutio euaderet; </s> <s xml:id="echoid-s14417" xml:space="preserve">id cælo noſtris votis cumulatè reſpondente, ex ſententia <lb/>omnino ſucceſſit; </s> <s xml:id="echoid-s14418" xml:space="preserve">non ſolum enim Cometam, ſed & </s> <s xml:id="echoid-s14419" xml:space="preserve">pręterea ante ipſam ingen@em Trabem, veluti eius pro-<lb/>dromum, nobis cælum oſtentauit. </s> <s xml:id="echoid-s14420" xml:space="preserve">de ijs igitur, cum plures fuſius ſcripſerint, ego pariter ex inſtituto, nõnul-<lb/>l<unsure/>a proferam, quæ egomet, vel obſeruaui, vel ex obſeruatione commentus ſum.</s> <s xml:id="echoid-s14421" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14422" xml:space="preserve">Anno igitur 1618. </s> <s xml:id="echoid-s14423" xml:space="preserve">die 18. </s> <s xml:id="echoid-s14424" xml:space="preserve">Nouembris, vt tradit diſputatio aſtronomica Collegij Rom. </s> <s xml:id="echoid-s14425" xml:space="preserve">Soc. </s> <s xml:id="echoid-s14426" xml:space="preserve">noſtræ, Trabs <lb/>ingens ante Lucano tempore, quippe quę in cælo 40. </s> <s xml:id="echoid-s14427" xml:space="preserve">gradus occupabat, mundo affulſit. </s> <s xml:id="echoid-s14428" xml:space="preserve">perſeuerauit dies 11. <lb/></s> <s xml:id="echoid-s14429" xml:space="preserve">quibus a Cratere ad cor Hydrę proprio motu gradus penè 24. </s> <s xml:id="echoid-s14430" xml:space="preserve">progreſſa eſt. </s> <s xml:id="echoid-s14431" xml:space="preserve">porrò præter proprium motum, <lb/>diurnam quoq; </s> <s xml:id="echoid-s14432" xml:space="preserve">conuerſionem, non ſecus ac ſydera, & </s> <s xml:id="echoid-s14433" xml:space="preserve">Cometæ hor. </s> <s xml:id="echoid-s14434" xml:space="preserve">24. </s> <s xml:id="echoid-s14435" xml:space="preserve">abſoluebat; </s> <s xml:id="echoid-s14436" xml:space="preserve">tandiuq; </s> <s xml:id="echoid-s14437" xml:space="preserve">ſupra horizon-<lb/>tem cernebatur, quandiu etiam ſydera, quibus proxima apparebat. </s> <s xml:id="echoid-s14438" xml:space="preserve">quod certum mihi argumentum eſt, eam <lb/>non in aerea regione, ſed ſublimius, ſaltem apud Lunares circuitus circulatam eſſe; </s> <s xml:id="echoid-s14439" xml:space="preserve">quod eadem ratione, & </s> <s xml:id="echoid-s14440" xml:space="preserve"><lb/>figura, quibus ſuperius cap. </s> <s xml:id="echoid-s14441" xml:space="preserve">3. </s> <s xml:id="echoid-s14442" xml:space="preserve">vſus ſum in oſtendenda Cometarum altitudine, oſtendi poteſt. </s> <s xml:id="echoid-s14443" xml:space="preserve">quod eo libẽtius <lb/>annotare placuit, cum illud pleriq; </s> <s xml:id="echoid-s14444" xml:space="preserve">omnes, quotquot ego legerim, huius Cometæ ſcriptores, præterierint. </s> <s xml:id="echoid-s14445" xml:space="preserve">ex <lb/>quibus præterea ſequi videtur huiuſmodi Trabes eſſe Cometis valde affines, ac promde iuris aſtronomici, cũ <lb/>& </s> <s xml:id="echoid-s14446" xml:space="preserve">ſublimes incedant, & </s> <s xml:id="echoid-s14447" xml:space="preserve">diu perſeuerent; </s> <s xml:id="echoid-s14448" xml:space="preserve">motuq; </s> <s xml:id="echoid-s14449" xml:space="preserve">non ſolum diurno, ſed etiam proprio cieantur; </s> <s xml:id="echoid-s14450" xml:space="preserve">& </s> <s xml:id="echoid-s14451" xml:space="preserve">tandem <lb/>figuram non eis abſimiles ſint: </s> <s xml:id="echoid-s14452" xml:space="preserve">cum ego enim die 39. </s> <s xml:id="echoid-s14453" xml:space="preserve">Nouembris mane eam ad meridiem, & </s> <s xml:id="echoid-s14454" xml:space="preserve">propè horizon-<lb/>zem extenſam conſpexiſſe, viſa mihi eſt eadem veluti magna alterius Cometæ cauda; </s> <s xml:id="echoid-s14455" xml:space="preserve">videram enim paulo <lb/>ante Cometam nouum, de quo mox dicam: </s> <s xml:id="echoid-s14456" xml:space="preserve">natura igitur Cometarum huiuſmodi Trabes omnino imitantur.</s> <s xml:id="echoid-s14457" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14458" xml:space="preserve">Die igitur 29. </s> <s xml:id="echoid-s14459" xml:space="preserve">Nouembris, quo mihi vltimo apparuit Trabs, eodem primo apparuit Cometa: </s> <s xml:id="echoid-s14460" xml:space="preserve">quo viſo, ma-<lb/>gnopere gauiſus ſum, ſperans me iamiam voti compotem eſſe, eum igitur ſtatim non ſolum ipſe, ſed alij etiã <lb/>ex noſtris ſocij, optimis Teleſcopij perſcrutati ſumus. </s> <s xml:id="echoid-s14461" xml:space="preserve">verum nihil aliud inſpeximus, quam veluti ſydus in-<lb/>gens, cuius lumen circa medium rubidum, ad inſtar Martis rutilum erat, circumquaque vero rarius flaueſce-<lb/>bat. </s> <s xml:id="echoid-s14462" xml:space="preserve">idem ſequentibus quoq; </s> <s xml:id="echoid-s14463" xml:space="preserve">diebus factitatum eſt, atq; </s> <s xml:id="echoid-s14464" xml:space="preserve">idem ſemper abſq; </s> <s xml:id="echoid-s14465" xml:space="preserve">vlla nouitate conſpectum eſt. </s> <s xml:id="echoid-s14466" xml:space="preserve">vn-<lb/>de argumentor eum non ſublunarem, ſed cæleſtem fuiſſe: </s> <s xml:id="echoid-s14467" xml:space="preserve">nam ſi ſublunaris fuiſſet, conſpecta in eo, ni fallor, <lb/>partium diuerſitas, ac varietas eſſet, præſertim ſi ex elementari materia conſtitiſſet; </s> <s xml:id="echoid-s14468" xml:space="preserve">ſi enim tanta rerum di-<lb/>uerſitatem videmns in Luna per Teleſcopium, quidni etiam in Cometa vidiſſemus, ſi quam Luna humilior, <lb/>ac propior inceſſiſſet. </s> <s xml:id="echoid-s14469" xml:space="preserve">præterea ſi idem inſtrumentum in Venere diuerſitates illuminationum, in Sole macu-<lb/>las, & </s> <s xml:id="echoid-s14470" xml:space="preserve">faculas aperuit, apud louem ſatellites, in Saturno binos nigrores detegit, profecto veriſimile videtur <lb/>idem in Cometam detecturum fuiſſe, ſi humilius, non altius affulſiſſet; </s> <s xml:id="echoid-s14471" xml:space="preserve">atqui more altiſſimorum ſyderum, eum <lb/>nobis purum lumen oſtendit, ſine vllis penè diuerſitatibus, ergo apud altiſſima ſydera collocandus eſt.</s> <s xml:id="echoid-s14472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14473" xml:space="preserve">Poſthęc eodem mane hora 13<emph style="super">1</emph>. </s> <s xml:id="echoid-s14474" xml:space="preserve">ciuili, ad orientẽ quadrante ſatis magno locum eius per diſtantiam a Mer-<lb/>curio, cum vix vlla alia ſtella videretur, obſeruaui. </s> <s xml:id="echoid-s14475" xml:space="preserve">erat autem ſupra Mercurium directè gr. </s> <s xml:id="echoid-s14476" xml:space="preserve">7 {1/2}. </s> <s xml:id="echoid-s14477" xml:space="preserve">Mercurius ve-<lb/>ro in gr. </s> <s xml:id="echoid-s14478" xml:space="preserve">20. </s> <s xml:id="echoid-s14479" xml:space="preserve">Scorpij. </s> <s xml:id="echoid-s14480" xml:space="preserve">vnde adhibito giobo ſtellarum Tychonico, conieci ipſum eſſe infra Lancem borealem, <lb/>gradu fermè vno, ſed parum verſus meridiem. </s> <s xml:id="echoid-s14481" xml:space="preserve">inibi propè obſeruatus eſt etiam Romę eodem mane hor. </s> <s xml:id="echoid-s14482" xml:space="preserve">12. <lb/></s> <s xml:id="echoid-s14483" xml:space="preserve">can<unsure/>dam autem videbatur auertere à Sole.</s> <s xml:id="echoid-s14484" xml:space="preserve"/> </p> <pb o="162" file="0184" n="189" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s14485" xml:space="preserve">Dies 30. </s> <s xml:id="echoid-s14486" xml:space="preserve">hora 14. </s> <s xml:id="echoid-s14487" xml:space="preserve">vrbis, diſtabat à Boote gr. </s> <s xml:id="echoid-s14488" xml:space="preserve">30. </s> <s xml:id="echoid-s14489" xml:space="preserve">à Spica gr. </s> <s xml:id="echoid-s14490" xml:space="preserve">25.</s> <s xml:id="echoid-s14491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14492" xml:space="preserve">Die 2. </s> <s xml:id="echoid-s14493" xml:space="preserve">Decembris hora 13 {3/4}. </s> <s xml:id="echoid-s14494" xml:space="preserve">diſtabat a Boote gr. </s> <s xml:id="echoid-s14495" xml:space="preserve">24. </s> <s xml:id="echoid-s14496" xml:space="preserve">a Spica 25. </s> <s xml:id="echoid-s14497" xml:space="preserve">à Lance borea 8.</s> <s xml:id="echoid-s14498" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14499" xml:space="preserve">Die 3. </s> <s xml:id="echoid-s14500" xml:space="preserve">hora 13 {1/2}. </s> <s xml:id="echoid-s14501" xml:space="preserve">a Boote gr. </s> <s xml:id="echoid-s14502" xml:space="preserve">21. </s> <s xml:id="echoid-s14503" xml:space="preserve">a Spica 26 {1/3}.</s> <s xml:id="echoid-s14504" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14505" xml:space="preserve">Die 4. </s> <s xml:id="echoid-s14506" xml:space="preserve">hora 14. </s> <s xml:id="echoid-s14507" xml:space="preserve">à Boote gr. </s> <s xml:id="echoid-s14508" xml:space="preserve">18. </s> <s xml:id="echoid-s14509" xml:space="preserve">porrò hic notandus eſt mirus obſeruationum conſenſus, nam etiam Romæ <lb/>hiſce tribus diebus à noſtris PP. </s> <s xml:id="echoid-s14510" xml:space="preserve">depræhenſæ ſunt eædem penè diſtantia, ab ijſdem ſtellis, eodem tempore.</s> <s xml:id="echoid-s14511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14512" xml:space="preserve">Die 6. </s> <s xml:id="echoid-s14513" xml:space="preserve">hora 13. </s> <s xml:id="echoid-s14514" xml:space="preserve">a Boote 12<emph style="super">1</emph>. </s> <s xml:id="echoid-s14515" xml:space="preserve">a coxendice Bootis 17 {1/5}. </s> <s xml:id="echoid-s14516" xml:space="preserve">a Spica 27 {1/3}.</s> <s xml:id="echoid-s14517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14518" xml:space="preserve">Die 11. </s> <s xml:id="echoid-s14519" xml:space="preserve">hora 14. </s> <s xml:id="echoid-s14520" xml:space="preserve">Bootes, & </s> <s xml:id="echoid-s14521" xml:space="preserve">coxendix æquidiſtabant ab horizonte, infra quas parum propior tamen coxen-<lb/>dici erat Cometa.</s> <s xml:id="echoid-s14522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14523" xml:space="preserve">Die 12. </s> <s xml:id="echoid-s14524" xml:space="preserve">hora 13. </s> <s xml:id="echoid-s14525" xml:space="preserve">à Boote 8 {1/2}. </s> <s xml:id="echoid-s14526" xml:space="preserve">à Coxa 3. </s> <s xml:id="echoid-s14527" xml:space="preserve">exceſſit tropicum Cancri.</s> <s xml:id="echoid-s14528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14529" xml:space="preserve">Die 14. </s> <s xml:id="echoid-s14530" xml:space="preserve">hora 13. </s> <s xml:id="echoid-s14531" xml:space="preserve">à Boote 13. </s> <s xml:id="echoid-s14532" xml:space="preserve">à Coxa 6. </s> <s xml:id="echoid-s14533" xml:space="preserve">conſentit obſeruatio Oenipontana à noſtris habita. </s> <s xml:id="echoid-s14534" xml:space="preserve">Porrò ſex hor. <lb/></s> <s xml:id="echoid-s14535" xml:space="preserve">prius, ideſt, hora noctis 8. </s> <s xml:id="echoid-s14536" xml:space="preserve">qua Cometa oriebatur, ad eius parallaxim explorandam, cum adhuc apud horizon-<lb/>tem eſſet, afſurreximus. </s> <s xml:id="echoid-s14537" xml:space="preserve">ac primò obiter obſeruaui longitudinem caudæ gr. </s> <s xml:id="echoid-s14538" xml:space="preserve">36. </s> <s xml:id="echoid-s14539" xml:space="preserve">quæ ſemper eo maior appa-<lb/>ruit, quo aer obſcurior, aut quo horizonti erat propior. </s> <s xml:id="echoid-s14540" xml:space="preserve">adhibito igitur filo obſeruauimus eum in concurſu <lb/>duarum diametrorum quadrilateri, quod 4. </s> <s xml:id="echoid-s14541" xml:space="preserve">inerrantes ſtellæ circa ipſam efficiebant; </s> <s xml:id="echoid-s14542" xml:space="preserve">eratq; </s> <s xml:id="echoid-s14543" xml:space="preserve">ſimul apud quan-<lb/>dam ſtellulam 4. </s> <s xml:id="echoid-s14544" xml:space="preserve">ferè digitis, deinde hor. </s> <s xml:id="echoid-s14545" xml:space="preserve">14. </s> <s xml:id="echoid-s14546" xml:space="preserve">ideſt, ſex horis poſtea elapſis, cum mu@tum eleuata eſſet ab hori-<lb/>zo nte, verticique accederet, iterum diligenter per filum inſpeximus an eundem ſitum ad prænotatas ſtellas <lb/>retineret, atq; </s> <s xml:id="echoid-s14547" xml:space="preserve">depræhendimus eundem planè locum retinere, ſtellulæq; </s> <s xml:id="echoid-s14548" xml:space="preserve">illi vti antea adhærere, niſi quantũ <lb/>motus eius proprius poſtularet. </s> <s xml:id="echoid-s14549" xml:space="preserve">quod euidens ſignum eſt nullam ſubijſſe parallaxim ſenſibilem.</s> <s xml:id="echoid-s14550" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14551" xml:space="preserve">Die 20. </s> <s xml:id="echoid-s14552" xml:space="preserve">hora 13. </s> <s xml:id="echoid-s14553" xml:space="preserve">diſtitit ad ſenſum à prima caudæ Vrſa maioris, quæ ſcilicet eſt in extrema cauda, ſeu etiam <lb/>quæ eſt prima temonis plauſtri, gr. </s> <s xml:id="echoid-s14554" xml:space="preserve">7. </s> <s xml:id="echoid-s14555" xml:space="preserve">in directum ſui itineris per circulum maximum, quem proportio motu <lb/>deſcribebat.</s> <s xml:id="echoid-s14556" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14557" xml:space="preserve">Die 28. </s> <s xml:id="echoid-s14558" xml:space="preserve">hora 12 {1/2}. </s> <s xml:id="echoid-s14559" xml:space="preserve">à ſecunda cauda Vrſæ maioris gr. </s> <s xml:id="echoid-s14560" xml:space="preserve">5. </s> <s xml:id="echoid-s14561" xml:space="preserve">à tertia cauda Serpentis 6 {1/2}. </s> <s xml:id="echoid-s14562" xml:space="preserve">eratiam valde immi-<lb/>nutus.</s> <s xml:id="echoid-s14563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14564" xml:space="preserve">Die 29. </s> <s xml:id="echoid-s14565" xml:space="preserve">hora 12 {1/2}. </s> <s xml:id="echoid-s14566" xml:space="preserve">à ſecunda cauda Vrſæ 5 {1/2}. </s> <s xml:id="echoid-s14567" xml:space="preserve">à tertia cauda Serpentis 5 {1/2}. </s> <s xml:id="echoid-s14568" xml:space="preserve">in recta linea cum eis ad ſenſum.</s> <s xml:id="echoid-s14569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14570" xml:space="preserve">Die 30. </s> <s xml:id="echoid-s14571" xml:space="preserve">hora 12 {1/2}. </s> <s xml:id="echoid-s14572" xml:space="preserve">à tertia cauda Vrſæ 7<emph style="super">3</emph>. </s> <s xml:id="echoid-s14573" xml:space="preserve">a tertia cauda Serpentis 5 {1/4}. </s> <s xml:id="echoid-s14574" xml:space="preserve">cum vtraque in recta linea.</s> <s xml:id="echoid-s14575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14576" xml:space="preserve">Die 31. </s> <s xml:id="echoid-s14577" xml:space="preserve">hora 13 {1/2}. </s> <s xml:id="echoid-s14578" xml:space="preserve">aliquantulum proceſſerat vltra prædictas ſtellas, adeo colore, motu, & </s> <s xml:id="echoid-s14579" xml:space="preserve">magnitudine im-<lb/>minutus, vt vix conſpicuus eſſet. </s> <s xml:id="echoid-s14580" xml:space="preserve">quare neq; </s> <s xml:id="echoid-s14581" xml:space="preserve">amplius a nobis conſpectus eſt.</s> <s xml:id="echoid-s14582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14583" xml:space="preserve">Habitus igitur hiſce diſtantijs, eiſq; </s> <s xml:id="echoid-s14584" xml:space="preserve">accuratè circino in globum ſtellarum translatis, apparuerunt ſingula <lb/>ſui itineris loca, ſeu ſtationes, pro ſingulis obſeruationibus; </s> <s xml:id="echoid-s14585" xml:space="preserve">quę omnia erant ſecundum ſenſus æſtimationem, <lb/>in eodem ferè circulo maximo. </s> <s xml:id="echoid-s14586" xml:space="preserve">quod ſi quid deflexiſſe videbatur, id aut obſeruationum, aut globi imperfe-<lb/>ctioni aſcribendum putaui. </s> <s xml:id="echoid-s14587" xml:space="preserve">porrò motum, lumen, & </s> <s xml:id="echoid-s14588" xml:space="preserve">magnitudinem in dies remittebat, quouſq; </s> <s xml:id="echoid-s14589" xml:space="preserve">euanuit. </s> <s xml:id="echoid-s14590" xml:space="preserve">cau-<lb/>damq; </s> <s xml:id="echoid-s14591" xml:space="preserve">ſemper in auerſas Soli partes dirigebat. </s> <s xml:id="echoid-s14592" xml:space="preserve">Poſtremo cum noſtræ obſeruationes Parmenſes, cum Ro-<lb/>manis, Antuerpienſibus, & </s> <s xml:id="echoid-s14593" xml:space="preserve">alijs conſenſerint, palam mihi eſſe videtur, neq; </s> <s xml:id="echoid-s14594" xml:space="preserve">vllam ex diuerſis, atq; </s> <s xml:id="echoid-s14595" xml:space="preserve">adeo diſſi-<lb/>tis locis exhibuiſſe parallaxim, ac proinde in ſupremis cæli regionibus ſpatiatum eſſe.</s> <s xml:id="echoid-s14596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14597" xml:space="preserve">Cæterum vt in futurum etiam caueamus, obſeruandum erit in poſteris Cometis, an eclipſentur à Luna, & </s> <s xml:id="echoid-s14598" xml:space="preserve"><lb/>an planeta quiſpiam ſub eis, vel ſupra eos incedat: </s> <s xml:id="echoid-s14599" xml:space="preserve">item an vmbra terræ, vel Lunę, aliuſue planetæ ipſos aliqua <lb/>ex parte obſcurare valeant; </s> <s xml:id="echoid-s14600" xml:space="preserve">quæ aliquando futura non dubitamus.</s> <s xml:id="echoid-s14601" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14602" xml:space="preserve">In confirmationen@ horum omnium, ſciat Lector me hoc mcnſe Ianuarij anno 1620. </s> <s xml:id="echoid-s14603" xml:space="preserve">accepifſe litteras <lb/>Goa Indiæ orientalis ad me datas a noſtris PP. </s> <s xml:id="echoid-s14604" xml:space="preserve">qui Euangelij cauſa ad Sinas anni 1618. </s> <s xml:id="echoid-s14605" xml:space="preserve">ex Europa ſoluerunt. <lb/></s> <s xml:id="echoid-s14606" xml:space="preserve">quibus continetur compendioſa narratio quarundam obſeruationum, quas ſe habituros ante diſceſſum re-<lb/>ceperant, circa Magnetis inclinationem, & </s> <s xml:id="echoid-s14607" xml:space="preserve">declinationem; </s> <s xml:id="echoid-s14608" xml:space="preserve">circa Maris æſtum, quem vbique marium pen-<lb/>dere a Luna compererunt<unsure/>; </s> <s xml:id="echoid-s14609" xml:space="preserve">circa ventos, circa ſtellarum antarcticarum deſcriptionem. </s> <s xml:id="echoid-s14610" xml:space="preserve">Et quod magis ad <lb/>rem noſtram facit, quodque ſcitu dignum pariter, & </s> <s xml:id="echoid-s14611" xml:space="preserve">iucundum eſt, eorum obſeruationes Goæ habitas de <lb/>Trabe, & </s> <s xml:id="echoid-s14612" xml:space="preserve">Cometa anni 1618. </s> <s xml:id="echoid-s14613" xml:space="preserve">omnino conſentire cum noſtris Romæ, Parmæ, atque Antuerpiæ peractis, <lb/>ideſt, vtrumq; </s> <s xml:id="echoid-s14614" xml:space="preserve">conſpectum eſſe ab eis apud eaſdem ſtellas eodem tempore; </s> <s xml:id="echoid-s14615" xml:space="preserve">& </s> <s xml:id="echoid-s14616" xml:space="preserve">præterea ijſdem motibus, ſecus <lb/>eadem ſydera vias ſuas in cælo deſcripſiſſe, quas nos etiam Europæi delineaſſe tunc vidimus, ac typis poſtea <lb/>mandauimus. </s> <s xml:id="echoid-s14617" xml:space="preserve">vnde certo certius iam liceat affirmare, eos nullam exhibuiſſe parallaxim, cum ex locis tanto <lb/>terrarum, ac marium interuallo ſeiunctis, eundem locum viſum in Firmamento ſortiti ſint. </s> <s xml:id="echoid-s14618" xml:space="preserve">quæ omnia ad-<lb/>huc clariora, ae iucundiora euadent, cum quod ipſi promittunt, iſthæc omnia prolixa Tractatione membra-<lb/>tim expoſita, in Studioſorum gratiam ad nos tranſinittent.</s> <s xml:id="echoid-s14619" xml:space="preserve"/> </p> <pb o="163" file="0185" n="190"/> </div> <div xml:id="echoid-div342" type="section" level="1" n="243"> <head xml:id="echoid-head258" xml:space="preserve">LIBER DECIMVSSEPTIMVS <lb/>DE FIRMAMENTO, <lb/>ET INERRANTIBVS STELLIS.</head> <head xml:id="echoid-head259" style="it" xml:space="preserve">Locus Firmamenti. Cap. 1.</head> <p> <s xml:id="echoid-s14620" xml:space="preserve">ABſoluta iam errantium ſyderum regione, ſupereſt, vt ad Firmamentum, quod inerrantium <lb/>Stellarum ſedes eſt, aſcendamus. </s> <s xml:id="echoid-s14621" xml:space="preserve">nec dubium, quin ſupremum hunc locum in hac Mundi <lb/>Fabrica eæ ſibi vindicent: </s> <s xml:id="echoid-s14622" xml:space="preserve">videmus namq; </s> <s xml:id="echoid-s14623" xml:space="preserve">eas ſupra omnes planet@s reuolui, cum illę ab his <lb/>occultentur, non contra. </s> <s xml:id="echoid-s14624" xml:space="preserve">Secundo ex proprio earum motu, qui ardiſſimus eſt, vt videbi-<lb/>mus; </s> <s xml:id="echoid-s14625" xml:space="preserve">ſunt autem illa ſydera cæteris ſuperiora, quorum propriæ motiones ſunt tardiores, vt <lb/>alias docuimus. </s> <s xml:id="echoid-s14626" xml:space="preserve">Quantum autem diſtet Firmamentum à mundi centro, certo affirmare dif-<lb/>ficilè eſt; </s> <s xml:id="echoid-s14627" xml:space="preserve">non enim conſtat an ſupra Saturni circuitum proximè ſtatuendum ſit, cum non-<lb/>nulli illud immenſo interuallo ſupra Saturnum extollant. </s> <s xml:id="echoid-s14628" xml:space="preserve">Quod ſi Saturni gyrum proximè ambiat, erit eius <lb/>diſtãtia eadem quæ Saturni maxima. </s> <s xml:id="echoid-s14629" xml:space="preserve">ſi vero altius euehatur incerta omnino remanebit; </s> <s xml:id="echoid-s14630" xml:space="preserve">Tycho tamen pru-<lb/>denter exiſtimat eam continere ſemid. </s> <s xml:id="echoid-s14631" xml:space="preserve">terræ 14000. </s> <s xml:id="echoid-s14632" xml:space="preserve">incertum præterea eſt num ſtellæ omnes ei affixæ à mun <lb/>di centro æquidiſtent; </s> <s xml:id="echoid-s14633" xml:space="preserve">ſunt enim qui ſuſpicientur, alias alijs eſſe nobis propiores; </s> <s xml:id="echoid-s14634" xml:space="preserve">ac propterea alias alijs ma-<lb/>iores apparere. </s> <s xml:id="echoid-s14635" xml:space="preserve">Dicuntur autem fixæ, quod eaſdem diſtantias, ſitus, & </s> <s xml:id="echoid-s14636" xml:space="preserve">poſitiones, ad inuicem habent, perpe-<lb/>tuo ſeruant, v.</s> <s xml:id="echoid-s14637" xml:space="preserve">g. </s> <s xml:id="echoid-s14638" xml:space="preserve">illæ ſeptem ſtellæ, quæ carrum vulgo appellant perpetuo eandem carri figuram, & </s> <s xml:id="echoid-s14639" xml:space="preserve">eandem <lb/>in Firmamento poſitionem conſtanter retinuerunt, vt teſtantur veterum, Hipparchi, Ptolemæi, ac recen-<lb/>tiorum omnes obſeruationes inuicem collatæ: </s> <s xml:id="echoid-s14640" xml:space="preserve">hinc etiam ipſarum regio, ſeu cælum appellari meruit Firma-<lb/>mentum. </s> <s xml:id="echoid-s14641" xml:space="preserve">Plura huiuſmodi exempla habes apud Tychonem tom. </s> <s xml:id="echoid-s14642" xml:space="preserve">1. </s> <s xml:id="echoid-s14643" xml:space="preserve">pag. </s> <s xml:id="echoid-s14644" xml:space="preserve">234.</s> <s xml:id="echoid-s14645" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div343" type="section" level="1" n="244"> <head xml:id="echoid-head260" style="it" xml:space="preserve">Partitio Stellarum in 48. conſtellationes, ſeu imagines.</head> <p> <s xml:id="echoid-s14646" xml:space="preserve">IN prima porrò illa aurea, ſed rudi tamen ætate Mundi; </s> <s xml:id="echoid-s14647" xml:space="preserve">vt eleganter cecinit Seneca:</s> <s xml:id="echoid-s14648" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14649" xml:space="preserve">Nondum quiſquam ſydera norat;</s> <s xml:id="echoid-s14650" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14651" xml:space="preserve">Stellis quibus ping@tur æther,</s> </p> <p style="it"> <s xml:id="echoid-s14652" xml:space="preserve">Non erat vſus: </s> <s xml:id="echoid-s14653" xml:space="preserve">nondum Pleiadas,</s> </p> <p style="it"> <s xml:id="echoid-s14654" xml:space="preserve">Hyadas poterant vitare rates;</s> <s xml:id="echoid-s14655" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14656" xml:space="preserve">Non Olenia ſydera Capræ,</s> </p> <p style="it"> <s xml:id="echoid-s14657" xml:space="preserve">Non qua ſequitur, flectitque ſenex</s> </p> <p style="it"> <s xml:id="echoid-s14658" xml:space="preserve">Arctica tardus plaustra Bootes.</s> <s xml:id="echoid-s14659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14660" xml:space="preserve">Succedentibus poſtea ſeculis primi omnium poetæ veteres initium, quoduis aliud agentes, ſyderali ſcien-<lb/>@iæ dedere; </s> <s xml:id="echoid-s14661" xml:space="preserve">ij enim Stellarum omnium confuſam, ac palantem multitudinem ſuis ludentes fabulis in ordinem <lb/>redigere, atque in partes quaſdam diſtribuere cæperunt. </s> <s xml:id="echoid-s14662" xml:space="preserve">hoc pacto dum ipſi Cynoſuram, aut Helicem in <lb/>Vrſas à Ioue conuerſas, & </s> <s xml:id="echoid-s14663" xml:space="preserve">in cælum translatas eſſe confinxerunt, Stellas complures in duas veluti Prouin-<lb/>cias ab alijs diuiſas diſtinxerunt. </s> <s xml:id="echoid-s14664" xml:space="preserve">idem de Arcturo, Perſeo, & </s> <s xml:id="echoid-s14665" xml:space="preserve">reliquis præſtiterunt. </s> <s xml:id="echoid-s14666" xml:space="preserve">Poetis ſuppetias tule-<lb/>runt Nautæ, qui Nauticæ artis neceſſitate compulſi, ac Stellarum cognitione propterea indigi, eas obſer-<lb/>uare, ac denominare cæperunt. </s> <s xml:id="echoid-s14667" xml:space="preserve">ſicque,</s> </p> </div> <div xml:id="echoid-div344" type="section" level="1" n="245"> <head xml:id="echoid-head261" style="it" xml:space="preserve">Nauita tum Stellis numeros, & nomina fecit.</head> <p> <s xml:id="echoid-s14668" xml:space="preserve">Quibus poſtea Aſtronomi ſuccurrentes tandem totam Firmamenti faciem in 48. </s> <s xml:id="echoid-s14669" xml:space="preserve">vel 49. </s> <s xml:id="echoid-s14670" xml:space="preserve">in 50. </s> <s xml:id="echoid-s14671" xml:space="preserve">veluti regiones <lb/>diſtribuerunt, vt facilius hac diſtinctione, atque ordine in cognitionem omnium Stellarum peruenirent. </s> <s xml:id="echoid-s14672" xml:space="preserve">has <lb/>vero Stellarum figuras appellarunt Aſteriſmos, ſeu conſtellationes, quorum nomina, & </s> <s xml:id="echoid-s14673" xml:space="preserve">ordines in catalogo <lb/>Stellarum infra apparebunt. </s> <s xml:id="echoid-s14674" xml:space="preserve">ſic legimus Thaletem Mileſium inuentorem fuiſſe Vrſę minoris, ideſt, eam con-<lb/>ſtellationem ſtatuiſſe: </s> <s xml:id="echoid-s14675" xml:space="preserve">Cononem etiam in gratiam Regis Ptolemæi, Bereces comam in cælum tranſtuliſſe: <lb/></s> <s xml:id="echoid-s14676" xml:space="preserve">ideſt, Stellas quaſdam inde denominaſſe: </s> <s xml:id="echoid-s14677" xml:space="preserve">noſtra pariter ætate Galilæus iure inuẽtionis Stellas Mediceas nun-<lb/>cupauit. </s> <s xml:id="echoid-s14678" xml:space="preserve">quo autem conſilio poetæ illi vetuſtiſſimi Heroas illos, aut animalia illa in cælum tranſtulerint, & </s> <s xml:id="echoid-s14679" xml:space="preserve"><lb/>quinam, ij fuerint, ne ego longior ſim, vide apud Aratum, Q. </s> <s xml:id="echoid-s14680" xml:space="preserve">Manilium, & </s> <s xml:id="echoid-s14681" xml:space="preserve">Higinium poetas veteres. </s> <s xml:id="echoid-s14682" xml:space="preserve">an-<lb/>s<unsure/>iquifſimas porro eſſe haſce ſyderum appellationes apparet ex libro lob antiquiſſimo (quem putant ſacræ <lb/>Scripturæ expoſitores eſſe ipſo Moyſe antiquiorem) qui cap. </s> <s xml:id="echoid-s14683" xml:space="preserve">9. </s> <s xml:id="echoid-s14684" xml:space="preserve">ait, qui facit Arcturum, & </s> <s xml:id="echoid-s14685" xml:space="preserve">Oriona, & </s> <s xml:id="echoid-s14686" xml:space="preserve">Hya-<lb/>das. </s> <s xml:id="echoid-s14687" xml:space="preserve">& </s> <s xml:id="echoid-s14688" xml:space="preserve">Amos cap. </s> <s xml:id="echoid-s14689" xml:space="preserve">5. </s> <s xml:id="echoid-s14690" xml:space="preserve">facientem Arcturum, & </s> <s xml:id="echoid-s14691" xml:space="preserve">Oriona, apud etiam Heſiodum, & </s> <s xml:id="echoid-s14692" xml:space="preserve">Homerum antiquiſſimos <lb/>poetas plurium Aſteriſmorum nomina leguntur. </s> <s xml:id="echoid-s14693" xml:space="preserve">Heſiodum quidem, qui parum poſt Troiani belli tempo-<lb/>ra floruit, in lib. </s> <s xml:id="echoid-s14694" xml:space="preserve">2. </s> <s xml:id="echoid-s14695" xml:space="preserve">operum, ac dierum plurium conſtellat: </s> <s xml:id="echoid-s14696" xml:space="preserve">meminit, quæ loca infra adducentur, cum de <lb/>ortu, & </s> <s xml:id="echoid-s14697" xml:space="preserve">occaſum ſyderum erit ſermo.</s> <s xml:id="echoid-s14698" xml:space="preserve"/> </p> <pb o="164" file="0186" n="191" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div345" type="section" level="1" n="246"> <head xml:id="echoid-head262" style="it" xml:space="preserve">Numerus Stellarum. Cap. I.</head> <p> <s xml:id="echoid-s14699" xml:space="preserve">HOc iam veluti apparatu præmiſſo, peruetuſtos illos ſyderum cultores inceſſit cupido multitudines Stel-<lb/>larum dignoſcendæ, ac ſi fieri poſſet earum omnium numerum aſſequi. </s> <s xml:id="echoid-s14700" xml:space="preserve">cum igitur iam omnis earum <lb/>mui<unsure/>titudo eſſetin 48. </s> <s xml:id="echoid-s14701" xml:space="preserve">conſtellationes diſtributa, facilè ijs fuit ſingularum conſtellationum ſtellas enumerare, <lb/>ſicque tandem omnium conſtellationum numeros (paruulis tamen non paucis, quæ ægre diſcerni paterant, <lb/>omiſſis) in vnam ſuminam redigere; </s> <s xml:id="echoid-s14702" xml:space="preserve">harum autem ſumma fuit 1022. </s> <s xml:id="echoid-s14703" xml:space="preserve">quos quidam alioquin doctiſſimus vir <lb/>ſequutus, dum l<unsure/>cripſit omnes omnino ſtellas eſſe tantum 1022. </s> <s xml:id="echoid-s14704" xml:space="preserve">falſus eſt. </s> <s xml:id="echoid-s14705" xml:space="preserve">quod erratum inde cõuincitur, quod <lb/>Tycho in ſuo Stellarum catalogo exhibet 100. </s> <s xml:id="echoid-s14706" xml:space="preserve">ferè Stellas a ſe viſas amplius, præter antiquis numeratas, atq; <lb/></s> <s xml:id="echoid-s14707" xml:space="preserve">in ſola Caſſiopea 13. </s> <s xml:id="echoid-s14708" xml:space="preserve">amplius obſeruauit præter recenſitas a maioribus. </s> <s xml:id="echoid-s14709" xml:space="preserve">Cæterum Stellarum numerum eſſe <lb/>propemodum humanæ menti infinitum ex Teleſcopio perſpicuum eſt, per ipſum enim non ſolum in lacteo <lb/>circulo, & </s> <s xml:id="echoid-s14710" xml:space="preserve">in nebulo ſis ſtellis, innumeræ ſtellulæ deteguntur; </s> <s xml:id="echoid-s14711" xml:space="preserve">verum etiam in quamuis cæli partem per illud <lb/> <anchor type="note" xlink:label="note-0186-01a" xlink:href="note-0186-01"/> inſpexeris, quam | lurimas oculis alioquin noſtris inuiſibiles, conſpi-<lb/>cere licebit. </s> <s xml:id="echoid-s14712" xml:space="preserve">Dum igitur in hoc ſtellarum cenſu verl<unsure/>arentur, aduer-<lb/>terunt eas inter ſe, tum apparenti magnitudine, tum colore differt, <lb/>quare eas iuxta magnitudinem in ſex claſſes redegere; </s> <s xml:id="echoid-s14713" xml:space="preserve">maximas om-<lb/>nium in prima claſſe reponẽtes, quas primæ magnitudinis dixerunt, <lb/>quæ ſunt 15. </s> <s xml:id="echoid-s14714" xml:space="preserve">alias prædictis proximè minores, ſecundę c@afſis, ac ma-<lb/>gnitudinis fecerunt: </s> <s xml:id="echoid-s14715" xml:space="preserve">eodem modo relinquas in reliquos ordines, ter-<lb/>tium, quartum, quintum, & </s> <s xml:id="echoid-s14716" xml:space="preserve">ſextum diſtribuerunt: </s> <s xml:id="echoid-s14717" xml:space="preserve">quas etiam pro-<lb/>prijs characteribus diſtinxerunt, quibus in globis aſtronomicis de-<lb/>pingendis, ad ſtellarum ordines diſtinguendos, adhibent. </s> <s xml:id="echoid-s14718" xml:space="preserve">Reſpe-<lb/>ctu autem coloris, alias claras, alias nebuloſas, alias obſcura ſtatue-<lb/>runt: </s> <s xml:id="echoid-s14719" xml:space="preserve">quorum ordo, in ſequenti Tabella exponuntur.</s> <s xml:id="echoid-s14720" xml:space="preserve"/> </p> <div xml:id="echoid-div345" type="float" level="2" n="1"> <note position="right" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve"> <lb/>Magnitudines # Numeri <lb/>Primæ # 15 <lb/>Secundæ # 45 <lb/>Tertiæ # 208 <lb/>Quartæ # 474 <lb/>Quintæ # 217 <lb/>Sextæ # 49 <lb/>Nebuloſæ # 5 <lb/>Obſcuræ # 9 <lb/>Summa # 1022 <lb/></note> </div> <p> <s xml:id="echoid-s14721" xml:space="preserve">Stellas autem omnes ſex clafſium claræ dicuntur, ſuntq; </s> <s xml:id="echoid-s14722" xml:space="preserve">numero <lb/>1008. </s> <s xml:id="echoid-s14723" xml:space="preserve">reliquæ vt in Tabella. </s> <s xml:id="echoid-s14724" xml:space="preserve">Nebuloſæ ſunt quaſi particulæ quædam <lb/>lactei circuli. </s> <s xml:id="echoid-s14725" xml:space="preserve">Porrò præter has ſtellas animaduerterunt in Firmamento albedinem quandã oblongam à Bo-<lb/>rea in Auſtrum inordinatè incedentem, totumq; </s> <s xml:id="echoid-s14726" xml:space="preserve">cælum cingentem quam Galaxiam, ſeu viam lacteam poe-<lb/>tæ cognominarunt. </s> <s xml:id="echoid-s14727" xml:space="preserve">pariter propè Antarcticum polum, vt referunt Vectores Indici, conſpiciuntur Nubecu-<lb/>læ duæ ſiue maculæ, quæ ſimiles ſunt Nebuloſis Stellis, aut Galaxiæ partibus. </s> <s xml:id="echoid-s14728" xml:space="preserve">quid vero hæc omnia ſint, an-<lb/>teactis omnibus ſeculis incompertum fuit. </s> <s xml:id="echoid-s14729" xml:space="preserve">noſtra tamen ætate, admirandi Teleſcopij beneficio, apertè vide-<lb/>mus Galaxiam nihil aliud eſſe, quam oblongum ſtellarum agmen adeo exilium, vt nullæ perſe ob @uminis <lb/>paruitatem diſtinctè cerni queant, omnes autem ſimul candorem illum lacteum oculis exhibeant. </s> <s xml:id="echoid-s14730" xml:space="preserve">Idem <lb/>prorſus contingit Nebuloſis, quas idem inſtrumentum oſtendit eſſe quoſdam ſtellularum greges. </s> <s xml:id="echoid-s14731" xml:space="preserve">Idem exi-<lb/>ſtimandum eſt de Maculis ad Antarticum polum ſitis. </s> <s xml:id="echoid-s14732" xml:space="preserve">vide Nuncium ſydereum Galilæi, qui omnium pri-<lb/>mus iſthæc Mundo miracula patefecit.</s> <s xml:id="echoid-s14733" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div347" type="section" level="1" n="247"> <head xml:id="echoid-head263" style="it" xml:space="preserve">Loca Stellarum in Firmamento. Cap. III.</head> <p> <s xml:id="echoid-s14734" xml:space="preserve">PRoxima Aſtronomis cura ſucceſſit ſingulis Stellis propria aſſignare loca in Firmamento; </s> <s xml:id="echoid-s14735" xml:space="preserve">quod præſtite-<lb/>runt inueſtigantes longitudines, ac altitudines ſingularum (ſupra autem in tractatu officij Zodiaci, & </s> <s xml:id="echoid-s14736" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0186-01a" xlink:href="fig-0186-01"/> eclipticæ dictum eſt, quid ſit vtraque) ex cognita enim longi-<lb/>tudine, & </s> <s xml:id="echoid-s14737" xml:space="preserve">latitudine alicuius ſyderis, cognoſcitur determina-<lb/>tus ipſius in cælo ſitus, vt ex conſideratione præſenti figuræ <lb/>patebit, in qua ecliptica fit B D, circulus A B C D, referat ip-<lb/>ſum Firmamentum, in quo ſit Stella E. </s> <s xml:id="echoid-s14738" xml:space="preserve">cuius locum in Firma-<lb/>mento oporteat determinare; </s> <s xml:id="echoid-s14739" xml:space="preserve">A C, ſint poli eclipticæ; </s> <s xml:id="echoid-s14740" xml:space="preserve">A, Bo-<lb/>reus; </s> <s xml:id="echoid-s14741" xml:space="preserve">C. </s> <s xml:id="echoid-s14742" xml:space="preserve">Auſtrinus. </s> <s xml:id="echoid-s14743" xml:space="preserve">tranſeat igitur per ipſam, & </s> <s xml:id="echoid-s14744" xml:space="preserve">per polos ecli-<lb/>pticæ circulus latitudinis A E G C, ſecans eclipticam in G, qui <lb/>fit 25. </s> <s xml:id="echoid-s14745" xml:space="preserve">gradus Tauri, ſitque atcus G E, notus, v.</s> <s xml:id="echoid-s14746" xml:space="preserve">g. </s> <s xml:id="echoid-s14747" xml:space="preserve">gr. </s> <s xml:id="echoid-s14748" xml:space="preserve">40. </s> <s xml:id="echoid-s14749" xml:space="preserve">ad Bo-<lb/>ream, qui arcus erit eius ſtellę latitudo Borealis; </s> <s xml:id="echoid-s14750" xml:space="preserve">longitudo au-<lb/>tem eiuſdem ſtellæ erit arcus B G, gr. </s> <s xml:id="echoid-s14751" xml:space="preserve">55. </s> <s xml:id="echoid-s14752" xml:space="preserve">ab initio Arietis com-<lb/>putatus: </s> <s xml:id="echoid-s14753" xml:space="preserve">ex quibus cognoſcitur vbinam in cælo ſtella E, fit affi-<lb/>xa, ideſt, eius proprius locus in Firmamento, relatus ad Zodia-<lb/>ci polos, & </s> <s xml:id="echoid-s14754" xml:space="preserve">ad eclipticam manifeſtatur. </s> <s xml:id="echoid-s14755" xml:space="preserve">Iam ſtella F, ſit in par-<lb/>te Auſtrali, circulus eius latitudinis A F C, ſecans eclipticam <lb/>in H, 28. </s> <s xml:id="echoid-s14756" xml:space="preserve">gr. </s> <s xml:id="echoid-s14757" xml:space="preserve">Cancri, arcus H F, erit eius lactitudo auſtralis gr. <lb/></s> <s xml:id="echoid-s14758" xml:space="preserve">43. </s> <s xml:id="echoid-s14759" xml:space="preserve">lõgitudo arcus B H, gr. </s> <s xml:id="echoid-s14760" xml:space="preserve">118. </s> <s xml:id="echoid-s14761" xml:space="preserve">ex quibus eius in cælo ſitus exa-<lb/>ctè deſignatur. </s> <s xml:id="echoid-s14762" xml:space="preserve">Inquirunt igitur Aſtronomi ſtellarum præci-<lb/>puarum longitudines, & </s> <s xml:id="echoid-s14763" xml:space="preserve">latitudines, vt ex ijs, vera earum loca <lb/>in cælo definiant. </s> <s xml:id="echoid-s14764" xml:space="preserve">Primi autem, qui in hanc præclaram curam incubuerunt fuere Ariſtillus, & </s> <s xml:id="echoid-s14765" xml:space="preserve">Timocharis, <lb/>qui a morte, Alexandri Magniannis circiter 41. </s> <s xml:id="echoid-s14766" xml:space="preserve">plurimarum ſtellarum loca obſeruarũt: </s> <s xml:id="echoid-s14767" xml:space="preserve">poſtea Hipparchus, <pb o="165" file="0187" n="192" rhead="Liber decimusſeptimus."/> inde Ptolen@ęus, hinc Albategnius, & </s> <s xml:id="echoid-s14768" xml:space="preserve">tandem Tycho, omnem in hanc curam, diligentiam adhibuerunt. </s> <s xml:id="echoid-s14769" xml:space="preserve">qui-<lb/>bus vero modis id præſtiterint, nunc dicendum.</s> <s xml:id="echoid-s14770" xml:space="preserve"/> </p> <div xml:id="echoid-div347" type="float" level="2" n="1"> <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a"> <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-01"/> </figure> </div> <p> <s xml:id="echoid-s14771" xml:space="preserve">Veteres ad hoc vtebantur inſtrumento quodam, quod Aſtrolabium, & </s> <s xml:id="echoid-s14772" xml:space="preserve">Armillas vocarunt, quod Ptolo-<lb/>æus initio ilb. </s> <s xml:id="echoid-s14773" xml:space="preserve">5. </s> <s xml:id="echoid-s14774" xml:space="preserve">deſcribit. </s> <s xml:id="echoid-s14775" xml:space="preserve">erat autem hoc inſtrumentum perſimile magnæ ſphęræ armillari; </s> <s xml:id="echoid-s14776" xml:space="preserve">quare ſi ſphæ-<lb/>ra adſit ſatis magna, atque accuratè fabricata, vſui nunc eſſe poterit, ſi tamen in ea incluſus fuerit cir<unsure/>culus, <lb/>quem ſecundi motus appellauimus; </s> <s xml:id="echoid-s14777" xml:space="preserve">nunc autem dici poterit, ab offitio quod præſtabit, circulus latitudinis, <lb/>vti in apparatu docuimus, qui ſcilicet in polis eclipticæ conuertatur: </s> <s xml:id="echoid-s14778" xml:space="preserve">eſt tamen nunc addenda Dioptra, quæ <lb/>circa centrum eius, ſeu eclipticæ, vertatur quęque habeat in vtraque extremitate pinnulas perforatas, vt per <lb/>ca foramina liceat in ſydera collimare. </s> <s xml:id="echoid-s14779" xml:space="preserve">Secundo neceſſe eſt tempore obſeruationes (quæ nõ niſi noctu ha-<lb/>beri poteſt, in die enim ſtellæ non videntur) habere locum Solis in Zodiaco accuratè notum. </s> <s xml:id="echoid-s14780" xml:space="preserve">Tertio vere-<lb/>res Hipparchus, & </s> <s xml:id="echoid-s14781" xml:space="preserve">Ptolemæus habebant etiam locum Lunæ notum in Zodiaco per calculum; </s> <s xml:id="echoid-s14782" xml:space="preserve">ſeu quod me-<lb/>lius eſt tempore alicuius eclypſis lunaris, quia tunc locus Lunæ exactè Soli opponitur. </s> <s xml:id="echoid-s14783" xml:space="preserve">pro Luna induſtrius, <lb/>& </s> <s xml:id="echoid-s14784" xml:space="preserve">ſolers Tycho Venerem aſſumpſit, quia locus eius in Zodiaco, & </s> <s xml:id="echoid-s14785" xml:space="preserve">diſtantia eius à Sole, certius haberi poteſt, <lb/>quam Lunæ: </s> <s xml:id="echoid-s14786" xml:space="preserve">eius enim motus magis obſeruabilis eſt. </s> <s xml:id="echoid-s14787" xml:space="preserve">habito igitur loco Lunæ aut Veneris in Zodiaco, ideſt, <lb/>in quo ſis gradu per eius à Sole diſtantiam; </s> <s xml:id="echoid-s14788" xml:space="preserve">noctu adhibita armillari ſphæra, ſtellam quampiam Lunę aut Ve-<lb/>neri proximam obſeruabant, quantum ſcilicet locus eius locum Veneris in Zodiaco pręcederet, vel ſequere-<lb/>t<unsure/>ur. </s> <s xml:id="echoid-s14789" xml:space="preserve">præcedere autem eſt eſſe propius initio Zodiaci ſecundum ſignorum ordinem, ſic ſtella in 20. </s> <s xml:id="echoid-s14790" xml:space="preserve">gra. </s> <s xml:id="echoid-s14791" xml:space="preserve">Arie-<lb/>t<unsure/>is præcedit alteram, quæ ſit in 25. </s> <s xml:id="echoid-s14792" xml:space="preserve">gra. </s> <s xml:id="echoid-s14793" xml:space="preserve">vel quæ ſit in Tauro, aut Geminis, &</s> <s xml:id="echoid-s14794" xml:space="preserve">c. </s> <s xml:id="echoid-s14795" xml:space="preserve">id autem per noſtram armil-<lb/>larem ſphæram ſic aſſequemur. </s> <s xml:id="echoid-s14796" xml:space="preserve">ea Aſtronomicè, ſplendente Luna, aut Venere, eorumquelocis iam præco-<lb/>gnitis, collocetur, poſſea circulus latitidinis ita moueatur, vt viſiuus radius illi adhærens; </s> <s xml:id="echoid-s14797" xml:space="preserve">tranſeat per me-<lb/>diam Venerem; </s> <s xml:id="echoid-s14798" xml:space="preserve">quo facto ſtatim ad ſtellam obſeruandã idem circulus transferatur ita, vt viſus per Dioptram <lb/>peruadens in ſtellam dirigatur, atque in terram gradus eclipticæ notetur, per quem circulus tranſit, quantus <lb/>enim erit arcus inter locum Veneris, & </s> <s xml:id="echoid-s14799" xml:space="preserve">hunc, is erit diſtantia ſtellæ à Venere ſecundum Zodiaci longitudi-<lb/>nem, quare ſi ei addatur Veneris longitudo, ſi eam Venus præcedat, conflabitum tota ſtellæ longitudo, v. </s> <s xml:id="echoid-s14800" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s14801" xml:space="preserve">Venus ſit in 10. </s> <s xml:id="echoid-s14802" xml:space="preserve">gra. </s> <s xml:id="echoid-s14803" xml:space="preserve">Tauri, ſtella vero obſeruata diſtetà Venere gradus 4. </s> <s xml:id="echoid-s14804" xml:space="preserve">erit igitur ſtella in 14. </s> <s xml:id="echoid-s14805" xml:space="preserve">gra. </s> <s xml:id="echoid-s14806" xml:space="preserve">Tauri, <lb/>ac proinde eius longitudo erit grad. </s> <s xml:id="echoid-s14807" xml:space="preserve">44. </s> <s xml:id="echoid-s14808" xml:space="preserve">diſtantia ſcilicet ab Æquinoctio, quæ primo quærebatur. </s> <s xml:id="echoid-s14809" xml:space="preserve">Arcus vero <lb/>circuli, latitudinis inter ſtellam, & </s> <s xml:id="echoid-s14810" xml:space="preserve">eclipticam interceptus, erit latitudo ſtellæ obſeruatæ borea vel auſtrina, <lb/>prout citra ad boream, vel vltra ad auſtrum ab ecliptica fuerit obſeruata: </s> <s xml:id="echoid-s14811" xml:space="preserve">quæ erat ſecundo loco inueſtigan-<lb/>da ex duabus hiſce diſtantijs verus, & </s> <s xml:id="echoid-s14812" xml:space="preserve">proprius ſtellę locus in Firmamento dignoſcitur. </s> <s xml:id="echoid-s14813" xml:space="preserve">ſic igitur omuium <lb/>ſtellarum poſſunt loca definiri, totiuſque Firmamenti ordinem, ac configurationem determinari. </s> <s xml:id="echoid-s14814" xml:space="preserve">Non eſt <lb/>autem neceſſe ſingularum ſtellarum longitudines, & </s> <s xml:id="echoid-s14815" xml:space="preserve">latitudines adeo laboriose inquirere, ſed ſatis eſt non-<lb/>nullis præſtitiſſe, vti fecerunt in prima Arietis ſtella, atque in ſpica Virginis, quæ olim erant propè æquino-<lb/>ctia; </s> <s xml:id="echoid-s14816" xml:space="preserve">aut in Baſiliſco, &</s> <s xml:id="echoid-s14817" xml:space="preserve">c. </s> <s xml:id="echoid-s14818" xml:space="preserve">conſtituitis enim harum locis poſſunt aliarum loca per diſtantias ab eis inuentas de-<lb/>terminari. </s> <s xml:id="echoid-s14819" xml:space="preserve">Hoc igitur modo deſcribunt Catalogum fixarum, in quo quælibet ſtella habet propriam longi-<lb/>tudinem, & </s> <s xml:id="echoid-s14820" xml:space="preserve">latitudinem, atque etiam magnitudinem. </s> <s xml:id="echoid-s14821" xml:space="preserve">Talem Catalogum videbis apud Ptolemæum, ſed cor-<lb/>rectiorem a pud Copernicum, & </s> <s xml:id="echoid-s14822" xml:space="preserve">correctiſſimum apud Tychonem, tom. </s> <s xml:id="echoid-s14823" xml:space="preserve">1. </s> <s xml:id="echoid-s14824" xml:space="preserve">qui ſumma cura ac diligentia ſtel-<lb/>larum loca ad noſtra ſæcula definiuit, ideſt, ad annum Chriſti 1600. </s> <s xml:id="echoid-s14825" xml:space="preserve">completum.</s> <s xml:id="echoid-s14826" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14827" xml:space="preserve">Totus igitur Calogus diuiditur in tres partes. </s> <s xml:id="echoid-s14828" xml:space="preserve">quarum vna continet omnes ſtellas apud Zodiacum. </s> <s xml:id="echoid-s14829" xml:space="preserve">ſecun-<lb/>da ſtellas, quæ extra Zodiacum ſunt Boreales. </s> <s xml:id="echoid-s14830" xml:space="preserve">tertia Auſtrales. </s> <s xml:id="echoid-s14831" xml:space="preserve">rurſus totus conſtat columnis 4. </s> <s xml:id="echoid-s14832" xml:space="preserve">prima conti-<lb/>net nomina ſtellarum, in qua illa dicitur præcedens, quæ minorem habet longitudinem, illa ſequens, quæ <lb/>maiorem. </s> <s xml:id="echoid-s14833" xml:space="preserve">ſitum vero earum explicatur iuxta imaginis illius membra, in qua exiſtunt. </s> <s xml:id="echoid-s14834" xml:space="preserve">Secunda columna conti-<lb/>net longitudines è regione ſtellæ ſitas. </s> <s xml:id="echoid-s14835" xml:space="preserve">Tertia eodem modo latitudines, & </s> <s xml:id="echoid-s14836" xml:space="preserve">in Zodiaco additur littera B. </s> <s xml:id="echoid-s14837" xml:space="preserve">quæ <lb/>Boreales, & </s> <s xml:id="echoid-s14838" xml:space="preserve">littera A. </s> <s xml:id="echoid-s14839" xml:space="preserve">quæ Auſtrales denotat. </s> <s xml:id="echoid-s14840" xml:space="preserve">Quar a Magnitudines, aut colores, ſic. </s> <s xml:id="echoid-s14841" xml:space="preserve">1. </s> <s xml:id="echoid-s14842" xml:space="preserve">ſignificat primam <lb/>magnitudinem. </s> <s xml:id="echoid-s14843" xml:space="preserve">2. </s> <s xml:id="echoid-s14844" xml:space="preserve">ſecundam, &</s> <s xml:id="echoid-s14845" xml:space="preserve">c. </s> <s xml:id="echoid-s14846" xml:space="preserve">Ne- ſignificat Nebuloſam. </s> <s xml:id="echoid-s14847" xml:space="preserve">Obſ. </s> <s xml:id="echoid-s14848" xml:space="preserve">obſcuram.</s> <s xml:id="echoid-s14849" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14850" xml:space="preserve">Quoniam vero apud ſcriptores eadem ſæpè ſtella varijs nominibus appellatur, placuit hoc loco hanc ſtel-<lb/>larum Polyonymiam explicare, vnde ſcriptores intelligi poſſint de qua ſtella loquantur: </s> <s xml:id="echoid-s14851" xml:space="preserve">ſunt autem nomina <lb/>@æc partim Hebræa, vel Arabica, partim Græca, & </s> <s xml:id="echoid-s14852" xml:space="preserve">Latina.</s> <s xml:id="echoid-s14853" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div349" type="section" level="1" n="248"> <head xml:id="echoid-head264" style="it" xml:space="preserve">Polyonymia Stellarum, & Asteriſmorum. Cap. IV.</head> <p> <s xml:id="echoid-s14854" xml:space="preserve">AQuila, Vultur volans, idem.</s> <s xml:id="echoid-s14855" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14856" xml:space="preserve">Caput Meduſæ, Arabicè Algol.</s> <s xml:id="echoid-s14857" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14858" xml:space="preserve">Bootes, Arctophylax, Arcturus.</s> <s xml:id="echoid-s14859" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14860" xml:space="preserve">Capra, Capella, Hircus, Arabes Alaiot.</s> <s xml:id="echoid-s14861" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14862" xml:space="preserve">Cygnus, Gallina auis.</s> <s xml:id="echoid-s14863" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14864" xml:space="preserve">Erictonius, Auriga, Agitator, Heniochus.</s> <s xml:id="echoid-s14865" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14866" xml:space="preserve">Vrſa minor, Cynoſura.</s> <s xml:id="echoid-s14867" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14868" xml:space="preserve">Vrſa maior, Helice, in ea Carrnm, vel Plauſtrum.</s> <s xml:id="echoid-s14869" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14870" xml:space="preserve">Corona Ariadnæ, Gnoſſia.</s> <s xml:id="echoid-s14871" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14872" xml:space="preserve">Serpentanus, Ophiueus.</s> <s xml:id="echoid-s14873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14874" xml:space="preserve">Lyra, Vultur, cadens.</s> <s xml:id="echoid-s14875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14876" xml:space="preserve">Triangulum, Deltoton.</s> <s xml:id="echoid-s14877" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14878" xml:space="preserve">Hercules, Engonafi.</s> <s xml:id="echoid-s14879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14880" xml:space="preserve">Regulus, Stella regia, Baſiliſcus, Cor Leonis.</s> <s xml:id="echoid-s14881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14882" xml:space="preserve">Pleiades, Virgiliæ, in Tauri dorſo.</s> <s xml:id="echoid-s14883" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14884" xml:space="preserve">Hyades, Suculæ, Atlantides, in capite Tauri.</s> <s xml:id="echoid-s14885" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14886" xml:space="preserve">Oculus Tauri vna Hyadum; </s> <s xml:id="echoid-s14887" xml:space="preserve">Arabicè Aldebaran; </s> <s xml:id="echoid-s14888" xml:space="preserve">eſt <lb/>oculus Tauri auſtralis, latinè Palilium.</s> <s xml:id="echoid-s14889" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14890" xml:space="preserve">Spica Virginis, Arabicè Alacel, & </s> <s xml:id="echoid-s14891" xml:space="preserve">Aſimech, in ſini-<lb/>ſtra manu Virginis.</s> <s xml:id="echoid-s14892" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14893" xml:space="preserve">Vindemiatrix, Arab. </s> <s xml:id="echoid-s14894" xml:space="preserve">Alaſaph. </s> <s xml:id="echoid-s14895" xml:space="preserve">Protrygetes Græcè: <lb/></s> <s xml:id="echoid-s14896" xml:space="preserve">eſt in Virgine.</s> <s xml:id="echoid-s14897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14898" xml:space="preserve">Caſtor, Apollo, eſt caput boreum Geminorum.</s> <s xml:id="echoid-s14899" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14900" xml:space="preserve">Pollux, Hercules, eſt caput auſtrinum Geminorum.</s> <s xml:id="echoid-s14901" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14902" xml:space="preserve">Cor Scorpionis, Antares, apud Ptolemæũ Græcum.</s> <s xml:id="echoid-s14903" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14904" xml:space="preserve">Libra, Chelæ, ideſt, branchiæ Scorpionis.</s> <s xml:id="echoid-s14905" xml:space="preserve"/> </p> <pb o="166" file="0188" n="193" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s14906" xml:space="preserve">Canis maior, Canis Syrius. </s> <s xml:id="echoid-s14907" xml:space="preserve">Arabicè Alhabor, vel <lb/>Elhabor.</s> <s xml:id="echoid-s14908" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14909" xml:space="preserve">Canis minor, Procyon: </s> <s xml:id="echoid-s14910" xml:space="preserve">Anticanis, Canicula, Algo-<lb/>meiſa Arabicé.</s> <s xml:id="echoid-s14911" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14912" xml:space="preserve">Os piſcij notij: </s> <s xml:id="echoid-s14913" xml:space="preserve">vltima Aquarij, Fomabant Arabicè.</s> <s xml:id="echoid-s14914" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14915" xml:space="preserve">Canobus, Canopus, in extremo temonis Argonauis.</s> <s xml:id="echoid-s14916" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14917" xml:space="preserve">Lar, Thuribulum, Ara, Puteus.</s> <s xml:id="echoid-s14918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14919" xml:space="preserve">Eridanus: </s> <s xml:id="echoid-s14920" xml:space="preserve">Fluuius, Amnis.</s> <s xml:id="echoid-s14921" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14922" xml:space="preserve">Argus, Nauis, Argonauis.</s> <s xml:id="echoid-s14923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14924" xml:space="preserve">Lupus, Beſtia Centauri.</s> <s xml:id="echoid-s14925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14926" xml:space="preserve">Corona auſtrina, Rota Ixionis.</s> <s xml:id="echoid-s14927" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14928" xml:space="preserve">Crater, Vas.</s> <s xml:id="echoid-s14929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14930" xml:space="preserve">Inter has Palilium, & </s> <s xml:id="echoid-s14931" xml:space="preserve">Antares diametraliter oppo-<lb/>nuntur.</s> <s xml:id="echoid-s14932" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14933" xml:space="preserve">Stella quædam Enonyma.</s> <s xml:id="echoid-s14934" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14935" xml:space="preserve">Scheat Arabicè, in dextra tibia Aquarij.</s> <s xml:id="echoid-s14936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14937" xml:space="preserve">Scheder, in pectore Caſſiopeæ, Arabicè.</s> <s xml:id="echoid-s14938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14939" xml:space="preserve">Marchab in ala Pegaſi, Arabicè.</s> <s xml:id="echoid-s14940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14941" xml:space="preserve">Regel, ſiniſter pes Orionis, Arabicè.</s> <s xml:id="echoid-s14942" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14943" xml:space="preserve">Acarnar, extrema Eridani, Arabicè.</s> <s xml:id="echoid-s14944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14945" xml:space="preserve">Hædi, duæ paruæ Stellæ in manu Aurigæ.</s> <s xml:id="echoid-s14946" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14947" xml:space="preserve">Aſelli, duæ Stellæ in Cancro, iuxta præſepe.</s> <s xml:id="echoid-s14948" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14949" xml:space="preserve">Præſepe, Stella Nebuloſa inter Aſellos.</s> <s xml:id="echoid-s14950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14951" xml:space="preserve">Propus, quaſi propes, ideſt, ante pedes Gemino-<lb/>rum.</s> <s xml:id="echoid-s14952" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14953" xml:space="preserve">Chelæ, branchiæ Scorpij.</s> <s xml:id="echoid-s14954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14955" xml:space="preserve">Polaris Stella eſt tertia, & </s> <s xml:id="echoid-s14956" xml:space="preserve">vltima cauda Cynoſuræ, <lb/>reliquæ vero duæ dicuntur Vigiles, & </s> <s xml:id="echoid-s14957" xml:space="preserve">Circitores, <lb/>quia circa polum circinent: </s> <s xml:id="echoid-s14958" xml:space="preserve">vulgo dicuntur, guar-<lb/>die, cuſtodi, quaſi poli cuſtodes, & </s> <s xml:id="echoid-s14959" xml:space="preserve">vigiles ſint: </s> <s xml:id="echoid-s14960" xml:space="preserve">à <lb/>Græcis teſte Hyginio, χορευται, ideſt, chorum ef-<lb/>ficientes.</s> <s xml:id="echoid-s14961" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div350" type="section" level="1" n="249"> <head xml:id="echoid-head265" xml:space="preserve">CATALOGVS ASTERISMORVM, <lb/>& Stellarum inerrantium præcipuarum ad annum <lb/>Chriſti completum 1600.</head> <head xml:id="echoid-head266" style="it" xml:space="preserve">Primo de Stellis, quæ à Zodiaco in Boream vergunt.</head> <note position="right" xml:space="preserve"> <lb/>Forma, & nomina Stellarum. # # ## Longitudo. # ## Latit. # Magn. <lb/>VRSA MINOR. # Sig. # Gra. # ′. # Gra. # ′. <lb/>QVæ in extremo caudæ, Polaris dicta. # ♊ # 23 # 2 # 66 # 2 # 2 <lb/>Sequens in cauda. # ♊ # 23 # 36 # 69 # 60 # 4 <lb/>In eductione caudæ. # ♋ # 3 # 24 # 73 # 50 # 4 <lb/>In latere quadranguli præcedente. # ♋ # 21 # 25 # 75 # 0 # 4 <lb/>In eodem latere altera. # ♋ # 24 # 52 # 77 # 38 # 5 <lb/>In latere ſequente. # ♌ # 7 # 16 # 72 # 51 # 2 <lb/>In eodem latere altera. # ♌ # 14 # 41 # 75 # 23 # 3 <lb/></note> </div> <div xml:id="echoid-div351" type="section" level="1" n="250"> <head xml:id="echoid-head267" style="it" xml:space="preserve">Prædictæ ſeptem Stellæ efficiunt figuram parui plauſtri, ei perſimile quod est <lb/>in Vrſa maiori, ſed contrario ſitu.</head> <note position="right" xml:space="preserve"> <lb/>VRSA MAIOR. 2. <lb/>Superior præcedentium in quadrangulo. # ♌ # 1 # 34 # 49 # 40 # 2 <lb/>Inferior præcedentium in eodem quadrangulo. # ♌ # 13 # 42 # 45 # 3 # 2 <lb/>Superiori ſequentium in eodem quadrangulo. # ♌ # 25 # 25 # 51 # 17 # 2 <lb/>Inferior ſequentium in eodem quadrangulo. # ♌ # 24 # 45 # 47 # 6 # 2 <lb/>Prima caudæ poſt eductionem. # ♍ # 3 # 10 # 54 # 18 # 2 <lb/>Secundæ caudæ. # ♍ # 9 # 56 # 56 # 22 # 2 <lb/>Vltimæ caudæ. # ♍ # 21 # 12 # 34 # 25 # 2 <lb/>Informis, ideſt, extra Vrſæ figuram. # ♍ # 17 # 43 # 40 # 6 # 2 <lb/>In genu ſiniſtro anteriori. # ♌ # 0 # 32 # 34 # 34 # 3 <lb/>Appellationes Stellarum. # # ## Longitudo. # ## Latit. # Magn. <lb/># Sig. # Gra. # ′. # Gra. # ′. <lb/>Borealior duarum in dextro pede. # ♋ # 25 # 56 # 29 # 15 # 3 <lb/>Altera auſtralior. # ♋ # 27 # 10 # 28 # 38 # 3 <lb/>DRACO. 3. <lb/>In capite lucidarum duarum prima. # ♐ # 6 # 19 # 75 # 21 # 3 <lb/>Lucida capitis dicta. # ♐ # 22 # 24 # 75 # 3 # 3 <lb/></note> <pb o="167" file="0189" n="194" rhead="Liber Decimusſeptimus."/> <note position="right" xml:space="preserve"> <lb/>In ſecunda ſſexura. # ♈ # 12 # 26 # 82 # 49 # 3 <lb/>Quædam. # ♈ # 27 # 47 # 79 # 25 # 3 <lb/>In flexura tertij nodi. # ♌ # 29 # 44 # 81 # 4 # 3 <lb/>Polo Zodiaci prima. # ♍ # 26 # 51 # 84 # 48 # 3 <lb/>Ad extremam flexionem. # ♎ # 7 # 54 # 78 # 32 # 3 <lb/>Præcedens flexuram. # ♎ # 12 # 28 # 74 # 11 # 3 <lb/>Ad eandem flexuram. # ♍ # 29 # 22 # 11 # 4 # 3 <lb/>Quæ flexuram proximè ſequitur. # ♍ # 2 # 10 # 66 # 36 # 2 <lb/>Penultima caudæ. # ♌ # 10 # 26 # 61 # 33 # 3 <lb/>Vltima caudæ. # ♌ # 4 # 37 # 57 # 7 # 3 <lb/>CEPHEVS. 4. <lb/>In cingulo. # ♉ # 0 # 13 # 71 # 7 # 3 <lb/>Lucida in humero. # ♈ # 7 # 13 # 68 # 54 # 3 <lb/>In ſiniſtro humero. # ♈ # 27 # 53 # 62 # 36 # 4 <lb/>Apud tiaram. # ♈ # 8 # 29 # 61 # 3 # 4 <lb/>BOOTES. 5. <lb/>In humero ſiniſtro. # ♎ # 13 # 5 # 49 # 33 # 3 <lb/>In capite dextro. # ♎ # 18 # 43 # 54 # 15 # 3 <lb/>In dextro humero. # ♎ # 27 # 29 # 49 # 1 # 3 <lb/>In coxendice. # ♎ # 22 # 29 # 40 # 40 # 3 <lb/>In crure dextro. # ♎ # 27 # 36 # 27 # 57 # 3 <lb/>In tibia ſiniſtra. # ♎ # 13 # 42 # 28 # 9 # 3 <lb/>In fimbria tunicæ, Arcturus dicta. # ♎ # 18 # 39 # 31 # 2 # 1 <lb/>CORONA BOREA. 6. <lb/>Lucida Coronæ. # ♎ # 18 # 39 # 31 # 2 # 1 <lb/>Nomina Stellarum. # # ## Longitudo. # ## Latit. # Magn. <lb/># Sig. # Gra. # ′. # Gra. # ′. <lb/>Præcedens. # ♏ # 3 # 37 # 46 # 8 # 4 <lb/>Sequens lucidam. # ♏ # 9 # 14 # 44 # 33 # 4 <lb/>Proximè ſequens. # ♏ # 11 # 25 # 44 # 51 # 4 <lb/>Quæ hanc comitatur. # ♏ # 13 # 42 # 36 # 9 # 4 <lb/>HERCVLES. 7. <lb/>In capite. # ♐ # 10 # 31 # 37 # 23 # 3 <lb/>In humero dextro. # ♏ # 25 # 27 # 42 # 48 # 3 <lb/>In brachio dextro. # ♏ # 23 # 39 # 40 # 5 # 3 <lb/>In ſiniſtro humero. # ♐ # 9 # 10 # 47 # 47 # 3 <lb/>In coxa ſiniſtra. # ♏ # 26 # 2 # 53 # 10 # 3 <lb/>In femore ſiniſtro. # ♐ # 2 # 45 # 53 # 21 # 3 <lb/>In geuu ſiniſtro. # ♐ # 22 # 56 # 60 # 47 # 3 <lb/>In ſiniſtra ſura. # ♐ # 14 # 17 # 69 # 22 # neb. <lb/>Nebuloſa in pede ſiniſtro. # ♐ # 18 # 0 # 71 # 5 <lb/>In femore dextro. # ♏ # 23 # 8 # 60 # 22 # 3 <lb/>LYRA. 8. <lb/>Lucida, Lyra, & Fidicula dicta. # ♑ # 9 # 43 # 61 # 43 # 1 <lb/>In iugo. # ♑ # 13 # 16 # 56 # 5 # 3 <lb/>In iugo altera. # ♑ # 16 # 11 # 53 # 6 # 3 <lb/>CYGNVS. 9. <lb/>In roſtro. # ♑ # 25 # 44 # 49 # 2 # 3 <lb/>In pectore. # ♒ # 19 # 25 # 57 # 9 # 3 <lb/>In cauda. # ♒ # 29 # 53 # 59 # 6 # 2 <lb/>Lucidiſſima in ancone alæ ſuperioris. # ♒ # 10 # 53 # 64 # 28 # 3 <lb/>In ancone inferioris alæ. # ♒ # 22 # 9 # 49 # 26 # 3 <lb/>Extrema inferioris alæ. # ♒ # 27 # 43 # 43 # 44 # 3 <lb/>Noua, quæ adhuc perſeuerat in imo collo. # ♒ # 16 # 18 # 55 # 37 # 3 <lb/></note> <pb o="168" file="0190" n="195" rhead="De Mundi Fabrica,"/> <note position="right" xml:space="preserve"> <lb/>CASSIOPEA. 10. <lb/>In pectore, Schedir. # ♉ # 2 # 17 # 46 # 35 # 3 <lb/>In flexura ad coxas. # ♉ # 8 # 27 # 48 # 46 # 3 <lb/>Ad genu. # ♉ # 12 # 21 # 46 # 22 # 3 <lb/>In crure. # ♉ # 19 # 13 # 47 # 29 # 3 <lb/>Appellationes Stellarum- # # ## Longitudo. # ## Latit. # Magn. <lb/># Sig. # Gra. # ′. # Gra. # ′. <lb/>Lucida Cathedra. # ♈ # 29 # 35 # 51 # 14 # 3 <lb/>Noua anno 1572. quæ poſtea euanuit. # ♉ # 6 # 54 # 53 # 55 # max. <lb/>PERSEVS. 11. <lb/>In dextro humero. # ♉ # 24 # 26 # 34 # 30 # 3 <lb/>Fulgens in dextro latere. # ♉ # 26 # 17 # 30 # 5 # 2 <lb/>Ad flexuram eiuſdem lateris. # ♉ # 29 # 15 # 27 # 14 # 3 <lb/>In ſiniſtro genu. # ♊ # 0 # 8 # 19 # 4 # 3 <lb/>In ſiniſtro pede. # ♉ # 27 # 36 # 11 # 17 # 3 <lb/>Caput Meduſæ. # ♉ # 20 # 38 # 22 # 22 # 3 <lb/>ERICTHONIVS. 12. <lb/>In ſiniſtro humero, Capella. # ♊ # 16 # 16 # 22 # 51 # 1 <lb/>Lucida in dextro humero. # ♊ # 15 # 52 # 21 # 27 # 2 <lb/>Hædus præcedens. # ♊ # 13 # 5 # 18 # 8 # 4 <lb/>Hædus ſequens. # ♊ # 13 # 49 # 16 # 11 # 4 <lb/>In ſiniſtro talo. # ♊ # 10 # 47 # 10 # 10 # 3 <lb/>In dextro pede, cornu ♉. # ♊ # 16 # 37 # 5 # 0 # 3 <lb/>COMA BERENICES. 13. <lb/>In cuſpide trianguli. # ♍ # 18 # 17 # 28 # 25 # 3 <lb/>Hanc ſequens. # ♍ # 18 # 42 # 27 # 23 # 4 <lb/>Inferior ijs. # ♍ # 18 # 46 # 27 # 20 # 4 <lb/>SERPENTARIVS. 14. <lb/>In capite. # ♐ # 16 # 50 # 35 # 47 # 3 <lb/>In humero dextro. # ♐ # 19 # 45 # 28 # 1 # 3 <lb/>Inferior in dextro humero. # ♐ # 21 # 5 # 26 # 11 # 3 <lb/>In ſiniſtra manu. # ♏ # 26 # 44 # 17 # 19 # 3 <lb/>Eam ſequens. # ♏ # 27 # 57 # 16 # 30 # 3 <lb/>In dextro genu. # ♐ # 12 # 24 # 7 # 18 # 3 <lb/>In ſiniſtro genu. # ♐ # 3 # 39 # 11 # 30 # 3 <lb/>In dextra tibia. # ♐ # 14 # 37 # 2 # 13 # 3 <lb/>Noua, quæ euanuit anno 1604. # ♐ # 18 # 0 # 2 # 0 # max. <lb/>SERPENS. 15. <lb/>Inore. # ♏ # 14 # 24 # 39 # 6 # 3 <lb/>Nomina Stellarum. # # ## Longitudo. # ## Latit. # Magn. <lb/># Sig. # Gra. # ′. # Gra. # ′. <lb/>In temporibus. # ♏ # 17 # 6 # 35 # 25 # 3 <lb/>In eductione colli. # ♏ # 14 # 21 # 37 # 27 # 3 <lb/>In collo ſecunda. # ♏ # 12 # 46 # 28 # 58 # 3 <lb/>In nexu colli. # ♏ # 16 # 30 # 25 # 35 # 2 <lb/>Auſtralior trium. # ♏ # 18 # 46 # 24 # 5 # 3 <lb/>Tertia caudæ. # ♐ # 24 # 34 # 19 # 57 # 3 <lb/>Penultima caudæ. # ♑ # 0 # 12 # 20 # 37 # 3 <lb/>Vltima caudæ. # ♑ # 10 # 10 # 26 # 59 # 3 <lb/>SAGITTA. 16. <lb/>Superior. # ♒ # 1 # 32 # 39 # 13 # 4 <lb/>Superior in glyphide. # ♑ # 35 # 30 # 38 # 53 # 4 <lb/>Inferior in glyphide. # ♑ # 25 # 39 # 38 # 18 # 4 <lb/></note> <pb o="169" file="0191" n="196" rhead="Liber Decimusſeptimus."/> <note position="right" xml:space="preserve"> <lb/>AQVILA. 17. <lb/>In collo. # ♑ # 26 # 53 # # 86 # 49 # 3 <lb/>Lucida in ſcapulis, ala. # ♑ # 29 # 9 # # 29 # 21 # 2 <lb/>In @iniſtro humero. # ♑ # 25 # 26 # # 31 # 18 # 3 <lb/>In cauda, Galaxiam tangens. # ♑ # 14 # 15 # # 36 # 16 # 3 <lb/>ANTINOVS. 18. <lb/>Manus ſiniſtra. # ♑ # 29 # 21 # # 18 # 48 # 3 <lb/>Latus dextrum. # ♑ # 20 # 17 # # 20 # 14 # 3 <lb/>Genu. # ♑ # 19 # 17 # # 14 # 28 # 3 <lb/>DELPHINVS. 19. <lb/>In cauda. # ♒ # 8 # 82 # # 29 # 8 # 3 <lb/>In rhomboide lateris primi. # ♒ # 10 # 56 # # 31 # 57 # 3 <lb/>In eodem latere borealior. # ♒ # 11 # 50 # # 33 # 5 # 3 <lb/>Sequentis lateris auſtralior. # ♒ # 13 # 36 # # 32 # 0 # 3 <lb/>Eiuſdem lateris borea. # ♒ # 14 # 27 # # 33 # 10 # 3 <lb/>Appellationes Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>######### EQVICVLVS. 20. <lb/>Sunt quatuor obſcuræ circa. # ♒ # 17 # # # 20 # # obſc. <lb/># ♒19 # # # 23 # # obſc. <lb/>PEGASVS. 21. <lb/>Os Pegaſi. # ♒ # 26 # 22 # # 22 # 7 # 3 <lb/>Lucida colli. # ♓ # 10 # 39 # # 17 # 41 # 3 <lb/>Dextrum genu. # ♓ # 20 # 10 # # 35 # 7 # 3 <lb/>Prima alæ. Marchab. # ♓ # 17 # 56 # # 19 # 26 # 2 <lb/>In eductione cruris. # ♓ # 23 # 49 # # 31 # 7 # 2 <lb/>Extrema alæ. # ♓ # 3 # 38 # # 12 # 35 # 2 <lb/>ANDROMEDA. 22 <lb/>Caput. # ♈ # 8 # 47 # # 25 # 42 # 2 <lb/>In cingulo. # ♈ # 24 # 49 # # 25 # 59 # 2 <lb/>In Auſtrali pede lucida. # ♉ # 8 # 39 # # 27 # 46 # 2 <lb/>In ſiniſtra ſcapula. # ♈ # 16 # 19 # # 24 # 20 # 2 <lb/>TRIANGVLVS. 23. <lb/>In apice iri<unsure/>anguli. # ♉ # 1 # 19 # # 16 # 49 # 4 <lb/>In baſi præcedens borea. # ♉ # 6 # 49 # # 20 # 33 # 4 <lb/>In baſi Auſtralior. # ♉ # 7 # 58 # # 18 # 57 # 4 <lb/>######### Secundo, de ſignts 12. Zodiac. b, Borealem. a, Australem ſignificat. <lb/>ARIES. 24. <lb/>Prima omnium in cornu dextrum duarum præced. # ♈ # 27 # 37 # # 7 # 8 # 4 # b. <lb/>Lucida in capite. # ♉ # 2 # 6 # # 9 # 57 # 3 # b. <lb/>In cauda. # ♉ # 15 # 15 # # 1 # 46 # 4 # b. <lb/>Sequens in codem cornu. # ♈ # 28 # 23 # # 8 # 29 # 4 # b. <lb/>TAVRVS. 25. <lb/>In naribus, Sucularum prima. # ♊ # 0 # 12 # # 5 # 46 # 3 # a. <lb/>Apud oculum boreum. # ♊ # 1 # 16 # # 4 # 2 # 3 # a. <lb/>Nomina Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>In oculo auſtrali. Aldebaram. Palilium. # ♊ # 4 # 12 # # 5 # 31 # 1 # a. <lb/>In oculo boreo. # ♊ # 2 # 53 # # 2 # 36 # 3 # a. <lb/>In fine cornu auſtralis. # ♊ # 12 # 12 # # 2 # 14 # 3 # b. <lb/>In ſummo cornu boreo. # ♊ # 16 # 59 # # 5 # 20 # 2 # b. <lb/>Media, & lucida Pleiadum. # ♉ # 24 # 24 # # 4 # 0 # 3 # b. <lb/></note> <pb o="170" file="0192" n="197" rhead="De Mundi Fabrica."/> <note position="right" xml:space="preserve"> <lb/>GEMINI. 26. <lb/>In ſuperiori capite. Caſtor. # ♋ # 14 # 41 # # 10 # 2 # 2 # b. <lb/>In inferiori capite. Pollux. # ♋ # 17 # 43 # # 6 # 38 # 2 # b. <lb/>In genu ſuperioris Gemini. # ♋ # 4 # 22 # # 2 # 11 # 3 # b. <lb/>In genu inferioris Gemini. # ♋ # 9 # 26 # # 2 # 2 # 3 # a. <lb/>In ventre inferioris Gemini. # ♋ # 12 # 56 # # 0 # 13 # 3 # a. <lb/>Calx ſuperioris Gemini. # ♋ # 29 # 44 # # 0 # 53 # 3 # a. <lb/>Lucida pedis ſuperioris. # ♋ # 3 # 31 # # 6 # 48 # 2 # a. <lb/>CANCER. 27. <lb/>Nebuloſa in pectore. # ♌ # 1 # 46 # # 1 # 14 # ## neb. <lb/>Aſellus boreus. # ♌ # 1 # 57 # # 3 # 8 # 4 # a. <lb/>Aſellus auftralis. # ♌ # 3 # 8 # # 0 # 4 # 4 # a. <lb/>In brachio auſtrino. # ♌ # 8 # 3 # # 5 # 8 # 3 # a. <lb/>Lucidor in radice caudæ. # ♋ # 25 # 45 # # 2 # 18 # 4 # a. <lb/>LEO. 28. <lb/>In capite. # ♌ # 15 # 5 # # 9 # 40 # 3 # b. <lb/>In collo. # ♌ # 21 # 57 # # 11 # 50 # 3 # b. <lb/>Media, & lucida colli. # ♌ # 23 # 59 # # 8 # 47 # 2 # b. <lb/>In collo ſequens. # ♌ # 22 # 20 # # 4 # 52 # 3 # b. <lb/>Cor, Regul<unsure/>us, Baſiliſcus. # ♌ # 24 # 17 # # 0 # 26 # 2 # b. <lb/>Lucida in lumbis. # ♍ # 5 # 41 # # 14 # 20 # 3 # b. <lb/>In clune. # ♍ # 7 # 50 # # 6 # 7 # 3 # b. <lb/>In femore. # ♍ # 11 # 58 # # 12 # 18 # 1 # b. <lb/>Lucida in extremo caudæ. # ♍ # 16 # 13 # # 12 # 18 # 1 # b. <lb/>VIRGO. 29. <lb/>In extremo alæ ſiniſtræ. # ♎ # 21 # 32 # # 0 # 43 # 3 # b. <lb/>Sequens in ſiniſtra ala. # ♍ # 4 # 35 # # 2 # 50 # 3 # b. <lb/>Appellationes Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>In dextro latere. # ♎ # 18 # 16 # # 1 # 59 # 1 # a. <lb/>Vindemiatrix. # ♎ # 15 # 22 # # 8 # 10 # 3 # b. <lb/>LIBRA. 30. <lb/>Lanx auſtrina. # ♍ # 9 # 31 # # 0 # 26 # 2 # b. <lb/>Lanx borea. # ♍ # 13 # 48 # # 8 # 55 # 2 # b. <lb/>Ab auſtrina lance ad ortum. # ♍ # 19 # 33 # # 4 # 28 # 3 # b. <lb/>SCORPIVS. 31. <lb/>Suprema in fronte. # ♍ # 27 # 36 # # 1 # 5 # 2 # b. <lb/>Media in fronte. # ♍ # 27 # 0 # # 1 # 54 # 3 # a. <lb/>Tertia in fronte. # ♍ # 27 # 25 # # 5 # 22 # 3 # a. <lb/>Cor Scorpionis. Antares. # ♐ # 4 # 13 # # 4 # 27 # 1 # a. <lb/>Nebuloſa propè aculeum Scorpionis. # ♐ # 22 # 7 # # 13 # 15 # ne. # a. <lb/>SAGITTARIVS. 32. <lb/>In cuſpide ſagittæ. # ♐ # 25 # 0 # # 6 # 30 # 3 # a. <lb/>In ſiniſtra manu. # ♐ # 29 # 27 # # 6 # 30 # 3 # a. <lb/>In arcus parte auſtrali. # ♐ # 29 # 49 # # 10 # 50 # 3 # a. <lb/>In parte arcus borea. # ♐ # 0 # 49 # 1 # 30 # 3 # a. <lb/>In extremo arcu boreo. # ♐ # 27 # 37 # # 2 # 50 # 4 # b. <lb/>In humero ſiniſtro. # ♑ # 9 # 40 # # 3 # 10 # 3 # a. <lb/>In oculo, nebuloſa. # ♑ # 8 # 30 # # 0 # 45 # ne. # b. <lb/>Sub axilla. # ♑ # 7 # 17 # # 6 # 45 # 3 # a. <lb/>In ſuffragine ſiniſtra priori. # ♑ # 8 # 37 # # 23 # 0 # 2 # a. <lb/>In genu eiuſdem cruris. # ♑ # 7 # 17 # # 18 # 0 # 2 # a. <lb/>In dextra priori ſuftragiue. # ♐ # 23 # 27 # # 13 # 0 # 3 # a. <lb/>In ſiniſtra ſcapul<unsure/>a. # ♑ # 18 # 17 # # 13 # 30 # 3 # a. <lb/>In priori dextro genu. # ♑ # 17 # 37 # # 20 # 10 # 3 # a. <lb/></note> <pb o="171" file="0193" n="198" rhead="Liber Decimusſeptimus."/> <note position="right" xml:space="preserve"> <lb/>CAPRICORNVS. 33. <lb/>In cornu præcedenti. # ♑ # 28 # 18 # # 7 # 2 # 3 # b. <lb/>Altera in eodem cornu. # ♑ # 28 # 31 # # 4 # 41 # 3 # b. <lb/>Nebuloſa præcedens cornua. # ♑ # 27 # 8 # # 7 # 16 # ne. # b. <lb/>Nomina Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>Nebuloſa in fronte. # ♑ # 27 # 57 # # 0 # 48 # ne. # b. <lb/>Altera nebuloſa ididem. # ♑ # 29 # 41 # # 0 # 28 # ne. # b. <lb/>Tertia nebuloſa inibi. # ♑ # 27 # 13 # # 0 # 24 # ne. # b. <lb/>Lucida in cauda præcedens. # ♒ # 16 # 14 # # 2 # 26 # 3 # a. <lb/>Lucida ſequens in cauda. # ♒ # 18 # 0 # # 2 # 29 # 3 # a. <lb/>AQVARIVS. 34. <lb/>In humero dextro clarior. # ♒ # 27 # 49 # # 10 # 42 # 3 # b. <lb/>In humero deſtro clarior. # ♒ # 17 # 51 # # 8 # 82 # 3 # b. <lb/>In brachio dextro. # ♓ # 1 # 10 # # 8 # 17 # 3 # b. <lb/>In dextra tibia, Scheat. # ♓ # 3 # 22 # # 8 # 10 # 3 # a. <lb/>Sub@axilla. # ♓ # 18 # 17 # # 6 # 15 # 3 # b. <lb/>Sub ſiniſtra manu. # ♓ # 7 # 37 # # 5 # 30 # 3 # b. <lb/>Altera inibi. # ♓ # 5 # 37 # # 8 # 30 # 3 # b. <lb/>In dextra manu. # ♓ # 0 # 37 # # 10 # 45 # 3 # b. <lb/>In eadem manu. # ♓ # 2 # 57 # # 9 # 0 # 3 # b. <lb/>Vltima effuſionis. Fomahant. # ♒ # 28 # 11 # # 21 # 0 # 1 # a. <lb/>PISCES. <lb/>In ore Piſcis prioris. # ♓ # 13 # 2 # # 9 # 4 # 4 # b. <lb/>In occipite eiuſdem. # ♓ # 15 # 50 # # 7 # 17 # 4 # b. <lb/>In cauda eiuſdem. # ♓ # 27 # 2 # # 6 # 23 # 4 # b. <lb/>In lino auſtrali præcedens. # ♈ # 8 # 36 # # 2 # 11 # 4 # b. <lb/>Al<unsure/>tera ibidem. # ♈ # 11 # 58 # # 1 # 5 # 4 # b. <lb/>Tertia inibi. # ♈ # 14 # 19 # # 0 # 57 # 4 # b. <lb/>In nexu linorum lucidior. # ♈ # 23 # 47 # # 9 # 4 # 4 # b. <lb/>In nexu boreo lucidior. # ♈ # 27 # 16 # # 5 # 21 # 4 # b. <lb/>In extremitate caudæ borei Piſcis. # ♈ # 21 # 37 # # 9 # 24 # 4 # b. <lb/>In ore borei Piſcis. # ♈ # 22 # 49 # # 20 # 43 # 5 # b. <lb/>In ſpina. # ♈ # 17 # 56 # # 13 # 21 # 5 # b. <lb/>In aluo duarnm præeedens. # ♈ # 20 # 58 # # 15 # 30 # 5 # b. <lb/>Sequens inibi. # ♈ # 23 # 18 # # 17 # 26 # 5 # b. <lb/>######### Tertio de Stellis à Zodiaco meridionalibus. <lb/>CETE. 36. <lb/>Lucida mandibula Cete. # ♉ # 8 # 47 # # 12 # 37 # 3 <lb/>Appellationes Stellarum- # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>In ore. # ♉ # 3 # 57 # # 12 # 2 # 3 <lb/>Ing enu. # ♉ # 2 # 2 # # 14 # 32 # 3 <lb/>In pectore. # ♈ # 27 # 47 # # 25 # 58 # 3 <lb/>In ventre. # ♈ # 16 # 25 # # 20 # 19 # 3 <lb/>In dorſo. # ♈ # 10 # 42 # # 15 # 46 # 3 <lb/>Ibidem. # ♈ # 6 # 11 # # 16 # 55 # 3 <lb/>In cauda. # ♓ # 25 # 23 # # 10 # 1 # 3 <lb/>Ibidem lucida. # ♓ # 26 # 56 # # 20 # 47 # 2 <lb/>ORION. 37. <lb/>In capite nebuloſa. # ♊ # 18 # 0 # # 16 # 30 # neb. <lb/>Lucidus humerus dexter. # ♊ # 23 # 12 # # 16 # 6 # 2 <lb/>Siniſter humerus præcedens. # ♊ # 15 # 23 # # 17 # 0 # 2 <lb/>In dextra manu. # ♊ # 7 # 23 # # 9 # 15 # 4 <lb/></note> <pb o="172" file="0194" n="199" rhead="De Mundi Fabrica,"/> <note position="right" xml:space="preserve"> <lb/>In clypeo. # ♊ # 7 # 53 # # 8 # 11 # 4 <lb/>Prima baltei. # ♊ # 16 # 50 # # 23 # 38 # 2 <lb/>Media baltei. # ♊ # 18 # 0 # # 24 # 33 # 2 <lb/>In manubrio enſis. # ♊ # 14 # 37 # # 26 # 0 # 3 <lb/>In medio enſe. # ♊ # 17 # 0 # # 19 # 0 # 3 <lb/>In enſe pariter. # ♊ # 17 # 27 # # 29 # 0 # 3 <lb/>In ſiniſtro. Regel. # ♊ # 11 # 0 # # 31 # 0 # 1 <lb/>In genu dextro. # ♊ # 21 # 0 # # 33 # 0 # 3 <lb/>Vltima baltei. # ♊ # 19 # 0 # # 25 # 0 # 2 <lb/>ERIDANVS. 38. <lb/>Supra pedem Orionis. # ♊ # 10 # 0 # # 28 # 0 # 3 <lb/>Ex quatuor præcedens. # ♉ # 13 # 0 # # 27 # 2 # 3 <lb/>Hanc ſequens. # ♉ # 15 # 0 # # 29 # 0 # 4 <lb/>Tertia ſequens. # ♉ # 16 # 0 # # 31 # 0 # 3 <lb/>Quarta ſequens. # ♉ # 8 # 0 # # 33 # {1/2} # 3 <lb/>Alia præcedens has. # ♉ # 8 # 0 # # 25 # {1/2} # 3 <lb/>Alia adhuc pręcedens. # ♉ # 6 # 0 # # 24 # 0 # 4 <lb/>Tertia adhuc præcedens. # ♉ # 2 # {1/2} # # 23 # 0 # 3 <lb/>In extremo fluuij. Phæton. # ♈ # 21 # 0 # # 53 # 0 # 1 <lb/>Nomina Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>LEPVS. 39. <lb/>In pedibus prioribus. # ♊ # 6 # {1/2} # # 45 # 0 # 4 <lb/>In dorſo. # ♊ # 16 # 0 # # 41 # 0 # 3 <lb/>In armo ſiniſtro. # ♊ # 14 # 0 # # 44 # 0 # 3 <lb/>In poſterioribus pedibus. # ♊ # 19 # 21 # # 46 # 0 # 3 <lb/>Alia ſequens inibi. # ♊ # 21 # {1/2} # # 44 # 0 # 3 <lb/>CANIS MAIOR. 40. <lb/>Inore ſplendida, Sirius. # ♋ # 8 # 15 # # 39 # 30 # 1 <lb/>Sub ſiniſtra aure. # ♋ # 14 # 0 # # 38 # 0 # 3 <lb/>In extremo pede priore. # ♋ # 2 # 0 # # 41 # 0 # 2 <lb/>In ventre. # ♋ # 18 # 0 # # 46 # {1/2} # 3 <lb/>Inter femora poſteriora. # ♋ # 15 # 0 # # 51 # 20 # 3 <lb/>In dextro pede priori. # ♋ # 1 # 7 # # 52 # 0 # 3 <lb/>In cauda. # ♋ # 24 # 0 # # 51 # 0 # 3 <lb/>Apud Canem duarum lucidarum prima. # ♊ # 20 # 6 # # 60 # 0 # 2 <lb/>Secunda earum. # ♊ # 17 # 0 # # 58 # 0 # 2 <lb/>CANIS MINOR. Procyon. 41. <lb/>In collo. # ♋ # 16 # 30 # # 13 # 30 # 3 <lb/>In femore Procyon. # ♋ # 20 # 20 # # 18 # 0 # 1 <lb/>ARGVS. NAVIS. 42. <lb/>In ſuprema puppi. # ♌ # 56 # 0 # # 43 # 0 # 3 <lb/>Suprema clypei nauis. # ♌ # 0 # 35 # # 49 # 0 # 3 <lb/>Præcedens clypei. # ♋ # 28 # 0 # # 47 # 30 # 3 <lb/>In carina. # ♋ # 25 # 0 # # 59 # 0 # 3 <lb/>Lucida in tranſtro. # ♌ # 12 # 7 # # 58 # 0 # 2 <lb/>Propè ſcutum. # ♌ # 6 # 7 # # 54 # 30 # 2 <lb/>In ſectione ſtrati. # ♌ # 8 # 27 # # 66 # 0 # 2 <lb/>Lucida in ſtatione. # ♌ # 21 # 0 # # 64 # 0 # 2 <lb/>Intra carinam fulgens. # ♌ # 29 # 30 # # 70 # 0 # 2 <lb/>Ibidem altera. # ♍ # 14 # 50 # # 66 # 0 # 3 <lb/>Tertia ibidem. # ♍ # 19 # 0 # # 66 # 0 # 3 <lb/>Quarta inibi. # ♍ # 16 # 0 # # 66 # 0 # 2 <lb/></note> <pb o="173" file="0195" n="200" rhead="Liber Decimusſeptimus."/> <note position="right" xml:space="preserve"> <lb/>Appellationes Stellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>In temone. Canopus. # ♋ # 6 # 0 # # 75 # 0 # 1 <lb/>Canopum ſequens. # ♋ # 18 # 0 # # 72 # 0 # 3 <lb/>Apud ſectionem. # ♋ # 22 # 0 # # 63 # 0 # 3 <lb/>Altera inibi. # ♋ # 29 # 0 # # 62 # 0 # 3 <lb/>Apud Canopum altera. # ♋ # 9 # 10 # # 66 # 0 # 3 <lb/>HYDRA. 34. <lb/>Lucida. Cor Hydræ. # ♌ # 21 # 45 # # 22 # 30 # 1 <lb/>Quæ in rectam lineam. 3. præcedit. # ♍ # 9 # 0 # # 24 # 30 # 3 <lb/>Media earum. # ♍ # 11 # 0 # # 23 # 0 # 4 <lb/>Tertia ſequens. # ♍ # 14 # 0 # # 22 # 0 # 3 <lb/>Poſt cornum vicina caudæ. # ♎ # 20 # 57 # # 14 # 0 # 4 <lb/>In quodam triangulo præcedens.<unsure/> # ♎ # 7 # 7 # # 31 # 0 # 3 <lb/>Propè caput in auſtrum. # ♌ # 2 # 50 # # 13 # 0 # 3 <lb/>Apud collum. # ♍ # 1 # 57 # # 16 # 0 # 3 <lb/>CRATER, VRNA. 44. <lb/>In baſi crateris. # ♍ # 18 # 0 # # 23 # 0 # 3 <lb/>Sequens duarum in medio. # ♍ # 24 # 0 # # 20 # 0 # 3 <lb/>Earundem præcedens. # ♍ # 21 # 0 # # 17 # 25 # 3 <lb/>CORVVS. 46. <lb/>Quæ ad oculum. # ♎ # 6 # 0 # # 20 # 0 # 3 <lb/>Præcedens d@arum fup@riorum. # ♎ # 5 # 13 # # 14 # 25 # 3 <lb/>Sequens e<unsure/>arum. # ♎ # 8 # 0 # # 12 # 7 # 3 <lb/>In ala. # ♎ # 7 # 37 # # 12 # 3 # 3 <lb/>Sequens inferiorum in quadrangulo. # ♎ # 12 # 0 # # 18 # 0 # 4 <lb/>CENTAVRVS. 46. <lb/>In humero ſiniſtro. # ♎ # 27 # 7 # # 26 # 0 # 3 <lb/>In humero dextro. # ♏ # 7 # 7 # # 22 # 30 # 3 <lb/>In dextro cubito. # ♏ # 14 # 0 # # 25 # 0 # 3 <lb/>In eductione corporis. # ♏ # 9 # 0 # # 33 # 30 # 3 <lb/>In lumbis. # ♏ # 26 # 47 # # 40 # 0 # 3 <lb/>In dextra coxa. # ♏ # 24 # 0 # # 46 # 0 # 3 <lb/>Sub aluo duarum præcedens<unsure/>. # ♏ # 7 # 17 # # 46 # 0 # 2 <lb/>Sequens. # ♏ # 9 # 17 # # 44 # 0 # 3 <lb/>NominaStellarum. # Sig. # ## Longitudo. \\ Gra. ′. # # ## Latit. \\ Gra. ′. # Magn. <lb/>In dextro pede. # ♏ # 1 # 0 # # 51 # 0 # 2 <lb/>In ſura dextra. # ♏ # 6 # 7 # # 52 # 0 # 2 <lb/>In muſculo ſiniſtri pepis. # ♏ # 2 # 0 # # 56 # 0 # 2 <lb/>In dextro pede priore. # ♏ # 29 # 17 # # 41 # 0 # 1 <lb/>In genu ſiniſtro. # ♏ # 14 # 0 # # 45 # 0 # 2 <lb/>LVPVS. 47. <lb/>In pede poſteriore. # ♏ # 19 # 0 # # 25 # 0 # 3 <lb/>In cauo eiuſdem pedis. # ♏ # 17 # 0 # # 29 # 0 # 3 <lb/>In medio corpore. # ♏ # 24 # 0 # # 25 # 0 # 4 <lb/>In priore pede. # ♏ # 18 # 10 # # 11 # 0 # 4 <lb/>LAR. ARA. 48. <lb/>In baſi. # ♐ # 18 # 0 # # 25 # 0 # 4 <lb/>In media arula. # ♐ # 16 # 30 # # 26 # 30 # 4 <lb/>In media flam@a. # ♐ # 11 # 47 # # 30 # 0 # 4 <lb/>In foculo. # ♐ # 11 # 34 # # 30 # 0 # 5 <lb/>ROTA IXIONIS. Corona auſtralis. 49. <lb/>Omnium auſtraliſſima. # ♐ # 29 # 27 # # 21 # 30 # 4 <lb/>Apud genu Sagittarij. # ♑ # 8 # 0 # # 17 # 0 # 4 <lb/></note> <pb o="174" file="0196" n="201" rhead="De Mundi Fabrica,"/> <note position="right" xml:space="preserve"> <lb/>Hanc præcedens. # ♑ # 7 # 40 # # 16 # 0 # 4 <lb/>Hanc præcedens. # ♑ # 6 # 30 # # 15 # 0 # 4 <lb/>PISCIS NOTIVS. 50. <lb/>In ore eadem, quæ in extrema Aquario. Fohamant. # ♒ # 28 # 11 # # 21 # 0 # 1 <lb/>In capite 3. pręcedens. # ♒ # 22 # 30 # # 21 # 20 # 4 <lb/>Media earum. # ♒ # 26 # 50 # # 22 # 0 # 4 <lb/>Sequens. # ♒ # 27 # 20 # # 22 # 30 # 4 <lb/>Extra piſcem 3. præcedens. # ♑ # 29 # 0 # # 22 # 0 # 3 <lb/>Media. # ♒ # 2 # 10 # # 22 # 10 # 3 <lb/>Sequens. # ♒ # 5 # 0 # # 21 # 0 # 3 <lb/></note> <p> <s xml:id="echoid-s14962" xml:space="preserve">Omiſſæ ſunt Stellæ magnitudinis 5. </s> <s xml:id="echoid-s14963" xml:space="preserve">& </s> <s xml:id="echoid-s14964" xml:space="preserve">6. </s> <s xml:id="echoid-s14965" xml:space="preserve">ferè omnes, quartæ verò nonnullæ. </s> <s xml:id="echoid-s14966" xml:space="preserve">primæ verò 2. </s> <s xml:id="echoid-s14967" xml:space="preserve">& </s> <s xml:id="echoid-s14968" xml:space="preserve">3. </s> <s xml:id="echoid-s14969" xml:space="preserve">omnes <lb/>ſunt adſcriptæ: </s> <s xml:id="echoid-s14970" xml:space="preserve">ſatis enim hæ ſunt noſtro inſtituto, & </s> <s xml:id="echoid-s14971" xml:space="preserve">breuitati. </s> <s xml:id="echoid-s14972" xml:space="preserve">Ex Tychone accepimus quas ipſe dedit, <lb/>reliquas ex alijs Catalogis correctioribus.</s> <s xml:id="echoid-s14973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14974" xml:space="preserve">Cæterum apud Polum Antarcticum tradunt eſſe duas maculas atrori Lunæ deficientis ſimiles, quarum. <lb/></s> <s xml:id="echoid-s14975" xml:space="preserve">maior propè polum Zodiaci, minor verò ad polum mundi vergit: </s> <s xml:id="echoid-s14976" xml:space="preserve">& </s> <s xml:id="echoid-s14977" xml:space="preserve">præterea plures Stellas, quarũ vix vna, <lb/>aut altera eſt ſecundæ magnitudinis, nulla enim cæli pars minoribus, & </s> <s xml:id="echoid-s14978" xml:space="preserve">paucioribus tellis ornatur, quem <lb/>hæc auſtrina circumpolaris, quarum loca, & </s> <s xml:id="echoid-s14979" xml:space="preserve">nomina nondum ſatis comperta ſunt; </s> <s xml:id="echoid-s14980" xml:space="preserve">diſtinctæ tamen ſunt in <lb/>12. </s> <s xml:id="echoid-s14981" xml:space="preserve">nouas conſtellationes, quarum hæc ſunt nomina, Pauo, Toucan auis, Phænix, Aurata, Pilcis volans, Hy-<lb/>drus Chamaleon, Apis, Apis Indica. </s> <s xml:id="echoid-s14982" xml:space="preserve">Triangulum Auſtrale, Indus. </s> <s xml:id="echoid-s14983" xml:space="preserve">vide Vranometriam lo: </s> <s xml:id="echoid-s14984" xml:space="preserve">Bapt. </s> <s xml:id="echoid-s14985" xml:space="preserve">Bayeri, ex <lb/>qua ſequentem figuram accepimus, vt ſaltem in ea Stellas illas antarcticas, necnon duas nubeculas. </s> <s xml:id="echoid-s14986" xml:space="preserve">abſq; </s> <s xml:id="echoid-s14987" xml:space="preserve">vl-<lb/>lis figurarum inuolucris, quandoquidem eas oculis cernere minimè poſſumus contemplari liceat.</s> <s xml:id="echoid-s14988" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14989" xml:space="preserve">Porrò hæc figura refert Stellarum poſitio-<lb/> <anchor type="figure" xlink:label="fig-0196-01a" xlink:href="fig-0196-01"/> nem, quæ in conuexo cæli, apparent, vti ſo-<lb/>lent ſphæræ Arateæ, in ea B, eſt polus mun-<lb/>di; </s> <s xml:id="echoid-s14990" xml:space="preserve">A, polus Zodiaci. </s> <s xml:id="echoid-s14991" xml:space="preserve">A B C, colurus ſolſtit. <lb/></s> <s xml:id="echoid-s14992" xml:space="preserve">D E B, colurus æquin. </s> <s xml:id="echoid-s14993" xml:space="preserve">A D C E, circulus po-<lb/>laris antarcticus. </s> <s xml:id="echoid-s14994" xml:space="preserve">F, nubecula maior ad polum <lb/>Zodiaci. </s> <s xml:id="echoid-s14995" xml:space="preserve">G, nubecula minor. </s> <s xml:id="echoid-s14996" xml:space="preserve">1. </s> <s xml:id="echoid-s14997" xml:space="preserve">2. </s> <s xml:id="echoid-s14998" xml:space="preserve">3. </s> <s xml:id="echoid-s14999" xml:space="preserve">4. </s> <s xml:id="echoid-s15000" xml:space="preserve">ſunt 4. </s> <s xml:id="echoid-s15001" xml:space="preserve"><lb/>Stellæ in poſterioribus pedibus Centauri re-<lb/>ferentes Crucem, Hiſpanis il Croſero. </s> <s xml:id="echoid-s15002" xml:space="preserve">Stella <lb/>verò magna infra crucem, eſt prior pes dex-<lb/>ter Centauri, quam ſupra iu Catalogo recen-<lb/>ſuimus.</s> <s xml:id="echoid-s15003" xml:space="preserve"/> </p> <div xml:id="echoid-div351" type="float" level="2" n="1"> <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a"> <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0196-01"/> </figure> </div> <p> <s xml:id="echoid-s15004" xml:space="preserve">In pręmiſſis Stellis, quindecim ſunt primę <lb/>magnitudinis, ac miræ pulchitudinis, videli-<lb/>cet, Arcturus, Lyra, Capella, Pal lium, Baſi-<lb/>liſcu<unsure/>s, Cauda Leonis, Spica Virginis, os Pi-<lb/>ſcis notij, dexter humerus Orionis, ſiniſter <lb/>pes Orionis, quę eadem eſt cum initio Erida-<lb/>ni, Acarnar, ideſt, extrema Eridani, Canis <lb/>maior, vel Syrius, Procyon, Canopus, Pes <lb/>Centauri dexter in ſummo pede. </s> <s xml:id="echoid-s15005" xml:space="preserve">vtrum au-<lb/>tem Canicula illa, quæ vulgo tam malè audit, atq; </s> <s xml:id="echoid-s15006" xml:space="preserve">infamis eſt, ſit Canis maior, an minor, alij vt Copernicus <lb/>volunt eſſe minorem, alij maiorem malunt; </s> <s xml:id="echoid-s15007" xml:space="preserve">ego libentius aſſentirer Copernico, quia Canis minor, & </s> <s xml:id="echoid-s15008" xml:space="preserve">Cani-<lb/>cula magis conueniunt.</s> <s xml:id="echoid-s15009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15010" xml:space="preserve">Nebuloſæ verò ſunt in ſequentibus locis. </s> <s xml:id="echoid-s15011" xml:space="preserve">In dextro genu Cigni vna. </s> <s xml:id="echoid-s15012" xml:space="preserve">In extrema manu dextra Perſei <lb/>vna præſepe in Cancro. </s> <s xml:id="echoid-s15013" xml:space="preserve">Vna quæ ſequitur aculeum Scorpij. </s> <s xml:id="echoid-s15014" xml:space="preserve">In oculo Sagittarij vna, & </s> <s xml:id="echoid-s15015" xml:space="preserve">in ipſa ecliptica. <lb/></s> <s xml:id="echoid-s15016" xml:space="preserve">In capite Orionis vna. </s> <s xml:id="echoid-s15017" xml:space="preserve">Tres nebuloſas ponit Tycho in capite Capricorni. </s> <s xml:id="echoid-s15018" xml:space="preserve">Ego tandem exiſtimo duas il-<lb/>las nubeculas, quas apud polum Antarcticum ponunt, eſſe duas Stellas nebuloſas, quod Teleſco pium@ <lb/>manifeſtum reddet.</s> <s xml:id="echoid-s15019" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div353" type="section" level="1" n="251"> <head xml:id="echoid-head268" style="it" xml:space="preserve">Sphæræ Aratææ, idest, Globi Aſtronomici constructio. Cap. V.</head> <p> <s xml:id="echoid-s15020" xml:space="preserve">IMmenſo iam labore Stellarum Catalogi conficiendi exant lato adiecerunt Aſtronomi animum ad omne@ <lb/>Stellas, ita in Globo depingendas, vt Globus ſic depictus inerrantium Sphæram imitaretur. </s> <s xml:id="echoid-s15021" xml:space="preserve">Globum hu-<lb/>iuſmodi Sphæram Aratæã dixere, propterea quod Aratus Poeta Græcus, qui Alexandri Magni æuo floruit, <lb/>de huiuſmodi Sphæra eleganter cecinit; </s> <s xml:id="echoid-s15022" xml:space="preserve">omnes ſcilicet conſtellationes, earumque fabulas eleganti ordine <lb/>proſequutus. </s> <s xml:id="echoid-s15023" xml:space="preserve">Neque vero difficilè fuerit habitis iam ſingularum Stellarum longitudinibus, & </s> <s xml:id="echoid-s15024" xml:space="preserve">latitudinibus <lb/>cas omnes Globo appingere, hoc ſcilicet modo.</s> <s xml:id="echoid-s15025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15026" xml:space="preserve">In Globo exactè tornatili, inuenias primo, duo puncta diametraliter oppoſita, quę pro Zodiaci polis erũt; <lb/></s> <s xml:id="echoid-s15027" xml:space="preserve">hoc modo, accipe circinum, cuius crura ſint introrſum curua, & </s> <s xml:id="echoid-s15028" xml:space="preserve">ex quouis puncto deſcribe duos, vel tres cir- <pb o="175" file="0197" n="202" rhead="Liber Decimusſeptimus."/> culos ſatis magnos, eoſque ſingulos diuide in quatuor partes æquales. </s> <s xml:id="echoid-s15029" xml:space="preserve">poſtea huic puncto qui ho-<lb/> <anchor type="figure" xlink:label="fig-0197-01a" xlink:href="fig-0197-01"/> rum circulorum polus eſt, affige ex altero extremo regulam flexibilem, oblongam, ſed anguſtam. <lb/></s> <s xml:id="echoid-s15030" xml:space="preserve">hanc, manente illa extremitate in polo, extende per puncta quadrifariam circulos ſecantia, de-<lb/>ſcribendo ſecus eam, lineam in ſuperficie globi, ſic deſcribes quattuor lineas, ſeu quattuor ſemi-<lb/>circulos tranſeuntes per quattuor circulorum diuiſiones, qui ſemicirculi concurrent in punctum. </s> <s xml:id="echoid-s15031" xml:space="preserve"><lb/>priori puncto diametraliter oppoſitum: </s> <s xml:id="echoid-s15032" xml:space="preserve">eruntque ambo eclipticæ poli. </s> <s xml:id="echoid-s15033" xml:space="preserve">Ex quibus deſcribe ecli-<lb/>pticam ipſam, necnon Zodiacum, Aequatorem, Tropicos, ac Circulos polares, vt in apparatu <lb/>de conſtructione Sphæræ materialis docuimus. </s> <s xml:id="echoid-s15034" xml:space="preserve">deinde diuide Eclipticam, & </s> <s xml:id="echoid-s15035" xml:space="preserve">Aequatorem in. </s> <s xml:id="echoid-s15036" xml:space="preserve"><lb/>gr. </s> <s xml:id="echoid-s15037" xml:space="preserve">360. </s> <s xml:id="echoid-s15038" xml:space="preserve">initio facto a ſectione, quam Verni Aequinoctij eſſe volueris. </s> <s xml:id="echoid-s15039" xml:space="preserve">in ecliptica diſtincta ſint 12. </s> <s xml:id="echoid-s15040" xml:space="preserve"><lb/>ſigna, cum ſuis characteribus ♈, ♉, &</s> <s xml:id="echoid-s15041" xml:space="preserve">c. </s> <s xml:id="echoid-s15042" xml:space="preserve">poſtea prædictam regulam ita diſpone, vt vtroque extremo <lb/>in polis iam inuentis affixa, ſit inſtar ſemicirculi volubilis circa globum, ipſum leniter radens: </s> <s xml:id="echoid-s15043" xml:space="preserve">latus <lb/>verò vnum regulæ tranſeat præcisè per polos eclipticæ ſi producatur, quod latus ſolet dici linea, <lb/>fiduciæ. </s> <s xml:id="echoid-s15044" xml:space="preserve">ſed huius ſemicircularis regulæ inſpice hanc figuram, cuius duo extrema A B. </s> <s xml:id="echoid-s15045" xml:space="preserve">ſunt perfo-<lb/>rata, vt axi globi extra polos extanti affigi poſſit, atq; </s> <s xml:id="echoid-s15046" xml:space="preserve">in eo conuolui, latus A C B. </s> <s xml:id="echoid-s15047" xml:space="preserve">quod eſt linea fi-<lb/>duciæ tranſiens per polos A B. </s> <s xml:id="echoid-s15048" xml:space="preserve">diuidatur bifariam in C. </s> <s xml:id="echoid-s15049" xml:space="preserve">à quo verſus vtrumq; </s> <s xml:id="echoid-s15050" xml:space="preserve">extremum diuidatur <lb/>in gr. </s> <s xml:id="echoid-s15051" xml:space="preserve">90. </s> <s xml:id="echoid-s15052" xml:space="preserve">ad ipſos polos deſinentes, ſicut figura indicat. </s> <s xml:id="echoid-s15053" xml:space="preserve">Adaptatur igitur hic ſemicirculus vt ſit mo-<lb/>bilis in polis eclip@icæ, erit inſtar omnium circulorum latitudinis, qui concipi poſſunt. </s> <s xml:id="echoid-s15054" xml:space="preserve">Iam diuide <lb/>totum globum in 12. </s> <s xml:id="echoid-s15055" xml:space="preserve">ſectiones æquales, ducendo lineas à polis eclipticæ tranſeuntes per ſingula ſin-<lb/>gulorum initia, ſic enim erit totus globus diuiſus in 12. </s> <s xml:id="echoid-s15056" xml:space="preserve">oblongas ſectiones, quæ erunt inſtar 11. </s> <s xml:id="echoid-s15057" xml:space="preserve">Pe-<lb/>ponis ſectiones æquales, & </s> <s xml:id="echoid-s15058" xml:space="preserve">vnaquæq; </s> <s xml:id="echoid-s15059" xml:space="preserve">erit eiuſdem appellationis cum eo ſigno, quod in eius medio <lb/>exiſtet. </s> <s xml:id="echoid-s15060" xml:space="preserve">Globo igitur ſic parato, ei ſic vnamquamq; </s> <s xml:id="echoid-s15061" xml:space="preserve">Stellam loco ſibi debito appinges. </s> <s xml:id="echoid-s15062" xml:space="preserve">Stellæ illius, <lb/>quæ in globo pingenda eſt, accipe ex ſuperiori Catalogo primo eius longitudinem, eamq; </s> <s xml:id="echoid-s15063" xml:space="preserve">in ecli-<lb/>ptica numera ab initio Arietis, & </s> <s xml:id="echoid-s15064" xml:space="preserve">vbi terminabitur eius longitudo, ibi ſtatue ſemicirculum mobilẽ: </s> <s xml:id="echoid-s15065" xml:space="preserve"><lb/>deinde ex Catalogo accipe eiuſdem Stellæ latitudinem Boream, vel Auſtrinam, eamq; </s> <s xml:id="echoid-s15066" xml:space="preserve">numera in <lb/>ipſo ſemicirculo facto initio ab ecliptica verſus Boream, vel Auſtrum, prout oportuerit, atq; </s> <s xml:id="echoid-s15067" xml:space="preserve">in fi-<lb/>ne, ſeu termino huius numerationis, ſeu latitudinis, depinge colore aureo aſſumptam Stellam, cum <lb/>charactere magnitudinis eius, aut coloris: </s> <s xml:id="echoid-s15068" xml:space="preserve">exemplum. </s> <s xml:id="echoid-s15069" xml:space="preserve">Arcturi Stellam ſic inſcribes; </s> <s xml:id="echoid-s15070" xml:space="preserve">ex catalogo <lb/>præmiſſo accipe eius longitudinem, quæ terminatur in gr. </s> <s xml:id="echoid-s15071" xml:space="preserve">18. </s> <s xml:id="echoid-s15072" xml:space="preserve">min. </s> <s xml:id="echoid-s15073" xml:space="preserve">30. </s> <s xml:id="echoid-s15074" xml:space="preserve">Libræ; </s> <s xml:id="echoid-s15075" xml:space="preserve">ideo ad hunc gradum <lb/>ſtatue ſemicirculum, quo ibi manente accipe eiuſdem latitudinem, quæ eſt gr. </s> <s xml:id="echoid-s15076" xml:space="preserve">31. </s> <s xml:id="echoid-s15077" xml:space="preserve">min. </s> <s xml:id="echoid-s15078" xml:space="preserve">2. </s> <s xml:id="echoid-s15079" xml:space="preserve">Borealis: </s> <s xml:id="echoid-s15080" xml:space="preserve"><lb/>numera igitur eam in ſemicirculo verſus Boream gr. </s> <s xml:id="echoid-s15081" xml:space="preserve">31. </s> <s xml:id="echoid-s15082" xml:space="preserve">2. </s> <s xml:id="echoid-s15083" xml:space="preserve">ibiq; </s> <s xml:id="echoid-s15084" xml:space="preserve">depinge Stellam auream, cum cha <lb/>ractere primæ Magnitudinis, quæ Arcturum referet: </s> <s xml:id="echoid-s15085" xml:space="preserve">idem facito cum reliquis Arcturi Stellis: </s> <s xml:id="echoid-s15086" xml:space="preserve">po-<lb/>ſtea figuram ipſius Arcturi circa haſce ſtellas colore intermortuo, vel debili delinea, ne cõſtellatio-<lb/>nis huius Stellæ nimis offuſcentur. </s> <s xml:id="echoid-s15087" xml:space="preserve">in quo hodie plurimum peccatur, dum potius animalia quæ-<lb/>dam, authomines, quam Stellæ pingi videntur. </s> <s xml:id="echoid-s15088" xml:space="preserve">eodem modo omnes Aratææ Sphæræ aſteriſmos <lb/>delineabis.</s> <s xml:id="echoid-s15089" xml:space="preserve"/> </p> <div xml:id="echoid-div353" type="float" level="2" n="1"> <figure xlink:label="fig-0197-01" xlink:href="fig-0197-01a"> <image file="0197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0197-01"/> </figure> </div> <p> <s xml:id="echoid-s15090" xml:space="preserve">Porrò Galaxiam ſic delineabis. </s> <s xml:id="echoid-s15091" xml:space="preserve">color totius Globi ſit cæruleus, viæ verò lacteæ ſubalbidus: </s> <s xml:id="echoid-s15092" xml:space="preserve">ea au <lb/>tem has conſtellationes peruadit, Centaurum Nauim; </s> <s xml:id="echoid-s15093" xml:space="preserve">inter Oriona, & </s> <s xml:id="echoid-s15094" xml:space="preserve">minorẽ Canem, pedes Eri-<lb/>chthonij, Perſeum, Caſſiopeam, caput Cephei, Cygnum, Sagittarium, Aquilam, Antinoum, Sa-<lb/>gittarium, Aram. </s> <s xml:id="echoid-s15095" xml:space="preserve">in Cygno tamen diuiditur in duos ramos, quorum vnus per dictos aſteriſmos <lb/>tranſit, alter verò inter Lyram, & </s> <s xml:id="echoid-s15096" xml:space="preserve">Aquilam deſcendit ad Ophiucum per Serpentem, & </s> <s xml:id="echoid-s15097" xml:space="preserve">per caudam <lb/>Scorpij incedens, quoad cum priori ramo ad Centaurum vniatur. </s> <s xml:id="echoid-s15098" xml:space="preserve">Ex hac tandem Stellarum de-<lb/>ſcriptione oritur eorum noua in 12. </s> <s xml:id="echoid-s15099" xml:space="preserve">Zodiaci ſigna diuiſio; </s> <s xml:id="echoid-s15100" xml:space="preserve">nam ductis, vti d ximus, ex polis ecl pti-<lb/>cæ 12. </s> <s xml:id="echoid-s15101" xml:space="preserve">latitudinem circulis, totum cælum inſtar Peponis in 12. </s> <s xml:id="echoid-s15102" xml:space="preserve">ſegmenta diuiditur, quæ ab vno polo <lb/>ad alterum pertinent; </s> <s xml:id="echoid-s15103" xml:space="preserve">continentq; </s> <s xml:id="echoid-s15104" xml:space="preserve">ſingula ſigna, & </s> <s xml:id="echoid-s15105" xml:space="preserve">omnes etiã Stellas, denominantq; </s> <s xml:id="echoid-s15106" xml:space="preserve">ab eo ſigno, <lb/>quod in medio cuiuſq; </s> <s xml:id="echoid-s15107" xml:space="preserve">eſt: </s> <s xml:id="echoid-s15108" xml:space="preserve">omnes igitur Stellæ, quæ ſunt v. </s> <s xml:id="echoid-s15109" xml:space="preserve">g. </s> <s xml:id="echoid-s15110" xml:space="preserve">in eo ſegmẽto, quod tranſit per Arie-<lb/>tem, dicuntur eſſe in Ariete, etiamſi ſint Zodiaci poli vicinæ, aliæ eodem modo in Tauro, &</s> <s xml:id="echoid-s15111" xml:space="preserve">c.</s> <s xml:id="echoid-s15112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15113" xml:space="preserve">Hiſce peractis globo Meridianum, & </s> <s xml:id="echoid-s15114" xml:space="preserve">Horizontem accommoda, ita tamen, vt circa polos æqua-<lb/>toris diurno motu expeditè reuoluatur. </s> <s xml:id="echoid-s15115" xml:space="preserve">adde tandem circuli quartam in gr. </s> <s xml:id="echoid-s15116" xml:space="preserve">90. </s> <s xml:id="echoid-s15117" xml:space="preserve">diuiſam, quæ altero <lb/>extremo hærens Meridiano in vertice Horizontis, poſſit circa ſuperius hemiſphærium circumduci, ad om-<lb/>nes videlicet verticales, hæc dicitur quarta altitudinum, cuius officium mox apparebit.</s> <s xml:id="echoid-s15118" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div355" type="section" level="1" n="252"> <head xml:id="echoid-head269" style="it" xml:space="preserve">De Stellis in Cælo dignoſcendis. Cap. VI.</head> <p> <s xml:id="echoid-s15119" xml:space="preserve">QVoniam iucundum, atq; </s> <s xml:id="echoid-s15120" xml:space="preserve">vtile eſt Stellas cæli non de facie tantum, ſed eas diſtinctè internoſcere, atque <lb/>vnamquamq; </s> <s xml:id="echoid-s15121" xml:space="preserve">proprio nomine compellare: </s> <s xml:id="echoid-s15122" xml:space="preserve">ideò per Aratæam Sphæram id facilè ſic aſſequemur. </s> <s xml:id="echoid-s15123" xml:space="preserve">Eam <lb/>igitur primò omnium oportet aſtronomicè collocare, eo modo, quo etiam Sphæram Armillarem <lb/>collocare docuimus; </s> <s xml:id="echoid-s15124" xml:space="preserve">ſed amplius oportet aſſumere gradum Solis in Zodiaco, eumq; </s> <s xml:id="echoid-s15125" xml:space="preserve">infra horizontem occi-<lb/>duum iuxta nocturnas horas elapſas deprimere: </s> <s xml:id="echoid-s15126" xml:space="preserve">quod fiet ſi pro ſingulis horis ab occaſu Solis deſcendent gr. <lb/></s> <s xml:id="echoid-s15127" xml:space="preserve">15. </s> <s xml:id="echoid-s15128" xml:space="preserve">Aequatoris cum ipſo gradu Solis: </s> <s xml:id="echoid-s15129" xml:space="preserve">in hoc enim Globi ſtatu omnes Stellæ, & </s> <s xml:id="echoid-s15130" xml:space="preserve">conſtellationes in Globo de-<lb/>pictas directè reſpicient ſtellas, & </s> <s xml:id="echoid-s15131" xml:space="preserve">conſtellationes, & </s> <s xml:id="echoid-s15132" xml:space="preserve">omnes, quarum ſunt imagines; </s> <s xml:id="echoid-s15133" xml:space="preserve">vnde quodammodo eas <lb/>nobis oſtendent, & </s> <s xml:id="echoid-s15134" xml:space="preserve">notificabunt. </s> <s xml:id="echoid-s15135" xml:space="preserve">Aliter ſic, ſi nota ſit tibi Stella quæpiam, quam tunc videas, accipe eius alti-<lb/>tudinem ſupra horizontem per Quadrantem; </s> <s xml:id="echoid-s15136" xml:space="preserve">deinde Sphæram motu diurno ita reuolue, donec Stella illa <lb/>in Globo depicta eadem altitudinem ſupra materialem horizontem obtineat; </s> <s xml:id="echoid-s15137" xml:space="preserve">quam altitudinem in quarta à <pb o="176" file="0198" n="203" rhead="De Mundi Fabrica,"/> vertice horizontis deſcendente numerabis; </s> <s xml:id="echoid-s15138" xml:space="preserve">nam manente hac Stella picta in hac poſitione, erit Globus aſtro-<lb/>nomicè collocatus. </s> <s xml:id="echoid-s15139" xml:space="preserve">in quo Globi ſtatu omnes eius ſtellæ ſtellas cæli non ſolum referent, ſed etiam indicabunt; <lb/></s> <s xml:id="echoid-s15140" xml:space="preserve">nam vnaquæque Globi conſtellatio erit è regione, ſeu directè aſpiciet cæleſtem ſibi cognominem: </s> <s xml:id="echoid-s15141" xml:space="preserve">vel vna <lb/>quæque cæli Stella directè ſuæ imagini Globo appictæ imminebit, ac ſuis radijs eam directè intuebitur. </s> <s xml:id="echoid-s15142" xml:space="preserve">vnde <lb/>licebit paulatim aſtra omnia in cælo dignoſcere, atque vnamquamque proprio nomine compellare operæ-<lb/>pretium autem eſt primum cognoſcere Stellam polarẽ, cum propè eam fit polus arct cus diurnæ totius Mun-<lb/>di conuerſionis cardo ſpectabilis. </s> <s xml:id="echoid-s15143" xml:space="preserve">quam etiam inde cognoſcere poſſumus, quia ad ſenſum non videtur moue-<lb/>ri, ſed ſemper in eodem cæli loco, & </s> <s xml:id="echoid-s15144" xml:space="preserve">in eadem ab horizonte altitudine conſiſtere videtur. </s> <s xml:id="echoid-s15145" xml:space="preserve">deinde Vrſam mi-<lb/>norem, & </s> <s xml:id="echoid-s15146" xml:space="preserve">maiorem, ac deinceps omnes boreales conſtellationes cognoſcemus. </s> <s xml:id="echoid-s15147" xml:space="preserve">Secundo loco ſeorſim om-<lb/>nes 12. </s> <s xml:id="echoid-s15148" xml:space="preserve">Zodiaci conſtellationes. </s> <s xml:id="echoid-s15149" xml:space="preserve">Tertio cæteras omnes auſtrales. </s> <s xml:id="echoid-s15150" xml:space="preserve">Iuuat etiam hanc Stellarum cognitionem <lb/>earum magnitudo, nam Stellæ. </s> <s xml:id="echoid-s15151" xml:space="preserve">15. </s> <s xml:id="echoid-s15152" xml:space="preserve">primæ magnitudinis inter cæteras ſunt fulgidiores, eaſque multo magni-<lb/>tudine ſuperant, vnde facilè intuentium oculos in ſe conuertunt.</s> <s xml:id="echoid-s15153" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15154" xml:space="preserve">Nebuloſæ pariter ob colorẽ ſubalbidum facilè dignoſcuntur. </s> <s xml:id="echoid-s15155" xml:space="preserve">Poſtremò conducit etiam ipſarum configu-<lb/>ratio, vt quia duæ poſtremæ Plauſtri rotæ ſunt in recta linea cum Stella polari, facilè erit ipſam polarem co-<lb/>gnoſcere, ducendo per imaginationem lineam rectam per duas illas eſt eam partem, vbi polus eſſe putatur; <lb/></s> <s xml:id="echoid-s15156" xml:space="preserve">hæc enim pollari Stellæ occurrens, eam manifeſtabit. </s> <s xml:id="echoid-s15157" xml:space="preserve">Sic etiam Aldebaram, Numerus ſiniſter Orionis, & </s> <s xml:id="echoid-s15158" xml:space="preserve"><lb/>Canis maior, in eadem ſunt rectitudine; </s> <s xml:id="echoid-s15159" xml:space="preserve">pariter Capella, Pes Aurigæ, & </s> <s xml:id="echoid-s15160" xml:space="preserve">Palilium. </s> <s xml:id="echoid-s15161" xml:space="preserve">quatuor rotæ Plau <lb/>ſtri quadrangulum conſtituunt. </s> <s xml:id="echoid-s15162" xml:space="preserve">Corona Gnoſſia circulum ferè repreſentat. </s> <s xml:id="echoid-s15163" xml:space="preserve">Hyades formant figuram lite-<lb/>ræ V. </s> <s xml:id="echoid-s15164" xml:space="preserve">Pleiades Botri figuram. </s> <s xml:id="echoid-s15165" xml:space="preserve">Delphinus Rhombi figuram efficit. </s> <s xml:id="echoid-s15166" xml:space="preserve">In Aquila ſunt tres in eadem rectitudine <lb/>inuicem æquidiſtantes, quarum media eſt primæ magnitudinis, quæ etiam Aquila dicitur. </s> <s xml:id="echoid-s15167" xml:space="preserve">ſtellæ omnes Ca-<lb/>pricorni ſunt in forma cuiuſdam magni trianguli. </s> <s xml:id="echoid-s15168" xml:space="preserve">porrò ex ipſo Globo ritè ſtellis inſignito licebit plures <lb/>huinſmodi configurationes elicere, quæ ad inſtitutum conducant.</s> <s xml:id="echoid-s15169" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div356" type="section" level="1" n="253"> <head xml:id="echoid-head270" style="it" xml:space="preserve">De motibus affixarum, & Aequinoctij præceſſione. Cap. VII.</head> <p> <s xml:id="echoid-s15170" xml:space="preserve">HIs omnibus iam fæliciter peractis ab antiquoribus illis ſyderum cultoribus, Thalete, Metone, Arato, <lb/>Ariſtillo, Timocharide, & </s> <s xml:id="echoid-s15171" xml:space="preserve">alijs; </s> <s xml:id="echoid-s15172" xml:space="preserve">cùm poſtea Hipparchus ſummus Aſtronomiæ conditor poſt Timocha-<lb/>ridem annis 150. </s> <s xml:id="echoid-s15173" xml:space="preserve">ſuas haberet obſeruationes, eaſque cum Timocharidis obſeruation. </s> <s xml:id="echoid-s15174" xml:space="preserve">conferet, reperit affi-<lb/>xas non ſolum motu primi mobilis diurno circunuerti, ſed præterea motu proprio ad ſignorum conſequen-<lb/>tia inſtar planetarum tardiſſimè promoueri, ſiue pſa Æquinoctiorum puncta in præcedentia paulatim repe-<lb/>dare. </s> <s xml:id="echoid-s15175" xml:space="preserve">idque hoc modo; </s> <s xml:id="echoid-s15176" xml:space="preserve">Timocharis reperit primam Arietis Stellam poſt ſectionem vernam gradibus 2. </s> <s xml:id="echoid-s15177" xml:space="preserve">ſeu <lb/>vt modo loquimur in ſecundo gradu ſigni ♈. </s> <s xml:id="echoid-s15178" xml:space="preserve">Hipparchus vero eandem ſtellam reperit poſt eandem vernam <lb/>ſectionem grad. </s> <s xml:id="echoid-s15179" xml:space="preserve">4. </s> <s xml:id="echoid-s15180" xml:space="preserve">Rurſus Timocharis reperit ſpicam Virginis ante ſectionem autumnalem gra. </s> <s xml:id="echoid-s15181" xml:space="preserve">8. </s> <s xml:id="echoid-s15182" xml:space="preserve">eandem <lb/>vero Hipparchus 6. </s> <s xml:id="echoid-s15183" xml:space="preserve">tantum gr. </s> <s xml:id="echoid-s15184" xml:space="preserve">eandem ſectionem præcederi inuenit. </s> <s xml:id="echoid-s15185" xml:space="preserve">Idem accidit in omnibus alijs ſtellis, <lb/>quarum obſeruationes horum duorum Aſtronomorum ſunt inuicẽ collatæ. </s> <s xml:id="echoid-s15186" xml:space="preserve">Vnde Hipparchus primus ani-<lb/>maduertit, ac poſteris tradidit, inerrantes quoque ſtellas paulatim in conſequentia promoueri. </s> <s xml:id="echoid-s15187" xml:space="preserve">quod poſtea <lb/>ſuccedentibus ſeculis alij ſyderum obſeruatores confirmarunt. </s> <s xml:id="echoid-s15188" xml:space="preserve">nam Menelaus annis 224. </s> <s xml:id="echoid-s15189" xml:space="preserve">poſt Hipparcum <lb/>eandem primam Arietis Stellam comperit diſtare gr. </s> <s xml:id="echoid-s15190" xml:space="preserve">6. </s> <s xml:id="echoid-s15191" xml:space="preserve">ab Aequinoctio verno. </s> <s xml:id="echoid-s15192" xml:space="preserve">poſt quem Ptolemæus annis <lb/>41. </s> <s xml:id="echoid-s15193" xml:space="preserve">eandem reperit in grad. </s> <s xml:id="echoid-s15194" xml:space="preserve">6. </s> <s xml:id="echoid-s15195" xml:space="preserve">min. </s> <s xml:id="echoid-s15196" xml:space="preserve">40. </s> <s xml:id="echoid-s15197" xml:space="preserve">Albategnius poſtea annis 741. </s> <s xml:id="echoid-s15198" xml:space="preserve">à Pt<unsure/>olemæo, eandem depræhendit in <lb/>grad. </s> <s xml:id="echoid-s15199" xml:space="preserve">18. </s> <s xml:id="echoid-s15200" xml:space="preserve">deinde ab Albategnio annis 381. </s> <s xml:id="echoid-s15201" xml:space="preserve">Alphonſus Rex eandem inuenit in grad. </s> <s xml:id="echoid-s15202" xml:space="preserve">26. </s> <s xml:id="echoid-s15203" xml:space="preserve">min. </s> <s xml:id="echoid-s15204" xml:space="preserve">54. </s> <s xml:id="echoid-s15205" xml:space="preserve">poſtea Co-<lb/>pernicus annis inde 265. </s> <s xml:id="echoid-s15206" xml:space="preserve">elapſis in in gra. </s> <s xml:id="echoid-s15207" xml:space="preserve">27. </s> <s xml:id="echoid-s15208" xml:space="preserve">21. </s> <s xml:id="echoid-s15209" xml:space="preserve">tandem Tycho ann. </s> <s xml:id="echoid-s15210" xml:space="preserve">60. </s> <s xml:id="echoid-s15211" xml:space="preserve">inde elapſis eam in grad. </s> <s xml:id="echoid-s15212" xml:space="preserve">27 min. </s> <s xml:id="echoid-s15213" xml:space="preserve">37. <lb/></s> <s xml:id="echoid-s15214" xml:space="preserve">obſeruauit: </s> <s xml:id="echoid-s15215" xml:space="preserve">Idem ſtud um contulit Hipparchus ad ſpicam Virginis, quam Timocharis repererat ante Aequi-<lb/>noctium autumnale. </s> <s xml:id="echoid-s15216" xml:space="preserve">8. </s> <s xml:id="echoid-s15217" xml:space="preserve">partibus: </s> <s xml:id="echoid-s15218" xml:space="preserve">ipſe vero ſex tantum, ex quibus Hipparchus Aſtronomiæ conſultiſſimus <lb/>concluſit Affixas omnes in cõſequentia promoueri: </s> <s xml:id="echoid-s15219" xml:space="preserve">reliqua enim ſydera cum duabus prędictis perpetuò con-<lb/>ſeruant eaſdem diſtantias, & </s> <s xml:id="echoid-s15220" xml:space="preserve">configurationes; </s> <s xml:id="echoid-s15221" xml:space="preserve">quare hiſce promotis reliquas omnes progredi neceſſe eſt. </s> <s xml:id="echoid-s15222" xml:space="preserve"><lb/>Hic porrò motus aptè dicitur motus Fixarum in longitudinem, ſicuti in Planetis.</s> <s xml:id="echoid-s15223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15224" xml:space="preserve">Hinc idem Hipparchus nouum aliud inuentum inuexit: </s> <s xml:id="echoid-s15225" xml:space="preserve">duos videlicet Zodiacos; </s> <s xml:id="echoid-s15226" xml:space="preserve">cum enim vidiſſet Ae-<lb/>quinoctia, & </s> <s xml:id="echoid-s15227" xml:space="preserve">Solſtitia certis ſtellis haudquaquam eſſe alligata, ſed eas paulatim magis ac magis præcedere, ea <lb/>propter cenſuit deinceps figna 12. </s> <s xml:id="echoid-s15228" xml:space="preserve">Zodiaci inchoanda eſie à puncto æquinoctij Verni: </s> <s xml:id="echoid-s15229" xml:space="preserve">vnde factũ eſt vt. </s> <s xml:id="echoid-s15230" xml:space="preserve">12. <lb/></s> <s xml:id="echoid-s15231" xml:space="preserve">conſtellationes illæ Zodiaci, Aries, Taurus, &</s> <s xml:id="echoid-s15232" xml:space="preserve">c. </s> <s xml:id="echoid-s15233" xml:space="preserve">quæ prius 12. </s> <s xml:id="echoid-s15234" xml:space="preserve">ſigna conſtituebant, ac denominabant, ab ijs <lb/>ſepararentur. </s> <s xml:id="echoid-s15235" xml:space="preserve">Quoniam enim vetuſtiſſimi Aſtronomorum, Thales, Eudoxus, &</s> <s xml:id="echoid-s15236" xml:space="preserve">c. </s> <s xml:id="echoid-s15237" xml:space="preserve">videbant æquinoctia fie-<lb/>ri initio ferè Aſteriſmi Arietis ideſt circa primam eius Stellam, id@o initium Zodiaci ſimul, etiam, & </s> <s xml:id="echoid-s15238" xml:space="preserve">quidem <lb/>aptè idem conſtituerunt cum initio 12. </s> <s xml:id="echoid-s15239" xml:space="preserve">ſignorum. </s> <s xml:id="echoid-s15240" xml:space="preserve">verum Zodiaci diuiſionem in Zodiacum ſignorum, & </s> <s xml:id="echoid-s15241" xml:space="preserve"><lb/>in Zodiacum Aſteriſmorum ob prædictam rationem Hipparchus inuexit, quam deinceps ſuccedentes Aſtro-<lb/>nomi retinuerunt.</s> <s xml:id="echoid-s15242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15243" xml:space="preserve">Columella refert Fauſtos Eudoxi, & </s> <s xml:id="echoid-s15244" xml:space="preserve">Mctonis (qui Hipparchum 300. </s> <s xml:id="echoid-s15245" xml:space="preserve">ferè annis pręceſſerunt) conſtituiſ-<lb/>ſe in octonis partibus, ſignorum æquinoctia, & </s> <s xml:id="echoid-s15246" xml:space="preserve">ſolſtitia. </s> <s xml:id="echoid-s15247" xml:space="preserve">idemque aſieritur in antiquiſſima cuiuſdam præfa-<lb/>tione in Ara@i Phœnomena: </s> <s xml:id="echoid-s15248" xml:space="preserve">quod intelligendum eſt de ſignis, & </s> <s xml:id="echoid-s15249" xml:space="preserve">ſimul Aſteriſmis, quia ea nondum Hippar-<lb/>chus diſtinxerat: </s> <s xml:id="echoid-s15250" xml:space="preserve">At verò tempore Eudoxi, (vt ex retrograda motus Stellarum computatione colligitur) ne-<lb/>quiuerunt eſ@e in octonis partibus, verum id multis retro ſæculis circa videlicet Troiani belli tempora con-<lb/>tigiſſe oportuit. </s> <s xml:id="echoid-s15251" xml:space="preserve">Vtrumque igitur Hipparchi placitum poſteritas omnis, vſque ad hæc ſæcula complexa eſt; <lb/></s> <s xml:id="echoid-s15252" xml:space="preserve">quod ſciſ<unsure/>ilicet Affixæ in longitudinem moueantur, ſiue quod æquinoctia præcedant; </s> <s xml:id="echoid-s15253" xml:space="preserve">& </s> <s xml:id="echoid-s15254" xml:space="preserve">quod duo ſint Zodia- <pb o="177" file="0199" n="204" rhead="Liber decimusſeptimus."/> ci diſtinguendi; </s> <s xml:id="echoid-s15255" xml:space="preserve">vnus Aſteriſinorum, qui à prima Arietis Stella incipiat; </s> <s xml:id="echoid-s15256" xml:space="preserve">Alter verò Signorum, qui ab æqui-<lb/>noctio verno, qui Zodiacus ſignorum, atque etiam Zodiacus primi mobilis appelletur.</s> <s xml:id="echoid-s15257" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div357" type="section" level="1" n="254"> <head xml:id="echoid-head271" style="it" xml:space="preserve">Motum hunc inerrantium fieri ſuper polis eclipticæ.</head> <p> <s xml:id="echoid-s15258" xml:space="preserve">DVm hunc Stellarum motum diligentius obſeruarent, aduerterũt eas ſemper eandem latitudinem ſerua-<lb/>re, hoc eſt, pari interuallo ſecus eclipticam incedere, ita vt. </s> <s xml:id="echoid-s15259" xml:space="preserve">v. </s> <s xml:id="echoid-s15260" xml:space="preserve">g. </s> <s xml:id="echoid-s15261" xml:space="preserve">ſpica Virginis, quæ tempore Timo-<lb/>char. </s> <s xml:id="echoid-s15262" xml:space="preserve">gra. </s> <s xml:id="echoid-s15263" xml:space="preserve">2. </s> <s xml:id="echoid-s15264" xml:space="preserve">ab eliptica in boream diſtabat, etiam tempore Ptolemæi, & </s> <s xml:id="echoid-s15265" xml:space="preserve">poſterorum totidem pariter gradi-<lb/>bus diſtiterit. </s> <s xml:id="echoid-s15266" xml:space="preserve">quapropter ſequitur eam deſcribere circulum eclipticæ paralellum ad boream. </s> <s xml:id="echoid-s15267" xml:space="preserve">Stellæ vero, <lb/>quæ in ipſa ecliptica exiſtunt, per ipſam perpetuo, ne latum quidem vnguem exorbitantes, directè ineceſſe-<lb/>runt. </s> <s xml:id="echoid-s15268" xml:space="preserve">plura huius rei exempla affert ſeries Aſtronomorum, vſque ad Tychonem. </s> <s xml:id="echoid-s15269" xml:space="preserve">qui tamen in hac re aliquid <lb/>innouare conatur: </s> <s xml:id="echoid-s15270" xml:space="preserve">illud tamen ex imperſectione obſeruationum ob multa, quæ incurrũt impedimenta pro-<lb/>uenire cenſeo; </s> <s xml:id="echoid-s15271" xml:space="preserve">quare cum, & </s> <s xml:id="echoid-s15272" xml:space="preserve">illud exiguum quid ſit, ac proinde noſtro inſtituto haud neceſſarium, omitten-<lb/>dum duxi. </s> <s xml:id="echoid-s15273" xml:space="preserve">cum igitur affixæ deſcribant hoc motu circulos eclipticæ paralelos, aut ipſam eclipticam, neceſ-<lb/>ſario ſequitur eum eclipticæ polis inniti. </s> <s xml:id="echoid-s15274" xml:space="preserve">Hunc porrò motum eſſe proprium Firmamenti communiter <lb/>Aſtronomi ſentiunt.</s> <s xml:id="echoid-s15275" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div358" type="section" level="1" n="255"> <head xml:id="echoid-head272" style="it" xml:space="preserve">Quantitas, vel periodus huius motus.</head> <p> <s xml:id="echoid-s15276" xml:space="preserve">PRæcipua hæc ſemper fuit circa inerrantes inueſtigatio, quam ſic peregerunt: </s> <s xml:id="echoid-s15277" xml:space="preserve">in annis 265. </s> <s xml:id="echoid-s15278" xml:space="preserve">inter Hippar-<lb/>chum, & </s> <s xml:id="echoid-s15279" xml:space="preserve">Ptolemæum elapſis, ſtellæ promotæ ſunt grad. </s> <s xml:id="echoid-s15280" xml:space="preserve">2. </s> <s xml:id="echoid-s15281" xml:space="preserve">min. </s> <s xml:id="echoid-s15282" xml:space="preserve">40. </s> <s xml:id="echoid-s15283" xml:space="preserve">quibus in annos 265. </s> <s xml:id="echoid-s15284" xml:space="preserve">diſtributis, com-<lb/>perit Ptolemæus eas annis ferè 100. </s> <s xml:id="echoid-s15285" xml:space="preserve">vnum gradum confeciſſe. </s> <s xml:id="echoid-s15286" xml:space="preserve">Albategnius autem Arabs ex ſuis obſeruatio-<lb/>nibus, cum obſeruationibus Menelai Geometræ collatis, reperit ſtellas in annis 782. </s> <s xml:id="echoid-s15287" xml:space="preserve">gradus 12. </s> <s xml:id="echoid-s15288" xml:space="preserve">min. </s> <s xml:id="echoid-s15289" xml:space="preserve">55. </s> <s xml:id="echoid-s15290" xml:space="preserve">pe-<lb/>ragraſſe; </s> <s xml:id="echoid-s15291" xml:space="preserve">vnde facta diuiſione, ideſt, tribuendo ſingulis gradibus ſuam temporis portionem, cenſuit vni gra-<lb/>dui deberi annos quaſi 66. </s> <s xml:id="echoid-s15292" xml:space="preserve">Tandem Tycho Brahe noſtro ſeculo, hoc modo, aliam reperit quantitatem pri-<lb/>mo enim annum ſyderalem, vt iam dixi, conſtituit. </s> <s xml:id="echoid-s15293" xml:space="preserve">dierum 365. </s> <s xml:id="echoid-s15294" xml:space="preserve">hor. </s> <s xml:id="echoid-s15295" xml:space="preserve">6. </s> <s xml:id="echoid-s15296" xml:space="preserve">min. </s> <s xml:id="echoid-s15297" xml:space="preserve">9. </s> <s xml:id="echoid-s15298" xml:space="preserve">&</s> <s xml:id="echoid-s15299" xml:space="preserve">c. </s> <s xml:id="echoid-s15300" xml:space="preserve">tanto enim tempore Sol <lb/>reuertitur ad eandem ſtellam fixam. </s> <s xml:id="echoid-s15301" xml:space="preserve">annum vero æquinoctialem definit dierum 365. </s> <s xml:id="echoid-s15302" xml:space="preserve">hor. </s> <s xml:id="echoid-s15303" xml:space="preserve">5. </s> <s xml:id="echoid-s15304" xml:space="preserve">min. </s> <s xml:id="echoid-s15305" xml:space="preserve">48. </s> <s xml:id="echoid-s15306" xml:space="preserve">&</s> <s xml:id="echoid-s15307" xml:space="preserve">c. </s> <s xml:id="echoid-s15308" xml:space="preserve">qui <lb/>deficit à ſydereo min. </s> <s xml:id="echoid-s15309" xml:space="preserve">horarum 20′. </s> <s xml:id="echoid-s15310" xml:space="preserve">ſec. </s> <s xml:id="echoid-s15311" xml:space="preserve">42″. </s> <s xml:id="echoid-s15312" xml:space="preserve">tantillum enim temporis requiritur, vt Sol emenſo toto Zodia-<lb/>ci curriculo, ſtellam aliquam interim aliquantulum progreſſam, iterum aſſequatur. </s> <s xml:id="echoid-s15313" xml:space="preserve">quo tempore Sol pro-<lb/>prio motu conficit ſec. </s> <s xml:id="echoid-s15314" xml:space="preserve">51″. </s> <s xml:id="echoid-s15315" xml:space="preserve">exacte quare tantilla erit ad noſtra ſæcula annua ſtellarum promotio. </s> <s xml:id="echoid-s15316" xml:space="preserve">quod etiam <lb/>more maiorum collatis ſuis cum vterum obſeruationibus, comprobauit. </s> <s xml:id="echoid-s15317" xml:space="preserve">Vnde ſequitur eas annis 70. </s> <s xml:id="echoid-s15318" xml:space="preserve">& </s> <s xml:id="echoid-s15319" xml:space="preserve"><lb/>menſibus 7. </s> <s xml:id="echoid-s15320" xml:space="preserve">vnum gradum ſuperare.</s> <s xml:id="echoid-s15321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15322" xml:space="preserve">Et in annis 10. </s> <s xml:id="echoid-s15323" xml:space="preserve">conficere gr. </s> <s xml:id="echoid-s15324" xml:space="preserve">0. </s> <s xml:id="echoid-s15325" xml:space="preserve">min. </s> <s xml:id="echoid-s15326" xml:space="preserve">8. </s> <s xml:id="echoid-s15327" xml:space="preserve">ſec. </s> <s xml:id="echoid-s15328" xml:space="preserve">30″.</s> <s xml:id="echoid-s15329" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15330" xml:space="preserve">In annis 100. </s> <s xml:id="echoid-s15331" xml:space="preserve">conficere gr. </s> <s xml:id="echoid-s15332" xml:space="preserve">1. </s> <s xml:id="echoid-s15333" xml:space="preserve">min. </s> <s xml:id="echoid-s15334" xml:space="preserve">25. </s> <s xml:id="echoid-s15335" xml:space="preserve">ſec. </s> <s xml:id="echoid-s15336" xml:space="preserve">0.</s> <s xml:id="echoid-s15337" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15338" xml:space="preserve">In annis 200. </s> <s xml:id="echoid-s15339" xml:space="preserve">conficere gr. </s> <s xml:id="echoid-s15340" xml:space="preserve">2. </s> <s xml:id="echoid-s15341" xml:space="preserve">min. </s> <s xml:id="echoid-s15342" xml:space="preserve">50. </s> <s xml:id="echoid-s15343" xml:space="preserve">ſec. </s> <s xml:id="echoid-s15344" xml:space="preserve">0.</s> <s xml:id="echoid-s15345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15346" xml:space="preserve">In annis 400. </s> <s xml:id="echoid-s15347" xml:space="preserve">conficere gr. </s> <s xml:id="echoid-s15348" xml:space="preserve">5. </s> <s xml:id="echoid-s15349" xml:space="preserve">min. </s> <s xml:id="echoid-s15350" xml:space="preserve">0. </s> <s xml:id="echoid-s15351" xml:space="preserve">ſec. </s> <s xml:id="echoid-s15352" xml:space="preserve">0.</s> <s xml:id="echoid-s15353" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15354" xml:space="preserve">Iam ſi gradus 5. </s> <s xml:id="echoid-s15355" xml:space="preserve">requirunt annos 400. </s> <s xml:id="echoid-s15356" xml:space="preserve">grad. </s> <s xml:id="echoid-s15357" xml:space="preserve">360. </s> <s xml:id="echoid-s15358" xml:space="preserve">ideſt, totus Zodiacus quotannis peragrabitur? </s> <s xml:id="echoid-s15359" xml:space="preserve">inuenie-<lb/>mus per auream proportionum regulam, requiri annos 28, 800. </s> <s xml:id="echoid-s15360" xml:space="preserve">in tanto igitur annorum interuallo inerrãtia <lb/>aſtra ſuam circa polos periodum abſoluent.</s> <s xml:id="echoid-s15361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15362" xml:space="preserve">Hunc porrò annorum numerum Philoſophi Annum magnum nuncuparunt: </s> <s xml:id="echoid-s15363" xml:space="preserve">exiſtimantque corum com-<lb/>plures, aliquando à certo initio deducta periodo, ſimul cum prædicto anno magno, abſolui etiam reliquorum <lb/>ſyderum errantium circulationes: </s> <s xml:id="echoid-s15364" xml:space="preserve">quibus abſolutis, in eaque tunc cœli conſtitutione, putant Mundum, vel <lb/>Igne, vel Aqua ſæpius interijſſe, atque in poſterum interiturum eſſe. </s> <s xml:id="echoid-s15365" xml:space="preserve">ea propter Mundum ſæpius renouari, <lb/>atque omnia iterum renaſci ſimulque cum renouatis ſyderum curſibus, quę prius exiſterant redire; </s> <s xml:id="echoid-s15366" xml:space="preserve">ſicque ite-<lb/>rum ad Troiam magnus mittetur Achilles. </s> <s xml:id="echoid-s15367" xml:space="preserve">hanc præcipuè aiunt fuiſſe Platonis mentem; </s> <s xml:id="echoid-s15368" xml:space="preserve">vnde, & </s> <s xml:id="echoid-s15369" xml:space="preserve">annum <lb/>hunc Platonis annum dixere: </s> <s xml:id="echoid-s15370" xml:space="preserve">ipſe enim in Timæo ſic inquit: </s> <s xml:id="echoid-s15371" xml:space="preserve">Perfectus temporis numerus perfectum annum <lb/>tunc complet, cum omnium octo circuituum velocitates inter ſe completæ caput attigerint eiuſdem, & </s> <s xml:id="echoid-s15372" xml:space="preserve">ſimi-<lb/>liter progredientes circulo menſuratæ. </s> <s xml:id="echoid-s15373" xml:space="preserve">Quoniam vero non æqualem, vt vidimus, prædicti Aſtronomi mo-<lb/>tum hunc prodiderunt, ideo plurimi putant hanc inæqualitatem ex ipſo firmamento prouenire. </s> <s xml:id="echoid-s15374" xml:space="preserve">verum in <lb/>motu adeo tardo, vt vix compręhendatur aliqua obſeruationibus fallacia accidere potuit, vel accuratiſſimis, <lb/>vnde hæc anomalia firmamento imputetur. </s> <s xml:id="echoid-s15375" xml:space="preserve">hoc igitur, veluti nobis dubium in medio relinquatur.</s> <s xml:id="echoid-s15376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15377" xml:space="preserve">Verùm cum in rebus Aſtronomicis recentioribus ſemper magis inhærendum fit, quòd ipſi maioribus tem-<lb/>porum interuallis ſuas obſeruationes veteribus conferentes certiores, & </s> <s xml:id="echoid-s15378" xml:space="preserve">exquiſitiores propterea habeant: <lb/></s> <s xml:id="echoid-s15379" xml:space="preserve">idcirco nouiſſimi Tychonis de hoc motu ſententiam amplecti conſul<unsure/>tius videtur.</s> <s xml:id="echoid-s15380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15381" xml:space="preserve">Tandem non omittam illud, quod tradit Ioannes Chriſtmanus in ſuis obſeruationibus Solaribus; </s> <s xml:id="echoid-s15382" xml:space="preserve">Stel-<lb/>lam videlicet polarem ad polum mundi ac cedere ſingulis annis, 20″. </s> <s xml:id="echoid-s15383" xml:space="preserve">ſecundis: </s> <s xml:id="echoid-s15384" xml:space="preserve">anno autem, 1618. </s> <s xml:id="echoid-s15385" xml:space="preserve">fuiſſe <lb/>polo vicinam grad. </s> <s xml:id="echoid-s15386" xml:space="preserve">2.</s> <s xml:id="echoid-s15387" xml:space="preserve">44′.</s> <s xml:id="echoid-s15388" xml:space="preserve">30″.</s> <s xml:id="echoid-s15389" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div359" type="section" level="1" n="256"> <head xml:id="echoid-head273" style="it" xml:space="preserve">Appendix de Calculo huius Motus. Cap. VIII.</head> <p> <s xml:id="echoid-s15390" xml:space="preserve">FAcilè erit ex calculo loca ſtellarum in futurum indagare, cum enim in ſuperiori Catalogo aſcriptæ ſint <lb/>earum longitudines, & </s> <s xml:id="echoid-s15391" xml:space="preserve">latitudines ad annum Domini completum 160. </s> <s xml:id="echoid-s15392" xml:space="preserve">eruntillæ horum motuum Radi- <pb o="178" file="0200" n="205" rhead="De Mundi Fabrica,"/> <anchor type="note" xlink:label="note-0200-01a" xlink:href="note-0200-01"/> ces propterea cum ponamus eas vno anno promoueri ſec. </s> <s xml:id="echoid-s15393" xml:space="preserve">51″. <lb/></s> <s xml:id="echoid-s15394" xml:space="preserve">conſtruximus ſequentem Tabellam, in qua vſque ad annos 10. </s> <s xml:id="echoid-s15395" xml:space="preserve"><lb/>ſingulis ſuus numerus aſcribitur, ex qua poſtea reliquorum an-<lb/>norum, v. </s> <s xml:id="echoid-s15396" xml:space="preserve">g. </s> <s xml:id="echoid-s15397" xml:space="preserve">20. </s> <s xml:id="echoid-s15398" xml:space="preserve">30. </s> <s xml:id="echoid-s15399" xml:space="preserve">&</s> <s xml:id="echoid-s15400" xml:space="preserve">c. </s> <s xml:id="echoid-s15401" xml:space="preserve">duplicando, aut triplicando motum an <lb/>norum 10. </s> <s xml:id="echoid-s15402" xml:space="preserve">facilè reperiemus, necnon annorum intermedio-<lb/>rum: </s> <s xml:id="echoid-s15403" xml:space="preserve">vt exemplo patebit, v. </s> <s xml:id="echoid-s15404" xml:space="preserve">g. </s> <s xml:id="echoid-s15405" xml:space="preserve">hoc anno 1616. </s> <s xml:id="echoid-s15406" xml:space="preserve">currente, libet <lb/>ſcire quantum diſtet prima Arietis ſtella ab Æquinoctio, ſeu <lb/>quanta ſit eius longitudo.</s> <s xml:id="echoid-s15407" xml:space="preserve"/> </p> <div xml:id="echoid-div359" type="float" level="2" n="1"> <note position="right" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve"> <lb/>Anni ſin \\ guli. # ## Motus eis re- \\ ſpondentes. <lb/># # Min. # Sec. <lb/>1 # 0 # 51 <lb/>2 # 1 # 42 <lb/>3 # 2 # 33 <lb/>4 # 3 # 24 <lb/>5 # 4 # 15 <lb/>6 # 5 # 6 <lb/>7 # 5 # 57 <lb/>8 # 6 # 48 <lb/>9 # 7 # 39 <lb/>10 # 8 # 30 <lb/></note> </div> <p> <s xml:id="echoid-s15408" xml:space="preserve">Accipe igitur ex Catalogo eius longitudinem quæ eſt Ra-<lb/>dix huius motus, eſtque gr. </s> <s xml:id="echoid-s15409" xml:space="preserve">27. </s> <s xml:id="echoid-s15410" xml:space="preserve">37.</s> <s xml:id="echoid-s15411" xml:space="preserve">′. </s> <s xml:id="echoid-s15412" xml:space="preserve">0″. </s> <s xml:id="echoid-s15413" xml:space="preserve">poſtea accipe ex hac <lb/>Tabella motum annorum 10. </s> <s xml:id="echoid-s15414" xml:space="preserve">& </s> <s xml:id="echoid-s15415" xml:space="preserve">poſtea motum annorum ſex <lb/>quibus ſimul poatis, vt in formula vides, atque in vnam ſum-<lb/>mam redactis, habebis eius longitudinem, ſeu locum eius in <lb/>Zodiaco. </s> <s xml:id="echoid-s15416" xml:space="preserve">latitudinem vero ſuppono eſſe ſemper eandem, <lb/>quam Catalogus oſtendit quæ eſt gr. </s> <s xml:id="echoid-s15417" xml:space="preserve">7. </s> <s xml:id="echoid-s15418" xml:space="preserve">borealis. </s> <s xml:id="echoid-s15419" xml:space="preserve">ex quibus lo-<lb/>cum Stellæ in cælo definitum habes.</s> <s xml:id="echoid-s15420" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15421" xml:space="preserve">Illud etiam notandum longitudinem huius primæ Arietis <lb/>eſſe tantam, quanta etiam eſt præceſſio Aequino&</s> <s xml:id="echoid-s15422" xml:space="preserve">ij. </s> <s xml:id="echoid-s15423" xml:space="preserve">Neque <lb/>vero neceſſe eſt ad datos dies aut menſes hunc motum com-<lb/>putare, cum ob ipſius tarditatem, ne vno quidem anno mi-<lb/>nutum vnum conficiant.</s> <s xml:id="echoid-s15424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div361" type="section" level="1" n="257"> <head xml:id="echoid-head274" style="it" xml:space="preserve">FORMVLA EXEMPLI.</head> <note position="right" xml:space="preserve"> <lb/># Gra. # Min. # Sec. <lb/># 0 # ′ # ″. <lb/>Rad. 1600 # 27 # 37 # 0 <lb/>Anni 10 # 0 # 0 # 30 <lb/>Summa. # 27 # 50 # 36. Longitudo. <lb/></note> <p> <s xml:id="echoid-s15425" xml:space="preserve">Libet nunc curioſitas per pulchræ gratia inda-<lb/>gare quibuſnam in Stellis fuerit æquinoctiũ ver-<lb/>num initio Orbis conditi, quod pro altero huius <lb/>calculi exemplo erit. </s> <s xml:id="echoid-s15426" xml:space="preserve">Erat igitur prima Arietis <lb/>anno ab Vrbe condita 466. </s> <s xml:id="echoid-s15427" xml:space="preserve">ab orbe vero condito <lb/>3832. </s> <s xml:id="echoid-s15428" xml:space="preserve">ſecudnum noſtram clarorum Mathemati-<lb/>corum Chronologiam, poſt æquinoctium gr. </s> <s xml:id="echoid-s15429" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s15430" xml:space="preserve">nam vt refert Ptolemęus tunc eam ibi Timocha-<lb/>ris depræhendit: </s> <s xml:id="echoid-s15431" xml:space="preserve">cum igitur, ſecundum noſtram <lb/>hypotheſim, ſtellæ conficiant gr. </s> <s xml:id="echoid-s15432" xml:space="preserve">1. </s> <s xml:id="echoid-s15433" xml:space="preserve">in annis 70. </s> <s xml:id="echoid-s15434" xml:space="preserve"><lb/>menſibus 7. </s> <s xml:id="echoid-s15435" xml:space="preserve">ſequitur duos illos gradus ſuperaſie <lb/>in annis 141. </s> <s xml:id="echoid-s15436" xml:space="preserve">quibus detractis ex 3832. </s> <s xml:id="echoid-s15437" xml:space="preserve">remanent <lb/>3691. </s> <s xml:id="echoid-s15438" xml:space="preserve">anno igitur ab Orbe condito 3691. </s> <s xml:id="echoid-s15439" xml:space="preserve">erat prima Arietis in ipſiſſima ſectione verna. </s> <s xml:id="echoid-s15440" xml:space="preserve">Eratautem is annus <lb/>ab Vrbe condita 325. </s> <s xml:id="echoid-s15441" xml:space="preserve">(qui remanent detractis annis 141. </s> <s xml:id="echoid-s15442" xml:space="preserve">ab annis 466. </s> <s xml:id="echoid-s15443" xml:space="preserve">ab Vrbe condita, quando Timocharis <lb/>obſeruauit) quod tempus ferè incidit in tempus obſeruationum Metonis, & </s> <s xml:id="echoid-s15444" xml:space="preserve">Euctemonis, qui ſolſtitia, & </s> <s xml:id="echoid-s15445" xml:space="preserve"><lb/>æquinoctia obſeruarunt; </s> <s xml:id="echoid-s15446" xml:space="preserve">qua tempeſtate Zodiacus eſſ aſteriſmorum coincidebat cum Zodiaco ſignorum, ſeu <lb/>primi Mobilis: </s> <s xml:id="echoid-s15447" xml:space="preserve">cum pręterea oſtenſum ſit inerrantes totum Zodiacum recurrere annis 28′ 800′. </s> <s xml:id="echoid-s15448" xml:space="preserve">perauręam <lb/>regulam inuenies eas in annis 3691. </s> <s xml:id="echoid-s15449" xml:space="preserve">progreſſas fuiſſe gr. </s> <s xml:id="echoid-s15450" xml:space="preserve">46. </s> <s xml:id="echoid-s15451" xml:space="preserve">nam ſi annis 28800. </s> <s xml:id="echoid-s15452" xml:space="preserve">dant gr. </s> <s xml:id="echoid-s15453" xml:space="preserve">360. </s> <s xml:id="echoid-s15454" xml:space="preserve">anni 3691. </s> <s xml:id="echoid-s15455" xml:space="preserve">dabũt <lb/>annos 49. </s> <s xml:id="echoid-s15456" xml:space="preserve">Quare prima Arietis erat in ipſa mudi exordio ante æquinoctium gr. </s> <s xml:id="echoid-s15457" xml:space="preserve">ferè 46. </s> <s xml:id="echoid-s15458" xml:space="preserve">hoc eſt in gr. </s> <s xml:id="echoid-s15459" xml:space="preserve">14. </s> <s xml:id="echoid-s15460" xml:space="preserve">ſigni <lb/>Aquarij. </s> <s xml:id="echoid-s15461" xml:space="preserve">Aequinoctium autem erat propè finem aſteriſmi Tauri: </s> <s xml:id="echoid-s15462" xml:space="preserve">diſtant enim cornua Tauri a prima Stella <lb/>Arietis gr. </s> <s xml:id="echoid-s15463" xml:space="preserve">circiter 46. </s> <s xml:id="echoid-s15464" xml:space="preserve">in qua diſtantia erat etiam æquinoctij punctum. </s> <s xml:id="echoid-s15465" xml:space="preserve">Atq; </s> <s xml:id="echoid-s15466" xml:space="preserve">hæc dicta ſint non tanquam vſ-<lb/>quequaque vera, ſed ex noſtris ſuppoſitis, non leui coniectura. </s> <s xml:id="echoid-s15467" xml:space="preserve">Ecce tibi quo peruadat humana ſubtilitas.</s> <s xml:id="echoid-s15468" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div362" type="section" level="1" n="258"> <head xml:id="echoid-head275" style="it" xml:space="preserve">Velocitas diurni motus affixarum.</head> <p> <s xml:id="echoid-s15469" xml:space="preserve">LAudabilis profecto curioſitas quærere quot milliaria ſingulis horis affixæ percurrãt, eæ præſertim, quæ <lb/>propè æquatorem ſitæ reuoluuntur. </s> <s xml:id="echoid-s15470" xml:space="preserve">cui ſic ſatis ſaciendum puto; </s> <s xml:id="echoid-s15471" xml:space="preserve">circumferentia maximi circuli firma-<lb/>menti, vt infra oſtendam, continet ſemidiametros 88′ 000′. </s> <s xml:id="echoid-s15472" xml:space="preserve">qnibus diuiſis in partes, ſeu hor. </s> <s xml:id="echoid-s15473" xml:space="preserve">24. </s> <s xml:id="echoid-s15474" xml:space="preserve">vni horę ob-<lb/>ueniunt 3666 {2/3} ſemidiametri terræ; </s> <s xml:id="echoid-s15475" xml:space="preserve">vna autem ſemidiameter continet milliaria Aſtronomica 3436 {1/2}. </s> <s xml:id="echoid-s15476" xml:space="preserve">quare <lb/>ſi 3666 {2/3}. </s> <s xml:id="echoid-s15477" xml:space="preserve">per 3436 {1/2}. </s> <s xml:id="echoid-s15478" xml:space="preserve">multiplicentur, producetur 12,589,045. </s> <s xml:id="echoid-s15479" xml:space="preserve">nnmerus milliariorum, in vna igitur hora tot <lb/>milliariorum milliones conficit ſtella propè æquatorem motu primi mobilis, ſeu diurno delata. </s> <s xml:id="echoid-s15480" xml:space="preserve">Vtrum ſtel-<lb/>la fixa plures gyros diurnos peragat, quam Sol aut Luna?</s> <s xml:id="echoid-s15481" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div363" type="section" level="1" n="259"> <head xml:id="echoid-head276" style="it" xml:space="preserve">Motus trepidationis firmamenti. Cap. IX.</head> <p> <s xml:id="echoid-s15482" xml:space="preserve">PRæter motum in longitudinem, & </s> <s xml:id="echoid-s15483" xml:space="preserve">motum diurnum, tertium nonnullis ſtellis addunt, quem trepidatio-<lb/>nem vocant: </s> <s xml:id="echoid-s15484" xml:space="preserve">quo firmamentum verſus Mundi polos lentiſſimè reciprocari, ſeu accedere, & </s> <s xml:id="echoid-s15485" xml:space="preserve">recedere ad <lb/>interuallum min. </s> <s xml:id="echoid-s15486" xml:space="preserve">24′. </s> <s xml:id="echoid-s15487" xml:space="preserve">putant. </s> <s xml:id="echoid-s15488" xml:space="preserve">Quam quantitatem colligunt ex maxima, & </s> <s xml:id="echoid-s15489" xml:space="preserve">minima Solis declinatione, cuius <lb/>ſupra Tabeli<unsure/>am expoſuimus; </s> <s xml:id="echoid-s15490" xml:space="preserve">vnde colligunt maximam, & </s> <s xml:id="echoid-s15491" xml:space="preserve">minimam eclipticæ declinationem, quam putant <pb o="179" file="0201" n="206" rhead="Liber Decimusſeptimus."/> prou@@ire ex motu cuiuſdam orbis ſuperioris, qui primo firmamentum, deinde reliquum inferius cælũ im-<lb/>pellat. </s> <s xml:id="echoid-s15492" xml:space="preserve">maxima vero. </s> <s xml:id="echoid-s15493" xml:space="preserve">differentia inter maximam, & </s> <s xml:id="echoid-s15494" xml:space="preserve">minimam eclipticæ declinationem eſt min. </s> <s xml:id="echoid-s15495" xml:space="preserve">24′. </s> <s xml:id="echoid-s15496" xml:space="preserve">quæ ex <lb/>eo oritur, quod poli eclipticæ reciprocentur verſus Mundi polos perſpatium 24′. </s> <s xml:id="echoid-s15497" xml:space="preserve">min. </s> <s xml:id="echoid-s15498" xml:space="preserve">idque ſecus Colurum <lb/>ſolſtitiorum, in quo ſunt vtriq; </s> <s xml:id="echoid-s15499" xml:space="preserve">poli, & </s> <s xml:id="echoid-s15500" xml:space="preserve">mundi, & </s> <s xml:id="echoid-s15501" xml:space="preserve">eclipticæ. </s> <s xml:id="echoid-s15502" xml:space="preserve">Hanc trepidationem conijciunt abſolui in an-<lb/>@is circiter 3434. </s> <s xml:id="echoid-s15503" xml:space="preserve">Aegyptijs. </s> <s xml:id="echoid-s15504" xml:space="preserve">Verùm cum iſte motus ob ſuam tarditatem nondum ſatis exploratius ſit; </s> <s xml:id="echoid-s15505" xml:space="preserve">cumq; <lb/></s> <s xml:id="echoid-s15506" xml:space="preserve">parua 24′. </s> <s xml:id="echoid-s15507" xml:space="preserve">differentia oriri potuerit ex obſeruationum imperfectione, vt benè Tycho ſuſpicatur, non admo-<lb/>dum ſolliciti eſſe debemus de hac inerrantium vacillatione. </s> <s xml:id="echoid-s15508" xml:space="preserve">ad hunc porrò motum efficiendum ſuperiores <lb/>Aſtronomi ſupponunt nonam ſphæram, cuius motus poli ſint in punctis æquinoctiorum, quibus innixa mo-<lb/>ueatur ſecumq; </s> <s xml:id="echoid-s15509" xml:space="preserve">pariter moueat firmamentũ eo modo quo diximus. </s> <s xml:id="echoid-s15510" xml:space="preserve">Primus eius inuentor fuit Thebit Arabs <lb/>anno Domini 1270. </s> <s xml:id="echoid-s15511" xml:space="preserve">vt patet ex noſtra clarorum Mathematicorum Chronologia.</s> <s xml:id="echoid-s15512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15513" xml:space="preserve">Tandem ex tribus hiſce motibus, quibus fixę agitantur, conflatur vltimus earum motum ſpiralis, vtin pla-<lb/>netis: </s> <s xml:id="echoid-s15514" xml:space="preserve">nam v. </s> <s xml:id="echoid-s15515" xml:space="preserve">g. </s> <s xml:id="echoid-s15516" xml:space="preserve">Stella, quæ olim erat in Tropico Cancri, ab eo ſenſim motu proprio recedens, quotidie no-<lb/>uam reuolutionem ob diurnam conuerſionem verſus alterum Tropicum agglomerat, ad quem perueniet in <lb/>fine Magnianni, ideſt, in annis ſolaribus 28,7000,.</s> <s xml:id="echoid-s15517" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div364" type="section" level="1" n="260"> <head xml:id="echoid-head277" style="it" xml:space="preserve">Orius, & Occaſus Inerrantium. Cap. X.</head> <p> <s xml:id="echoid-s15518" xml:space="preserve">PRædictos inerrantium motus ſequuntur Ortus earum, & </s> <s xml:id="echoid-s15519" xml:space="preserve">Occaſus varij. </s> <s xml:id="echoid-s15520" xml:space="preserve">omnis autem Ortus, & </s> <s xml:id="echoid-s15521" xml:space="preserve">Occaſus <lb/>ſtellarum, vel eſt Horizontalis, vel Solaris, quem Græcè Heliacum vocant. </s> <s xml:id="echoid-s15522" xml:space="preserve">Ortus horizontalis eſt eleua-<lb/>tio, ſeu aſcenſio aſtri ſupra horizontem. </s> <s xml:id="echoid-s15523" xml:space="preserve">Occaſus horizontalis eſt depreſſio, ſeu deſcenſio aſtri infra horizon-<lb/>tem: </s> <s xml:id="echoid-s15524" xml:space="preserve">hic autem Ortus, & </s> <s xml:id="echoid-s15525" xml:space="preserve">Occaſus conſequitur ad inortum diurnum, & </s> <s xml:id="echoid-s15526" xml:space="preserve">ideo quotidianus eſt; </s> <s xml:id="echoid-s15527" xml:space="preserve">& </s> <s xml:id="echoid-s15528" xml:space="preserve">ſubdiuiditur <lb/>in alias ſpecies. </s> <s xml:id="echoid-s15529" xml:space="preserve">Ortus Heliacus eſt apparitio Aſtri, quod antea ob Solis vicinitatem non conſpiciebatur. </s> <s xml:id="echoid-s15530" xml:space="preserve">Oc-<lb/>caſus Heliacus eſt occultatio Aſtri, ita vtamplius ob Solis prupinquitatem cerni nequeat. </s> <s xml:id="echoid-s15531" xml:space="preserve">hic etiam in alias <lb/>ſpecies diuiditur. </s> <s xml:id="echoid-s15532" xml:space="preserve">inde autem oritur, quia Affixæ motu proprio in longitudinem tardiſſimè progrediuntur, <lb/>Solautem reſpectu earum ocyſſimè; </s> <s xml:id="echoid-s15533" xml:space="preserve">vnde fit vt Sol ſingulis annis inerrantes omnes aſſequatur, & </s> <s xml:id="echoid-s15534" xml:space="preserve">proinde <lb/>fulgore ſuo contengat; </s> <s xml:id="echoid-s15535" xml:space="preserve">quod eſt Heliacè occidere; </s> <s xml:id="echoid-s15536" xml:space="preserve">eaſdem poſtea prætereat, ſuoque fulgore liberet, vtite-<lb/>rum apparere poſſint; </s> <s xml:id="echoid-s15537" xml:space="preserve">quod eſt Heliacè oriri. </s> <s xml:id="echoid-s15538" xml:space="preserve">Ortus horizontalis matutinus eſt, quando Aſtrum vna cum <lb/>Sole mane oritur: </s> <s xml:id="echoid-s15539" xml:space="preserve">hunc ineptè nonnulli Coſmicum appellant. </s> <s xml:id="echoid-s15540" xml:space="preserve">Quod ſi Solem ita præcedat vt primo conſpi-<lb/>ci mane incipiat dicitur Ortus Heliacus. </s> <s xml:id="echoid-s15541" xml:space="preserve">´de hoc ortu intelligendus eſt Heſiodus, cum canit ſic.</s> <s xml:id="echoid-s15542" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15543" xml:space="preserve">Pleiadibus Atlante natis exorientibus, incipè Meſsem.</s> <s xml:id="echoid-s15544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15545" xml:space="preserve">Illæ enim Menſe Iunio, quo Meſſis initur manè heliacè apparere incipiunt. </s> <s xml:id="echoid-s15546" xml:space="preserve">Idem Heſiodus hæc rurſus <lb/>ahbet; </s> <s xml:id="echoid-s15547" xml:space="preserve">cum verò Orione, & </s> <s xml:id="echoid-s15548" xml:space="preserve">Syrius in medium venerit cælum, Arcturum autem inſpexerit Aurora. </s> <s xml:id="echoid-s15549" xml:space="preserve">indicat <lb/>Autumni tempus, quo Auroræ tempore Arcturus Heliacè apparet, & </s> <s xml:id="echoid-s15550" xml:space="preserve">tunc illa duo Aſtra, Orion, & </s> <s xml:id="echoid-s15551" xml:space="preserve">Syrius <lb/>Meridianum obſident: </s> <s xml:id="echoid-s15552" xml:space="preserve">quod accidit poſt æquinoctium Autumnale. </s> <s xml:id="echoid-s15553" xml:space="preserve">Ouid. </s> <s xml:id="echoid-s15554" xml:space="preserve">lib. </s> <s xml:id="echoid-s15555" xml:space="preserve">2. </s> <s xml:id="echoid-s15556" xml:space="preserve">Faſt. </s> <s xml:id="echoid-s15557" xml:space="preserve">hunc etiam ortum <lb/>innuit, fic,</s> </p> <p style="it"> <s xml:id="echoid-s15558" xml:space="preserve">Iam leuis obliqua ſubſidit Aquarius vrna <lb/>Proximus æthereos accipe Piſcis equos.</s> <s xml:id="echoid-s15559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15560" xml:space="preserve">Vbi verbum, ſubſidit, ſignificat à Sole derelinqui, qui prius ipſum occultabat ſua præſentia, vnde poſtea <lb/>conſpici poſſit. </s> <s xml:id="echoid-s15561" xml:space="preserve">Eodem conſilio Virg. </s> <s xml:id="echoid-s15562" xml:space="preserve">Georg. </s> <s xml:id="echoid-s15563" xml:space="preserve">1.</s> <s xml:id="echoid-s15564" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15565" xml:space="preserve">Ggnoſſiaque ardentis decedat stella Coronæ. <lb/></s> <s xml:id="echoid-s15566" xml:space="preserve">Debita quam ſulcis committas ſemina.</s> <s xml:id="echoid-s15567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15568" xml:space="preserve">Vbi verbum, decedat, ſignificat à Sole decedere, vel recedere, ipſo ſcilicet Sole prætereunte, ſicq; </s> <s xml:id="echoid-s15569" xml:space="preserve">manè an-<lb/>te Solem apparere, ideſt, heliacè oriri. </s> <s xml:id="echoid-s15570" xml:space="preserve">Ariſtoteles tandem, ſecundo Meteor. </s> <s xml:id="echoid-s15571" xml:space="preserve">cum ait, quapropter & </s> <s xml:id="echoid-s15572" xml:space="preserve">circa <lb/>ortum Orionis, maximè fit tranquillitas; </s> <s xml:id="echoid-s15573" xml:space="preserve">hunc ortum Orionis, maximè fit tranquillitas; </s> <s xml:id="echoid-s15574" xml:space="preserve">hunc ortum intelli-<lb/>git; </s> <s xml:id="echoid-s15575" xml:space="preserve">vt ibi in noſtris Comment. </s> <s xml:id="echoid-s15576" xml:space="preserve">in loca eius Mathematica explicauimus. </s> <s xml:id="echoid-s15577" xml:space="preserve">de eodem ortu ſunt etiam illa eiuſdẽ <lb/>loci, Eteſiæ autem ſtant poſt verſionem, & </s> <s xml:id="echoid-s15578" xml:space="preserve">Canis ortum, ideſt, heliacum matutinum.</s> <s xml:id="echoid-s15579" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15580" xml:space="preserve">Ortus horizontalis veſpertinus eſt cum veſperi occidente Sole, Stella ex oriente emergit. </s> <s xml:id="echoid-s15581" xml:space="preserve">qui ortus Græ-<lb/>tè dicitur Acronychus, vti alias dictum eſt, quem vulgus Latinorum Græcè neſcientium Cronicum, & </s> <s xml:id="echoid-s15582" xml:space="preserve">hinc <lb/>temporalem ineptè appellauit. </s> <s xml:id="echoid-s15583" xml:space="preserve">Ouid. </s> <s xml:id="echoid-s15584" xml:space="preserve">lib. </s> <s xml:id="echoid-s15585" xml:space="preserve">1. </s> <s xml:id="echoid-s15586" xml:space="preserve">de Ponto Elogia 9. </s> <s xml:id="echoid-s15587" xml:space="preserve">hunc innuit:</s> <s xml:id="echoid-s15588" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15589" xml:space="preserve">Vt careo vobis ſcythicas detruſus in oras <lb/>Quatuor Autumnos Pleias orta facit.</s> <s xml:id="echoid-s15590" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15591" xml:space="preserve">Autumni enim tempore veſperi demerſo iam Sole oriuntur Pleiades in oriente, tuncque primo appare-<lb/>reincipiunt.</s> <s xml:id="echoid-s15592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15593" xml:space="preserve">Occaſus horizontalis matutinus fit quando oriente Sole, Stella in occidente deſcendit infra horizontem. <lb/></s> <s xml:id="echoid-s15594" xml:space="preserve">ad hunc alludit Heſiodus, his; </s> <s xml:id="echoid-s15595" xml:space="preserve">Arationem vero videlicet incipe, Pleiadibus occidentibus; </s> <s xml:id="echoid-s15596" xml:space="preserve">hæ quidem no-<lb/>cteſque, & </s> <s xml:id="echoid-s15597" xml:space="preserve">dies quadraginta latent; </s> <s xml:id="echoid-s15598" xml:space="preserve">rurſum verò circumuertente ſe anno apparent. </s> <s xml:id="echoid-s15599" xml:space="preserve">Virgilius etiam He-<lb/>ſiodum ſequutus Georg. </s> <s xml:id="echoid-s15600" xml:space="preserve">1. </s> <s xml:id="echoid-s15601" xml:space="preserve">ſic,</s> </p> <p style="it"> <s xml:id="echoid-s15602" xml:space="preserve">Ante tibi Eoæ Atlantides abſcondantur, <lb/>Debita quam ſulcis committas ſemina.</s> <s xml:id="echoid-s15603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15604" xml:space="preserve">Intelligit enim tempus Autumni, quod tempus ſationis eſt, & </s> <s xml:id="echoid-s15605" xml:space="preserve">quo Sole Scorpionem poſſidente, Pleiades in <lb/>oppoſito Tauri ſigno exiſtentes, matutino tempore occidunt, nec amplius cernuntur. </s> <s xml:id="echoid-s15606" xml:space="preserve">hunc ineptè quidam <lb/>occaſum Coſmicum appellauere.</s> <s xml:id="echoid-s15607" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15608" xml:space="preserve">Occaſus horizontalis veſpertinus, qui Græcè Acronychus, & </s> <s xml:id="echoid-s15609" xml:space="preserve">barbare cronicus dicitur; </s> <s xml:id="echoid-s15610" xml:space="preserve">fit cũ Stella ſimul <pb o="180" file="0202" n="207" rhead="De Mundi Fabrica,"/> @um Sole infra horizontem deprimitur. </s> <s xml:id="echoid-s15611" xml:space="preserve">quod ſi Stella, quæ in occidente veſpeti videbatur, appropinquan-<lb/>te ei Sole apparere deſierit. </s> <s xml:id="echoid-s15612" xml:space="preserve">is erit occaſus Heliacus, ad quem Ouid. </s> <s xml:id="echoid-s15613" xml:space="preserve">reſpicit lib. </s> <s xml:id="echoid-s15614" xml:space="preserve">2. </s> <s xml:id="echoid-s15615" xml:space="preserve">Faſt. </s> <s xml:id="echoid-s15616" xml:space="preserve">ſit,</s> </p> <p style="it"> <s xml:id="echoid-s15617" xml:space="preserve">Quem modo cælatum. </s> <s xml:id="echoid-s15618" xml:space="preserve">stellis Delphina videbas. <lb/></s> <s xml:id="echoid-s15619" xml:space="preserve">Is fugiet viſus nocte ſequente tuos.</s> <s xml:id="echoid-s15620" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15621" xml:space="preserve">Loquitur enim de tertio Februarij die, cuius pridie poſt Solis occaſum apparebat Delphinus in occidente, <lb/>ſcd tertio die a ſuperueniente Sole occultatus, vna eum eo occidebat inuiſus. </s> <s xml:id="echoid-s15622" xml:space="preserve">Et Virg.</s> <s xml:id="echoid-s15623" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15624" xml:space="preserve">-- Et aduerſo cedens Canis occidit Astro.</s> <s xml:id="echoid-s15625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15626" xml:space="preserve">Ideſt, Canis cedens locum aduerſo Soli appropinquanti heliacè occidit. </s> <s xml:id="echoid-s15627" xml:space="preserve">Porrò ex prædictis manifeſtum eſt <lb/>hunc ortuum, & </s> <s xml:id="echoid-s15628" xml:space="preserve">occaſuum cognitionem neceſſariam eſſe ad intelligenda plurima loca tam Poetarum, quam <lb/>Philoſophorum, tum rei ruſticæ Scriptorum; </s> <s xml:id="echoid-s15629" xml:space="preserve">ſed & </s> <s xml:id="echoid-s15630" xml:space="preserve">maximè Medicorum; </s> <s xml:id="echoid-s15631" xml:space="preserve">hi enim omnes rerũ tempora pet <lb/>ortus, & </s> <s xml:id="echoid-s15632" xml:space="preserve">occaſus ferè ſemper heliacos deſcribunt. </s> <s xml:id="echoid-s15633" xml:space="preserve">quam neceſſitatem ſic Virgilius exprimit:</s> <s xml:id="echoid-s15634" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15635" xml:space="preserve">Præterea tam ſunt Arcturi, ſydera nobis <lb/>Hædorumq; </s> <s xml:id="echoid-s15636" xml:space="preserve">dies ſeruandi, & </s> <s xml:id="echoid-s15637" xml:space="preserve">lucidus Anguis, <lb/>Quam quibus in patriam ventoſa per æquora vectis, <lb/>Pontus, & </s> <s xml:id="echoid-s15638" xml:space="preserve">ostriferi fauces tentantur Abydi.</s> <s xml:id="echoid-s15639" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15640" xml:space="preserve">Idem affirmat Aetius Medicinæ conſultiſſimus ſermone 3. </s> <s xml:id="echoid-s15641" xml:space="preserve">cap. </s> <s xml:id="echoid-s15642" xml:space="preserve">4. </s> <s xml:id="echoid-s15643" xml:space="preserve">ſic; </s> <s xml:id="echoid-s15644" xml:space="preserve">quandoquidem etiam ſtellæ orientes, <lb/>& </s> <s xml:id="echoid-s15645" xml:space="preserve">occidentes aera mutant: </s> <s xml:id="echoid-s15646" xml:space="preserve">vnde contingit etiam alios ventos aliter ſpirare, necceſſarium duxi hic tempora <lb/>indi care, in quibus earum, quæ aerem palam alterant, Ortus, & </s> <s xml:id="echoid-s15647" xml:space="preserve">Occaſus fiunt: </s> <s xml:id="echoid-s15648" xml:space="preserve">nam ſanorum corpora, & </s> <s xml:id="echoid-s15649" xml:space="preserve"><lb/>multo magis ægrorum iuxta aeris ſtatum alterantur ea igitur ſunt, Equus cum mane oritur; </s> <s xml:id="echoid-s15650" xml:space="preserve">cum Pleiades <lb/>oriuntur manè, cum veſperi occidunt, & </s> <s xml:id="echoid-s15651" xml:space="preserve">c. </s> <s xml:id="echoid-s15652" xml:space="preserve">quæ apud eum reperies. </s> <s xml:id="echoid-s15653" xml:space="preserve">Galenus ipſe Medicorum princeps mo-<lb/>net ægrotos ne ſe manibus Medicorum Aſtrologiam ignorantium committant, quia inquit, medicamina <lb/>parum iuuant imo ſæpè nocent, temporibus incommodis exhibita: </s> <s xml:id="echoid-s15654" xml:space="preserve">tempora autem ex ortibus, & </s> <s xml:id="echoid-s15655" xml:space="preserve">occaſibus <lb/>ſtellarum pendent. </s> <s xml:id="echoid-s15656" xml:space="preserve">ſed primus omnium Hippocrates in lib. </s> <s xml:id="echoid-s15657" xml:space="preserve">de aere, & </s> <s xml:id="echoid-s15658" xml:space="preserve">aquis, int<unsure/>er cætera hæc habet; </s> <s xml:id="echoid-s15659" xml:space="preserve">oportet <lb/>autem, & </s> <s xml:id="echoid-s15660" xml:space="preserve">Aſtrorum ortus conſiderare, præcipuè Canis, deinde Arcturi, & </s> <s xml:id="echoid-s15661" xml:space="preserve">Pleiadum occaſum, morbi enim <lb/>in his maximè diebus iudicantur, alijque perimunt, alij vero deſinunt, & </s> <s xml:id="echoid-s15662" xml:space="preserve">c. </s> <s xml:id="echoid-s15663" xml:space="preserve">Quamobrem operæpretium eſt, <lb/>cognoſcere quo anni tempore, quæuis ſtella oriatur, & </s> <s xml:id="echoid-s15664" xml:space="preserve">occidit. </s> <s xml:id="echoid-s15665" xml:space="preserve">quod pulchre, ac commode indicabit ſphæ-<lb/>ra Arathæa, ſeu Globus Aſtronomicus, qucm ſupra conſtruximus; </s> <s xml:id="echoid-s15666" xml:space="preserve">hoc modo; </s> <s xml:id="echoid-s15667" xml:space="preserve">eum colloca aſtronomicè, de-<lb/>inde Stellam illam, cuius ortus, tempus quæris, ſtatue in horizonte orientali, notaque gradum eclipticæ, qui <lb/>tunc ſimul horizontem tangit; </s> <s xml:id="echoid-s15668" xml:space="preserve">cum enim Sol ad illum gradum peruenerit, orientur Stella illa horizontali-<lb/>ter, & </s> <s xml:id="echoid-s15669" xml:space="preserve">poſt aliquot dies etiam heliacè. </s> <s xml:id="echoid-s15670" xml:space="preserve">poſita item Stella in horizonte occiduo, notetur pariter gradus ecli-<lb/>pticæ eundem horizontem contingens, cum enim eo Soloccupauerit: </s> <s xml:id="echoid-s15671" xml:space="preserve">Stella ea veſperi horizontaliter oc-<lb/>cumbet, cum aliquot diebus prius heliacè occiderit. </s> <s xml:id="echoid-s15672" xml:space="preserve">quando verò Sol fuerit in gradu huic oppoſito, Stella <lb/>eadem manè occidet. </s> <s xml:id="echoid-s15673" xml:space="preserve">Maginus in ſuis Ephemeridibus exhibet Tabulam ortuum, & </s> <s xml:id="echoid-s15674" xml:space="preserve">occaſuum præcipuarum <lb/>Stellarum. </s> <s xml:id="echoid-s15675" xml:space="preserve">De ortu, & </s> <s xml:id="echoid-s15676" xml:space="preserve">occaſum inerrantium extat Autolycus antiquus Aſtronomus, qui Olimpiade circi-<lb/>ter 120. </s> <s xml:id="echoid-s15677" xml:space="preserve">floruit: </s> <s xml:id="echoid-s15678" xml:space="preserve">eum Ioſephus Auria, & </s> <s xml:id="echoid-s15679" xml:space="preserve">traduxit, & </s> <s xml:id="echoid-s15680" xml:space="preserve">illuſtrauit.</s> <s xml:id="echoid-s15681" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div365" type="section" level="1" n="261"> <head xml:id="echoid-head278" style="it" xml:space="preserve">Aliter de Ortu, & Occaſu ſyderum ſecundum Astronom. Cap. XI.</head> <p> <s xml:id="echoid-s15682" xml:space="preserve">PRædicta ortuum, & </s> <s xml:id="echoid-s15683" xml:space="preserve">occaſuum acceptiones, communes ſunt Aſtronomis, & </s> <s xml:id="echoid-s15684" xml:space="preserve">cæteris ſcriptoribus, quæ ve-<lb/>rò ſequuntur ſolis Aſtronomis ſeruiunt: </s> <s xml:id="echoid-s15685" xml:space="preserve">eas Ptolemæus coortus, & </s> <s xml:id="echoid-s15686" xml:space="preserve">cooccaſus appellat: </s> <s xml:id="echoid-s15687" xml:space="preserve">Latini Aſcenſio-<lb/>nes, & </s> <s xml:id="echoid-s15688" xml:space="preserve">Deſcenſiones; </s> <s xml:id="echoid-s15689" xml:space="preserve">quarum vſus eſt, vt per eas tempus menſuretur, quod inſumitur in ortu, vel occaſu ali-<lb/>cuius ſigni, vel arcus Zodiaci, vel Stellæ, vel puncti cuiuſpiam. </s> <s xml:id="echoid-s15690" xml:space="preserve">quæ mẽſura ſumitor penes æquatorem, quip-<lb/>pe qui vniformiter moueatur, & </s> <s xml:id="echoid-s15691" xml:space="preserve">horizontem pertranſeat, & </s> <s xml:id="echoid-s15692" xml:space="preserve">ideo communis mẽſura ſic cæleſtium motuum, <lb/>vt alias diximus: </s> <s xml:id="echoid-s15693" xml:space="preserve">Zodiacus verò ob ſui obliquitatem inęqualiter aſcendit, & </s> <s xml:id="echoid-s15694" xml:space="preserve">deſcendit ſupra, & </s> <s xml:id="echoid-s15695" xml:space="preserve">infra horizon <lb/>tem, & </s> <s xml:id="echoid-s15696" xml:space="preserve">ideo menſurationi ineptus eſt.</s> <s xml:id="echoid-s15697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15698" xml:space="preserve">Aſcenſio igitur Stellæ alicuius eſt arcus æquatoris à ſectione verna inchoatus, & </s> <s xml:id="echoid-s15699" xml:space="preserve">numeratus ſecundum ſi-<lb/>gnorum ſucceſſionem vſq; </s> <s xml:id="echoid-s15700" xml:space="preserve">ad horizontem ortiuum, dum Stella oriens, ipſum pariter horizontem attingit. <lb/></s> <s xml:id="echoid-s15701" xml:space="preserve">v. </s> <s xml:id="echoid-s15702" xml:space="preserve">g. </s> <s xml:id="echoid-s15703" xml:space="preserve">in hac Parmenſi eleuatione polari, quia quando Canicula, ſeu Procyon oritur, ſiue quando ortiuum ho-<lb/>rizontem attingit, tunc arcus æquatoris inchoatus ab æquinoctio verno vſq; </s> <s xml:id="echoid-s15704" xml:space="preserve">ad eundem horizontem nume-<lb/>ratus, continet gr. </s> <s xml:id="echoid-s15705" xml:space="preserve">102. </s> <s xml:id="echoid-s15706" xml:space="preserve">erit aſcenfio Procyonis gr. </s> <s xml:id="echoid-s15707" xml:space="preserve">102. </s> <s xml:id="echoid-s15708" xml:space="preserve">æquatoris. </s> <s xml:id="echoid-s15709" xml:space="preserve">Deſcenſio pariter Stellæ eſt arcus æqua-<lb/>toris eodem modo computatus, qui demerſus eſt ſub occiduo horizonte, dum ſtella occidens eundem hori-<lb/>zontem attingit, v. </s> <s xml:id="echoid-s15710" xml:space="preserve">g. </s> <s xml:id="echoid-s15711" xml:space="preserve">occidente eadem Canicula in noſtrc eleuatione tunc prædictus arcus eſt gr. </s> <s xml:id="echoid-s15712" xml:space="preserve">117. </s> <s xml:id="echoid-s15713" xml:space="preserve">eiu@ <lb/>videlicet deſcenſio.</s> <s xml:id="echoid-s15714" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15715" xml:space="preserve">Aſtronomi præterea conſiderant aſcenſionem, & </s> <s xml:id="echoid-s15716" xml:space="preserve">deſcenſionem arcus cuiuſuis eclipticæ, ideſt, arcũ æqua-<lb/>toris ſimul cum oblato arcu coorientem, aut coocidentem, vnde tempus menſurant, quo totus ille arcus Zo-<lb/>diaci emergit ab horizonte, vel ſub eo demergitur; </s> <s xml:id="echoid-s15717" xml:space="preserve">tantum enim eſt tempus, quantum arcus ille æquatoris <lb/>importat; </s> <s xml:id="echoid-s15718" xml:space="preserve">15. </s> <s xml:id="echoid-s15719" xml:space="preserve">enim gra. </s> <s xml:id="echoid-s15720" xml:space="preserve">vnam horam efficiunt, & </s> <s xml:id="echoid-s15721" xml:space="preserve">c. </s> <s xml:id="echoid-s15722" xml:space="preserve">Has præterea omnes aſcenſiones, & </s> <s xml:id="echoid-s15723" xml:space="preserve">deſcenſiones dupli-<lb/>citer conſiderant; </s> <s xml:id="echoid-s15724" xml:space="preserve">in ſphæra videlicet obliqua, & </s> <s xml:id="echoid-s15725" xml:space="preserve">recta; </s> <s xml:id="echoid-s15726" xml:space="preserve">vnde eas in obliquas, & </s> <s xml:id="echoid-s15727" xml:space="preserve">rectas diuidunt. </s> <s xml:id="echoid-s15728" xml:space="preserve">Aſcenſio, <lb/>a@t deſcenſio obliqua eſt arcus æquatoris cooriens, aut coocidens alicui arcui eclipticæ in ſphæra obliqua. <lb/></s> <s xml:id="echoid-s15729" xml:space="preserve">Aſcenſio, & </s> <s xml:id="echoid-s15730" xml:space="preserve">deſcenſio recta arcus æquatoris, & </s> <s xml:id="echoid-s15731" xml:space="preserve">c. </s> <s xml:id="echoid-s15732" xml:space="preserve">cooriens, & </s> <s xml:id="echoid-s15733" xml:space="preserve">c. </s> <s xml:id="echoid-s15734" xml:space="preserve">in ſphæra recta. </s> <s xml:id="echoid-s15735" xml:space="preserve">Vbi illud ſciendum media-<lb/>tionem cæli cuiuſuis puncti, vel arcus eclipticæ eſſe pariter arcum æquatoris, qui ſimul cum aſſumpto ecli-<lb/>pticæ arcu Meridianum circulum pertranſit, vel eſt arcus æquatoris numeratus ab æquinoctio qui pertran-<lb/>ſijt Meridianum, dum punctum aſſumptum, vel Stella Meridianum attingit: </s> <s xml:id="echoid-s15736" xml:space="preserve">quapropter mediatio cæli, &</s> <s xml:id="echoid-s15737" xml:space="preserve"> <pb o="181" file="0203" n="208" rhead="Liber decimusſeptimus."/> aſ@enſio recta ſunt ſemper æquales, nec differunt nifi quia aſcenſio recta refertur ad horizontem ſphæræ re-<lb/>ctæ; </s> <s xml:id="echoid-s15738" xml:space="preserve">Mediatio verò ad Meridianum: </s> <s xml:id="echoid-s15739" xml:space="preserve">ſed Meridianus eodem modo ſe habet ad Aequatorem, & </s> <s xml:id="echoid-s15740" xml:space="preserve">Zodiacum, <lb/>atq; </s> <s xml:id="echoid-s15741" xml:space="preserve">horizon rectæ ſphæræ, omnis enim Meridianus eſt etiam alicubi horizon ſphæræ rectæ; </s> <s xml:id="echoid-s15742" xml:space="preserve">& </s> <s xml:id="echoid-s15743" xml:space="preserve">omnis ho-<lb/>rizon rectus eſt etiam alicubi Meridianus. </s> <s xml:id="echoid-s15744" xml:space="preserve">Cæterum Aſtronomi condiderunt Tabulas aſcenſionum recta-<lb/>rum, ac proinde etiam mediationum cæli; </s> <s xml:id="echoid-s15745" xml:space="preserve">necnon aſcenſionum obliquarum omnium arcuum eclipticæ in-<lb/>cipientium ab initio Arietis, quas huc tranſcribere noſtro inſtituto oneroſius duxi, quam vtilius; </s> <s xml:id="echoid-s15746" xml:space="preserve">ponam <lb/>tamen ſolam hanc Tabellam.</s> <s xml:id="echoid-s15747" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div366" type="section" level="1" n="262"> <head xml:id="echoid-head279" style="it" xml:space="preserve">Aſcenſiones rectæ, ſiue Cæli mediationes 12. ſigni Zodiaci.</head> <note position="right" xml:space="preserve"> <lb/># # # # Gra. # ′. <lb/>♈ # ♍ # ♎ # ♓ # 27 # 54 <lb/>♉ # ♌ # ♏ # ♒ # 29 # 54 <lb/>♊ # ♋ # ♐ # ♑ # 32 # 12 <lb/></note> <p> <s xml:id="echoid-s15748" xml:space="preserve">Vbi vides quatuor ſigna ſuperiora oriri, & </s> <s xml:id="echoid-s15749" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15750" xml:space="preserve">cælum mediare cum gr. </s> <s xml:id="echoid-s15751" xml:space="preserve">27. </s> <s xml:id="echoid-s15752" xml:space="preserve">54′. </s> <s xml:id="echoid-s15753" xml:space="preserve">quæ eſt eo-<lb/>rum aſcenſio recta, & </s> <s xml:id="echoid-s15754" xml:space="preserve">cæli mediatio. </s> <s xml:id="echoid-s15755" xml:space="preserve">ſic qua-<lb/>tuor ſigna media cum gr. </s> <s xml:id="echoid-s15756" xml:space="preserve">29. </s> <s xml:id="echoid-s15757" xml:space="preserve">54′. </s> <s xml:id="echoid-s15758" xml:space="preserve">tãdem qua-<lb/>tuor inferiora cũ gr. </s> <s xml:id="echoid-s15759" xml:space="preserve">32. </s> <s xml:id="echoid-s15760" xml:space="preserve">12′. </s> <s xml:id="echoid-s15761" xml:space="preserve">quæ ſunt eorum <lb/>aſcenſiones rectæ, ſeu cæli mediationes. </s> <s xml:id="echoid-s15762" xml:space="preserve">Por-<lb/>rò<unsure/> ex ſphæra materiali fabrefacta facilè erit <lb/>vnicuiq; </s> <s xml:id="echoid-s15763" xml:space="preserve">volenti, aſcenfiones omnes rectas, & </s> <s xml:id="echoid-s15764" xml:space="preserve"><lb/>obliquas cuiuſuis puncti, vel arcus inuenire. </s> <s xml:id="echoid-s15765" xml:space="preserve">hac ratione rectas aſcenſiones reperies, applica gradum eclipti-<lb/>cæ oblatum circulo meridiano, & </s> <s xml:id="echoid-s15766" xml:space="preserve">numera gradus ab initio ęquatoris vſq; </s> <s xml:id="echoid-s15767" xml:space="preserve">ad meridianum procedendo ab oc-<lb/>caſu ad ortum, ij enim conflant aſcenſionem rectam illius gradus, ſeu etiam mediationem cæli. </s> <s xml:id="echoid-s15768" xml:space="preserve">ſimiliter pote-<lb/>ris reperire omnes aſcenſiones obliquas graduum omnium apud horizontem quemuis; </s> <s xml:id="echoid-s15769" xml:space="preserve">necnõ omnes aſcen-<lb/>ſiones tam rectas, quam obliquas, quorumlibet arcuum eclipticæ. </s> <s xml:id="echoid-s15770" xml:space="preserve">verum quiddam hic mirum conſiderandum <lb/>occurrit, arcus nimirum omnes primæ quartæ Zodiaci quæ habet gr. </s> <s xml:id="echoid-s15771" xml:space="preserve">90. </s> <s xml:id="echoid-s15772" xml:space="preserve">inchoati ab initio ♈, & </s> <s xml:id="echoid-s15773" xml:space="preserve">deſinentes <lb/>vbicumq; </s> <s xml:id="echoid-s15774" xml:space="preserve">habere aſcenſiones rectas ſe minores, in fine tamen quartæ, ideſt, in fine ♊, totam quartam habere <lb/>aſcenſionem rectam ſibi æqualem. </s> <s xml:id="echoid-s15775" xml:space="preserve">ſic in preſenti Tabella, vides arcum ♈, habere aſcenſionem rectam 25. </s> <s xml:id="echoid-s15776" xml:space="preserve">54′. <lb/></s> <s xml:id="echoid-s15777" xml:space="preserve">ſe minorem, & </s> <s xml:id="echoid-s15778" xml:space="preserve">arcum conſtantem ex ♈, & </s> <s xml:id="echoid-s15779" xml:space="preserve">♉, ideſt, gr. </s> <s xml:id="echoid-s15780" xml:space="preserve">60. </s> <s xml:id="echoid-s15781" xml:space="preserve">habere aſcenſionem rectam gr. </s> <s xml:id="echoid-s15782" xml:space="preserve">57. </s> <s xml:id="echoid-s15783" xml:space="preserve">48′. </s> <s xml:id="echoid-s15784" xml:space="preserve">adhuc ſe mi-<lb/>norem: </s> <s xml:id="echoid-s15785" xml:space="preserve">totam verò quartam, ideſt, ♈, ♉, ♊, quæ habet gr. </s> <s xml:id="echoid-s15786" xml:space="preserve">90. </s> <s xml:id="echoid-s15787" xml:space="preserve">habere aſcenſionem rectam gr. </s> <s xml:id="echoid-s15788" xml:space="preserve">90. </s> <s xml:id="echoid-s15789" xml:space="preserve">ſibi æqua-<lb/>lem. </s> <s xml:id="echoid-s15790" xml:space="preserve">idem pulchrè contemplari poteris inſphæra materiali promouendo lente primum mobile ad occiden <lb/>tem, & </s> <s xml:id="echoid-s15791" xml:space="preserve">interim dum partes Zodiaci meridianum pertranſeunt, vel horizontem rectũ, intuere partes æqua-<lb/>toris eas concomitantes, & </s> <s xml:id="echoid-s15792" xml:space="preserve">oculis ipſis rem totam percipies, & </s> <s xml:id="echoid-s15793" xml:space="preserve">intelliges. </s> <s xml:id="echoid-s15794" xml:space="preserve">de alijs verò quartis tibi iudi-<lb/>candum relinquo.</s> <s xml:id="echoid-s15795" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div367" type="section" level="1" n="263"> <head xml:id="echoid-head280" style="it" xml:space="preserve">Lumen affixarum. Cap. XII.</head> <p> <s xml:id="echoid-s15796" xml:space="preserve">QVæritur num recipiant lumen à Sole, ac proinde aliena Solis luce reſplendeant, ſicuti Luna, Venus, & </s> <s xml:id="echoid-s15797" xml:space="preserve"><lb/>cæteri planetæ. </s> <s xml:id="echoid-s15798" xml:space="preserve">Reſpondeo igitur probabiliter exiſtimandum eſſe, eas a Sole luminum parente collu-<lb/>ſtrari, lucemq; </s> <s xml:id="echoid-s15799" xml:space="preserve">ab eo gratis acceptam, gratis quoque terrigenis mortalibus reflectere: </s> <s xml:id="echoid-s15800" xml:space="preserve">vmbras vero <lb/>omnes ſurſum proijcere: </s> <s xml:id="echoid-s15801" xml:space="preserve">quæ quantæ ſint nimis curioſum eſt indagare. </s> <s xml:id="echoid-s15802" xml:space="preserve">Ego tamen poſita earum à Sole di-<lb/>ſtantia 13000. </s> <s xml:id="echoid-s15803" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s15804" xml:space="preserve">terræ, comperi ſtellas primæ magnitudinis vmbram proijcere ſemid. </s> <s xml:id="echoid-s15805" xml:space="preserve">terræ 65000. </s> <s xml:id="echoid-s15806" xml:space="preserve">lon-<lb/>gam, quod ſane mirum eſt. </s> <s xml:id="echoid-s15807" xml:space="preserve">conicæ tamen erunt, quoniam affixæ primæ magnitudinis ſunt minores Sole, <lb/>vt mox apparebit.</s> <s xml:id="echoid-s15808" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15809" xml:space="preserve">Sed cur ſcintillant, & </s> <s xml:id="echoid-s15810" xml:space="preserve">præ cæteris nonnullæ maximè, vti Procyon, & </s> <s xml:id="echoid-s15811" xml:space="preserve">Syrius? </s> <s xml:id="echoid-s15812" xml:space="preserve">Exiſtimo ſcintillationem <lb/>ſtellarum nihil aliud eſſe quam tremorem quendam luminis apparẽtem propter intercurſantium vaporum <lb/>variam infractionem. </s> <s xml:id="echoid-s15813" xml:space="preserve">cuius rei primum ſit argumentum, quòd illæ, magis ſcintillant, quæ horizonti propio-<lb/>res ſunt, vbi ſcilicet maior halituum aſcendentium turba exiſtit; </s> <s xml:id="echoid-s15814" xml:space="preserve">quæ verò vertici propiores, minus, vbi vide-<lb/>licet halituum minor multiplicatio exiſtit, ita vt ſupra 45. </s> <s xml:id="echoid-s15815" xml:space="preserve">gr. </s> <s xml:id="echoid-s15816" xml:space="preserve">altitudinis ab horizonte (vbi ſecundum proba-<lb/>tiores Aſtronomos, ſenſibilis refractio deſinit) nihil micent. </s> <s xml:id="echoid-s15817" xml:space="preserve">ſecundum ſit, quod Luna, Sol, & </s> <s xml:id="echoid-s15818" xml:space="preserve">quoduis aliud <lb/>obiectum ob fumum interpoſitum tremere videntur, qui tremor, ſi parua eſſent obiecta ſecundum apparen-<lb/>tiam, vti ſunt ſtellæ, diceretur ſcintillatio. </s> <s xml:id="echoid-s15819" xml:space="preserve">qui tremor tanto magis apparet, quãto longius à nobis obiectum <lb/>fuerit. </s> <s xml:id="echoid-s15820" xml:space="preserve">quare minimè mirum ſit, ſi cæteris paribus planetæ, qui nobis propiores ſunt quam fixæ, minorem <lb/>quoq; </s> <s xml:id="echoid-s15821" xml:space="preserve">quam ipſæ ſcintilationem exhibent. </s> <s xml:id="echoid-s15822" xml:space="preserve">præterea planetæ cum ſint affixis maiores, magnitudine hac ſua, <lb/>melius refractioni, ac tremori reſiſtunt, vti de Sole, & </s> <s xml:id="echoid-s15823" xml:space="preserve">Luna ſupra tactum eſt. </s> <s xml:id="echoid-s15824" xml:space="preserve">Lapilli ſub currenti aqua tre-<lb/>muli, & </s> <s xml:id="echoid-s15825" xml:space="preserve">veluti ſcintillantes ſpectantur; </s> <s xml:id="echoid-s15826" xml:space="preserve">quippe quod in ſtellis efficlt intercurſans halitus, in lapillis ſupra cur-<lb/>rens aqua efficiat. </s> <s xml:id="echoid-s15827" xml:space="preserve">Porrò Procyon, & </s> <s xml:id="echoid-s15828" xml:space="preserve">Sirius, quamuis magnitudine ſua nonnullos planetas adæquent, valde <lb/>tamenſcintillant, quoniam in noſtris regionibus vix ad altitudinem 45. </s> <s xml:id="echoid-s15829" xml:space="preserve">graduum aſcendunt, ſed vt pluri-<lb/>mum propè horizontem pone multos vapores incedunt, ac propterea tremuli, & </s> <s xml:id="echoid-s15830" xml:space="preserve">micantes apparent, idque <lb/>minus quò altius meant. </s> <s xml:id="echoid-s15831" xml:space="preserve">vide P. </s> <s xml:id="echoid-s15832" xml:space="preserve">Chriſtophorum Scheiner de cæleſtibus refractionibus.</s> <s xml:id="echoid-s15833" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div368" type="section" level="1" n="264"> <head xml:id="echoid-head281" style="it" xml:space="preserve">Figura affixarum. Cap. XIII.</head> <p> <s xml:id="echoid-s15834" xml:space="preserve">OStenſum eſt Terrã, Aquam, Lunam, Venerem, Solem, globoſa eſſe corpora; </s> <s xml:id="echoid-s15835" xml:space="preserve">vnde pariter reliquos Pla-<lb/>netos globoſos eſſe credidimus. </s> <s xml:id="echoid-s15836" xml:space="preserve">ijſdem igitur rationibus exiſtimandum eſt inerrantes quoq; </s> <s xml:id="echoid-s15837" xml:space="preserve">ſphærica fi-<lb/>gura eſſe præditas.</s> <s xml:id="echoid-s15838" xml:space="preserve"/> </p> <pb o="182" file="0204" n="209" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div369" type="section" level="1" n="265"> <head xml:id="echoid-head282" style="it" xml:space="preserve">Magnitudines affixarum. Cap. XIIII.</head> <p> <s xml:id="echoid-s15839" xml:space="preserve">QVemadmodum in cæter is aſtris duo neceſſaria fuerunt ad eorum veras magnitudines indagandas, ita <lb/>etiam in affixis, diſtantia videlicet earum a<unsure/> medio Mundi; </s> <s xml:id="echoid-s15840" xml:space="preserve">necnon earum apparens diameter. </s> <s xml:id="echoid-s15841" xml:space="preserve">Porrò <lb/>veteres Aſtrologiæ cultores, Hipparchus, & </s> <s xml:id="echoid-s15842" xml:space="preserve">Ptolemæus hanc partem veluti abſtruſam, & </s> <s xml:id="echoid-s15843" xml:space="preserve">altam, <lb/>attingere non ſunt auſi. </s> <s xml:id="echoid-s15844" xml:space="preserve">Albategnius tamen vir Arabs improbo auxu affixarum etiam magnitudines ſubti-<lb/>liter admodum aggreſſus eſt; </s> <s xml:id="echoid-s15845" xml:space="preserve">quas poſtea recentiores multo adhuc certius depræhenderunt: </s> <s xml:id="echoid-s15846" xml:space="preserve">vt igitur vtro-<lb/>rumq; </s> <s xml:id="echoid-s15847" xml:space="preserve">ſubtiliſſimas indagationes explicemus, præmittenda prius ſunt illa duo, quæ modo commemoraui. <lb/></s> <s xml:id="echoid-s15848" xml:space="preserve">Ac primo de earum diſtantia à medio ſic ſtatuendum; </s> <s xml:id="echoid-s15849" xml:space="preserve">cum oſtenſum ſit ex Tychone ſupremos Saturni cir-<lb/>cuitus à medio attolli ſemidiametris terræ 12′900′. </s> <s xml:id="echoid-s15850" xml:space="preserve">conueniens eſſe putandum eſt, affixas paulò altius collo-<lb/>catas eſie. </s> <s xml:id="echoid-s15851" xml:space="preserve">præterea cùm craſſities firmamenti incerta ſit, ac proinde incertnm an omnes affixæ ſint in eadem <lb/>altitudine, vtaliquid medio loco ſtatuamus, ſtatuemus cum recentioribus affixas à centro terræ ſemidiam. </s> <s xml:id="echoid-s15852" xml:space="preserve"><lb/>terræ 14′000′. </s> <s xml:id="echoid-s15853" xml:space="preserve">plus minus attolli. </s> <s xml:id="echoid-s15854" xml:space="preserve">Secundo de earum apparenti diametro: </s> <s xml:id="echoid-s15855" xml:space="preserve">diligenti inſpectatione habita <lb/>depræhenſa eſt diameter apparens ſtellarum primæ magnitudinis minuta 2′. </s> <s xml:id="echoid-s15856" xml:space="preserve">adimplere. </s> <s xml:id="echoid-s15857" xml:space="preserve">talibus præmiſſis <lb/>hanc Albategnius in libro de ſcientia Stellarum inibat rationem. </s> <s xml:id="echoid-s15858" xml:space="preserve">imaginabatur triangulum vti præſens, in <lb/>quo E C. </s> <s xml:id="echoid-s15859" xml:space="preserve">referret mediocrem Solis à terra diſtantiam, quæ eſt 1142. </s> <s xml:id="echoid-s15860" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s15861" xml:space="preserve">terra. </s> <s xml:id="echoid-s15862" xml:space="preserve">C D. </s> <s xml:id="echoid-s15863" xml:space="preserve">referret ſemidiame-<lb/> <anchor type="figure" xlink:label="fig-0204-01a" xlink:href="fig-0204-01"/> trum Solis apparentem, min. <lb/></s> <s xml:id="echoid-s15864" xml:space="preserve">15 {1/2}. </s> <s xml:id="echoid-s15865" xml:space="preserve">E A, referret diſtantiam <lb/>affixarum prædictam, ideſt, <lb/>ſemidiam. </s> <s xml:id="echoid-s15866" xml:space="preserve">14′000′. </s> <s xml:id="echoid-s15867" xml:space="preserve">A B. </s> <s xml:id="echoid-s15868" xml:space="preserve">refer-<lb/>ret ſemidiametrum Solis ap-<lb/>parentem in firmamento, vbi <lb/>ſunt aſſixæ, ſiue interuallum <lb/>illud, quodapparẽs ſemidiam. </s> <s xml:id="echoid-s15869" xml:space="preserve"><lb/>Solis in firmamento occupare <lb/>videtur. </s> <s xml:id="echoid-s15870" xml:space="preserve">quoniam vero diame-<lb/>ter apparens Stellæ primi ordinis eſt min. </s> <s xml:id="echoid-s15871" xml:space="preserve">2′. </s> <s xml:id="echoid-s15872" xml:space="preserve">ideo erit ferè pars octaua totius A B. </s> <s xml:id="echoid-s15873" xml:space="preserve">repræſentetur igitur in <lb/>A F. </s> <s xml:id="echoid-s15874" xml:space="preserve">parte octaua totius A B. </s> <s xml:id="echoid-s15875" xml:space="preserve">quoniam igitur ſunt duo triangula ſimilia E C D. </s> <s xml:id="echoid-s15876" xml:space="preserve">E A B. </s> <s xml:id="echoid-s15877" xml:space="preserve">erit vt E C. </s> <s xml:id="echoid-s15878" xml:space="preserve">ad C D. </s> <s xml:id="echoid-s15879" xml:space="preserve"><lb/>ita E A. </s> <s xml:id="echoid-s15880" xml:space="preserve">ad A B. </s> <s xml:id="echoid-s15881" xml:space="preserve">ideſt, erit vt 1142. </s> <s xml:id="echoid-s15882" xml:space="preserve">ad min. </s> <s xml:id="echoid-s15883" xml:space="preserve">15 {1/2}. </s> <s xml:id="echoid-s15884" xml:space="preserve">ita 14′000′. </s> <s xml:id="echoid-s15885" xml:space="preserve">ad 190. </s> <s xml:id="echoid-s15886" xml:space="preserve">ferè per auream regulã. </s> <s xml:id="echoid-s15887" xml:space="preserve">qui numerus 190. </s> <s xml:id="echoid-s15888" xml:space="preserve"><lb/>ſignificat in interuallo A B. </s> <s xml:id="echoid-s15889" xml:space="preserve">contineri min. </s> <s xml:id="echoid-s15890" xml:space="preserve">190. </s> <s xml:id="echoid-s15891" xml:space="preserve">ex ijs, ſiue eiuſdem magnitudinis cum min. </s> <s xml:id="echoid-s15892" xml:space="preserve">15 {1/2} quæ ſunt in <lb/>C D. </s> <s xml:id="echoid-s15893" xml:space="preserve">quia verò A F. </s> <s xml:id="echoid-s15894" xml:space="preserve">eſt pars ferè octaua totius A B. </s> <s xml:id="echoid-s15895" xml:space="preserve">ſiue min. </s> <s xml:id="echoid-s15896" xml:space="preserve">190. </s> <s xml:id="echoid-s15897" xml:space="preserve">erit A F. </s> <s xml:id="echoid-s15898" xml:space="preserve">min. </s> <s xml:id="echoid-s15899" xml:space="preserve">circiter 24′. </s> <s xml:id="echoid-s15900" xml:space="preserve">ex ijs, quorum <lb/>15 {1/2}. </s> <s xml:id="echoid-s15901" xml:space="preserve">conflant ſemidiam. </s> <s xml:id="echoid-s15902" xml:space="preserve">Solis. </s> <s xml:id="echoid-s15903" xml:space="preserve">31′. </s> <s xml:id="echoid-s15904" xml:space="preserve">verò totam diametrum Solis. </s> <s xml:id="echoid-s15905" xml:space="preserve">quare proportio diametri Stellæ ad diame-<lb/>trum Solis, erit vt 24. </s> <s xml:id="echoid-s15906" xml:space="preserve">ad 31. </s> <s xml:id="echoid-s15907" xml:space="preserve">ſiue fere vt 4. </s> <s xml:id="echoid-s15908" xml:space="preserve">ad 5. </s> <s xml:id="echoid-s15909" xml:space="preserve">quare & </s> <s xml:id="echoid-s15910" xml:space="preserve">proportio ſphærarum erit ferè ſubdupla, ideſt, vna ex <lb/>dictis Stellis erit quaſi dimidia Solis, porrò cum Sol ad terram ſit vt 140. </s> <s xml:id="echoid-s15911" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s15912" xml:space="preserve">Stella, quæ eſt Solis medietas <lb/>erit vt 70 ad terram, ideſt, terram ſeptuagies adæquabit.</s> <s xml:id="echoid-s15913" xml:space="preserve"/> </p> <div xml:id="echoid-div369" type="float" level="2" n="1"> <figure xlink:label="fig-0204-01" xlink:href="fig-0204-01a"> <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0204-01"/> </figure> </div> <p> <s xml:id="echoid-s15914" xml:space="preserve">Aliter ex ijſdem præmiſſis ex Tychone ſic; </s> <s xml:id="echoid-s15915" xml:space="preserve">cum habeamus ſemidiametrum firmamenti cognitam in ſe-<lb/>midiametris terræ, habebimus etiam eiuſdem ſemicircumferentiam in ijſdem ſemidiametris, eſt enim ſe-<lb/>midiameter ad circumferentiam vt 7. </s> <s xml:id="echoid-s15916" xml:space="preserve">ad 22. </s> <s xml:id="echoid-s15917" xml:space="preserve">igitur per auream regulam, erit vt 7. </s> <s xml:id="echoid-s15918" xml:space="preserve">ad 22. </s> <s xml:id="echoid-s15919" xml:space="preserve">ita 14′000′. </s> <s xml:id="echoid-s15920" xml:space="preserve">ad <lb/>44′000′. </s> <s xml:id="echoid-s15921" xml:space="preserve">ſemicirculum firmamenti. </s> <s xml:id="echoid-s15922" xml:space="preserve">videndum nunc eſt, vnum minutum firmamenti quot ſemid ametros <lb/>contineat. </s> <s xml:id="echoid-s15923" xml:space="preserve">diuidantur ergo 44′000′. </s> <s xml:id="echoid-s15924" xml:space="preserve">vel breuitatis cauſa 22000. </s> <s xml:id="echoid-s15925" xml:space="preserve">ſemidiametri per gradus 90. </s> <s xml:id="echoid-s15926" xml:space="preserve">ideſt, per mi-<lb/>nuta 5400. </s> <s xml:id="echoid-s15927" xml:space="preserve">ſic enim diuidetur quadrans per quadrantem; </s> <s xml:id="echoid-s15928" xml:space="preserve">erit autem quotiens 4 {1/15} ferè. </s> <s xml:id="echoid-s15929" xml:space="preserve">quare vnum minu-<lb/>tum firmamenti continet ſemidiam. </s> <s xml:id="echoid-s15930" xml:space="preserve">4 {1/13}. </s> <s xml:id="echoid-s15931" xml:space="preserve">Et quia diameter apparens Stellæ eſt min. </s> <s xml:id="echoid-s15932" xml:space="preserve">2. </s> <s xml:id="echoid-s15933" xml:space="preserve">ideo apparens Stellæ <lb/>diameter continebit 8 {2/13}. </s> <s xml:id="echoid-s15934" xml:space="preserve">ſemidiam. </s> <s xml:id="echoid-s15935" xml:space="preserve">terræ, ideſt, diametros terra 4 {1/3}. </s> <s xml:id="echoid-s15936" xml:space="preserve">cum ergo nota ſit proportio diametro-<lb/>rum, nota quoq; </s> <s xml:id="echoid-s15937" xml:space="preserve">euadet proportio ſphærarum, eadem ferè quæ ſupra, vt 70. </s> <s xml:id="echoid-s15938" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s15939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15940" xml:space="preserve">Aliter tandem practicè ex conſtructione trianguli iſoſcelis, cuius latera contineant ſemidiam. </s> <s xml:id="echoid-s15941" xml:space="preserve">terræ 1400 <lb/>baſis vero contineat min. </s> <s xml:id="echoid-s15942" xml:space="preserve">2. </s> <s xml:id="echoid-s15943" xml:space="preserve">vt in planetis fecimus.</s> <s xml:id="echoid-s15944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15945" xml:space="preserve">Eadem methodo reperit Tycho Stel@as ſecundæ claſſis terræ molem continere vicies, & </s> <s xml:id="echoid-s15946" xml:space="preserve">octies, ideſt, eas <lb/>eſſe ad terram, vt 28. </s> <s xml:id="echoid-s15947" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s15948" xml:space="preserve">Stellas tertij ordinis eſſe ad terram, vt 11. </s> <s xml:id="echoid-s15949" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s15950" xml:space="preserve">quarti honoris eſſe ad terram vt 27. <lb/></s> <s xml:id="echoid-s15951" xml:space="preserve">ad 8. </s> <s xml:id="echoid-s15952" xml:space="preserve">quinti paulo terram ſuperare. </s> <s xml:id="echoid-s15953" xml:space="preserve">ſexti paulo a terra ſuperari. </s> <s xml:id="echoid-s15954" xml:space="preserve">Atq; </s> <s xml:id="echoid-s15955" xml:space="preserve">hæc de affixis iam inde ab origine mun-<lb/>di cognitis ſufficiant, nunc ad nuper cognitas, ac mortalibus noua tranſeamus.</s> <s xml:id="echoid-s15956" xml:space="preserve"/> </p> <pb o="183" file="0205" n="210"/> </div> <div xml:id="echoid-div371" type="section" level="1" n="266"> <head xml:id="echoid-head283" xml:space="preserve">LIBER DECIMVSOCTAVVS <lb/>DE NOVIS STELLIS.</head> <head xml:id="echoid-head284" style="it" xml:space="preserve">Nouas Stellas aliquando apparere. Cap. I.</head> <p> <s xml:id="echoid-s15957" xml:space="preserve">QVemadmodum in ea cæli parte, quæ planetarum regio eſt, non rarò adſcititij, ac neoterici <lb/>planetæ apparent, qui Cometæ dicuntur, quippe qui naturam illius regionis errat cam @@o <lb/>particulari modo imitantur: </s> <s xml:id="echoid-s15958" xml:space="preserve">ita etiam in firmamento, quæ affixarum regio eſt, noua Mun-<lb/>do ſpectacula aliquando præbent repentina ſydera, quæ firmam cæleſtis illius partis natu-<lb/>ram ſequuntur; </s> <s xml:id="echoid-s15959" xml:space="preserve">atque omnia inerrantium accidentia pro tempore, imitantur. </s> <s xml:id="echoid-s15960" xml:space="preserve">conuenien@ <lb/>igitur eſt, vt abſoluta ęternarum ſtellarum tractatione de nouis nunc diſſeramus. </s> <s xml:id="echoid-s15961" xml:space="preserve">Naſci igi-<lb/>tur noua interdum ſydera teſtis eſt Plinius qui lib. </s> <s xml:id="echoid-s15962" xml:space="preserve">2. </s> <s xml:id="echoid-s15963" xml:space="preserve">cap. </s> <s xml:id="echoid-s15964" xml:space="preserve">24. </s> <s xml:id="echoid-s15965" xml:space="preserve">de repentinis ſyderibus, ſic in-<lb/>quit; </s> <s xml:id="echoid-s15966" xml:space="preserve">namque & </s> <s xml:id="echoid-s15967" xml:space="preserve">in ipſo cælo ſtellæ repente naſcuntur. </s> <s xml:id="echoid-s15968" xml:space="preserve">rurſus cap. </s> <s xml:id="echoid-s15969" xml:space="preserve">26. </s> <s xml:id="echoid-s15970" xml:space="preserve">de quadam tempore Hipparchi exorta <lb/>ſtella, hæc habet illuſtria, atq; </s> <s xml:id="echoid-s15971" xml:space="preserve">magnifica verba. </s> <s xml:id="echoid-s15972" xml:space="preserve">Idem Hipparchus nunquam ſatis laudatus, vt quo nemo ma-<lb/>gis approbauerit cognationem cum homine ſyderum, animaſq; </s> <s xml:id="echoid-s15973" xml:space="preserve">noſtras cœlo dignas eſſe; </s> <s xml:id="echoid-s15974" xml:space="preserve">Nouam Stellam, <lb/>& </s> <s xml:id="echoid-s15975" xml:space="preserve">aliam ſuo æuo genitam depræhendit, eiuſq; </s> <s xml:id="echoid-s15976" xml:space="preserve">motu, quo die fulſit ad dubitationem eſt adductus anne hoc <lb/>ſæpius fieret, mouerenturque & </s> <s xml:id="echoid-s15977" xml:space="preserve">eæ, quas putamus affixas: </s> <s xml:id="echoid-s15978" xml:space="preserve">idemq; </s> <s xml:id="echoid-s15979" xml:space="preserve">auſus rem etiam Deo improbam annume-<lb/>rare poſteris ſtellas, ſyderaq; </s> <s xml:id="echoid-s15980" xml:space="preserve">ad normam expangere organis excogitatis, per quæ ſingularum loca, & </s> <s xml:id="echoid-s15981" xml:space="preserve">magni-<lb/>tudines ſignaret, vt facilè ex eo decerni poſſet, non modo an obirent, naſcerenturuè; </s> <s xml:id="echoid-s15982" xml:space="preserve">item an creſcerent, mi-<lb/>nuerenturuè, cælo in hæreditate cunctis relicto, ſi quiſpiam, qui rationẽ eam caperet inuentus eſſet. </s> <s xml:id="echoid-s15983" xml:space="preserve">hæc Pli-<lb/>nius. </s> <s xml:id="echoid-s15984" xml:space="preserve">vixit autem Hipparchus ſecũdum noſtra clarorum Mathematicorum Chronologiam ante Chriſti Do-<lb/>mini aduentum annis ferè 125.</s> <s xml:id="echoid-s15985" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15986" xml:space="preserve">Hanc vero Hipparchi re vera Stellam, non autem Cometam fuiſſe omnes fermè præſertim probatiſſimi <lb/>noſtri temporis Aſtronomi conſenſere. </s> <s xml:id="echoid-s15987" xml:space="preserve">quod mirum enim ſi Cometa tunc apparuiſſet? </s> <s xml:id="echoid-s15988" xml:space="preserve">nonne Cometarum <lb/>apparitiones adeò frequentes ſunt, vt nulla ſit penè cuiuſuis hominis ætas, quin plures ſe conſpiciendos præ-<lb/>beant. </s> <s xml:id="echoid-s15989" xml:space="preserve">quorſum enim tanta huius ſyderis commemoratio? </s> <s xml:id="echoid-s15990" xml:space="preserve">Præterea ſi Cometas fuiſſet; </s> <s xml:id="echoid-s15991" xml:space="preserve">cur inde Hipparchus <lb/>fuiſſet impulſus, vt inſtar alterius Atlantis, onus illum aſſumeret grauiſſimum, vt omnes firmamento affixas <lb/>organis obſeruatas, ac dinumeratas poſteris commendaret, vt inde conſtare poſſet, anne aliæ nouæ ſtellæ in <lb/>poſterum orirentur? </s> <s xml:id="echoid-s15992" xml:space="preserve">Quare nemini dubium ſit Hipparchum ſydus aliquod re vera recens cæteris perſimile, <lb/>& </s> <s xml:id="echoid-s15993" xml:space="preserve">à Cometis diuerſum ſuo tempore obſeruaſſe. </s> <s xml:id="echoid-s15994" xml:space="preserve">quale tamen, aut quantum tuerit, & </s> <s xml:id="echoid-s15995" xml:space="preserve">quandiu luxerit, cætera-<lb/>que accidentia ignorantur; </s> <s xml:id="echoid-s15996" xml:space="preserve">cum nec Plinius ea tradat, nec in operibus Hipparchi ſuperſtitibus, quod ſciam, <lb/>de ea, mentio vlla habeatur. </s> <s xml:id="echoid-s15997" xml:space="preserve">Atq; </s> <s xml:id="echoid-s15998" xml:space="preserve">hæc eſt prima ſtella, quam repentinam Mundo affulſiſſe ex hiſtorijs certo <lb/>affirmare liceat: </s> <s xml:id="echoid-s15999" xml:space="preserve">quamuis anteactis ſæculis plures alias; </s> <s xml:id="echoid-s16000" xml:space="preserve">ſed tamen non obſeruatas, effulſiſſe par ſit credere. <lb/></s> <s xml:id="echoid-s16001" xml:space="preserve">Hiſtoriographi enim non diſcernere norunt inter ſtellas nouiter exortas & </s> <s xml:id="echoid-s16002" xml:space="preserve">Cometas; </s> <s xml:id="echoid-s16003" xml:space="preserve">ſed quod magis ſolẽne <lb/>eſt omnes nuperas Cometis accenſent. </s> <s xml:id="echoid-s16004" xml:space="preserve">qui autem eas noſſent, aut animaduerterent pauciſſimi olim reprie-<lb/>bantur: </s> <s xml:id="echoid-s16005" xml:space="preserve">quapropter niſi magnæ, atq; </s> <s xml:id="echoid-s16006" xml:space="preserve">illuſtres valdè ext@terint, nemine eas adſpectante, ac ſuſpiciente ignotę <lb/>præterierunt. </s> <s xml:id="echoid-s16007" xml:space="preserve">quod maximè hinc comprobatur, quia hac noſtra ætate, qua non pauci ſtellarum obſeruatores <lb/>extiterunt, iam tres nouæ ſunt depræhenſæ, de quibus infra dicemus. </s> <s xml:id="echoid-s16008" xml:space="preserve">plures videlicet in annis 35. </s> <s xml:id="echoid-s16009" xml:space="preserve">quam in <lb/>anteactis quinque annorum millibus. </s> <s xml:id="echoid-s16010" xml:space="preserve">Quapropter ſi ſtellarum, ac cæleſtis militiæ haberemus excubias, non <lb/>deeſſent ſingulis ætatibus ſua ſydera aduentitia.</s> <s xml:id="echoid-s16011" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div372" type="section" level="1" n="267"> <head xml:id="echoid-head285" style="it" xml:space="preserve">De Stella noua Caſſiopeæ anni 1572. Cap. II.</head> <p> <s xml:id="echoid-s16012" xml:space="preserve">ASæculo Hipparchi vſq; </s> <s xml:id="echoid-s16013" xml:space="preserve">ad annum Domini 1572. </s> <s xml:id="echoid-s16014" xml:space="preserve">interceſſere anni amplius 1170. </s> <s xml:id="echoid-s16015" xml:space="preserve">quibus nouum ſydus in <lb/>octaua ſphæra effulſiſle certo affirmare non auſim, etiamſi ob rationes ante allatas id credam, idemque <lb/>nonnulli, dubia tamen ſcriptorum authoritate, affirmare cupiant. </s> <s xml:id="echoid-s16016" xml:space="preserve">de hoc igitur, quoniam in ſe multa conti-<lb/>net admiranda deinceps ſummatim dicendum erit. </s> <s xml:id="echoid-s16017" xml:space="preserve">Igitur circa initium Nouembris anni 1572. </s> <s xml:id="echoid-s16018" xml:space="preserve">labentis, hęc <lb/>primo toti mundo in conſtellatione Caſſiopeæ illuxit, atq; </s> <s xml:id="echoid-s16019" xml:space="preserve">oculos omniũ ad ſe alliciens conſpecta eſt; </s> <s xml:id="echoid-s16020" xml:space="preserve">quam-<lb/>uis putem prius exortam eſſe, & </s> <s xml:id="echoid-s16021" xml:space="preserve">quidem minorem, ſed non animaduerſam, quis enim ad ſtellas ſingulis no-<lb/>ctibus cuſtodias, aut vigilias adhibet? </s> <s xml:id="echoid-s16022" xml:space="preserve">at niſi nouum ſydus ſua magnitudine, ac ſplendore ſe oſtentet, quis il-<lb/>lud animaduertat? </s> <s xml:id="echoid-s16023" xml:space="preserve">Durauit autem per totum annum ſequentem 1573. </s> <s xml:id="echoid-s16024" xml:space="preserve">& </s> <s xml:id="echoid-s16025" xml:space="preserve">inſuper vſque ad menſem Martij <lb/>anni 1574. </s> <s xml:id="echoid-s16026" xml:space="preserve">Forma eius fuit rotunda ſicuti aliarum ſtellarum, ſcintillantes radios vndiq; </s> <s xml:id="echoid-s16027" xml:space="preserve">eiaculans. </s> <s xml:id="echoid-s16028" xml:space="preserve">Magni-<lb/>tudo eius apparens ab initio omnes affixas, etiam primi honoris excedebat, ita vt maximum Veneris iubar <lb/>proximè æmularetur, albicante, claro, ac ſplendenti lumine. </s> <s xml:id="echoid-s16029" xml:space="preserve">& </s> <s xml:id="echoid-s16030" xml:space="preserve">non ſecus ac Venus in ipſo meridie, aere, ſe-<lb/>reno diſcretè videretur; </s> <s xml:id="echoid-s16031" xml:space="preserve">quam magnitudinem paulatim minuebat, donec prorſus euaneſceret.</s> <s xml:id="echoid-s16032" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16033" xml:space="preserve">LOCVS eius in firmamento fuit inter Caſſiopeæ ſtellas in cathedra, in confinio via lactea boreali, diſta-<lb/>bat à polo mundi arctico gr. </s> <s xml:id="echoid-s16034" xml:space="preserve">28. </s> <s xml:id="echoid-s16035" xml:space="preserve">13′. </s> <s xml:id="echoid-s16036" xml:space="preserve">igitur eius declinatio fuit gr. </s> <s xml:id="echoid-s16037" xml:space="preserve">61. </s> <s xml:id="echoid-s16038" xml:space="preserve">47′. </s> <s xml:id="echoid-s16039" xml:space="preserve">longitudo eius gr. </s> <s xml:id="echoid-s16040" xml:space="preserve">36. </s> <s xml:id="echoid-s16041" xml:space="preserve">54′. </s> <s xml:id="echoid-s16042" xml:space="preserve">ideſt, in <lb/>gr. </s> <s xml:id="echoid-s16043" xml:space="preserve">7. </s> <s xml:id="echoid-s16044" xml:space="preserve">♉. </s> <s xml:id="echoid-s16045" xml:space="preserve">latitudo eius gr. </s> <s xml:id="echoid-s16046" xml:space="preserve">54. </s> <s xml:id="echoid-s16047" xml:space="preserve">Porrò retinuit ſemper eandem circumuicinis ſtellis diſtantiam, & </s> <s xml:id="echoid-s16048" xml:space="preserve">poſitionem <lb/>vſq; </s> <s xml:id="echoid-s16049" xml:space="preserve">ad finem quare in firmamento mobili hæſit.</s> <s xml:id="echoid-s16050" xml:space="preserve"/> </p> <pb o="184" file="0206" n="211" rhead="De Mundi Fabrica,"/> <p> <s xml:id="echoid-s16051" xml:space="preserve">MOTVS igitur ei proprius nullus fuit, ſed ſola conuerſione diurna reuoluebatur.</s> <s xml:id="echoid-s16052" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16053" xml:space="preserve">DISTANTIA eius à centro Mundi. </s> <s xml:id="echoid-s16054" xml:space="preserve">Aio vna cum omnibus Aſtronomiæ conſultiſſimis, qui eam ſum-<lb/>ma diligentia obſeruarunt, eam ſupra omnia elementa, ac ſupra omnes planetarum regiones in ſirmamento <lb/>inter affixas effulſiſſe. </s> <s xml:id="echoid-s16055" xml:space="preserve">Primo quia forma eius, & </s> <s xml:id="echoid-s16056" xml:space="preserve">ſpecies cæteris inerrantibus erat ſimillima. </s> <s xml:id="echoid-s16057" xml:space="preserve">Secundo quia <lb/>lumine claro, & </s> <s xml:id="echoid-s16058" xml:space="preserve">puro genuinas firmamenti ſtellas æmulabatur. </s> <s xml:id="echoid-s16059" xml:space="preserve">Tertio ſcintillatio eximia, ac præ cæteris lu-<lb/>minibus corruſcans apertè indicabat eam inter micantia ſydera, quibus propriè, ac ſemper ea competit ſibi <lb/>locum vindicaſſe. </s> <s xml:id="echoid-s16060" xml:space="preserve">Quarto immobilitas eius in eodem firmamenti loco idem atteſtatur; </s> <s xml:id="echoid-s16061" xml:space="preserve">quod euidens argu-<lb/>mentum eſt eam in parte cæli inerrante extitiſſe. </s> <s xml:id="echoid-s16062" xml:space="preserve">Cometæ enim quia in parte cæli errante exoriuntur, ideo <lb/>ſicuti planetæ genuini, motu proprio pererrant.</s> <s xml:id="echoid-s16063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16064" xml:space="preserve">Verum Aſtronomicas rationes, & </s> <s xml:id="echoid-s16065" xml:space="preserve">quidem fortiores afferamus, eas nimirum quæ à parallaxibus petuntur. <lb/></s> <s xml:id="echoid-s16066" xml:space="preserve">Primus modus indagandæ parallaxeos eſt hic. </s> <s xml:id="echoid-s16067" xml:space="preserve">ſi ſtella in diurna conuerſione ſeruauerit ſemper eandem di-<lb/>ſtantiam a vicinioribus ſtellis, ideſt, tam propè horizontem, quam propè verticem, nullam exhibet paralla. </s> <s xml:id="echoid-s16068" xml:space="preserve"><lb/> <anchor type="figure" xlink:label="fig-0206-01a" xlink:href="fig-0206-01"/> xim. </s> <s xml:id="echoid-s16069" xml:space="preserve">ſi verò diſtantiam variat parallaxim habet. </s> <s xml:id="echoid-s16070" xml:space="preserve">Exemplo ſit figu. <lb/></s> <s xml:id="echoid-s16071" xml:space="preserve">ra, in qua terra E F. </s> <s xml:id="echoid-s16072" xml:space="preserve">I K. </s> <s xml:id="echoid-s16073" xml:space="preserve">cælum ſtellæ nouæ obſeruandæ H L G <lb/>meridiano in firmamento deſcriptus. </s> <s xml:id="echoid-s16074" xml:space="preserve">L, polus arcticus circa quem <lb/>ſtella noua gybat. </s> <s xml:id="echoid-s16075" xml:space="preserve">Loca eius obſeruata erant in meridiano, in eo <lb/>enim modo apparebat humillima, vt in B, inferiori; </s> <s xml:id="echoid-s16076" xml:space="preserve">modo altiſſi-<lb/>ma vt in B, ſuperiori. </s> <s xml:id="echoid-s16077" xml:space="preserve">obſeruator ſit in E, ſuperficie terræ: </s> <s xml:id="echoid-s16078" xml:space="preserve">ſi igitur <lb/>ſtella obſeruanda fuerit infra firmamentum in gyro I K, obſerua-<lb/>tor eam videat primo in B, inferiori in firmamento eritque B, lo-<lb/>cus verus viſus, verus vero ſit A, & </s> <s xml:id="echoid-s16079" xml:space="preserve">ducatur linea F A: </s> <s xml:id="echoid-s16080" xml:space="preserve">erit igitur <lb/>arcus B A, parallaxis ſtellæ. </s> <s xml:id="echoid-s16081" xml:space="preserve">ſit etiam apud ſtellam C, fixam. </s> <s xml:id="echoid-s16082" xml:space="preserve">poſtea <lb/>ob conuerſionem diurnam quando ſtella erit in I, apparebit in al-<lb/>tero B, altiſſima, eritq; </s> <s xml:id="echoid-s16083" xml:space="preserve">eius locus verus A, ſupra B, viſum, vt prius; </s> <s xml:id="echoid-s16084" xml:space="preserve"><lb/>ſed tamen propinquior eidem ſtellæ C, quæ modo infra A, erit, ſed <lb/>vicinior loco viſo B. </s> <s xml:id="echoid-s16085" xml:space="preserve">hæc autem diſtantia inter B C, erit nunc mi-<lb/>nor, quia vt alias dictum eſt, parallaxis B A, minor eſt propè verti-<lb/>cem, quam propè horizontem. </s> <s xml:id="echoid-s16086" xml:space="preserve">quod quidem euenit ſi ſtella ſit in-<lb/>fra firmamentum. </s> <s xml:id="echoid-s16087" xml:space="preserve">ſi verò ſtella obſeruanda ſit in ipſo firmamento-<unsure/> <lb/>vtin B, vbi apparet, retinebit ſemper e<unsure/>andem diſtantiam ab affixa C, tam infra polum, quam ſupra. </s> <s xml:id="echoid-s16088" xml:space="preserve">ratio eſt, <lb/>quia linea viſiua E B, nullibi ſecabit linea F A, ſed in firmamento vtraque ſeparatim deſinet, ideſt, nulla erit <lb/>parallaxis, quæ ſtellam B, nouam, ſtellæ fixæ C, apud verticem magis vniat, quàm apud horizontem, vt fi-<lb/>guram conſideranti patet. </s> <s xml:id="echoid-s16089" xml:space="preserve">quoniam verò ſtella noua anni 1572. </s> <s xml:id="echoid-s16090" xml:space="preserve">ſeruauit ſemper eandem diſtantiam ab ijſdẽ <lb/>vicinis ſtellis, tam propè horizontem, quam propè verticem, ideo nullam habebat parallaxim, & </s> <s xml:id="echoid-s16091" xml:space="preserve">conſequen-<lb/>ter altiſſima erat à medio.</s> <s xml:id="echoid-s16092" xml:space="preserve"/> </p> <div xml:id="echoid-div372" type="float" level="2" n="1"> <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a"> <image file="0206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0206-01"/> </figure> </div> <p> <s xml:id="echoid-s16093" xml:space="preserve">Aliter parallaxim ad polum L, perſcrutantur; </s> <s xml:id="echoid-s16094" xml:space="preserve">ſi enim Stella B, tam infra, quam ſupra polum ſemper æqui-<lb/>diſtiterit a polo, ſignum eſt nullam adeſſe parallaxim. </s> <s xml:id="echoid-s16095" xml:space="preserve">quod ſi propè horizontem infra polum, magis a polo <lb/>diſtiterit, quam ſupra, parallaxis adeſt. </s> <s xml:id="echoid-s16096" xml:space="preserve">vndc neceſſario ea ſtella infra firmamentum in regionibus erraticis <lb/>exiſtet. </s> <s xml:id="echoid-s16097" xml:space="preserve">Atqui noſtra ſtella in vtroq; </s> <s xml:id="echoid-s16098" xml:space="preserve">ſitu ſemper diſtitita polo exactè gr. </s> <s xml:id="echoid-s16099" xml:space="preserve">28. </s> <s xml:id="echoid-s16100" xml:space="preserve">13′. </s> <s xml:id="echoid-s16101" xml:space="preserve">ergo nulla ſuberat parallexis, <lb/>quæ eam in fra firmamentum detraheret.</s> <s xml:id="echoid-s16102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16103" xml:space="preserve">Aliter etiam, & </s> <s xml:id="echoid-s16104" xml:space="preserve">quidem ſolertur per ſolum filum, eo modo quo in Cometis.</s> <s xml:id="echoid-s16105" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16106" xml:space="preserve">Prædicti tres modi vſui ſunt in eodem obſeruatoris loco; </s> <s xml:id="echoid-s16107" xml:space="preserve">verum etiam ex diuetſis locis, diuerſiſq; </s> <s xml:id="echoid-s16108" xml:space="preserve">obſer-<lb/>uatoribus eam rimantur, vti ſuperius de Cometis diximus; </s> <s xml:id="echoid-s16109" xml:space="preserve">nam ſi aſtrum ſit infra firmamentum, atq; </s> <s xml:id="echoid-s16110" xml:space="preserve">ex locis <lb/>valdè diſſitis conſpiciatur, non apparebit vbiq; </s> <s xml:id="echoid-s16111" xml:space="preserve">locorum in eodem cæli puncto; </s> <s xml:id="echoid-s16112" xml:space="preserve">ſicuti enim cum plures in eo-<lb/>dem templo ex diuerſis locis pendentem Lychnum intuentur, eum iuxta diuerſum lacunaris punctum putãt <lb/>eſſe, quæ viſus varietas eſt quædam parallaxis. </s> <s xml:id="echoid-s16113" xml:space="preserve">ſi verò Lychnus ſit laqueari affixus, omnibus, qui ſunt in tẽplo <lb/>videtur eſſe in eodem loco, ideſt, nullam aſpectus diuerſitatem efficiet; </s> <s xml:id="echoid-s16114" xml:space="preserve">ſic firmamentum eſt Mundi lacunar, <lb/>Lychni ſunt ſydera; </s> <s xml:id="echoid-s16115" xml:space="preserve">quornm quæ infra ipſum ceu penſilia ſunt, vti ſunt planetæ, & </s> <s xml:id="echoid-s16116" xml:space="preserve">Cometæ. </s> <s xml:id="echoid-s16117" xml:space="preserve">quæ propterea <lb/>in diuerſis firmamenti locis, ex diuerſis terræ locis, conſpecta cernuntur. </s> <s xml:id="echoid-s16118" xml:space="preserve">vnde nec eandem cum proximis<unsure/> <lb/>ſtellis configurationem, vel diſtantiam habere videntur. </s> <s xml:id="echoid-s16119" xml:space="preserve">At ſtella hæc noua Caſſiopeæ vbiq; </s> <s xml:id="echoid-s16120" xml:space="preserve">loco rum viſa <lb/>eſt in eodem cæli puncto; </s> <s xml:id="echoid-s16121" xml:space="preserve">nam Valentiæ in Hiſpania Hieronymus Muſonius Mathematicum profeſſor, in <lb/>Sicilia Franciſcus Maurolycus inſignis Mathematicus, demum in Dania Tycho magnus ille obſeruator, in <lb/>locis adeò diſiunctis, eam cum vicinis ſtellis eandem ſemper ſeruaſſe diſtantiam, ac proinde nullam habuiſſe <lb/>parallaxim depræhenderunt. </s> <s xml:id="echoid-s16122" xml:space="preserve">Vnde conſequens eſt eam ſupra omnes errantium regiones conſtitiſſe.</s> <s xml:id="echoid-s16123" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16124" xml:space="preserve">FIGVRAM eius fuſſſe ſphæricam exiſtimo ijſdem rationibus, quibus & </s> <s xml:id="echoid-s16125" xml:space="preserve">reliquas mundo coæuas eſſe <lb/>rotundas. </s> <s xml:id="echoid-s16126" xml:space="preserve">omnia enim eius accidentia vti ſupra vidimus erant communia cum alijs inerrantibus, quare idem <lb/>de figura exiſtimandum eſt.</s> <s xml:id="echoid-s16127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16128" xml:space="preserve">MAGNITVDO eius vera, eodem prorſus modo, quo in ſtellis perpetuis, reperitur; </s> <s xml:id="echoid-s16129" xml:space="preserve">eandem diſtan-<lb/>tiam à medio mundi obtinent, quæ eſt ſemidiam. </s> <s xml:id="echoid-s16130" xml:space="preserve">terræ 14′000′. </s> <s xml:id="echoid-s16131" xml:space="preserve">diameter autem apparens huius, cum ma-<lb/>xima apparuit, fuit 3 {1/2}. </s> <s xml:id="echoid-s16132" xml:space="preserve">ex quibus duobus principijs, modis alias traditis, elicitur eius magnitudo ad terram <lb/>collata, quæ ſanè mira eſt, nam terram 360. </s> <s xml:id="echoid-s16133" xml:space="preserve">vicibus adæquauit. </s> <s xml:id="echoid-s16134" xml:space="preserve">De hac Tycho edidit integrum Tomum, <lb/>& </s> <s xml:id="echoid-s16135" xml:space="preserve">alij plures de eadem varia Opuſcula conſcripſerunt, quæ omnia cum eodem Tychonis Tomo ſunt edita.</s> <s xml:id="echoid-s16136" xml:space="preserve"/> </p> <pb o="185" file="0207" n="212" rhead="Liber Decimusoctauus."/> </div> <div xml:id="echoid-div374" type="section" level="1" n="268"> <head xml:id="echoid-head286" style="it" xml:space="preserve">De recenti Stella in Cygno exorta anno 1600. Cap. III.</head> <p> <s xml:id="echoid-s16137" xml:space="preserve">DISTANTIA eius à centro mundi. </s> <s xml:id="echoid-s16138" xml:space="preserve">eodem Rurſus enim anno 1600. </s> <s xml:id="echoid-s16139" xml:space="preserve">nouum mundo ſpecta culum edi-<lb/>dit firmamentum, nouã videlicet Stellam in ſummo Cygni pectore, quæ prę pręter alia hoc vnum maximè <lb/>mirũ habet, quod iam per annos 16. </s> <s xml:id="echoid-s16140" xml:space="preserve">ibi affixa, & </s> <s xml:id="echoid-s16141" xml:space="preserve">immota inter alias inerrantes, ceu cæleſti ciuitate donat<unsure/>a pe-<lb/>rennat. </s> <s xml:id="echoid-s16142" xml:space="preserve">altitudo igitur eius à<unsure/> centro mundi, erit vt in præcedenti ſemid. </s> <s xml:id="echoid-s16143" xml:space="preserve">terræ 14000.</s> <s xml:id="echoid-s16144" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16145" xml:space="preserve">LOCVS eius in firmamento, & </s> <s xml:id="echoid-s16146" xml:space="preserve">in confinio colli, & </s> <s xml:id="echoid-s16147" xml:space="preserve">pectoris Cygui, eiuſq; </s> <s xml:id="echoid-s16148" xml:space="preserve">longitudo eſt in gr. </s> <s xml:id="echoid-s16149" xml:space="preserve">16. </s> <s xml:id="echoid-s16150" xml:space="preserve">18′. <lb/></s> <s xml:id="echoid-s16151" xml:space="preserve">Aquarij. </s> <s xml:id="echoid-s16152" xml:space="preserve">Latitudo borealis gr. </s> <s xml:id="echoid-s16153" xml:space="preserve">55 {1/2}.</s> <s xml:id="echoid-s16154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16155" xml:space="preserve">MOTVS in ea nullus præter diurnum, eundem enim ſemper retinuit ſitum in Cygno, ideſt, nullam ſor-<lb/>tita eſt parallaxim.</s> <s xml:id="echoid-s16156" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16157" xml:space="preserve">FIGVRA eius rotunda, vtin alijs.</s> <s xml:id="echoid-s16158" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16159" xml:space="preserve">MAGNITVDO eius eſt tertij ordinis, vnde non admodum ſpectabilis, quapropter nonnulli de eius <lb/>nouitate dubitarunt; </s> <s xml:id="echoid-s16160" xml:space="preserve">putarunt enim eam vnam eſſe perennium ſtellarum, ſed tamen propter ipſius medio-<lb/>critatem nemini antea, aut obſeruatam, aut à<unsure/> præteritis ſtellarum cenſoribus prętermiſſam: </s> <s xml:id="echoid-s16161" xml:space="preserve">quam dubitatio-<lb/>nem ſic tollam. </s> <s xml:id="echoid-s16162" xml:space="preserve">Primo. </s> <s xml:id="echoid-s16163" xml:space="preserve">Hæc ſtella omiſſa eſt ab Hipparcho, qui auſus fuit annumerare poſteris ſtellas, eaſq; <lb/></s> <s xml:id="echoid-s16164" xml:space="preserve">ſuis loci s in firmamento conſignare, ſuaſq; </s> <s xml:id="echoid-s16165" xml:space="preserve">ſingulis magnitudines def<unsure/>inire, vt facilè inde poſteri diſcernere <lb/>poſſent non modo an obirent, naſcerenturuè, ſed an omninò aliquæ tranſirent, mouerenturue<unsure/>. </s> <s xml:id="echoid-s16166" xml:space="preserve">item an cre-<lb/>ſcerent minue renturuè, cælo in hæreditatem cunctis relicto: </s> <s xml:id="echoid-s16167" xml:space="preserve">ex Plin. </s> <s xml:id="echoid-s16168" xml:space="preserve">lib. </s> <s xml:id="echoid-s16169" xml:space="preserve">2. </s> <s xml:id="echoid-s16170" xml:space="preserve">cap. </s> <s xml:id="echoid-s16171" xml:space="preserve">6. </s> <s xml:id="echoid-s16172" xml:space="preserve">cum ergo nec in eius catalo-<lb/>go, nec in eius Commentario in Aratum, vbi de ſtellis Cygni de induſtria agitur (quæ opera adhunc extant) <lb/>eam ſilentio prætereat, quid aliud nos docet, quam poſt tot ſæcula tandem illud accidere, quod ipſe dubitare <lb/>cæperat, in ſummo videlicet cælo nouas, diuturnaſq; </s> <s xml:id="echoid-s16173" xml:space="preserve">ſtellas naſci poſſe? </s> <s xml:id="echoid-s16174" xml:space="preserve">Secundo, neq; </s> <s xml:id="echoid-s16175" xml:space="preserve">Ptolem. </s> <s xml:id="echoid-s16176" xml:space="preserve">in ſuo ſyde-<lb/>rum catalogo huius ſtellę meminit, quem ab Hipparcho acceptum correxit, & </s> <s xml:id="echoid-s16177" xml:space="preserve">locupletauit. </s> <s xml:id="echoid-s16178" xml:space="preserve">Tertio tandem <lb/>Tycho Brahe, qui noſtra tempeſtate veterem illam Hipparchi curam, per tot ſæcula neglectam reſumpſit, vt <lb/>ſtellas omnes accuratè dinumerarit, ſuiſq; </s> <s xml:id="echoid-s16179" xml:space="preserve">locis, ac magnitudinibus cenſuerit, cur hanc tacitam, & </s> <s xml:id="echoid-s16180" xml:space="preserve">incomme-<lb/>moratam reliquit? </s> <s xml:id="echoid-s16181" xml:space="preserve">præſertim cùm ducentas alias a veteribus omiſſas, & </s> <s xml:id="echoid-s16182" xml:space="preserve">quidem hac minores numerauerit <lb/>diligenter? </s> <s xml:id="echoid-s16183" xml:space="preserve">veruntamen hæc in eius monumentis nuſquam reperiri poteſt. </s> <s xml:id="echoid-s16184" xml:space="preserve">Quarto, accedit hiſce mutis te-<lb/>ſtibus loquentium authoritas, Gulielmus enim lanſonius primus profitetur ſe hanc ſtellam nouam annotaſ-<lb/>ſe, cum anno 1600. </s> <s xml:id="echoid-s16185" xml:space="preserve">nouam globi Aſtronomici editionem pararet. </s> <s xml:id="echoid-s16186" xml:space="preserve">Eius vero authoritas plurimum valere <lb/>debet, quippe qui vnus ex Tychonis diſcipulis in aſtrorum notitia, & </s> <s xml:id="echoid-s16187" xml:space="preserve">obſeruatione erat verſatiſſimus. </s> <s xml:id="echoid-s16188" xml:space="preserve">Quin-<lb/>to, ne ſim longior, loannes Keplerus, & </s> <s xml:id="echoid-s16189" xml:space="preserve">P. </s> <s xml:id="echoid-s16190" xml:space="preserve">Clauius cæteriq; </s> <s xml:id="echoid-s16191" xml:space="preserve">ſydernm ſtudioſi, eam proculdubio nouam re-<lb/>cipiunt.</s> <s xml:id="echoid-s16192" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16193" xml:space="preserve">MAGNITVDO autem eius vera eadem erit cum ſtellis tertiæ magnitudinis quæ adæquabat, terram <lb/>igitur continebit vndecies.</s> <s xml:id="echoid-s16194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16195" xml:space="preserve">Cæterum ſtella hæc, omnes tam Cometas, quam nouas ſtellas diuturnitatem iam ſuperat. </s> <s xml:id="echoid-s16196" xml:space="preserve">hoc enim anno <lb/>1616. </s> <s xml:id="echoid-s16197" xml:space="preserve">iam annum agens decimum ſextum inuariata adhuc perſeuerat. </s> <s xml:id="echoid-s16198" xml:space="preserve">vide Kepleri opuſculum de hac ſtella.</s> <s xml:id="echoid-s16199" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div375" type="section" level="1" n="269"> <head xml:id="echoid-head287" style="it" xml:space="preserve">De Stella noua in Serpentario exorta anno 1601. Cap. IV.</head> <p> <s xml:id="echoid-s16200" xml:space="preserve">ANno tandem 1604. </s> <s xml:id="echoid-s16201" xml:space="preserve">die 9. </s> <s xml:id="echoid-s16202" xml:space="preserve">Octobris, nouum ſydus ac mirè fl<unsure/>ammans affulſit in ſerpentario.</s> <s xml:id="echoid-s16203" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16204" xml:space="preserve">FIGVRA rotundam ſine vllo cincinno, aut barba, clarè ſcintillans, fixis ſimillimum, emicanſq; </s> <s xml:id="echoid-s16205" xml:space="preserve">colo-<lb/>res Iridis circumquaque. </s> <s xml:id="echoid-s16206" xml:space="preserve">Magnitudine apparenti ſuperabat omnes ſtellas primi honoris, adeo vt Venerem <lb/>fulgidiſſimam adæquaret.</s> <s xml:id="echoid-s16207" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16208" xml:space="preserve">MOTV nullo proprio ciebatur, ſed ſolum diurna vertigine; </s> <s xml:id="echoid-s16209" xml:space="preserve">eandem enim ſemper poſitionem cum ſtel-<lb/>lis Serpentarij retinuit; </s> <s xml:id="echoid-s16210" xml:space="preserve">hæſit enim in ipſius genu ſiniſtro, & </s> <s xml:id="echoid-s16211" xml:space="preserve">in limbo Galaxiæ. </s> <s xml:id="echoid-s16212" xml:space="preserve">Longitudo eius fuit in gr. </s> <s xml:id="echoid-s16213" xml:space="preserve">18. <lb/></s> <s xml:id="echoid-s16214" xml:space="preserve">Sagittarij. </s> <s xml:id="echoid-s16215" xml:space="preserve">Latitudo borealis gr. </s> <s xml:id="echoid-s16216" xml:space="preserve">ferè duorum. </s> <s xml:id="echoid-s16217" xml:space="preserve">Parallaxis nulla durauit vſq; </s> <s xml:id="echoid-s16218" xml:space="preserve">ad anuum 1605<unsure/>. </s> <s xml:id="echoid-s16219" xml:space="preserve">initioq; </s> <s xml:id="echoid-s16220" xml:space="preserve">Februa-<lb/>rij extincta eſt. </s> <s xml:id="echoid-s16221" xml:space="preserve">quare per ſeſquiannum quaſi illuxit. </s> <s xml:id="echoid-s16222" xml:space="preserve">Cum igitur magnitudine, ſplendore, ſcintillatione, im-<lb/>mobilitate, atq; </s> <s xml:id="echoid-s16223" xml:space="preserve">omnes parallaxeos carentia, cæteris affixis eſſet ſimillima, eam merito Aſtronomi inter cæ-<lb/>teras affixa in firmamento locarunt.</s> <s xml:id="echoid-s16224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16225" xml:space="preserve">DISTANTIA eius igitur fuit 14′000′. </s> <s xml:id="echoid-s16226" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s16227" xml:space="preserve">terræ, & </s> <s xml:id="echoid-s16228" xml:space="preserve">quia eius apparens magnitudo fuit eadem cum <lb/>noua Caſſiopeæ, ideo etiam.</s> <s xml:id="echoid-s16229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16230" xml:space="preserve">MAGNITVDO eius vera fuerit eadem, terræque 360. </s> <s xml:id="echoid-s16231" xml:space="preserve">vicibus adæquabitur. </s> <s xml:id="echoid-s16232" xml:space="preserve">vide Ioannem Keple-<lb/>rum de ea.</s> <s xml:id="echoid-s16233" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16234" xml:space="preserve">Illud porrò conſideratione dignum eſt, tria hæc noua ſydera in Galaxia effulſiſſe, vt quemadmodum ea <lb/>quoddam ſtellularum agmen eſt, ita etiam nouarum ſtellarum quoddam ſeminarium.</s> <s xml:id="echoid-s16235" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16236" xml:space="preserve">Cum itaque tam breui annorum 34. </s> <s xml:id="echoid-s16237" xml:space="preserve">interuallo, mea hac ætate, tria noua effulſerint aſtra, ſeu potius ob-<lb/>ſeruata ſint, quis addubitare poterit cæteris ætatibns ſua ſydera defuiſſe, niſi vigiles ſtellarum defuiſſent <lb/>obſeruatores?</s> <s xml:id="echoid-s16238" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div376" type="section" level="1" n="270"> <head xml:id="echoid-head288" style="it" xml:space="preserve">Appendix de generatione, & materia nouarum Stellarum. Cap. V.</head> <p> <s xml:id="echoid-s16239" xml:space="preserve">HIc Phyſiologi valde ſolliciti ſunt de hac ſtellarum nouitate, deque materia, cum cęlum à nouitate, ac ge-<lb/>neratione immune exiſtiment. </s> <s xml:id="echoid-s16240" xml:space="preserve">Iudiciarij vero circa cauſam finalem valdè ſomniant, ac multa commi- <pb o="186" file="0208" n="213" rhead="De Mundi Fabrica,"/> niſcuntur. </s> <s xml:id="echoid-s16241" xml:space="preserve">Verum nos iſthæc miſſa faciamus, cum extram noſtram ſint ſphæram. </s> <s xml:id="echoid-s16242" xml:space="preserve">Non abſurdam tamen opi-<lb/>nionem puto dicentium ſtellas haſce nuperas non eſſe nouiter generatas; </s> <s xml:id="echoid-s16243" xml:space="preserve">ſed ſimiliter ac de Cometis dixi, <lb/>nouiter tantum apparere, eo quòd in firmamento rectè aſcendant, ac deſcendant, vnde etiam earum apparẽs <lb/>magnitudo reddatur varia. </s> <s xml:id="echoid-s16244" xml:space="preserve">ſed cur ſtella Cygni non mutat apparentem magnitudinem? </s> <s xml:id="echoid-s16245" xml:space="preserve">fortè quia hæc adeò <lb/>lentè mouetur, vt nondum ſenſibiliter inde mutata ſit. </s> <s xml:id="echoid-s16246" xml:space="preserve">hæc autem opinanter circa quæſtiones phyſicas de <lb/>materia, aut generatione, &</s> <s xml:id="echoid-s16247" xml:space="preserve">c. </s> <s xml:id="echoid-s16248" xml:space="preserve">de his ſtellis pluras habent Tycho, & </s> <s xml:id="echoid-s16249" xml:space="preserve">Keplerus, non pauca etiam Clauius in ſua <lb/>Sphæra, qui ferè omnia prædicta affirmat.</s> <s xml:id="echoid-s16250" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div377" type="section" level="1" n="271"> <head xml:id="echoid-head289" style="it" xml:space="preserve">Conſectarium de ipſo Firmamento. Cap. VI.</head> <p> <s xml:id="echoid-s16251" xml:space="preserve">SI qua pars cæli duritie, ac firmitate Prædita eſt, proculdubio erit firmamentum; </s> <s xml:id="echoid-s16252" xml:space="preserve">videmus enim in eo ſtel-<lb/>las affixas atque adinuicem immotas omnes ſimul ſupra mundi polos ordinatè, ac ſphæricè moueri, ideſt, <lb/>perinde ac ſi corpori ſphærico affixæ vna cum eo reuoluerentur. </s> <s xml:id="echoid-s16253" xml:space="preserve">quod euidens ſignum eſt firmitatis illius, & </s> <s xml:id="echoid-s16254" xml:space="preserve"><lb/>cauſa ſimul cur vocatum ſit firmamentum.</s> <s xml:id="echoid-s16255" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16256" xml:space="preserve">LOCVS eius ſiue diſtantia a terra patet ex prædictis.</s> <s xml:id="echoid-s16257" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16258" xml:space="preserve">FIGVRAM autem eius eſſ<unsure/>e ſphæricam motus ipſe ſtellarum indicat, vt ſuperius cum de figura mundi <lb/>tractaremus oſtendimus; </s> <s xml:id="echoid-s16259" xml:space="preserve">vnde cum oſtenſum ſit mundũ eſſe ſphęricum, ſequitur pariter firmamentum pręſer-<lb/>tim@ſecundũ extimam, ac conuexam ſuperficiem eſſe globoſum, cum hoc ſupremum ac vltimum cęlum ſit, ex <lb/>ijs quæ Aſtronomi probatiores norunt, ſitq; </s> <s xml:id="echoid-s16260" xml:space="preserve">propterea veluti totius mundi tectum, ac culmen ſphæricum.</s> <s xml:id="echoid-s16261" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16262" xml:space="preserve">MOTVS eius ijdem ſunt, qui affixarum de quibus ſuperius ſatis.</s> <s xml:id="echoid-s16263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16264" xml:space="preserve">MAGNITVDO eius ſic habetur; </s> <s xml:id="echoid-s16265" xml:space="preserve">oſtendimus diſtantiam affixarum eſſe 14000. </s> <s xml:id="echoid-s16266" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s16267" xml:space="preserve">terræ, quare to-<lb/>ta diameter firmamenti, ſeu mundi totius contin ebit 28′000. </s> <s xml:id="echoid-s16268" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s16269" xml:space="preserve">terræ, ac proinde maximus firmamenti <lb/>gyrus continebit ſemid. </s> <s xml:id="echoid-s16270" xml:space="preserve">88′000. </s> <s xml:id="echoid-s16271" xml:space="preserve">quæ efficiunt milliaria aſtronomica 312′412000. </s> <s xml:id="echoid-s16272" xml:space="preserve">quanto verò ſit eius ſolidi-<lb/>tas vel craſſities, quamuis par ſit eam putare immenſam, nihil tamen certi aſſerimus. </s> <s xml:id="echoid-s16273" xml:space="preserve">Cum autem firmamen-<lb/>tum ſit mundi pars ſuprema, quæ cęteras omnes complectitur, eiuſq; </s> <s xml:id="echoid-s16274" xml:space="preserve">diam. </s> <s xml:id="echoid-s16275" xml:space="preserve">nota ſit in diametris terræ, ſaltem <lb/>qua ſtellæ fixæ a terra diſtare neceſſe eſt, facilè erit totius mundanæ ſphæræ magnitudinem ad terræ magni-<lb/>tudinem conferre; </s> <s xml:id="echoid-s16276" xml:space="preserve">ſi nimirum cubi diametrorum vtriuſq; </s> <s xml:id="echoid-s16277" xml:space="preserve">exhibeantur. </s> <s xml:id="echoid-s16278" xml:space="preserve">diam. </s> <s xml:id="echoid-s16279" xml:space="preserve">terræ eſt 1. </s> <s xml:id="echoid-s16280" xml:space="preserve">diam. </s> <s xml:id="echoid-s16281" xml:space="preserve">totius mundi <lb/>ſaltẽ eſt 14000. </s> <s xml:id="echoid-s16282" xml:space="preserve">terræ eorum cubi ſunt 1. </s> <s xml:id="echoid-s16283" xml:space="preserve">& </s> <s xml:id="echoid-s16284" xml:space="preserve">2′744′000′000′000′. </s> <s xml:id="echoid-s16285" xml:space="preserve">ea igitur eſt proportio terræ ad totum mundũ.</s> <s xml:id="echoid-s16286" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div378" type="section" level="1" n="272"> <head xml:id="echoid-head290" style="it" xml:space="preserve">COROLLARIVM. <lb/>De noua Sphæra, & primo mobili ſupra firmamentum, confictis ad omnes motus <lb/>fixarum ſaluandos. Cap. VII.</head> <p> <s xml:id="echoid-s16287" xml:space="preserve">SVpra firmamentum ſolent communiter Aſtronomi nonum cælum, ſeu ſphæram nullo aſtro, aut lumine <lb/>inſignitam ſupponere; </s> <s xml:id="echoid-s16288" xml:space="preserve">cuius officium ſit, vt ſupra diximus, mouere firmamentũ motu trepidationis. </s> <s xml:id="echoid-s16289" xml:space="preserve">cum <lb/>enim putent ipſum firmamentum a ſe moueri in long itudinem, conſequenter etiam putant ipſum motu tre-<lb/>pidationis non a ſe, ſed ab alio cieri debere; </s> <s xml:id="echoid-s16290" xml:space="preserve">quandoqu@dem philoſophicum dogma ſit,<unsure/> corpus vnum ſimplex <lb/>natura ſua, moueri vno tantum ſimplici motu; </s> <s xml:id="echoid-s16291" xml:space="preserve">extrinſecè autem, ſi pluribus motibus percellatur.</s> <s xml:id="echoid-s16292" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16293" xml:space="preserve">Eadem ratione ſupra hanc nonam ſphæram circumponit vltimum cælum, nec aſtris, nec lumine præditũ, <lb/>quod primum mobile appellant, cuius poli ſint poli mundi ſimul & </s> <s xml:id="echoid-s16294" xml:space="preserve">æquatoris. </s> <s xml:id="echoid-s16295" xml:space="preserve">eius autem officium ſit moue-<lb/>re inferiores omnes ſphæras, ſeu totam ferè mundi machinam motu d@urno, ſeu ſpatio 24. </s> <s xml:id="echoid-s16296" xml:space="preserve">horarum ab orien-<lb/>te in occidentem verſare. </s> <s xml:id="echoid-s16297" xml:space="preserve">Aliqui tamen ex recentioribus, vt apparet ex lib. </s> <s xml:id="echoid-s16298" xml:space="preserve">epiſt. </s> <s xml:id="echoid-s16299" xml:space="preserve">Tychonis, & </s> <s xml:id="echoid-s16300" xml:space="preserve">aliorum ad <lb/>ipſum ſcribentium) inclinant nullum exiſtere cælum anaſtron, atq; </s> <s xml:id="echoid-s16301" xml:space="preserve">ob ſolum motum quempiam efficiẽdum: <lb/></s> <s xml:id="echoid-s16302" xml:space="preserve">quapropter probabilius eſſe putant diurnam mundi conuerſionem a nullo primo mobili ab alijs diſtincto ef-<lb/>fici, ſed a tota cæleſti regione, hoc eſt, totum cælum ſimul moueri in polis mundi, vi propria, ab oriente in <lb/>o caſum ſpatio 24. </s> <s xml:id="echoid-s16303" xml:space="preserve">horarum. </s> <s xml:id="echoid-s16304" xml:space="preserve">in quo cælo interim ſydera omnia, & </s> <s xml:id="echoid-s16305" xml:space="preserve">planetæ proprijs motibus ab occaſu in or-<lb/>tum in pol s Zod aci, quaſi contra primum motum, conuertantur, eo modo, quo ſupra ex poſui. </s> <s xml:id="echoid-s16306" xml:space="preserve">quamobrem <lb/>de hoc prim<unsure/>o mobili, & </s> <s xml:id="echoid-s16307" xml:space="preserve">motu eius nihi<unsure/>l mihi aliud dicendum ſupereſt, quam quæ dicta ſunt.</s> <s xml:id="echoid-s16308" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div379" type="section" level="1" n="273"> <head xml:id="echoid-head291" xml:space="preserve">EPILOGVS.</head> <head xml:id="echoid-head292" xml:space="preserve">Viſum eſt ſequentes Tabellas apponere, in quibus vnico iutuitu, præcipua exſupe-<lb/>rioribus in vnum collecta, conſpicere liceat.</head> <head xml:id="echoid-head293" style="it" xml:space="preserve">I. Semidiametri Sphærarum, & Orbium, vna cum distantijs planetarum, <lb/>& inerrantium à centro terræ.</head> <note position="right" xml:space="preserve"> <lb/>SEmidiameter terræ continet milliaria. # 3′436′{@/2}. <lb/>Semidiameter conuexi aeris continet milliaria. # 3′489′. <lb/>Semidiam. conuexi ætheris, ſeu putati ignis, continet ſemidiam. terræ 52. ſeu milliaria. # 178′672′. <lb/>Lunæ mediocris diſtantia a centro terræ conſtatſemidiametristerræ. # 56. <lb/>Solis, Mercurij, Veneris, ſemidiam. terræ. # 1142 <lb/></note> <pb o="187" file="0209" n="214" rhead="Liber Decimusoctauus."/> <note position="right" xml:space="preserve"> <lb/>Martis med. diſtant. continet ſemidiam. terræ. # 1745. <lb/>Iouis. # 3′990′. <lb/>Saturni. # 10′550′. <lb/>Cometarum varia in regione planetarum. <lb/>Inerrantium veterum, ac nouarum diſtancia, ac proinde. <lb/>Semidiameter firmamenri, ac totius mundi, conſtat ſemidiam. terræ ſaltem. # 14′000′. <lb/></note> </div> <div xml:id="echoid-div380" type="section" level="1" n="274"> <head xml:id="echoid-head294" style="it" xml:space="preserve">II. Proportiones ſemidiametri terræ, ad ſemid. planet. & ſvderum.</head> <note position="right" xml:space="preserve"> <lb/>## SEmidiameter terræ, # #### ad ſemidiametros planet. & ſyderum. <lb/>eſt vti # 3 {2/5}. # ad # 1 # ſemidiam. # ***. <lb/>Vel # 17 # ad # 5 <lb/>Vti # 1 # ad # 5 {1/5} # ſemidiam. # ***. <lb/>Vel # 5 # ad # 26 <lb/>Vti # 2 {2/3}. # ad # 1 # ſemidiam. # ☿. <lb/>Vel # 8 # ad # 3 <lb/>Vti # 1 {5/6}. # ad # 1 # ſemidiam. # ♀. <lb/>Vel # 11 # ad # 6 <lb/>Vti # 2 {2/5}. # ad # 1 # ſemidiam. # ♂. <lb/>Vel # 12 # ad # 5 <lb/>Vti # 1 # ad # 2 {2/5} # ſemidiam. # ♃. <lb/>Vel # 5 # ad # 12 <lb/>Vti # 1 # ad # 2 {0/11} # ſemidiam. # ♄. <lb/>Vel # 11 # ad # 31 <lb/>Vti # 1 # ad # 4 {1/3} # ſemidiam. Stellæ primæ magnit. <lb/>Vel # 3 # ad # 13 <lb/></note> </div> <div xml:id="echoid-div381" type="section" level="1" n="275"> <head xml:id="echoid-head295" style="it" xml:space="preserve">III. Magnitudinis Sphærarum, ac ſyderum collata ad terram.</head> <figure> <image file="0209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0209-01"/> </figure> <note position="right" xml:space="preserve"> <lb/>TErra continet milliara cubica # 170′032′521′600′. ad Maris ſoliditatem eſt ſicuti # 2290′ad 1. ad Aeris ſoliditatem, vt # 27. ad 1. ad Aetheris ſoliditatem, vt # 1. ad 140′708. ad Lunam, vt # 40. ad 1. ad Solem, vt # 1. ad 140. ad Mercurium, vt # 19. ad 1. ad Venerem, vt # 6. ad 1. ad Martem, vt # 13. ad 1. ad Iouem, vt # 1. ad 14. ad Saturnum, vt # 1. ad 22. ad Cometam anni 1577. vt # 100. ad 1. ad Stellas primæ magnit. vt # 1. ad 70. Secundæ magnit. vt # 1. ad 28. Tertiæ magnit. vt # 1. ad 11. Quartæ magnit. vt # 1. ad 3 {3/8}. Quintæ magnit. vt # 1. ad 1 {1/50}. Sextæ magnit. vt # 1. ad 1. Ad Stellam nouam Caffiopeæ, vt # 1. ad 360. Cygni, vt # 1. ad 11. Serpentarij, vt # 1. ad 360. ## Ad Mundi Sphæram, vt 1. ad 2′744′000′000′000′. Quæomnia in adiecta figu- \\ ra ad ſenſum intueri licebit. </note> </div> <div xml:id="echoid-div382" type="section" level="1" n="276"> <head xml:id="echoid-head296" style="it" xml:space="preserve">IV. Proportiones diametri Solis ad diametros terræ planet. & ſyd.</head> <figure> <image file="0209-10" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0209-10"/> </figure> <note position="right" xml:space="preserve"> <lb/># 5. # diamet. Terræ. <lb/># 1 {8/17}. # diamet. ***. <lb/># 1 {7/8}. # diamet. # ☿. <lb/>Diameter ***. cſt ſicuti 26. ad # 2 {1/12}. # diamet. # ♀. <lb/># {1/12}. # diamet. ♂. <lb/># 5. # diamet. ♃. <lb/># 24 {1/11}. # diamet. ♄. <lb/># 23 {2/3}. # diamet. Stellæ primæ magnit. <lb/></note> <pb o="188" file="0210" n="215" rhead="De Mundi Fabrica,"/> </div> <div xml:id="echoid-div383" type="section" level="1" n="277"> <head xml:id="echoid-head297" style="it" xml:space="preserve">V. Eorundem maxima distantia à Sole.</head> <note position="right" xml:space="preserve"> <lb/>## TErra diſtat à ***. apogæo, ſemidiam. Terra # 1181 <lb/>***. # In oppoſitione a ***. apogæo. # 1246 <lb/>☿. # # 571 <lb/>♀. # # 855 <lb/>♂. # à ***. apogæo. # 1628 <lb/>♃. # à ***. apogæo. # 3652 <lb/>♃. # in ☍. à ***. apogæo. # 10′588 <lb/>*. # minimum. # 14000 <lb/></note> </div> <div xml:id="echoid-div384" type="section" level="1" n="278"> <head xml:id="echoid-head298" style="it" xml:space="preserve">VI. Ex hiſce duabus Tabellis præcedentibus deduxi maximas vmbrarum longitudines, v@i <lb/>docui in vmbra Terra inueſtiganda: ſunt autem ſequentes.</head> <head xml:id="echoid-head299" xml:space="preserve">EORVNDEM VMBRÆ MAXIMÆ.</head> <note position="right" xml:space="preserve"> <lb/>TErræ vmbra maxima conſtat ſemidiam. Terræ. # 264. <lb/>Quapropter Lunam eclipſat, quæ à Terra maximè diſtat. # 60 {1/2}. <lb/>Lunæ vmbra maxima conſtat ſemidiam. Terræ. # 67. <lb/>Quare Terram attingere poteſt, à qua diſtat aliquando ſemidiam. Terræ tantum. # 52. <lb/>Eius autem mucro diſtat a Terræ. # 132. <lb/>Quare nullum aliũ planetarũ attingere poteſt, cum Venus quę reliquorum citiſſima eſt, diſtet ſaltem. # 287. <lb/>Mercurij vmbra maxima conſtat ſemidiam. Terræ. # 43. <lb/>Eiuſque apex diſtat à Sole ſemidiam. Terræ. # 614. <lb/>Quare ad Venerem non pertinet, quæ diſtat à Sole. # 855. <lb/>Veneris vmbra maxima conſtat ſemidiam. Terræ. # 102. <lb/>Eius acumen diſtat à Sole ſemidiam. Terræ. # 957. <lb/>Quare Lunam aſſequi nequit, quæ à Sole diſtat ſaltem. # 1034. <lb/>Martis vmbra maxima conſtat ſemidiam. Terræ. # 147. <lb/>Eius vertex diſtat à Sole. # 1775. <lb/>Iouem igitur non attinget, qui diſtat à Sole. # 2652. <lb/>Iouls vmbra maxima conſtat ſemidiam. Terræ. # 869. <lb/>Eius ſummitas recedit à Sole. # 4521. <lb/>Saturnum igitur non attinget, qui diſtat à Sole. # 10′588. <lb/>Saturni vmbra maxima conſtat ſemidiam. Terræ. # 12′532. <lb/>Cimaeius à Sole recedit. # 23′124. <lb/>Quare poterit inerrantes eclipſare, ſi earum diſtantia a Terra ſit tantum 14000. aut à Sole. # 12′858. <lb/>Stellarum primæ magnit. vmbra maxima conſtat ſemidiam. Terræ ſaltem. # 65′000. <lb/></note> </div> <div xml:id="echoid-div385" type="section" level="1" n="279"> <head xml:id="echoid-head300" style="it" xml:space="preserve">VII. Medij motus.</head> <note position="right" xml:space="preserve"> <lb/>## TErra in medio Mundi quieſcit, circa quam Maris æſtus Lunæ du- # Annis. # Dieb. # Hor. <lb/># ctu circumit. # 0 # 0 # 25 <lb/>## Lunæ totum Zodiacum percurrit. # 0 # 27 # 8 <lb/># Epicyclum percurrit. Anomalia. # 0 # 29 # 13 <lb/>## Solem aſſequitur. # 0 # 27 # 13 <lb/>## Motus ☊. annis Aegyptijs. # 18 # 223 # 0 <lb/>## Soltotum Zodiacum conf<unsure/>icit anno communi. # 1 # 0 # 0 <lb/>## Seu. # 0 # 365 # 5 {5/6} <lb/>## Apogæum Solis totum Zodiacum abſoluit. # 28′800′ # 0 # 0 <lb/>## Maculæ totum Solis diſcum ſubeunt. # 0 # 15 # 0 <lb/>## Mercur us totum Zodiacum cum Sole. # 1 # 0 # 0 <lb/># Epicyclum abſoluit. # 0 # 115 # 21 <lb/>## Venus, totum Zodiacum cum Sole. # 1 # 0 # 0 <lb/># Epicyclum, menſibus 19. & diebus 8. ideſt. # 1 # 218 # 0 <lb/>## Mars, totum Zodiacum. # 1 # 322 # 0 <lb/># Epicyclum. # 2 # 50 # 0 <lb/>## Iupiter totum Zodiacum. # 11 # 215 # 0 <lb/># Epicyclum. # 1 # 34 # 0 <lb/>## Comites 4. louis circa ipſum hiſce periodis voluuntur. <lb/># Primus, eique propior. # 0 # 1 # 18 {1/2} <lb/></note> <pb o="189" file="0211" n="216" rhead="Liber Decimusoctamus."/> <note position="right" xml:space="preserve"> <lb/>Secundus. # 0 # 3 # 13 <lb/>Tertius. # 0 # 7 # 4 <lb/>Quartus. # 0 # 16 # 18 <lb/>Saturnus totum Zodiacum. # 29 # 174 # 0 <lb/>Epicyclum. # 1 # 13 # 0 <lb/>Comites Saturni adhuc incomperti motus. <lb/>Inerrantes Stellæ totum Zodiacum obibunt. # 28′800′ # 0 # 0 <lb/>Motus primi mobilis, ſeu totius cæleſtis regio. # 0 # 1 # 0 <lb/></note> </div> <div xml:id="echoid-div386" type="section" level="1" n="280"> <head xml:id="echoid-head301" style="it" xml:space="preserve">Colophon. De Cælo Empyre@.</head> <p> <s xml:id="echoid-s16309" xml:space="preserve">POſtremo omnium ſupra Firmamentum Theologhi aliud Cœlum eſſe affirmant, nulla quidem præditum <lb/>ſtella, aut motu, ſed fælicem Beatorum mentium ſedem, quod Empyreum ab igne, ſeu claritate vocant, <lb/>Hoc tamen ab Aſtronomis vllo modo cognoſci nequit, cum nihil inde noſtris ſenſibus ingeratur.</s> <s xml:id="echoid-s16310" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div387" type="section" level="1" n="281"> <head xml:id="echoid-head302" style="it" xml:space="preserve">Appendix. De vſu Sphæra<unsure/> Armillaris.</head> <p> <s xml:id="echoid-s16311" xml:space="preserve">SOlent nonnulli ſcriptores ſeorſim de vſu Sphæræ materialis, & </s> <s xml:id="echoid-s16312" xml:space="preserve">armillaris agere, docentes qua ratione <lb/>per eam inueniamus ſequentia; </s> <s xml:id="echoid-s16313" xml:space="preserve">locum Solis in Zodiaco ſiue, gradum Solis quouis die dato. </s> <s xml:id="echoid-s16314" xml:space="preserve">Secundo, De-<lb/>clinatione@ omnium graduu eclipticæ. </s> <s xml:id="echoid-s16315" xml:space="preserve">Tertio, Aſcenſionem rectam cuiuſuis dati arcus, necnon gradus ecli-<lb/>pticæ. </s> <s xml:id="echoid-s16316" xml:space="preserve">Quarto, Altitudinem Solis ſupra horizontem. </s> <s xml:id="echoid-s16317" xml:space="preserve">Quinto, Lineam meridianam. </s> <s xml:id="echoid-s16318" xml:space="preserve">Sexto, Poli altitu <lb/>dinem. </s> <s xml:id="echoid-s16319" xml:space="preserve">Septimo, Quatuor mundi plagas, ac ventum flantem. </s> <s xml:id="echoid-s16320" xml:space="preserve">Octauo, Latitudinem ortiuam, occiduamue <lb/>Solis. </s> <s xml:id="echoid-s16321" xml:space="preserve">Nono, Arcum ſemidiurnum, ac diurnum, nocturnumque. </s> <s xml:id="echoid-s16322" xml:space="preserve">Decimo, Qua hora Sol oriatur, ſit meri-<lb/>dies, & </s> <s xml:id="echoid-s16323" xml:space="preserve">media nox. </s> <s xml:id="echoid-s16324" xml:space="preserve">Vndecimo, Horam labentem interdiu. </s> <s xml:id="echoid-s16325" xml:space="preserve">Duodecimo, Quantitatem Auroræ, ſeu crepu-<lb/>ſculi. </s> <s xml:id="echoid-s16326" xml:space="preserve">Decimotertio, Diem, & </s> <s xml:id="echoid-s16327" xml:space="preserve">hora æquinoctij. </s> <s xml:id="echoid-s16328" xml:space="preserve">quæ omnia, & </s> <s xml:id="echoid-s16329" xml:space="preserve">quidem ni fallor aptius ſuperius ſuis locis <lb/>inſeruimus, tantum in hunc locum differentes ſequens problema.</s> <s xml:id="echoid-s16330" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div388" type="section" level="1" n="282"> <head xml:id="echoid-head303" style="it" xml:space="preserve">Constructio Horologij Italici horizontalis auxilio Sphæra materialis.</head> <p> <s xml:id="echoid-s16331" xml:space="preserve">INter cæteros hui@s Sphæræ vſus egregius ille eſt, quo Solaria Horologia conſtrui poſſunt.</s> <s xml:id="echoid-s16332" xml:space="preserve"><unsure/> idque in hunc <lb/>modum: </s> <s xml:id="echoid-s16333" xml:space="preserve">Oportet primo Sphæram huic negotio ſic adaptare; </s> <s xml:id="echoid-s16334" xml:space="preserve">eleua polum iuxta tuam habitationem, po-<lb/>ſtea collocato vno colurorum ſub meridiano, obfirma partem Sphæræ, quam primum mobile diximus, cum <lb/>meridiano, & </s> <s xml:id="echoid-s16335" xml:space="preserve">horizonte, ita vt moueri nequeat. </s> <s xml:id="echoid-s16336" xml:space="preserve">Secundo diuide vtrumq; </s> <s xml:id="echoid-s16337" xml:space="preserve">Tropicum, & </s> <s xml:id="echoid-s16338" xml:space="preserve">Æquatorem in par-<lb/>tes 24. </s> <s xml:id="echoid-s16339" xml:space="preserve">æquales, facto initio ab horizonte occiduo, & </s> <s xml:id="echoid-s16340" xml:space="preserve">procedendo ſupra horizontem verſus orientem; </s> <s xml:id="echoid-s16341" xml:space="preserve">hæ <lb/>autem diuiſiones oportet attingant ipſam lineam tropici, & </s> <s xml:id="echoid-s16342" xml:space="preserve">æquatoris, quibus appone numeros horarum; <lb/></s> <s xml:id="echoid-s16343" xml:space="preserve">ſic, in ipſo horizõte occiduo iuxta primas tres diuiſiones ſint tres num. </s> <s xml:id="echoid-s16344" xml:space="preserve">24. </s> <s xml:id="echoid-s16345" xml:space="preserve">duo in tropicis, reliquus in æqua-<lb/>tione; </s> <s xml:id="echoid-s16346" xml:space="preserve">ſic, ternis diuiſionibus ſecundis, adde tres numerns 23. </s> <s xml:id="echoid-s16347" xml:space="preserve">duos in tropicis, reliquum in æquationem. </s> <s xml:id="echoid-s16348" xml:space="preserve">idem <lb/>fac tertijs, adſcribendo illis ter. </s> <s xml:id="echoid-s16349" xml:space="preserve">22. </s> <s xml:id="echoid-s16350" xml:space="preserve">eodem modo cum alijs ternis punctis facies vſque ad vltimum tropici æſti-<lb/>ui punctum, quod eſt ſupra horizontem, notando ternos numeros, etiamſi puncta æquatoris, aut tropici hy-<lb/>berni, correſpondentia punctis æſtiui tropici, ſint infra horizontem.</s> <s xml:id="echoid-s16351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16352" xml:space="preserve">Sed hoc loco addenda eſt horizonti ortiuo ſponda quædam aliquantulum ſupra ipſum erecta inter tropi-<lb/>cos, in cuius ſummitate notanda ſunt puncta, & </s> <s xml:id="echoid-s16353" xml:space="preserve">numeri pro ijs punctis, & </s> <s xml:id="echoid-s16354" xml:space="preserve">numeris æquatoris, & </s> <s xml:id="echoid-s16355" xml:space="preserve">tropi-<lb/>ci hyberni, quæ infra horizontem ceciderint; </s> <s xml:id="echoid-s16356" xml:space="preserve">quæ ſcilicet correſpondent in eadem numeratione punctis, <lb/>& </s> <s xml:id="echoid-s16357" xml:space="preserve">numeris tropici æſtiui exiſtentibus ſupra. </s> <s xml:id="echoid-s16358" xml:space="preserve">ſunt autem notanda hac ratione, extende filum ſuper tres nu-<lb/>meros eiuſdem appellationis a tropico æſtiuo per æquatorem, vſque ad hybernum@, & </s> <s xml:id="echoid-s16359" xml:space="preserve">vbi hoc filum teti-<lb/>gerit interius ſpondam, ibi notabis in ſummitate ſpondæ punctum, & </s> <s xml:id="echoid-s16360" xml:space="preserve">numerum eundem, qui erat infra <lb/>horizontem, hic enim numerus inſeruit pro numero infra exiſtente. </s> <s xml:id="echoid-s16361" xml:space="preserve">in eleuatione Parmenſi gi<unsure/>ad. </s> <s xml:id="echoid-s16362" xml:space="preserve">ferè 45. <lb/></s> <s xml:id="echoid-s16363" xml:space="preserve">puncta, & </s> <s xml:id="echoid-s16364" xml:space="preserve">numeros horarum 9. </s> <s xml:id="echoid-s16365" xml:space="preserve">10. </s> <s xml:id="echoid-s16366" xml:space="preserve">11. </s> <s xml:id="echoid-s16367" xml:space="preserve">12. </s> <s xml:id="echoid-s16368" xml:space="preserve">13. </s> <s xml:id="echoid-s16369" xml:space="preserve">14. </s> <s xml:id="echoid-s16370" xml:space="preserve">15. </s> <s xml:id="echoid-s16371" xml:space="preserve">tropici Capricorni, ſunt infra. </s> <s xml:id="echoid-s16372" xml:space="preserve">in æquatore ſunttan-<lb/>tum infra hi, 9. </s> <s xml:id="echoid-s16373" xml:space="preserve">10. </s> <s xml:id="echoid-s16374" xml:space="preserve">11. </s> <s xml:id="echoid-s16375" xml:space="preserve">12. </s> <s xml:id="echoid-s16376" xml:space="preserve">tamen eſt in ipſo horizonte, ſed notandus eſt in ſponda. </s> <s xml:id="echoid-s16377" xml:space="preserve">in tropico autem Cancri <lb/>omnes ſunt ſupra. </s> <s xml:id="echoid-s16378" xml:space="preserve">in ſponda autem notandi ſunt omnes prędicti 9. </s> <s xml:id="echoid-s16379" xml:space="preserve">10. </s> <s xml:id="echoid-s16380" xml:space="preserve">11. </s> <s xml:id="echoid-s16381" xml:space="preserve">12. </s> <s xml:id="echoid-s16382" xml:space="preserve">13. </s> <s xml:id="echoid-s16383" xml:space="preserve">14. </s> <s xml:id="echoid-s16384" xml:space="preserve">15. </s> <s xml:id="echoid-s16385" xml:space="preserve">vt inſeruiant pro exi-<lb/>ſtentibus inſra, vti per nuper diximus. </s> <s xml:id="echoid-s16386" xml:space="preserve">quanta autem eſſe debeat altitudo ſpondæ, vſus docebit. </s> <s xml:id="echoid-s16387" xml:space="preserve">Tertio, axis <lb/>materialis auferatur; </s> <s xml:id="echoid-s16388" xml:space="preserve">poſtea filum extende ab ortu, ad occaſum in ſuperficie horizontis, quod referat diame-<lb/>trum horizontis; </s> <s xml:id="echoid-s16389" xml:space="preserve">in cuius medio, quod exacte ſit centrum horizontis, ſiue ſphæræ, notetur punctum appa-<lb/>renti colore. </s> <s xml:id="echoid-s16390" xml:space="preserve">Quarto, accipiatur tabella exacte complanata, in qua deſcribendum eſt horologium, tantæ <lb/>magnitudinis, vt poſſit intra ſphæram collocari. </s> <s xml:id="echoid-s16391" xml:space="preserve">è medio eius perpendiculariter erigatur ſtylus acutus ſatis <lb/>breuis, quantus autem depeat eſſe hic ſtylus, vſus poſtea docebit; </s> <s xml:id="echoid-s16392" xml:space="preserve">debet enim tantus eſſe, vt radius, de quo <lb/>mox dicam, per apicem eius tranſieus tabellæ occurrere poſſit. </s> <s xml:id="echoid-s16393" xml:space="preserve">Hæc intra ſphæram collocetur, ita vt ſit in fra <lb/>horizontem, ſed ei tamen æquidiſtans, apexque ſtyli præcisè pungat punctum fili medium, quod ſphæræ eſt <lb/>centrum, in quo ſtatu tabela obfirmetur, vt dimoueri nequeat poſtea filum auferatur. </s> <s xml:id="echoid-s16394" xml:space="preserve">Quinto, accipe filum <lb/>æneum ſubtiliſſimum, atque rectiſſimum, qui Solaris radijs vices gerat tantę longitudinis, quanta eſt ſphæ-<lb/>ræ diameter ſitque ex altero capite acuminatus.</s> <s xml:id="echoid-s16395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16396" xml:space="preserve">Hiſce paratis ad linearum horariam deſcriptionem ſic aggredere; </s> <s xml:id="echoid-s16397" xml:space="preserve">velis exempli gratia, horam 23. </s> <s xml:id="echoid-s16398" xml:space="preserve">ſeu li-<lb/>neam eius in tabella delineare; </s> <s xml:id="echoid-s16399" xml:space="preserve">immitte igitur radium, qua parte accuminatus eſt, per punctum horæ 23. </s> <s xml:id="echoid-s16400" xml:space="preserve">tro- <pb o="190" file="0212" n="217" rhead="De Mundi Fabrica,"/> pici æſtiui, & </s> <s xml:id="echoid-s16401" xml:space="preserve">ſimul per apicem ſtyli, donec leuiter punctim tabellam attingat, ibique in ea punctum notabis. <lb/></s> <s xml:id="echoid-s16402" xml:space="preserve">idem fac per punctum horæ pariter 23. </s> <s xml:id="echoid-s16403" xml:space="preserve">æquatoris notando punctum in tabella tandem idem fac ad punctum <lb/>pariter 23. </s> <s xml:id="echoid-s16404" xml:space="preserve">alterius tropici, notando tertium punctum in tabella; </s> <s xml:id="echoid-s16405" xml:space="preserve">quæ tria puncta, ſi rectè operatus fueris, <lb/>erunt in directum conſtituta, ſiue in recta linea recta per tria hæc puncta, erit ea linea horararia horæ 13. </s> <s xml:id="echoid-s16406" xml:space="preserve">eo-<lb/>dem modo reperies terna puncta pro hora 22. </s> <s xml:id="echoid-s16407" xml:space="preserve">& </s> <s xml:id="echoid-s16408" xml:space="preserve">pro cæteris omnibus, quorum puncta, & </s> <s xml:id="echoid-s16409" xml:space="preserve">numeri vtriuſque <lb/>tropici ſunt ſupra horizontem. </s> <s xml:id="echoid-s16410" xml:space="preserve">At vero in horis quarum puncta, & </s> <s xml:id="echoid-s16411" xml:space="preserve">numeri ſunt notata partim in tropico <lb/>æſtiuo, vel æquatore, partim in prędicta iam ſponda, aſſumenda ſunt ea quæ ſignata ſunt in ſponda vice eo-<lb/>rum, quæ ſunt infra horizontem: </s> <s xml:id="echoid-s16412" xml:space="preserve">v. </s> <s xml:id="echoid-s16413" xml:space="preserve">g. </s> <s xml:id="echoid-s16414" xml:space="preserve">in eleuatione noſtra boreali gr. </s> <s xml:id="echoid-s16415" xml:space="preserve">44. </s> <s xml:id="echoid-s16416" xml:space="preserve">ſit deſcribenda linea h. </s> <s xml:id="echoid-s16417" xml:space="preserve">13. </s> <s xml:id="echoid-s16418" xml:space="preserve">immiſ-<lb/>ſo igitur radio per punctum horæ 13<unsure/>. </s> <s xml:id="echoid-s16419" xml:space="preserve">in tropico Cancri, & </s> <s xml:id="echoid-s16420" xml:space="preserve">per verticem ſtyli vſque ad tabellæ occurſum, <lb/>ibique notato puncto, & </s> <s xml:id="echoid-s16421" xml:space="preserve">ſimiliter per punctum æquatoris hor. </s> <s xml:id="echoid-s16422" xml:space="preserve">13 inuento ſecundo puncto in tabella, tandem <lb/>per punctum horæ 13. </s> <s xml:id="echoid-s16423" xml:space="preserve">in ſponda, & </s> <s xml:id="echoid-s16424" xml:space="preserve">per verticem ſtyli tranſmiſſo radio, vſque ad tabellam notetur tertium <lb/>punctum: </s> <s xml:id="echoid-s16425" xml:space="preserve">per hæc tria puncta tranſibit linea recta, quæ horam 13. </s> <s xml:id="echoid-s16426" xml:space="preserve">indicatura eſt: </s> <s xml:id="echoid-s16427" xml:space="preserve">quod ſi radius ſpondam, & </s> <s xml:id="echoid-s16428" xml:space="preserve"><lb/>ſtyli verticem tangens non occurreret tabellæ, ſponda nimis humilis eſſe, & </s> <s xml:id="echoid-s16429" xml:space="preserve">propterea eo vſque eleuanda fo-<lb/>ret, quouſque radius ſtyli verttice attingens tabelllæ accidat@. </s> <s xml:id="echoid-s16430" xml:space="preserve">Idem ſiat, pro horis 12. </s> <s xml:id="echoid-s16431" xml:space="preserve">11. </s> <s xml:id="echoid-s16432" xml:space="preserve">10. </s> <s xml:id="echoid-s16433" xml:space="preserve">9. </s> <s xml:id="echoid-s16434" xml:space="preserve">quæ duobu@ <lb/>tantum punctis indigent, vno in tropico ſupra horizontem, altero in ſponda.</s> <s xml:id="echoid-s16435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16436" xml:space="preserve">Poſtremo per tria puncta, quibus Meridianus ſecat tropicos, & </s> <s xml:id="echoid-s16437" xml:space="preserve">æquatorem, necnon per verticem ſtyli im-<lb/>miſſo radio, reperiantur tria puncta in tabella, quæ ita ſignentur, vt ab alijs dignoſcantur, ſunt enim pro li-<lb/>nea meridiana. </s> <s xml:id="echoid-s16438" xml:space="preserve">His punctorum ternarijs in tabella notatis, extrahatur è ſphæra, & </s> <s xml:id="echoid-s16439" xml:space="preserve">quælibettria puncta, quæ <lb/>ad eandem horam pertinet, iungantur line is rectis. </s> <s xml:id="echoid-s16440" xml:space="preserve">ſimiliter bina puncta horarum 12. </s> <s xml:id="echoid-s16441" xml:space="preserve">11. </s> <s xml:id="echoid-s16442" xml:space="preserve">10. </s> <s xml:id="echoid-s16443" xml:space="preserve">9. </s> <s xml:id="echoid-s16444" xml:space="preserve">iungatur li-<lb/>ne@ quibus aſcribantur numeri horarum, qui eis debentur; </s> <s xml:id="echoid-s16445" xml:space="preserve">erunt enim hæ lineæ horariæ: </s> <s xml:id="echoid-s16446" xml:space="preserve">tria pariter pun-<lb/>cta vltimo inuenta per puncta tria meridiani, linea recta iungantur, hæc enim erit linea meridiana, quæ ſci-<lb/>licet meridiem indicabit.</s> <s xml:id="echoid-s16447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16448" xml:space="preserve">Omnia deinde puncta media, quæ ſcilicet per puncta æquatoris inuenta ſunt, copulentur linea, quæ erit <lb/>recta, eritq: </s> <s xml:id="echoid-s16449" xml:space="preserve">æquinoctialis linea, quæ videlicet æquinoctia indicabit. </s> </p> </div> <div xml:id="echoid-div389" type="section" level="1" n="283"> <figure xlink:label="fig-0212-01a" xlink:href="fig-0212-01"> <caption xml:id="echoid-caption1" style="it" xml:space="preserve">Horol. Ital. orizontale<unsure/> ad latitudinem 45.</caption> </figure> <p> <s xml:id="echoid-s16450" xml:space="preserve">puncta verò extrema inuenta ex tropi-<lb/></s> <s xml:id="echoid-s16451" xml:space="preserve">coæſtiuo, quia non ſunt in di- rectum conſtituta, iungantur linea punctuali introrſum cur- ua, quæ ſolſtitium æſtiuũ mon- ſtrabit. </s> <s xml:id="echoid-s16452" xml:space="preserve">eodem modo deſcriba- tur altera linea punctualis per reliqua extrema pũcta alterius tropici, quæ brumalis ſolſtitij eritindicatiua. </s> <s xml:id="echoid-s16453" xml:space="preserve">Ex quibus de- ſcriptum erit Horologium ho- rizontale Italicum, ad latitudi- nem gr. </s> <s xml:id="echoid-s16454" xml:space="preserve">45. </s> <s xml:id="echoid-s16455" xml:space="preserve">quale ſequens figu- ra oſtendit, in qua lineæ hora- rum ex appoſitis numeris co- gnoſcuntur. </s> <s xml:id="echoid-s16456" xml:space="preserve">linea E B, eſt me- ridiana. </s> <s xml:id="echoid-s16457" xml:space="preserve">linea C D. </s> <s xml:id="echoid-s16458" xml:space="preserve">eſt æquino- ctialis, quæ horarijs tranſuerſa eſt. </s> <s xml:id="echoid-s16459" xml:space="preserve">Lineæ punctuales tropicos referunt, &</s> <s xml:id="echoid-s16460" xml:space="preserve">c. </s> <s xml:id="echoid-s16461" xml:space="preserve">Quod vt officio officio ſuo rectè fungatur, col- locandũ eſt ad libellam in apri- @o loco, lineaq; </s> <s xml:id="echoid-s16462" xml:space="preserve">ipſius meridiana congruere debet veræ lineæ meridianæ inibi prius inuentæ; </s> <s xml:id="echoid-s16463" xml:space="preserve">ſtylua ſit ad meridiem, collucente enim Sole vertex vmbræ ſtyli oſtendet horas Italicas, ſeu ab occaſu, meridiem, æqui- noctia, & </s> <s xml:id="echoid-s16464" xml:space="preserve">ſolſtitia, vt facilè ipſius figurationem conſideranti patere poteſt.</s> <s xml:id="echoid-s16465" xml:space="preserve"/> </p> <div xml:id="echoid-div389" type="float" level="2" n="1"> <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a"> <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0212-01"/> </figure> </div> </div> <div xml:id="echoid-div391" type="section" level="1" n="284"> <head xml:id="echoid-head304" style="it" xml:space="preserve">De Horologijs verticalibus, ſeu muralibus.</head> <p> <s xml:id="echoid-s16466" xml:space="preserve">SI Tabella collocetur intra ſphæram, ita vt faciat angulos rectos cum horizonte, vti faciunt muri cum ho-<lb/>rizonte naturali, & </s> <s xml:id="echoid-s16467" xml:space="preserve">ita vt imitetur ſitum muri, cui velles Horologium appingere: </s> <s xml:id="echoid-s16468" xml:space="preserve">apexq; </s> <s xml:id="echoid-s16469" xml:space="preserve">ſtyli attingat <lb/>centrum ſphæræ, & </s> <s xml:id="echoid-s16470" xml:space="preserve">poſtea puncta terna, pro ſingulis horis reperiantur, vt ſupra in horizõtali docui, factum <lb/>crit Horologium murale, quod horas, & </s> <s xml:id="echoid-s16471" xml:space="preserve">cætera oſtendet in muro, cuius ſitum intra ſphæram imitabatur. <lb/></s> <s xml:id="echoid-s16472" xml:space="preserve">Porrò ſi ſphæra aſtronomicè apud murum aſſumptum collocetur, eique muro Tabella intra ſphærã exiſtens <lb/>ſit æquidiſtans, ſimulq; </s> <s xml:id="echoid-s16473" xml:space="preserve">horizonti perpendicularis, tunc optimè murum illum referet.</s> <s xml:id="echoid-s16474" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16475" xml:space="preserve">Illud ſcitu dignum eſt, ac pariter vtile, in eleuatione poli gr. </s> <s xml:id="echoid-s16476" xml:space="preserve">45. </s> <s xml:id="echoid-s16477" xml:space="preserve">qualis ſerè eſt totus Lombardiæ tractus, <lb/>idem Horologium horizontale commutari poſſe in duo verticalia, ſeu muralia primaria, ideſt, in vnũ quod <lb/>meridiem directè aſpiciat, & </s> <s xml:id="echoid-s16478" xml:space="preserve">in alterum huic auerſum, quod ad Boream pariter directè proſpiciat: </s> <s xml:id="echoid-s16479" xml:space="preserve">idque mu- <pb o="191" file="0213" n="218" rhead="Liber Decimũsoctauus."/> tis tantummodo horarum numereris. </s> <s xml:id="echoid-s16480" xml:space="preserve">ſi igitur iſtud Horologium, ita muro exactè auſtrali applicetur, vt <lb/>linea meridiana ſit horlzonti perpendicularis, ſimulque linea horæ 12. </s> <s xml:id="echoid-s16481" xml:space="preserve">ſit horizonti paralella, & </s> <s xml:id="echoid-s16482" xml:space="preserve">hora 23. <lb/></s> </p> </div> <div xml:id="echoid-div392" type="section" level="1" n="285"> <figure xlink:label="fig-0213-01a" xlink:href="fig-0213-01"> <caption xml:id="echoid-caption2" style="it" xml:space="preserve">Horol. Ital. verticale auſtrale primarium ad latit. 45.</caption> </figure> <p> <s xml:id="echoid-s16483" xml:space="preserve">appelletur 13. </s> <s xml:id="echoid-s16484" xml:space="preserve">22. </s> <s xml:id="echoid-s16485" xml:space="preserve">appelletur 14. </s> <s xml:id="echoid-s16486" xml:space="preserve">21.</s> <s xml:id="echoid-s16487" xml:space="preserve"> dicatur 15. </s> <s xml:id="echoid-s16488" xml:space="preserve">& </s> <s xml:id="echoid-s16489" xml:space="preserve">ſic deinceps vſque ad 12. </s> <s xml:id="echoid-s16490" xml:space="preserve">quæ in 24. </s> <s xml:id="echoid-s16491" xml:space="preserve">commutanda eſt: </s> <s xml:id="echoid-s16492" xml:space="preserve">pa- riter tropicus Cancri euadat Capri- corni, & </s> <s xml:id="echoid-s16493" xml:space="preserve">contra: </s> <s xml:id="echoid-s16494" xml:space="preserve">factum erit Horo- logium verticale, & </s> <s xml:id="echoid-s16495" xml:space="preserve">auſtrale prima- rium. </s> <s xml:id="echoid-s16496" xml:space="preserve">Porrò notandum eſt in hoc Horologio lineas horarum 9. </s> <s xml:id="echoid-s16497" xml:space="preserve">10. </s> <s xml:id="echoid-s16498" xml:space="preserve">11.</s> <s xml:id="echoid-s16499" xml:space="preserve"> & </s> <s xml:id="echoid-s16500" xml:space="preserve">ſimiliter partes horarum 23. </s> <s xml:id="echoid-s16501" xml:space="preserve">22 21.</s> <s xml:id="echoid-s16502" xml:space="preserve"> quæ omnes ſunt ſupra lineam horæ 12. </s> <s xml:id="echoid-s16503" xml:space="preserve">quæ modo euaſit 24. </s> <s xml:id="echoid-s16504" xml:space="preserve">eſſe ſuper- fluas: </s> <s xml:id="echoid-s16505" xml:space="preserve">huius figuram inſpice.</s> <s xml:id="echoid-s16506" xml:space="preserve"/> </p> <div xml:id="echoid-div392" type="float" level="2" n="1"> <figure xlink:label="fig-0213-01" xlink:href="fig-0213-01a"> <image file="0213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0213-01"/> </figure> </div> <p> <s xml:id="echoid-s16507" xml:space="preserve">Pro Horologio autem boreali primario, accipiatur ea pars Horologij horizontalis, quam modo diximus <lb/>in verticale auſtrali eſſe ſuperuacaneam, atque ita muro boreali applicetur, vt lineæ horæ 12. </s> </p> </div> <div xml:id="echoid-div394" type="section" level="1" n="286"> <figure xlink:label="fig-0213-02a" xlink:href="fig-0213-02"> <caption xml:id="echoid-caption3" style="it" xml:space="preserve">Horol. Ital. veritcale primarium boreale ad latitudinem 45. </caption> </figure> <p> <s xml:id="echoid-s16508" xml:space="preserve">quæ commu-<lb/></s> <s xml:id="echoid-s16509" xml:space="preserve">ta eſt in 24. </s> <s xml:id="echoid-s16510" xml:space="preserve">in verticale; </s> <s xml:id="echoid-s16511" xml:space="preserve">ſit horizonti paralella, ſitque omnium ſuprema, vn- de ſequetur lineam meridianam deor- ſum perpendiculariter cadere, ſic au- tem ipſarum numeri ſunt commutan- di, hora 12. </s> <s xml:id="echoid-s16512" xml:space="preserve">commutatur, vt prius in 24. </s> <s xml:id="echoid-s16513" xml:space="preserve">hor. </s> <s xml:id="echoid-s16514" xml:space="preserve">11. </s> <s xml:id="echoid-s16515" xml:space="preserve">in 23. </s> <s xml:id="echoid-s16516" xml:space="preserve">10. </s> <s xml:id="echoid-s16517" xml:space="preserve">in 22. </s> <s xml:id="echoid-s16518" xml:space="preserve">9. </s> <s xml:id="echoid-s16519" xml:space="preserve">in 21. </s> <s xml:id="echoid-s16520" xml:space="preserve">hæ autem erunt ad partem orienris. </s> <s xml:id="echoid-s16521" xml:space="preserve">por- tiones verò horarum 23. </s> <s xml:id="echoid-s16522" xml:space="preserve">22. </s> <s xml:id="echoid-s16523" xml:space="preserve">21. </s> <s xml:id="echoid-s16524" xml:space="preserve">quæ re- manent infra lineam 24. </s> <s xml:id="echoid-s16525" xml:space="preserve">ſiue horizon- talem, ſic immutantur, portio 21. </s> <s xml:id="echoid-s16526" xml:space="preserve">mutantur in 9. </s> <s xml:id="echoid-s16527" xml:space="preserve">portio 22. </s> <s xml:id="echoid-s16528" xml:space="preserve">in 10. </s> <s xml:id="echoid-s16529" xml:space="preserve">portio 23. </s> <s xml:id="echoid-s16530" xml:space="preserve">in 11. </s> <s xml:id="echoid-s16531" xml:space="preserve">hæ autem ſunt ad par- tem, cuius talis eſt præſens figura.</s> <s xml:id="echoid-s16532" xml:space="preserve"/> </p> <div xml:id="echoid-div394" type="float" level="2" n="1"> <figure xlink:label="fig-0213-02" xlink:href="fig-0213-02a"> <image file="0213-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0213-02"/> </figure> </div> </div> <div xml:id="echoid-div396" type="section" level="1" n="287"> <head xml:id="echoid-head305" style="it" xml:space="preserve">De alijs Horologijs Aſtronomicis, & Babylonicis.</head> <p> <s xml:id="echoid-s16533" xml:space="preserve">EX præmiſſis facilè erit cuiq; </s> <s xml:id="echoid-s16534" xml:space="preserve">ſtudioſo, ac induſtrioſo, reliqua Horologiorum genera ex materiali ſphæ-<lb/>ra deſcribere: </s> <s xml:id="echoid-s16535" xml:space="preserve">nam pro Aſtronomico diuiſio tropicorum, & </s> <s xml:id="echoid-s16536" xml:space="preserve">æquatoris in 24. </s> <s xml:id="echoid-s16537" xml:space="preserve">partes, debet à meridia-<lb/>no incipere, ac in eundem deſinere, procedendo verſus occidentem. </s> <s xml:id="echoid-s16538" xml:space="preserve">pro Babylonico inchoanda eſt diuiſio <lb/>ab horizonte ortiuo, procedendo ſupernè occaſum verſus, contra quam factum eſt in Italico, quia hæc duo <lb/>Horologia ſunt alterum alterius inuerſum: </s> <s xml:id="echoid-s16539" xml:space="preserve">vnde ſequitur Horologium Italicum conuerti poſſe in Babylo-<lb/>nicum, hac ratione.</s> <s xml:id="echoid-s16540" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16541" xml:space="preserve">Italicum Horologium ſit primo conſtitutum in ſua poſitione Aſtronomica, in qua horas oſtendere de-<lb/>bet, & </s> <s xml:id="echoid-s16542" xml:space="preserve">poſtea ita inuertatur, vt pars occidentalis fiat orientalis, & </s> <s xml:id="echoid-s16543" xml:space="preserve">contra. </s> <s xml:id="echoid-s16544" xml:space="preserve">quæ conuerſio ſiat circa lineam <lb/>meridianam, tanquam axem manentem. </s> <s xml:id="echoid-s16545" xml:space="preserve">Hac facta conuerſione lineæ omnes erunt infra, ideſt, in ſuper-<lb/>ficie, quæ nunc deorſum aſpiciet; </s> <s xml:id="echoid-s16546" xml:space="preserve">ſtylus etiam deorſum tendet. </s> <s xml:id="echoid-s16547" xml:space="preserve">Imaginemur iam haſce lineas ſurſum tran-<lb/>ſparere, vti facerent in ſubtiliori charta delineatæ. </s> <s xml:id="echoid-s16548" xml:space="preserve">hæ lineæ ſic tranſparentes adamuſſim repræſentabunt <lb/>Horologium Babylonicum. </s> <s xml:id="echoid-s16549" xml:space="preserve">ſi igitur in parte ſuperiori, vbi tranſparent delineentur, pro vt tranſpa ent, <lb/>ſtiluſque etiam ſurſum inuertatur, abſolutum erit Horologium, quod horas ab ortu indicabit. </s> <s xml:id="echoid-s16550" xml:space="preserve">Rurſus hoc <lb/>Horologium Babylonicum ſi conſtitutum ſit ad latitudinem gr. </s> <s xml:id="echoid-s16551" xml:space="preserve">45. </s> <s xml:id="echoid-s16552" xml:space="preserve">commutari poteſt in duo Horologia <lb/>verticalia primaria, auſtrale, & </s> <s xml:id="echoid-s16553" xml:space="preserve">boreale, commutatis numeris, & </s> <s xml:id="echoid-s16554" xml:space="preserve">cæteris proportionaliter factis, vt in Ita-<lb/>lico. </s> <s xml:id="echoid-s16555" xml:space="preserve">Quapropter eadem opera, qua Italicum conſtruitur, conſtruuntur ſimul ſex Horologia, quod ſanè <lb/>iucundum, ac mirum eſt: </s> <s xml:id="echoid-s16556" xml:space="preserve">tria videlicet Italica; </s> <s xml:id="echoid-s16557" xml:space="preserve">& </s> <s xml:id="echoid-s16558" xml:space="preserve">tria itidem Babylonica. </s> <s xml:id="echoid-s16559" xml:space="preserve">Hæc ſatis ſint pro inſti@uto. </s> <s xml:id="echoid-s16560" xml:space="preserve">plu-<lb/>ra alia ſolers lector ex materiali ſphæra deducere poteſt ex prædictis. </s> <s xml:id="echoid-s16561" xml:space="preserve">præſertim qua ratione ex ea accipi poſ-<lb/>ſint altitudines Solis ſupra horizontem pro ſingulis horis in tropicis, & </s> <s xml:id="echoid-s16562" xml:space="preserve">æquatore, ex quibus poſtea confici <lb/>poſſint varia Horologium genera.</s> <s xml:id="echoid-s16563" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div397" type="section" level="1" n="288"> <head xml:id="echoid-head306" xml:space="preserve">L. D. D. P. V.</head> <pb file="0214" n="219"/> <pb o="193" file="0215" n="220"/> </div> <div xml:id="echoid-div398" type="section" level="1" n="289"> <head xml:id="echoid-head307" xml:space="preserve">ADDITAMENTVM <lb/>IN QVO,</head> <p> <s xml:id="echoid-s16564" xml:space="preserve">1. </s> <s xml:id="echoid-s16565" xml:space="preserve">Introductio ad Geographiam.</s> <s xml:id="echoid-s16566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16567" xml:space="preserve">2. </s> <s xml:id="echoid-s16568" xml:space="preserve">Apparatus ad Mathematicarum Studium.</s> <s xml:id="echoid-s16569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16570" xml:space="preserve">3. </s> <s xml:id="echoid-s16571" xml:space="preserve">Echometria.</s> <s xml:id="echoid-s16572" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div399" type="section" level="1" n="290"> <head xml:id="echoid-head308" style="it" xml:space="preserve">BREVIS INTRODVCTIO AD GEOGRAPHIAM.</head> <p> <s xml:id="echoid-s16573" xml:space="preserve">CVm animaduertiſſem quam plurimos poſt Sphæræ auſcultationem, magno iucun-<lb/>dæ æquè ac vtilis Geographiæ deſiderio teneri, iuſto eorum voluntati breui hac <lb/>Introductione ſatisfaciendum putaui: </s> <s xml:id="echoid-s16574" xml:space="preserve">enimuero præterquam quod per ſe iucun-<lb/>diſſima eſt hæc totius Terræ deſcriptio, eſt etiam ad hiſtoricorum, ac poetarum le-<lb/>ctionem, necnon ad familiaria de rerum ſtatu colloquia perneceſſaria.</s> <s xml:id="echoid-s16575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16576" xml:space="preserve">Coſmographia igitur vt nomen indicat, eſt totius Mundi deſcriptio, ſeu totius <lb/>mundanę Fabricę explicatio, quæ perficitur ex deſcriptione ſingularum mundi par-<lb/>tium, Elementorum ſcilicet, & </s> <s xml:id="echoid-s16577" xml:space="preserve">Cælorum, ex ponenendo loca, motus, figuras, ma-<lb/>gnitudines, & </s> <s xml:id="echoid-s16578" xml:space="preserve">illuminationes ſingularum, vti nos fecimus in tertia ſphæræ parte, <lb/>quam propterea Coſmographiam appellauimus.</s> <s xml:id="echoid-s16579" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16580" xml:space="preserve">Geographia, vt nomen indicat, & </s> <s xml:id="echoid-s16581" xml:space="preserve">de qua nunc eſt ſermo, eſt Terræ ſeu terreni globi deſcriptio, quæ ta-<lb/>men differt ab ea diſcriptione terræ, quam nos ſupra in tractatu de Terra exhibuimus quod hæc tantum ver-<lb/>ſatur circa ſuperficiem terreſtris globi deſcribendo omnes terræ partes, ſeu Prouincias, Inſulas, Vrbes, Ma-<lb/>ria, Lacus, &</s> <s xml:id="echoid-s16582" xml:space="preserve">c. </s> <s xml:id="echoid-s16583" xml:space="preserve">ita vt appareat horum omnium mutua ad inuicem collocatio, & </s> <s xml:id="echoid-s16584" xml:space="preserve">magnitudo, necnon eorum <lb/>ſitus reſpectu celi, ac proinde totius ſuperficiei terræ deſcriptio, vt infra melius patebit.</s> <s xml:id="echoid-s16585" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16586" xml:space="preserve">Chorographia, vt nomen indicat, eſt alicuius particularis regionis deſcriptio.</s> <s xml:id="echoid-s16587" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16588" xml:space="preserve">Primo igitur oportet Geographiæ ſtudioſum intellexiſſe, ac probè tenere ea, quæ tradita ſunt à nobis in <lb/>ſecunda parte ſphæræ de Circulis, videlicet de Horizonte, Meridiano, &</s> <s xml:id="echoid-s16589" xml:space="preserve">c. </s> <s xml:id="echoid-s16590" xml:space="preserve">Secundo paret ſibi globum Geo-<lb/>graphicum, ſine eo enim male omnia percipi poſſunt. </s> <s xml:id="echoid-s16591" xml:space="preserve">in eo igitur recognoſcat omnes ſphæræ circulos præ-<lb/>dictos, eumq; </s> <s xml:id="echoid-s16592" xml:space="preserve">aſtronomicè ſciat collocare, vt de ſphæra docuimus in Meridiano.</s> <s xml:id="echoid-s16593" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16594" xml:space="preserve">Nunc reliquum eſt vt ea, quæ Geographiæ ſunt propria breuiter explicemus, ac primo.</s> <s xml:id="echoid-s16595" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div400" type="section" level="1" n="291"> <head xml:id="echoid-head309" style="it" xml:space="preserve">De quinque Zonis.</head> <p> <s xml:id="echoid-s16596" xml:space="preserve">EXplicatis ſphæræ circulis facilè eſt intelligere quidnam ſint Zonæ, quiſque earum vſus. </s> <s xml:id="echoid-s16597" xml:space="preserve">Zonæ enim ſunt <lb/>quinquæ faſciæ (ζωνη enim faſciam ſignificat) quæ totum cælum ac terram circumcingunt. </s> <s xml:id="echoid-s16598" xml:space="preserve">omneſque <lb/>inter quatuor circulos æquatori parallellos continentur. </s> <s xml:id="echoid-s16599" xml:space="preserve">Ea quæ Torrida appellatur inter vtrunque Tropi-<lb/>cum contenta, mundum ambit.</s> <s xml:id="echoid-s16600" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s16601" xml:space="preserve">Semper Sole rubens, & </s> <s xml:id="echoid-s16602" xml:space="preserve">torrida ſempen ab igne.</s> <s xml:id="echoid-s16603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16604" xml:space="preserve">Duæ vero Temperatæ huic vtrinque aſſident, continenturque intra Tropicos, & </s> <s xml:id="echoid-s16605" xml:space="preserve">Polares circulos Lati-<lb/>tudinum; </s> <s xml:id="echoid-s16606" xml:space="preserve">quarum vna eſt borealis, altera auſtralis.</s> <s xml:id="echoid-s16607" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s16608" xml:space="preserve">--- quibus cura Dei <lb/>Temperiemque dedit mixta cum frigore flamma.</s> <s xml:id="echoid-s16609" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16610" xml:space="preserve">Reliquæ duæ Frigidæ, impropriè Zonæ dicuntur, cum enim vna contineatur intra circulum polarem bo-<lb/>realem, altera intra auſtralem, terminenturque eorum peripherijs, ſequitur eas nullatenus Zonæ figuram <lb/>habere, ſed circularem, & </s> <s xml:id="echoid-s16611" xml:space="preserve">rotundam; </s> <s xml:id="echoid-s16612" xml:space="preserve">in quarum medio ſint poli mundi, ſunt autem.</s> <s xml:id="echoid-s16613" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div401" type="section" level="1" n="292"> <head xml:id="echoid-head310" style="it" xml:space="preserve">Cær<unsure/>ulea glacie concretæ, atque imbribus atris.</head> <p> <s xml:id="echoid-s16614" xml:space="preserve">Zonarum vſus maximè in Geographia apparet, terreſtris enim globus ſecundnm cæleſtes Zonas, ac polos, <lb/>diſtinguitur, & </s> <s xml:id="echoid-s16615" xml:space="preserve">inſignitur. </s> <s xml:id="echoid-s16616" xml:space="preserve">a qualitatibus autem Zonarum, ideſt, a calore, temperie, frigore, etiam earum <lb/>habitatores, animalia, plantæ, &</s> <s xml:id="echoid-s16617" xml:space="preserve">c. </s> <s xml:id="echoid-s16618" xml:space="preserve">afficiuntur, vt in tractatu de Habitationibus melius patebit.</s> <s xml:id="echoid-s16619" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div402" type="section" level="1" n="293"> <head xml:id="echoid-head311" style="it" xml:space="preserve">De Paralellis.</head> <p> <s xml:id="echoid-s16620" xml:space="preserve">GEographi vt adhuc melius Terram cognitam in partes diſtribuerent, præter prædictos circulos, & </s> <s xml:id="echoid-s16621" xml:space="preserve">Zo-<lb/>nas, alios circulos, & </s> <s xml:id="echoid-s16622" xml:space="preserve">Zonulas etiam, ſeu climata excogitarunt. </s> <s xml:id="echoid-s16623" xml:space="preserve">Ptolemęus igitur deſignauit in ſ@perſi-<lb/>cie terræ circulos quoſdam æquatori paralellos, eoſque procedendo ab æquatore verſus bor<unsure/>eam, tanto ſpa-<lb/>@io inter ie diſtantes, quantũ requiritur, vt maxima dies vnius differat quadrãte horę a maxima die alterius pa- <pb o="194" file="0216" n="221" rhead="TRACTATVS"/> ralelli proximè ſequentis. </s> <s xml:id="echoid-s16624" xml:space="preserve">Porrò recentiores plures paralellos cõſtituunt quam Ptolemæus, quod maior por-<lb/>tio terræ nunc cognita, pluribus diſtinguenda ſit paralellis; </s> <s xml:id="echoid-s16625" xml:space="preserve">neq; </s> <s xml:id="echoid-s16626" xml:space="preserve">omnes in hoc numero conueniunt. </s> <s xml:id="echoid-s16627" xml:space="preserve">plures <lb/>ponunt 48. </s> <s xml:id="echoid-s16628" xml:space="preserve">paralellos, quorum vltimus d@ſtat ab æquatore gr. </s> <s xml:id="echoid-s16629" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s16630" xml:space="preserve">ſiue habet poli eleuationem, gr. </s> <s xml:id="echoid-s16631" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s16632" xml:space="preserve">vbi <lb/>videlicet dies max mus eſt horarum 24. </s> <s xml:id="echoid-s16633" xml:space="preserve">quare vltimus hic paralellus coincidit cũ circulo polari arctico, qui <lb/>confinium eſt Zonæ @emperatæ, & </s> <s xml:id="echoid-s16634" xml:space="preserve">frigidæ. </s> <s xml:id="echoid-s16635" xml:space="preserve">Alij paralellos vſq; </s> <s xml:id="echoid-s16636" xml:space="preserve">ad polum extendunt; </s> <s xml:id="echoid-s16637" xml:space="preserve">quos ſolent in meri-<lb/>d@ano globi<unsure/> Geographici deſcribere: </s> <s xml:id="echoid-s16638" xml:space="preserve">vel ad margines Mapparum vniuerſalium. </s> <s xml:id="echoid-s16639" xml:space="preserve">ſubi<unsure/>jciam autem Tabellam <lb/>paraleli<unsure/>os, ac climata continentem, in qua deſcripti erunt 48. </s> <s xml:id="echoid-s16640" xml:space="preserve">paralelli prędicti, vna cum maxima die eorum, <lb/>altitudine poli, & </s> <s xml:id="echoid-s16641" xml:space="preserve">locis inſign@oribus, per quæ incedunt.</s> <s xml:id="echoid-s16642" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div403" type="section" level="1" n="294"> <head xml:id="echoid-head312" style="it" xml:space="preserve">De Climatilius.</head> <p> <s xml:id="echoid-s16643" xml:space="preserve">CL@ma eſt Zonula quædam æquatori paralella duobus circulis æquatori paralellis terminata totam terrã <lb/>circumcingens, cuius latitudo tanta ſit, vt à termino ipſius auſtrali ad borealem, dies maxima excreuerit <lb/>perſemihoram. </s> <s xml:id="echoid-s16644" xml:space="preserve">cum autem dictum ſit vnum paralellum ab altero ſequenti differre per horæ quadrantem. <lb/></s> <s xml:id="echoid-s16645" xml:space="preserve">ſequitur ad clima vnum conſtituendum tres paralellos conuenire, duos quidem ipſum terminantes, tertium <lb/>verò<unsure/> eorum medium per ipſum incedens, qui dicitur paralellus per medium climatis: </s> <s xml:id="echoid-s16646" xml:space="preserve">non quod bifariam id <lb/>omnino ſecet, magis enim diſtant ab inuicem paralelli verſus Auſtrum, quam verſus Boream; </s> <s xml:id="echoid-s16647" xml:space="preserve">quemadmodũ <lb/>etiam climata anguſtiora ſunt, quanto borealiora; </s> <s xml:id="echoid-s16648" xml:space="preserve">ſed quoniam diſſerentia temporis, quæ eſt inter primum, <lb/>& </s> <s xml:id="echoid-s16649" xml:space="preserve">ſecundum, ſeu medium para ellum, æqua is eſt differentiæ, quę eſt inter eundem medium, & </s> <s xml:id="echoid-s16650" xml:space="preserve">tertium, nam <lb/>vtrobiq; </s> <s xml:id="echoid-s16651" xml:space="preserve">eſt horæ qua lrans<unsure/>, ideſt medius hic paralellus diuidit bifariam tempus illud ſemihoræ, quo extre-<lb/>mi paralelli clima terminantes ab inuicem diſcrepant. </s> <s xml:id="echoid-s16652" xml:space="preserve">In Tabula porro ſequenti intueri poteris non ſoium <lb/>paralellos, ſed e<unsure/>tiam climata ipſis connexa: </s> <s xml:id="echoid-s16653" xml:space="preserve">quorum prima ſeptem ſunt etiam antiquis Geographis vſitata: </s> <s xml:id="echoid-s16654" xml:space="preserve"><lb/>reliqua a recentioribus addita ſimul cum ſeptem prædictis explent numerum 23. </s> <s xml:id="echoid-s16655" xml:space="preserve">climatum. </s> <s xml:id="echoid-s16656" xml:space="preserve">In prima Tabel-<lb/>læ c@lumna ſunt numeri 48. </s> <s xml:id="echoid-s16657" xml:space="preserve">paralellorum. </s> <s xml:id="echoid-s16658" xml:space="preserve">in ſecunda numeri climatum 23. </s> <s xml:id="echoid-s16659" xml:space="preserve">in tertia maxima dies vni cuique <lb/>paralello conueniens. </s> <s xml:id="echoid-s16660" xml:space="preserve">In quarta eorundem altitudines poli, ſiue diſtantiæ ab æquator<unsure/>e. </s> <s xml:id="echoid-s16661" xml:space="preserve">In quinta climatum <lb/>amplitudines, ſiue latitudines, quarum borealiores ſunt ſemper minores. </s> <s xml:id="echoid-s16662" xml:space="preserve">In ſexta ſunt loca a quibus climata <lb/>denominantur, quod medij climatum paralelli per ea tranſeant. </s> <s xml:id="echoid-s16663" xml:space="preserve">Eadem omnia in hemiſphærio quoque <lb/>Auſtrali recentiores concipiunt.</s> <s xml:id="echoid-s16664" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div404" type="section" level="1" n="295"> <head xml:id="echoid-head313" style="it" xml:space="preserve">Tahula Paralellorum, & Climatum ſecundum rècentiores.</head> <note position="right" xml:space="preserve"> <lb/>Paral- \\ leli. # Clima- \\ ta. # ## Maxima \\ dies. # ## Altitudo \\ poli. # ## Amplitudo \\ Climatum. # Loca inſigniora per quæ \\ tranſeunt. <lb/># # H. # M. # Gr. # M. # Gr. # M. <lb/>1 # # 12 # 15 # 4 # 18 <lb/>2 # # 12 # 30 # 8 # 34 <lb/>3 # # 12 # 45 # 12 # 43 <lb/>4 # I # 13 # 0 # 16 # 43 # 7 # 50 # Per Meroem. <lb/>5 # # 13 # 15 # 20 # 33 <lb/>6 # II # 13 # 30 # 23 # 11 # 7 # 3 # Per S<unsure/>yenem ſub tropico ♋. <lb/>7 # # 13 # 45 # 27 # 36 <lb/>8 # III # 14 # 0 # 30 # 47 # 6 # 9 # Per Alexandriam. <lb/>9 # # 14 # 15 # 33 # 45 <lb/>10 # IIII # 14 # 30 # 36 # 30 # 5 # 17 # Per Rhodum, & Babylonem. <lb/>11 # V # 14 # 45 # 39 # 2 <lb/>12 # # 15 # 0 # 41 # 12 # 4 # 30 # Per Rom. Corſic. & Hell, <lb/>13 # VI # 15 # 15 # 43 # 32 <lb/>14 # # 15 # 30 # 44 # 29 # 3 # 48 # Per Venetias. <lb/>15 # VII # 15 # 45 # 47 # 20 <lb/>16 # # 16 # 0 # 49 # 1 # 3 # 13 # Per Podoliam. <lb/>17 # VIII # 16 # 15 # 50 # 53 <lb/>18 # # 16 # 30 # 51 # 58 # 2 # 44 # Per Vitebergam. <lb/>19 # IX # 16 # 45 # 53 # 17 <lb/>20 # # 17 # 0 # 54 # 19 # 2 # 17 # Per Roſtochium. <lb/>21 # X # 17 # 15 # 55 # 34 <lb/>22 # # 17 # 30 # 56 # 37 # 2 # 0 # Per Hyberniam. <lb/>23 # XI # 17 # 45 # 57 # 34 <lb/>24 # # 18 # 0 # 58 # 46 # 1 # 40 # Per Bous Caſtrum Noruegiæ. <lb/></note> <pb o="195" file="0217" n="222" rhead="AD GEOGRAPHIAM."/> <note position="right" xml:space="preserve"> <lb/>Paral- \\ leli. # Clima- \\ ta. # ## Maxima \\ dies. # ## Altitudo \\ poli. # ## Amplitudo \\ Climatum. # Loca inſigniora per quæ \\ tranſeunt. <lb/># # H. # M. # Gr. # M. # Gr. # M. <lb/>25 # # 18 # 15 # 59 # 14 <lb/>26 # XII # 18 # 30 # 59 # 59 # 1 # 16 # Per Gothiam. <lb/>27 # # 18 # 45 # 60 # 40 <lb/>28 # XIII # 19 # 0 # 61 # 18 # 1 # 13 # Per Bergis Nouergiæ. <lb/>29 # # 19 # 15 # 61 # 53 <lb/>30 # XIIII # 19 # 30 # 62 # 25 # 1 # 1 # Per Viburgum Filandiæ. <lb/>31 # # 19 # 45 # 62 # 53 <lb/>32 # XV # 20 # 0 # 63 # 22 # 0 # 52 # Per Arotiam Sueciæ. <lb/>33 # # 20 # 15 # 63 # 40 <lb/>34 # XVI # 20 # 30 # 64 # 6 # 0 # 44 # Per ſluuij Dalecanlij oſtia. <lb/>35 # # 20 # 45 # 64 # 30 <lb/>36 # XVII # 21 # 0 # 64 # 49 # 0 # 36 # Per reliqua <lb/>37 # # 21 # 15 # 65 # 9 <lb/>38 # XVIII # 21 # 30 # 65 # 21 # 0 # 29 # loca Nor. <lb/>39 # # 21 # 45 # 65 # 35 <lb/>40 # XIX # 22 # 0 # 65 # 47 # 0 # 23 # uegiæ. <lb/>41 # # 22 # 15 # 65 # 57 <lb/>42 # XX # 22 # 30 # 66 # 0 # 0 # 16 # Sueciæ. <lb/>43 # # 22 # 45 # 66 # 14 <lb/>44 # XXI # 23 # 0 # 66 # 20 # 0 # 11 # Alba Ruſſiæ, <lb/>45 # # 23 # 15 # 66 # 25 <lb/>46 # XXII # 23 # 30 # 66 # 28 # 0 # 0 # & Inſularum <lb/>47 # # 23 # 45 # 66 # 30 <lb/>48 # XIII # 24 # 0 # 66 # 31 # 0 # 0 # vicinarum. <lb/></note> </div> <div xml:id="echoid-div405" type="section" level="1" n="296"> <head xml:id="echoid-head314" style="it" xml:space="preserve">De Meridianis.</head> <p> <s xml:id="echoid-s16665" xml:space="preserve">VT adhuc melius totam terram, ac partes eius diſtinguerent, ac dignoſcerent, deſignarunt infinitos me-<lb/>ridianos, ſeu per ſingula puncta æquatoris intelligunt duci ſingulos meridianos, ita vt nullus ſit in terra <lb/>locus, qui non ſit ſub eorum aliquo. </s> <s xml:id="echoid-s16666" xml:space="preserve">Porrò ex iſtis meridianum vnum eſſe omnium primum ſt<unsure/>atuerunt, illum <lb/>videlicet, qui per extremum terræ cognitæ occidentale duceretur, iſque fuit meridianus Inſularum Fortu-<lb/>natarum, nihil enim certi vltra eas antiqui cognouerunt. </s> <s xml:id="echoid-s16667" xml:space="preserve">ab hoc itaque meridiano alij numerabantur proce-<lb/>dendo verſus orientem; </s> <s xml:id="echoid-s16668" xml:space="preserve">quapropter gradus etiam æquatoris terreſtris ab hoc meridiano numerari incipiunt <lb/>procedendo verſus orientem, quemadmodum in cęlo gradus Zodiaci numerantur à<unsure/> puncto æquinoctij ver-<lb/>ni, ſeu à primo gradus Arietis verſus orientem procedendo; </s> <s xml:id="echoid-s16669" xml:space="preserve">ita vt ibi Zodiaci initium conſtituatur.</s> <s xml:id="echoid-s16670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16671" xml:space="preserve">In globis autem Geographicis, & </s> <s xml:id="echoid-s16672" xml:space="preserve">vniuerſalibus Tabulis ſcribi ſolent meridiani per quinos tantummodo <lb/>gradus æquatoris, plures enim parerent confuſionem; </s> <s xml:id="echoid-s16673" xml:space="preserve">quare erunt omnes 36. </s> <s xml:id="echoid-s16674" xml:space="preserve">qui tamen totum globum in <lb/>partes 72. </s> <s xml:id="echoid-s16675" xml:space="preserve">diuidunt quaſi in ſegmenta quædam ab vno polo ad alterum pertinentia. </s> <s xml:id="echoid-s16676" xml:space="preserve">Primus meridianus eſt <lb/>Inſularum Fortunatarum. </s> <s xml:id="echoid-s16677" xml:space="preserve">ſecundus tranſit per 5. </s> <s xml:id="echoid-s16678" xml:space="preserve">grad. </s> <s xml:id="echoid-s16679" xml:space="preserve">æquatoris. </s> <s xml:id="echoid-s16680" xml:space="preserve">tertius per 10. </s> <s xml:id="echoid-s16681" xml:space="preserve">quartus per 15. </s> <s xml:id="echoid-s16682" xml:space="preserve">& </s> <s xml:id="echoid-s16683" xml:space="preserve">ſic dein-<lb/>ceps orientem verſus. </s> <s xml:id="echoid-s16684" xml:space="preserve">Cæterum de vſu horum meridianorum apud Geographos. </s> <s xml:id="echoid-s16685" xml:space="preserve">vide quæ ſupra de vſu me-<lb/>ridi ani in Sphæra ſcripſimus, poſt<unsure/>ea lege quæ ſequuntur.</s> <s xml:id="echoid-s16686" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div406" type="section" level="1" n="297"> <head xml:id="echoid-head315" style="it" xml:space="preserve">De longitudine, & latitudine Terræ, & locorum omni@m.</head> <p> <s xml:id="echoid-s16687" xml:space="preserve">QVemadmodum Aſtronomi in cœlo fingularum ſtellarum loca per earum longitudines, ae latitudines <lb/>determinant: </s> <s xml:id="echoid-s16688" xml:space="preserve">ita etiam Geographi ſingulorum locorum ſitum in terra definia<unsure/>nt, & </s> <s xml:id="echoid-s16689" xml:space="preserve">conſtitutint medio <lb/>longitudinum, ac latitudinum. </s> <s xml:id="echoid-s16690" xml:space="preserve">vt autem melius hæc percipias, vide quæ ſupra ſcripſimus de locis <lb/>ſtellarum, necnon de longitudine, & </s> <s xml:id="echoid-s16691" xml:space="preserve">latitudine earum in tractatu de Zodiaco, & </s> <s xml:id="echoid-s16692" xml:space="preserve">Ecliptica: </s> <s xml:id="echoid-s16693" xml:space="preserve">ex quibus aduer-<lb/>tere debes longitudines, & </s> <s xml:id="echoid-s16694" xml:space="preserve">latitudines Aſtronomorum, & </s> <s xml:id="echoid-s16695" xml:space="preserve">Geographorum differre, quod illæ referuntur ad <lb/>eclipticam auxilio circulorum latitudinum, qui tranſeu<unsure/>nt per polos eclipticæ; </s> <s xml:id="echoid-s16696" xml:space="preserve">hæ vero referantur ad æqua-<lb/>torem terreſtrem auxilio meridianorum, qui pariter tranſeunt per polos æquatoris: </s> <s xml:id="echoid-s16697" xml:space="preserve">Quare quod ibi latitu-<lb/>dinum circuli præſtant, hic meridiani efficiunt. </s> <s xml:id="echoid-s16698" xml:space="preserve">Quid longitudo, & </s> <s xml:id="echoid-s16699" xml:space="preserve">latitudo ſit Geographis, dictum eſt in <lb/>cap. </s> <s xml:id="echoid-s16700" xml:space="preserve">de meridiano, num. </s> <s xml:id="echoid-s16701" xml:space="preserve">8. </s> <s xml:id="echoid-s16702" xml:space="preserve">& </s> <s xml:id="echoid-s16703" xml:space="preserve">9. </s> <s xml:id="echoid-s16704" xml:space="preserve">de officijs eius. </s> <s xml:id="echoid-s16705" xml:space="preserve">vbi iterum aduertendum eſt, quod quamuis latitudines in ter-<lb/>ra ſint diſtantiæ ab æquatore verſus alterutrum polorum, in cælo tamen diſtantiæ ab æquatore ad vtrumuis <lb/>polorum dicuntur declinationes, vt in cap. </s> <s xml:id="echoid-s16706" xml:space="preserve">de æquatore dictum eſt. </s> <s xml:id="echoid-s16707" xml:space="preserve">Auctor quidam duplicem facit longi- <pb o="196" file="0218" n="223" rhead="INTRODVCTIO"/> tudinem orientalem, & </s> <s xml:id="echoid-s16708" xml:space="preserve">occidentalem; </s> <s xml:id="echoid-s16709" xml:space="preserve">illa continet gr. </s> <s xml:id="echoid-s16710" xml:space="preserve">180. </s> <s xml:id="echoid-s16711" xml:space="preserve">verſus orientem incipientes à meridiano Fortu-<lb/>natarum; </s> <s xml:id="echoid-s16712" xml:space="preserve">hæc vero numerat alios 180. </s> <s xml:id="echoid-s16713" xml:space="preserve">ab eodem meridiano verſus occidentem quæ m@hi probantur<unsure/>; </s> <s xml:id="echoid-s16714" xml:space="preserve">ſicut <lb/>enim duplex latitudo ſtatuitur Borealis, & </s> <s xml:id="echoid-s16715" xml:space="preserve">Auſtralis, ita duplex longitudo oriẽ<unsure/>talis, & </s> <s xml:id="echoid-s16716" xml:space="preserve">occide<unsure/>talis vtilis erit.</s> <s xml:id="echoid-s16717" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div407" type="section" level="1" n="298"> <head xml:id="echoid-head316" style="it" xml:space="preserve">Qua ratione locorum latitudines inueſtigentur.</head> <p> <s xml:id="echoid-s16718" xml:space="preserve">ALias in tractatu de circulis Sphæræ oſtendimus tantam eſſe cuiuſuis loci latitudinem, ſiue diſtant@am ab <lb/>æquatore, quanta eſt e@uſdem loci, poli eleuatio: </s> <s xml:id="echoid-s16719" xml:space="preserve">Inuenias igitur altitudinem poli, quo diximus modo <lb/>in capite de meridiano, & </s> <s xml:id="echoid-s16720" xml:space="preserve">ſimul inueneris eiuſdem lat@tudinem.</s> <s xml:id="echoid-s16721" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div408" type="section" level="1" n="299"> <head xml:id="echoid-head317" style="it" xml:space="preserve">Qua ratione locorum longitudines inueſtigentur.</head> <p> <s xml:id="echoid-s16722" xml:space="preserve">DIffie<unsure/>ilior multo eſt hæc inueſtigatio præcedenti, nec adeo certa; </s> <s xml:id="echoid-s16723" xml:space="preserve">cauſa difficultatis eſt, quod nullum ſit <lb/>in cælo punctum propè æquatorem fixum ac ſtabile, ad quod, ſicuti ad polum, diſtantiæ @ocorum referri <lb/>poſſint: </s> <s xml:id="echoid-s16724" xml:space="preserve">modus tamen Geographis vſitatior eſt hic. </s> <s xml:id="echoid-s16725" xml:space="preserve">Primo ex mẽſuratione aliqua nautica cognouerunt quan-<lb/>tum diſtarent nonnulla loca occidentaliſſima Africæ, aut Hiſpaniæ, à meridiano Fortunatarum; </s> <s xml:id="echoid-s16726" xml:space="preserve">quę diſtan-<lb/>tia erat ipſa eorum longitudo: </s> <s xml:id="echoid-s16727" xml:space="preserve">Idem cognoſcere etiam potuerunt per Lunares eclipſes hac ratione, exem-<lb/>pli gratia tempore alicuius eclipſis Lunaris, vnus obſeruator in Inſulis Fortunatis obſeruauit initium eclipſis <lb/>Lunæ contigiſſe hora 12. </s> <s xml:id="echoid-s16728" xml:space="preserve">abſoluta præcisè, ſiue media nocte: </s> <s xml:id="echoid-s16729" xml:space="preserve">alius obſeruator exiſtens Vlyſſipone in Hiſpa-<lb/>nia eiuſdem eclipſis initium notauit accidiſſe hora 12 {1/3}. </s> <s xml:id="echoid-s16730" xml:space="preserve">poſt meridiem, hoc eſt, vna tertia parte horæ poſt <lb/>mediam noctem. </s> <s xml:id="echoid-s16731" xml:space="preserve">differentia igitur temporis, quæ eſt {1/3}. </s> <s xml:id="echoid-s16732" xml:space="preserve">horæ qua Vlyſſipone tardius incipit Lunæ defectus, <lb/>indicat Vlyſſiponem eſſe orientaliorem, quam locus alter Fortunatarum; </s> <s xml:id="echoid-s16733" xml:space="preserve">cum enim illi tardius reſpectu ſui <lb/>meridiani eadem defectio apparue<unsure/>rit, ſignum eſt Solem prius eum attigiſſe, quam alterum quoniam vero <lb/>Sol motu diurno hora conficit gr. </s> <s xml:id="echoid-s16734" xml:space="preserve">15. </s> <s xml:id="echoid-s16735" xml:space="preserve">vna horæ tertia conficiet gr. </s> <s xml:id="echoid-s16736" xml:space="preserve">5. </s> <s xml:id="echoid-s16737" xml:space="preserve">cum ergo Sol prætereat meridianum <lb/>Vlyſſiponenſem vna horæ tertia prius quam Fortunatarum, diſtabit ille ab hoc gr. </s> <s xml:id="echoid-s16738" xml:space="preserve">5. </s> <s xml:id="echoid-s16739" xml:space="preserve">quod erat propoſitum. <lb/></s> <s xml:id="echoid-s16740" xml:space="preserve">Cognita longitudine vnius loci obſeruant deinde eclipſium momenta alterius loci, cuius longitudo ſit inue-<lb/>ſtiganda, eaq; </s> <s xml:id="echoid-s16741" xml:space="preserve">comparant cum temporibus, quibus in priori loco accid@t; </s> <s xml:id="echoid-s16742" xml:space="preserve">ex quorum differentia erunt diſtan-<lb/>tia meridiani loci aſſumpti à meridiano Fortunatarum, quæ eſt ipſa eius longitudo. </s> <s xml:id="echoid-s16743" xml:space="preserve">Loco ecl@pſis aſſumere <lb/>poſſumus planetæ cuiuſpiam coniunctionem, vel cum alio planeta, vel cum quapiam affixarum.</s> <s xml:id="echoid-s16744" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16745" xml:space="preserve">Cum primum in Mathematicis tyrocinium ponerem, venit in mentem alius modus, qui certiſſimus eſſet <lb/>ſi Horologium exactiſſimum, ac diuturnum fabricari poſſet. </s> <s xml:id="echoid-s16746" xml:space="preserve">is eſt hui@ſmodi. </s> <s xml:id="echoid-s16747" xml:space="preserve">aſſumo Horologium, quod <lb/>exactè diem totum oſtendat, ſeu quod indicat diem totum elapſum eſſe, ſeu iam 24. </s> <s xml:id="echoid-s16748" xml:space="preserve">horas præterijſſe; </s> <s xml:id="echoid-s16749" xml:space="preserve">Volo <lb/>igitur exempli gratia, inuenire quantum Roma ſit orientalior Mediolano, ſeu quanta ſit differentia longi-<lb/>tudinum inter Romam, & </s> <s xml:id="echoid-s16750" xml:space="preserve">Mediolanum; </s> <s xml:id="echoid-s16751" xml:space="preserve">exiſtens ego primum Mediolani obſeruo de media nocte ſtellam <lb/>quampiam dum meridianum attingit, atq; </s> <s xml:id="echoid-s16752" xml:space="preserve">in eodem momento Horologium, quod prius ſilebat ſoluo; </s> <s xml:id="echoid-s16753" xml:space="preserve">quo <lb/>facto ſtatim Romam peto, Horologium ferens mecum; </s> <s xml:id="echoid-s16754" xml:space="preserve">illud ſtatim ac vnam diem elapſam eſſe indicauerit, <lb/>iterum ad priſtinum reſtituens; </s> <s xml:id="echoid-s16755" xml:space="preserve">ſicqu<unsure/>e ſemper facio quouſque Romam peruenerim; </s> <s xml:id="echoid-s16756" xml:space="preserve">vbi cum Horologium <lb/>ſuas integras periodos exegerit, neceſſario ſtella Mediolani aſſumpta, obtinebit eundem Mediolanenſem <lb/>meridianum quia ſingulis diebus eundem meridianum repetit: </s> <s xml:id="echoid-s16757" xml:space="preserve">abſolutis autem Horologij periodis, neceſ-<lb/>ſario etiam abſoluti erunt totidem dies; </s> <s xml:id="echoid-s16758" xml:space="preserve">quare ſtella eadem eundem meridianum obtinebit ſtatim ac Horo-<lb/>@ogium Romę fuerit abſolutum. </s> <s xml:id="echoid-s16759" xml:space="preserve">quo temporis momento Mediolan erit media nox, Romę autem erit hora <lb/>tardior, v. </s> <s xml:id="echoid-s16760" xml:space="preserve">g. </s> <s xml:id="echoid-s16761" xml:space="preserve">vna horæ tertia poſt mediam noctem, quæ differentia temporis indicat Romanam longitudi-<lb/>nem maiorem eſſe Mediolanenſi gr. </s> <s xml:id="echoid-s16762" xml:space="preserve">5.</s> <s xml:id="echoid-s16763" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16764" xml:space="preserve">Poſtquam igitur Geographi locorum latitudines, & </s> <s xml:id="echoid-s16765" xml:space="preserve">longirudines compererint, conſcribunt Tabulas lo-<lb/>corum cum ſuis longit. </s> <s xml:id="echoid-s16766" xml:space="preserve">& </s> <s xml:id="echoid-s16767" xml:space="preserve">latit. </s> <s xml:id="echoid-s16768" xml:space="preserve">vt videre eſt apud Ptolemęum, & </s> <s xml:id="echoid-s16769" xml:space="preserve">alios; </s> <s xml:id="echoid-s16770" xml:space="preserve">huiuſmodi Tabulam, ſed breuem, quã <lb/>ſupra in cap. </s> <s xml:id="echoid-s16771" xml:space="preserve">de meridiano promiſſimus, nunc exhibemus, videlicet ſequentem.</s> <s xml:id="echoid-s16772" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div409" type="section" level="1" n="300"> <head xml:id="echoid-head318" style="it" xml:space="preserve">Tabula continens longitudines, latitudineſq; præcipuærum vrbium, & locorum.</head> <note position="right" xml:space="preserve"> <lb/># Longit. # ## Latit. # # Longit. # ## Latit. <lb/># Gr. # G. # M. # # Gr. # G. # M. <lb/>AEtna mons Siciliæ. # 39 # 38 # 20 # Babylon Chaldæorum. # 83 # 34 # 0 <lb/>Alba Græ. Belgrado. # 45 # 47 # 40 # Bamberga. # 32 # 49 # 56 <lb/>Alexandria Aegypti. # 60 # 30 # 0 # Barcino. # 17 # 41 # 36 <lb/>Ancona. # 38 # 43 # 40 # Bengala Indiæ. # 138 # 23 # 0 <lb/>Andegaui. # 19 # 47 # 30 # Bethlehem. # 56 # 32 # 0 <lb/>Antuerpia. # 24 # 51 # 48 # Bononia Italiæ. # 33 # 44 # 30 <lb/>Adem in Arabia. # 83 # 13 # 0 # Brixia. # 32 # 45 # 0 <lb/>Aretium Hetruriæ. # 35 # 42 # 50 # Buda. # 47 # 47 # 0 <lb/>Armutia, Ormus. # 95 # 27 # 24 # Calicut Indiæ. # 112 # 17 # 0 <lb/>Athenæ. # 53 # 37 # 15 # Calaris Sardiniæ. # 31 # 36 # 30 <lb/>Auenio, Auignone. # 23 # 50 # 10 # Cayrum Aegypti. # 64 # 29 # 40 <lb/></note> <pb o="197" file="0219" n="224" rhead="AD GEOGRAPHIAM."/> <note position="right" xml:space="preserve"> <lb/># Longit. # 35 # 15 # # Longit. # ## Latit. <lb/># Gr. # 41 # 45 # # Gr. # Gr. # M. <lb/>Candia, Cretæ. # 54 # 37 # 15 # Mexicum. # 182 # 20 # 0 <lb/>Cæſarauguſta. # 14 # 51 # 0 # Mons regius Franconiæ, patria \\ Io: Regiom. <lb/>Catanea. # 40 # 44 # 0 # # 31 # 50 # 15 <lb/>Colonia Agrippina. # 28 # 40 # 30 # Mozambique. # 67 # 15 # 0 <lb/>Compoſtella. # 7 # ## Latit. # Mutina. # 21 # 44 # 3@ <lb/>Conimbrica Luſitaniæ. # 6 # Gr. # M. # Narbona. # 21 # 43 # 0 <lb/>Conſtantinopolis. # 56 # 43 # 0 # Neapolis Campani@. # 39 # 41 # 0 <lb/>Cracouia Poloniæ. # 43 # 50 # 12 # Nicea. # 75 # 42 # 0 <lb/>Cremona. # 33 # 44 # 0 # Nurſia S. Bened. patr. # 38 # 43 # 0 <lb/>Cuzcum in Peru. # 312 # 15 auſt. # 0 # Oenipontum, Iſpruch. # 33 # 47 # 0 <lb/>Damaſcus. # 69 # 32 # 0 # Panhormus, Palermo. # 37 # 38 # 0 <lb/>Dantiſcum. # 45 # 55 # 0 # Papia. # 31 # 44 # 50 <lb/>Dyrrachium. # 45 # 41 # 0 # Parma, hic ſcribo. # 32 # 44 # 30 <lb/>Ecbatana, Tauris. # 89 # 41 # 0 # Patauium. # 33 # 45 # 0 <lb/>Edemburgum Scotiæ. # 27 # 59 # 20 # Piſtorium, Piſtoia. # 33 # 43 # 0 <lb/>Epheſus in Ionia. # 68 # 37 # 40 # Placentia. # 32 # 44 # 0 <lb/>Epidaurus. # 52 # 36 # 25 # Quitum in Peru. # 303 # 20 # 0 <lb/>Feſſa in Africa. # 10 # 35 # 0 # Rauenna. # 35 # 44 # 20 <lb/>Florentia. # 34 # 43 # 40 # Regium Lepidi. # 36 # 44 # 30 <lb/>Francfordia ad Mœnum. # 30 # 50 # 30 # ROMA. # 36 # 41 # 56 <lb/>Francfordia ad Oderam. # 34 # 52 # 30 # Salamantica. # 9 # 40 # 0 <lb/>Gades. # 6 # 22 # 20 # Saſſarum in Sardinia<unsure/>. # 31 # 39 # 0 <lb/>Gandauum. # 20 # 51 # 30 # Senæ, Siena. # 34 # 43 # 0 <lb/>Gaza. # 63 # 32 # 0 # Strigonium. # 42 # 48 # 0 <lb/>Genua. # 30 # 44 # 0 # Syene, Aſna. # 62 # 23 # 30 <lb/>Goa Indiæ. # 115 # 17 # 0 # Syracuſæ. # 40 # 37 # 30 <lb/>Granata. # 11 # 38 # 0 # Tarentum. # 45 # 40 # 0 <lb/>Hadrianopolis. # 52 # 42 # 45 # Tarracona. # 16 # 41 # 0 <lb/>Hierapolis, Aleppo. # 71 # 38 # 0 # Tauris Perſiæ. # 82 # 41 # 0 <lb/>Hiſpalis, Siuiglia. # 7 # 37 # 0 # Thebæ. # 51 # 38 # 0 <lb/>leroſolyma. # 66 # 31 # 40 # Theodoſia, Caſſa. # 62 # 49 # 20 <lb/>Iuſtinopolis Iſtriæ. # 35 # 46 # 0 # D. Thomæ Inſula. # 33 # 41 # 0 <lb/>Lacædemonia. # 50 # 35 # 30 # Toletum. # 10 # 40 # 0 <lb/>Lauretum. # 37 # 43 # 0 # Trapezus. # 71 # 40 # 0 <lb/>Leopolis Ruſſiæ. # 43 # 50 # 30 # Tunetum. # 33 # 32 # 0 <lb/>Londunum, Londra. # 10 # 52 # 30 # Valentia Hiſpaniæ. # 14 # 39 # 30 <lb/>Lugdunum, Lione. # 28 # 45 # 0 # Venetiæ. # 34 # 45 # 0 <lb/>Lutetia, Parigi. # 23 # 48 # 40 # Verona. # 33 # 45 # 0 <lb/>Malepur in India. # 424 # 14 # 0 # Vienna Auſtriæ. # 38 # 48 # 0 <lb/>Mantua. # 33 # 44 # 30 # Vlyſſipona, Lisbona. # 5 # 39 # 38 <lb/>Marſilia. # 24 # 43 # 10 # Vormatia. # 28 # 49 # 45 <lb/>Mediolanum. # 31 # 45 # 0 # Zofa<unsure/>la Africæ auſtralis. # 64 # 20 au@. # 0 <lb/></note> <p> <s xml:id="echoid-s16773" xml:space="preserve">Vtinam verò Geographicum iſtud ſtudium, non obiter tantum, ſed nauiter hoc etiam@ſęculo coleretur: <lb/></s> <s xml:id="echoid-s16774" xml:space="preserve">non enim tanta præſertim longitudinum differentia, ac diſcordia inter authores cernetur. </s> <s xml:id="echoid-s16775" xml:space="preserve">qua de cauſa nos <lb/>tantum gradus integros longitudinum ſine vllis minutis ſcripſimus. </s> <s xml:id="echoid-s16776" xml:space="preserve">Sed<unsure/> fortè in hac re Regum, ac Princi-<lb/>pum captanda eſt liberalitas, quam pro eorum in hæc pulcherrima ſtudia amore, ſpero non defuturam. </s> <s xml:id="echoid-s16777" xml:space="preserve">ſru-<lb/>@tus autem, & </s> <s xml:id="echoid-s16778" xml:space="preserve">vſus hui<unsure/>us Tabellæ eſt cognoſcere exactè in ſuperficie terræ locum, ſeu ſitum cuiuſuis V@bis@. </s> <s xml:id="echoid-s16779" xml:space="preserve"><lb/>Oppidi, &</s> <s xml:id="echoid-s16780" xml:space="preserve">c. </s> <s xml:id="echoid-s16781" xml:space="preserve">quod per eius longitudinem, & </s> <s xml:id="echoid-s16782" xml:space="preserve">latitudinem aſſequimur, vti Geographi docent.</s> <s xml:id="echoid-s16783" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div410" type="section" level="1" n="301"> <head xml:id="echoid-head319" style="it" xml:space="preserve">Qua ratione globus Geographicus constituatur.</head> <p> <s xml:id="echoid-s16784" xml:space="preserve">EOdem prorſus modo, quo ſ@ellas omnes per earũ longitudines, & </s> <s xml:id="echoid-s16785" xml:space="preserve">latitudines depingunt in globo Aſtro-<lb/>nomico, de cuius conſtr@cti<unsure/>one in trac@. </s> <s xml:id="echoid-s16786" xml:space="preserve">de Steilis ſatis diximus, ita depingunt etiam in globo Geogra-<lb/>p@ico omnia terræ loca, quo@um longitudines, & </s> <s xml:id="echoid-s16787" xml:space="preserve">latitudines depræhenſæ fuerint.</s> <s xml:id="echoid-s16788" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16789" xml:space="preserve">In globo Geographico deſignant ante omnia æquatorem, tropicos, & </s> <s xml:id="echoid-s16790" xml:space="preserve">circulos polares; </s> <s xml:id="echoid-s16791" xml:space="preserve">præterea meri-<lb/>dianos ſaltem per qui nos gradus æquatoris, qui erunt 36. </s> <s xml:id="echoid-s16792" xml:space="preserve">horum vnum ſtatuunt pro meridiano Fortunata-<lb/>rum, qui ſcilicet ſit omnium primus, eumq; </s> <s xml:id="echoid-s16793" xml:space="preserve">facto initio ab æquatore diuidunt in gradus, quorum numera-<lb/>tio incipit ab æquatore, & </s> <s xml:id="echoid-s16794" xml:space="preserve">deſinit in po@is, ita vt in polis ſint nonageſimi gradus: </s> <s xml:id="echoid-s16795" xml:space="preserve">ſed relege conſtructione@ <lb/>@lobi ſtelliferi, quæ huic ſimillima eſt, & </s> <s xml:id="echoid-s16796" xml:space="preserve">omnia<unsure/> tibi perſpicua reddentur.</s> <s xml:id="echoid-s16797" xml:space="preserve"/> </p> <pb o="198" file="0220" n="225" rhead="INTRODVCTIO"/> </div> <div xml:id="echoid-div411" type="section" level="1" n="302"> <head xml:id="echoid-head320" style="it" xml:space="preserve">Antipodes, Antæci, Periæci.</head> <p> <s xml:id="echoid-s16798" xml:space="preserve">DEſcriptis in Geographíco globo locis<unsure/> omnibus cognitis, & </s> <s xml:id="echoid-s16799" xml:space="preserve">conſequenter tota ferè terra habitabili, <lb/>quædam inter eorum habitatores notandæ ſunt habitudines, vnde quidam dicuntur Anti<unsure/>podes, An-<lb/>tæci, Periæci.</s> <s xml:id="echoid-s16800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16801" xml:space="preserve">Antipodes ij dicuntur, qui diametr@liter opponuntur, i@demq; </s> <s xml:id="echoid-s16802" xml:space="preserve">ſunt ſub eodem meridiano: </s> <s xml:id="echoid-s16803" xml:space="preserve">ſed præterea <lb/>(extra ſphæram rectam, & </s> <s xml:id="echoid-s16804" xml:space="preserve">parale@@am) ſunt in oppoſitis paralellis, quo rum vnus eſt b@@ealis, alt<unsure/>er auſtralis; <lb/></s> <s xml:id="echoid-s16805" xml:space="preserve">vnde habent æquales latitudines, ſed diuerſas, vna enimeſt borealis, alter auſtralis. </s> <s xml:id="echoid-s16806" xml:space="preserve"><gap/> ſtr is <lb/> <anchor type="figure" xlink:label="fig-0220-01a" xlink:href="fig-0220-01"/> A B C D. </s> <s xml:id="echoid-s16807" xml:space="preserve">in quo circu<unsure/>lus A E C G B H D F, ſit meridianus, æqu@@oris autem <lb/>C D. </s> <s xml:id="echoid-s16808" xml:space="preserve">ſint E F. </s> <s xml:id="echoid-s16809" xml:space="preserve">& </s> <s xml:id="echoid-s16810" xml:space="preserve">G H. </s> <s xml:id="echoid-s16811" xml:space="preserve">diametri duorum paralellorum oppoſirorum, quo-<lb/>rum ille ſit borealis, hic auſtralis. </s> <s xml:id="echoid-s16812" xml:space="preserve">A. </s> <s xml:id="echoid-s16813" xml:space="preserve">polus arcticus, B. </s> <s xml:id="echoid-s16814" xml:space="preserve">antarcticus: </s> <s xml:id="echoid-s16815" xml:space="preserve">lam ha@i-<lb/>tatores duo G. </s> <s xml:id="echoid-s16816" xml:space="preserve">& </s> <s xml:id="echoid-s16817" xml:space="preserve">F. </s> <s xml:id="echoid-s16818" xml:space="preserve">ſunt mutuo Antipodes, opponun@ur enim lecundum <lb/>diametrum G F. </s> <s xml:id="echoid-s16819" xml:space="preserve">ſuntque iu oppoſitis paralellis E F G H. </s> <s xml:id="echoid-s16820" xml:space="preserve">& </s> <s xml:id="echoid-s16821" xml:space="preserve">@ub eodem meri-<lb/>diano. </s> <s xml:id="echoid-s16822" xml:space="preserve">eadem ratione A B. </s> <s xml:id="echoid-s16823" xml:space="preserve">ſunt Antipodes, ſimiliter C D. </s> <s xml:id="echoid-s16824" xml:space="preserve">quamuis non ſint <lb/>ſub oppoſitis paralellis. </s> <s xml:id="echoid-s16825" xml:space="preserve">Parmenſes, & </s> <s xml:id="echoid-s16826" xml:space="preserve">ij qui degunt ſu<unsure/>b altitudine pol@ au-<lb/>ſtralis gri 45. </s> <s xml:id="echoid-s16827" xml:space="preserve">ſeu in oppoſito paralello, ſuntque ſub eodem meridiano in par-<lb/>te dia@@ traliter oppoſita, ſunt inuicem Antipodes; </s> <s xml:id="echoid-s16828" xml:space="preserve">dicuntur etiam Anti-<lb/>cthones. </s> <s xml:id="echoid-s16829" xml:space="preserve">qui ſunt ſub diuerſis polis, extra omnes paralellos, ſunt tamen Anti-<lb/>podes. </s> <s xml:id="echoid-s16830" xml:space="preserve">Porrò Antipodibus contraria omnia accidunt, quamuis enim ha-<lb/>beant eundem horizontem, eius tamen auerſas fa<unsure/>cies inhabitant, & </s> <s xml:id="echoid-s16831" xml:space="preserve">oppoſita<unsure/> <lb/>hæmiſpheria. </s> <s xml:id="echoid-s16832" xml:space="preserve">quando nos Aeſtatem habemus: </s> <s xml:id="echoid-s16833" xml:space="preserve">illi Hyeme@ habent: </s> <s xml:id="echoid-s16834" xml:space="preserve">quan-<lb/>do nos diem, ij noctem: </s> <s xml:id="echoid-s16835" xml:space="preserve">quando nobis occidit Sol, ijs or tur: </s> <s xml:id="echoid-s16836" xml:space="preserve">cum nobis dies longiſſima, is breuiſſima, &</s> <s xml:id="echoid-s16837" xml:space="preserve">c.</s> <s xml:id="echoid-s16838" xml:space="preserve"/> </p> <div xml:id="echoid-div411" type="float" level="2" n="1"> <figure xlink:label="fig-0220-01" xlink:href="fig-0220-01a"> <image file="0220-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0220-01"/> </figure> </div> <p> <s xml:id="echoid-s16839" xml:space="preserve">Antæci, ideſt, Anticolæ ſunt, qui habitant ſub oppoſitis paralellis, ſuntque ſub eodem meri@iano, non ta-<lb/>men diametraliter, quia ſunt ſub eodem ſemicirculo meridiani inter polos intercepto, ſic E G. </s> <s xml:id="echoid-s16840" xml:space="preserve">ſunt Antæ-<lb/>ci, necnon F G. </s> <s xml:id="echoid-s16841" xml:space="preserve">ſic Parmenſes habent ſuos Antæcos ſub eodem meridiano ſitos, ſed tãtum vltra æquatorem <lb/>ad Auſtrum, quantum Parmenſes ab Boream. </s> <s xml:id="echoid-s16842" xml:space="preserve">habent Antæci diuerſo tempore Aeſtatem & </s> <s xml:id="echoid-s16843" xml:space="preserve">Hyemem, item <lb/>diem maximum, & </s> <s xml:id="echoid-s16844" xml:space="preserve">minimum. </s> <s xml:id="echoid-s16845" xml:space="preserve">eodem tamen temporis momento habent meridiem, & </s> <s xml:id="echoid-s16846" xml:space="preserve">mediam noctem, <lb/>quamuis non ſemper eodem tempore Sol vtriſq; </s> <s xml:id="echoid-s16847" xml:space="preserve">oriatur, & </s> <s xml:id="echoid-s16848" xml:space="preserve">occidat, &</s> <s xml:id="echoid-s16849" xml:space="preserve">c.</s> <s xml:id="echoid-s16850" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16851" xml:space="preserve">Periæci, ideſt Circuncolæ, habitant ſub eodem paralello, & </s> <s xml:id="echoid-s16852" xml:space="preserve">meridiano, ſed inter eos medius eſt mundi po-<lb/>lus: </s> <s xml:id="echoid-s16853" xml:space="preserve">opponunturq; </s> <s xml:id="echoid-s16854" xml:space="preserve">diametraliter reſpectu diametri paralelli, ſub quo exiſtunt, vnde eundem polum, eodem <lb/>modo eleuatum aſpiciunt, tales ſunt in figura E F. </s> <s xml:id="echoid-s16855" xml:space="preserve">necnon G H. </s> <s xml:id="echoid-s16856" xml:space="preserve">ſi Parma quis ambularet verſus polum ar-<lb/>cticum, tantundemq; </s> <s xml:id="echoid-s16857" xml:space="preserve">vltra illum proficiſceretur, ibi ſuos Perię@os reperiret. </s> <s xml:id="echoid-s16858" xml:space="preserve">quando nobis eſt nox, illis dies <lb/>eſt, reliqua omnia ſunt communia, Aeſtas, Hyems, dies maxima, &</s> <s xml:id="echoid-s16859" xml:space="preserve">c.</s> <s xml:id="echoid-s16860" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16861" xml:space="preserve">Poſtremo aduertendum eſt, ſequi ex prædictis habitatores æquatoris C. </s> <s xml:id="echoid-s16862" xml:space="preserve">& </s> <s xml:id="echoid-s16863" xml:space="preserve">D. </s> <s xml:id="echoid-s16864" xml:space="preserve">eſſe tantum Antipodes, & </s> <s xml:id="echoid-s16865" xml:space="preserve"><lb/>eoſdem ſimul Periæcos, non autem Antæcos, quia nullus paral@llus æquatori opponitur. </s> <s xml:id="echoid-s16866" xml:space="preserve">Habitatores verò <lb/>ſub polis eſſe tantum Antipodes, & </s> <s xml:id="echoid-s16867" xml:space="preserve">Antæcos eoſdem ſim@l, non autem Periæcos, quia non ſunt ſub parale l-<lb/>lis. </s> <s xml:id="echoid-s16868" xml:space="preserve">cum autem volueris ſcire, quinam habitatores ſint inuicem Antipodes, aut Antæci, aut Per@æci, @acilèid <lb/>aſſequeris ex globo Aſtronomico, ſi ea quæ nunc dicta ſunt rectè percepiſti.</s> <s xml:id="echoid-s16869" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div413" type="section" level="1" n="303"> <head xml:id="echoid-head321" style="it" xml:space="preserve">De varijs Habitationibus.</head> <p> <s xml:id="echoid-s16870" xml:space="preserve">PRæterea in globo Geographico iam conſtructo, cõſiderant Geographi quænam loca ſeu Prouinciæ @int <lb/>in vna quaque Zonarum; </s> <s xml:id="echoid-s16871" xml:space="preserve">quas quidem explicauimus in ſecunda par@ Sp@æræ in finem. </s> <s xml:id="echoid-s16872" xml:space="preserve">Tandem ijdem <lb/>Geographi conſiderant ſeptem varias Sphę@æ mundi conſtitutiones ſeu habitationes, quarũ prima eſt Sphę-<lb/>ra recta. </s> <s xml:id="echoid-s16873" xml:space="preserve">Secunda Sphæra obliqua, cuius vertex eſt inter alterutrum tropicorum, & </s> <s xml:id="echoid-s16874" xml:space="preserve">æquatorem. </s> <s xml:id="echoid-s16875" xml:space="preserve">Tertia obli-<lb/>qua, cuius vertex eſt in alterutro tropicorum. </s> <s xml:id="echoid-s16876" xml:space="preserve">Quarta ob@iqua, cuius vertex eſt in alterutra @onarum tem-<lb/>peratarum, ſeu inter tropicos, & </s> <s xml:id="echoid-s16877" xml:space="preserve">polares circellos. </s> <s xml:id="echoid-s16878" xml:space="preserve">Quinta obliqua, cuius vertex eſt in alterutro circellorum <lb/>polarium. </s> <s xml:id="echoid-s16879" xml:space="preserve">Sexta obliqua, cuius vertex eſt intra prædictos circellos polares, non tamen ſub polis ipſis. </s> <s xml:id="echoid-s16880" xml:space="preserve">Septi-<lb/>ma eſt Sphæra paralella, cuius vertex eſt alter polorum, alter verò cęli imum; </s> <s xml:id="echoid-s16881" xml:space="preserve">n qua omnes paralleli æquato-<lb/>ris, ſunt etiam horizontis paralelli, quia æquator ipſe coincidit cum horizonte. </s> <s xml:id="echoid-s16882" xml:space="preserve">Porrò Sphæra recta nec bo-<lb/>realis, nec auſtralis eſt, ſed in medio. </s> <s xml:id="echoid-s16883" xml:space="preserve">Reliquę verò ſex duplices ſunt: </s> <s xml:id="echoid-s16884" xml:space="preserve">ſex enim boreales, & </s> <s xml:id="echoid-s16885" xml:space="preserve">ſex auſtrales, prout <lb/>polut arcticus, aut antarcticus eis eleuatur.</s> <s xml:id="echoid-s16886" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16887" xml:space="preserve">Proprietates autem harum habitationum, quas Aſtronomi conſiderant ſunt quinque. </s> <s xml:id="echoid-s16888" xml:space="preserve">1. </s> <s xml:id="echoid-s16889" xml:space="preserve">Ortus, & </s> <s xml:id="echoid-s16890" xml:space="preserve">occa-<lb/>ſus aſtrorum, ac ſignorum. </s> <s xml:id="echoid-s16891" xml:space="preserve">2. </s> <s xml:id="echoid-s16892" xml:space="preserve">Dies, & </s> <s xml:id="echoid-s16893" xml:space="preserve">noctes. </s> <s xml:id="echoid-s16894" xml:space="preserve">3. </s> <s xml:id="echoid-s16895" xml:space="preserve">Aequinoctia, & </s> <s xml:id="echoid-s16896" xml:space="preserve">Solſtitia. </s> <s xml:id="echoid-s16897" xml:space="preserve">4. </s> <s xml:id="echoid-s16898" xml:space="preserve">Quatuor anni tempora. <lb/></s> <s xml:id="echoid-s16899" xml:space="preserve">5. </s> <s xml:id="echoid-s16900" xml:space="preserve">Vmbræ ſolares.</s> <s xml:id="echoid-s16901" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div414" type="section" level="1" n="304"> <head xml:id="echoid-head322" style="it" xml:space="preserve">De prima Sphæra, idest recta, cuius vertex eſt ſub æquatore, poli veroin Horizonte.</head> <p> <s xml:id="echoid-s16902" xml:space="preserve">1 IN hac mundi coni<unsure/>titutione, exceptis mundi polis, omnia cęli puncta, omniaq; </s> <s xml:id="echoid-s16903" xml:space="preserve">ſydera quotidie oriũ<unsure/>tur <lb/>& </s> <s xml:id="echoid-s16904" xml:space="preserve">occidunt; </s> <s xml:id="echoid-s16905" xml:space="preserve">aſcenduntque, & </s> <s xml:id="echoid-s16906" xml:space="preserve">deſcẽdunt, facientes angulos rectos cum horizonte, ſicu@i etiam æquator, <lb/>& </s> <s xml:id="echoid-s16907" xml:space="preserve">tropici recta aſcendunt & </s> <s xml:id="echoid-s16908" xml:space="preserve">deſcendunt: </s> <s xml:id="echoid-s16909" xml:space="preserve">vnde & </s> <s xml:id="echoid-s16910" xml:space="preserve">recta Sphæra dicta eſt.</s> <s xml:id="echoid-s16911" xml:space="preserve"/> </p> <pb o="199" file="0221" n="226" rhead="AD GEOGRAPHIAM."/> <p> <s xml:id="echoid-s16912" xml:space="preserve">2 In ea dierum nulla ſun,<unsure/> in<unsure/>cremen<unsure/>ta, aut decrementa.</s> <s xml:id="echoid-s16913" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16914" xml:space="preserve">3 Sed perpetuum eſt æquinoctium; </s> <s xml:id="echoid-s16915" xml:space="preserve">quia vt perſpicuum eſt, adhibita Sphæra materiali, eaque ſic conſti-<lb/>@@ta, vt Sphæram hanc rectam, repræſentet, horizon bifariam ſecab@t æquatorem, tropicos, rel q́<unsure/>uoſq; </s> <s xml:id="echoid-s16916" xml:space="preserve">om-<lb/>ne@ circulos vel potius ſpiras, quas Sol ſinguſis anni diebus deſcribit. </s> <s xml:id="echoid-s16917" xml:space="preserve">Sim<unsure/>il ter reliqua ſydera tantum ſupra <lb/>horizontem, quantum infra morantur, ita vt ſemic reulos tam ſupra, quam infra horizontem ducant.</s> <s xml:id="echoid-s16918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16919" xml:space="preserve">4 Habitatores hi habent duas æſtates, & </s> <s xml:id="echoid-s16920" xml:space="preserve">duas hyemes; </s> <s xml:id="echoid-s16921" xml:space="preserve">b@s enim in anno@ol per verticem eorum tranſit, <lb/>ideſt, in vtroque æquinoctio; </s> <s xml:id="echoid-s16922" xml:space="preserve">quando videlicet æqua@o@em, attingit, @ub quo eorum vertex eſt@ duas ig@@r <lb/>æſtates habent in æquinoctijs, quia tunc Sol capitibus eorum imminens radijs maximè perpen<gap/>ibus <lb/>@erram impetit duas verò hyem@s@dum Sol circa t@opicos verſatu@, vbi max mèa vertice eorum recedit. </s> <s xml:id="echoid-s16923" xml:space="preserve">re <lb/>vera tamen hæ hyemes, ita appellantur reſpectu æſtatu@ calidiſſimarum, non quòd admodum frigidæ ſint. <lb/></s> <s xml:id="echoid-s16924" xml:space="preserve">ex accidenti tamen aliquo multis inlocis res aliter ſe habet, cuius rationes reddere eſt Geographi<unsure/>, & </s> <s xml:id="echoid-s16925" xml:space="preserve">nos eas, <lb/>in locis Mathematicis Ariſtotelis in ſecundo Meteororum numero marginali 159. </s> <s xml:id="echoid-s16926" xml:space="preserve">huic rei ſ@tisfeci<unsure/>@us.</s> <s xml:id="echoid-s16927" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16928" xml:space="preserve">5 Habent quatuor vmbrarum diſcrimina; </s> <s xml:id="echoid-s16929" xml:space="preserve">oriente enim Sole habent vmb@am occidentalem; </s> <s xml:id="echoid-s16930" xml:space="preserve">occidente <lb/>vero orientalem. </s> <s xml:id="echoid-s16931" xml:space="preserve">Sole borealia ſigna obeunte vmbram meridianam proijciunt ad auſtrum. </s> <s xml:id="echoid-s16932" xml:space="preserve">e<unsure/> contra vero <lb/>in f<unsure/>ignis auſtralibus vmbram borealem efficiunt. </s> <s xml:id="echoid-s16933" xml:space="preserve">ratione harum duarum vmbrarum meridianarum, dicun-<lb/>tur Amphiſcij, quaſi Amphiumbræ, σκια, enim eſt vmbra. </s> <s xml:id="echoid-s16934" xml:space="preserve">in æquinoctijs nuſſam efficiunt vmbram meri-<lb/>dianam, quia in meridie Sol directè vertici incumbit, eoſque propterea circumqua<unsure/>q; </s> <s xml:id="echoid-s16935" xml:space="preserve">illum@nat; </s> <s xml:id="echoid-s16936" xml:space="preserve">vnde & </s> <s xml:id="echoid-s16937" xml:space="preserve">pu-<lb/>tei toti vſq; </s> <s xml:id="echoid-s16938" xml:space="preserve">ad imum, totuſq; </s> <s xml:id="echoid-s16939" xml:space="preserve">eorum fundus illuſtratur. </s> <s xml:id="echoid-s16940" xml:space="preserve">Porro hæc Sphæra cæ@erarum nobiliſſima eſt, tum <lb/>ob perpetuum æquinoctium, tum ob quo idianam totius cœli apparentiam, vn<unsure/>de paricer de vtraque mundi <lb/>plagaboreali, & </s> <s xml:id="echoid-s16941" xml:space="preserve">auſtrali participant, totoq; </s> <s xml:id="echoid-s16942" xml:space="preserve">cœlo, ac ſtellis omn bus perfruuntur.</s> <s xml:id="echoid-s16943" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div415" type="section" level="1" n="305"> <head xml:id="echoid-head323" style="it" xml:space="preserve">De ſecunda Sphæra, ideſt obliqua, cuius vertex eſt inter æquatorem, <lb/>& alterum Tropicorum.</head> <p> <s xml:id="echoid-s16944" xml:space="preserve">1 IN horizonte huius Sphæræ non omnia ſydera orinntur, & </s> <s xml:id="echoid-s16945" xml:space="preserve">occidunt, ſed illa tantũ, quæ ſunt intra duos <lb/>circulosęquator<unsure/>i paralellos, & </s> <s xml:id="echoid-s16946" xml:space="preserve">horizontem tangentes, quorum vnus eſt maximus ſemper apparentium, <lb/>alter vero maximus ſemperoco<unsure/>u<unsure/>ltorum. </s> <s xml:id="echoid-s16947" xml:space="preserve">Ea vero ſydera quæ continentur intra paralel@um ſemper appa-<lb/>rentem verſus polum conſpicuum, nec oriuntur, nec occidunt, ſed perpetuo ſupra horizontem cirea polum <lb/>mouentur. </s> <s xml:id="echoid-s16948" xml:space="preserve">quæ vero clauduntur intra alterum ſemper occultum, perpetuo latent infra horizontem, fimiſi-<lb/>@er ortus, & </s> <s xml:id="echoid-s16949" xml:space="preserve">occaſus expertia, vt in Spliæra Aratæa, vel etiam Armillari videre eſt.</s> <s xml:id="echoid-s16950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16951" xml:space="preserve">2 Habeant incrementa, & </s> <s xml:id="echoid-s16952" xml:space="preserve">decrementa dierum, & </s> <s xml:id="echoid-s16953" xml:space="preserve">noctium.</s> <s xml:id="echoid-s16954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16955" xml:space="preserve">3 Habent bis æquinoctium, vernum, & </s> <s xml:id="echoid-s16956" xml:space="preserve">autumnale, necnon duo ſolſtitia.</s> <s xml:id="echoid-s16957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16958" xml:space="preserve">4 Bis æſtatem, b@ſque hyemem, eis Solaffert, cuius cauſa eſt, quia bis per eorum vertices tranſit, biſque <lb/>ad tropicos recedit.</s> <s xml:id="echoid-s16959" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16960" xml:space="preserve">5 Quad ruplicem vmbram projciunt; </s> <s xml:id="echoid-s16961" xml:space="preserve">& </s> <s xml:id="echoid-s16962" xml:space="preserve">ratione vmbrarum meridianarum Amphiſcij, vti etiam ſupe-<lb/>@iores dicuntur.</s> <s xml:id="echoid-s16963" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div416" type="section" level="1" n="306"> <head xml:id="echoid-head324" style="it" xml:space="preserve">De tertia Sphæra, ideſt obliqua, cuius veriex eſt in vno Tropicorum.</head> <p> <s xml:id="echoid-s16964" xml:space="preserve">HAbet hæc Sphæra determinatam poli eleuationem gr. </s> <s xml:id="echoid-s16965" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s16966" xml:space="preserve">præterea circelli po@ares coincidunt cum <lb/>maxim@s circulis, quorum vnus eſt<unsure/>ſemper apparen@um maximus, alterſemper latentium itidem ma-<lb/>@imus.</s> <s xml:id="echoid-s16967" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16968" xml:space="preserve">1 In ea omnia ſydera, quæ intra polarem circulem conſpicuum continentur, ſemper ſupra horizontem <lb/>verſantur: </s> <s xml:id="echoid-s16969" xml:space="preserve">quæ vero intra al@erum polarem occultum contin@ntur, ſimul cum eo infra horizontem latent. <lb/></s> <s xml:id="echoid-s16970" xml:space="preserve">reliqua tandem quæ inter vtrumq; </s> <s xml:id="echoid-s16971" xml:space="preserve">circellum exiſtu@t, oriuntur, & </s> <s xml:id="echoid-s16972" xml:space="preserve">occidunt quotidie.</s> <s xml:id="echoid-s16973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16974" xml:space="preserve">2 Dids creſcunt, & </s> <s xml:id="echoid-s16975" xml:space="preserve">decreſcunt.</s> <s xml:id="echoid-s16976" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16977" xml:space="preserve">3 Vtrumque ſolſ@@ium, & </s> <s xml:id="echoid-s16978" xml:space="preserve">vtrumque æquinoct@um rec@rrit.</s> <s xml:id="echoid-s16979" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16980" xml:space="preserve">4 Aeſtatem vnam, vnamque hyemem ſent@unt.</s> <s xml:id="echoid-s16981" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16982" xml:space="preserve">5 Tres tan@um vmbras eſf<unsure/>iciunt, occidenta@em, orientalem, & </s> <s xml:id="echoid-s16983" xml:space="preserve">meridianam, quæ ad polum conſpicuum <lb/>vergit, ratione cuius dicuntur Eteroſcij, quaſi alteriumbrę. </s> <s xml:id="echoid-s16984" xml:space="preserve">huius cauſa eſt Sol, qui non pertranſit vltr<unsure/> eorũ <lb/>verticem ad polum conſpicuum, ſed tantum ſeni<unsure/>el in anno ad ipſum peruenit, quãdo, videlicet atting i@ tro-<lb/>picum illum, ſub quo eorum vertex ſitus eſt. </s> <s xml:id="echoid-s16985" xml:space="preserve">prædictæ tertiæ habitationes ſunt in Zona torrida.</s> <s xml:id="echoid-s16986" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div417" type="section" level="1" n="307"> <head xml:id="echoid-head325" style="it" xml:space="preserve">De quart<unsure/>a Sphæra, ideſt obliqua, cuius vertex eſt inter Tropicum, & polarem circulum.</head> <p> <s xml:id="echoid-s16987" xml:space="preserve">HÆceſt Zonæ temperatæ h<unsure/>abita@io. </s> <s xml:id="echoid-s16988" xml:space="preserve">In ea ortus, & </s> <s xml:id="echoid-s16989" xml:space="preserve">occaſus ſyderum habet ſe proportionaliter, vt in <lb/>præ@eden@i, ideſt, pars ſemper apparen@, pars ſemper latent, pars oriuntur, & </s> <s xml:id="echoid-s16990" xml:space="preserve">occidunt, quæ tria diffi-<lb/><gap/>tur a duobus circu@is, quorum vnus eſt maxim@siſemper apparentium, alter @em<unsure/>per occul@or@@ dier@m <lb/>@ncrementa, a quinoctia, & </s> <s xml:id="echoid-s16991" xml:space="preserve">to@ſtitia, æſtatem, & </s> <s xml:id="echoid-s16992" xml:space="preserve">hyemem vnam tantum experiuntur. </s> <s xml:id="echoid-s16993" xml:space="preserve">ratione vmbraiũ ſunt, <lb/>vt in præcedenti Eteroſcij, quia Sol nunquam ad eorum verticem peruenit, & </s> <s xml:id="echoid-s16994" xml:space="preserve">ideo in meri<unsure/>die proijciunt <lb/>vmbram ad polum eleuatum. </s> <s xml:id="echoid-s16995" xml:space="preserve">cæterum in hac temperata Zona, vbi polus eleuatur gr. </s> <s xml:id="echoid-s16996" xml:space="preserve">45. </s> <s xml:id="echoid-s16997" xml:space="preserve">ſuntin<unsure/> eius medio, <pb o="200" file="0222" n="227" rhead="INTRODVCTIO."/> tantumq; </s> <s xml:id="echoid-s16998" xml:space="preserve">ab eorum verticibus diſtat polus, quantum æquator; </s> <s xml:id="echoid-s16999" xml:space="preserve">tantũmq; </s> <s xml:id="echoid-s17000" xml:space="preserve">polusab horizonte eleuatur, quan-<lb/>tum æquator; </s> <s xml:id="echoid-s17001" xml:space="preserve">vnde caloræſtatis tantus eſt, quantum hyemis frigus: </s> <s xml:id="echoid-s17002" xml:space="preserve">& </s> <s xml:id="echoid-s17003" xml:space="preserve">Horologium ſolare horizontale in-<lb/>ſeruit etiam pro verticali.</s> <s xml:id="echoid-s17004" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div418" type="section" level="1" n="308"> <head xml:id="echoid-head326" style="it" xml:space="preserve">De quinta Sphæra, ideſt obliqua, cuius vertex eſtin circulo polari.</head> <p> <s xml:id="echoid-s17005" xml:space="preserve">HIc polus præcisè eleuatur gr. </s> <s xml:id="echoid-s17006" xml:space="preserve">66 {1/2}. </s> <s xml:id="echoid-s17007" xml:space="preserve">& </s> <s xml:id="echoid-s17008" xml:space="preserve">tropicus vnus totus ect ſupra horizontem, alter vero totus infra; </s> <s xml:id="echoid-s17009" xml:space="preserve">il-<lb/>le coincidit cum maximo paralello ſemper apparentium, hic verò cum maximo ſemper latentium. </s> <s xml:id="echoid-s17010" xml:space="preserve">qui-<lb/>bus ſit vt aſtra, quæ ſunt intra Zonam torridam oriantur, & </s> <s xml:id="echoid-s17011" xml:space="preserve">occidant. </s> <s xml:id="echoid-s17012" xml:space="preserve">quæ ſunt extra ad polum eleuatũ ſem-<lb/>per lateant. </s> <s xml:id="echoid-s17013" xml:space="preserve">habent dierum varietates, maxin uſq; </s> <s xml:id="echoid-s17014" xml:space="preserve">dies eſt horarum 24. </s> <s xml:id="echoid-s17015" xml:space="preserve">quando videlicet Sol percurrit tro-<lb/>picum extantem; </s> <s xml:id="echoid-s17016" xml:space="preserve">in altero vero tropico nox eſt horarum 24. </s> <s xml:id="echoid-s17017" xml:space="preserve">æquinoctia, & </s> <s xml:id="echoid-s17018" xml:space="preserve">ſolſtitia ſortiuntur, vt pręceden-<lb/>t<unsure/>es: </s> <s xml:id="echoid-s17019" xml:space="preserve">pariter & </s> <s xml:id="echoid-s17020" xml:space="preserve">quatuor anni tempora. </s> <s xml:id="echoid-s17021" xml:space="preserve">Eteroſcij ſunt, quia vmbram meridiei ad polum tantum conſpicuum <lb/>emittunt. </s> <s xml:id="echoid-s17022" xml:space="preserve">peculiare illis eſt, quod eclipticæ polus, qui circulum polarem deſcribit, ſemel per eorum verticem<unsure/> <lb/>tranſeat: </s> <s xml:id="echoid-s17023" xml:space="preserve">quo temporis momento ecliptica cum horizonte congruit, & </s> <s xml:id="echoid-s17024" xml:space="preserve">ſtatim poſt, bifariam ſe mutuo ſec@t.</s> <s xml:id="echoid-s17025" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div419" type="section" level="1" n="309"> <head xml:id="echoid-head327" style="it" xml:space="preserve">De ſexta Sphæra, ideſt obliqua, cuius vertex eſt intra polarem circulum, <lb/>& polum conſpicuum.</head> <p> <s xml:id="echoid-s17026" xml:space="preserve">HÆc eſt frigidæ Zonæ habitatio. </s> <s xml:id="echoid-s17027" xml:space="preserve">habet dies maximos, & </s> <s xml:id="echoid-s17028" xml:space="preserve">noctes maximas conſtantes ex pluribus horis, <lb/>quam 24. </s> <s xml:id="echoid-s17029" xml:space="preserve">imo prout magis ad polum vertex appropinquat, conſtabunt ex pluribus diebus, & </s> <s xml:id="echoid-s17030" xml:space="preserve">noctibus; </s> <s xml:id="echoid-s17031" xml:space="preserve">& </s> <s xml:id="echoid-s17032" xml:space="preserve"><lb/>criam ex menſibus, ratio eſt, quia hic pars quædam eclipticæ ſemper manet ſupra horizontem verſus polum <lb/>eleuatum, & </s> <s xml:id="echoid-s17033" xml:space="preserve">altera huic oppoſita ſemper infra manet, quare Sole per eas incedente, erit ib:</s> <s xml:id="echoid-s17034" xml:space="preserve"><unsure/> dies continua, hic <lb/>vero nox: </s> <s xml:id="echoid-s17035" xml:space="preserve">quæ vt me ius intelligas conſtitue ſphæram materialem, vt propoſitum requirit, eamque motu <lb/>diurno conuerte, interim obſeruans eclipticam ad polum ſublimem, videbiſq; </s> <s xml:id="echoid-s17036" xml:space="preserve">portionem eius aliquam ſem-<lb/>per ſupra horizontem extare, tantumq; </s> <s xml:id="echoid-s17037" xml:space="preserve">ad polum depreſſum latere. </s> <s xml:id="echoid-s17038" xml:space="preserve">Sole igitur illam motu proprio obeun-<lb/>te, erit dies continuus, & </s> <s xml:id="echoid-s17039" xml:space="preserve">quidem tot ferè dierum, quot gradus erunt in ea: </s> <s xml:id="echoid-s17040" xml:space="preserve">hanc vero obeunte Sole, erit nox <lb/>continua. </s> <s xml:id="echoid-s17041" xml:space="preserve">vbi aduertendum eſt, quod quamuis hæ duę portiones æquales ſint, non tamen ſequitun<unsure/> diem con-<lb/>tinuum æqualem eſſe nocti continuæ, cauſa eſt apogæum Solis, quod nunc eſt in Cancro, propter quod Sol <lb/>tardius incedit per ſigna ſolſtitialia Cancri, quam in oppoſiris Capricorni, & </s> <s xml:id="echoid-s17042" xml:space="preserve">conſequenter dies ille conti-<lb/>nuus longior erit nocte continua, in boreali habitatione: </s> <s xml:id="echoid-s17043" xml:space="preserve">in auſtrali nox erit longior. </s> <s xml:id="echoid-s17044" xml:space="preserve">Ex ſphæra materiali <lb/>facilè eſt reperire quantitatem horum arcuum, ac proinde etiam dierum, ac noctium continuarum quæ illis <lb/>debentur. </s> <s xml:id="echoid-s17045" xml:space="preserve">quas quantitates videre potes in Tabula temporis diurni, aut<unsure/>ſemidiurni, quam ſupra in Sole dedi-<lb/>mus, præterea ſigna exiſtentia circa vernum æquinoctium, præpoſterẽ oriuntur, ideſt, Taurus ante Arietem, <lb/>Aries ante Piſces: </s> <s xml:id="echoid-s17046" xml:space="preserve">ſigna vero ad autumnale æquinoctium præpoſterè occidunt, ideſf, Sagittarius ante Scor-<lb/>pionem, Scorpio ante Libram, quæ vt impoſſibilia videantur, adhibita tamen materiali ſphæra, qua ratione <lb/>fiant clarè percipitur. </s> <s xml:id="echoid-s17047" xml:space="preserve">ortus, & </s> <s xml:id="echoid-s17048" xml:space="preserve">occaſus, æquinoctia, & </s> <s xml:id="echoid-s17049" xml:space="preserve">ſolſtitia, quatuor anni tempora, vmbræ tandem hic ſe <lb/>habent proportionaliter, vt in præcedentibus ſphæris obliquis.</s> <s xml:id="echoid-s17050" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div420" type="section" level="1" n="310"> <head xml:id="echoid-head328" style="it" xml:space="preserve">De ſeptima, & vltima Sphæra, ideſt paralella, cuius vertex eſt alter polorum, <lb/>alter vero i@um cœli.</head> <p> <s xml:id="echoid-s17051" xml:space="preserve">HIc æquator horizonti congruit; </s> <s xml:id="echoid-s17052" xml:space="preserve">dimidiumq; </s> <s xml:id="echoid-s17053" xml:space="preserve">eclipticæ ſemper eſt ſupra, dimidiumq; </s> <s xml:id="echoid-s17054" xml:space="preserve">alterum infra ho-<lb/>rizontem vnde, nulla affixa ſydera diurna conuerſione oriuntur. </s> <s xml:id="echoid-s17055" xml:space="preserve">aut occidunt, ſed motu diurno deſcri-<lb/>bunt circulos horizonti paralellos, perpetuo enim dimidium cæli conſpicuum eſt, dimidium etiam occultũ: <lb/></s> <s xml:id="echoid-s17056" xml:space="preserve">quare planetæ ibi oriuntur, & </s> <s xml:id="echoid-s17057" xml:space="preserve">occidunt, non ratione motus diurni, ſed proprij. </s> <s xml:id="echoid-s17058" xml:space="preserve">vnde Sol ſupra horizonrem <lb/>perpetuo moratur dum obit ſex ſigna conſpicua, moueturq; </s> <s xml:id="echoid-s17059" xml:space="preserve">primo radendo horizontem, pararelloſque ei, <lb/>vel potius ſpiras quotidie altiores deſcribendo. </s> <s xml:id="echoid-s17060" xml:space="preserve">quocirca ibi eſt dies vna, & </s> <s xml:id="echoid-s17061" xml:space="preserve">nox vna tantum in toto anno, <lb/>vtraque conſtans ſex menſibus. </s> <s xml:id="echoid-s17062" xml:space="preserve">aduertendum tamen eſt in eo Zodiaci ſemicirculo, in quo eſt apogæum So-<lb/>lis Solem immorari ſeptem diebus amplius, quam in altero; </s> <s xml:id="echoid-s17063" xml:space="preserve">ideo vel dies, vel nox longior erit ſeptem diebus <lb/>nocte, vel die. </s> <s xml:id="echoid-s17064" xml:space="preserve">quod ſi in partem vulgo crepuſculum computemus, erit dies continuus per nouem menſes, & </s> <s xml:id="echoid-s17065" xml:space="preserve"><lb/>amplius. </s> <s xml:id="echoid-s17066" xml:space="preserve">Sol enim crepuſculum efficit exiſtens infra horizontem gr. </s> <s xml:id="echoid-s17067" xml:space="preserve">18. </s> <s xml:id="echoid-s17068" xml:space="preserve">quia vero 21. </s> <s xml:id="echoid-s17069" xml:space="preserve">gr. </s> <s xml:id="echoid-s17070" xml:space="preserve">Scorpij, & </s> <s xml:id="echoid-s17071" xml:space="preserve">9. </s> <s xml:id="echoid-s17072" xml:space="preserve">Aqua-<lb/>rij declinant gr. </s> <s xml:id="echoid-s17073" xml:space="preserve">18. </s> <s xml:id="echoid-s17074" xml:space="preserve">ab æquatore, & </s> <s xml:id="echoid-s17075" xml:space="preserve">proinde etiam ab hoc horizonte, ideo in tota Libra vſq; </s> <s xml:id="echoid-s17076" xml:space="preserve">ad gr. </s> <s xml:id="echoid-s17077" xml:space="preserve">21. </s> <s xml:id="echoid-s17078" xml:space="preserve">Scor-<lb/>pij; </s> <s xml:id="echoid-s17079" xml:space="preserve">& </s> <s xml:id="echoid-s17080" xml:space="preserve">a 9. </s> <s xml:id="echoid-s17081" xml:space="preserve">gr. </s> <s xml:id="echoid-s17082" xml:space="preserve">Aquarij per totos Piſces, fiet crepuſculum, quod tempus erit trium menſium, dierum 12. </s> <s xml:id="echoid-s17083" xml:space="preserve">die@ <lb/>igitur artificialis vulgaris erit menſium 9. </s> <s xml:id="echoid-s17084" xml:space="preserve">dierum 12. </s> <s xml:id="echoid-s17085" xml:space="preserve">imo ſi etiam refractionis ratio habeatur, quæ Solem ſu-<lb/>pra horizontem eleuat, antequam reuera eum conſcendat, dies erunt longiores, crepuſcula vero breuiora. </s> <s xml:id="echoid-s17086" xml:space="preserve"><lb/>Aequinoctium hic propriè nullum; </s> <s xml:id="echoid-s17087" xml:space="preserve">quamuis dici poſſit eſſe ibi perpetuum, quia nox illa eſt ſemper ferè diei <lb/>æqualis, cum vterque ſit ferè ſex menſium. </s> <s xml:id="echoid-s17088" xml:space="preserve">habent duo ſolſtitia, vt alij. </s> <s xml:id="echoid-s17089" xml:space="preserve">quatuor etiam anni tempora perſenti-<lb/>ſcunt. </s> <s xml:id="echoid-s17090" xml:space="preserve">ab vmbris dicuntur periſcij, ideſt, circumumbræ; </s> <s xml:id="echoid-s17091" xml:space="preserve">cum enim Sol circa horizontem æquidiſtanter ſem-<lb/>per gyret, vmbræ quoque in gyrum quoquouerſus proijcientur. </s> <s xml:id="echoid-s17092" xml:space="preserve">Luna per dies 14 {1/2} ſupra horizontem exi-<lb/>ſtit. </s> <s xml:id="echoid-s17093" xml:space="preserve">Venus, & </s> <s xml:id="echoid-s17094" xml:space="preserve">Mercurius Solem comitantur. </s> <s xml:id="echoid-s17095" xml:space="preserve">Mars conſpicitur per menſes ferè 10. </s> <s xml:id="echoid-s17096" xml:space="preserve">@upiter per annos ferè 6. </s> <s xml:id="echoid-s17097" xml:space="preserve"><lb/>Saturnus per 15. </s> <s xml:id="echoid-s17098" xml:space="preserve">ac per tautumdem temporum latent poſtea.</s> <s xml:id="echoid-s17099" xml:space="preserve"/> </p> <pb o="201" file="0223" n="228" rhead="AD GEOGRAPHIAM."/> <p> <s xml:id="echoid-s17100" xml:space="preserve">Hæc porrò Sphœra videtur omnium ignobiliſſima, quod dimidio tantum mundo perfruatur, maximiſ-<lb/>que frigoribus horreſcat. </s> <s xml:id="echoid-s17101" xml:space="preserve">Vtrum autem hæc habitatio habeat habitatores, hactenus Geographis incom-<lb/>pertum eſt.</s> <s xml:id="echoid-s17102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17103" xml:space="preserve">Atque in hunc modum inuentis longitudinibus, & </s> <s xml:id="echoid-s17104" xml:space="preserve">latitudinibus locorum præcipuè valdè diſſitorum, per-<lb/>agitur vniuerſalis terræ deſcriptio, atq; </s> <s xml:id="echoid-s17105" xml:space="preserve">cognitio, quæ Geographia propriè appellatur. </s> <s xml:id="echoid-s17106" xml:space="preserve">In deſcriptione ve-<lb/>rò particularium prouinciarum, aut regionum, difficilè eſt per longitudinem, & </s> <s xml:id="echoid-s17107" xml:space="preserve">latitudinem id aſſequi, quo-<lb/>niam cum loca ſint ſatis vicina, difficilè earum differentiam latitudinum ex prædictis obſeruationibus haberi <lb/>poteſt, quod parua ſit: </s> <s xml:id="echoid-s17108" xml:space="preserve">difficilius etiam differentia longitudinum percipitur, non ſolum ob paruitatem ip-<lb/>ſius, ſed ob multas alias difficultates, quæ in obſeruatione eclipſium contingunt, quapropter alia ratio inſti-<lb/>tuenda eſt, vt mox dicam.</s> <s xml:id="echoid-s17109" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div421" type="section" level="1" n="311"> <head xml:id="echoid-head329" style="it" xml:space="preserve">De particularis regionis deſcriptione quæ Chorographia dicitur.</head> <p> <s xml:id="echoid-s17110" xml:space="preserve">CVm volueris igitur particularis alicuius regionis deſcriptionẽ aggredi, duc in plano aliquo, vt in char-<lb/>ta lineam rectam, quam meridianam appellabis, quoniam pro meridiana poſtea inſeruiet, qualis eſt in <lb/> <anchor type="figure" xlink:label="fig-0223-01a" xlink:href="fig-0223-01"/> figura linea A B. </s> <s xml:id="echoid-s17111" xml:space="preserve">ad cuius extremitates adſcribes, <lb/>Auſt. </s> <s xml:id="echoid-s17112" xml:space="preserve">Boreas: </s> <s xml:id="echoid-s17113" xml:space="preserve">& </s> <s xml:id="echoid-s17114" xml:space="preserve">ad latera Occid. </s> <s xml:id="echoid-s17115" xml:space="preserve">Or. </s> <s xml:id="echoid-s17116" xml:space="preserve">ſecundum <lb/>loci exigentiam. </s> <s xml:id="echoid-s17117" xml:space="preserve">poſthæc manens tu in loco, v.</s> <s xml:id="echoid-s17118" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s17119" xml:space="preserve">A. </s> <s xml:id="echoid-s17120" xml:space="preserve">qui prima ſtatio dicitur, conſcende turrim <lb/>quampiam ex qua circumiacentia caſtra, villas, <lb/>vrbes, & </s> <s xml:id="echoid-s17121" xml:space="preserve">c. </s> <s xml:id="echoid-s17122" xml:space="preserve">poſſis circumſpicere: </s> <s xml:id="echoid-s17123" xml:space="preserve">atq; </s> <s xml:id="echoid-s17124" xml:space="preserve">inibi collo-<lb/>ca planum iam paratum cum linea meridiana <lb/>Aſtronomicè, ideſt, ita vt linea hæc meridiana <lb/>congruat veræ lineæ meridianę aliquo modo in-<lb/>uentæ, vt in ſphæra docuimus, & </s> <s xml:id="echoid-s17125" xml:space="preserve">ſimul quatuor <lb/>mundi plagæ veras mundi plagas, quas referunt, <lb/>reſpiciant. </s> <s xml:id="echoid-s17126" xml:space="preserve">plano hoc in tali poſitione obfirma-<lb/>to, ei Dioptram ſuperpone, quæ circa punctum <lb/>A. </s> <s xml:id="echoid-s17127" xml:space="preserve">conuerti poſſit, & </s> <s xml:id="echoid-s17128" xml:space="preserve">per quam inſpicere, aut col-<lb/>li mari poſſis ad loca circumiacentia.</s> <s xml:id="echoid-s17129" xml:space="preserve"/> </p> <div xml:id="echoid-div421" type="float" level="2" n="1"> <figure xlink:label="fig-0223-01" xlink:href="fig-0223-01a"> <image file="0223-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0223-01"/> </figure> </div> <p> <s xml:id="echoid-s17130" xml:space="preserve">Primo igitur per eam aſpice directè adlocum <lb/>E. </s> <s xml:id="echoid-s17131" xml:space="preserve">& </s> <s xml:id="echoid-s17132" xml:space="preserve">ſecus eam ſic directam duc lineam A F. </s> <s xml:id="echoid-s17133" xml:space="preserve">infi-<lb/>nitæ longitudinis. </s> <s xml:id="echoid-s17134" xml:space="preserve">pariter directa Dioptra ad lo-<lb/>cum G. </s> <s xml:id="echoid-s17135" xml:space="preserve">ſecus eam ducas lineam A G. </s> <s xml:id="echoid-s17136" xml:space="preserve">in infinitũ. <lb/></s> <s xml:id="echoid-s17137" xml:space="preserve">quæ tranſeat etiam per locum E. </s> <s xml:id="echoid-s17138" xml:space="preserve">ſit etiam B. </s> <s xml:id="echoid-s17139" xml:space="preserve">lo-<lb/>cus quiſpiam, vt villa, vel caſtellum, in ipſa meri-<lb/>diana ſitum, pro quo ſufficit ipſa meridiana. </s> <s xml:id="echoid-s17140" xml:space="preserve">idẽ <lb/>facies cum reliquis locis C. </s> <s xml:id="echoid-s17141" xml:space="preserve">& </s> <s xml:id="echoid-s17142" xml:space="preserve">D. </s> <s xml:id="echoid-s17143" xml:space="preserve">& </s> <s xml:id="echoid-s17144" xml:space="preserve">alijs quot-<lb/>cunque.</s> <s xml:id="echoid-s17145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17146" xml:space="preserve">Quibus peractis perge ad vnum ex prænotatis locis, v.</s> <s xml:id="echoid-s17147" xml:space="preserve">g. </s> <s xml:id="echoid-s17148" xml:space="preserve">ad D. </s> <s xml:id="echoid-s17149" xml:space="preserve">quæ flatio ſecunda erit, ibique conſcende <lb/>ſpeculam aliquam, & </s> <s xml:id="echoid-s17150" xml:space="preserve">plano iterum Aſtronomicè collocato, & </s> <s xml:id="echoid-s17151" xml:space="preserve">obfirmato, accipe in linea A D. </s> <s xml:id="echoid-s17152" xml:space="preserve">locum D. </s> <s xml:id="echoid-s17153" xml:space="preserve">ſiue <lb/>diſtantia A D. </s> <s xml:id="echoid-s17154" xml:space="preserve">cuiuſuis longitudinis, ad magnitudinem enim eius, reliquæ omnes diſtantiæ proportionales <lb/>erunt. </s> <s xml:id="echoid-s17155" xml:space="preserve">Ad hunc locum D. </s> <s xml:id="echoid-s17156" xml:space="preserve">ſic determinatum transfert Dioptram, vt poſſit circa ipſum verti, atq; </s> <s xml:id="echoid-s17157" xml:space="preserve">ad obſer-<lb/>uata loca dirigi. </s> <s xml:id="echoid-s17158" xml:space="preserve">ſecus eam igitur collimans iterum ad caſtrum F. </s> <s xml:id="echoid-s17159" xml:space="preserve">ducas lineam D F. </s> <s xml:id="echoid-s17160" xml:space="preserve">eodem modo duc cæte-<lb/>ras lineas C D G. </s> <s xml:id="echoid-s17161" xml:space="preserve">D E. </s> <s xml:id="echoid-s17162" xml:space="preserve">D B, & </s> <s xml:id="echoid-s17163" xml:space="preserve">c. </s> <s xml:id="echoid-s17164" xml:space="preserve">nam in punctis concurſum F G C, & </s> <s xml:id="echoid-s17165" xml:space="preserve">c. </s> <s xml:id="echoid-s17166" xml:space="preserve">ſunt pingenda caſtra prædicta, vr-<lb/>bes, villæ, & </s> <s xml:id="echoid-s17167" xml:space="preserve">c. </s> <s xml:id="echoid-s17168" xml:space="preserve">eritq; </s> <s xml:id="echoid-s17169" xml:space="preserve">figura parua ſimilis omnino regioni deſcriptæ: </s> <s xml:id="echoid-s17170" xml:space="preserve">conſtat enim ex triangulis paruis ſimili-<lb/>bus ijs, quæ in ipſa prouincia deſcribi poſſunt: </s> <s xml:id="echoid-s17171" xml:space="preserve">ſic ex loco D. </s> <s xml:id="echoid-s17172" xml:space="preserve">poterunt aſpici, & </s> <s xml:id="echoid-s17173" xml:space="preserve">notari multa alia loca; </s> <s xml:id="echoid-s17174" xml:space="preserve">quæ <lb/>poſtea ex tertia ſtagione, repertis concurſuum punctis, in pictura definientur. </s> <s xml:id="echoid-s17175" xml:space="preserve">Atq; </s> <s xml:id="echoid-s17176" xml:space="preserve">ſic per totam prouinciã <lb/>procedendo, eius abſolues chorographiam.</s> <s xml:id="echoid-s17177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17178" xml:space="preserve">Quod ſi nota fuerit vna ex diſtantijs, v.</s> <s xml:id="echoid-s17179" xml:space="preserve">g. </s> <s xml:id="echoid-s17180" xml:space="preserve">diſtantia A D. </s> <s xml:id="echoid-s17181" xml:space="preserve">in milliarijs, reliquæ omnes diſtantiæ notæ eua-<lb/>dent, vt v.</s> <s xml:id="echoid-s17182" xml:space="preserve">g. </s> <s xml:id="echoid-s17183" xml:space="preserve">A D. </s> <s xml:id="echoid-s17184" xml:space="preserve">milliaria 10. </s> <s xml:id="echoid-s17185" xml:space="preserve">diuide igitur lineam A D. </s> <s xml:id="echoid-s17186" xml:space="preserve">in partes 10. </s> <s xml:id="echoid-s17187" xml:space="preserve">æquales, poſtea per circinum exami-<lb/>na quot huiuſmodi partes contineantur in diſtantia A F. </s> <s xml:id="echoid-s17188" xml:space="preserve">tot enim milliaria pariter in ea cõtinebuntur; </s> <s xml:id="echoid-s17189" xml:space="preserve">A F. <lb/></s> <s xml:id="echoid-s17190" xml:space="preserve">v.</s> <s xml:id="echoid-s17191" xml:space="preserve">g. </s> <s xml:id="echoid-s17192" xml:space="preserve">ſint partes 5. </s> <s xml:id="echoid-s17193" xml:space="preserve">ergo quinque milliarijs diſtat caſtellum F. </s> <s xml:id="echoid-s17194" xml:space="preserve">ab vrbe A. </s> <s xml:id="echoid-s17195" xml:space="preserve">& </s> <s xml:id="echoid-s17196" xml:space="preserve">ſic de reliquis.</s> <s xml:id="echoid-s17197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17198" xml:space="preserve">Iam vero ſi alicuius vrbis lociue huius regionis comperta ſit longitudo, & </s> <s xml:id="echoid-s17199" xml:space="preserve">latitudo, reliquorum quoq; </s> <s xml:id="echoid-s17200" xml:space="preserve">lo-<lb/>corum, ex diſtantijs iam cognitis, longitudo, & </s> <s xml:id="echoid-s17201" xml:space="preserve">latitudo latere non poterit. </s> <s xml:id="echoid-s17202" xml:space="preserve">Alios modos ſed minus idoneos, <lb/>vide apud Gemmam Friſium, à quo hunc pariter in compendium redegimus. </s> <s xml:id="echoid-s17203" xml:space="preserve">Hac ratione facile Patres no-<lb/>ſtræ Societatis poterunt nobile Sinarum regnum ad veram deſcriptionem aliquando redigere.</s> <s xml:id="echoid-s17204" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div423" type="section" level="1" n="312"> <head xml:id="echoid-head330" style="it" xml:space="preserve">Diuiſiones ſuperficiei terreſtris Globi.</head> <p> <s xml:id="echoid-s17205" xml:space="preserve">DEſcriptione terreſtri Globi ex præcedenti doctrina abſoluta, ſtatim apparet eam totam diuidi in duas <lb/>partes, in terreſtrem videlicet, & </s> <s xml:id="echoid-s17206" xml:space="preserve">aqueam, ſeu maritimam: </s> <s xml:id="echoid-s17207" xml:space="preserve">& </s> <s xml:id="echoid-s17208" xml:space="preserve">qua ratione terra, & </s> <s xml:id="echoid-s17209" xml:space="preserve">mare ſe inuicem com- <pb o="202" file="0224" n="229" rhead="INTRODVCTIO"/> plectantur, & </s> <s xml:id="echoid-s17210" xml:space="preserve">intercurſent: </s> <s xml:id="echoid-s17211" xml:space="preserve">ſtatimq; </s> <s xml:id="echoid-s17212" xml:space="preserve">manifeſtum fit, quæ pars terræ, aut maris ſit in Zona torrida, quæ in fri-<lb/>gidis; </s> <s xml:id="echoid-s17213" xml:space="preserve">quæ earum climata, & </s> <s xml:id="echoid-s17214" xml:space="preserve">paralelli; </s> <s xml:id="echoid-s17215" xml:space="preserve">quæ longitudines, & </s> <s xml:id="echoid-s17216" xml:space="preserve">latitudines. </s> <s xml:id="echoid-s17217" xml:space="preserve">porrò ex mutua terræ ac maris inter-<lb/>curſatione, oriuntur aliæ terrę, & </s> <s xml:id="echoid-s17218" xml:space="preserve">aquæ diuiſiones; </s> <s xml:id="echoid-s17219" xml:space="preserve">nam omnis terra, vel Continens eſt, vel Inſula, vel Penin-<lb/>ſula, vel Iſthmus. </s> <s xml:id="echoid-s17220" xml:space="preserve">Continens dicitur omnis terræ ſuperficies adeo magna, quæ a mari vulgò non putatur <lb/>ambiri, vt Aſia, Europa, & </s> <s xml:id="echoid-s17221" xml:space="preserve">c. </s> <s xml:id="echoid-s17222" xml:space="preserve">I<unsure/>nſula dicitur terra pars, quæ vndique mari alluitur, vt Sicilia, Corſica, Sardi-<lb/>nia, & </s> <s xml:id="echoid-s17223" xml:space="preserve">c. </s> <s xml:id="echoid-s17224" xml:space="preserve">Peninſula, vt nomen indicat, terra eſt quæ penè tota mari circumdatur, relicta tantum anguſta ter-<lb/>ræ parte, qua veluti collo, aut ceruice quadam continenti annectitur, quæ anguſta terra dicitur Iſthmus græ-<lb/>cis: </s> <s xml:id="echoid-s17225" xml:space="preserve">ſicuti etiam Peninſula dicitur Cherſoneſus. </s> <s xml:id="echoid-s17226" xml:space="preserve">Peninſula eſt Peloponeſus, Taurica Cherſoneſus, Cimbrica <lb/>Cherſoneſus. </s> <s xml:id="echoid-s17227" xml:space="preserve">ſunt præterea complura alia Geograpſis vſitata nomina ad terram pertinentia, litus, promon-<lb/>torium, regio, regnum, & </s> <s xml:id="echoid-s17228" xml:space="preserve">c. </s> <s xml:id="echoid-s17229" xml:space="preserve">quæ omnia Grammatici in ſuis Dictionarijs explicant.</s> <s xml:id="echoid-s17230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17231" xml:space="preserve">Pariter omnis Aqua, aut eſt ſalſa, & </s> <s xml:id="echoid-s17232" xml:space="preserve">Mare dicitur, aut dulcis. </s> <s xml:id="echoid-s17233" xml:space="preserve">Mare eſt vel Oceanus, vel Mediterraneum <lb/>mare. </s> <s xml:id="echoid-s17234" xml:space="preserve">Oceanus eſt mare magnum, videtur vniuerſam terram circumplecti. </s> <s xml:id="echoid-s17235" xml:space="preserve">Mediterraneum quod intra <lb/>terram eſt, vt Caſpium, & </s> <s xml:id="echoid-s17236" xml:space="preserve">Mediterraneum, quod inter Africam, Europam, & </s> <s xml:id="echoid-s17237" xml:space="preserve">Aſiam, ſitum eſt. </s> <s xml:id="echoid-s17238" xml:space="preserve">Sinus maris <lb/>dicitur, quod intra terram ſe inſinuat, vt ſinus Arabicus, Perſicus, & </s> <s xml:id="echoid-s17239" xml:space="preserve">alij. </s> <s xml:id="echoid-s17240" xml:space="preserve">Fretum eſt anguſtum mare, quod <lb/>intra binas terras arectè intercurrens, fremit. </s> <s xml:id="echoid-s17241" xml:space="preserve">Aquæ dulces ſunt lacus, paludes, fluuij, torrentes, fontes, oſtia, <lb/>& </s> <s xml:id="echoid-s17242" xml:space="preserve">c. </s> <s xml:id="echoid-s17243" xml:space="preserve">quæ Grammatici exponunt. </s> <s xml:id="echoid-s17244" xml:space="preserve">Conſiderandum hic etiam, vtra ſuperficies ſit maior, an minor, terræne, <lb/>an aquæ, quæ dubitatio ſolet multos inceſiere. </s> <s xml:id="echoid-s17245" xml:space="preserve">at cum nondum neutra ſit omnino tota cognita; </s> <s xml:id="echoid-s17246" xml:space="preserve">lis adhuc <lb/>pendet: </s> <s xml:id="echoid-s17247" xml:space="preserve">Cæterum globus Geographicus accuratè iuxta recentiores Nautarum, ac Viatorum traditiones <lb/>conſtructus, indicat eſſe ferè æquales.</s> <s xml:id="echoid-s17248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17249" xml:space="preserve">Solet etiam hic@quæri quantus ſit terræ ambi@us, quanta eius ſuperficies, & </s> <s xml:id="echoid-s17250" xml:space="preserve">ſoliditas, quibus ſatisfactum eſt <lb/>ſupra in cap. </s> <s xml:id="echoid-s17251" xml:space="preserve">de terræ magnitddine, & </s> <s xml:id="echoid-s17252" xml:space="preserve">cap. </s> <s xml:id="echoid-s17253" xml:space="preserve">de magnitudine maris.</s> <s xml:id="echoid-s17254" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div424" type="section" level="1" n="313"> <head xml:id="echoid-head331" style="it" xml:space="preserve">De terraipſa, ſeu ſuperficie terræ in vniuerſum.</head> <p> <s xml:id="echoid-s17255" xml:space="preserve">IAm tota terra ſecundum ſuperficiem diuiditur in quatuor partes præcipuas, Europam, Aſiam, Africam, <lb/>Nouum Orbem, ſeu Americam. </s> <s xml:id="echoid-s17256" xml:space="preserve">Debet igitur Geographiæ ſtudioſus has quatuor partes in globo conſio<unsure/>e-<lb/>rare, quem ſitum habeant inuicem earum vnaquæque, quibus confinijs inuicem ſeparentur; </s> <s xml:id="echoid-s17257" xml:space="preserve">Item ſingularũ <lb/>magnitudinem, ſitum cæleſtem, quæ pars ſit Orientalis, quæ Occidentalis, & </s> <s xml:id="echoid-s17258" xml:space="preserve">c. </s> <s xml:id="echoid-s17259" xml:space="preserve">quę vt ritè percipiantur, con-<lb/>ſtitue globum Aſtronomicè iuxta tuam habitationem, ideſt, ita vt habitatio tua ſit ſupra horizõtem ſub ver-<lb/>tice, ideſt, horizon globi ſit terræ horizon, & </s> <s xml:id="echoid-s17260" xml:space="preserve">c. </s> <s xml:id="echoid-s17261" xml:space="preserve">ſi videbis, & </s> <s xml:id="echoid-s17262" xml:space="preserve">concipies ritè poſitionem omnium partium ter-<lb/>ræ. </s> <s xml:id="echoid-s17263" xml:space="preserve">Ex quo cognoſcitur in qua Zona, in quo climate, ſub quibus paralellis ſit, vnde & </s> <s xml:id="echoid-s17264" xml:space="preserve">dies maxima, altitudo <lb/>poli, ſeu latitudines, & </s> <s xml:id="echoid-s17265" xml:space="preserve">longitudines innoteſcunt. </s> <s xml:id="echoid-s17266" xml:space="preserve">præterea quinam Amphiſcij, Eteroſcij, & </s> <s xml:id="echoid-s17267" xml:space="preserve">c. </s> <s xml:id="echoid-s17268" xml:space="preserve">quinam quo-<lb/>rumuis locorum ſint Antipodes, Antæci, Periæci. </s> <s xml:id="echoid-s17269" xml:space="preserve">Atq; </s> <s xml:id="echoid-s17270" xml:space="preserve">hæc ſunt quæ propriè cognoſcere debet Geogra-<lb/>phus, & </s> <s xml:id="echoid-s17271" xml:space="preserve">quæ Geographica appellantur. </s> <s xml:id="echoid-s17272" xml:space="preserve">verum præterea, & </s> <s xml:id="echoid-s17273" xml:space="preserve">quidem magna cum voluptate conſiderat alia <lb/>plura, quæ tamen ad duo capita reduci poſſunt, ideſt, ad Naturalia, & </s> <s xml:id="echoid-s17274" xml:space="preserve">Humana.</s> <s xml:id="echoid-s17275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17276" xml:space="preserve">Naturalia in vnaquaque mundi parte, atque etiam regione notanda hæc ſunt, primo Elementa ipſa, <lb/>v.</s> <s xml:id="echoid-s17277" xml:space="preserve">g. </s> <s xml:id="echoid-s17278" xml:space="preserve">terræ qualitates, plana, an montuoſa, montes celebres, lacus, ſtagna, flum@na, præſertim quæ aliqua <lb/>proprietates celebrantur, vt aquæ thermales, & </s> <s xml:id="echoid-s17279" xml:space="preserve">c. </s> <s xml:id="echoid-s17280" xml:space="preserve">Aer, venti, & </s> <s xml:id="echoid-s17281" xml:space="preserve">c. </s> <s xml:id="echoid-s17282" xml:space="preserve">Ignes ſubterranei, vulcani, foſſilia, fodi-<lb/>næ, plantæ peculiares, animalia peculiaria: </s> <s xml:id="echoid-s17283" xml:space="preserve">ſingulæ enim regiones proprijs rebus præditæ ſunt, nam, non <lb/>omnis fert omnia tellus, vnde</s> </p> <p style="it"> <s xml:id="echoid-s17284" xml:space="preserve">India mittit ebur, molles ſua thura Sabæi, & </s> <s xml:id="echoid-s17285" xml:space="preserve">e.</s> <s xml:id="echoid-s17286" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s17287" xml:space="preserve">Palmas Epirus equarnm.</s> <s xml:id="echoid-s17288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17289" xml:space="preserve">Secundo loco humana conſideranda ſunt, ac primo Homines ipſi, quales corpore, qui mores eorum, ſtudia, <lb/>idiomata, religio, reſpublica potentia, viri illuſtres. </s> <s xml:id="echoid-s17290" xml:space="preserve">loca pariter notanda ſunt, in quibus aliquid præclarum <lb/>geſtum fuerit, v.</s> <s xml:id="echoid-s17291" xml:space="preserve">g. </s> <s xml:id="echoid-s17292" xml:space="preserve">locus pugnæ Hannibalis cum Romanis ad Cannas, ad Trebiam. </s> <s xml:id="echoid-s17293" xml:space="preserve">loca vrbium deletarum: <lb/></s> <s xml:id="echoid-s17294" xml:space="preserve">tandem vrbes illuſtriores, præſertim in quibus Reges, aut Duces reſident, quæ Metropoles appellantur, <lb/>notandæ etiam antiquitatis reliquiæ, quæ paſſim occurrunt, Aquæductus, Via, Templa, & </s> <s xml:id="echoid-s17295" xml:space="preserve">c. </s> <s xml:id="echoid-s17296" xml:space="preserve">Oſtendan-<lb/>tur tandem maximi Monarchæ cum ſuis imperijs; </s> <s xml:id="echoid-s17297" xml:space="preserve">Rex Sinarum videtur maximus, Rex Hiſpaniarum ſe-<lb/>cundus, Magnus Turca tertius, & </s> <s xml:id="echoid-s17298" xml:space="preserve">c.</s> <s xml:id="echoid-s17299" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div425" type="section" level="1" n="314"> <head xml:id="echoid-head332" style="it" xml:space="preserve">DE EVROPA.</head> <p> <s xml:id="echoid-s17300" xml:space="preserve">DIuiſa iam tota terra in quatuor partes primarias, reliquum eſt tradere methodum, qua ſingularum geo-<lb/>graphicam doctrinam acquiras; </s> <s xml:id="echoid-s17301" xml:space="preserve">quamuis autem methodum modo in vniuerſum innuerimus, videtur ta-<lb/>men neceſſarium veluti exemplo geographico eam Europæ applicare.</s> <s xml:id="echoid-s17302" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17303" xml:space="preserve">Quæratur igitur primo Europæ etymon; </s> <s xml:id="echoid-s17304" xml:space="preserve">ſic autẽ dicta eſt ab Europa Agenoris Regis filia, quam ex Phæ-<lb/>nicia Iupiter in Cretam abduxiſſe poetæ fabulant<unsure/>ur.</s> <s xml:id="echoid-s17305" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17306" xml:space="preserve">Secundo definitio Europę. </s> <s xml:id="echoid-s17307" xml:space="preserve">eſt autem Europa vna ex quatuor mundi partibus, eſtq; </s> <s xml:id="echoid-s17308" xml:space="preserve">partim Cõtinens par-<lb/>tim Inſulæ, partim Peninſulæ; </s> <s xml:id="echoid-s17309" xml:space="preserve">cuius termini ſunt hi: </s> <s xml:id="echoid-s17310" xml:space="preserve">A meridie terminatur mari Mediterraneo, ab Occi-<lb/>dente Oceano; </s> <s xml:id="echoid-s17311" xml:space="preserve">à Septentrione Oceano glaciali, quamuis huius plagæ termini nondum ſint ſatis cogniti; <lb/></s> <s xml:id="echoid-s17312" xml:space="preserve">ab Oriente ſeparatur ab Aſia ſinu Granuico, poſtea Tanai fluuio, nam,</s> </p> <pb o="203" file="0225" n="230" rhead="AD GEOGRAPHIAM."/> <p style="it"> <s xml:id="echoid-s17313" xml:space="preserve">Europam atque Aſiam Tanais disterminat amnis.</s> <s xml:id="echoid-s17314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17315" xml:space="preserve">Poſtea palude Meotide, hincmari. </s> <s xml:id="echoid-s17316" xml:space="preserve">Euxino Propontide, ac tandem Aegeomari, quæ membra ſunt Me-<lb/>diterranei maris; </s> <s xml:id="echoid-s17317" xml:space="preserve">vt autem probè hæc omnia percipias ſtatue globum Aſtronomicè, ſecundum tuam hab ta-<lb/>tionem, ita vt habitatio tua ſit ſupra horizontẽ in medio hemiſpærij ſuperioris, ideſt, horizon globi euadat <lb/>tuus horizon; </s> <s xml:id="echoid-s17318" xml:space="preserve">ſic enim videbis quæ pars ſit orientalis, quæoccidentalis, & </s> <s xml:id="echoid-s17319" xml:space="preserve">c.</s> <s xml:id="echoid-s17320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17321" xml:space="preserve">Tertio figuram Europa: </s> <s xml:id="echoid-s17322" xml:space="preserve">S@rabo eam ſerpenti aſſi@@ilat, cuius caput ſit Hiſpania; </s> <s xml:id="echoid-s17323" xml:space="preserve">bina alæ ſint Italia, & </s> <s xml:id="echoid-s17324" xml:space="preserve">An-<lb/>glia; </s> <s xml:id="echoid-s17325" xml:space="preserve">cauda ſit Baltica peninſula, ſeu ſcandia; </s> <s xml:id="echoid-s17326" xml:space="preserve">pectus Gallia, & </s> <s xml:id="echoid-s17327" xml:space="preserve">Germania: </s> <s xml:id="echoid-s17328" xml:space="preserve">reliquę Polonia, Gręcia, Moſco-<lb/>uiam ventrem eſſiciant.</s> <s xml:id="echoid-s17329" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17330" xml:space="preserve">Quarto, quantitas ſeu magnitudo, quæ conſtat ex longitudine, & </s> <s xml:id="echoid-s17331" xml:space="preserve">latitudine, necnon ambitu. </s> <s xml:id="echoid-s17332" xml:space="preserve">hæc autem <lb/>longitudo, & </s> <s xml:id="echoid-s17333" xml:space="preserve">latitudo differunt ab eis, quas ſuperius explicauimus: </s> <s xml:id="echoid-s17334" xml:space="preserve">illę enim poſitionem loci in globo terre-<lb/>ſtri demonſtrant, hæ autem magnitudinem regionis, ideſt, quam longa, quamque lata ſit oſtendunt. </s> <s xml:id="echoid-s17335" xml:space="preserve">Longi-<lb/>tudo igitur Europa à Gadibus vſq; </s> <s xml:id="echoid-s17336" xml:space="preserve">ad Tanaim protenditur, eſtque milliaria 3000. </s> <s xml:id="echoid-s17337" xml:space="preserve">Latitudo ab extrema Si-<lb/>cilia vſq; </s> <s xml:id="echoid-s17338" xml:space="preserve">ad Sinum Granuicum milliaria 2400. </s> <s xml:id="echoid-s17339" xml:space="preserve">qnam in globo reperies ſic, pede vno circini poſito in Gadi-<lb/>bus, alterum extende vſq; </s> <s xml:id="echoid-s17340" xml:space="preserve">ad Tanaim, hanc circini aperturam applica 6 quatori initio facto à meridiano For-<lb/>tunatarum verſus orientem, & </s> <s xml:id="echoid-s17341" xml:space="preserve">vide quot gradus ęquatoris in ea contineantur: </s> <s xml:id="echoid-s17342" xml:space="preserve">pro ſingulis autem gr 60. </s> <s xml:id="echoid-s17343" xml:space="preserve">mil-<lb/>liaria computanda ſunt: </s> <s xml:id="echoid-s17344" xml:space="preserve">idem fac pro latitudine habenda: </s> <s xml:id="echoid-s17345" xml:space="preserve">& </s> <s xml:id="echoid-s17346" xml:space="preserve">pro quau@s alia diſtantia capienda.</s> <s xml:id="echoid-s17347" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17348" xml:space="preserve">Quinto ſitus cęleſtis, qui determinatur per latitudinem, & </s> <s xml:id="echoid-s17349" xml:space="preserve">longitu linem extremitatum ipſius; </s> <s xml:id="echoid-s17350" xml:space="preserve">ſic in glo-<lb/>bo apparet extremitates eius Auſtrales eſſe in latitudine gr. </s> <s xml:id="echoid-s17351" xml:space="preserve">35. </s> <s xml:id="echoid-s17352" xml:space="preserve">Boreales vero gr. </s> <s xml:id="echoid-s17353" xml:space="preserve">70. </s> <s xml:id="echoid-s17354" xml:space="preserve">quod indicant gradus, <lb/>quibus diuiditur meridianus Fortunatarum, nam paralelli ducti per extremitates Europæ tranſeunt, vnus <lb/>per gr. </s> <s xml:id="echoid-s17355" xml:space="preserve">35. </s> <s xml:id="echoid-s17356" xml:space="preserve">alter per gr. </s> <s xml:id="echoid-s17357" xml:space="preserve">70. </s> <s xml:id="echoid-s17358" xml:space="preserve">In lõgitudine verò ſituatur inter gr. </s> <s xml:id="echoid-s17359" xml:space="preserve">10. </s> <s xml:id="echoid-s17360" xml:space="preserve">& </s> <s xml:id="echoid-s17361" xml:space="preserve">75. </s> <s xml:id="echoid-s17362" xml:space="preserve">Meridiani enim eius extremi, ideſt, <lb/>occidentaliſſimus, & </s> <s xml:id="echoid-s17363" xml:space="preserve">orientali ſſimus tranſeunt per prędictos gradus æquatoris. </s> <s xml:id="echoid-s17364" xml:space="preserve">hinc patet totam eſſe in Zo-<lb/>na temperata, præter paruam quandam partem Balteæ peninſulæ, quę Zonam frigidam ingreditur: </s> <s xml:id="echoid-s17365" xml:space="preserve">patet <lb/>ſub quibus climatibus ſita ſit, necnon quinam ſint extremi eius paralelli, quos ſupra vna cum climatibus in <lb/>eadem Tabula dedimus: </s> <s xml:id="echoid-s17366" xml:space="preserve">ex qua appareteam eſſe extra priora tria climata, ſed ſub reliquis 19. </s> <s xml:id="echoid-s17367" xml:space="preserve">vt indicant la-<lb/>titudines exttemæ gr. </s> <s xml:id="echoid-s17368" xml:space="preserve">35. </s> <s xml:id="echoid-s17369" xml:space="preserve">& </s> <s xml:id="echoid-s17370" xml:space="preserve">70. </s> <s xml:id="echoid-s17371" xml:space="preserve">patet etiam diem eius maximum ſub auſtrali paralello eſſe horarum 14. </s> <s xml:id="echoid-s17372" xml:space="preserve">min. <lb/></s> <s xml:id="echoid-s17373" xml:space="preserve">15. </s> <s xml:id="echoid-s17374" xml:space="preserve">circiter: </s> <s xml:id="echoid-s17375" xml:space="preserve">ſub boreali vero eſſe horarum 24. </s> <s xml:id="echoid-s17376" xml:space="preserve">& </s> <s xml:id="echoid-s17377" xml:space="preserve">amplius propter partem illam, quæ in Zonam frigidam ex-<lb/>currit. </s> <s xml:id="echoid-s17378" xml:space="preserve">præterea Europæos omnes eſſe Eteroſcios. </s> <s xml:id="echoid-s17379" xml:space="preserve">quin etiam patet quinam ſint Europęis Antipodes, item <lb/>Periæci, & </s> <s xml:id="echoid-s17380" xml:space="preserve">Antæci, & </s> <s xml:id="echoid-s17381" xml:space="preserve">c. </s> <s xml:id="echoid-s17382" xml:space="preserve">atque hęc primario ad Geographum ſpectant. </s> <s xml:id="echoid-s17383" xml:space="preserve">Hoc loco mouendus eſt Geographus <lb/>Tyro, caueat ab vniuerſalibus terrę Tabulis, ſeu Mappis, in ferendo iudicio de magnitudine Regnorum, aut <lb/>Prouinciarum; </s> <s xml:id="echoid-s17384" xml:space="preserve">quoniam huiuſmodi Mappæ plus iuſto ampliant Regiones, quæ ſunt propè polos. </s> <s xml:id="echoid-s17385" xml:space="preserve">ratio eſt <lb/>quia Mapoa vniuerſalis debet repręſentare in plano terræ ſuperficiem, quę ſphęrica eſt; </s> <s xml:id="echoid-s17386" xml:space="preserve">impoſſibile autem <lb/>eſt ſphęricum ita in planum proijcere, vt illud re vera imitetur. </s> <s xml:id="echoid-s17387" xml:space="preserve">pręterea in huiuſmodi Mappis difficile eſt <lb/>concipere mutuos ſitus prouinciarum; </s> <s xml:id="echoid-s17388" xml:space="preserve">vnde ſtudioſi prauas imaginationes ex eis ſæpè concipiunt. </s> <s xml:id="echoid-s17389" xml:space="preserve">Conſu-<lb/>lo igitur lectori, vt ptimum Globo Geographico det operam, is enim rectè cum ſphæricus ſit, ſphæricam <lb/>Terram referre poteſt.</s> <s xml:id="echoid-s17390" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div426" type="section" level="1" n="315"> <head xml:id="echoid-head333" style="it" xml:space="preserve">NATVRALIA.</head> <p> <s xml:id="echoid-s17391" xml:space="preserve">PRęterea conſiderant qualitatem totius regionis, qua rerum ſit fertilis, vbi commodè habitabilis: </s> <s xml:id="echoid-s17392" xml:space="preserve">tota igi-<lb/>tur Europa fertilis, ac habitabilis eſt; </s> <s xml:id="echoid-s17393" xml:space="preserve">abundat metallis, ac reliquis foſſibilibus, plures habet proprias <lb/>plantas, & </s> <s xml:id="echoid-s17394" xml:space="preserve">animalia. </s> <s xml:id="echoid-s17395" xml:space="preserve">Caret tamen Aromatibus, Vnionibus, Leonibus, & </s> <s xml:id="echoid-s17396" xml:space="preserve">Elephantibus, & </s> <s xml:id="echoid-s17397" xml:space="preserve">c. </s> <s xml:id="echoid-s17398" xml:space="preserve">quæapud Ma-<lb/>ginum in Geographia, & </s> <s xml:id="echoid-s17399" xml:space="preserve">apud Boterum in Relationibus vniuerſalibus fusè narrantur: </s> <s xml:id="echoid-s17400" xml:space="preserve">quamuis Auctores <lb/>hæc tria Geographica, Naturalia, & </s> <s xml:id="echoid-s17401" xml:space="preserve">Humana confundant.</s> <s xml:id="echoid-s17402" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div427" type="section" level="1" n="316"> <head xml:id="echoid-head334" style="it" xml:space="preserve">HVMANA.</head> <p> <s xml:id="echoid-s17403" xml:space="preserve">EVropæi homines, ſtrenui, fortes, atque etiam ingenio pollentes: </s> <s xml:id="echoid-s17404" xml:space="preserve">in hac maxima Imperia Græcorom, <lb/>& </s> <s xml:id="echoid-s17405" xml:space="preserve">Latinorum extitere, atque adhuc Imperator, ac Summus Pontifex veluti Reipublicæ Chriſtianę ca-<lb/>put reſidet. </s> <s xml:id="echoid-s17406" xml:space="preserve">Eximij nunc ſunt Nautici. </s> <s xml:id="echoid-s17407" xml:space="preserve">In ea pluſquam alibi omnes ſcientię, & </s> <s xml:id="echoid-s17408" xml:space="preserve">artes floruerunt, ac etiam-<lb/>num florent. </s> <s xml:id="echoid-s17409" xml:space="preserve">Varij nunc ſunt Europæi, lingua, moribus, religione, ſtatura corporis, & </s> <s xml:id="echoid-s17410" xml:space="preserve">ſimilibus. </s> <s xml:id="echoid-s17411" xml:space="preserve">Bote-<lb/>tus opinatur probabili eoniectura in tota Europa eontineri 70. </s> <s xml:id="echoid-s17412" xml:space="preserve">milliones hominum. </s> <s xml:id="echoid-s17413" xml:space="preserve">Vrbes pręclaræ, Ro-<lb/>ma, Conſtantinopolis, Lutetiæ, Vlyſſippo, Venetię, Mediolanum, & </s> <s xml:id="echoid-s17414" xml:space="preserve">c. </s> <s xml:id="echoid-s17415" xml:space="preserve">In ea nunc latè dominantur Rex <lb/>Britanniæ, Rex Hiſpaniarum, Rex Galliæ, Imperator, Magnus Turca, Rex Poloniæ, Dux Moſcouiæ, <lb/>Rex Suetiæ, Rex Daniæ. </s> <s xml:id="echoid-s17416" xml:space="preserve">His de Europa in vniuerſum cognitis, tota debet diuidi in ſua regna, Britan-<lb/>niam, Hiſpaniam, Galliam, Italiam, Germaniam, Illyricum, Gręciam, Thraciam, Miſiam, Vngariam, <lb/>Moldauiam, Poloniam, Moſcouiam, Scandiam, ſeu Balticam. </s> <s xml:id="echoid-s17417" xml:space="preserve">porrò de ſingulis regnis ea cognoſcenda <lb/>ſunt, atque eadem methodo, qua vſi ſumus in Europa tota. </s> <s xml:id="echoid-s17418" xml:space="preserve">Incipiunt autem à regnis occidentalibus, vt à <lb/>Britannia, Hiſpania, proceduntque paulatim ad orientalia. </s> <s xml:id="echoid-s17419" xml:space="preserve">ſunt autem apud Geographos Tabulæ, ſeu pi-<lb/>cturæ ſingulorum regnorum, & </s> <s xml:id="echoid-s17420" xml:space="preserve">prouinciarum, quibus antequam des operam, debes earum ſitum prius in <lb/>globo Aſtronomicè collocato cognoſcere, præſertim reſpectu tuæ habitationis, ita vt domi tuæ manen@ <lb/>ſcias indigitare ad quam mundi partem ſita ſunt ſingula regna, vr<unsure/>bes, & </s> <s xml:id="echoid-s17421" xml:space="preserve">c. </s> <s xml:id="echoid-s17422" xml:space="preserve">Tabulæ enim, vt ſingulas partes <pb o="204" file="0226" n="231" rhead="TRACTATVS"/> melius manifeftant, peius tamen ſitum, ac poſitionem in orbe terreſtri monſtrant, quam globus. </s> <s xml:id="echoid-s17423" xml:space="preserve">in hiſce <lb/>Tabulis vt plurimum, pars dextra eſt oriens, ſiniſtra occidens: </s> <s xml:id="echoid-s17424" xml:space="preserve">ſuperior Boreas, inferior Auſter. </s> <s xml:id="echoid-s17425" xml:space="preserve">quapro-<lb/>pter in appoſi@a ſequenti figura, Vienna eſt in parte orientis, Monachium in parte occidentis, Praga verò <lb/>borealis, &</s> <s xml:id="echoid-s17426" xml:space="preserve">c. </s> <s xml:id="echoid-s17427" xml:space="preserve">Gradus in boreali, & </s> <s xml:id="echoid-s17428" xml:space="preserve">auſtrali <lb/> <anchor type="figure" xlink:label="fig-0226-01a" xlink:href="fig-0226-01"/> latere notati ſunt gradus lõgitudinis qui in-<lb/>cipiunt a 28. </s> <s xml:id="echoid-s17429" xml:space="preserve">& </s> <s xml:id="echoid-s17430" xml:space="preserve">deſinunt in 37. </s> <s xml:id="echoid-s17431" xml:space="preserve">ſuntque vel <lb/>in æquatore, vel in paralello æquatoris in <lb/>pręſenti autem figura ſunt in duobus ęqua-<lb/>tori paralellis, vt oſtendunt gradus ad lęuã, <lb/>& </s> <s xml:id="echoid-s17432" xml:space="preserve">dexteram poſiti, qui ſunt gradus latitudi-<lb/>num, ſuntque in meridianis regionem illam <lb/>claudentibus. </s> <s xml:id="echoid-s17433" xml:space="preserve">qui cum incipiant a gr. </s> <s xml:id="echoid-s17434" xml:space="preserve">46. </s> <s xml:id="echoid-s17435" xml:space="preserve">& </s> <s xml:id="echoid-s17436" xml:space="preserve"><lb/>deſinant in 52. </s> <s xml:id="echoid-s17437" xml:space="preserve">grad. </s> <s xml:id="echoid-s17438" xml:space="preserve">indicant paralellum au-<lb/>ſtralem in quo ſunt num. </s> <s xml:id="echoid-s17439" xml:space="preserve">28. </s> <s xml:id="echoid-s17440" xml:space="preserve">29. </s> <s xml:id="echoid-s17441" xml:space="preserve">&</s> <s xml:id="echoid-s17442" xml:space="preserve">c. </s> <s xml:id="echoid-s17443" xml:space="preserve">diſtare <lb/>ab æquatore gr. </s> <s xml:id="echoid-s17444" xml:space="preserve">45. </s> <s xml:id="echoid-s17445" xml:space="preserve">borealem verò gr. </s> <s xml:id="echoid-s17446" xml:space="preserve">52. </s> <s xml:id="echoid-s17447" xml:space="preserve">ſeu <lb/>habere latitudines gr. </s> <s xml:id="echoid-s17448" xml:space="preserve">45. </s> <s xml:id="echoid-s17449" xml:space="preserve">& </s> <s xml:id="echoid-s17450" xml:space="preserve">52. </s> <s xml:id="echoid-s17451" xml:space="preserve">pariter in <lb/>eadem figura, linea quæ ducitur a borea in <lb/>auſtrum per gr. </s> <s xml:id="echoid-s17452" xml:space="preserve">33. </s> <s xml:id="echoid-s17453" xml:space="preserve">& </s> <s xml:id="echoid-s17454" xml:space="preserve">per Pragam, oſtendit <lb/>longitudinem Pragæ eſſe gr. </s> <s xml:id="echoid-s17455" xml:space="preserve">33. </s> <s xml:id="echoid-s17456" xml:space="preserve">altera vero <lb/>linea prædictæ perpendicularis duæa ab oc-<lb/>cidente 50. </s> <s xml:id="echoid-s17457" xml:space="preserve">in oriente 50. </s> <s xml:id="echoid-s17458" xml:space="preserve">indicat latitudinem <lb/>Pragæ ſiue altitudinem poli, eſſe gr. </s> <s xml:id="echoid-s17459" xml:space="preserve">50. </s> <s xml:id="echoid-s17460" xml:space="preserve">quæ <lb/>omnia alijs etiam Tabulis eadem ratione <lb/>applicari debent. </s> <s xml:id="echoid-s17461" xml:space="preserve">Abſolutis Europę Tabu-<lb/>lis, ad Aſiam aut Africam ſimili methodo <lb/>perluſtrandam aggrediaris. </s> <s xml:id="echoid-s17462" xml:space="preserve">Atq; </s> <s xml:id="echoid-s17463" xml:space="preserve">hæc ſuf-<lb/>ficiunt ſtudioſo, ac cupido Geographiæ in-<lb/>troducendo. </s> <s xml:id="echoid-s17464" xml:space="preserve">reliqua per ſe prudenter inue-<lb/>ueniet. </s> <s xml:id="echoid-s17465" xml:space="preserve">habeat ſi poteſt Abrahami Ortelij <lb/>Theatrum Mundi. </s> <s xml:id="echoid-s17466" xml:space="preserve">Vide infra in Appara-<lb/>tu ad Mathematicas addiſcendas; </s> <s xml:id="echoid-s17467" xml:space="preserve">vbi de Geographia, & </s> <s xml:id="echoid-s17468" xml:space="preserve">ſcriptoribus eius agitur. </s> <s xml:id="echoid-s17469" xml:space="preserve">Habes igitur Coſmogra-<lb/>phiam, Geographiam, & </s> <s xml:id="echoid-s17470" xml:space="preserve">Chorographiam, à me in hoc opere explicatas.</s> <s xml:id="echoid-s17471" xml:space="preserve"/> </p> <div xml:id="echoid-div427" type="float" level="2" n="1"> <figure xlink:label="fig-0226-01" xlink:href="fig-0226-01a"> <image file="0226-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0226-01"/> </figure> </div> <pb o="205" file="0227" n="232"/> </div> <div xml:id="echoid-div429" type="section" level="1" n="317"> <head xml:id="echoid-head335" xml:space="preserve">APPARATVS <lb/>AD MATHEMATICAS <lb/>ADDISCENDAS, ET PROMOVENDAS</head> <p> <s xml:id="echoid-s17472" xml:space="preserve">CVm ego tum in me ipſo, tum in alijs plunibus experientia didicerim quant is labori-<lb/>bus, quantiſque ſtudiorum diſpendijs, ij Mathematicis dent operam, qui eas nullo <lb/>doctore præuio, nullaq; </s> <s xml:id="echoid-s17473" xml:space="preserve">eræeedenti nſtructione aggrediuntur, breui hoc apparatu <lb/>huic malo remedium afferre decreui. </s> <s xml:id="echoid-s17474" xml:space="preserve">Qua in re fortè Gemio<unsure/>u mimitabor, qui vt <lb/>tradit Pappus lib. </s> <s xml:id="echoid-s17475" xml:space="preserve">8. </s> <s xml:id="echoid-s17476" xml:space="preserve">de Mathematicarum ordine ſeripſerat. </s> <s xml:id="echoid-s17477" xml:space="preserve">præ cæteris veroſcien-<lb/>tijs Mathematicæ prccipuè tali auxilio indigere videntur, tum propter earum mul-<lb/>titudinem, mutuam connexionem, ac depẽdentiam; </s> <s xml:id="echoid-s17478" xml:space="preserve">tum quod hac tempeſtate, qua <lb/>ipſę reuiuiſcere, ac reflorere incipiunt, perpauci, rariq; </s> <s xml:id="echoid-s17479" xml:space="preserve">ea@n profeſlores reperian-<lb/>tur, pauci ſſimique, qui earum totam Encyclopęd am p@ritè, ſcienterq; </s> <s xml:id="echoid-s17480" xml:space="preserve">percalleant, <lb/>quique varijs ſtudioſorum finibus latis facere queant, Verum (quod magis dolen-<lb/>dum eſt) plurimi paſſim reperiuntur, qui ſe Mathematicos venditant, propterea quòd ſphæræ circulos vt-<lb/>cunque nouerint, aut quod nudam Horologij deſcriptionem teneant. </s> <s xml:id="echoid-s17481" xml:space="preserve">quot ſunt qui totam Mutheſeos vim <lb/>in eo conſiſtere putant, vt ſciat quis, vt aiunt, alicuius Natiuitatem conſtruere? </s> <s xml:id="echoid-s17482" xml:space="preserve">totiq; </s> <s xml:id="echoid-s17483" xml:space="preserve">ſunt ferè omnes, vt Iu-<lb/>diciariam Aſtrologiam exiſtiment eſſe totius Matheſ@os columen, quæ tamen nuna ratione nomen ſcien-<lb/>tiæ Mathematicæ meretur. </s> <s xml:id="echoid-s17484" xml:space="preserve">Quam rari hodie Geome@ræ, qui Archimedis, Apollonij, Pappi, admiranda. <lb/></s> <s xml:id="echoid-s17485" xml:space="preserve">monumenta perlegerint? </s> <s xml:id="echoid-s17486" xml:space="preserve">Quam @ari inter Arichmeticos ad Algebræ penetralia ſcienter perueniunt? </s> <s xml:id="echoid-s17487" xml:space="preserve">tan-<lb/>dem qui Muſici habentur, & </s> <s xml:id="echoid-s17488" xml:space="preserve">probantur, nulla Arithmeticæ aut Geometrię cognitione, nulla de Muſicæ na-<lb/>tura, officio, aut fine tractatione, eam tradunt, ac profitentur. </s> <s xml:id="echoid-s17489" xml:space="preserve">vnde reliqua noſtræ Muſicæ detrimẽta, de qui-<lb/>bus nos alibi diximus oriuntur. </s> <s xml:id="echoid-s17490" xml:space="preserve">Idem de reliquis Mathematicis dici poſlet, fed ne longior ſim, rem propo-<lb/>ſitam aggrediar, & </s> <s xml:id="echoid-s17491" xml:space="preserve">totum apparatum in quinque partes diſtribuam.</s> <s xml:id="echoid-s17492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17493" xml:space="preserve">Prima, erit Mathematicarum omnium expoſitio, & </s> <s xml:id="echoid-s17494" xml:space="preserve">diuiſio.</s> <s xml:id="echoid-s17495" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17496" xml:space="preserve">Secunda, Bibliotheca Authorum ſelectorum pro ſingulis Mathematicis.</s> <s xml:id="echoid-s17497" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17498" xml:space="preserve">Tertia, Variæ methodi earum addiſcenda@un.</s> <s xml:id="echoid-s17499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17500" xml:space="preserve">Quarta, Mathematici ſtudij promotio.</s> <s xml:id="echoid-s17501" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17502" xml:space="preserve">Quinta, Chronologia clarorum Mathematicorum, quam edidimus iam cum locis Mathematicis Ariſt.</s> <s xml:id="echoid-s17503" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div430" type="section" level="1" n="318"> <head xml:id="echoid-head336" style="it" xml:space="preserve">Mathematicarum diuiſio, & expl. catio. ‘Pars prima.</head> <p> <s xml:id="echoid-s17504" xml:space="preserve">COnueniens imo nec ſſarium omninò eſſe videtur, ante omnia breu@m quandam ac ſimplicem Mathe-<lb/>maticarum expl cationem tradere. </s> <s xml:id="echoid-s17505" xml:space="preserve">breuem m<unsure/>quam quoniam quamuis pluribus dequauis ſcienci@@ſ-<lb/>ſeratur, nunquam tamen naturam illius probè percipies, niſi ſcientiam ipſam animo totam compræhen-<lb/>deris.</s> <s xml:id="echoid-s17506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17507" xml:space="preserve">Mathematicæ igitur ſcientiæ al@æ ſunt ſpeculatiuæ, aliæ practicæ; </s> <s xml:id="echoid-s17508" xml:space="preserve">item aliæ puræ, aliæ mediæ; </s> <s xml:id="echoid-s17509" xml:space="preserve">tandem <lb/>aliæ ſubalternantes, aliæ ſubalternatæ. </s> <s xml:id="echoid-s17510" xml:space="preserve">Per ſpeculatiuas eas intelligo quæ conſiderant quan@itatem a mate-<lb/>ria abſtractam, ideſt, nulla habita ratione mater æ in qua ipſa quantitas detinetur. </s> <s xml:id="echoid-s17511" xml:space="preserve">quod ſi quæ concretam <lb/>conſiderant, non tamen conſiderationem dirigunt ad opus.</s> <s xml:id="echoid-s17512" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div431" type="section" level="1" n="319"> <head xml:id="echoid-head337" style="it" xml:space="preserve">Speculatiuæ Mathematicæ ſunt ſex ſequentes.</head> <p> <s xml:id="echoid-s17513" xml:space="preserve">1 GEometria quam primam facere libet, tractat de quantitate continua terminata, cuius ſunt tria gene-<lb/>ra, linea, ſuperficie, corpus: </s> <s xml:id="echoid-s17514" xml:space="preserve">uxta tres dimenſiones, longitudinem, latitudinem, & </s> <s xml:id="echoid-s17515" xml:space="preserve">profunditatem. </s> <s xml:id="echoid-s17516" xml:space="preserve">Li-<lb/>nea terminata eſt, v.</s> <s xml:id="echoid-s17517" xml:space="preserve">g. </s> <s xml:id="echoid-s17518" xml:space="preserve">linea bipedalis, diameter alicuius circuli, vel quadrati, latus alicui<unsure/>us trianguli, quadra-<lb/>ti, rhombi, &</s> <s xml:id="echoid-s17519" xml:space="preserve">c. </s> <s xml:id="echoid-s17520" xml:space="preserve">ſuperficies terminata eſt, v.</s> <s xml:id="echoid-s17521" xml:space="preserve">g. </s> <s xml:id="echoid-s17522" xml:space="preserve">triangu um, quadratum, circulus, &</s> <s xml:id="echoid-s17523" xml:space="preserve">c. </s> <s xml:id="echoid-s17524" xml:space="preserve">corpus terminatum eſt, vt <lb/>cubus, conus, cylindrus, ſphæra, &</s> <s xml:id="echoid-s17525" xml:space="preserve">c. </s> <s xml:id="echoid-s17526" xml:space="preserve">de quibus omnibus ſubtiliſſime Geometria oſtendit admir<unsure/>abiles pro-<lb/>prietates. </s> <s xml:id="echoid-s17527" xml:space="preserve">pars quæ tractat de corporibus, ſeu ſolidis proprio no@ine dicitur Stereometria.</s> <s xml:id="echoid-s17528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17529" xml:space="preserve">2 Arithmetica agit de quantitate diſcreta, finita, & </s> <s xml:id="echoid-s17530" xml:space="preserve">terminata, ſiue denumeris finicis, & </s> <s xml:id="echoid-s17531" xml:space="preserve">terminatis, vt <lb/>ſunt numeri quadrati, cubi, &</s> <s xml:id="echoid-s17532" xml:space="preserve">c. </s> <s xml:id="echoid-s17533" xml:space="preserve">con@poſiti, incompoſiti, &</s> <s xml:id="echoid-s17534" xml:space="preserve">c. </s> <s xml:id="echoid-s17535" xml:space="preserve">horum naturam, & </s> <s xml:id="echoid-s17536" xml:space="preserve">accidentiam, eoru@ que mu-<lb/>tuas actiones perſcrutatur.</s> <s xml:id="echoid-s17537" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17538" xml:space="preserve">Hæ porrò duę dicuntur puræ, quod tractent de pura quantitate abſtracta a maleria, ideſt, Geometria con-<lb/>ſiderat triangulum ſecundum ſe, nulla habita ratione materię in qua ſit triangulum, ſiue enim ſit in ligno, ſi-<lb/>ue in ære, ſiue in cęlo, ſiue in terra, illud eodem modo conſiderat. </s> <s xml:id="echoid-s17539" xml:space="preserve">Similiter Arithmetica conſiderat nume- <pb o="206" file="0228" n="233" rhead="APPARATVS"/> ros abſtractos, ideſt, abſque eo quod illis res vllæ ſenſibiles ſubſint. </s> <s xml:id="echoid-s17540" xml:space="preserve">reliquæ vero quatuor quoniam quantita-<lb/>tes prædictas in rebus materialibus, aut ſenſibilibus cõſtitutas contemplantur, propterea medię vocã tur, me-<lb/>diæ enim ſunt inter puras Mathematicas, & </s> <s xml:id="echoid-s17541" xml:space="preserve">naturalem Philoſophiam. </s> <s xml:id="echoid-s17542" xml:space="preserve">Prædictæ duæ vocantur ſubalter-<lb/>nantes, reliquæ verò quatuor ſubalternatæ: </s> <s xml:id="echoid-s17543" xml:space="preserve">quidautem ſit hæc ſubalternatio mox apparebit.</s> <s xml:id="echoid-s17544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17545" xml:space="preserve">3 Ex medijs, & </s> <s xml:id="echoid-s17546" xml:space="preserve">ſubalternatis prima ſit Optica, ſeu Perſpectiua, quæ de radijs viſus, & </s> <s xml:id="echoid-s17547" xml:space="preserve">lucis, ideſt, de Vi-<lb/>ſione, & </s> <s xml:id="echoid-s17548" xml:space="preserve">Lumine tractat, quamuis a Viſione ſola ſit denominata. </s> <s xml:id="echoid-s17549" xml:space="preserve">quia vero in prædictis radijs conſiderat li-<lb/>neas, angulos, atq; </s> <s xml:id="echoid-s17550" xml:space="preserve">hinc ſuperficies, pyramides, conos, axes, &</s> <s xml:id="echoid-s17551" xml:space="preserve">c. </s> <s xml:id="echoid-s17552" xml:space="preserve">quæ ad Geometriæ obiectum pertinent, ijſq; <lb/></s> <s xml:id="echoid-s17553" xml:space="preserve">vtitur in demonſtrando accidentia viſus, & </s> <s xml:id="echoid-s17554" xml:space="preserve">illuminationis, ideo Geometriæ dicitur ſubalternari. </s> <s xml:id="echoid-s17555" xml:space="preserve">eius ſunt <lb/>tres partes.</s> <s xml:id="echoid-s17556" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17557" xml:space="preserve">Prima, eſt de Directione, ideſt, viſione, & </s> <s xml:id="echoid-s17558" xml:space="preserve">illuminatione directa, ideſt, quæ fit per lineas rectas ſimpli-<lb/>ces, quod accidit quotieſcumque per vnicum medium, vt per ſolum aerem, & </s> <s xml:id="echoid-s17559" xml:space="preserve">ſine ſpeculo fit viſio, & </s> <s xml:id="echoid-s17560" xml:space="preserve">illu-<lb/>minatio.</s> <s xml:id="echoid-s17561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17562" xml:space="preserve">Secunda, eſt de Reflexione, ideſt, de viſione, & </s> <s xml:id="echoid-s17563" xml:space="preserve">illuminatione reflexa, quę per ſpeculum fiunt, hęc propri@ <lb/>dicitur Catoptrica, ſiue Specularia; </s> <s xml:id="echoid-s17564" xml:space="preserve">de admirandis enim ſpeculorum accidentibus demonſtrat.</s> <s xml:id="echoid-s17565" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17566" xml:space="preserve">Tertia, de Refractione, ideſt, viſione, & </s> <s xml:id="echoid-s17567" xml:space="preserve">illuminatione refracta, quæ per radios fractos fiunt; </s> <s xml:id="echoid-s17568" xml:space="preserve">quod accidit <lb/>cum radij per plura media, ideſt, diuerſæ tranſparentiæ, vt per aerem, & </s> <s xml:id="echoid-s17569" xml:space="preserve">aquam tranſeunt; </s> <s xml:id="echoid-s17570" xml:space="preserve">hæc propriè dici-<lb/>tur Dioptrica.</s> <s xml:id="echoid-s17571" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17572" xml:space="preserve">Quarta, Mechanica, quæ de Machinis agit, ſiue vt ait Ariſtoteles verſatur circa artificiata, ſicuti naturali@ <lb/>circa naturalia: </s> <s xml:id="echoid-s17573" xml:space="preserve">de ſex Machinis præcipuis, Libra, Vecte, Trochlea, Axe in Peritrochio, Cuneo, Cochlea <lb/>egregia demonſtrat: </s> <s xml:id="echoid-s17574" xml:space="preserve">& </s> <s xml:id="echoid-s17575" xml:space="preserve">quia in eis conſiderat quantitates virium mouentium, ponderum, motuum, tempo-<lb/>rum, quibus mouentur, & </s> <s xml:id="echoid-s17576" xml:space="preserve">Machinas ipſas tanquam lineas quaſdam circa centra reuolutas, ideo Geometriæ <lb/>ſubalternatur, ideſt, Geometricè demonſtrat. </s> <s xml:id="echoid-s17577" xml:space="preserve">Eius pars ſubtiliſſima eſt, quæ centra grauitatis in planis, a@ <lb/>ſolidis perſcrutatur.</s> <s xml:id="echoid-s17578" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17579" xml:space="preserve">Quinta, Muſica, quæ quoniam conſiderat quantitatem diſcretam in ſonis, & </s> <s xml:id="echoid-s17580" xml:space="preserve">vocibus, ſeu numerum ſono-<lb/>rum ſonoſq; </s> <s xml:id="echoid-s17581" xml:space="preserve">reducit ad numeros, ideo in demonſtrando Arithmetica indiget, vnde & </s> <s xml:id="echoid-s17582" xml:space="preserve">Arithmeticè demon-<lb/>ſtrat, Arithmeticæque ſubalternatur: </s> <s xml:id="echoid-s17583" xml:space="preserve">præcipuè vero circa conſonantiarum omnium naturam, & </s> <s xml:id="echoid-s17584" xml:space="preserve">rationem, <lb/>& </s> <s xml:id="echoid-s17585" xml:space="preserve">accidentia verſatur.</s> <s xml:id="echoid-s17586" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17587" xml:space="preserve">Sexta, eſt Aſtronomia omnium nobiliſſ@a, cuius eſt totam Mundi Fabricam dęſcribere. </s> <s xml:id="echoid-s17588" xml:space="preserve">quod perficit <lb/>demonſtrando de ſingulis mundi partibus Planetis, & </s> <s xml:id="echoid-s17589" xml:space="preserve">Stellis, Locum, Figuram, Motum, Magnitudinem, <lb/>Illuminationem, & </s> <s xml:id="echoid-s17590" xml:space="preserve">Vmbram, v. </s> <s xml:id="echoid-s17591" xml:space="preserve">g. </s> <s xml:id="echoid-s17592" xml:space="preserve">oſtendit terram eſſe in medio Mundi, eſſe ſphæricam, quieſcentem, vt à <lb/>Sole illuſtretur, qualem vmbram efficiat. </s> <s xml:id="echoid-s17593" xml:space="preserve">hæc Geometriæ ſubalternatur quod haſce mundanas quantitates <lb/>contempletur, ſubordinatur etiam Arithmeticę quatenus cæleſles motus diſcretos facit, vnde paſſim nume-<lb/>ris vtitur. </s> <s xml:id="echoid-s17594" xml:space="preserve">Aſtronomicæ partes cenſentur Tractatus de Sphæra, Thcoricæ Planetarum, Tabulæ Aſtrono-<lb/>micæ, Computus Eccleſiaſticus, Gnomonica, quæ Solis vmbras obſeruat, cuius pręcipuum munus eſt ſolaria, <lb/>& </s> <s xml:id="echoid-s17595" xml:space="preserve">ſcioterica Horologia conſtruere: </s> <s xml:id="echoid-s17596" xml:space="preserve">Geographia, quæ totam terræ ſuperficiem, atque omnes eius prouin-<lb/>cias, & </s> <s xml:id="echoid-s17597" xml:space="preserve">loca etiam reſpectu cęli deſcribit: </s> <s xml:id="echoid-s17598" xml:space="preserve">Aſtrologia, ſeu ludiciaria, cuius eſt futura prædicere etiam vul-<lb/>go pars Aſtronomiæ putatur, ſed immeritò, quia etſi nihil ferè demonſtret conatur tamen per cauſas natura-<lb/>les, non Mathen aticas demonſtrare, quare pars phyficæ cenſenda eſt. </s> <s xml:id="echoid-s17599" xml:space="preserve">Verum quidem eſt hoſce Aſtro-<lb/>logos nonnulla rerum Aſtronomicarum cognitione indigere, præſertim calculo, vnde ſibi Aſtrologię no-<lb/>men vſurparunt. </s> <s xml:id="echoid-s17600" xml:space="preserve">Atque hæ ſunt ſex ſcientiæ Mathematicæ ſpeculatiuæ, quibus reſpondent totidem <lb/>practicæ ſequentes.</s> <s xml:id="echoid-s17601" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div432" type="section" level="1" n="320"> <head xml:id="echoid-head338" style="it" xml:space="preserve">Mathematicarum practica ſex.</head> <p> <s xml:id="echoid-s17602" xml:space="preserve">1 GEometria practica, cuius eſt menſurare altitudines turrium, montium, profunditates puteorum, di-<lb/>ſtantias locorum, ſuperficies agrorum, &</s> <s xml:id="echoid-s17603" xml:space="preserve">c. </s> <s xml:id="echoid-s17604" xml:space="preserve">Idque etiam per ſolum vll<unsure/>um. </s> <s xml:id="echoid-s17605" xml:space="preserve">metitur etiam ſoliditates <lb/>corporum, quæ paffim militares Duces, & </s> <s xml:id="echoid-s17606" xml:space="preserve">Agrimenſores operantur.</s> <s xml:id="echoid-s17607" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17608" xml:space="preserve">2 Arithmetica practica, ſeu ſupputatrix, cuius pars mirabilis eſt Algebra.</s> <s xml:id="echoid-s17609" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17610" xml:space="preserve">3 Perſpectiua practica, quæ Pictoribus, Sculptoribus, & </s> <s xml:id="echoid-s17611" xml:space="preserve">Architectoribus maximè vſui eſt. </s> <s xml:id="echoid-s17612" xml:space="preserve">Huius pa@ <lb/>pulcherrima eſt Scenographia, quæ ſcenarum receſſus perbelle mentitur.</s> <s xml:id="echoid-s17613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17614" xml:space="preserve">4 Mechanica practica, quam qui profitentur hodie vulgo dicuntur, Ingegnieri; </s> <s xml:id="echoid-s17615" xml:space="preserve">huius aſt varias machi-<lb/>nas conſtruere, quibus parua vi ingentia pondera, imo quæuis pondera mouere, ac transferre poſſint, hæc nõ <lb/>ſolum domi, ſed militiæ maximè neceſſaria eſt.</s> <s xml:id="echoid-s17616" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17617" xml:space="preserve">5 Muſica practica, quæ duplex eſt; </s> <s xml:id="echoid-s17618" xml:space="preserve">altera docet cantilenas & </s> <s xml:id="echoid-s17619" xml:space="preserve">ſonationes muſicis modulis cõponere, quæ <lb/>Melopoeia græcis dicitur. </s> <s xml:id="echoid-s17620" xml:space="preserve">eam nunc vulgo vocant, II Contrapunto. </s> <s xml:id="echoid-s17621" xml:space="preserve">Altera eſt ipſa Cantatrix, & </s> <s xml:id="echoid-s17622" xml:space="preserve">Pulſatrix, <lb/>quæ ad actum cantilenas, & </s> <s xml:id="echoid-s17623" xml:space="preserve">ſonationes tam vocibus, quam inſtrumentorum ſonis reducit.</s> <s xml:id="echoid-s17624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17625" xml:space="preserve">6 Aſtronomia practica, quæ ſyderum motus ope. </s> <s xml:id="echoid-s17626" xml:space="preserve">Tabularum Aſtronomicarum ad calculum reuocat, <lb/>luminarium defectus, planetarum aſpectus prædicit, cœli thema ad quoduis tempus conſtituit. </s> <s xml:id="echoid-s17627" xml:space="preserve">Gnomo-<lb/>nica practica, quę Horologia deſcribit; </s> <s xml:id="echoid-s17628" xml:space="preserve">Varij vſus inſtrumentorum, Aſtrolabij, Sphæræ, Globi, practici <lb/>ſunt, &</s> <s xml:id="echoid-s17629" xml:space="preserve">c.</s> <s xml:id="echoid-s17630" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17631" xml:space="preserve">Prædictæ practicæ habent ſuarum effectionum demonſtrationes, vnde veræ ſunt ſcientiæ; </s> <s xml:id="echoid-s17632" xml:space="preserve">quod ſi vt paſ-<lb/>ſim fit ſine demonſtratione tradantur, puræ practicæ appellan@ur.</s> <s xml:id="echoid-s17633" xml:space="preserve"/> </p> <pb o="207" file="0229" n="234" rhead="AD MATHEMATICAS."/> <p> <s xml:id="echoid-s17634" xml:space="preserve">Si plura de natura, ac pręſtantia Mathematicarum cupis, adeas tractationem noſtram editam vna cum lo@ <lb/>cis Mathematicis Ariſt. </s> <s xml:id="echoid-s17635" xml:space="preserve">vbi plura nuper obſeruata reperies, quæq; </s> <s xml:id="echoid-s17636" xml:space="preserve">tibi plenè ſatisfacient.</s> <s xml:id="echoid-s17637" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div433" type="section" level="1" n="321"> <head xml:id="echoid-head339" style="it" xml:space="preserve">Selectorum librorum Bibliotheca. Pars ſecunda.</head> <p> <s xml:id="echoid-s17638" xml:space="preserve">IN recenſendis operibus non eum ſeruabo ordinem temporis, quo ſcripta ſunt, id enim Chronologum at <lb/>tinet; </s> <s xml:id="echoid-s17639" xml:space="preserve">ſed eum quem doctrinæ ratio poſtulat, quo nimirum ſunt addiſcenda, & </s> <s xml:id="echoid-s17640" xml:space="preserve">perlegenda.</s> <s xml:id="echoid-s17641" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div434" type="section" level="1" n="322"> <head xml:id="echoid-head340" style="it" xml:space="preserve">Geometræ ſcientes.</head> <p> <s xml:id="echoid-s17642" xml:space="preserve">INter Mathematica monumenta primum eſt Euclidis opus Elementorum non tantum antiquitate, & </s> <s xml:id="echoid-s17643" xml:space="preserve">di-<lb/>gnitate, verum etiam doctrinæ ordine; </s> <s xml:id="echoid-s17644" xml:space="preserve">eſt enim totius Matheſeos baſis, & </s> <s xml:id="echoid-s17645" xml:space="preserve">fundamentum. </s> <s xml:id="echoid-s17646" xml:space="preserve">in ipſum plures <lb/>ſcripſerunt. </s> <s xml:id="echoid-s17647" xml:space="preserve">Primus omnium Proclus Diadochus cuius comment. </s> <s xml:id="echoid-s17648" xml:space="preserve">Latinitate donata a F. </s> <s xml:id="echoid-s17649" xml:space="preserve">Barocio extant. <lb/></s> <s xml:id="echoid-s17650" xml:space="preserve">Secundus eſt Campanus, qui illud ex Arabico, Latinum fecit. </s> <s xml:id="echoid-s17651" xml:space="preserve">Tertius Zambertus qui ex Græco idem in La-<lb/>tinum tranſtulit, vterq; </s> <s xml:id="echoid-s17652" xml:space="preserve">tamen in multis peccauit. </s> <s xml:id="echoid-s17653" xml:space="preserve">Quarto F. </s> <s xml:id="echoid-s17654" xml:space="preserve">Candalla idem Latinum, ſed non fideliter fe-<lb/>cit. </s> <s xml:id="echoid-s17655" xml:space="preserve">Quintus Federicus Comandinus illud ſumma fide è Græco tranſtulit, ac commentarijs illuſtrauit. </s> <s xml:id="echoid-s17656" xml:space="preserve">Sex-<lb/>tus eſt P. </s> <s xml:id="echoid-s17657" xml:space="preserve">Clauius qui etſi paraphraſim potius quam tranſlationem dederit, totum tamen illud opus ſartum <lb/>tectum præſtitit, ac locupletauit; </s> <s xml:id="echoid-s17658" xml:space="preserve">hi duo Comandinus, & </s> <s xml:id="echoid-s17659" xml:space="preserve">Clauius cæteris præferuntur.</s> <s xml:id="echoid-s17660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17661" xml:space="preserve">Eiuſdem Euclidis opus, Datorum ſecũdum occupat locum, quod neceſſarium eſt ad Archimedem, Apol-<lb/>lonium, Pappum, &</s> <s xml:id="echoid-s17662" xml:space="preserve">c. </s> <s xml:id="echoid-s17663" xml:space="preserve">intelligendos. </s> <s xml:id="echoid-s17664" xml:space="preserve">quamdiu opus hoc negligetur tandiu Geometria, ac tota Matheſis clau-<lb/>dicabit. </s> <s xml:id="echoid-s17665" xml:space="preserve">iacet adhuc ſub Zamberti tranſlatione adeo obſcurus, ac mendoſus, vt ſummo labore vix intelligi <lb/>queat. </s> <s xml:id="echoid-s17666" xml:space="preserve">audio Ioſephum Auriam Neapolitanum illud rectè latinum feciſſe, ac illuſtraſſe, ſed eo iam mor@uo <lb/>Neapoli apud quendam adhuc magno Geometriæ diſpendio in teneb@is latet. </s> <s xml:id="echoid-s17667" xml:space="preserve">Vtinam Mecænas aliquis il-<lb/>lud communi bono, ac luci committat.</s> <s xml:id="echoid-s17668" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17669" xml:space="preserve">Tertio loco danda eſt opera Apollonij pergæi Conicis Elementis, quæ Federicus Comandinus tranſtulit, <lb/>ac ill@ftrauit; </s> <s xml:id="echoid-s17670" xml:space="preserve">quamuis nonnullis in locis non omnino ſatisfaciat, nec omnino ab iniuria eum vindicat, quam <lb/>illi Barocius in ſuo admirando Problemate inuſſit. </s> <s xml:id="echoid-s17671" xml:space="preserve">hic ob ſubtilitatem, & </s> <s xml:id="echoid-s17672" xml:space="preserve">profunditatem demonſtrationum <lb/>magnus Geometra cognominatus eſt.</s> <s xml:id="echoid-s17673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17674" xml:space="preserve">Apollonio ſuccedunt libri duo Sereni de ſectione cylindri, & </s> <s xml:id="echoid-s17675" xml:space="preserve">coni à Comandino vna cum Apollonio il-<lb/>luſtrati, atque editi.</s> <s xml:id="echoid-s17676" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17677" xml:space="preserve">Quarto loco legenda ſunt Archimedis opera hæc: </s> <s xml:id="echoid-s17678" xml:space="preserve">de circuli dimẽſione, de lineis ſpiralibus: </s> <s xml:id="echoid-s17679" xml:space="preserve">hæc enim mul <lb/>tis in locis ſupponunt doctrinam de conicis traditam ab Apollonio, & </s> <s xml:id="echoid-s17680" xml:space="preserve">Sereno. </s> <s xml:id="echoid-s17681" xml:space="preserve">Eadem legenda ſunt ex tra-<lb/>ditione Comandini vna cum eiuſdem, necnon Eutocij co nmentarijs. </s> <s xml:id="echoid-s17682" xml:space="preserve">poſtea opus Archimedis de Sphęra, <lb/>ac cylindro, cum comment. </s> <s xml:id="echoid-s17683" xml:space="preserve">Eutocij latinitate quidem donatum, ſed multis in locis aut male tranſlatum, aut <lb/>mutilum opus. </s> <s xml:id="echoid-s17684" xml:space="preserve">alioquin pulcherrimum, cuius gratia ſepuichro Archim. </s> <s xml:id="echoid-s17685" xml:space="preserve">Sphæra, & </s> <s xml:id="echoid-s17686" xml:space="preserve">cylindrus fuerant inſcul-<lb/>pta, vt teſtatur Cicero. </s> <s xml:id="echoid-s17687" xml:space="preserve">Vtinam Comandinus quiſpiam reperiatur, qui illud nitori ſuo reſtituat. </s> <s xml:id="echoid-s17688" xml:space="preserve">Ego qui-<lb/>dem nonnulla in ipſum notaui, transſlationemq; </s> <s xml:id="echoid-s17689" xml:space="preserve">reſtauraui, quæ aliquando forſitan ſi opus fuerit edentur-<lb/>Archimedi poſtea a multis attribuitur opuſculum de Iſoperimetris figuris, quod habes in Geometria practi-<lb/>ca Clauij, Theon Græcus Ptolemæi commentator illud Zenedoro aſcribit; </s> <s xml:id="echoid-s17690" xml:space="preserve">cuiuſuis ſit egregium eſt monu-<lb/>mentum, hoc loco legendum. </s> <s xml:id="echoid-s17691" xml:space="preserve">Opuſcula duo Archim. </s> <s xml:id="echoid-s17692" xml:space="preserve">de Arenæ numero, & </s> <s xml:id="echoid-s17693" xml:space="preserve">de Inſidentibus aquæ, quam-<lb/>uis non ſint pura Geometrica, poſſunt tamen hic legi, vt omnia eius opera ſimul abſoluantur. </s> <s xml:id="echoid-s17694" xml:space="preserve">Extant <lb/>præterea Romæ in Bibliotheca Medicea, Archim. </s> <s xml:id="echoid-s17695" xml:space="preserve">opera duo nondum typis mandata, Lemmata, & </s> <s xml:id="echoid-s17696" xml:space="preserve">de Se-<lb/>ctione circuli, vtrumq; </s> <s xml:id="echoid-s17697" xml:space="preserve">nunc Arabicè ſcriptum, quæ vt latio donentur, & </s> <s xml:id="echoid-s17698" xml:space="preserve">publici iuris fiant, Matheſeos ſtu-<lb/>dioſi deſiderant.</s> <s xml:id="echoid-s17699" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17700" xml:space="preserve">Quinto loco ſuccedunt Pappi Alexandrini Collectiones Mathematicæ à Comandino transſlatæ, & </s> <s xml:id="echoid-s17701" xml:space="preserve">illu-<lb/>ſtratæ. </s> <s xml:id="echoid-s17702" xml:space="preserve">vbi ſciendum eſt in eo opere non omnia perfectè Geometrice demonſtrari, vti ſunt quadratura cir-<lb/>culi, anguli dati diuiſio, &</s> <s xml:id="echoid-s17703" xml:space="preserve">c. </s> <s xml:id="echoid-s17704" xml:space="preserve">Octauus eius liber ad Mechanicam pertinet, poſtea legi poſſunt ſine vllo diſcri-<lb/>mine ſequentes Authores, Mahometes Bagdadinus de ſuperficierum diuiſionibus, Ioanne Dee Londenſis, <lb/>Comandini opera in lucem editus; </s> <s xml:id="echoid-s17705" xml:space="preserve">libellum hunc nonnulli putant Euclidis eſſe, nam teſte Proclo in Eu-<lb/>clidem, Euclides de diuiſione ſcripſit. </s> <s xml:id="echoid-s17706" xml:space="preserve">Theodoſij Tripolitæ Sphęrica, & </s> <s xml:id="echoid-s17707" xml:space="preserve">Męnelai Romani Triangula Sphę-<lb/>rica, quorum doctrinam vnico volumine complexus eſt Clauius, addiditq; </s> <s xml:id="echoid-s17708" xml:space="preserve">tractatum de Triangulis planis, <lb/>de Sinubus, Tangentibus, & </s> <s xml:id="echoid-s17709" xml:space="preserve">Secantibus, omnia ad Aſtronomiam neceſſariam. </s> <s xml:id="echoid-s17710" xml:space="preserve">Eandẽ doctrinam vnico ope-<lb/>re tractat F. </s> <s xml:id="echoid-s17711" xml:space="preserve">Maurolycus vir acutiſſimus. </s> <s xml:id="echoid-s17712" xml:space="preserve">Io: </s> <s xml:id="echoid-s17713" xml:space="preserve">Buteo de antiquis circuli quadraturis. </s> <s xml:id="echoid-s17714" xml:space="preserve">Heronis Alexandrini in-<lb/>troductiones in vniuerſam Geometriam; </s> <s xml:id="echoid-s17715" xml:space="preserve">hunc Ioſephus Auria parauerat, vt ederet. </s> <s xml:id="echoid-s17716" xml:space="preserve">Ben Muſa de fi-<lb/>guris planis, & </s> <s xml:id="echoid-s17717" xml:space="preserve">ſphæricis, adhuc Arabicus aſſeruatur in Bibliotheca Medicea. </s> <s xml:id="echoid-s17718" xml:space="preserve">Petri Antonij Cattaldi Geo-<lb/>metrica transformatio. </s> <s xml:id="echoid-s17719" xml:space="preserve">Vietæ, & </s> <s xml:id="echoid-s17720" xml:space="preserve">Marini Ghetaldi Apollonius rediuimus. </s> <s xml:id="echoid-s17721" xml:space="preserve">his igitur authoribus Geome-<lb/>trica omnia continentur, quæ hactenus humani ingenij acumen excogitare potuerit: </s> <s xml:id="echoid-s17722" xml:space="preserve">omnia adeo admiran-<lb/>da vt ambigas magiſnè rerum naturam, an hominum ſolertiam mireris; </s> <s xml:id="echoid-s17723" xml:space="preserve">atque hæc omnia callere debet, <lb/>qui pro dignitate Geometriam profiteri poſſe deſiderant.</s> <s xml:id="echoid-s17724" xml:space="preserve"/> </p> <pb o="208" file="0230" n="235" rhead="APPARATVS"/> </div> <div xml:id="echoid-div435" type="section" level="1" n="323"> <head xml:id="echoid-head341" style="it" xml:space="preserve">Geometræ practici.</head> <p> <s xml:id="echoid-s17725" xml:space="preserve">PErfectus Geometra non ſimplici Theorica contentus eſſe debet, ſed vt Reipubl. </s> <s xml:id="echoid-s17726" xml:space="preserve">vtilis, & </s> <s xml:id="echoid-s17727" xml:space="preserve">domi, & </s> <s xml:id="echoid-s17728" xml:space="preserve">mili-<lb/>tiæ eſſe poſſit, ſequentes etiam authores, qui praxim continent callere debet. </s> <s xml:id="echoid-s17729" xml:space="preserve">Geometras verò practi-<lb/>cos eos intelligo, qui non puram quantitatem abſtractam conſiderant, ſed eam in in rebus materialis, & </s> <s xml:id="echoid-s17730" xml:space="preserve">ſenſi-<lb/>bilibus in ordine ad praxim, ſeu ad menſurationem conſiderant, vt altitudines turrium, latitudines fluuio-<lb/>rum, &</s> <s xml:id="echoid-s17731" xml:space="preserve">c. </s> <s xml:id="echoid-s17732" xml:space="preserve">qua ratione Euclidis, & </s> <s xml:id="echoid-s17733" xml:space="preserve">aliorum problemata censenda non ſunt practica, & </s> <s xml:id="echoid-s17734" xml:space="preserve">ideo in ſuperiori claſſe <lb/>fuerunt connumeranda.</s> <s xml:id="echoid-s17735" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17736" xml:space="preserve">Scriptores huius ex antiquis fuerunt hi, Hero Mechanicus de Geodæſia, antiqui enim vt ait Barocius per <lb/>Geodæſiam intelligebant illam, quæ viſu ſiue radio viſiuo, ope variorum inſtrumentorum, altitudines, lon-<lb/>gitudines, ſuperficies, & </s> <s xml:id="echoid-s17737" xml:space="preserve">ſolida, metiri docet: </s> <s xml:id="echoid-s17738" xml:space="preserve">quamuis Geodeſiæ nomen propriè terræ diuiſionem ſignificet, <lb/>vnde ortum fortè habuit. </s> <s xml:id="echoid-s17739" xml:space="preserve">Porrò liber hic rectè tranſlatus, ac illuſtratus ab eodem Barocio editus eſt ſimul <lb/>cum alio opere cui titulus eſt, Heronis tranſlatio de Machinis bellicis, necnon liber de Geodęſia à F. </s> <s xml:id="echoid-s17740" xml:space="preserve">Barocio <lb/>tranſlata, &</s> <s xml:id="echoid-s17741" xml:space="preserve">c. </s> <s xml:id="echoid-s17742" xml:space="preserve">Secundus ſit alter Hero qui dicitur Alexandrinus, cuius liber ſic inſcribitur, Heronis Alexan-<lb/>drini Geometrumenon, in quo, vt ait Ioſephus Auria, Geometria practica continetur; </s> <s xml:id="echoid-s17743" xml:space="preserve">nondum tamen edi-<lb/>tum eſſe puto; </s> <s xml:id="echoid-s17744" xml:space="preserve">mortuus enim eſt ipſe Auria, qui ſe eum translaturum, atq; </s> <s xml:id="echoid-s17745" xml:space="preserve">editurum profitebatur. </s> <s xml:id="echoid-s17746" xml:space="preserve">quod au-<lb/>tem hi duo Herones differant, inde patet, quoniam Hero Mechanicus in proæmio de Machinis citat alterũ <lb/>hunc Heronem, eumq; </s> <s xml:id="echoid-s17747" xml:space="preserve">Mathematicum appellat. </s> <s xml:id="echoid-s17748" xml:space="preserve">Boetius primus ex Latinis ſemipriſcis, hanc praxim duo-<lb/>bus libris ſuæ Geometriæ paſſim attigit. </s> <s xml:id="echoid-s17749" xml:space="preserve">ex recentioribus verò complures, & </s> <s xml:id="echoid-s17750" xml:space="preserve">Italicè, & </s> <s xml:id="echoid-s17751" xml:space="preserve">Latinè hanc artem <lb/>conſcripſerunt: </s> <s xml:id="echoid-s17752" xml:space="preserve">ex Latinis dno tantum proferantur; </s> <s xml:id="echoid-s17753" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s17754" xml:space="preserve">Antonius Maginus de dimetiendi arte, & </s> <s xml:id="echoid-s17755" xml:space="preserve">P. </s> <s xml:id="echoid-s17756" xml:space="preserve">Cla-<lb/>uij Geometria practica; </s> <s xml:id="echoid-s17757" xml:space="preserve">Italicè verò Franc. </s> <s xml:id="echoid-s17758" xml:space="preserve">Lucas de Burgo, Coſmus Bartholus, Siluius Bellus, Nicolaus <lb/>Tartalia, Petri Antonij Cattaldi opera Italica, Elementi de numeri Aritmetici, Elementi de numeri Geo-<lb/>metrici, Algebra proportionale, Algebra numerale, lineale, & </s> <s xml:id="echoid-s17759" xml:space="preserve">applicata, della regola aurea, de numeri per-<lb/>fetti, & </s> <s xml:id="echoid-s17760" xml:space="preserve">della radice quadrata.</s> <s xml:id="echoid-s17761" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div436" type="section" level="1" n="324"> <head xml:id="echoid-head342" style="it" xml:space="preserve">Arithmetici ſcientes.</head> <p> <s xml:id="echoid-s17762" xml:space="preserve">PRimus omnium Euclides in 7. </s> <s xml:id="echoid-s17763" xml:space="preserve">8. </s> <s xml:id="echoid-s17764" xml:space="preserve">& </s> <s xml:id="echoid-s17765" xml:space="preserve">9. </s> <s xml:id="echoid-s17766" xml:space="preserve">Elemento. </s> <s xml:id="echoid-s17767" xml:space="preserve">ſubtiliſſimè agit de numeris, quę primo loco addiſcen-<lb/>da ſunt; </s> <s xml:id="echoid-s17768" xml:space="preserve">poſtea legendus eſt Iordanus Nemorarius cum comment. </s> <s xml:id="echoid-s17769" xml:space="preserve">Fabri Stapulenſis, qui libris 10. </s> <s xml:id="echoid-s17770" xml:space="preserve">Arith-<lb/>meticæ theoriam explicat: </s> <s xml:id="echoid-s17771" xml:space="preserve">deinde Nicomachus Græcus nondum tranſlatus, pro quo interim legatur Arith-<lb/>metica Boetij, qui ſe eum ſequi fatetur; </s> <s xml:id="echoid-s17772" xml:space="preserve">deinde Maurolyci Arithmeticorum lib. </s> <s xml:id="echoid-s17773" xml:space="preserve">2. </s> <s xml:id="echoid-s17774" xml:space="preserve">ſuccedat his Diophantes <lb/>Alexandrinus a Guilelmo Xilandro illuſtratus, hunc Algebræ inuentorem faciunt, à quo eam Arabes acce-<lb/>ptam Algebram poſtea appellarunt. </s> <s xml:id="echoid-s17775" xml:space="preserve">deinceps legãtur hi, Michaelis Stifelij Arithmetica integra, vbi etiam <lb/>Algebram exponit; </s> <s xml:id="echoid-s17776" xml:space="preserve">Cardani Arithmetica, P. </s> <s xml:id="echoid-s17777" xml:space="preserve">Clauij Algebra, Bombelli Algebra Italica, Leonardus Piſa-<lb/>nus qui primus Italicè de Algebra ſcripſit, ſed nondum editus. </s> <s xml:id="echoid-s17778" xml:space="preserve">Fr. </s> <s xml:id="echoid-s17779" xml:space="preserve">Lucas de Burgo, Barlaam Monachus <lb/>Græcè, nondum editus, vt puto. </s> <s xml:id="echoid-s17780" xml:space="preserve">Petrus Bungus de myſterijs numerorum.</s> <s xml:id="echoid-s17781" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div437" type="section" level="1" n="325"> <head xml:id="echoid-head343" style="it" xml:space="preserve">Arithmetici practici, qui ſupputatores, & logistæ dicuntur.</head> <p> <s xml:id="echoid-s17782" xml:space="preserve">HI ſunt qui numeros rebus ſenſibilibus, vt numis, & </s> <s xml:id="echoid-s17783" xml:space="preserve">mercibus, gradibus, applicatos pertractant. </s> <s xml:id="echoid-s17784" xml:space="preserve">Innu-<lb/>meri ſunt huius rei ſcriptores, ſed nobis hi ſufficiant; </s> <s xml:id="echoid-s17785" xml:space="preserve">P. </s> <s xml:id="echoid-s17786" xml:space="preserve">Clauij Arithmetica practica; </s> <s xml:id="echoid-s17787" xml:space="preserve">Gemmæ Friſi@ <lb/>Arithmetica practica. </s> <s xml:id="echoid-s17788" xml:space="preserve">Orontius etiam in ſuis operibus, Nicolaus Tartalea, &</s> <s xml:id="echoid-s17789" xml:space="preserve">c.</s> <s xml:id="echoid-s17790" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div438" type="section" level="1" n="326"> <head xml:id="echoid-head344" style="it" xml:space="preserve">Perſpectiui ſeu Optici ſcientes.</head> <p> <s xml:id="echoid-s17791" xml:space="preserve">PRimum locum occupant Euclidis Optica, & </s> <s xml:id="echoid-s17792" xml:space="preserve">Catoptrica, vt antiquitate ita, & </s> <s xml:id="echoid-s17793" xml:space="preserve">ordine doctrinę, ſunt enim <lb/>veluti introductio ad hanc ſcientiam; </s> <s xml:id="echoid-s17794" xml:space="preserve">eorum interpretatione a Ioanne Pena editam cęteris præferri au-<lb/>dio; </s> <s xml:id="echoid-s17795" xml:space="preserve">verſio Zamberti indiget correctione, & </s> <s xml:id="echoid-s17796" xml:space="preserve">expoſitione. </s> <s xml:id="echoid-s17797" xml:space="preserve">Italica verſio, & </s> <s xml:id="echoid-s17798" xml:space="preserve">expoſitio Ignatij Dantis multis <lb/>ſcatet paralogiſmis, & </s> <s xml:id="echoid-s17799" xml:space="preserve">mutila apparet. </s> <s xml:id="echoid-s17800" xml:space="preserve">Maurolycus in indice ſuorum operum teſtatur ſe ea tranſtuliſſe, & </s> <s xml:id="echoid-s17801" xml:space="preserve"><lb/>expoſuiſſe, ſed editorem aliquem expectant. </s> <s xml:id="echoid-s17802" xml:space="preserve">Poſtea ſuccedat Theſaurus Opticæ in quo Alhazeni Arabis <lb/>acutiſſimi Optica, & </s> <s xml:id="echoid-s17803" xml:space="preserve">Vitellionis ſimul continetur; </s> <s xml:id="echoid-s17804" xml:space="preserve">quamuis Vitellio paſſim indigeat correctione; </s> <s xml:id="echoid-s17805" xml:space="preserve">ſuũ enim <lb/>opus ex Euclide, Archim. </s> <s xml:id="echoid-s17806" xml:space="preserve">Ptolemæo, Alhazeno confarcinauit. </s> <s xml:id="echoid-s17807" xml:space="preserve">Deinde Optica Aguillonij non ſine caute-<lb/>la legenda. </s> <s xml:id="echoid-s17808" xml:space="preserve">Rogerij Bacconis, lo: </s> <s xml:id="echoid-s17809" xml:space="preserve">Petſan, Orontij de ſpeculo vſtorio. </s> <s xml:id="echoid-s17810" xml:space="preserve">Maurolyci Photiſmi, & </s> <s xml:id="echoid-s17811" xml:space="preserve">Diaphana, <lb/>de Specillis, & </s> <s xml:id="echoid-s17812" xml:space="preserve">Iride vnico volumine. </s> <s xml:id="echoid-s17813" xml:space="preserve">lo Baptiſta Porta lib. </s> <s xml:id="echoid-s17814" xml:space="preserve">9. </s> <s xml:id="echoid-s17815" xml:space="preserve">de hac re: </s> <s xml:id="echoid-s17816" xml:space="preserve">Ioan: </s> <s xml:id="echoid-s17817" xml:space="preserve">Kepleri Paralipomena ad <lb/>Vitellionem, eiuſdem Optica, & </s> <s xml:id="echoid-s17818" xml:space="preserve">Dioptrica. </s> <s xml:id="echoid-s17819" xml:space="preserve">Guidiubaldi Marchionis perſpectiua Scenographica, qua ar-<lb/>tem Democriti, & </s> <s xml:id="echoid-s17820" xml:space="preserve">Anaxagoræ reſtaurauit. </s> <s xml:id="echoid-s17821" xml:space="preserve">Marinus Chetaldus breuiter de Parabola, & </s> <s xml:id="echoid-s17822" xml:space="preserve">Speculo vſtorio. <lb/></s> <s xml:id="echoid-s17823" xml:space="preserve">Tractatus de radijs viſus, & </s> <s xml:id="echoid-s17824" xml:space="preserve">lucis in vitris perſpectiuis, & </s> <s xml:id="echoid-s17825" xml:space="preserve">Iride, vbi Teleſcopij demonſtratio inchoata habe-<lb/>tur. </s> <s xml:id="echoid-s17826" xml:space="preserve">Extat præterea libellus Archimedis de ſpeculis vſtorijs parabolicis, & </s> <s xml:id="echoid-s17827" xml:space="preserve">Ptolemæi etiam, vt ait Mauroly- <pb o="209" file="0231" n="236" rhead="AD MATHEMATICAS."/> cus in indice ſuorum operum, ſed ea lucem deſiderant. </s> <s xml:id="echoid-s17828" xml:space="preserve">Extant præterea Heliodori Lariſſei eapita optico-<lb/>rum, fragmentum quoddam editum ab Ignatio Dante, cum ſua Euclidis optica, Italica. </s> <s xml:id="echoid-s17829" xml:space="preserve">Oculus, ſeu Funda-<lb/>mentum Opticum P. </s> <s xml:id="echoid-s17830" xml:space="preserve">Chriſtophori Scheiner Societatis noſtræ, opus recens editum, verùm abſtruſis expe-<lb/>rimentis, ac noua neceſſariaque rerum cognitione refertum.</s> <s xml:id="echoid-s17831" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div439" type="section" level="1" n="327"> <head xml:id="echoid-head345" style="it" xml:space="preserve">Perspectiui practici.</head> <p> <s xml:id="echoid-s17832" xml:space="preserve">PLures ex prędictis paſſim ſunt practici, ſiquidem problemata eorum omnia ordinantur ad praxim in ma-<lb/>teria ſenſibili. </s> <s xml:id="echoid-s17833" xml:space="preserve">nonnulli Italicè nudas praxes circa Scenographicam tantum exhibuerunt, vt ſunt, la Per-<lb/>ſpectiua del Vignola, di Sebaſtiano Serlio, di Daniele Barbaro, &</s> <s xml:id="echoid-s17834" xml:space="preserve">c.</s> <s xml:id="echoid-s17835" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div440" type="section" level="1" n="328"> <head xml:id="echoid-head346" style="it" xml:space="preserve">Me@hanici ſcientes.</head> <p> <s xml:id="echoid-s17836" xml:space="preserve">@OMnes antiquitate, & </s> <s xml:id="echoid-s17837" xml:space="preserve">ordine pręcedat Ariſtoteles, cuius Mechanicæ quæſt. </s> <s xml:id="echoid-s17838" xml:space="preserve">continent prima huius ſcien-<lb/>tiæ fundamenta, & </s> <s xml:id="echoid-s17839" xml:space="preserve">iſagogem; </s> <s xml:id="echoid-s17840" xml:space="preserve">eas nos commẽtarijs illuſtrauimus vna cum alijs locis Mathem. </s> <s xml:id="echoid-s17841" xml:space="preserve">apud Ari-<lb/>ſtotelem. </s> <s xml:id="echoid-s17842" xml:space="preserve">eaſdem etiam, & </s> <s xml:id="echoid-s17843" xml:space="preserve">latinitate, & </s> <s xml:id="echoid-s17844" xml:space="preserve">expoſitione optima donauit Henricus Monontolius, cum quo in <lb/>omnibus ferè, quamuis in locis valde diſſitis, ille enim Burdegalę, ego Parmæ eodem tempore interpretaba-<lb/>mur ad vnguem conueni. </s> <s xml:id="echoid-s17845" xml:space="preserve">Ariſtotelem ſequatur doctiſſima Paraphraſis Guidiubaldi in Archim. </s> <s xml:id="echoid-s17846" xml:space="preserve">de Aeque-<lb/>ponderantibus: </s> <s xml:id="echoid-s17847" xml:space="preserve">cui ſuccedat Lucas Valerius de Centro grauitatis ſolidorũ: </s> <s xml:id="echoid-s17848" xml:space="preserve">deinceps legantur Iordanus Ne-<lb/>morarius de Ponderibus lib. </s> <s xml:id="echoid-s17849" xml:space="preserve">8. </s> <s xml:id="echoid-s17850" xml:space="preserve">Pappi. </s> <s xml:id="echoid-s17851" xml:space="preserve">Guidiubaldi Mechanica, opus egregium. </s> <s xml:id="echoid-s17852" xml:space="preserve">Archimedes de ijs, quæ ve-<lb/>huntur in aqua, cui ſuccedat Marini Ghetaldi promotus Archimedes. </s> <s xml:id="echoid-s17853" xml:space="preserve">Galilęus Italicè de his, quæ vehuntur <lb/>vel mouentur in aqua. </s> <s xml:id="echoid-s17854" xml:space="preserve">Guiduſubaldus de Cochlea aquatica, opus poſthumum, & </s> <s xml:id="echoid-s17855" xml:space="preserve">ideo demonſtrationes ali-<lb/>quot non ſatis perfectæ ſunt, ſed dignæ, quæ ab aliquo perfecto G@ometra corrigantur. </s> <s xml:id="echoid-s17856" xml:space="preserve">10: </s> <s xml:id="echoid-s17857" xml:space="preserve">Bapt. </s> <s xml:id="echoid-s17858" xml:space="preserve">Benedictus <lb/>in ſuis ſpeculationibus tractatum vnicum habet de Mechanicis, vbi multa contra Ariſt. </s> <s xml:id="echoid-s17859" xml:space="preserve">diſputat.</s> <s xml:id="echoid-s17860" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div441" type="section" level="1" n="329"> <head xml:id="echoid-head347" style="it" xml:space="preserve">Mechanici practici.</head> <p> <s xml:id="echoid-s17861" xml:space="preserve">HEronis Alexandrini Spiritalia à Comandino tranſlata, ſed quæ vti poſthuma, extremam authoris ma-<lb/>num deſiderant: </s> <s xml:id="echoid-s17862" xml:space="preserve">eiuſdem Automata quę nuper Italica fecit Bernardinus Abbas Guaſtallẽſis, Hero Me-<lb/>chanicus de machinis bellicis, ex editione Barocij: </s> <s xml:id="echoid-s17863" xml:space="preserve">Heronis Creſibij Belopæia, ideſt, Telifactiua Bernardi-<lb/>no Baldo Guaſtallæ Abbate interprete. </s> <s xml:id="echoid-s17864" xml:space="preserve">Ioſephus Cedrenus dc Cochlea Archim. </s> <s xml:id="echoid-s17865" xml:space="preserve">Italicè. </s> <s xml:id="echoid-s17866" xml:space="preserve">10: </s> <s xml:id="echoid-s17867" xml:space="preserve">Bapt. </s> <s xml:id="echoid-s17868" xml:space="preserve">Portæ <lb/>Pneumatica: </s> <s xml:id="echoid-s17869" xml:space="preserve">An vero extet Atheneus de machinis bellicis, & </s> <s xml:id="echoid-s17870" xml:space="preserve">eiuſdem Mechanica, mihi dubium eſt. </s> <s xml:id="echoid-s17871" xml:space="preserve">ex re-<lb/>centioribus Auguſtinus Ramelius de machinis Italicè, & </s> <s xml:id="echoid-s17872" xml:space="preserve">Iacobi Beſſonis Theatrum inſtrumentorum.</s> <s xml:id="echoid-s17873" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div442" type="section" level="1" n="330"> <head xml:id="echoid-head348" style="it" xml:space="preserve">Muſici ſcientes.</head> <p> <s xml:id="echoid-s17874" xml:space="preserve">EXiſtimo initium faciendum eſſe à Muſica Iacobi Fabri Stapulenſis, quam ipſe quatuor libris perſpicuè, <lb/>& </s> <s xml:id="echoid-s17875" xml:space="preserve">breuiter exponit, appellatq; </s> <s xml:id="echoid-s17876" xml:space="preserve">Elementa muſicalia. </s> <s xml:id="echoid-s17877" xml:space="preserve">edita eſt vna cum Arithm. </s> <s xml:id="echoid-s17878" xml:space="preserve">lordani; </s> <s xml:id="echoid-s17879" xml:space="preserve">poſtea legatur <lb/>Muſica Boetij, quibus perceptis patefacta erit via ad antiquorum intelligentiam. </s> <s xml:id="echoid-s17880" xml:space="preserve">omnlum antiquiſſimus eſt <lb/>Ariſtoxenus, cuius extant lib. </s> <s xml:id="echoid-s17881" xml:space="preserve">3. </s> <s xml:id="echoid-s17882" xml:space="preserve">Harmonicorum vna cum Ptolemæi Harmonicis ex traditione An. </s> <s xml:id="echoid-s17883" xml:space="preserve">Goga-<lb/>uini. </s> <s xml:id="echoid-s17884" xml:space="preserve">hos ſequatur Euclidis Muſica, quam habes in Bibliotheca ſcelecta P. </s> <s xml:id="echoid-s17885" xml:space="preserve">Poſſeuini. </s> <s xml:id="echoid-s17886" xml:space="preserve">Caſſiodori Muſicæ <lb/>compendium. </s> <s xml:id="echoid-s17887" xml:space="preserve">Martianus Capella in nuptijs, &</s> <s xml:id="echoid-s17888" xml:space="preserve">c.</s> <s xml:id="echoid-s17889" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17890" xml:space="preserve">Venerabilis Bedæ Muſica ſpeculatiua. </s> <s xml:id="echoid-s17891" xml:space="preserve">Recentiores ſint, Guido Aretinus Monachus edidit 500. </s> <s xml:id="echoid-s17892" xml:space="preserve">ab hinc <lb/>annis, Introductorum Muſicæ. </s> <s xml:id="echoid-s17893" xml:space="preserve">Ludouicus Folianus Mutinenſis, Franchinus Gaſſurius Laudentis, Ioſephus <lb/>Zarlinus Italicè ſcripſit Inſtitutioni harmoniche, Demonſtrationi harmoniche, Supplementi muſicali. </s> <s xml:id="echoid-s17894" xml:space="preserve">Vin-<lb/>centius Galilæus Italicè, cinque Dialogi della Muſica antica, & </s> <s xml:id="echoid-s17895" xml:space="preserve">moderna, opus neceſſarium ad muſicam no-<lb/>ſtri temporis corrigendam, & </s> <s xml:id="echoid-s17896" xml:space="preserve">reſtaurandami alij nondum editi infra ſuo loco ponentur.</s> <s xml:id="echoid-s17897" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div443" type="section" level="1" n="331"> <head xml:id="echoid-head349" style="it" xml:space="preserve">Muſici practici, ſiue Melopæi.</head> <p> <s xml:id="echoid-s17898" xml:space="preserve">EX antiquis nullus quòd ſciam extat, qui rem hãc nobis obſcuram illuſtret: </s> <s xml:id="echoid-s17899" xml:space="preserve">qua videlicet ratione veteres <lb/>illi ſuas Cantilenas contexerent. </s> <s xml:id="echoid-s17900" xml:space="preserve">Beda ſcribit lib. </s> <s xml:id="echoid-s17901" xml:space="preserve">2. </s> <s xml:id="echoid-s17902" xml:space="preserve">de Muſica practica ſed obſcurè: </s> <s xml:id="echoid-s17903" xml:space="preserve">Zarlinus lib. </s> <s xml:id="echoid-s17904" xml:space="preserve">4. </s> <s xml:id="echoid-s17905" xml:space="preserve">Inſtitu-<lb/>cionum Muſic. </s> <s xml:id="echoid-s17906" xml:space="preserve">& </s> <s xml:id="echoid-s17907" xml:space="preserve">Franc. </s> <s xml:id="echoid-s17908" xml:space="preserve">Vaneus, & </s> <s xml:id="echoid-s17909" xml:space="preserve">alij plures hanc artem docent, quam vulgò vocant, il Contrapunto.</s> <s xml:id="echoid-s17910" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div444" type="section" level="1" n="332"> <head xml:id="echoid-head350" style="it" xml:space="preserve">Astronomi ſcientes.</head> <p> <s xml:id="echoid-s17911" xml:space="preserve">PRimum O<unsure/>udium impendatur tractatibus de Sphęra; </s> <s xml:id="echoid-s17912" xml:space="preserve">ego autem ni philautia me fallit, Sphęram hanc meã <lb/>tibi primò legendam conſulo: </s> <s xml:id="echoid-s17913" xml:space="preserve">deinde obantiquita@em legatur Sphęra Procli Diadochi, Cleomedis me- <pb o="210" file="0232" n="237" rhead="APPARATVS"/> teora Valla interprete; </s> <s xml:id="echoid-s17914" xml:space="preserve">Euclidis Phænomena Auria interprete. </s> <s xml:id="echoid-s17915" xml:space="preserve">Campani Sphęra, Maurolyci Coſmogra-<lb/>phia, Alfagrani Elementa Aſtronomica, ex traductione Iacobi Chriſtmanni. </s> <s xml:id="echoid-s17916" xml:space="preserve">Sphęra Piccolominei Italica. <lb/></s> <s xml:id="echoid-s17917" xml:space="preserve">Clauij Sphæra. </s> <s xml:id="echoid-s17918" xml:space="preserve">Autolycus de Sphæra quæ mouetur; </s> <s xml:id="echoid-s17919" xml:space="preserve">item de vario ortu, & </s> <s xml:id="echoid-s17920" xml:space="preserve">occaſu aſtrorum, Ioſepho Auria <lb/>interprete. </s> <s xml:id="echoid-s17921" xml:space="preserve">Theodoſius Tripolita de diebus, ac noctibus, item de Habitationibus Auria interprete. </s> <s xml:id="echoid-s17922" xml:space="preserve">Iulius <lb/>Higinius de Sphæra, ac ſignis cæleſtibus. </s> <s xml:id="echoid-s17923" xml:space="preserve">deinceps ſuccedat Epitome Ioan. </s> <s xml:id="echoid-s17924" xml:space="preserve">de Monteregio in magnam Pto-<lb/>lemæi conſtructionem; </s> <s xml:id="echoid-s17925" xml:space="preserve">eſt quidem obſcura ſed tamen auxilio Geometriæ, & </s> <s xml:id="echoid-s17926" xml:space="preserve">doctrinæ de triangul s planis, <lb/>& </s> <s xml:id="echoid-s17927" xml:space="preserve">ſphæricis, de quibus ſupra, adhibito ſtudio intelligi poteſt, quamuis multum obeſt impreſſio mendoſa. </s> <s xml:id="echoid-s17928" xml:space="preserve">de-<lb/>inde Ariſtarcus Samius de diſtantijs Solis, & </s> <s xml:id="echoid-s17929" xml:space="preserve">Lunæ interprete Comandito. </s> <s xml:id="echoid-s17930" xml:space="preserve">deinde Ptolemæi magna con-<lb/>ſtructio Arabicè Almageſtum, opus mirum, & </s> <s xml:id="echoid-s17931" xml:space="preserve">in quo tota Aſtronomia Hipparchi, & </s> <s xml:id="echoid-s17932" xml:space="preserve">Ptolemæi continetur. </s> <s xml:id="echoid-s17933" xml:space="preserve"><lb/>duæ ipſius verſiones circumferuntur, vna ex Arabica lingua, aitera ex Græca Georgij Trapezuntij. </s> <s xml:id="echoid-s17934" xml:space="preserve">haben-<lb/>tur in ea commentaria Theonis Græca, quę Græcè ſcienti auxilio eſſe poterunt, ſunt enim edita. </s> <s xml:id="echoid-s17935" xml:space="preserve">huius com-<lb/>pendium fecit Proclus ſub nomine Hypotypofis Aſtronomicarum poſitionum. </s> <s xml:id="echoid-s17936" xml:space="preserve">Geber Arabs opus Aſtro-<lb/>nomicum eſt inſtar Almageſti, imo Almageſtum exponit, & </s> <s xml:id="echoid-s17937" xml:space="preserve">paſſim Ptolemæum redarguit. </s> <s xml:id="echoid-s17938" xml:space="preserve">Albategnius, <lb/>ſiue Mahometes Aracenfis de ſcientia ſtellarum nunc pariter legendus. </s> <s xml:id="echoid-s17939" xml:space="preserve">his ſuccedat Nicolaus Copernicus, <lb/>qui præter abſurdam hypotheſim de motu terræ eximius eſt Aſtronomus, ſed nunc cum Eccleſiæ facultute <lb/>legendus. </s> <s xml:id="echoid-s17940" xml:space="preserve">tandem opera Tichonis Brahe, ideſt Progymnaſmata, de Cometis, Mechanica, Epiſtolæ claudãt <lb/>hoc ſtudium. </s> <s xml:id="echoid-s17941" xml:space="preserve">poſtea ſine ordine adiri poſſunt hi, Ioan: </s> <s xml:id="echoid-s17942" xml:space="preserve">Keplerus de Stella noua in Serpentario, idem de alia <lb/>noua in Cygno; </s> <s xml:id="echoid-s17943" xml:space="preserve">Galilæi nuncius ſy dereus, idem de Maculis ſolaribus Italicè; </s> <s xml:id="echoid-s17944" xml:space="preserve">Apelles poſt tabulam latens <lb/>de ilſdem maculis. </s> <s xml:id="echoid-s17945" xml:space="preserve">Guidiubaldi problemata Aſtroncmica. </s> <s xml:id="echoid-s17946" xml:space="preserve">Arati ſolenſis phænomena verſibus decantata: </s> <s xml:id="echoid-s17947" xml:space="preserve"><lb/>extant in ea commentaria Hipparchi Græce, & </s> <s xml:id="echoid-s17948" xml:space="preserve">Latine edita: </s> <s xml:id="echoid-s17949" xml:space="preserve">Germanici Cæſaris, Ciceronis, & </s> <s xml:id="echoid-s17950" xml:space="preserve">Rufi Auie-<lb/>ni, traſlationes verſibus latin@s eiuſdem Arati legil poſſunt ad eruditionem. </s> <s xml:id="echoid-s17951" xml:space="preserve">Item Hypparchus de Aſteriſ-<lb/>mis editus cum prædicto commentario. </s> <s xml:id="echoid-s17952" xml:space="preserve">Archim. </s> <s xml:id="echoid-s17953" xml:space="preserve">de Arenæ numero, videtur llber Aſtronomicus hic collo-<lb/>candus. </s> <s xml:id="echoid-s17954" xml:space="preserve">Alhazen, & </s> <s xml:id="echoid-s17955" xml:space="preserve">Vitello de Crepuſculis; </s> <s xml:id="echoid-s17956" xml:space="preserve">Petri Nonij varia.</s> <s xml:id="echoid-s17957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17958" xml:space="preserve">Authores vero Theoricarum Planetarum videntur mihi inanis laboris, & </s> <s xml:id="echoid-s17959" xml:space="preserve">imaginationis pleni, pro qui-<lb/>bus ſufficiant abundè recenſiti. </s> <s xml:id="echoid-s17960" xml:space="preserve">alij nondum editi in Catalogo proprio ſcribentur.</s> <s xml:id="echoid-s17961" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div445" type="section" level="1" n="333"> <head xml:id="echoid-head351" style="it" xml:space="preserve">Meteoroſcopij, & Organici, qui de inſtrumentis astronom. agunt.</head> <p> <s xml:id="echoid-s17962" xml:space="preserve">PTolemæi Planiſphærium Comandino interprete. </s> <s xml:id="echoid-s17963" xml:space="preserve">Venerabilis Beda de Aſtrolabio. </s> <s xml:id="echoid-s17964" xml:space="preserve">Gemma Friſius <lb/>de Afi<unsure/>rolabio Catholico, & </s> <s xml:id="echoid-s17965" xml:space="preserve">de vſu Globi Aſt onomici: </s> <s xml:id="echoid-s17966" xml:space="preserve">Ioannes Steflerus de Aſtrolabio. </s> <s xml:id="echoid-s17967" xml:space="preserve">Iordanus de <lb/>Planiphærij figuratione. </s> <s xml:id="echoid-s17968" xml:space="preserve">Ioannes Roias in Aſtrolabium. </s> <s xml:id="echoid-s17969" xml:space="preserve">Guidiubaldi Pleniſphæriorum vniuerſalium <lb/>Theorica: </s> <s xml:id="echoid-s17970" xml:space="preserve">Clauij Aſtrolabium: </s> <s xml:id="echoid-s17971" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s17972" xml:space="preserve">Gallucij Theatrum inſtrumentorum Aſtronomicorom. </s> <s xml:id="echoid-s17973" xml:space="preserve">Tychonis <lb/>Mechanica ad cæleſtes obſeruationes neceſſaria.</s> <s xml:id="echoid-s17974" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div446" type="section" level="1" n="334"> <head xml:id="echoid-head352" style="it" xml:space="preserve">PRACTICI.</head> <p> <s xml:id="echoid-s17975" xml:space="preserve">OMnes qui de calculo Aſtronomico, & </s> <s xml:id="echoid-s17976" xml:space="preserve">de Tabulis Aſtronomicis tractat huc pertinent. </s> <s xml:id="echoid-s17977" xml:space="preserve">hanc partem Pto-<lb/>lemæus, Copernicus, Tycho in ſuis libris Aſtronomicis pertractant. </s> <s xml:id="echoid-s17978" xml:space="preserve">alij vero hãc ſolam partem ſeorſim <lb/>tradunt ſuntq; </s> <s xml:id="echoid-s17979" xml:space="preserve">ij magis practici, vti ſunt Tabulæ Alfonſi Regis, Tabulæ ſchoneri omnium facillimæ; </s> <s xml:id="echoid-s17980" xml:space="preserve">Tabu-<lb/>læ Pructenicæ Eraſmi Reinoldi eruditiſſimæ, quæ Copernici doctrinam ſequuntur. </s> <s xml:id="echoid-s17981" xml:space="preserve">Georgij Purbachij <lb/>Tabulæ Eclipſi; </s> <s xml:id="echoid-s17982" xml:space="preserve">Tabula primi mobilis Ioan. </s> <s xml:id="echoid-s17983" xml:space="preserve">de Monteregio. </s> <s xml:id="echoid-s17984" xml:space="preserve">Tabulæ Tichonicæ magna expectatione de-<lb/>ſiderantur. </s> <s xml:id="echoid-s17985" xml:space="preserve">Ex his Tabulis conficiunt Ephemerides ad multos annos, vti ſunt Ephemerides Magini, Ori-<lb/>gani, &</s> <s xml:id="echoid-s17986" xml:space="preserve">c. </s> <s xml:id="echoid-s17987" xml:space="preserve">Ioan. </s> <s xml:id="echoid-s17988" xml:space="preserve">Antonij Magini Tabulæ Nouæ Directionum, quas poſthumas, & </s> <s xml:id="echoid-s17989" xml:space="preserve">imperfectas. </s> <s xml:id="echoid-s17990" xml:space="preserve">R. </s> <s xml:id="echoid-s17991" xml:space="preserve">P. </s> <s xml:id="echoid-s17992" xml:space="preserve">Anto-<lb/>nius Roncho Bonon. </s> <s xml:id="echoid-s17993" xml:space="preserve">eius diſcipulus Aſtronomiæ peritiſſimus addita extrema manu ſuppleuit. </s> <s xml:id="echoid-s17994" xml:space="preserve">Tabulæ So-<lb/>lis, & </s> <s xml:id="echoid-s17995" xml:space="preserve">Martis partim à Ioan. </s> <s xml:id="echoid-s17996" xml:space="preserve">Antonio Magino, partim à Cæſare Marſilio patritio Bonon. </s> <s xml:id="echoid-s17997" xml:space="preserve">ex obſeruationi-<lb/>bus Tychonis, a Kepleri excerptæ, & </s> <s xml:id="echoid-s17998" xml:space="preserve">ſupputatæ.</s> <s xml:id="echoid-s17999" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div447" type="section" level="1" n="335"> <head xml:id="echoid-head353" style="it" xml:space="preserve">Computistæ qui de Calendario agunt.</head> <p> <s xml:id="echoid-s18000" xml:space="preserve">EX calculo, & </s> <s xml:id="echoid-s18001" xml:space="preserve">Tabulis Aſtronomicis pendet tota ratio temporum, & </s> <s xml:id="echoid-s18002" xml:space="preserve">annorum, ac proinde Calendarij <lb/>conſtructio, & </s> <s xml:id="echoid-s18003" xml:space="preserve">correctio, qua ſacrorum geſtorum ſeries, & </s> <s xml:id="echoid-s18004" xml:space="preserve">tempora conſtanter ſeruentur. </s> <s xml:id="echoid-s18005" xml:space="preserve">quę omnia per <lb/>computum Eccleſiaſticũ peraguntur. </s> <s xml:id="echoid-s18006" xml:space="preserve">ſcripſerunt hac de re olim Dionyſius Exiguus Abbas Rom. </s> <s xml:id="echoid-s18007" xml:space="preserve">Venerab. <lb/></s> <s xml:id="echoid-s18008" xml:space="preserve">Beda, Ioan. </s> <s xml:id="echoid-s18009" xml:space="preserve">de Sacroboſco, Campanus; </s> <s xml:id="echoid-s18010" xml:space="preserve">lo Lucidus de temporum emendatione; </s> <s xml:id="echoid-s18011" xml:space="preserve">Petrus de Aliaco Cardi-<lb/>nalis Cameracenſis; </s> <s xml:id="echoid-s18012" xml:space="preserve">10: </s> <s xml:id="echoid-s18013" xml:space="preserve">de Regio Monte; </s> <s xml:id="echoid-s18014" xml:space="preserve">Paulus de Midelburgo Epiſcopus; </s> <s xml:id="echoid-s18015" xml:space="preserve">P. </s> <s xml:id="echoid-s18016" xml:space="preserve">Clauius edidit Calendarij <lb/>Romani explicationem; </s> <s xml:id="echoid-s18017" xml:space="preserve">Iacobus Chriſtmanus poſt ſua in Alfagranum comment. </s> <s xml:id="echoid-s18018" xml:space="preserve">addidit tract. </s> <s xml:id="echoid-s18019" xml:space="preserve">de Calenda-<lb/>rijs variarum nationum, ac temporum connexione, opuſculum magna eruditione plenum, &</s> <s xml:id="echoid-s18020" xml:space="preserve">c.</s> <s xml:id="echoid-s18021" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div448" type="section" level="1" n="336"> <head xml:id="echoid-head354" style="it" xml:space="preserve">Gnomonici, & qui de Horologijs.</head> <p> <s xml:id="echoid-s18022" xml:space="preserve">ANtiquiſſimus omnium qui de Horologijs agant, eſt Vitruuius, qui lib. </s> <s xml:id="echoid-s18023" xml:space="preserve">9. </s> <s xml:id="echoid-s18024" xml:space="preserve">principia quædam de rationi-<lb/>bus Gnomonicis attingit, ex ipſo tamen patet plures ante ipſum de hac re ſcripſiſſe. </s> <s xml:id="echoid-s18025" xml:space="preserve">Secundus eſt Clau- <pb o="211" file="0233" n="238" rhead="AD MATHEMATICAS."/> dius Ptolemæus de Analemate, Commandino interpretc, & </s> <s xml:id="echoid-s18026" xml:space="preserve">illuſtratore: </s> <s xml:id="echoid-s18027" xml:space="preserve">deinceps Venerab. </s> <s xml:id="echoid-s18028" xml:space="preserve">Beda de Horo-<lb/>logij Solaris menſura. </s> <s xml:id="echoid-s18029" xml:space="preserve">Albategnius ad finem operis de ſcientia ſtellarum tradit modum deſcribendi Horo-<lb/>logia ſolaria. </s> <s xml:id="echoid-s18030" xml:space="preserve">Maurolycus Abbas edidit tres libros acutiſſimos de lineis horarjs. </s> <s xml:id="echoid-s18031" xml:space="preserve">Andreæ Schoneri Gno-<lb/>monica ſubtiliſſima; </s> <s xml:id="echoid-s18032" xml:space="preserve">Io: </s> <s xml:id="echoid-s18033" xml:space="preserve">Bapt. </s> <s xml:id="echoid-s18034" xml:space="preserve">Vimercatus Italicè de Horologijs Solaribus; </s> <s xml:id="echoid-s18035" xml:space="preserve">Clauij Gno nonica; </s> <s xml:id="echoid-s18036" xml:space="preserve">item Ho-<lb/>rologiorum noua deſcriptio per tangen@es. </s> <s xml:id="echoid-s18037" xml:space="preserve">10: </s> <s xml:id="echoid-s18038" xml:space="preserve">P. </s> <s xml:id="echoid-s18039" xml:space="preserve">Galluc us Salodienſis, Italicè ſcripſit de Fabrica, & </s> <s xml:id="echoid-s18040" xml:space="preserve">vſu in-<lb/>ſtrumenti ad Horologia deſcribenda ad omnem poli eleuationem, quod mihi maximè probatur.</s> <s xml:id="echoid-s18041" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div449" type="section" level="1" n="337"> <head xml:id="echoid-head355" style="it" xml:space="preserve">GEOGRAPHI.</head> <p> <s xml:id="echoid-s18042" xml:space="preserve">PRimo legatur noſtra introductio ad Geographiam, quam ſupra præmifimus, poſtea Ptolemæi Geogra-<lb/>graphia a Mercatore reſtaurata; </s> <s xml:id="echoid-s18043" xml:space="preserve">ſuccedat his Theatrum Abrahami Ortelij, opus regium. </s> <s xml:id="echoid-s18044" xml:space="preserve">Appiani, & </s> <s xml:id="echoid-s18045" xml:space="preserve"><lb/>Gemmæ Friſij Coſmographia; </s> <s xml:id="echoid-s18046" xml:space="preserve">Ptolemæi Geographia cum comment. </s> <s xml:id="echoid-s18047" xml:space="preserve">Magini. </s> <s xml:id="echoid-s18048" xml:space="preserve">Iulius Solinus Polyhiſtor. <lb/></s> <s xml:id="echoid-s18049" xml:space="preserve">Pomp. </s> <s xml:id="echoid-s18050" xml:space="preserve">Mela, & </s> <s xml:id="echoid-s18051" xml:space="preserve">Strabo de ſitu orbis; </s> <s xml:id="echoid-s18052" xml:space="preserve">Theſaurus Geographicus Abrahami Ortelij omnino neceſſarius. </s> <s xml:id="echoid-s18053" xml:space="preserve">huc <lb/>etiam pertinent Scriptores itinerum, & </s> <s xml:id="echoid-s18054" xml:space="preserve">nauigationum, vti ſunt Marcus Polus Venetus de rebus mundi mi-<lb/>rabilibus; </s> <s xml:id="echoid-s18055" xml:space="preserve">item antiquæ ac nouæ nauigationes a Petro Ramuſio tribus tomis collectæ. </s> <s xml:id="echoid-s18056" xml:space="preserve">Petrus Bellonius <lb/>Gallicè ſcribit ſuas in Oriente obſeruationes. </s> <s xml:id="echoid-s18057" xml:space="preserve">Ioanni Boteri Relationes vniuerſales, quibus Strabonem <lb/>optimè imitatus eſt.</s> <s xml:id="echoid-s18058" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div450" type="section" level="1" n="338"> <head xml:id="echoid-head356" style="it" xml:space="preserve">Aſtrologi, ſiue Iudiciarij.</head> <p> <s xml:id="echoid-s18059" xml:space="preserve">QVamuis Aſtrologia hæc, vt ſupra docuimus, non ſit verè pars Aſtronomiæ, quia tamen ſæpiſſimè ea in-<lb/>diget, ideo ea ſolet hic annumerari. </s> <s xml:id="echoid-s18060" xml:space="preserve">duplex porrò eſt, aut enim ea prædicit quæ Agricolationi, Nauiga-<lb/>tioni, & </s> <s xml:id="echoid-s18061" xml:space="preserve">Medicinæ conferunt, & </s> <s xml:id="echoid-s18062" xml:space="preserve">hac parte licita eſt, nec vllis legibus proſcripta, aut liberos hominis <lb/>euentus, quaſi neceſſarios diuinatur, qua parre illicita, ac legibus diuinis, ac humanis prohibita. </s> <s xml:id="echoid-s18063" xml:space="preserve">Studium <lb/>profecto vaniſſimum, ac indignum, in quo bonæ horæ collocentur, quod tum plures, tum duo ſummi noſtrę <lb/>ætatis Aſtronomi eius vanitatis conſult<unsure/>iſſimi; </s> <s xml:id="echoid-s18064" xml:space="preserve">Ticho, & </s> <s xml:id="echoid-s18065" xml:space="preserve">Keplerus pluribus repræhendunt. </s> <s xml:id="echoid-s18066" xml:space="preserve">lehe Picum Mi-<lb/>randulanum contra Aſtrologos. </s> <s xml:id="echoid-s18067" xml:space="preserve">cum autem non ſit hæc ars tota omnino interdicta, vt diximus, paucos eius <lb/>authores enumerabo ex ijs, qui minus humanę libertati derogant, nec fortè ſunt damnati. </s> <s xml:id="echoid-s18068" xml:space="preserve">Q. </s> <s xml:id="echoid-s18069" xml:space="preserve">Manilij Aſtro-<lb/>nomicon verſibus deſcriptum. </s> <s xml:id="echoid-s18070" xml:space="preserve">Ptolemæi Quadripartitum; </s> <s xml:id="echoid-s18071" xml:space="preserve">Centiloquium, inerrantium Stellarum ſignifica-<lb/>tiones. </s> <s xml:id="echoid-s18072" xml:space="preserve">Iulius Firmicus Maternus de Iudicijs, ſub Conſtante, & </s> <s xml:id="echoid-s18073" xml:space="preserve">Conſtantio Imp. </s> <s xml:id="echoid-s18074" xml:space="preserve">cæteros Arabes, & </s> <s xml:id="echoid-s18075" xml:space="preserve">Latinos <lb/>recentior s nugis, & </s> <s xml:id="echoid-s18076" xml:space="preserve">ſuperſtitionibus plenos indignos recenſeri, miſſos faciamus.</s> <s xml:id="echoid-s18077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18078" xml:space="preserve">Atq; </s> <s xml:id="echoid-s18079" xml:space="preserve">hi ſunt Authores qui hactenus in lucẽ prodierunt quiq; </s> <s xml:id="echoid-s18080" xml:space="preserve">Bibliochecæ conſtruendæ ſufficere poſſint.</s> <s xml:id="echoid-s18081" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div451" type="section" level="1" n="339"> <head xml:id="echoid-head357" style="it" xml:space="preserve">Variæ methodi in addiſcendis Mathematicis iuxta varios adiſcentium <lb/>fines ſeruandæ. Pars tærtia.</head> <p> <s xml:id="echoid-s18082" xml:space="preserve">EOrum qui ſe Mathematicis addicunt varij poſſunt eſſe fines, quibus totidem methodi reſpondeant. </s> <s xml:id="echoid-s18083" xml:space="preserve">alij <lb/>enim ſola Geometria, aut ſola Arithmetica delectantur. </s> <s xml:id="echoid-s18084" xml:space="preserve">alij Optica, alij Muſica, alij alijs detinentur, <lb/>alij totius Matheſeos curriculum abſoluere cupiunt: </s> <s xml:id="echoid-s18085" xml:space="preserve">nonnulli Mathematicæ non ſui gratia dant operam, <lb/>ſed aut ad Phyſiologiam, aut ad Militiam, aut ad alias artes melius capeſlendas earum ſtudium dirigunt: </s> <s xml:id="echoid-s18086" xml:space="preserve">ſin-<lb/>gulis igitur ſingulas methodos, & </s> <s xml:id="echoid-s18087" xml:space="preserve">modos tradere oportet.</s> <s xml:id="echoid-s18088" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div452" type="section" level="1" n="340"> <head xml:id="echoid-head358" style="it" xml:space="preserve">Methodus ad ſolam Geometriam.</head> <p> <s xml:id="echoid-s18089" xml:space="preserve">PRimo nauetur diligens opera Elementis Euclidis, non ea leuiter ac feſtinanter percurrendo, ſed ſæpius <lb/>eadem repetendo. </s> <s xml:id="echoid-s18090" xml:space="preserve">ſeruentur autem hæ duæ regulæ. </s> <s xml:id="echoid-s18091" xml:space="preserve">Prima. </s> <s xml:id="echoid-s18092" xml:space="preserve">Notet ſtudioſus cuiuſuis Demonſtratio-<lb/>nis medium præcipuum, quod eſt illud ex quo proximè concluſio infertur. </s> <s xml:id="echoid-s18093" xml:space="preserve">porrò in demonftrationibus ad <lb/>impoſſibile, illud ipſum impoſſibile, quod infertur, habetur pro medio illius demonſtrationis. </s> <s xml:id="echoid-s18094" xml:space="preserve">ſic in ſexta de-<lb/>monſtratione Primi, probat Euclides latera illa eſſe æqualia, quia alioquin ſequeretur partem eſſe æqualem <lb/>toti, quod eſt abſurdum, vel impoſſibile, & </s> <s xml:id="echoid-s18095" xml:space="preserve">hoc abſurdum eſt meſiium huius demonſtrationis. </s> <s xml:id="echoid-s18096" xml:space="preserve">in demonſtra-<lb/>tionibus vero oſtenſiuis medium ſemper eſt principium aliquod, ſic in ſecunda demonſtratione primi, duæ <lb/>lineæ B C. </s> <s xml:id="echoid-s18097" xml:space="preserve">& </s> <s xml:id="echoid-s18098" xml:space="preserve">A G. </s> <s xml:id="echoid-s18099" xml:space="preserve">probantur æquales, quia ſunt æquales vni tertię lineæ G E. </s> <s xml:id="echoid-s18100" xml:space="preserve">per 1. </s> <s xml:id="echoid-s18101" xml:space="preserve">pronunciatum, quę ſunt <lb/>æquales vni tertio ſunt æqualia inuicem: </s> <s xml:id="echoid-s18102" xml:space="preserve">ex hoc enim axiomate infertur illa concluſio. </s> <s xml:id="echoid-s18103" xml:space="preserve">propoſito enim ſibi <lb/>@anquam ſcopo hoc demonſtrationis medio, facillimè memoria tenentur, & </s> <s xml:id="echoid-s18104" xml:space="preserve">repetuntur omnes demonſtra-<lb/>@iones. </s> <s xml:id="echoid-s18105" xml:space="preserve">hac de cauſa Ariſtoteles prudens Philoſophus hæc media obieruabat, quod inde apparet, quia cum <lb/>alicuius demonſtrationis meminit, eius medium præcipuum ſemper innuit, ſic cum inquit, cur angulus in ſe-<lb/>@nicirculus rectus eſt? </s> <s xml:id="echoid-s18106" xml:space="preserve">ſubdit rationem ſeu medium, quia ſcilicet eſt dimidium duorum rectorum. </s> <s xml:id="echoid-s18107" xml:space="preserve">Vide Ap-<lb/>pendicem ad finem noſtri operis delocis Mathem. </s> <s xml:id="echoid-s18108" xml:space="preserve">apud Ariſtotelem, in qua omnes demonſtrationes primi <lb/>Elem. </s> <s xml:id="echoid-s18109" xml:space="preserve">ad normam logicam expenduntur, & </s> <s xml:id="echoid-s18110" xml:space="preserve">earum media enucleantur. </s> <s xml:id="echoid-s18111" xml:space="preserve">hac porrò obſeruatione adhibita <pb o="212" file="0234" n="239" rhead="APPARATVS"/> perfectius, & </s> <s xml:id="echoid-s18112" xml:space="preserve">ſecundum Logicæ præcepta percipitur ipſa Geometria. </s> <s xml:id="echoid-s18113" xml:space="preserve">Secunda regula: </s> <s xml:id="echoid-s18114" xml:space="preserve">In difficilioribus <lb/>demonſtrationibus aliquando augetur difficultas. </s> <s xml:id="echoid-s18115" xml:space="preserve">propterea quod in ijs percipiendis neceſſe eſt fatigari ima-<lb/>ginationem circa plures figuras quæ ibi ſupponuntur, & </s> <s xml:id="echoid-s18116" xml:space="preserve">deſiderantur concipiendas, ac retinendas, vt intel-<lb/>lectus circa eas poſſit diſcurrere, quod primo accidit in 12. </s> <s xml:id="echoid-s18117" xml:space="preserve">ſecundi Elem. </s> <s xml:id="echoid-s18118" xml:space="preserve">in qua dicitur, quadratum|lateris <lb/>A C. </s> <s xml:id="echoid-s18119" xml:space="preserve">maius eſſe quadratis laterum A B. </s> <s xml:id="echoid-s18120" xml:space="preserve">B C. </s> <s xml:id="echoid-s18121" xml:space="preserve">rectangulo bis compræhenſo ſub C C. </s> <s xml:id="echoid-s18122" xml:space="preserve">B D. </s> <s xml:id="echoid-s18123" xml:space="preserve">quę tamen quadra-<lb/>ta, & </s> <s xml:id="echoid-s18124" xml:space="preserve">rectangula, & </s> <s xml:id="echoid-s18125" xml:space="preserve">aliæ figuræ ibi deſiderantur: </s> <s xml:id="echoid-s18126" xml:space="preserve">vnde difficilis euadit intelligentia illius: </s> <s xml:id="echoid-s18127" xml:space="preserve">facilis tamen red-<lb/>ditur ſi prædictæ figuræ ibi vtcunque addantur, eo modo, quo citantur. </s> <s xml:id="echoid-s18128" xml:space="preserve">Tertſa regula aliquando obſcuritas <lb/>oritur ex longo diſcurſu per plures æqualitates, quæ ſubinde variantur addendo, demendo, transferendo, <lb/>commutando, quo caſu vtile eſt rem ad calculum redigere, ideſt, in pagella notare membra æqualitatis hinc <lb/>inde ſe poſita, ideſt, figuras æquales contradiſtinctas, eaſque ſecundum diſcurſus exigentiam addere, deme-<lb/>re, transferre, commutare, &</s> <s xml:id="echoid-s18129" xml:space="preserve">c. </s> <s xml:id="echoid-s18130" xml:space="preserve">hac enim calculatione iuuatur imaginatio, & </s> <s xml:id="echoid-s18131" xml:space="preserve">diſcurſus, vt poſſit vſq; </s> <s xml:id="echoid-s18132" xml:space="preserve">ad fi-<lb/>nem peruenire, alioquin in medio ſæpè curſu frangitur, & </s> <s xml:id="echoid-s18133" xml:space="preserve">coincidit. </s> <s xml:id="echoid-s18134" xml:space="preserve">hoc etiam vſu venit in 12. </s> <s xml:id="echoid-s18135" xml:space="preserve">& </s> <s xml:id="echoid-s18136" xml:space="preserve">13. </s> <s xml:id="echoid-s18137" xml:space="preserve">ſecun-<lb/>di Elementorum.</s> <s xml:id="echoid-s18138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18139" xml:space="preserve">Secundò tandem ſciat lector neminem poſſe euadere perfectum Geometram ſine Arith. </s> <s xml:id="echoid-s18140" xml:space="preserve">neq; </s> <s xml:id="echoid-s18141" xml:space="preserve">perfectum <lb/>Arithm. </s> <s xml:id="echoid-s18142" xml:space="preserve">ſine Geometria; </s> <s xml:id="echoid-s18143" xml:space="preserve">ſunt enim hæ duæ ſcientiæ veluti duæ ſorores, vt ait Eutocius, quæ ſibi mutuas tra-<lb/>dunt operas. </s> <s xml:id="echoid-s18144" xml:space="preserve">hac de cauſa Euclides ſapientiſſimè tres Arithm. </s> <s xml:id="echoid-s18145" xml:space="preserve">libros inter ſua Geometrica Elem. </s> <s xml:id="echoid-s18146" xml:space="preserve">@inſeruit. <lb/></s> <s xml:id="echoid-s18147" xml:space="preserve">hinc videmus multa in 10. </s> <s xml:id="echoid-s18148" xml:space="preserve">lib. </s> <s xml:id="echoid-s18149" xml:space="preserve">ſecundum numerorum rationes demonſtrari; </s> <s xml:id="echoid-s18150" xml:space="preserve">ſic omnia ferè quæ à Geometris <lb/>demonſtrantur etiam per numeros, ſiue rationales, ſiue irrationales, ſumma iucunditate peraguntur, atq; </s> <s xml:id="echoid-s18151" xml:space="preserve">ob <lb/>oculos ponuntur, v. </s> <s xml:id="echoid-s18152" xml:space="preserve">g. </s> <s xml:id="echoid-s18153" xml:space="preserve">demonſtratio 47. </s> <s xml:id="echoid-s18154" xml:space="preserve">primi, oſtendit quadratum illud lateris angulum rectum ſubtenden-<lb/>tis, eſſe ęquales quadratis reliquorum duorum laterum; </s> <s xml:id="echoid-s18155" xml:space="preserve">hoc idem numeris exequi poſſumus, ſi enim fiat trian <lb/>gulum rectangulum cuius baſis ſit linea quinque vnciarum, alterum latus ſit quatuor vnciarum, tertium ſit <lb/>@rium vnciarum, & </s> <s xml:id="echoid-s18156" xml:space="preserve">quadrati horum numerorum ſumantur, erit quadratus num. </s> <s xml:id="echoid-s18157" xml:space="preserve">quinque nimirum 25. </s> <s xml:id="echoid-s18158" xml:space="preserve">æqua-<lb/>lis duc<unsure/>bus quadratis reliquorum, nam quadratus numeri 4. </s> <s xml:id="echoid-s18159" xml:space="preserve">eſt 16. </s> <s xml:id="echoid-s18160" xml:space="preserve">quadratus numeri 3. </s> <s xml:id="echoid-s18161" xml:space="preserve">eſt 9. </s> <s xml:id="echoid-s18162" xml:space="preserve">qui duo quadra-<lb/>ti ſimul conficiunt 25. </s> <s xml:id="echoid-s18163" xml:space="preserve">Sed hoc magis manifeſtum eſt in Algebra, quæ quamuis Arithmet. </s> <s xml:id="echoid-s18164" xml:space="preserve">fit, vtitur ta-<lb/>men Geometricis demonſtrationibus, & </s> <s xml:id="echoid-s18165" xml:space="preserve">problemata Geometrica præſertim 10. </s> <s xml:id="echoid-s18166" xml:space="preserve">Element. </s> <s xml:id="echoid-s18167" xml:space="preserve">per numeros <lb/>reſoluit.</s> <s xml:id="echoid-s18168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18169" xml:space="preserve">Tertio poſtquam quis probè in Elementis Euclidianis verſatus fuerit, alios Geometras aggrediatur, eo <lb/>ordine quo ſuper in Bibliotheca recenſiti ſunt.</s> <s xml:id="echoid-s18170" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div453" type="section" level="1" n="341"> <head xml:id="echoid-head359" style="it" xml:space="preserve">Methodus ad Arithmeticam.</head> <p> <s xml:id="echoid-s18171" xml:space="preserve">OB affinitatem, & </s> <s xml:id="echoid-s18172" xml:space="preserve">connexionem quæ inter Geometriam’<unsure/>, & </s> <s xml:id="echoid-s18173" xml:space="preserve">Arithmeticam intercedit, nulla ratione <lb/>merebitur quiſpiam Arithmetici cognomen; </s> <s xml:id="echoid-s18174" xml:space="preserve">quin Element. </s> <s xml:id="echoid-s18175" xml:space="preserve">ſaltem Euclidis probè percipiat, quibus <lb/>perceptis debet poſtea operam Arithm. </s> <s xml:id="echoid-s18176" xml:space="preserve">illis impendere, quos ſuper recenſuimus, atque ex eodem ordine <lb/>quo ſunt recenſiti. </s> <s xml:id="echoid-s18177" xml:space="preserve">occurrentibus vero difficultatibus. </s> <s xml:id="echoid-s18178" xml:space="preserve">Primum ſit remedium adhibere paruos numeros pro <lb/>magnis, atque in illis prius experiri veritatem anteqnam aggrediaris, aut ſuperes totam oblatam demon-<lb/>ſtrationem. </s> <s xml:id="echoid-s18179" xml:space="preserve">Secundum ſit, in numeris irrationalibus, & </s> <s xml:id="echoid-s18180" xml:space="preserve">radicalibus Algebræ, quando occurrunt obſcuri-<lb/>tates, pro eis ſupponantur prius facilitatis gratia numeri rationales, & </s> <s xml:id="echoid-s18181" xml:space="preserve">communes, ijque parui; </s> <s xml:id="echoid-s18182" xml:space="preserve">in iſtis <lb/>enim apparet etiam veritas illa, quæ de Algebraticis proponitur, ſicque intellectus illuminatur, vt Alge<unsure/> <lb/>braticas tenebras diſijcere queat.</s> <s xml:id="echoid-s18183" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div454" type="section" level="1" n="342"> <head xml:id="echoid-head360" style="it" xml:space="preserve">Methodus ad Opticam.</head> <p> <s xml:id="echoid-s18184" xml:space="preserve">QVoniam Optica Geometriæ ſubalternatur, ideo ad eam rectè capeſſendam neceſſario præcedere de-<lb/>bent ſaltem ſex primi libri Euclidis: </s> <s xml:id="echoid-s18185" xml:space="preserve">poſtea ſtudium impendatur Authoribus Opticæ ſupra recenſitis, <lb/>atque eodem ordine. </s> <s xml:id="echoid-s18186" xml:space="preserve">proderit autem multum ea experiri præſertim in ſpeculis, & </s> <s xml:id="echoid-s18187" xml:space="preserve">vitris, & </s> <s xml:id="echoid-s18188" xml:space="preserve">pili@ <lb/>vitreis, & </s> <s xml:id="echoid-s18189" xml:space="preserve">chriſtallinis, nam experientia rerum magiſtra.</s> <s xml:id="echoid-s18190" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div455" type="section" level="1" n="343"> <head xml:id="echoid-head361" style="it" xml:space="preserve">Methodus ad Mechanicam.</head> <p> <s xml:id="echoid-s18191" xml:space="preserve">QVoniam Mechanici Geometricè demonſtrant, ideo neceſſaria eſt hic quoque ſaltem ſex primorum <lb/>Euclidis pręcognitio, poſt quam ſequatur ſtudium Authorum ſupra numeratorum, atq; </s> <s xml:id="echoid-s18192" xml:space="preserve">eodem ordine.</s> <s xml:id="echoid-s18193" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div456" type="section" level="1" n="344"> <head xml:id="echoid-head362" style="it" xml:space="preserve">Methodus ad Muſicam.</head> <p> <s xml:id="echoid-s18194" xml:space="preserve">HÆc Arithmeticè demonſtrat, ideo neceſſe eſt præcedat cognitio mediocris Arithmeticæ,|præſertim <lb/>proportionum Arithmeticarum quas ad 5. </s> <s xml:id="echoid-s18195" xml:space="preserve">Fuclidis P. </s> <s xml:id="echoid-s18196" xml:space="preserve">Clauius fusè exponit, necnõ ad finem 9. </s> <s xml:id="echoid-s18197" xml:space="preserve">Euclidis, <lb/>vtitur etiam aliquando figuris Geometricis, vnde primorum ſex elementorum Euclidis aliqua præcognitio <lb/>neceſſaria eſt: </s> <s xml:id="echoid-s18198" xml:space="preserve">deinde ſuperiores Authores eo ordine, adhibito ſtudio legantur, quo enumerati ſunt.</s> <s xml:id="echoid-s18199" xml:space="preserve"/> </p> <pb o="213" file="0235" n="240" rhead="AD MATHEMATICAS."/> </div> <div xml:id="echoid-div457" type="section" level="1" n="345"> <head xml:id="echoid-head363" style="it" xml:space="preserve">Methodus ad Aſtronomiam, & partes eius.</head> <p> <s xml:id="echoid-s18200" xml:space="preserve">QVoniam Aſtronomiam, vt rectè Plato aduertit, duabus veluti alis Geometria, & </s> <s xml:id="echoid-s18201" xml:space="preserve">Arithmetica in cæ-<lb/>lum euolat, ideo primo neceſſaria eſt totius Euclidis præcognitio, necnon Arithmeticæ vulgaris, il-<lb/>lius præſertim, quæ de Aſtronomicis fractionibus agit, quibus præmiſſis aggredi poteris Autho-<lb/>res ſuper recenſitos, eodem ordine ſeruato.</s> <s xml:id="echoid-s18202" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div458" type="section" level="1" n="346"> <head xml:id="echoid-head364" style="it" xml:space="preserve">Pro Gnomonica.</head> <p> <s xml:id="echoid-s18203" xml:space="preserve">ADres Gnomonicas facilè, & </s> <s xml:id="echoid-s18204" xml:space="preserve">rectè percipiendas plurimum confert conſtructio Sphæræ Gnomonicæ. <lb/></s> <s xml:id="echoid-s18205" xml:space="preserve">appello Sphæram Gnomonicam eam in cuius ſuperficie deſcripti ſunt pimò Tropici, Aequator, & </s> <s xml:id="echoid-s18206" xml:space="preserve">duo <lb/>paralelli horizontem tangentes, vnus maximus apparentium, alter occultorum maximus. </s> <s xml:id="echoid-s18207" xml:space="preserve">deinde omnes cir-<lb/>culi horarij, tam hi qui indicant horas Aſtronomicas à meridie inchoatas, quique tranſeunt per polos mun-<lb/>di, & </s> <s xml:id="echoid-s18208" xml:space="preserve">quorum vnus eſt meridianus; </s> <s xml:id="echoid-s18209" xml:space="preserve">quam ij, qui indicant horas ab ortu, vel occaſu numeratas, quorum vnus <lb/>eſt horizon, & </s> <s xml:id="echoid-s18210" xml:space="preserve">tangunt duos circulos æquatori paralellos, quorum vnus eſt maximus ſemper apparentium, <lb/>altet maximus ſemper latentium. </s> <s xml:id="echoid-s18211" xml:space="preserve">Conſtructio hæc innuitur a P. </s> <s xml:id="echoid-s18212" xml:space="preserve">Clauio in Gnomonica lib. </s> <s xml:id="echoid-s18213" xml:space="preserve">1. </s> <s xml:id="echoid-s18214" xml:space="preserve">propoſitione 9. </s> <s xml:id="echoid-s18215" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s18216" xml:space="preserve">10. </s> <s xml:id="echoid-s18217" xml:space="preserve">& </s> <s xml:id="echoid-s18218" xml:space="preserve">inde elici poteſt. </s> <s xml:id="echoid-s18219" xml:space="preserve">in hac pila ſumma iucunditate, vti expertus ſum, licebit intueri omnes horum cir-<lb/>culorum poſitus, & </s> <s xml:id="echoid-s18220" xml:space="preserve">interſectiones; </s> <s xml:id="echoid-s18221" xml:space="preserve">& </s> <s xml:id="echoid-s18222" xml:space="preserve">in quibus diurnis circulis omnes tres ſe mutuo ſecent; </s> <s xml:id="echoid-s18223" xml:space="preserve">vt in arcubus <lb/>diurnis horarum 14. </s> <s xml:id="echoid-s18224" xml:space="preserve">& </s> <s xml:id="echoid-s18225" xml:space="preserve">10. </s> <s xml:id="echoid-s18226" xml:space="preserve">& </s> <s xml:id="echoid-s18227" xml:space="preserve">in quibus duo tantum; </s> <s xml:id="echoid-s18228" xml:space="preserve">& </s> <s xml:id="echoid-s18229" xml:space="preserve">alia omnia quæ alioquin obſcuriſſima ſunt, quęq; </s> <s xml:id="echoid-s18230" xml:space="preserve">Cla-<lb/>uius prolixo tædio ad propoſitionem 20. </s> <s xml:id="echoid-s18231" xml:space="preserve">explicat. </s> <s xml:id="echoid-s18232" xml:space="preserve">hæc porrò Sphæræ conſtructio fieri debet ad datam poli <lb/>cleuationem, vnica enim nequit eſſe vniuerſalis. </s> <s xml:id="echoid-s18233" xml:space="preserve">Reliquæ Aſtronomiæ partes non alia indigent directio-<lb/>ne præter eam, quam ſupra in Auth. </s> <s xml:id="echoid-s18234" xml:space="preserve">Biblioth. </s> <s xml:id="echoid-s18235" xml:space="preserve">innuimus.</s> <s xml:id="echoid-s18236" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div459" type="section" level="1" n="347"> <head xml:id="echoid-head365" style="it" xml:space="preserve">Methodus vniuerſalis ad totius Matheſos curriculum ineundum.</head> <p> <s xml:id="echoid-s18237" xml:space="preserve">SIomnes aut præcipuè Authores ſingularum Mathematicarum, quos ſupra in Bibliotheca recenſuimus, <lb/>eodem ordine percipiantur, res confecta erit. </s> <s xml:id="echoid-s18238" xml:space="preserve">Sed vtile imo neceſſarium puto ſeorſim ſingulis diſtinctè <lb/>dare operam. </s> <s xml:id="echoid-s18239" xml:space="preserve">Primo Geometriæ. </s> <s xml:id="echoid-s18240" xml:space="preserve">Secundo Arithmeticæ, & </s> <s xml:id="echoid-s18241" xml:space="preserve">ſic deinceps: </s> <s xml:id="echoid-s18242" xml:space="preserve">hac enim ratione tollitur omnis <lb/>confuſio, & </s> <s xml:id="echoid-s18243" xml:space="preserve">melius, ac clarius omnia intelliguntur, nam pluribus intentus minor eſt ad ſingula ſenſus.</s> <s xml:id="echoid-s18244" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div460" type="section" level="1" n="348"> <head xml:id="echoid-head366" style="it" xml:space="preserve">Methodus ad Phyſicam, & Methaphyſicam, & Moralem.</head> <p> <s xml:id="echoid-s18245" xml:space="preserve">QVam neceſſariæ ſint Mathematicæ ad reliquas Philoſophiæ partes rectè capeſſendas, optimè Plato de-<lb/>clarauit, edicto illo pro foribus Gymnaſij propoſito, nullus ingrediatur ageometretos. </s> <s xml:id="echoid-s18246" xml:space="preserve">ſed melius re ip-<lb/>ſa id confirmabat, cum quotidie ſuis auditoribus problema aliquod Geometricum reſoluẽdum pro-<lb/>poneret. </s> <s xml:id="echoid-s18247" xml:space="preserve">idem etiam manifeſtum eſt ex opere noſtro de locis Mathematicis apud Ariſtotelem, in quo loca <lb/>num. </s> <s xml:id="echoid-s18248" xml:space="preserve">400. </s> <s xml:id="echoid-s18249" xml:space="preserve">expoſuimus, quæ abſq; </s> <s xml:id="echoid-s18250" xml:space="preserve">Mathematicis intelligi nequeunt. </s> <s xml:id="echoid-s18251" xml:space="preserve">Iacobus Zabarella fatetur ſe bis totum <lb/>Euclidem diligenter perlegiſſe, vt ad germanum Ariſt, ſenſum in libris Logicis penetraret. </s> <s xml:id="echoid-s18252" xml:space="preserve">quis libro de cę-<lb/>lo ſine Sphæra tractatu, quis Meteora, quis tractatum de Viſu, ſine Perſpectiua aſſequi poterit? </s> <s xml:id="echoid-s18253" xml:space="preserve">certè nullus. <lb/></s> <s xml:id="echoid-s18254" xml:space="preserve">Quicunq; </s> <s xml:id="echoid-s18255" xml:space="preserve">igitur voluerit pro dignitate Philoſophiam profiteri, is nõ mediocrem Mathematis operam im-<lb/>pendat oportet, & </s> <s xml:id="echoid-s18256" xml:space="preserve">præterea opus noſtrum prædictum conetur intelligere, in eo enim omnia ferè quæ Pe-<lb/>ripateticis neceſſaria ſunt in vnum collecta, & </s> <s xml:id="echoid-s18257" xml:space="preserve">declarata reperiet.</s> <s xml:id="echoid-s18258" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div461" type="section" level="1" n="349"> <head xml:id="echoid-head367" style="it" xml:space="preserve">Methodus ad Militiam.</head> <p> <s xml:id="echoid-s18259" xml:space="preserve">AD exercitum varijs modis, & </s> <s xml:id="echoid-s18260" xml:space="preserve">ordinibus diſponendum, neceſſaria eſt Arithmetica: </s> <s xml:id="echoid-s18261" xml:space="preserve">ad varias Machi-<lb/>nas tam ad oppugnationem, quam ad defenſionem neceſſarias, item ad aquas deducenda neceſſarias eſt <lb/>Mechanica; </s> <s xml:id="echoid-s18262" xml:space="preserve">ad menſurandas à longè per radium viſiuum tum altitudines, tum diſtantias, & </s> <s xml:id="echoid-s18263" xml:space="preserve">ad inacceſſarum <lb/>arcium deſcriptionem neceſſaria eſt Geometria practica. </s> <s xml:id="echoid-s18264" xml:space="preserve">miles igitur peritus, vt ſit dicaturque Ingegniero, <lb/>intelligat ſaltem ſex priores libros Euclidis, deinde Arithmeticam practicam, & </s> <s xml:id="echoid-s18265" xml:space="preserve">Geometriam practicam, <lb/>his enim inſtructus optimè ſtudere poterit libris militaribus, & </s> <s xml:id="echoid-s18266" xml:space="preserve">qui de Munitione ſiue, vt aiunt Fortificatio-<lb/>netractant.</s> <s xml:id="echoid-s18267" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18268" xml:space="preserve">Architectores, & </s> <s xml:id="echoid-s18269" xml:space="preserve">Pictores poſſim etiam Mathematicis indigent præſertim Perſpectiua. </s> <s xml:id="echoid-s18270" xml:space="preserve">Atque hi ſunt <lb/>præcipui fines quibus viſum eſt ſuas methodos indicare.</s> <s xml:id="echoid-s18271" xml:space="preserve"/> </p> <pb o="214" file="0236" n="241" rhead="APPARATVS"/> </div> <div xml:id="echoid-div462" type="section" level="1" n="350"> <head xml:id="echoid-head368" style="it" xml:space="preserve">Mathematici studij promoti@. Pars quarta.</head> <head xml:id="echoid-head369" style="it" xml:space="preserve">Index operum quæ quidem extant, ſed nondum edita, aut ſi edita nondum latini@ate donata, v@ <lb/>tum Mecænates, tum viri doctiea in lucem edere aut in latinum transferre non ſine <lb/>ipſorum gloria, & studioſorum vtilitate poſſint.</head> <p> <s xml:id="echoid-s18272" xml:space="preserve">EVclidis data noua indigent tranſlatione; </s> <s xml:id="echoid-s18273" xml:space="preserve">Maurolycus primum, poſtea Ioſephus Auria ea, vt ederent pa-<lb/>rauerant, ſed apud eorum hæredes adhuc latent. </s> <s xml:id="echoid-s18274" xml:space="preserve">Maurolyci liber de Figuris planis, & </s> <s xml:id="echoid-s18275" xml:space="preserve">ſolidis locum re-<lb/>plentibus. </s> <s xml:id="echoid-s18276" xml:space="preserve">Io:</s> <s xml:id="echoid-s18277" xml:space="preserve">de Regiomonte de ijſdem acutè ſcripſerat teſte Maurolyco. </s> <s xml:id="echoid-s18278" xml:space="preserve">Modus ſecandi Sphæram ad da-<lb/>tam rationem ex Dionyſodoro à Maurol. </s> <s xml:id="echoid-s18279" xml:space="preserve">tranſlatus. </s> <s xml:id="echoid-s18280" xml:space="preserve">Data Arithm. </s> <s xml:id="echoid-s18281" xml:space="preserve">Iordani, & </s> <s xml:id="echoid-s18282" xml:space="preserve">Maurolyci. </s> <s xml:id="echoid-s18283" xml:space="preserve">Euclidis Opti-<lb/>ca, & </s> <s xml:id="echoid-s18284" xml:space="preserve">Catoptrica à Maurolyco illuſtrata. </s> <s xml:id="echoid-s18285" xml:space="preserve">Ptolemæi Specula ab eodem expoſita. </s> <s xml:id="echoid-s18286" xml:space="preserve">Archimedes de Speculis <lb/>comburentibus ab eodem excultus. </s> <s xml:id="echoid-s18287" xml:space="preserve">Albategnij traditiones ab eodem expoſitæ. </s> <s xml:id="echoid-s18288" xml:space="preserve">Hęronis Spiritalia ab eo-<lb/>dem tranſlata. </s> <s xml:id="echoid-s18289" xml:space="preserve">Speculationes Mathematicæ eiuſdem. </s> <s xml:id="echoid-s18290" xml:space="preserve">Hæc omnia deſcripſi ex indice ante ipſius Coſmo-<lb/>graphiam, quæ apud eius hæredes adhuc aſſeruantur.</s> <s xml:id="echoid-s18291" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18292" xml:space="preserve">Qui vero ſequuntur continentur in præfatione Ioſephi Auriæ ad Theodoſium tripolitam de diebus, & </s> <s xml:id="echoid-s18293" xml:space="preserve"><lb/>noctibus. </s> <s xml:id="echoid-s18294" xml:space="preserve">Barlaam Monachi Arithm. </s> <s xml:id="echoid-s18295" xml:space="preserve">& </s> <s xml:id="echoid-s18296" xml:space="preserve">Logiſtices lib. </s> <s xml:id="echoid-s18297" xml:space="preserve">6. </s> <s xml:id="echoid-s18298" xml:space="preserve">erat apud Auriam. </s> <s xml:id="echoid-s18299" xml:space="preserve">Theonis Smirnæi de locis Ma-<lb/>thematicis apud Platonem, eiuſdem de Aſtronomia; </s> <s xml:id="echoid-s18300" xml:space="preserve">aſſeruatur Venetijs in Bibliotheca Card. </s> <s xml:id="echoid-s18301" xml:space="preserve">Beſſarionis.</s> <s xml:id="echoid-s18302" xml:space="preserve"><unsure/> <lb/>Logotheti expoſitio in Almageſtum. </s> <s xml:id="echoid-s18303" xml:space="preserve">Porfirij expoſitio in Harmonica Ptolemæi,|qui duo Græci aſſeruan-<lb/>tur in Vaticana, cum alijs nonnullis, vt videre eſt apud Auriam.</s> <s xml:id="echoid-s18304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18305" xml:space="preserve">Qui ſequuntur ſunt in Bibliotheca Medicea lingua Arabica ſcripti: </s> <s xml:id="echoid-s18306" xml:space="preserve">Archimedes de Sectione circuli, eiuſ-<lb/>dem Lemmata. </s> <s xml:id="echoid-s18307" xml:space="preserve">Ariſtarcus de corporibus Luminoſis. </s> <s xml:id="echoid-s18308" xml:space="preserve">Ypſicles de Aſcenſionibus. </s> <s xml:id="echoid-s18309" xml:space="preserve">ThebitBen Cora rerum <lb/>ſelectarum. </s> <s xml:id="echoid-s18310" xml:space="preserve">Apollonij Conicorum lib. </s> <s xml:id="echoid-s18311" xml:space="preserve">8. </s> <s xml:id="echoid-s18312" xml:space="preserve">Mænelai de Figuris ſphæricis lib. </s> <s xml:id="echoid-s18313" xml:space="preserve">3. </s> <s xml:id="echoid-s18314" xml:space="preserve">Ben Muſa de Figuris planis, <lb/>& </s> <s xml:id="echoid-s18315" xml:space="preserve">ſphæricis, hactenus ex Auria. </s> <s xml:id="echoid-s18316" xml:space="preserve">Diophantis Arithmeticorum lib. </s> <s xml:id="echoid-s18317" xml:space="preserve">13. </s> <s xml:id="echoid-s18318" xml:space="preserve">ait Bombellus extare in Vaticana, quo-<lb/>rum ſex tantum editi ſunt: </s> <s xml:id="echoid-s18319" xml:space="preserve">ipſe quidem Diophantes pag. </s> <s xml:id="echoid-s18320" xml:space="preserve">7. </s> <s xml:id="echoid-s18321" xml:space="preserve">aſſe<unsure/>rit ſe lib. </s> <s xml:id="echoid-s18322" xml:space="preserve">13. </s> <s xml:id="echoid-s18323" xml:space="preserve">Arithm. </s> <s xml:id="echoid-s18324" xml:space="preserve">ſcribere. </s> <s xml:id="echoid-s18325" xml:space="preserve">Abifeldea Ara-<lb/>bs Geographus reperitur in Blbliotheca Palatina Hidelbergenſi, ex Iacobo Chriſtmano in Alfagranum. </s> <s xml:id="echoid-s18326" xml:space="preserve">Vl-<lb/>timò reſtant Theonis Alexandrini Græca commentaria in Ptolemęi magnam conſtructionem, edita quidẽ, <lb/>ſed nondum in latinum traſlata, quamuis multi eam tranſlationem ſint aggreſſi, & </s> <s xml:id="echoid-s18327" xml:space="preserve">multi etiam eam ſe maxi-<lb/>mè deſiderare ſcribant. </s> <s xml:id="echoid-s18328" xml:space="preserve">In alijs præterea Regum, ac Principum Biblioth. </s> <s xml:id="echoid-s18329" xml:space="preserve">non dubito reperiri alia complu-<lb/>ra, quæ deinceps à ſtudioſis ac benè mereri de omnibus litteratis cupientibus, in lucem prodibunt.</s> <s xml:id="echoid-s18330" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div463" type="section" level="1" n="351"> <head xml:id="echoid-head370" style="it" xml:space="preserve">Alter Index, Operum, quæ temporis iniuria perierunt, vt recentiores, quod nonnulli iam præ-<lb/>stiterunt, ea reſtaurare, aut imi<unsure/>tari poſſint.</head> <p> <s xml:id="echoid-s18331" xml:space="preserve">HEron Alexandrinus de Aquaticis Horologijs, Barocius in Heronem. </s> <s xml:id="echoid-s18332" xml:space="preserve">ſequentes Authores accepimus <lb/>ex Proclo in Euclidem: </s> <s xml:id="echoid-s18333" xml:space="preserve">Eudemus de Angulo; </s> <s xml:id="echoid-s18334" xml:space="preserve">eiuſdem Geometricæ enarrationes. </s> <s xml:id="echoid-s18335" xml:space="preserve">Euclides de Falla <lb/>cijs eiuſdem Corollaria, idem de Reſolutione, quem Marinus Ghetaldus ſe reſtauraturum promiſſit. </s> <s xml:id="echoid-s18336" xml:space="preserve">idem <lb/>de Diuiſionibus, quem Bagdadinus reſtaurauit. </s> <s xml:id="echoid-s18337" xml:space="preserve">Ptolemæus demonſtrauit, quod à minoribus quam duo re-<lb/>cti productæ coincidant, quod P. </s> <s xml:id="echoid-s18338" xml:space="preserve">Glauius reſtaurauit ad decimum tertium pronunciatum Euclidis. </s> <s xml:id="echoid-s18339" xml:space="preserve">Geminus <lb/>de Ortu linearum ſpiralium, conchoidum, earumq; </s> <s xml:id="echoid-s18340" xml:space="preserve">paſſionibus. </s> <s xml:id="echoid-s18341" xml:space="preserve">Nichomedes de Lineis conchoidibus. </s> <s xml:id="echoid-s18342" xml:space="preserve">Hip-<lb/>pias de Lineis quadratricibus. </s> <s xml:id="echoid-s18343" xml:space="preserve">Perſeus de Lineis Spiricis. </s> <s xml:id="echoid-s18344" xml:space="preserve">Apollonius de Perturbaris proportionibus, de <lb/>Tactionibus, quem partim Vieta, partim Ghetaldus refecerunt.</s> <s xml:id="echoid-s18345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18346" xml:space="preserve">Theodoſij Tripolitæ Delinationes ædium: </s> <s xml:id="echoid-s18347" xml:space="preserve">de Vere, ex Suida. </s> <s xml:id="echoid-s18348" xml:space="preserve">Comment. </s> <s xml:id="echoid-s18349" xml:space="preserve">in Archimedis Viaticum. </s> <s xml:id="echoid-s18350" xml:space="preserve">Ge-<lb/>mini Geometricæ narrationes, quas tanquam extantes citat Barocius in margine quarti libri Procli in Eu-<lb/>clidem. </s> <s xml:id="echoid-s18351" xml:space="preserve">eaſdem citat Heniſchius in Sphæram Procli.</s> <s xml:id="echoid-s18352" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18353" xml:space="preserve">Sequentes Authores accepimus ex Pappi collectionibus. </s> <s xml:id="echoid-s18354" xml:space="preserve">Archimedes de 13. </s> <s xml:id="echoid-s18355" xml:space="preserve">ſolidis à ſe inuentis æquian-<lb/>gulis, & </s> <s xml:id="echoid-s18356" xml:space="preserve">æquilaterit quidem polygonis, non autem ſimilibus contenta, pag. </s> <s xml:id="echoid-s18357" xml:space="preserve">83. </s> <s xml:id="echoid-s18358" xml:space="preserve">item de Libra, & </s> <s xml:id="echoid-s18359" xml:space="preserve">Viat<unsure/>icum <lb/>apud Auriam. </s> <s xml:id="echoid-s18360" xml:space="preserve">item de Sphæræ conſtructione.</s> <s xml:id="echoid-s18361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18362" xml:space="preserve">Euclides de Reſolutione, de qua etiam Apollonius, & </s> <s xml:id="echoid-s18363" xml:space="preserve">Ariſtęus ſenior. </s> <s xml:id="echoid-s18364" xml:space="preserve">vide Pappum initio ſeptimi, & </s> <s xml:id="echoid-s18365" xml:space="preserve">no-<lb/>ſtra loca Mathematica Ariſt. </s> <s xml:id="echoid-s18366" xml:space="preserve">ad titulum Reſolutiuorum, & </s> <s xml:id="echoid-s18367" xml:space="preserve">intra iterum egemus. </s> <s xml:id="echoid-s18368" xml:space="preserve">hanc ſe reſtituturum rece-<lb/>pit Marinus Ghetaldus. </s> <s xml:id="echoid-s18369" xml:space="preserve">eiuſdem Poriſmata lib. </s> <s xml:id="echoid-s18370" xml:space="preserve">3. </s> <s xml:id="echoid-s18371" xml:space="preserve">& </s> <s xml:id="echoid-s18372" xml:space="preserve">delocis ad ſuperficiem libri duo Ariſtæi locorum ſoli-<lb/>dorum lib. </s> <s xml:id="echoid-s18373" xml:space="preserve">3. </s> <s xml:id="echoid-s18374" xml:space="preserve">Eratoſthenes de Medietatibus lib. </s> <s xml:id="echoid-s18375" xml:space="preserve">2. </s> <s xml:id="echoid-s18376" xml:space="preserve">vide Pappum lib. </s> <s xml:id="echoid-s18377" xml:space="preserve">7. </s> <s xml:id="echoid-s18378" xml:space="preserve">de ordine legendorum horum operũ. <lb/></s> <s xml:id="echoid-s18379" xml:space="preserve">Geminus de Mathematicarum ordine. </s> <s xml:id="echoid-s18380" xml:space="preserve">Ptolemęi Mechanica, & </s> <s xml:id="echoid-s18381" xml:space="preserve">Momenta. </s> <s xml:id="echoid-s18382" xml:space="preserve">Heronis Alexandrini Barulcon, <lb/>ideſt, Onuſtrahens, & </s> <s xml:id="echoid-s18383" xml:space="preserve">Mechanica, in quibus de quinque facultatibus, Vecte, Libra, &</s> <s xml:id="echoid-s18384" xml:space="preserve">c. </s> <s xml:id="echoid-s18385" xml:space="preserve">quæ ſumma laude vi-<lb/>detur renouaſſe Marchio Guiduſubal<unsure/>dus. </s> <s xml:id="echoid-s18386" xml:space="preserve">idem de Rotulis, & </s> <s xml:id="echoid-s18387" xml:space="preserve">aliud in 40. </s> <s xml:id="echoid-s18388" xml:space="preserve">inuenta Archimedis.</s> <s xml:id="echoid-s18389" xml:space="preserve">|Pappus pro-<lb/>poſitione 10. </s> <s xml:id="echoid-s18390" xml:space="preserve">lib. </s> <s xml:id="echoid-s18391" xml:space="preserve">8. </s> <s xml:id="echoid-s18392" xml:space="preserve">Erycemi Paradoxa. </s> <s xml:id="echoid-s18393" xml:space="preserve">Eratoſthenis Meſolabia, cuius fragmentum ext<unsure/>at in comment. </s> <s xml:id="echoid-s18394" xml:space="preserve">Eu-<lb/>tocij in Archimedem. </s> <s xml:id="echoid-s18395" xml:space="preserve">Demetrius Alexandrinus de linearibus aggreſſionibus pag. </s> <s xml:id="echoid-s18396" xml:space="preserve">61. </s> <s xml:id="echoid-s18397" xml:space="preserve">Philo Tianæus ex <lb/>implicatione πληκτοειδων, pag. </s> <s xml:id="echoid-s18398" xml:space="preserve">61. </s> <s xml:id="echoid-s18399" xml:space="preserve">Hi ex Pappo. </s> <s xml:id="echoid-s18400" xml:space="preserve">Tandem Democritus, & </s> <s xml:id="echoid-s18401" xml:space="preserve">Anaxagoras, vt refert Vitruuius <lb/>lib. </s> <s xml:id="echoid-s18402" xml:space="preserve">7. </s> <s xml:id="echoid-s18403" xml:space="preserve">de eadem re ſcripſerunt, quemadmodum oporteat ad aciem oculorum, radiorum extenſionem certo <lb/>loco, centro conſtituto, ad lineas ratione naturali reſpondere, vti de incerta re certæ imagines ædificiorum <pb o="215" file="0237" n="242" rhead="AD MATHEMATICAS."/> in ſcenar@m picturis redderent ſpeciem, & </s> <s xml:id="echoid-s18404" xml:space="preserve">quæ in directio planiſq; </s> <s xml:id="echoid-s18405" xml:space="preserve">frontibu@ fint figuratæ, alia abſcenden-<lb/>tia, aiia prominentia eſſe videantur. </s> <s xml:id="echoid-s18406" xml:space="preserve">horum doctrinam, videtur innouaſſe Marchio Guiduſubaldus in ſua <lb/>Perſpectiua. </s> <s xml:id="echoid-s18407" xml:space="preserve">Federicus etiam Comandinus putat veteres de centro grauitatis ſolidorum ſcripſiſſe, cum Ar-<lb/>chimedes deinſidentibus aquæ centri grauitatis conoidis fecerit mentionem. </s> <s xml:id="echoid-s18408" xml:space="preserve">quam partem ipſe conatus eſt <lb/>renou<unsure/>are, ſedeam Lucas Valerius multo magis ampliauit. </s> <s xml:id="echoid-s18409" xml:space="preserve">Hæc ſunt igitur diuina illa veterum monumen-<lb/>ta, quæ obſæculorum barbariẽ intercidiſſe dolemus:</s> <s xml:id="echoid-s18410" xml:space="preserve"><unsure/> quæ fortèapud Arabes, aut alias nationes ſub alio idio-<lb/>mate latitant, donec Principum noſtrorum induftria ea requiſierit.</s> <s xml:id="echoid-s18411" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div464" type="section" level="1" n="352"> <head xml:id="echoid-head371" style="it" xml:space="preserve">De Geometriæ promotione, ex arte Geometricè demonſtr andi, vbi de Reſolutione.</head> <p> <s xml:id="echoid-s18412" xml:space="preserve">HOcloc<unsure/>o mei muneris eſſe animaduerti nonnulla de arte Geometricè demonſſrandi in medium aſſerre; <lb/></s> <s xml:id="echoid-s18413" xml:space="preserve">quandoquidem ea eſt quæ cæteris omnibus Mathem. </s> <s xml:id="echoid-s18414" xml:space="preserve">ſpiritum ac vitam quodammodo infundit, & </s> <s xml:id="echoid-s18415" xml:space="preserve">qua<unsure/> <lb/>reliquæ deſtitutæ ſcientiæ, ac Philoſophiæ nomine prorſus indignę videantur. </s> <s xml:id="echoid-s18416" xml:space="preserve">præterea quoiure quiſpiam <lb/>fibi Mathematici nomen arrogare audeat, qui nec ſua rectè demonſtrar<unsure/>e, nec de alienis rectè iudicare queat. </s> <s xml:id="echoid-s18417" xml:space="preserve"><lb/>hac veteres magni illi Geometræ ſuffulti mirabiles illas demonſtrationes@,|quæ noſtris ingenijs impoſſibi-<lb/>les videtur, fęliciter excogitarunt. </s> <s xml:id="echoid-s18418" xml:space="preserve">Vtinam autem extarent ea quæ de ea Euclides, Apollonius, & </s> <s xml:id="echoid-s18419" xml:space="preserve">Ari-<lb/>ftæus conſcripſerunt; </s> <s xml:id="echoid-s18420" xml:space="preserve">non enim opus nunc eſſet nos in ea vtcunque adumbranda laborare. </s> <s xml:id="echoid-s18421" xml:space="preserve">Quamuis au-<lb/>tem hanc artem, vt bene ait Petrus Nonnius cap. </s> <s xml:id="echoid-s18422" xml:space="preserve">4. </s> <s xml:id="echoid-s18423" xml:space="preserve">de err. </s> <s xml:id="echoid-s18424" xml:space="preserve">Orontij, ex quotidiano librorum Euclidis, & </s> <s xml:id="echoid-s18425" xml:space="preserve"><lb/>aliorum Geometrarum ſtudio, & </s> <s xml:id="echoid-s18426" xml:space="preserve">imitatione conſequi poſſimus, facilius tamen additis ſequentibus anno-<lb/>tationibus, eam conſequemur.</s> <s xml:id="echoid-s18427" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div465" type="section" level="1" n="353"> <head xml:id="echoid-head372" style="it" xml:space="preserve">Quid ſit Geometrica demonstratio.</head> <p> <s xml:id="echoid-s18428" xml:space="preserve">DEmonf<unsure/>tratio Geometrica eſt diſeurſus certus, & </s> <s xml:id="echoid-s18429" xml:space="preserve">euidens ex veris, & </s> <s xml:id="echoid-s18430" xml:space="preserve">proprijs Geometrię principijs per <lb/>Enthymemata ad concluſionem procedens. </s> <s xml:id="echoid-s18431" xml:space="preserve">vt autem bene intelligatur quid ſit veritas conclufionis <lb/>Geometricæ, & </s> <s xml:id="echoid-s18432" xml:space="preserve">alia huc ſpectantia, lege tractatum de natura Mathematicarum in fine operis noſtri de locis <lb/>Mathem. </s> <s xml:id="echoid-s18433" xml:space="preserve">vbi dictum eſt quid ſit materia intelligibilis, quæ ſola capax eſt Geometricæ veritatis, & </s> <s xml:id="echoid-s18434" xml:space="preserve">perfectio-<lb/>nis: </s> <s xml:id="echoid-s18435" xml:space="preserve">ea autem eſt quantitas abſtracta, &</s> <s xml:id="echoid-s18436" xml:space="preserve">c. </s> <s xml:id="echoid-s18437" xml:space="preserve">ſic vera, & </s> <s xml:id="echoid-s18438" xml:space="preserve">Geometrica æqualitas ea eſt, quæ duæ, v.</s> <s xml:id="echoid-s18439" xml:space="preserve">g. </s> <s xml:id="echoid-s18440" xml:space="preserve">lineæ ita ſunt <lb/>æquales, vt nullum omnino diſcrimen interſit, non ſolum ſenſibile, ſed nec intelligibile. </s> <s xml:id="echoid-s18441" xml:space="preserve">quædam enim ad <lb/>ſenſum videri poſſunt æqualia, quæ tamen Geometricè, & </s> <s xml:id="echoid-s18442" xml:space="preserve">verè non ſunt æqualia. </s> <s xml:id="echoid-s18443" xml:space="preserve">vbi notandum eſt Geo-<lb/>metram, dum demonſtrat, ſupponere ſe habere hanc materiam intelligibilem præſentem’, atque in ipſa <lb/>poſſe ſe operari, ideſt, ducere in eas lineas, angulos, tria@gula, &</s> <s xml:id="echoid-s18444" xml:space="preserve">c. </s> <s xml:id="echoid-s18445" xml:space="preserve">quamuis in ſuo Abaco delineet lineas, <lb/>& </s> <s xml:id="echoid-s18446" xml:space="preserve">figuras ſenfibiles, non tamen propterea (vt ait Ariſt. </s> <s xml:id="echoid-s18447" xml:space="preserve">text 25. </s> <s xml:id="echoid-s18448" xml:space="preserve">primi poſter.) </s> <s xml:id="echoid-s18449" xml:space="preserve">falſum ſupponit. </s> <s xml:id="echoid-s18450" xml:space="preserve">quia deli-<lb/>m<unsure/>eationesillas ſenſibiles pro intelligibilibus ſupponit, vt melius intelligatur. </s> <s xml:id="echoid-s18451" xml:space="preserve">& </s> <s xml:id="echoid-s18452" xml:space="preserve">vt ait Ariſtoteles Geome-<lb/>tra nihil concludit eò quod hæc eſt linea ſenfibilis, quam ipſe exponit, ſed virtute illius intelligibilis, quæ <lb/>per ſenfibilem oſtenditur. </s> <s xml:id="echoid-s18453" xml:space="preserve">& </s> <s xml:id="echoid-s18454" xml:space="preserve">quamuis hæc materia intelligibilis nulla nunc extaret, ſatis eſt ſi poſſit extare, <lb/>ſcientia enim abſtrahit ab exiſtentia ſui ſub@ecti.</s> <s xml:id="echoid-s18455" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div466" type="section" level="1" n="354"> <head xml:id="echoid-head373" style="it" xml:space="preserve">Form<unsure/>a<unsure/> Geometricæ Demonſtrationis.</head> <p> <s xml:id="echoid-s18456" xml:space="preserve">HAhe debemus elicere ex Euclidis, & </s> <s xml:id="echoid-s18457" xml:space="preserve">aliorum demonſtrationibus qui Primo loco ponit Propoſitionem, <lb/>quæ ſcilicet proponitur vt probetur, vel vt effic<unsure/>iatur; </s> <s xml:id="echoid-s18458" xml:space="preserve">illud dicitur Theorema, hoc Problema. </s> <s xml:id="echoid-s18459" xml:space="preserve">Secun-<lb/>do Propoſitionem explie<unsure/>at appoſita figura, quæ in problemate continet quædam Data, dantur enim vel <lb/>puncta, vel lineæ, vel anguli, &</s> <s xml:id="echoid-s18460" xml:space="preserve">c. </s> <s xml:id="echoid-s18461" xml:space="preserve">ſic in prima Euclidis, datur linea vna, in ſecunda datur linea, & </s> <s xml:id="echoid-s18462" xml:space="preserve">punctum. <lb/></s> <s xml:id="echoid-s18463" xml:space="preserve">in Theoremate exibetur figura de qua paſſio demonſtranda eſt, ideſt, quæ eſt ſubiectum demonſtrationis: </s> <s xml:id="echoid-s18464" xml:space="preserve"><lb/>ſic in quarta exibentur duo triangula, de quibus demonſtrandæ ſunt aliquot æqualitates, & </s> <s xml:id="echoid-s18465" xml:space="preserve">in ijs explicatur <lb/>propoſitio. </s> <s xml:id="echoid-s18466" xml:space="preserve">Tertio, ſequitur Conſtructio, vt plurimum enim præter data, & </s> <s xml:id="echoid-s18467" xml:space="preserve">ſubiectum neceſſe eſt ad de-<lb/>monſtrandum conſtruere alias lin<unsure/>e<unsure/>as, vel angulos, vel circulos, &</s> <s xml:id="echoid-s18468" xml:space="preserve">c. </s> <s xml:id="echoid-s18469" xml:space="preserve">ſic in Prima Euclidis conſtruuntur duo <lb/>circuli, & </s> <s xml:id="echoid-s18470" xml:space="preserve">duæ lineæ. </s> <s xml:id="echoid-s18471" xml:space="preserve">in omni problemate necceſſaria eſt conſtructio ſaltem ipſius problematis. </s> <s xml:id="echoid-s18472" xml:space="preserve">in Theore-<lb/>mate, nulla aliquando opus eſt conſtructione, vt patet in 15. </s> <s xml:id="echoid-s18473" xml:space="preserve">primi. </s> <s xml:id="echoid-s18474" xml:space="preserve">Quarto, ſequitur diſcurſus circa ſigu-<lb/>ram conftructam, qui propriè eſt ipſa Demonſtratio procedens per enthymemata, quæ probat aut factum <lb/>eſſe, aut verum eſſe, quod proponebatur. </s> <s xml:id="echoid-s18475" xml:space="preserve">hi autem diſcurſus geometrici debent eſſe breues, & </s> <s xml:id="echoid-s18476" xml:space="preserve">ſimplices, & </s> <s xml:id="echoid-s18477" xml:space="preserve"><lb/>propterea n@hil in eis reperitur, quod ex præcedentibus non ſit iam manifeſtum, & </s> <s xml:id="echoid-s18478" xml:space="preserve">ideo procedit enthyme-<lb/>maticè non ſyllogiſticè; </s> <s xml:id="echoid-s18479" xml:space="preserve">quamuis poſſit ad formam ſyllogiſticam reduci, vt patet in ſcholio P. </s> <s xml:id="echoid-s18480" xml:space="preserve">Claudij ad <lb/>primam primi, ſed id eſſet longum, & </s> <s xml:id="echoid-s18481" xml:space="preserve">tædioſum ac minus perſpicuum, & </s> <s xml:id="echoid-s18482" xml:space="preserve">multa eſſent ſępius repetenda, & </s> <s xml:id="echoid-s18483" xml:space="preserve"><lb/>ſuperuacanea. </s> <s xml:id="echoid-s18484" xml:space="preserve">demonſtratio porrò quo b<unsure/>reuior, ac ſimplicior, eo melior. </s> <s xml:id="echoid-s18485" xml:space="preserve">Eſt autem omn s demonſtratio aut <lb/>ad impoſſibile. </s> <s xml:id="echoid-s18486" xml:space="preserve">Oſtenſiua oſtendit per cauſam materialem, aut formalem, aut à ſigno: </s> <s xml:id="echoid-s18487" xml:space="preserve">Quæ ad impoſſibile <lb/>eſt, vel deducit contra principia, vel contra demonſtrata, vel contra hypoteſim, ſeu ſuppoſitionem. </s> <s xml:id="echoid-s18488" xml:space="preserve">Sexta <lb/>primi repugnant principio illi totum eſt maius ſua parte. </s> <s xml:id="echoid-s18489" xml:space="preserve">vij. </s> <s xml:id="echoid-s18490" xml:space="preserve">eſt contra v. </s> <s xml:id="echoid-s18491" xml:space="preserve">xxv. </s> <s xml:id="echoid-s18492" xml:space="preserve">eſt contra hypotheſim. </s> <s xml:id="echoid-s18493" xml:space="preserve">Quin-<lb/>tò. </s> <s xml:id="echoid-s18494" xml:space="preserve">Tandem vltima pars huius diſcurſus eſt concluſio, quæ eſt ipſa propoſitio iam demonſtrata, cui in P<unsure/>ro- <pb o="216" file="0238" n="243" rhead="APPARATVS"/> blemate ſubditur, quod erat faciendum; </s> <s xml:id="echoid-s18495" xml:space="preserve">in Theoremate vero, quod erat demonſtrandum, ſciendum præte-<lb/>rea Lemma eſſe quandam demonſtrationem in gratiam alterius demonſtrationis ne ipſa demonſtratio pro-<lb/>lixior euadat. </s> <s xml:id="echoid-s18496" xml:space="preserve">Vide Clauium duobus capit. </s> <s xml:id="echoid-s18497" xml:space="preserve">vltimis prolegom: </s> <s xml:id="echoid-s18498" xml:space="preserve">in Euclidem.</s> <s xml:id="echoid-s18499" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div467" type="section" level="1" n="355"> <head xml:id="echoid-head374" style="it" xml:space="preserve">De Fallacijs, vel Paralogiſmis, vel Pſeudographijs.</head> <p> <s xml:id="echoid-s18500" xml:space="preserve">QVoniam Paralogiſmus, ſeu Pſeudographia, eſt fallax demonſ<unsure/>ſ<unsure/>ratio, ſequitur vt nunc de ea breuiter tra-<lb/>ctemus, hoc eſt de fallacijs, ſeu erratis, quæ aduerſus rectũ demonſtrandi vſum committi ſolẽt quarum.</s> <s xml:id="echoid-s18501" xml:space="preserve"/> </p> <figure> <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-01"/> </figure> <p> <s xml:id="echoid-s18502" xml:space="preserve">Prima ſit, ſi quid ab Authoritate probetur; </s> <s xml:id="echoid-s18503" xml:space="preserve">hæc enim ratio, nec conuincit, nec Geo-<lb/>metrica eſt, ideſt, non procedit ex proprijs Geometriæ principijs, aut demonſtratis.</s> <s xml:id="echoid-s18504" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18505" xml:space="preserve">Secunda eſt, cum quis ratione, ſeu experientia ſenſus vtitur, vt ſi quis probaret in <lb/>præſenti triangulo lineam D E. </s> <s xml:id="echoid-s18506" xml:space="preserve">quæ eſt baſi B C. </s> <s xml:id="echoid-s18507" xml:space="preserve">paralella, eſſe eadem baſi minorem, <lb/>ex eo quod ipſius oculis id percipiatur, eſſet fallacia, quia Geometria tractat de mate-<lb/>ria intelligibili, non ſenſibili, nec ſenſus poteſt ſemper percipere inæqualitatem; </s> <s xml:id="echoid-s18508" xml:space="preserve">poteſt <lb/>enim linea D E. </s> <s xml:id="echoid-s18509" xml:space="preserve">eſſe adeo proxima baſi B C. </s> <s xml:id="echoid-s18510" xml:space="preserve">vt oculus vel linceus nullam cernat diſſe-<lb/>rentiam; </s> <s xml:id="echoid-s18511" xml:space="preserve">ſemper tamen Geometricè oſtendetur minor. </s> <s xml:id="echoid-s18512" xml:space="preserve">ad hanc fallaciam reducitur <lb/>menſuratio, vt ſi quis aut Circino, aut alio inſtrumento, vtranque, ex dictis lineis me-<lb/>tietur, indeque probaret illam eſſe minorem.</s> <s xml:id="echoid-s18513" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18514" xml:space="preserve">Tertia deceptio in qua Tyrones ferè omnes incidunt, eſt vti circulo ſenſibili ad oſtendendam æqualita-<lb/>tem linearum, v.</s> <s xml:id="echoid-s18515" xml:space="preserve">g. </s> <s xml:id="echoid-s18516" xml:space="preserve">in præſenti Iſoſcele A B C. </s> <s xml:id="echoid-s18517" xml:space="preserve">ducta D E. </s> <s xml:id="echoid-s18518" xml:space="preserve">paralella baſi B C. </s> <s xml:id="echoid-s18519" xml:space="preserve">probandum ſit duas lineas A D. <lb/></s> <s xml:id="echoid-s18520" xml:space="preserve">A E. </s> <s xml:id="echoid-s18521" xml:space="preserve">abſcindi æquales, & </s> <s xml:id="echoid-s18522" xml:space="preserve">ad id conſtruat quis circulum ex A. </s> <s xml:id="echoid-s18523" xml:space="preserve">interuallo A D. </s> <s xml:id="echoid-s18524" xml:space="preserve">hic circulus tranſibit etiam per <lb/> <anchor type="figure" xlink:label="fig-0238-02a" xlink:href="fig-0238-02"/> E. </s> <s xml:id="echoid-s18525" xml:space="preserve">ad ſenſum euidenter. </s> <s xml:id="echoid-s18526" xml:space="preserve">ſi igitur diſcurat ſic, lineæ A D. </s> <s xml:id="echoid-s18527" xml:space="preserve">A E. </s> <s xml:id="echoid-s18528" xml:space="preserve">ſunt ductæ à centro <lb/>A. </s> <s xml:id="echoid-s18529" xml:space="preserve">ad circumferentiam D E. </s> <s xml:id="echoid-s18530" xml:space="preserve">ergo ſunt æquales. </s> <s xml:id="echoid-s18531" xml:space="preserve">erit fallacia ſenſus quia inde pro-<lb/>bat, quia oculo id cernit. </s> <s xml:id="echoid-s18532" xml:space="preserve">certum quidem eſt lineam A D. </s> <s xml:id="echoid-s18533" xml:space="preserve">pertinere à centro ad <lb/>circumferentiam, ſed auxilio ſenſus non eſt certum lineam A E. </s> <s xml:id="echoid-s18534" xml:space="preserve">præcisè terminari <lb/>in ipſa circumferentia, quia non eſt ducta poſt deſcriptum circulum, nec ſupponi-<lb/>tur circulum tranſire per E. </s> <s xml:id="echoid-s18535" xml:space="preserve">& </s> <s xml:id="echoid-s18536" xml:space="preserve">quamuis Euclides in Prima, & </s> <s xml:id="echoid-s18537" xml:space="preserve">alijs, vtatur circulo <lb/>ad oſtendas lineas æquales, id bene habet, quia in Prima lineæ ducuntur ſaltem. <lb/></s> <s xml:id="echoid-s18538" xml:space="preserve">vna poſt factum circulum, qui per extremum alterius lineæ tranſit ex hypotheſi. </s> <s xml:id="echoid-s18539" xml:space="preserve"><lb/>in Secunda vero propoſitione ductis iam lineis circulus deſcribitur interuallo mi-<lb/>noris ſecans maiorem, quare pars maioris intra circulum intercepta neceſſario ducitur à cẽtro ad circumfe-<lb/>rentiam, & </s> <s xml:id="echoid-s18540" xml:space="preserve">ſic illæ duæ probantur æquales.</s> <s xml:id="echoid-s18541" xml:space="preserve"/> </p> <div xml:id="echoid-div467" type="float" level="2" n="1"> <figure xlink:label="fig-0238-02" xlink:href="fig-0238-02a"> <image file="0238-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-02"/> </figure> </div> <p> <s xml:id="echoid-s18542" xml:space="preserve">Quartò, fallaciter demonſtramus, quando in conſtructione aſſumitur aliquid, cuius conſtructio ignora-<lb/>tur, vt ſi ad quadrandum circulum dicat quis, ſumatur linea recta æqualis peripherię circuli; </s> <s xml:id="echoid-s18543" xml:space="preserve">hoc enim Geo-<lb/>metricè non dum inuentum eſt, & </s> <s xml:id="echoid-s18544" xml:space="preserve">ſi mechanicè, vel organicè fiat nititur ſenſu; </s> <s xml:id="echoid-s18545" xml:space="preserve">ſimiliter peccant omnes de-<lb/>monſtrationes in quibus vſui ſunt lineę punctuales, vt eſt linea Cõchiodis Nicodemis apud Clauium in Geo-<lb/>metria pract. </s> <s xml:id="echoid-s18546" xml:space="preserve">lib. </s> <s xml:id="echoid-s18547" xml:space="preserve">8. </s> <s xml:id="echoid-s18548" xml:space="preserve">pag. </s> <s xml:id="echoid-s18549" xml:space="preserve">25. </s> <s xml:id="echoid-s18550" xml:space="preserve">& </s> <s xml:id="echoid-s18551" xml:space="preserve">linea Quadratix apud Clauium ad finem 6. </s> <s xml:id="echoid-s18552" xml:space="preserve">Euclid. </s> <s xml:id="echoid-s18553" xml:space="preserve">huiuſmodi enim lineæ non <lb/>ſunt quid continuum, cum ex punctis conoſcent, & </s> <s xml:id="echoid-s18554" xml:space="preserve">propterea nequeunt partes ipſarum præcisè haberi, cum <lb/>incertum ſit vbinam ſint puncta lineam conſtituentia. </s> <s xml:id="echoid-s18555" xml:space="preserve">in Quadrantice præterea vltimum punctum haberi <lb/>nequit. </s> <s xml:id="echoid-s18556" xml:space="preserve">Nicodemes paralogizat ducens lineam quandam quæ terminatur ad Conchilem punctualem, quia <lb/>incertum eſt an ad vnum ex punctis illis deſinat, ſecus terminari ab ea nequit.</s> <s xml:id="echoid-s18557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18558" xml:space="preserve">Quinta, eſt cum vtimur communibus principis aliarum ſcientiarum, ſic Bryſo in quadrando circulo vte-<lb/>batur, hoc principio, quæcunque ſunt ſimul maiora, & </s> <s xml:id="echoid-s18559" xml:space="preserve">minora ijſdem, ſunt inuicem æqualia, quod com-<lb/>mune eſt magnitudinibus, numeris temporibus, & </s> <s xml:id="echoid-s18560" xml:space="preserve">qualitatibus, & </s> <s xml:id="echoid-s18561" xml:space="preserve">ideo ab Ariſt. </s> <s xml:id="echoid-s18562" xml:space="preserve">repræhenditur text. </s> <s xml:id="echoid-s18563" xml:space="preserve">primi <lb/>poſter. </s> <s xml:id="echoid-s18564" xml:space="preserve">vide noſtram illius loci explicationem: </s> <s xml:id="echoid-s18565" xml:space="preserve">Hinc etiam non licet Geometræ vti illo principio quæ ſunt <lb/>eadem vni tertio ſunt eadem inter ſe, quia eſt cõmune alijs ſcientijs, ſed pro eo vt debet hoc; </s> <s xml:id="echoid-s18566" xml:space="preserve">quæ ſunt æqua-<lb/>lia vni tertio, &</s> <s xml:id="echoid-s18567" xml:space="preserve">c.</s> <s xml:id="echoid-s18568" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18569" xml:space="preserve">Sexta, Rationes probabiles apud Geometras habentur pro paralogiſmis, vt ſi quis probaret ſuperiorcm li-<lb/>neam D E quæ eſt baſi æquidiſtans, eſſe minorem baſi B C. </s> <s xml:id="echoid-s18570" xml:space="preserve">ex eo, quod ſit in anguſtiori loco, quam ſit baſis; <lb/></s> <s xml:id="echoid-s18571" xml:space="preserve">deciperetur quia ibi poni poteſt linea maior baſi, quæ tamen non ſit ei æquidiſtans.</s> <s xml:id="echoid-s18572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18573" xml:space="preserve">Septima, Dicitur principij petitio, eſtque, quando in diſcurſu aſſumitur pro vero id, quod eſt demon-<lb/>ſtrandum, ideſt, quod in principio poſitum eſt, Ariſt. </s> <s xml:id="echoid-s18574" xml:space="preserve">2. </s> <s xml:id="echoid-s18575" xml:space="preserve">priorum cap. </s> <s xml:id="echoid-s18576" xml:space="preserve">31. </s> <s xml:id="echoid-s18577" xml:space="preserve">af<unsure/>ſ<unsure/>ert hoc exemplum; </s> <s xml:id="echoid-s18578" xml:space="preserve">vult quiſpiam <lb/> <anchor type="figure" xlink:label="fig-0238-03a" xlink:href="fig-0238-03"/> oſtendere duas in ſequenti figura lineas A B. </s> <s xml:id="echoid-s18579" xml:space="preserve">C D. </s> <s xml:id="echoid-s18580" xml:space="preserve">eſſe paralellas, <lb/>quod faciant angulos alternos A G H. </s> <s xml:id="echoid-s18581" xml:space="preserve">G H D. </s> <s xml:id="echoid-s18582" xml:space="preserve">æquales, nam hoc <lb/>poſito per vigeſimam ſeptimam primi, id ſequitur volens poſtea <lb/>probare tales angulos eſſe æquales, id probat, ex eo quòd ſunt pa-<lb/>ralellæ, quod ſequitur per 29. </s> <s xml:id="echoid-s18583" xml:space="preserve">primi, petit quod in principio poſi-<lb/>tum eſt pro bandum, ſcilicet, lineas A B. </s> <s xml:id="echoid-s18584" xml:space="preserve">C D. </s> <s xml:id="echoid-s18585" xml:space="preserve">eſſe paralellas Ean-<lb/>dem peccaret fallaciam qui demonſtrationem aliquam citaret, quę <lb/>ex demonſtranda penderet, ſeu ſequeretur, vt ſi quis probaret 10. <lb/></s> <s xml:id="echoid-s18586" xml:space="preserve">p. </s> <s xml:id="echoid-s18587" xml:space="preserve">per 32. </s> <s xml:id="echoid-s18588" xml:space="preserve">primi.</s> <s xml:id="echoid-s18589" xml:space="preserve"/> </p> <div xml:id="echoid-div468" type="float" level="2" n="2"> <figure xlink:label="fig-0238-03" xlink:href="fig-0238-03a"> <image file="0238-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-03"/> </figure> </div> <p> <s xml:id="echoid-s18590" xml:space="preserve">Octaua, aliquando Tyrones dum demonſtrat@ones Euclidis repetunt falluntur ob ſimilitudinem demon- <pb o="217" file="0239" n="244" rhead="AD MATHEMATICAS."/> ſtrationũ, ſic aliquando probant angulos ad baſim eſſe æquales in 5. </s> <s xml:id="echoid-s18591" xml:space="preserve">per 4. </s> <s xml:id="echoid-s18592" xml:space="preserve">nam illi anguli opponuntur æqua-<lb/>libus lateribus, ergo inferunt per 4. </s> <s xml:id="echoid-s18593" xml:space="preserve">ſunt æquales. </s> <s xml:id="echoid-s18594" xml:space="preserve">error eſt quia in 4. </s> <s xml:id="echoid-s18595" xml:space="preserve">id probatum eſt in duobus diuerſis trian-<lb/>gulis, in 5. </s> <s xml:id="echoid-s18596" xml:space="preserve">autem probandum eſt in vno tant<unsure/>um.</s> <s xml:id="echoid-s18597" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18598" xml:space="preserve">Nona dicitur fallacia vniuerſalis, debet enim propoſicio eſſe talis, vt omnibus ſubiectis ſpeciebus, & </s> <s xml:id="echoid-s18599" xml:space="preserve">om-<lb/>nibus caſibus aptari poſſit: </s> <s xml:id="echoid-s18600" xml:space="preserve">ſi quis vellet oſtendere, in omni triangulo paralellam baſi, eſſe baſi minorem, in <lb/>demonſtratione vero id ſolum oſtẽderet in figura Iſoſcelis, & </s> <s xml:id="echoid-s18601" xml:space="preserve">ex natura eius, eſſet pſeudographus. </s> <s xml:id="echoid-s18602" xml:space="preserve">ſic etiam <lb/>quando habet varios caſus; </s> <s xml:id="echoid-s18603" xml:space="preserve">conſidera ſecundum primi, quæ varios habet eaſus pro varietate locorum puncti <lb/>adati, & </s> <s xml:id="echoid-s18604" xml:space="preserve">tamen demonſtrationem Euclidis conuenit omnibus illis caſibus.</s> <s xml:id="echoid-s18605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18606" xml:space="preserve">Decima, eſt contra C<unsure/>eometriæ principia; </s> <s xml:id="echoid-s18607" xml:space="preserve">ſic errabat Antiphon dum ad quadrandum circulum aſſumebat <lb/>lineam curuam conſtare ex minimis rectis lineolis, quod ſalſum eſt. </s> <s xml:id="echoid-s18608" xml:space="preserve">vide Ariſt. </s> <s xml:id="echoid-s18609" xml:space="preserve">vlt. </s> <s xml:id="echoid-s18610" xml:space="preserve">cap. </s> <s xml:id="echoid-s18611" xml:space="preserve">Elench. </s> <s xml:id="echoid-s18612" xml:space="preserve">cum noſtra <lb/>explicatione.</s> <s xml:id="echoid-s18613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18614" xml:space="preserve">Vndecima, cum aliquod falſum vel impoſſibile aſſumitur. </s> <s xml:id="echoid-s18615" xml:space="preserve">ſic fallit Hippocrates in ſua circuli quadratio-<lb/>ne, qui cum lunn<unsure/>lam quadraſſet, aſſumit poſtea ex quodam trapezin accipi poſſe tria triangula æqualia tri-<lb/>bus lunulis, eo modo quo antea ex quadrato quodam triangulum æquale lunulæ acceperat; </s> <s xml:id="echoid-s18616" xml:space="preserve">quod falſum eſt. <lb/></s> <s xml:id="echoid-s18617" xml:space="preserve">vide cap. </s> <s xml:id="echoid-s18618" xml:space="preserve">31. </s> <s xml:id="echoid-s18619" xml:space="preserve">ſecundi priorum Ariſt. </s> <s xml:id="echoid-s18620" xml:space="preserve">cum noſtra explicatione.</s> <s xml:id="echoid-s18621" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18622" xml:space="preserve">Duodecima, cum aliquid aſſumitur, quod non ſit euidens, aut quod non ſit demonſtratum, etiamſi verum <lb/>ſit. </s> <s xml:id="echoid-s18623" xml:space="preserve">Obijcies fortè, Euclides in prima aſſumit duos illos circulos ſe mutuo ſecare, quod non probat. </s> <s xml:id="echoid-s18624" xml:space="preserve">Reſpon-<lb/>deo id eſſe euidens, quid enim euidentius eſt, quam ſi vnus circulus habebt centrum in circumferentia alte-<lb/>rius, ſimulq; </s> <s xml:id="echoid-s18625" xml:space="preserve">per centrum illius tranſeat, ipſum ſecare. </s> <s xml:id="echoid-s18626" xml:space="preserve">Alia ſimilia ſunt apud Euclidem, & </s> <s xml:id="echoid-s18627" xml:space="preserve">alios Geometra@, <lb/>quæ tamen fi benè conſiderentureuidentiſſima ſunt, & </s> <s xml:id="echoid-s18628" xml:space="preserve">propterea ſine probatione aſſumuntur.</s> <s xml:id="echoid-s18629" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18630" xml:space="preserve">Decimatertia, cum malam illationem admittimus, vt ſi quis ſic inferret, trãſitur a minori ad maius, & </s> <s xml:id="echoid-s18631" xml:space="preserve">per <lb/>omnia media, ergo per æquale; </s> <s xml:id="echoid-s18632" xml:space="preserve">vide Clauium ad 16. </s> <s xml:id="echoid-s18633" xml:space="preserve">propoſitionem 3. </s> <s xml:id="echoid-s18634" xml:space="preserve">Elem. </s> <s xml:id="echoid-s18635" xml:space="preserve">in fine illius longiſſimi Scholij. <lb/></s> <s xml:id="echoid-s18636" xml:space="preserve">ſic fallebat Auerr. </s> <s xml:id="echoid-s18637" xml:space="preserve">dum ſic ratiocinabatur, vt eſt 6. </s> <s xml:id="echoid-s18638" xml:space="preserve">ad 3. </s> <s xml:id="echoid-s18639" xml:space="preserve">ita 4. </s> <s xml:id="echoid-s18640" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s18641" xml:space="preserve">ergo permutando,|vt 6. </s> <s xml:id="echoid-s18642" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s18643" xml:space="preserve">ita 4. </s> <s xml:id="echoid-s18644" xml:space="preserve">ad 3. </s> <s xml:id="echoid-s18645" xml:space="preserve">hæc <lb/>enim non eſt permutata proportio, nec vllus alius modus argumentandi ex ijs, qui ab Euclide comproban-<lb/>tur, & </s> <s xml:id="echoid-s18646" xml:space="preserve">apparet falſitas in numeris. </s> <s xml:id="echoid-s18647" xml:space="preserve">nec pariter valet inferre, duæ hæ rectę lineæ non ſunt æquidiſtantes, ergo <lb/>concurrunt.</s> <s xml:id="echoid-s18648" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18649" xml:space="preserve">Decimaquarta, cum aliquid aſſumitur, quod æquè obſcurum eſt, ac ipſa propoſitio; </s> <s xml:id="echoid-s18650" xml:space="preserve">debet enim ex notio-<lb/>ribus deduci; </s> <s xml:id="echoid-s18651" xml:space="preserve">ſic Proclus decipitur dum ad probandum axioma 13. </s> <s xml:id="echoid-s18652" xml:space="preserve">Euclidis aſſumit illud æquè ignotum, ſi <lb/>ab vno puncto duæ reææ angulo fac<unsure/>ientes infinitè producerentur, earum diſtantia excedet omnem finitam <lb/>magnitudinem. </s> <s xml:id="echoid-s18653" xml:space="preserve">vide Clauium in ſcholio 28. </s> <s xml:id="echoid-s18654" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s18655" xml:space="preserve">primi Elem. </s> <s xml:id="echoid-s18656" xml:space="preserve">pag. </s> <s xml:id="echoid-s18657" xml:space="preserve">150.</s> <s xml:id="echoid-s18658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18659" xml:space="preserve">Decimaquinta, oritur ex ignoratione terminorum Geometricorum. </s> <s xml:id="echoid-s18660" xml:space="preserve">ſic Tyrones aberrant, dum putant <lb/>ſe quadrare circulum, ſi conſtruant quadratum cuius quatuor latera ſint æqualia peri pheriæ dati circuli: </s> <s xml:id="echoid-s18661" xml:space="preserve">vi-<lb/>de Geometriam practicam P. </s> <s xml:id="echoid-s18662" xml:space="preserve">Clauij pag. </s> <s xml:id="echoid-s18663" xml:space="preserve">357.</s> <s xml:id="echoid-s18664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18665" xml:space="preserve">Tandem lectorẽ monitum volo ad vitandas fallacias vtile eſſe legere Io: </s> <s xml:id="echoid-s18666" xml:space="preserve">Buteonem de varijs circuli qua-<lb/>draturis: </s> <s xml:id="echoid-s18667" xml:space="preserve">& </s> <s xml:id="echoid-s18668" xml:space="preserve">Petrum Nonium de Orontij erratis, & </s> <s xml:id="echoid-s18669" xml:space="preserve">Io: </s> <s xml:id="echoid-s18670" xml:space="preserve">Regiomontanum de quadratura Nicolai Cuſani. </s> <s xml:id="echoid-s18671" xml:space="preserve">hi <lb/>enim aliorum varios paralogiſmos, & </s> <s xml:id="echoid-s18672" xml:space="preserve">fallacias detegunt, vnde nos aliorum damno proſiciamus.</s> <s xml:id="echoid-s18673" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div470" type="section" level="1" n="356"> <head xml:id="echoid-head375" style="it" xml:space="preserve">De reſolutione, & compoſitione.</head> <p> <s xml:id="echoid-s18674" xml:space="preserve">VT ars quæuis benè tractetur non ſolum neceſſarium eſt, vitia illi contraria, vt vitari|poſſint, cognoſcere, <lb/>ſed etiam, & </s> <s xml:id="echoid-s18675" xml:space="preserve">quidem præcipuum|, præcepta tenere quibus facilè, & </s> <s xml:id="echoid-s18676" xml:space="preserve">optimè artis finem conſequamur; <lb/></s> <s xml:id="echoid-s18677" xml:space="preserve">cum ergo de fallacijs egerimus, quæ arti hui<unsure/>c contrariæ ſunt, ſequitur vt de reſolutione, & </s> <s xml:id="echoid-s18678" xml:space="preserve">compoſitione <lb/>nonnulla dicamus, per eas enim, & </s> <s xml:id="echoid-s18679" xml:space="preserve">optimè & </s> <s xml:id="echoid-s18680" xml:space="preserve">facilè Geometricè demonſtrationes inueniri poſſunt.</s> <s xml:id="echoid-s18681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18682" xml:space="preserve">Reſolutionem hanc Geometricam primus omnium Plato adinuenit, eamque Laodamãtem Theſium do-<lb/>cuit, cuius auxilio, & </s> <s xml:id="echoid-s18683" xml:space="preserve">ipſe, & </s> <s xml:id="echoid-s18684" xml:space="preserve">reliqui iuniores Geometrę plurimis ſubtiliter inuentis Geometriam magnope-<lb/>re amplificarunt. </s> <s xml:id="echoid-s18685" xml:space="preserve">de hac reſolutione, vt refert Pappus initio 7. </s> <s xml:id="echoid-s18686" xml:space="preserve">ſcripſerat Euclides, Apollonius, & </s> <s xml:id="echoid-s18687" xml:space="preserve">Ariſtæus, <lb/>ſed opera eorum interciderunt. </s> <s xml:id="echoid-s18688" xml:space="preserve">Marinus autem Ghetaldus in ſuo Apollonio rediuiuo reſolutionem hanc <lb/>pariter rediuiuam ſe propediem daturum recipit: </s> <s xml:id="echoid-s18689" xml:space="preserve">nos tamen interim de ſtac nonnulla diximus in locis Ma-<lb/>@hem. </s> <s xml:id="echoid-s18690" xml:space="preserve">ad titulum, Lib. </s> <s xml:id="echoid-s18691" xml:space="preserve">reſolutor. </s> <s xml:id="echoid-s18692" xml:space="preserve">& </s> <s xml:id="echoid-s18693" xml:space="preserve">hic etiam nonnulla in medius afferemus. </s> <s xml:id="echoid-s18694" xml:space="preserve">quid autem ipſa ſit ex veterum <lb/>de ea reliquijs primo videamus. </s> <s xml:id="echoid-s18695" xml:space="preserve">Euclides igitur in ſcholio propoſ. </s> <s xml:id="echoid-s18696" xml:space="preserve">primæ 13. </s> <s xml:id="echoid-s18697" xml:space="preserve">Elem. </s> <s xml:id="echoid-s18698" xml:space="preserve">iuxta fideliſſimam Go-<lb/>mand. </s> <s xml:id="echoid-s18699" xml:space="preserve">ex Zamberti, & </s> <s xml:id="echoid-s18700" xml:space="preserve">Græco interpretationem (quod ſchol. </s> <s xml:id="echoid-s18701" xml:space="preserve">cum quatuor reſolutiones, pretioſum antiqui-<lb/>tatis monumentum nonnulli interpretes perperam omiſerunt) eam ſic definit. </s> <s xml:id="echoid-s18702" xml:space="preserve">Reſolntio eſt ſumptio tan-<lb/>quam conceſſi, per ea quę conſequuntur in aliquod verum conceſſum. </s> <s xml:id="echoid-s18703" xml:space="preserve">poſtea addit. </s> <s xml:id="echoid-s18704" xml:space="preserve">Compoſitio eſt ſumptio <lb/>conceſſi per ea quæ conſequuntur in quęſiti concluſionem ſiue depręhenſionem. </s> <s xml:id="echoid-s18705" xml:space="preserve">Eaſdem definit Proclus lib. <lb/></s> <s xml:id="echoid-s18706" xml:space="preserve">6. </s> <s xml:id="echoid-s18707" xml:space="preserve">primi pag. </s> <s xml:id="echoid-s18708" xml:space="preserve">145. </s> <s xml:id="echoid-s18709" xml:space="preserve">& </s> <s xml:id="echoid-s18710" xml:space="preserve">Pappus initio lib. </s> <s xml:id="echoid-s18711" xml:space="preserve">7. </s> <s xml:id="echoid-s18712" xml:space="preserve">quos tu conſule. </s> <s xml:id="echoid-s18713" xml:space="preserve">Senſus autem Euclidis eſt hic: </s> <s xml:id="echoid-s18714" xml:space="preserve">Reſolutio eſt diſcur-<lb/>ſus, quo inueſtigamus veritatem Theorematis, aut poſſibilitas Problematis quæſiti hoc modo; </s> <s xml:id="echoid-s18715" xml:space="preserve">ſi quæſitũ eſt <lb/>Theorema accipimus illud tanquam verum, & </s> <s xml:id="echoid-s18716" xml:space="preserve">conceſſum. </s> <s xml:id="echoid-s18717" xml:space="preserve">ſi vero eſt Problema, aſſumimus illud tanquam <lb/>factum, ideſt, ſupponimus illud verum eſſe, iſtud vero poſſibile, & </s> <s xml:id="echoid-s18718" xml:space="preserve">iam factum; </s> <s xml:id="echoid-s18719" xml:space="preserve">ex qua ſuppoſitione ratioci-<lb/>namur per ea, quæ ex ſuppoſitis veré deducuntur, donec aliquod verum vel falſum oecurrat: </s> <s xml:id="echoid-s18720" xml:space="preserve">ſi enim occur-<lb/>rat aliquod verum, & </s> <s xml:id="echoid-s18721" xml:space="preserve">conceſſum, ſignum euidens eſt etiam ſuppoſitum illud, ex quo iſtud ſequitur verum eſ-<lb/>ſe, ſeu poſſibile eſſe. </s> <s xml:id="echoid-s18722" xml:space="preserve">quæ conſequentia nititur hoc logico fundamento, verum non niſi ex vero in bona ma-<lb/>teria, & </s> <s xml:id="echoid-s18723" xml:space="preserve">forma ſequitur.</s> <s xml:id="echoid-s18724" xml:space="preserve"/> </p> <pb o="218" file="0240" n="245" rhead="APPARATVS"/> <p> <s xml:id="echoid-s18725" xml:space="preserve">Inuento autem vero illo, demonſtrationis compoſitionem poſtea ordine retrogrado faciebant, ideſt, de-<lb/>monſtrationem quæſiti ordine compoſitiuo conſtruebant, ratiocinantes ex vero illo inuento ad quęſiti con-<lb/>cluſionei<unsure/>n. </s> <s xml:id="echoid-s18726" xml:space="preserve">Quod ſi falſum vel impoſſibile occurrat, euidẽs ſignum eſt quęſitum eſſe falſum, vel impoſſibile. <lb/></s> <s xml:id="echoid-s18727" xml:space="preserve">quæ conſequutio hoc nititur principio logico; </s> <s xml:id="echoid-s18728" xml:space="preserve">falſum non niſi ex falſo in bona materia, & </s> <s xml:id="echoid-s18729" xml:space="preserve">forma deducitur. </s> <s xml:id="echoid-s18730" xml:space="preserve"><lb/>quæ argumentatio dicitur ad impoſſibile. </s> <s xml:id="echoid-s18731" xml:space="preserve">Verum hæc multo melius intelliges ſi attente legeris, ac conſide-<lb/>raueris illas. </s> <s xml:id="echoid-s18732" xml:space="preserve">5. </s> <s xml:id="echoid-s18733" xml:space="preserve">Reſolutiones, ac compoſitiones Euclidis in 13. </s> <s xml:id="echoid-s18734" xml:space="preserve">Elem. </s> <s xml:id="echoid-s18735" xml:space="preserve">& </s> <s xml:id="echoid-s18736" xml:space="preserve">alias quas paſſim apud Apollonium, <lb/>Archimedem, & </s> <s xml:id="echoid-s18737" xml:space="preserve">Pappum reperies, quæ tibi pro perſpicuis exemplis inſeruient (melius enim exemplis, quã <lb/>multis pręceptionibus proficimus.) </s> <s xml:id="echoid-s18738" xml:space="preserve">ex quibus facultatem Geometricè demonſtrandi facilè tibi comparabis.</s> <s xml:id="echoid-s18739" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18740" xml:space="preserve">Tandem ſcias opus datorum Euclidis huic reſolutionis arti ſubſeruire in eo enim ex varijs datis varia in-<lb/>feruntur, & </s> <s xml:id="echoid-s18741" xml:space="preserve">conſequuntur, quæ illationes, & </s> <s xml:id="echoid-s18742" xml:space="preserve">conſequutiones citantur poſtea in reſolutionibus faciendis, vt <lb/>videbis apud Euclidem, Apollonium, & </s> <s xml:id="echoid-s18743" xml:space="preserve">Pappum. </s> <s xml:id="echoid-s18744" xml:space="preserve">Porrò de opere datorum reſtaurãdo dictum eſt ſuperius. <lb/></s> <s xml:id="echoid-s18745" xml:space="preserve">Atq; </s> <s xml:id="echoid-s18746" xml:space="preserve">hæc ſunt quæ de arte demonſtrandi apud Geometras ex veterum naufragijs colligere licuit. </s> <s xml:id="echoid-s18747" xml:space="preserve">Percepta <lb/>igitur hac arte, auxilio eius poterimus magna animi iucunditate ſubtiliſſimis demonſtrationibus, non ſolum <lb/>Geometriam, ſed etiam Arithmeticam, qnæ eodem modo demonſtrat, locupletare, ac nõnulla tandem per-<lb/>tinaci labore, & </s> <s xml:id="echoid-s18748" xml:space="preserve">ſtudio inueſtigare, quorum difficultas veterum ingenia hactenus incaſſum vexauit, & </s> <s xml:id="echoid-s18749" xml:space="preserve">torſit; </s> <s xml:id="echoid-s18750" xml:space="preserve"><lb/>vti ſunt angulum datum in quotuis partes diuidere; </s> <s xml:id="echoid-s18751" xml:space="preserve">ſimiliter, arcum circuli datum in quotuis pattes diuide-<lb/>re, circulum quadrare, rectam lineam circulari æqualem exhibere; </s> <s xml:id="echoid-s18752" xml:space="preserve">duplare cubum, duas medias lineas pro-<lb/>portionales inuenire, Heptagonum regulare deſcribere, I ſoſceles habens angulum ad baſim triplum eius <lb/>qui ad verticem conſtruere, &</s> <s xml:id="echoid-s18753" xml:space="preserve">c.</s> <s xml:id="echoid-s18754" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18755" xml:space="preserve">Sed maximè omnium proderit ipſa demonſtr<unsure/>andi exercitatio. </s> <s xml:id="echoid-s18756" xml:space="preserve">quapropter Geometriæ Doctoris præci-<lb/> <anchor type="figure" xlink:label="fig-0240-01a" xlink:href="fig-0240-01"/> puum munns exiſtimo, ſubinde auditoribus ſuis faciles quaſdam propoſitiones propo-<lb/>nere, quod quotidie Plato, quamuis aliud agens, factitaſſe legimus. </s> <s xml:id="echoid-s18757" xml:space="preserve">Ego quidem ſin-<lb/>gulis annis auditoribus meis prooono publicè demõſtrandum illud, quod ſuper in pri-<lb/>ma figura exhibetur, videlicet, in quolibet triangulo linea baſi paaralella, ipſa baſi mi-<lb/>nor eſt. </s> <s xml:id="echoid-s18758" xml:space="preserve">id autem non parua eorum iucunditate, & </s> <s xml:id="echoid-s18759" xml:space="preserve">vtilitate pluſquam quindecim mo-<lb/>dis demonſtrarunt. </s> <s xml:id="echoid-s18760" xml:space="preserve">vel iſtud; </s> <s xml:id="echoid-s18761" xml:space="preserve">ſi trianguli æquilateri ſingula latera bifariam diuidan-<lb/>tur, ducanturque ad tria diuiſionum puncta tres rectæ lineæ, exurgunt quatuor trian-<lb/>gula pariter æquilatera, & </s> <s xml:id="echoid-s18762" xml:space="preserve">inuicem omnino æqualia, necnon tria parai<unsure/>ellogramma <lb/>æqualia: </s> <s xml:id="echoid-s18763" xml:space="preserve">cuius ſiguram hanc conſidera.</s> <s xml:id="echoid-s18764" xml:space="preserve"/> </p> <div xml:id="echoid-div470" type="float" level="2" n="1"> <figure xlink:label="fig-0240-01" xlink:href="fig-0240-01a"> <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0240-01"/> </figure> </div> </div> <div xml:id="echoid-div472" type="section" level="1" n="357"> <head xml:id="echoid-head376" style="it" xml:space="preserve">De aliarum Mathematicarum promotione.</head> <p> <s xml:id="echoid-s18765" xml:space="preserve">AArithmetica, eadem arte, vt dictum eſt multis adinuentis ditari poteſt. </s> <s xml:id="echoid-s18766" xml:space="preserve">Mechanica facultas eadem arte <lb/>pariter locupletari poteſt, præſertim cum nondum centra grauitatis omniũ figurarum tam planarum, <lb/>quam ſolidarum comperta ſint, v.</s> <s xml:id="echoid-s18767" xml:space="preserve">g. </s> <s xml:id="echoid-s18768" xml:space="preserve">centrum grauitatis ſemicirculi, & </s> <s xml:id="echoid-s18769" xml:space="preserve">aliarum circuli portionũ adhuc igno-<lb/>rantur. </s> <s xml:id="echoid-s18770" xml:space="preserve">ſimiliter portionum Ellipſi, Hyperboles etiam, & </s> <s xml:id="echoid-s18771" xml:space="preserve">Fruſtorum eius, centra grauitatis adhuc latent <lb/>expectanturque. </s> <s xml:id="echoid-s18772" xml:space="preserve">Opticam facultatem non ſolum demonſtrationibus, ſed multo magis aſſiduis reflexionum, <lb/>& </s> <s xml:id="echoid-s18773" xml:space="preserve">refractionum experimentis ampliare valemus, ſicuti nuper P. </s> <s xml:id="echoid-s18774" xml:space="preserve">Chriſtophorus Scheiner noſtræ Soc. </s> <s xml:id="echoid-s18775" xml:space="preserve">ſoler-<lb/>ter in ſuo oculo, ſeu fundamento optico præſtitit. </s> <s xml:id="echoid-s18776" xml:space="preserve">nunc omnes Teleſcopij inſtrumenti optici adeo præſtan-<lb/>tis demonſtrationes, aut deſiderant, aut inquirunt, ſed nondum emerſit.</s> <s xml:id="echoid-s18777" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18778" xml:space="preserve">Muſicam corrigere, & </s> <s xml:id="echoid-s18779" xml:space="preserve">illuſtrare debemus, non ſolum ex Theoricis traditionibus vete rum, ſed multo ma-<lb/>gis ex eis quæ Plato, Ariſtoteles, & </s> <s xml:id="echoid-s18780" xml:space="preserve">Plutarchus de eius materia, officio, & </s> <s xml:id="echoid-s18781" xml:space="preserve">ſine ſcripta reliquerunt. </s> <s xml:id="echoid-s18782" xml:space="preserve">Aſtrono-<lb/>miam maximè exemplo Tichonis promouere oportet adhibitis ſcilicet magnis, & </s> <s xml:id="echoid-s18783" xml:space="preserve">exquiſitis inſtrumentis, <lb/>aſſiduas obſeruationes peragere, eaſque cum antiquorum obſeruationibus conferre. </s> <s xml:id="echoid-s18784" xml:space="preserve">Alijs tandem pluribus <lb/>modis, & </s> <s xml:id="echoid-s18785" xml:space="preserve">quidem nouis (neq; </s> <s xml:id="echoid-s18786" xml:space="preserve">enim humanum ingenium vllis artium regulis, quaſi carceribus concludi po-<lb/>teſt) hiſce nobiliſſimis, & </s> <s xml:id="echoid-s18787" xml:space="preserve">pulcherrimis ſcientijs incrementum afferri poteſt. </s> <s xml:id="echoid-s18788" xml:space="preserve">Nos etiam Echometriam, <lb/>nouam Matheſeos partem, in fine dabimus, in qua ſonum, & </s> <s xml:id="echoid-s18789" xml:space="preserve">voces per lineas, angulos, &</s> <s xml:id="echoid-s18790" xml:space="preserve">c. </s> <s xml:id="echoid-s18791" xml:space="preserve">iuris Geometrici <lb/>fecimus, ac plura de ijs noua demonſtrauimus.</s> <s xml:id="echoid-s18792" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div473" type="section" level="1" n="358"> <head xml:id="echoid-head377" style="it" xml:space="preserve">Clarorum Mathematicorum Chronologia. Pars quinta.</head> <p> <s xml:id="echoid-s18793" xml:space="preserve">AD huius Apparatus perfectionem addendam eſſe cenſeo clarorum Mathematicorum Chronologiam, <lb/>quam cum locis Mathematicis Ariſt. </s> <s xml:id="echoid-s18794" xml:space="preserve">iam edidimus: </s> <s xml:id="echoid-s18795" xml:space="preserve">non modicam enim vtilitatem ſtudijs afferre lon-<lb/>go vſu & </s> <s xml:id="echoid-s18796" xml:space="preserve">experientia didici, noſſe quibus temporibus, ij Authores ſcripſerint, quibus operam, & </s> <s xml:id="echoid-s18797" xml:space="preserve">ſtudiũ im-<lb/>pendimus. </s> <s xml:id="echoid-s18798" xml:space="preserve">quod optimè ij etiam norunt, qui ſuauiſſimum eruditionis ſtudium vna cum Philoſophia con-<lb/>iungere ſolent. </s> <s xml:id="echoid-s18799" xml:space="preserve">Enimuero non paruum vidctur inconueniens, authorem quempiam ſedulo verſare, eumq; <lb/></s> <s xml:id="echoid-s18800" xml:space="preserve">quo ſæculo floruerit, ac ſcripſerit, hoc eſt, quibus ſcriptoribus ſit iunior, quibus contemporaneus, quibuſq; </s> <s xml:id="echoid-s18801" xml:space="preserve"><lb/>ſenior extitericignorare. </s> <s xml:id="echoid-s18802" xml:space="preserve">Ego qnidem eius ſum genij, vt nullum vnquam opus legendum aggrediar, quin <lb/>mihi prius auth<unsure/>oris ipſius tempus, vtcunq; </s> <s xml:id="echoid-s18803" xml:space="preserve">conſtiterit; </s> <s xml:id="echoid-s18804" xml:space="preserve">conſule igitur noſtram clarorum Mathematicorum <lb/>Chronologiam vna cum locis Mathematicis Ariſt. </s> <s xml:id="echoid-s18805" xml:space="preserve">editam, ne eam iterum hic imprimendo, actum agamus.</s> <s xml:id="echoid-s18806" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div474" type="section" level="1" n="359"> <head xml:id="echoid-head378" xml:space="preserve">LAVS DEO.</head> <pb o="219" file="0241" n="246"/> </div> <div xml:id="echoid-div475" type="section" level="1" n="360"> <head xml:id="echoid-head379" xml:space="preserve">ECHOMETRIA <lb/>SIVE DE NATVRA ECHVS <lb/>GEOMETRICA TRACTATIO, <lb/>Publicè habita à quodam Academico. <lb/>PROLVSIO, ET OCCASIO COMMENTATIONIS.</head> <p> <s xml:id="echoid-s18807" xml:space="preserve">SVperiori Autumno, cum in ſcholis Halcyonia eſſent, relicta in vrbe Philoſophia, in ſubur-<lb/>banum relaxandi animi, acpurioris cæli captandi gratia conceſſeramus. </s> <s xml:id="echoid-s18808" xml:space="preserve">cumq; </s> <s xml:id="echoid-s18809" xml:space="preserve">ſimul non-<lb/>nulli ſuauioris Muſæ comites deambulatum iſſemus, accidit vt ex noſtris quidam Muſica, <lb/>ſimulq; </s> <s xml:id="echoid-s18810" xml:space="preserve">clariori voce præditus, carmen quoddam altius modularetur. </s> <s xml:id="echoid-s18811" xml:space="preserve">& </s> <s xml:id="echoid-s18812" xml:space="preserve">ecce tibi, carmen <lb/>idem, ex quadam ſatis remota turri, continuo pari ſuauitate recantatum excepimus. </s> <s xml:id="echoid-s18813" xml:space="preserve">primo <lb/>putatum eſt ſodalium aliquem inibi latentem ioculariter, ac blandè nobis illuſiſſe. </s> <s xml:id="echoid-s18814" xml:space="preserve">tandem <lb/>iterata, atque iterum relata modulatione, illa depræhenſa eſt,</s> </p> <p style="it"> <s xml:id="echoid-s18815" xml:space="preserve">-- quæ nec reticere loquenti, <lb/>Nec prior ipſa loqui didicit reſonabilis Echo:</s> <s xml:id="echoid-s18816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18817" xml:space="preserve">Pergratas noſtrarum vocum imagines reddidiſſe. </s> <s xml:id="echoid-s18818" xml:space="preserve">diutius igitur illius ſuauitate detenti, varij varios cantus <lb/>ei recinendos accinebamus. </s> <s xml:id="echoid-s18819" xml:space="preserve">cùm interim Geometria, quam ſimul cum reliqua Philoſophiæ familia in vrbe <lb/>reliqueramus, ſe nobis iterum comitem præbet, grateq; </s> <s xml:id="echoid-s18820" xml:space="preserve">ſuadet minimè inſtituto noſtro, relaxationiuè obeſ-<lb/>ſe, ſi latentem Echus naturam indagaremus; </s> <s xml:id="echoid-s18821" xml:space="preserve">quandoquidem id philoſophandi genus, iucundè per amæna <lb/>collium, & </s> <s xml:id="echoid-s18822" xml:space="preserve">vallium ambulationibus obiri poſſit. </s> <s xml:id="echoid-s18823" xml:space="preserve">Ego itaque veluti Pan alter, per ſaltus, per ſyluas, hac il-<lb/>lac vociferans Echum perſequi, & </s> <s xml:id="echoid-s18824" xml:space="preserve">captare; </s> <s xml:id="echoid-s18825" xml:space="preserve">ipſaque noſtris votis reſpondente, ipſi</s> </p> <p style="it"> <s xml:id="echoid-s18826" xml:space="preserve">-- pulſati colles clamore reſultant</s> </p> <p style="it"> <s xml:id="echoid-s18827" xml:space="preserve">& </s> <s xml:id="echoid-s18828" xml:space="preserve">-- gemitu nemus omne remugit.</s> <s xml:id="echoid-s18829" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18830" xml:space="preserve">Perſequebar, inquam, captabamque, contemplabar videlicet locorum reſonantium poſitionem, figuram, <lb/>qualitatem, quæ hanc vocis imaginem effinxiſſent. </s> <s xml:id="echoid-s18831" xml:space="preserve">atque ni fallor, Panos inſtar Echum depræhendi, natu-<lb/>ram eius videlicet, cauſaſque perueſtigaui. </s> <s xml:id="echoid-s18832" xml:space="preserve">Pan enim, vti tradunt Mythologi, fuit vir doctus, qui primus <lb/>Echus cauſam inueſtigauit, ductuſque ſuauitate noſcendi, diu collibus, montibuſque quaſi Echum perſe-<lb/>quens oberrauit. </s> <s xml:id="echoid-s18833" xml:space="preserve">vnde ipſum eam deperijſſe vetus fabula emanauit. </s> <s xml:id="echoid-s18834" xml:space="preserve">quæ igitur tunc temporis de hoc vocis <lb/>fimulacro, Geometriæ ope commentati ſumus, ea nunc in medium allata, non iniucunda fore ſperamus. <lb/></s> <s xml:id="echoid-s18835" xml:space="preserve">quæ vt ordine tradantur, opus eſt more Mathematicorum, nonnulla præmittere, ac primò definitiones <lb/>aliquot, quarum prima erit ipſius Echus nominis Etymon, nomina enim teſte Platonis Cratylo, quædam <lb/>ſunt perbreues rerum definitiones.</s> <s xml:id="echoid-s18836" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div476" type="section" level="1" n="361"> <head xml:id="echoid-head380" style="it" xml:space="preserve">DEFINITIONES.</head> <p> <s xml:id="echoid-s18837" xml:space="preserve">PRima erit ipſius nominis definitio, ſeu Etymologia. </s> <s xml:id="echoid-s18838" xml:space="preserve">Echo Græcè dicitur Hχω, à verbo Hχεω, ideſt, re-<lb/>ſono, vnde Latinis aptè redditus reſonantia. </s> <s xml:id="echoid-s18839" xml:space="preserve">Poetæ Latini eam modo Echo, modo imaginem vocis ap-<lb/>pellat, ſic Virg. </s> <s xml:id="echoid-s18840" xml:space="preserve"># Saxa ſonant, vociſque offenſa reſultat imago, <lb/>Philoſophis vox reflexa, repercuſſa, reciproca etiam dicitur. </s> <s xml:id="echoid-s18841" xml:space="preserve">hinc ad ipſius definitionem commodius iam <lb/>tranſire licebit.</s> <s xml:id="echoid-s18842" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18843" xml:space="preserve">Secunda. </s> <s xml:id="echoid-s18844" xml:space="preserve">Echo enim nihil aliud eſt, quam vocis articulatæ, aut modulatæ ſonus reflexus, hoc videlicet <lb/>modo, cum vox noſtra prolata, ac motuaeris quoquouerſus delata, obiecto directè corpori plano, cauo-<lb/>ue, ac ſatis læuigato occurrens, inde pilæ inſtar ad noſmet reucrtitur. </s> <s xml:id="echoid-s18845" xml:space="preserve">vbi diſtinguendum eſt inter Bom-<lb/>bum, & </s> <s xml:id="echoid-s18846" xml:space="preserve">Echum.</s> <s xml:id="echoid-s18847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18848" xml:space="preserve">Tertia. </s> <s xml:id="echoid-s18849" xml:space="preserve">Bombus enim eſt quidem ſonus reflexus, ſed ob defectum alicuius circumſtantiæ, ex ijs, quæ ne-<lb/>@eſſariæ ſunt ad Echum perſiciendam, confusſus, & </s> <s xml:id="echoid-s18850" xml:space="preserve">inarticulatus. </s> <s xml:id="echoid-s18851" xml:space="preserve">Echo autem propriè eſt, quæ vocesarti-<lb/>culatas, aut modulatas diſtinctè reſtituit. </s> <s xml:id="echoid-s18852" xml:space="preserve">Cuius naturam, vt melius perſcrutemur, animaduertimus non ſo-<lb/>lum communi Phy ſiologia, ſed præterea opus eſſe eam legibus Geometriæ, atq; </s> <s xml:id="echoid-s18853" xml:space="preserve">adeo linearibus demonſtra-<lb/>tionibus ſubijcere. </s> <s xml:id="echoid-s18854" xml:space="preserve">more videlicet opticorum, qui viſionis, atq; </s> <s xml:id="echoid-s18855" xml:space="preserve">illuminationis naturam per lineas, & </s> <s xml:id="echoid-s18856" xml:space="preserve">angu-<lb/>los optimè ſolent explicare. </s> <s xml:id="echoid-s18857" xml:space="preserve">quod ſi id cuipiam nouum, ac mirum videatur, non tamen impoſſibile videri <lb/>debet, eum enim hæc reſonantia fiat per reflexionem, reflexio autem omnis fiat per lineas, & </s> <s xml:id="echoid-s18858" xml:space="preserve">angulos meri-<lb/>to eam lineis, & </s> <s xml:id="echoid-s18859" xml:space="preserve">angulis reſerendam eſſe duximus. </s> <s xml:id="echoid-s18860" xml:space="preserve">ſed in primis exponendæ ſunt ſequentes deſinitiones.</s> <s xml:id="echoid-s18861" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18862" xml:space="preserve">Quarta. </s> <s xml:id="echoid-s18863" xml:space="preserve">Sonorum, ſiue canorum nobis hic eſt omne corpus ſonum, aut vocem primam emittens.</s> <s xml:id="echoid-s18864" xml:space="preserve"/> </p> <pb o="220" file="0242" n="247" rhead="DE ECHO."/> <p> <s xml:id="echoid-s18865" xml:space="preserve">Quinta. </s> <s xml:id="echoid-s18866" xml:space="preserve">Linea recta ſonora, ſeu vocalis eſt, ſecundum quam vox in directum propagatur.</s> <s xml:id="echoid-s18867" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18868" xml:space="preserve">Quod pręterea ſonus in aperto, ac libero quoquouerſus per lineas diſſundatur, hiſce rationibus palam fiet; <lb/></s> <s xml:id="echoid-s18869" xml:space="preserve">quarum prima fit ab experientia; </s> <s xml:id="echoid-s18870" xml:space="preserve">nam multo melius ad omnes plagas ſonum audimus, cum inter nos, & </s> <s xml:id="echoid-s18871" xml:space="preserve">ſo-<lb/>norum nihil directè interponitur, quod eius directæ ad nos productioni obſtet, quam cum quippiam interij-<lb/>citur. </s> <s xml:id="echoid-s18872" xml:space="preserve">Secunda, Echo ipſa idem manifeſtat, ipſa etenim nuſq; </s> <s xml:id="echoid-s18873" xml:space="preserve">reſonat, niſi vbi vox per lineam rectam à ſo-<lb/>noro ad reflectens procurrit, vnde poſtea reſilit. </s> <s xml:id="echoid-s18874" xml:space="preserve">Tertia, ſicuti in lumine, & </s> <s xml:id="echoid-s18875" xml:space="preserve">viſione in confeſſo eſt, rectas vn-<lb/>diq; </s> <s xml:id="echoid-s18876" xml:space="preserve">lineas dari oportere, quidni etiam in iono, & </s> <s xml:id="echoid-s18877" xml:space="preserve">voce? </s> <s xml:id="echoid-s18878" xml:space="preserve">Quarta, huius rei cauſa eſt, quod natura agit per li-<lb/>neas breuiſſimas, breuiſſimæ autem ſunt rectæ, ad quaſuis plagas extendantur.</s> <s xml:id="echoid-s18879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18880" xml:space="preserve">Cæterum dixi (in loco aperto, aclibero) quod, vt vulgo notum eſt, ſonus, & </s> <s xml:id="echoid-s18881" xml:space="preserve">vox vel tenuiſſima per tu-<lb/>bos, & </s> <s xml:id="echoid-s18882" xml:space="preserve">canales, etiam curuos, ceu per ſon@ ductus, optimè defertur, ac longius quam in aperto propagatur. <lb/></s> <s xml:id="echoid-s18883" xml:space="preserve">hac ratione in cænationibus concameratis, in quibus anguli caui parietum cont nuantur cauis angulis, qui <lb/>per fornicem diametraliter tranſcendunt ad oppoſitum angulum parietum, etiamſi quis ſubmiſſe loquatur <lb/>in vno parietum angulo, ore in angulum obuerſo, exauditur tamen ab altero. </s> <s xml:id="echoid-s18884" xml:space="preserve">in altero angulo oppoſito au-<lb/>ſcultante, nihil interim audientibus intermedijs. </s> <s xml:id="echoid-s18885" xml:space="preserve">id multis in locis licet experiri, ſed præcipuè celebr s eſt <lb/>Aula Sereniſs. </s> <s xml:id="echoid-s18886" xml:space="preserve">Ducis Mantuæ. </s> <s xml:id="echoid-s18887" xml:space="preserve">cauſa eſt, quia vox per angulum veluti per canalem vnita, & </s> <s xml:id="echoid-s18888" xml:space="preserve">clauſa, aſcendit <lb/>etiam per fornicis canalem, & </s> <s xml:id="echoid-s18889" xml:space="preserve">ad oppoſitum murorum angulum deſcendit vbi exauditur. </s> <s xml:id="echoid-s18890" xml:space="preserve">quod ſi in fornice <lb/>ſint anguli non caui, ſed conuexi, & </s> <s xml:id="echoid-s18891" xml:space="preserve">prominentes, ſeu adſit planum laqueare, vox illuc offendens, non vnita <lb/>pergit, ſed latè diſpergitur. </s> <s xml:id="echoid-s18892" xml:space="preserve">Porro huluſmodi vocum propagationes, cum non fiant per reflexionem, inſti-<lb/>tutæ tractationi cenſendæ ſunt alienæ.</s> <s xml:id="echoid-s18893" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18894" xml:space="preserve">Sexta. </s> <s xml:id="echoid-s18895" xml:space="preserve">Linea ſonora actiuitatis, actioniſuè, eſt ea ſecundum quam ſonus quam longiſſimè propagari po-<lb/>teſt. </s> <s xml:id="echoid-s18896" xml:space="preserve">dicitur etiam ſemidiameter ſphæræ actionis.</s> <s xml:id="echoid-s18897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18898" xml:space="preserve">Septima. </s> <s xml:id="echoid-s18899" xml:space="preserve">Reflectens eſt omne corpus, quod ſonum modulatum, aut articulatum reflectere poteſt ad ip-<lb/>ſum ſonorum, ad aliumuè, quod nos aliquando, & </s> <s xml:id="echoid-s18900" xml:space="preserve">murum, & </s> <s xml:id="echoid-s18901" xml:space="preserve">parietem dicemus.</s> <s xml:id="echoid-s18902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18903" xml:space="preserve">Octaua. </s> <s xml:id="echoid-s18904" xml:space="preserve">Sonora linea directa, ſeu incldens eſt ea, ſecundum quam ſonus primus ã ſonoro manans rectà in <lb/>obiectum aliquod corpus incidit.</s> <s xml:id="echoid-s18905" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18906" xml:space="preserve">Nona. </s> <s xml:id="echoid-s18907" xml:space="preserve">Linea vocalis reflexa eſt ea, ſecundum quam ſonus ad obiectum corpus colliſus reflectitur. </s> <s xml:id="echoid-s18908" xml:space="preserve">Quæ <lb/>omnia vt probè percipiantur, prænotandum eſt, quatuor eſſe, quæ eadem ratione per lineas incidentes, & </s> <s xml:id="echoid-s18909" xml:space="preserve"><lb/>reflexus explicari oporteat, lumen, & </s> <s xml:id="echoid-s18910" xml:space="preserve">viſionem; </s> <s xml:id="echoid-s18911" xml:space="preserve">ſonum, & </s> <s xml:id="echoid-s18912" xml:space="preserve">auditionem ſicuti enim perſpectiui in luminis <lb/>profuſione, & </s> <s xml:id="echoid-s18913" xml:space="preserve">reflexione conſiderant lineam radioſam, ſeu radium incidentem, & </s> <s xml:id="echoid-s18914" xml:space="preserve">reflexum in viſione pari-<lb/> <anchor type="figure" xlink:label="fig-0242-01a" xlink:href="fig-0242-01"/> ter concipiunt lineam incidentem, & </s> <s xml:id="echoid-s18915" xml:space="preserve">reflexam. </s> <s xml:id="echoid-s18916" xml:space="preserve">eadem ratione <lb/>par eſt in ſoni prolatione, & </s> <s xml:id="echoid-s18917" xml:space="preserve">reflexione lineas ſonoras, & </s> <s xml:id="echoid-s18918" xml:space="preserve">voca-<lb/>les ſtatuere, quarum aliæ ſint incidentes, aliæ reflexæ. </s> <s xml:id="echoid-s18919" xml:space="preserve">Earum <lb/>autem productio melius figuræ huius exemplo percipietur. </s> <s xml:id="echoid-s18920" xml:space="preserve">in <lb/>qua ſonorum ſit vbi A. </s> <s xml:id="echoid-s18921" xml:space="preserve">corpus autem ſonum reflectens ſit paries <lb/>C B D. </s> <s xml:id="echoid-s18922" xml:space="preserve">dum igitur ſonus ab A. </s> <s xml:id="echoid-s18923" xml:space="preserve">quaquauerſum diffunditur, in <lb/>oppoſitum parietem impingit. </s> <s xml:id="echoid-s18924" xml:space="preserve">in qua vocis diffuſione licebit <lb/>concipere innumeras lineas, quarum tres tantum hic depingun-<lb/>tur A B. </s> <s xml:id="echoid-s18925" xml:space="preserve">A C. </s> <s xml:id="echoid-s18926" xml:space="preserve">A D. </s> <s xml:id="echoid-s18927" xml:space="preserve">ſecundum quas vox parieti incidit, ideoq; <lb/></s> <s xml:id="echoid-s18928" xml:space="preserve">lineæ incidentiæ dicuntur, harum omnium vna A B. </s> <s xml:id="echoid-s18929" xml:space="preserve">propriè eſt <lb/>parieti perpendicularis, ſeu normalis, quia ad angulos rectos ei <lb/>accidit. </s> <s xml:id="echoid-s18930" xml:space="preserve">reliquę omnes, quales ſunt A C. </s> <s xml:id="echoid-s18931" xml:space="preserve">A D. </s> <s xml:id="echoid-s18932" xml:space="preserve">eidem obliquè oc-<lb/>currunt. </s> <s xml:id="echoid-s18933" xml:space="preserve">licebit pariter innumeras lineas à pariete reflexas ima-<lb/>ginari, quæ totidẽ incidentibus reſpondeant: </s> <s xml:id="echoid-s18934" xml:space="preserve">harum hic tantum <lb/>tres depinguntur; </s> <s xml:id="echoid-s18935" xml:space="preserve">C F. </s> <s xml:id="echoid-s18936" xml:space="preserve">reflexa ipſius A C. </s> <s xml:id="echoid-s18937" xml:space="preserve">B A. </s> <s xml:id="echoid-s18938" xml:space="preserve">reflexa ipſius <lb/>A B. </s> <s xml:id="echoid-s18939" xml:space="preserve">normalis; </s> <s xml:id="echoid-s18940" xml:space="preserve">normales enim in ſe ipſas reciprocantur: </s> <s xml:id="echoid-s18941" xml:space="preserve">D E. </s> <s xml:id="echoid-s18942" xml:space="preserve"><lb/>tandem reflexa ipſius A D. </s> <s xml:id="echoid-s18943" xml:space="preserve">vbi notandum eſt, lineam reflexam obliquam ſemper reflecti in partem alteram, <lb/>ſeu directè oppoſitam ſuæ incidentis, ita vtambæ, & </s> <s xml:id="echoid-s18944" xml:space="preserve">incidens, & </s> <s xml:id="echoid-s18945" xml:space="preserve">roflexa poſſint eſſe in eadem plana ſuperfi-<lb/>cie, quæ tranſiret per lineam normalem A B. </s> <s xml:id="echoid-s18946" xml:space="preserve">necnon per lineas incidentes A C. </s> <s xml:id="echoid-s18947" xml:space="preserve">A D. </s> <s xml:id="echoid-s18948" xml:space="preserve">faceretque in pariete <lb/>lineam G C B D H. </s> <s xml:id="echoid-s18949" xml:space="preserve">hæc de ſonoris lineis, nunc de angulis earundem.</s> <s xml:id="echoid-s18950" xml:space="preserve"/> </p> <div xml:id="echoid-div476" type="float" level="2" n="1"> <figure xlink:label="fig-0242-01" xlink:href="fig-0242-01a"> <image file="0242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0242-01"/> </figure> </div> <p> <s xml:id="echoid-s18951" xml:space="preserve">Decima. </s> <s xml:id="echoid-s18952" xml:space="preserve">Angulus incidentiæ lineæ obliquæ hic eſt quem facit linea obliquà incidens, cum linea in pa-<lb/>riete ducta à termino lineæ normalis per terminum lineæ obliquæ incidentis (qualis in præſenti figura eſt <lb/>linea B C G. </s> <s xml:id="echoid-s18953" xml:space="preserve">tranſit enim per B. </s> <s xml:id="echoid-s18954" xml:space="preserve">& </s> <s xml:id="echoid-s18955" xml:space="preserve">C. </s> <s xml:id="echoid-s18956" xml:space="preserve">terminos linearum A B. </s> <s xml:id="echoid-s18957" xml:space="preserve">A C. </s> <s xml:id="echoid-s18958" xml:space="preserve">talis eſt etiam linea B D H. </s> <s xml:id="echoid-s18959" xml:space="preserve">trannens <lb/>per terminos B D. </s> <s xml:id="echoid-s18960" xml:space="preserve">linearum A B. </s> <s xml:id="echoid-s18961" xml:space="preserve">A D.) </s> <s xml:id="echoid-s18962" xml:space="preserve">anguli igitur incidentiæ ſunt A C B. </s> <s xml:id="echoid-s18963" xml:space="preserve">A D B. </s> <s xml:id="echoid-s18964" xml:space="preserve">angulus incidentiæ <lb/>lineæ normalis eſt quem ipſa facit cum quauis linea in pariete ducta per ſuum terminum B. </s> <s xml:id="echoid-s18965" xml:space="preserve">qualis erit an-<lb/>gulus A B C. </s> <s xml:id="echoid-s18966" xml:space="preserve">& </s> <s xml:id="echoid-s18967" xml:space="preserve">A B D.</s> <s xml:id="echoid-s18968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18969" xml:space="preserve">Vndecima. </s> <s xml:id="echoid-s18970" xml:space="preserve">Angulus reflexionis lineæ obliquæ is eſt, quem facit linea reflexa obliqua cum prædicta linea <lb/>in pariete: </s> <s xml:id="echoid-s18971" xml:space="preserve">tales ſunt anguli F C G. </s> <s xml:id="echoid-s18972" xml:space="preserve">E D H. </s> <s xml:id="echoid-s18973" xml:space="preserve">angulus reflexionis lineę normalis is eſt quem ipſa facit cum prę-<lb/>dicta linea, quales ſunt anguli C B A. </s> <s xml:id="echoid-s18974" xml:space="preserve">B D A. </s> <s xml:id="echoid-s18975" xml:space="preserve">notandum eſt angulum hunc reflexionis ſemper vergere ad <lb/>partem directè auerſam angulo incidentiæ, quoniam fit a linea reflexa, quæ vti ſupra notatnm eſt, illuc pa-<lb/>riter tendit. </s> <s xml:id="echoid-s18976" xml:space="preserve">porrò ex prænotatis facile eſt varias Echus diuiſiones; </s> <s xml:id="echoid-s18977" xml:space="preserve">acſpecies definire; </s> <s xml:id="echoid-s18978" xml:space="preserve">nam,</s> </p> <p> <s xml:id="echoid-s18979" xml:space="preserve">Duodecima, alia eſt normalis, & </s> <s xml:id="echoid-s18980" xml:space="preserve">reciproca, quæ ſcilieet reflectitur per eandem lineam: </s> <s xml:id="echoid-s18981" xml:space="preserve">alia vero obliqua, <lb/>quæ obliquè per diuerſam lineam a primaria reflectitur, quaſi & </s> <s xml:id="echoid-s18982" xml:space="preserve">ad alium auditorem, quam ad ſonorum. </s> <s xml:id="echoid-s18983" xml:space="preserve">hęc <lb/>autem aut fit per vnam tantum reflexionem, aut per plures.</s> <s xml:id="echoid-s18984" xml:space="preserve"/> </p> <pb o="221" file="0243" n="248" rhead="DE ECHO."/> <p> <s xml:id="echoid-s18985" xml:space="preserve">Decimatertia, alia item eſt ad ipſum ſonorum reflexa, & </s> <s xml:id="echoid-s18986" xml:space="preserve">hæc aut normalis aut obliqua, & </s> <s xml:id="echoid-s18987" xml:space="preserve">per plures refle-<lb/>xiones. </s> <s xml:id="echoid-s18988" xml:space="preserve">alia verò eſt ad alterum auditorem; </s> <s xml:id="echoid-s18989" xml:space="preserve">hæcq; </s> <s xml:id="echoid-s18990" xml:space="preserve">aut normalis, aut obliqua.</s> <s xml:id="echoid-s18991" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18992" xml:space="preserve">Decimaquarta, alia eſt monoſyllaba, alia diſſyllaba, alia triſyllaba, & </s> <s xml:id="echoid-s18993" xml:space="preserve">c. </s> <s xml:id="echoid-s18994" xml:space="preserve">pro numero ſyllabarum, quas <lb/>repetit.</s> <s xml:id="echoid-s18995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18996" xml:space="preserve">Decimaquinta, alia eſt Echo monophona, ſeu ſimplex, quæ ſemel ſcilicet tantum reſonat; </s> <s xml:id="echoid-s18997" xml:space="preserve">alia verò poly-<lb/>phona, quæ ſæpius; </s> <s xml:id="echoid-s18998" xml:space="preserve">diphona quæ bis, triphona quæ ter, heptaphona quæ ſepties, & </s> <s xml:id="echoid-s18999" xml:space="preserve">c. </s> <s xml:id="echoid-s19000" xml:space="preserve">reſpondet.</s> <s xml:id="echoid-s19001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19002" xml:space="preserve">Decimaſexta, alia tandem clara, & </s> <s xml:id="echoid-s19003" xml:space="preserve">ſonora; </s> <s xml:id="echoid-s19004" xml:space="preserve">alia vero ſubmiſſa, ac taciturna. </s> <s xml:id="echoid-s19005" xml:space="preserve">Quæ omnia ex demon-<lb/>ſtrandis reddentur clariora.</s> <s xml:id="echoid-s19006" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div478" type="section" level="1" n="362"> <head xml:id="echoid-head381" style="it" xml:space="preserve">Anguli incidentiæ, & reflexionis lineæ ſonoræ ſunt inuicem æquales. Theorema I.</head> <p> <s xml:id="echoid-s19007" xml:space="preserve">SIcuti in radijs lucis, & </s> <s xml:id="echoid-s19008" xml:space="preserve">viſus, prædicti anguli æquales exiſtunt, vt optimè optici oſtendunt: </s> <s xml:id="echoid-s19009" xml:space="preserve">ijdem eadem <lb/>ratione exiſtimandi hic quoq; </s> <s xml:id="echoid-s19010" xml:space="preserve">ſunt æquales. </s> <s xml:id="echoid-s19011" xml:space="preserve">quod probè experientia confirmat, ſi enim duo ſint ab eo-<lb/> <anchor type="figure" xlink:label="fig-0243-01a" xlink:href="fig-0243-01"/> dem pariete, necnon ab inuicem ita diſtantes, <lb/>vt vnus audiat alterius Echum, fiunt prædicti <lb/>anguliæquales. </s> <s xml:id="echoid-s19012" xml:space="preserve">vt in ſequẽti figura, ſi ſonorum <lb/>fit vbi A. </s> <s xml:id="echoid-s19013" xml:space="preserve">audiens autem Echum ipſius ex reper-<lb/>cuſſu parietis D B E. </s> <s xml:id="echoid-s19014" xml:space="preserve">ſit v. </s> <s xml:id="echoid-s19015" xml:space="preserve">g. </s> <s xml:id="echoid-s19016" xml:space="preserve">vbi C. </s> <s xml:id="echoid-s19017" xml:space="preserve">obſeruatio <lb/>docet reflexionem fieri, in tali pariet s loco, vt <lb/>lineæ ductę ab eo, ad ſonorum vna altera ad au-<lb/>dientem, faciant angulos D B A. </s> <s xml:id="echoid-s19018" xml:space="preserve">E B C. </s> <s xml:id="echoid-s19019" xml:space="preserve">æqua-<lb/>les. </s> <s xml:id="echoid-s19020" xml:space="preserve">ratio vero, ſeu cauſa huius æqualitatis eſt <lb/>quia natura (niſi quod obſiet) agit per lineas <lb/>breuiſſimas, breuiſſimæ autem ſunt in caſu no-<lb/>ſtro, quæ faciunt prædictos angulos compares, <lb/>ideſt, ex omnibus lineis, quæ poſſunt duci ab A. <lb/></s> <s xml:id="echoid-s19021" xml:space="preserve">per parietem D B C. </s> <s xml:id="echoid-s19022" xml:space="preserve">ad C. </s> <s xml:id="echoid-s19023" xml:space="preserve">breuiſſimę omnium <lb/>illæ ſunt, quæ faciunt prædictos angulos æqua-<lb/>les. </s> <s xml:id="echoid-s19024" xml:space="preserve">quod demonſtratum habesà Vitellione lib. </s> <s xml:id="echoid-s19025" xml:space="preserve">1. </s> <s xml:id="echoid-s19026" xml:space="preserve">num. </s> <s xml:id="echoid-s19027" xml:space="preserve">17. </s> <s xml:id="echoid-s19028" xml:space="preserve">Tandem, hanc angulorum æqualitatem agnouit <lb/>etiam Ariſtoteles, qui 2. </s> <s xml:id="echoid-s19029" xml:space="preserve">de Anim. </s> <s xml:id="echoid-s19030" xml:space="preserve">tex. </s> <s xml:id="echoid-s19031" xml:space="preserve">80. </s> <s xml:id="echoid-s19032" xml:space="preserve">appoſitè docet, hanc reflexionem fieri eo modo quo pila luioria <lb/>reflectitur, ea enim normaliter parieti, aut pauimento alliſa, etiam normaliter reſilit. </s> <s xml:id="echoid-s19033" xml:space="preserve">ſi verò obliquè, ea quo-<lb/>que obliquè, necnon compari angulo in auerſam partem reſultat. </s> <s xml:id="echoid-s19034" xml:space="preserve">imo expreſsè in Probl. </s> <s xml:id="echoid-s19035" xml:space="preserve">ſect. </s> <s xml:id="echoid-s19036" xml:space="preserve">11. </s> <s xml:id="echoid-s19037" xml:space="preserve">num. </s> <s xml:id="echoid-s19038" xml:space="preserve">23. </s> <s xml:id="echoid-s19039" xml:space="preserve">aſ-<lb/>ſerit hanc reflexionem fieri per angulos æquales.</s> <s xml:id="echoid-s19040" xml:space="preserve"/> </p> <div xml:id="echoid-div478" type="float" level="2" n="1"> <figure xlink:label="fig-0243-01" xlink:href="fig-0243-01a"> <image file="0243-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243-01"/> </figure> </div> </div> <div xml:id="echoid-div480" type="section" level="1" n="363"> <head xml:id="echoid-head382" style="it" xml:space="preserve">Echo reſonat ex corporihus planis, & ſolidis. Theorema 11.</head> <p> <s xml:id="echoid-s19041" xml:space="preserve">VEritas huius propoſitionis multis obſeruationibus nobis conſtitit: </s> <s xml:id="echoid-s19042" xml:space="preserve">experti enim ſumus omnes muros <lb/>domorum, & </s> <s xml:id="echoid-s19043" xml:space="preserve">omnia mænia vrbium, ſi ſatis ſint complanata, in debita diſtantia, ac debito ſitu ſonori ad <lb/>ipſa, noſtra verba repetere: </s> <s xml:id="echoid-s19044" xml:space="preserve">etiamſi intus omninò ſint ſolida, fine vllo cõelaui, ſine vllis feneſtris: </s> <s xml:id="echoid-s19045" xml:space="preserve">vti ſunt mæ-<lb/>nia intus congeſta humo ſtipata. </s> <s xml:id="echoid-s19046" xml:space="preserve">idem præſtant rupes montium, & </s> <s xml:id="echoid-s19047" xml:space="preserve">ripæ fluminum, quamuis in eis nihil ca-<lb/>uernoſum, aut anfractuoſum ſit, quod reſonantium iuuare videatur. </s> <s xml:id="echoid-s19048" xml:space="preserve">quaproptes huiuſmodi corpus vocem <lb/>reflectens, eſt quaſi planum ſpeculum vocis; </s> <s xml:id="echoid-s19049" xml:space="preserve">vnde & </s> <s xml:id="echoid-s19050" xml:space="preserve">vox ipſa reflexa aptè dicitur à Poetis imago vocis. </s> <s xml:id="echoid-s19051" xml:space="preserve">ru-<lb/>pes vero, & </s> <s xml:id="echoid-s19052" xml:space="preserve">cliui herboſi, vel arui, alioquin plani, neutiquam reſonant, cum non ſatis complanati ſunt. </s> <s xml:id="echoid-s19053" xml:space="preserve">por-<lb/>rò complanatio hæc reflectentis corporis efficit, vt plures lineæ ad ſenſum ferè normales reflectantur. </s> <s xml:id="echoid-s19054" xml:space="preserve">con-<lb/>trarium autem inæqualitas, & </s> <s xml:id="echoid-s19055" xml:space="preserve">aſperitas (qualis eſt in muris cæmentitijs nullo tectorio illitis efficiunt; </s> <s xml:id="echoid-s19056" xml:space="preserve">quo-<lb/>niam inter lapides, & </s> <s xml:id="echoid-s19057" xml:space="preserve">cæmenta ſunt concauitates, & </s> <s xml:id="echoid-s19058" xml:space="preserve">prominentiæ, quæ lineas vocales incidentes tumultua-<lb/>riè huc illuc diſpergunt, & </s> <s xml:id="echoid-s19059" xml:space="preserve">confundunt, quare aut nullam, aut imperfectam valdè Echum reddere poſſunt. <lb/></s> <s xml:id="echoid-s19060" xml:space="preserve">Quæ omnia, etſi nulla experientia fulcirentur, ratio tamen ipſa conuinceret. </s> <s xml:id="echoid-s19061" xml:space="preserve">qua enim de cauſa pila in parie-<lb/>tem alliſa reſilit, & </s> <s xml:id="echoid-s19062" xml:space="preserve">lumen in ſpeculum incidens, reflectitur, eadem etiam ratione vox planis corporibus oc-<lb/>currens, ex ijs reſultare, & </s> <s xml:id="echoid-s19063" xml:space="preserve">repeili neceſſe eſt.</s> <s xml:id="echoid-s19064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19065" xml:space="preserve">Cæterum cum dicimus reflectens eſſe corpus ſolidum, id ita accipiendum eſt, vt ſolum tantæ ſit ſoli@ita-<lb/>tis, ſeu duritiei, vt aeri ob ſonum commoto, nihil cedat, ſed ei ita obſiſtat, vt eam reflectat. </s> <s xml:id="echoid-s19066" xml:space="preserve">qua ratione aqua, <lb/>quamuis fluida, aeri tamen comparata, ſolida, & </s> <s xml:id="echoid-s19067" xml:space="preserve">dura cenſeri debet id quod experientia in aqua puteorum <lb/>manifectè probat, nam ſuperficies aquæ puteanæ tantæ profunditatis, quanta debet eſſe diſtantia ſonori a <lb/>reflectente (de qua poſtea dicemus) Echũ perfectè ſurium reflectit. </s> <s xml:id="echoid-s19068" xml:space="preserve">quod ipſe in puteis 50. </s> <s xml:id="echoid-s19069" xml:space="preserve">vlnis, ſeu 24. </s> <s xml:id="echoid-s19070" xml:space="preserve">paſſi-<lb/>bus Geometricis circiter altis expertus ſum, qui adeo loquaces, & </s> <s xml:id="echoid-s19071" xml:space="preserve">garruli erant, vt etiã @ubmiſſę voci perbel <lb/>lè reſponderent. </s> <s xml:id="echoid-s19072" xml:space="preserve">Vbi illud obſeruaui, quod etiam ſatis profundi ſint putęi, non tamen niſi ſub dio ſint, Echũ <lb/>reſonant. </s> <s xml:id="echoid-s19073" xml:space="preserve">ratio, ni fallor eſt, quia quando ſunt ſub tecto, aut cõcameratione, fiunt ſimul duę reflect onis inui-<lb/>cem cõtrariæ, vox enim primo reflectitur ex tecto, vel fornice deorſum, ſecundo ex aqua ſurſum; </s> <s xml:id="echoid-s19074" xml:space="preserve">illa deſcen-<lb/>dens occurrit huic alteri aſcendenti, eiq; </s> <s xml:id="echoid-s19075" xml:space="preserve">obuians impedimento eſt, ne clara ac diſtincta ref@ecti poſſit. </s> <s xml:id="echoid-s19076" xml:space="preserve">cũ au-<lb/>tem ſub dio puteus eſt, fit vnica tantum reflexio ſurſum, abſq; </s> <s xml:id="echoid-s19077" xml:space="preserve">vllo impedimento, ſicq; </s> <s xml:id="echoid-s19078" xml:space="preserve">clariſſimè reſonant.</s> <s xml:id="echoid-s19079" xml:space="preserve"/> </p> <pb o="222" file="0244" n="249" rhead="DE ECHO."/> </div> <div xml:id="echoid-div481" type="section" level="1" n="364"> <head xml:id="echoid-head383" style="it" xml:space="preserve">Echo reſonat ex planis, quibus ſonus per lineam normalem occurrit. Theorema III.</head> <p> <s xml:id="echoid-s19080" xml:space="preserve">ID primo docet obſeruatio, vt in pręcedenti prima figura, ſi ſonorũ in A. </s> <s xml:id="echoid-s19081" xml:space="preserve">ſit in eo fitu ad parietem C B D. <lb/></s> <s xml:id="echoid-s19082" xml:space="preserve">vt vox per lineam A B. </s> <s xml:id="echoid-s19083" xml:space="preserve">delata, normaliter offenſet ad parietem in B. </s> <s xml:id="echoid-s19084" xml:space="preserve">eadem vox articulata repercutitur ad <lb/>idem A. </s> <s xml:id="echoid-s19085" xml:space="preserve">ſi vero ſit in tali ſitu, vnde vox obliquè tantum in murum incidat, vox non reuertitur ad idem A. </s> <s xml:id="echoid-s19086" xml:space="preserve"><lb/>quod præterea ratio ſuadet, cum enim probatum ſi@ reflexionem hanc fieri per angulos æquales angulis in-<lb/>cidentiæ; </s> <s xml:id="echoid-s19087" xml:space="preserve">angulis autem incidentiæ ſint recti, ſequitur angulos etiam reflexionis eſſe rectos, ac propterea vo-<lb/>cem à muro reflecti per eandem lineam, per quam muro incidit, hacq; </s> <s xml:id="echoid-s19088" xml:space="preserve">ratione ad ipſum A. </s> <s xml:id="echoid-s19089" xml:space="preserve">ſonorum reuer-<lb/>ti. </s> <s xml:id="echoid-s19090" xml:space="preserve">Porrò quamuis ex innumeris lineis, quæ ex A. </s> <s xml:id="echoid-s19091" xml:space="preserve">ad parietem tendunt, vna tantum Geometricè loquendo <lb/>normalis ſit, vti A B. </s> <s xml:id="echoid-s19092" xml:space="preserve">cæteræ tamen ei propiores ſecundum ſenſum, pro normalibus aſſumi debent, vt om-<lb/>nes ſimul ad Echum efficiendam ſufficiant; </s> <s xml:id="echoid-s19093" xml:space="preserve">omnes enim ſimul aerem circa ſonorum A. </s> <s xml:id="echoid-s19094" xml:space="preserve">exiſtentem commo-<lb/>uent. </s> <s xml:id="echoid-s19095" xml:space="preserve">Ea propter exiſtimo paruam eſſe muri partem, quæ reaſpe reflectit ad ſonorum A. </s> <s xml:id="echoid-s19096" xml:space="preserve">quod etiam obſer-<lb/>uationi conguit; </s> <s xml:id="echoid-s19097" xml:space="preserve">ſæpius enim obſeruaui exiguos parietes, vti tripedales, aut modicas rupes, humanas voces <lb/>perbellè ementiri. </s> <s xml:id="echoid-s19098" xml:space="preserve">Quod ſi Echo exaudiretur tantum per lineas reflexas a reflectente ad aures ſonori ipſum <lb/>reflectẽs exiguum admodum euaderet, eius ſcilicet latitudinis, quæ æqualis eſſet dimidio interuallo aurium <lb/>audientis, quod ſic oſtendo. </s> <s xml:id="echoid-s19099" xml:space="preserve">ſit in ſequenti figura linea B C. </s> <s xml:id="echoid-s19100" xml:space="preserve">interuallum aurium, medium eius A. </s> <s xml:id="echoid-s19101" xml:space="preserve">reflectens <lb/> <anchor type="figure" xlink:label="fig-0244-01a" xlink:href="fig-0244-01"/> ſit D E. </s> <s xml:id="echoid-s19102" xml:space="preserve">æquale ipſi A B. </s> <s xml:id="echoid-s19103" xml:space="preserve">vel A C. </s> <s xml:id="echoid-s19104" xml:space="preserve">medium eius <lb/>ſit F. </s> <s xml:id="echoid-s19105" xml:space="preserve">ſitque linea A F. </s> <s xml:id="echoid-s19106" xml:space="preserve">ipſi normalis. </s> <s xml:id="echoid-s19107" xml:space="preserve">iam intel-<lb/>ligatur linea vocalis incidens, & </s> <s xml:id="echoid-s19108" xml:space="preserve">r@flexa ſimul <lb/>A D B. </s> <s xml:id="echoid-s19109" xml:space="preserve">ad aurem B. </s> <s xml:id="echoid-s19110" xml:space="preserve">pariter ad aurem C. </s> <s xml:id="echoid-s19111" xml:space="preserve">ſit linea <lb/>vocalis incidens, & </s> <s xml:id="echoid-s19112" xml:space="preserve">reflexa A E C. </s> <s xml:id="echoid-s19113" xml:space="preserve">erũt enim an <lb/>guli ad D. </s> <s xml:id="echoid-s19114" xml:space="preserve">& </s> <s xml:id="echoid-s19115" xml:space="preserve">E. </s> <s xml:id="echoid-s19116" xml:space="preserve">incidentiæ, & </s> <s xml:id="echoid-s19117" xml:space="preserve">reflexioni<unsure/>s æqua-<lb/>les, quare totum reflectens D F E. </s> <s xml:id="echoid-s19118" xml:space="preserve">non amplius <lb/>patebit quam D E. </s> <s xml:id="echoid-s19119" xml:space="preserve">quod ex ſuppoſitione a qua-<lb/>le eſt ipſi A B. </s> <s xml:id="echoid-s19120" xml:space="preserve">dimidio aurium interſtitio. </s> <s xml:id="echoid-s19121" xml:space="preserve">Ve-<lb/>rum quia hæc vocis reflexa propagatur videtur <lb/>indigere adhuc maiori aeris commotione, cu-<lb/>ius certa quãtitas ignoratur, ideo difficile quo-<lb/>que erit reflectentis paruitatem determinare.</s> <s xml:id="echoid-s19122" xml:space="preserve"/> </p> <div xml:id="echoid-div481" type="float" level="2" n="1"> <figure xlink:label="fig-0244-01" xlink:href="fig-0244-01a"> <image file="0244-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-01"/> </figure> </div> <p> <s xml:id="echoid-s19123" xml:space="preserve">Cæterum cum hæc reflexio à B. </s> <s xml:id="echoid-s19124" xml:space="preserve">ad A. </s> <s xml:id="echoid-s19125" xml:space="preserve">in prima figura neceſſario fiat per lineam B A. </s> <s xml:id="echoid-s19126" xml:space="preserve">& </s> <s xml:id="echoid-s19127" xml:space="preserve">alias ei propiores, <lb/>manifeſtum euadit vocalem hanc reflexionem fieri per lineas reflexas, quæ ſint eædem cum incidentibus, <lb/>ſicuti reflexa B A. </s> <s xml:id="echoid-s19128" xml:space="preserve">eſt eadem cum incidente A B. </s> <s xml:id="echoid-s19129" xml:space="preserve">& </s> <s xml:id="echoid-s19130" xml:space="preserve">præterea fieri per angulos reflexionis, angulis inciden-<lb/>tiæ æquales; </s> <s xml:id="echoid-s19131" xml:space="preserve">ſic in figura angulis incidentiæ A B C. </s> <s xml:id="echoid-s19132" xml:space="preserve">A B D. </s> <s xml:id="echoid-s19133" xml:space="preserve">æquales ſunt angult reflexion@s C B A. </s> <s xml:id="echoid-s19134" xml:space="preserve">D B A. <lb/></s> <s xml:id="echoid-s19135" xml:space="preserve">cum ſint ijdem re vera cum illis, ac proinde omnes ſint recti.</s> <s xml:id="echoid-s19136" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div483" type="section" level="1" n="365"> <head xml:id="echoid-head384" style="it" xml:space="preserve">Muri plant quibus ſonus oblique tantum occurrit, non reflectunt Echum <lb/>ad ipſum ſonorum. Theorema IV.</head> <p> <s xml:id="echoid-s19137" xml:space="preserve">ID ex præmiſſis facilè deducitur, ſi enim omnes lineæ murum obliquè petunt, obliquè pariter, & </s> <s xml:id="echoid-s19138" xml:space="preserve">quidem <lb/>in auerſam partem excurrent; </s> <s xml:id="echoid-s19139" xml:space="preserve">quare omnis illa vox reflexa, neutiquam ad ſonorum reuertitur, ſed in <lb/>auerſam ab eo partem deflectet. </s> <s xml:id="echoid-s19140" xml:space="preserve">quod etiam experientia comprobat. </s> <s xml:id="echoid-s19141" xml:space="preserve">vt in ſuperiori ſecunda figura, ſit ſono-<lb/>rum A. </s> <s xml:id="echoid-s19142" xml:space="preserve">in eo ſitu ad murum D B E. </s> <s xml:id="echoid-s19143" xml:space="preserve">ſupra horizontem erectum, ad quem omnis linea vocalis obliquè ſatis <lb/>occurrat, vti facit@linea A E. </s> <s xml:id="echoid-s19144" xml:space="preserve">eius reflexa iuxta leges angulorum incidentiæ, & </s> <s xml:id="echoid-s19145" xml:space="preserve">reflexionis ſit B C. </s> <s xml:id="echoid-s19146" xml:space="preserve">palam eſt <lb/>Echum exaudiri ab altero. </s> <s xml:id="echoid-s19147" xml:space="preserve">quare ſi paries ſit adeo magnus, vt ei in orbem vox obliquè accidat, Echo pariter <lb/>in orbem exaudi ri poterit, ab auditoribus ſcilicet in orbem è regione muri conſtitutis.</s> <s xml:id="echoid-s19148" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div484" type="section" level="1" n="366"> <head xml:id="echoid-head385" style="it" xml:space="preserve">Conſectarium.</head> <figure> <image file="0244-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-02"/> </figure> <p> <s xml:id="echoid-s19149" xml:space="preserve">HInc palam fit cur ædificia in edito ſita, ſonoro in planitie <lb/>conſtituto, non ei reſonent Echo. </s> <s xml:id="echoid-s19150" xml:space="preserve">ratio eſt quoniam omnes <lb/>lineæ a ſonoro ſurſum aſcendentes obliquè hiſce muris occurrunt, <lb/>ac proinde ſurſum verſum reflectuntur; </s> <s xml:id="echoid-s19151" xml:space="preserve">vnde tota illa vox, iuxta <lb/>leges angulorum incidentiæ, & </s> <s xml:id="echoid-s19152" xml:space="preserve">reflexionis in altum reuerbera-<lb/>tur. </s> <s xml:id="echoid-s19153" xml:space="preserve">vtin hac ſequenti figura omnes lineæ ductæ a ſonoro A. </s> <s xml:id="echoid-s19154" xml:space="preserve">ad <lb/>murum E. </s> <s xml:id="echoid-s19155" xml:space="preserve">neceſſario ſurſum verſus E. </s> <s xml:id="echoid-s19156" xml:space="preserve">repelluntur; </s> <s xml:id="echoid-s19157" xml:space="preserve">debet enim <lb/>angulus reflexionis C B E. </s> <s xml:id="echoid-s19158" xml:space="preserve">eſſe æqualis angulo incidentiæ D B A. <lb/></s> <s xml:id="echoid-s19159" xml:space="preserve">atque in partem auerſam, videlicet ſurſum vergere. </s> <s xml:id="echoid-s19160" xml:space="preserve">Eadem de <lb/>cauſa cliuus propugnaculorum ei ſonoro non reddit Echo, quod <lb/>exiſtit in horizontali planitie ſupra quam propugnaculum erigi-<lb/>tur: </s> <s xml:id="echoid-s19161" xml:space="preserve">quoniam cum in oppoſitam parcem ſit inclinatum, videli-<lb/>cet in altum reuerberat. </s> <s xml:id="echoid-s19162" xml:space="preserve">hactenus de ſi@u inter ſonorum, & </s> <s xml:id="echoid-s19163" xml:space="preserve">refle <lb/>ctens, nunc de interuallo eorumdem.</s> <s xml:id="echoid-s19164" xml:space="preserve"/> </p> <pb o="223" file="0245" n="250" rhead="DE ECHO."/> </div> <div xml:id="echoid-div485" type="section" level="1" n="367"> <head xml:id="echoid-head386" style="it" xml:space="preserve">De interuallo ſeu diſtantia inter ſonorum, & reflectens.</head> <p> <s xml:id="echoid-s19165" xml:space="preserve">PRæter prædictas conditiones reflectentis, ac pręter ſitum eius ad ſonorum, neceſſe eſt, vt interuallum in-<lb/>ter vtrumque ſit omnino liberum, ac patens; </s> <s xml:id="echoid-s19166" xml:space="preserve">experientia enim docet multo melius ſonum, & </s> <s xml:id="echoid-s19167" xml:space="preserve">vocem re-<lb/>currere, cum nullæ intercedunt arbores, nullæ ſegetes, herbæ nullæ. </s> <s xml:id="echoid-s19168" xml:space="preserve">optimè autem vbi interijcitur aqua ſta-<lb/>gnans, aut ſine murmure fluens. </s> <s xml:id="echoid-s19169" xml:space="preserve">quorum ratio eſt, quoniam vox defertur nõ ſine agitatione aeris, aer autem <lb/>celerius moueri poteſt per medium omnino liberum ac patens, quod nimirum neutiquam reſiſtit. </s> <s xml:id="echoid-s19170" xml:space="preserve">vbi aduer-<lb/>tendum eſt, quod quamuis in prolatione vocis, nihil interponatur in linea normali inter ſonorum, & </s> <s xml:id="echoid-s19171" xml:space="preserve">refle-<lb/>ctens, aer tamen qui iuxta eam commouetur, cõnexus eſt cum aere proximo, quem ſecum ſimul commouet, <lb/>quare ſi proximus hæſerit herbis, ſegetibus, arboribus, difficilius ab eo commouebitur, ac proinde eum ali-<lb/>quantulum retardabit, vnde nec ſonitus poterit celerrimè parieti accurrere, & </s> <s xml:id="echoid-s19172" xml:space="preserve">recurrere. </s> <s xml:id="echoid-s19173" xml:space="preserve">hac de cauſa ſecus <lb/>flumina, non obſtrepentia, & </s> <s xml:id="echoid-s19174" xml:space="preserve">lacus, perfectè audiuntur voces, & </s> <s xml:id="echoid-s19175" xml:space="preserve">ſoni vel ad maximam diſtantiam. </s> <s xml:id="echoid-s19176" xml:space="preserve">addenda <lb/>eſt etiam alia cauſa, ideſt, angulus factus à ſuperficie aquæ, aut ripæ; </s> <s xml:id="echoid-s19177" xml:space="preserve">vt in Theor. </s> <s xml:id="echoid-s19178" xml:space="preserve">17. </s> <s xml:id="echoid-s19179" xml:space="preserve">apparebit. </s> <s xml:id="echoid-s19180" xml:space="preserve">è cõtrario vox <lb/>quæ in concluſis locis (cuiuſmodi ſunt longiſſimi Xyſti, vndiq; </s> <s xml:id="echoid-s19181" xml:space="preserve">muris, ac lacunaribus concluſi) profertur, <lb/>nequit diſtinctè reflecti in Echum, ſed in Bombum confunditur, vox enim inibi concluſa, per varios, & </s> <s xml:id="echoid-s19182" xml:space="preserve">inæ-<lb/>quales parietum, pauimenti, lacunariſq; </s> <s xml:id="echoid-s19183" xml:space="preserve">offenſiones ac repulſas agitatur, atq; </s> <s xml:id="echoid-s19184" xml:space="preserve">confunditur. </s> <s xml:id="echoid-s19185" xml:space="preserve">pręterea ſæpè re-<lb/>ſonantia fit ſimul ab vtroque extremo pariete Xyſti, quare duæ reſonantiæ ſunt ſibi inuicem impedimento, <lb/>eadem ratione, ob quam dixi in puteis quibus ſupra concameratio, aut lacunar ſit, non fieri Echum. </s> <s xml:id="echoid-s19186" xml:space="preserve">proinde <lb/>ſi Xyſtus ſit ex vna parte omnino apertus, ideſt, abſque pariete, erit tanquam puteus proſtratus, & </s> <s xml:id="echoid-s19187" xml:space="preserve">conſe-<lb/>quenter Echum reſpondebit. </s> <s xml:id="echoid-s19188" xml:space="preserve">Quantum autem, oporteat eſſe interuallum, ſeu diſtantia inter ſonorum, & </s> <s xml:id="echoid-s19189" xml:space="preserve"><lb/>reflectens, mox dicemus.</s> <s xml:id="echoid-s19190" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div486" type="section" level="1" n="368"> <head xml:id="echoid-head387" style="it" xml:space="preserve">Minima distantia inter ſonorum, & reflectens est paſſuum Geometricerum <lb/>ferè 24. Theorema V.</head> <p> <s xml:id="echoid-s19191" xml:space="preserve">MInima diſtantia ea cenſenda eſt, ex qua vna tantum ſyllaba reflexa, vel vnus tantum ictus reflexus ſta-<lb/>tim poſt primariam, vel primarium diſtinctè auditur a ſonoro. </s> <s xml:id="echoid-s19192" xml:space="preserve">quam eſſe paſſuum Geometricorũ cir-<lb/>citer 24. </s> <s xml:id="echoid-s19193" xml:space="preserve">pluribus experimentis depræhenſum eſt. </s> <s xml:id="echoid-s19194" xml:space="preserve">in hac igitur diſtantia Echo monoſyllaba eſſicitur.</s> <s xml:id="echoid-s19195" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div487" type="section" level="1" n="369"> <head xml:id="echoid-head388" style="it" xml:space="preserve">Maxima diſtantia inter ſonorum, & reflectens est æqualis dimidiæ <lb/>lineæ actionis. Theorema VI.</head> <p> <s xml:id="echoid-s19196" xml:space="preserve">CVm ſoni vociſq; </s> <s xml:id="echoid-s19197" xml:space="preserve">propagatio fiat per aeris agitationem, ac proinde per interuallum aliquod, necnon in <lb/>tempore aliquo, propterea requiritur tanta diſtantia, quę tanto tẽpore a voce percurratur, vt ſonus pri-<lb/>marius, cùm re@lexus ad fonorum reuertitur, ita ſiluerit, vt eum reuertentem non ita ſuperet, quin audiri ab <lb/>eodem ſonoro diſtinctè poſſit:</s> <s xml:id="echoid-s19198" xml:space="preserve">neq; </s> <s xml:id="echoid-s19199" xml:space="preserve">adeo magna, vt reflexus ſonus nequeat ad ſonorum peruenire: </s> <s xml:id="echoid-s19200" xml:space="preserve">ſit igitur <lb/> <anchor type="figure" xlink:label="fig-0245-01a" xlink:href="fig-0245-01"/> in figura, linea actiuitatis A B. </s> <s xml:id="echoid-s19201" xml:space="preserve">ideſt, vox ſonori A. </s> <s xml:id="echoid-s19202" xml:space="preserve">audiatur <lb/>vltimo in B. </s> <s xml:id="echoid-s19203" xml:space="preserve">diuidatur bifariam in C. </s> <s xml:id="echoid-s19204" xml:space="preserve">dico A C. </s> <s xml:id="echoid-s19205" xml:space="preserve">eſſe maximam <lb/>diſtantiam, ſecundum quam ex pariete in C. </s> <s xml:id="echoid-s19206" xml:space="preserve">erecto Echo re-<lb/>flecti poſſit ad A. </s> <s xml:id="echoid-s19207" xml:space="preserve">nam pariter hic, atq; </s> <s xml:id="echoid-s19208" xml:space="preserve">in luminis reflexione <lb/>diſcurrendum eſt. </s> <s xml:id="echoid-s19209" xml:space="preserve">atqui ex doctrina Catoptricorum, tanta eſ-<lb/>ſe poteſt linea radioſa reflexa, quanta eadem eſſet ſi non refſe-<lb/>cteretur, ſed recta tenderet. </s> <s xml:id="echoid-s19210" xml:space="preserve">vel linea directa, & </s> <s xml:id="echoid-s19211" xml:space="preserve">reflexa ſimul ſemper ſunt æquales lineæ actiuitatis, v.</s> <s xml:id="echoid-s19212" xml:space="preserve">g. </s> <s xml:id="echoid-s19213" xml:space="preserve">re-<lb/>flectens in C. </s> <s xml:id="echoid-s19214" xml:space="preserve">poterit reflectere reliquum radium C B. </s> <s xml:id="echoid-s19215" xml:space="preserve">& </s> <s xml:id="echoid-s19216" xml:space="preserve">non amplius. </s> <s xml:id="echoid-s19217" xml:space="preserve">cum igitur C B. </s> <s xml:id="echoid-s19218" xml:space="preserve">æqualis ſit ipſi C A. <lb/></s> <s xml:id="echoid-s19219" xml:space="preserve">lumen vſq; </s> <s xml:id="echoid-s19220" xml:space="preserve">ad A. </s> <s xml:id="echoid-s19221" xml:space="preserve">exactè, & </s> <s xml:id="echoid-s19222" xml:space="preserve">nihil vlterius reffectetur. </s> <s xml:id="echoid-s19223" xml:space="preserve">quoniam vero eodem modo de linearum vocalium re-<lb/>flexione, vt ſupra oſtendimus, aſſerendum eſt, ſequitur reflectẽs in C. </s> <s xml:id="echoid-s19224" xml:space="preserve">poſſe reflectere reliquam lineam ſono-<lb/>ram C B. </s> <s xml:id="echoid-s19225" xml:space="preserve">normaliter vſque ad ſonorum A. </s> <s xml:id="echoid-s19226" xml:space="preserve">& </s> <s xml:id="echoid-s19227" xml:space="preserve">non amplius. </s> <s xml:id="echoid-s19228" xml:space="preserve">quod ſi reffectens ſit inter C. </s> <s xml:id="echoid-s19229" xml:space="preserve">& </s> <s xml:id="echoid-s19230" xml:space="preserve">B. </s> <s xml:id="echoid-s19231" xml:space="preserve">vt in D. </s> <s xml:id="echoid-s19232" xml:space="preserve">nullo <lb/>pacto reflectere valebit vſq; </s> <s xml:id="echoid-s19233" xml:space="preserve">ad A. </s> <s xml:id="echoid-s19234" xml:space="preserve">cum reliqua D B. </s> <s xml:id="echoid-s19235" xml:space="preserve">quæ reflectenda eſt, minor ſit quam A D. </s> <s xml:id="echoid-s19236" xml:space="preserve">ex quibus pa-<lb/>@et omnes Echus reflexiones exiſtere inter A. </s> <s xml:id="echoid-s19237" xml:space="preserve">& </s> <s xml:id="echoid-s19238" xml:space="preserve">C. </s> <s xml:id="echoid-s19239" xml:space="preserve">quarum remotiſſima erit in C. </s> <s xml:id="echoid-s19240" xml:space="preserve">ac proinde maximam re-<lb/>ſſectentis a ſonoro diſtantiam æqualem eſſe ſemiſſi lineæ actiuitatis, quod erat probandum. </s> <s xml:id="echoid-s19241" xml:space="preserve">vbi nõ omitten-<lb/>dum huiuſmodi Echum fore debiliſſimæ, & </s> <s xml:id="echoid-s19242" xml:space="preserve">quaſi moriturientis vocis, qualis ſcilicet exaudiretur in B. </s> <s xml:id="echoid-s19243" xml:space="preserve">ex-<lb/>tremo lineæ actiuitatis. </s> <s xml:id="echoid-s19244" xml:space="preserve">vltimo notandum: </s> <s xml:id="echoid-s19245" xml:space="preserve">ſi verum eſt reflexionem debilitare aliquantulum vocem, non <lb/>crit vox reflexa omnino, ſed ferè æqualis voci primariæ.</s> <s xml:id="echoid-s19246" xml:space="preserve"/> </p> <div xml:id="echoid-div487" type="float" level="2" n="1"> <figure xlink:label="fig-0245-01" xlink:href="fig-0245-01a"> <image file="0245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0245-01"/> </figure> </div> </div> <div xml:id="echoid-div489" type="section" level="1" n="370"> <head xml:id="echoid-head389" style="it" xml:space="preserve">Conſectarium.</head> <p> <s xml:id="echoid-s19247" xml:space="preserve">EX præmiſſis de ſitu, & </s> <s xml:id="echoid-s19248" xml:space="preserve">diſtantia inter ſonorum, & </s> <s xml:id="echoid-s19249" xml:space="preserve">reflectens, conſequens eſt, omnes parietes ſolo, ſeu ho-<lb/>rizonti @@ectos Echo reſonare poſſe, ſi ablatis impedimetis in eos linea vocalis debitæ longitudinis nor- <pb o="224" file="0246" n="251" rhead="DE ECHO."/> maliter acciderit. </s> <s xml:id="echoid-s19250" xml:space="preserve">quod multis antea videbatur paradoxum. </s> <s xml:id="echoid-s19251" xml:space="preserve">nullos è contrario quibus vox ſatis obliquè, aut <lb/>citra debitam diſtantiam occurrat, ſonoro ipſi reſonare poſſe. </s> <s xml:id="echoid-s19252" xml:space="preserve">quæ omnia etiam pluribus experimentis a me <lb/>comprobata ſunt. </s> <s xml:id="echoid-s19253" xml:space="preserve">Porrò ex ignoratione harum circũſtantiarum, ſitus ſcilicet, & </s> <s xml:id="echoid-s19254" xml:space="preserve">diſtantiæ prouenit, vt mul-<lb/>ti perſæpè mirentur cum paries vnus reſonet, alter vero minimè, etiamſi ſecundum cætera, ſint ſimillimi.</s> <s xml:id="echoid-s19255" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div490" type="section" level="1" n="371"> <head xml:id="echoid-head390" style="it" xml:space="preserve">Qua ratione eximis vallibus Echo reſonare poſſit. Theorema VII.</head> <p> <s xml:id="echoid-s19256" xml:space="preserve">SEd enim dubitabit forte quiſpiam in hunc modum, ſi vera <lb/> <anchor type="figure" xlink:label="fig-0246-01a" xlink:href="fig-0246-01"/> ſunt hactenus tradita, curigitur ſi quis ex alta torrentis rupe <lb/>vociferetur, ei non raro, & </s> <s xml:id="echoid-s19257" xml:space="preserve">quidem ab ima valle Echo ſuccine-<lb/>re, aut ſucclamare ſolet? </s> <s xml:id="echoid-s19258" xml:space="preserve">Reſpondemus igitur Echum huiuſ-<lb/>modi reſonare ex ima atque oppoſita rupe, cui vox ſonori nor-<lb/>maliter dimittatur. </s> <s xml:id="echoid-s19259" xml:space="preserve">vt in hac ſiguratione licet contemplari. </s> <s xml:id="echoid-s19260" xml:space="preserve">vox <lb/>enim à ſonoro A. </s> <s xml:id="echoid-s19261" xml:space="preserve">normaliter per lineam A B. </s> <s xml:id="echoid-s19262" xml:space="preserve">decurrit in imam, <lb/>& </s> <s xml:id="echoid-s19263" xml:space="preserve">oppoſitam rupem C B D. </s> <s xml:id="echoid-s19264" xml:space="preserve">atque inde per eandem viam, iux-<lb/>ta leges reflexionis reuertitur ad idem A. </s> <s xml:id="echoid-s19265" xml:space="preserve">oportet autem partem <lb/>rupis oppoſitæ reſonantem eſſe planam, aut modicè concauam, <lb/>& </s> <s xml:id="echoid-s19266" xml:space="preserve">præterea ſatis terſam.</s> <s xml:id="echoid-s19267" xml:space="preserve"/> </p> <div xml:id="echoid-div490" type="float" level="2" n="1"> <figure xlink:label="fig-0246-01" xlink:href="fig-0246-01a"> <image file="0246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0246-01"/> </figure> </div> </div> <div xml:id="echoid-div492" type="section" level="1" n="372"> <head xml:id="echoid-head391" style="it" xml:space="preserve">Car in minori diſtantia Echo pauciores ſyllabas, in maiore plures repetat. <lb/>Theorema VIII.</head> <p> <s xml:id="echoid-s19268" xml:space="preserve">HIc conſideranda eſt duplex duratio vocis. </s> <s xml:id="echoid-s19269" xml:space="preserve">prima eſt duratio vocis primariæ circa ipſum ſonorum, quæ <lb/>tandiu durat, quandiu profertur. </s> <s xml:id="echoid-s19270" xml:space="preserve">pręterea notandum eſt, hanc vocem primariam eſſe multo maiorem, <lb/>& </s> <s xml:id="echoid-s19271" xml:space="preserve">r<unsure/>ortiorem quam reflexam, quanto enim longius tendit, tanto magis debilitaur. </s> <s xml:id="echoid-s19272" xml:space="preserve">ſecunda duratio, eſt du-<lb/>ratio propagationis vocis per lineam actionis, quę duratio includit primam, non ſolum enim dum vox pri-<lb/>maria ſonat, vel durat circa ſonorum, eodem tempore longè propagatur, ſed etiam poſtquam ibi ſiluerit ad-<lb/>huc propagatur: </s> <s xml:id="echoid-s19273" xml:space="preserve">& </s> <s xml:id="echoid-s19274" xml:space="preserve">in ipſa propagatione aliquando reflectitur, vnde & </s> <s xml:id="echoid-s19275" xml:space="preserve">Echo generatur, ſicque propagatio <lb/>fit partim per directam, partim pet reflexam lineam. </s> <s xml:id="echoid-s19276" xml:space="preserve">porrò & </s> <s xml:id="echoid-s19277" xml:space="preserve">experientia, & </s> <s xml:id="echoid-s19278" xml:space="preserve">ratione palam eſt hanc ſecun-<lb/>dam durationem eſſe prima diuturniorem, audimus enim aliquando multo poſt primariam vocem, vocem <lb/>eandem ab Echo reflexam. </s> <s xml:id="echoid-s19279" xml:space="preserve">præterea conſiderare oportet, quod hęc ſecunda duratio commenſuratur diſtan-<lb/>tiæ, ſeu longitudini illi toti per quam vox producitur, & </s> <s xml:id="echoid-s19280" xml:space="preserve">reflectitur; </s> <s xml:id="echoid-s19281" xml:space="preserve">quare in minori diſtãtia, minor erit hæc <lb/>duratio, hoc eſt, citius vox reflexa reuertetur ad ſonorum: </s> <s xml:id="echoid-s19282" xml:space="preserve">in maiori autem diſtantia, maior erit duratio, hoc <lb/>eſt, tardius vox reflexa reuertetur ad ſonorum. </s> <s xml:id="echoid-s19283" xml:space="preserve">quoniam vero in minori diſtantia minor eſt durario, ſeu tem <lb/>pus breue intercedit, ideo pauciores ſyllabas reflectere poteſt, quæ poſt primam durationem exaudiantur, <lb/>hoc eſt, extincta priori voce, vox enim prima quia fortior, & </s> <s xml:id="echoid-s19284" xml:space="preserve">maior eſt hac ſecunda reflexa, ideo impedit ne <lb/>quidquam de ea diſtinctè percipiatur, quandiu ipſa durat. </s> <s xml:id="echoid-s19285" xml:space="preserve">vbi ſciendum eſt omne reflectens repetere omnes <lb/>ſyllabas, quæ in ipſum diriguntur, non tamen omnes exaudiri poſſe à ſonoro, ſed eas tantummodo, quæ poſt <lb/>primariam vocem ad eum reflectuntur. </s> <s xml:id="echoid-s19286" xml:space="preserve">priores autem, quę durante prima voce ad eum reflectuntur, ob ſtre-<lb/>pitum eius diſtinctè exaudiri ab eo nequeunt, ſed cum ſtrepitu primæ vocis in bombum confunduntur. </s> <s xml:id="echoid-s19287" xml:space="preserve">è <lb/>contrario quando maior eſt diſtantia, maior eſt etiam duratio ſecunda, ideſt, plus temporis intercedit inter <lb/>primam vocem, & </s> <s xml:id="echoid-s19288" xml:space="preserve">ſecundam: </s> <s xml:id="echoid-s19289" xml:space="preserve">quare poterunt in maiori hoc tempore plures quoque ſyllabæ diſtinctè refle-<lb/>cti, & </s> <s xml:id="echoid-s19290" xml:space="preserve">exaudiri. </s> <s xml:id="echoid-s19291" xml:space="preserve">ex quibus propoſitum patere poteſt.</s> <s xml:id="echoid-s19292" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div493" type="section" level="1" n="373"> <head xml:id="echoid-head392" style="it" xml:space="preserve">Cùm c<unsure/>cho ſtatim poſt primam vocem, repetit omnes illius ſyllabas, neceſſe eſt durationem propa-<lb/>gationis eſſe duplam orationis tam primariæ vocis, quam reflexæ. Theor. I X.</head> <p> <s xml:id="echoid-s19293" xml:space="preserve">DVratio enim propagationis, vti ſupra explicauimus, continet etiam durationem primariæ vocis, quia <lb/>ſonante illa ſimul ſit propagatio, & </s> <s xml:id="echoid-s19294" xml:space="preserve">præterea continet durationem vocis reſlexæ, ſed duratio vocis re-<lb/>flexæ eſt æqualis durationi vocis primariæ, cùm vna, & </s> <s xml:id="echoid-s19295" xml:space="preserve">eadem ſit prima, & </s> <s xml:id="echoid-s19296" xml:space="preserve">reflexa. </s> <s xml:id="echoid-s19297" xml:space="preserve">tota igitur propagatio <lb/>conſtat in hoc caſu ex duabus durationibus æqualibus, & </s> <s xml:id="echoid-s19298" xml:space="preserve">inuicem continuis, ideſt, ex duratione primarię vo-<lb/>cis, & </s> <s xml:id="echoid-s19299" xml:space="preserve">reflexæ. </s> <s xml:id="echoid-s19300" xml:space="preserve">quare tota ſimul erit dupla tam primæ, quam reflexæ vocis. </s> <s xml:id="echoid-s19301" xml:space="preserve">vera igitur eſt propoſitio.</s> <s xml:id="echoid-s19302" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div494" type="section" level="1" n="374"> <head xml:id="echoid-head393" style="it" xml:space="preserve">Conſectarium.</head> <p> <s xml:id="echoid-s19303" xml:space="preserve">EX quibus ſequitur in ea Echo, quæ non ſtatim poſt primam vocem, ſed aliquanto poſt reſonat, duratio-<lb/>nem propagationis eſſe pluſquam duplam primariæ. </s> <s xml:id="echoid-s19304" xml:space="preserve">& </s> <s xml:id="echoid-s19305" xml:space="preserve">quidem tanto plus, quantum eſt illud temporis, <pb o="225" file="0247" n="252" rhead="DE ECHO"/> quod inter primam, & </s> <s xml:id="echoid-s19306" xml:space="preserve">reflexam vocem interlabitur. </s> <s xml:id="echoid-s19307" xml:space="preserve">è contrario etiam deducitur, in ea Echo, quæ non re-<lb/>petit primam vocem integram, durationem propagationis eſſe minorem quam duplam primæ durationis; <lb/></s> <s xml:id="echoid-s19308" xml:space="preserve">quoniam in hoc caſu prior pars vocis reflexæ ſuperuenit voci primæ adhuc perſeueranti, a qua i<unsure/>mpeditur ne <lb/>audiri poſſit. </s> <s xml:id="echoid-s19309" xml:space="preserve">vt melius mox explicabitur.</s> <s xml:id="echoid-s19310" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div495" type="section" level="1" n="375"> <head xml:id="echoid-head394" style="it" xml:space="preserve">Cur Echo aliquando repetat vliimas tantum ſyllabas. Theorema X.</head> <p> <s xml:id="echoid-s19311" xml:space="preserve">ID vſu venit, cum plures ſyllabas Echo accinimus recinendas, quàm ipſius ferat diſtantia<unsure/>; </s> <s xml:id="echoid-s19312" xml:space="preserve">tunc enim prio-<lb/>res ſyllabæ prolatæ, priores etiam reuertuntur, quæ quoniam diſtantia minor eſt, quam par ſit, ideo per-<lb/>tingunt ad ſonorum, nondum tono primariæ vocis remiſſo, a quo opprimuntur ne audiri diſtinctè poſſint <lb/>extincto autem primæ vocis tono ſubſequuntur vltimæ ſyllabæ, quæ proinde, ablato iam primæ vocis im-<lb/>pedimento, Solæ diſl<unsure/>incteque exaudiuntur. </s> <s xml:id="echoid-s19313" xml:space="preserve">conſidera in prima figura verbum Dominus, quod in primaria <lb/>voce ſcribitur, ſeu imprimitur in aere præpoſtere, ſeu Hebræorum more: </s> <s xml:id="echoid-s19314" xml:space="preserve">in ſecunda, ſeu reflexa ſcribitur <lb/>recto ordine, ac more noſtro. </s> <s xml:id="echoid-s19315" xml:space="preserve">in noſtro igitur caſu prior ſyllaba reflexa Do- confunditur cum vltima pri-<lb/>mæ vocis nus; </s> <s xml:id="echoid-s19316" xml:space="preserve">quare duæ ſyllabæ minus, poſteriores, ex reflexis, ſolæ ſine concurſus illio<unsure/>s ſyllabæ prima-<lb/>riæ vocis exaudiri poſſunt.</s> <s xml:id="echoid-s19317" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div496" type="section" level="1" n="376"> <head xml:id="echoid-head395" style="it" xml:space="preserve">Sit ſonorum ſimul cum alio Audiente in maxima distantia à reflectente, abeantque in contrarias <lb/>partes æqualibus interuallis, ſonorum, quidem recta à pariete, audiens autem <lb/>ad parietem, ſonorum nuſquam amplius Echum, audiens, verò <lb/>vbique exaudiet. Theorema XI.</head> <p> <s xml:id="echoid-s19318" xml:space="preserve">CAuſam huiuslibet primò explicare hac ſimilitudine. </s> <s xml:id="echoid-s19319" xml:space="preserve">imaginemur lineam vocalem eſſe inſtat funiculi, <lb/>qui in dato caſu incipiat ab ore ſonori, tendatq; </s> <s xml:id="echoid-s19320" xml:space="preserve">normaliter in parietem, vbi per trochleam ibi affixam <lb/>reuolutus, reuertatur iterum ad locum ſonori, vbi audientis auribus religatus deſinat: </s> <s xml:id="echoid-s19321" xml:space="preserve">in hac enim maxima <lb/>diſtantia linea directa æqualis eſt reflexæ per 6. </s> <s xml:id="echoid-s19322" xml:space="preserve">Theorema. </s> <s xml:id="echoid-s19323" xml:space="preserve">iam manifeſtum eſt, ſi ſonorum abiens recta a pa-<lb/> <anchor type="figure" xlink:label="fig-0247-01a" xlink:href="fig-0247-01"/> riete ſecum traxerit ore funiculum, tracta-<lb/>turum quoq; </s> <s xml:id="echoid-s19324" xml:space="preserve">ipſo funiculo audientem ver-<lb/>ſus parietem; </s> <s xml:id="echoid-s19325" xml:space="preserve">tantumque futurum ſonori <lb/>receſſum, quantus audientis acceſſus. </s> <s xml:id="echoid-s19326" xml:space="preserve">cùm <lb/>igitur hac ratione ſonorum ſemper rece-<lb/>dat a fine lineæ actiuitatis, audiens verò ſit <lb/>ſemper in extremo eiuſdem lineæ, neceſ-<lb/>ſario ſequitur ſonorum nuſquam amplius <lb/>Echum, audientem vero vbiq; </s> <s xml:id="echoid-s19327" xml:space="preserve">audire poſ-<lb/>ſe. </s> <s xml:id="echoid-s19328" xml:space="preserve">Idem Geometricè ſic; </s> <s xml:id="echoid-s19329" xml:space="preserve">ſint vt in ſigura <lb/>ſonorum A. </s> <s xml:id="echoid-s19330" xml:space="preserve">& </s> <s xml:id="echoid-s19331" xml:space="preserve">audiens C. </s> <s xml:id="echoid-s19332" xml:space="preserve">ſimul, in maxi-<lb/>ma diſtantia a pariete B. </s> <s xml:id="echoid-s19333" xml:space="preserve">linea actiuitatis <lb/>ſit A B C. </s> <s xml:id="echoid-s19334" xml:space="preserve">recedat ſonorum quouis ſpatio <lb/>A D. </s> <s xml:id="echoid-s19335" xml:space="preserve">audiens vero accedat pari interuallo <lb/>C E. </s> <s xml:id="echoid-s19336" xml:space="preserve">dico ſonorum non amplius Echum <lb/>audientem vero auditurum. </s> <s xml:id="echoid-s19337" xml:space="preserve">ſumatur F B. </s> <s xml:id="echoid-s19338" xml:space="preserve">æqualis ipſi A D. </s> <s xml:id="echoid-s19339" xml:space="preserve">vel C E. </s> <s xml:id="echoid-s19340" xml:space="preserve">quia igitur D F. </s> <s xml:id="echoid-s19341" xml:space="preserve">& </s> <s xml:id="echoid-s19342" xml:space="preserve">A B. </s> <s xml:id="echoid-s19343" xml:space="preserve">ſunt æquales, <lb/>necnon F B E. </s> <s xml:id="echoid-s19344" xml:space="preserve">B E C. </s> <s xml:id="echoid-s19345" xml:space="preserve">erunt per 2. </s> <s xml:id="echoid-s19346" xml:space="preserve">pronunt. </s> <s xml:id="echoid-s19347" xml:space="preserve">1. </s> <s xml:id="echoid-s19348" xml:space="preserve">Euclid. </s> <s xml:id="echoid-s19349" xml:space="preserve">totæ D F B E. </s> <s xml:id="echoid-s19350" xml:space="preserve">A B C. </s> <s xml:id="echoid-s19351" xml:space="preserve">æquales; </s> <s xml:id="echoid-s19352" xml:space="preserve">quapropter ſonorum <lb/>in D. </s> <s xml:id="echoid-s19353" xml:space="preserve">abeſt ab E. </s> <s xml:id="echoid-s19354" xml:space="preserve">extremo lineæ reflexæ vbi deſinit Echo, Echum igitur non audiet. </s> <s xml:id="echoid-s19355" xml:space="preserve">Audiens autem ſem-<lb/>per erit in E. </s> <s xml:id="echoid-s19356" xml:space="preserve">quo Echo pertinet, eam igitur audiet.</s> <s xml:id="echoid-s19357" xml:space="preserve"/> </p> <div xml:id="echoid-div496" type="float" level="2" n="1"> <figure xlink:label="fig-0247-01" xlink:href="fig-0247-01a"> <image file="0247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0247-01"/> </figure> </div> </div> <div xml:id="echoid-div498" type="section" level="1" n="377"> <head xml:id="echoid-head396" style="it" xml:space="preserve">Corollarium. De deceptionibus ab Echo reciprocæ.</head> <p> <s xml:id="echoid-s19358" xml:space="preserve">VT hæc noſtra Echometria aſſimilis ſit opticæ, non deſunt ei ſuæ deceptiones, & </s> <s xml:id="echoid-s19359" xml:space="preserve">fallaciæ. </s> <s xml:id="echoid-s19360" xml:space="preserve">& </s> <s xml:id="echoid-s19361" xml:space="preserve">primò qui-<lb/>dem in hac prima Echo reciproca. </s> <s xml:id="echoid-s19362" xml:space="preserve">accidit aliquando, vt quis nihil de Echo cogitans, noctu præſertim <lb/>altius loquatur, aut vocitet, eique Echo, & </s> <s xml:id="echoid-s19363" xml:space="preserve">quidem ad rem, ſeu ad mentem illius abundè reſpõdeat, vnde ipſe <lb/>deceptus putat aliquem alium inde ſibi reſpondere. </s> <s xml:id="echoid-s19364" xml:space="preserve">Cardanus lib. </s> <s xml:id="echoid-s19365" xml:space="preserve">18. </s> <s xml:id="echoid-s19366" xml:space="preserve">de ſubt. </s> <s xml:id="echoid-s19367" xml:space="preserve">mira narrat cuiuſdã deceptio-<lb/>nem. </s> <s xml:id="echoid-s19368" xml:space="preserve">quidam ait, amicus noſter, cum iter ageret iuxta flumen, nec vadum ſciret, exclamare cæpit, on<unsure/>? </s> <s xml:id="echoid-s19369" xml:space="preserve">cui la-<lb/>tens Echo reſpondit, oh? </s> <s xml:id="echoid-s19370" xml:space="preserve">ille exiſtimans hominem eſſe, interrogat Italicè, vnde debo paſſa? </s> <s xml:id="echoid-s19371" xml:space="preserve">paſſa? </s> <s xml:id="echoid-s19372" xml:space="preserve">reſpon-<lb/>detur. </s> <s xml:id="echoid-s19373" xml:space="preserve">tum ille, qui? </s> <s xml:id="echoid-s19374" xml:space="preserve">qui? </s> <s xml:id="echoid-s19375" xml:space="preserve">replicatur. </s> <s xml:id="echoid-s19376" xml:space="preserve">at ibi prpfundo gurgite aquæ admodum perſtrepebant, vnde illi terri-<lb/>tus iterum interrogat, debo paſſa qui? </s> <s xml:id="echoid-s19377" xml:space="preserve">Echo reſpondet, paſſa qui. </s> <s xml:id="echoid-s19378" xml:space="preserve">cui ſæpius idem interroganti, idem reſpon <lb/>debat. </s> <s xml:id="echoid-s19379" xml:space="preserve">quare cum amicus inter metum, & </s> <s xml:id="echoid-s19380" xml:space="preserve">neceſſitatem vadandi eſſet, noxq; </s> <s xml:id="echoid-s19381" xml:space="preserve">obſcura atq; </s> <s xml:id="echoid-s19382" xml:space="preserve">intempeſta vrge-<lb/>ret, exiſtimauit Dæmonem aliquem ſibi perſuadere velle, vt ſe in torrentem illum præcipitaret; </s> <s xml:id="echoid-s19383" xml:space="preserve">quare inde <lb/>reuerſu<unsure/>s Cardano rem tota<unsure/>m narrauit, qui poſtea Echus, non Dæmonis fallaciam eſſe depræhendit.</s> <s xml:id="echoid-s19384" xml:space="preserve"/> </p> <pb o="226" file="0248" n="253" rhead="DE ECHO."/> </div> <div xml:id="echoid-div499" type="section" level="1" n="378"> <head xml:id="echoid-head397" style="it" xml:space="preserve">De Echo obliqua.</head> <p> <s xml:id="echoid-s19385" xml:space="preserve">QVemadmodum cùm in ſpeculum planum lineæ viſiuæ perpendiculariter accidunt, & </s> <s xml:id="echoid-s19386" xml:space="preserve">reflectuntur, ipfi <lb/>noſtram intuemur imaginem. </s> <s xml:id="echoid-s19387" xml:space="preserve">cum verò obliquè ei occurrunt, non ipſi ſed alius quiſpiam noſtam ima-<lb/>ginem intuetur. </s> <s xml:id="echoid-s19388" xml:space="preserve">pari ratione idem Echo accidit. </s> <s xml:id="echoid-s19389" xml:space="preserve">porrò hactenus de Echo quæ norm<unsure/>aliter reſona@ <lb/>egimus, nunc nonnulla de ea, quæ ex obliquo repercuſſu, ab alio quam à ſonoro exaudiri ſolet.</s> <s xml:id="echoid-s19390" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div500" type="section" level="1" n="379"> <head xml:id="echoid-head398" style="it" xml:space="preserve">Echum ab alio, quam à ſonoro audiri, cum vox parieti oblique occurrit. <lb/>Theorema XII.</head> <p> <s xml:id="echoid-s19391" xml:space="preserve">IN hac Echo præter ſonorum, neceſſarius eſt alius qui Echum exaudiat, vt in ſecunda figura. </s> <s xml:id="echoid-s19392" xml:space="preserve">ſit ſonorum <lb/>A. </s> <s xml:id="echoid-s19393" xml:space="preserve">cuius in parietem D B E. </s> <s xml:id="echoid-s19394" xml:space="preserve">oblique incidat, vti per lineam A B. </s> <s xml:id="echoid-s19395" xml:space="preserve">quę faciens angulum A B D. </s> <s xml:id="echoid-s19396" xml:space="preserve">deflectatur <lb/>ad audientem C. </s> <s xml:id="echoid-s19397" xml:space="preserve">faciens angulum C B E. </s> <s xml:id="echoid-s19398" xml:space="preserve">æqualem e<unsure/>lteri A B D. </s> <s xml:id="echoid-s19399" xml:space="preserve">iam experientia conſrat in tali caſu audien-<lb/>tem C. </s> <s xml:id="echoid-s19400" xml:space="preserve">audire Echum ipſius A. </s> <s xml:id="echoid-s19401" xml:space="preserve">A vero neutiquam. </s> <s xml:id="echoid-s19402" xml:space="preserve">cuius ratio ſuperius tacta eſt, quoniã ſcilicet natura agit <lb/>per lineas breuiſſimas; </s> <s xml:id="echoid-s19403" xml:space="preserve">omnium autem breuiſſimæ ſunt quæ faciunt prædictos angulos æquales, vti conſtat <lb/>per 1. </s> <s xml:id="echoid-s19404" xml:space="preserve">Theor. </s> <s xml:id="echoid-s19405" xml:space="preserve">huius. </s> <s xml:id="echoid-s19406" xml:space="preserve">Diſtantia porrò ſonori à refiectente tantum eſſe oportet, vt binæ lineæ A B. </s> <s xml:id="echoid-s19407" xml:space="preserve">B C. </s> <s xml:id="echoid-s19408" xml:space="preserve">fi <lb/>mul non ſint maiores linea actionis.</s> <s xml:id="echoid-s19409" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div501" type="section" level="1" n="380"> <head xml:id="echoid-head399" style="it" xml:space="preserve">Conſectarium.</head> <p> <s xml:id="echoid-s19410" xml:space="preserve">HInc ſequitur Echum audiri poſſe ab audientibus in orbem ſitis, ſi enim adeo magnus ſit paries, vt ab eo <lb/>reflexiones fieri poſſint circumquaque, ideſt, a dextris, & </s> <s xml:id="echoid-s19411" xml:space="preserve">à ſiniſtris, ſupernè, & </s> <s xml:id="echoid-s19412" xml:space="preserve">infernè; </s> <s xml:id="echoid-s19413" xml:space="preserve">omnes autem <lb/>reflexionum anguli ſint inuicem æquales, manifeſtum eſt omnia puncta incidentie fore in peripheria circu-<lb/> <anchor type="figure" xlink:label="fig-0248-01a" xlink:href="fig-0248-01"/> li deſcripta in pariete, quare linea omnes <lb/>ref<unsure/>lexę, cum reflectantur ad conſimiles an-<lb/>gulos, erunt omnes in ſuperficie conica <lb/>reflexa, cuius baſis erit circulus, in cuius <lb/>circuli peripheria auditores poſiti omnes <lb/>Echum exaudient. </s> <s xml:id="echoid-s19414" xml:space="preserve">porrò ſi<unsure/> hæc fuſius ex-<lb/>plicare velim, intelligenda eſſet prius py-<lb/>ramis incidentiæ, more opticorum, cuius <lb/>vertex eſſet in A. </s> <s xml:id="echoid-s19415" xml:space="preserve">figuræ, baſis verò in pa-<lb/>riete E B D. </s> <s xml:id="echoid-s19416" xml:space="preserve">quæ baſis eſſet circulus cuius <lb/>centrum D. </s> <s xml:id="echoid-s19417" xml:space="preserve">circumferentia verò per B E. <lb/></s> <s xml:id="echoid-s19418" xml:space="preserve">tranſiret, ex qua circumferentia reflecte-<lb/>rentur omnes lineæ efficientes reliquann <lb/>pyramidem reflexionis; </s> <s xml:id="echoid-s19419" xml:space="preserve">cuius baſis eſſet <lb/>orbis, in cuius peripheria auditores poſi-<lb/>ti varias Echus exaudirent. </s> <s xml:id="echoid-s19420" xml:space="preserve">quæ omnia eſſent eodem modo demonſtranda, quo demonſtrantur in tracta-<lb/>tu de figura Iridis. </s> <s xml:id="echoid-s19421" xml:space="preserve">Sed hæc fortè nimis breuiter.</s> <s xml:id="echoid-s19422" xml:space="preserve"/> </p> <div xml:id="echoid-div501" type="float" level="2" n="1"> <figure xlink:label="fig-0248-01" xlink:href="fig-0248-01a"> <image file="0248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-01"/> </figure> </div> </div> <div xml:id="echoid-div503" type="section" level="1" n="381"> <head xml:id="echoid-head400" style="it" xml:space="preserve">Echum ſecundariam manifeſtare. Theorema XIII.</head> <p> <s xml:id="echoid-s19423" xml:space="preserve">SInt exempli gratia, duo reflectentia C S. </s> <s xml:id="echoid-s19424" xml:space="preserve">A B. </s> <s xml:id="echoid-s19425" xml:space="preserve">ab inuicem diſtantia ſaltem 25. </s> <s xml:id="echoid-s19426" xml:space="preserve">paſſus Geometricos, inui-<lb/>cemq; </s> <s xml:id="echoid-s19427" xml:space="preserve">non omnino paralella, ſed ad partes C A. </s> <s xml:id="echoid-s19428" xml:space="preserve">modicum diuergentia. </s> <s xml:id="echoid-s19429" xml:space="preserve">ſitq; </s> <s xml:id="echoid-s19430" xml:space="preserve">linea actiuitatis paulo maior <lb/>quam tripla prædictæ diſtantiæ, v.</s> <s xml:id="echoid-s19431" xml:space="preserve">g. </s> <s xml:id="echoid-s19432" xml:space="preserve">paſſuum 80. </s> <s xml:id="echoid-s19433" xml:space="preserve">ſonorum ſit S. </s> <s xml:id="echoid-s19434" xml:space="preserve">cuius linea prima ſonora S B. </s> <s xml:id="echoid-s19435" xml:space="preserve">feratur in pa-<lb/> <anchor type="figure" xlink:label="fig-0248-02a" xlink:href="fig-0248-02"/> rietem A B. </s> <s xml:id="echoid-s19436" xml:space="preserve">recta. </s> <s xml:id="echoid-s19437" xml:space="preserve">reflectetur igitur ad S. </s> <s xml:id="echoid-s19438" xml:space="preserve">ſonorum, ex demonſtra-<lb/>tis, eique Echum reſonabit. </s> <s xml:id="echoid-s19439" xml:space="preserve">rurſus conſidero aliam lineam S I. </s> <s xml:id="echoid-s19440" xml:space="preserve">quæ <lb/>obliquè parieti A I B. </s> <s xml:id="echoid-s19441" xml:space="preserve">occurrat, quare reflectetur vltra in alterũ pa-<lb/>rietem in C. </s> <s xml:id="echoid-s19442" xml:space="preserve">eritq; </s> <s xml:id="echoid-s19443" xml:space="preserve">I C. </s> <s xml:id="echoid-s19444" xml:space="preserve">vnde iterum reflecti poterit ad A. </s> <s xml:id="echoid-s19445" xml:space="preserve">vbi ſit au-<lb/>ditor, per lineã C A. </s> <s xml:id="echoid-s19446" xml:space="preserve">quare ab audiente A. </s> <s xml:id="echoid-s19447" xml:space="preserve">exaudiri poterit: </s> <s xml:id="echoid-s19448" xml:space="preserve">eſt enim <lb/>tota linea S I C A. </s> <s xml:id="echoid-s19449" xml:space="preserve">75. </s> <s xml:id="echoid-s19450" xml:space="preserve">ex hypoth eſi paulò minor tota linea actionis <lb/>80. </s> <s xml:id="echoid-s19451" xml:space="preserve">igitur A. </s> <s xml:id="echoid-s19452" xml:space="preserve">exaudiet vocem ſonori S. </s> <s xml:id="echoid-s19453" xml:space="preserve">ei ſecũdò reflexam ex C. </s> <s xml:id="echoid-s19454" xml:space="preserve">erit <lb/>tamen Echo iſthæc diuerſa ab ea, quam percipit ſonorum S. </s> <s xml:id="echoid-s19455" xml:space="preserve">imò illa <lb/>tardior in ratione ſeſquialtera, nam eius diſtantia à ſonoro conſtat <lb/>tribus lineis S I. </s> <s xml:id="echoid-s19456" xml:space="preserve">I C. </s> <s xml:id="echoid-s19457" xml:space="preserve">C A. </s> <s xml:id="echoid-s19458" xml:space="preserve">diſl<unsure/>antia autem per quam recurrit Echo ad ipſum ſonorum conſtat tantum dua-<lb/>bus S B. </s> <s xml:id="echoid-s19459" xml:space="preserve">B S. </s> <s xml:id="echoid-s19460" xml:space="preserve">vnde patet propoſitum. </s> <s xml:id="echoid-s19461" xml:space="preserve">eodem modo Echum tertiariam in ratione dupla, &</s> <s xml:id="echoid-s19462" xml:space="preserve">c. </s> <s xml:id="echoid-s19463" xml:space="preserve">ſimiles faci-<lb/>lè demonſtrabimus</s> </p> <div xml:id="echoid-div503" type="float" level="2" n="1"> <figure xlink:label="fig-0248-02" xlink:href="fig-0248-02a"> <image file="0248-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-02"/> </figure> </div> <pb o="227" file="0249" n="254" rhead="DE ECHO."/> </div> <div xml:id="echoid-div505" type="section" level="1" n="382"> <head xml:id="echoid-head401" style="it" xml:space="preserve">Corollarium, De deceptionibus ab Echo obliqua.</head> <p> <s xml:id="echoid-s19464" xml:space="preserve">ACcidit ſæpè nos decipi ab hac obliqua Echo circa ſitum ſonori, cuius cauſa eſt, quod ſepè ob aliquod im-<lb/>pedimentum, nequimus audire vocem primariam, ſed reflexam tantum audimus. </s> <s xml:id="echoid-s19465" xml:space="preserve">quare auditus iudicat <lb/>ſe audire non per reflexouem, ſed per directionem: </s> <s xml:id="echoid-s19466" xml:space="preserve">& </s> <s xml:id="echoid-s19467" xml:space="preserve">conſequenter exiſtimat ſonorum ad parte<unsure/>m illam ſitũ <lb/>eſſe, ex qua ſonum ipſius percipit. </s> <s xml:id="echoid-s19468" xml:space="preserve">ſenſus enim auditus, ſicuti & </s> <s xml:id="echoid-s19469" xml:space="preserve">viſus, niſi corrigantur ab intellectu, puta<unsure/>nt ſe <lb/>per lineas tantum directas ſem per videre, & </s> <s xml:id="echoid-s19470" xml:space="preserve">audire: </s> <s xml:id="echoid-s19471" xml:space="preserve">ſic oculus imaginem vltra ſpeculum in linea recta ſe vi-<lb/>dere iudicat; </s> <s xml:id="echoid-s19472" xml:space="preserve">pariter auditus exiſtimat ſonum reflexum propagari a ſonoro ad ſe per vnicam lineam rectam <lb/>ſic me Parmæ, ſæpiſſimè ſonitus campanarum S. </s> <s xml:id="echoid-s19473" xml:space="preserve">Andreæ decipit, cuius cauſa eſt ædifi ciorum vrbis multitu-<lb/>do, quæ interponuntur inter illas, & </s> <s xml:id="echoid-s19474" xml:space="preserve">meum cubiculum, ſicque impediunt ne directum earum ſonum exau-<lb/>diam. </s> <s xml:id="echoid-s19475" xml:space="preserve">vbi è contrario paries quidam, cui directus illarum ſonitus per via quandam accidit, eum mihi in <lb/>meum cubiculum reflectit, quare exiſtimo campanas prædictas exiſtere ad partes illius parietis, qui mihi ea-<lb/>rum ſonum reflectit, cum tamen ſint in oppoſita p<unsure/>arte.</s> <s xml:id="echoid-s19476" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div506" type="section" level="1" n="383"> <head xml:id="echoid-head402" style="it" xml:space="preserve">Cur Echus vox debilior, imbecilliorque ſit quam primaria.</head> <p> <s xml:id="echoid-s19477" xml:space="preserve">CAuſa eſt eadem, quæ exilioris vocis directæ, & </s> <s xml:id="echoid-s19478" xml:space="preserve">nunquam reflexę:</s> <s xml:id="echoid-s19479" xml:space="preserve">nam vocis ſonus quò longius propaga-<lb/>tur, eo magis gracileſcit, & </s> <s xml:id="echoid-s19480" xml:space="preserve">languet, donec in extrema diſtantia, qua exaudiri poſſit, vbi videlicet eſt ter-<lb/>minus lineæ actionis, penitus euaneſcat. </s> <s xml:id="echoid-s19481" xml:space="preserve">quie igitur mirum ſi reflexa idem patiatur, quæ eſt eadem cum ea <lb/>directa, quæ ablato impedimento refl<unsure/>ectentis, longius rectà tenderet. </s> <s xml:id="echoid-s19482" xml:space="preserve">adde quòd ipſa reflexio per ſe, ob re-<lb/>flectentis, aut medij reſiſtentiam, ſolet ſemper rem reflexam debilitare. </s> <s xml:id="echoid-s19483" xml:space="preserve">Hactenus de reflectentibus planis, <lb/>nunc de concauis, & </s> <s xml:id="echoid-s19484" xml:space="preserve">conuexis.</s> <s xml:id="echoid-s19485" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div507" type="section" level="1" n="384"> <head xml:id="echoid-head403" style="it" xml:space="preserve">Si reflectens ſit Sphæricum concauum, Echum perfectiſſimam ad ſuum <lb/>centrum reſonabit. Theorema XIV.</head> <p> <s xml:id="echoid-s19486" xml:space="preserve">CAuſa huius eſt, quoniam omnes lineæ à<unsure/> centro ad circumferentiam ſunt æquales, & </s> <s xml:id="echoid-s19487" xml:space="preserve">perpendiculares; <lb/></s> <s xml:id="echoid-s19488" xml:space="preserve">quare omnes reflectentur in ſeipſas ad centrum, ſiue omnium reflexio fiet ad centrum, vbi ſonorum <lb/>ſitum eſſe ſupponimus. </s> <s xml:id="echoid-s19489" xml:space="preserve">cùm præterea ſint æquales, fiet omnium reflexio eodem tempore ad ſonorum, qua-<lb/>re Echo admodum elegans, ac reſonabilis euadet. </s> <s xml:id="echoid-s19490" xml:space="preserve">vt in adiecto ſchemate, fit reflectens ſphæricum conca-<lb/>uum C B D. </s> <s xml:id="echoid-s19491" xml:space="preserve">in cuius centro A. </s> <s xml:id="echoid-s19492" xml:space="preserve">ſit ſonorum. </s> <s xml:id="echoid-s19493" xml:space="preserve">lineæ vocales A B. </s> <s xml:id="echoid-s19494" xml:space="preserve">A C. </s> <s xml:id="echoid-s19495" xml:space="preserve">A D. </s> <s xml:id="echoid-s19496" xml:space="preserve">omnes ſunt normales, quare <lb/>omnes normaliter reffectent ſonum per eaſdem C A. </s> <s xml:id="echoid-s19497" xml:space="preserve">B A. </s> <s xml:id="echoid-s19498" xml:space="preserve">D A. </s> <s xml:id="echoid-s19499" xml:space="preserve">ad ſonorum A. </s> <s xml:id="echoid-s19500" xml:space="preserve">ſed etiam eodem tempore, <lb/>cùm ſint æqualis diſtantiæ, perfectiſſima, igitur Echo reſonabit. </s> <s xml:id="echoid-s19501" xml:space="preserve">Quod ſi reflectens C B D. </s> <s xml:id="echoid-s19502" xml:space="preserve">ſit cylindricum, <lb/>non eadem prorſus perfectione, ſed tamen eieganter admodum recantabit. </s> <s xml:id="echoid-s19503" xml:space="preserve">Vbi notandum eſt Theatra <lb/>fuiſſe antiquitus cylindrica, qua re ex modo dictis, minimè mirum ſit, ea fuiſſe, ſicuti veteres ſcriptores tra-<lb/>dunt, magnopere ac perbellè reſonantia.</s> <s xml:id="echoid-s19504" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div508" type="section" level="1" n="385"> <head xml:id="echoid-head404" style="it" xml:space="preserve">Quanto ſonorum fuer it extra centrum concaui, tantum Echo reddetur imperfectior. <lb/>Theorema XV.</head> <p> <s xml:id="echoid-s19505" xml:space="preserve">CAuſa huius ex pręcedenti propoſitione patere poteſt. </s> <s xml:id="echoid-s19506" xml:space="preserve">ſi enim ſonorum extra centrum ponatur, non am-<lb/>plius erunt omnes lineæ ęquales;</s> <s xml:id="echoid-s19507" xml:space="preserve">neq; </s> <s xml:id="echoid-s19508" xml:space="preserve">omnes normales, ſed vna tantum. </s> <s xml:id="echoid-s19509" xml:space="preserve">vti ſi ſonorum ſit in G. </s> <s xml:id="echoid-s19510" xml:space="preserve">vna tan-<lb/> <anchor type="figure" xlink:label="fig-0249-01a" xlink:href="fig-0249-01"/> tum G B. </s> <s xml:id="echoid-s19511" xml:space="preserve">norma-<lb/>lis erit; </s> <s xml:id="echoid-s19512" xml:space="preserve">aliæ duæ <lb/>G C. </s> <s xml:id="echoid-s19513" xml:space="preserve">G D. </s> <s xml:id="echoid-s19514" xml:space="preserve">obli-<lb/>què reflectẽti oc-<lb/>curent. </s> <s xml:id="echoid-s19515" xml:space="preserve">quare ſe-<lb/>cundũ leges refle <lb/>ctionis, reflecten <lb/>tur non ad ſono-<lb/>rum G. </s> <s xml:id="echoid-s19516" xml:space="preserve">ſed ad H. <lb/></s> <s xml:id="echoid-s19517" xml:space="preserve">per reflexas CH. </s> <s xml:id="echoid-s19518" xml:space="preserve"><lb/>D H. </s> <s xml:id="echoid-s19519" xml:space="preserve">aliæ porrò <lb/>innumeræ, quæ <lb/>incidunt extra <lb/>C D. </s> <s xml:id="echoid-s19520" xml:space="preserve">reflectẽtur <lb/>ad alia pũcta pro <lb/>piora ipſi B. </s> <s xml:id="echoid-s19521" xml:space="preserve">quã <lb/>H. </s> <s xml:id="echoid-s19522" xml:space="preserve">quæ verò in-<lb/>cidũt extra C. </s> <s xml:id="echoid-s19523" xml:space="preserve">& </s> <s xml:id="echoid-s19524" xml:space="preserve"><lb/>D. </s> <s xml:id="echoid-s19525" xml:space="preserve">reflectẽtur ad <lb/>alia pũcta remo- <pb o="228" file="0250" n="255" rhead="DE ECHO."/> tiora à B. </s> <s xml:id="echoid-s19526" xml:space="preserve">quam ſit H. </s> <s xml:id="echoid-s19527" xml:space="preserve">quare non poterunt omnes ſimul concorditer reflectere vocem ad G. </s> <s xml:id="echoid-s19528" xml:space="preserve">qua propter re-<lb/>ſonantia imperfectior, euadet. </s> <s xml:id="echoid-s19529" xml:space="preserve">ſi verò ſonorum ſit intra centrum A. </s> <s xml:id="echoid-s19530" xml:space="preserve">vti in H. </s> <s xml:id="echoid-s19531" xml:space="preserve">erit pariter vna tantum norma-<lb/>lis H B. </s> <s xml:id="echoid-s19532" xml:space="preserve">& </s> <s xml:id="echoid-s19533" xml:space="preserve">aliæ incidentes obliquæ H C. </s> <s xml:id="echoid-s19534" xml:space="preserve">quæ reflectentur per lineas C G. </s> <s xml:id="echoid-s19535" xml:space="preserve">D H. </s> <s xml:id="echoid-s19536" xml:space="preserve">ad alium locu n G. </s> <s xml:id="echoid-s19537" xml:space="preserve">quare tũc <lb/>pariter Echo fiet imperfectior. </s> <s xml:id="echoid-s19538" xml:space="preserve">Veruntamen Echo hnius concaui erit ſemper perfectior, quam plani:</s> <s xml:id="echoid-s19539" xml:space="preserve">ſi enim <lb/>ex plano tot lineæ normali propiores reflecti poſſunt, quæ ad Echum ſufficiant, multò pi<unsure/>ures ex concauo, <lb/>normali propiores reffecti poterunt, quæ cum normali reſonent ad ſonorum G. </s> <s xml:id="echoid-s19540" xml:space="preserve">vel H. </s> <s xml:id="echoid-s19541" xml:space="preserve">concaua enim figura <lb/>vnit magis lineas reflexas, quàm plana, vt conſtat ex catoptricis. </s> <s xml:id="echoid-s19542" xml:space="preserve">Cæterum quæ ſuperius, cum de planis refle-<lb/>ctentibus agebatur, de diſtantia, ac ſitu dicta ſunt, hic quoq; </s> <s xml:id="echoid-s19543" xml:space="preserve">& </s> <s xml:id="echoid-s19544" xml:space="preserve">in ſequentibus valere debent.</s> <s xml:id="echoid-s19545" xml:space="preserve"/> </p> <div xml:id="echoid-div508" type="float" level="2" n="1"> <figure xlink:label="fig-0249-01" xlink:href="fig-0249-01a"> <image file="0249-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0249-01"/> </figure> </div> </div> <div xml:id="echoid-div510" type="section" level="1" n="386"> <head xml:id="echoid-head405" style="it" xml:space="preserve">Corollarium.</head> <p> <s xml:id="echoid-s19546" xml:space="preserve">SI reflectens fuerit cauum parabolicuw, aut ellipticum, & </s> <s xml:id="echoid-s19547" xml:space="preserve">ſonorum ſit ab eis adeo diſtans, vt vocales líneæ <lb/>eis occurrentes ſumi poſſint tanquam paralellæ, reflectenter omnes ad vnum locũ, ad quem ſcilicet refle-<lb/>ctentur radij Solis, & </s> <s xml:id="echoid-s19548" xml:space="preserve">in quo ſolet fieri accenſio. </s> <s xml:id="echoid-s19549" xml:space="preserve">qui locus quia eſt propè ſpeculum, propterea Echo erit n@n <lb/>reciproca, ſed ad alterũ. </s> <s xml:id="echoid-s19550" xml:space="preserve">Cæterum niſi huiuſmodi reflectentia ſint magnorum conoideon, aut ſphæroideon <lb/>portiones, pũctum concurſus erit tam reflectenti vicinum, vt audiens ægrè vocem reflexam a directa diſtin-<lb/>ctam percepturus ſit. </s> <s xml:id="echoid-s19551" xml:space="preserve">Quod ſi magnę fuerint, tunc puto ad ſenſum fore adeo ſphæricis ſimilia, vt ab eis in re-<lb/>flexione nõ differant. </s> <s xml:id="echoid-s19552" xml:space="preserve">huiuſmodi igitur concaua Echoi taciturnæ reſeruẽtur. </s> <s xml:id="echoid-s19553" xml:space="preserve">de qua vltimo dicendum erit.</s> <s xml:id="echoid-s19554" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div511" type="section" level="1" n="387"> <head xml:id="echoid-head406" style="it" xml:space="preserve">Reflect@ns Sphæricum conuexum ineptum eſt Echo efficiendæ. Theorena XVI.</head> <p> <s xml:id="echoid-s19555" xml:space="preserve">RAtio eſt, quia talis figura lineas nullas, pręter vnam normalem reflectit ad ſonorũ, ſed valde eas aliorſum <lb/>detorquet. </s> <s xml:id="echoid-s19556" xml:space="preserve">idq; </s> <s xml:id="echoid-s19557" xml:space="preserve">propterea quòd anguli incidentiæ, & </s> <s xml:id="echoid-s19558" xml:space="preserve">reflexionis oporteat eſſe compares. </s> <s xml:id="echoid-s19559" xml:space="preserve">vt dato ſphæ-<lb/>rico conuexo C B D. </s> <s xml:id="echoid-s19560" xml:space="preserve">ſonorum I. </s> <s xml:id="echoid-s19561" xml:space="preserve">in illud inſonet, vna tantum I B. </s> <s xml:id="echoid-s19562" xml:space="preserve">normalis erit; </s> <s xml:id="echoid-s19563" xml:space="preserve">reliquæ vero omnes, quales <lb/>ſunt I C. </s> <s xml:id="echoid-s19564" xml:space="preserve">I D. </s> <s xml:id="echoid-s19565" xml:space="preserve">aliorſum valde deflectuntur per lineas C E. </s> <s xml:id="echoid-s19566" xml:space="preserve">D F. </s> <s xml:id="echoid-s19567" xml:space="preserve">quanto autẽ reflectens hoc fuerit maioris ſphæ <lb/>rę portio, tanto minorem habebit curuitatem, ſeu magis ad naturam plani reflectentis accedet, qua re minus <lb/>Lineas reflexa@ diſperget. </s> <s xml:id="echoid-s19568" xml:space="preserve">ſicque pote runt nonnullæ perpendiculari propiores, ſimui cum ipſa aliquantulam <lb/>Echum reſonare. </s> <s xml:id="echoid-s19569" xml:space="preserve">atque hæc eſt ratio cur rotunda propugnacula, & </s> <s xml:id="echoid-s19570" xml:space="preserve">ſimilia nullam Echum efficiant.</s> <s xml:id="echoid-s19571" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div512" type="section" level="1" n="388"> <head xml:id="echoid-head407" style="it" xml:space="preserve">Concauum rectiplanum, vti est angulus concauus duorum parietum clariorem <lb/>Echum reſonat. Theorema XVII.</head> <p> <s xml:id="echoid-s19572" xml:space="preserve">HOc me varie experientem docuit experientia in angulo duorum parietum recto, cõtra quàm prius opi-<lb/>nabar. </s> <s xml:id="echoid-s19573" xml:space="preserve">eram autem ab eo diſtans minimum 24. </s> <s xml:id="echoid-s19574" xml:space="preserve">paſſus geometricos, & </s> <s xml:id="echoid-s19575" xml:space="preserve">ita ex aduerſo ipſius, vt linea in ip-<lb/>ſum angulum incidens faceret angulos ſemirectos cum vtroq; </s> <s xml:id="echoid-s19576" xml:space="preserve">pariete, ſeu diuideret ipſum angulum bifariã. <lb/></s> <s xml:id="echoid-s19577" xml:space="preserve"> <anchor type="figure" xlink:label="fig-0250-01a" xlink:href="fig-0250-01"/> vt in appoſit<unsure/>a ſigu <lb/>ra, ſit angulus ca-<lb/>uus C B D. </s> <s xml:id="echoid-s19578" xml:space="preserve">ſonorũ <lb/>in A. </s> <s xml:id="echoid-s19579" xml:space="preserve">linea incidẽs <lb/>A B. </s> <s xml:id="echoid-s19580" xml:space="preserve">faciat angulos <lb/>ſem<unsure/>irectos A B C. <lb/></s> <s xml:id="echoid-s19581" xml:space="preserve">A B D. </s> <s xml:id="echoid-s19582" xml:space="preserve">quare in di-<lb/>ſtantia 24. </s> <s xml:id="echoid-s19583" xml:space="preserve">paſſuum <lb/>aliæ lineæ inciden <lb/>tes, & </s> <s xml:id="echoid-s19584" xml:space="preserve">ipſi propio-<lb/>res, faciunt pariter <lb/>angulos ad ſenſum <lb/>ſemirectos, aut ſal-<lb/>tẽ paulò minores, <lb/>quales eſſent A C I. </s> <s xml:id="echoid-s19585" xml:space="preserve"><lb/>A D K. </s> <s xml:id="echoid-s19586" xml:space="preserve">quare reflectentur etiam per angulos ſemirectos, atq; </s> <s xml:id="echoid-s19587" xml:space="preserve">in parietes viciſſim oppoſitos, ideſt, linea A C. </s> <s xml:id="echoid-s19588" xml:space="preserve"><lb/>reflectetur per lineam C D. </s> <s xml:id="echoid-s19589" xml:space="preserve">facietq; </s> <s xml:id="echoid-s19590" xml:space="preserve">angulum reflexionis B C D. </s> <s xml:id="echoid-s19591" xml:space="preserve">ferè ſemirectum. </s> <s xml:id="echoid-s19592" xml:space="preserve">pariter lineæ incidentis <lb/>A D. </s> <s xml:id="echoid-s19593" xml:space="preserve">reflexa erit D C. </s> <s xml:id="echoid-s19594" xml:space="preserve">ad angulum ſemirectum B D C. </s> <s xml:id="echoid-s19595" xml:space="preserve">poſtea vtraque iterum ex locis C D. </s> <s xml:id="echoid-s19596" xml:space="preserve">reflectetur verſus <lb/>ſonorum per lineas C A. </s> <s xml:id="echoid-s19597" xml:space="preserve">D A. </s> <s xml:id="echoid-s19598" xml:space="preserve">ſecundum angulos pariter ſemirectos; </s> <s xml:id="echoid-s19599" xml:space="preserve">qua ratione eãdem vocem referent ad <lb/>ſonorum A. </s> <s xml:id="echoid-s19600" xml:space="preserve">Porrò claritatis huius angularis Echus maioris, quam plani reflectentis, cauſa eſſe puto plurium <lb/>reflexarum linearum vnionem ſeu concurſum ad idem ſonorum A. </s> <s xml:id="echoid-s19601" xml:space="preserve">vt conſideranti, & </s> <s xml:id="echoid-s19602" xml:space="preserve">comparanti figurnm <lb/>hanc cum ſuperioribus figuris planorum reflectentium, facilè patebit; </s> <s xml:id="echoid-s19603" xml:space="preserve">ex plano enim pauciſſimæ lineę reuer-<lb/>tuntur ad eundem locum A. </s> <s xml:id="echoid-s19604" xml:space="preserve">vt propterea admittendæ ſint aliæ propiores normali, quæ neq; </s> <s xml:id="echoid-s19605" xml:space="preserve">cum ipſa, neq; </s> <s xml:id="echoid-s19606" xml:space="preserve"><lb/>inuicem concurrunt ad A. </s> <s xml:id="echoid-s19607" xml:space="preserve">ex quibus etiam manifeſta eſt cauſa cur clariſſimæ Echus ex aduerſis fluminum ri-<lb/>pis reſonent, quia videlicet reſonant ex angulis aquæ ac ripę ad ſonorum, vt plurimum è regione anguli ele-<lb/>uatum. </s> <s xml:id="echoid-s19608" xml:space="preserve">ſed vide quæ ſupra vbi de interuallo inter ſonorum, & </s> <s xml:id="echoid-s19609" xml:space="preserve">reflectens annotauimus.</s> <s xml:id="echoid-s19610" xml:space="preserve"/> </p> <div xml:id="echoid-div512" type="float" level="2" n="1"> <figure xlink:label="fig-0250-01" xlink:href="fig-0250-01a"> <image file="0250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0250-01"/> </figure> </div> <pb o="229" file="0251" n="256" rhead="DE ECHO."/> <p> <s xml:id="echoid-s19611" xml:space="preserve">Sed hic dubitatur cur in concurſu linearum refl<unsure/>exarum C D. </s> <s xml:id="echoid-s19612" xml:space="preserve">& </s> <s xml:id="echoid-s19613" xml:space="preserve">D C. </s> <s xml:id="echoid-s19614" xml:space="preserve">cum normali A B. </s> <s xml:id="echoid-s19615" xml:space="preserve">non fiat bombus; <lb/></s> <s xml:id="echoid-s19616" xml:space="preserve">verùm reſpondetur, ſicuti diuerſa lumina impermixta eundem aerem illuminant; </s> <s xml:id="echoid-s19617" xml:space="preserve">& </s> <s xml:id="echoid-s19618" xml:space="preserve">ficuti in eadem aqua <lb/>contrarij, & </s> <s xml:id="echoid-s19619" xml:space="preserve">concurrentes circuli, & </s> <s xml:id="echoid-s19620" xml:space="preserve">tamen impermixti tendunt in partes contrarias, idem accidere etiam <lb/>ſono. </s> <s xml:id="echoid-s19621" xml:space="preserve">quod etiam experientia ab ipſa Echo deſumpta confirmatur; </s> <s xml:id="echoid-s19622" xml:space="preserve">nam ſi ſonorum ſit longè à pariete, au-<lb/>diens autem alter propè<unsure/> parietem, audiet vtramq; </s> <s xml:id="echoid-s19623" xml:space="preserve">vocem ſimul diſtinctè, primam ſcilicet, & </s> <s xml:id="echoid-s19624" xml:space="preserve">refl<unsure/>exam. </s> <s xml:id="echoid-s19625" xml:space="preserve">opor-<lb/>tet autem in eo caſu, primariam vocem ob diſtantiam ſonori ſatis magnam ab audiente, eſſe adeo remiſſam, <lb/>ac tenuem, vt refl<unsure/>exam minimè offuſcare aut opprimere valeat.</s> <s xml:id="echoid-s19626" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div514" type="section" level="1" n="389"> <head xml:id="echoid-head408" style="it" xml:space="preserve">Conuexum rectiplanum, vti est angulus conuexus domorum ineptiſſimum <lb/>est ad Echum. Theorema XVIII.</head> <p> <s xml:id="echoid-s19627" xml:space="preserve">RAtio eſt eadem, quæ in ſphærico conuexo. </s> <s xml:id="echoid-s19628" xml:space="preserve">vt in eadem præcedenti figura, ſit conuexus angulus C B D. <lb/></s> <s xml:id="echoid-s19629" xml:space="preserve">ſonorum ſit in H. </s> <s xml:id="echoid-s19630" xml:space="preserve">vnica erit perpendicularis H B. </s> <s xml:id="echoid-s19631" xml:space="preserve">reliquæ omnes quales ſunt H C. </s> <s xml:id="echoid-s19632" xml:space="preserve">H D. </s> <s xml:id="echoid-s19633" xml:space="preserve">magnopere in <lb/>partes diuerſas, & </s> <s xml:id="echoid-s19634" xml:space="preserve">alteras, ob æqualitatem angulorum incidentiæ, & </s> <s xml:id="echoid-s19635" xml:space="preserve">reflexionis diſpcrguntur. </s> <s xml:id="echoid-s19636" xml:space="preserve">quare ne-<lb/>que propiores ipſi normali, eam iuuare poterunt ad Echum reſonandam. </s> <s xml:id="echoid-s19637" xml:space="preserve">Hactenus de Echo monopho-<lb/>na, reliquum eſt nunc de polyphona agere.</s> <s xml:id="echoid-s19638" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div515" type="section" level="1" n="390"> <head xml:id="echoid-head409" style="it" xml:space="preserve">De Echo polyphona, ſiue multiplici.</head> <p> <s xml:id="echoid-s19639" xml:space="preserve">PRofectò iucunda æquè ac mirabilis eſt natura Echus vniuerſim, verum illius maximè, quæ non ſemel <lb/>tantum noſtras voces repetit, ſed eaſdem etiam eleganter, concinneque ſolet ſæpius ingeminare. </s> <s xml:id="echoid-s19640" xml:space="preserve">vt pro-<lb/>pterea tum antiquis, tum etiam recentioribus Scriptoribus digna ſit habita, quæ memoriæ literis conſigna-<lb/>retur; </s> <s xml:id="echoid-s19641" xml:space="preserve">Lucretius enim poeta antiquiſſimus, ſic de ea cecinit;</s> <s xml:id="echoid-s19642" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19643" xml:space="preserve">Sex etiam, aut ſeptem loca vidi reddere voces, <lb/>Vnam cùm faceres: </s> <s xml:id="echoid-s19644" xml:space="preserve">ita colles collibus ipſis <lb/>Verba repulſantes iterabant dicta referre.</s> <s xml:id="echoid-s19645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19646" xml:space="preserve">poſtea Plinius lib. </s> <s xml:id="echoid-s19647" xml:space="preserve">36. </s> <s xml:id="echoid-s19648" xml:space="preserve">cap. </s> <s xml:id="echoid-s19649" xml:space="preserve">15. </s> <s xml:id="echoid-s19650" xml:space="preserve">hęc habet; </s> <s xml:id="echoid-s19651" xml:space="preserve">in vrbe Cuaici iuxta portam quandam, Turres ſeptem acceptas voces <lb/>numeroſiores repercuſſu muultiplicant: </s> <s xml:id="echoid-s19652" xml:space="preserve">nomenq; </s> <s xml:id="echoid-s19653" xml:space="preserve">huic miraculo Echo eſt. </s> <s xml:id="echoid-s19654" xml:space="preserve">Olympiæ autem arce, mirabili <lb/>modo, in porticu, quod ob id Heptaphonon appellant, quoniam ſepties eadem vox redditur. </s> <s xml:id="echoid-s19655" xml:space="preserve">demum Pauſa-<lb/>nias in Corinthiacis alterius ſic meminit, apud Hermonienſes porticus eſt, quam Echus incolæ vocant, eius <lb/>ea natura eſt, vt miſſa vox, vt minimum triplicetur. </s> <s xml:id="echoid-s19656" xml:space="preserve">Recentiores nonnulli aliam adhuc magis miram tradunt <lb/>audiri propè Mediolanum, in villa cui nomen Simoneta, quæ magno audientium ſtupore, eandem vocem, & </s> <s xml:id="echoid-s19657" xml:space="preserve"><lb/>quidem diſſylabam, vti, Arma, vigeties replicet. </s> <s xml:id="echoid-s19658" xml:space="preserve">Ego tandem cum aliquando varias Echus, ſimul cũ meis ſo-<lb/>dalibus oblectandi animi cauſa indagaremus, vnã pentaphonam, quę ſcilicet quinquies concinnè admodum <lb/>noſtras voces recantabat, inuenimus. </s> <s xml:id="echoid-s19659" xml:space="preserve">ad quam ſubinde adhibitis etiam ſonoris inſtrumentis, tibijs, tubis, tym <lb/>panis accedere ſolebamus, vt eam ſuauiter noſtras modulationes recantitantem iucunda animi oblectatio-<lb/>ne, auſcultaremus. </s> <s xml:id="echoid-s19660" xml:space="preserve">atqui multo nunc iucundius forè exiſtimo, admirandi huius effectus cauſam aperire.</s> <s xml:id="echoid-s19661" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div516" type="section" level="1" n="391"> <head xml:id="echoid-head410" style="it" xml:space="preserve">Multiplicis Echus cauſam aperire. Theorema XIX.</head> <p> <s xml:id="echoid-s19662" xml:space="preserve">QVam nobis partim præmiſſa doctrina de Echo ſimplici, partim loci huius noſtri pentaphonę Echus for <lb/>ma, & </s> <s xml:id="echoid-s19663" xml:space="preserve">conſtitutio patefecit, erant enim quinque rupes, ſeu crepidines è ripa cuiuſdam profundi torren-<lb/>tis prominẽtes vna poſt alteram ordinatim, quales præ-<lb/> <anchor type="figure" xlink:label="fig-0251-01a" xlink:href="fig-0251-01"/> ſens delineatio vtcunq; </s> <s xml:id="echoid-s19664" xml:space="preserve">refert A B C D E. </s> <s xml:id="echoid-s19665" xml:space="preserve">Sonorum in <lb/>ſitu ad eas recto erat, vti in F. </s> <s xml:id="echoid-s19666" xml:space="preserve">ſic enim lineæ vocales plu-<lb/>rimæ in illarum ſingulas ad ſenſum normaliter incurre-<lb/>bant. </s> <s xml:id="echoid-s19667" xml:space="preserve">prima igitur rupes A. </s> <s xml:id="echoid-s19668" xml:space="preserve">vocem miſſam primò repe-<lb/>tebat; </s> <s xml:id="echoid-s19669" xml:space="preserve">ſecunda B. </s> <s xml:id="echoid-s19670" xml:space="preserve">ſecundo; </s> <s xml:id="echoid-s19671" xml:space="preserve">tertia C. </s> <s xml:id="echoid-s19672" xml:space="preserve">tertio, & </s> <s xml:id="echoid-s19673" xml:space="preserve">cæterę, ſta-<lb/>tim vna poſt alteram, eandem voeem ingeminabunt. <lb/></s> <s xml:id="echoid-s19674" xml:space="preserve">Erant enim ſingulæ rupes ſingula reflectentia reſpectu <lb/>eiuſdem ſonori, erantq; </s> <s xml:id="echoid-s19675" xml:space="preserve">ſitus eorum conueniens. </s> <s xml:id="echoid-s19676" xml:space="preserve">verum <lb/>quia variæ erant diſtantiæ à ſonoro F. </s> <s xml:id="echoid-s19677" xml:space="preserve">fiebat vt propior <lb/>citius, ſecunda paulò tardius, & </s> <s xml:id="echoid-s19678" xml:space="preserve">ſic deinceps vſque ad vl-<lb/>timam reſonarent. </s> <s xml:id="echoid-s19679" xml:space="preserve">ex quibus patet nihil aliud eſſe mul-<lb/>tiplicem Echum, quam plura refleſtentia cum diuerſis <lb/>diſtantijs ab eodem ſonoro. </s> <s xml:id="echoid-s19680" xml:space="preserve">Cæterum quæ hactenus diſ-<lb/>ſeruimus ad Theoriam pertinent: </s> <s xml:id="echoid-s19681" xml:space="preserve">quæ verò ſequuntur <lb/>etiam ad opus, & </s> <s xml:id="echoid-s19682" xml:space="preserve">praxim.</s> <s xml:id="echoid-s19683" xml:space="preserve"/> </p> <div xml:id="echoid-div516" type="float" level="2" n="1"> <figure xlink:label="fig-0251-01" xlink:href="fig-0251-01a"> <image file="0251-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0251-01"/> </figure> </div> <pb o="230" file="0252" n="257" rhead="DE ECHO."/> </div> <div xml:id="echoid-div518" type="section" level="1" n="392"> <head xml:id="echoid-head411" style="it" xml:space="preserve">Dati ſonori lineam actionis reperire. Problema I.</head> <p> <s xml:id="echoid-s19684" xml:space="preserve">IDexperimẽto diſees, tanta eſt enim linea actionis, quanta eſt maxima diſtãtia, ex qua vox tua ab alio audiri <lb/>poterit. </s> <s xml:id="echoid-s19685" xml:space="preserve">vel abſq; </s> <s xml:id="echoid-s19686" xml:space="preserve">auxilio alterius, ſed tantũ auxilio ipſius Echus: </s> <s xml:id="echoid-s19687" xml:space="preserve">ſi enim a pariete tibi reſonã@e eouſq; </s> <s xml:id="echoid-s19688" xml:space="preserve">pau <lb/>l<unsure/>atim recedas donec vltimo Echũ exaudias, erit diſtadtia hæc dimidia lineę actionis, vt ex 6. </s> <s xml:id="echoid-s19689" xml:space="preserve">Theor. </s> <s xml:id="echoid-s19690" xml:space="preserve">apparet.</s> <s xml:id="echoid-s19691" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div519" type="section" level="1" n="393"> <head xml:id="echoid-head412" style="it" xml:space="preserve">Dato quouis reflectente, & quouis ſonoro, locum reperire vnde ſonorum <lb/>ſibi Echum eliciat. Problema II.</head> <p> <s xml:id="echoid-s19692" xml:space="preserve">PRimò ſonorum conſtituendum eſt in eo loco, vnde vocalis eius linea normaliter teflectenti occurrat. <lb/></s> <s xml:id="echoid-s19693" xml:space="preserve">Secundo, in tanta ab eo diſtantia, quæ maior non ſit ſemiſſe lineæ actionis inuentæ ex problem. </s> <s xml:id="echoid-s19694" xml:space="preserve">præce-<lb/>denti, nec minor 24. </s> <s xml:id="echoid-s19695" xml:space="preserve">paſſibus geometricis.</s> <s xml:id="echoid-s19696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19697" xml:space="preserve">His enim præhabitis, palam eſt ex 3. </s> <s xml:id="echoid-s19698" xml:space="preserve">5. </s> <s xml:id="echoid-s19699" xml:space="preserve">6. </s> <s xml:id="echoid-s19700" xml:space="preserve">Theorematibus, Echum noſtras voces alternaturam eſſe; </s> <s xml:id="echoid-s19701" xml:space="preserve">ſic-<lb/>que ex quolibet pariete Echum audire poterimus.</s> <s xml:id="echoid-s19702" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div520" type="section" level="1" n="394"> <head xml:id="echoid-head413" style="it" xml:space="preserve">Adato quolibet plano pariete Echum obliquam elicere. Problema III.</head> <p> <s xml:id="echoid-s19703" xml:space="preserve">SOnorum, & </s> <s xml:id="echoid-s19704" xml:space="preserve">audiens in diuerſas parietis partes<unsure/> vtrinq; </s> <s xml:id="echoid-s19705" xml:space="preserve">abeant, ita vt vt vterq; </s> <s xml:id="echoid-s19706" xml:space="preserve">obliquè parietem mediũ, <lb/>necnon quantũ fieri poteſt ad angulos ęquales aſpici<unsure/>ant; </s> <s xml:id="echoid-s19707" xml:space="preserve">ſicuti ſecunda figura indicat; </s> <s xml:id="echoid-s19708" xml:space="preserve">vbi ex ſonoro A. </s> <s xml:id="echoid-s19709" xml:space="preserve">li-<lb/>nea ſonora A B. </s> <s xml:id="echoid-s19710" xml:space="preserve">in parietem D B E. </s> <s xml:id="echoid-s19711" xml:space="preserve">oblique incidens reflectitur ad audientem C. </s> <s xml:id="echoid-s19712" xml:space="preserve">per lineam B C. </s> <s xml:id="echoid-s19713" xml:space="preserve">fiuntq; </s> <s xml:id="echoid-s19714" xml:space="preserve">an-<lb/>guli incidentiæ A B D. </s> <s xml:id="echoid-s19715" xml:space="preserve">& </s> <s xml:id="echoid-s19716" xml:space="preserve">reflexionis C B E. </s> <s xml:id="echoid-s19717" xml:space="preserve">æquales, quare per 12. </s> <s xml:id="echoid-s19718" xml:space="preserve">Theor. </s> <s xml:id="echoid-s19719" xml:space="preserve">audiens in C. </s> <s xml:id="echoid-s19720" xml:space="preserve">audiet Echum ipſius <lb/>A. </s> <s xml:id="echoid-s19721" xml:space="preserve">hoc eſt audiet vocem eius reflexam. </s> <s xml:id="echoid-s19722" xml:space="preserve">& </s> <s xml:id="echoid-s19723" xml:space="preserve">poterit aliquando etiam audire primariam.</s> <s xml:id="echoid-s19724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19725" xml:space="preserve">Eodem modò facilè erit Echum ſecundariam, tertiariam, &</s> <s xml:id="echoid-s19726" xml:space="preserve">c. </s> <s xml:id="echoid-s19727" xml:space="preserve">ex Theor. </s> <s xml:id="echoid-s19728" xml:space="preserve">conſtruere.</s> <s xml:id="echoid-s19729" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div521" type="section" level="1" n="395"> <head xml:id="echoid-head414" style="it" xml:space="preserve">Echum circularem construere. Problema IV.</head> <p> <s xml:id="echoid-s19730" xml:space="preserve">AD hanc pulcherrimam conſtructionẽ opus eſt duobus planis parietibus inuicem paralellis ſatis magnis, <lb/>ſatiſq; </s> <s xml:id="echoid-s19731" xml:space="preserve">inuicem diſtantibus. </s> <s xml:id="echoid-s19732" xml:space="preserve">in horum alterius feneſtris ſonorum ſimul cum alijs auditoribus collocandi <lb/>ſunt: </s> <s xml:id="echoid-s19733" xml:space="preserve">Sonorum quidem in medio, alij vero auditores circa ipium in gyrum. </s> <s xml:id="echoid-s19734" xml:space="preserve">alter autem paries erit pro re-<lb/>flectente. </s> <s xml:id="echoid-s19735" xml:space="preserve">quibus paratis (ex dictis ad 5. </s> <s xml:id="echoid-s19736" xml:space="preserve">definit.) </s> <s xml:id="echoid-s19737" xml:space="preserve">vox ſonori non ſolum normaliter incidet in oppoſitum re-<lb/>flectens, ſed etiam circumquaq; </s> <s xml:id="echoid-s19738" xml:space="preserve">obliquè, & </s> <s xml:id="echoid-s19739" xml:space="preserve">in eadem diſtantia a normali, ideſt, ad ſiniſtram, ad dexteram, ſu@ <lb/>ſum, deorſum æquè longè à<unsure/> perpendiculari. </s> <s xml:id="echoid-s19740" xml:space="preserve">quare etiam obliquè reflectentur per plurimas lineas in diuer-<lb/>ſas partes per angulos æquales angulis incidentium, vnde & </s> <s xml:id="echoid-s19741" xml:space="preserve">ad priorem murum reuertentur, in quo ſonorũ, <lb/>& </s> <s xml:id="echoid-s19742" xml:space="preserve">alij circa ipſum audientes ſiti ſunt. </s> <s xml:id="echoid-s19743" xml:space="preserve">linea igitur normalis reuertetur ad ipſum ſonorum; </s> <s xml:id="echoid-s19744" xml:space="preserve">aliæ verò ad alios <lb/>auditores ipfum ſatis longè circumdantes, ac proinde ij omnes proprias Echus exaudient. </s> <s xml:id="echoid-s19745" xml:space="preserve">vt patet ex Con-<lb/>ſectario Theor. </s> <s xml:id="echoid-s19746" xml:space="preserve">12. </s> <s xml:id="echoid-s19747" xml:space="preserve">& </s> <s xml:id="echoid-s19748" xml:space="preserve">partim intelligi poteſt ex figura eiuſdem; </s> <s xml:id="echoid-s19749" xml:space="preserve">in qua ſicuti duas Echus dextram, & </s> <s xml:id="echoid-s19750" xml:space="preserve">ſiniſtrã <lb/>ab eodem ſonoro A. </s> <s xml:id="echoid-s19751" xml:space="preserve">ad auditores C H. </s> <s xml:id="echoid-s19752" xml:space="preserve">depingimus; </s> <s xml:id="echoid-s19753" xml:space="preserve">ſic etian, innumeras alias ex plurimis punctis eiuſdem <lb/>parietis circa D. </s> <s xml:id="echoid-s19754" xml:space="preserve">in eundem orbem cum B E. </s> <s xml:id="echoid-s19755" xml:space="preserve">ſitis, concipere debemus reflexas ad alios auditores circa ipſum <lb/>A. </s> <s xml:id="echoid-s19756" xml:space="preserve">in circulum in feneſtris parietis ſimul cum A. </s> <s xml:id="echoid-s19757" xml:space="preserve">ſonoro, conſtitutos.</s> <s xml:id="echoid-s19758" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div522" type="section" level="1" n="396"> <head xml:id="echoid-head415" style="it" xml:space="preserve">Dato loco ſonori, vna cum eius linea actionis, eireflectus Echum conſtruere <lb/>Problema V.</head> <p> <s xml:id="echoid-s19759" xml:space="preserve">ALoco ſonori metire rectam diſtantiam noh maiorem ſemiſſe lineæ actionis eiuſddem: </s> <s xml:id="echoid-s19760" xml:space="preserve">metire etiam ab <lb/>eodem loco verſus eandem partem minimã reflectentis diſtantiam, videlicet paſſus geometricos 24. </s> <s xml:id="echoid-s19761" xml:space="preserve">plus <lb/>minus. </s> <s xml:id="echoid-s19762" xml:space="preserve">atq; </s> <s xml:id="echoid-s19763" xml:space="preserve">inter vtrumq; </s> <s xml:id="echoid-s19764" xml:space="preserve">terminum cõſtrue reflectens aliquod è ſuperioribus, in ſitu tamen perpendiculari <lb/>ad lineam actionis. </s> <s xml:id="echoid-s19765" xml:space="preserve">manifeſtum enim eſt ex Theor. </s> <s xml:id="echoid-s19766" xml:space="preserve">3. </s> <s xml:id="echoid-s19767" xml:space="preserve">5. </s> <s xml:id="echoid-s19768" xml:space="preserve">6. </s> <s xml:id="echoid-s19769" xml:space="preserve">Echum inde auditum iri. </s> <s xml:id="echoid-s19770" xml:space="preserve">Cæterum ſi diſtantia <lb/>fererit 24. </s> <s xml:id="echoid-s19771" xml:space="preserve">paſſuum, erit Echo monoſyllaba; </s> <s xml:id="echoid-s19772" xml:space="preserve">ſi 48. </s> <s xml:id="echoid-s19773" xml:space="preserve">diſſyllaba; </s> <s xml:id="echoid-s19774" xml:space="preserve">ſi 70. </s> <s xml:id="echoid-s19775" xml:space="preserve">ferè triſyl@aba, &</s> <s xml:id="echoid-s19776" xml:space="preserve">c.</s> <s xml:id="echoid-s19777" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div523" type="section" level="1" n="397"> <head xml:id="echoid-head416" style="it" xml:space="preserve">Echum polyphonam conſtruere. Problema VI.</head> <p> <s xml:id="echoid-s19778" xml:space="preserve">PRimo in planitie quapiam ſatis magna, eligatur locus ſonori; </s> <s xml:id="echoid-s19779" xml:space="preserve">poſtea ex præced. </s> <s xml:id="echoid-s19780" xml:space="preserve">Probl. </s> <s xml:id="echoid-s19781" xml:space="preserve">conſtruantur plu-<lb/>ra ad eum locum reflectentia, cum diuerſis ac talibus ab eo diſtantijs vt primũ, ſeu quod ei propius fuerit, <lb/>Echum mono@yllabam reſohet: </s> <s xml:id="echoid-s19782" xml:space="preserve">ſecundum quod ferè duplo diſtabit diſſyllabam: </s> <s xml:id="echoid-s19783" xml:space="preserve">tertium quod quaſi triplo <lb/>aberit, triſyllabam. </s> <s xml:id="echoid-s19784" xml:space="preserve">& </s> <s xml:id="echoid-s19785" xml:space="preserve">ſic deinceps prout libuerit Echum efficere numeroſiorem ea igitur totuplicem Echũ <lb/>conſtituent, quot ipſa erunt reflectentia; </s> <s xml:id="echoid-s19786" xml:space="preserve">repetentq; </s> <s xml:id="echoid-s19787" xml:space="preserve">ſingula vnã eandemq; </s> <s xml:id="echoid-s19788" xml:space="preserve">ſyllabam, continuò poſt alteram <pb o="231" file="0253" n="258" rhead="DE ECHO."/> toties quot ipſa ſunt, vt ex demonſtratis conſtat. </s> <s xml:id="echoid-s19789" xml:space="preserve">Porrò reflectentia hac ratione, & </s> <s xml:id="echoid-s19790" xml:space="preserve">ordine cõſtructa Echum <lb/>eſſicient, vt ex ipſa conſtructione patet, poly phonam quidem, ſed monoſyllabam: </s> <s xml:id="echoid-s19791" xml:space="preserve">quamuis enim ſecundum <lb/>poſſit repetere duas ſyllabas, & </s> <s xml:id="echoid-s19792" xml:space="preserve">tertium tres, &</s> <s xml:id="echoid-s19793" xml:space="preserve">c. </s> <s xml:id="echoid-s19794" xml:space="preserve">quia tamen primum vnam eandemq; </s> <s xml:id="echoid-s19795" xml:space="preserve">cum eo pariter reſo-<lb/>nent. </s> <s xml:id="echoid-s19796" xml:space="preserve">quod ſi velimus Echum polyphonam diſſylabam, quæ ſcilicet verbum diſſyllabum referat; </s> <s xml:id="echoid-s19797" xml:space="preserve">conſtruen-<lb/>dum eſt ex præced. </s> <s xml:id="echoid-s19798" xml:space="preserve">Probl. </s> <s xml:id="echoid-s19799" xml:space="preserve">primum reflectens, quod ſit diſſyllabum, cuius diſtantia |erit ferè 46. </s> <s xml:id="echoid-s19800" xml:space="preserve">paſſuum. <lb/></s> <s xml:id="echoid-s19801" xml:space="preserve">ſecundum vero cuius diſtantia ſit paulo minor quà<unsure/>m dupla præcedentis, & </s> <s xml:id="echoid-s19802" xml:space="preserve">reliqua eadem ratione. </s> <s xml:id="echoid-s19803" xml:space="preserve">ſi verò <lb/>velimus Echum triſyllabam, aut tetraſyllabam, ea couſtruemus ex præcedenti Probl. </s> <s xml:id="echoid-s19804" xml:space="preserve">proportionaliter ad <lb/>prædicta.</s> <s xml:id="echoid-s19805" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19806" xml:space="preserve">Ex quibus pat@t, ſi à priori ſerie reflectentium, auferantur ea, quæ numero impari afficiuntur, ideſt, pri-<lb/>mum, tertium, &</s> <s xml:id="echoid-s19807" xml:space="preserve">c. </s> <s xml:id="echoid-s19808" xml:space="preserve">imparia, ea quæ relinquentur eſſectura eſſe Echum polyphonam diſſyllabam, &</s> <s xml:id="echoid-s19809" xml:space="preserve">c. </s> <s xml:id="echoid-s19810" xml:space="preserve">Porro <lb/>pro numero reflectentinm erit Echo ant diphona, aut triphona, aut tetraphona, pentaphona, &</s> <s xml:id="echoid-s19811" xml:space="preserve">c. </s> <s xml:id="echoid-s19812" xml:space="preserve">Sciẽdum <lb/>præterea poſſe hæc reflectentia vario ordine collocari, ideſt, aut omnia ſecundum eandem horizontis plagã <lb/>ſermè in directum; </s> <s xml:id="echoid-s19813" xml:space="preserve">aut ſecundum diuerſas plagas, & </s> <s xml:id="echoid-s19814" xml:space="preserve">quaſi in gyrum loco ſonori circundantia, ante, retro, a <lb/>dextris, à<unsure/> ſiniſtris: </s> <s xml:id="echoid-s19815" xml:space="preserve">quouis enim modo audiemus Echum multiplicem. </s> <s xml:id="echoid-s19816" xml:space="preserve">priori tamen modo, Echo euadet igna-<lb/>ris mirabilior, quòd tunc minimè agnoſcant multitudinem reflectentium, putetq; </s> <s xml:id="echoid-s19817" xml:space="preserve">eſſe vnum tantum, atque <lb/>vnam tantum Echum, quæ ſæpius miro quodam modo, reflectat. </s> <s xml:id="echoid-s19818" xml:space="preserve">quod ſi ex diuerſis partibus exaudiatur re-<lb/>flexio, manifeſtiora euadunt plura reflectentia, & </s> <s xml:id="echoid-s19819" xml:space="preserve">plures Echi; </s> <s xml:id="echoid-s19820" xml:space="preserve">quapropter cognita @@ultiplicis reſonantiæ <lb/>cauſa, ijdem nihil amplius mirantur. </s> <s xml:id="echoid-s19821" xml:space="preserve">Tandem illud non omittam, diſtantias horum reflectentium non vi-<lb/>deri ſeruare eandem inter ſe proportionem Arithmeticam, ita vt diſtantia ſecundi reflectentis ſit omninò <lb/>dupla diſtantiæ primi, & </s> <s xml:id="echoid-s19822" xml:space="preserve">diſtantia tertij ſit ſeſquialtera diſtantiæ ſecundi; </s> <s xml:id="echoid-s19823" xml:space="preserve">& </s> <s xml:id="echoid-s19824" xml:space="preserve">diſtantia quarti, ſit ſeſquitertia <lb/>diſtantiæ tcrtij. </s> <s xml:id="echoid-s19825" xml:space="preserve">ſed videntur ſemper magis decreſcere, & </s> <s xml:id="echoid-s19826" xml:space="preserve">minui, quo longius abeunt, ideſi, ſecunda diſtantia <lb/>eſt paulo minor quam dupla primæ, & </s> <s xml:id="echoid-s19827" xml:space="preserve">diſtantia tertia eſt paulo minor quàm ſeſquialtera ſecundæ; </s> <s xml:id="echoid-s19828" xml:space="preserve">pariter <lb/>diſtantia quarta adhuc multo minor eſt quãm vt ſit ſeſquitertia tertiæ; </s> <s xml:id="echoid-s19829" xml:space="preserve">& </s> <s xml:id="echoid-s19830" xml:space="preserve">ſic deinceps. </s> <s xml:id="echoid-s19831" xml:space="preserve">quod fortè inde pro-<lb/>uenit, quod vox quo longius propagatur, eo tardius propagatur: </s> <s xml:id="echoid-s19832" xml:space="preserve">tardius autem propagatur eadem de cauſa <lb/>qua cæteræ actiones naturales in progreſſu debilitantur; </s> <s xml:id="echoid-s19833" xml:space="preserve">ſit enim vox cum quadam aeris motione violenta, <lb/>violentæ autem motiones ſolent citò debilitari ac remitti, ob hancigitur tarditatem minori opus eſt diſtan-<lb/>tia, vt poſſit vox reflexa, primaria iam extincta, reuerti ad ſonorum.</s> <s xml:id="echoid-s19834" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19835" xml:space="preserve">ALITER MECHANICE. </s> <s xml:id="echoid-s19836" xml:space="preserve">Conſtruatur refl<unsure/>ectens mobile, ac geſtabile ex aſſeribus (Tabulatum <lb/>enim ſatis planum ex aſſeribus, non ſecus ac paries Echum reſonat) illud deinde à loco ſonori adeo longè, <lb/>atq; </s> <s xml:id="echoid-s19837" xml:space="preserve">in eo ſitu erigatur, vt inde vnam tantum ſyllabam refl<unsure/>ectat. </s> <s xml:id="echoid-s19838" xml:space="preserve">hinc poſtea eo vſq; </s> <s xml:id="echoid-s19839" xml:space="preserve">trãsferatur, donec duas <lb/>ſyllabas, ſeu verbum diſſyllabum repetat. </s> <s xml:id="echoid-s19840" xml:space="preserve">tertio adhuc vlterius ſe ponatur. </s> <s xml:id="echoid-s19841" xml:space="preserve">vnde triſyllabum verbum reſo-<lb/>net; </s> <s xml:id="echoid-s19842" xml:space="preserve">& </s> <s xml:id="echoid-s19843" xml:space="preserve">ſic deinceps prout numeroſiorem Echum conſtruere placuerit. </s> <s xml:id="echoid-s19844" xml:space="preserve">notentur autem, loca ex quibus refl<unsure/>e-<lb/>ctens mobile refl<unsure/>ectebat, vnam, duas, tres, &</s> <s xml:id="echoid-s19845" xml:space="preserve">c. </s> <s xml:id="echoid-s19846" xml:space="preserve">ſyllabas; </s> <s xml:id="echoid-s19847" xml:space="preserve">atq; </s> <s xml:id="echoid-s19848" xml:space="preserve">in ijſdem locis totidem ſtabilia refl<unsure/>ectentia ijſ-<lb/>dem legibus quibus ſuperiora conſtruantur: </s> <s xml:id="echoid-s19849" xml:space="preserve">quæ ſi erratum non fuerit erunt eadem cum ijs quæ ſuperius re-<lb/>perta ſunt. </s> <s xml:id="echoid-s19850" xml:space="preserve">nihiligitur aliud de his dicendum ſupereſt, quam quod de illis dictum eſt.</s> <s xml:id="echoid-s19851" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div524" type="section" level="1" n="398"> <head xml:id="echoid-head417" style="it" xml:space="preserve">Colophon. De Echo ſuhmiſſa, ac taciturna.</head> <p> <s xml:id="echoid-s19852" xml:space="preserve">HActenus NN. </s> <s xml:id="echoid-s19853" xml:space="preserve">Echum ſonorum, atq; </s> <s xml:id="echoid-s19854" xml:space="preserve">apertè reſpondentem inſequentes, quantumuis ſylueſtrem, & </s> <s xml:id="echoid-s19855" xml:space="preserve">fu-<lb/>gientem, nihilominus tamen depræhendimus, atq; </s> <s xml:id="echoid-s19856" xml:space="preserve">in conſpectum veſtrum adduximus. </s> <s xml:id="echoid-s19857" xml:space="preserve">quod quidem, <lb/>ſi vobis (vt præ vobis fertis) iucundum, gratumq; </s> <s xml:id="echoid-s19858" xml:space="preserve">contigit ſpectaculum, iucundius multo gratiuſque acci-<lb/>dere neceſſe eſt, Echum alteram penè taciturnam, ac omnino non vt prior, rudibus in antris, concauiſque <lb/>ſpecubus abditam, ſed mirum; </s> <s xml:id="echoid-s19859" xml:space="preserve">in læuigatis ac concauis ſpeculis mirè latitantem, tandem inuentam, captam-<lb/>que, atq; </s> <s xml:id="echoid-s19860" xml:space="preserve">è ſuis latebris in publicum euocatam, hodie pro libito conſpicere. </s> <s xml:id="echoid-s19861" xml:space="preserve">Hanc igitur nunc poſt priorem <lb/>alteram, veluti in triumphum vobis ſpectantibus traducemus. </s> <s xml:id="echoid-s19862" xml:space="preserve">primus Hector Auſonius Venetijs, & </s> <s xml:id="echoid-s19863" xml:space="preserve">poſtea <lb/>loan. </s> <s xml:id="echoid-s19864" xml:space="preserve">Baptiſta Porta ſecretorum naturæ particeps, & </s> <s xml:id="echoid-s19865" xml:space="preserve">veluti canis ſagax, quamuis latentem indicauit tamen, <lb/>vnde nos eam non magno labore, ſed magna cum voluptate cæpimus. </s> <s xml:id="echoid-s19866" xml:space="preserve">Sed vt rem aperiamus, dicimus hanc <lb/>ſubmiſl<unsure/>am Echum eſſe refl<unsure/>exionem vocis primæ adeo tenuis ac ſubmiſſę, vt in ea audiatur vox tantum refle-<lb/>xa, non autem primaria: </s> <s xml:id="echoid-s19867" xml:space="preserve">neq; </s> <s xml:id="echoid-s19868" xml:space="preserve">fieri niſi reflectens ſit ſpeculum ſatis magnam concauum ac terſum, vnumque <lb/>ex tribus quæ vſtoria appellantur, videlicet, ſphæricum, parabolicum, ellipticum: </s> <s xml:id="echoid-s19869" xml:space="preserve">Neq; </s> <s xml:id="echoid-s19870" xml:space="preserve">præterea audiri ab <lb/>vllo, præterquam ab vno auditore, & </s> <s xml:id="echoid-s19871" xml:space="preserve">quidem auſcultante. </s> <s xml:id="echoid-s19872" xml:space="preserve">quæ vt ſuccedant neceſſe eſt, vt audiens alteram <lb/>puncto illi apponat, in quem hæc ſpecula reflexum lumen congregant, ſeu in quo comburunt; </s> <s xml:id="echoid-s19873" xml:space="preserve">ſonorum au-<lb/>tem ſeu loquens, quod hic illuminantis corporis vices gerit, multum à ſpeculo diſtare debet, verum ſingilla-<lb/>tim nonnulla ſunt explicanda.</s> <s xml:id="echoid-s19874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19875" xml:space="preserve">Pro ſpeculo igitur Sphærico hæc ſunt obſeruanda. </s> <s xml:id="echoid-s19876" xml:space="preserve">primo collocetur ſpeculum in loco ſatis obſcuro ac ſi-<lb/>lenti, ita vt facies concaua ſit erecta ad horizontem. </s> <s xml:id="echoid-s19877" xml:space="preserve">ſecundo lumine candelæ accenſæ è regione ſpeculi vl-<lb/>tro citroque delatæ, inueniendus eſt locus vnionis radiorum reflexorum, in quo fit combuſtio ad Solem non <lb/>me latet locum hunc eſſe in quarta parte diametri, vnde poſſet aliter inueniri, ſed pręſtat nunc, eum per can-<lb/>delam ſic breuiter inuenire. </s> <s xml:id="echoid-s19878" xml:space="preserve">porro vt hæc luminis congregatio appareat, ea corpore quopiam aere opacio-<lb/>ri ſpeculoque oppoſito, atque hac illac commoto excipienda eſt. </s> <s xml:id="echoid-s19879" xml:space="preserve">huic igitur loco Audiens aurem alteram <lb/>adhibere opportet, altera à<unsure/> ſpeculo auerſa. </s> <s xml:id="echoid-s19880" xml:space="preserve">melius ſuccedet ſi ſocius aurem alterius applicet illi puncto, &</s> <s xml:id="echoid-s19881" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s19882" xml:space="preserve">vbi conſultum fuerit candelam non omnino directe contra ſpeculum eſſe, ſed parum extra axem, ſeu ad la- <pb o="232" file="0254" n="259" rhead="DE ECHO."/> tus, vt reflexio ad alterum latus, non autem omnino contra medium ſpeculum fiat: </s> <s xml:id="echoid-s19883" xml:space="preserve">hac enim ratione caput <lb/>auſcultantis minus aduentanti voci erit impedimẽto. </s> <s xml:id="echoid-s19884" xml:space="preserve">tertio locus loquentis vel ſonori, ſit vel vbi fuerat can-<lb/>dela, vel ſaltem in eadem rectitudine ad ſpeculum; </s> <s xml:id="echoid-s19885" xml:space="preserve">atque in ea diſtantia, vt vox ipſius ſubmiſſa ſpeculo inci-<lb/>dens, ac reflexa, audiri poſſitab auſcultante. </s> <s xml:id="echoid-s19886" xml:space="preserve">quibus adhibitis vox tantum reflexa percipitur. </s> <s xml:id="echoid-s19887" xml:space="preserve">cuius ratio eſt, <lb/>quia ſicut hoc ſpeculum vi figuræ ac terſitiei, in illud punctum lumen ſic congregat, vt ibi adeò intendatur <lb/>vt comburat; </s> <s xml:id="echoid-s19888" xml:space="preserve">vocem pariter ad illud idem punctum reuerberat, & </s> <s xml:id="echoid-s19889" xml:space="preserve">vnit, vt ex hac vnione vox paulò quam <lb/>primaria ſonantior euadat, ac propterea ab auſcultãte ſecretò audiri poſſit. </s> <s xml:id="echoid-s19890" xml:space="preserve">vocales enim lineæ caſdem cum <lb/>luminoſis reflexionis patiuntur. </s> <s xml:id="echoid-s19891" xml:space="preserve">liuius experientiæ fidelem teſtem habeo D. </s> <s xml:id="echoid-s19892" xml:space="preserve">Cæſarem Carauagium, virum <lb/>non minus ingenio, quam manu induſtrium.</s> <s xml:id="echoid-s19893" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19894" xml:space="preserve">In ſpeculo verò parabolico, eodem artificio inueniemus. </s> <s xml:id="echoid-s19895" xml:space="preserve">punctum auſcultationis, necnon diſtantiam in <lb/>illud obloquentis dixi, punctum auſcultat. </s> <s xml:id="echoid-s19896" xml:space="preserve">quoniam ex cauo parabolico omnes lineæ paralellæ incidentes <lb/>reflectuntur ad vnicum punctum, non autem ad lineam, vt in Sphærico; </s> <s xml:id="echoid-s19897" xml:space="preserve">ex Orontio, & </s> <s xml:id="echoid-s19898" xml:space="preserve">Vitell. </s> <s xml:id="echoid-s19899" xml:space="preserve">de Speculo <lb/>vſtorio, & </s> <s xml:id="echoid-s19900" xml:space="preserve">alijs, quapropter hinc paulo perfectior, cæteris paribus, reddetur Echo, quam illinc. </s> <s xml:id="echoid-s19901" xml:space="preserve">dummodo <lb/>ſonorum ab eo ita diſtet, vt lineæ incidentes aſlumi poſſint ad ſenſum pro paralellis.</s> <s xml:id="echoid-s19902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19903" xml:space="preserve">In ſpeculo tandem elliptico perfectiſſima Echo reddetur. </s> <s xml:id="echoid-s19904" xml:space="preserve">(verum hic ſuppono doctrinam peracuti opu-<lb/>ſculi de ſpeculo vſtorio, editi à D. </s> <s xml:id="echoid-s19905" xml:space="preserve">Franc. </s> <s xml:id="echoid-s19906" xml:space="preserve">Gheuara, vbi P. </s> <s xml:id="echoid-s19907" xml:space="preserve">Chriſtophorus Gruembergerius noſtræ Societ. </s> <s xml:id="echoid-s19908" xml:space="preserve">ex <lb/>data diſtantia puncti combuſtionis, & </s> <s xml:id="echoid-s19909" xml:space="preserve">luminis, nunc vero ſonori, & </s> <s xml:id="echoid-s19910" xml:space="preserve">audientis docet elliptici ſpeculi conſtru-<lb/>ctionem) cæterum m@iori hic opus eſt induſtria, cum neceſſe ſit ſonorum, & </s> <s xml:id="echoid-s19911" xml:space="preserve">audientem eſſe in duobus de-<lb/>terminatis axis ſpeculis punctis, quæ Apollonius Pergæus lib. </s> <s xml:id="echoid-s19912" xml:space="preserve">3. </s> <s xml:id="echoid-s19913" xml:space="preserve">pr. </s> <s xml:id="echoid-s19914" xml:space="preserve">48. </s> <s xml:id="echoid-s19915" xml:space="preserve">appellat puncta ex comparatione fa-<lb/>cta: </s> <s xml:id="echoid-s19916" xml:space="preserve">poſito enim ſonoro in remotiori, omnes lineæ reuerberantur ad alterum ſpeculo propinquum, non ſe-<lb/>eus ac in parabolico, vt ex allegata Apoll. </s> <s xml:id="echoid-s19917" xml:space="preserve">prop. </s> <s xml:id="echoid-s19918" xml:space="preserve">conſtat. </s> <s xml:id="echoid-s19919" xml:space="preserve">vtrumq; </s> <s xml:id="echoid-s19920" xml:space="preserve">igitur punctum ope candellæ, vt prius, in-<lb/>ueniemus, nam lumen propè ſpeculum in quopiam plano exceptum, ac maximè intẽtum indicabit alterum <lb/>videlicet auſcultantis. </s> <s xml:id="echoid-s19921" xml:space="preserve">locus vero candellæ erit alter obloquentis. </s> <s xml:id="echoid-s19922" xml:space="preserve">Erit autem hæc omnium perfectiſſima <lb/>Echo, cum propter concurſum ad vnicum punctum, tum propter æqualitatem linearum, qua fit vt om-<lb/>nes lineæ fimul ad vnum, & </s> <s xml:id="echoid-s19923" xml:space="preserve">idem auſcultationis punctum concurrant: </s> <s xml:id="echoid-s19924" xml:space="preserve">nam ex Apoll. </s> <s xml:id="echoid-s19925" xml:space="preserve">lib. </s> <s xml:id="echoid-s19926" xml:space="preserve">3. </s> <s xml:id="echoid-s19927" xml:space="preserve">prop. </s> <s xml:id="echoid-s19928" xml:space="preserve">52. </s> <s xml:id="echoid-s19929" xml:space="preserve">om-<lb/>nes lineæ rectæ ex punctis à comparatione factis ad ſuperficiem ellipticam inclinatæ ipſi axi ſunt æquales. <lb/></s> <s xml:id="echoid-s19930" xml:space="preserve">Speculum igitur ellipticum cæteris antecellet.</s> <s xml:id="echoid-s19931" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div525" type="section" level="1" n="399"> <head xml:id="echoid-head418" style="it" xml:space="preserve"><emph style="sc">Corollarivm</emph>.</head> <p> <s xml:id="echoid-s19932" xml:space="preserve">EX quibus etiam manifeſtum eſt, qua ratione horum ſpeculorum beneficio, ſecreto ac ſubmiſſe ad ami-<lb/>cum ſatis diſtantem loqui valeamus.</s> <s xml:id="echoid-s19933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19934" xml:space="preserve">Atque hæc ſunt quæ ſuperiori æſtate, rura relaxationis cauſa incolentes, non ex aliorum libris, ſed ab ex-<lb/>perimentis, vobis de hoc vocis miraculo, vt ait Plato, geometricauimus.</s> <s xml:id="echoid-s19935" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div526" type="section" level="1" n="400"> <head xml:id="echoid-head419" style="it" xml:space="preserve">Aliorum Sententiæ.</head> <p> <s xml:id="echoid-s19936" xml:space="preserve">CÆterùm quod alij dixerint Echum reſonare ex locis tantum concauis, cauernoſis, & </s> <s xml:id="echoid-s19937" xml:space="preserve">anfractuoſis, ex <lb/>ſpeluncis, & </s> <s xml:id="echoid-s19938" xml:space="preserve">antris, ex muris ſaltem feneſtratis: </s> <s xml:id="echoid-s19939" xml:space="preserve">item in nimia diſtantia vltimas tantum ſyllabas conſer-<lb/>uari, eaſque tantum audiri, quod aeris motus debilitatus minus perfectè poteſt ſequentem aerem formare, <lb/>ac mouere. </s> <s xml:id="echoid-s19940" xml:space="preserve">vel quod alij dicant vltima tantum exaudiri, quia licet fiat reflexio totius vocis, priores tamen <lb/>vocis partes ab vltimis à tergo vrgentibus turbentur. </s> <s xml:id="echoid-s19941" xml:space="preserve">tandem quod cum Ariſt. </s> <s xml:id="echoid-s19942" xml:space="preserve">ait vocem reflecti ſicuti pilam, <lb/>intelligendum eſſe ſicuti circulum. </s> <s xml:id="echoid-s19943" xml:space="preserve">iſthæc inquam omnia, qua ratione veritati congruant, iudicio eorum, <lb/>qui à nobis ſuperius demonſtrata perceperint committimus. </s> <s xml:id="echoid-s19944" xml:space="preserve">nos enim minime amamus contentioſas diſſer-<lb/>tationes, ſed humanioribus, placidlſque Muſis perpetuo oblectamur, & </s> <s xml:id="echoid-s19945" xml:space="preserve">conſtruendo libentius, quam de-<lb/>ſtruendo operam damus.</s> <s xml:id="echoid-s19946" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div527" type="section" level="1" n="401"> <head xml:id="echoid-head420" style="it" xml:space="preserve">Gratiarum Actio.</head> <p> <s xml:id="echoid-s19947" xml:space="preserve">VErum enimuero N. </s> <s xml:id="echoid-s19948" xml:space="preserve">N. </s> <s xml:id="echoid-s19949" xml:space="preserve">& </s> <s xml:id="echoid-s19950" xml:space="preserve">ſi ea, quæ hactenus de Echo diſſeruimus iucunditate, atque admirabilitate <lb/>ſint plena; </s> <s xml:id="echoid-s19951" xml:space="preserve">admirandum tamen adhuc magis vnum preſtabitis vos ipſi, Echum videlicet, quæ nemine <lb/>loquente, ſed ſilentibus omnibus, non ſemel, nec bis tantum, ſed perpetuò reſonet. </s> <s xml:id="echoid-s19952" xml:space="preserve">vos nimirum Ornatiſſi-<lb/>mi Viri, grato, ac continuo ſilentio nos dicentes proſequuti eſtis, gratiſſima auditione dignati eſtis, quod <lb/>ſilentium, quæ auditio in nobis perpetuam gratiarum actionis Echum efficiet. </s> <s xml:id="echoid-s19953" xml:space="preserve">quodque ad huc magis mi-<lb/>randum eſt, nos ijdem, & </s> <s xml:id="echoid-s19954" xml:space="preserve">corpora Sonora, & </s> <s xml:id="echoid-s19955" xml:space="preserve">grates haſce Reflectentia erimus. </s> <s xml:id="echoid-s19956" xml:space="preserve">quin imo exoptamus, inſtar <lb/>Echus in vocem, ſi fas ſit, transformari, quæ veſtras laudes, veſtraſque grates perpetuo reſonare poſſit.</s> <s xml:id="echoid-s19957" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div528" type="section" level="1" n="402"> <head xml:id="echoid-head421" xml:space="preserve">LAVS DEO.</head> <pb file="0255" n="260"/> </div> <div xml:id="echoid-div529" type="section" level="1" n="403"> <head xml:id="echoid-head422" xml:space="preserve">CONSTRVCTIO <lb/>INSTRVMENTI <lb/>AD HOROLOGIA SOLARIA <lb/>deſcribenda per opportuni.</head> <head xml:id="echoid-head423" xml:space="preserve">Quo facilius, ac breuius, quam vnquam antea, in qualibet ſuperficie, & ad quam-<lb/>uis Poli altitudinem Horologia Italica, Aſtronomica, <lb/>& Babylonica deſcribuntur.</head> <p style="it"> <s xml:id="echoid-s19958" xml:space="preserve">Vna cum noua Ratione conſtruendiin Quadrante Solare Horologium Viatorium, quod Horas <lb/>multo diſtinctiores exhibeat, quam vſitatus antea Quadrans, & </s> <s xml:id="echoid-s19959" xml:space="preserve">quo alios vſus <lb/>nonos, etiam in vmbra poſiti vti poßumus.</s> <s xml:id="echoid-s19960" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div530" type="section" level="1" n="404"> <head xml:id="echoid-head424" xml:space="preserve">AVCTORE P. IOSEPHO BLANCANO SOC. IESV <lb/>OPVS POSTHVMVM.</head> <figure> <image file="0255-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-01"/> </figure> </div> <div xml:id="echoid-div531" type="section" level="1" n="405"> <head xml:id="echoid-head425" xml:space="preserve">MVTINÆ.</head> <head xml:id="echoid-head426" xml:space="preserve">Ex Typographia, Iuliani Caſsiani. M. DC. XXXV. <lb/>Superiorum permiſſu.</head> <pb file="0256" n="261"/> <pb o="3" file="0257" n="262"/> </div> <div xml:id="echoid-div532" type="section" level="1" n="406"> <head xml:id="echoid-head427" xml:space="preserve">PRÆFATIO.</head> <p style="it"> <s xml:id="echoid-s19961" xml:space="preserve">ADagium illud, facilè est inuentis addero<unsure/>, veriſſimum eſſe, in inuentione ac <lb/>varia ad perfectionem vſq; </s> <s xml:id="echoid-s19962" xml:space="preserve">Inſtrumenti huius, de quo acturus ſum ad-<lb/>ditt<unsure/>one mihi, ſi vnquam alias perſpicue patuit. </s> <s xml:id="echoid-s19963" xml:space="preserve">nam cum illud P. </s> <s xml:id="echoid-s19964" xml:space="preserve">Clauius <lb/>lib. </s> <s xml:id="echoid-s19965" xml:space="preserve">7. </s> <s xml:id="echoid-s19966" xml:space="preserve">Gnomon primo, vt videbatur ſatis abſolutũ edidiſſet; </s> <s xml:id="echoid-s19967" xml:space="preserve">illud idem <lb/>postea in meliorem formam redactum ſeorſum proprio libello iterum ex-<lb/>plicauit. </s> <s xml:id="echoid-s19968" xml:space="preserve">Idipſum 10: </s> <s xml:id="echoid-s19969" xml:space="preserve">Paulus Galluccius ſublata quadam difficult<unsure/>ate ad-<lb/>huc perfectius tertio in lucẽ dedit. </s> <s xml:id="echoid-s19970" xml:space="preserve">& </s> <s xml:id="echoid-s19971" xml:space="preserve">cum illud quarto quidam ex nostris <lb/>auditoribus expeditius adhuc reddidiſſet: </s> <s xml:id="echoid-s19972" xml:space="preserve">& </s> <s xml:id="echoid-s19973" xml:space="preserve">nos ipſi tandẽ huic additioni ſuper addentes, illud ad <lb/>abſolutiſſimã perfectionem (ni fallor) productum quinto emittimus. </s> <s xml:id="echoid-s19974" xml:space="preserve">Porro quamuis nihil ei am-<lb/>plius addi poſſe videatur, id tamen prædicta experientia edoctus, minimè auſim affirmare; </s> <s xml:id="echoid-s19975" xml:space="preserve">quiæ<unsure/> <lb/>potius exiſtimem non defuturũ qui illud adbuc auctius ſexto, & </s> <s xml:id="echoid-s19976" xml:space="preserve">ſeptimo in lucem ſit prolaturus.</s> <s xml:id="echoid-s19977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19978" xml:space="preserve">Noſtro autem hoc Inſtrumento deſcribi poſſunt Horæ tam ab ortu, quam ab occaſu, necnon à <lb/>meridie, ideſt, Babylonicæ, Italicæ, & </s> <s xml:id="echoid-s19979" xml:space="preserve">Astronomicæ, vna cum arcubus ſignorum, necnon diur-<lb/>norum; </s> <s xml:id="echoid-s19980" xml:space="preserve">& </s> <s xml:id="echoid-s19981" xml:space="preserve">quidem vna eademq; </s> <s xml:id="echoid-s19982" xml:space="preserve">opera mira facilitate, ac breuitate, eaq; </s> <s xml:id="echoid-s19983" xml:space="preserve">in quauis ſuperficie <lb/>tam plana, quam inæquali, tam rectam ad horizontem, quam inclinata, aut de lina<unsure/>ta, & </s> <s xml:id="echoid-s19984" xml:space="preserve">tam <lb/>concaua quam conuexa, idque ſine vlla declinationis, aut inclinationis muri conſideratione: <lb/></s> <s xml:id="echoid-s19985" xml:space="preserve">quodque magnifaciendum eſt, haberi poſſunt ſingula puncta cuiuſuis horariæ lineæ, quæ huius <lb/>Inſtrumenti ſingularis, ac præcipua eſt præſtantia. </s> <s xml:id="echoid-s19986" xml:space="preserve">Omiſi horas antiquas, quibus dies artificia-<lb/>lis in duodecim ſemper hor<unsure/> as inter ſe æquales diuidebatur, cum earum nullus amplius ſit vſus; </s> <s xml:id="echoid-s19987" xml:space="preserve"><lb/>eas tamen eodem Inſtrumento quilibet ſolers, ac industrius lector ſibi deſcribere poterit.</s> <s xml:id="echoid-s19988" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19989" xml:space="preserve">Ad huius autem Instrumenti ſpec<unsure/>ulationẽ me impulerunt errata nonnulla à me animaduer-<lb/>ſain zona illa materiali ſecundum horas Italicas feneſtrata, necnon in eius portione, quæ dicitur <lb/>Horarium: </s> <s xml:id="echoid-s19990" xml:space="preserve">quibus paſſim plures pro Instrumentis ad Horologia conſtruenda vtuntur: </s> <s xml:id="echoid-s19991" xml:space="preserve">de qui<unsure/>-<lb/>bus erratis ſuo loco dicemus.</s> <s xml:id="echoid-s19992" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19993" xml:space="preserve">Addam præterea nouam rationem deſcribendi Horologij mobilis, & </s> <s xml:id="echoid-s19994" xml:space="preserve">Viatorij in Quadran-<lb/>te, quod horas circa meridiem explicatiores exhibeat, quam vſitatus antea Quadrans; </s> <s xml:id="echoid-s19995" xml:space="preserve">quod ei <lb/>vnum obijeiebatur; </s> <s xml:id="echoid-s19996" xml:space="preserve">quam mihi D. </s> <s xml:id="echoid-s19997" xml:space="preserve">Petrus Dordellus Placentinus pictor à ſe excogitatam primus <lb/>@lim communicauit. </s> <s xml:id="echoid-s19998" xml:space="preserve">Porro vtriuſq; </s> <s xml:id="echoid-s19999" xml:space="preserve">Quadrantis vſus nonnullos, non ſolum reconditos, ve-<lb/>rum etiam vtiles à me excogitatos proferam; </s> <s xml:id="echoid-s20000" xml:space="preserve">cuiuſmodi eo vti in vmbra: </s> <s xml:id="echoid-s20001" xml:space="preserve">quod prima fronte <lb/>incredibile cuipl<unsure/>am videri poſſit.</s> <s xml:id="echoid-s20002" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div533" type="section" level="1" n="407"> <head xml:id="echoid-head428" xml:space="preserve">PARTITIO TOTIVS OPERIS.</head> <p> <s xml:id="echoid-s20003" xml:space="preserve">Prima pars erit de Inſtrumento prædicto, cuius erunt tria capita.</s> <s xml:id="echoid-s20004" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20005" xml:space="preserve">Primum caput de conſtructione Inſtrumenti.</s> <s xml:id="echoid-s20006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20007" xml:space="preserve">Secundum caput de Horario plano.</s> <s xml:id="echoid-s20008" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20009" xml:space="preserve">Tertium caput de Horario Cylindrico.</s> <s xml:id="echoid-s20010" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20011" xml:space="preserve">Secunda pars erit de nouo Quadrante, cuius erunt capita tria.</s> <s xml:id="echoid-s20012" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20013" xml:space="preserve">Primum de conſtructione Horologij in Quadrante.</s> <s xml:id="echoid-s20014" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20015" xml:space="preserve">Secundum de vſu eiuſdem Quadrantis.</s> <s xml:id="echoid-s20016" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20017" xml:space="preserve">Tertium de conſtruendis Tabulis altitudinis Solis.</s> <s xml:id="echoid-s20018" xml:space="preserve"/> </p> <pb o="4" file="0258" n="263" rhead="TRACTATVS"/> </div> <div xml:id="echoid-div534" type="section" level="1" n="408"> <head xml:id="echoid-head429" xml:space="preserve">PARS PRIMA <lb/>DE INSTRVMENTO PROPOSITO.</head> <head xml:id="echoid-head430" style="it" xml:space="preserve">Conſtructio eiuſdem Instrumenti. Cap. I.</head> <p> <s xml:id="echoid-s20019" xml:space="preserve">ANte omnia monendus eſt Lector, nihil ferri ponendum eſſe in hoc Inſtrumento, ne <lb/>ab eo acus magnetica, quæ eiuſdem pars futura eſt, à propria poſitione diſtrahatur. <lb/></s> <s xml:id="echoid-s20020" xml:space="preserve">quapropter neq; </s> <s xml:id="echoid-s20021" xml:space="preserve">bractea illa, quæ latitudine vulgò lata appellatur, cum partim ex <lb/>ferro, partim ex ſtanno conſtet, huic conſtructioni idonea eſt. </s> <s xml:id="echoid-s20022" xml:space="preserve">fiat igitur ante om-<lb/> <anchor type="note" xlink:label="note-0258-01a" xlink:href="note-0258-01"/> nia ex ligno, vel ære circulus ſeu tympanum ſimile huic in prima figura deſcripto. <lb/></s> <s xml:id="echoid-s20023" xml:space="preserve">is diuidendus eſt primo in quatuor partes æquales per duas diametros A B, C D, <lb/>inuicem perpendiculares. </s> <s xml:id="echoid-s20024" xml:space="preserve">deinde quælibet quarta in ſex partes æquales, ea ratione, <lb/> <anchor type="note" xlink:label="note-0258-02a" xlink:href="note-0258-02"/> quam tradidimus prima propoſ. </s> <s xml:id="echoid-s20025" xml:space="preserve">noſtræ Sphæræ; </s> <s xml:id="echoid-s20026" xml:space="preserve">ſicque totus erit in 24. </s> <s xml:id="echoid-s20027" xml:space="preserve">partes æquales diuiſus, quæ <lb/>horas diei 24. </s> <s xml:id="echoid-s20028" xml:space="preserve">referent. </s> <s xml:id="echoid-s20029" xml:space="preserve">quod ſi quis ſemiſſibus, atq; </s> <s xml:id="echoid-s20030" xml:space="preserve">etiam quadrantibus horarum delectetur, rurſus <lb/>ſingulas horas bifariam, atque etiam quadrifariam ſubdiuidat. </s> <s xml:id="echoid-s20031" xml:space="preserve">Quoniam verò tria horarum genera <lb/>ſunt hodie in vſu, videlicet, Italicæ, quæ ab occaſu Solis: </s> <s xml:id="echoid-s20032" xml:space="preserve">Babilonicæ, quæ ab ortu; </s> <s xml:id="echoid-s20033" xml:space="preserve">& </s> <s xml:id="echoid-s20034" xml:space="preserve">Aſtronomicæ, <lb/>quæ à meridie numerantur; </s> <s xml:id="echoid-s20035" xml:space="preserve">propterea diuiſionibus tympani adſcribantur tres numerorum ordines, <lb/>vti vides in figura. </s> <s xml:id="echoid-s20036" xml:space="preserve">exterior refert horas ab occaſu: </s> <s xml:id="echoid-s20037" xml:space="preserve">medius horas ab ortu: </s> <s xml:id="echoid-s20038" xml:space="preserve">interior horas à<unsure/> meridie, vel, <lb/>a media nocte. </s> <s xml:id="echoid-s20039" xml:space="preserve">linea A B, eſt pro linea meridiana: </s> <s xml:id="echoid-s20040" xml:space="preserve">C D, pro linea æquinoctiali: </s> <s xml:id="echoid-s20041" xml:space="preserve">poſtremo in centro E, <lb/>fiat foramen. </s> <s xml:id="echoid-s20042" xml:space="preserve">quale in exemplo cernitur. </s> <s xml:id="echoid-s20043" xml:space="preserve">& </s> <s xml:id="echoid-s20044" xml:space="preserve">apud A, foraminulum adſit, per quod axiculo poſſit ſuæ <lb/>baſi, de qua mox dicam, affigi, vt poſtea dicemus. </s> <s xml:id="echoid-s20045" xml:space="preserve">Porrò hoc tympanum in vſu Inſtrumenti refert <lb/>æquatorem, & </s> <s xml:id="echoid-s20046" xml:space="preserve">quamuis ſit extra locum eius, eſt tamen ei paralellum.</s> <s xml:id="echoid-s20047" xml:space="preserve"/> </p> <div xml:id="echoid-div534" type="float" level="2" n="1"> <note position="left" xlink:label="note-0258-01" xlink:href="note-0258-01a" xml:space="preserve">Conſtru-<lb/>c<unsure/>t@o tym-<lb/>pani.</note> <note position="left" xlink:label="note-0258-02" xlink:href="note-0258-02a" xml:space="preserve">Prima ſi-<lb/>gura.</note> </div> <p> <s xml:id="echoid-s20048" xml:space="preserve">Conſtruatur ex ligno prædicti tympani baſis, eius ſaltem magnitudinis, qualem vides in ſecunda <lb/> <anchor type="note" xlink:label="note-0258-03a" xlink:href="note-0258-03"/> figura, in qua A B, eſt baſis manubrium, cuius pars ſuperior A P, teres eſt, vt per eam inſeri poſſit ſu-<lb/>ſpenſorio, de quo poſtea dicam. </s> <s xml:id="echoid-s20049" xml:space="preserve">Apud A, eſt foramen, cuius vſus poſtea patebit. </s> <s xml:id="echoid-s20050" xml:space="preserve">reliquum P B, eſt <lb/>regula quadrangula C E D, eſt perpendiculum ex clauiculo C, pendens, & </s> <s xml:id="echoid-s20051" xml:space="preserve">tranſiens per foramen <lb/>E. </s> <s xml:id="echoid-s20052" xml:space="preserve">D. </s> <s xml:id="echoid-s20053" xml:space="preserve">eſt ipſum perpendiculi pondus. </s> <s xml:id="echoid-s20054" xml:space="preserve">Debet autem filum iſtud perpendiculi in vſu Inſtrumenti pen-<lb/>dere intra canaliculum in angulo<unsure/> manubrij A B, excauatum, ducendæque ſunt duæ lineæ in duobus <lb/>canaliculi lateribus deſcendentes perpendiculariter, ad quas ambas in vſu Inſtrumenti filum dirigen <lb/>dum eſt, vti poſtea dicemus. </s> <s xml:id="echoid-s20055" xml:space="preserve">Foramen ad B, eſt loculus, in quo D, pondus perpendiculi extra vſum <lb/>Inſtrumenti collocandum eſt. </s> <s xml:id="echoid-s20056" xml:space="preserve">Iam ſi facienda ſit baſis pro particulari poli altitudine, ſatis erit face-<lb/>re triangulum O I K, cuius angulus ad I, ſit rectus, angulus verò ad O, contineat poli aſſumpti alti-<lb/>tudinem; </s> <s xml:id="echoid-s20057" xml:space="preserve">ſicque conſequenter angulus ad K, erit complementum altitudinis poli, quæ eſt eleuatio <lb/>æquatoris ſupra horizontem. </s> <s xml:id="echoid-s20058" xml:space="preserve">linea F K, erit linea meridiana, ideſt, communis ſectio æquatoris, & </s> <s xml:id="echoid-s20059" xml:space="preserve"><lb/>meridiani, nam planum trianguli O I K, refert meridianum circulum. </s> <s xml:id="echoid-s20060" xml:space="preserve">L M, eſt axis ex aurichalco <lb/>referens axem mundi, cuius longitudo poſtea taxabitur: </s> <s xml:id="echoid-s20061" xml:space="preserve">apex eius M, tefert centrum mundi. </s> <s xml:id="echoid-s20062" xml:space="preserve">Mr. </s> <s xml:id="echoid-s20063" xml:space="preserve">eſt <lb/>eſt tenue filum ab eius apice egrediens radij ſolaris vicarium. </s> <s xml:id="echoid-s20064" xml:space="preserve">Porrò in hunc axem inſerendum eſt <lb/>tympanum per foramen E, factum iam in centro eius, congruens craſſitiei axis; </s> <s xml:id="echoid-s20065" xml:space="preserve">atq; </s> <s xml:id="echoid-s20066" xml:space="preserve">tympanum ba-<lb/>ſi huic aptetur, vt linea A B, tympani meridiana congruat lineæ F K, mer dianę baſis, & </s> <s xml:id="echoid-s20067" xml:space="preserve">planum tym <lb/>pani cum plano trianguli O I B, rectos angulos efficiat, in quo ſitu clauiculis æneis aut coch leis apud <lb/>A, in circumferentia ſitis obfirmetur cum opus fuerit; </s> <s xml:id="echoid-s20068" xml:space="preserve">vt autem melius inuicem cohæreant addi po-<lb/>teſt regula tranſuerſa S R, exiſtens in eodem plano, cũ ſupe@ficie O Q K, lateris trianguli, vt ſit quaſi <lb/>fulcrum tympani.</s> <s xml:id="echoid-s20069" xml:space="preserve"/> </p> <div xml:id="echoid-div535" type="float" level="2" n="2"> <note position="left" xlink:label="note-0258-03" xlink:href="note-0258-03a" xml:space="preserve">Baſis <lb/>tympani. <lb/>Secunda <lb/>figura.</note> </div> <p> <s xml:id="echoid-s20070" xml:space="preserve">Quod ſi conſtruenda ſit baſis vniuerſalis, quæ inſeruiat ad omnes poli altitudines loco prædicti <lb/>trianguli ponendus eſt quadrans O H G, mobilis circa axiculum O Q, quempiam per centrum O, tra-<lb/>iectum, ac manubrixio affixum. </s> <s xml:id="echoid-s20071" xml:space="preserve">Huius arcus G H, diuidatur in gr. </s> <s xml:id="echoid-s20072" xml:space="preserve">90. </s> <s xml:id="echoid-s20073" xml:space="preserve">per propoſ. </s> <s xml:id="echoid-s20074" xml:space="preserve">1. </s> <s xml:id="echoid-s20075" xml:space="preserve">noſtræ Sphæræ: <lb/></s> <s xml:id="echoid-s20076" xml:space="preserve">qui numerandi ſuntà G, verſus H, debet autem eſſe mobilis circa axiculum O Q, vt cuiuis poli alti-<lb/>tudini fieri poſſit I O K, æqualis. </s> <s xml:id="echoid-s20077" xml:space="preserve">in quo ſtatu cochlea c<unsure/>uapiam propè I, conſt<unsure/>ringendus erit cum <lb/>oportuerit. </s> <s xml:id="echoid-s20078" xml:space="preserve">lateri autem O Q K, tanquam baſi debet tympanum inniti, eo modo, ac ſitu, quo de late-<lb/>re trianguli diximus.</s> <s xml:id="echoid-s20079" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20080" xml:space="preserve">Vltima pars huius baſis eſt pyxis acus magneticæ, qualem cernis in tertia figura: </s> <s xml:id="echoid-s20081" xml:space="preserve">quæ cum vſus po-<lb/> <anchor type="note" xlink:label="note-0258-04a" xlink:href="note-0258-04"/> ſtulauerit affigenda eſt in auerſa parte baſis per inciſuram inibi factam, in quam inſerenda eſt pyxidis <lb/>margo A B C D, ita vt linea A B, paralella ſit plano baſis, ſeu ei congruat; </s> <s xml:id="echoid-s20082" xml:space="preserve">ſitque planum ſeu fundus, <lb/>aut baxis pyxidis E F A B, normale baſi inſtrumenti: </s> <s xml:id="echoid-s20083" xml:space="preserve">in quo ſitu linea G. </s> <s xml:id="echoid-s20084" xml:space="preserve">H. </s> <s xml:id="echoid-s20085" xml:space="preserve">quæ eſt linea meridiana <lb/>pyxidis erit ipſa paralella ſuperficiei baſis Inſtrumẽti. </s> <s xml:id="echoid-s20086" xml:space="preserve">linea I K, in fundo pyxidis eſt linea magnetis, <lb/>quæ in Italia vulgò putatur delineare a meridiana G H. </s> <s xml:id="echoid-s20087" xml:space="preserve">ſex fermè grad. </s> <s xml:id="echoid-s20088" xml:space="preserve">P, tamen, Chriſtoph. </s> <s xml:id="echoid-s20089" xml:space="preserve">Gruẽb. <lb/></s> <s xml:id="echoid-s20090" xml:space="preserve">noſtræ Soc. </s> <s xml:id="echoid-s20091" xml:space="preserve">ſcribit ſe obſeruaſſe declinationẽ hanc Romæ eſſe gr. </s> <s xml:id="echoid-s20092" xml:space="preserve">3 {1/2}. </s> <s xml:id="echoid-s20093" xml:space="preserve">ego autem Parmæ eam reperio <lb/>paulo minorem tribus gradibus L M, eſt ipſa arcus magnetica ſupra ſtylum O P, æquilibrata, ac vo- <pb o="5" file="0259" n="264" rhead="DE HOROLOGIIS."/> lubilis. </s> <s xml:id="echoid-s20094" xml:space="preserve">Oportet autem, vt acus hæc ſit ſatis magna, & </s> <s xml:id="echoid-s20095" xml:space="preserve">optimè magnete illita, aliter inſtrumentum <lb/>perperam collocabitur in deſcriptione Horologiorum, nam a vera meridiana deflectet; </s> <s xml:id="echoid-s20096" xml:space="preserve">quam vnam <lb/>acus magneticæ imperfectionem. </s> <s xml:id="echoid-s20097" xml:space="preserve">cauſam eſſe exiſtimo, cur pauca adeo ſolaria Horologia abſque pa-<lb/>tentibus erratis conſpiciantur.</s> <s xml:id="echoid-s20098" xml:space="preserve"/> </p> <div xml:id="echoid-div536" type="float" level="2" n="3"> <note position="left" xlink:label="note-0258-04" xlink:href="note-0258-04a" xml:space="preserve">Pyxis ma <lb/>gnetis. <lb/>Tertia ſi <lb/>gura.</note> </div> <p> <s xml:id="echoid-s20099" xml:space="preserve">Conſtructa hoc modo baſi, opus eſt pręterea ſuſpenſorio, cui in vſu Inſtrumentum ſuſpendi debet, <lb/> <anchor type="note" xlink:label="note-0259-01a" xlink:href="note-0259-01"/> ita vt ab eo ex muro pendeat: </s> <s xml:id="echoid-s20100" xml:space="preserve">male enim ſibi conſulunt ij, qui Inſtrumentũ non parieti ſuſpendunt, <lb/>ſed illud ſupra pontem ligneum, qui ante murum conſtrui ſolet, collocant; </s> <s xml:id="echoid-s20101" xml:space="preserve">dum enim horologij ar-<lb/> <anchor type="note" xlink:label="note-0259-02a" xlink:href="note-0259-02"/> tifex per pontem huc illuc mouetur, pons tremit, & </s> <s xml:id="echoid-s20102" xml:space="preserve">vacillat, ac proinde Inſtrumentum in certo, ac <lb/>vero ſitu manere nequit. </s> <s xml:id="echoid-s20103" xml:space="preserve">Fiat igitur tale, quale quarta figura oſtendit; </s> <s xml:id="echoid-s20104" xml:space="preserve">quod conſtat duabus partibus. <lb/></s> <s xml:id="echoid-s20105" xml:space="preserve">Prima eſt regula quadrata ſaltem quinque palmos longa (quæ cum opus fuerio maior ſumi poterit) <lb/>in ea ſunt crebra foramina, eius magnitudinis, vt in ea caput baſis A P, inſerit ſatis arctè poſſit; </s> <s xml:id="echoid-s20106" xml:space="preserve">ſur-<lb/>ſum extra regulam emergat foramen A, per quod immiſſo clauiculo retineatur. </s> <s xml:id="echoid-s20107" xml:space="preserve">Hæc regula altero <lb/>extremo A, eſt rotunda, vt ea immitti poſſit in tabellæ foramen D, quam tabellam figura oſtendit, <lb/>quæque eſt altera pars ſuſpenſorij. </s> <s xml:id="echoid-s20108" xml:space="preserve">Hæc tabella clauis ferreis per parua eius foramina e, f, g, h, m, <lb/>affigenda eſt parieti ſupra locum horologij fabricandi. </s> <s xml:id="echoid-s20109" xml:space="preserve">claui hi quamuis ſint ferrei, quia tamen mul-<lb/>tum diſtantab acu, eam non attrahent; </s> <s xml:id="echoid-s20110" xml:space="preserve">Regula autem inſerenda eſt in tabellæ foramen D, non tam <lb/>ante quin in eo reuolui poſſit: </s> <s xml:id="echoid-s20111" xml:space="preserve">pars autem vbi foramen D, cum muro affigitur, ſit inferior, alte-<lb/>ra verò vbi claui, ſit ſuperior. </s> <s xml:id="echoid-s20112" xml:space="preserve">Porro hæc, quæ hactenus deſcripſimus, ſunt huius Inſtrumenti pars <lb/>immobilis, & </s> <s xml:id="echoid-s20113" xml:space="preserve">ignobilior, & </s> <s xml:id="echoid-s20114" xml:space="preserve">quaſi materialis; </s> <s xml:id="echoid-s20115" xml:space="preserve">nunc ad partem alteram mobilem, & </s> <s xml:id="echoid-s20116" xml:space="preserve">præcipuam, <lb/>ac veluti Inſtrumenti formam.</s> <s xml:id="echoid-s20117" xml:space="preserve"/> </p> <div xml:id="echoid-div537" type="float" level="2" n="4"> <note position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">Suſpen ſo<unsure/>-<lb/>rium.</note> <note position="right" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">Quarta <lb/>figura.</note> </div> </div> <div xml:id="echoid-div539" type="section" level="1" n="409"> <head xml:id="echoid-head431" style="it" xml:space="preserve">De Horario. Cap. II.</head> <p> <s xml:id="echoid-s20118" xml:space="preserve">HÆe eſt præcipua pars huius Inſtrumenti, in ea enim deſcribendi ſunt non ſolum omnes arcus <lb/>Horarij, à quibus Horarium denominatur; </s> <s xml:id="echoid-s20119" xml:space="preserve">ſed præterea puncta quæd<unsure/>am hyperbolarum, qua-<lb/>rum aliæ arcus ſignorum, aliæ vero arcus diurnos referant: </s> <s xml:id="echoid-s20120" xml:space="preserve">immo ſolem ipſum ſuo motu, vel potius <lb/>radium ſolis imitatur, quæ omnia ſubtili ratione perficienda ſunt.</s> <s xml:id="echoid-s20121" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20122" xml:space="preserve">Prima pars, quæ eſt veluti baſis ipſius Horarij, eſt regula extenui ærea lamina, qualẽ vides in quin-<lb/> <anchor type="note" xlink:label="note-0259-03a" xlink:href="note-0259-03"/> ta figura. </s> <s xml:id="echoid-s20123" xml:space="preserve">eius pars B A, eſt æqualis ſemidiametro tympani; </s> <s xml:id="echoid-s20124" xml:space="preserve">altera vero A C, aliquanto longior. </s> <s xml:id="echoid-s20125" xml:space="preserve">linea <lb/>B A C, dicitur linea fiduciæ, quæ tranſit per centrum foraminis A, in medio regulæ; </s> <s xml:id="echoid-s20126" xml:space="preserve">quod foramen <lb/> <anchor type="note" xlink:label="note-0259-04a" xlink:href="note-0259-04"/> debet congruere foramini E, tympani, & </s> <s xml:id="echoid-s20127" xml:space="preserve">proinde craſſiciei axis. </s> <s xml:id="echoid-s20128" xml:space="preserve">poni enim debet hæc regula ſuper <lb/>tympanum inſerta axi, ita vt eius foramen A, congruat foramini E, ibiq; </s> <s xml:id="echoid-s20129" xml:space="preserve">per axiculum traiectũ per <lb/>foraminulum m, in axe conſtringatur leniter ſupra tympanum, vt ſupra ipſius faciem circa prædi-<lb/>ctum axem gyrari poſſit.</s> <s xml:id="echoid-s20130" xml:space="preserve"/> </p> <div xml:id="echoid-div539" type="float" level="2" n="1"> <note position="right" xlink:label="note-0259-03" xlink:href="note-0259-03a" xml:space="preserve">Regula <lb/>He<unsure/>r@rij.</note> <note position="right" xlink:label="note-0259-04" xlink:href="note-0259-04a" xml:space="preserve">Quinta <lb/>figura.</note> </div> <p> <s xml:id="echoid-s20131" xml:space="preserve">Huius regulæ capiti D E G F, per tria eius foramina G C F, affigenda eſt altera pars præcipua, quę <lb/>eſt Horarium ipſum. </s> <s xml:id="echoid-s20132" xml:space="preserve">Horarium ergo iſtud, quod deſcripturi ſumus, nihil eſt aliud, quam portio Ho-<lb/> <anchor type="note" xlink:label="note-0259-05a" xlink:href="note-0259-05"/> rologij polaris dicti, ideſt deſcripti in plano axi mundo paralello, ſeu æquidiſtanti plano per polos <lb/>mundi tranſeunti, de quo vide Gnom. </s> <s xml:id="echoid-s20133" xml:space="preserve">Clauij: </s> <s xml:id="echoid-s20134" xml:space="preserve">hæc autem portio continet tres lineas horarias, Itali-<lb/>cam, Babylonicam, Aſtronomicam, ſe mutuo in eodem puncto æquatoris ſecantes; </s> <s xml:id="echoid-s20135" xml:space="preserve">& </s> <s xml:id="echoid-s20136" xml:space="preserve">præterea pun-<lb/>cta in ijſdem lineis, perquæ tranſeunt arcus ſignorum, necnon arcus diurni. </s> <s xml:id="echoid-s20137" xml:space="preserve">qui igitur callent huiuſ-<lb/>modi horologij deſcriptionẽ, noſtra hæc doctrina non indigent: </s> <s xml:id="echoid-s20138" xml:space="preserve">cæteri vtantur ſequentibus regulis.</s> <s xml:id="echoid-s20139" xml:space="preserve"/> </p> <div xml:id="echoid-div540" type="float" level="2" n="2"> <note position="right" xlink:label="note-0259-05" xlink:href="note-0259-05a" xml:space="preserve">Horari-<lb/>um quid.</note> </div> </div> <div xml:id="echoid-div542" type="section" level="1" n="410"> <head xml:id="echoid-head432" style="it" xml:space="preserve">Apparatus Radiarij ad Horarium deſcribendum.</head> <p> <s xml:id="echoid-s20140" xml:space="preserve">PRimo parare opus eſt figuram Radiorum Solis, à quibus eam placet Radiarium appellare, quam <lb/>ſic deſcribes. </s> <s xml:id="echoid-s20141" xml:space="preserve">Habeas duas Tabellas, quales ſunt duæ in prima columna ſequentium Tabella-<lb/> <anchor type="note" xlink:label="note-0259-06a" xlink:href="note-0259-06"/> rum, quarum prima continet declinationes paralellorum per initia ſignorum, necnon grad. </s> <s xml:id="echoid-s20142" xml:space="preserve">15. </s> <s xml:id="echoid-s20143" xml:space="preserve">♏, <lb/>& </s> <s xml:id="echoid-s20144" xml:space="preserve">♎; </s> <s xml:id="echoid-s20145" xml:space="preserve">vt titulus eius indicat. </s> <s xml:id="echoid-s20146" xml:space="preserve">Porro hæc Tabula eſt vniuerſ<unsure/>alis, non enim ex variatione altitudinis <lb/> <anchor type="note" xlink:label="note-0259-07a" xlink:href="note-0259-07"/> poli variantur declinationes graduum eclipticæ, ſed eædem vbique manent. </s> <s xml:id="echoid-s20147" xml:space="preserve">Altera continet decli-<lb/>nationes arcuum diurnorum horarum integrarum ad altitudinem poli 44 {1/2}. </s> <s xml:id="echoid-s20148" xml:space="preserve">hanc vides in ſecunda <lb/>parte columnæ primæ ſequentium Tabellarum.</s> <s xml:id="echoid-s20149" xml:space="preserve"/> </p> <div xml:id="echoid-div542" type="float" level="2" n="1"> <note position="right" xlink:label="note-0259-06" xlink:href="note-0259-06a" xml:space="preserve">Radiari-<lb/>um.</note> <note position="right" xlink:label="note-0259-07" xlink:href="note-0259-07a" xml:space="preserve">Sexta ſi-<lb/>gura.</note> </div> <p> <s xml:id="echoid-s20150" xml:space="preserve">Huiuſmodi Tabellas excerpes ex Tabulis declinationum ſignorum, necnon arcuum diurnorum, <lb/>quæ paſſim reperiuntur apud Authores de Gnomonicis, præſertim apud Clauium in Sphæra, atque <lb/>in noua deſcriptione de Horol. </s> <s xml:id="echoid-s20151" xml:space="preserve">necnon in Tabulis pro ea ſeorſim editis.</s> <s xml:id="echoid-s20152" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20153" xml:space="preserve">2. </s> <s xml:id="echoid-s20154" xml:space="preserve">Iam ad interuallum A C, ex præmiſſa regula circino acceptum, ſeorſim in quapiam ſuper-<lb/>ficie ex centro deſcribatur E, arcus, in quo arcus G A F, contineat vtrinque ab A, grad. </s> <s xml:id="echoid-s20155" xml:space="preserve">23 {1/2} ideſt. <lb/></s> <s xml:id="echoid-s20156" xml:space="preserve">vterque arcus G A, A F, ſit gr. </s> <s xml:id="echoid-s20157" xml:space="preserve">23 {1/2}. </s> <s xml:id="echoid-s20158" xml:space="preserve">quanta eſt maxima tropicorum declinatio, & </s> <s xml:id="echoid-s20159" xml:space="preserve">quanta apparet ex <lb/>prima Tabella. </s> <s xml:id="echoid-s20160" xml:space="preserve">Poſtea à puncto pariter A, hinc inde notentur reliquæ declinationes reliquorum <lb/>fignorum Zodiaci acceptæ ex eadem Tabella. </s> <s xml:id="echoid-s20161" xml:space="preserve">Ex ſecunda autem Tabella ſatis erit accipere declina-<lb/>r<unsure/>iones duorum arcuum, ideſt horarum 14. </s> <s xml:id="echoid-s20162" xml:space="preserve">& </s> <s xml:id="echoid-s20163" xml:space="preserve">horarum 10. </s> <s xml:id="echoid-s20164" xml:space="preserve">eaſq; </s> <s xml:id="echoid-s20165" xml:space="preserve">inibi eodem modo notare vti vides <pb o="6" file="0260" n="265" rhead="TRACTATVS"/> factum in appoſita figura. </s> <s xml:id="echoid-s20166" xml:space="preserve">Si quis tamen voluerit reliquas quoque arcuum declinationes, vt per eas <lb/>arcus diurnos reliquos in ſuis Horol. </s> <s xml:id="echoid-s20167" xml:space="preserve">deſcribere poſſit, eas pro arbitrio ex eadem Tabella accipiat, <lb/>atq; </s> <s xml:id="echoid-s20168" xml:space="preserve">in radiario ſimiliter notet. </s> <s xml:id="echoid-s20169" xml:space="preserve">Poſtea per ſingula declinationum puncta notata ducantur ex centro <lb/>E, lineæ rectæ aliquantulum extra peripheriam egredientes, & </s> <s xml:id="echoid-s20170" xml:space="preserve">per punctum A, ducantur linea H I, <lb/>recta tangens arcũ in A, ſeu normalis ipſi B A, ſecans productas lineas in punctis H K L M N O P I, <lb/>vt vides in figura. </s> <s xml:id="echoid-s20171" xml:space="preserve">erunt A N, A O, A P, A I, & </s> <s xml:id="echoid-s20172" xml:space="preserve">totidem ex altera parte tangens arcuum ſibi reſpon-<lb/>dentium. </s> <s xml:id="echoid-s20173" xml:space="preserve">Porro hæ lineæ è centro egredientes referunt radios Solis tranſeuntes per tales declina-<lb/> <anchor type="note" xlink:label="note-0260-01a" xlink:href="note-0260-01"/> tiones exiſtente Sole in ijſdem declinationibus: </s> <s xml:id="echoid-s20174" xml:space="preserve">arcus vero ipſe refert portionem coluri ſolſtitiorũ, <lb/>vel meridiani inter tropicos interceptam. </s> <s xml:id="echoid-s20175" xml:space="preserve">Radius E A, eſt radius Solis exiſtentis in principio ♎, vel <lb/>♈, radij E H, E I, ſunt radij Solis exiſtentis in ♋, & </s> <s xml:id="echoid-s20176" xml:space="preserve">♌, &</s> <s xml:id="echoid-s20177" xml:space="preserve">c. </s> <s xml:id="echoid-s20178" xml:space="preserve">vt apparet ex characteribus ſignorum <lb/>adſcriptis. </s> <s xml:id="echoid-s20179" xml:space="preserve">Sit tandem recta E Q, æqualis rectæ A I, hoc eſt parti axis m M, extantis ſupra regulam <lb/>tympano ſuperpoſitam. </s> <s xml:id="echoid-s20180" xml:space="preserve">Aduertendum Radiarium huiuſmodi eſſe vniuerſale ſecundum declina-<lb/>tiones ſignorum, non autem ſecundum declinationes arcuum diurnorum, vt ſupra tetigi. </s> <s xml:id="echoid-s20181" xml:space="preserve">Hoc Ra-<lb/>diarium fieri poteſt Geometricè per analemma. </s> <s xml:id="echoid-s20182" xml:space="preserve">vide Gnom. </s> <s xml:id="echoid-s20183" xml:space="preserve">Clau. </s> <s xml:id="echoid-s20184" xml:space="preserve">lib. </s> <s xml:id="echoid-s20185" xml:space="preserve">1.</s> <s xml:id="echoid-s20186" xml:space="preserve"/> </p> <div xml:id="echoid-div543" type="float" level="2" n="2"> <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">Ratio<unsure/> <lb/>huius <lb/>Radiarij.</note> </div> <p> <s xml:id="echoid-s20187" xml:space="preserve">3. </s> <s xml:id="echoid-s20188" xml:space="preserve">Breuius. </s> <s xml:id="echoid-s20189" xml:space="preserve">ſi quis in ſuis Horologijs contentus ſit ſola deſcriptione horarum abſque arcubus <lb/>ſignorum, necnon arcubus diurnis, ſatis ei fuerit in ſuo Radiario ponere tantum maximas declina-<lb/>tiones tropicorum, & </s> <s xml:id="echoid-s20190" xml:space="preserve">tres tantũ lineas è centro E, egredientes E G H, E A, E F I, quare nec ei opus <lb/>eſt totis Tabellis præmiſſis, ſed ſatis erit habere declinationes extremas ♋, & </s> <s xml:id="echoid-s20191" xml:space="preserve">♌, vna cum tempori-<lb/>bus ſemidiurnis, meridiebus, interuallis, & </s> <s xml:id="echoid-s20192" xml:space="preserve">arcubus illis correſpondentibus in cęteris columnis.</s> <s xml:id="echoid-s20193" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20194" xml:space="preserve">4. </s> <s xml:id="echoid-s20195" xml:space="preserve">Habeantur tempora ſemidiurna competentia paralellis, & </s> <s xml:id="echoid-s20196" xml:space="preserve">arcubus in prima columna, <lb/>quorum radij inſcripti ſunt in Radiario. </s> <s xml:id="echoid-s20197" xml:space="preserve">quę tempora haberi poſſunt ex Tabula temporis ſemidiur-<lb/>ni ad datam latitudinem, quæ paſſim reperitur apud Authores; </s> <s xml:id="echoid-s20198" xml:space="preserve">optima vero in Sphæra P. </s> <s xml:id="echoid-s20199" xml:space="preserve">Clauij: <lb/></s> <s xml:id="echoid-s20200" xml:space="preserve">ſunt autem in ſecunda columna congruentia latitudini, ſeu altitudini 44 {1/2}. </s> <s xml:id="echoid-s20201" xml:space="preserve">vt indicat titulus eius co-<lb/>lumnæ.</s> <s xml:id="echoid-s20202" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20203" xml:space="preserve">5. </s> <s xml:id="echoid-s20204" xml:space="preserve">Ex tempore ſemidiurno cuiuſuis paralelli poſito in ſecunda columna inquirendum eſt, quo-<lb/>ta hora Italica ſit meridies Sole eundem paralellum percurrente, hac ratione. </s> <s xml:id="echoid-s20205" xml:space="preserve">Detrahatur tem-<lb/>pus ſemid. </s> <s xml:id="echoid-s20206" xml:space="preserve">aſſumpti paralellis ab horis 24. </s> <s xml:id="echoid-s20207" xml:space="preserve">reliquæ enim horæ indicabunt meridiem ſecundum horas <lb/>I@alicas, v. </s> <s xml:id="echoid-s20208" xml:space="preserve">g. </s> <s xml:id="echoid-s20209" xml:space="preserve">quia detracto tempore ſemid. </s> <s xml:id="echoid-s20210" xml:space="preserve">paralelli ♋, quod eſt hor. </s> <s xml:id="echoid-s20211" xml:space="preserve">7. </s> <s xml:id="echoid-s20212" xml:space="preserve">41. </s> <s xml:id="echoid-s20213" xml:space="preserve">ex 24. </s> <s xml:id="echoid-s20214" xml:space="preserve">remanent hor. </s> <s xml:id="echoid-s20215" xml:space="preserve">16. <lb/></s> <s xml:id="echoid-s20216" xml:space="preserve">19. </s> <s xml:id="echoid-s20217" xml:space="preserve">ideo hora meridiana erit hora 16. </s> <s xml:id="echoid-s20218" xml:space="preserve">19. </s> <s xml:id="echoid-s20219" xml:space="preserve">& </s> <s xml:id="echoid-s20220" xml:space="preserve">ſic de cęteris. </s> <s xml:id="echoid-s20221" xml:space="preserve">Hac ratione inuentæ ſunt horæ merid. </s> <s xml:id="echoid-s20222" xml:space="preserve">ter-<lb/>tiæ columnæ competentis paralellis primæ columnæ.</s> <s xml:id="echoid-s20223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20224" xml:space="preserve">6. </s> <s xml:id="echoid-s20225" xml:space="preserve">Inueſtigare oportet interuallum temporis inter horam 18. </s> <s xml:id="echoid-s20226" xml:space="preserve">Italicam, & </s> <s xml:id="echoid-s20227" xml:space="preserve">12. </s> <s xml:id="echoid-s20228" xml:space="preserve">aſtronomicam, <lb/>ſeu meridianam in quouis paralello, ſic. </s> <s xml:id="echoid-s20229" xml:space="preserve">Accipe differentiam inter tempus ſemidiurnum aſſumpti <lb/>paralello, & </s> <s xml:id="echoid-s20230" xml:space="preserve">horas 6. </s> <s xml:id="echoid-s20231" xml:space="preserve">ea enim eſt interuallum temporis inter horam 18. </s> <s xml:id="echoid-s20232" xml:space="preserve">Italicam, & </s> <s xml:id="echoid-s20233" xml:space="preserve">meridiem, v.</s> <s xml:id="echoid-s20234" xml:space="preserve">g. </s> <s xml:id="echoid-s20235" xml:space="preserve">in <lb/>paralello ♋, tempus ſemidiurnum eſt hor. </s> <s xml:id="echoid-s20236" xml:space="preserve">7. </s> <s xml:id="echoid-s20237" xml:space="preserve">42. </s> <s xml:id="echoid-s20238" xml:space="preserve">quod ſuperat hor. </s> <s xml:id="echoid-s20239" xml:space="preserve">6. </s> <s xml:id="echoid-s20240" xml:space="preserve">hor. </s> <s xml:id="echoid-s20241" xml:space="preserve">1. </s> <s xml:id="echoid-s20242" xml:space="preserve">41. </s> <s xml:id="echoid-s20243" xml:space="preserve">ergo hora 1. </s> <s xml:id="echoid-s20244" xml:space="preserve">41. </s> <s xml:id="echoid-s20245" xml:space="preserve">eſt di-<lb/>ſtantia hor. </s> <s xml:id="echoid-s20246" xml:space="preserve">18. </s> <s xml:id="echoid-s20247" xml:space="preserve">Italicæ à meridie, ſeu ab hora 12. </s> <s xml:id="echoid-s20248" xml:space="preserve">a ſtronomica. </s> <s xml:id="echoid-s20249" xml:space="preserve">In paralello ♎, cum tempus ſemidlur-<lb/>num ſit hor. </s> <s xml:id="echoid-s20250" xml:space="preserve">6. </s> <s xml:id="echoid-s20251" xml:space="preserve">nulla erit differentia, quare neq; </s> <s xml:id="echoid-s20252" xml:space="preserve">vllum interuallum. </s> <s xml:id="echoid-s20253" xml:space="preserve">In paralello ♌, tempus ſemidiur-<lb/>num eſt hor. </s> <s xml:id="echoid-s20254" xml:space="preserve">4. </s> <s xml:id="echoid-s20255" xml:space="preserve">19. </s> <s xml:id="echoid-s20256" xml:space="preserve">eius diſſerentia ad hor. </s> <s xml:id="echoid-s20257" xml:space="preserve">6. </s> <s xml:id="echoid-s20258" xml:space="preserve">eſt hor. </s> <s xml:id="echoid-s20259" xml:space="preserve">1. </s> <s xml:id="echoid-s20260" xml:space="preserve">41. </s> <s xml:id="echoid-s20261" xml:space="preserve">quare tantumdem erit interuallum inter <lb/>horam Italicam, & </s> <s xml:id="echoid-s20262" xml:space="preserve">merid.</s> <s xml:id="echoid-s20263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20264" xml:space="preserve">Notandum eadem eſſe interualla in oppoſitis paralellis; </s> <s xml:id="echoid-s20265" xml:space="preserve">ſic in vtroq; </s> <s xml:id="echoid-s20266" xml:space="preserve">tropico eſt hor. </s> <s xml:id="echoid-s20267" xml:space="preserve">1. </s> <s xml:id="echoid-s20268" xml:space="preserve">41. </s> <s xml:id="echoid-s20269" xml:space="preserve">vt vidi-<lb/>ſti. </s> <s xml:id="echoid-s20270" xml:space="preserve">In borealibus tamen ſignis eſt exceſſus ſupra 6. </s> <s xml:id="echoid-s20271" xml:space="preserve">in auſtralibus autem eſt defectus à 6. </s> <s xml:id="echoid-s20272" xml:space="preserve">Hæc inter-<lb/>ualla ſunt in quarta columna reſpondentia paralellis primæ columnæ. </s> <s xml:id="echoid-s20273" xml:space="preserve">Idem aſſequeris ſumendo de-<lb/>fectum horæ cuiuſuis meridiei tertiæ columnæ vſq; </s> <s xml:id="echoid-s20274" xml:space="preserve">ad hor. </s> <s xml:id="echoid-s20275" xml:space="preserve">18. </s> <s xml:id="echoid-s20276" xml:space="preserve">in borealibus, exceſſum autem ſupra <lb/>18. </s> <s xml:id="echoid-s20277" xml:space="preserve">in auſtralibus.</s> <s xml:id="echoid-s20278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20279" xml:space="preserve">7. </s> <s xml:id="echoid-s20280" xml:space="preserve">Hæc interualla conuertenda ſunt in arcus, ſeu in grad. </s> <s xml:id="echoid-s20281" xml:space="preserve">paralellorum aſſumptorum, qui in-<lb/>tercipiuntur inter hor. </s> <s xml:id="echoid-s20282" xml:space="preserve">18. </s> <s xml:id="echoid-s20283" xml:space="preserve">Italicam, & </s> <s xml:id="echoid-s20284" xml:space="preserve">12. </s> <s xml:id="echoid-s20285" xml:space="preserve">aſtronomicam, v.</s> <s xml:id="echoid-s20286" xml:space="preserve">g. </s> <s xml:id="echoid-s20287" xml:space="preserve">in ♋, interuallum eſt hor. </s> <s xml:id="echoid-s20288" xml:space="preserve">1. </s> <s xml:id="echoid-s20289" xml:space="preserve">41. </s> <s xml:id="echoid-s20290" xml:space="preserve">qui <lb/>nihil aliud eſt, quam arcus tropici ♋, intercepti inter horam 18. </s> <s xml:id="echoid-s20291" xml:space="preserve">Italicam, & </s> <s xml:id="echoid-s20292" xml:space="preserve">12. </s> <s xml:id="echoid-s20293" xml:space="preserve">aſtronomicam, qui <lb/>arcus continet gr. </s> <s xml:id="echoid-s20294" xml:space="preserve">25. </s> <s xml:id="echoid-s20295" xml:space="preserve">15. </s> <s xml:id="echoid-s20296" xml:space="preserve">vna enim hora continet gr. </s> <s xml:id="echoid-s20297" xml:space="preserve">15. </s> <s xml:id="echoid-s20298" xml:space="preserve">41. </s> <s xml:id="echoid-s20299" xml:space="preserve">autem minuta efficiunt gr. </s> <s xml:id="echoid-s20300" xml:space="preserve">10. </s> <s xml:id="echoid-s20301" xml:space="preserve">15. </s> <s xml:id="echoid-s20302" xml:space="preserve">quare <lb/>omnes ſimul ſunt gr. </s> <s xml:id="echoid-s20303" xml:space="preserve">25. </s> <s xml:id="echoid-s20304" xml:space="preserve">15. </s> <s xml:id="echoid-s20305" xml:space="preserve">Omnes porro arcus facti ex grad. </s> <s xml:id="echoid-s20306" xml:space="preserve">& </s> <s xml:id="echoid-s20307" xml:space="preserve">minutis, ex interuallis, ſunt in quin-<lb/>ta columna è directo ſuorum interuallorum, &</s> <s xml:id="echoid-s20308" xml:space="preserve">c. </s> <s xml:id="echoid-s20309" xml:space="preserve">Extat Tabula apud Authores conuertendi horas, & </s> <s xml:id="echoid-s20310" xml:space="preserve"><lb/>min. </s> <s xml:id="echoid-s20311" xml:space="preserve">in grad. </s> <s xml:id="echoid-s20312" xml:space="preserve">& </s> <s xml:id="echoid-s20313" xml:space="preserve">minuta, quæ hic vſui erit.</s> <s xml:id="echoid-s20314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20315" xml:space="preserve">8. </s> <s xml:id="echoid-s20316" xml:space="preserve">Quæ vt melius intelligantur ponam ob oculos Lectoris Horarij deſcribendi figuram præ-<lb/> <anchor type="note" xlink:label="note-0260-02a" xlink:href="note-0260-02"/> ſentem ſeptimam, in qua tres lineæ E C F, D C B, G C H, ſunt horariæ, 18. </s> <s xml:id="echoid-s20317" xml:space="preserve">Italica, 12. </s> <s xml:id="echoid-s20318" xml:space="preserve">Aſtronomi-<lb/>ca, & </s> <s xml:id="echoid-s20319" xml:space="preserve">6. </s> <s xml:id="echoid-s20320" xml:space="preserve">Babylonica. </s> <s xml:id="echoid-s20321" xml:space="preserve">linea curua E D G. </s> <s xml:id="echoid-s20322" xml:space="preserve">eſt hyperbole referens paralellum ♌. </s> <s xml:id="echoid-s20323" xml:space="preserve">tranſeuntem per tria <lb/>puncta E D G. </s> <s xml:id="echoid-s20324" xml:space="preserve">Altera curua R T S. </s> <s xml:id="echoid-s20325" xml:space="preserve">refert paralellum ♂<unsure/>, vti characteres ſignorum appoſiti indicant. <lb/></s> <s xml:id="echoid-s20326" xml:space="preserve">Tertia refert arcum diurnum hor. </s> <s xml:id="echoid-s20327" xml:space="preserve">10. </s> <s xml:id="echoid-s20328" xml:space="preserve">& </s> <s xml:id="echoid-s20329" xml:space="preserve">ſic de reliquis. </s> <s xml:id="echoid-s20330" xml:space="preserve">Interualla porro prędicta inter hor. </s> <s xml:id="echoid-s20331" xml:space="preserve">Italicam, <lb/>& </s> <s xml:id="echoid-s20332" xml:space="preserve">meridianam nihil aliud ſunt quam arcus prædictorum paralellorum inter lineam Italicam E F. </s> <s xml:id="echoid-s20333" xml:space="preserve">& </s> <s xml:id="echoid-s20334" xml:space="preserve"><lb/>meridianam D B, v.</s> <s xml:id="echoid-s20335" xml:space="preserve">g. </s> <s xml:id="echoid-s20336" xml:space="preserve">arcus E D, eſt interuallum inter eas in paralello ♌, arcus R T. </s> <s xml:id="echoid-s20337" xml:space="preserve">eſt interuallum <lb/>inter eaſdem in paralello ♂, & </s> <s xml:id="echoid-s20338" xml:space="preserve">ſic de cęteris. </s> <s xml:id="echoid-s20339" xml:space="preserve">quare B F, eſt interuallum earundem in ♋, &</s> <s xml:id="echoid-s20340" xml:space="preserve">c. </s> <s xml:id="echoid-s20341" xml:space="preserve">Eadem <lb/>prędictis ſunt interualla inter Babylon. </s> <s xml:id="echoid-s20342" xml:space="preserve">& </s> <s xml:id="echoid-s20343" xml:space="preserve">merid. </s> <s xml:id="echoid-s20344" xml:space="preserve">vt ex figura patet.</s> <s xml:id="echoid-s20345" xml:space="preserve"/> </p> <div xml:id="echoid-div544" type="float" level="2" n="3"> <note position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">Septima <lb/>figura <lb/>Horarij.</note> </div> <pb o="7" file="0261" n="266" rhead="DE HOROLOGIIS."/> </div> <div xml:id="echoid-div546" type="section" level="1" n="411"> <head xml:id="echoid-head433" xml:space="preserve">TABELLÆ.</head> <note position="right" xml:space="preserve"> <lb/>### Declinationes paralello- \\ rũ per initia ſignorũ, nec \\ non per gr. 15. ♍, & ♎. # ## Tẽpora ſemi- \\ diurna eorun- \\ dem paralel- \\ lorum. # ## Meridies eo- \\ rundem. # ## Interualla inter \\ h. 18. Ital. & me- \\ ridianam in ijſ- \\ dem paralellis. # ## Eadẽ interual- \\ la conuerſa in \\ arcus. <lb/># ## Declinationes <lb/>Sig. # Gr. # M. # Horę # Min. # Horę # Min. # Horæ # Min. # Gr. # Min. <lb/>♋ # 23 # 30 # 7 # 51 # 16 # 19 # 1 # 41 # 25 # 15 <lb/>♌ # 20 # 12 # 7 # 25 # 16 # 35 # 1 # 25 # 21 # 15 <lb/>♏ # 11 # 30 # 6 # 46 # 17 # 14 # 0 # 46 # 11 # 30 <lb/>15 ♍ # 5 # 56 # 6 # 23 # 17 # 37 # 0 # 23 # 5 # 45 <lb/>♎ # 0 # 0 # 6 # 0 # 18 # 0 # 0 # 0 # 0 # 0 <lb/>15 ♎ # 5 # 56 # 5 # 37 # 18 # 23 # 0 # 23 # 5 # 45 <lb/>♒ # 11 # 30 # 5 # 14 # 18 # 46 # 0 # 46 # 11 # 30 <lb/>♂ # 20 # 12 # 4 # 35 # 19 # 25 # 1 # 25 # 21 # 15 <lb/>☊ # 23 # 30 # 4 # 19 # 19 # 41 # 1 # 41 # 25 # 15 <lb/>### Declinationes arcuum \\ diurnorũ horar. integra \\ rum ad altit. poli 44 {1/2}. # ## Tempora ſe- \\ midiurna eo- \\ rundem ar- \\ cuum d. # ## Meridies eo- \\ rundem ar- \\ cuum. # ## Interualla inter \\ hor. 18. Itali- \\ cam, & meri- \\ dianam in ijſ- \\ dem arcubus d. # ## Eadem inter- \\ ualla conuer- \\ ſa in arcus. <lb/>Arcus diur- \\ ni horarum # ## Declina- \\ tiones. <lb/># Gr. # M. # Horę # Min. # Horę # Min. # Horę # Min. # Gr. # Min. <lb/>15 # 21 # 17 # 7 # 30 # 16 # 30 # 1 # 30 # 22 # 30 <lb/>14 # 14 # 45 # 7 # 0 # 17 # 0 # 1 # 0 # 15 # 0 <lb/>13 # 7 # 34 # 6 # 30 # 17 # 30 # 0 # 30 # 7 # 30 <lb/>12 # 0 # 0 # 6 # 0 # 18 # 0 # 0 # 0 # 0 # 0 <lb/>11 # 7 # 34 # 5 # 30 # 18 # 30 # 0 # 30 # 7 # 30 <lb/>10 # 14 # 45 # 5 # 0 # 19 # 0 # 1 # 0 # 15 # 0 <lb/>9 # 21 # 17 # 4 # 30 # 19 # 30 # 1 # 30 # 22 # 30 <lb/>### Prima columna. # ## Secũda colũna # ## Tertia colũna. # ## Quarta colũna. # ## Quarta colũna <lb/></note> </div> <div xml:id="echoid-div547" type="section" level="1" n="412"> <head xml:id="echoid-head434" style="it" xml:space="preserve">De Horario plano, & particulari.</head> <p> <s xml:id="echoid-s20346" xml:space="preserve">9 EX quinta columna interuallorum deſcribatur figura (quam propterea figura interuallorũ ap-<lb/> <anchor type="note" xlink:label="note-0261-02a" xlink:href="note-0261-02"/> pello) hoc modo. </s> <s xml:id="echoid-s20347" xml:space="preserve">Accepto ſemidiametro A B, æquali ſemidiametro E A, Radiarij deſcriba <lb/>tur arcus I B K, & </s> <s xml:id="echoid-s20348" xml:space="preserve">arcus B I, B K, vterque ſit interuallũ maximum, quod eſt gr. </s> <s xml:id="echoid-s20349" xml:space="preserve">25. </s> <s xml:id="echoid-s20350" xml:space="preserve">15. </s> <s xml:id="echoid-s20351" xml:space="preserve">quæ ſunt duæ <lb/>diſtantiæ hor. </s> <s xml:id="echoid-s20352" xml:space="preserve">18. </s> <s xml:id="echoid-s20353" xml:space="preserve">Italica à meridiana. </s> <s xml:id="echoid-s20354" xml:space="preserve">Deinde ducta recta T B V, normali ſemidiametro A B, ſeu tan-<lb/>gente arcum in puncto B, ducantur duæ rectæ A I T, A K V, occurrentes tangenti in punctis T V, & </s> <s xml:id="echoid-s20355" xml:space="preserve"><lb/>producta A B, in directum, ita vt B D, ſit æqualis tangenti H A I, Radiarij; </s> <s xml:id="echoid-s20356" xml:space="preserve">ſitq; </s> <s xml:id="echoid-s20357" xml:space="preserve">ſicuti eſt illa diuiſa <lb/>in punctis H K M A N P I. </s> <s xml:id="echoid-s20358" xml:space="preserve">ita hæc in totidem partes illis æquales, & </s> <s xml:id="echoid-s20359" xml:space="preserve">medio puncto apponatur C, <lb/> <anchor type="note" xlink:label="note-0261-03a" xlink:href="note-0261-03"/> atq; </s> <s xml:id="echoid-s20360" xml:space="preserve">hæc linea erit 12. </s> <s xml:id="echoid-s20361" xml:space="preserve">Aſtronomica. </s> <s xml:id="echoid-s20362" xml:space="preserve">Deinde ex centro C, deſcribatur arcus X Y, in quo eius portio <lb/>X Y, contineat tot grad. </s> <s xml:id="echoid-s20363" xml:space="preserve">quot conſtat altitudo poli eius loci, pro quo particulare Inſtrumentum nunc <lb/>eſt fabricandum, v.</s> <s xml:id="echoid-s20364" xml:space="preserve">g. </s> <s xml:id="echoid-s20365" xml:space="preserve">quia Parmæ cuius altitudo poli eſt gr. </s> <s xml:id="echoid-s20366" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s20367" xml:space="preserve">conſtruimus Inſtrumentum, faciam <lb/>arcum X Y, gr. </s> <s xml:id="echoid-s20368" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s20369" xml:space="preserve">Vtile erit ex altera parte verſus B F, delcribere pariter ex C, alterũ arcum Z, ♎, <lb/>æqualem prædicto, ſic enim melius operabimur. </s> <s xml:id="echoid-s20370" xml:space="preserve">lam per puncta Y C Z, quæ debent eſſe in directum <lb/>poſita, ducatur recta Y C Z, quæ erit 18. </s> <s xml:id="echoid-s20371" xml:space="preserve">Italica, ſimiliter ad eoſdem angulos cum meridiana ducatur <lb/>G C H, quæ erit 6. </s> <s xml:id="echoid-s20372" xml:space="preserve">Babylonica. </s> <s xml:id="echoid-s20373" xml:space="preserve">Ratio eſt, quia, vt probatur in Gnomon. </s> <s xml:id="echoid-s20374" xml:space="preserve">hora 18. </s> <s xml:id="echoid-s20375" xml:space="preserve">Italica, 6. </s> <s xml:id="echoid-s20376" xml:space="preserve">Babylo-<lb/>nica, & </s> <s xml:id="echoid-s20377" xml:space="preserve">12. </s> <s xml:id="echoid-s20378" xml:space="preserve">Aſtronomica ſe mutuo bifariam ſecant in codem puncto æquatoris, quod in Horario eſt <lb/>eſt C, & </s> <s xml:id="echoid-s20379" xml:space="preserve">præterea tangunt circulum maximum ſemper apparentium in punctis per quadrantem re-<lb/>motis. </s> <s xml:id="echoid-s20380" xml:space="preserve">a puncto vbi 12. </s> <s xml:id="echoid-s20381" xml:space="preserve">Aſtronomica eundem ſecat; </s> <s xml:id="echoid-s20382" xml:space="preserve">qui circulus cum tangat Horizontem, & </s> <s xml:id="echoid-s20383" xml:space="preserve">polus <lb/>eius ſit etiam polus mundi, neceſſario eius peripheria diſtat à polo mundi tantum, quanta eſt altitu-<lb/>do poli; </s> <s xml:id="echoid-s20384" xml:space="preserve">quare hora Italica, & </s> <s xml:id="echoid-s20385" xml:space="preserve">Babylonica facient cum Aſtronomica angulos æquales altitudini poli.</s> <s xml:id="echoid-s20386" xml:space="preserve"> <pb o="8" file="0262" n="267" rhead="TRACTATVS"/> Noſtræ porto lineæ rectæ in plano Horarij ſunt communes ſectiones planorum circulorũm Ital. </s> <s xml:id="echoid-s20387" xml:space="preserve">& </s> <s xml:id="echoid-s20388" xml:space="preserve"><lb/>Babylon. </s> <s xml:id="echoid-s20389" xml:space="preserve">cum plano Horarij, quod Sphæram tangit in C. </s> <s xml:id="echoid-s20390" xml:space="preserve">eſtque paralellum circulo horę 6. </s> <s xml:id="echoid-s20391" xml:space="preserve">Aſtrono-<lb/>micę, quare etiam in plano Horarij hæ ſectiones facient eoſdem angulos.</s> <s xml:id="echoid-s20392" xml:space="preserve"/> </p> <div xml:id="echoid-div547" type="float" level="2" n="1"> <note position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">Octau@ <lb/>figura <lb/>diſtanti@ <lb/>rum.</note> <note position="right" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">Horari-<lb/>um, im-<lb/>plex, pla-<lb/>num, & <lb/>partic@ <lb/>lare.</note> </div> <p> <s xml:id="echoid-s20393" xml:space="preserve">Iam Ital. </s> <s xml:id="echoid-s20394" xml:space="preserve">& </s> <s xml:id="echoid-s20395" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20396" xml:space="preserve">terminandæ ſunt hac ra@ione. </s> <s xml:id="echoid-s20397" xml:space="preserve">Per puncta I V, ducantur duæ rectæ norma-<lb/>les ipſi tangenti T B V, donec occurrant lineis Italicæ, & </s> <s xml:id="echoid-s20398" xml:space="preserve">Babylonicæ productis in punctis E F G H, <lb/>ſicque E F, erit Italica terminata, & </s> <s xml:id="echoid-s20399" xml:space="preserve">G H, Babylonica pariter terminata, cuius ratio poſtea patebit. <lb/></s> <s xml:id="echoid-s20400" xml:space="preserve">Atq; </s> <s xml:id="echoid-s20401" xml:space="preserve">ex his tribus lineis erit abſolutum Horarium, ſed ſimplex, & </s> <s xml:id="echoid-s20402" xml:space="preserve">quo tantum horas terminatas de-<lb/>ſcribere poſſes. </s> <s xml:id="echoid-s20403" xml:space="preserve">Si quis igitur contentus ſit hac breuitate, ei iam ſatis factum erit. </s> <s xml:id="echoid-s20404" xml:space="preserve">Opus tamen erit <lb/>Horarium iſtud in laminam ſolidam tranſcribere, atque ad vſum accommodare, vt poſt modum di-<lb/>cemus.</s> <s xml:id="echoid-s20405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20406" xml:space="preserve">10 Verum vt nos Horarium habeamus quo videlicet. </s> <s xml:id="echoid-s20407" xml:space="preserve">præter horas etiam paralellos ſignorum, <lb/>necnon arcus diurnos in noſtris Horologiis delineare poſſimus. </s> <s xml:id="echoid-s20408" xml:space="preserve">addantur quæ ſequuntur.</s> <s xml:id="echoid-s20409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20410" xml:space="preserve">In arcu I B K, ponantur reliqua interualla accepta ex quinta columna, ideſt, arcus B L, & </s> <s xml:id="echoid-s20411" xml:space="preserve">B M, ſint <lb/> <anchor type="note" xlink:label="note-0262-01a" xlink:href="note-0262-01"/> vterq; </s> <s xml:id="echoid-s20412" xml:space="preserve">gr. </s> <s xml:id="echoid-s20413" xml:space="preserve">21. </s> <s xml:id="echoid-s20414" xml:space="preserve">15. </s> <s xml:id="echoid-s20415" xml:space="preserve">arcus B N, B O, ſint gr. </s> <s xml:id="echoid-s20416" xml:space="preserve">15. </s> <s xml:id="echoid-s20417" xml:space="preserve">0. </s> <s xml:id="echoid-s20418" xml:space="preserve">qui accipiendi ſunt ex ſecunda parte columnæ quintæ <lb/>ſunt enim interualla in arcubus diurnis hor. </s> <s xml:id="echoid-s20419" xml:space="preserve">14. </s> <s xml:id="echoid-s20420" xml:space="preserve">& </s> <s xml:id="echoid-s20421" xml:space="preserve">hor. </s> <s xml:id="echoid-s20422" xml:space="preserve">10. </s> <s xml:id="echoid-s20423" xml:space="preserve">arcus B P, B Q, ſint ſint gr. </s> <s xml:id="echoid-s20424" xml:space="preserve">11. </s> <s xml:id="echoid-s20425" xml:space="preserve">30. </s> <s xml:id="echoid-s20426" xml:space="preserve">arcus B r, <lb/>B q, ſint gr. </s> <s xml:id="echoid-s20427" xml:space="preserve">5. </s> <s xml:id="echoid-s20428" xml:space="preserve">45. </s> <s xml:id="echoid-s20429" xml:space="preserve">Deinde ex centr@ A, per puncta, L N P r q QOM, ducantur rectæ vſque ad tan-<lb/>gentem T B V, in punctis 0. </s> <s xml:id="echoid-s20430" xml:space="preserve">1. </s> <s xml:id="echoid-s20431" xml:space="preserve">2. </s> <s xml:id="echoid-s20432" xml:space="preserve">3. </s> <s xml:id="echoid-s20433" xml:space="preserve">ex vtraq; </s> <s xml:id="echoid-s20434" xml:space="preserve">parte ex prædictis lineis adſcribantur characteres ſigno-<lb/>rum, per quorum interualla tranieunt: </s> <s xml:id="echoid-s20435" xml:space="preserve">duabus vero A N, A D, apponantur hor. </s> <s xml:id="echoid-s20436" xml:space="preserve">10 & </s> <s xml:id="echoid-s20437" xml:space="preserve">hor. </s> <s xml:id="echoid-s20438" xml:space="preserve">14. </s> <s xml:id="echoid-s20439" xml:space="preserve">quia, <lb/>tranſeunt per finem interuallorum in arcubus diurnis hor. </s> <s xml:id="echoid-s20440" xml:space="preserve">10. </s> <s xml:id="echoid-s20441" xml:space="preserve">& </s> <s xml:id="echoid-s20442" xml:space="preserve">14. </s> <s xml:id="echoid-s20443" xml:space="preserve">vt apparet in figura. </s> <s xml:id="echoid-s20444" xml:space="preserve">poſtea ſecus <lb/>puncta 1. </s> <s xml:id="echoid-s20445" xml:space="preserve">2. </s> <s xml:id="echoid-s20446" xml:space="preserve">3. </s> <s xml:id="echoid-s20447" xml:space="preserve">omiſſis in præſentia 0. </s> <s xml:id="echoid-s20448" xml:space="preserve">0. </s> <s xml:id="echoid-s20449" xml:space="preserve">applicata regula normaliter ad tangentem B V. </s> <s xml:id="echoid-s20450" xml:space="preserve">vbi ipſa regu-<lb/> <anchor type="note" xlink:label="note-0262-02a" xlink:href="note-0262-02"/> la ſecuerit lineas horarias Italicam, & </s> <s xml:id="echoid-s20451" xml:space="preserve">Babylonicam, vbi imprime puncta, vnum pro ſingulis. </s> <s xml:id="echoid-s20452" xml:space="preserve">ſic ap-<lb/>plicata, v.</s> <s xml:id="echoid-s20453" xml:space="preserve">g. </s> <s xml:id="echoid-s20454" xml:space="preserve">regula ſecus punctum 3. </s> <s xml:id="echoid-s20455" xml:space="preserve">ſecabit Italicam, & </s> <s xml:id="echoid-s20456" xml:space="preserve">Babylonicam in punctis notatis litera s. </s> <s xml:id="echoid-s20457" xml:space="preserve">Idem <lb/>fac ex puncto 2. </s> <s xml:id="echoid-s20458" xml:space="preserve">& </s> <s xml:id="echoid-s20459" xml:space="preserve">habebis alia duo pũcta in Ital. </s> <s xml:id="echoid-s20460" xml:space="preserve">& </s> <s xml:id="echoid-s20461" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20462" xml:space="preserve">& </s> <s xml:id="echoid-s20463" xml:space="preserve">ſic de cęteris, etiam ex altera parte tan-<lb/>gentis B T. </s> <s xml:id="echoid-s20464" xml:space="preserve">Porro ſi erratum non eſt, erunt omnia puncta hor. </s> <s xml:id="echoid-s20465" xml:space="preserve">Ital. </s> <s xml:id="echoid-s20466" xml:space="preserve">& </s> <s xml:id="echoid-s20467" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20468" xml:space="preserve">conſimiliter poſita <lb/>in vna, a tq; </s> <s xml:id="echoid-s20469" xml:space="preserve">in altera. </s> <s xml:id="echoid-s20470" xml:space="preserve">Et ſi imaginemur lineam curuam ductam per tria extrema E D G, linearum ho-<lb/>rariarum ipſa reſpondebit tropico ♌, ſeu erit portio hyperboles reſpondens paralello per initium, <lb/>♌, pariter linea per@ria puncta ſequentia R T S, leniter curua, erit portio hyperboles reſpondens pa-<lb/>ralello per initium ♑, ducto, & </s> <s xml:id="echoid-s20471" xml:space="preserve">ſic de cęteris. </s> <s xml:id="echoid-s20472" xml:space="preserve">quibus apponantur proprij characteres, & </s> <s xml:id="echoid-s20473" xml:space="preserve">notæ, vt fi-<lb/>gura per ſe oſtendi@:</s> <s xml:id="echoid-s20474" xml:space="preserve">eritq; </s> <s xml:id="echoid-s20475" xml:space="preserve">Horarium abſolutum in plano deſcriptum.</s> <s xml:id="echoid-s20476" xml:space="preserve"/> </p> <div xml:id="echoid-div548" type="float" level="2" n="2"> <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Horæviũ <lb/>parfectũ <lb/>planum, <lb/>& parti-<lb/>culare.</note> <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">Deſcri-<lb/>prio para <lb/>lellorum <lb/>in Hera-<lb/>ri@.</note> </div> <p> <s xml:id="echoid-s20477" xml:space="preserve">11 Notanda quædam. </s> <s xml:id="echoid-s20478" xml:space="preserve">Primo, quamuis prædicta interualla omnia ponantur in eodem arcu I K, <lb/>debet tamen quodlibet illorum intelligi in proprijs eſſe paralellis, v. </s> <s xml:id="echoid-s20479" xml:space="preserve">g. </s> <s xml:id="echoid-s20480" xml:space="preserve">I B in tropico ♑. </s> <s xml:id="echoid-s20481" xml:space="preserve">B K, in tro-<lb/>pico ♋, L B, in paralello ♐, B M, in paralello ♌, prout characteres lineis ea termi ã@ bus indicant. <lb/></s> <s xml:id="echoid-s20482" xml:space="preserve">Ratio huius eſt, quia idem arcus I B K, ſecundum varia interualla in eo notata refert etiã varios pa-<lb/>ralellos, quibus ea interualla competunt: </s> <s xml:id="echoid-s20483" xml:space="preserve">quare ob interuallum I B, refer@ tropicum ♑, ob interuallũ <lb/>L B, paralellum ♐ &</s> <s xml:id="echoid-s20484" xml:space="preserve">c.</s> <s xml:id="echoid-s20485" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20486" xml:space="preserve">Secundo, notandum lineas à centro A, egredientes per puncta interuallorum eſſe ſingulas ſecan-<lb/>tes ſingulorum dictorũ interuallorum quibus interuallis reſpondent ſingulæ tangentes B 1. </s> <s xml:id="echoid-s20487" xml:space="preserve">B 2. </s> <s xml:id="echoid-s20488" xml:space="preserve">B 3. <lb/></s> <s xml:id="echoid-s20489" xml:space="preserve">B V, ex vna parte. </s> <s xml:id="echoid-s20490" xml:space="preserve">ex altera vero ſimiliter B 1. </s> <s xml:id="echoid-s20491" xml:space="preserve">B 2. </s> <s xml:id="echoid-s20492" xml:space="preserve">B 3. </s> <s xml:id="echoid-s20493" xml:space="preserve">B T.</s> <s xml:id="echoid-s20494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20495" xml:space="preserve">12 Aliter ſine altitudine poli poſſunt inueniri linea Italica, & </s> <s xml:id="echoid-s20496" xml:space="preserve">Babylonica, & </s> <s xml:id="echoid-s20497" xml:space="preserve">quidem termina-<lb/>tæ. </s> <s xml:id="echoid-s20498" xml:space="preserve">Oportet igitur primo diuidere, ac terminare ſimul duo latera Horarij F G, H E, in punctis de-<lb/>clinationum paralellorum aſſumptorum in Horario, ope Rad@arij: </s> <s xml:id="echoid-s20499" xml:space="preserve">ſi u@i etiam diuiſa eſt Aſtronomi-<lb/>ca B D. </s> <s xml:id="echoid-s20500" xml:space="preserve">Accipiatur igitur circino alterutra duarum ſecantium A T, vel A V, & </s> <s xml:id="echoid-s20501" xml:space="preserve">ponatur in Radiario, <lb/>ſitque E r, & </s> <s xml:id="echoid-s20502" xml:space="preserve">per punctum r, acta normalis S r T, ſecetur ſaltem a duobus radijs ex remis in punctis <lb/>S T, deinde a puncto C, Horarij applicata normali vſq; </s> <s xml:id="echoid-s20503" xml:space="preserve">ad latus G F, in a, erit a, punctum medium <lb/>ipſius. </s> <s xml:id="echoid-s20504" xml:space="preserve">iam ab a, ſupra, & </s> <s xml:id="echoid-s20505" xml:space="preserve">infra ponantur a G, & </s> <s xml:id="echoid-s20506" xml:space="preserve">a F, æquales ip is @ S, r @. </s> <s xml:id="echoid-s20507" xml:space="preserve">Radiarij. </s> <s xml:id="echoid-s20508" xml:space="preserve">ſimiſiter reliquæ <lb/>diuiſiones transferri hinc ad latus Horarij poterunt. </s> <s xml:id="echoid-s20509" xml:space="preserve">Idem aciendum eſt cum latere H E, eruntque <lb/>æqualia inuicem. </s> <s xml:id="echoid-s20510" xml:space="preserve">Iam ſi per puncta E F, & </s> <s xml:id="echoid-s20511" xml:space="preserve">per puncta G H, ducantur duæ rect@e, tranſibunt ambæ <lb/>per C, ipſæque erunt lineæ horariæ Italica, & </s> <s xml:id="echoid-s20512" xml:space="preserve">Babylonica, vt prius. </s> <s xml:id="echoid-s20513" xml:space="preserve">Porro ſi ab reliquis extremis <lb/>punctis ſecantium 3. </s> <s xml:id="echoid-s20514" xml:space="preserve">2. </s> <s xml:id="echoid-s20515" xml:space="preserve">1. </s> <s xml:id="echoid-s20516" xml:space="preserve">erigantur latera alia normali@er, eaque eadem ra@oiſe ope Radiarij diui-<lb/>dantur, diuidentur in ijſdem punctis, in quibus ipſa ſecat horarias Italicam, & </s> <s xml:id="echoid-s20517" xml:space="preserve">Baby onicam, v.</s> <s xml:id="echoid-s20518" xml:space="preserve">g. </s> <s xml:id="echoid-s20519" xml:space="preserve">la-<lb/>tus ex 3. </s> <s xml:id="echoid-s20520" xml:space="preserve">erectum, ſecaretur in punctiss, s, a Radiario, in quibus ipſum ſ@ca ſineas Italicam, & </s> <s xml:id="echoid-s20521" xml:space="preserve">Baby <lb/>lonicam.</s> <s xml:id="echoid-s20522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20523" xml:space="preserve">13 Quorum rationes, vt intelligantur; </s> <s xml:id="echoid-s20524" xml:space="preserve">debemus primo imaginari Horarium ſitum in ſuo ſitu na-<lb/> <anchor type="note" xlink:label="note-0262-03a" xlink:href="note-0262-03"/> turali, in quo ſupponitur deſcriptum, ideſt, in plano paralello circulo horæ 6. </s> <s xml:id="echoid-s20525" xml:space="preserve">Aſtronomicæ, quare & </s> <s xml:id="echoid-s20526" xml:space="preserve"><lb/>paralello axi mundi, necnon tangenti Sphæram mundi in puncto commun æquatoris, & </s> <s xml:id="echoid-s20527" xml:space="preserve">lineæ me-<lb/>ridianæ; </s> <s xml:id="echoid-s20528" xml:space="preserve">quod in Radiario eſt A, in Horario vero eſt C. </s> <s xml:id="echoid-s20529" xml:space="preserve">Debemus igitur concipere Radiarium ere-<lb/>ctum normaliter ſupra planum circuli interuallorum, & </s> <s xml:id="echoid-s20530" xml:space="preserve">linea tangens Radiarij A I, pariter normalis <lb/>ſupra B, circuli diſtantiarum. </s> <s xml:id="echoid-s20531" xml:space="preserve">quibus ſic poſitis, erigatur Horarium circa rectam T B V, nonmaliter <lb/>ſupra planum circuli diſtantiarum, ita vt linea B C D, Aſtronomica coincidat cum I A H, Radiarij, <lb/>ſicq; </s> <s xml:id="echoid-s20532" xml:space="preserve">erit in ſuo ſitu naturali: </s> <s xml:id="echoid-s20533" xml:space="preserve">in quo ſitu manifeſtum eſt radios Radiarij diuidere lineam B D, Hora-<lb/>rij in ijſdem punctis, quibus eam ſupra diuifimus. </s> <s xml:id="echoid-s20534" xml:space="preserve">Poſtea moueatur Radiarium, ſeu giretur circa ma-<lb/>nentem E Q, normalem donec Q I, linea eius ſit ſupra alterutram extremarum ſecantium circuli di-<lb/>ſtantiarum, v. </s> <s xml:id="echoid-s20535" xml:space="preserve">g. </s> <s xml:id="echoid-s20536" xml:space="preserve">coincidat cum ſecante A K V, eritq; </s> <s xml:id="echoid-s20537" xml:space="preserve">Radiarium directe è regione lateris<unsure/> F G, quod <pb o="9" file="0263" n="268" rhead="DE HOROLOGIIS."/> diſtabit aliquantulum à linea Radiarij H A I, cum totum Horarium cadat extra arcum diſtantiarum; <lb/></s> <s xml:id="echoid-s20538" xml:space="preserve">incumbit enim tangenti T V, quare radij non ſecabunt illud niſi producantur vitra lineã H A I, qua-<lb/>re producti facient in eo diuiſiones laxiores quam in B D, ſic generatim quãto magis diſtabunt a me-<lb/>dia B D, tanto magis etiam a Radiario, & </s> <s xml:id="echoid-s20539" xml:space="preserve">proinde laxioribus ſpatijs diuidentur.</s> <s xml:id="echoid-s20540" xml:space="preserve"/> </p> <div xml:id="echoid-div549" type="float" level="2" n="3"> <note position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">Demon-<lb/>stratio <lb/>praceden <lb/>@ium.</note> </div> <p> <s xml:id="echoid-s20541" xml:space="preserve">14 Hinc pariter neceſſe erit hyperbolas, quas ſupra innuimus, ſeu puncta illarum eſſe illa eadem, <lb/>quæ reperta ſunt in lineis horarijs per latera erecta normaliter ſupra ſecantium extrema puncta, V, <lb/>3. </s> <s xml:id="echoid-s20542" xml:space="preserve">2. </s> <s xml:id="echoid-s20543" xml:space="preserve">1. </s> <s xml:id="echoid-s20544" xml:space="preserve">&</s> <s xml:id="echoid-s20545" xml:space="preserve">c. </s> <s xml:id="echoid-s20546" xml:space="preserve">ſeu per applicatam regulam normaliter, nam radius, v. </s> <s xml:id="echoid-s20547" xml:space="preserve">g. </s> <s xml:id="echoid-s20548" xml:space="preserve">♋, E I T, in prædicto ſitu ſecat <lb/>latus G F, in F, vt vidimus, infra ſecantem A V, diſtantiæ horæ Italicæ in ♋. </s> <s xml:id="echoid-s20549" xml:space="preserve">Idem accidet reliquis <lb/>punctis extremis linearum Ital. </s> <s xml:id="echoid-s20550" xml:space="preserve">& </s> <s xml:id="echoid-s20551" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20552" xml:space="preserve">Idem intelligendum de alijs punctis, v.</s> <s xml:id="echoid-s20553" xml:space="preserve">g.</s> <s xml:id="echoid-s20554" xml:space="preserve">s.</s> <s xml:id="echoid-s20555" xml:space="preserve">s. </s> <s xml:id="echoid-s20556" xml:space="preserve">quia in il-<lb/>lis occurrunt radij ♌ & </s> <s xml:id="echoid-s20557" xml:space="preserve">♐, & </s> <s xml:id="echoid-s20558" xml:space="preserve">pariter in ijſmet ſecatur a regula normaliter applicata ſecus punctu@ 3. <lb/></s> <s xml:id="echoid-s20559" xml:space="preserve">extremum ſecãtis horæ Italicæ a meridie in paralello ♌, &</s> <s xml:id="echoid-s20560" xml:space="preserve">c. </s> <s xml:id="echoid-s20561" xml:space="preserve">res per ſe obſcura indiget ſpeculatione. </s> <s xml:id="echoid-s20562" xml:space="preserve"><lb/>Quare patet aliter reperiri poſſe Italicam, & </s> <s xml:id="echoid-s20563" xml:space="preserve">Babylonicam, quam per altitudinem poli, quod pro-<lb/>poſueram.</s> <s xml:id="echoid-s20564" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20565" xml:space="preserve">15 Notandum tres prædictas lineas 18. </s> <s xml:id="echoid-s20566" xml:space="preserve">Italicam 12. </s> <s xml:id="echoid-s20567" xml:space="preserve">Aſtronomicam, & </s> <s xml:id="echoid-s20568" xml:space="preserve">6. </s> <s xml:id="echoid-s20569" xml:space="preserve">Babylonicam poſſe in-<lb/>ſeruire in vſu Inſtrumenti etiam pro cęteris omnibus horis: </s> <s xml:id="echoid-s20570" xml:space="preserve">quod patebit conſideranti primo lineas <lb/>omnes horarias Italicas, & </s> <s xml:id="echoid-s20571" xml:space="preserve">Babylonicas habere vbiq; </s> <s xml:id="echoid-s20572" xml:space="preserve">eundem ſitum vel inclinationem ad æquatorẽ; <lb/></s> <s xml:id="echoid-s20573" xml:space="preserve">cum enim omnes earum circuli horarij tangant paralellum maximum ſemper apparentium, necnon <lb/>ſemper occultorum habebunt omnes eandem inclinationem, quæ æqualis erit altitudini poli propo-<lb/>ſitæ regionis. </s> <s xml:id="echoid-s20574" xml:space="preserve">De Aſtronomicis etiam perſpicuum eſt, cum omnes circuli earum horarij faciant cum <lb/>æquatore angulos rectos: </s> <s xml:id="echoid-s20575" xml:space="preserve">cum igitur tres noſtræ lineę fint tangentes trium horum circulorum hora-<lb/>riorum, in mutuis eorum ſectionibus cum æquatore, ſequitur eas habere eandem inclinationem, & </s> <s xml:id="echoid-s20576" xml:space="preserve"><lb/>poſitionem ad æquatorem, quam habent cęteræ omnes tangentes cęterorum omnium arcuum, quas-<lb/>libet cum quibuslibet ſui generis comparando, ideſt 18. </s> <s xml:id="echoid-s20577" xml:space="preserve">Italicam coincidere poſſe cum qualibet alia <lb/>Italica, & </s> <s xml:id="echoid-s20578" xml:space="preserve">Babylonicam cum qualibet Babilonica, & </s> <s xml:id="echoid-s20579" xml:space="preserve">Aſtronomicam cum qualibet Aſtronomica, ſi <lb/>horarium transferatur ad aliam quamuis diuiſionem æquatoris factam in 24. </s> <s xml:id="echoid-s20580" xml:space="preserve">partes competentes 24. </s> <s xml:id="echoid-s20581" xml:space="preserve"><lb/>horis, &</s> <s xml:id="echoid-s20582" xml:space="preserve">c. </s> <s xml:id="echoid-s20583" xml:space="preserve">quemadmodum accidit in vſu Inſtrumenti: </s> <s xml:id="echoid-s20584" xml:space="preserve">nam Horarium transfertur ad ſingulas partes <lb/>24. </s> <s xml:id="echoid-s20585" xml:space="preserve">æquatoris. </s> <s xml:id="echoid-s20586" xml:space="preserve">ex quibus patet propoſitum.</s> <s xml:id="echoid-s20587" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20588" xml:space="preserve">16 Deſcripto iam in charta Horario tranſcribendum illud eſt in laminam ęneam, aut in regulas <lb/> <anchor type="note" xlink:label="note-0263-01a" xlink:href="note-0263-01"/> ęneas. </s> <s xml:id="echoid-s20589" xml:space="preserve">Si quis vellet eo vti ad horas tantum Italicas deſcribendas, ſatis eſſet tranſcribere triangulum <lb/>E F H, cum ſuis punctis. </s> <s xml:id="echoid-s20590" xml:space="preserve">Si tantum Aſtronomicas, ſatis ei fuerit in regulam ęneam tranſcribere li-<lb/>neam D C B, cum ſuis purctis. </s> <s xml:id="echoid-s20591" xml:space="preserve">Si tantum Babylonicam triangulum G H F, ſufficiet cum ſuis pun-<lb/>ctis. </s> <s xml:id="echoid-s20592" xml:space="preserve">Quod ſi latus E H, vel latus G E, ſint diuiſa vt ſupra, ea poſſunt inſeruire ad horas Aſtronomi-<lb/>cas delineandas. </s> <s xml:id="echoid-s20593" xml:space="preserve">ſatius tamen exiſtimo integrum Horarium in lamina ænea incidere hoc modo: </s> <s xml:id="echoid-s20594" xml:space="preserve">aſ-<lb/>ſumptum laminam feneſtrare ſecundum tres lineas horarias, ideſt excidere in ea tres feneſtellas ęqua-<lb/>les ſecundum longitudinem tribus lineis horarijs: </s> <s xml:id="echoid-s20595" xml:space="preserve">Obſeruando tamen vt latus vnum tantum fene-<lb/>ſtellę referat ſuam lineam horariam, ideſt ſit rectum omnino, & </s> <s xml:id="echoid-s20596" xml:space="preserve">diuiſum, &</s> <s xml:id="echoid-s20597" xml:space="preserve">c. </s> <s xml:id="echoid-s20598" xml:space="preserve">ſicuti illa: </s> <s xml:id="echoid-s20599" xml:space="preserve">alterum vero <lb/>latus eiuſdem feneſtellę ſit modicè curuum, vt apparet in pręſenti figura 9. </s> <s xml:id="echoid-s20600" xml:space="preserve">Exurgunt ex hac exciſio-<lb/> <anchor type="note" xlink:label="note-0263-02a" xlink:href="note-0263-02"/> ne ſex triangula, quorum apices deſinent ad centrum C, Horarij: </s> <s xml:id="echoid-s20601" xml:space="preserve">Diligenter igitur curandum eſt, <lb/>vt ij apices quam proximè ad centrum accedant, & </s> <s xml:id="echoid-s20602" xml:space="preserve">quaſi concurrant, vt punctum C, centrum Hora-<lb/>rij tutò adiri filo poſſit. </s> <s xml:id="echoid-s20603" xml:space="preserve">Hoc modo haberi poterunt omnia, & </s> <s xml:id="echoid-s20604" xml:space="preserve">ſingula puncta horaria in Horologij <lb/>deſcriptione, quod valde vtile, ac ſingulare huic Inſtrumento eſt.</s> <s xml:id="echoid-s20605" xml:space="preserve"/> </p> <div xml:id="echoid-div550" type="float" level="2" n="4"> <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">Horari-<lb/>um ma-<lb/>teriale.</note> <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">9 figura.</note> </div> <p> <s xml:id="echoid-s20606" xml:space="preserve">Alij illud in tribus oblongis laminis ponunt, qualem altera figura 10. </s> <s xml:id="echoid-s20607" xml:space="preserve">oſtendit, ſed non ſine quopiã <lb/> <anchor type="note" xlink:label="note-0263-03a" xlink:href="note-0263-03"/> incommodo quod propè centrum C, aliquanta pars linearum filo adiri nequit. </s> <s xml:id="echoid-s20608" xml:space="preserve">Atque hęc ſufficiant <lb/>pro Horario plano, & </s> <s xml:id="echoid-s20609" xml:space="preserve">partieulari.</s> <s xml:id="echoid-s20610" xml:space="preserve"/> </p> <div xml:id="echoid-div551" type="float" level="2" n="5"> <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">10. figu-<lb/>ra.</note> </div> <p> <s xml:id="echoid-s20611" xml:space="preserve">17 Erit vniuerſale ſi circa centrum C, ita tres prędictę materiales lineę connectãtur, vt duę, Ital. <lb/></s> <s xml:id="echoid-s20612" xml:space="preserve"> <anchor type="note" xlink:label="note-0263-04a" xlink:href="note-0263-04"/> & </s> <s xml:id="echoid-s20613" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20614" xml:space="preserve">efficere poſſint cum Aſtronom. </s> <s xml:id="echoid-s20615" xml:space="preserve">angulum ęqualem cuiuis altitudini poli. </s> <s xml:id="echoid-s20616" xml:space="preserve">Curandum por-<lb/>ro vt punctum C, quantum fieri poteſt apertum maneat:</s> <s xml:id="echoid-s20617" xml:space="preserve">neq; </s> <s xml:id="echoid-s20618" xml:space="preserve">ſunt faciendę diuiſiones iu Italica, & </s> <s xml:id="echoid-s20619" xml:space="preserve"><lb/>Babylonica, ſed tantum in Aſtronomica. </s> <s xml:id="echoid-s20620" xml:space="preserve">Pręterea Italica, & </s> <s xml:id="echoid-s20621" xml:space="preserve">Babylonica ſint paulo longiores quam <lb/> <anchor type="note" xlink:label="note-0263-05a" xlink:href="note-0263-05"/> ſupra determinauimus; </s> <s xml:id="echoid-s20622" xml:space="preserve">maiori enim altitudini maiores, minori minores inſeruient; </s> <s xml:id="echoid-s20623" xml:space="preserve">quapropter ne-<lb/>que certis diuiſionibus queunt notari. </s> <s xml:id="echoid-s20624" xml:space="preserve">Vt autem quemuis angulum cum Aſtronomica efficere poſ-<lb/>ſint, apponatur ſemicirculus ad ima earum diuiſus in duos quadrantes, qui diuiſi ſint in ſuos 90. </s> <s xml:id="echoid-s20625" xml:space="preserve">grad. <lb/></s> <s xml:id="echoid-s20626" xml:space="preserve">facto initio a medio ſemicirculi. </s> <s xml:id="echoid-s20627" xml:space="preserve">ſicuti videre eſt in adiecta figura.</s> <s xml:id="echoid-s20628" xml:space="preserve"/> </p> <div xml:id="echoid-div552" type="float" level="2" n="6"> <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">Horariũ <lb/>vniuer-<lb/>ſale.</note> <note position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">11. figu-<lb/>ra.</note> </div> <p> <s xml:id="echoid-s20629" xml:space="preserve">18 Abſolutum hoc modo Horarium ſeu particulare, ſeu vniuerſale, capiti D C E, regulę, quam <lb/>initium huius capitis pro baſi Horarij deſcripſimus, aut glutine, aut cochleis per foramina r, s, t, im-<lb/>miſſis, conſolidetur, ita vt normaliter ſupra eam erigatur, & </s> <s xml:id="echoid-s20630" xml:space="preserve">linea B D, Aſtronomica applicetur exa-<lb/>cte lineę fiducię B A C, faciens non ſolum cum eam rectum angulum, ſed etiam cum plano ipſius re-<lb/>gulę; </s> <s xml:id="echoid-s20631" xml:space="preserve">tantumque totum Horarium ſupra ipſam emineat, vt cum regula, cum Horario ſibi annexo, po-<lb/>ſita fuerit ſupra tympanum per axem mundi, partes Horarij inferiores a filo procedente ab axe attin <lb/>gi commodè poſſint: </s> <s xml:id="echoid-s20632" xml:space="preserve">ſicq; </s> <s xml:id="echoid-s20633" xml:space="preserve">Horarium erit etiam normale plano tympani, & </s> <s xml:id="echoid-s20634" xml:space="preserve">linea B D, erit pararella <lb/>axi, quod oportet. </s> <s xml:id="echoid-s20635" xml:space="preserve">Tantus præterea ſit axis ſupra regulam, vt apex eius exacte centro C, Horarij re-<lb/>ſpondeat, ideſt apex eius M, & </s> <s xml:id="echoid-s20636" xml:space="preserve">C, centrum Horarij æque alta ſint ſupra tympanum. </s> <s xml:id="echoid-s20637" xml:space="preserve">Tandem regu-<lb/>la axiculo per foramen m, ad pedem axis factum leniter confirmetur, vt poſſit ſupra ipſum ægre ali-<lb/>quantulum ad quamlibet partem conuolui, inibiq; </s> <s xml:id="echoid-s20638" xml:space="preserve">ſatis firma manere.</s> <s xml:id="echoid-s20639" xml:space="preserve"/> </p> <pb o="10" file="0264" n="269" rhead="TRACTATVS"/> <p> <s xml:id="echoid-s20640" xml:space="preserve">19 Ex hiſce partibus iam abſolutis totum Inſtrumentum componendum eſt, vt totalis hæc figura <lb/> <anchor type="note" xlink:label="note-0264-01a" xlink:href="note-0264-01"/> 12. </s> <s xml:id="echoid-s20641" xml:space="preserve">oſtendit. </s> <s xml:id="echoid-s20642" xml:space="preserve">Ex vſu tamen erit ſi totum ſit ſolutile, vt commodius geſtari poſſit.</s> <s xml:id="echoid-s20643" xml:space="preserve"/> </p> <div xml:id="echoid-div553" type="float" level="2" n="7"> <note position="left" xlink:label="note-0264-01" xlink:href="note-0264-01a" xml:space="preserve">22. figu-<lb/>ra to@-<lb/>lis.</note> </div> </div> <div xml:id="echoid-div555" type="section" level="1" n="413"> <head xml:id="echoid-head435" style="it" xml:space="preserve">De vſu Instrumenti generatim.</head> <p> <s xml:id="echoid-s20644" xml:space="preserve">ABſoluto ex omni parte Inſtrumento ſequitur, vt de vſu eius primo generatim, deinde etiam par-<lb/>ticulatim agamus ſequentibus regulis.</s> <s xml:id="echoid-s20645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20646" xml:space="preserve">Prima eſt, vt illud Aſtronomicè collocemus: </s> <s xml:id="echoid-s20647" xml:space="preserve">Aſtronomicè autem collocari dicitur Inſtrumentum <lb/> <anchor type="note" xlink:label="note-0264-02a" xlink:href="note-0264-02"/> quoduis Aſtronomicum, ſicut in Sphæra expoſui, cum ita ſituatur, vt omnes eius partes propria po-<lb/>ſitiones illas mundi partes, ſeu circulos, quorum vicariæ ſunt, imitantur. </s> <s xml:id="echoid-s20648" xml:space="preserve">Vt igitur hoc Inſtrumentum <lb/>Aſtronomicè collocetur dum pendeat ex ſuſpenſorio alicui ſuperficiei, v.</s> <s xml:id="echoid-s20649" xml:space="preserve">g. </s> <s xml:id="echoid-s20650" xml:space="preserve">pariete affixo, vt figura, <lb/>præcedens indicat. </s> <s xml:id="echoid-s20651" xml:space="preserve">Primo, ſi Inſtrumentum eſt vniuerſale, tympanum, quia refert ęquatorem, debet <lb/>in ipſo Inſtrumento accommodari ſecundum loci dati altitudinem. </s> <s xml:id="echoid-s20652" xml:space="preserve">Si vero particulari fuerit, non <lb/>eſt opus hac regula, quia iam ex ipſa Inſtrumenti conſtructione accommodatum eſt. </s> <s xml:id="echoid-s20653" xml:space="preserve">Eadem ratione <lb/>ſi Horarium ſit vniuerſale, accommodandum eſt ad eandem altitudinem cum tympano. </s> <s xml:id="echoid-s20654" xml:space="preserve">Secundo, <lb/>conuertatur manubrium baſis in foramine haſtæ ſuſpẽſorij donec acus magnetica exacte ſupra ſuam <lb/>punctualem lineam immineat, ibiq; </s> <s xml:id="echoid-s20655" xml:space="preserve">obfirmetur. </s> <s xml:id="echoid-s20656" xml:space="preserve">Porro hic cauendum eſt a vicinis ferramentis, nec-<lb/>non à lateribus, quia magnetica virtute ſunt præditi, ſæpeq; </s> <s xml:id="echoid-s20657" xml:space="preserve">in muris latentes acum magneticam oc-<lb/>cultè diſturbant. </s> <s xml:id="echoid-s20658" xml:space="preserve">Propterea tutius eſſet, ſi vacaret, prius inibi lineam meridianam in plano horizon-<lb/>tali Aſtronomicè inueniſſe (vti in Sphæra docuimus) atq; </s> <s xml:id="echoid-s20659" xml:space="preserve">ſecundum eam dirigere planum baſis, vti <lb/>meridianum, quem refert, ſua poſitione imitaretur; </s> <s xml:id="echoid-s20660" xml:space="preserve">in qua præterea axis, m M, debet vergere ad po-<lb/>lum conſpicuum, ideſt paralellus eſſe axi mundi, quem refert. </s> <s xml:id="echoid-s20661" xml:space="preserve">Tertio, debet perpendiculum in ſuo <lb/>canaliculo ita liberè pendere, vt filum eius per medium foraminis inferioris tranſeat, vnaq; </s> <s xml:id="echoid-s20662" xml:space="preserve">reſpon-<lb/>deat duabus lineis in lateribus canaliculi notatis. </s> <s xml:id="echoid-s20663" xml:space="preserve">Id fiet conu ertendo haſtam ſuſpenſorij huc illuc in <lb/>foramine Tabellæ, haſtamque aliquantulum eleuando, aut deprimendo, donec filum præſcriptum ſi-<lb/>tum obtineat: </s> <s xml:id="echoid-s20664" xml:space="preserve">tuncq; </s> <s xml:id="echoid-s20665" xml:space="preserve">paruis cuneis in Tabelle foramen immiſſis obfirmetur, interim ſimul obſeruan-<lb/>do ne acus magnetica à ſitu ſuo deuiet. </s> <s xml:id="echoid-s20666" xml:space="preserve">ſic erit Inſtrumentum Aſtronomicè ſitum.</s> <s xml:id="echoid-s20667" xml:space="preserve"/> </p> <div xml:id="echoid-div555" type="float" level="2" n="1"> <note position="left" xlink:label="note-0264-02" xlink:href="note-0264-02a" xml:space="preserve">Aſtre@ <lb/>mice col-<lb/>locare.</note> </div> <p> <s xml:id="echoid-s20668" xml:space="preserve">Secunda, vt intelligas rationem huius Inſtrumenti, memineris primo apicem axis M, referre cen-<lb/> <anchor type="note" xlink:label="note-0264-03a" xlink:href="note-0264-03"/> trum terræ ſeu Sphærę Solis, ſeu etiam mundi; </s> <s xml:id="echoid-s20669" xml:space="preserve">quamuis enim ſimus in ſuperficie terræ longè a cen-<lb/>tro eius, quia tamen magnitudo terræ reſpectu totius Sphærę Solis adeo exigua eſt, vt ſemidiameter <lb/>eius euadat inſenſibilis, propterea in praxi, & </s> <s xml:id="echoid-s20670" xml:space="preserve">ad ſenſum perinde eſt, ac ſi eſſemus in eius centro. </s> <s xml:id="echoid-s20671" xml:space="preserve">At-<lb/>que hæc eſt ratio cur omnes Gnomorum vertices omniũ Horologiorum rectè horas indicent, quam-<lb/>uis Horologia ſint conſtructa ſupponendo vertices eorum eſſe in centro terræ. </s> <s xml:id="echoid-s20672" xml:space="preserve">Secundo, memine-<lb/>ris diuiſiones 24. </s> <s xml:id="echoid-s20673" xml:space="preserve">tympani referre 24. </s> <s xml:id="echoid-s20674" xml:space="preserve">horas, in quas ęquator diuiditur à circulis horarijs. </s> <s xml:id="echoid-s20675" xml:space="preserve">Tertio, tres <lb/>lineas horarij referre quoslibet ternos arcus horarios veros, quos in cœlo Gnomonici imaginantur; <lb/></s> <s xml:id="echoid-s20676" xml:space="preserve">& </s> <s xml:id="echoid-s20677" xml:space="preserve">puncta declinationum in eis notata referre varios paralellos ęquatoris, qua ratione dum horarium <lb/>ſuper tympanum Aſtronomicè ſitum mouetur referre poteſt ſucceffiuè omnes partes Zonę torridę, <lb/>ideſt omnes circulos horarios, omnes paralellos æquatori, ipſumq; </s> <s xml:id="echoid-s20678" xml:space="preserve">æquatorem: </s> <s xml:id="echoid-s20679" xml:space="preserve">punctum enim C, me-<lb/>dium eius gyrando deſignat æquatorem; </s> <s xml:id="echoid-s20680" xml:space="preserve">punctum D, tropicum ♑, punctum B, tropicum ♋, & </s> <s xml:id="echoid-s20681" xml:space="preserve">ſic <lb/>cętera puncta ſuos referunt paralellos. </s> <s xml:id="echoid-s20682" xml:space="preserve">Quarto filum M r, egrediens a vertice axis centrum terrę re-<lb/>ferente, atque extenſum ſecus quoduis punctum cuiuſuis lineæ horariæ vſq; </s> <s xml:id="echoid-s20683" xml:space="preserve">ad aliquam ſuperficiem, <lb/>v. </s> <s xml:id="echoid-s20684" xml:space="preserve">g. </s> <s xml:id="echoid-s20685" xml:space="preserve">muri alicuius, fungi vice radij ſolaris tranſeuntis per centrum terræ, & </s> <s xml:id="echoid-s20686" xml:space="preserve">per punctum illud hora-<lb/>rium vſq; </s> <s xml:id="echoid-s20687" xml:space="preserve">ad illum parie em: </s> <s xml:id="echoid-s20688" xml:space="preserve">hic enim radius centralis eſt ille, qui vmbras apud nos efficit à Gnomo-<lb/>nicis conſideratas, quare vbi radius hic termina@ur, ibi etiam vmbra axis deſinit, ſeu ibidem vertex vm <lb/>bræ eius eſt; </s> <s xml:id="echoid-s20689" xml:space="preserve">vmbra enim, & </s> <s xml:id="echoid-s20690" xml:space="preserve">radius ſunt comites perpetui. </s> <s xml:id="echoid-s20691" xml:space="preserve">Ex his omnibus ſequitur, quod applicata <lb/>regula horarij alicui horæ tympani, ſi filum extenſum ſit, v.</s> <s xml:id="echoid-s20692" xml:space="preserve">g.</s> <s xml:id="echoid-s20693" xml:space="preserve">per punctum E, horarij vſq; </s> <s xml:id="echoid-s20694" xml:space="preserve">ad parie-<lb/>tem ibi, vbi parieti occurrerit, deſignabit extremum illius horę Italicæ in ♑, cui applicatum erit ho-<lb/>rarium in tympano, ſi per C, in æquatore, ſi per F, in ♋. </s> <s xml:id="echoid-s20695" xml:space="preserve">(Idem proportionaliter de horis Aſtrono-<lb/>micis, & </s> <s xml:id="echoid-s20696" xml:space="preserve">Babylonicis intellige) & </s> <s xml:id="echoid-s20697" xml:space="preserve">ſi per D, ſummum horæ Aſtronomicę filum parieti occurrens de-<lb/>feratur ab horario ſuper tympano gyrante, quod deſcribet in muro hyperbolem, aut parabolam re-<lb/>ferentem tropicum ♑.</s> <s xml:id="echoid-s20698" xml:space="preserve"/> </p> <div xml:id="echoid-div556" type="float" level="2" n="2"> <note position="left" xlink:label="note-0264-03" xlink:href="note-0264-03a" xml:space="preserve">Ratio In-<lb/>ſtrumen-<lb/>ti.</note> </div> <p> <s xml:id="echoid-s20699" xml:space="preserve">Tertia, Tandem quanto remotius fuerit à muro Inſtrumentum, tanto maiores lineas horarias, & </s> <s xml:id="echoid-s20700" xml:space="preserve"><lb/>proinde maiora Horologia delineabit.</s> <s xml:id="echoid-s20701" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div558" type="section" level="1" n="414"> <head xml:id="echoid-head436" style="it" xml:space="preserve">De vſu Instrumenti in particulari exemplo.</head> <p> <s xml:id="echoid-s20702" xml:space="preserve">1 PRo oblato pariete, quem nunc ſuppono eſſe planum, atque erectum ab horizontem, in quo de-<lb/>ſcribendum ſit Horologium habenda eſt ratio proſpectus, ideſt loci vnde vt plurimum ſpectato-<lb/> <anchor type="note" xlink:label="note-0264-04a" xlink:href="note-0264-04"/> res illud ſunt intuituri, ne ſcilicet maius, aut minus, quam par ſit illud deſcribamus; </s> <s xml:id="echoid-s20703" xml:space="preserve">in quo ij Pictores <lb/>ſunt imitandi, qui picturarum magnitudines ad aſpectantium diſtantiam definiunt. </s> <s xml:id="echoid-s20704" xml:space="preserve">Si igitur paries ſit <lb/>fatis magnus, eam nobis deligemus aream quę idouea videatur; </s> <s xml:id="echoid-s20705" xml:space="preserve">ſi vero ſpatium ſit determinatum, in <lb/>eo, in quo fieri poterit commodius curabimus Horologium delineare.</s> <s xml:id="echoid-s20706" xml:space="preserve"/> </p> <div xml:id="echoid-div558" type="float" level="2" n="1"> <note position="left" xlink:label="note-0264-04" xlink:href="note-0264-04a" xml:space="preserve">Magni-<lb/>de Horo-<lb/>logij.</note> </div> <p> <s xml:id="echoid-s20707" xml:space="preserve">2 Curandum eſt, vt vna cum magnitudine competenti adſint etiam omnes horę in eo muro poſ- <pb o="11" file="0265" n="270" rhead="DE HOROLOGIIS."/> ſibiles, ideſt inſcribatur numerus horarum omnium poſſibilium in dato pariete, ſeu quotquot datus <lb/>paries recipere poteſt; </s> <s xml:id="echoid-s20708" xml:space="preserve">nulla enim plana ſuperficie recta ad horizõtem, cuiuſmodi ſunt communiter <lb/>parietes omnes horas diurnas per totum annum exh bere poteſt. </s> <s xml:id="echoid-s20709" xml:space="preserve">in quo nonnulli non mediocriter <lb/>errant, dumtemere, & </s> <s xml:id="echoid-s20710" xml:space="preserve">quaſi fortuito huiuſmodi deſcriptionem aggrediuntur. </s> <s xml:id="echoid-s20711" xml:space="preserve">Sed omne tulit pun-<lb/>ctum, qui iunxit numero magnum. </s> <s xml:id="echoid-s20712" xml:space="preserve">Hoc vero hac ratione aſſequemur. </s> <s xml:id="echoid-s20713" xml:space="preserve">Sit exempli gratia Parmæ <lb/>ad altitudinem gr. </s> <s xml:id="echoid-s20714" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s20715" xml:space="preserve">oblatus paries; </s> <s xml:id="echoid-s20716" xml:space="preserve">tympano, & </s> <s xml:id="echoid-s20717" xml:space="preserve">horario ad hanc altitudinem aptatis in Inſtru-<lb/>mento, accedentes ad parietem, & </s> <s xml:id="echoid-s20718" xml:space="preserve">manu Inſtrumentum tenentes, rudiq; </s> <s xml:id="echoid-s20719" xml:space="preserve">Minerua illud Aſtronomi-<lb/>cè collocantes, primo ſatis propè par@etem filum per horarium vſq; </s> <s xml:id="echoid-s20720" xml:space="preserve">ad parietem extendentes videbi-<lb/>mus ad quam partem plures, quotq; </s> <s xml:id="echoid-s20721" xml:space="preserve">horæ cadant: </s> <s xml:id="echoid-s20722" xml:space="preserve">poſtea remotius a pariete, atq; </s> <s xml:id="echoid-s20723" xml:space="preserve">ex alia parte eãdem <lb/>experientiam habebimus, ſicq; </s> <s xml:id="echoid-s20724" xml:space="preserve">ſæpius variata diſtantia, & </s> <s xml:id="echoid-s20725" xml:space="preserve">ſitu, tandem iudicabimus in qua parte ſit <lb/>affigendum muro inſtrumentum, vt omnes horæ poſſibiles, ac ſatis magnæ haberi poſſint.</s> <s xml:id="echoid-s20726" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20727" xml:space="preserve">3 Inibi igitur affigendum ſuſpenſorium ſupra Horologij ſpatiũ, vt pars Tabellæ acutior, in qua <lb/>figendi ſunt ferrei claui ſit ſuperior, & </s> <s xml:id="echoid-s20728" xml:space="preserve">remorior à magnete, neq; </s> <s xml:id="echoid-s20729" xml:space="preserve">ſit impedimento lineis in muro du-<lb/>cendis. </s> <s xml:id="echoid-s20730" xml:space="preserve">Tandem accepta conuenienti diſtantia in haſta ſuſpenſorij, inſeratur ibi caput baſis totum-<lb/>que Inſtrumentum omni cura, & </s> <s xml:id="echoid-s20731" xml:space="preserve">diligentia, Aſtronomicè ſtatuatur, & </s> <s xml:id="echoid-s20732" xml:space="preserve">obfirmetur. </s> <s xml:id="echoid-s20733" xml:space="preserve">Quoniam vero <lb/>ſolet in Horologiorum conſtructione ob varia accidentia Inſtrumẽtum a ſuo ſitu Aſtronomico ſub-<lb/>inde luxari, ideo neceſſe eſt identidem, tum ad magneticam acum, tum ad perpendiculum oculos <lb/>conuertere.</s> <s xml:id="echoid-s20734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20735" xml:space="preserve">4 Antequam ſerio rem aggrediaris probandum eſt an Inſtrumentum ſit ritè collocatum hiſce <lb/> <anchor type="note" xlink:label="note-0265-01a" xlink:href="note-0265-01"/> probationibus. </s> <s xml:id="echoid-s20736" xml:space="preserve">Primo, applicata regula ſecundum lineam fiduciæ lineæ meridianæ tympani filum <lb/>extenſum ſecus lineam Merid@anam, ſeu Aſtronomicam 12. </s> <s xml:id="echoid-s20737" xml:space="preserve">horarij vſque ad parietem in eo plura <lb/>duobus puncta deſignet; </s> <s xml:id="echoid-s20738" xml:space="preserve">nã ſi ea omnia puncta fuerint in linea recta deorſum perpendiculariter ten-<lb/>dente, ritè & </s> <s xml:id="echoid-s20739" xml:space="preserve">Aſtronomicè ſtabit Inſtrumentum, ideſt oportet vt linea meridiana quæ hac ratione <lb/>deſignanda eſt, congruat filo perpendiculi alicuius ſibi applicati. </s> <s xml:id="echoid-s20740" xml:space="preserve">Secundo, applicato Horario horæ <lb/> <anchor type="note" xlink:label="note-0265-02a" xlink:href="note-0265-02"/> 24. </s> <s xml:id="echoid-s20741" xml:space="preserve">Italicæ tympani, oportet vt ipſa hora Italica horar@j ſit horizonti paralella, quod libella exami-<lb/>nandum erit. </s> <s xml:id="echoid-s20742" xml:space="preserve">Similiter applicato horario horæ 24. </s> <s xml:id="echoid-s20743" xml:space="preserve">Babylonicæ tympani, debet hora Babylonica <lb/>horarij horizonti æquidiſtare. </s> <s xml:id="echoid-s20744" xml:space="preserve">Præterea ſi ambæ in muro per ſilum notentur, & </s> <s xml:id="echoid-s20745" xml:space="preserve">producantur, con-<lb/>current ad meridianam normaliter, & </s> <s xml:id="echoid-s20746" xml:space="preserve">in eodem puncto: </s> <s xml:id="echoid-s20747" xml:space="preserve">quapropter efficient vnicam lineam rectam <lb/>quæ horizontalis dicitur. </s> <s xml:id="echoid-s20748" xml:space="preserve">Tertio demum filum etiam extra horarium extenſum muro normaliter <lb/> <anchor type="note" xlink:label="note-0265-03a" xlink:href="note-0265-03"/> occurrens, in prædicta linea horizontali occurrat oportet. </s> <s xml:id="echoid-s20749" xml:space="preserve">Si igitur hæ probationes benè ſuccedant, <lb/>ritè collocatum erit ſin minus corrigendum. </s> <s xml:id="echoid-s20750" xml:space="preserve">Caue ne nimis fi@um tendas; </s> <s xml:id="echoid-s20751" xml:space="preserve">nam filum nimis tenſum <lb/>luxat Inſtrumentum.</s> <s xml:id="echoid-s20752" xml:space="preserve"/> </p> <div xml:id="echoid-div559" type="float" level="2" n="2"> <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">Proba-<lb/>tiones col <lb/>locati In <lb/>strumen-<lb/>ti.</note> <note position="right" xlink:label="note-0265-02" xlink:href="note-0265-02a" xml:space="preserve">Linea <lb/>meridia-<lb/>na.</note> <note position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">Linea <lb/>Horizo@ <lb/>talis.</note> </div> <p> <s xml:id="echoid-s20753" xml:space="preserve">5 Probata, & </s> <s xml:id="echoid-s20754" xml:space="preserve">correcta, ſi oportuerit, Inſtrumenti poſitione, ſic horam quamlibet deſcribes. </s> <s xml:id="echoid-s20755" xml:space="preserve">ex. <lb/></s> <s xml:id="echoid-s20756" xml:space="preserve"> <anchor type="note" xlink:label="note-0265-04a" xlink:href="note-0265-04"/> gr. </s> <s xml:id="echoid-s20757" xml:space="preserve">velis primo deſcribere horam 18. </s> <s xml:id="echoid-s20758" xml:space="preserve">Italicam: </s> <s xml:id="echoid-s20759" xml:space="preserve">dirige horarium ſecundum lineam fiduciæ regulæ ad <lb/>18. </s> <s xml:id="echoid-s20760" xml:space="preserve">Italicam tympani, ibiq; </s> <s xml:id="echoid-s20761" xml:space="preserve">horario manente extende filum ſecus horam eius Italicam, ideſt ita vt fi-<lb/>lum extenſum radens exactè quodlibet punctum horæ Italicę attingat parietem: </s> <s xml:id="echoid-s20762" xml:space="preserve">& </s> <s xml:id="echoid-s20763" xml:space="preserve">notabis punctum <lb/>illud in pariete: </s> <s xml:id="echoid-s20764" xml:space="preserve">ſic notabis ſa@tem tria puncta pro ſingulis horis. </s> <s xml:id="echoid-s20765" xml:space="preserve">Per extremum E, notabitur pun-<lb/>ctum in ♑, per C, in ♎, per F, in ♋. </s> <s xml:id="echoid-s20766" xml:space="preserve">Hæc tria puncta ſufficient pro ſimplici Horologio: </s> <s xml:id="echoid-s20767" xml:space="preserve">Vtile ta-<lb/>men erit notare præterea alia duo puncta declinationum arcuum diurnorum hor. </s> <s xml:id="echoid-s20768" xml:space="preserve">10. </s> <s xml:id="echoid-s20769" xml:space="preserve">& </s> <s xml:id="echoid-s20770" xml:space="preserve">14. </s> <s xml:id="echoid-s20771" xml:space="preserve">quia in-<lb/>ſeruiunt ad examen Horologij, vt poſtea videbis. </s> <s xml:id="echoid-s20772" xml:space="preserve">Si vero volueris Horologium Italicum perfectum, <lb/>notanda ſunt præterea cętera puncta declinationum arcuum ſignorum. </s> <s xml:id="echoid-s20773" xml:space="preserve">Examen. </s> <s xml:id="echoid-s20774" xml:space="preserve">ſi rectè operatus <lb/> <anchor type="note" xlink:label="note-0265-05a" xlink:href="note-0265-05"/> fueris, erunt omnia puncta eiuſdem lineæ conſ@ituta in directum, ideſt in linea recta. </s> <s xml:id="echoid-s20775" xml:space="preserve">poſtea ducta in <lb/>muro linea recta ex color coniungens omnia puncta notata, ea erit linea horaria Italica eiuſdem ap-<lb/>pellationis cum ea, cui in tympano horarium applicatum fuerit; </s> <s xml:id="echoid-s20776" xml:space="preserve">quapropter ei adſcribẽdus eſt idem <lb/>numerus, v.</s> <s xml:id="echoid-s20777" xml:space="preserve">g. </s> <s xml:id="echoid-s20778" xml:space="preserve">18. </s> <s xml:id="echoid-s20779" xml:space="preserve">qui eſt in tympano.</s> <s xml:id="echoid-s20780" xml:space="preserve"/> </p> <div xml:id="echoid-div560" type="float" level="2" n="3"> <note position="right" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve">Hora@um <lb/>deſcriptio <lb/>Horę Ita <lb/>lica.</note> <note position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">Examen.</note> </div> <p> <s xml:id="echoid-s20781" xml:space="preserve">6 Si volueris in tuo Horologio etiam horas Aſtronomicas, aut Babylonicas perſiſtente inibi ho-<lb/>rario eadem omnia facies proportionaliter auxilio horæ Aſtronomicæ, & </s> <s xml:id="echoid-s20782" xml:space="preserve">Babylonicæ horarij. </s> <s xml:id="echoid-s20783" xml:space="preserve">Ho-<lb/>ra Aſtronomica erit in muro 12. </s> <s xml:id="echoid-s20784" xml:space="preserve">Babylonica vero erit 6. </s> <s xml:id="echoid-s20785" xml:space="preserve">vt numeri in tympano adnotati indicant: <lb/></s> <s xml:id="echoid-s20786" xml:space="preserve">ſicque eadem ferè opera tria horarum genera delineabis. </s> <s xml:id="echoid-s20787" xml:space="preserve">Aliquando ob ſitum parietis non poſſunt <lb/>omnia puncta eiuſdem horæ haberi; </s> <s xml:id="echoid-s20788" xml:space="preserve">omnia tamen poſſibilia per hoc Horologium haberi poſſunt, <lb/>quæ eius ſingulari, & </s> <s xml:id="echoid-s20789" xml:space="preserve">præcipua vtilitas eſt. </s> <s xml:id="echoid-s20790" xml:space="preserve">Quamuis enim filum tranſeat ſecus lineam horarij, vbi <lb/>nullum ſit notatum punctum declinationum, dabit tamen in muro punctum eiuſdem lineæ eidem <lb/>reſpondens.</s> <s xml:id="echoid-s20791" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20792" xml:space="preserve">7 Poſt hæc dextere, ac leniter promoue horam, v.</s> <s xml:id="echoid-s20793" xml:space="preserve">g. </s> <s xml:id="echoid-s20794" xml:space="preserve">19. </s> <s xml:id="echoid-s20795" xml:space="preserve">vel 17. </s> <s xml:id="echoid-s20796" xml:space="preserve">Italicam, cauendo interim ne In-<lb/>ſtrumentum luxetur, ibique eadem omnia operare ſimiliter quæ in præcedenti poſicione. </s> <s xml:id="echoid-s20797" xml:space="preserve">H@nc ad <lb/>alias, atq; </s> <s xml:id="echoid-s20798" xml:space="preserve">alias horas progredere, donec omnes horas illi muro poſſibiles cum ſuis numeris delinea-<lb/>ueris. </s> <s xml:id="echoid-s20799" xml:space="preserve">Si horarum ſemiſſibus, aut etiam quadrantibus delecteris, eas partes in tympano prius habeas, <lb/>& </s> <s xml:id="echoid-s20800" xml:space="preserve">poſteas ſecundum eas modo, quo dictum eſt de integris, operaberis, eriſq; </s> <s xml:id="echoid-s20801" xml:space="preserve">voti compos.</s> <s xml:id="echoid-s20802" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20803" xml:space="preserve">8 Si extremitates omnium hora@um ſuperiores linea punctuali leniter inflexa coniungantur, ea <lb/>referet tropicum ♑. </s> <s xml:id="echoid-s20804" xml:space="preserve">ſi inferiores referet tropicum ♋. </s> <s xml:id="echoid-s20805" xml:space="preserve">ſi media puncta, quę ſunt in æquatore iungan-<lb/>tur linea, ea recta @rit (ſi rectè fneris operatus) eritq; </s> <s xml:id="echoid-s20806" xml:space="preserve">linea æquinoctialis ♈, aut ♎. </s> <s xml:id="echoid-s20807" xml:space="preserve">Pariter ſi reliqua <lb/>terna puncta eiuſdem declinationis, ſeu paralelli ♌, aut ♍, quæ ſingula ſunt in ſingulis trium linearũ <lb/>ltal. </s> <s xml:id="echoid-s20808" xml:space="preserve">Aſtronom. </s> <s xml:id="echoid-s20809" xml:space="preserve">Babyl. </s> <s xml:id="echoid-s20810" xml:space="preserve">iungantur lineis punctualibus leniter curuis, eæ indicabunt eoſdem ſuo tem- <pb o="12" file="0266" n="271" rhead="TRACTATVS"/> pore paralellos à Sole percurri. </s> <s xml:id="echoid-s20811" xml:space="preserve">Pariter ſi tria puncta arcus diurni hor. </s> <s xml:id="echoid-s20812" xml:space="preserve">14. </s> <s xml:id="echoid-s20813" xml:space="preserve">vel 10. </s> <s xml:id="echoid-s20814" xml:space="preserve">quæ ſunt ſingula in <lb/>ſingulis trium linearum, iungantur linea curua punctuali indicabunt tempus eorundem arcuum. </s> <s xml:id="echoid-s20815" xml:space="preserve">ex <lb/>quibus omnibus erit abſolutum Horologium.</s> <s xml:id="echoid-s20816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20817" xml:space="preserve">Poſtremo adhibenda ſunt quædam examina. </s> <s xml:id="echoid-s20818" xml:space="preserve">Primum, ſi erratum non eſt, ternæ horæ Italica, <lb/> <anchor type="note" xlink:label="note-0266-01a" xlink:href="note-0266-01"/> Aſtronomica, & </s> <s xml:id="echoid-s20819" xml:space="preserve">Babylonica debent ſe mutuo interſecare in ijſdem punctis æquatoris, ideſt, ternę il-<lb/>læ quæ ſunt deſcriptæ ad eundem locum tympani. </s> <s xml:id="echoid-s20820" xml:space="preserve">Secundum, aliæ ternæ Italica, Aſtronomica, & </s> <s xml:id="echoid-s20821" xml:space="preserve"><lb/>Babylonica, ſe mutuo ſecant in eodem puncto arcus diurni hor. </s> <s xml:id="echoid-s20822" xml:space="preserve">10. </s> <s xml:id="echoid-s20823" xml:space="preserve">necnon hor. </s> <s xml:id="echoid-s20824" xml:space="preserve">14. </s> <s xml:id="echoid-s20825" xml:space="preserve">vti ſequentes <lb/>Tabellæ indicant.</s> <s xml:id="echoid-s20826" xml:space="preserve"/> </p> <div xml:id="echoid-div561" type="float" level="2" n="4"> <note position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">Examina</note> </div> </div> <div xml:id="echoid-div563" type="section" level="1" n="415"> <head xml:id="echoid-head437" style="it" xml:space="preserve">Ternæ horæ huius Tabellæ ſe mutuo fecant in linea Æquin. ſiue in arcu diurno horar. 12. <lb/>tam in verticali, quam in horiz. horol. excepta hor. 12. Ital. in horizontali.</head> <note position="right" xml:space="preserve"> <lb/># Bab. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ # Aſtr. # 7 # 8 # 9 # 10 # 11 # 12 # 1 # 2 # 3 # 4 # 5 # 6 <lb/># Ital. # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 12 <lb/></note> </div> <div xml:id="echoid-div564" type="section" level="1" n="416"> <head xml:id="echoid-head438" style="it" xml:space="preserve">Ternæ horæ ſeq. tab. ſe ſecant in arcu diurno hor. 14.</head> <note position="right" xml:space="preserve"> <lb/># Bab. # 24 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 13 # 14 <lb/>Horæ # Aſtr. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 1 # 2 # 3 # 4 # 5 # 6 # 7 <lb/># Ital. # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 <lb/></note> </div> <div xml:id="echoid-div565" type="section" level="1" n="417"> <head xml:id="echoid-head439" style="it" xml:space="preserve">Ternæ horæ ſeq. tab. ſe ſecant in arcu diurno hor. 10.</head> <note position="right" xml:space="preserve"> <lb/># Bab. # 24 # 1 # 2 # 4 # 3 # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 13 <lb/>Horæ # Aſtr. # 7 # 8 # 9 # 11 # 12 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 <lb/># Ital. # 14 # 15 # 16 # 18 # 19 # 20 # 21 # 22 # 23 # 24 # 1 # 2 # 3 <lb/></note> </div> <div xml:id="echoid-div566" type="section" level="1" n="418"> <head xml:id="echoid-head440" style="it" xml:space="preserve">Binæ horæſeq. Tab. ſe mutuo ſecant in linea meridiana, ſiue in linea hor. 12. Aſtron. <lb/>In meridiano tamen ſunt æquidistantes.</head> <note position="right" xml:space="preserve"> <lb/>Bab. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 <lb/>Ital. # 23 # 22 # 21 # 20 # 19 # 18 # 17 # 16 # 15 # 14 # 13 # 12 # 11 # 10 # 9 # 8 # 7 # 6 <lb/>Bab. # 19 # 20 # 21 # 22 # 23 # 24 <lb/>Ital. # 5 # 4 # 3 # 2 # 1 # 24 <lb/></note> </div> <div xml:id="echoid-div567" type="section" level="1" n="419"> <head xml:id="echoid-head441" style="it" xml:space="preserve">De vſu Inſtrumenti<unsure/> vniuerſalis.</head> <p> <s xml:id="echoid-s20827" xml:space="preserve">ERit tympanum erigendum in quadrante, cui incumbit, ad altitudinem poli dati loci, vt in no-<lb/>ſtro exemplo Parmæ ad gr. </s> <s xml:id="echoid-s20828" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s20829" xml:space="preserve">pariter in Horario duæ lineæ Italica, & </s> <s xml:id="echoid-s20830" xml:space="preserve">Babylonica debent fa-<lb/>cere quælibet in ſuo quadrante eundem angulum altitudinis poli cum linea Aſtronomica.</s> <s xml:id="echoid-s20831" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20832" xml:space="preserve">Quoniam in hoc vniuerſali Horario nec hora Italica, nec Babylonica terminatæ ſunt, neque pun-<lb/>ctis declinationum aliorum paralellorum notatę, ideo primo opus eſt deſcribere tropicos, ac ſi libue-<lb/>rit, reliquos paralellos auxilio horæ Aſtronomicæ, quæ in huiuſmodi punctis diuiſa, ac terminata <lb/>eſt, hoc modo. </s> <s xml:id="echoid-s20833" xml:space="preserve">Manente Inſtrumento aſtronomicè ſito filium extremitati ſuperiori lineæ Aſtrono-<lb/>micæ, ideſt, puncto D. </s> <s xml:id="echoid-s20834" xml:space="preserve">Horarij applicatum atque extenſum pertingat vſque ad parietem, ibique vbi-<lb/>cunque fuerit horarium notetur punctum, ſicque gyrando horarium ſuper tympanum, notentur in <lb/>muro crebra puncta, quæ repræſentent tropicum ♑. </s> <s xml:id="echoid-s20835" xml:space="preserve">eodem modo delineandus eſt alter tropicum ♋. <lb/></s> <s xml:id="echoid-s20836" xml:space="preserve">necnon reliqui paralelli. </s> <s xml:id="echoid-s20837" xml:space="preserve">Poſtea eadem ratione, qua ſupra cum particulari Inſtrumento, deſcriban-<lb/>tur in muro lineæ Ital. </s> <s xml:id="echoid-s20838" xml:space="preserve">Aſtronom. </s> <s xml:id="echoid-s20839" xml:space="preserve">& </s> <s xml:id="echoid-s20840" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20841" xml:space="preserve">vſque ad tropicos tãtum; </s> <s xml:id="echoid-s20842" xml:space="preserve">ſiue enim lineæ horarij ltal. </s> <s xml:id="echoid-s20843" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s20844" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s20845" xml:space="preserve">ſint longiores, ſiue breuiores, quam pro data altitudine poli, ſemper tamen earum ter-<lb/>mini in muro debent eſ@e tropici. </s> <s xml:id="echoid-s20846" xml:space="preserve">Quando ſunt longiores, filum continendum eſt intra trop. </s> <s xml:id="echoid-s20847" xml:space="preserve">in pa-<lb/>riete; </s> <s xml:id="echoid-s20848" xml:space="preserve">quando ſunt breuiores, earum portiones deſcribendæ ſunt maiores quæ haberi poſſunt: </s> <s xml:id="echoid-s20849" xml:space="preserve">& </s> <s xml:id="echoid-s20850" xml:space="preserve">po-<lb/>ſtea producendæ ſunt auxilio regulæ recta vſq; </s> <s xml:id="echoid-s20851" xml:space="preserve">ad vtrunq; </s> <s xml:id="echoid-s20852" xml:space="preserve">tropicum; </s> <s xml:id="echoid-s20853" xml:space="preserve">hac énim ratione non tantum <lb/>terminabũtur à tropicis, ſed etiam à cęteris paralellis ſignorum, & </s> <s xml:id="echoid-s20854" xml:space="preserve">arcuum diurnorum 10. </s> <s xml:id="echoid-s20855" xml:space="preserve">& </s> <s xml:id="echoid-s20856" xml:space="preserve">14. </s> <s xml:id="echoid-s20857" xml:space="preserve">prius <lb/>deſcriptis, ritè ſecabuntur. </s> <s xml:id="echoid-s20858" xml:space="preserve">In cęteris igitur agendum eſt ſicuti in vſu particularis Inſtrumenti.</s> <s xml:id="echoid-s20859" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20860" xml:space="preserve">3 Tandem notandum eſt poſſe eodem modo in quouis plano quantumuis inclinato atque etiam <lb/>horizontali horologia deſcribi. </s> <s xml:id="echoid-s20861" xml:space="preserve">Si in ſuperficie inæquali concaua, aut conuexa; </s> <s xml:id="echoid-s20862" xml:space="preserve">lineamenta tamen <lb/>eſſent fimiliter curua, quæ quia raro contingunt, & </s> <s xml:id="echoid-s20863" xml:space="preserve">ex dictis facilia, ideo Lectoris prudentiæ re-<lb/>linquantur.</s> <s xml:id="echoid-s20864" xml:space="preserve"/> </p> <pb o="13" file="0267" n="272" rhead="DE HOROLOGIIS."/> </div> <div xml:id="echoid-div568" type="section" level="1" n="420"> <head xml:id="echoid-head442" style="it" xml:space="preserve">De Guomone, ſeu ſtylo figendo.</head> <p> <s xml:id="echoid-s20865" xml:space="preserve">1 PRopriè loquendo ſtyli longitudo tanta eſt, quanta eſt diſtantia inter verticem M. </s> <s xml:id="echoid-s20866" xml:space="preserve">axis, & </s> <s xml:id="echoid-s20867" xml:space="preserve">parie-<lb/>tem; </s> <s xml:id="echoid-s20868" xml:space="preserve">ſeu lineæ normali à vertice axis ad parietem. </s> <s xml:id="echoid-s20869" xml:space="preserve">Quamobrem è re erit punctũ illud, in quod <lb/>hęc normalis cadit, notare; </s> <s xml:id="echoid-s20870" xml:space="preserve">cadit autem ſemper in lineam horizontalem, vt ſupra dictum eſt, & </s> <s xml:id="echoid-s20871" xml:space="preserve">ab eo <lb/>in linea horizontali notare lineam rectam æqualem huic diſtantiæ, ſeu vero ſtylo, eique adſcribere <lb/>hæc verba (longitudo ſtyli,) vt ſi accidat aliquando ſtylum à ſuo ſitu detorquerr<unsure/>, poſſit per eam reſti-<lb/>r<unsure/>ui ad priſtinum. </s> <s xml:id="echoid-s20872" xml:space="preserve">Illud autem punctum ſic inuenies. </s> <s xml:id="echoid-s20873" xml:space="preserve">Si murus ſit planus, & </s> <s xml:id="echoid-s20874" xml:space="preserve">ad horizontem rectus, ex <lb/>vertice M. </s> <s xml:id="echoid-s20875" xml:space="preserve">notentur filo extenſo tria in muro puncta eadem ſemper fili longitudine retenta; </s> <s xml:id="echoid-s20876" xml:space="preserve">nam <lb/>horum trium punctorum centrum per ſchol. </s> <s xml:id="echoid-s20877" xml:space="preserve">prop. </s> <s xml:id="echoid-s20878" xml:space="preserve">5. </s> <s xml:id="echoid-s20879" xml:space="preserve">lib. </s> <s xml:id="echoid-s20880" xml:space="preserve">4. </s> <s xml:id="echoid-s20881" xml:space="preserve">Euclidis, erit locus ſtyli proprius. </s> <s xml:id="echoid-s20882" xml:space="preserve">Quod ſi <lb/>murus non ſit ſatis planus, aut ſit inclinatus, ineptus erit huic modo, quare opus erit libella, amuſſi, & </s> <s xml:id="echoid-s20883" xml:space="preserve"><lb/>perpendiculo. </s> <s xml:id="echoid-s20884" xml:space="preserve">Si igitur inibi figatur ſtylus (qui ferreus ſit oportet) tantæ longitudinis, vt apex eius <lb/>congruatapici M. </s> <s xml:id="echoid-s20885" xml:space="preserve">axis, vel puncto illi vbi erat M. </s> <s xml:id="echoid-s20886" xml:space="preserve">rectè habebit; </s> <s xml:id="echoid-s20887" xml:space="preserve">horaſq; </s> <s xml:id="echoid-s20888" xml:space="preserve">& </s> <s xml:id="echoid-s20889" xml:space="preserve">alia, apice ſuæ vmbræ re-<lb/>ctè indicabit. </s> <s xml:id="echoid-s20890" xml:space="preserve">Dicitur autem talis ſtylus Gnomon, eo quod normalis ſit ad parietem; </s> <s xml:id="echoid-s20891" xml:space="preserve">norma enim <lb/> <anchor type="note" xlink:label="note-0267-01a" xlink:href="note-0267-01"/> Græcis dicitur Gnomon.</s> <s xml:id="echoid-s20892" xml:space="preserve"/> </p> <div xml:id="echoid-div568" type="float" level="2" n="1"> <note position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">Gnomo@@ <lb/>quid.</note> </div> <p> <s xml:id="echoid-s20893" xml:space="preserve">2 Rectè porrò vertex vmbræ eius horas, & </s> <s xml:id="echoid-s20894" xml:space="preserve">reliqua indicabit; </s> <s xml:id="echoid-s20895" xml:space="preserve">quia ſicut M. </s> <s xml:id="echoid-s20896" xml:space="preserve">apex axis referebat <lb/> <anchor type="note" xlink:label="note-0267-02a" xlink:href="note-0267-02"/> centrum mundi, ita nunc apex ſtyli cum ſit loco eius idem referet: </s> <s xml:id="echoid-s20897" xml:space="preserve">& </s> <s xml:id="echoid-s20898" xml:space="preserve">ſicut filum inde extenſum vſq; <lb/></s> <s xml:id="echoid-s20899" xml:space="preserve">ad murum referebat radium Solis in muri punctum terminatum, ſit apex vmbræ ſtyli in idem pun-<lb/>ctum parietis accidet; </s> <s xml:id="echoid-s20900" xml:space="preserve">radius enim Solis tangens apicem ſtyli eſt comes indiuiduus vmbræ illius.</s> <s xml:id="echoid-s20901" xml:space="preserve"/> </p> <div xml:id="echoid-div569" type="float" level="2" n="2"> <note position="right" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">Ratio.</note> </div> <p> <s xml:id="echoid-s20902" xml:space="preserve">3 Si ſtylo figendo Inſtrumentum ſit impedimento, amouendum eſt: </s> <s xml:id="echoid-s20903" xml:space="preserve">quod ſi timeas ne amoto <lb/>Inſtrumento amittas verum locum verticis M. </s> <s xml:id="echoid-s20904" xml:space="preserve">adhibeas tale remedium. </s> <s xml:id="echoid-s20905" xml:space="preserve">In ſublimi loco parietis af-<lb/>ſige baculum quempiam, ex quo liberè deſcendat perpendiculum deſinens exactè in pũctum M. </s> <s xml:id="echoid-s20906" xml:space="preserve">nam <lb/>amoto poſtea Inſtrumento ſtylus commodè figi poterit. </s> <s xml:id="echoid-s20907" xml:space="preserve">Neq; </s> <s xml:id="echoid-s20908" xml:space="preserve">verò neceſſe eſt ſtylum eius eſſe lon-<lb/>gitudinis, quam ei antea definiuimus, immo ſolet fieri longior, altiuſque propterea figi, dummodo <lb/>apex eius puncto M. </s> <s xml:id="echoid-s20909" xml:space="preserve">congruat; </s> <s xml:id="echoid-s20910" xml:space="preserve">ſolus enim apex eſt qui indicat. </s> <s xml:id="echoid-s20911" xml:space="preserve">Fitautem longior, vt longiorem quo-<lb/>que vmbram, ac proinde vi<unsure/>ſibiliorem efficiat.</s> <s xml:id="echoid-s20912" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20913" xml:space="preserve">4 Stylo collocato delenda ſunt omnia lineamenta, quæſunt tam ſupra lineam horizontalem, <lb/>quam extra tropicos, tanquam inutilia: </s> <s xml:id="echoid-s20914" xml:space="preserve">actum demum lineæ coloribus depingendæ. </s> <s xml:id="echoid-s20915" xml:space="preserve">Si ſolæ adſint <lb/>Italicæ, eæ nigro colore, ſi vero vna adſint etiam Aſtronomicæ, & </s> <s xml:id="echoid-s20916" xml:space="preserve">Babylonicæ diſtinguendæ ſunt <lb/>colorum varietate: </s> <s xml:id="echoid-s20917" xml:space="preserve">paralelli verò ſignorum, & </s> <s xml:id="echoid-s20918" xml:space="preserve">arcuum diurnorum meridiana, æquinoctialis diuerſo <lb/>ab alijs pariter colore tingendæ ſunt. </s> <s xml:id="echoid-s20919" xml:space="preserve">Adduntur aliquando characteres ſignorum ſuis paralellis ſi-<lb/>cuti horarium indicat. </s> <s xml:id="echoid-s20920" xml:space="preserve">Numeri adſcribendi ſunt lineis horarijs ad eam partem, in qua lineæ ſunt la-<lb/>xiores. </s> <s xml:id="echoid-s20921" xml:space="preserve">Tandem in angulis vacuis addi ſolet ſententia quæpiam moralis de breuitate vitæ, aut fu-<lb/>ga temporis. </s> <s xml:id="echoid-s20922" xml:space="preserve">Volat irreuocabile tempus. </s> <s xml:id="echoid-s20923" xml:space="preserve">Dies noſtri ſicut vmbra prætereunt. </s> <s xml:id="echoid-s20924" xml:space="preserve">Puluis, & </s> <s xml:id="echoid-s20925" xml:space="preserve">vmbra <lb/>ſumus, & </s> <s xml:id="echoid-s20926" xml:space="preserve">ſimilia.</s> <s xml:id="echoid-s20927" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div571" type="section" level="1" n="421"> <head xml:id="echoid-head443" style="it" xml:space="preserve">Vſus deſcripti Horologij.</head> <p> <s xml:id="echoid-s20928" xml:space="preserve">1 PRæcipua eius vtilitas eſt horas indicare, vt propterea Horologium denominetur. </s> <s xml:id="echoid-s20929" xml:space="preserve">eam namque <lb/>horam indicat adeſſe, aut labi, quam vmbræ vertex propius attingit.</s> <s xml:id="echoid-s20930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20931" xml:space="preserve">2 Indicat eodem vmbræ vertice horam meridianam.</s> <s xml:id="echoid-s20932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20933" xml:space="preserve">3 Si adſint arcus diurni, indicat per eos quantitatem diei. </s> <s xml:id="echoid-s20934" xml:space="preserve">Horam ortus, & </s> <s xml:id="echoid-s20935" xml:space="preserve">occaſus.</s> <s xml:id="echoid-s20936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20937" xml:space="preserve">4 Aliquando ſine paralellis, ſed tantum ex loco in linea horizontali notato, in quem cadit vmbra <lb/>Sole oriente, innoteſcit hora ortus, & </s> <s xml:id="echoid-s20938" xml:space="preserve">conſequenter reliqua.</s> <s xml:id="echoid-s20939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20940" xml:space="preserve">5 Indicat vmbra alterum tropicorum percurrente, Solem illum cũdem percurrere, eſſeque Sol-<lb/>ſtitium, aut Æſtiuum, aut Hyemale. </s> <s xml:id="echoid-s20941" xml:space="preserve">Æquinoctium vero fieri percurrente lineam æquinoctialem.</s> <s xml:id="echoid-s20942" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20943" xml:space="preserve">6 Si adſint arcus ſignorum cum ſuis characteribus, manifeſtabit in quo ſigno Zodiaci, atq; </s> <s xml:id="echoid-s20944" xml:space="preserve">etiam <lb/>in quanta eius parte Sol verſetur.</s> <s xml:id="echoid-s20945" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div572" type="section" level="1" n="422"> <head xml:id="echoid-head444" style="it" xml:space="preserve">De alio Horario Cylindrico. Cap. III.</head> <p> <s xml:id="echoid-s20946" xml:space="preserve">SIcuti ſuperius conſtruximus Horarium in plano planum; </s> <s xml:id="echoid-s20947" xml:space="preserve">ita nunc alterum in concauo Cylindrico <lb/>conſtruemus, cylindricumq; </s> <s xml:id="echoid-s20948" xml:space="preserve">dicemus. </s> <s xml:id="echoid-s20949" xml:space="preserve">quod nihil aliud eſt, quã portio Horologij deſcripti in con-<lb/>cauo cilindri continens tres tantum horas Italicam, Aſtronomicam, Babylonicam. </s> <s xml:id="echoid-s20950" xml:space="preserve">quæ inquam por-<lb/>tio ſupponitur tangere ſpæram mundi in ęquatore; </s> <s xml:id="echoid-s20951" xml:space="preserve">axemq; </s> <s xml:id="echoid-s20952" xml:space="preserve">hui<unsure/>us cilindri eſſe eundem cum axe mun-<lb/>di. </s> <s xml:id="echoid-s20953" xml:space="preserve">Quare latus cylindri@, quod coincidet cum linea Aſtronomica erit duplex tangens maximę decli-<lb/>nationis, acproinde eadem quam Aſtronomica in horario plano. </s> <s xml:id="echoid-s20954" xml:space="preserve">Huius imaginem infra poſitam <lb/>nunc intuere in figura 13. </s> <s xml:id="echoid-s20955" xml:space="preserve">in qua linea menta ſunt ſimilia lineamentis horarij plani. </s> <s xml:id="echoid-s20956" xml:space="preserve">linea G B K. </s> <s xml:id="echoid-s20957" xml:space="preserve">eſt <lb/> <anchor type="note" xlink:label="note-0267-03a" xlink:href="note-0267-03"/> Italica I B C. </s> <s xml:id="echoid-s20958" xml:space="preserve">Aſtronomica H B I. </s> <s xml:id="echoid-s20959" xml:space="preserve">Babylonica decuſſantes ſemutuo bifariam in B. </s> <s xml:id="echoid-s20960" xml:space="preserve">vti ſupra. </s> <s xml:id="echoid-s20961" xml:space="preserve">lineæ <lb/>tranſuerſales ſunt paralelli ſignorum, & </s> <s xml:id="echoid-s20962" xml:space="preserve">arcum hor. </s> <s xml:id="echoid-s20963" xml:space="preserve">10. </s> <s xml:id="echoid-s20964" xml:space="preserve">& </s> <s xml:id="echoid-s20965" xml:space="preserve">14. </s> <s xml:id="echoid-s20966" xml:space="preserve">Reliqua ſuo loco patebunt.</s> <s xml:id="echoid-s20967" xml:space="preserve"/> </p> <div xml:id="echoid-div572" type="float" level="2" n="1"> <note position="right" xlink:label="note-0267-03" xlink:href="note-0267-03a" xml:space="preserve">Figura <lb/>13.</note> </div> <p> <s xml:id="echoid-s20968" xml:space="preserve">Neque vero lector exiſtimet hoc noſtrum horarium cylindricum eſſe idem cum eo, quodantea <lb/>circumterebatur, quodque erat portio faſciæ cylindricæ Zonam torridam referentis cum arcubus, <pb o="14" file="0268" n="273" rhead="TRACTATVS"/> ſeu lineis hora<unsure/>rijs in ea exciſis: </s> <s xml:id="echoid-s20969" xml:space="preserve">Nam huiuſmodi Zona, & </s> <s xml:id="echoid-s20970" xml:space="preserve">conſequententer horarium, quod erat eius <lb/>portio, erant perperam, vt patebit, conſtructa. </s> <s xml:id="echoid-s20971" xml:space="preserve">Quod cum ego animaduertiſſ<unsure/>@m, cæpicogitare de <lb/>modo correctionis, inueniq; </s> <s xml:id="echoid-s20972" xml:space="preserve">modum horarij plani ſuperius traditi, & </s> <s xml:id="echoid-s20973" xml:space="preserve">cylind@ici, quem nunc tra-<lb/>dam, quo ritè explicato patebunt errata veteris horarij, necnon Zonæillius, cuius erat portio.</s> <s xml:id="echoid-s20974" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20975" xml:space="preserve">Vt igitur ad datam poli altitudinem v. </s> <s xml:id="echoid-s20976" xml:space="preserve">g. </s> <s xml:id="echoid-s20977" xml:space="preserve">44. </s> <s xml:id="echoid-s20978" xml:space="preserve">{1/2}. </s> <s xml:id="echoid-s20979" xml:space="preserve">vti ſuperius, horariom iſtud con ſtruas.</s> <s xml:id="echoid-s20980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20981" xml:space="preserve">Primo, habeas figuram diſtant iarum ad eandem altitudinem deſcriptam, qualis eſt ea, quam ſupra <lb/>pro horario plano deſcripfimus.</s> <s xml:id="echoid-s20982" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s20983" xml:space="preserve">2 Adſit altera regula B A C. </s> <s xml:id="echoid-s20984" xml:space="preserve">æqualis, ac ſimilis´ſuperiori, præter quam quod exparte C. </s> <s xml:id="echoid-s20985" xml:space="preserve">termi-<lb/> <anchor type="note" xlink:label="note-0268-01a" xlink:href="note-0268-01"/> netur arcu I C K. </s> <s xml:id="echoid-s20986" xml:space="preserve">æquali arcui I B K. </s> <s xml:id="echoid-s20987" xml:space="preserve">diſtantiarum, in quo arcu per circinum notentur omnes diſtan-<lb/>tiæ, quæ ſunt in figura diſtantiarum, & </s> <s xml:id="echoid-s20988" xml:space="preserve">notentur ijſdem litteris, ita vt diſtantiæ B r. </s> <s xml:id="echoid-s20989" xml:space="preserve">B q. </s> <s xml:id="echoid-s20990" xml:space="preserve">ſint æqua-<lb/>les diſtantias regulæ C r. </s> <s xml:id="echoid-s20991" xml:space="preserve">C q. </s> <s xml:id="echoid-s20992" xml:space="preserve">& </s> <s xml:id="echoid-s20993" xml:space="preserve">ſic cęteræ cęteris, quæ notatæ ſunt ijſdem litteris ſicuti figura 14. <lb/></s> <s xml:id="echoid-s20994" xml:space="preserve">appoſita indicat.</s> <s xml:id="echoid-s20995" xml:space="preserve"/> </p> <div xml:id="echoid-div573" type="float" level="2" n="2"> <note position="left" xlink:label="note-0268-01" xlink:href="note-0268-01a" xml:space="preserve">14. figu-<lb/>ra. Regu-<lb/>la Hora-<lb/>@ij cylin-<lb/>drici.</note> </div> <p> <s xml:id="echoid-s20996" xml:space="preserve">3 Paretur charta ſolidior quadrangula qualis eſt regalis vel lamina pro deſcriptione huius hora-<lb/>rij, cuius vnum latus, quod erit baſis eius ſit aliquanto maius arcu I C K. </s> <s xml:id="echoid-s20997" xml:space="preserve">regulæ: </s> <s xml:id="echoid-s20998" xml:space="preserve">iuxta hoc latus duca-<lb/>tur linea recta notata ijſdem litteris I C K. </s> <s xml:id="echoid-s20999" xml:space="preserve">quibus no tatur arcus regulæ, cuius medium ſit punctum <lb/>C. </s> <s xml:id="echoid-s21000" xml:space="preserve">Hæc charta, curuo capiti regulæ curuando eam, ipſi applicentur, ita vt eius baſis I C K. </s> <s xml:id="echoid-s21001" xml:space="preserve">congruat <lb/>capiti curuo regulæ I C K. </s> <s xml:id="echoid-s21002" xml:space="preserve">& </s> <s xml:id="echoid-s21003" xml:space="preserve">punctum C. </s> <s xml:id="echoid-s21004" xml:space="preserve">illius congruat puncto C. </s> <s xml:id="echoid-s21005" xml:space="preserve">huius, & </s> <s xml:id="echoid-s21006" xml:space="preserve">pariter reliqua puncta <lb/>reliquis punctis congruentia, notentur ijſdem litteris. </s> <s xml:id="echoid-s21007" xml:space="preserve">Quare baſis horarij I K. </s> <s xml:id="echoid-s21008" xml:space="preserve">æqualis omnino eua-<lb/>det arcui diſtantiarum I K. </s> <s xml:id="echoid-s21009" xml:space="preserve">& </s> <s xml:id="echoid-s21010" xml:space="preserve">ſic reliquæ diſtantiæ notatæ ijſdem litteris L. </s> <s xml:id="echoid-s21011" xml:space="preserve">N. </s> <s xml:id="echoid-s21012" xml:space="preserve">P. </s> <s xml:id="echoid-s21013" xml:space="preserve">r. </s> <s xml:id="echoid-s21014" xml:space="preserve">q. </s> <s xml:id="echoid-s21015" xml:space="preserve">q. </s> <s xml:id="echoid-s21016" xml:space="preserve">o. </s> <s xml:id="echoid-s21017" xml:space="preserve">m. </s> <s xml:id="echoid-s21018" xml:space="preserve">poſt <lb/>hæc, charta explanata, erit baſis I K. </s> <s xml:id="echoid-s21019" xml:space="preserve">linea recta æqualis arcui I K. </s> <s xml:id="echoid-s21020" xml:space="preserve">regulæ, quam hoc modo mecha-<lb/>nicè inuenire oportet, cum nondum inuen ta ſit ars geometrica inueniendæ rectæ æqualis vlli peri-<lb/>pheriæ.</s> <s xml:id="echoid-s21021" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21022" xml:space="preserve">4 Ex tribus punctis I. </s> <s xml:id="echoid-s21023" xml:space="preserve">C. </s> <s xml:id="echoid-s21024" xml:space="preserve">K. </s> <s xml:id="echoid-s21025" xml:space="preserve">baſis prędictæ erigãtur normaliter tres rectę lineæ I G. </s> <s xml:id="echoid-s21026" xml:space="preserve">C I. </s> <s xml:id="echoid-s21027" xml:space="preserve">H K. </s> <s xml:id="echoid-s21028" xml:space="preserve">ſin-<lb/>gulæ ęquales lineę H I. </s> <s xml:id="echoid-s21029" xml:space="preserve">Radiarij notenturque in ijs reliqua puncta declinationum reſpondentia pun-<lb/>ctis lineę Radiarij H. </s> <s xml:id="echoid-s21030" xml:space="preserve">K. </s> <s xml:id="echoid-s21031" xml:space="preserve">L. </s> <s xml:id="echoid-s21032" xml:space="preserve">M. </s> <s xml:id="echoid-s21033" xml:space="preserve">A. </s> <s xml:id="echoid-s21034" xml:space="preserve">N. </s> <s xml:id="echoid-s21035" xml:space="preserve">O. </s> <s xml:id="echoid-s21036" xml:space="preserve">P. </s> <s xml:id="echoid-s21037" xml:space="preserve">I. </s> <s xml:id="echoid-s21038" xml:space="preserve">ſeruatis videlicet ijſdem interuallis. </s> <s xml:id="echoid-s21039" xml:space="preserve">punctum medium <lb/>omnium trium linearum erit B. </s> <s xml:id="echoid-s21040" xml:space="preserve">& </s> <s xml:id="echoid-s21041" xml:space="preserve">c. </s> <s xml:id="echoid-s21042" xml:space="preserve">& </s> <s xml:id="echoid-s21043" xml:space="preserve">per hæc puncta ducantur lineę tranſuerſim, ideſt, paralellę baſi <lb/>I K. </s> <s xml:id="echoid-s21044" xml:space="preserve">harum ſuprema erit G I H. </s> <s xml:id="echoid-s21045" xml:space="preserve">referens paralellum ♑. </s> <s xml:id="echoid-s21046" xml:space="preserve">proxima illi X R Y. </s> <s xml:id="echoid-s21047" xml:space="preserve">refert paralellum ♒, & </s> <s xml:id="echoid-s21048" xml:space="preserve"><lb/>♐. </s> <s xml:id="echoid-s21049" xml:space="preserve">tertia arcum diurnum hor. </s> <s xml:id="echoid-s21050" xml:space="preserve">10. </s> <s xml:id="echoid-s21051" xml:space="preserve">&</s> <s xml:id="echoid-s21052" xml:space="preserve">c. </s> <s xml:id="echoid-s21053" xml:space="preserve">media æquatorem infima trop. </s> <s xml:id="echoid-s21054" xml:space="preserve">♋, vt in figura characteres ſi-<lb/>gnorum, & </s> <s xml:id="echoid-s21055" xml:space="preserve">aliæ notæ indicant.</s> <s xml:id="echoid-s21056" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21057" xml:space="preserve">5 Ex punctis L. </s> <s xml:id="echoid-s21058" xml:space="preserve">N. </s> <s xml:id="echoid-s21059" xml:space="preserve">P. </s> <s xml:id="echoid-s21060" xml:space="preserve">r. </s> <s xml:id="echoid-s21061" xml:space="preserve">&</s> <s xml:id="echoid-s21062" xml:space="preserve">c. </s> <s xml:id="echoid-s21063" xml:space="preserve">erecta regula quapiam normaliter, quæ ſecuerit paralellos corre-<lb/>ſpondentes diſtantijs prædictorum punctorum; </s> <s xml:id="echoid-s21064" xml:space="preserve">Notentur diligenter puncta, in quibus eos ſecat, nam <lb/>per talia puncta ducendæ ſunt lineæ horariæ Italica, & </s> <s xml:id="echoid-s21065" xml:space="preserve">Babilonica, hac ratione regula ex I. </s> <s xml:id="echoid-s21066" xml:space="preserve">erecta ſe-<lb/>cat paralellum G H. </s> <s xml:id="echoid-s21067" xml:space="preserve">in puncto G. </s> <s xml:id="echoid-s21068" xml:space="preserve">lineæ Italicæ, quia ille paralellus reſpondent diſtantiæ I C. </s> <s xml:id="echoid-s21069" xml:space="preserve">quam <lb/>videlicet habet hora Italica 18. </s> <s xml:id="echoid-s21070" xml:space="preserve">à meridie in trop. </s> <s xml:id="echoid-s21071" xml:space="preserve">♑. </s> <s xml:id="echoid-s21072" xml:space="preserve">quare regula ſecabit illum in puncto G. </s> <s xml:id="echoid-s21073" xml:space="preserve">extre-<lb/>molineæ Italicæ. </s> <s xml:id="echoid-s21074" xml:space="preserve">Pariter quia diſtantia L C. </s> <s xml:id="echoid-s21075" xml:space="preserve">eſt diſtantia horæ Italicæ à meridie in paralello ♒, ideo <lb/>regula erecta ex L. </s> <s xml:id="echoid-s21076" xml:space="preserve">ſecabit paralellum ♒, in R. </s> <s xml:id="echoid-s21077" xml:space="preserve">puncto Italicæ. </s> <s xml:id="echoid-s21078" xml:space="preserve">eadem ratione ſecabit penultimum <lb/>paralellum in t. </s> <s xml:id="echoid-s21079" xml:space="preserve">puncto Babilonicæ, quia prædicta diſtantia à meridie competit horæ Babilonicæ in <lb/>co paralello, & </s> <s xml:id="echoid-s21080" xml:space="preserve">ſic ordinatim deinceps ex ſequentibus punctis erecta regula, ſecabit ſequentes para-<lb/>lellos in punctis Italicæ, & </s> <s xml:id="echoid-s21081" xml:space="preserve">Babilonicæ ex utraque parte horarij vſque ad mediam Aſtronomicam, vt <lb/>videre eſt in figura. </s> <s xml:id="echoid-s21082" xml:space="preserve">Erecta autem ex puncto C. </s> <s xml:id="echoid-s21083" xml:space="preserve">nullam habente diſtantiam à meridiana coincidit <lb/>cum ipſa meridiana, & </s> <s xml:id="echoid-s21084" xml:space="preserve">ſecat paralellum ♎, ♈, in B. </s> <s xml:id="echoid-s21085" xml:space="preserve">eius medio, in quo paralello Italica, & </s> <s xml:id="echoid-s21086" xml:space="preserve">Babyloni-<lb/>ca nullam habent diſtantiam à meridiana. </s> <s xml:id="echoid-s21087" xml:space="preserve">quare B. </s> <s xml:id="echoid-s21088" xml:space="preserve">erit punctum commune etiam Italicæ, & </s> <s xml:id="echoid-s21089" xml:space="preserve">Babylo-<lb/>nicæ. </s> <s xml:id="echoid-s21090" xml:space="preserve">Si igitur ducantur duę lineæ punctuales per prædicta puncta vt in figura linea G R B s K. </s> <s xml:id="echoid-s21091" xml:space="preserve">ipſa <lb/>erit Italica, & </s> <s xml:id="echoid-s21092" xml:space="preserve">H B t I, erit Babylonica.</s> <s xml:id="echoid-s21093" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21094" xml:space="preserve">6 Demonſtratio huius conſtructionis ſic habebitur. </s> <s xml:id="echoid-s21095" xml:space="preserve">Concipe Radiarium normaliter erectum <lb/> <anchor type="note" xlink:label="note-0268-02a" xlink:href="note-0268-02"/> ſupra planum figuræ diſtantiarum, ſicuti etiam in demonſtratione horarij plani ſitque præſens ho-<lb/>rarium cylindricum curuatum ſecundum euruitatem arcus figuræ diſtantiarum, & </s> <s xml:id="echoid-s21096" xml:space="preserve">baſis horarij <lb/>I C K, curuata, congruat arcui I C K. </s> <s xml:id="echoid-s21097" xml:space="preserve">diſtantiarum, in quo ſitu linea horarij C B I. </s> <s xml:id="echoid-s21098" xml:space="preserve">congruet lineæ <lb/>H A I. </s> <s xml:id="echoid-s21099" xml:space="preserve">Radiarij, & </s> <s xml:id="echoid-s21100" xml:space="preserve">puncta declinationum vnius congruent punctis declinationum, alterius ſi po-<lb/>ſtea imaginemur Radiarium moueri circa manentem axem E Q. </s> <s xml:id="echoid-s21101" xml:space="preserve">linea H I. </s> <s xml:id="echoid-s21102" xml:space="preserve">ſemper radet hora-<lb/>rium cylindricum, quare puncta declinationum in ea gyratione deſcriberent lineas paralellas, <lb/>ſeu arcus ſignorum, & </s> <s xml:id="echoid-s21103" xml:space="preserve">diurnos. </s> <s xml:id="echoid-s21104" xml:space="preserve">Iam latera erecta ſuper fines diſtantiarum ſecabunt hos paralel-<lb/>los, & </s> <s xml:id="echoid-s21105" xml:space="preserve">quidem in punctis horæ, & </s> <s xml:id="echoid-s21106" xml:space="preserve">Babylonicæ, v. </s> <s xml:id="echoid-s21107" xml:space="preserve">g. </s> <s xml:id="echoid-s21108" xml:space="preserve">I G. </s> <s xml:id="echoid-s21109" xml:space="preserve">ſecabit in puncto G. </s> <s xml:id="echoid-s21110" xml:space="preserve">Italicam, & </s> <s xml:id="echoid-s21111" xml:space="preserve">Ba-<lb/>bylonicam in ipſo I. </s> <s xml:id="echoid-s21112" xml:space="preserve">linea vero, vel regula ex L. </s> <s xml:id="echoid-s21113" xml:space="preserve">erecta ſecabit Italicam in R. </s> <s xml:id="echoid-s21114" xml:space="preserve">Babylonicam in t@ quæ <lb/>puncta dico eſſe in prædictis lineis, quia linea L R. </s> <s xml:id="echoid-s21115" xml:space="preserve">nihil eſt aliud, quam tangens H I. </s> <s xml:id="echoid-s21116" xml:space="preserve">Radiarij, quan-<lb/>do Radiarium gypando peruenit ad finem diſtantię L C. </s> <s xml:id="echoid-s21117" xml:space="preserve">quę eſt diſtantia prędictarum horarum a me-<lb/>ridiana in paralello, ♒, x. </s> <s xml:id="echoid-s21118" xml:space="preserve">y. </s> <s xml:id="echoid-s21119" xml:space="preserve">pro Italica, & </s> <s xml:id="echoid-s21120" xml:space="preserve">diſtantia Babylonicę à meridiana in paralello ☊, ♊. </s> <s xml:id="echoid-s21121" xml:space="preserve">eſt au-<lb/>tem R u. </s> <s xml:id="echoid-s21122" xml:space="preserve">æqualis ipſi L C. </s> <s xml:id="echoid-s21123" xml:space="preserve">ergo punctum R. </s> <s xml:id="echoid-s21124" xml:space="preserve">eſt terminus pariter diſtantiæ Italicę a<unsure/> meridiana in ♒, <lb/>& </s> <s xml:id="echoid-s21125" xml:space="preserve">conſequenter erit punctum lineæ Italicę inibi. </s> <s xml:id="echoid-s21126" xml:space="preserve">Idem valeat de alijs punctis, atq; </s> <s xml:id="echoid-s21127" xml:space="preserve">etiam de punctis <lb/>horæ Babylonicæ.</s> <s xml:id="echoid-s21128" xml:space="preserve"/> </p> <div xml:id="echoid-div574" type="float" level="2" n="3"> <note position="left" xlink:label="note-0268-02" xlink:href="note-0268-02a" xml:space="preserve">Demon-<lb/>stratio <lb/>praceden-<lb/>tium.</note> </div> <p> <s xml:id="echoid-s21129" xml:space="preserve">7 Sciendum eſt haſce lineas pũctuales Italicam, & </s> <s xml:id="echoid-s21130" xml:space="preserve">Babylonicam in charta explanata, neq; </s> <s xml:id="echoid-s21131" xml:space="preserve">eſſe re-<lb/>ctas, neq; </s> <s xml:id="echoid-s21132" xml:space="preserve">debere eſſe, quia quando lamina cylindrico curuatur, ſi eſſent lineę rectę euaderent ſpirales, <lb/>quarum nulla puncta, præter extrema G. </s> <s xml:id="echoid-s21133" xml:space="preserve">K. </s> <s xml:id="echoid-s21134" xml:space="preserve">H. </s> <s xml:id="echoid-s21135" xml:space="preserve">I. </s> <s xml:id="echoid-s21136" xml:space="preserve">& </s> <s xml:id="echoid-s21137" xml:space="preserve">medium B. </s> <s xml:id="echoid-s21138" xml:space="preserve">eſſent in eodem plano per prop. </s> <s xml:id="echoid-s21139" xml:space="preserve">24.</s> <s xml:id="echoid-s21140" xml:space="preserve"> <pb o="15" file="0269" n="274" rhead="DE HOROLOGIIS."/> lib. </s> <s xml:id="echoid-s21141" xml:space="preserve">8. </s> <s xml:id="echoid-s21142" xml:space="preserve">Pappi. </s> <s xml:id="echoid-s21143" xml:space="preserve">& </s> <s xml:id="echoid-s21144" xml:space="preserve">per prop. </s> <s xml:id="echoid-s21145" xml:space="preserve">1. </s> <s xml:id="echoid-s21146" xml:space="preserve">de Cochlea mechanicorum Guidubaldi, qui docent ex hypotemuſa trian-<lb/>guli plani eirca cylindum circumuoluti fieri Helicem. </s> <s xml:id="echoid-s21147" xml:space="preserve">vide etiam prop. </s> <s xml:id="echoid-s21148" xml:space="preserve">4. </s> <s xml:id="echoid-s21149" xml:space="preserve">& </s> <s xml:id="echoid-s21150" xml:space="preserve">8. </s> <s xml:id="echoid-s21151" xml:space="preserve">lib. </s> <s xml:id="echoid-s21152" xml:space="preserve">2. </s> <s xml:id="echoid-s21153" xml:space="preserve">de Cochlea <lb/>aquatica eiuſdem Guidubaldi vbi oſtendit Helicem, ſeu ſpiralem habere puncta primæ medietatis <lb/>altiora iuſto puncta vero ſecundæ medietatis depreſſiora iuſto;</s> <s xml:id="echoid-s21154" xml:space="preserve">|illa enim ſunt ſupra ellipſim deſcri-<lb/>ptam per extrema puncta, ac medium Helicis, iſta vero infra. </s> <s xml:id="echoid-s21155" xml:space="preserve">Ea propter ſi in lamina horarij huius <lb/>plana duceretur linea recta per tria puncta G B K. </s> <s xml:id="echoid-s21156" xml:space="preserve">ea poſtea cylindricata haberet puncta omnia me-<lb/>dietatis primæ B K. </s> <s xml:id="echoid-s21157" xml:space="preserve">altiora iuſto; </s> <s xml:id="echoid-s21158" xml:space="preserve">alerius vero medietatis B G. </s> <s xml:id="echoid-s21159" xml:space="preserve">depreſſiora.</s> <s xml:id="echoid-s21160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21161" xml:space="preserve">8 Vnde apertè apparet errare, qui Zonas illas explanatas linets rectis horarijs ad horas Italicas <lb/> <anchor type="note" xlink:label="note-0269-01a" xlink:href="note-0269-01"/> deſcribendas prius excidunt; </s> <s xml:id="echoid-s21162" xml:space="preserve">nam Zonis illis cylindricè poſtea curuatis, neceſſe eſt lineas rectas eua-<lb/>dere ſpirales ſeu Helices, quorum omnia puncta non ſunt in eodem plano: </s> <s xml:id="echoid-s21163" xml:space="preserve">deberent autem omnia <lb/>eſſe in communi ſectione plani circuli horarij Italici ſecantis cylindricum, & </s> <s xml:id="echoid-s21164" xml:space="preserve">conſequemer eſſe in li-<lb/>nea elliptica ſeu ouali; </s> <s xml:id="echoid-s21165" xml:space="preserve">ſectio enim cylindri à plano facta ellipſis eſt, ex Sereno de ſectione cylindri: <lb/></s> <s xml:id="echoid-s21166" xml:space="preserve">neceſſe pariter eſt mendoſum eſſe horarium illud, quod iſtius Zonæ portio eſt, vti ſupra innuebamus.</s> <s xml:id="echoid-s21167" xml:space="preserve"/> </p> <div xml:id="echoid-div575" type="float" level="2" n="4"> <note position="right" xlink:label="note-0269-01" xlink:href="note-0269-01a" xml:space="preserve">Errata <lb/>Zonæ fe-<lb/>neſtratæ, <lb/>necnon <lb/>Horarij <lb/>cylindri-<lb/>ci antea <lb/>viſitati.</note> </div> <p> <s xml:id="echoid-s21168" xml:space="preserve">9 Sequitur tandem ex pręmiſſis noſtras lineas Italicas, & </s> <s xml:id="echoid-s21169" xml:space="preserve">Babylonicas punctuales in plano factas, <lb/>curuata cylindricè lamina euadere ellipticas ſeu ouales; </s> <s xml:id="echoid-s21170" xml:space="preserve">cum enim oſtenſum ſit omnia earum puncta <lb/>eſſe in lineis horarijs Ital. </s> <s xml:id="echoid-s21171" xml:space="preserve">& </s> <s xml:id="echoid-s21172" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s21173" xml:space="preserve">erunt conſequenter in planis circulorum horariorum earum, <lb/>cruntq; </s> <s xml:id="echoid-s21174" xml:space="preserve">in ſectione facta ab ijs planis in ſuperficie cylindri, quæ ſectio ellipſis eſt, ex Sereno de ſect. <lb/></s> <s xml:id="echoid-s21175" xml:space="preserve">cylindri. </s> <s xml:id="echoid-s21176" xml:space="preserve">Praxis porrò noſtra, eſt fere eandem cum ea quam docet Guidubaldus prop. </s> <s xml:id="echoid-s21177" xml:space="preserve">28. </s> <s xml:id="echoid-s21178" xml:space="preserve">lib. </s> <s xml:id="echoid-s21179" xml:space="preserve">2. </s> <s xml:id="echoid-s21180" xml:space="preserve">de Co-<lb/>chela; </s> <s xml:id="echoid-s21181" xml:space="preserve">eſt tamen breuior, quia omifi deſcriptionem cuiuſdam paralellogrammi.</s> <s xml:id="echoid-s21182" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21183" xml:space="preserve">10 Notandum angulos G B i. </s> <s xml:id="echoid-s21184" xml:space="preserve">H B i. </s> <s xml:id="echoid-s21185" xml:space="preserve">quos faciunt Italica, & </s> <s xml:id="echoid-s21186" xml:space="preserve">Babylonica cum Aſtronomica in ſu-<lb/>perficie explanata, minime debere eſſe æquales altitudini polari ſicuti in hor. </s> <s xml:id="echoid-s21187" xml:space="preserve">plano, ſed eſſe paulo <lb/>maiores: </s> <s xml:id="echoid-s21188" xml:space="preserve">cylindricata enim lamina deberent eſſe æquales altitudini poli, ſed eam curuando fiunt mi-<lb/>nores ergo prius debant eſſe maiores. </s> <s xml:id="echoid-s21189" xml:space="preserve">Idem patebit per circinum experienti: </s> <s xml:id="echoid-s21190" xml:space="preserve">deſcripto enim ex cẽtro <lb/>B. </s> <s xml:id="echoid-s21191" xml:space="preserve">arcu G Z. </s> <s xml:id="echoid-s21192" xml:space="preserve">reperies eum eſſe maiorem altitudine poli, ideſt, plures gradus continere. </s> <s xml:id="echoid-s21193" xml:space="preserve">quapropter <lb/>ij erroris conuincuntur, qui præcipiunt, & </s> <s xml:id="echoid-s21194" xml:space="preserve">Zonas prædictas, & </s> <s xml:id="echoid-s21195" xml:space="preserve">horaria pariter earum portiones con-<lb/>ſtruenda eſſe ſecundum angulos æquales altitudini poli. </s> <s xml:id="echoid-s21196" xml:space="preserve">Vnde tandem ſequitur Ital. </s> <s xml:id="echoid-s21197" xml:space="preserve">& </s> <s xml:id="echoid-s21198" xml:space="preserve">Babylon. </s> <s xml:id="echoid-s21199" xml:space="preserve">per <lb/>altitudinem hanc haberi non poſſe.</s> <s xml:id="echoid-s21200" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21201" xml:space="preserve">11 Exiſtimo tamen errorem nullum ſenſibilem committi, ſi in loeo minoris altitudinis quam gr. <lb/></s> <s xml:id="echoid-s21202" xml:space="preserve">43. </s> <s xml:id="echoid-s21203" xml:space="preserve">vel 44. </s> <s xml:id="echoid-s21204" xml:space="preserve">prædicti anguli ſiant æquales altitudini poli; </s> <s xml:id="echoid-s21205" xml:space="preserve">nam in altitudine 43. </s> <s xml:id="echoid-s21206" xml:space="preserve">& </s> <s xml:id="echoid-s21207" xml:space="preserve">44. </s> <s xml:id="echoid-s21208" xml:space="preserve">incipit appare-<lb/>reſenſibilis curuitas helicis, & </s> <s xml:id="echoid-s21209" xml:space="preserve">diſcrepantia ab ellipſi; </s> <s xml:id="echoid-s21210" xml:space="preserve">quæ quidem ſemper maior| euadit, quanto <lb/>maiores fiunt dicti anguli, quia quanto creſcit altitudo poli, tanto creſcunt hi anguli, & </s> <s xml:id="echoid-s21211" xml:space="preserve">conſequen-<lb/>@ar Italica, & </s> <s xml:id="echoid-s21212" xml:space="preserve">Babybilonica longiores euadunt, & </s> <s xml:id="echoid-s21213" xml:space="preserve">ideo Helices etiam longiores, atque adeo magis <lb/>ſenſibiliter ab ellipſi diſcrepantes.</s> <s xml:id="echoid-s21214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21215" xml:space="preserve">12 De vſu eius nihil noui occurit, præter ea quæ deplano dicta ſunt: </s> <s xml:id="echoid-s21216" xml:space="preserve">Sicut enim omnia huic <lb/> <anchor type="note" xlink:label="note-0269-02a" xlink:href="note-0269-02"/> communia, & </s> <s xml:id="echoid-s21217" xml:space="preserve">applicabilia. </s> <s xml:id="echoid-s21218" xml:space="preserve">Si quis tamen velit eo vti ad horas tantum Italicas ſolo triangulo G I K. <lb/></s> <s xml:id="echoid-s21219" xml:space="preserve">opus habet, quo præterea potuit horas Aſtronom icas deſcribere, ſi vtatur latere G I. </s> <s xml:id="echoid-s21220" xml:space="preserve">& </s> <s xml:id="echoid-s21221" xml:space="preserve">latere regu-<lb/>læ A I. </s> <s xml:id="echoid-s21222" xml:space="preserve">quæ illi reſpondent, vtatur pro linea fiduciæ, illam applicando horis tympani deſcribendis, <lb/>ſicuti vtitur. </s> <s xml:id="echoid-s21223" xml:space="preserve">linea B A C. </s> <s xml:id="echoid-s21224" xml:space="preserve">pro Italicis. </s> <s xml:id="echoid-s21225" xml:space="preserve">Hic pariter idem examen per tabellas interſectionum adhiben-<lb/>dum eſt; </s> <s xml:id="echoid-s21226" xml:space="preserve">& </s> <s xml:id="echoid-s21227" xml:space="preserve">ſtylus eodem modo fingendum, & </s> <s xml:id="echoid-s21228" xml:space="preserve">Horologium euadet idem cum ſuperiori, quare, & </s> <s xml:id="echoid-s21229" xml:space="preserve"><lb/>idem vſus, &</s> <s xml:id="echoid-s21230" xml:space="preserve">c.</s> <s xml:id="echoid-s21231" xml:space="preserve"/> </p> <div xml:id="echoid-div576" type="float" level="2" n="5"> <note position="right" xlink:label="note-0269-02" xlink:href="note-0269-02a" xml:space="preserve">Vſus <lb/>eius.</note> </div> </div> <div xml:id="echoid-div578" type="section" level="1" n="423"> <head xml:id="echoid-head445" xml:space="preserve">Laus Deo O. M.</head> <pb o="16" file="0270" n="275"/> </div> <div xml:id="echoid-div579" type="section" level="1" n="424"> <head xml:id="echoid-head446" xml:space="preserve">PARS SECVNDA.</head> <head xml:id="echoid-head447" xml:space="preserve">DE NOVO HOROLOGIO VIATORIO</head> <head xml:id="echoid-head448" xml:space="preserve">IN QVADRANTE</head> <head xml:id="echoid-head449" xml:space="preserve">Per altitudines Solis deſcribendo. Cap. I.</head> <p> <s xml:id="echoid-s21232" xml:space="preserve">QVoniam Horologium hoc deſcribitur per| Tabulam altitudinũ Solis in ſingulis horis <lb/>ſupra horizontem loci illius, pro quo Horologium deſcribendum eſt: </s> <s xml:id="echoid-s21233" xml:space="preserve">ideo paratam <lb/>habere oportet huiuſmodi tabulam, conſtructam ad latitudinem dati loci, qualis eſt <lb/>ſequens, conſtructa à D. </s> <s xml:id="echoid-s21234" xml:space="preserve">Alfonſo Iſæo nobili Parmenſi, atque in Mathematicis ver-<lb/>ſatiffimo ad latit. </s> <s xml:id="echoid-s21235" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s21236" xml:space="preserve">vti eſt Parmenſis. </s> <s xml:id="echoid-s21237" xml:space="preserve">vbi nunc in exemplo trademus regulas hu-<lb/>ius Horologij deſcribendi.</s> <s xml:id="echoid-s21238" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div580" type="section" level="1" n="425"> <head xml:id="echoid-head450" xml:space="preserve">LOCVS TABVLÆ.</head> <p> <s xml:id="echoid-s21239" xml:space="preserve">SEd ante omnia præmiſſa Tabula declaranda eſt. </s> <s xml:id="echoid-s21240" xml:space="preserve">in ea igitur conſiderandi ſunt duo proceſſus. <lb/></s> <s xml:id="echoid-s21241" xml:space="preserve">Primus qui tendit a ſiniſtra in dexte@ã, & </s> <s xml:id="echoid-s21242" xml:space="preserve">dicitur verſus alter tendit à ſumo ad imum, & </s> <s xml:id="echoid-s21243" xml:space="preserve">dicitur co-<lb/>lumna. </s> <s xml:id="echoid-s21244" xml:space="preserve">Verſus ſunt 22. </s> <s xml:id="echoid-s21245" xml:space="preserve">quorum. </s> <s xml:id="echoid-s21246" xml:space="preserve">primus continet titulum. </s> <s xml:id="echoid-s21247" xml:space="preserve">ſecundus numeros Horarum ab ortu 1. </s> <s xml:id="echoid-s21248" xml:space="preserve">2. </s> <s xml:id="echoid-s21249" xml:space="preserve"><lb/>3. </s> <s xml:id="echoid-s21250" xml:space="preserve">&</s> <s xml:id="echoid-s21251" xml:space="preserve">c. </s> <s xml:id="echoid-s21252" xml:space="preserve">& </s> <s xml:id="echoid-s21253" xml:space="preserve">ab occaſu 23. </s> <s xml:id="echoid-s21254" xml:space="preserve">22. </s> <s xml:id="echoid-s21255" xml:space="preserve">21. </s> <s xml:id="echoid-s21256" xml:space="preserve">&</s> <s xml:id="echoid-s21257" xml:space="preserve">c. </s> <s xml:id="echoid-s21258" xml:space="preserve">ternus continet varios characteres; </s> <s xml:id="echoid-s21259" xml:space="preserve">quorum primus M. </s> <s xml:id="echoid-s21260" xml:space="preserve">ſig n@ficat <lb/>Menſes ſecundus D. </s> <s xml:id="echoid-s21261" xml:space="preserve">dies, 8. </s> <s xml:id="echoid-s21262" xml:space="preserve">ſigna, G. </s> <s xml:id="echoid-s21263" xml:space="preserve">gradus, M. </s> <s xml:id="echoid-s21264" xml:space="preserve">minuta. </s> <s xml:id="echoid-s21265" xml:space="preserve">poſtea iterum ſequuntur M. </s> <s xml:id="echoid-s21266" xml:space="preserve">D. </s> <s xml:id="echoid-s21267" xml:space="preserve">S. </s> <s xml:id="echoid-s21268" xml:space="preserve">G. </s> <s xml:id="echoid-s21269" xml:space="preserve">M. </s> <s xml:id="echoid-s21270" xml:space="preserve"><lb/>&</s> <s xml:id="echoid-s21271" xml:space="preserve">c. </s> <s xml:id="echoid-s21272" xml:space="preserve">idem ſignificantia poſtea ad finem huius verſus, ſunt hor. </s> <s xml:id="echoid-s21273" xml:space="preserve">M. </s> <s xml:id="echoid-s21274" xml:space="preserve">ideſt, Horæ, minuta. </s> <s xml:id="echoid-s21275" xml:space="preserve">reliqui ver ſus <lb/>intelligentur partim ex columnarum expoſitione, partim ex vſu tabulæ.</s> <s xml:id="echoid-s21276" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21277" xml:space="preserve">Secundum columnas tota tabula diuitur in tres partes, in Annum, in Altitudines, in Tempora. <lb/></s> <s xml:id="echoid-s21278" xml:space="preserve"> <anchor type="note" xlink:label="note-0270-01a" xlink:href="note-0270-01"/> Prima pars, quæ Annus eſt conſtat ex octo columnis, quarum prima continet nomina ſex Menſium <lb/>incipiendo à ſolſtitio hyemali vſque ad æſtiuum, vt indicat litera M, ei in tertio verſu præfixa. </s> <s xml:id="echoid-s21279" xml:space="preserve">Se-<lb/>cunda continet aliquot dies menſium, ſeu numeros dierum menſium primæ columnæ, cui ideo litera <lb/>D. </s> <s xml:id="echoid-s21280" xml:space="preserve">inſcribitur. </s> <s xml:id="echoid-s21281" xml:space="preserve">Tertia cui S. </s> <s xml:id="echoid-s21282" xml:space="preserve">inſcribitur habet ſex ſigna, ſeu ſex characteres ſignorum Zodiaci aſcen-<lb/>dentium, quæ reſpondent ſex menſibus primæ columnæ. </s> <s xml:id="echoid-s21283" xml:space="preserve">Quarta cui ſuperponitur G. </s> <s xml:id="echoid-s21284" xml:space="preserve">M. </s> <s xml:id="echoid-s21285" xml:space="preserve">continet <lb/>numeros graduum, & </s> <s xml:id="echoid-s21286" xml:space="preserve">minutorum ſex ſignorum præcedentis columnæ, qui numeri reſpondent fin-<lb/>guli numeris ſingulis dierum ſecundæ columnæ, qui ſunt ſecum in eodem verſu. </s> <s xml:id="echoid-s21287" xml:space="preserve">Qu@nta continet <lb/>reliquos fex menſes, ideo ei M. </s> <s xml:id="echoid-s21288" xml:space="preserve">iterum præſcribitur. </s> <s xml:id="echoid-s21289" xml:space="preserve">Sexta dies aliquot menſium. </s> <s xml:id="echoid-s21290" xml:space="preserve">Septima, reli-<lb/>quorum ſex ſignorum deſcendentium characteres reſpondentium diebus menſium quintæ, & </s> <s xml:id="echoid-s21291" xml:space="preserve">ſextæ <lb/>columnæ. </s> <s xml:id="echoid-s21292" xml:space="preserve">Octaua habet numeros graduum, & </s> <s xml:id="echoid-s21293" xml:space="preserve">min. </s> <s xml:id="echoid-s21294" xml:space="preserve">præcedentium ſignorum, qui gradus, & </s> <s xml:id="echoid-s21295" xml:space="preserve">min. </s> <s xml:id="echoid-s21296" xml:space="preserve">re-<lb/>ſpondent diebus præcedentis columnæ, qui ſunt ſecum in ijſdem ver@bus. </s> <s xml:id="echoid-s21297" xml:space="preserve">Quapropter duo primi <lb/>verſus harum 8. </s> <s xml:id="echoid-s21298" xml:space="preserve">columna rum ſignificant menſis Iunij diem 22. </s> <s xml:id="echoid-s21299" xml:space="preserve">reſpondere gr. </s> <s xml:id="echoid-s21300" xml:space="preserve">30. </s> <s xml:id="echoid-s21301" xml:space="preserve">min. </s> <s xml:id="echoid-s21302" xml:space="preserve">0. </s> <s xml:id="echoid-s21303" xml:space="preserve">♊. </s> <s xml:id="echoid-s21304" xml:space="preserve">& </s> <s xml:id="echoid-s21305" xml:space="preserve">pariter <lb/>eiuſdem menſis eandem diem 22. </s> <s xml:id="echoid-s21306" xml:space="preserve">reſpondere gr. </s> <s xml:id="echoid-s21307" xml:space="preserve">o. </s> <s xml:id="echoid-s21308" xml:space="preserve">min. </s> <s xml:id="echoid-s21309" xml:space="preserve">o. </s> <s xml:id="echoid-s21310" xml:space="preserve">♋. </s> <s xml:id="echoid-s21311" xml:space="preserve">quæ omnia indicant prædicta die 22. <lb/></s> <s xml:id="echoid-s21312" xml:space="preserve">Solem tranſire a Geminis ad Cancrum, ſeu deſcribere tropicum Cancri. </s> <s xml:id="echoid-s21313" xml:space="preserve">Tertius verſus earundem <lb/>columnarum indicat die 6. </s> <s xml:id="echoid-s21314" xml:space="preserve">Iunij Solem percurrere paralellum tranſeuntem per gr. </s> <s xml:id="echoid-s21315" xml:space="preserve">25. </s> <s xml:id="echoid-s21316" xml:space="preserve">min. </s> <s xml:id="echoid-s21317" xml:space="preserve">o. </s> <s xml:id="echoid-s21318" xml:space="preserve">♊. </s> <s xml:id="echoid-s21319" xml:space="preserve">die <lb/>verò 8. </s> <s xml:id="echoid-s21320" xml:space="preserve">Iulij Solem percurrere paralellum tranſeuntem per gr. </s> <s xml:id="echoid-s21321" xml:space="preserve">15. </s> <s xml:id="echoid-s21322" xml:space="preserve">min. </s> <s xml:id="echoid-s21323" xml:space="preserve">o. </s> <s xml:id="echoid-s21324" xml:space="preserve">♋.</s> <s xml:id="echoid-s21325" xml:space="preserve"/> </p> <div xml:id="echoid-div580" type="float" level="2" n="1"> <note position="left" xlink:label="note-0270-01" xlink:href="note-0270-01a" xml:space="preserve">Prima <lb/>pars ta-<lb/>bul@ in <lb/>qua An-<lb/>nus.</note> </div> <p> <s xml:id="echoid-s21326" xml:space="preserve">Igitur numeri gr. </s> <s xml:id="echoid-s21327" xml:space="preserve">& </s> <s xml:id="echoid-s21328" xml:space="preserve">min. </s> <s xml:id="echoid-s21329" xml:space="preserve">Signorum, qui ſunt iu quarta, & </s> <s xml:id="echoid-s21330" xml:space="preserve">octaua columna denotant totidem para-<lb/> <anchor type="note" xlink:label="note-0270-02a" xlink:href="note-0270-02"/> lellus æquatoris tranſeuntes per tot, taleſq; </s> <s xml:id="echoid-s21331" xml:space="preserve">gradus. </s> <s xml:id="echoid-s21332" xml:space="preserve">alij porrò ſunt paralelli per initia Signorum, qui <lb/>notantur per gr. </s> <s xml:id="echoid-s21333" xml:space="preserve">0. </s> <s xml:id="echoid-s21334" xml:space="preserve">min. </s> <s xml:id="echoid-s21335" xml:space="preserve">0. </s> <s xml:id="echoid-s21336" xml:space="preserve">alij per gr. </s> <s xml:id="echoid-s21337" xml:space="preserve">10. </s> <s xml:id="echoid-s21338" xml:space="preserve">vel 15. </s> <s xml:id="echoid-s21339" xml:space="preserve">&</s> <s xml:id="echoid-s21340" xml:space="preserve">c. </s> <s xml:id="echoid-s21341" xml:space="preserve">alij ſunt ſimul paralelli, & </s> <s xml:id="echoid-s21342" xml:space="preserve">arcus diurni horarum in-<lb/>tegrarum, vti ſunt qui tranſeunt per gr. </s> <s xml:id="echoid-s21343" xml:space="preserve">24. </s> <s xml:id="echoid-s21344" xml:space="preserve">min. </s> <s xml:id="echoid-s21345" xml:space="preserve">25. </s> <s xml:id="echoid-s21346" xml:space="preserve">♋. </s> <s xml:id="echoid-s21347" xml:space="preserve">per eos enim tranſit arcus diurnus horarum <lb/>15. </s> <s xml:id="echoid-s21348" xml:space="preserve">vt apparet procedẽdo in eodem verſu vſq; </s> <s xml:id="echoid-s21349" xml:space="preserve">ad columnam temporis diurni, ibi enim ſunt hor. </s> <s xml:id="echoid-s21350" xml:space="preserve">15. </s> <s xml:id="echoid-s21351" xml:space="preserve">0. <lb/></s> <s xml:id="echoid-s21352" xml:space="preserve">Pariter in gr. </s> <s xml:id="echoid-s21353" xml:space="preserve">20. </s> <s xml:id="echoid-s21354" xml:space="preserve">min. </s> <s xml:id="echoid-s21355" xml:space="preserve">20. </s> <s xml:id="echoid-s21356" xml:space="preserve">☊. </s> <s xml:id="echoid-s21357" xml:space="preserve">eſt arcus diurnus horarum 10. </s> <s xml:id="echoid-s21358" xml:space="preserve">vt apparet procedẽdo in eodem ver@u vſq; </s> <s xml:id="echoid-s21359" xml:space="preserve"><lb/>ad colum. </s> <s xml:id="echoid-s21360" xml:space="preserve">temp. </s> <s xml:id="echoid-s21361" xml:space="preserve">diurni, vbi horæ 10. </s> <s xml:id="echoid-s21362" xml:space="preserve">0. </s> <s xml:id="echoid-s21363" xml:space="preserve">& </s> <s xml:id="echoid-s21364" xml:space="preserve">ſic de reliquis. </s> <s xml:id="echoid-s21365" xml:space="preserve">Hi autem arcus aſſumpti ſunt propter eo-<lb/>rum vtilitatem in horologij propoſiti deſcriptione; </s> <s xml:id="echoid-s21366" xml:space="preserve">in paralellis enim horologij (quos poſtea vide-<lb/>bis) correſpondentibus hil<unsure/>ce arcubus diurnis, ſe mutuò ſecantbinæ horæ, ita vt nulla hora ſit in ijs <lb/>ſolitaria, & </s> <s xml:id="echoid-s21367" xml:space="preserve">præterea habetur in ſingulis eorum punctum vnum in horizonte pro ortu Solis in quoli-<lb/>bet arcu diurno. </s> <s xml:id="echoid-s21368" xml:space="preserve">quæ res plurimum confert ad rectam horologij deſcriptionem. </s> <s xml:id="echoid-s21369" xml:space="preserve">ſunt autem in toto <lb/>hoc anno 19. </s> <s xml:id="echoid-s21370" xml:space="preserve">paralelli, quorum ſingulis è directo reſpondent ſinguli verl<unsure/>us continentes gr. </s> <s xml:id="echoid-s21371" xml:space="preserve">& </s> <s xml:id="echoid-s21372" xml:space="preserve">min. </s> <s xml:id="echoid-s21373" xml:space="preserve"><lb/>altitudinem Solis pro ſingulis horis in præcedentibus paralellis, quæ eſt ſecunda pars Tabulæ, de qua <lb/>modo dicendum.</s> <s xml:id="echoid-s21374" xml:space="preserve"/> </p> <div xml:id="echoid-div581" type="float" level="2" n="2"> <note position="left" xlink:label="note-0270-02" xlink:href="note-0270-02a" xml:space="preserve">Areus <lb/>@iur@i.</note> </div> <p> <s xml:id="echoid-s21375" xml:space="preserve">Poſt haſce octo columnas, ſequitur ſecunda pars Tabulæ, quæ continet columnas 16. </s> <s xml:id="echoid-s21376" xml:space="preserve">quarum prima <lb/> <anchor type="note" xlink:label="note-0270-03a" xlink:href="note-0270-03"/> eſt ſub hora 23. </s> <s xml:id="echoid-s21377" xml:space="preserve">& </s> <s xml:id="echoid-s21378" xml:space="preserve">continet gradus, & </s> <s xml:id="echoid-s21379" xml:space="preserve">min. </s> <s xml:id="echoid-s21380" xml:space="preserve">altitudinum in hora 23. </s> <s xml:id="echoid-s21381" xml:space="preserve">in ſingulis aſſumptis paralellis, v.</s> <s xml:id="echoid-s21382" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s21383" xml:space="preserve">gr. </s> <s xml:id="echoid-s21384" xml:space="preserve">9. </s> <s xml:id="echoid-s21385" xml:space="preserve">min. </s> <s xml:id="echoid-s21386" xml:space="preserve">21. </s> <s xml:id="echoid-s21387" xml:space="preserve">quæ ſunt in verſu reſpondente primo verſui anni, in quo eſt paralellus per finem ♊, & </s> <s xml:id="echoid-s21388" xml:space="preserve"><lb/>initium ♋, qui dicitur tropicus Cancri, ſignificant in tali paralello Solem hora 23. </s> <s xml:id="echoid-s21389" xml:space="preserve">ſiue horam 23. </s> <s xml:id="echoid-s21390" xml:space="preserve">eſſe <pb o="17" file="0271" n="276" rhead="DE HOROLOGIIS."/> altam ſupra horizontem gr. </s> <s xml:id="echoid-s21391" xml:space="preserve">9. </s> <s xml:id="echoid-s21392" xml:space="preserve">min. </s> <s xml:id="echoid-s21393" xml:space="preserve">21. </s> <s xml:id="echoid-s21394" xml:space="preserve">Pariter gr. </s> <s xml:id="echoid-s21395" xml:space="preserve">9. </s> <s xml:id="echoid-s21396" xml:space="preserve">27. </s> <s xml:id="echoid-s21397" xml:space="preserve">qui ſequuntur in eadem columna, ſuntque in <lb/>directum ſecundi verſus anni, in quo eſt paralellus per gr. </s> <s xml:id="echoid-s21398" xml:space="preserve">15. </s> <s xml:id="echoid-s21399" xml:space="preserve">0′. </s> <s xml:id="echoid-s21400" xml:space="preserve">♊. </s> <s xml:id="echoid-s21401" xml:space="preserve">& </s> <s xml:id="echoid-s21402" xml:space="preserve">♋. </s> <s xml:id="echoid-s21403" xml:space="preserve">denotant altitudinem Solis <lb/>hora 23. </s> <s xml:id="echoid-s21404" xml:space="preserve">in eo exiſtentis. </s> <s xml:id="echoid-s21405" xml:space="preserve">quod ſi rectà perga@ per quartum verſum Tabulæ, qui proximè eſt ſub tertio <lb/>verſu graduum, & </s> <s xml:id="echoid-s21406" xml:space="preserve">min. </s> <s xml:id="echoid-s21407" xml:space="preserve">quiq; </s> <s xml:id="echoid-s21408" xml:space="preserve">continet verſum primi paralelli, ſeu ♋. </s> <s xml:id="echoid-s21409" xml:space="preserve">habebis omnes alritudines om-<lb/>nium horarum in tropico ♋. </s> <s xml:id="echoid-s21410" xml:space="preserve">pariter in ſequenti quinto verſu habebis altitudines omnium horarum <lb/>in paralello per gr. </s> <s xml:id="echoid-s21411" xml:space="preserve">15. </s> <s xml:id="echoid-s21412" xml:space="preserve">@′. </s> <s xml:id="echoid-s21413" xml:space="preserve">Cancri. </s> <s xml:id="echoid-s21414" xml:space="preserve">ſic etiam in ſexto reperies altitudines in paralello per gr. </s> <s xml:id="echoid-s21415" xml:space="preserve">24. </s> <s xml:id="echoid-s21416" xml:space="preserve">25. </s> <s xml:id="echoid-s21417" xml:space="preserve">eiuſ-<lb/>dem Cancri, qui eſt arcus diurnus horarum 15. </s> <s xml:id="echoid-s21418" xml:space="preserve">& </s> <s xml:id="echoid-s21419" xml:space="preserve">ſic de alijs.</s> <s xml:id="echoid-s21420" xml:space="preserve"/> </p> <div xml:id="echoid-div582" type="float" level="2" n="3"> <note position="left" xlink:label="note-0270-03" xlink:href="note-0270-03a" xml:space="preserve">S@@@@da <lb/>pars ta-<lb/>bula in <lb/>qua @it. <lb/>@erarum.</note> </div> <p> <s xml:id="echoid-s21421" xml:space="preserve">Porrò ſecunda hæc pars Tabulæ, quæ ſcilicet continet prædictas altitudines, ſubdiuiditur in tres <lb/>partes. </s> <s xml:id="echoid-s21422" xml:space="preserve">in partem antemeridianam, & </s> <s xml:id="echoid-s21423" xml:space="preserve">pomeridianam a linea ſcalari, quæ incedit inter maximas alti-<lb/>tudines Tabulæ. </s> <s xml:id="echoid-s21424" xml:space="preserve">& </s> <s xml:id="echoid-s21425" xml:space="preserve">meridianam, quæ conſtat vnica columna, cui titulus eſt, altit. </s> <s xml:id="echoid-s21426" xml:space="preserve">merid. </s> <s xml:id="echoid-s21427" xml:space="preserve">numeri enim <lb/>graduum, & </s> <s xml:id="echoid-s21428" xml:space="preserve">min. </s> <s xml:id="echoid-s21429" xml:space="preserve">eius indicant altitudines Solis meridianas in paralellis quibuſcum ſunt in ijſdem <lb/>verſibus; </s> <s xml:id="echoid-s21430" xml:space="preserve">ſic gr. </s> <s xml:id="echoid-s21431" xml:space="preserve">69. </s> <s xml:id="echoid-s21432" xml:space="preserve">0′. </s> <s xml:id="echoid-s21433" xml:space="preserve">ſunt altitudo Solis meridiana in tropico ♋.</s> <s xml:id="echoid-s21434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21435" xml:space="preserve">Tert@a, & </s> <s xml:id="echoid-s21436" xml:space="preserve">vltima pars Tabulæ continet vltimas 4. </s> <s xml:id="echoid-s21437" xml:space="preserve">columnas continuantes eoſdem prædictos ver-<lb/> <anchor type="note" xlink:label="note-0271-01a" xlink:href="note-0271-01"/> ſus, ijſdemq; </s> <s xml:id="echoid-s21438" xml:space="preserve">reſpondentes; </s> <s xml:id="echoid-s21439" xml:space="preserve">quæ appellari poſſunt temporales, quòd varia tempora contineant, earũ <lb/>tituli manifeſtant. </s> <s xml:id="echoid-s21440" xml:space="preserve">igitur ſub his titulis tempus diurnum, & </s> <s xml:id="echoid-s21441" xml:space="preserve">hor. </s> <s xml:id="echoid-s21442" xml:space="preserve">min. </s> <s xml:id="echoid-s21443" xml:space="preserve">numeri 15. </s> <s xml:id="echoid-s21444" xml:space="preserve">22′. </s> <s xml:id="echoid-s21445" xml:space="preserve">ideſt, horæ 15. <lb/></s> <s xml:id="echoid-s21446" xml:space="preserve">22′. </s> <s xml:id="echoid-s21447" xml:space="preserve">ſignificant tempus diurnum tropici ♋. </s> <s xml:id="echoid-s21448" xml:space="preserve">continere totidem horas, & </s> <s xml:id="echoid-s21449" xml:space="preserve">min. </s> <s xml:id="echoid-s21450" xml:space="preserve">eſt enim in eodem ver-<lb/>ſu cum eo.</s> <s xml:id="echoid-s21451" xml:space="preserve"/> </p> <div xml:id="echoid-div583" type="float" level="2" n="4"> <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Tertia <lb/>pi<unsure/>rs tabu <lb/>læ in quæ <lb/>Var@a tẽ-<lb/>pora.</note> </div> <p> <s xml:id="echoid-s21452" xml:space="preserve">Tertia exhibet tempus nocturnum, vnaq; </s> <s xml:id="echoid-s21453" xml:space="preserve">tempus ortus Solis; </s> <s xml:id="echoid-s21454" xml:space="preserve">quapropter hor. </s> <s xml:id="echoid-s21455" xml:space="preserve">8. </s> <s xml:id="echoid-s21456" xml:space="preserve">38′. </s> <s xml:id="echoid-s21457" xml:space="preserve">in verſu ♋. </s> <s xml:id="echoid-s21458" xml:space="preserve">eſt <lb/>@empus nocturnum illius paralelli, in quo etiam Sol oritur hora 8. </s> <s xml:id="echoid-s21459" xml:space="preserve">38′. </s> <s xml:id="echoid-s21460" xml:space="preserve">eodem modo de cęteris colum-<lb/>nis, necnon earum verſibus intelligas, quæ tamen melius partim ex vſu Tabulæ, partim ex eius con-<lb/>ſtructione percipientur.</s> <s xml:id="echoid-s21461" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21462" xml:space="preserve">Quoniam verò conſtructio eius prolixior eſt, ideo ne præcipuus finis noſter, qui eſt Horologij <lb/>propoſiti deſcriptio interrumpatur, eam in fine reijciemus. </s> <s xml:id="echoid-s21463" xml:space="preserve">eius tamen vſus maximè in Horologij <lb/>delineatione de qua nunc dicemus, apparebit.</s> <s xml:id="echoid-s21464" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div585" type="section" level="1" n="426"> <head xml:id="echoid-head451" style="it" xml:space="preserve">DESCRIPTIO HOROLOGII <lb/>per præcedentem Tabulam.</head> <p> <s xml:id="echoid-s21465" xml:space="preserve">1 IN plana quapiam ſuperficie, vt in charta regali, deſcribatur primo ex centro A. </s> <s xml:id="echoid-s21466" xml:space="preserve">quadrans A B C. <lb/></s> <s xml:id="echoid-s21467" xml:space="preserve"> <anchor type="note" xlink:label="note-0271-02a" xlink:href="note-0271-02"/> quantus ferè eſt in figura 15. </s> <s xml:id="echoid-s21468" xml:space="preserve">cuius arcus C B. </s> <s xml:id="echoid-s21469" xml:space="preserve">diuidatur (per primã prop. </s> <s xml:id="echoid-s21470" xml:space="preserve">noſtræ Sphæræ) in gr. <lb/></s> <s xml:id="echoid-s21471" xml:space="preserve">90. </s> <s xml:id="echoid-s21472" xml:space="preserve">initio facto in C. </s> <s xml:id="echoid-s21473" xml:space="preserve">intra quem alij duo ſint quadrantes ei proximi ex eodem centro A. </s> <s xml:id="echoid-s21474" xml:space="preserve">vt apparet in <lb/>figura. </s> <s xml:id="echoid-s21475" xml:space="preserve">Latus A C. </s> <s xml:id="echoid-s21476" xml:space="preserve">ſumatur pro linea horizontali; </s> <s xml:id="echoid-s21477" xml:space="preserve">in qua pars D E. </s> <s xml:id="echoid-s21478" xml:space="preserve">ſit tanta ferè quanta eſt in figura. </s> <s xml:id="echoid-s21479" xml:space="preserve"><lb/>dico ferè, quia quantitates hę ſunt ad libitum, comodiores tamen vt in figura. </s> <s xml:id="echoid-s21480" xml:space="preserve">obſeruaui totã A C. </s> <s xml:id="echoid-s21481" xml:space="preserve">di-<lb/>uiſam eſſe in partes 9. </s> <s xml:id="echoid-s21482" xml:space="preserve">æquales, quarum duæ ſunt in A D. </s> <s xml:id="echoid-s21483" xml:space="preserve">ſex in ipſa D E. </s> <s xml:id="echoid-s21484" xml:space="preserve">vna in E C. </s> <s xml:id="echoid-s21485" xml:space="preserve">Iam ab ipſa D E. </s> <s xml:id="echoid-s21486" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0271-03a" xlink:href="note-0271-03"/> ducantur 19. </s> <s xml:id="echoid-s21487" xml:space="preserve">paralelli, ſeu lineæ paralellæ æqualibus interuallis; </s> <s xml:id="echoid-s21488" xml:space="preserve">quot ſcilicet ſunt in Zodiaco, ſeu in <lb/>Anno Tabulæ altitudinum (quamuis non ſit neceſſe eſſe paralellas, nec ſpatia æqualia.) </s> <s xml:id="echoid-s21489" xml:space="preserve">Porrò hi pa-<lb/>ralelli habent miram connexionem cum paralellis Tabulæ altit. </s> <s xml:id="echoid-s21490" xml:space="preserve">in h@ſce enim paralellis notãdæ ſunt <lb/>altitudines paralellorum Tabulæ; </s> <s xml:id="echoid-s21491" xml:space="preserve">nam in paralello D F. </s> <s xml:id="echoid-s21492" xml:space="preserve">Horolog@j referente tropicum ♋. </s> <s xml:id="echoid-s21493" xml:space="preserve">notandæ <lb/>ſunt altitudines horarum poſitæ in verſu Tabulæ in quo eſt paralellus per initium ♋. </s> <s xml:id="echoid-s21494" xml:space="preserve">qui eſt tropi-<lb/>cus. </s> <s xml:id="echoid-s21495" xml:space="preserve">in ſecundo paralello notandæ ſunt altitudines ſecundi paralelli Tab. </s> <s xml:id="echoid-s21496" xml:space="preserve">qui eſt per gr. </s> <s xml:id="echoid-s21497" xml:space="preserve">15 0′. </s> <s xml:id="echoid-s21498" xml:space="preserve">♋. </s> <s xml:id="echoid-s21499" xml:space="preserve">quo-<lb/>cum ſunt in eodem verſu. </s> <s xml:id="echoid-s21500" xml:space="preserve">in tertio notandæ ſunt in altit. </s> <s xml:id="echoid-s21501" xml:space="preserve">tertij paralelli per gr. </s> <s xml:id="echoid-s21502" xml:space="preserve">24. </s> <s xml:id="echoid-s21503" xml:space="preserve">25′. </s> <s xml:id="echoid-s21504" xml:space="preserve">♋. </s> <s xml:id="echoid-s21505" xml:space="preserve">ſeu arcus <lb/>diurni horarum 15. </s> <s xml:id="echoid-s21506" xml:space="preserve">in quo Sol oritur hora 9. </s> <s xml:id="echoid-s21507" xml:space="preserve">& </s> <s xml:id="echoid-s21508" xml:space="preserve">ideo punctum primum horæ 9. </s> <s xml:id="echoid-s21509" xml:space="preserve">erit illud in linea ho-<lb/>rizontali, a quo ducitur tertius hic paralellus. </s> <s xml:id="echoid-s21510" xml:space="preserve">Quartus paralellus Horol. </s> <s xml:id="echoid-s21511" xml:space="preserve">competit paralello Tabulę <lb/>per initium Leonis. </s> <s xml:id="echoid-s21512" xml:space="preserve">& </s> <s xml:id="echoid-s21513" xml:space="preserve">fic deinceps de reliquis. </s> <s xml:id="echoid-s21514" xml:space="preserve">quapropter medius paralellus erit æquator. </s> <s xml:id="echoid-s21515" xml:space="preserve">vltimus <lb/>vero E G. </s> <s xml:id="echoid-s21516" xml:space="preserve">erit pro tropico ♑. </s> <s xml:id="echoid-s21517" xml:space="preserve">atq; </s> <s xml:id="echoid-s21518" xml:space="preserve">in eo notabuntur altitudines vltimi paralelli Tabulæ, quę ſcilicet <lb/>ſunt in vltimo verſu Tabulæ cum eo. </s> <s xml:id="echoid-s21519" xml:space="preserve">Vltimo obſeruandum eſt, vt paralelli per initia ſignorum ſint <lb/>lineæ cęteris craſſiores; </s> <s xml:id="echoid-s21520" xml:space="preserve">vt in ſigura. </s> <s xml:id="echoid-s21521" xml:space="preserve">primi eorum tres ſunt in ♋. </s> <s xml:id="echoid-s21522" xml:space="preserve">alij tres ſunt in ♌. </s> <s xml:id="echoid-s21523" xml:space="preserve">alij tres ſunt in ♍. <lb/></s> <s xml:id="echoid-s21524" xml:space="preserve">&</s> <s xml:id="echoid-s21525" xml:space="preserve">c. </s> <s xml:id="echoid-s21526" xml:space="preserve">vt ſuperpoſiti characteres ſignorum indicant.</s> <s xml:id="echoid-s21527" xml:space="preserve"/> </p> <div xml:id="echoid-div585" type="float" level="2" n="1"> <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">15. figu-<lb/>ra.</note> <note position="right" xlink:label="note-0271-03" xlink:href="note-0271-03a" xml:space="preserve">Parale@i <lb/>horologij.</note> </div> <p> <s xml:id="echoid-s21528" xml:space="preserve">2 Adſit regula ex tenui lamina, latere quadrantis paulò longior, ſimilis huic depictæ in figura 16. <lb/></s> <s xml:id="echoid-s21529" xml:space="preserve"> <anchor type="note" xlink:label="note-0271-04a" xlink:href="note-0271-04"/> cuius latus fiduciæ ſit A B. </s> <s xml:id="echoid-s21530" xml:space="preserve">in puncto A. </s> <s xml:id="echoid-s21531" xml:space="preserve">ſit paruum foramen. </s> <s xml:id="echoid-s21532" xml:space="preserve">vtile autem fuerit ſi latus A B. </s> <s xml:id="echoid-s21533" xml:space="preserve">ſit ſuper-<lb/>nè exangulatum (quod vulgò dicitur ſmuſſato) ſic enim linea fiduciæ A B. </s> <s xml:id="echoid-s21534" xml:space="preserve">exactius oſten det quæſi-<lb/> <anchor type="note" xlink:label="note-0271-05a" xlink:href="note-0271-05"/> ta puncta. </s> <s xml:id="echoid-s21535" xml:space="preserve">hęc regula ponenda eſt ſupra quadrantem, vt eius foramen A. </s> <s xml:id="echoid-s21536" xml:space="preserve">exactè congruat centro qua. <lb/></s> <s xml:id="echoid-s21537" xml:space="preserve">drantis: </s> <s xml:id="echoid-s21538" xml:space="preserve">aciculaq; </s> <s xml:id="echoid-s21539" xml:space="preserve">per foramen, centrumq; </s> <s xml:id="echoid-s21540" xml:space="preserve">quadrantis immiſſa, ita configatur, vt circa hoc centrum <lb/>linea fiduciæ moueri poſſit ad quemlibet quadrantis gradum.</s> <s xml:id="echoid-s21541" xml:space="preserve"/> </p> <div xml:id="echoid-div586" type="float" level="2" n="2"> <note position="right" xlink:label="note-0271-04" xlink:href="note-0271-04a" xml:space="preserve">Regula <lb/>mobilis.</note> <note position="right" xlink:label="note-0271-05" xlink:href="note-0271-05a" xml:space="preserve">Figura <lb/>16.</note> </div> <p> <s xml:id="echoid-s21542" xml:space="preserve">3 His paratis, primo loco, in Horologio deſcribendus eſt annus ex anno Tabulæ, ideſt characte-<lb/> <anchor type="note" xlink:label="note-0271-06a" xlink:href="note-0271-06"/> res ſignorum Zodiaci, & </s> <s xml:id="echoid-s21543" xml:space="preserve">Menſes ſuis ſignis correſpondentes, ſicuti correſpondentin Tabula. </s> <s xml:id="echoid-s21544" xml:space="preserve">Chara-<lb/>cteres igitur Signorum ponendi iuxta paralellos ſibi debitos, ſeu reſpondentes paralellis tabulæ ſibi <lb/>debitis: </s> <s xml:id="echoid-s21545" xml:space="preserve">hoc ordine: </s> <s xml:id="echoid-s21546" xml:space="preserve">ſupra lineam horizontalem ſint duo ſpatia in quorum inferiori ponantur ſex <lb/>characteres ♋. </s> <s xml:id="echoid-s21547" xml:space="preserve">♌. </s> <s xml:id="echoid-s21548" xml:space="preserve">♍, &</s> <s xml:id="echoid-s21549" xml:space="preserve">c in altero ponantur Menſes, & </s> <s xml:id="echoid-s21550" xml:space="preserve">partes Menſium reſpondentes Signis, & </s> <s xml:id="echoid-s21551" xml:space="preserve">par-<lb/>@ibus Signorum. </s> <s xml:id="echoid-s21552" xml:space="preserve">ſimiliter in interiori ſpatio, quod eſt inter duos arcus quadratum ponantur reliquo <lb/>ſex ſigna ♑. </s> <s xml:id="echoid-s21553" xml:space="preserve">♒, &</s> <s xml:id="echoid-s21554" xml:space="preserve">c. </s> <s xml:id="echoid-s21555" xml:space="preserve">& </s> <s xml:id="echoid-s21556" xml:space="preserve">in altero ſpatio exteriori ponantur eorum Menſes, & </s> <s xml:id="echoid-s21557" xml:space="preserve">partes Menſium, ſicuti <lb/>figura indicat. </s> <s xml:id="echoid-s21558" xml:space="preserve">ſic 22. </s> <s xml:id="echoid-s21559" xml:space="preserve">dies Iunij reſpondet tropico ♋, &</s> <s xml:id="echoid-s21560" xml:space="preserve">c. </s> <s xml:id="echoid-s21561" xml:space="preserve">ſicut annus tabulæ monet.</s> <s xml:id="echoid-s21562" xml:space="preserve"/> </p> <div xml:id="echoid-div587" type="float" level="2" n="3"> <note position="right" xlink:label="note-0271-06" xlink:href="note-0271-06a" xml:space="preserve">Annid@. <lb/>ſcripti@.</note> </div> <pb o="18" file="0272" n="277" rhead="TRACTATVS"/> <p> <s xml:id="echoid-s21563" xml:space="preserve">4 Poſtea ad horarum deſcriptionem ſic aggrediemur. </s> <s xml:id="echoid-s21564" xml:space="preserve">ſit v. </s> <s xml:id="echoid-s21565" xml:space="preserve">g. </s> <s xml:id="echoid-s21566" xml:space="preserve">deſcribenda hora nona Italica ad <lb/> <anchor type="note" xlink:label="note-0272-01a" xlink:href="note-0272-01"/> altit. </s> <s xml:id="echoid-s21567" xml:space="preserve">poli 44 {1/2}. </s> <s xml:id="echoid-s21568" xml:space="preserve">pro qua eriam conſtructa eſt tabula. </s> <s xml:id="echoid-s21569" xml:space="preserve">primo in ſecundo verſu tab. </s> <s xml:id="echoid-s21570" xml:space="preserve">in quo numeri hora-<lb/>rum Italicarum continentur, inuen@as 9. </s> <s xml:id="echoid-s21571" xml:space="preserve">poſtea deicende per columnam eius infra gr. </s> <s xml:id="echoid-s21572" xml:space="preserve">& </s> <s xml:id="echoid-s21573" xml:space="preserve">min. </s> <s xml:id="echoid-s21574" xml:space="preserve">& </s> <s xml:id="echoid-s21575" xml:space="preserve">inue-<lb/>nies numeros altitudinum Solis horæ nonę in tribus verſibus deſcendentibus, ſunt aute n hi gr. </s> <s xml:id="echoid-s21576" xml:space="preserve">3. </s> <s xml:id="echoid-s21577" xml:space="preserve">22′. <lb/></s> <s xml:id="echoid-s21578" xml:space="preserve"> <anchor type="note" xlink:label="note-0272-02a" xlink:href="note-0272-02"/> quæ eſt altitudo in tropico Cancri. </s> <s xml:id="echoid-s21579" xml:space="preserve">infra quos ſunt gr. </s> <s xml:id="echoid-s21580" xml:space="preserve">2. </s> <s xml:id="echoid-s21581" xml:space="preserve">6′. </s> <s xml:id="echoid-s21582" xml:space="preserve">ſcilicet altitudo in paralello per gr. </s> <s xml:id="echoid-s21583" xml:space="preserve">15. <lb/></s> <s xml:id="echoid-s21584" xml:space="preserve">Cancri. </s> <s xml:id="echoid-s21585" xml:space="preserve">infra quos ſunt gr. </s> <s xml:id="echoid-s21586" xml:space="preserve">0. </s> <s xml:id="echoid-s21587" xml:space="preserve">0′. </s> <s xml:id="echoid-s21588" xml:space="preserve">qui denotant in paralello per gr. </s> <s xml:id="echoid-s21589" xml:space="preserve">24. </s> <s xml:id="echoid-s21590" xml:space="preserve">25. </s> <s xml:id="echoid-s21591" xml:space="preserve">♋. </s> <s xml:id="echoid-s21592" xml:space="preserve">Solem nullam habe-<lb/>re altitudinem ſupra horizontem, ſed eſſe in ipſo horizonte. </s> <s xml:id="echoid-s21593" xml:space="preserve">quapropter initium horæ nonæ erit <lb/>etiam initium tertij paralelli ♋. </s> <s xml:id="echoid-s21594" xml:space="preserve">in Horologio, ſeu primum punctum horæ 9. </s> <s xml:id="echoid-s21595" xml:space="preserve">erit pariter punctum <lb/>primum huius paralelli in horizonte. </s> <s xml:id="echoid-s21596" xml:space="preserve">hoc puncto ſic animaduerſo, vt inuenias aliud punctum eiuſ-<lb/>dem horæ, aſcende ad ſecundum numerum 2. </s> <s xml:id="echoid-s21597" xml:space="preserve">6′. </s> <s xml:id="echoid-s21598" xml:space="preserve">& </s> <s xml:id="echoid-s21599" xml:space="preserve">ſecundum eum applica lineam fiduciæ regulæ <lb/>præcisè ad totidem gr. </s> <s xml:id="echoid-s21600" xml:space="preserve">& </s> <s xml:id="echoid-s21601" xml:space="preserve">min. </s> <s xml:id="echoid-s21602" xml:space="preserve">quadrantis, ideſt ad gr. </s> <s xml:id="echoid-s21603" xml:space="preserve">2. </s> <s xml:id="echoid-s21604" xml:space="preserve">6′. </s> <s xml:id="echoid-s21605" xml:space="preserve">& </s> <s xml:id="echoid-s21606" xml:space="preserve">vbi interim linea fiduciæ ſecuerit para-<lb/>rellum ſecundum ♋. </s> <s xml:id="echoid-s21607" xml:space="preserve">quadrantis, qui reſpondet pararello ſecundo tab. </s> <s xml:id="echoid-s21608" xml:space="preserve">per gr. </s> <s xml:id="echoid-s21609" xml:space="preserve">15. </s> <s xml:id="echoid-s21610" xml:space="preserve">o′. </s> <s xml:id="echoid-s21611" xml:space="preserve">Cancri, inibi pun-<lb/>ctum imprime. </s> <s xml:id="echoid-s21612" xml:space="preserve">poſtea vt tertium punctum habeas, aſſume numerum 3. </s> <s xml:id="echoid-s21613" xml:space="preserve">22′. </s> <s xml:id="echoid-s21614" xml:space="preserve">primi paralelli ♋. </s> <s xml:id="echoid-s21615" xml:space="preserve">tabulæ; </s> <s xml:id="echoid-s21616" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s21617" xml:space="preserve">ſecundum hunc numerum applica regulam totidem gradibus quadrantis, ſcilicet gr. </s> <s xml:id="echoid-s21618" xml:space="preserve">3. </s> <s xml:id="echoid-s21619" xml:space="preserve">22′. </s> <s xml:id="echoid-s21620" xml:space="preserve">& </s> <s xml:id="echoid-s21621" xml:space="preserve">vbi ab <lb/>ea ſecabitur paralellus primus ♋ quadrantis, inibi fac punctum. </s> <s xml:id="echoid-s21622" xml:space="preserve">iam ſi per tria hæc puncta in his tribus <lb/>paralellis notata, ducatur linea congruenter inſlexa, ea erit linea horæ 9. </s> <s xml:id="echoid-s21623" xml:space="preserve">ideſt quę horam 9. </s> <s xml:id="echoid-s21624" xml:space="preserve">indicabit, <lb/>cui propterea adſcribendus eſt numerus 9. </s> <s xml:id="echoid-s21625" xml:space="preserve">Percommodum autem eſt, incipere (vti nunc fecimus) a <lb/> <anchor type="note" xlink:label="note-0272-03a" xlink:href="note-0272-03"/> numeris columnæ imis, & </s> <s xml:id="echoid-s21626" xml:space="preserve">paulatim ad ſuperiores aſcendere, ac ſecundum eorum ſingulos reperire <lb/>puncta in paralellis quadrantis. </s> <s xml:id="echoid-s21627" xml:space="preserve">hac enim ratione melius numerantur gradus, & </s> <s xml:id="echoid-s21628" xml:space="preserve">minuta quadrantis, <lb/>& </s> <s xml:id="echoid-s21629" xml:space="preserve">manifeſtè apparet quinam ex paralellis Horol. </s> <s xml:id="echoid-s21630" xml:space="preserve">ſit pungendus; </s> <s xml:id="echoid-s21631" xml:space="preserve">& </s> <s xml:id="echoid-s21632" xml:space="preserve">puncta iam notata, per regulam <lb/>nec tegunrur, nec delentur ab ea, ſicuti vſus edocet.</s> <s xml:id="echoid-s21633" xml:space="preserve"/> </p> <div xml:id="echoid-div588" type="float" level="2" n="4"> <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Horarũ <lb/>deſcripsio</note> <note position="left" xlink:label="note-0272-02" xlink:href="note-0272-02a" xml:space="preserve">Horæ 9.</note> <note position="left" xlink:label="note-0272-03" xlink:href="note-0272-03a" xml:space="preserve">Quoordi <lb/>@@.</note> </div> <p> <s xml:id="echoid-s21634" xml:space="preserve">Eodem modo agendum eſt pro hora 10. </s> <s xml:id="echoid-s21635" xml:space="preserve">ideſt, ex columna ſub hora 10. </s> <s xml:id="echoid-s21636" xml:space="preserve">accipiendæ ſunt altitu-<lb/> <anchor type="note" xlink:label="note-0272-04a" xlink:href="note-0272-04"/> dines, & </s> <s xml:id="echoid-s21637" xml:space="preserve">ſecundum eas applicata regula gradibus quadrantis, notandæ ſunt ſectiones eius cum para-<lb/>lellis horologij reſpondentibus p@raleliis tabulæ per quas ſectiones ducta linea congruenter flexa, ea <lb/>erit hora 10. </s> <s xml:id="echoid-s21638" xml:space="preserve">cui ideo adſcribendum eſt 10. </s> <s xml:id="echoid-s21639" xml:space="preserve">vti figura monet. </s> <s xml:id="echoid-s21640" xml:space="preserve">codem modo cum reliquis agendum. <lb/></s> <s xml:id="echoid-s21641" xml:space="preserve">ſolent nonnulli horas matutinas notare lineis continuis, veſpertinas vero lineis punctualibus vt figu-<lb/>ra oſtendit quod tamen non eſt neceſſe.</s> <s xml:id="echoid-s21642" xml:space="preserve"/> </p> <div xml:id="echoid-div589" type="float" level="2" n="5"> <note position="left" xlink:label="note-0272-04" xlink:href="note-0272-04a" xml:space="preserve">De ca@e-<lb/>ris horis. <lb/>Hora 10.</note> </div> <p> <s xml:id="echoid-s21643" xml:space="preserve">5 Poterit autem hoc examen adhiberi; </s> <s xml:id="echoid-s21644" xml:space="preserve">nam ſi rectè operatus fueris, horæ pomeridianæ, & </s> <s xml:id="echoid-s21645" xml:space="preserve">ante-<lb/> <anchor type="note" xlink:label="note-0272-05a" xlink:href="note-0272-05"/> meridianæ ſe mutuo ſecabunt in paralellis horarum inſignarum, ſeu in quibus Sol orirur hora inte-<lb/>gra: </s> <s xml:id="echoid-s21646" xml:space="preserve">ſic vides in figura hora n 23. </s> <s xml:id="echoid-s21647" xml:space="preserve">ſecare horam 10. </s> <s xml:id="echoid-s21648" xml:space="preserve">in para. </s> <s xml:id="echoid-s21649" xml:space="preserve">ello horarum integrarum 15. </s> <s xml:id="echoid-s21650" xml:space="preserve">ſeu quo Sol <lb/>oritur hora 9. </s> <s xml:id="echoid-s21651" xml:space="preserve">qui eſt tertius ♋. </s> <s xml:id="echoid-s21652" xml:space="preserve">pariter eandem 23. </s> <s xml:id="echoid-s21653" xml:space="preserve">ſecare 11. </s> <s xml:id="echoid-s21654" xml:space="preserve">in paralello, quo Sol oritur hora 10. </s> <s xml:id="echoid-s21655" xml:space="preserve">& </s> <s xml:id="echoid-s21656" xml:space="preserve"><lb/>ſecare 12. </s> <s xml:id="echoid-s21657" xml:space="preserve">in paralello quo Sol oritur hora 11. </s> <s xml:id="echoid-s21658" xml:space="preserve">& </s> <s xml:id="echoid-s21659" xml:space="preserve">ſecare 13. </s> <s xml:id="echoid-s21660" xml:space="preserve">in paralello ortus hora 12. </s> <s xml:id="echoid-s21661" xml:space="preserve">& </s> <s xml:id="echoid-s21662" xml:space="preserve">ſecare 14. </s> <s xml:id="echoid-s21663" xml:space="preserve">in <lb/>paralello ortus horæ 13. </s> <s xml:id="echoid-s21664" xml:space="preserve">& </s> <s xml:id="echoid-s21665" xml:space="preserve">ſic deinceps, vt videre eſt in figura. </s> <s xml:id="echoid-s21666" xml:space="preserve">quæ obſeruatio plurimum iuuat, non <lb/>ſolum ad horologia recte, ſed etiam facilius deſcribenda: </s> <s xml:id="echoid-s21667" xml:space="preserve">eadem cnim puncta iam inuenta in præ-<lb/>dictis paralellis pro horis matutinis inſeruiunt etiam pro veſpertinis. </s> <s xml:id="echoid-s21668" xml:space="preserve">ſic vides pro hora 23. </s> <s xml:id="echoid-s21669" xml:space="preserve">inuenta <lb/>iam fuiſſe prædicta ſeptem puncta. </s> <s xml:id="echoid-s21670" xml:space="preserve">ratio huius eſt quia horæ veſpertinæ @n prædictis paralellis habent <lb/>in tabula altitudines eaſdem cum altitudinibus horarũ matutinarum; </s> <s xml:id="echoid-s21671" xml:space="preserve">vt cõſideranti tabulam patebit.</s> <s xml:id="echoid-s21672" xml:space="preserve"/> </p> <div xml:id="echoid-div590" type="float" level="2" n="6"> <note position="left" xlink:label="note-0272-05" xlink:href="note-0272-05a" xml:space="preserve">Examen.</note> </div> <p> <s xml:id="echoid-s21673" xml:space="preserve">6 Linea meridiana nõ videtur neceſſaria, etenim ſi deſcribatur incedit tam propè ima lineamen-<lb/> <anchor type="note" xlink:label="note-0272-06a" xlink:href="note-0272-06"/> ta horarum 16. </s> <s xml:id="echoid-s21674" xml:space="preserve">17. </s> <s xml:id="echoid-s21675" xml:space="preserve">18. </s> <s xml:id="echoid-s21676" xml:space="preserve">19. </s> <s xml:id="echoid-s21677" xml:space="preserve">20. </s> <s xml:id="echoid-s21678" xml:space="preserve">vt ea paſſim contingat, ac proinde confuſionem pariat. </s> <s xml:id="echoid-s21679" xml:space="preserve">Quare ipſa prę-<lb/>dictarum horarum ima lineamenta ſatis poterunt indicare meridiem. </s> <s xml:id="echoid-s21680" xml:space="preserve">Veruntamen (ſi libuerit) eam <lb/>deſcribere per altitudines meridianas in propr a columna exiſtentes, eodem modo applicando regu-<lb/>lam quadranti ſecundum ſingulas altitudines, no@ãdo ſectiones eius cum paralellis horologij reſpon-<lb/>dentibus paralellis tabulæ. </s> <s xml:id="echoid-s21681" xml:space="preserve">ſed ea poſtea pingenda è vel colore, vel lineamento ab alijs diuerſo ad <lb/>confuſionem tollendam.</s> <s xml:id="echoid-s21682" xml:space="preserve"/> </p> <div xml:id="echoid-div591" type="float" level="2" n="7"> <note position="left" xlink:label="note-0272-06" xlink:href="note-0272-06a" xml:space="preserve">Linea <lb/>meridia-<lb/>na.</note> </div> <p> <s xml:id="echoid-s21683" xml:space="preserve">7 Alij aliter hanc horarum deſcriptionem ſic inſtituunt; </s> <s xml:id="echoid-s21684" xml:space="preserve">nam vt in linea horizontali ſigant pun-<lb/> <anchor type="note" xlink:label="note-0272-07a" xlink:href="note-0272-07"/> cta extremorum paralellorum, ſeu tropicorum, primo accipiunt ex tabula maximam omnium altitu-<lb/>dinem, quæ ſunt in tropico cancri in verſu tabulæ in quo eſt tropicus cancri, quæ eſt gr. </s> <s xml:id="echoid-s21685" xml:space="preserve">68. </s> <s xml:id="echoid-s21686" xml:space="preserve">39′. </s> <s xml:id="echoid-s21687" xml:space="preserve">ſub <lb/>hora, ibidem a@q; </s> <s xml:id="echoid-s21688" xml:space="preserve">in quadrante applicata regula repertis grad. </s> <s xml:id="echoid-s21689" xml:space="preserve">68. </s> <s xml:id="echoid-s21690" xml:space="preserve">39. </s> <s xml:id="echoid-s21691" xml:space="preserve">& </s> <s xml:id="echoid-s21692" xml:space="preserve">ex puncto F. </s> <s xml:id="echoid-s21693" xml:space="preserve">vbi regula ſe-<lb/>cuerit quadrantem interiorem ducunt lineam rectam F D. </s> <s xml:id="echoid-s21694" xml:space="preserve">normalem horizontali A C. </s> <s xml:id="echoid-s21695" xml:space="preserve">eamque ſta-<lb/>@uunt eſſe para@ellũ primum ſeu trop. </s> <s xml:id="echoid-s21696" xml:space="preserve">♋. </s> <s xml:id="echoid-s21697" xml:space="preserve">pariter accepta maxima altitudine tropici Capricorni, quę <lb/>eſt gr. </s> <s xml:id="echoid-s21698" xml:space="preserve">21. </s> <s xml:id="echoid-s21699" xml:space="preserve">55′. </s> <s xml:id="echoid-s21700" xml:space="preserve">ſub hora 20. </s> <s xml:id="echoid-s21701" xml:space="preserve">ideo ex puncto G. </s> <s xml:id="echoid-s21702" xml:space="preserve">quadrantis interioris terminante gr. </s> <s xml:id="echoid-s21703" xml:space="preserve">21. </s> <s xml:id="echoid-s21704" xml:space="preserve">55′. </s> <s xml:id="echoid-s21705" xml:space="preserve">eriguntalte-<lb/>ram lineam G E. </s> <s xml:id="echoid-s21706" xml:space="preserve">normalter ad horizontalẽ A C. </s> <s xml:id="echoid-s21707" xml:space="preserve">eamq; </s> <s xml:id="echoid-s21708" xml:space="preserve">aſiumunt pro paralello ſeu tropico ♑. </s> <s xml:id="echoid-s21709" xml:space="preserve">hacq; <lb/></s> <s xml:id="echoid-s21710" xml:space="preserve">ratione partem D E. </s> <s xml:id="echoid-s21711" xml:space="preserve">lineæ horizontalis aſſumũt pro loco omnium paralellorum: </s> <s xml:id="echoid-s21712" xml:space="preserve">in qua eorum loca <lb/>non ad æqualia interualla, ſed habita ratione declinationum paralellorum, ſic reperiunt.</s> <s xml:id="echoid-s21713" xml:space="preserve"/> </p> <div xml:id="echoid-div592" type="float" level="2" n="8"> <note position="left" xlink:label="note-0272-07" xlink:href="note-0272-07a" xml:space="preserve">Al@ter.</note> </div> <p> <s xml:id="echoid-s21714" xml:space="preserve">8 Conſtruunt huius rei gratia Radiarium, quod contineat declinationes omnium 19. </s> <s xml:id="echoid-s21715" xml:space="preserve">paralello-<lb/> <anchor type="note" xlink:label="note-0272-08a" xlink:href="note-0272-08"/> rum tabulæ, quale eſt preſens. </s> <s xml:id="echoid-s21716" xml:space="preserve">accipi autem poſſunt hæ declinationes ex Tabula declinat. </s> <s xml:id="echoid-s21717" xml:space="preserve">quæ eſt in <lb/>Sphæra Clauij, eſt enim valde copioſa. </s> <s xml:id="echoid-s21718" xml:space="preserve">in hoc Radiario accomodant l@neam D E. </s> <s xml:id="echoid-s21719" xml:space="preserve">quæ ſit æqualis alte-<lb/> <anchor type="note" xlink:label="note-0272-09a" xlink:href="note-0272-09"/> ri lineæ D E. </s> <s xml:id="echoid-s21720" xml:space="preserve">horizontali quadrantis, ſitq; </s> <s xml:id="echoid-s21721" xml:space="preserve">normalis cum paralello omnium medio, qui eſt ♎, & </s> <s xml:id="echoid-s21722" xml:space="preserve">♈. <lb/></s> <s xml:id="echoid-s21723" xml:space="preserve">iam ijſdem punctis, & </s> <s xml:id="echoid-s21724" xml:space="preserve">interuallis quibus ſecatur a paralellis Radiarij, ijſdem omnino diuidunt D E. </s> <s xml:id="echoid-s21725" xml:space="preserve"><lb/>quadrantis. </s> <s xml:id="echoid-s21726" xml:space="preserve">atq; </s> <s xml:id="echoid-s21727" xml:space="preserve">ex punctis diuiſionum ducunt reliquos omnes paralellos quadrantis, vt in figura 17. </s> <s xml:id="echoid-s21728" xml:space="preserve"><lb/>apparent. </s> <s xml:id="echoid-s21729" xml:space="preserve">quibus peractis horarum deſcriptionem peragunt per altitudines tabulæ, & </s> <s xml:id="echoid-s21730" xml:space="preserve">per gr. </s> <s xml:id="echoid-s21731" xml:space="preserve">qua-<lb/>drantis, notando puncta horaria in hiſce paralellis ſicuti in ſuperioribus. </s> <s xml:id="echoid-s21732" xml:space="preserve">quę puncta lineis vniformi-<lb/>ter inflexis coniuncta efficiunt lineas horarias, & </s> <s xml:id="echoid-s21733" xml:space="preserve">quidem pulchriores, quod non tam diformiter ſi- <pb o="19" file="0273" n="278" rhead="DE HOROLOGIIS."/> nuoſas ſicuti ſuperiores. </s> <s xml:id="echoid-s21734" xml:space="preserve">atque hoc vnum lucri, ſeu pulchritudinis bonum aſſequuntur. </s> <s xml:id="echoid-s21735" xml:space="preserve">huius exem-<lb/>plum vides in adiecta figura 18′. </s> <s xml:id="echoid-s21736" xml:space="preserve">Alij vtuntur alia tabula, a noſtra, in qua calculatæ ſunt altitudines <lb/> <anchor type="note" xlink:label="note-0273-01a" xlink:href="note-0273-01"/> per ſingulas graduum decurias ſignorum Zodiaci; </s> <s xml:id="echoid-s21737" xml:space="preserve">breuius quidem, ſed non exactius horologia con-<lb/>ſtruunt, de qua tabula in fine breuiter dicam.</s> <s xml:id="echoid-s21738" xml:space="preserve"/> </p> <div xml:id="echoid-div593" type="float" level="2" n="9"> <note position="left" xlink:label="note-0272-08" xlink:href="note-0272-08a" xml:space="preserve">17. figu-<lb/>ra.</note> <note position="left" xlink:label="note-0272-09" xlink:href="note-0272-09a" xml:space="preserve">Radiarij.</note> <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">18. figu-<lb/>ra 2. qua <lb/>drantis.</note> </div> <p> <s xml:id="echoid-s21739" xml:space="preserve">Deſcripſis Anno, & </s> <s xml:id="echoid-s21740" xml:space="preserve">horis, ponantur an aliquo ſpatio vacuo hæc, Ad lat. </s> <s xml:id="echoid-s21741" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s21742" xml:space="preserve">vna cum quapiam <lb/> <anchor type="note" xlink:label="note-0273-02a" xlink:href="note-0273-02"/> ſententia morali de breuitate vitæ, de fuga temporis, vel alia.</s> <s xml:id="echoid-s21743" xml:space="preserve"/> </p> <div xml:id="echoid-div594" type="float" level="2" n="10"> <note position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">De alia <lb/>tab. altit.</note> </div> <p> <s xml:id="echoid-s21744" xml:space="preserve">9 Tandem deſignandæ ſunt duæ pinnulæ ciuſdem altitudinis, vna apud A, altera apud B. </s> <s xml:id="echoid-s21745" xml:space="preserve">Poſtea <lb/>hæc omnia lineamenta tranſcribantur in aliquam mundam ſaperficiem ſolidiorem; </s> <s xml:id="echoid-s21746" xml:space="preserve">vel ipſum hoc <lb/>horologium tali ſuperficiei agglutinetur. </s> <s xml:id="echoid-s21747" xml:space="preserve">omnia autem quæ ſunt extra quadrantẽ præter Annum, & </s> <s xml:id="echoid-s21748" xml:space="preserve"><lb/>pinnulas circuncidantur. </s> <s xml:id="echoid-s21749" xml:space="preserve">demum ex centro A, tenui filo paulo @ongiori quam latus quadrantis perpen-<lb/>diculum pendeat. </s> <s xml:id="echoid-s21750" xml:space="preserve">eritq; </s> <s xml:id="echoid-s21751" xml:space="preserve">abſolutum horologium viatorium, ſeu mobile de cuius vſu modò dicendum.</s> <s xml:id="echoid-s21752" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21753" xml:space="preserve">10 Sciat lector poſſe per præmiſſam ad lat. </s> <s xml:id="echoid-s21754" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s21755" xml:space="preserve">altitudinum tabulam, deſcribi eodem modo ci-<lb/>tra ſenſibilem errorem horologia ad lat. </s> <s xml:id="echoid-s21756" xml:space="preserve">44. </s> <s xml:id="echoid-s21757" xml:space="preserve">& </s> <s xml:id="echoid-s21758" xml:space="preserve">45. </s> <s xml:id="echoid-s21759" xml:space="preserve">vel quod idem eſt, Horologium ipſum deſcriptum <lb/>ad lat. </s> <s xml:id="echoid-s21760" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s21761" xml:space="preserve">inſeruire etiam pro lat. </s> <s xml:id="echoid-s21762" xml:space="preserve">44. </s> <s xml:id="echoid-s21763" xml:space="preserve">& </s> <s xml:id="echoid-s21764" xml:space="preserve">45.</s> <s xml:id="echoid-s21765" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div596" type="section" level="1" n="427"> <head xml:id="echoid-head452" style="it" xml:space="preserve">Varij vſus Horologij in Quadranti deſcripti; quorum nonnulli noui ſunt, <lb/>ac valde vtiles. Cap. II.</head> <p> <s xml:id="echoid-s21766" xml:space="preserve">1 VT rationem vſuum tradendorum intelligamus, conſiderandum eſt in primis, qua ratione Qua-<lb/> <anchor type="note" xlink:label="note-0273-03a" xlink:href="note-0273-03"/> drans ſit col ocandus aſtronomicè, vt eo recte vtamur. </s> <s xml:id="echoid-s21767" xml:space="preserve">Primo igitur quoniam latus eius A C. </s> <s xml:id="echoid-s21768" xml:space="preserve">re-<lb/>fert horizontem, indubium eſt, ipſum ſtatuendũ eſſe horizonti paralellum 2. </s> <s xml:id="echoid-s21769" xml:space="preserve">quia in eo Horologium <lb/>conſtructum eſt per altitudines Solis vt ſcilicet ex altitudine Solis horam cognoſcamus, ideo vt So-<lb/>lis altitudinem quouis momento temporis habeamus, ex centro A, exeat normaliter tenuis ſtylus <lb/>vel arcus A I, cuiuſuis longitudinis. </s> <s xml:id="echoid-s21770" xml:space="preserve">poſtea Sole ſplendente Quadrantem manibus tenens, latere <lb/>A C, ſuperius exiſtente, latere A B. </s> <s xml:id="echoid-s21771" xml:space="preserve">deorſum tendente perpendiculoq; </s> <s xml:id="echoid-s21772" xml:space="preserve">liberè congruente (ſic enim <lb/>A C, erit horizonti æquidiſtans) obuertemus in Solem, ita vt radij eius vix illuminent faciem Horo-<lb/>logij, ſeu eam radant. </s> <s xml:id="echoid-s21773" xml:space="preserve">in quo ſitu erit planum eius in circulo Solis verticali, & </s> <s xml:id="echoid-s21774" xml:space="preserve">vmbra A H, ſtyli A I, <lb/>proiecta in faciem Horologij tantum cadet infra horizontalem lineam A C, quantum Sol ſupra ho-<lb/>rizontem eleuabitur, ſecabitq; </s> <s xml:id="echoid-s21775" xml:space="preserve">arcum quadrantis ſecundum gradus altitudinis Solis. </s> <s xml:id="echoid-s21776" xml:space="preserve">ſecabit etiã om-<lb/>nes paralellos, quare & </s> <s xml:id="echoid-s21777" xml:space="preserve">paralellum currentem, ideſt debitum diei eurrenti; </s> <s xml:id="echoid-s21778" xml:space="preserve">ſeu qui eſt è regione diei <lb/>currentis in anno Horologij; </s> <s xml:id="echoid-s21779" xml:space="preserve">ſecabitque illum in eo puncto, in quo ſecabuntur a regula applica a tali <lb/>altitudini debitæ tali horæ tabulæ, dum Horologium conſtruebatur: </s> <s xml:id="echoid-s21780" xml:space="preserve">atque idcirco linea horaria illi <lb/>puncto propior matutina ſi mane, veſpertina ſi veſpere, labentem horam neceſſariò indicabit, v. </s> <s xml:id="echoid-s21781" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s21782" xml:space="preserve">ſit diei 18. </s> <s xml:id="echoid-s21783" xml:space="preserve">Auguſti poſt meridiem indaganda hora in tali temporis momento, quo collocato aſtro-<lb/>nomicè quadrante, vti docuimus, Sole S. </s> <s xml:id="echoid-s21784" xml:space="preserve">ſplendente vmbra A H. </s> <s xml:id="echoid-s21785" xml:space="preserve">ſtyli A I. </s> <s xml:id="echoid-s21786" xml:space="preserve">ſecans omnes paralel-<lb/>los, ſecet etiam paralellum currentem, ideſt debitum diei 18. </s> <s xml:id="echoid-s21787" xml:space="preserve">Auguſti (qui dies quamuis non ſit in <lb/>quadrante expreſſus, tamen ſecundum iudicij æſtimationem, cum ſit poſt 14. </s> <s xml:id="echoid-s21788" xml:space="preserve">diem ibi expreſſum <lb/>per paralellum 6. </s> <s xml:id="echoid-s21789" xml:space="preserve">qui eſt tertius ♌. </s> <s xml:id="echoid-s21790" xml:space="preserve">imaginor eum paulo poſt 14. </s> <s xml:id="echoid-s21791" xml:space="preserve">ſimiliter imaginor paralellum corre-<lb/>ſpondentem huic diei, & </s> <s xml:id="echoid-s21792" xml:space="preserve">conſequenter ſatis propinquum paralello tertio ♌. </s> <s xml:id="echoid-s21793" xml:space="preserve">ad dexteram) ſecet au-<lb/>tem in puncto K. </s> <s xml:id="echoid-s21794" xml:space="preserve">quod cadat inter 4. </s> <s xml:id="echoid-s21795" xml:space="preserve">lineas horarias, ideſt inter 11. </s> <s xml:id="echoid-s21796" xml:space="preserve">& </s> <s xml:id="echoid-s21797" xml:space="preserve">12. </s> <s xml:id="echoid-s21798" xml:space="preserve">necnon inter 22. </s> <s xml:id="echoid-s21799" xml:space="preserve">& </s> <s xml:id="echoid-s21800" xml:space="preserve">23. </s> <s xml:id="echoid-s21801" xml:space="preserve">cum <lb/>vero priores duæ ſint matutinæ, tempus autem præſens ſit veſpertinum, eæ non facient ad rem; </s> <s xml:id="echoid-s21802" xml:space="preserve">ideo <lb/>ſecundæ tantum inſeruient, ideoq; </s> <s xml:id="echoid-s21803" xml:space="preserve">indicatur elapſam eſie horam 22. </s> <s xml:id="echoid-s21804" xml:space="preserve">& </s> <s xml:id="echoid-s21805" xml:space="preserve">quidem paulò ante, cum pun-<lb/>ctum K. </s> <s xml:id="echoid-s21806" xml:space="preserve">paululum cadat ſupra 22. </s> <s xml:id="echoid-s21807" xml:space="preserve">ſi dies currens fuiſſet 14. </s> <s xml:id="echoid-s21808" xml:space="preserve">aſſumendus fuiſſet paralellus tertius ♌. </s> <s xml:id="echoid-s21809" xml:space="preserve">qui <lb/>ſectus fuiſſet ab vmbra propè K. </s> <s xml:id="echoid-s21810" xml:space="preserve">indicaſſetq; </s> <s xml:id="echoid-s21811" xml:space="preserve">horam ferè eandem.</s> <s xml:id="echoid-s21812" xml:space="preserve"/> </p> <div xml:id="echoid-div596" type="float" level="2" n="1"> <note position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">Primus <lb/>modus <lb/>per vm-<lb/>bram ſty-<lb/>li.</note> </div> <p> <s xml:id="echoid-s21813" xml:space="preserve">Si aliunde non conſtaret tempus eſſe pomeridianum, obſertiandum eſſet bis ex vmbra ſtyli (inter-<lb/> <anchor type="note" xlink:label="note-0273-04a" xlink:href="note-0273-04"/> poſita aliqua temporis mora) an Solis altitudo creſcat, vel decreſcat; </s> <s xml:id="echoid-s21814" xml:space="preserve">qua creſcente eſt matutinum, <lb/>decreſcente v@ſpertinum: </s> <s xml:id="echoid-s21815" xml:space="preserve">circa meridiem vero inſenſibiliter variatur.</s> <s xml:id="echoid-s21816" xml:space="preserve"/> </p> <div xml:id="echoid-div597" type="float" level="2" n="2"> <note position="right" xlink:label="note-0273-04" xlink:href="note-0273-04a" xml:space="preserve">An tem-<lb/>pus ſit an <lb/>remerid. <lb/>vel pome. <lb/>merid.</note> </div> <p> <s xml:id="echoid-s21817" xml:space="preserve">Nonnulli pro ſtylo, vtuntur pinnacidio A. </s> <s xml:id="echoid-s21818" xml:space="preserve">normaliter eleuato cum vſui fuerit, obſeruantes vm-<lb/>bram lateris eius A L. </s> <s xml:id="echoid-s21819" xml:space="preserve">quod centro A. </s> <s xml:id="echoid-s21820" xml:space="preserve">coniungitur pro vmbra ſtyli, neq; </s> <s xml:id="echoid-s21821" xml:space="preserve">adhibent perpendiculum, <lb/>ſed tantum ſecundum ſenſus æſtimationem ſtatuunt latus A C. </s> <s xml:id="echoid-s21822" xml:space="preserve">ad libeliã, ſeu horizonti æquidiſtans.</s> <s xml:id="echoid-s21823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21824" xml:space="preserve">Atq; </s> <s xml:id="echoid-s21825" xml:space="preserve">hic primus eſt modus, magis quidem naturalis quam ſequens: </s> <s xml:id="echoid-s21826" xml:space="preserve">ſequens tamen eſt magis vtilis, <lb/>vt mox patebit. </s> <s xml:id="echoid-s21827" xml:space="preserve">qua propter in eo exponam omnes vſus, tam ei propius quam ſuperiori, atque etiam <lb/>communis alteri quadrantiiam vſitato.</s> <s xml:id="echoid-s21828" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div599" type="section" level="1" n="428"> <head xml:id="echoid-head453" style="it" xml:space="preserve">De ſecundo modo præstantiori vtendi Quadrante per perpendiculum, <lb/>& pinnulas.</head> <p> <s xml:id="echoid-s21829" xml:space="preserve">1. </s> <s xml:id="echoid-s21830" xml:space="preserve">REquirit hic modus binas pinnulas, & </s> <s xml:id="echoid-s21831" xml:space="preserve">perpendiculum, non enim obſeruat vmbram ſtyli, ſed <lb/> <anchor type="note" xlink:label="note-0273-05a" xlink:href="note-0273-05"/> loco vmbræ filum perpendiculi conſiderat. </s> <s xml:id="echoid-s21832" xml:space="preserve">& </s> <s xml:id="echoid-s21833" xml:space="preserve">propterea in vſu eius requirit diuerſam qua-<lb/>drantis poſitionem a ſuperiori, nam collocandus eſt in verticali Solis, ita vt centrum A. </s> <s xml:id="echoid-s21834" xml:space="preserve">vergat in So-<lb/>lem, & </s> <s xml:id="echoid-s21835" xml:space="preserve">latus A B. </s> <s xml:id="echoid-s21836" xml:space="preserve">pinnularum congruat radio Solis. </s> <s xml:id="echoid-s21837" xml:space="preserve">quod fiet, ſi obuerſo in ſplendentem Solem cen- <pb o="20" file="0274" n="279" rhead="TRACTATVS"/> tro A. </s> <s xml:id="echoid-s21838" xml:space="preserve">ſiue pinnula ad A. </s> <s xml:id="echoid-s21839" xml:space="preserve">alteram pinnulam eleuemus, aut deprimamus quouſq; </s> <s xml:id="echoid-s21840" xml:space="preserve">vmbra pinnulæ ad <lb/>A. </s> <s xml:id="echoid-s21841" xml:space="preserve">obumbret adæquatè totam pinnulam B. </s> <s xml:id="echoid-s21842" xml:space="preserve">(citius fit excipiendo vtriuſque pinnulæ vmbram in pal-<lb/>mam manus ei proximam, donec ambæ vmbræ in ea ſint æquè altæ) tunc enim radius Solis radit <lb/>vtriuſq, pinnulæ ſummitatem, latuſque A B. </s> <s xml:id="echoid-s21843" xml:space="preserve">ei congruens eandem eleuationem ſupra horizontem <lb/>cum Sole obtinebit; </s> <s xml:id="echoid-s21844" xml:space="preserve">quod in omni operatione neceſlarium eſt. </s> <s xml:id="echoid-s21845" xml:space="preserve">iam manente quadrante in hac eleua-<lb/>tione, interim perpendiculum liberè pendens radat oportet faciem Horolog j, ſicque tunc exactè <lb/>erit in verticali Solis, & </s> <s xml:id="echoid-s21846" xml:space="preserve">ideo filum ſecans omnes paralellos ſecabit arcum quadrantis ſecundum gra-<lb/>dus altitudinis Solis, perinde ac in primo ſecabat vmbra ſtyli. </s> <s xml:id="echoid-s21847" xml:space="preserve">cuius rationem ſic percip@emus. </s> <s xml:id="echoid-s21848" xml:space="preserve">ſtatua-<lb/> <anchor type="note" xlink:label="note-0274-01a" xlink:href="note-0274-01"/> tur latus A B. </s> <s xml:id="echoid-s21849" xml:space="preserve">pinnularum horizonti paralellum, vti oporteret oriente Sole; </s> <s xml:id="echoid-s21850" xml:space="preserve">tunc latus A C. </s> <s xml:id="echoid-s21851" xml:space="preserve">congruet <lb/>filo perpendiculi, & </s> <s xml:id="echoid-s21852" xml:space="preserve">ſi ſecundum ſucceſſiuam Solis eleuationem pariter eleuetur latus A B. </s> <s xml:id="echoid-s21853" xml:space="preserve">conſe-<lb/>quenter tantundem latus A C. </s> <s xml:id="echoid-s21854" xml:space="preserve">recedet a ſtabili perpendiculo; </s> <s xml:id="echoid-s21855" xml:space="preserve">quantum igitur radius eleuabitur, tan-<lb/>tum diſtabit filum à latere A C. </s> <s xml:id="echoid-s21856" xml:space="preserve">quantum ſcilicet diſtabat etiam vmbra ſtyli in priori modo. </s> <s xml:id="echoid-s21857" xml:space="preserve">quare ne-<lb/>ceſſario eadem omnia filum hic, quæ ibi vmbra, manifeſtabit. </s> <s xml:id="echoid-s21858" xml:space="preserve">cum ergo eadem præſtet hic hlum, <lb/>quod illic vmbra, eius vtilitates breuiter percurramus.</s> <s xml:id="echoid-s21859" xml:space="preserve"/> </p> <div xml:id="echoid-div599" type="float" level="2" n="1"> <note position="right" xlink:label="note-0273-05" xlink:href="note-0273-05a" xml:space="preserve">Secisndus <lb/>modus <lb/>per per-<lb/>pendicu-<lb/>lum.</note> <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">D@mon-<lb/>stratio <lb/>huius ſe-<lb/>cũdi mo-<lb/>di.</note> </div> <p> <s xml:id="echoid-s21860" xml:space="preserve">11. </s> <s xml:id="echoid-s21861" xml:space="preserve">Quarum prima, ac præcipua fit horam currentem cognoſcere. </s> <s xml:id="echoid-s21862" xml:space="preserve">quam quidem ſplendente So-<lb/> <anchor type="note" xlink:label="note-0274-02a" xlink:href="note-0274-02"/> le inueniemus, ſi (vti modo dictum eſt) ſtatuamus Horologium, obſeruemuſq; </s> <s xml:id="echoid-s21863" xml:space="preserve">vbinam filum ſecet <lb/>currentem paralellum; </s> <s xml:id="echoid-s21864" xml:space="preserve">inde enim eadem ratione qua ſupra per vmbram ſ@yli horam labentem co-<lb/>gnoſcemus.</s> <s xml:id="echoid-s21865" xml:space="preserve"/> </p> <div xml:id="echoid-div600" type="float" level="2" n="2"> <note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">Cognoſce <lb/>re horam <lb/>laben@e.</note> </div> <p> <s xml:id="echoid-s21866" xml:space="preserve">Secunda eſt, eadem opera, qua horam cognoſcimus, cognoſcere etiam altitud nem Solis ſupra ho-<lb/> <anchor type="note" xlink:label="note-0274-03a" xlink:href="note-0274-03"/> rizontem, hanc enim indicabit filum ſecans arcum quadrantis ſecundum gradum ſolaris al@i@udinis.</s> <s xml:id="echoid-s21867" xml:space="preserve"/> </p> <div xml:id="echoid-div601" type="float" level="2" n="3"> <note position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">Solis alti <lb/>@@dinem.</note> </div> <p> <s xml:id="echoid-s21868" xml:space="preserve">Tertia eſt, cognoſcere inſtans meridiei; </s> <s xml:id="echoid-s21869" xml:space="preserve">quando enim filum ſecuerit paralel ũ currentem, lineamq, <lb/> <anchor type="note" xlink:label="note-0274-04a" xlink:href="note-0274-04"/> meridianam in puncto vtrique communi: </s> <s xml:id="echoid-s21870" xml:space="preserve">vel tranſierit per communem ſectionem paralelli curren-<lb/>tis, & </s> <s xml:id="echoid-s21871" xml:space="preserve">meridianæ, tunc exactè meridies erit; </s> <s xml:id="echoid-s21872" xml:space="preserve">& </s> <s xml:id="echoid-s21873" xml:space="preserve">planum quadrantis in tali obſeruatione congruet pla-<lb/>no meridiani circuli. </s> <s xml:id="echoid-s21874" xml:space="preserve">Si meridiana deſit, meridiem plus minus cognoſces per inferiora horarum li-<lb/>neamenta.</s> <s xml:id="echoid-s21875" xml:space="preserve"/> </p> <div xml:id="echoid-div602" type="float" level="2" n="4"> <note position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve">Meridiẽ</note> </div> <p> <s xml:id="echoid-s21876" xml:space="preserve">Quarta eſt, præter Italicas horas, indicare etiam Babylonicas, nam eædem lineæ horariæ ab occa-<lb/> <anchor type="note" xlink:label="note-0274-05a" xlink:href="note-0274-05"/> ſu, euadunt in lineas horarias ab ortu; </s> <s xml:id="echoid-s21877" xml:space="preserve">hac ratione, mutantur appellation@s Italicarum in earum com-<lb/>plementa vſq; </s> <s xml:id="echoid-s21878" xml:space="preserve">ad 24. </s> <s xml:id="echoid-s21879" xml:space="preserve">v.</s> <s xml:id="echoid-s21880" xml:space="preserve">g. </s> <s xml:id="echoid-s21881" xml:space="preserve">23. </s> <s xml:id="echoid-s21882" xml:space="preserve">Italica euadet 1. </s> <s xml:id="echoid-s21883" xml:space="preserve">Babylonica, ſi eius denominatio fiat ab 1. </s> <s xml:id="echoid-s21884" xml:space="preserve">ideſt ab vni-<lb/>tate, quæ eſt complementum 23. </s> <s xml:id="echoid-s21885" xml:space="preserve">vſque ad 24. </s> <s xml:id="echoid-s21886" xml:space="preserve">ſicque appellabitur vna, vel prima ab ortu. </s> <s xml:id="echoid-s21887" xml:space="preserve">pariter 22. <lb/></s> <s xml:id="echoid-s21888" xml:space="preserve">ab occaſu, euadet 2. </s> <s xml:id="echoid-s21889" xml:space="preserve">ab ortu, quia denominabitur a 2. </s> <s xml:id="echoid-s21890" xml:space="preserve">quod eſt eius complementum vſque ad 24. </s> <s xml:id="echoid-s21891" xml:space="preserve">ſic 21. </s> <s xml:id="echoid-s21892" xml:space="preserve"><lb/>euadet 3. </s> <s xml:id="echoid-s21893" xml:space="preserve">20. </s> <s xml:id="echoid-s21894" xml:space="preserve">commutabitur in quarta, &</s> <s xml:id="echoid-s21895" xml:space="preserve">c. </s> <s xml:id="echoid-s21896" xml:space="preserve">hac ratione in ſuperiori fuit inchoata 13. </s> <s xml:id="echoid-s21897" xml:space="preserve">ab ortu, quia <lb/>punctum K. </s> <s xml:id="echoid-s21898" xml:space="preserve">cadit ſupra lineam 12. </s> <s xml:id="echoid-s21899" xml:space="preserve">Italicam, quæ euadit etiam 12. </s> <s xml:id="echoid-s21900" xml:space="preserve">Babylonica quia complementum <lb/>eius eſt 12.</s> <s xml:id="echoid-s21901" xml:space="preserve"/> </p> <div xml:id="echoid-div603" type="float" level="2" n="5"> <note position="left" xlink:label="note-0274-05" xlink:href="note-0274-05a" xml:space="preserve">Babylo-<lb/>nicam <lb/>etiam ho <lb/>ram.</note> </div> <p> <s xml:id="echoid-s21902" xml:space="preserve">Quinta, quota hora oriatur Sol ſic cognoſcitur: </s> <s xml:id="echoid-s21903" xml:space="preserve">in linea horizontali D E. </s> <s xml:id="echoid-s21904" xml:space="preserve">ſunt initia horarum 9. <lb/></s> <s xml:id="echoid-s21905" xml:space="preserve"> <anchor type="note" xlink:label="note-0274-06a" xlink:href="note-0274-06"/> 10. </s> <s xml:id="echoid-s21906" xml:space="preserve">11. </s> <s xml:id="echoid-s21907" xml:space="preserve">12. </s> <s xml:id="echoid-s21908" xml:space="preserve">13. </s> <s xml:id="echoid-s21909" xml:space="preserve">14. </s> <s xml:id="echoid-s21910" xml:space="preserve">15. </s> <s xml:id="echoid-s21911" xml:space="preserve">quę initia ſunt etiam communia tot@dem paralellis. </s> <s xml:id="echoid-s21912" xml:space="preserve">ſi igitur paralellus currens <lb/>fuerit vnus ex illis, Sol oritur hora illa, quę cum illo ortum habet in linea horizon@ali. </s> <s xml:id="echoid-s21913" xml:space="preserve">ſin minus con-<lb/>ſidera cuinam ex prædictis paralellis currẽs fuer@t propior, & </s> <s xml:id="echoid-s21914" xml:space="preserve">facilè iudicab@s de hora ortus Solis, v.</s> <s xml:id="echoid-s21915" xml:space="preserve">g. <lb/></s> <s xml:id="echoid-s21916" xml:space="preserve">in præmiſſo exemplo, quia paralellus prædictæ diei 18. </s> <s xml:id="echoid-s21917" xml:space="preserve">Auguſti, eſt inter horam 10. </s> <s xml:id="echoid-s21918" xml:space="preserve">& </s> <s xml:id="echoid-s21919" xml:space="preserve">11. </s> <s xml:id="echoid-s21920" xml:space="preserve">in linea ho-<lb/>rizontali, eſtque propior initio horæ 10 ideo ſignificat Solem oriri paululum poſt horam 10. </s> <s xml:id="echoid-s21921" xml:space="preserve">quod ſi <lb/>dies currens fuiſſet 14. </s> <s xml:id="echoid-s21922" xml:space="preserve">Auguſti, e@us paralellus idem fuiſſet cum eo, qui incipit cum hora 10. </s> <s xml:id="echoid-s21923" xml:space="preserve">qu@re or-<lb/>tus contigiſſet hora 10.</s> <s xml:id="echoid-s21924" xml:space="preserve"/> </p> <div xml:id="echoid-div604" type="float" level="2" n="6"> <note position="left" xlink:label="note-0274-06" xlink:href="note-0274-06a" xml:space="preserve">Ortus So. <lb/>lis.</note> </div> <p> <s xml:id="echoid-s21925" xml:space="preserve">Sexta, facilè erit cognoſcere ex præcedenti tempus nocturnum, & </s> <s xml:id="echoid-s21926" xml:space="preserve">diurnum, ſeu quantitatem diei, <lb/> <anchor type="note" xlink:label="note-0274-07a" xlink:href="note-0274-07"/> & </s> <s xml:id="echoid-s21927" xml:space="preserve">noctis. </s> <s xml:id="echoid-s21928" xml:space="preserve">quantitas noctis indicatur per horam ortus, nam ſi Sol oritur hora 10. </s> <s xml:id="echoid-s21929" xml:space="preserve">nox eſt horarum 10. <lb/></s> <s xml:id="echoid-s21930" xml:space="preserve">quibus detractis à 24. </s> <s xml:id="echoid-s21931" xml:space="preserve">remanent 14. </s> <s xml:id="echoid-s21932" xml:space="preserve">pro tempore diurno.</s> <s xml:id="echoid-s21933" xml:space="preserve"/> </p> <div xml:id="echoid-div605" type="float" level="2" n="7"> <note position="left" xlink:label="note-0274-07" xlink:href="note-0274-07a" xml:space="preserve">Tempus <lb/>noctu-<lb/>num, & <lb/>d@u@@ ũ-<lb/>Locũ So-<lb/>lis in Zo-<lb/>diaco.</note> </div> <p> <s xml:id="echoid-s21934" xml:space="preserve">Septima, cognoicimus locum Solis in Zodiaco quem indicabit currens paralellus, v.</s> <s xml:id="echoid-s21935" xml:space="preserve">g. </s> <s xml:id="echoid-s21936" xml:space="preserve">in ſuperio-<lb/>ri exemplo diei 18. </s> <s xml:id="echoid-s21937" xml:space="preserve">Auguſti, paralellus currens occurrit gradui 24. </s> <s xml:id="echoid-s21938" xml:space="preserve">Leonis, Soligitur verſatur in eo <lb/>gradu.</s> <s xml:id="echoid-s21939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s21940" xml:space="preserve">Octaua, ſimiliter cognoſces ſolſtitia, & </s> <s xml:id="echoid-s21941" xml:space="preserve">æquinoctia; </s> <s xml:id="echoid-s21942" xml:space="preserve">nam cùm paralellus currens, fuerit alter extre-<lb/>morum, erit alterum ſolſtitiorum; </s> <s xml:id="echoid-s21943" xml:space="preserve">ſi Cancri æſtiuum; </s> <s xml:id="echoid-s21944" xml:space="preserve">ſi Capricorni, hybernum. </s> <s xml:id="echoid-s21945" xml:space="preserve">ſi medius paralellus <lb/> <anchor type="note" xlink:label="note-0274-08a" xlink:href="note-0274-08"/> cucurrerit erit alter æquinoctiorum, vernum ſcilicet, vel autumnale.</s> <s xml:id="echoid-s21946" xml:space="preserve"/> </p> <div xml:id="echoid-div606" type="float" level="2" n="8"> <note position="left" xlink:label="note-0274-08" xlink:href="note-0274-08a" xml:space="preserve">Solstitia <lb/>æquino-<lb/>stia.</note> </div> </div> <div xml:id="echoid-div608" type="section" level="1" n="429"> <head xml:id="echoid-head454" style="it" xml:space="preserve">Alij modi non tam noui, acreconditi, quam vtiles.</head> <p> <s xml:id="echoid-s21947" xml:space="preserve">1 PRimus ſit, non ſplendente Sole, ſed ita tamen nebula, aut nubibus inuoluto, vt locus eius in c@ <lb/> <anchor type="note" xlink:label="note-0274-09a" xlink:href="note-0274-09"/> lo vtcunq; </s> <s xml:id="echoid-s21948" xml:space="preserve">appareat: </s> <s xml:id="echoid-s21949" xml:space="preserve">nam ſi per ſummitates pinnularum in Sole coſſimauer@t, perpendiculo in-<lb/>terim liberè pendente, ac radente faciẽ Horologij, ſecabi@ur ab eo paralellus currens in eodem pun-<lb/>cto, ac ſi radius per ſummitates pinnularum excurreret. </s> <s xml:id="echoid-s21950" xml:space="preserve">ratio eſt quia in eadem altitudine eſt linea vi-<lb/>ſiua tendens ab oculo per ſummitates pinnularum in Solem, ac radius procedens a Sole per apices <lb/>pinnularum ad oculum. </s> <s xml:id="echoid-s21951" xml:space="preserve">quare vtroq; </s> <s xml:id="echoid-s21952" xml:space="preserve">modo Horologium eandem obtinebi@ alt@t@dinem. </s> <s xml:id="echoid-s21953" xml:space="preserve">Hic por-<lb/>rò modus magnifaciendus eſt, cum ſæpe Sole nullatenus radiante, neceſſe habeamus horam cogno-<lb/>ſcere, quam tunc temporis cętera ſcyotherica, quæ perpendiculo non vtuntur, nullo modo exhibere <lb/>queant, ſed penitus inutilia reddantur.</s> <s xml:id="echoid-s21954" xml:space="preserve"/> </p> <div xml:id="echoid-div608" type="float" level="2" n="1"> <note position="left" xlink:label="note-0274-09" xlink:href="note-0274-09a" xml:space="preserve">Sole nu-<lb/>@ilo.</note> </div> <p> <s xml:id="echoid-s21955" xml:space="preserve">2 Exiſtentibus nobis vna cum Horologio in vmbra (quod videtur paradoxum) ſecus aquam <pb o="21" file="0275" n="280" rhead="DE HOROLOGIIS."/> quampiam, in qua videamus Solem per reflexionem, collimandum eſt deorſum in ipſum, ſuperiori <lb/> <anchor type="note" xlink:label="note-0275-01a" xlink:href="note-0275-01"/> tamen pinnula A. </s> <s xml:id="echoid-s21956" xml:space="preserve">oculo applicata, interim perpendiculo liberè pendente, & </s> <s xml:id="echoid-s21957" xml:space="preserve">faciem Horol. </s> <s xml:id="echoid-s21958" xml:space="preserve">radente, <lb/>nam paralellus currens ab eo ſecabitur, ac ſi in Solem ipſum ſupra horizontem præcedenti modo col-<lb/>limauerimus ratio eſt, quia radius ex aqua reflexus facit angulum cum ſuperficie aquæ æqualem an-<lb/>gulo radij incidentis, ideſt eodem modo eleuatur ſupra horizontem ac directus, vt optici demon-<lb/>ſtrant. </s> <s xml:id="echoid-s21959" xml:space="preserve">radius autẽ viſiuus in hac operatione coincidit cum radio Solis reflexo, ac proinde latus A B. <lb/></s> <s xml:id="echoid-s21960" xml:space="preserve">quod congruit radio viſiuo, congruet pariter radio Solis reflexo, ac proinde eleuatum erit quantum <lb/>Sol ipſe.</s> <s xml:id="echoid-s21961" xml:space="preserve"/> </p> <div xml:id="echoid-div609" type="float" level="2" n="2"> <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">In vm-<lb/>bra per <lb/>reflexio-<lb/>nem.</note> </div> <p> <s xml:id="echoid-s21962" xml:space="preserve">3 Exiſtentibus nobis vnà cum quadrante pariter in vmbra (alterum paradoxum) veluti intra cu-<lb/> <anchor type="note" xlink:label="note-0275-02a" xlink:href="note-0275-02"/> biculum, vel ſub porticu, abſq; </s> <s xml:id="echoid-s21963" xml:space="preserve">eo quod in Solem prodeamus, per vmbram cuiuſuis corporis, vti arbo-<lb/>ris alicuius, etiam ſatis diſtantis, ſic horam labentem venabimur. </s> <s xml:id="echoid-s21964" xml:space="preserve">ſed primo cõſiderandum eſt radium <lb/>Solis tranſire per verticem arboris aſſumptæ, & </s> <s xml:id="echoid-s21965" xml:space="preserve">ſimul definere ad verticem vmbræ illius. </s> <s xml:id="echoid-s21966" xml:space="preserve">huic igitur <lb/>radio debet latus pinnarum A B. </s> <s xml:id="echoid-s21967" xml:space="preserve">eſſe paralellum, vt ſit in eadem cum eo eleuatione ſupra horizon-<lb/>tem. </s> <s xml:id="echoid-s21968" xml:space="preserve">quod fiet ſi primo radius noſter viſiuus ſit ferè normalis plano illius verticalis, in quo eſt illic <lb/>radius Solis; </s> <s xml:id="echoid-s21969" xml:space="preserve">& </s> <s xml:id="echoid-s21970" xml:space="preserve">planum quadrantis ſtatuatur ad ſenſum plano prædicto paralellum. </s> <s xml:id="echoid-s21971" xml:space="preserve">debet autem pin-<lb/>na A. </s> <s xml:id="echoid-s21972" xml:space="preserve">eſſe ad partes arboris, pinna verò B. </s> <s xml:id="echoid-s21973" xml:space="preserve">ad partes vmbrę. </s> <s xml:id="echoid-s21974" xml:space="preserve">poſtea latus A B. </s> <s xml:id="echoid-s21975" xml:space="preserve">ante oculos noſtros tranſ-<lb/>miſſum, ita ex parte A. </s> <s xml:id="echoid-s21976" xml:space="preserve">eleuetur, vt alter oculorũ ſolus (altero clauſo) collimans ſecundum ipſum latus <lb/>A B. </s> <s xml:id="echoid-s21977" xml:space="preserve">modo ad verticem arboris, modò ad verticem vmbræ, videatur ſibi videre ipſum latus; </s> <s xml:id="echoid-s21978" xml:space="preserve">quodam <lb/>modo tranſire per vtrumque verticem, fic enim ad ſenſum e@it radio illi paralellum, & </s> <s xml:id="echoid-s21979" xml:space="preserve">cum eo æquè <lb/>altum. </s> <s xml:id="echoid-s21980" xml:space="preserve">Idem exactius aſſequemur ſi dum aſpicimus, manente A. </s> <s xml:id="echoid-s21981" xml:space="preserve">centro quadrantis, B. </s> <s xml:id="echoid-s21982" xml:space="preserve">verò acceden-<lb/>te, & </s> <s xml:id="echoid-s21983" xml:space="preserve">recedente à plano verticalis prædicti, interim perpendiculum liberè pendens, radenſq; </s> <s xml:id="echoid-s21984" xml:space="preserve">quadran <lb/>tem, ſecuerit plurimos gradus eius, ideſt latus A B. </s> <s xml:id="echoid-s21985" xml:space="preserve">maximam habuerit altitudinem ſub tali collima-<lb/>tione. </s> <s xml:id="echoid-s21986" xml:space="preserve">in tali igitur ſituatione quadrans erit eleuatns perinde, ac ſi radius ille tranſiret per pinnarum <lb/>apices: </s> <s xml:id="echoid-s21987" xml:space="preserve">& </s> <s xml:id="echoid-s21988" xml:space="preserve">conſequenter perpendiculum ſecabit currentem paralellum, ac ſi eſſemus in Sole; </s> <s xml:id="echoid-s21989" xml:space="preserve">& </s> <s xml:id="echoid-s21990" xml:space="preserve">pro-<lb/>inde ea omnia præſtabit, & </s> <s xml:id="echoid-s21991" xml:space="preserve">manifeſtabit, quæ ſuperius in Sole cognouimus. </s> <s xml:id="echoid-s21992" xml:space="preserve">Idem quoque ſimili via <lb/>aſſequemur ex vmbris verſis, ideſt ex vmbris corporum ex parietibus extantium; </s> <s xml:id="echoid-s21993" xml:space="preserve">quod induſtriæ cu-<lb/>iuſuis relinquimus.</s> <s xml:id="echoid-s21994" xml:space="preserve"/> </p> <div xml:id="echoid-div610" type="float" level="2" n="3"> <note position="right" xlink:label="note-0275-02" xlink:href="note-0275-02a" xml:space="preserve">In vm-<lb/>bra per <lb/>arborem.</note> </div> <p> <s xml:id="echoid-s21995" xml:space="preserve">4 Nocturnas quoque horas indagabis, ſi Planetam, aut Stellam Soli oppoſitam, vice Solis aſſum-<lb/> <anchor type="note" xlink:label="note-0275-03a" xlink:href="note-0275-03"/> pſeris, aſſumpto pariter paralello oppoſito paralello currenti; </s> <s xml:id="echoid-s21996" xml:space="preserve">horiſq; </s> <s xml:id="echoid-s21997" xml:space="preserve">Italicis commutatis in Baby-<lb/>lonicas: </s> <s xml:id="echoid-s21998" xml:space="preserve">ea enim Stella, occidente Sole, oritur, deſcribitq; </s> <s xml:id="echoid-s21999" xml:space="preserve">motu diuruo paralellum Soli oppoſitum, <lb/>qua propter ſortietur de nocte eaſdem altitudines ſupra horizontem, quas Sol noctu infra horizon-<lb/>@em in oppoſito paralello, in oppoſitis enim paralellis arcus diurnus vnius eſt æqualis arcui nocturno <lb/>alterius. </s> <s xml:id="echoid-s22000" xml:space="preserve">indicabit igitur horas ab ortu ſuo, quæ eædem erunt cum horis ab occaſu Solis: </s> <s xml:id="echoid-s22001" xml:space="preserve">& </s> <s xml:id="echoid-s22002" xml:space="preserve">propterea <lb/>horæ Italicæ commutandæ ſunt in Babylonicas vti ſupra docui, ideſt 23. </s> <s xml:id="echoid-s22003" xml:space="preserve">erit 1. </s> <s xml:id="echoid-s22004" xml:space="preserve">22. </s> <s xml:id="echoid-s22005" xml:space="preserve">erit 2. </s> <s xml:id="echoid-s22006" xml:space="preserve">21. </s> <s xml:id="echoid-s22007" xml:space="preserve">erit 3. </s> <s xml:id="echoid-s22008" xml:space="preserve">&</s> <s xml:id="echoid-s22009" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s22010" xml:space="preserve">quæ tamen eædem erunt cum horis ab occaſu Solis. </s> <s xml:id="echoid-s22011" xml:space="preserve">cognita igitur hora quapiam ab ortu Stellæ, ea <lb/>erit eadem cum hora ab o ccaſu Solis.</s> <s xml:id="echoid-s22012" xml:space="preserve"/> </p> <div xml:id="echoid-div611" type="float" level="2" n="4"> <note position="right" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">Horas no <lb/>cturnas <lb/>cognoſce-<lb/>re.</note> </div> </div> <div xml:id="echoid-div613" type="section" level="1" n="430"> <head xml:id="echoid-head455" style="it" xml:space="preserve">De conſtruendis Tabulis pro alijs latitudini bus. Cap. III.</head> <p> <s xml:id="echoid-s22013" xml:space="preserve">1 VT huius Horologij tractatio vniuerſalior euadat, ac partim defectum Tabularum quę pro plu-<lb/>ribus locis, ſeu latitudinibus neceſſariæ eſſent, compenſemus, placet nunc mirifica aliquot <lb/>compendia tradere, quibus maximopere minuitur labor, & </s> <s xml:id="echoid-s22014" xml:space="preserve">tædium conſtruendæ tabulæ altit. </s> <s xml:id="echoid-s22015" xml:space="preserve">Solis <lb/>pro quauis latitudine. </s> <s xml:id="echoid-s22016" xml:space="preserve">hac enim difficultate ſuperata, poterit quilibet in quauis regione, conſtructa <lb/>prius tabula, Horol. </s> <s xml:id="echoid-s22017" xml:space="preserve">ſibi facilè conſtruere. </s> <s xml:id="echoid-s22018" xml:space="preserve">Suppono autem primo Lectorem eſſe aliquantulum ver-<lb/>ſatum in Tabula ſinuum, atq; </s> <s xml:id="echoid-s22019" xml:space="preserve">adeò in Additione, Subtractione, Multiplicatione, Diuiſione, huic ne-<lb/>gotio neceſſarijs.</s> <s xml:id="echoid-s22020" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22021" xml:space="preserve">2 Habeat Tabulam ſinuum 10,000,000. </s> <s xml:id="echoid-s22022" xml:space="preserve">vel ſaltem 100,000. </s> <s xml:id="echoid-s22023" xml:space="preserve">quales ſunt Tabulæ P. </s> <s xml:id="echoid-s22024" xml:space="preserve">Clauij, & </s> <s xml:id="echoid-s22025" xml:space="preserve">Ma-<lb/>gnus Canon 10: </s> <s xml:id="echoid-s22026" xml:space="preserve">Magini in ſuo primo Mobili, qui cæteris tabulis eſt commodior, quia eadem tabula <lb/>exhibet ſinus rectos, & </s> <s xml:id="echoid-s22027" xml:space="preserve">verſos, quorum perpetuus eſt vſus in hac calculatione.</s> <s xml:id="echoid-s22028" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22029" xml:space="preserve">3 Sequatur modum calculandi traditũ a P. </s> <s xml:id="echoid-s22030" xml:space="preserve">Clauio in noua deſcriptione Horol. </s> <s xml:id="echoid-s22031" xml:space="preserve">probl. </s> <s xml:id="echoid-s22032" xml:space="preserve">15. </s> <s xml:id="echoid-s22033" xml:space="preserve">& </s> <s xml:id="echoid-s22034" xml:space="preserve">lib. </s> <s xml:id="echoid-s22035" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s22036" xml:space="preserve">Gnom. </s> <s xml:id="echoid-s22037" xml:space="preserve">probl. </s> <s xml:id="echoid-s22038" xml:space="preserve">15. </s> <s xml:id="echoid-s22039" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s22040" xml:space="preserve">36. </s> <s xml:id="echoid-s22041" xml:space="preserve">proximè ante rationem ex triangulis ſphęricis deſumptam. </s> <s xml:id="echoid-s22042" xml:space="preserve">de quo etiam <lb/>tractat inibi in ſcholio pag. </s> <s xml:id="echoid-s22043" xml:space="preserve">139. </s> <s xml:id="echoid-s22044" xml:space="preserve">linea 26. </s> <s xml:id="echoid-s22045" xml:space="preserve">paragr. </s> <s xml:id="echoid-s22046" xml:space="preserve">At verò eſt autem hic:</s> <s xml:id="echoid-s22047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22048" xml:space="preserve">Fiat vt ſinus totus ad ſinum verſum diſtantiæ Solis a meridie,</s> </p> <p> <s xml:id="echoid-s22049" xml:space="preserve">Ita ſemiſſis aggregati ex ſinibus altitudinis ac depreſſionis meridianæ ad aliud:</s> <s xml:id="echoid-s22050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22051" xml:space="preserve">Nam inuentum illud ſubtractum ex ſinu altitudinis meridia@æ, relinquet ſinum quæſitæ altitudi. <lb/></s> <s xml:id="echoid-s22052" xml:space="preserve">nis ſolaris.</s> <s xml:id="echoid-s22053" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22054" xml:space="preserve">4 Seruanda eſt hęc methodus, vt prius inueniamus altitudines Solis ad ſingulas horas eiuſdem pa-<lb/>ralelli, & </s> <s xml:id="echoid-s22055" xml:space="preserve">eadem ferè opera, altitudines oppoſiti paralelli, v.</s> <s xml:id="echoid-s22056" xml:space="preserve">g. </s> <s xml:id="echoid-s22057" xml:space="preserve">inueniantur primo altitudines ad ſin-<lb/>gulas horas primi paralelli ♋. </s> <s xml:id="echoid-s22058" xml:space="preserve">& </s> <s xml:id="echoid-s22059" xml:space="preserve">oppoſiti ♑. </s> <s xml:id="echoid-s22060" xml:space="preserve">poſtea idem faciendum pro paralello per gr. </s> <s xml:id="echoid-s22061" xml:space="preserve">15. </s> <s xml:id="echoid-s22062" xml:space="preserve">0′. </s> <s xml:id="echoid-s22063" xml:space="preserve">♋. <lb/></s> <s xml:id="echoid-s22064" xml:space="preserve">necnon oppoſiti per gr. </s> <s xml:id="echoid-s22065" xml:space="preserve">15. </s> <s xml:id="echoid-s22066" xml:space="preserve">0′. </s> <s xml:id="echoid-s22067" xml:space="preserve">♑, &</s> <s xml:id="echoid-s22068" xml:space="preserve">c.</s> <s xml:id="echoid-s22069" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22070" xml:space="preserve">5 Vtautem ſecundum prædictam analogiam, per regulam auream, vti oportet, operemur, opus <lb/> <anchor type="note" xlink:label="note-0275-04a" xlink:href="note-0275-04"/> eſt præmittere Apparatum quendam, in quo continentur omnes termini neceſſarij ad hanc calcula- <pb o="22" file="0276" n="281" rhead="TRACTATVS"/> tionem. </s> <s xml:id="echoid-s22071" xml:space="preserve">ſunt autem hi, ſinus totus, diſtantiæ ſingularum horarum à meridie in aſſumpto paralello; <lb/></s> <s xml:id="echoid-s22072" xml:space="preserve">altitudo, & </s> <s xml:id="echoid-s22073" xml:space="preserve">depreſſio meridiana, vt fiat aggregatum ex vtriuſque ſinubus. </s> <s xml:id="echoid-s22074" xml:space="preserve">quæ omnia melius perci-<lb/>pientur ex ſequenti exemplo. </s> <s xml:id="echoid-s22075" xml:space="preserve">ſint igitur exempli gratia ad latit. </s> <s xml:id="echoid-s22076" xml:space="preserve">44. </s> <s xml:id="echoid-s22077" xml:space="preserve">calculandæ per regulam auream <lb/> <anchor type="note" xlink:label="note-0276-01a" xlink:href="note-0276-01"/> ſecundum præditam analogiam altitudines pro ſingulis horis Italicis paralellorum oppoſitorum ♋. <lb/></s> <s xml:id="echoid-s22078" xml:space="preserve">& </s> <s xml:id="echoid-s22079" xml:space="preserve">♑. </s> <s xml:id="echoid-s22080" xml:space="preserve">ſeu tropicorum, cuius gratia fiat apparatus qualis eſt ſequens,</s> </p> <div xml:id="echoid-div613" type="float" level="2" n="1"> <note position="right" xlink:label="note-0275-04" xlink:href="note-0275-04a" xml:space="preserve">Apparat. <lb/>ad calcu-<lb/>lu@.</note> <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">Ex@mplũ</note> </div> </div> <div xml:id="echoid-div615" type="section" level="1" n="431"> <head xml:id="echoid-head456" xml:space="preserve">LOCVS APPARATVS.</head> <p> <s xml:id="echoid-s22081" xml:space="preserve">PRo conſtruendo hoc apparatu ſecundũ præcepta P. </s> <s xml:id="echoid-s22082" xml:space="preserve">Clauij tradita, tum probl. </s> <s xml:id="echoid-s22083" xml:space="preserve">15. </s> <s xml:id="echoid-s22084" xml:space="preserve">Nouæ deſcript. <lb/></s> <s xml:id="echoid-s22085" xml:space="preserve">tum in Gnom. </s> <s xml:id="echoid-s22086" xml:space="preserve">lib. </s> <s xml:id="echoid-s22087" xml:space="preserve">propoſ. </s> <s xml:id="echoid-s22088" xml:space="preserve">35. </s> <s xml:id="echoid-s22089" xml:space="preserve">in ſcholio, inſeruiunt Tabellæ, quæ ſunt partim in Sphæra eius, par-<lb/>tim in noua deſcript. </s> <s xml:id="echoid-s22090" xml:space="preserve">partim in Tabulis ſeorſim editis pro habẽdis arcubus, & </s> <s xml:id="echoid-s22091" xml:space="preserve">temporibus ſemidiur-<lb/>nis. </s> <s xml:id="echoid-s22092" xml:space="preserve">ſinus autem recti, & </s> <s xml:id="echoid-s22093" xml:space="preserve">verſi eadem opera commodè habentur ex Magno Canone Magini. </s> <s xml:id="echoid-s22094" xml:space="preserve">In hoc <lb/>igitur apparatu parauimus, omnes terminos neceſſarios ad operandum per regulam auream ſecundũ <lb/>ſuperiorem analogiam, vt altitudines Solis in quauis hora dati paralelli per calculum indagemus. </s> <s xml:id="echoid-s22095" xml:space="preserve">in <lb/>qua analogia primus terminus eſt ſinus totus ſaltem 100,000. </s> <s xml:id="echoid-s22096" xml:space="preserve">qui ſemper idem manet in caiculo om-<lb/>nium horarum atq; </s> <s xml:id="echoid-s22097" xml:space="preserve">in omni paralello. </s> <s xml:id="echoid-s22098" xml:space="preserve">Secundus terminus eſt ſinus verſus diſtantiæ illius horæ pro-<lb/>prius pro qua c lculus inſtituitur, qui in apparatu ſcribitur è regione ſuæ horæ: </s> <s xml:id="echoid-s22099" xml:space="preserve">quare hic variatur in <lb/>ſingulis horis. </s> <s xml:id="echoid-s22100" xml:space="preserve">ij tamen qui reſpondent horis ♑. </s> <s xml:id="echoid-s22101" xml:space="preserve">reſpondent etiam totidem horis ♋. </s> <s xml:id="echoid-s22102" xml:space="preserve">quare ijde dua-<lb/>bus horis reſpondent. </s> <s xml:id="echoid-s22103" xml:space="preserve">Tertius terminus eſt ſemiſſis aggregati ex ſinubus rectis altit. </s> <s xml:id="echoid-s22104" xml:space="preserve">& </s> <s xml:id="echoid-s22105" xml:space="preserve">depreſſionis <lb/>meridianæ, qui cum primo termino ſemper idem manet in duobus oppoſitis paralellis. </s> <s xml:id="echoid-s22106" xml:space="preserve">Multipli-<lb/>candus eſt igitur ſinus verſus horæ aſſumptæ in prædictam ſemiſſem: </s> <s xml:id="echoid-s22107" xml:space="preserve">productum autem diuidendum <lb/>per ſinum totum: </s> <s xml:id="echoid-s22108" xml:space="preserve">& </s> <s xml:id="echoid-s22109" xml:space="preserve">quotiens inuentus, qui eſt quartus terminus huius analogiæ, demendus eſt ex ſi-<lb/>nu recto altitudinis meridianæ; </s> <s xml:id="echoid-s22110" xml:space="preserve">nam relictum erit ſinus altitudinis quæſitæ. </s> <s xml:id="echoid-s22111" xml:space="preserve">exe plo ſoquent@ res <lb/>melius percipietur.</s> <s xml:id="echoid-s22112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22113" xml:space="preserve">Sit v.</s> <s xml:id="echoid-s22114" xml:space="preserve">g. </s> <s xml:id="echoid-s22115" xml:space="preserve">calculanda altit. </s> <s xml:id="echoid-s22116" xml:space="preserve">23. </s> <s xml:id="echoid-s22117" xml:space="preserve">horæ (ab ea enim vt ordine procedamus incipendum eſt.) </s> <s xml:id="echoid-s22118" xml:space="preserve">in aſſumpto <lb/> <anchor type="note" xlink:label="note-0276-02a" xlink:href="note-0276-02"/> paralello ♋. </s> <s xml:id="echoid-s22119" xml:space="preserve">datæ latit. </s> <s xml:id="echoid-s22120" xml:space="preserve">gr. </s> <s xml:id="echoid-s22121" xml:space="preserve">44. </s> <s xml:id="echoid-s22122" xml:space="preserve">Duco igitur ſinum verſum 117,078,. </s> <s xml:id="echoid-s22123" xml:space="preserve">in ſemiſſem aggregati 65,967. <lb/></s> <s xml:id="echoid-s22124" xml:space="preserve">verum quia valdè tædioſum, laborioſum, pluribuſq; </s> <s xml:id="echoid-s22125" xml:space="preserve">erroribus obnoxium eſſet pro ſingulis 24. </s> <s xml:id="echoid-s22126" xml:space="preserve">noris <lb/>huiuſmodi multi plicationes iterare (in duobus enim oppoſitis paralellis ſunt 24 horæ) v@em@r miri-<lb/>fica, atque compendioſa hac induſtria, qua ſine labore multiplicationis, magna cum voluptate, fru-<lb/>ctum illius capiemus.</s> <s xml:id="echoid-s22127" xml:space="preserve"/> </p> <div xml:id="echoid-div615" type="float" level="2" n="1"> <note position="left" xlink:label="note-0276-02" xlink:href="note-0276-02a" xml:space="preserve">Exemplũ <lb/>calculi <lb/>horæ 23.</note> </div> <p> <s xml:id="echoid-s22128" xml:space="preserve">I Parentur igitur circiter 20. </s> <s xml:id="echoid-s22129" xml:space="preserve">regulæ ſeu tabellę ex ligno, quales apparatus oſtendit ad dexteram. <lb/></s> <s xml:id="echoid-s22130" xml:space="preserve"> <anchor type="note" xlink:label="note-0276-03a" xlink:href="note-0276-03"/> earum ſuperior ſuperficies ſit palimpſeſtus, ſeu deletiua, vt inſeruire poſſit pro alils etiam paralellis. <lb/></s> <s xml:id="echoid-s22131" xml:space="preserve">earum aliæ notentur nota 1. </s> <s xml:id="echoid-s22132" xml:space="preserve">aliæ 2. </s> <s xml:id="echoid-s22133" xml:space="preserve">aliæ 3. </s> <s xml:id="echoid-s22134" xml:space="preserve">aliæ o, & </s> <s xml:id="echoid-s22135" xml:space="preserve">c. </s> <s xml:id="echoid-s22136" xml:space="preserve">quæ notæ nunquam delendę ſunt. </s> <s xml:id="echoid-s22137" xml:space="preserve">his paratis ac-<lb/>cedo ad multiplicationem hoc modo; </s> <s xml:id="echoid-s22138" xml:space="preserve">ſcribo ſinum verſum prædictum ſub ſemiſie aggregati, vti vi-<lb/>des in Apparatu; </s> <s xml:id="echoid-s22139" xml:space="preserve">& </s> <s xml:id="echoid-s22140" xml:space="preserve">quia prima figura multiplicans eſt 8. </s> <s xml:id="echoid-s22141" xml:space="preserve">ideo accipio regulam iam prænotatam figu-<lb/>ra eadem 8. </s> <s xml:id="echoid-s22142" xml:space="preserve">quam pono ſub numero multiplicante; </s> <s xml:id="echoid-s22143" xml:space="preserve">vt vides in exemplo apparatus. </s> <s xml:id="echoid-s22144" xml:space="preserve">Duco igitur 8. </s> <s xml:id="echoid-s22145" xml:space="preserve">in <lb/>ſingulas figuras ſemiſſis (omitto tamen fractionem {1/2}. </s> <s xml:id="echoid-s22146" xml:space="preserve">quæ tamen non eſt omittenda quotieſcunque <lb/> <anchor type="note" xlink:label="note-0276-04a" xlink:href="note-0276-04"/> dimidium ſinus verſi habet plures figuras quinque) excipiendo in tabella 8. </s> <s xml:id="echoid-s22147" xml:space="preserve">productum huius multi-<lb/>plicationis, ſcilicet 527,736. </s> <s xml:id="echoid-s22148" xml:space="preserve">deinde vtor probatione per 9. </s> <s xml:id="echoid-s22149" xml:space="preserve">quæ c tiſſimè perficitur: </s> <s xml:id="echoid-s22150" xml:space="preserve">præſertim quia <lb/>figura 6. </s> <s xml:id="echoid-s22151" xml:space="preserve">quæ re nanet ex dimidio aggregati, ſemper eadem manet per vtrumque paralellum decuſ-<lb/>ſato deinde 8. </s> <s xml:id="echoid-s22152" xml:space="preserve">aſſumo ſequentem figuram 7. </s> <s xml:id="echoid-s22153" xml:space="preserve">& </s> <s xml:id="echoid-s22154" xml:space="preserve">pariter tabellam 7 pono ſub priore tabella 8. </s> <s xml:id="echoid-s22155" xml:space="preserve">eo ſitu <lb/>quem vides in formula Apparatus; </s> <s xml:id="echoid-s22156" xml:space="preserve">atque in ea excipio multiplicationem 7. </s> <s xml:id="echoid-s22157" xml:space="preserve">in totam ſemiſſem, cum <lb/>probatione per 9. </s> <s xml:id="echoid-s22158" xml:space="preserve">Similiter decuſſata figura 7. </s> <s xml:id="echoid-s22159" xml:space="preserve">quia ſequens figura eſt o. </s> <s xml:id="echoid-s22160" xml:space="preserve">ſuppono tabellam 0. </s> <s xml:id="echoid-s22161" xml:space="preserve">duabus <lb/>præcedentibus, in quo deſcribo productum ex multipſicationeo. </s> <s xml:id="echoid-s22162" xml:space="preserve">in ſemiſſem. </s> <s xml:id="echoid-s22163" xml:space="preserve">Idem facio cum ſe-<lb/>quenti 7. </s> <s xml:id="echoid-s22164" xml:space="preserve">& </s> <s xml:id="echoid-s22165" xml:space="preserve">altera regula 7. </s> <s xml:id="echoid-s22166" xml:space="preserve">ſed abſq; </s> <s xml:id="echoid-s22167" xml:space="preserve">nouo labore multiplicandi deſcribo in ea productum prioris 7. <lb/></s> <s xml:id="echoid-s22168" xml:space="preserve">Tandem propter binas 1, 1,. </s> <s xml:id="echoid-s22169" xml:space="preserve">ſuppono alijs duas regulas 1, 1,. </s> <s xml:id="echoid-s22170" xml:space="preserve">& </s> <s xml:id="echoid-s22171" xml:space="preserve">in vtraque deſcribo ipſam ſemiſſem <lb/>aggregati, quia 1,. </s> <s xml:id="echoid-s22172" xml:space="preserve">ducta in quemuis numerum, eundem numerum producit. </s> <s xml:id="echoid-s22173" xml:space="preserve">poſtremo ex omnibus <lb/>hiſce multiplicationibus fit ſumma; </s> <s xml:id="echoid-s22174" xml:space="preserve">vna cum probatione per 9 quo facto tabellas hiſce productis in-<lb/>ſcriptas ad partes ſeruo, erunt enim vſui, & </s> <s xml:id="echoid-s22175" xml:space="preserve">patebit.</s> <s xml:id="echoid-s22176" xml:space="preserve"/> </p> <div xml:id="echoid-div616" type="float" level="2" n="2"> <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">Induſtria <lb/>mirifica <lb/>in multi-<lb/>pl.</note> <note position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">Quando <lb/>fractio <lb/>non ſit <lb/>omitten-<lb/>da.</note> </div> <p> <s xml:id="echoid-s22177" xml:space="preserve">2 Abſoluta hac prima multiplicatione, quæ eſt ſecundi termini analogiæ in tertium; </s> <s xml:id="echoid-s22178" xml:space="preserve">diuiden-<lb/> <anchor type="note" xlink:label="note-0276-05a" xlink:href="note-0276-05"/> dus eſt productus, ſumma ſcilicet prædicta per primum tern inum, ideſt, per ſinum totum, 100, 000. <lb/></s> <s xml:id="echoid-s22179" xml:space="preserve">quę diuiſio abſque vllo labore fit demendo a numero diuidendo tot figuras ad dexteram ſitas, quot <lb/>ſunt cifræ in ſinu toto, ſcilicet quinq; </s> <s xml:id="echoid-s22180" xml:space="preserve">vt factum vides in formula apparatus. </s> <s xml:id="echoid-s22181" xml:space="preserve">Quotiens autem hui@s <lb/>diuiſionis erit reliquas numerus 77, 232. </s> <s xml:id="echoid-s22182" xml:space="preserve">& </s> <s xml:id="echoid-s22183" xml:space="preserve">quartus terminus analogiæ inuentus per auream regulam <lb/>quam quotiens ſeruandus eſt quando hora ♋. </s> <s xml:id="echoid-s22184" xml:space="preserve">habet aliam horam ſib in ♑, reſpondentem. </s> <s xml:id="echoid-s22185" xml:space="preserve">poſtea hic <lb/>quartus terminus detrahendus eſt ex ſinu altitudinis meridianæ 93, 667. </s> <s xml:id="echoid-s22186" xml:space="preserve">nam reliquus 16, 435. </s> <s xml:id="echoid-s22187" xml:space="preserve">erit <lb/>ſinus altitudinis horæ 23. </s> <s xml:id="echoid-s22188" xml:space="preserve">♋. </s> <s xml:id="echoid-s22189" xml:space="preserve">Igitur in Tabula ſinuum reperio hunc reliquum numerum (aut @altem <lb/>ei propinquiorem) cui in eadem tabula competunt gr. </s> <s xml:id="echoid-s22190" xml:space="preserve">9. </s> <s xml:id="echoid-s22191" xml:space="preserve">28. </s> <s xml:id="echoid-s22192" xml:space="preserve">altitudo ſcilicet Solis quæſita hora 23. </s> <s xml:id="echoid-s22193" xml:space="preserve"><lb/>in ♋. </s> <s xml:id="echoid-s22194" xml:space="preserve">quam altitudinem ſcribo in apparatu è regione horæ 23.</s> <s xml:id="echoid-s22195" xml:space="preserve"/> </p> <div xml:id="echoid-div617" type="float" level="2" n="3"> <note position="left" xlink:label="note-0276-05" xlink:href="note-0276-05a" xml:space="preserve">Diuiſio <lb/>facillima</note> </div> <p> <s xml:id="echoid-s22196" xml:space="preserve">3 Deinde ſimiliter multiplico ſinum verſum horę 22, in eandẽ ſemiſſem, & </s> <s xml:id="echoid-s22197" xml:space="preserve">quoniam prima ſigu-<lb/> <anchor type="note" xlink:label="note-0276-06a" xlink:href="note-0276-06"/> ra multiplicans eſt 4. </s> <s xml:id="echoid-s22198" xml:space="preserve">& </s> <s xml:id="echoid-s22199" xml:space="preserve">tabella 4. </s> <s xml:id="echoid-s22200" xml:space="preserve">adhuc vacua eſt, eam propterea accipio, ponoq; </s> <s xml:id="echoid-s22201" xml:space="preserve">ſub numeris mul-<lb/>ti plicandis, eorumq; </s> <s xml:id="echoid-s22202" xml:space="preserve">multiplicationem excipio in eadem tabella 4. </s> <s xml:id="echoid-s22203" xml:space="preserve">adhibita probatione per 9. </s> <s xml:id="echoid-s22204" xml:space="preserve">de-<lb/>inde volens multiplicare per ſecundam figuram, quę eſſe 99. </s> <s xml:id="echoid-s22205" xml:space="preserve">accipio tabellam 9. </s> <s xml:id="echoid-s22206" xml:space="preserve">pariter vacuam, atq;</s> <s xml:id="echoid-s22207" xml:space="preserve"> <pb o="23" file="0277" n="282" rhead="DEHOROLOGIIS."/> in ea ſcribo productum. </s> <s xml:id="echoid-s22208" xml:space="preserve">poſtea eadem ratione propter tertiam figuram 9. </s> <s xml:id="echoid-s22209" xml:space="preserve">tranſeribo eundem produ-<lb/>ctum ſine noua multiplicatione deinde propter quartam figuram o.</s> <s xml:id="echoid-s22210" xml:space="preserve">accipio tabellam o. </s> <s xml:id="echoid-s22211" xml:space="preserve">iam cifris no-<lb/>tatam, eamque præcedentibus ſuppono. </s> <s xml:id="echoid-s22212" xml:space="preserve">tandem ob vltimam 9. </s> <s xml:id="echoid-s22213" xml:space="preserve">aliam tabellam 9. </s> <s xml:id="echoid-s22214" xml:space="preserve">inſcribo eodem <lb/>producto, quo aliæ duæ 9. </s> <s xml:id="echoid-s22215" xml:space="preserve">eamque ſuo loco cæteris appono. </s> <s xml:id="echoid-s22216" xml:space="preserve">ex quibus omnibus fit ſumma cum pro-<lb/>batione per 9. </s> <s xml:id="echoid-s22217" xml:space="preserve">quę ſumma diuiditur vt ſupra per 100,000, abiectis quinq; </s> <s xml:id="echoid-s22218" xml:space="preserve">figuris dexteris, & </s> <s xml:id="echoid-s22219" xml:space="preserve">Quotiens <lb/>hinc proueniens detractus ex ſinu recto altit. </s> <s xml:id="echoid-s22220" xml:space="preserve">meridianę relinquat ſinum rectũ altitudinis hor. </s> <s xml:id="echoid-s22221" xml:space="preserve">22. </s> <s xml:id="echoid-s22222" xml:space="preserve">cui <lb/>in Tabula finuum dantur gra. </s> <s xml:id="echoid-s22223" xml:space="preserve">19. </s> <s xml:id="echoid-s22224" xml:space="preserve">40′. </s> <s xml:id="echoid-s22225" xml:space="preserve">quos ideo ſcribo è regione horæ 22. </s> <s xml:id="echoid-s22226" xml:space="preserve">in Apparatu. </s> <s xml:id="echoid-s22227" xml:space="preserve">tabellas ve-<lb/>rò ſeorſum repono. </s> <s xml:id="echoid-s22228" xml:space="preserve">Quotientem hunc ſeruare non eſſe opus ex dictis ſuperius.</s> <s xml:id="echoid-s22229" xml:space="preserve"/> </p> <div xml:id="echoid-div618" type="float" level="2" n="4"> <note position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">Calculus <lb/>her@, 22.</note> </div> <p> <s xml:id="echoid-s22230" xml:space="preserve">4 Iam multiplicandus eſt ſinus verſus horæ 21,. </s> <s xml:id="echoid-s22231" xml:space="preserve">in eandem ſemiſsem. </s> <s xml:id="echoid-s22232" xml:space="preserve">eius prima figura multipli-<lb/> <anchor type="note" xlink:label="note-0277-01a" xlink:href="note-0277-01"/> cans eſt 4. </s> <s xml:id="echoid-s22233" xml:space="preserve">ſed quia tabella 4. </s> <s xml:id="echoid-s22234" xml:space="preserve">eſt inſcripta, eam ſine vllollabore multiplicationis pono ſub numeris <lb/>multiplicandis, deinde propter ſecundam figuram 2. </s> <s xml:id="echoid-s22235" xml:space="preserve">cuius tabella adhuc vacua eſt multiplico ſemiſ-<lb/>ſe per 2. </s> <s xml:id="echoid-s22236" xml:space="preserve">excipiendo in tabella 2. </s> <s xml:id="echoid-s22237" xml:space="preserve">productum ſimiliter facio cum duabus figuris duabus 5, 5,. </s> <s xml:id="echoid-s22238" xml:space="preserve">& </s> <s xml:id="echoid-s22239" xml:space="preserve">dua-<lb/>bus tabellis 5, 5,. </s> <s xml:id="echoid-s22240" xml:space="preserve">& </s> <s xml:id="echoid-s22241" xml:space="preserve">idem cum ſigura 6,. </s> <s xml:id="echoid-s22242" xml:space="preserve">ſcribendo in tabula 6. </s> <s xml:id="echoid-s22243" xml:space="preserve">&</s> <s xml:id="echoid-s22244" xml:space="preserve">c. </s> <s xml:id="echoid-s22245" xml:space="preserve">facta poſtea ſumma, eaque diuiſa <lb/>per ſinum totum, & </s> <s xml:id="echoid-s22246" xml:space="preserve">quotiente demptio ex ſinu altitudinis meridie, reliquus ſinus ex hibebit in tabula <lb/>ſinuum altitudinem horæ 21. </s> <s xml:id="echoid-s22247" xml:space="preserve">ſcilicet gr. </s> <s xml:id="echoid-s22248" xml:space="preserve">30. </s> <s xml:id="echoid-s22249" xml:space="preserve">18,. </s> <s xml:id="echoid-s22250" xml:space="preserve">quos è directo horæ 21. </s> <s xml:id="echoid-s22251" xml:space="preserve">in apparatu ſcribo, neque eſt <lb/>opus ſeruare hunc quotientem.</s> <s xml:id="echoid-s22252" xml:space="preserve"/> </p> <div xml:id="echoid-div619" type="float" level="2" n="5"> <note position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">Calculas <lb/>horæ 21.</note> </div> <p> <s xml:id="echoid-s22253" xml:space="preserve">5 Iam per multiplicationem ſinus verſi horæ 20. </s> <s xml:id="echoid-s22254" xml:space="preserve">nihil ferè laborandum eſt, cum omnes eius figu-<lb/> <anchor type="note" xlink:label="note-0277-02a" xlink:href="note-0277-02"/> ræ habeant ſuam multiplicationem in tabellis ſibi cognominibus. </s> <s xml:id="echoid-s22255" xml:space="preserve">ſolius figuræ 4. </s> <s xml:id="echoid-s22256" xml:space="preserve">erit bis repetenda <lb/>multiplicatio, quare eius ſuperior multiplicatio tranſcribenda erit in noua tabella 4. </s> <s xml:id="echoid-s22257" xml:space="preserve">atque hoc mo-<lb/>do procedendo habebis citò omnes multiplicationes in tabellis, vnde etiam earum ſummam, & </s> <s xml:id="echoid-s22258" xml:space="preserve">diui-<lb/>ſionem, & </s> <s xml:id="echoid-s22259" xml:space="preserve">quotientem nunc ſeruandum, & </s> <s xml:id="echoid-s22260" xml:space="preserve">detrahendum ex ſinu altitudinis meridianæ, atq; </s> <s xml:id="echoid-s22261" xml:space="preserve">hinc re-<lb/>liquum ſinum, qui in tabula ſinuum dabit altitudinem horæ 20. </s> <s xml:id="echoid-s22262" xml:space="preserve">atq; </s> <s xml:id="echoid-s22263" xml:space="preserve">eodem modo agendum eſt in cæ-<lb/>teris horis.</s> <s xml:id="echoid-s22264" xml:space="preserve"/> </p> <div xml:id="echoid-div620" type="float" level="2" n="6"> <note position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">Her@ 20.</note> </div> <p> <s xml:id="echoid-s22265" xml:space="preserve">Hic quotiens ſeruandus eſt, quoties oritur ex calculo alicuius horæ ♋. </s> <s xml:id="echoid-s22266" xml:space="preserve">vel alius paralelli, quæ ha-<lb/> <anchor type="note" xlink:label="note-0277-03a" xlink:href="note-0277-03"/> beat eundem ſinum verſum cum hora oppoſiti paralelli, v.</s> <s xml:id="echoid-s22267" xml:space="preserve">g. </s> <s xml:id="echoid-s22268" xml:space="preserve">♑. </s> <s xml:id="echoid-s22269" xml:space="preserve">vti nunc eſt hora 20 ♋. </s> <s xml:id="echoid-s22270" xml:space="preserve">reſpectu ho-<lb/>ræ 16. </s> <s xml:id="echoid-s22271" xml:space="preserve">♑. </s> <s xml:id="echoid-s22272" xml:space="preserve">quia mihi quotientem inſeruiunt etiam pro horis oppoſiti paralelli, vti nunc ♑.</s> <s xml:id="echoid-s22273" xml:space="preserve"/> </p> <div xml:id="echoid-div621" type="float" level="2" n="7"> <note position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">Quando <lb/>quotiens <lb/>ſeruãdus <lb/>ſit.</note> </div> </div> <div xml:id="echoid-div623" type="section" level="1" n="432"> <head xml:id="echoid-head457" style="it" xml:space="preserve">De Paralello oppoſito, qui est Capricorni.</head> <p> <s xml:id="echoid-s22274" xml:space="preserve">1 IAm pro oppoſito paralello ♑. </s> <s xml:id="echoid-s22275" xml:space="preserve">parum laboris ſupereſt; </s> <s xml:id="echoid-s22276" xml:space="preserve">ſunt enim omnia ferè huius paralelli com-<lb/> <anchor type="note" xlink:label="note-0277-04a" xlink:href="note-0277-04"/> munia cum paralello ♋. </s> <s xml:id="echoid-s22277" xml:space="preserve">ſed inuerſa, & </s> <s xml:id="echoid-s22278" xml:space="preserve">commutata. </s> <s xml:id="echoid-s22279" xml:space="preserve">ſic altitudo meridiana vnius eſt deprefſio <lb/>meridiana alterius, & </s> <s xml:id="echoid-s22280" xml:space="preserve">viceuerſa. </s> <s xml:id="echoid-s22281" xml:space="preserve">quare erit eadem ſemiſſis aggregati ex ſinubus earum, vt apparet in <lb/>apparatu. </s> <s xml:id="echoid-s22282" xml:space="preserve">ſim iliter tempus nocturnum illlus eſt diurnum huius, &</s> <s xml:id="echoid-s22283" xml:space="preserve">c. </s> <s xml:id="echoid-s22284" xml:space="preserve">pręterea diſtantię horarum diur-<lb/>narum in ♑. </s> <s xml:id="echoid-s22285" xml:space="preserve">ſunt æquales totidem diſtantijs in ♋. </s> <s xml:id="echoid-s22286" xml:space="preserve">quod inde patet quia portio diurna ♑. </s> <s xml:id="echoid-s22287" xml:space="preserve">eſt æqualis <lb/>portioni nocturnæ ♋. </s> <s xml:id="echoid-s22288" xml:space="preserve">ſed media nox in ♋. </s> <s xml:id="echoid-s22289" xml:space="preserve">eſt hora 4. </s> <s xml:id="echoid-s22290" xml:space="preserve">21,. </s> <s xml:id="echoid-s22291" xml:space="preserve">meridies quoque in ♋. </s> <s xml:id="echoid-s22292" xml:space="preserve">eſt hora 16. </s> <s xml:id="echoid-s22293" xml:space="preserve">21,. <lb/></s> <s xml:id="echoid-s22294" xml:space="preserve">quare tantum diſtat à meridiano nocturno 4. </s> <s xml:id="echoid-s22295" xml:space="preserve">hora noctis, quantum 16. </s> <s xml:id="echoid-s22296" xml:space="preserve">diurna à meridiano diurno. </s> <s xml:id="echoid-s22297" xml:space="preserve"><lb/>Quod etiam patebit conſideranti, quod cum in ♋. </s> <s xml:id="echoid-s22298" xml:space="preserve">ſit meridies hora 16. </s> <s xml:id="echoid-s22299" xml:space="preserve">21,. </s> <s xml:id="echoid-s22300" xml:space="preserve">ſi ei addantur horæ 12. </s> <s xml:id="echoid-s22301" xml:space="preserve"><lb/>quæ intercedunt vſque ad mediam noctem, neceſiariò hora proximè præcedens mediam noctem di-<lb/>ſtabit min. </s> <s xml:id="echoid-s22302" xml:space="preserve">21. </s> <s xml:id="echoid-s22303" xml:space="preserve">à meridiano nocturno: </s> <s xml:id="echoid-s22304" xml:space="preserve">Quare quatuor horæ antemerinocturnæ tantum ſingulæ di-<lb/>ſtabunt à meridiano nocturno, & </s> <s xml:id="echoid-s22305" xml:space="preserve">inſeriori, quantum aliæ quatuor diurnæ proximè meridiem præ <lb/>cedentes diſtantà meridiano diurno, & </s> <s xml:id="echoid-s22306" xml:space="preserve">ſuperiori: </s> <s xml:id="echoid-s22307" xml:space="preserve">igitur diſtantiæ nocturnarum horarum 1, 2, 3, 4,. </s> <s xml:id="echoid-s22308" xml:space="preserve"><lb/>æquales erunt diſtantijs diurnarum 13. </s> <s xml:id="echoid-s22309" xml:space="preserve">14. </s> <s xml:id="echoid-s22310" xml:space="preserve">15. </s> <s xml:id="echoid-s22311" xml:space="preserve">16 & </s> <s xml:id="echoid-s22312" xml:space="preserve">conſequenter reliquarum pomerinocturnarum <lb/>5, 6, 7, 8,. </s> <s xml:id="echoid-s22313" xml:space="preserve">diſtantię æquales erunt diſtantijs diurnarum 17, 18, 19, 20,. </s> <s xml:id="echoid-s22314" xml:space="preserve">Præterea conſiderandum, quod <lb/>cum portio nocturna ♋. </s> <s xml:id="echoid-s22315" xml:space="preserve">ſit eadem cum portione diurna ♑ ſi illa transferatur in locum huius, ita vt <lb/>pars antemerinocturna ♋. </s> <s xml:id="echoid-s22316" xml:space="preserve">euadat pomeridiana ♑; </s> <s xml:id="echoid-s22317" xml:space="preserve">pars vero pomerinocturna ♋. </s> <s xml:id="echoid-s22318" xml:space="preserve">euadat antemeri-<lb/>diana ♑, erunt horarum appellationes incipiendo ab occaſu in ♋, hæ 1, 2, 3, 4, 5, 6, 7, 8,. </s> <s xml:id="echoid-s22319" xml:space="preserve">in horas <lb/>24, 22, 21, 20, 19, 18, 17, 16. </s> <s xml:id="echoid-s22320" xml:space="preserve">& </s> <s xml:id="echoid-s22321" xml:space="preserve">habebimus arcum diurnum Capricorni ipſiſſimum, &</s> <s xml:id="echoid-s22322" xml:space="preserve">c. </s> <s xml:id="echoid-s22323" xml:space="preserve">ac propterea <lb/>(vti dictum eſt) earum diſtantiæ eædem erunt cum diſtantijs totidem horarum Cancri. </s> <s xml:id="echoid-s22324" xml:space="preserve">qua de cau-<lb/>ſa has horas ♑. </s> <s xml:id="echoid-s22325" xml:space="preserve">ſcripſimus in Apparatu è regione illarum horarum ♋, quæ æqualiter cum illis diſtãt <lb/>à meridie.</s> <s xml:id="echoid-s22326" xml:space="preserve"/> </p> <div xml:id="echoid-div623" type="float" level="2" n="1"> <note position="right" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">Portio <lb/>noctur-<lb/>na ♋, <lb/>æqualis <lb/>eſt diur-<lb/>nę oppo-<lb/>ſitipa-<lb/>ralelli <lb/>♑, &c. <lb/>permu-<lb/>tatim.</note> </div> <p> <s xml:id="echoid-s22327" xml:space="preserve">2 Vnde ſequitur horas Capricorni habere præterea eaſdem ſinus verſos diſtantiarum cum præ-<lb/>dictis horis Cancri: </s> <s xml:id="echoid-s22328" xml:space="preserve">& </s> <s xml:id="echoid-s22329" xml:space="preserve">conſequenter ex ductu eorum in ſemiſſem aggregati fore idem productum, & </s> <s xml:id="echoid-s22330" xml:space="preserve"><lb/>eundem quotientem ex eius diuiſionem per ſinum totum. </s> <s xml:id="echoid-s22331" xml:space="preserve">qui quotiens detrahendus eſt ex ſinu alti-<lb/>tudinis meridianæ Capricorni, qui eſt 38, 268. </s> <s xml:id="echoid-s22332" xml:space="preserve">qui cum differat à ſinu altitudinis meridianæ Cancri <lb/>relinquet neceſſariò alium numerum, qui reliquus numerus erit ſinus altitudinis horæ ſibi compe-<lb/>tentis. </s> <s xml:id="echoid-s22333" xml:space="preserve">cum vero hi quotientes ſint in Cancro ſeruati (vt monuimus) ijs nunc abſque vllo multipli-<lb/>candi, aut diuidendi labore vtemur. </s> <s xml:id="echoid-s22334" xml:space="preserve">hoc compendio altitudines horarum in ♑. </s> <s xml:id="echoid-s22335" xml:space="preserve">quas in Apparatu vi-<lb/>des, inuenimus.</s> <s xml:id="echoid-s22336" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22337" xml:space="preserve">3 Abſoluo calculo delendæ ſunt tabellarum multiplicationes, vt ſequentibus duobus oppoſitis <lb/>paralellis inſeruire poſſint. </s> <s xml:id="echoid-s22338" xml:space="preserve">quorum vnus eſſe per gra. </s> <s xml:id="echoid-s22339" xml:space="preserve">15. </s> <s xml:id="echoid-s22340" xml:space="preserve">0′ ♋. </s> <s xml:id="echoid-s22341" xml:space="preserve">alter vero ei oppoſitus per gra. </s> <s xml:id="echoid-s22342" xml:space="preserve">15. </s> <s xml:id="echoid-s22343" xml:space="preserve">0′ <lb/>♐. </s> <s xml:id="echoid-s22344" xml:space="preserve">in quibus eadem methodo cum ſuperioribus calculandum eſt, ideſt, prius pro boreali, poſtea per <lb/>auſtrali.</s> <s xml:id="echoid-s22345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22346" xml:space="preserve">4 Aliud compendium ex vſu erit, ſi inter paralellos calculandos, aſſumamus paralellos arcuum <lb/> <anchor type="note" xlink:label="note-0277-05a" xlink:href="note-0277-05"/> <pb o="24" file="0278" n="283" rhead="TRACTATVS"/> diurnorum horarum integrarum, ſicuti factum eſt in conſtruenda Tabula ad latit. </s> <s xml:id="echoid-s22347" xml:space="preserve">44 {1/2}. </s> <s xml:id="echoid-s22348" xml:space="preserve">tum quia per <lb/>eos exactius horologia conficiuntur, tum quia dimidio labore minus, quam in alijs computandum <lb/>eſt; </s> <s xml:id="echoid-s22349" xml:space="preserve">ſatis eſt enim computare pro horis pomeridianis, quia earum diſtantiæ a meridie æquales ſunt <lb/>diſtantijs à meridie horarum antemeridianarum; </s> <s xml:id="echoid-s22350" xml:space="preserve">quare, & </s> <s xml:id="echoid-s22351" xml:space="preserve">cætera erunt æqualia, ſcilicet ſinus verſi, <lb/>& </s> <s xml:id="echoid-s22352" xml:space="preserve">altitudines (vti vſus docebit.) </s> <s xml:id="echoid-s22353" xml:space="preserve">Aequatoris calculatio eſſe omnium facillima, tum quia nullum <lb/>habet oppoſitum paralellum, tum quia computandum eſt per horis paucioris, quam in alijs.</s> <s xml:id="echoid-s22354" xml:space="preserve"/> </p> <div xml:id="echoid-div624" type="float" level="2" n="2"> <note position="right" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">Aliudcõ <lb/>pendi{us}.</note> </div> <p> <s xml:id="echoid-s22355" xml:space="preserve">5 Tandem ex omnibus Apparatibus omnium paralellorum tranſcribendæ ſunt altitudines, & </s> <s xml:id="echoid-s22356" xml:space="preserve"><lb/>Annum, &</s> <s xml:id="echoid-s22357" xml:space="preserve">c. </s> <s xml:id="echoid-s22358" xml:space="preserve">in propriam Tabulam, quæ euadat ſimilis noſtræ ſuperiori ad lat. </s> <s xml:id="echoid-s22359" xml:space="preserve">44 {1/2}.</s> <s xml:id="echoid-s22360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s22361" xml:space="preserve">6 Alij conſtrũnt has tabulas ex paralellis tranſeuntibus per ſingulas decurias graduum Zodiaci@, <lb/> <anchor type="note" xlink:label="note-0278-01a" xlink:href="note-0278-01"/> v.</s> <s xml:id="echoid-s22362" xml:space="preserve">g. </s> <s xml:id="echoid-s22363" xml:space="preserve">per gr. </s> <s xml:id="echoid-s22364" xml:space="preserve">20. </s> <s xml:id="echoid-s22365" xml:space="preserve">0′. </s> <s xml:id="echoid-s22366" xml:space="preserve">♋. </s> <s xml:id="echoid-s22367" xml:space="preserve">per grad. </s> <s xml:id="echoid-s22368" xml:space="preserve">10. </s> <s xml:id="echoid-s22369" xml:space="preserve">0′. </s> <s xml:id="echoid-s22370" xml:space="preserve">♋. </s> <s xml:id="echoid-s22371" xml:space="preserve">per grad. </s> <s xml:id="echoid-s22372" xml:space="preserve">20. </s> <s xml:id="echoid-s22373" xml:space="preserve">0. </s> <s xml:id="echoid-s22374" xml:space="preserve">♋. </s> <s xml:id="echoid-s22375" xml:space="preserve">per grad. </s> <s xml:id="echoid-s22376" xml:space="preserve">0. </s> <s xml:id="echoid-s22377" xml:space="preserve">0. </s> <s xml:id="echoid-s22378" xml:space="preserve">♌ & </s> <s xml:id="echoid-s22379" xml:space="preserve">ſic vſq; </s> <s xml:id="echoid-s22380" xml:space="preserve">ad finem.</s> <s xml:id="echoid-s22381" xml:space="preserve"/> </p> <div xml:id="echoid-div625" type="float" level="2" n="3"> <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">Aliata-<lb/>bul@.</note> </div> <p> <s xml:id="echoid-s22382" xml:space="preserve">7 Monitos volo Tyrones, ne ob multa, ac varia errata, quæ in hiſce calculis contingere ſolent, <lb/>animum deſpondeant, nam labor omnia vincit improbus. </s> <s xml:id="echoid-s22383" xml:space="preserve">neq; </s> <s xml:id="echoid-s22384" xml:space="preserve">nimis ſuis fidant operationibus, ſed <lb/>eas conferant cum virorum doctorum ealculis ſeu Tabulis, quæ paſſim editæ reperiuntur: </s> <s xml:id="echoid-s22385" xml:space="preserve">præterea <lb/>vſus ſuarum tabularum in deſcribendis horologijs propria errata detegere ſolet.</s> <s xml:id="echoid-s22386" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div627" type="section" level="1" n="433"> <head xml:id="echoid-head458" xml:space="preserve">LAVSDEO:</head> <pb file="0279" n="284"/> <figure> <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0279-01"/> </figure> <figure> <image file="0279-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0279-02"/> </figure> <pb file="0280" n="285"/> <figure> <image file="0280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0280-01"/> </figure> <pb file="0281" n="286"/> <figure> <image file="0281-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0281-01"/> </figure> <pb file="0282" n="287"/> <figure> <image file="0282-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0282-01"/> </figure> <pb file="0283" n="288"/> <figure> <image file="0283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0283-01"/> </figure> <pb file="0284" n="289"/> <figure> <image file="0284-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0284-01"/> </figure> <pb file="0285" n="290"/> <pb file="0286" n="291"/> <pb file="0287" n="292"/> </div> <div xml:id="echoid-div628" type="section" level="1" n="434"> <head xml:id="echoid-head459" xml:space="preserve">Apparatus ad calculandas altit ſingularum horarum aboccaſu <lb/>in vtroque Tropico ad latit. 44.</head> <note position="right" xml:space="preserve"> <lb/># H. # M. <lb/># 24 # 0 <lb/>Tempus ſemidiurnum in tropico ♋. # 7 # 18 <lb/>Diurnum verò # 15 # 39 <lb/>Quare eius meridies # 16 # 21 <lb/>Ortus Solis erit # 8 # 42 <lb/>Quare tempus diurnum in tropico ♑. erit # 8 # 42 <lb/>Meridies autem in tropico ♑. erit # 19 # 39 <lb/>### Arcus ſemidiurnus, ſeu diſ@a@a hor. 24. à meridie in trop. Cancri eſt gr. 114. 50″<unsure/> <lb/>Quare cæterarum diſtantiæ à meridie erunt ſequentes. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Horæ in \\ trop. ♑. # Horæ in \\ trop. ♋. # ## Diſtantię \\ à meridie. # Har. diſ@ã. \\ ſinus verſi. # ## Altit. hor. in trop. ♋. # ## Altit. hor. \\ in trop ♑. <lb/># # G. # M. # # G. # M. # G. # M. <lb/># 24 # 114 # 50 # 117,078 # 9 # 28 # 5 # 55 <lb/># 23 # 99 # 50 # 90,994 # 19 # 40 # 13 # 16 <lb/># 22 # 84 # 50 # 65,524 # 30 # 18 # 18 # 46 <lb/>Ort. 15. 18′ # 21 # 59 # 50 # 42,404 # 41 # 4 # 21 # 54 <lb/>16 # 20 # 54 # 50 # 23,208 # 51 # 35 # 22 # 20 <lb/>17 # 19 # 39 # 50 # 9,246 # 61 # 7 # 20 # 1 <lb/>18 # 18 # 24 # 50 # 1,469 # 62 # 58 # 15 # 13 <lb/>19 # 17 # 9 # 50 # 406 # 69 # 4 # 8 # 22 <lb/>Mer. 19. 39′ # Mer. 16. 21′ # 5 # 10 # 6,130 # 13 # 40 <lb/>20 # 15 # 20 # 10 # 18,251 # 54 # 43 <lb/>21 # 14 # 35 # 10 # 39,944 # 44 # 24 <lb/>22 # 13 # 50 # 10 # 58,001 # 33 # 39 <lb/>23 # 12 # 65 # 10 # 82,921 # 22 # 56 <lb/># 11 # 80 # 10 # 109,005 # 12 # 33 <lb/># 10 # 95 # 10 # 117,651 # 2 # 50 <lb/># 9 # 110 # 10 <lb/># Ort. 8. 42′ <lb/></note> <note position="right" xml:space="preserve"> <lb/>## Complementum latitudinis eſt gr. 46. 0′. <lb/>## Tropicorum declinatio gr. 23. 30. <lb/>Quare altitudo meridiana ♋. # erit gr. 69.30-93,667. eius ſinus rectus <lb/>Depreſſio autem meridiana ♑. <lb/>Et depreſſio meridiana ♋. # erit gr. 22. 30-38,268, eius ſinus rectus. <lb/>Altera verò meridiana ♑. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Aggregatum ex # 131,935. ſinubus rectis. <lb/>Semiſſis aggregati # 65967 {1/2}. <lb/>Sinus vero nor. 23. # 117078. <lb/>8 # 527,736 <lb/>7 # 461,769 <lb/>0 # 000000 <lb/>7 # 461769 <lb/>1 # 65967 <lb/>1 # 65967 <lb/># 77332 ſumma. <lb/>## Quotiens, & quartus terminus. <lb/></note> <figure> <image file="0287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0287-01"/> </figure> <note position="right" xml:space="preserve"> <lb/>Subtractio # 93,667. # ſinus rectus altit. merid. à quo <lb/># 77,232. # quartus terminus ſubtrahitur. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Horæabocc. # Sinus \\ recti. <lb/>1 # 65,967 <lb/>1 # 65,967 <lb/>2 # 131,934 <lb/>3 <lb/>4 # 263,868 <lb/>4 # 263,868 <lb/>5 # 329,835 <lb/>5 # 329,835 <lb/>6 # 395,802 <lb/>6 <lb/>7 # 461,769 <lb/>7 # 461,769 <lb/>8 # 527,736 <lb/>9 # 593,703 <lb/>9 # 593,703 <lb/>0 # 593,703 <lb/>0 # 000,000 <lb/></note> <pb file="0288" n="293"/> <pb file="0289" n="294"/> <pb file="0289a" n="295"/> </div> <div xml:id="echoid-div629" type="section" level="1" n="435"> <head xml:id="echoid-head460" xml:space="preserve">Tabula altitudinum Solis ſupra horizontem latit. ſeu altit. Poli 44 {1/2} pro horis ab ortu, & ab occaſu in paralellis Signorum infraſcriptis.</head> <note position="right" xml:space="preserve"> <lb/>########## Horæ abortu. # ## 1 # ## 2 # ## 3 # ## 4 # ## 5 # ## 6 # ## 7 # ## 8 # ## 9 # ## 10 # ## 11 # ## 12 # ## 13 # ## 14 # ## 15 # ## Altit. # ## Tẽpus # ## Tẽp. no. # ## Tẽpus # ## Tẽpus <lb/>########## Horæ ab occaſu. # ## 23 # ## 22 # ## 21 # ## 20 # ## 19 # ## 18 # ## 17 # ## 16 # ## 15 # ## 14 # ## 13 # ## 12 # ## 11 # ## 10 # ## 9 # ## merid. # ## diurnũ. # ## Ort. *** # ## ſemid. # ## merid. <lb/>M. # D. # S. # G. # M. # M. # D. # S. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # G. # M. # H. # M. # H. # M. # H. # M. # H. # M. <lb/>NI- # 22 # # 30 # 0 # VS. # 22 # ♋ # 0 # 0 # 9 # 21 # 19 # 28 # 29 # 59 # 40 # 41 # 51 # 6 # 60 # 34 # 67 # 23 # 68 # 39 # 63 # 33 # 54 # 48 # 44 # 38 # 33 # 59 # 23 # 21 # 13 # 2 # 3 # 22 # 69 # 0 # 15 # 22 # 8 # 38 # 7 # 41 # 16 # 19 <lb/>IV- # 6 # # 15 # 0 # IV- # 8 # # 15 # 0 # 9 # 27 # 19 # 38 # 30 # 13 # 40 # 53 # 51 # 14 # 60 # 28 # 66 # 52 # 67 # 39 # 62 # 19 # 53 # 32 # 43 # 21 # 32 # 42 # 22 # 4 # 11 # 40 # 2 # 6 # 68 # 9 # 15 # 14 # 8 # 46 # 7 # 37 # 16 # 23 <lb/>VS. # 28 # # 5 # 35 # LI- # 17 # # 24 # 25 # 9 # 39 # 19 # 56 # 30 # 35 # 41 # 14 # 51 # 25 # 60 # 17 # 65 # 58 # 65 # 58 # 60 # 17 # 51 # 25 # 41 # 14 # 30 # 35 # 19 # 56 # 9 # 39 # 0 # 0 # 66 # 47 # 15 # 0 # 9 # 0 # 7 # 30 # 16 # 30 <lb/>I- # 22 # ♊ # 0 # 0 # VS. # 24 # ♌ # 0 # 0 # 9 # 46 # 20 # 9 # 30 # 49 # 41 # 25 # 51 # 28 # 60 # 0 # 65 # 9 # 64 # 37 # 58 # 42 # 49 # 47 # 39 # 35 # 28 # 57 # 18 # 19 # 8 # 2 # # # 65 # 42 # 14 # 50 # 9 # 10 # 7 # 25 # 16 # 35 <lb/>MA # 11 # # 20 # 0 # AV- # 3 # # 10 # 0 # 10 # 7 # 20 # 38 # 31 # 19 # 41 # 47 # 51 # 27 # 59 # 13 # 63 # 9 # 61 # 32 # 55 # 8 # 46 # 7 # 35 # 54 # 25 # 16 # 14 # 38 # 4 # 21 # # # 63 # 17 # 14 # 26 # 9 # 34 # 7 # 13 # 16 # 47 <lb/>S. # 30 # # 9 # 40 # GV- # 14 # # 20 # 20 # 10 # 16 # 20 # 54 # 31 # 34 # 41 # 46 # 50 # 52 # 57 # 38 # 60 # 15 # 57 # 38 # 50 # 52 # 41 # 46 # 31 # 34 # 20 # 54 # 10 # 16 # 0 # 0 # # 60 # 15 # 14 # 0 # 10 # 0 # 7 # 0 # 17 # 0 <lb/>LI- # 21 # ♉ # 0 # 0 # ST- # 24 # ♍ # 0 # 0 # 10 # 29 # 21 # 10 # 31 # 41 # 41 # 31 # 49 # 55 # 55 # 33 # 56 # 52 # 53 # 23 # 46 # 17 # 37 # 6 # 26 # 52 # 16 # 13 # 5 # 36 # # # # # 57 # 0 # 13 # 32 # 10 # 28 # 6 # 46 # 17 # 14 <lb/>RI- # 10 # # 19 # 18 # SE- # 3 # # 10 # 42 # 10 # 37 # 21 # 17 # 31 # 31 # 40 # 47 # 47 # 19 # 52 # 30 # 52 # 30 # 47 # 19 # 40 # 47 # 31 # 31 # 21 # 17 # 10 # 37 # 0 # 0 # # # # # 53 # 4 # 13 # 0 # 11 # 0 # 6 # 30 # 17 # 30 <lb/>AP- # 2 # # 10 # 0 # PT- # 14 # # 20 # 0 # 10 # 37 # 21 # 8 # 31 # 1 # 39 # 40 # 46 # 10 # 49 # 19 # 48 # 19 # 43 # 29 # 35 # 50 # 26 # 31 # 16 # 16 # 5 # 38 # # # # # # # 49 # 28 # 12 # 32 # 11 # 28 # 6 # 16 # 17 # 44 <lb/>IVS. # 21 # ♈ # 0 # 0 # EM. # 24 # ♎ # 0 # 0 # 10 # 38 # 20 # 53 # 30 # 17 # 38 # 9 # 43 # 33 # 45 # 30 # 43 # 33 # 38 # 9 # 30 # 17 # 20 # 53 # 10 # 38 # 0 # 0 # # # # # # # 45 # 30 # 12 # 0 # 12 # 0 # 6 # 0 # 18 # 0 <lb/>RT- # 11 # # 20 # 0 # OC- # 4 # # 10 # 0 # 10 # 23 # 20 # 18 # 29 # 6 # 36 # 8 # 40 # 30 # 41 # 25 # 38 # 42 # 32 # 54 # 24 # 52 # 15 # 26 # 5 # 11 # # # # # # # # # 41 # 32 # 11 # 28 # 12 # 32 # 5 # 44 # 18 # 16 <lb/>MA # 2 # # 10 # 42 # TO # 13 # # 19 # 18 # 10 # 16 # 19 # 46 # 27 # 57 # 34 # 7 # 37 # 30 # 37 # 30 # 34 # 7 # 27 # 57 # 19 # 46 # 10 # 16 # 0 # 0 # # # # # # # # # 37 # 56 # 11 # 0 # 13 # 0 # 5 # 30 # 18 # 30 <lb/>BR. # 19 # ♓ # 0 # 0 # BER. # 24 # *** # 0 # 0 # 9 # 56 # 18 # 53 # 26 # 18 # 31 # 33 # 33 # 55 # 33 # 2 # 29 # 3 # 22 # 32 # 14 # 13 # 4 # 41 # # # # # # # # # # # 34 # 0 # 10 # 28 # 13 # 32 # 5 # 14 # 18 # 46 <lb/>FE- # 9 # # 20 # 20 # NO- # 3 # # 9 # 40 # 9 # 35 # 18 # 1 # 24 # 46 # 29 # 12 # 30 # 45 # 29 # 12 # 24 # 46 # 18 # 1 # 9 # 35 # 0 # 0 # # # # # # # # # # # 30 # 45 # 10 # 0 # 14 # 0 # 5 # 0 # 19 # 0 <lb/>IVS. # 30 # # 10 # 0 # VE- # 13 # # # 20 # 0 # 9 # 7 # 17 # 1 # 23 # 6 # 27 # 18 # 27 # 59 # 25 # 32 # 20 # 44 # 13 # 47 # 5 # 15 # # # # # # # # # # # # # 27 # 43 # 9 # 34 # 14 # 26 # 4 # 47 # 19 # 13 <lb/>AR- # 21 # ♒ # 0 # 0 # M- # 23 # ♐ # 0 # 0 # 8 # 49 # 16 # 14 # 21 # 44 # 24 # 48 # 25 # 3 # 22 # 27 # 17 # 21 # 10 # 14 # 1 # 36 # # # # # # # # # # # # # 25 # 18 # 9 # 10 # 14 # 50 # 4 # 35 # 19 # 25 <lb/>NV- # 15 # # 24 # 25 # BER. # 29 # # 5 # 35 # 8 # 38 # 15 # 50 # 21 # 5 # 23 # 52 # 23 # 52 # 21 # 5 # # 15 # 50 # 8 # 38 # 0 # 0 # # # # # # # # # # # # # 24 # 13 # 9 # 0 # 15 # 0 # 4 # 30 # 19 # 30 <lb/>IA- # 6 # # 15 # 0 # DE- # 8 # # 15 # 0 # 8 # 26 # 15 # 20 # 20 # 13 # 22 # 29 # 22 # 19 # 19 # 17 # 13 # 53 # 6 # 35 # # # # # # # # # # # # # # # 22 # 51 # 8 # 46 # 15 # 14 # 4 # 23 # 19 # 37 <lb/>BER. # 22 # ♑ # 30 # 0 # CEM # 22 # # 30 # 0 # 8 # 15 # 14 # 58 # 19 # 39 # 21 # 55 # 21 # 21 # 18 # 10 # 12 # 40 # 5 # 20 # # # # # # # # # # # # # # # 22 # 0 # 8 # 38 # 15 # 22 # 4 # 19 # 19 # 41 <lb/># # # # # # # # # ###### Altitudines pomeridianæ. ###### Altitudo antemeridianæ. <lb/>1 # 2 # 3 # ## 4 # 5 # 6 # 7 # ## 8 # ## 9 # ## 10 <lb/></note> <pb file="0290" n="296"/> <pb file="0291" n="297"/> <pb file="0292" n="298"/> <pb file="0293" n="299"/> <pb file="0294" n="300"/> </div></text> </echo>