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diff texts/XML/echo/la/Biancani_1635_GWS4WXH4.xml @ 6:22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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| date | Fri, 07 Dec 2012 17:05:22 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/texts/XML/echo/la/Biancani_1635_GWS4WXH4.xml Fri Dec 07 17:05:22 2012 +0100 @@ -0,0 +1,28518 @@ +<?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> \ No newline at end of file