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DESpecs 2.0 Autumn 2009
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Thu, 02 May 2013 11:14:40 +0200
parents 22d6a63640c6
children
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">
  <info>
    <author>Biancani, Giuseppe</author>
    <title>Aristotelis loca mathematica</title>
    <date>1615</date>
    <place>Bologna</place>
    <translator/>
    <lang>la</lang>
    <cvs_file>bianc_locam_009_la_1615</cvs_file>
    <cvs_version/>
    <locator>009.xml</locator>
  </info>
  <text>
    <front>
      <pb xlink:href="009/01/001.jpg"/>
      <section>
        <p type="head">
          <s id="s.000001">ARISTOTELIS <lb/>LOCA MATHEMATICA <lb/>
Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>
&amp; explicata.</s>
        </p>
        <p type="head">
          <s id="s.000002"><emph type="italics"/>Aristotelic&aelig; videlicet expo&longs;itionis complementum <lb/>
hactenus de&longs;ideratum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000003">Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/>
<expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s>
        </p>
        <p type="head">
          <s id="s.000004"><emph type="italics"/>Authore IOSEPHO BLANCANO Bononien&longs;i &egrave; Societate Ie&longs;u, <lb/>
Mathematicarum in Gymna&longs;io Parmen&longs;i Profe&longs;&longs;ore.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000005">Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum <lb/>PETRVM FRANCISCVM MALASPINAM <lb/>
Aedificiorum Marchionem, apud C&aelig;&longs;. <!-- REMOVE S-->Maie&longs;tatem <lb/>
pro Sereni&longs;s. <!-- REMOVE S-->Parmen&longs;ium Duce Legatum.</s>
        </p>
        <p type="head">
          <s id="s.000006">BONONI&AElig; M. <!-- REMOVE S-->D C. <!-- KEEP S--><!-- REMOVE S-->X V.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000007">Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>
          <s id="s.000008">Superiorum permi&longs;&longs;u.</s>
        </p>
        <p type="head">
          <s id="s.000009">Sumptibus Hieronymi Tamburini.</s>
        </p>
        <pb xlink:href="009/01/002.jpg"/>
        <pb pagenum="3" xlink:href="009/01/003.jpg"/>
      </section>
      <section>
        <p type="head">
          <s id="s.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO <lb/>PETRO FRANCISCO <lb/>MALASPINAE <lb/>
&AElig;DIFICIORVM MARCHIONI.</s>
        </p>
        <p type="main">
          <s id="s.000011"><emph type="italics"/>En tandem Illustri&szlig;. <!-- REMOVE S-->Marchio opus no&shy;<lb/>
strum de Locis Mathematicis apud Ari&shy;<lb/>
stotelem, vn&agrave; cum Tractatione de natura <lb/>
&longs;cientiarum Mathematicarum, necnon <lb/>
Clarorum <expan abbr="Mathematicor&utilde;">Mathematicorum</expan> Chronologia; <lb/>
quod tibi Mec&oelig;nati meo munificenti&longs;simo iure merit&ograve; <lb/>
dicare, ac &longs;ub clari&szlig;imi tui nominis patrocinio in lucem <lb/>
dare con&longs;titui. </s>
          <s id="s.000012">prim&ugrave;m quidem, vt mei perpetui erga te <lb/>
amoris, &amp; ob&longs;eruanti&aelig; hoc vnum &longs;altem specimen exta&shy;<lb/>
ret: t&ugrave;m vt idoneum, &aelig;quumque propo&longs;it&aelig; rei iudicem <lb/>
nanci&longs;cerer. </s>
          <s id="s.000013">c&ugrave;m enim ad iu&longs;tum <expan abbr="arbitr&utilde;">arbitrum</expan> duo poti&szlig;im&ugrave;m <lb/>
requirantur, rerum &longs;cilicet cognitio, atque prudentia, quem <lb/>
te rei, de qua agitur peritiorem, quemu&egrave; prudentiorem <lb/>
inuenire potuerim? </s>
          <s id="s.000014">tu enim c&ugrave;m Phy&longs;iologi&aelig;, ac Mathe&shy;<lb/>
maticarum omnium Encyclop&aelig;diam mirum in modum<emph.end type="italics"/> <pb pagenum="4" xlink:href="009/01/004.jpg"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>
per&longs;ua&longs;i&longs;ti, vt Archimedis, &amp; Apollonij admirandis, ac <lb/>
&longs;ubtili&szlig;imis Demon&longs;trationibus detinearis. </s>
          <s id="s.000015">Quanta por&shy;<lb/>
r&ograve; in rebus agendis prudentia valeas, toti pen&egrave; Europ&aelig; <lb/>
innotuit, c&ugrave;m pro no&longs;tris Sereni&szlig;. <!-- REMOVE S-->Ducibus, non &longs;ol&ugrave;m ad <lb/>
omnes fer&egrave; Itali&aelig;, atque Germani&aelig; Principes, ver&ugrave;m etiam <lb/>
ad C&aelig;&longs;aream Maie&longs;tatem rebus f&oelig;liciter ge&longs;tis Legatus <lb/>
decim&ugrave;m extiteris; ac dem&ugrave;m &agrave; Sereni&szlig;. <!-- REMOVE S-->Duce Ranutio <lb/>
inter primarios de Rep. <!-- KEEP S--></s>
          <s id="s.000016">Con&longs;iliorum Authores ad&longs;citus <lb/>
fueris. </s>
          <s id="s.000017">C&aelig;ter&ugrave;m in Clarorum Mathematicorum Chro&shy;<lb/>
nologia perlegenda, &longs;&aelig;pi&szlig;im&egrave; tibi nobili&szlig;imi &aelig;qu&egrave;, ac do&shy;<lb/>
cti&szlig;imi Viri, tui omnino per&longs;imiles occurrent, quod tibi <lb/>
nonni&longs;i grati&szlig;imum accidere po&longs;&longs;e arbitror. </s>
          <s id="s.000018">Complectere <lb/>
igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu&shy;<lb/>
dia promouere, mea h&aelig;c quantulacumque munu&longs;cula. <lb/>
</s>
          <s id="s.000019">qu&aelig; &longs;i tibi accepta e&longs;&longs;e intellexero, iam tandem ma&shy;<lb/>
ximorum munerum loco habenda e&longs;&longs;e cen&longs;e&shy;<lb/>
bo. </s>
          <s id="s.000020">incolumem tibi, ac f&oelig;licem D. Opt. <lb/>
<!-- REMOVE S-->Max. <!-- REMOVE S-->long&aelig;uitatem tueatur. <lb/>
</s>
          <s id="s.000021">Vale.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000022"><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/>
<!-- KEEP S--></s>
        </p>
      </section>
      <pb pagenum="5" xlink:href="009/01/005.jpg"/>
      <section>
        <p type="head">
          <s id="s.000023">Liber de &longs;e ip&longs;o.</s>
        </p>
        <p type="head">
          <s id="s.000024"><emph type="italics"/>Nec di&longs;cet Lector me &longs;olo interprete totum, <lb/>
Nec &longs;ine me totum di&longs;cet Aristotelem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000025">Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>
Ie&longs;u, ex auctoritate Adm. <!-- REMOVE S-->Reuer. <!-- REMOVE S-->P. no&longs;tro Pr&aelig;po&longs;iti Generalis P. <!-- REMOVE S-->Claudij <lb/>
Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. <!-- REMOVE S-->Io&longs;ephi Blancani eiu&longs;dem <lb/>
Societatis, quod in&longs;cribitur, Ari&longs;t. Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>
operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>
probatum typis mandari po&longs;&longs;it. </s>
          <s id="s.000026">Parm&aelig; die 15. Ianuarij 1615.</s>
        </p>
        <p type="main">
          <s id="s.000027"><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/><!-- REMOVE S--><lb/>
Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s>
          <s id="s.000028">&amp; Reuerendi&longs;s. <!-- REMOVE S-->Archiepi&longs;c. <!-- REMOVE S-->Bonon.</s>
        </p>
        <p type="main">
          <s id="s.000029">Imprimatur</s>
          <s id="s.000030">Fr. <!-- REMOVE S-->Hieronymus Onuphrius pro Reuerendi&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Inqui&longs;itore Bonon.</s>
        </p>
      </section>
      <pb pagenum="6" xlink:href="009/01/006.jpg"/>
      <section>
        <p type="head">
          <s id="s.000031">LECTORI.</s>
        </p>
        <p type="main">
          <s id="s.000032">Qvod pri&longs;cis olim temporibus &lpar;humani&longs;&longs;ime Lector&rpar; &longs;um&shy;<lb/>
mi duo Philo&longs;ophi, Philippus Mendeus, ac Theon Smyr&shy;<lb/>
n&aelig;us in Platonis Dialogis egregi&egrave; perfecerunt, vt videli&shy;<lb/>
cet qu&aelig; pa&longs;&longs;im &longs;ummus hic Philo&longs;ophus de Mathemati&shy;<lb/>
cis &longs;cripta reliquit, eadem ip&longs;a ab illis &longs;electa, &amp; in vnum <lb/>
qua&longs;i corpus redacta lucubrationibus illu&longs;trarent: idem ego quoque in <lb/>
Ari&longs;totelis operibus efficere &longs;um conatus, vt qu&aelig; de Mathematicis re&shy;<lb/>
bus in vniuer&longs;is eiu&longs;dem monumentis &longs;par&longs;a leguntur, eadem in vnum <lb/>
&agrave; me collecta, &amp; explicata ijs Philo&longs;ophi&aelig; &longs;tudio&longs;is maxime &longs;eruirent, <lb/>
qui pri&longs;ca illa con&longs;uetudine relicta, Mathematicarum omnium ignari <lb/>
non &longs;ine graui &longs;tudiorum &longs;uorum detrimento Philo&longs;ophi&aelig; curriculum <lb/>
aggrediuntur. </s>
          <s id="s.000033">Vt autem huius operis nece&longs;&longs;itas, <expan abbr="vari&aelig;&qacute;">vari&aelig;que</expan>; vtilitates pla&shy;<lb/>
nius cogno&longs;cantur oper&aelig;pretium erit initio illius cau&longs;as exponere; qu&aelig; <lb/>
me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s>
        </p>
        <p type="main">
          <s id="s.000034">Prima &longs;it, quod h&aelig;c Ari&longs;t. loca Mathematica, qu&aelig; quidem fer&egrave; 408. <lb/>
numerantur, pe&longs;&longs;im&egrave; latinis literis con&longs;ignata &longs;unt v&longs;que ade&ograve;, vt Ari&shy;<lb/>
&longs;totelem ip&longs;um, vel inuitum &lpar;quod po&longs;tea multis in locis planum fiet&rpar; in <lb/>
ab&longs;urdi&longs;&longs;ima errata &longs;&aelig;pi&longs;&longs;im&egrave; compellant.</s>
        </p>
        <p type="main">
          <s id="s.000035">Secunda, qu&ograve;d plurima huiu&longs;modi loca &agrave; nemine, quod &longs;ciam, adhuc <lb/>
declarata in tenebris magno no&longs;trorum malo delite&longs;cunt: cuiu&longs;modi <lb/>
&longs;unt ad &longs;exaginta problemata, libellus de lineis in &longs;ecabilibus, libellus <lb/>
de mundo, &longs;i tamen Ari&longs;totelis e&longs;t, &amp; Mechanic&aelig; qu&aelig;&longs;tiones, quamuis <lb/>
enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif&shy;<lb/>
ficiliora non &longs;atis illu&longs;trauit. </s>
          <s id="s.000036">Vt autem dixi 408. in vniuer&longs;um loca mi&shy;<lb/>
nim&ugrave;m numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">agaiome/trhtos <lb/>
udei/s eisi/to</foreign>; &amp; in quibus Mathematic&aelig; di&longs;ciplin&aelig; rudes, &amp; imperiti, quem <lb/>
&longs;equuntur ducem Ari&longs;t. eum &longs;&aelig;pe de&longs;erere non &longs;ine turpi dedecoris no&shy;<lb/>
ta coguntur; quo fit vt exempla illa Mathematica lucem rebus aliquan&shy;<lb/>
do allatura, tenebras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/>
obducant.</s>
        </p>
        <p type="main">
          <s id="s.000037">Tertia, quia Gr&aelig;ci eorumdem locorum commentatores breuiter, &amp; <lb/>
ob&longs;cur&egrave; admodum ea, qu&aelig; ad Mathematicum &longs;pectant, attingunt, hoc <lb/>
enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, Lectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>
Philo &longs;ophorum, Mathematicis imbutum; at ver&ograve; no&longs;tra &aelig;tate magna <lb/>
cum Philo&longs;ophi&aelig; iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti&shy;<lb/>
tuti pr&aelig;&longs;idijs, ne Gr&aelig;corum quidem Interpretum explanationes, ne&shy;<lb/>
dum Ari&longs;t. ob&longs;cur&egrave; dicta intelligunt.</s>
        </p>
        <pb pagenum="7" xlink:href="009/01/007.jpg"/>
        <p type="main">
          <s id="s.000038">Quarta. </s>
          <s id="s.000039">Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati&shy;<lb/>
corum puluere con&longs;per&longs;us, ade&ograve; tamen peruer&longs;a e&longs;t eorumdem Gr&aelig;co&shy;<lb/>
rum in Latinum tran&longs;latio, <expan abbr="tanta&qacute;">tantaque</expan>; figurarum, qu&aelig; nece&longs;&longs;ari&aelig; erant <lb/>
confu&longs;io, &amp; deprauatio, vt nec abeo, qui &longs;it Mathematicarum &longs;cientia <lb/>
excultus, &longs;ine magno labore percipi po&longs;&longs;int. </s>
          <s id="s.000040">Quin etiam figur&aelig; ill&aelig;, qu&aelig; <lb/>
omnino nece&longs;&longs;ari&aelig; &longs;unt ob Scriptorum, &amp; Typographorum in&longs;citiam, <lb/>
aut inertiam pluribus in locis de&longs;iderantur. </s>
          <s id="s.000041">Latini ver&ograve; multo minus, <lb/>
qu&agrave;m Gr&aelig;ci Mathematic&aelig; periti, qua ratione eadem loca pertractaue&shy;<lb/>
rint, facilius e&longs;t conijcere, qu&agrave;m vt dici oporteat.</s>
        </p>
        <p type="main">
          <s id="s.000042">Quinta. </s>
          <s id="s.000043">Ex his omnibus in aliud incommodum, vel maximum Phi&shy;<lb/>
lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta&shy;<lb/>
citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t. percipiendam <lb/>
&longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;&shy;<lb/>
&longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s>
          <s id="s.000044">Eorum ver&ograve; nonnulli eorumdem <lb/>
locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri&shy;<lb/>
les ill&aelig;, ac ridicul&aelig; expo&longs;itiones pa&longs;&longs;im audit&aelig;, cuiu&longs;modi e&longs;t illa, quan&shy;<lb/>
do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha&shy;<lb/>
bet tres; nihil aliud &longs;ignificari volunt, qu&agrave;m omnem triangulum habe&shy;<lb/>
re tres angulos. </s>
          <s id="s.000045">quod &longs;i dicat, omnis triangulus habet tres &aelig;quales duo&shy;<lb/>
bus rectis: hic h&aelig;rent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/>
&longs;e minim&egrave; expedire valeant, aurea verba illa, quibus ingentes &longs;apienti&aelig; <lb/>
the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/>
cogit in&longs;citia: vnde illud, quod Gr&aelig;c&aelig; lingu&aelig; imperitis mutata oratio&shy;<lb/>
ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s>
          <s id="s.000046">Nec mi&shy;<lb/>
nus elegans illa altera expo&longs;itio; Diametrum e&longs;&longs;e incommen&longs;urabilem <lb/>
co&longs;t&aelig;; quod &longs;&aelig;pe apud Ari&longs;t. legentibus occurrit, nihil aliud &longs;ibi velle, <lb/>
quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetri&aelig; huius <lb/>
ignorantiam Plato de legibus dial. 7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco&shy;<lb/>
rumque</expan> appellare non dubitauit. </s>
          <s id="s.000047">Quid illa? </s>
          <s id="s.000048">cum Ari&longs;t. ait duo cubi, cu&shy;<lb/>
bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>
uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/>
</s>
          <s id="s.000049">Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. <!-- REMOVE S-->15. qu&agrave;m &longs;e Mathematicis, <lb/>
reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>
tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>
tum, argumentari,</s>
        </p>
        <p type="main">
          <s id="s.000050"><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>
It a voluntas antiqua ad effectum antiquum. <lb/>
</s>
          <s id="s.000051">Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>
antiquum, ita voluntas antiqua ad effectum nouum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000052"><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i ri&longs;um teneatis amici? </s>
          <s id="s.000053">nego, ait; qui&longs;piam con&longs;equen&shy;


<pb pagenum="8" xlink:href="009/01/008.jpg"/>tiam, non enim hoc e&longs;t argumentari &agrave; permutata ratione, deberet enim <lb/>
inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad&shy;<lb/>
modum effectus nouus ad antiquum. </s>
          <s id="s.000054">qu&aelig; vitio&longs;a argumentatio quan&shy;<lb/>
tumuis l&aelig;uis &longs;it, &amp; manife&longs;ta, quo&longs;dam tamen magni nominis philo&longs;o&shy;<lb/>
phantes ade&ograve; tor&longs;it, vt adhuc torqueat.</s>
        </p>
        <p type="main">
          <s id="s.000055">Quanta autem mi&longs;eratione digni, qui public&egrave; aliquando apud &longs;uos <lb/>
auditores totam Per&longs;pectiuam, qua nihil iucundius e&longs;t, de medio tolle&shy;<lb/>
re conati &longs;unt, propterea quod ill&aelig; vi&longs;uales line&aelig;, illi anguli, ill&aelig; pyra&shy;<lb/>
mides, aut coni, quibus vi&longs;io perficitur nullibi extarent, &longs;ed e&longs;&longs;ent vana <lb/>
qu&aelig;dam opticorum figmenta. </s>
          <s id="s.000056">Qu&igrave; ver&ograve; fieri potuit, vt non aduerterint <lb/>
i&longs;ti &longs;e Ari&longs;toteli &longs;uo manife&longs;te repugnare, qui &longs;&aelig;pius de lineis vi&longs;ualibus <lb/>
per&longs;pectiuum pertractare a&longs;&longs;erit, <expan abbr="di&longs;crimen&qacute;">di&longs;crimenque</expan>; inter lineam phy&longs;icam, &amp; <lb/>
opticam a&longs;&longs;ignat, <expan abbr="ip&longs;ius&qacute;">ip&longs;iusque</expan>; optices tanquam ver&aelig; &longs;cienti&aelig; mentionem <lb/>
&longs;&aelig;pius facit.</s>
        </p>
        <p type="main">
          <s id="s.000057">Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/>
epiciclos omnes de c&oelig;lo detrahere cupientes. </s>
          <s id="s.000058">Verum id i&longs;ti nulla ex&shy;<lb/>
pre&longs;&longs;a nedum probabili ratione faciunt, fals&ograve; exi&longs;timantes A&longs;tronomos <lb/>
admirandam illam C&oelig;lorum fabricam a&longs;&longs;erere, non autem &longs;upponere: <lb/>
&longs;ed a&longs;tronomi illam &longs;upponunt, <expan abbr="eam&qacute;">eamque</expan>; propterea hypothe&longs;im <expan abbr="appell&atilde;t">appellant</expan>, <lb/>
non a&longs;&longs;erunt. </s>
          <s id="s.000059">Quod &longs;i aliqua probabili ratione id facerent, vti nonnulli <lb/>
ex recentioribus, quorum Ticho Coripheus e&longs;t, laudandi potius, quam <lb/>
vituperandi e&longs;&longs;ent. </s>
          <s id="s.000060">Impugnant <expan abbr="itaq;">itaque</expan> a&longs;tronomachi i&longs;ti hypothe&longs;im pro <lb/>
a&longs;&longs;ertione; <expan abbr="tales&qacute;">talesque</expan>; &longs;&aelig;p&egrave; hi &longs;unt, vt non &longs;atis intelligant, quid &longs;it Aequa&shy;<lb/>
tor, aut Zodiacus, ne dum quid Epiciclus, aut Eccentricus. </s>
          <s id="s.000061">Nec defuit <lb/>
qui viginti duo argumenta excogitarit, <expan abbr="atq;">atque</expan> in medium protulerit, qui&shy;<lb/>
bus contra A&longs;tronomos probare conatus e&longs;t, nullo modo Solem, aut <lb/>
Lunam moueri po&longs;&longs;e motibus contrarijs, ide&longs;t, ab oriente in <expan abbr="occid&etilde;tem">occidentem</expan> <lb/>
motu diurno, &amp; proprio ab occidente in orientem. </s>
          <s id="s.000062">Sed exi&longs;timandum <lb/>
e&longs;t <expan abbr="i&longs;t&utilde;">i&longs;tum</expan> Lunam nouam &agrave; Sole quotidie magis, ac magis ver&longs;us orientem <lb/>
recedere, nunquam animaduerti&longs;&longs;e; ab ea enim hanc motuum concor&shy;<lb/>
diam didici&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.000063">Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om&shy;<lb/>
nium tamen <expan abbr="Mathematicar&utilde;">Mathematicarum</expan> experte, qui in publica di&longs;putatione axio&shy;<lb/>
ma illud Mathematicum, omne totum e&longs;t maius &longs;ua parte, in &longs;en&longs;u in <lb/>
quo &agrave; Mathematicis effertur negare non erubuit, e&ograve;, quod in infinito, <lb/>
vt aiebat non concederetur ab omnibus. </s>
          <s id="s.000064">&longs;cilicet non intelligebat ma&shy;<lb/>
thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/>
in qua axioma pr&aelig;dictum ab omnibus conceditur. </s>
          <s id="s.000065">Neque vero hic <lb/>
nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/>
e&ograve; progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien&shy;


<pb pagenum="9" xlink:href="009/01/009.jpg"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu&shy;<lb/>
gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/>
qu&agrave;m quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/>
qu&aelig; cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi&shy;<lb/>
bus vafr&egrave; per&longs;uadere conabatur. </s>
          <s id="s.000066">Verum enim ver&ograve; optim&egrave; &longs;cio, ea, <lb/>
qu&etail; hactenus dicta &longs;unt non in omnes no&longs;tri temporis Philo&longs;ophos qua&shy;<lb/>
drare, cum non pauci hodie quoque &longs;int, qui more antiquorum Mathe&shy;<lb/>
maticis &longs;uffulti, optim&egrave; &longs;uis &longs;tudijs con&longs;ulentes, reliquam Philo&longs;ophiam <lb/>
non &longs;ine magno compendio aggrediuntur. </s>
          <s id="s.000067">Quo fit, vt c&aelig;teros ageo&shy;<lb/>
metretos ita antecellant, vt eorum Magi&longs;tri appellari po&longs;&longs;int, &amp; <expan abbr="debe&atilde;t">debeant</expan>; <lb/>
tales fuerunt in primis Vicomercatus, Cardanus, Zabarella, Toletus, <lb/>
Bonamicus, &amp; alij, quibus paulo antiquiores fuerunt D. Tho. <!-- REMOVE S-->&amp; Scotus, <lb/>Hi omnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o&shy;<lb/>
phantes excelluerint, nemo e&longs;t qui non nouerit. </s>
          <s id="s.000068">Illud hoc loco minim&egrave; <lb/>
tacendum, Iacobum Zabarellam in &longs;uis logic&aelig; commentarijs te&longs;tari &longs;e <lb/>
bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfect&egrave; Ari&longs;t. de <lb/>
demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.000069">Hi ridiculas illas, ac pueriles expo&longs;itiones &longs;uperius allatas minim&egrave; <lb/>
effutierunt, neque reliquis &longs;upra recen&longs;itis incommodis obnoxij fue&shy;<lb/>
runt, quibus magno etiam cum dedecore alij Mathematicarum ope ca&shy;<lb/>
rentes afficiuntur.</s>
        </p>
        <p type="main">
          <s id="s.000070">In horum igitur gratiam operam diligenter dedi, vt quantum in me <lb/>
e&longs;&longs;et damna &agrave; me &longs;upra enarrata aliqua ex parte re&longs;arcirem. </s>
          <s id="s.000071">Quaprop&shy;<lb/>
ter loca h&aelig;c mathematica num rect&egrave; e&longs;&longs;ent &egrave; gr&aelig;co in latinum tran&longs;lata <lb/>
diligenter prius expendi. </s>
          <s id="s.000072">Deinde claritate, qu&agrave;m potui maxima eadem <lb/>
loca interpretatus &longs;um, &amp; in horum, de quibus dixi gratiam, qu&aelig;dam <lb/>
fan&egrave; tenuia pro&longs;equutus &longs;um, qu&aelig; alioquin libenter omi&longs;i&longs;&longs;em. </s>
          <s id="s.000073">Tum fi&shy;<lb/>
guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s>
          <s id="s.000074">Hoc igitur <lb/>
no&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere, <lb/>
<expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo &agrave; Lectore ma&shy;<lb/>
thematicarum experte requiram, vt principia &longs;altem illa, &longs;cilicet defini&shy;<lb/>
tiones, po&longs;tulata, &amp; axiomata, qu&aelig; prim&ograve; Euclideis libro pr&aelig;ponuntur, <lb/>
diligenter prius perlegat cum illa &longs;ua per&longs;picuitate omnibus &longs;int obuia; <lb/>
c&aelig;tera ego explicanda recipio. </s>
          <s id="s.000075">Obiter etiam auctaria nonnulla partim <lb/>
mathematica, partim naturalia in&longs;erui, qu&aelig; ob nouitatem, ac pulchri&shy;<lb/>
tudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s>
        </p>
        <p type="main">
          <s id="s.000076">Sciat pr&aelig;terea Lector no&longs;trum in&longs;titutum e&longs;&longs;e loca h&aelig;c mathemati&shy;<lb/>
ca, quatenus mathematica &longs;unt declarare, &longs;iue ea &longs;upplere, qu&aelig; ex ma&shy;<lb/>
thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan&shy;<lb/>
tum harum rerum cum illis connexio po&longs;tulat.</s>
        </p>
        <pb pagenum="10" xlink:href="009/01/010.jpg"/>
        <p type="main">
          <s id="s.000077">His omnibus placuit appendices opportune nonnullas addere, qua&shy;<lb/>
rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes <lb/>
demon&longs;trationes primi libri Euclidis breuiter ad Logicam normam ex&shy;<lb/>
penduntur, vt pateat, quonam demon&longs;trationis genere <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> <expan abbr="vnaqu&etail;q;">vnaqu&etail;que</expan> <lb/>
debeat, &amp; ex illis de c&aelig;teris iudicium fiat. </s>
          <s id="s.000078">Tandem in gratiam etiam <lb/>
Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t. <lb/>
<!-- REMOVE S-->Geometrica ad Euclidis ordinem referuntur; vnde &amp; ip&longs;i ad &longs;uas pr&etail;le&shy;<lb/>
ctiones exornandas aliquid &longs;ubinde depromere queant.</s>
        </p>
        <p type="main">
          <s id="s.000079">Fruere igitur amice Lector hoc no&longs;tro qua liquali labore, quo ad ple&shy;<lb/>
nam totius Ari&longs;t. intelligentiam, cui adhuc mathematicarum ignoratio <lb/>
ob&longs;titit peruenire tandem po&longs;&longs;is: <expan abbr="illud&qacute;">illudque</expan>; experiaris, quod optimus qui&shy;<lb/>
dam Philo&longs;ophus, cum totum hunc librum perlegi&longs;&longs;et, effatus e&longs;t, vide&shy;<lb/>
licet, opus hoc <emph type="italics"/>Aristotelic&aelig; expo&longs;itionis complementum ad hanc v&longs;que <lb/>
diem de&longs;ideratum<emph.end type="italics"/> iure ac merit&ograve; nuncupari po&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.000080">Illud demum tanquam parergon addam, quod ego his elucubran&shy;<lb/>
dis experientia didici, ad veram &longs;cilicet, ac perfectam to&shy;<lb/>
tius Ari&longs;totelis intelligentiam lingu&aelig; in primis <lb/>
gr&aelig;c&aelig;, necnon mathematicarum om&shy;<lb/>
nium di&longs;ciplinarum haud medio&shy;<lb/>
crem cognitionem ne&shy;<lb/>
ce&longs;&longs;ariam e&longs;&longs;e. <lb/>
</s>
          <s id="s.000081">Vale.<!-- KEEP S--></s>
        </p>
      </section>
      <pb pagenum="11" xlink:href="009/01/011.jpg"/>
      <section>
        <p type="head">
          <s id="s.000082">Pr&etail;cipua qu&etail;dam, aut noua, aut re&longs;taurata, <lb/>
qu&aelig; obiter pertractantur.<lb/>
<arrow.to.target n="table1"/></s>
        </p>
        <table>
          <table.target id="table1"/>
          <row>
            <cell><emph type="italics"/>1<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De re&longs;olutione. numero marginali.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>4<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>2<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De figuris vacuum replentibus, vbi Aristotelis, &amp; expo-&longs;itorum erratum aperitur. num.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>121<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell/>
            <cell><emph type="italics"/>Inibi, Apum mirabilis qu&aelig;dam in cellis &longs;uis hexagonis   constituendis indu&longs;tria detegitur. num.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>120<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>3<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De ijs, qu&aelig; aqu&aelig; in&longs;ident, vn&agrave; cum noua demonstratione problema-tis illius Archimedis, quo metallorum mixtionem indi&longs;&longs;oluta Co-rona, explorauit. in additione. ante num.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>124<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>4<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Cometa, recentiorum &longs;ententia. num.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>136<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>5<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>148<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>6<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Terr&aelig; rotunditate, ac mundi duratione.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>151<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>7<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Iride. in additione.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>181<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>8<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Scytala quid.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>250<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>9<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Securis antiqua qu&aelig;, &amp; qua ratione fieret.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>258<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>10<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Statera antiqua qu&aelig;,<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>259<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>11<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Ae&longs;tu Maris.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>272<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>12<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Araneorum indu&longs;tria nuper patefacta: vbi Democritus contra Ari&longs;t.   defenditur.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>293<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>13<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Lucis figuratione, &amp; rerum &longs;imulacris in ob&longs;curo loco.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>345<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>14<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Pupilla oculi.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>408<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>15<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>De Mathematicarum natura. prop&egrave; finem operis.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>16<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Clarorum Mathematicorum Chronologia, in fine operis.<emph.end type="italics"/></cell>
            <cell/>
          </row>
        </table>
      </section>
      <pb pagenum="12" xlink:href="009/01/012.jpg"/>
      <section>
        <p type="head">
          <s id="s.000083"><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000084"><emph type="italics"/>Qu&aelig; in hoc opere explicantur, iuxta ordine librorum <lb/>
ip&longs;ius ex vulgata editione Lugdunen&longs;i.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000085">In Pr&aelig;dicamentis.</s>
        </p>
        <p type="main">
          <s id="s.000086"><emph type="italics"/>Capite s. </s>
          <s id="s.000087">de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000088"><emph type="italics"/>Cap. de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000089"><emph type="italics"/>Cap. de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000090">In Primo Priorum Re&longs;olutoriorum.</s>
        </p>
        <p type="main">
          <s id="s.000091"><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000092"><emph type="italics"/>Cap. 23. &longs;ect 1. libri 1. de Incommen&longs;urabilibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000093"><emph type="italics"/>Cap. 24. &longs;ecti 1. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000094"><emph type="italics"/>Cap. 2. &longs;ect 2. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000095"><emph type="italics"/>Cap. 3. &longs;ecti 2. lib. 1. de Incommen&longs;urabili.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000096"><emph type="italics"/>Cap. 1. &longs;ecti 3. lib. 1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales <lb/>
&aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000097"><emph type="italics"/>Cap. eodem, de exemplis, quibus vtuntur Geometr&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000098">In &longs;ecundo Priorum Re&longs;ol.<!-- REMOVE S--><emph type="italics"/>Cap. 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000099"><emph type="italics"/>Cap. eodem. </s>
          <s id="s.000100">de Paralellis, &amp; de triangulo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000101"><emph type="italics"/>Cap. 26. Quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000102"><emph type="italics"/>Cap. 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000103"><emph type="italics"/>Cap. codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000104">In primo Po&longs;teriorum.</s>
        </p>
        <p type="main">
          <s id="s.000105"><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000106"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000107"><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s>
          <s id="s.000108">Item De Mathematicarum Principijs.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000109"><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000110"><emph type="italics"/>T. 9. De Puncto, &amp; linea. </s>
          <s id="s.000111">Item de recto, &amp; circulari. </s>
          <s id="s.000112">Item de numero pari, impari; <lb/>
primo, &amp; compo&longs;ito; &aelig;quilatero, &amp; altera parte longiore.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000113"><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000114"><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s>
          <s id="s.000115">De I&longs;o&longs;cele. </s>
          <s id="s.000116">De Alterna Proportione, <lb/>
Item quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000117"><emph type="italics"/>T. 14. De ij&longs;dem cum pr&aelig;cedentibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000118"><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s>
          <s id="s.000119">Item, quod non duo cubi cubus. </s>
          <s id="s.000120">Item de <lb/>
Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000121"><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s>
          <s id="s.000122">Item per&longs;ectam illam e&longs;&longs;e Demon&shy;<lb/>
&longs;trationem, qua Geometr&aelig; o&longs;tendunt, quod Omnis triangulus habet tres, &amp; c. <lb/>
<!-- KEEP S--></s>
          <s id="s.000123">Per&longs;pectiuam, &amp; Mechanicam &longs;ubalternari Geometri&aelig;, Mu&longs;icam, Arithmetic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000124"><emph type="italics"/>T. 24. De numero pari, impari, quadrangulo, cubo. </s>
          <s id="s.000125">In Geometria quid irrationale, <lb/>
refrangi, concurrere. </s>
          <s id="s.000126">Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000127"><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000128"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <pb pagenum="13" xlink:href="009/01/013.jpg"/>
        <p type="main">
          <s id="s.000129"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s>
          <s id="s.000130">Item quid multiplicata propor&shy;<lb/>
tio. </s>
          <s id="s.000131">Quid C&aelig;neus dixerit. </s>
          <s id="s.000132">Cur Affectiones <expan abbr="Mathematicor&utilde;">Mathematicor&utilde;</expan> maxim&egrave; <expan abbr="conuert&atilde;tur">conuertantur</expan>.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000133"><emph type="italics"/>T. 30. De Lun&aelig; &longs;ph&aelig;ricitate. </s>
          <s id="s.000134">Quid &longs;tereometria. </s>
          <s id="s.000135">&amp; De &longs;ubalternatione, &amp;c. </s>
          <s id="s.000136">&amp; Ma&shy;<lb/>
thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum ver&ograve; &longs;cire Quod.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000137"><emph type="italics"/>T. 37. I&longs;o&longs;celes, &amp; Scalenum habere tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000138"><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000139"><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s>
          <s id="s.000140">Item, quod omnis figura habet &longs;uos angu&shy;<lb/>
los externos &aelig;quales quatuor tantum rectis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000141"><emph type="italics"/>T. 43. Triangulum tres &aelig;quales, &amp;c. </s>
          <s id="s.000142">De Eclyp&longs;i.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000143"><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;ph&aelig;ra vitrea. </s>
          <s id="s.000144">De principijs &longs;cientiarum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000145"><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000146">In 2. Po&longs;teriorum.</s>
        </p>
        <p type="main">
          <s id="s.000147"><emph type="italics"/>T. 1. Aequalitas, &amp; in&aelig;qualitas. </s>
          <s id="s.000148">Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per&shy;<lb/>
fect&egrave; demon&longs;tratur. </s>
          <s id="s.000149">Item Quid con&longs;onantia.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000150"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s>
          <s id="s.000151">Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000152"><emph type="italics"/>T. 7. Geometra, qu&aelig;dam accipit, qu&aelig;dam demon&longs;trat.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000153"><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari &agrave; Geometra per cau&longs;am materia&shy;<lb/>
lem. </s>
          <s id="s.000154">Zabarella correctus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000155"><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000156"><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000157">In primo lib. <!-- REMOVE S-->Topicorum.</s>
        </p>
        <p type="main">
          <s id="s.000158"><emph type="italics"/>Cap. 13. Diameter est incommen&longs;urabilis. </s>
          <s id="s.000159">Vox acuta velox, cur. </s>
          <s id="s.000160">&amp;c. </s>
          <s id="s.000161">Colores in <lb/>
Mu&longs;ica, qui. </s>
          <s id="s.000162">tria genera veteris Mu&longs;ic&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000163">In 4. libro.</s>
        </p>
        <p type="main">
          <s id="s.000164"><emph type="italics"/>Cap. 1. loco 1. line&aelig; in&longs;ecabiles.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000165">In 6. libro.</s>
        </p>
        <p type="main">
          <s id="s.000166"><emph type="italics"/>Cap. 2. loco 32. Definitio line&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000167">In 8. libro.</s>
        </p>
        <p type="main">
          <s id="s.000168"><emph type="italics"/>Cap. 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000169"><emph type="italics"/>Cap. 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000170">In Elenchorum lib. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000171"><emph type="italics"/>Cap. 10. Quid P&longs;eudographia. </s>
          <s id="s.000172">Quadratura rur&longs;us Hippocratis, &amp; Bry&longs;onis. </s>
          <s id="s.000173">Mathe&shy;<lb/>
matic&aelig; non contentio&longs;&aelig;. </s>
          <s id="s.000174">Quadratio Antiphontis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000175">Ex 1. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000176"><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, &amp; Antiphontis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000177">Ex 2. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000178"><emph type="italics"/>T. 20. Quatenus Per&longs;pectiuus con&longs;ideret lineam.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000179"><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000180"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes habere cau&longs;am, qu&aelig; reducitur ad defini&shy;<lb/>
tionem.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000181"><emph type="italics"/>T. 8. De nece&longs;&longs;ario, quod e&longs;t in Mathematicis. <!-- KEEP S--></s>
          <s id="s.000182">&amp; omnis triangulus habet tres an&shy;<lb/>
gulos, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000183">Ex 3. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000184"><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000185"><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000186"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <pb pagenum="14" xlink:href="009/01/014.jpg"/>
        <p type="head">
          <s id="s.000187">Ex 4. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000188"><emph type="italics"/>T. 120. De commen&longs;urab. </s>
          <s id="s.000189">&amp; incommen&longs;.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000190">Ex 5. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000191"><emph type="italics"/>T. 6. De chordis, graui, acuta; media, &amp; vltima.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000192">Ex 8. Phy&longs;ic.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000193"><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000194">Ex 1. de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000195"><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000196"><emph type="italics"/>T. 36. Ratione vtitur lineari; vt probet mundum e&longs;&longs;e finitum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000197"><emph type="italics"/>T. 48. Commen&longs;urab. <!-- REMOVE S-->&amp; incommen&longs;urab. </s>
          <s id="s.000198">quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000199"><emph type="italics"/>T. 119. Omnis triangulus habet tres, &amp;c. </s>
          <s id="s.000200">Item de commen&longs;urabili.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000201">Ex 2. de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000202"><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000203"><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000204"><emph type="italics"/>T. 31. Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000205"><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s>
          <s id="s.000206">Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000207"><emph type="italics"/>T. 57. De ordine C&oelig;lorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000208"><emph type="italics"/>T. 59. De rotunditate Lun&aelig;, bis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000209"><emph type="italics"/>T. 107. Centrum duplex grauit: &amp; molis. </s>
          <s id="s.000210">Qua ratione grauia ad mundi centrum <lb/>
aptarentur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000211"><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s>
          <s id="s.000212">alio item modo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000213"><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu C&oelig;li.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000214"><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000215"><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000216">Ex 3. de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000217"><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000218"><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000219"><emph type="italics"/>T. 66. Qu&aelig;nam planarum figurarum totum &longs;patium repleant. </s>
          <s id="s.000220">Hinc de admirabili <lb/>Apum ingenio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000221"><emph type="italics"/>T. eodem. </s>
          <s id="s.000222">Num plures Pyramides locum replere valeant, vbi Ari&longs;toteles, &amp; omnes <lb/>
expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000223"><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000224">Ex 4. de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000225"><emph type="italics"/>T. 33. Extare centrum Mundi, qu&ograve; grauia tendunt, &agrave; quo leuia abeant.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000226"><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grauiora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000227">Ex 2. de Generatione, &amp; Corruptione.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000228"><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000229">Ex 1. Meteororum.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000230"><emph type="italics"/>Summa prima cap. 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000231"><emph type="italics"/>Cap. eodem. </s>
          <s id="s.000232">De magnitudine A&longs;trorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000233"><emph type="italics"/>Cap. 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000234"><emph type="italics"/>Summa 2. cap. 3. de Mercurij stella. </s>
          <s id="s.000235">Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000236"><emph type="italics"/>Cap. 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000237"><emph type="italics"/>Cap. 5. De Glaxia.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000238"><emph type="italics"/>Cap. 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/>
aperitur.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="15" xlink:href="009/01/015.jpg"/>
        <p type="main">
          <s id="s.000239"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>
          <s id="s.000240">Mare extraneum, quod. </s>
          <s id="s.000241">Errata qu&aelig;&shy;<lb/>
dam veterum Geographorum, &amp; Ari&longs;t. corriguntur. </s>
          <s id="s.000242">Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000243"><emph type="italics"/>Cap. 2. De permutatione Aquarum, &amp; continentis. </s>
          <s id="s.000244">Noua ob&longs;eruatio de rotundi&shy;<lb/>
tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000245">Ex 2. Meteororum.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000246"><emph type="italics"/>Summa 1. cap. 1. De Mari rubro.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000247"><emph type="italics"/>Summa 2. cap. 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000248"><emph type="italics"/>Cap. eodem, De Canicula. </s>
          <s id="s.000249">De Zonis temperatis. </s>
          <s id="s.000250">Corona Ariadn&aelig;. </s>
          <s id="s.000251">Zonam torridam <lb/>
fals&ograve; putabant inho&longs;pitalem. </s>
          <s id="s.000252">cur habitabilis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000253"><emph type="italics"/>Cap. 3. De Ventorum &longs;itu.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000254">Ex 3. Meteor.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000255"><emph type="italics"/>Summa 2. cap. 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;tratio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000256"><emph type="italics"/>Cap. 4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s>
          <s id="s.000257">Noua de eadem <lb/>
tractatio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000258"><emph type="italics"/>Cap. 5. De Parelio. <!-- KEEP S--></s>
          <s id="s.000259">Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000260">Ex 1. De Anima.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000261"><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>
          <s id="s.000262">&amp; omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000263"><emph type="italics"/>T. 13. Sph&aelig;ra planum tangit in puncto.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000264">Ex 2. De Anima.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000265"><emph type="italics"/>T. 12. Definitionem formalem, &amp; cau&longs;alem explicat exemplo Quadrationis Geo&shy;<lb/>
metric&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000266"><emph type="italics"/>T. 86. Acutum, &amp; Graue, vt differant.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000267"><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000268">Ex 3. De Anima.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000269"><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000270"><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000271"><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000272">Ex lib. <!-- REMOVE S-->De Sen&longs;u.</s>
        </p>
        <p type="main">
          <s id="s.000273"><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000274"><emph type="italics"/>Cap. 8. Nete. </s>
          <s id="s.000275">Diapa&longs;on. <!-- KEEP S--></s>
          <s id="s.000276">Diapen&longs;e.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000277">Ex lib. <!-- REMOVE S-->De Memoria, &amp; Rem.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000278"><emph type="italics"/>Cap. 1. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000279"><emph type="italics"/>Cap. 3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000280">Ex lib. <!-- REMOVE S-->De Somnijs.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000281"><emph type="italics"/>Cap. 2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000282"><emph type="italics"/>Cap. 3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000283">Ex 1. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000284"><emph type="italics"/>Cap. 1. Initium Mathematicarum ab Aegyptiorum Sacerdotibus. </s>
          <s id="s.000285">Item, Automata, <lb/>
qu&aelig; &longs;olstitia. </s>
          <s id="s.000286">Diameter incommen&longs;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000287"><emph type="italics"/>Summa 2. cap. 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000288"><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000289">Ex 2. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000290"><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000291">Ex 3. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000292"><emph type="italics"/>Tex. <!-- KEEP S--></s>
          <s id="s.000293">Mathematicas puras carere cau&longs;is efficiente, &amp; finali. </s>
          <s id="s.000294">Ari&longs;tippus, vt Mathe&shy;<lb/>
maticas &longs;ugillaret. </s>
          <s id="s.000295">Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="16" xlink:href="009/01/016.jpg"/>
        <p type="main">
          <s id="s.000296"><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000297">Ex 4. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000298"><emph type="italics"/>T. 4. Qu&aelig; &longs;int prim&aelig;, &amp; qu&aelig; &longs;ecund&aelig; inter Mathematicas.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000299"><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000300">Ex 5. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000301"><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. <!-- KEEP S--></s>
          <s id="s.000302">Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000303"><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000304"><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000305"><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000306"><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>
          <s id="s.000307">Quid potentia vnius line&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000308"><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000309">Ex 6. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000310"><emph type="italics"/>T. 1. Principia, elementa, &amp; cau&longs;&aelig; in Mathem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000311"><emph type="italics"/>T. 8. Diameter. </s>
          <s id="s.000312">commen&longs;urab.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000313"><emph type="italics"/>T. 20. De&longs;criptiones. </s>
          <s id="s.000314">Omnis triangulus habet tres, &amp;c. </s>
          <s id="s.000315">Cur Angulus in &longs;emicir&shy;<lb/>
culo rectus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000316"><emph type="italics"/>T. 22. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000317">Ex 10. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000318"><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>
          <s id="s.000319">Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000320"><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s>
          <s id="s.000321">Diuer&longs;um in Math. quid.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000322">Ex 11. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000323"><emph type="italics"/>Cap. 2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000324">Ex 12. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000325"><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam <lb/>
pluralitatem C&oelig;lorum docere.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000326"><emph type="italics"/>T. 45. Numerus orbium c&oelig;le&longs;tium &longs;ecundum Eudoxum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000327"><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000328"><emph type="italics"/>T. 47. Orbium c&oelig;le&longs;tium numerus, &amp; fabrica ex Calippo.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000329">Ex 13. Methaphy&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000330"><emph type="italics"/>Cap. 3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000331">In Mechanicas Qu&aelig;&longs;tiones.</s>
        </p>
        <p type="main">
          <s id="s.000332"><emph type="italics"/>Cap. 1. Qu&aelig; &longs;it Mechanica facultas.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000333"><emph type="italics"/>Cap. 2. De Admirandis circuli.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000334"><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. <!-- KEEP S--></s>
          <s id="s.000335">cur maior, exactior. </s>
          <s id="s.000336">inibi Ari&longs;t. lap&longs;us.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000337"><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. <!-- KEEP S--></s>
          <s id="s.000338">Piccolomineus reiectus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000339"><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000340"><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist. correctio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000341"><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000342"><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000343"><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000344"><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000345"><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000346"><emph type="italics"/>Q&ugrave;&aelig;&longs;t. <!-- REMOVE S-->11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000347"><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>
          <s id="s.000348">De Succula.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000349"><emph type="italics"/>Qu&aelig;&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000350"><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="17" xlink:href="009/01/017.jpg"/>
        <p type="main">
          <s id="s.000351"><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000352"><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000353"><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>
          <s id="s.000354">Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>
eius mirabili.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000355"><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. <!-- KEEP S--></s>
          <s id="s.000356">Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000357"><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000358"><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000359"><emph type="italics"/>Qu&aelig;&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000360"><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000361"><emph type="italics"/>Qu&aelig;&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000362"><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000363"><emph type="italics"/>Qu&aelig;&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000364"><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000365"><emph type="italics"/>Qu&aelig;&longs;t. 29. De onere &agrave; duobus phalanga ge&longs;tato.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000366"><emph type="italics"/>Qu&aelig;&longs;t. 30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000367">In libello De Mundo ad Alex.<!-- REMOVE S--><emph type="italics"/>Cap. 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000368"><emph type="italics"/>Cap. 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000369"><emph type="italics"/>Cap. 5. De fluxu maris. </s>
          <s id="s.000370">noua de maris &aelig;&longs;tu &longs;ententia.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000371">In libro De Admirandis audit.</s>
        </p>
        <p type="main">
          <s id="s.000372"><emph type="italics"/>Num. <!-- REMOVE S-->8. De nouo orbe.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000373"><emph type="italics"/>Nu. </s>
          <s id="s.000374">100. De I&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000375">In libello De lineis in&longs;ecabilibus.</s>
        </p>
        <p type="main">
          <s id="s.000376"><emph type="italics"/>Primus locus. </s>
          <s id="s.000377">De commen&longs;urabili, &amp; incommen&longs;urabili.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000378"><emph type="italics"/>2. locus. </s>
          <s id="s.000379">De figuris incommen&longs;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000380"><emph type="italics"/>3. locus. </s>
          <s id="s.000381">Qu&aelig; linea rationalis, qu&aelig; irrationalis. </s>
          <s id="s.000382">Binomio, Apotome.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000383"><emph type="italics"/>4. locus. </s>
          <s id="s.000384">De communi men&longs;ura.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000385"><emph type="italics"/>5. locus. </s>
          <s id="s.000386">Line&aelig; rect&aelig; motus in &longs;emicirculum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000387"><emph type="italics"/>6. locus. </s>
          <s id="s.000388">Circulorum &aelig;qualium ab inuicem motus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000389"><emph type="italics"/>7. locus. </s>
          <s id="s.000390">Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000391"><emph type="italics"/>8. locus. </s>
          <s id="s.000392">Si extarent indiuidua, omnes line&aelig; e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000393"><emph type="italics"/>9. locus. </s>
          <s id="s.000394">Idem probat alite&racute;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000395"><emph type="italics"/>10. locus. </s>
          <s id="s.000396">Idem ex triangulo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000397"><emph type="italics"/>11. locus. </s>
          <s id="s.000398">Idem ex quadrato.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000399"><emph type="italics"/>12. Ex diui&longs;ione line&aelig; idem confirmatur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000400"><emph type="italics"/>13. Idem eodem fer&egrave; modo cum pr&aelig;cedenti.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000401"><emph type="italics"/>14. A quadrato cuiu&longs;uis line&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000402"><emph type="italics"/>15. Idem probat ex &longs;uperficie, &amp; ex corpore.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000403"><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000404">Ex lib. 9. Hi&longs;tori&aelig; Animalium.</s>
        </p>
        <p type="main">
          <s id="s.000405"><emph type="italics"/>Cap. 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000406">De Ince&longs;&longs;u Animal.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000407"><emph type="italics"/>Cap. 7. qua ratione in gre&longs;&longs;u fiat hypotenu&longs;a. </s>
          <s id="s.000408">&amp; ea quid &longs;it.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000409">De Motu Animal.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000410"><emph type="italics"/>Cap. 1. in flexuris animalium e&longs;&longs;e centrum, &amp; circulum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000411"><emph type="italics"/>Cap. 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <pb pagenum="18" xlink:href="009/01/018.jpg"/>
        <p type="head">
          <s id="s.000412">De Generatione Animal.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000413"><emph type="italics"/>Lib. 2. cap. 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000414"><emph type="italics"/>Lib. 2. cap. 4. Omnis triangulus habet tres, &amp;c. </s>
          <s id="s.000415">Ibidem Diametrum e&longs;&longs;e incommen&shy;<lb/>
&longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000416">In Ethicis ad Nicom.</s>
        </p>
        <p type="main">
          <s id="s.000417"><emph type="italics"/>Lib. 1. cap. 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000418"><emph type="italics"/>Lib. 2. cap. 6. De Arithmetica proportione.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000419"><emph type="italics"/>cap. 9. Centrum circuli reperire.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000420"><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>
trica: Quid de&longs;ignatio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000421"><emph type="italics"/>Lib. 5. cap. 3. Vnitarius numerus. </s>
          <s id="s.000422">Quid Proportionalitas. <!-- KEEP S--></s>
          <s id="s.000423">Eam in 4. terminis con&shy;<lb/>
&longs;i&longs;tere. </s>
          <s id="s.000424">Item quid Permutata proportio. </s>
          <s id="s.000425">Item quid Geometrica proportio. </s>
          <s id="s.000426">Propor&shy;<lb/>
tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000427"><emph type="italics"/>cap. 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000428"><emph type="italics"/>Lib. 6. cap. 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000429"><emph type="italics"/>cap. 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000430"><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000431">Ex 1. Magnorum Moralium.</s>
        </p>
        <p type="main">
          <s id="s.000432"><emph type="italics"/>Cap. 1. Numerus pariter par.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000433"><emph type="italics"/>Cap. 2. Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000434"><emph type="italics"/>Cap. 10 Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000435"><emph type="italics"/>Cap. 16. Quadratum quatuor rectis &aelig;quales habere.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000436"><emph type="italics"/>Cap. 30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000437">Ex 1. lib. <!-- REMOVE S-->Moralium Eudemiorum.</s>
        </p>
        <p type="main">
          <s id="s.000438"><emph type="italics"/>Cap. 5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000439">Ex 1. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
        </p>
        <p type="main">
          <s id="s.000440"><emph type="italics"/>Cap. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000441"><emph type="italics"/>Cap. 10. Diametrum commen&longs;. </s>
          <s id="s.000442">e&longs;&longs;e. </s>
          <s id="s.000443">Circuli quadratio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000444"><emph type="italics"/>Cap. 12. Triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000445">Ex 7. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
        </p>
        <p type="main">
          <s id="s.000446"><emph type="italics"/>Cap. 12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000447">Ex 3. lib. <!-- REMOVE S-->Politicorum.</s>
        </p>
        <p type="main">
          <s id="s.000448"><emph type="italics"/>Cap. 2. Modi Dorius, &amp; Phrygius apud Mu&longs;icos, qu&igrave;.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000449">Ex 4. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000450"><emph type="italics"/>Cap. 3. Modus Doricus, &amp; Phrygius.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000451">Ex 5. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000452"><emph type="italics"/>Cap. 1. Aequitas Arithmetica, &amp; qu&aelig; &longs;ecundum dignitatem.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000453">Ex 8. Polit.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000454"><emph type="italics"/>Cap. 5. Mu&longs;ica nuda, &amp; cum melodia. </s>
          <s id="s.000455">Rithmus quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000456"><emph type="italics"/>Harmonia lydia. </s>
          <s id="s.000457">Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000458"><emph type="italics"/>Cap. 7. Harmoni&aelig;, &amp; Rithmi, vt in pr&aelig;cedenti.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000459">Ex Problematibus.</s>
        </p>
        <p type="main">
          <s id="s.000460"><emph type="italics"/>Sectione 1. num. </s>
          <s id="s.000461">3. De ortu &longs;yderum inerrantium: Succul&aelig;, Hypades, Atlantides, <lb/>
Virgili&aelig;, Pleiades. </s>
          <s id="s.000462">num. </s>
          <s id="s.000463">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000464"><emph type="italics"/>Sectione 15. num. </s>
          <s id="s.000465">1. Diametri ethymon.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000466"><emph type="italics"/>num. </s>
          <s id="s.000467">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="19" xlink:href="009/01/019.jpg"/>
        <p type="main">
          <s id="s.000468"><emph type="italics"/>num. </s>
          <s id="s.000469">3. Denarius numerus cur perfectus. </s>
          <s id="s.000470">eius dignitates. </s>
          <s id="s.000471">Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000472"><emph type="italics"/>4. De in&aelig;quali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000473"><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotund&aelig;, quamuis per angulo&longs;a foramina ingre&shy;<lb/>
diantur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000474"><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>
          <s id="s.000475">vbi de illuminatione Lun&aelig;, <lb/>
qu&aelig; experientia docetur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000476"><emph type="italics"/>7. Cur Sol, &amp; Luna videantur plana?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000477"><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000478"><emph type="italics"/>9. Cur Lun&aelig;, qu&agrave;m Solis minores vmbr&aelig;?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000479"><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s>
          <s id="s.000480">modus commod&egrave; <lb/>
videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000481"><emph type="italics"/>Sect. <!-- REMOVE S-->16. nu. </s>
          <s id="s.000482">1. Cur ba&longs;es bullarum in aquis &longs;unt alb&aelig;?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000483"><emph type="italics"/>3. Opplumbati tali.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000484"><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000485"><emph type="italics"/>5. Cur conus, &amp; cylindrus diuers&egrave; moueantur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000486"><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000487"><emph type="italics"/>12. Idem cum pr&aelig;cedenti 3.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000488"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>
          <s id="s.000489">reflexio radior&ubreve;m pulchr&egrave; comparatur corpor&ubreve;m re&longs;ultationi.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000490">Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000491"><emph type="italics"/>num. </s>
          <s id="s.000492">2. Line&aelig; dupl&aelig; quadratum quadruplum. </s>
          <s id="s.000493">Hoc loco &longs;equentium probl. </s>
          <s id="s.000494">cau&longs;a, <lb/>
pr&aelig;mittitur totius Mu&longs;ic&aelig; ortus breuis tractatio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000495"><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000496"><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000497"><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000498"><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000499"><emph type="italics"/>8. Cur grauis &longs;onum potest acut&aelig;?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000500"><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000501"><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000502"><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000503"><emph type="italics"/>12. Grauior &egrave; fidibus cantilenam &longs;u&longs;cipit.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000504"><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000505"><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>
          <s id="s.000506">Punicum quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000507"><emph type="italics"/>15. Leges Mu&longs;ic&aelig;, qu&aelig;. </s>
          <s id="s.000508">Genera, Diatonicum, Chromaticum, Encharmonium. <lb/>
</s>
          <s id="s.000509">Tetrachorda qu&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000510"><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000511"><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>
          <s id="s.000512">Magadis quid. </s>
          <s id="s.000513">Magadare.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000514"><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000515"><emph type="italics"/>19. Cur Diapente, &amp; Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000516"><emph type="italics"/>20. Me&longs;e &longs;ola di&longs;&longs;onante, totum de&longs;&longs;onat p&longs;alterium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000517"><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000518"><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000519"><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000520"><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000521"><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>
          <s id="s.000522">Rithmus quid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000523"><emph type="italics"/>28. Cur cantilen&aelig; qu&aelig;dam leges decebantur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000524"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="20" xlink:href="009/01/020.jpg"/>
        <p type="main">
          <s id="s.000525"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melop&aelig;os.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000526"><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000527"><emph type="italics"/>33. Cur apt&egrave; de acuto in graue, non &egrave; contra canitur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000528"><emph type="italics"/>34. Cur bi&longs;diapente, aut bi&longs;diate&longs;&longs;aron con&longs;onantia non e&longs;t.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000529"><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000530"><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000531"><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000532"><emph type="italics"/>38. Cur Rythmo, &amp; harmonij omnes gaudent?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000533"><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000534"><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000535"><emph type="italics"/>41. Idem cum 5.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000536"><emph type="italics"/>42. Idem cum 34.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000537"><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete&shy;<lb/>
ris lyr&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000538"><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000539"><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000540"><emph type="italics"/>46. Idem cum 22.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000541"><emph type="italics"/>47. Idem cum 26.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000542"><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000543"><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus <lb/>
erat in v&longs;u.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000544"><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000545"><emph type="italics"/>51. Dolia duo &aelig;qualia, quorum alterum plenum &longs;it, alterum dimidium, Diapa&longs;on <lb/>
re&longs;onant.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000546">Ex &longs;ectione 23.</s>
        </p>
        <p type="main">
          <s id="s.000547"><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000548">Ex &longs;ectione 30.</s>
        </p>
        <p type="main">
          <s id="s.000549"><emph type="italics"/>6. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000550">Ex &longs;ectione 31.</s>
        </p>
        <p type="main">
          <s id="s.000551"><emph type="italics"/>7. Cur o culos, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla vi, ab inuicem di&longs;&longs;ociari nequimus?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000552"><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>
          <s id="s.000553">Cur aliquando rei vi&longs;&aelig; gemina&shy;<lb/>
tio accidat.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000554"><emph type="italics"/>11. Cur di&longs;tractis oculis res vna du&aelig; apparent?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000555"><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000556"><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000557">Auctarium De Oculi Pupilla.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000558"><emph type="italics"/>Oculi fabrica pr&aelig;mittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000559"><emph type="italics"/>Primo. </s>
          <s id="s.000560">De pupill&aelig; voce.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000561"><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000562"><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000563"><emph type="italics"/>4. Pupill&aelig; definitio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000564"><emph type="italics"/>5. Cur nigra in omnibus hominibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000565"><emph type="italics"/>6. Cur in Sole euane&longs;cat.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000566"><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000567"><emph type="italics"/>8. Cur modo maior, modo minor videatur, &amp; cui&longs;dam lepida deceptio.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="21" xlink:href="009/01/021.jpg"/>
        <p type="main">
          <s id="s.000568">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s>
        </p>
        <p type="main">
          <s id="s.000569"><emph type="italics"/>Primo. </s>
          <s id="s.000570">De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;<lb/>
nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000571">2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000572">3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumni&aelig; diluuntur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000573">4. <emph type="italics"/>De pr&aelig;stantia cognitionis, quam Geometria, &amp; Arithmetica gignunt.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000574">5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000575">6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000576">7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000577"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s>
        </p>
      </section>
      <pb pagenum="22" xlink:href="009/01/022.jpg"/>
      <section>
        <p type="head">
          <s id="s.000578"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000579"><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>
ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>
runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>
vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000580"><emph type="italics"/>In Primo Elem. Euclidis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000581">Ad verbum ip&longs;um <emph type="italics"/>&lpar;Elementum Euclidis&rpar;<emph.end type="italics"/> vide infra tex. <!-- REMOVE S-->4. quinti <lb/>
Methaph.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000582">Ad principia primi elementorum, vide infra tex. <!-- REMOVE S-->5. pri. <!-- REMOVE S-->Po&longs;ter.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000583">Ad definitionem 10. pri. <!-- REMOVE S-->pro angulo recto, vide 30. qu&aelig;&longs;t. </s>
          <s id="s.000584">Mecha&shy;<lb/>
nic. <!-- REMOVE S-->&amp; cap. 7. lib. 1. Eth.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000585">Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>
hoc vno axiomate qu&etail;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>
facile di&longs;&longs;olui. </s>
          <s id="s.000586">ea e&longs;t, vtrum marmor, aut adamas, aliudue quidpiam infle&shy;<lb/>
xibile &longs;ucce&longs;&longs;iu&egrave; findi, &amp; aperiri po&longs;&longs;it. </s>
          <s id="s.000587">qui enim aiunt, &longs;ic refelluntur, quia <lb/>
nimirum &longs;equeretur, duas rectas lineas habere &longs;egmentum commune: in&shy;<lb/>
telligantur enim du&aelig; line&aelig;, vna in vna &longs;uperficie, altera vero in altera, qu&aelig; <lb/>
antequam incipiat apertio, congruant; Quoniam igitur tota illa apertio <lb/>
non fit in in&longs;tanti, &longs;ed &longs;ucce&longs;&longs;iu&egrave;, facta iam aliqua apertionis parte con&longs;i&shy;<lb/>
derentur pr&aelig;dict&aelig; line&aelig;, erit igitur earum pars aliqua ab inuicem &longs;epara&shy;<lb/>
ta, altera ver&ograve; adhuc alteri congruens, ergo &longs;equetur, duas lineas habere <lb/>
&longs;egmentum commune, quod e&longs;t impo&longs;&longs;ibile, quia contra 10. axioma.</s>
        </p>
        <p type="main">
          <s id="s.000588">Ad Calcem axiomatum primi accommodetur tex. <!-- REMOVE S-->1. primi Po&longs;ter.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000589">Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>
Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>
tiones, vide cap. de Priori, &amp; cap. 24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>
tex. <!-- REMOVE S-->4. quinti Methaph. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->&amp; cap. 3. lib. 3. Ethic. <lb/>
<!-- KEEP S--></s>
          <s id="s.000590">Item ad primam primi, vide tex. <!-- REMOVE S-->7. &longs;ecundi Po&longs;ter. loco 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000591">Ad 5. primi, vide cap. 24. &longs;ecti 1 lib. 1. Priorum.</s>
        </p>
        <p type="main">
          <s id="s.000592">Ad 21. primi, vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000593">Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s>
        </p>
        <p type="main">
          <s id="s.000594">Ad 28. primi, vide cap. 21. &amp; cap. 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->13. primi Po&longs;ter.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000595">Ad 32. primi, vide cap. 1. &longs;ecti 3. lib. 1. Prior. <!-- REMOVE S-->&amp; cap. 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->2. <lb/>
primi Po&longs;ter. loco 4. &amp; tex. <!-- REMOVE S-->23. primi Po&longs;ter. <!-- REMOVE S-->vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam <lb/>
<expan abbr="dem&otilde;&longs;trationem">demon&longs;trationem</expan>. </s>
          <s id="s.000596">&amp; tex. <!-- REMOVE S-->37. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->39. primi Po&longs;ter. <!-- KEEP S--></s>
          <s id="s.000597">Ibidem <lb/>
loco 4. &amp; tex. <!-- REMOVE S-->43. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->2. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->bis. </s>
          <s id="s.000598">&amp; tex. <!-- REMOVE S-->89. &longs;e&shy;<lb/>
cundi Phy&longs;. &amp; tex. <!-- REMOVE S-->15. octaui Phy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>
          <s id="s.000599">&amp; tex. <!-- REMOVE S-->25. <lb/>
&longs;ecundi de C&oelig;lo. <!-- KEEP S--></s>
          <s id="s.000600">tex 11. primi de Anima. <!-- REMOVE S-->&amp; cap. 1. de mem. </s>
          <s id="s.000601">&amp; remini&longs;c. <lb/>
</s>
          <s id="s.000602">&amp; tex. <!-- REMOVE S-->35. quinti Methaphy&longs;. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaphy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->22. &longs;exti <lb/>
Methaphy&longs;. <!-- REMOVE S-->&amp; cap. 4. lib. 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>
          <s id="s.000603">&amp; cap. 5. lib. 6. Ethic. <!-- REMOVE S-->&amp; <lb/>
cap. 2. Magnorum Moral. &amp; cap. 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/>
<!-- REMOVE S-->&amp; cap. <!-- REMOVE S-->7. &longs;ecundi Eudem. &amp; cap. <!-- REMOVE S-->12. &longs;ecundi Eudem. <!-- REMOVE S-->&amp; problema 6. &longs;ectio&shy;


<pb pagenum="23" xlink:href="009/01/023.jpg"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica h&aelig;c Euclidis Demon&longs;tratio.</s>
        </p>
        <p type="main">
          <s id="s.000604">Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. <!-- REMOVE S-->39. primi Po&longs;ter. loco 3. Item <lb/>
tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->loco vlt.</s>
        </p>
        <p type="main">
          <s id="s.000605">Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s>
        </p>
        <p type="main">
          <s id="s.000606">Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s>
        </p>
        <p type="main">
          <s id="s.000607">Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s>
          <s id="s.000608">Item locum 14. de ij&longs;dem.</s>
        </p>
        <p type="head">
          <s id="s.000609"><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000610">Ad 2. definitionem 2. Gnomonis, vide cap. de Motu in Po&longs;tpr&aelig;dicam. </s>
          <s id="s.000611">Qua&shy;<lb/>
dratum augetur Gnomone circumpo&longs;ito.</s>
        </p>
        <p type="main">
          <s id="s.000612">Ad 14. propo&longs;. </s>
          <s id="s.000613">2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>
vide igitur cap. de relatione in pr&aelig;dicam. </s>
          <s id="s.000614">&amp; cap. 31. &longs;ecundi Priorum, &amp; <lb/>
tex. <!-- REMOVE S-->23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>
          <s id="s.000615">lege primam Ar&shy;<lb/>
chimedis de dimen&longs;ione circuli.</s>
        </p>
        <p type="head">
          <s id="s.000616"><emph type="italics"/>In tertio Elem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000617">Ad primam 3. vide cap. 9. lib. 2. Ethycorum.</s>
        </p>
        <p type="main">
          <s id="s.000618">Ad 2. tertij, vide tex. <!-- REMOVE S-->13. lib. 1. de Anima. <!-- REMOVE S-->&amp; locum 16. de lineis in&longs;ecab.</s>
        </p>
        <p type="main">
          <s id="s.000619">Ad 31. tertij, vide tex. <!-- REMOVE S-->11. &longs;ecundi Po&longs;ter. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000620"><emph type="italics"/>In quarto.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000621">Ad commentarium P. <!-- REMOVE S-->Clauij extremum lib. 4. elementorum. </s>
          <s id="s.000622">lege tex. <!-- REMOVE S-->66. <lb/>
tertij de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000623"><emph type="italics"/>In quinto.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000624">Ad 4. definitionem 5. vide cap. 3. lib. 2. Ethyc.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000625">Ad 9. definitionem 5. vide cap. 3. lib. 5. Ethyc. <!-- REMOVE S-->loco 4. &amp; cap. 31. primi Ma&shy;<lb/>
gnorum Moralium.</s>
        </p>
        <p type="main">
          <s id="s.000626">Ad 10. definitionem 5. vide tex. <!-- REMOVE S-->29. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000627">Ad 12. definitionem 5. vide tex. <!-- REMOVE S-->13. primi Po&longs;ter. <!-- REMOVE S-->loco 3. &amp; tex. <!-- REMOVE S-->25. &longs;ecundi <lb/>
Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->32. tertij de Anima. <!-- REMOVE S-->&amp; cap. 3. lib. 5. Ethyc. <!-- REMOVE S-->loco 4.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000628">Ad 16. propo&longs;. </s>
          <s id="s.000629">5. vide tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>
&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/>
<!-- REMOVE S-->comm. <!-- REMOVE S-->15. &longs;cilicet.</s>
        </p>
        <p type="main">
          <s id="s.000630">Vt &longs;e habet voluntas antiqua ad antiquum effectum, <lb/>
Ita &longs;e habet etiam voluntas noua ad effectum nouum: <lb/>
Ergo permutando, ita &longs;e habebit voluntas antiqua ad effectum nouum. <lb/>
</s>
          <s id="s.000631">Quemadmodum voluntas noua ad effectum antiquum.</s>
        </p>
        <p type="main">
          <s id="s.000632">Non enim in permutando confert antecedentem ad antecedentem, &amp; con&shy;<lb/>
&longs;equentem ad con&longs;equentem, vt par erat, &longs;ed confert antecedentem ad <lb/>
con&longs;equentem, quod non licet.</s>
        </p>
        <p type="head">
          <s id="s.000633"><emph type="italics"/>In &longs;exto.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000634">Ad 2. propo&longs;it. </s>
          <s id="s.000635">6. vide cap. 2. lib. 8. Topicorum loco 41.</s>
        </p>
        <p type="main">
          <s id="s.000636">Ad 13. &longs;exti, vide tex. <!-- REMOVE S-->12. &longs;ecundi de Anima, &amp; tex. <!-- REMOVE S-->3. tertij Methaphy&longs;.<!-- REMOVE S--><emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000637">Ad primam definitionem 7. vide tex. <!-- REMOVE S-->5. primi Po&longs;ter.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000638">Ad 8. definitionem 7. vide cap. 1. lib. 1. Magnorum Moral.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000639"><emph type="italics"/>In octauo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000640">Ad 4. propo&longs;. </s>
          <s id="s.000641">9. vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000642">Ad 8. propo&longs;. </s>
          <s id="s.000643">9. vide problem. </s>
          <s id="s.000644">3. &longs;ectionis 15. loco 4.<!-- KEEP S--></s>
        </p>
        <pb pagenum="24" xlink:href="009/01/024.jpg"/>
        <p type="head">
          <s id="s.000645"><emph type="italics"/>In decimo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000646">Ad primam definitionem 10. vide cap. 23. &longs;ecti 1. primi Priorum. </s>
          <s id="s.000647">&amp; tex. <!-- REMOVE S-->48. <lb/>
primi de C&oelig;lo.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000648">Ad 118. decimi, vide cap. 23. &longs;ecti 1. libri 1. Priorum. </s>
          <s id="s.000649">&amp; &longs;ecto 2. cap. 23. li&shy;<lb/>
bri 1. Priorum. </s>
          <s id="s.000650">&amp; cap. 22. lib. 2. Priorum. </s>
          <s id="s.000651">&amp; tex. <!-- REMOVE S-->5. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->44. <lb/>
primi Po&longs;ter. <!-- REMOVE S-->&amp; cap. 15. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>
          <s id="s.000652">&amp; tex. <lb/>
<!-- REMOVE S-->120. quarti Phy&longs;. &amp; tex. <!-- REMOVE S-->21. tertij de Anima. <!-- REMOVE S-->&amp; cap. 1. primi Methaphy&longs;. <lb/>
<!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->28. quarti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->34. quinti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->8. &longs;exti Met. <!-- REMOVE S-->&amp; cap. 4. <lb/>
lib. 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>
          <s id="s.000653">&amp; lib. 3. cap. 3. Ethyc. <!-- REMOVE S-->&amp; cap. 10. &longs;ecundi Eu&shy;<lb/>
dem. <!-- KEEP S--></s>
          <s id="s.000654">tot Ari&longs;t. loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s>
        </p>
        <p type="head">
          <s id="s.000655"><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000656">Ad primam propo&longs;. </s>
          <s id="s.000657">13. &longs;ecundum editionem Commandini, aut Zamberti. <lb/>
<!-- KEEP S--></s>
          <s id="s.000658">vide initio Priorum, in verbum &lpar;Re&longs;olutio&rpar;</s>
        </p>
        <p type="main">
          <s id="s.000659">Atque h&aelig;c &longs;unt, qu&aelig; ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/>
qu&aelig;que nos infra explicabimus.</s>
        </p>
        <p type="head">
          <s id="s.000660"><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s>
        </p>
        <p type="main">
          <s id="s.000661">Qu&aelig; ver&ograve; ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe&shy;<lb/>
ctiuam, Mechanicam, &amp; A&longs;tronomiam pertinens, facil&egrave; <lb/>
poterunt ex primo Indice ad vnamquamque earum &longs;eor&shy;<lb/>
&longs;um cum libuerit, &longs;ecerni.</s>
        </p>
      </section>
      <pb pagenum="25" xlink:href="009/01/025.jpg"/>
      <section>
        <p type="head">
          <s id="s.000662"><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000663"><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/><lb/>
<arrow.to.target n="table2"/></s>
        </p>
        <table>
          <table.target id="table2"/>
          <row>
            <cell><emph type="italics"/>A<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Abductio quid. eius inuentor. numero 16. marginali.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Acuti den&longs;um quid.<emph.end type="italics"/></cell>
            <cell>399</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aequalitas mathematica, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ae&longs;tus maris natura.<emph.end type="italics"/></cell>
            <cell>272</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aequitas arithmetica, &amp; &aelig;quitas &longs;ecundum dignitatem.<emph.end type="italics"/></cell>
            <cell>330</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Agathir&longs;i populi.<emph.end type="italics"/></cell>
            <cell>382</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Angulus quid. vt nominari debeat 10. angulum in &longs;emicirculo e&longs;&longs;e rectum o&longs;tendi   per cau&longs;am materialem.<emph.end type="italics"/></cell>
            <cell>71</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Angulus rectus vari&egrave; con&longs;ideratur &agrave; Geometra, &amp; &agrave; Fabro.<emph.end type="italics"/></cell>
            <cell>301</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Antiphontis quadratura circuli.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Antenn&aelig; nauis problema.<emph.end type="italics"/></cell>
            <cell>248</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Antiphon&aelig; voces.<emph.end type="italics"/> 358. 363. 370. 371.</cell>
            <cell>373</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Apum mirabilis indu&longs;tria.<emph.end type="italics"/></cell>
            <cell>120</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Apotome linea, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>279</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam ratione mathematica.<emph.end type="italics"/></cell>
            <cell>107</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Arithmetica proportio.<emph.end type="italics"/></cell>
            <cell>302</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aranei industria patefacta, qua ad res inaca&longs;&longs;as tran&longs;eat.<emph.end type="italics"/></cell>
            <cell>293</cell>
          </row>
          <row>
            <cell><emph type="italics"/>filum emittit ex &longs;ece&longs;&longs;u contra Ari&longs;totelem pro Democrito.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Astronomi&aelig; principia duo, Apparentia, &amp; Ob&longs;eruatio.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Automata, qu&aelig;.<emph.end type="italics"/> 199. 298.</cell>
            <cell><emph type="italics"/>a. b.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>B<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Ba&longs;is ballarum in aqua, cur &longs;it alba, &amp; cur non faciat vmbram.<emph.end type="italics"/></cell>
            <cell>351</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Binomium linea, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>279</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bra&longs;ilien&longs;es, qua ratione numerare &longs;oliti.<emph.end type="italics"/></cell>
            <cell>340</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bry&longs;onis quadratura circuli.<emph.end type="italics"/></cell>
            <cell>35</cell>
          </row>
          <row>
            <cell><emph type="italics"/>C<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Calippi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell>
            <cell>236</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cantilenam notam &longs;uauius, quam ignotam audimus.<emph.end type="italics"/></cell>
            <cell>362</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Centrum circuli reperire. 303. Centrum mundi mathematic&egrave; o&longs;tenditur. 123. Cen-trum grauitatis, &amp; molis.<emph.end type="italics"/> 38.</cell>
            <cell>112</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Chordarum veterum nomina.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Circuli quadratura quid. an po&longs;&longs;ibilis. num. 1. Circulorum concentricorum maiores   velocius moueri. 108. Circuli admiranda. 239. De circulorum concentricorum   volutatione.<emph.end type="italics"/></cell>
            <cell>263</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Coaltern&aelig; line&aelig;, qu&aelig;.<emph.end type="italics"/> 12. 14.</cell>
            <cell>44</cell>
          </row>
          <row>
            <cell><emph type="italics"/>C&oelig;lorum ordinem petendum ex A&longs;tronomis 109. item numerum<emph.end type="italics"/></cell>
            <cell>233</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Colores in mu&longs;ica 78. Colores oculorum vnde.<emph.end type="italics"/></cell>
            <cell>408</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cometarum tractatiuncula ex recentioribus, qui eas in C&oelig;lo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur mathematic&egrave;. 129. in additione.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Con&longs;onantia, quid. 64. quibus numeris con&longs;onanti&aelig; con&longs;tent.<emph.end type="italics"/></cell>
            <cell>210</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Conus, &amp; cylindrus, cur vari&egrave; mouentur.<emph.end type="italics"/></cell>
            <cell>355</cell>
          </row>
          <pb pagenum="26" xlink:href="009/01/026.jpg"/>
          <row>
            <cell><emph type="italics"/>Cubus numerus. duo cubi cubus, quid &longs;ignificet.<emph.end type="italics"/></cell>
            <cell>33</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Curru problema.<emph.end type="italics"/></cell>
            <cell>252</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cunei problema.<emph.end type="italics"/></cell>
            <cell>256</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cylindri, &amp; coni motus comparatio problematica.<emph.end type="italics"/></cell>
            <cell>335</cell>
          </row>
          <row>
            <cell><emph type="italics"/>D<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Definitiones mathematic&aelig; e&longs;&longs;e e&longs;&longs;entiales, &amp; perfe&longs;&longs;imas. cap. 1. de nat. Math.   definitionum v&longs;us in Mathematicis.<emph.end type="italics"/></cell>
            <cell>81</cell>
          </row>
          <row>
            <cell><emph type="italics"/>De&longs;criptio, &amp; de&longs;cribere, quid.<emph.end type="italics"/> 2. 6. 7.</cell>
            <cell>205</cell>
          </row>
          <row>
            <cell><emph type="italics"/>De&longs;ignatio pro demon&longs;tratione mathematica.<emph.end type="italics"/></cell>
            <cell>305</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Demon&longs;trationis perfect&aelig; exemplum. 36. demon&longs;trationum mathematicarum pr&aelig;-&longs;tantia. cap. 4. de nat. Mathem.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Dentiforcipis problema.<emph.end type="italics"/></cell>
            <cell>260</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Denarij numeri perfectio. 339. cur <expan abbr="v&longs;q;">v&longs;que</expan> ad denari&ubreve; omnes <expan abbr="g&etilde;tes">gentes</expan> <expan abbr="numer&etilde;t">numerent</expan>.<emph.end type="italics"/></cell>
            <cell>339. 8. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diameter incommen&longs;urabilis cost&aelig;. 5. diametri etymon.<emph.end type="italics"/></cell>
            <cell>337</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diapa&longs;on quid. 90. 350. omnium con&longs;onantiarum pulcherrima.<emph.end type="italics"/></cell>
            <cell>388</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diapa&longs;on diapente.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diapente con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diate&longs;&longs;aron con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Di&longs;d apa&longs;on con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Die&longs;is, quid.<emph.end type="italics"/> 53.</cell>
            <cell>226</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Dolia duo, quomodo aliquando Diapa&longs;on re&longs;onent.<emph.end type="italics"/></cell>
            <cell>402</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Duplum inter multiplicia primum e&longs;t.<emph.end type="italics"/></cell>
            <cell>322</cell>
          </row>
          <row>
            <cell><emph type="italics"/>E<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Elementa mundi non componi ex figuris geometricis.<emph.end type="italics"/></cell>
            <cell>120</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Elementa geometrica, qu&aelig;.<emph.end type="italics"/> 82.</cell>
            <cell>213</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Eudoxi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell>
            <cell>234</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Exempla mathematicorum, qualia. 11. non e&longs;&longs;e fal&longs;a.<emph.end type="italics"/></cell>
            <cell>43</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Exemplorum veritas, &amp; conformitas, quatenus requirantur.<emph.end type="italics"/></cell>
            <cell>36</cell>
          </row>
          <row>
            <cell><emph type="italics"/>F<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Figuram omnem planam habere &longs;uos angulos externos <expan abbr="quotc&ubreve;mq;">quotc&ubreve;mque</expan> &aelig;quales quatuor   rectis angulis, qu&aelig; e&longs;t mira proprietas.<emph.end type="italics"/></cell>
            <cell>59</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Figur&aelig; &longs;imiles, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>70</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Figurarum planarum ordo 88. qu&aelig; nam totum locum repleant.<emph.end type="italics"/></cell>
            <cell>96</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Figurarum &longs;olidarum, qu&aelig;nam totum locum repleant: vbi Ari&longs;t. &amp; omnium expo&longs;i-torum ratum aperitur.<emph.end type="italics"/></cell>
            <cell>121</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Figuratio lucis.<emph.end type="italics"/></cell>
            <cell>345</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Figurationes pro demon&longs;trationibus Mathem.<emph.end type="italics"/></cell>
            <cell>194</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, &amp; ex qua materia.<emph.end type="italics"/></cell>
            <cell>293</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fluxus, ac refluxus maris.<emph.end type="italics"/></cell>
            <cell>272</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Funium lectorum problema.<emph.end type="italics"/></cell>
            <cell>264</cell>
          </row>
          <row>
            <cell><emph type="italics"/>G<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Galaxia quid. 131. Ari&longs;toteles defen&longs;us.<emph.end type="italics"/> 132.</cell>
            <cell>140</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Galibei recens ob&longs;eruatio.<emph.end type="italics"/></cell>
            <cell>141</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Generatria Mu&longs;ic&aelig; veteris. 78. Fus&egrave; explicantur.<emph.end type="italics"/></cell>
            <cell>371</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Geod&aelig;&longs;ia.<emph.end type="italics"/></cell>
            <cell>207</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Geographi&aelig; veteris plura errata,<emph.end type="italics"/> 145. 146. 147. 148.</cell>
            <cell>149</cell>
          </row>
          <pb pagenum="27" xlink:href="009/01/027.jpg"/>
          <row>
            <cell><emph type="italics"/>Gnomon, quid. 3. &amp;<emph.end type="italics"/></cell>
            <cell>331</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Gnomones numeri.<emph.end type="italics"/></cell>
            <cell>93</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Graue qua ratione ad centrum mundi de&longs;cenderet, eiqu&eacute; aptaretur.<emph.end type="italics"/></cell>
            <cell>112</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Grauiden&longs;um, quid.<emph.end type="italics"/></cell>
            <cell>399</cell>
          </row>
          <row>
            <cell><emph type="italics"/>H<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Halonis demon&longs;tratio.<emph.end type="italics"/></cell>
            <cell>161</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hippocratis chij quadratura circuli. 17. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> quadratura lunul&aelig; optima.<emph.end type="italics"/></cell>
            <cell>17</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hyades, Atlantides, &amp; Succul&aelig;.<emph.end type="italics"/></cell>
            <cell>335</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hypate, quid.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hypotenu&longs;a in ince&longs;&longs;u animalium.<emph.end type="italics"/></cell>
            <cell>294</cell>
          </row>
          <row>
            <cell><emph type="italics"/>I<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Illuminationes Solis deficientis per foramina tran&longs;euntes, eur &longs;int defectiu&aelig;.<emph.end type="italics"/></cell>
            <cell>350</cell>
          </row>
          <row>
            <cell><emph type="italics"/>modus videndi eclyp&longs;im facilis, ac iucundus.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ince&longs;&longs;us animalium lineis explicatur.<emph.end type="italics"/></cell>
            <cell>294. <emph type="italics"/>&amp; <expan abbr="&longs;eqq.">&longs;eqque</expan><emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Incommen&longs;urabilia, qu&aelig;, &amp; eorum inuentores.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Indiui&longs;ibilia mathematica e&longs;&longs;e priuationes. 189. oriri ex diui&longs;ione. 231. eorum duo   genera.<emph.end type="italics"/></cell>
            <cell>276</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Infinito, qua ratione vtantur Mathematici.<emph.end type="italics"/> 94.</cell>
            <cell>96</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iridis demon&longs;tratio &longs;ecundum Ari&longs;t. 163. &amp; &longs;equentibus. Item noua de Iride tra-ctatio. ibidem in additione.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Iugum in lyra quid, &amp; eius figura.<emph.end type="italics"/></cell>
            <cell>396</cell>
          </row>
          <row>
            <cell><emph type="italics"/>L<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Leges mu&longs;icales.<emph.end type="italics"/></cell>
            <cell>204</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Libra maior, cur exactior. initio Mechanicarum qu&aelig;&longs;t.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Linea, qu&aelig; terminus est illuminationis in Luna, cur modo recta, modo curua vi-deatur.<emph.end type="italics"/></cell>
            <cell>346</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Line&aelig; rationales, &amp; irrationales, &amp;c.<emph.end type="italics"/></cell>
            <cell>279</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lumen oculorum noctu videntium, in qua oculi parte manet. in addit. de Pupilla.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Lumen Solis, cur &longs;it circulare, quamuis per foramina angulo&longs;a ingrediatur.<emph.end type="italics"/></cell>
            <cell>345</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Luna plana, cur appareat, cum &longs;it &longs;ph&aelig;rica. 347. cur in eadem altitudine cum Sole   &longs;upra horizontem, maiorem vmbram efficiat.<emph.end type="italics"/></cell>
            <cell>349</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lunam e&longs;&longs;e &longs;ph&aelig;ricam. 48. illuminari &longs;ph&aelig;ric&egrave; quid: ibidem &amp; de illuminatione Lu-n&aelig;. iterum e&longs;&longs;e &longs;ph&aelig;ricam ab eclyp&longs;ibus.<emph.end type="italics"/></cell>
            <cell>111</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Luminarium Solis, &amp; Lun&aelig; ordo.<emph.end type="italics"/></cell>
            <cell>133</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lychanos, quid.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lyr&aelig; veteris figura.<emph.end type="italics"/></cell>
            <cell>396</cell>
          </row>
          <row>
            <cell><emph type="italics"/>M<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Magalis, &longs;eu magas, &amp; magadi&longs;&longs;are.<emph.end type="italics"/> 373.</cell>
            <cell>393</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Materia intelligibilis. fus&egrave; ver&ograve;. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Mathematic&aelig; medi&aelig;, &longs;eu &longs;ubalternat&aelig; habent propter quid &longs;uarum demon&longs;iratio-nem.<emph.end type="italics"/></cell>
            <cell>50</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mathematici negant reperiri quantitatem indiui&longs;ibilem, &longs;eu minimam.<emph.end type="italics"/></cell>
            <cell>100</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mathematic&aelig; non &longs;unt contentio&longs;&aelig;. 83. ostendunt per cau&longs;am formalcm.<emph.end type="italics"/></cell>
            <cell>91</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mathematicas inuenerunt Aegyptij Sacerdotes.<emph.end type="italics"/></cell>
            <cell>198</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mathematic&aelig; o&longs;tendunt per cau&longs;am materialem, &amp; formalem. 205. earum vtilitas.   ibidem. De earum natura. in proprio tractatu.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <pb pagenum="28" xlink:href="009/01/028.jpg"/>
          <row>
            <cell><emph type="italics"/>Mathematic&aelig; maxim&egrave; tractant de Bono, &amp; Pulcro, qua ratione.<emph.end type="italics"/></cell>
            <cell>237</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mechanica facultas, qu&aelig;.<emph.end type="italics"/></cell>
            <cell>238</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Melodia.<emph.end type="italics"/></cell>
            <cell>331</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Melopeia quid.<emph.end type="italics"/></cell>
            <cell>384</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Medium Demonstrationum Mathem. in earum tractatu.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Me&longs;e quid.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mina in men&longs;uris quid.<emph.end type="italics"/></cell>
            <cell>53</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Monochordium.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Motus nauigij, &amp; remi comparatio. 247. Pulchra P. Nonij in id annotatio con-tra Ari&longs;t.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Modi mu&longs;ici.<emph.end type="italics"/></cell>
            <cell>383</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Modorum antiquorum ordo, numerus, &amp;c.<emph.end type="italics"/></cell>
            <cell>383</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Motus primi mobilis, &longs;eu diurnus e&longs;t men&longs;ura c&oelig;lestium motuum.<emph.end type="italics"/></cell>
            <cell>225</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. &amp; in fine Chronologi&aelig;.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Mu&longs;ic&aelig; totius elementa.<emph.end type="italics"/></cell>
            <cell>359</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mu&longs;ica nuda, &amp; cum melodia.<emph.end type="italics"/></cell>
            <cell>331</cell>
          </row>
          <row>
            <cell><emph type="italics"/>N<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Nete quid.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nucifragi in&longs;trumenti problema.<emph.end type="italics"/></cell>
            <cell>261</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Numerus, par, impar, primus, &amp; compo&longs;itus, quadratus, &longs;eu &aelig;quilaterus, altera   parte longior. 24. Cubus num.<emph.end type="italics"/></cell>
            <cell>33</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Numeri capitales, qui.<emph.end type="italics"/></cell>
            <cell>82</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Numerum parem e&longs;&longs;e cau&longs;am infiniti: imparem ver&ograve; finiti.<emph.end type="italics"/></cell>
            <cell>93</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Numerorum parium alij &longs;unt primi, alij non.<emph.end type="italics"/></cell>
            <cell>224</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Numerus vnitarius.<emph.end type="italics"/></cell>
            <cell>307</cell>
          </row>
          <row>
            <cell><emph type="italics"/>O<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Oculi cur moueantur con&longs;imiliter.<emph.end type="italics"/></cell>
            <cell>405</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Oculi anathome.<emph.end type="italics"/></cell>
            <cell>408. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Omophon&aelig; voces.<emph.end type="italics"/> 372.</cell>
            <cell>392</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Oppo&longs;itio diametralis e&longs;t omnium maxima.<emph.end type="italics"/></cell>
            <cell>327</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ortus, &amp; occa&longs;us &longs;yderum, quid, &amp; quotuplex: vbide Orione, &amp; Canicula.<emph.end type="italics"/></cell>
            <cell>153</cell>
          </row>
          <row>
            <cell><emph type="italics"/>P<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Paranete qu&aelig; voces, aut chord&aelig;.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Parame&longs;e<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Parhypate<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Parelia, cur appareant nondum &longs;atis explicari.<emph.end type="italics"/></cell>
            <cell>182</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Parna&longs;&longs;us mons, vbinam &longs;it. Item paropame&longs;&longs;us.<emph.end type="italics"/></cell>
            <cell>145</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Partes quantitatis &longs;unt materia illius.<emph.end type="italics"/></cell>
            <cell>211</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Per&longs;pectiuus, quatenus con&longs;ideret lineam.<emph.end type="italics"/></cell>
            <cell>89</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pa&longs;&longs;iones Mathematicorum cum &longs;ubiecto conuertuntur.<emph.end type="italics"/></cell>
            <cell>47</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pila chri&longs;tallina, vel vitrea, qua ratione comburat.<emph.end type="italics"/></cell>
            <cell>60</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Planet&aelig;, qua ratione moueantur duplici motu.<emph.end type="italics"/></cell>
            <cell>130</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Plato &longs;olida ex planis componebat. 105. cur Elementis figuras Geometricas attri-bueret.<emph.end type="italics"/></cell>
            <cell>122</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Planetarum ordo.<emph.end type="italics"/></cell>
            <cell>271</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Principia Mathematicorum.<emph.end type="italics"/> 2.</cell>
            <cell>118</cell>
          </row>
          <pb pagenum="29" xlink:href="009/01/029.jpg"/>
          <row>
            <cell><emph type="italics"/>Principia &longs;cientiarum duplicia. Ex quibus, &amp; circa quod.<emph.end type="italics"/></cell>
            <cell>61</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></cell>
            <cell>315</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proportio alterna. 28. multiplicata, &longs;eu multiplex &longs;ecundum C&aelig;neum.<emph.end type="italics"/></cell>
            <cell>46</cell>
          </row>
          <row>
            <cell><emph type="italics"/>P&longs;eudographia quid.<emph.end type="italics"/></cell>
            <cell>83</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proportionalitas quid.<emph.end type="italics"/></cell>
            <cell>308</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proportio continuata, &amp; di&longs;iuncta quid. 310. alterna, &longs;eu permutata quid.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>inibi.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proportio Geometrica. 311. Arithmetica.<emph.end type="italics"/></cell>
            <cell>302</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proportio &longs;ecundum dignitatem, e&longs;t Geometrica.<emph.end type="italics"/></cell>
            <cell>330</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Problemata mu&longs;icalia varia &agrave; 360. <expan abbr="v&longs;q;">v&longs;que</expan> ad finem &longs;ectionis 19. problematum.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Punicum, mu&longs;icum in&longs;trumentum.<emph.end type="italics"/></cell>
            <cell>370</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pupill&aelig; oculi etymon., &amp; natura. 408. cur in oculo no&longs;tro imago pupill&aelig; appareat.   problem.<emph.end type="italics"/> 2.</cell>
            <cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cur nigra in omnibus hominibus. probl.<emph.end type="italics"/> 5.</cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Cur in Sole euane&longs;cat. probl.<emph.end type="italics"/> 6.</cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Cur modo maior, modo minor appareat.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Pythagorici primi Mathematicis <expan abbr="oper&atilde;">operam</expan> dedere, easqu&eacute; ceteris &longs;cientijs pr&aelig;ponebat.<emph.end type="italics"/></cell>
            <cell>202</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Q<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Qvadratura circuli. vide circulus. de quadratura figurarum rectangularum, &amp;   quadratur&aelig; duplex definitio cau&longs;alis, &amp; formalis.<emph.end type="italics"/></cell>
            <cell>185</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Quantitas an con&longs;tet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis   mathematicis.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>R<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Remi problema.<emph.end type="italics"/></cell>
            <cell>245</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Re&longs;olutio logica, &amp; mathematica, vt conueniant. 4. &amp;<emph.end type="italics"/></cell>
            <cell>305</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Re&longs;ultus cadentium in terram, quibus angulis fiat.<emph.end type="italics"/></cell>
            <cell>354</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Rythmus fus&egrave; explicatur.<emph.end type="italics"/></cell>
            <cell>381</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Rubrum mare duplex.<emph.end type="italics"/></cell>
            <cell>152</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Scythala quid, &amp; eius figura 250. &amp;<emph.end type="italics"/></cell>
            <cell>252</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Securis problema, vbi de antiqu&aelig; &longs;ecuris figura, &amp; angulo pulchra demon&longs;tran-tur.<emph.end type="italics"/></cell>
            <cell>258</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Semitonium, quid.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Solem e&longs;&longs;e terra multo maiorem: probatur.<emph.end type="italics"/></cell>
            <cell>131</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Sph&aelig;ram planum tangit in puncto. demon&longs;tratur.<emph.end type="italics"/></cell>
            <cell>184</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Statera antiqua, qu&aelig;: eius figura, &amp; problema.<emph.end type="italics"/></cell>
            <cell>259</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Stereomatria, vt differat &agrave; Geometria.<emph.end type="italics"/></cell>
            <cell>49</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Succula.<emph.end type="italics"/></cell>
            <cell>253</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Symphon&aelig; voces.<emph.end type="italics"/> 372.</cell>
            <cell>392</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Symphonia.<emph.end type="italics"/></cell>
            <cell>391</cell>
          </row>
          <row>
            <cell><emph type="italics"/>T<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Temonis nauis problema.<emph.end type="italics"/></cell>
            <cell>246</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Terram e&longs;&longs;e rotundam ex eclyp&longs;i. 114. Item aliter. 115. e&longs;&longs;e re&longs;pectu C&oelig;li   paruam valde. 115. e&longs;&longs;e cubum cur Plato voluerit.<emph.end type="italics"/></cell>
            <cell>122</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Terr&aelig; quantitas.<emph.end type="italics"/></cell>
            <cell>115</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Terram paulatim reduci ad peff&eacute;ctam rotunditatem.<emph.end type="italics"/></cell>
            <cell>151</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Tetragoni&longs;mus. vide Quadratura.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <pb pagenum="30" xlink:href="009/01/030.jpg"/>
          <row>
            <cell><emph type="italics"/>Teretizare, quid.<emph.end type="italics"/></cell>
            <cell>366</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Tetrachordon, quid.<emph.end type="italics"/></cell>
            <cell>386</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Tollenonis problema.<emph.end type="italics"/></cell>
            <cell>267</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Tonus mu&longs;icus, qui; vnde oriatur.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Trochle&aelig; problemata.<emph.end type="italics"/> 249. 250.</cell>
            <cell>251</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Tunic&aelig; oculi. 408. in tractatu de Pupilla.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>V<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Ventorum nomina, &amp; &longs;itus.<emph.end type="italics"/></cell>
            <cell>160. <emph type="italics"/>a.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vectis quotuplex, &amp; c.<emph.end type="italics"/></cell>
            <cell>244</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Veteres canere &longs;olitos non &longs;olum in choris, &longs;ed etiam in &longs;cenis.<emph.end type="italics"/> 371. 384.</cell>
            <cell>400</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Virgili&aelig;, Pleiades.<emph.end type="italics"/></cell>
            <cell>335</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vi&longs;&aelig; res gemmantur di&longs;tractis oculis.<emph.end type="italics"/></cell>
            <cell>406</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vi&longs;&aelig; rei geminatio non fit altero oculo in latera torto, cur.<emph.end type="italics"/></cell>
            <cell>407</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vi&longs;us res vi&longs;as, cur non duplicet, etiam &longs;i duos oculos habeamus.<emph.end type="italics"/></cell>
            <cell>405</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vmbelici litoralis problema.<emph.end type="italics"/></cell>
            <cell>254</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vmbram terr&aelig; parum &longs;upra Lunam tran&longs;cendere.<emph.end type="italics"/></cell>
            <cell>137</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vmbrarum incrementa, &amp; decrementa, cur in&aelig;qualia.<emph.end type="italics"/> 344.</cell>
            <cell>348</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vi&longs;us res geminat, &longs;i alter oculorum digito pellatur, cur.<emph.end type="italics"/></cell>
            <cell>197</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vocum mu&longs;icalium antiqu&aelig; appellationes.<emph.end type="italics"/></cell>
            <cell>360</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vox acuta velocior, grauis ver&ograve; tarda, cur.<emph.end type="italics"/></cell>
            <cell>77</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Voluminum &longs;ectio modo rectam lineam, modo curuam refert, cur.<emph.end type="italics"/></cell>
            <cell>356</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vnitas, cur indiui&longs;ibilis.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Z<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Zonas terr&aelig;, vt Arist. de&longs;ignet: &amp; qu&aelig; &longs;ecundum ip&longs;um &longs;int habitabiles.<emph.end type="italics"/></cell>
            <cell>156</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Zonam torridam quatuor reddunt habitabilem.<emph.end type="italics"/></cell>
            <cell>159</cell>
          </row>
        </table>
        <p type="head">
          <s id="s.000664">Finis Tertij Indicis.</s>
        </p>
        <pb pagenum="31" xlink:href="009/01/031.jpg"/>
      </section>
      <section>
        <p type="main">
          <s id="s.000665">Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum <lb/>
loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma&shy;<lb/>
thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&etail;&longs;ertim Peripa&shy;<lb/>
tetici facilius ea inuenire, <expan abbr="atq;">atque</expan> de ij&longs;dem iudicium ferre <lb/>
po&longs;&longs;int.<lb/>
<arrow.to.target n="table3"/></s>
        </p>
        <table>
          <table.target id="table3"/>
          <row>
            <cell><emph type="italics"/>121<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Nvmero marginali: vbi ait plura Octaedra, &longs;eu Pyramides re-plere locum: in quo omnes pariter expo&longs;itores lap&longs;i &longs;unt.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>124<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Latitudinem figura, ait, cau&longs;am e&longs;&longs;e &longs;upernatationis. &amp; aquam   re&longs;i&longs;tere &longs;impliciter diui&longs;ioni.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>136<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Cometas in &longs;uprema aeris regione collocat; cuius contrarium ibi   line ari demon&longs;tratione ostenditur.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>147<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait Tanaim, &amp; Indum oriri ex monte Paropami&longs;&longs;o. &amp; c.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>148<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait, tertia parte noctis Cauca&longs;i verticem illuminari &agrave; Sole.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>149<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait Danubium ex Pyreneo monte defluere.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>150<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait fluuium quendam non minorem Rhodano in Liguria ab&longs;orberi,   &amp; iterum egredi.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>152<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait Rubrum mare parum Atlantico Oceano commi&longs;ceri.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>159<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Zonam torridam inhabitabilem exi&longs;timat.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>164<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Putat Iridis angulos non po&longs;&longs;e vnum &longs;upra alterum collocari, &longs;ed   tantummodo in orbem.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>182<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Rationes, quas in Parelij dubitationibus affert, videntur inanes.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>236<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>In &longs;ubducendo c&oelig;le&longs;tium orbium numero, memoria labitur.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>243<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait lineam O L, &longs;uperare lineam L R, quantitate P L, vt in figura.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>245<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Remum ad vectem primi generis reducit.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>246<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Temonem nauis reducit ad vectem primi generis.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>247<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>In motu Remi collato cum motu Nauigij, &agrave; Nonio erroris manifest&egrave;   arguitur. eodem modo in motu Temonis.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>250<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait maioribus trochleis, aut rotulis facilius onera &longs;ubleuari.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>256<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Reducit cuneum ad vectem primi generis.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>270<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Cur res in vorticibus ad medium ferantur, veram cau&longs;am a&longs;signa-re non videtur.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>275<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Ait Danubium altero ramo in Mediterraneum, altero in Pontum   effluere.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>293<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Negat Araneum filum ab intrin&longs;eco emittere, Democritum iniuria   refellens. quamuis hoc vltimum ad Phy&longs;icum pertineat.<emph.end type="italics"/></cell>
          </row>
          <row>
            <cell><emph type="italics"/>403<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>Problem. 2. &longs;ect. 2 3. non ben&egrave; videtur a&longs;signare cau&longs;am vari&aelig; im-mer&longs;ionis nauigij.<emph.end type="italics"/></cell>
          </row>
        </table>
        <pb xlink:href="009/01/032.jpg"/>
        <!--blank page -->
      </section>
    </front>
    <body>
      <chap>
        <pb pagenum="33" xlink:href="009/01/033.jpg"/>
        <p type="head">
          <s id="s.000666">LOCA <lb/>MATHEMATICA <lb/>EX LIBRO <lb/>PR&AElig;DICAMENTORVM <lb/>
Per ordinem declarata.</s>
        </p>
        <p type="main">
          <s id="s.000667"><arrow.to.target n="marg1"/></s>
        </p>
        <p type="margin">
          <s id="s.000668"><margin.target id="marg1"/>1</s>
        </p>
        <p type="main">
          <s id="s.000669">Ex c. <!-- REMOVE S-->3. De his, qu&aelig; ad aliquid. </s>
          <s id="s.000670">Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita <lb/>
<expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g. <lb/>
<!-- REMOVE S-->angulus B A C, vbi ait <emph type="italics"/>&lpar;Scientia ver&ograve; &longs;i non &longs;it, <lb/>
nihil probibet e&longs;&longs;e &longs;cibile, vt circuli quadratura, &longs;i e&longs;t &longs;cibilis, <lb/>
&longs;cientia quidem eius nondum e&longs;t&rpar;<emph.end type="italics"/> Cum velit Ari&longs;t. o&longs;tendere, <lb/>
n&oacute; omnia correlatiua &longs;imul e&longs;&longs;e natura, id de &longs;cibili, &amp; &longs;cien&shy;<lb/>
tia vari&egrave; probat, pr&aelig;&longs;ertim ver&ograve;, quia multa &longs;int &longs;cibilia, <lb/>
qu&aelig; tamen nondum &longs;ciantur, vt patet, inquit, in Quadratu&shy;<lb/>
ra circuli, &amp; &longs;cientia ip&longs;ius, quia quamuis ip&longs;a circuli quadratura &longs;it &longs;cibi&shy;<lb/>
lis, nondum tamen &longs;imul cum ip&longs;a, &longs;cientia illius extat. </s>
          <s id="s.000671">Qu&aelig; vt perfect&egrave; <lb/>
intelligantur, &longs;ciendum e&longs;t, quadraturam circuli, qu&aelig; &agrave; Gr&aelig;cis tetrago&shy;<lb/>
ni&longs;mus dicitur, nihil aliud e&longs;&longs;e, qu&agrave;m propo&longs;ito cuilibet circulo exhibere <lb/>
quadratum &aelig;quale. </s>
          <s id="s.000672">Qu&aelig; &aelig;qualitas debet intelligi de areis, &longs;eu &longs;patijs, ita <lb/>
vt area circuli, &longs;eu &longs;patium illud, &longs;iue &longs;uperficies illa circularis, &longs;it &aelig;qualis <lb/>
are&aelig;, &longs;eu &longs;uperficiei quadrat&aelig;. </s>
          <s id="s.000673">Qua in re plurimi decipiuntur exi&longs;timantes <lb/>
per quadraturam cir culi inquiri &aelig;qualitatem linearum, ita vt circumferen&shy;<lb/>
tia circuli debeat e&longs;&longs;e &aelig;qualis ambitui, &longs;eu quatuor lateribus quadrati: <lb/>
quod omnino fal&longs;um e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.000674">Quadratio porr&ograve; circuli dupliciter proponi pote&longs;t, vel tanquam Theo&shy;<lb/>
rema, vel tanquam Problema <emph type="italics"/>&lpar;theorema autem e&longs;t propo&longs;itio, in qua nihil fa&shy;<lb/>
ciendum proponitur; problema ver&ograve; aliquid fieri expo&longs;cit&rpar;<emph.end type="italics"/> neutrum autem tem&shy;<lb/>
pore Ari&longs;t. erat adinuentum nam theorema inuentum e&longs;t po&longs;t ip&longs;um ducen&shy;<lb/>
tis circiter annis ab Archimede: problema ver&ograve; nondum &agrave; quoquam per&shy;<lb/>
fect&egrave; potuit reperiri. </s>
          <s id="s.000675">qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius <lb/>
hoc loco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadratur&aelig; huius, &longs;i nimi&shy;<lb/>
rum intelligant theorema. </s>
          <s id="s.000676">&amp; alij etiam verum a&longs;&longs;erunt, dum negant hacte&shy;<lb/>
nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi&shy;


<pb pagenum="34" xlink:href="009/01/034.jpg"/>medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au&shy;<lb/>
tem huiu&longs;modi. </s>
          <s id="s.000677">Quilibet circulus &aelig;qualis e&longs;t triangulo rectangulo, cuius <lb/>
quidem &longs;emidiameter vni laterum, qu&aelig; circa rectum angulum &longs;unt, ambi&shy;<lb/>
tus ver&ograve; ba&longs;i eius e&longs;t &aelig;qualis.</s>
        </p>
        <figure id="id.009.01.034.1.jpg" place="text" xlink:href="009/01/034/1.jpg"/>
        <p type="main">
          <s id="s.000678">Sit, v.g. <!-- REMOVE S-->datus circulus, cuius &longs;emidiameter A B; &amp; fit triangulum rectangu&shy;<lb/>
lum A B C, cuius angulus B, &longs;it rectus, &amp; latus B A, <expan abbr="con&longs;titu&etilde;s">con&longs;tituens</expan> angulum re&shy;<lb/>
ctum B, cum ba&longs;i B C, &longs;it &aelig;quale &longs;emidiametro A B; ba&longs;is ver&ograve; B C, &longs;it &aelig;qua&shy;<lb/>
lis peripheri&aelig; eiu&longs;dem circuli dati. </s>
          <s id="s.000679">demon&longs;trat iam ibi Archimedes acuta <lb/>
&aelig;qu&egrave;, ac euidenti demon&longs;tratione triangulum i&longs;tud &aelig;quale e&longs;&longs;e circulo illi. <lb/>
</s>
          <s id="s.000680">quod perinde e&longs;t, ac &longs;i o&longs;tendi&longs;&longs;et cuinam quadrato &longs;it &aelig;qualis, cum per vl&shy;<lb/>
timam 2. Eucl. <!-- REMOVE S-->po&longs;&longs;imus triangulo huic quadratum &aelig;quale con&longs;truere, quod <lb/>
con&longs;equenter dato circulo &aelig;quale erit. </s>
          <s id="s.000681">Quod &longs;i in modum Problematis ita <lb/>
proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>
e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <lb/>
e&longs;t ad &aelig;qualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif&shy;<lb/>
ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>
neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s>
          <s id="s.000682">quam nullus hactenus <lb/>
geometric&egrave; illi &aelig;qualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra&shy;<lb/>
tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib. de <lb/>
lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>
&longs;tigauit. </s>
          <s id="s.000683">nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>
&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>
rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s>
          <s id="s.000684">tu ip&longs;um con&longs;ule, <lb/>
&longs;i admirandarum rerum contemplatione delectaris. </s>
          <s id="s.000685">Multa hac de re Pap&shy;<lb/>
pus Alexandrinus lib. 4. Math. coll. </s>
          <s id="s.000686">&amp; Ioannes Buteo vnico volumine om&shy;<lb/>
nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s>
          <s id="s.000687">Qua&shy;<lb/>
re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>
illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>
turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s>
          <s id="s.000688">&longs;olet autem &agrave; non&shy;<lb/>
nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>
cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>
nus adinuentam e&longs;&longs;e. </s>
          <s id="s.000689">ego quidem e&longs;&longs;e po&longs;&longs;ibilem exi&longs;timo, quis enim dubi&shy;<lb/>
tare pote&longs;t, po&longs;&longs;e exi&longs;tere quadratum &aelig;quale circulo propo&longs;ito? </s>
          <s id="s.000690">Quod &longs;i po&shy;<lb/>
te&longs;t fieri, quare non etiam demon&longs;trari? </s>
          <s id="s.000691">pr&etail;fertim cum videamus ab Archi&shy;<lb/>
mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s>
          <s id="s.000692">&amp; pr&aelig;terea con&longs;tet, Hip&shy;<lb/>
pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, &amp; Archimedem in libel&shy;


<pb pagenum="35" xlink:href="009/01/035.jpg"/>lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, qu&aelig; tamen du&aelig; fi&shy;<lb/>
gur&aelig;, lunula &longs;cilicet, &amp; parabola &longs;unt curuiline&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.000693"><arrow.to.target n="marg2"/></s>
        </p>
        <p type="margin">
          <s id="s.000694"><margin.target id="marg2"/>2</s>
        </p>
        <p type="main">
          <s id="s.000695">Ex cap. de Priori <emph type="italics"/>&lpar;in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>
elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>
matibus ordine&rpar;<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s>
          <s id="s.000696">qu&aelig; non &longs;unt in antiqua tran&shy;<lb/>
&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy;<lb/>
dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/>
<foreign lang="greek">ai/ gar arxai/ pro/terai tw=n qewrhma/twn th&verbar; ta/ch. </foreign> per &longs;cientias autem demon&longs;tra&shy;<lb/>
tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>
a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>
nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>
rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>
ba illa &agrave; nobis addita ex gr&aelig;co, optim&egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>
menta intelligantur principia, qualia &longs;unt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>
nes exponant theoremata. </s>
          <s id="s.000697">quod autem principia illa ordine priora &longs;int de&shy;<lb/>
mon&longs;trationibus, &longs;iue ip&longs;as pr&aelig;cedant, ex ip&longs;a primi Euclidis in&longs;pectione <lb/>
patere pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.000698"><arrow.to.target n="marg3"/></s>
        </p>
        <p type="margin">
          <s id="s.000699"><margin.target id="marg3"/>3</s>
        </p>
        <p type="main">
          <s id="s.000700">Ex cap. de motu <emph type="italics"/>&lpar;Quadratum augetur Gnomone circumpo&longs;ito&rpar;<emph.end type="italics"/> Gnomon vox <lb/>
gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/>
<figure id="id.009.01.035.1.jpg" place="text" xlink:href="009/01/035/1.jpg"/><lb/>
tum normam appellant, Itali ver&ograve;, Squadra, ad <lb/>
cuius &longs;imilitudinem Geometr&aelig; denominarunt fi&shy;<lb/>
guram quandam, &longs;eu portionem cuiu&longs;uis paralle&shy;<lb/>
logrammi, vt videre e&longs;t in definitione &longs;ecunda <lb/>
2. elem. </s>
          <s id="s.000701">&amp; in pr&aelig;&longs;enti figura, in qua quadratum <lb/>
A B C D, circumpo&longs;ito gnomone E F G, augetur, <lb/>
&amp; fit maius quadratum H B I L.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000702">Idem etiam verum e&longs;t in quadrato arithmeti&shy;<lb/>
co, &longs;iue in numero quadrato: is enim pariter ad&shy;<lb/>
dito Gnomone augetur. </s>
          <s id="s.000703">i. </s>
          <s id="s.000704">addito numero impari. <lb/>
</s>
          <s id="s.000705">quemadmodum infra 3. Phy&longs;. tex. <!-- REMOVE S-->26. fus&egrave; explicabimus.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.000706"><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000707"><arrow.to.target n="marg4"/></s>
        </p>
        <p type="margin">
          <s id="s.000708"><margin.target id="marg4"/>4</s>
        </p>
        <p type="main">
          <s id="s.000709">Aliquorum opinio e&longs;t, Ari&longs;totelem ho&longs;ce libros appella&longs;&longs;e re&longs;olu&shy;<lb/>
torios, quod per illos doceat &longs;yllogi&longs;mum, ac demon&longs;trationem <lb/>
iam factam in &longs;ua immediata principia re&longs;oluere, quam opinio&shy;<lb/>
nem meum non e&longs;t, nunc refellere. </s>
          <s id="s.000710">per&longs;ua&longs;um tamen mihi e&longs;t, rem <lb/>
multo aliter &longs;e habere, veram rationem huius tituli petendam e&longs;&longs;e ex peni&shy;<lb/>
tiori Mathematicorum eruditione. </s>
          <s id="s.000711">Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>
Alex. initio &longs;eptimi Mathem. collect. </s>
          <s id="s.000712">antiqui&longs;&longs;imos videlicet Geometras, <lb/>
Euclidem, Apollonium Perg&aelig;um, &amp; Ari&longs;t&etail;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio&shy;<lb/>
ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble&shy;<lb/>
mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri&shy;<lb/>
tatem, per quam deinde componerent illius, quod qu&aelig;rebatur, Demon&longs;tra&shy;<lb/>
tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem <lb/>
ver&ograve; nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento,


<pb pagenum="36" xlink:href="009/01/036.jpg"/>o&longs;tendebant conclu&longs;ionem. </s>
          <s id="s.000713">Porr&ograve; Diogenes Laert. <!-- REMOVE S-->huius re&longs;olutionis in&shy;<lb/>
uentorem facit Platonem: &agrave; quo eam Leodamas Tha&longs;ius didicit, cuius be&shy;<lb/>
neficio, pluries deinde Geometricas demon&longs;trationes adinuenit. </s>
          <s id="s.000714">definitio <lb/>
<expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t apud Euclidem ad primam propo&longs;. 13. Elem. iuxta tran&longs;latio&shy;<lb/>
nem Zamberti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy;<lb/>
m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy;<lb/>
quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s>
          <s id="s.000715">&longs;unt pr&aelig;terea fre&shy;<lb/>
quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>
pi. </s>
          <s id="s.000716">extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in&shy;<lb/>
&longs;eruiebat. </s>
          <s id="s.000717">vtinam extarent etiam alij de re&longs;olutione, quorum auxilio non <lb/>
tantopere recentiores Mathematici in inueniendis Demo&longs;trationibus la&shy;<lb/>
borarent; hanc re&longs;olutionem, &longs;ic Pappus fu&longs;ius, quam Euclides explicat; <lb/>
re&longs;olutio e&longs;t via &agrave; qu&aelig;&longs;ito tanquam conce&longs;&longs;o per ea, qu&aelig; ex ip&longs;o con&longs;equun&shy;<lb/>
tur ad aliquod certum, &amp; conce&longs;&longs;um: in re&longs;olutione enim id, quod qu&aelig;ritur <lb/>
tanquam factum, &amp; verum &longs;upponentes, quid ex hoc &longs;equatur, con&longs;idera&shy;<lb/>
mus, quou&longs;que incidamus in aliquod iam cognitum, vel quod &longs;it &egrave; numero <lb/>
principiorum. </s>
          <s id="s.000718">Quod quidem erat &longs;ignum euidens, qu&aelig;&longs;itum quoque verum <lb/>
e&longs;&longs;e. </s>
          <s id="s.000719">eadem omnino habet Proclus in comm. <!-- REMOVE S-->ad &longs;extam primi elem. </s>
          <s id="s.000720">Quod <lb/>
porr&ograve; Ari&longs;t. ip&longs;e hanc re&longs;olutionem Mathematicam cognouerit e&longs;&longs;e medij <lb/>
inqui&longs;itionem manife&longs;tum e&longs;t ex cap. 3. lib.  3. Ethyc. <!-- REMOVE S-->vbi &longs;ic ait <emph type="italics"/>&lpar;Qui enim <lb/>
con&longs;ultat, qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, quemadmodum de&longs;igna&shy;<lb/>
tiones&rpar;<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/>
&longs;upra innuimus, &amp; infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it, <lb/>
quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e <lb/>
&longs;imilem re&longs;olutioni Geometric&aelig;, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem <lb/>
e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s>
          <s id="s.000721">Exi&longs;timo igitur <lb/>
cum docti&longs;&longs;imis Zabarella, Burana, Toleto, &amp; alijs, Ari&longs;totilem non &longs;olum <lb/>
hanc &longs;uam logicam ad mathematicarum &longs;cientiarum typum compegi&longs;&longs;e, <lb/>
verum potius imitatum e&longs;&longs;e opus illud Euclidis de re&longs;olutione, atque ex eo <lb/>
non &longs;olum plurima exempla Geometrica, verum etiam titulum de&longs;ump&longs;i&longs;&longs;e, <lb/>pr&aelig;&longs;ertim cum argumentum e&longs;&longs;et fer&egrave; idem vtrobique, &longs;ed Ari&longs;t. intentio <lb/>
fuerit accommodare re&longs;olutionem omnibus <expan abbr="&longs;ci&etilde;tijs">&longs;cientijs</expan>; Euclidis ver&ograve;, &amp; alio&shy;<lb/>
rum Geometri&aelig; &longs;oli. </s>
          <s id="s.000722">hinc patere pote&longs;t, cur hi libri re&longs;olutorij in&longs;cribantur, <lb/>
quod &longs;cilicet tradunt methodum, qua valeamus qu&aelig;&longs;itum quoduis re&longs;olue&shy;<lb/>
re, ide&longs;t, ex qu&aelig;&longs;ito tanquam vero inue&longs;tare aliquam veritatem, per quam <lb/>
deinde propo&longs;it&aelig; qu&aelig;&longs;tionis rationem methodo compo&longs;itiua reddamus. </s>
          <s id="s.000723">Et <lb/>
ver&ograve; cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis, <lb/>
definitionum, po&longs;tulatorum, axiomatum, &amp; alia huiu&longs;modi ex Geometri&shy;<lb/>
cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s>
          <s id="s.000724">maxim&egrave; <lb/>
ver&ograve;, quia &longs;i horum lib. intentio e&longs;&longs;et docere iam factum &longs;yllogi&longs;mum in &longs;ua <lb/>
principia re&longs;oluere, parum e&longs;&longs;et vtilis; im&ograve; nec vtilis, &longs;ed &longs;uperfluum quid. <lb/>
</s>
          <s id="s.000725">at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s>
          <s id="s.000726">profecto nullibi. </s>
          <s id="s.000727">quid opus e&longs;t <lb/>
iam factum &longs;yllogi&longs;mum re&longs;oluere? </s>
          <s id="s.000728">at ver&ograve; propo&longs;itam qu&aelig;&longs;tionem re&longs;ol&shy;<lb/>
uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.000729">Hanc porr&ograve; re&longs;olutionem attendendam e&longs;&longs;e prim&ograve; penes formam, quam <lb/>
docet primis duobus analyticis; &longs;ecund&ograve; penes materiam, quam tradit duo&shy;


<pb pagenum="37" xlink:href="009/01/037.jpg"/>bus vltimis, non pr&aelig;tereundum. </s>
          <s id="s.000730">reliquas duas logic&aelig; partes, Topicam &longs;ci&shy;<lb/>
licet, &amp; Elenchos, qu&aelig; &longs;yllogi&longs;mos probabilem, &amp; apparentem docent, no&shy;<lb/>
luit appellare re&longs;olutorios, quamuis inuentionem mediorum doceant, quia <lb/>
iam mos i&longs;te inoleuerat apud Philo&longs;ophos, &amp; Mathematicos, vt illa &longs;ola <lb/>
pars, qu&aelig; ex materia nece&longs;&longs;aria doceret &longs;yllogi&longs;mum demon&longs;tratiuum con&shy;<lb/>
&longs;truere, diceretur re&longs;olutio: cum Mathematici, qui primi de re&longs;olutione <lb/>
&longs;crip&longs;erunt, talem materiam &longs;olum con&longs;iderent.</s>
        </p>
        <p type="main">
          <s id="s.000731"><arrow.to.target n="marg5"/></s>
        </p>
        <p type="margin">
          <s id="s.000732"><margin.target id="marg5"/>5</s>
        </p>
        <p type="main">
          <s id="s.000733">Ex cap. 23. &longs;ecti primi lib. 1. <emph type="italics"/>&lpar;Vt quod diameter incommen&longs;urabilis eo, quod <lb/>
imparia &aelig;qualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;urabilis. </s>
          <s id="s.000734">&aelig;qualia igitur fieri <lb/>
imparia paribus ratiocinantur, diametrum vtr&ograve; incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo&shy;<lb/>
&longs;itione <expan abbr="mon&longs;tr&atilde;t">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem&rpar;<emph.end type="italics"/> Euclides pri&shy;<lb/>
mis duabus definitionibus 10. elem. </s>
          <s id="s.000735">definit, qu&aelig; nam &longs;int magnitudines <lb/>
commen&longs;. </s>
          <s id="s.000736">&amp; qu&aelig; incommen&longs;. </s>
          <s id="s.000737">&longs;ic; commen&longs;. </s>
          <s id="s.000738">magnitudines dicuntur, quas <lb/>
<figure id="id.009.01.037.1.jpg" place="text" xlink:href="009/01/037/1.jpg"/><lb/>
eadem men&longs;ura metitur, vt &longs;i fuerint du&aelig; magnitu&shy;<lb/>
dines, A, &amp; B, quas eadem men&longs;ura C, ide&longs;t quan&shy;<lb/>
titas C, metiatur, ide&longs;t <expan abbr="qu&atilde;titas">quantitas</expan> C, applicata quan&shy;<lb/>
titati A, &amp; per ip&longs;am aliquoties replicata ip&longs;am ad&shy;<lb/>
&aelig;quat&egrave; ab&longs;umat, vt &longs;i linea C, quinquies &longs;uper li&shy;<lb/>
neam A, replicata eam pr&aelig;cis&egrave;, &amp; perfect&egrave; omnin&ograve; <lb/>
ad&aelig;quaret: &amp; eadem linea C, applicata line&aelig; B, &amp; &longs;uper illam ter, v.g. <!-- REMOVE S-->re&shy;<lb/>
petita ip&longs;am con&longs;umeret, diceretur <expan abbr="vtranq;">vtranque</expan> metiri, &amp; proinde duas lineas <lb/>
A, &amp; B, e&longs;&longs;e comm. <!-- REMOVE S-->definit po&longs;tea <expan abbr="incomm&etilde;&longs;">incommen&longs;.</expan> hoc modo, incomm. autem, qua&shy;<lb/>
rum nullam contingit communem men&longs;uram reperiri; vt &longs;i duarum linea&shy;<lb/>
<figure id="id.009.01.037.2.jpg" place="text" xlink:href="009/01/037/2.jpg"/><lb/>
rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u&shy;<lb/>
ra, qu&aelig; <expan abbr="vtranq;">vtranque</expan> ad&aelig;quat&egrave; metiretur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i linea <lb/>
C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta <lb/>
non ad&aelig;quaret omnino <expan abbr="line&atilde;">lineam</expan> B, &longs;ed deficeret, vel ex&shy;<lb/>
cederet aliquantulum, <expan abbr="atq;">atque</expan> hoc fieret in quauis alia <lb/>
men&longs;ura, loco ip&longs;ius C, a&longs;&longs;umpta, &longs;iue maior, &longs;iue <lb/>
minor ip&longs;a C, vt <expan abbr="vtranq;">vtranque</expan> nunquam perfect&egrave; metiretur, e&longs;&longs;ent du&aelig; ill&aelig; line&aelig; <lb/>
incommen&longs;. </s>
          <s id="s.000739">Extare porr&ograve; tales lineas, &amp; &longs;uperficies, &amp; corpora, <expan abbr="ea&qacute;">eaque</expan>; quam&shy;<lb/>
plurima, ac pen&egrave; infinita ex 10. Elem. manife&longs;tum e&longs;t. </s>
          <s id="s.000740">inuentum autem hu&shy;<lb/>
ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>
e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>
&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s>
          <s id="s.000741">Quapropter <lb/>
non immerit&ograve; diuinus ille Plato lib. 7. de legib. </s>
          <s id="s.000742">huius a&longs;ymmetri&aelig; ignora&shy;<lb/>
tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque <lb/>
ignorantiam cen&longs;uerit. </s>
          <s id="s.000743">inter lineas incommen&longs;. &longs;unt diameter, &amp; latus eiu&longs;&shy;<lb/>
dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti <lb/>
<figure id="id.009.01.037.3.jpg" place="text" xlink:href="009/01/037/3.jpg"/><lb/>
e&longs;t lineola E, in pr&aelig;&longs;enti quadrato, etiam&longs;i illam in <lb/>
infinitum &longs;ubdiuidas, qu&aelig; <expan abbr="vtranq;">vtranque</expan> lineam, diame&shy;<lb/>
trum &longs;cilicet A C, &amp; latus quoduis ex quatuor, v.<!-- REMOVE S-->g. <lb/>
<!-- REMOVE S-->latus B C, pr&aelig;cis&egrave; omnino metiatur. </s>
          <s id="s.000744">theorema <lb/>
i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me&shy;<lb/>
dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38" xlink:href="009/01/038.jpg"/>propo&longs;itionis, qu&aelig; fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm. <lb/>
<!-- REMOVE S-->deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t. fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>
licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/>
imparia &aelig;qualia paribus fiunt. </s>
          <s id="s.000745">ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>
ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. <!-- REMOVE S-->&amp; proinde altera pars con&shy;<lb/>
tradictionis, qu&aelig; e&longs;t, e&longs;&longs;e incomm. <!-- REMOVE S-->vera a&longs;truitur. </s>
          <s id="s.000746">ex quibus &longs;atis videtur ex&shy;<lb/>
plicari hic locus. </s>
          <s id="s.000747">videas igitur, qu&agrave;m leuiter nonnulli no&longs;tr&aelig; tempe&longs;tatis <lb/>
ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. <!-- REMOVE S-->co&longs;t&aelig;, nihil <lb/>
aliud &longs;ignificare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione <lb/>
nihil ineptius. </s>
          <s id="s.000748">Aduerte tandem figuram vulgat&aelig; editionis e&longs;&longs;e ineptam, <lb/>
cum habeat duo quadrata alterum &longs;uper diametro alterius, quorum maius <lb/>
&longs;uperuacaneum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.000749"><arrow.to.target n="marg6"/></s>
        </p>
        <p type="margin">
          <s id="s.000750"><margin.target id="marg6"/>6</s>
        </p>
        <p type="main">
          <s id="s.000751">Et cap. 24. &longs;ecti primi libri primi <emph type="italics"/>&lpar;Sed magis efficitur manife&longs;tum in de&longs;cri&shy;<lb/>
ptionibus, vt quod &aelig;quicruris, qui ad ba&longs;im &aelig;quales &longs;int, ad centrum duct&aelig; A B, <lb/>A C, &longs;i igitur &aelig;qualem accipiat A G, angulum ip&longs;i A B D, non omnino exi&longs;timans <lb/>
&aelig;quales, qui &longs;emicirculorum, &amp; rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e&shy;<lb/>
cti. </s>
          <s id="s.000752">amplius ab &aelig;qualibus existentibus totis angulis, &amp; ablatorum &aelig;quales e&longs;&longs;e re&shy;<lb/>
liquos E, F, quod ex principio petet, ni&longs;i acceperit ab &aelig;qualibus demptis &aelig;qualia <lb/>
derelinqui.&rpar;<emph.end type="italics"/> Primum &longs;cias characteres vulgat&aelig; editionis, vna cum figura ip&shy;<lb/>
&longs;is re&longs;pondente, e&longs;&longs;e mendo&longs;os; propterea ex textu gr&aelig;co vtrunque corri&shy;<lb/>
gendum putaui in hunc, quem vidi&longs;ti modum. </s>
          <s id="s.000753">Secundo, per de&longs;criptiones <lb/>
Ari&longs;t. intelligere <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> Geometricas &longs;upra diximus, quod ex hoc <lb/>
loco euidenter confirmatur, vbi manife&longs;t&egrave; loco de&longs;criptionis &longs;upponit li&shy;<lb/>
nearem demon&longs;trationem. </s>
          <s id="s.000754">In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t. illud demon&shy;<lb/>
&longs;trare, quod Euclides in 5. primi o&longs;tendit, alio tamen modo, &longs;cilicet I&longs;o&longs;ce&shy;<lb/>
lium triangulorum, qui ad ba&longs;im &longs;unt anguli, inter &longs;e &longs;unt &aelig;quales. </s>
          <s id="s.000755">e&longs;t au&shy;<lb/>
tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="r&egrave;&longs;t&imacr;tuendam">r&egrave;&longs;tituendam</expan> e&longs;&longs;e <lb/>
ex quodam gr&aelig;co codice, qui characteres hoc modo appo&longs;uerat. </s>
          <s id="s.000756">&longs;it I&longs;o&longs;ce&shy;<lb/>
<figure id="id.009.01.038.1.jpg" place="text" xlink:href="009/01/038/1.jpg"/><lb/>
les C A B, cuius ba&longs;is C B, Dico angulos &longs;upra ba&longs;im, <lb/>
in quibus liter&aelig; E F, e&longs;&longs;e inuicem &aelig;quales. </s>
          <s id="s.000757">facto centro <lb/>
in A, de&longs;cribatur circulus A B C, tran&longs;iens per puncta <lb/>
C B, iam &longs;ic. </s>
          <s id="s.000758">omnes anguli &longs;emicirculi &longs;unt &aelig;quales in&shy;<lb/>
ter &longs;e, ergo anguli A C G, A B D, &longs;unt &aelig;quales. </s>
          <s id="s.000759">Pr&aelig;te&shy;<lb/>
rea c&ugrave;m anguli eiu&longs;dem &longs;ectionis &longs;int &aelig;quales ad inui&shy;<lb/>
cem, erunt anguli &longs;ectionis C B D G, nimirum anguli, <lb/>
in quibus &longs;unt G, &amp; D, inter &longs;e &aelig;quales: <expan abbr="cum&qacute;">cumque</expan>; hi duo <lb/>
anguli &longs;ectionis &longs;int partes <expan abbr="angulor&utilde;">angulorum</expan> &longs;emicirculi A C G, <lb/>
A B D, &longs;i illi ab his auferantur, auferuntur &aelig;quales anguli ab &aelig;qualibus an&shy;<lb/>
gulis, ergo anguli, qui remanent, &longs;cilicet E, &amp; F, erunt &aelig;quales, quod erat <lb/>
demon&longs;trandum. </s>
          <s id="s.000760">hinc Ari&longs;t. infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo&shy;<lb/>
gi&longs;mo, reperiri vniuer&longs;ales, &amp; affirmatiuas propo&longs;itiones, vt Factum e&longs;t in <lb/>
pr&aelig;cedenti aliter e&longs;&longs;et petitio principij. </s>
          <s id="s.000761">Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>
Geometr&aelig; con&longs;iderant, infra cap. 1. &longs;ecti 3. explicabitur.</s>
        </p>
        <p type="main">
          <s id="s.000762"><arrow.to.target n="marg7"/></s>
        </p>
        <p type="margin">
          <s id="s.000763"><margin.target id="marg7"/>7</s>
        </p>
        <p type="main">
          <s id="s.000764">Ex cap. 2. &longs;ecti 2. lib. 1. <emph type="italics"/>&lpar;Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>
veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>
&longs;ecundum opinionem&rpar;<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39" xlink:href="009/01/039.jpg"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/k tw=n kata\ alhqei/an diagegramme/non </foreign> vbi manife&longs;t&egrave; vtitur <lb/>
verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari <lb/>
Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy;<lb/>
quentibus verbis, cum dixit &lpar;ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy;<lb/>
tionibus &longs;ecundum opinionem&rpar; hac adhibita con&longs;ideratione, quam inter&shy;<lb/>
pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s>
        </p>
        <p type="main">
          <s id="s.000765"><arrow.to.target n="marg8"/></s>
        </p>
        <p type="margin">
          <s id="s.000766"><margin.target id="marg8"/>8</s>
        </p>
        <p type="main">
          <s id="s.000767">Ex eodem loco paulo po&longs;t <emph type="italics"/>&lpar;Quare principia quidem, qu&aelig; &longs;ecundum <expan abbr="vnum-quodq;">vnum&shy;<lb/>
quodque</expan> &longs;unt experimenti est tradere: dico autem, vt a&longs;trologicam experientiam <lb/>
a&longs;trologic&aelig; &longs;cienti&aelig;: acceptis enim apparentibus <expan abbr="&longs;uffici&etilde;ter">&longs;ufficienter</expan>, ita inuent&aelig; &longs;unt a&longs;tro&shy;<lb/>
logic&aelig; demonstrationes&rpar;<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;cientijs <lb/>po&longs;&longs;e probari, aut demoν&longs;trari: principia enim &longs;cientiarum <expan abbr="n&otilde;">non</expan> demon&longs;tran&shy;<lb/>
tur, &longs;ed &longs;ola experientia manife&longs;ta &longs;unt; vt patet in A&longs;tronomia, qu&aelig; ab ex&shy;<lb/>
perientia &longs;ua &longs;olet &longs;tabilire principia: principijs autem <expan abbr="experim&etilde;to">experimento</expan> con&longs;ti&shy;<lb/>
tutis ex ip&longs;is reliqua problemata <expan abbr="demon&longs;tr&atilde;tur">demon&longs;trantur</expan>. </s>
          <s id="s.000768">duo autem &longs;unt apud a&longs;tro&shy;<lb/>
nomos genera experimenti, primum dicitur Ph&aelig;nomena, ide&longs;t, <expan abbr="appar&etilde;ti&aelig;">apparenti&aelig;</expan>; <lb/>
&amp; &longs;unt ea, qu&aelig; vulgo omnibus patent, vt Solem oriri, &amp; occidere; a&longs;tra fer&shy;<lb/>
ri circulariter, diem augeri modo, modo minui: &amp; his &longs;imilia. </s>
          <s id="s.000769">alterum ge&shy;<lb/>
nus dicitur ob&longs;eruationes, qu&aelig; tantummodo a&longs;tronomi&aelig; peritis per ob&longs;er&shy;<lb/>
uationem innote&longs;cunt, vt Solem in&aelig;qualiter ferri proprio motu per Zodia&shy;<lb/>
cum; aliquando maiorem, aliquando minorem videri; plures dies immo&shy;<lb/>
rari citra &aelig;quatiorem in parte Zodiaci boreali, quam in altera vltra &aelig;qua&shy;<lb/>
torem au&longs;trali. </s>
          <s id="s.000770">dies naturales e&longs;&longs;e inuicem in&aelig;quales, &amp;c. </s>
          <s id="s.000771">ex quibus deinde <lb/>
ponunt eccentricos, &amp; augem, ad &longs;aluandas tum apparentias, tum ob&longs;erua&shy;<lb/>
tiones; &amp; hac ratione a&longs;trologica &longs;cientia paulatim reperta e&longs;t, ac in dies <lb/>
reperitur.</s>
        </p>
        <p type="main">
          <s id="s.000772"><arrow.to.target n="marg9"/></s>
        </p>
        <p type="margin">
          <s id="s.000773"><margin.target id="marg9"/>9</s>
        </p>
        <p type="main">
          <s id="s.000774">Ex cap. 3. &longs;ecti 2. lib. 1. <emph type="italics"/>&lpar;Vt an ne diameter incomm.&rpar;<emph.end type="italics"/> loquitur de a&longs;ymme&shy;<lb/>
tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati, de qua fus&egrave; egimus &longs;uperius in <lb/>
cap. 23. &longs;ecti 1. huius libri; qu&aelig; &longs;i repetantur, optim&egrave; hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s>
        </p>
        <p type="main">
          <s id="s.000775"><arrow.to.target n="marg10"/></s>
        </p>
        <p type="margin">
          <s id="s.000776"><margin.target id="marg10"/>10</s>
        </p>
        <p type="main">
          <s id="s.000777">Ex cap. 1. &longs;ecti 3. lib. 1. <emph type="italics"/>&lpar;Sit A, duo recti, in quo B, triangulus, in quo C, <lb/>
&aelig;quicrus, ip&longs;i <expan abbr="itaq;">itaque</expan> C, ine&longs;t A. per B; ip&longs;i vero B, non amplius per aliud, per &longs;e <lb/>
namque triangulus habet duos rectos&rpar;<emph.end type="italics"/> nullum aliud exemplum tam frequenter <lb/>
v&longs;urpat Philo&longs;ophus, quam i&longs;tud ex Mathematicis de&longs;umptum de triangu&shy;<lb/>
lo, &longs;cilicet, omnis triangulus habet tres angulos &aelig;quales duobus rectis an&shy;<lb/>
gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem. quod, vt prob&egrave; intelliga&shy;<lb/>
tur, explicandum e&longs;t penes quid attendenda &longs;it &aelig;qualitas inter angulum, &amp; <lb/>
angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e inclinatio&shy;<lb/>
nem illam, quam du&aelig; line&aelig; non in directum po&longs;it&aelig; faciunt: &longs;iue etiam &lpar;vt <lb/>
melius percipiamus&rpar; angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem <lb/>
du&aelig; line&aelig; non in directum con&longs;titut&aelig; faciunt, vt duarum linearum A B, A C, <lb/>
<figure id="id.009.01.039.1.jpg" place="text" xlink:href="009/01/039/1.jpg"/><lb/>
inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>
e&longs;t ratio anguli. </s>
          <s id="s.000778">&longs;olum igitur duo anguli erunt &aelig;qua&shy;<lb/>
les, <expan abbr="qu&atilde;do">quando</expan> vnius acumen &aelig;quale erit acumini alterius; <lb/>
etiam &longs;i line&aelig; con&longs;tituentes vnum angulum &longs;int lon&shy;<lb/>
giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40" xlink:href="009/01/040.jpg"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, &amp; mucronem, quem faciunt: vnde etiam&longs;i <lb/>
du&aelig; line&aelig; pr&aelig;dict&aelig; A B, A C, product&aelig;, &longs;iue etiam decurtat&aelig; fuerint, dum&shy;<lb/>
modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur, <lb/>
erit &longs;emper eadem quantitas anguli A. <!-- KEEP S--></s>
          <s id="s.000779">Aduertendum pr&aelig;terea rationem <lb/>
anguli non po&longs;&longs;e &longs;aluari in &longs;olo puncto A, in quo line&aelig; concurrunt, &longs;ed ne&shy;<lb/>
ce&longs;&longs;ariam e&longs;&longs;e aliquam quantitatem, quamuis exiguam, linearum A B, A C. <lb/>
<!-- KEEP S--></s>
          <s id="s.000780">Notandum etiam, quod in nominatione angulorum, qu&aelig; fit per tres lite&shy;<lb/>
ras, &longs;emper literam illam e&longs;&longs;e medio loco proferendam, qu&aelig; ad acumen ip&shy;<lb/>
&longs;um po&longs;ita e&longs;t, vt in &longs;uperiori, litera A, debet &longs;emper media proferri, dicen&shy;<lb/>
do angulum B A C, &longs;iue C A B, <expan abbr="n&utilde;quam">nunquam</expan> tamen licet dicere angulum A C B, <lb/>
vel C B A. <!-- KEEP S--></s>
          <s id="s.000781">Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita <lb/>
<expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g. <lb/>
<!-- REMOVE S-->angulus B A C, diuidatur in duos angulos &agrave; linea A D. tunc enim duo angu&shy;<lb/>
<figure id="id.009.01.040.1.jpg" place="text" xlink:href="009/01/040/1.jpg"/><lb/>
li partiales B A D, D A C, erunt &aelig;quales totali angulo <lb/>
B A C, cum partes omnes &longs;imul &longs;umpt&aelig; &longs;int &longs;uo toti &aelig;qua&shy;<lb/>
les. </s>
          <s id="s.000782">pariter tres anguli po&longs;&longs;unt &aelig;quari &amp; vni, &amp; duobus <lb/>
alijs angulis, quando nimirum a cumina, &longs;iue mucrones il&shy;<lb/>
li &longs;imul ad vnum punctum con&longs;tituti <expan abbr="ad&aelig;quar&etilde;tur">ad&aelig;quarentur</expan> mucro&shy;<lb/>
ni illi, quem con&longs;tituerent alij duo anguli, quibus illi tres <lb/>
&longs;unt pares, v.g. <!-- REMOVE S-->&longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/>
<figure id="id.009.01.040.2.jpg" place="text" xlink:href="009/01/040/2.jpg"/><lb/>
quos linea perpendicularis D E, facit cum li&shy;<lb/>
nea F G; &longs;it <expan abbr="inqu&atilde;">inquam</expan> anguli recti D E F, D E G, <lb/>
tunc tres anguli illius <expan abbr="tri&atilde;guli">trianguli</expan> <expan abbr="dic&etilde;tur">dicentur</expan> &aelig;qua&shy;<lb/>
les duobus hi&longs;ce rectis, &longs;i tres illi mucrones <lb/>
trianguli &longs;imul &longs;umpti, &amp; vniti ad punctum <lb/>
E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum <lb/>
<figure id="id.009.01.040.3.jpg" place="text" xlink:href="009/01/040/3.jpg"/><lb/>
rectorum coeunt, congruent omnino duobus <lb/>
pr&aelig;dictis angulis rectis, &longs;iue duobus illis mu&shy;<lb/>
cronibus angulorum rectorum, &longs;iue con&longs;ti&shy;<lb/>
tuent lineam rectam F E G, &longs;icuti faciunt <lb/>
etiam duo illi anguli recti; &longs;iue etiam dica&shy;<lb/>
mus, occupabunt idem &longs;patium omnin&ograve;, &amp; <lb/>
pr&aelig;cis&egrave;, quod occupant duo recti: v.g. <!-- REMOVE S-->&longs;i mucro B, ibi poneretur, faceret <lb/>
angulum F E H, &amp; &longs;i ibi iuxta ip&longs;um apponeretur mucro A, faceret angulum <lb/>
H E I. quem &longs;i deinceps &longs;ub&longs;equetur reliquus angulus C, con&longs;titueret <expan abbr="reli-qu&utilde;">reli&shy;<lb/>
quum</expan> angulum I E G. iam, vt vides, illi tres anguli ad E, tran&longs;lati, &longs;unt &aelig;qua&shy;<lb/>
les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum <lb/>rector&uacute;m, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/>
con&longs;tituant. </s>
          <s id="s.000783">habet igitur omne triangulum &longs;iue &etail;quilaterum, &longs;iue &longs;calenum, <lb/>
&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian&shy;<lb/>
guli &longs;int &aelig;quales duobus rectis angulis. </s>
          <s id="s.000784">Quam demon&longs;trationem primi om&shy;<lb/>
nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli&shy;<lb/>
des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s>
          <s id="s.000785">Quod &longs;i <lb/>
quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam &lpar;cum &aelig;qua&shy;<lb/>
litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe qu&aelig; in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, &amp; cuius <pb pagenum="41" xlink:href="009/01/041.jpg"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>
vitare ob &longs;ui imperfectionem non licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>
&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reperire differentiam&rpar; &longs;umat <lb/>
inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po&shy;<lb/>te&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>
qu&aelig; &longs;cilicet faciat, cum illa duos angulos rectos. </s>
          <s id="s.000786">po&longs;tea ab&longs;cindat tres an&shy;<lb/>
gulos trianguli materialis, <expan abbr="eos&qacute;">eosque</expan>; ita &longs;imul componat, vt mucrones illorum <lb/>
&longs;int vniti, &amp; contigui ad punctum line&aelig; perpendicularis cum altera, vti e&longs;t <lb/>in &longs;uperiori figura punctum E; &amp; illic&ograve; apparebit tres illos angulos mate&shy;<lb/>
riales obtegere ad&aelig;quat&egrave; totum illud &longs;patium duorum rectorum, quos per&shy;<lb/>
pendicularis con&longs;tituit. </s>
          <s id="s.000787">Hoc autem experiri poteris in diuer&longs;is admodum <lb/>
triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &amp;c. </s>
          <s id="s.000788">non &longs;ine de&shy;<lb/>
lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet <lb/>
tres &etail;quales duobus rectis. </s>
          <s id="s.000789">Ab&longs;tineo &agrave; demon&longs;trationibus geometricis, quo&shy;<lb/>
niam ij, qui Mathematicis &longs;unt imbuti, no&longs;tra hac opera parum indigent. <lb/>
</s>
          <s id="s.000790">&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. <!-- KEEP S--></s>
          <s id="s.000791">Ex hac igitur declaratione <lb/>
licet cogno&longs;cere nonnullos ageometretos locum hunc, &amp; &longs;imiles &longs;ub&longs;equen&shy;<lb/>
tes non &longs;atis intelligere, dicentes, nihil aliud verba illa Ari&longs;t. velle &longs;ignifi&shy;<lb/>
care, qu&agrave;m omnem triangulum habere tres angulos, quod inquiunt, noti&longs;&shy;<lb/>
&longs;imum e&longs;t. </s>
          <s id="s.000792">Sed &longs;i incidant in &longs;equentia; &aelig;quales duobus rectis, tunc, cum <lb/>
h&aelig;c non intelligant, ab&longs;tinent etiam &agrave; priorum declaratione, quibus pr&aelig;&shy;<lb/>
mi&longs;&longs;is facile e&longs;t Ari&longs;t. textum percipere. </s>
          <s id="s.000793">&longs;it A, duo recti, ide&longs;t, duo anguli <lb/>
recti &longs;int pa&longs;&longs;io demon&longs;tranda, in quo B, triangulus, in quo C, &aelig;quicrus. </s>
          <s id="s.000794">ip&longs;i <lb/>
itaque C, ide&longs;t triangulo &aelig;quicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t <lb/>
&aelig;quicru&longs;i h&aelig;c, pa&longs;&longs;io habere tres angulos &aelig;quales duobus rectis per B, ide&longs;t <lb/>
per <expan abbr="triangul&utilde;">triangulum</expan> vniuer&longs;ale, quia h&aelig;c proprietas e&longs;t trianguli propria, &amp; <expan abbr="c&otilde;pe-tit">compe&shy;<lb/>
tit</expan> &aelig;quicru&longs;i, non vt &aelig;quicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non erit <lb/>
medium ip&longs;ius A, quia pr&aelig;dicta pa&longs;&longs;io. </s>
          <s id="s.000795">A, non competit triangulo B, per <lb/>
aliud, &longs;ed per &longs;e, de eo enim primo, &amp; per &longs;e demon&longs;tratur in 32. primi Elem. <lb/>
optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s>
        </p>
        <p type="main">
          <s id="s.000796"><arrow.to.target n="marg11"/></s>
        </p>
        <p type="margin">
          <s id="s.000797"><margin.target id="marg11"/>11</s>
        </p>
        <p type="main">
          <s id="s.000798">Ex eodem cap. <emph type="italics"/>&lpar;Non oportet autem exi&longs;timare penes id, quod exponimus, ali&shy;<lb/>
quid accidere ab&longs;urdum, nihil enim vtimur eo, quod e&longs;t hoc aliquid e&longs;&longs;e. </s>
          <s id="s.000799">&longs;ed &longs;icut <lb/>
Geometra pedalem, &amp; rectam hanc, &amp; &longs;ine latitudine dicit, qu&aelig; non &longs;unt. </s>
          <s id="s.000800">verum <lb/>
non &longs;ic vtitur, tanquam ex his ratiocinans&rpar;<emph.end type="italics"/> Quoniam Ari&longs;t. in exemplis affert <lb/>
pro rebus characteres, A, B, C, po&longs;&longs;et qui&longs;piam &longs;u&longs;picari aliquod propterea <lb/>
ab&longs;urdum accidere: cui &longs;u&longs;picioni Ari&longs;t. re&longs;pondet, dicens, nihil inde ab&longs;ur&shy;<lb/>
di accidere po&longs;&longs;e, quoniam ip&longs;e vtitur hi&longs;ce literis, <expan abbr="n&otilde;">non</expan> quatenus liter&aelig; &longs;unt, <lb/>
&longs;ed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum <lb/>
etiam Geometr&aelig; faciunt, qui lineam, qu&aelig; pedalis non e&longs;t, pedalem, &amp; qu&aelig; <lb/>
non e&longs;t recta, rectam; &amp; qu&aelig; lata e&longs;t, non latam, &longs;upponunt, &amp; tamen nihil <lb/>
inde ab&longs;urdi contingit. </s>
          <s id="s.000801">Ex quibus intelligimus per lineas illas &longs;en&longs;ibiles, &amp; <lb/>
phy&longs;icas, quas Geometr&aelig; in &longs;uis figuris ducunt, intelligendas e&longs;&longs;e lineas ve&shy;<lb/>
r&egrave; Mathematicas omni latitudine carentes; vtitur enim inquit Ari&longs;t. <!-- REMOVE S-->Geo&shy;<lb/>
metra lineis phy&longs;icis, non tanquam phy&longs;icis, nec de eis tanquam de phy&longs;icis <lb/>
lineis ratiocinatur, &longs;ed ijs vtitur tanquam ver&egrave; mathematicis. </s>
          <s id="s.000802">idem dicen&shy;<lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, qu&aelig; ijdem Geometr&aelig; de&shy;<lb/>
&longs;cribunt, vt per ea, de ver&egrave; mathematicis di&longs;currant.</s>
        </p>
      </chap>
      <pb pagenum="42" xlink:href="009/01/042.jpg"/>
      <chap>
        <p type="head">
          <s id="s.000803"><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000804"><arrow.to.target n="marg12"/></s>
        </p>
        <p type="margin">
          <s id="s.000805"><margin.target id="marg12"/>12</s>
        </p>
        <p type="main">
          <s id="s.000806">Ex cap. 21. <emph type="italics"/>&lpar;Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;e<lb/>&longs;e ip&longs;os talia accipientes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exi&longs;tentibus <lb/>
coalternis&rpar;<emph.end type="italics"/> Vult Ari&longs;t. exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>
titio principij. </s>
          <s id="s.000807">vbi per coalternas intelligit parallelas lineas, vox <lb/>
enim gr&aelig;ca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, &amp; coalternus. </s>
          <s id="s.000808">quoad <lb/>
exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/>
<figure id="id.009.01.042.1.jpg" place="text" xlink:href="009/01/042/1.jpg"/><lb/>
probat Euclides in 28. primi Elem. quod &longs;i <lb/>
linea recta qu&aelig;dam, vti E F, cadens &longs;uper <lb/>
duas rectas, vti &longs;unt A B, C D, fecerit angu&shy;<lb/>
los alternos &etail;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H, <lb/>
G H D, ij enim dicuntur alterni; &longs;iue alios <lb/>
duos, nimirum B G H, G H C, hi enim &longs;unt <lb/>
<expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li&shy;<lb/>
neas A B, C D, e&longs;&longs;e inuicem parallelas. </s>
          <s id="s.000809">Iam &longs;i quis vellet probare, &longs;e duas <lb/>
parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet faciunt pr&aelig;dictos angulos al&shy;<lb/>
ternos &aelig;quales; &amp; probaret facere angulos alternos &aelig;quales, quia &longs;unt pa&shy;<lb/>
rallel&aelig;, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="proband&utilde;">probandum</expan> erat, <lb/>
afferret pro ratione, &amp; cau&longs;a, quod dicitur peti principium, quia tunc pe&shy;<lb/>
timus, vt concedatur nobis, id, quod principio, &amp; primo omnium demon&shy;<lb/>
&longs;trare propo&longs;ueramus. </s>
          <s id="s.000810">aduerte, quod characteres, qui &longs;unt in &longs;equentibus <lb/>
verbis huius loci, non appellant characteres figur&aelig; appo&longs;it&aelig;; in quo quidam <lb/>
decepti, nullo pacto poterant locum hunc intelligere.</s>
        </p>
        <p type="main">
          <s id="s.000811"><arrow.to.target n="marg13"/></s>
        </p>
        <p type="margin">
          <s id="s.000812"><margin.target id="marg13"/>13</s>
        </p>
        <p type="main">
          <s id="s.000813">Ex cap. 22. lib. 2. Priorum <emph type="italics"/>&lpar;Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>
men&longs;. argueret Zenonis rationem, quod non e&longs;t moueri&rpar;<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. 1. <lb/>
fus&egrave; explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea&shy;<lb/>
dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com&shy;<lb/>munis, qu&aelig; debet vtramque, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, nimirum medietates medietatum in infinitum, <lb/>
e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, &amp; propterea <lb/>
non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="qu&atilde;titatibus">quantitatibus</expan>, qu&aelig; putaban&shy;<lb/>
tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t. non cau&longs;am pro cau&longs;a.</s>
        </p>
        <p type="main">
          <s id="s.000814"><arrow.to.target n="marg14"/></s>
        </p>
        <p type="margin">
          <s id="s.000815"><margin.target id="marg14"/>14</s>
        </p>
        <p type="main">
          <s id="s.000816">Ex eodem cap. <emph type="italics"/>&lpar;Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere <lb/>
nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; &amp; &longs;i maior e&longs;t extrin&longs;ecus <lb/>
angulus intrin&longs;eco; &amp; &longs;i triangulus habet plures rectos duobus&rpar;<emph.end type="italics"/> per plures po&longs;i&shy;<lb/>
tiones &longs;ubaudi fal&longs;as. </s>
          <s id="s.000817">per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>
rallelas, vt in &longs;uperiori cap. monuimus. </s>
          <s id="s.000818">C&aelig;terum Euclides propo&longs;. </s>
          <s id="s.000819">28. pri&shy;<lb/>
mi Elem. o&longs;tendit, quod &longs;i fuerint du&aelig; parallel&aelig; veluti in pr&aelig;cedenti figura, <lb/>
A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex&shy;<lb/>
trin&longs;ecum E G B, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;qualem interno, &amp; oppo&longs;ito, &amp; ad ea&longs;dem partes, <lb/>
angulo videlicet G H D. &longs;i ergo inquit Ari&longs;t &longs;upponamus i&longs;tud fal&longs;um, an&shy;<lb/>
gulum &longs;cilicet E G B, externum e&longs;&longs;e maiorem angulo interno G H D, &longs;equi&shy;<lb/>
tur etiam fal&longs;um, videlicet lineas <expan abbr="&aelig;quidi&longs;t&atilde;tes">&aelig;quidi&longs;tantes</expan> A B, C D, concurrere. </s>
          <s id="s.000820">&amp; pro&shy;<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb pagenum="43" xlink:href="009/01/043.jpg"/>G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli <lb/>
E G B, B G H, maiores, quam &longs;int duo B G H, G H D, quia &longs;i in&aelig;qualibus <lb/>
&aelig;qualia addantur, tota erunt in&aelig;qualia, vt prius per 4, axioma: hoc loco <lb/>
communis angulus additur &longs;emel maiori angulo, &amp; &longs;emel minori; &amp; ideo <lb/>
totum illud, in quo e&longs;t maior angulus, adhuc maius e&longs;t altero toto, in quo <lb/>
minor angulus continetur. </s>
          <s id="s.000821">at illi duo E G B, B G H, per 13. primi, &longs;unt <lb/>
&aelig;quales duobus rectis angulis, ergo duo <expan abbr="quoq;">quoque</expan> recti erunt maiores duobus <lb/>
internis B G H, D H G, &longs;iue hi duo interni erunt minores duobus rectis. <lb/>
</s>
          <s id="s.000822">At quando hi duo interni &longs;unt minores duobus rectis, tunc line&aelig; A B, C D, <lb/>
&longs;unt concurrentes, &longs;i protrahantur ad partes pr&aelig;dictorum <expan abbr="angulor&utilde;">angulorum</expan>. </s>
          <s id="s.000823">quod <lb/>
P. <!-- REMOVE S-->Clauius luculenti, &amp; hactenus de&longs;iderata demon&longs;tratione ad 28. primi <lb/>
demon&longs;trauit. </s>
          <s id="s.000824"><expan abbr="Atq;">Atque</expan> hoc pacto ex prima fal&longs;a &longs;uppo&longs;itione, nimirum angu&shy;<lb/>
lum illum externum e&longs;&longs;e maiorem interno, &amp; oppo&longs;ito; &longs;equitur fal&longs;um, ni&shy;<lb/>
mirum lineas parallelas concurrere.</s>
        </p>
        <p type="main">
          <s id="s.000825">Pr&aelig;terea &longs;i &longs;upponamus aliam fal&longs;itatem, &longs;cilicet triangulum habere tres <lb/>
angulos maiores duobus rectis, &longs;equetur eadem iterum fal&longs;itas, &longs;cilicet pa&shy;<lb/>
<figure id="id.009.01.043.1.jpg" place="text" xlink:href="009/01/043/1.jpg"/><lb/>
rallelas coincidere, &amp; probatur &longs;ic; &longs;int enim <lb/>
<expan abbr="tri&atilde;guli">trianguli</expan> A B C, tres anguli maiores, quam duo <lb/>
recti anguli, &amp; per punctum C, ducta &longs;it recta <lb/>
C D, parallela lateri B A. quia ergo angulus <lb/>
A, &aelig;qualis e&longs;t angulo &longs;ibi alterno A C D, per <lb/>
29. primi, &amp; quia totalis angulus B C D, &aelig;qua&shy;<lb/>
lis e&longs;t duobus angulis B C A, A C D, quos tanquam &longs;uas partes ad&aelig;quatas <lb/>
continet, quorum alter, &longs;cilicet A C D, e&longs;t &aelig;qualis angulo A. erit idem to&shy;<lb/>
talis angulus B C D, &aelig;qualis duobus angulis A, &amp; A C B, trianguli propo&longs;i&shy;<lb/>
ti. </s>
          <s id="s.000826">ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="tri&atilde;guli">trianguli</expan> angulo B. con&shy;<lb/>
&longs;tabit compo&longs;itionem ex tribus angulis trianguli dati: &amp; con&longs;equenter ta&shy;<lb/>
lis compo&longs;itio trium angulorum erit maior, quam &longs;int duo anguli recti. </s>
          <s id="s.000827">ex <lb/>
quo &longs;equitur duas rectas B A, C D, &longs;uper quas cadit linea B C, faciens duos <lb/>
angulos internos, &amp; ad ea&longs;dem partes, &longs;cilicet A B D, maiores duobus re&shy;<lb/>
ctis non e&longs;&longs;e parallelas, &longs;ed concurrentes &lpar;vt patet ex nuper citata demon&shy;<lb/>
&longs;tratione P. Clauij&rpar; quod fal&longs;um e&longs;t. </s>
          <s id="s.000828">&amp; &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio&shy;<lb/>
ne. </s>
          <s id="s.000829">ex quibus textus Ari&longs;t. videtur &longs;atis clarus.</s>
        </p>
        <p type="main">
          <s id="s.000830"><arrow.to.target n="marg15"/></s>
        </p>
        <p type="margin">
          <s id="s.000831"><margin.target id="marg15"/>15</s>
        </p>
        <p type="main">
          <s id="s.000832">Ex cap. 26. <emph type="italics"/>&lpar;Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibilis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis <lb/>
triangulus habet duos rectos: quare &longs;imul no&longs;cet, &amp; ignorabit idem. </s>
          <s id="s.000833">no&longs;ce enim <lb/>
omnem triangulum, quod duobus rectis, non &longs;implex e&longs;t: &longs;ed hoc quidem eo, quod <lb/>
vniuer&longs;alem habet &longs;cientiam: illud autem eo, quod &longs;ingularem. </s>
          <s id="s.000834">&longs;ic igitur, vt vni&shy;<lb/>
uer&longs;ale nouit C, quod duo recti; vt autem &longs;ingulare non nouit, quare non habebit <lb/>
contrarias&rpar;<emph.end type="italics"/> vide, qu&aelig; diximus lib. 1. &longs;ecto 3. cap. 1. ex quibus quidquid Ma&shy;<lb/>
thematicum e&longs;t hic, clarum redditur. </s>
          <s id="s.000835">reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>
ctant, huius loci commentatores pro&longs;equuntur.</s>
        </p>
        <p type="main">
          <s id="s.000836">In cap. 31. de Abductione.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000837"><arrow.to.target n="marg16"/></s>
        </p>
        <p type="margin">
          <s id="s.000838"><margin.target id="marg16"/>16</s>
        </p>
        <p type="main">
          <s id="s.000839">Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>
cap. agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">eamque</expan>; Ari&longs;t. quemadmodum multa <lb/>
alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>
          <s id="s.000840">e&longs;&longs;e <pb pagenum="44" xlink:href="009/01/044.jpg"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib. 3. <lb/>
in comm. <!-- REMOVE S-->Elem. Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/>
</s>
          <s id="s.000841">121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>
remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>
cuum e&longs;t. </s>
          <s id="s.000842">Exempli cau&longs;a, cum cubi duplicatio propo&longs;ita e&longs;&longs;et ad inue&longs;ti&shy;<lb/>
gandam qu&aelig;&longs;tionem in aliud tran&longs;tulere, quod illud propo&longs;itum con&longs;equi&shy;<lb/>
tur, ad duarum nempe mediarum linearum inuentionem tran&longs;lata e&longs;t qu&aelig;&shy;<lb/>
&longs;tio, &amp; &longs;ic qu&aelig;rebant deinceps, quonam modo datis duabus rectis lineis, <lb/>
du&aelig; medi&aelig; proportionales reperirentur. </s>
          <s id="s.000843">Primum autem dicunt Hippocra&shy;<lb/>
tem Chium pr&etail;dictorum titulorum, Abductionem feci&longs;&longs;e, qui &amp; lunul&aelig; qua&shy;<lb/>
dratum fecit &aelig;quale, &amp; alia multa in Geometria inuenit. </s>
          <s id="s.000844">h&aelig;c Proclus. <!-- KEEP S--></s>
          <s id="s.000845">vbi <lb/>
non di&longs;&longs;imulandum nos re&longs;titui&longs;&longs;e verbum, Abductionem, cuius loco inter&shy;<lb/>
pres Procli vtitur inductionis voce, &longs;equuti &amp; rationem, &amp; gr&aelig;cum textum, <lb/>
qui no&longs;tram hanc expo&longs;itionem euidenter po&longs;tulat, <foreign lang="greek">apagwgh\</foreign> enim valet &amp; <lb/>
inductionem, &amp; abductionem, &longs;ed abductio omnino rei propo&longs;it&aelig; quadrat.</s>
        </p>
        <p type="main">
          <s id="s.000846">Notandum pr&aelig;terea Hippocratem Chium fui&longs;&longs;e auctorem huius Abdu&shy;<lb/>
ctionis, <expan abbr="eum&qacute;">eumque</expan>; feci&longs;&longs;e Abductionem &agrave; propo&longs;ito Problemate quadrandi cir&shy;<lb/>
culi, vnde manife&longs;t&egrave; apparet, Ari&longs;totelem ex Mathematicis hunc terminum <lb/>
mutu&ograve; accepi&longs;&longs;e, quandoquidem ex ij&longs;dem accepit etiam exemplum Abdu&shy;<lb/>ctionis Mathematic&aelig;, im&ograve; etiam exemplum ip&longs;ius authoris Abductionis <lb/>
Mathematic&aelig;. </s>
          <s id="s.000847">&longs;yllogi&longs;mus autem Hippocratis, quo o&longs;tendebat circuli qua&shy;<lb/>
draturam reducebatur ad has propo&longs;itiones, omnis rectilinea figura qua&shy;<lb/>
dratur, &longs;ed circulus reducitur ad figuram rectilineam, ergo circulus qua&shy;<lb/>
dratur. </s>
          <s id="s.000848">in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re&shy;<lb/>
ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam, <lb/>
quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrin&utilde;">Alexandrinum</expan>, &amp; apud P. <!-- REMOVE S-->Cla&shy;<lb/>
uium in fine &longs;exti Elem. &amp; alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici ver&longs;antur; qu&aelig; pro&shy;<lb/>
batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro&shy;<lb/>
blema, nimirum circulus quadraretur; vide qu&aelig; &longs;crip&longs;imus in cap. 3. Pr&aelig;&shy;<lb/>
dicam. <!-- REMOVE S-->de hac re, quia plurimum hunc conferunt. </s>
          <s id="s.000849">&longs;ed iam ad textus expli&shy;<lb/>
cationem veniamus.</s>
        </p>
        <p type="main">
          <s id="s.000850"><arrow.to.target n="marg17"/></s>
        </p>
        <p type="margin">
          <s id="s.000851"><margin.target id="marg17"/>17</s>
        </p>
        <p type="main">
          <s id="s.000852">Ex eodem cap. <emph type="italics"/>&lpar;Veluti &longs;i K, e&longs;&longs;et quadrari, in quo autem E, rectilineum, in <lb/>
quo ver&ograve; F, circulus, &longs;i ip&longs;ius E F, vnum &longs;olum e&longs;&longs;et medium, hoc, quod e&longs;t, cum <lb/>
lunulis &aelig;qualem fieri circulum rectilineo, e&longs;&longs;e po&longs;&longs;et prop&egrave; ip&longs;um cogno&longs;cere, cum <lb/>
vero B C, neque credibilius &longs;it, quam A C, <expan abbr="neq;">neque</expan> pauca media, non dico Abductio&shy;<lb/>
nem: <expan abbr="neq;">neque</expan> quando B C, &longs;it immediatum, tale enim &longs;cientia est&rpar;<emph.end type="italics"/> Aduerte figuram <lb/>
vulgat&aelig; editionis e&longs;&longs;e mendo&longs;am, &amp; propterea re&longs;tituendam e&longs;&longs;e, qualis pri&shy;<lb/>
ma &longs;equens ex Simplicio ad tex. <!-- REMOVE S-->11. primi Phy&longs;ic. <!-- REMOVE S-->hoc modo Hippocrates <lb/>
Chius conabatur circulum ad quadrum redigere; fit circulus A B G C, qua&shy;<lb/>
drandus; con&longs;tituatur <expan abbr="itaq;">itaque</expan> &longs;uper diametro eius B C, quadratum B C D F, <lb/>
cuius diameter B D, &longs;ecatur bifariam in G, &agrave; circumferentia circuli dati, <lb/>
quod patet ducta &longs;emidiametro H G, perpendiculari ex B C, qu&aelig; &longs;uo extre&shy;<lb/>
mo puncto G, &longs;ecat bifariam, &amp; <expan abbr="diametr&utilde;">diametrum</expan> B D, &amp; circumferentiam B G C. <lb/>
facto ergo centro G, de&longs;cribatur alter circulus per puncta B C D F, <expan abbr="conne-ctatur&qacute;">conne&shy;<lb/>
ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb pagenum="45" xlink:href="009/01/045.jpg"/><figure id="id.009.01.045.1.jpg" place="text" xlink:href="009/01/045/1.jpg"/><lb/>
angulo recto C, ergo quadratum eius ex corol&shy;<lb/>
lario 47. primi, duplum erit quadrati B C, quare <lb/>
etiam circulus B C D F, duplus erit circuli A B&shy;<lb/>
G C, per 2. duodecimi, &amp; &longs;emicirculus B C D, <lb/>
duplus erit &longs;emicirculi B A C: &amp; quadrans B E&shy;<lb/>
C G, &aelig;qualis erit &longs;emicirculo B A C: ablato igi&shy;<lb/>
tur communi &longs;egmento B E C H, remanet lunu&shy;<lb/>
la B A C E, &aelig;qualis triangulo B C G, quod trian&shy;<lb/>
gulum &longs;i per vltimam &longs;ecundi quadretur, erit lu&shy;<lb/>
nula B A C, con&longs;equenter quadrata. </s>
          <s id="s.000853"><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be&shy;<lb/>
n&egrave; procedit Hippocrates. <!-- KEEP S--></s>
          <s id="s.000854">&longs;ed vt reliquum circu&shy;<lb/>
li quadret, &longs;ic pergit, ponatur recta L M, dupla <lb/>
ip&longs;ius B C, &longs;upra quam &longs;emicirculus de&longs;cribatur <lb/>
<figure id="id.009.01.045.2.jpg" place="text" xlink:href="009/01/045/2.jpg"/><lb/>
L O M, cui in&longs;cribatur hexagoni <lb/>
&aelig;quilateri dimidium L Q S M, &amp; &longs;u&shy;<lb/>
per tribus hexagoni lateribus, &longs;int <lb/>
tres &longs;emicirculi, vt in figura. </s>
          <s id="s.000855">&amp; <expan abbr="quo-ni&atilde;">quo&shy;<lb/>
niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;&shy;<lb/>
cuiu&longs;que</expan> <expan abbr="diametror&utilde;">diametrorum</expan> B C, L Q, Q S, <lb/>
S M, erit &longs;emicirculus L O M, &etail;qua&shy;<lb/>
lis quatuor &longs;emicirculis pr&aelig;dictis <lb/>
per 2. duodecimi, &amp; per 4. &longs;ecundi <lb/>
ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com&shy;<lb/>
munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, &aelig;quale &longs;e&shy;<lb/>
micirculo B A C, &amp; tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan&shy;<lb/>
tur <expan abbr="itaq;">itaque</expan> de trapezio tria triangula &aelig;qualia tribus lunulis, eo modo, quo &longs;u&shy;<lb/>
pra in prima figura factum e&longs;t, &amp; quod relinquetur &aelig;quale erit &longs;emicirculo <lb/>
B A C. quod deinde quadretur per vlt. </s>
          <s id="s.000856">&longs;ecundi, &longs;ed aduerte, quod quando <lb/>
ait, ab&longs;cindantur de trapezio tria triangula &aelig;qualia lunulis, eo modo, quo <lb/>
&longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minim&egrave; id fa&shy;<lb/>
cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la&shy;<lb/>
tus B C, quadrati B C D F, intra circulum de&longs;cripti, qui circulus facit cum <lb/>
B C, maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q, <lb/>
Q S, S M. &amp; propterea &longs;emicirculus i&longs;te non habet eandem proportionem <lb/>
ad vnamquamque lunularum &longs;uarum, quam habet &longs;emicirculus &longs;uperior <lb/>
B C D, ad lunulam B A C E. <expan abbr="atq;">atque</expan> h&aelig;c e&longs;t fallacia, quam authorem &longs;uum mi&shy;<lb/>
nim&egrave; latui&longs;&longs;e putandum, cuius Ari&longs;t. &longs;&aelig;pius mentionem in &longs;equentibus fa&shy;<lb/>
ciet : qu&igrave; enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro&shy;<lb/>
rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla&shy;<lb/>
cuit paralogy&longs;mus. </s>
          <s id="s.000857">mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>
quadratio. </s>
          <s id="s.000858">Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, qu&aelig; ad <expan abbr="Mathematic&utilde;">Mathematicum</expan> per&shy;<lb/>
tinent, ad locum hunc de Abductione declarandum. </s>
          <s id="s.000859">facta e&longs;t igitur abdu&shy;<lb/>
ctio ab Hippocrate in quadratione trium po&longs;teriorum lunularum, in qua&shy;<lb/>
rum quadratione diu immoratus, nunquam ni&longs;i cum paralogy&longs;mo quadra&shy;<lb/>
re valuit. </s>
          <s id="s.000860">H&aelig;c pluribus, vt &longs;equentibus etiam textibus, in quibus huius te&shy;<lb/>
tragoni&longs;mi fit mentio &longs;atisfacere po&longs;&longs;imus. </s>
          <s id="s.000861">Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46" xlink:href="009/01/046.jpg"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>
Aphrod. <!-- REMOVE S-->in Primum Meteororum de Cometis.<!-- KEEP S--></s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.000862"><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000863"><arrow.to.target n="marg18"/></s>
        </p>
        <p type="margin">
          <s id="s.000864"><margin.target id="marg18"/>18</s>
        </p>
        <p type="main">
          <s id="s.000865">Textu primo <emph type="italics"/>&lpar;Omnis doctrina, &amp; omnis di&longs;ciplina di&longs;cur&longs;iua ex pr&aelig;exi&shy;<lb/>
&longs;tenti fit cognitione. </s>
          <s id="s.000866">manife&longs;tum autem hoc &longs;peculantibus in omnibus, <lb/>
Mathematic&aelig; <expan abbr="namq;">namque</expan> &longs;cientiarum per hunc modum accedunt&rpar;<emph.end type="italics"/> quo mo&shy;<lb/>
do Mathematic&aelig; fiant ex pr&aelig;cedenti cognitione, &longs;cilicet Princi&shy;<lb/>
piorum per&longs;picu&egrave; quilibet videbit, qui &longs;altem primum <expan abbr="Elem&etilde;torum">Elementorum</expan> Eucli&shy;<lb/>
dis, vel &egrave; ianuis in&longs;pexerit; pr&etail;cedunt enim primo principiorum tria gene&shy;<lb/>
ra, quorum primum continet definitiones &longs;ubiecti Geometri&aelig;, vt definitio&shy;<lb/>
nes line&aelig;, &longs;uperficiei, trianguli, &amp;c: Secundum continet Po&longs;tulata. </s>
          <s id="s.000867">Tertium <lb/>
Axiomata, &longs;eu communes omnium conceptiones, &amp; &longs;ententias, ex quibus <lb/>tanquam ex vberrimis, &amp; chri&longs;tallinis fontibus Demon&longs;trationes Geome&shy;<lb/>
tric&aelig; deriuantur. </s>
          <s id="s.000868">Idem v&igrave;dere licet in operibus aliorum Geometrarum, <lb/>
Archimedis, Apollonij, Pappi, &amp; c&aelig;terorum. </s>
          <s id="s.000869">Ali&aelig; &longs;imiliter mathematic&aelig;, <lb/>
vt Arithmetica, Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia, non ni&longs;t ex <lb/>
pr&aelig;mi&longs;&longs;is, ac manife&longs;ti&longs;simis principijs &longs;uas demon&longs;trationes deducunt. <lb/>
</s>
          <s id="s.000870">Nulla porr&ograve; alia &longs;cientia tam di&longs;tinct&egrave; &longs;ua pr&aelig;mittit principia, <expan abbr="tam&qacute;">tamque</expan>; per&shy;<lb/>
&longs;picua, &longs;icuti Mathematic&aelig;, vt non immerit&ograve; Philo&longs;ophus eas, tamquam <lb/>
ver&aelig; &longs;cienti&aelig; <expan abbr="typ&utilde;">typum</expan>, <expan abbr="eum&qacute;">eumque</expan>; omnibus numeris ab&longs;olutum &longs;ibi ob oculos pro&shy;<lb/>
po&longs;uerit, ex quo ver&aelig; &longs;cienti&aelig; de&longs;criptionem hi&longs;ce libris complecteretur.</s>
        </p>
        <p type="main">
          <s id="s.000871"><arrow.to.target n="marg19"/></s>
        </p>
        <p type="margin">
          <s id="s.000872"><margin.target id="marg19"/>19</s>
        </p>
        <p type="main">
          <s id="s.000873">Tex. 2. <emph type="italics"/>&lpar;Quod enim omne triangulum habet duobus rectis &aelig;quales, pr&aelig;&longs;ciuit: <lb/>
quod autem hoc, quod e&longs;t in &longs;emicirculo triangulum e&longs;t, &longs;imul inducens cognouit&rpar;<emph.end type="italics"/><lb/>
vide primo, qu&aelig; &longs;upra libro 1. Prior. <!-- REMOVE S-->&longs;ecto 3. cap. 1. explicaui de angulis <lb/>
trianguli. </s>
          <s id="s.000874">deinde &longs;cias, quod quando Ari&longs;t. ait, hoc, quod e&longs;t in &longs;emicircu&shy;<lb/>
lo triangulum, &amp;c. </s>
          <s id="s.000875">alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>
rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem. Euclidis 31. in qua talis fi&shy;<lb/>
gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/>
<figure id="id.009.01.046.1.jpg" place="text" xlink:href="009/01/046/1.jpg"/><lb/>
micirculo. </s>
          <s id="s.000876">tunc autem dicitur triangulum in <lb/>
&longs;emicirculo, quando ba&longs;is ip&longs;ius e&longs;t diameter <lb/>
&longs;emicirculi, &amp; reliqua duo latera ita concur&shy;<lb/>runt &longs;imul in angulum B, vt ip&longs;um pariter in <lb/>
circumferentia con&longs;tituant, quibus pr&etail;mi&longs;sis <lb/>
&longs;ic textum explicaueris: quod enim omne <lb/>
triangulum habet tres angulos &aelig;quales duo&shy;<lb/>
bus rectis angulis pr&aelig;&longs;ciuit vniuer&longs;aliter per <lb/>
32. primi; quod autem hoc particulare triangulum A B C, quod e&longs;t in &longs;e&shy;<lb/>micirculo habeat eandem proprietatem, &longs;imul, ac qui&longs;piam animaduertit <lb/>
illud e&longs;&longs;e triangulum cogno&longs;cit, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla demon&longs;tratione, &longs;ed &longs;olum virtu&shy;<lb/>
te illius maioris propo&longs;itionis; omne triangulum habet tres, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.000877"><arrow.to.target n="marg20"/></s>
        </p>
        <p type="margin">
          <s id="s.000878"><margin.target id="marg20"/>20</s>
        </p>
        <p type="main">
          <s id="s.000879">Tex. 5. <emph type="italics"/>&lpar;Vera quidem igitur oportet e&longs;&longs;e, quoniam non e&longs;t non ens &longs;cire, vt quod <lb/>diameter &longs;it commen&longs;urabilis&rpar;<emph.end type="italics"/> con&longs;ule ea, qu&aelig; &longs;crip&longs;imus ad cap. 23. primi <lb/>
Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy;<lb/>
ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;


<pb pagenum="47" xlink:href="009/01/047.jpg"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com&shy;<lb/>
men&longs;urabilem pr&aelig;dicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur <lb/>
impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s>
        </p>
        <p type="main">
          <s id="s.000880"><arrow.to.target n="marg21"/></s>
        </p>
        <p type="margin">
          <s id="s.000881"><margin.target id="marg21"/>21</s>
        </p>
        <p type="main">
          <s id="s.000882">Hoc eodem cap. plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>
ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>
&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>
templatione primi libri Elem. Euclidis percipi pote&longs;t. </s>
          <s id="s.000883">vt propterea ben&egrave; ij <lb/>
&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/>
Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>
&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>
bris complectaretur.</s>
        </p>
        <p type="main">
          <s id="s.000884"><arrow.to.target n="marg22"/></s>
        </p>
        <p type="margin">
          <s id="s.000885"><margin.target id="marg22"/>22</s>
        </p>
        <p type="main">
          <s id="s.000886">Eodem tex. <!-- REMOVE S-->5. <emph type="italics"/>&lpar;Ponit enim Arithmeticus vnitatem indiui&longs;ibilem e&longs;&longs;e &longs;ecun&shy;<lb/>
dum quantum&rpar;<emph.end type="italics"/> hoc quamquam non ponatur ab Arithmeticis expre&longs;s&egrave;, pr&aelig;&shy;<lb/>
&longs;upponitur tamen ab eis: nu&longs;quam enim Euclides in totis tribus Arithme&shy;<lb/>
ticis libris, infra vnitatem de&longs;cendit, vt propterea appareat, ip&longs;am in quan&shy;<lb/>
titate di&longs;creta e&longs;&longs;e minimum, &amp; indiui&longs;ibile. </s>
          <s id="s.000887">Verum dubitabit fort&egrave; qui&longs;&shy;<lb/>
piam hoc modo, &longs;i vnitas minimum, <expan abbr="atq;">atque</expan> indiui&longs;ibile e&longs;t in quanto di&longs;creto, <lb/>
qua igitur ratione Arithmetici practici eam diuidunt in dimidium, in trien&shy;<lb/>
tem, in quadrantem, &amp; alijs &longs;imiliter modis, vnde numeri illi, qui fractio&shy;<lb/>
nes appellantur, exurgunt? </s>
          <s id="s.000888">Re&longs;pondemus, <expan abbr="quotie&longs;eunq;">quotie&longs;cunque</expan> vnitas diuiditur ab <lb/>
Arithmeticis, tunc ip&longs;i eam accipiunt tanquam totum quoddam <expan abbr="c&otilde;tinuum">continuum</expan> <lb/>
in plures partes diui&longs;ibile: &longs;iue tanquam aggregatum quoddam vnitatum, <lb/>
qu&aelig; vnitates &longs;unt partes illius, vt quando dicunt, vnum hor&aelig; quadrantem, <lb/>
vel duos hor&aelig; quadrantes, vel tres hor&aelig; quadrantes, accipiunt horam tan&shy;<lb/>
quam aggregatum quatuor quadrantum, &amp; propterea numeri illi 1/4. 2/4. 3/4. <lb/>
&amp; &longs;imiles fractiones, nihil aliud &longs;unt, quam numeri partium vnius hor&aelig;: ex <lb/>
quo patet huiu&longs;modi fractiones omnes reduci ad numeros integros, qui <lb/>
enim dicit tres quadrantes 3/4. dicit tres partes alicuius totius, quod intel&shy;<lb/>
ligitur diui&longs;um e&longs;&longs;e in 4. &aelig;quales partes, ex quibus ill&aelig; tres tantummodo <lb/>
numerat.</s>
        </p>
        <p type="main">
          <s id="s.000889"><arrow.to.target n="marg23"/></s>
        </p>
        <p type="margin">
          <s id="s.000890"><margin.target id="marg23"/>23</s>
        </p>
        <p type="main">
          <s id="s.000891">Tex. 9. <emph type="italics"/>&lpar;Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>
nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>
te, quid e&longs;t, in&longs;unt&rpar;<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>
tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s>
          <s id="s.000892">quorum primus e&longs;t, ea &longs;cilicet, <lb/>
per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>
iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in definitione enim trianguli ponitur linea recta, quia linea <lb/>
recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>
naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>
tribus lineis rectis terminata. </s>
          <s id="s.000893">&longs;imiliter in definitione line&aelig;, non infinit&aelig;, <lb/>
&longs;ed finit&aelig;, &amp; terminat&aelig; ponitur punctum, quia duo puncta, qu&aelig; &longs;unt extre&shy;<lb/>
ma illius, faciunt, vt ea &longs;it line a finita, &amp; definitur &longs;ic, linea finita e&longs;t lon&shy;<lb/>gitudo, cuius extrema &longs;unt puncta. </s>
          <s id="s.000894">quamuis autem h&aelig;c definitio apud Eu&shy;<lb/>
clidem expre&longs;&longs;a non habeatur, tamen ex definitionibus ip&longs;ius pr&aelig;&longs;ertim &longs;e&shy;<lb/>
cunda, tertia, &amp; quarta elici pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.000895"><arrow.to.target n="marg24"/></s>
        </p>
        <p type="margin">
          <s id="s.000896"><margin.target id="marg24"/>24</s>
        </p>
        <p type="main">
          <s id="s.000897">Eodem tex. <!-- REMOVE S-->9. <emph type="italics"/>&lpar;Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> inexi&longs;tentium ip&longs;is, ip&longs;&aelig; &longs;unt in oratione, quid<emph.end type="italics"/> <pb pagenum="48" xlink:href="009/01/048.jpg"/><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t line&aelig;, &amp; circulare: &amp; impar, &amp; par <lb/>
numero, &amp; primum, &amp; compo&longs;itum, &amp; &aelig;quilaterum, &amp; altera parte longius. &amp; <lb/>
<expan abbr="o&itilde;bus">omnibus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declar&atilde;te">declarante</expan>, ibi quidem linea, hic vero numerus&rpar;<emph.end type="italics"/><lb/>
quia locus hic ben&egrave; exponitur &agrave; Toleto, &amp; melius etiam &agrave; Conymbr. </s>
          <s id="s.000898">addam <lb/>
tantummodo qu&aelig;dam, qu&aelig; ad perfectam eius intelligentiam de&longs;iderantur. <lb/>
</s>
          <s id="s.000899">Sciendum igitur prim&ograve;, nu&longs;quam ab Euclide definiri rectum, circulare, <lb/>
impar, par, primum, compo&longs;itum, &aelig;quilaterum, nec altera parte longius: <lb/>
<expan abbr="ver&utilde;">verum</expan> ab ip&longs;o in definitionibus primi definiri lineam rectam, non tamen cir&shy;<lb/>
cularem expre&longs;s&egrave;. </s>
          <s id="s.000900">in definitionibus deinde &longs;eptimi definiri <expan abbr="numer&utilde;">numerum</expan> parem, <lb/>
&amp; imparem, item numerum primum, &amp; compo&longs;itum, &amp; &aelig;quilaterum, &amp; al&shy;<lb/>
tera parte longiorem. </s>
          <s id="s.000901">ex quibus definitionibus po&longs;&longs;unt erui definitiones re&shy;<lb/>
cti, circularis, imparis, &amp; c&aelig;terorum, quorum hic Ari&longs;toteles meminit. <lb/>
</s>
          <s id="s.000902">C&aelig;terum Euclides definitione 11. &longs;eptimi, &longs;ic definit numerum primum: <lb/>
primus numerus e&longs;t, quem vnitas &longs;ola metitur. </s>
          <s id="s.000903">numerus autem, vel vnitas <lb/>
metiri dicitur alium numerum, quando &longs;&aelig;pius repetita ip&longs;um omnino ad&shy;<lb/>
&aelig;quat, vt ternarius metitur nouenarium, quia ter repetitus ip&longs;um ad vn&shy;<lb/>
guem explet. </s>
          <s id="s.000904">illi igitur numeri dicuntur ab Arithmeticis primi, qui &agrave; nullo <lb/>
alio, pr&aelig;terquam ab vnitate men&longs;urantur, quales &longs;unt, 2. 3. 5. 7. &amp;c. </s>
          <s id="s.000905">Defi&shy;<lb/>
nitione ver&ograve; 13. definit numerum compo&longs;itum &longs;ic; compo&longs;itus numerus e&longs;t, <lb/>
quem numerus qui&longs;piam metitur, vt &longs;enarius erit compo&longs;itus, quia ip&longs;um <lb/>
binarius metitur, nam ter repetitus, ip&longs;i perfect&egrave; ad&aelig;quatur.</s>
        </p>
        <p type="main">
          <s id="s.000906">Per &aelig;quilaterum, intelligit quadratum, quadratus autem numerus defi&shy;<lb/>
nitione 18. &longs;eptimi &longs;ic explicatur: Quadratus numerus e&longs;t, qui &longs;ub duobus <lb/>
&aelig;qualibus numeris continetur, ide&longs;t, qui fit ex ductu vnius numeri in &longs;e ip&shy;<lb/>
<figure id="id.009.01.048.1.jpg" place="text" xlink:href="009/01/048/1.jpg"/><lb/>
&longs;um, vt &longs;i ducantur 3. in 3. fient 9. qui continetur &longs;ub duobus <lb/>
ternarijs; omnes autem ternarij &longs;unt &aelig;quales. </s>
          <s id="s.000907">is autem nu&shy;<lb/>
merus dicetur quadratus, quia, vt apparet in figura, nouem <lb/>
ip&longs;ius vnitates po&longs;&longs;unt in plano ita ad inuicem collocari, vt <lb/>
referant quadratum; &amp; &longs;icuti quadratum geometricum ha&shy;<lb/>
bet latera &aelig;qualia, ita etiam quadratum arithmeticum: &longs;i&shy;<lb/>
ue numerus quadratus, habet &longs;ua latera &aelig;qualia, quot enim vnitates &longs;unt <lb/>
in vno, tot etiam &longs;unt in reliquis, vt in pr&aelig;&longs;enti &longs;unt tres vnitates in &longs;ingulis <lb/>
lateribus. </s>
          <s id="s.000908">pr&etail;terea quemadmodum quadratum geometricum re&longs;olui pote&longs;t <lb/>
in plura quadrata, ita etiam arithmeticum, vt pr&aelig;&longs;ens, qui re&longs;oluitur in <lb/>
quatuor quadrata arithmetica. </s>
          <s id="s.000909"><expan abbr="Neq;">Neque</expan> enim pote&longs;t quilibet numerus, vt opi&shy;<lb/>
nantur ageometreti, in hunc modum di&longs;poni, &longs;ed &longs;olum ij, qui producuntur <lb/>
ex multiplicatione numeri alicuius in &longs;e ip&longs;um.</s>
        </p>
        <p type="main">
          <s id="s.000910">Per altera parte longius, intelligit numerum, qui producitur &agrave; duobus <lb/>
<figure id="id.009.01.048.2.jpg" place="text" xlink:href="009/01/048/2.jpg"/><lb/>
numeris in&aelig;qualibus inuicem multiplicatis, qualis e&longs;t <lb/>
duodenarius, qui ex ductu trium in quatuor produci&shy;<lb/>
tur, &amp; refert figuram altera parte longiorem, &longs;iue, vt <lb/>
ait Boetius longilateram, cuius vnum latus e&longs;t maius <lb/>
altero, vt in appo&longs;ita figura videre licet. </s>
          <s id="s.000911">atque h&aelig;c <lb/>
&longs;unt, qu&aelig; ex Mathematicis petenda erant, ad huius <lb/>
loci intelligentiam.</s>
        </p>
        <p type="main">
          <s id="s.000912"><arrow.to.target n="marg25"/></s>
        </p>
        <p type="margin">
          <s id="s.000913"><margin.target id="marg25"/>25</s>
        </p>
        <p type="main">
          <s id="s.000914">Tex. 11. <emph type="italics"/>&lpar;Per &longs;e autem, &amp; &longs;ecundum quod ip&longs;um, idem, vt per &longs;e line&aelig; inest<emph.end type="italics"/> <pb pagenum="49" xlink:href="009/01/049.jpg"/><emph type="italics"/>punctum, &amp; rectum; etenim &longs;ecundum quod linea, &amp; triangulo, &longs;ecundum quod <lb/>
triangulum duo recti: etenim per &longs;e triangulum duobus rectis &aelig;quale. </s>
          <s id="s.000915">Vniuer&longs;ale <lb/>
autem e&longs;t tunc, quando in quolibet, &amp; primo mon&longs;tratur, vt duos rectos habere, <lb/>
<expan abbr="neq;">neque</expan> figur&aelig; e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;trare de figura, quod duos rectos habet, <lb/>
&longs;ed non de qualibet figura, <expan abbr="neq;">neque</expan> vtitur qualibet figura monstrans, quadrangulum <lb/>
enim figura a quidem est, non habet autem duobus rectis &aelig;quales. </s>
          <s id="s.000916">Aequicrus ver&ograve; <lb/>habet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis &aelig;quales, &longs;ed non prim&ograve;, &longs;ed triangulum <lb/>
prius. </s>
          <s id="s.000917">quod igitur quoduis primum mon&longs;tratur duos rectos habens, aut <expan abbr="quodcunq;">quodcunque</expan> <lb/>
aliud, huic primo ine&longs;t vniuer&longs;ale, &amp; demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs <lb/>
ver&ograve; quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de &aelig;quicrure e&longs;t vniuer&longs;aliter, &longs;ed in plus&rpar;<emph.end type="italics"/> pro <lb/>
quorum intelligentia nece&longs;&longs;aria &longs;unt ea, qu&aelig; primo Priorum &longs;ecto 3. cap. 1. <lb/>
&longs;crip&longs;imus. </s>
          <s id="s.000918">deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>
angulum vniuer&longs;alius &aelig;quicrure. </s>
          <s id="s.000919">quando ait &lpar;vt duos rectos habere&rpar; vult <lb/>
dicere, habere duos angulos rectos non actu, &longs;ed potentia; qu&aelig; affectio e&longs;t <lb/>
trianguli, quia, vt &longs;uperius diximus, habet tres angulos &aelig;quales duobus <lb/>
rectis angulis: qu&aelig; proprietas vniuer&longs;aliter, &amp; prim&ograve; competit triangulo. <lb/>
</s>
          <s id="s.000920">non autem figur&aelig;, quia figura e&longs;t vniuer&longs;alior. </s>
          <s id="s.000921"><expan abbr="neq;">neque</expan> i&longs;o&longs;celi, quia i&longs;o&longs;celes e&longs;t <lb/>
re&longs;trictius triangulo. </s>
          <s id="s.000922">omittimus reliqua &longs;ingillatim exponere, tum quia &longs;a&shy;<lb/>
tis clara &longs;unt, tum quia ab interpretibus ben&egrave; explicantur.</s>
        </p>
        <p type="main">
          <s id="s.000923"><arrow.to.target n="marg26"/></s>
        </p>
        <p type="margin">
          <s id="s.000924"><margin.target id="marg26"/>26</s>
        </p>
        <p type="main">
          <s id="s.000925">Tex. 13. <emph type="italics"/>&lpar;Si quis igitur mon&longs;trauerit, quod rect&aelig; <expan abbr="n&otilde;">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan> <lb/>huius e&longs;&longs;e demonstratio, eo quod in omnibus e&longs;t rectis; non e&longs;t autem: &longs;i quidem <lb/>
non quoniam &longs;ic &aelig;quales, fit hoc, &longs;ed &longs;ecundum quod <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales&rpar;<emph.end type="italics"/> pro&shy;<lb/>
ponit tres errores, qui circa demon&longs;trationem de vniuer&longs;ali contingunt, <lb/>
quos omnes Geometricis exemplis illu&longs;trat; affert autem primo pro tertio <lb/>
errore duo exempla, quorum primum in pr&aelig;mi&longs;&longs;is verbis continetur, <expan abbr="atq;">atque</expan> <lb/>
ex 28. primi Elem. de&longs;umitur, quam propterea primo loco exponendam <lb/>
<figure id="id.009.01.049.1.jpg" place="text" xlink:href="009/01/049/1.jpg"/><lb/>
cen&longs;ui. </s>
          <s id="s.000926">Quando igitur du&aelig; rect&aelig; con&longs;titu&shy;<lb/>
t&aelig; fuerint, vt A B, C D, in quas alia recta, <lb/>
vt G F, incidens, faciat duos angulos in&shy;<lb/>
ternos, re&longs;pectu rectarum A B, C D, &amp; ad <lb/>
ea&longs;dem partes rect&aelig; E F, vt &longs;unt ex parte <lb/>
&longs;ini&longs;tra anguli A G H, C H G; exparte ve&shy;<lb/>
r&ograve; dextra B G H, D H G; &longs;i <expan abbr="inqu&atilde;">inquam</expan> linea E F, <lb/>
fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, &aelig;quales duobus <lb/>
rectis angulis, vel duos ex parte dextra pariter &aelig;quales duobus rectis, pro&shy;<lb/>
bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s>
          <s id="s.000927">Verum, <lb/>
quia linea E F, pote&longs;t facere aliquando pr&aelig;dictos angulos non <expan abbr="tant&utilde;">tantum</expan> &aelig;qua&shy;<lb/>
les duobus rectis, verum etiam rectos, quo etiam modo <expan abbr="probar&etilde;tur">probarentur</expan> c&aelig;dem <lb/>
line&aelig; e&longs;&longs;e parallel&aelig;, vt in &longs;equenti figura, cum &longs;int anguli A G I, C I G, re&shy;<lb/>
<figure id="id.009.01.049.2.jpg" place="text" xlink:href="009/01/049/2.jpg"/><lb/>
cti, probabitur de rectis A B, C D, &aelig;quidi&longs;tan&shy;<lb/>
tia. </s>
          <s id="s.000928">Ex his facile textum in hunc modum expo&shy;<lb/>
nemus; &longs;i quis igitur mon&longs;trauerit, quod rect&aelig; <lb/>A B, C D, nunquam coincidunt, etiam&longs;i in infi&shy;<lb/>
nitum producantur, &longs;eu quod &longs;unt &aelig;quidi&longs;tantes, <lb/>
quando anguli pr&aelig;dicti interni &longs;unt duo recti, <lb/>
videbitur <expan abbr="vtiq;">vtique</expan> huius e&longs;&longs;e demon&longs;tratio de vniuer&longs;ali per &longs;e, &amp; de primo &longs;u&shy;


<pb pagenum="50" xlink:href="009/01/050.jpg"/>biecto, vel &longs;ecundum quod ip&longs;um, e&ograve; quod probatur vniuer&longs;aliter de lineis <lb/>
omnibus habentibus pr&aelig;dictos angulos rectos. </s>
          <s id="s.000929">non autem de omni, &longs;ecun&shy;<lb/>
dum quod ip&longs;um, &longs;i quidem non competit affectio h&aelig;c, e&longs;&longs;e parallelas, li&shy;<lb/>
neis habentibus illos angulos rectos actu; &longs;ed prim&ograve;, &amp; vniuer&longs;aliter, &amp; &longs;e&shy;<lb/>
cundum quod ip&longs;um competit lineis habentibus illos angulos &aelig;quales duo&shy;<lb/>
bus rectis, <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales &longs;int duobus rectis, &longs;iue ambo &longs;int recti, <lb/>
&longs;iue vnus acutus, alter obtu&longs;us, &longs;ed tamen ambo &longs;imul &aelig;quentur duobus re&shy;<lb/>
ctis, quales &longs;unt line&aelig; prim&aelig; figur&aelig;. </s>
          <s id="s.000930">In tertio igitur errore, vniuer&longs;ale exi&shy;<lb/>
&longs;tit quidem, &amp; habet nomen, &longs;ed tamen pr&aelig;termittetur, &longs;eu &longs;trictius &longs;ume&shy;<lb/>
tur, quam oportet. </s>
          <s id="s.000931">alij latini, quos quidem viderim, pr&aelig;ter Zabarellana <lb/>
perperam omnino ob mathematicarum ignorantiam, exemplum i&longs;tud in&shy;<lb/>
terpretantur.</s>
        </p>
        <p type="main">
          <s id="s.000932"><arrow.to.target n="marg27"/></s>
        </p>
        <p type="margin">
          <s id="s.000933"><margin.target id="marg27"/>27</s>
        </p>
        <p type="main">
          <s id="s.000934">Ibidem <emph type="italics"/>&lpar;Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, &longs;ecundum quod I&longs;o&shy;<lb/>
&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e&rpar;<emph.end type="italics"/> i&longs;tud e&longs;t &longs;ecundum exemplum tertij erroris. </s>
          <s id="s.000935">Por&shy;<lb/>
r&ograve; cum tres &longs;int &longs;pecies triangulorum, &aelig;quilaterum, I&longs;o&longs;celes, Scalenum, &longs;i <lb/>
accideret, vt ex illis tribus vna tantum &longs;pecies, v. <!-- REMOVE S-->g. <!-- REMOVE S-->I&longs;o&longs;celes in mundo re&shy;<lb/>
periretur; <expan abbr="tunc&qacute;">tuncque</expan>; qui&longs;piam de I&longs;o&longs;cele o&longs;tenderet affectionem quampiam, <lb/>
putans &longs;e <expan abbr="o&longs;t&etilde;di&longs;&longs;e">o&longs;tendi&longs;&longs;e</expan> pa&longs;&longs;ionem de proprio &longs;ubiecto, &amp; primo, falleretur, quia <lb/>
aifectio illa competeret I&longs;o&longs;celi, non vt huic &longs;peciei I&longs;o&longs;celis, &longs;ed quatenus <lb/>
e&longs;t triangulum, cui primo, &amp; per &longs;e, &amp; &longs;ecundum quod ip&longs;um conuenit. </s>
          <s id="s.000936">hoc <lb/>
loco di&longs;ce&longs;&longs;imus &agrave; Zabarella, qui putat i&longs;tud e&longs;&longs;e exemplum primi erroris, <lb/>
cum verba textus adeo clara &longs;int, vt expo&longs;itionem illius nullo modo admit&shy;<lb/>
tant. </s>
          <s id="s.000937">&longs;unt autem h&aelig;c textus verba <emph type="italics"/>&lpar;Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&shy;<lb/>
&longs;celes, &longs;ecundum quod I&longs;o&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e&rpar;<emph.end type="italics"/> quibus verbis manife&longs;t&egrave; <lb/>
apparet Ari&longs;t. accipere pro &longs;ubiecto vniuer&longs;ali non indiuiduum vnum, vt in <lb/>
primo errore contingit, &longs;ed &longs;peciem loco generis, &longs;cilicet I&longs;o&longs;celes, quod <lb/>
e&longs;t &longs;pecies trianguli pro genere ip&longs;o, nimirum pro Triangulo. </s>
          <s id="s.000938">ait enim, &longs;i <lb/>
non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quod I&longs;o&longs;celes: quibus verbis cla&shy;<lb/>r&egrave; &longs;peciem, non indiuiduum, &longs;ignificat, ex his duobus exemplis manife&longs;tus <lb/>
e&longs;t tertius error, qui erat, quando erat <emph type="italics"/>&lpar;vt in parte totum&rpar;<emph.end type="italics"/> <expan abbr="quod&qacute;">quodque</expan>; illis verbis <lb/>
expo&longs;uerat <emph type="italics"/>&lpar;vel contingit etiam, vt in parte totum, in quo mon&longs;tratur: ijs enim, <lb/>
qu&aelig; &longs;unt in parte inerit quidem demon&longs;tratio, &amp; erit de omni, &longs;ed tamen non erit <lb/>
huius primi vniuer&longs;aliter demon&longs;tratio. </s>
          <s id="s.000939">dico autem huius primi, &longs;ecundum quod <lb/>
huius demonstrationem, quando &longs;it primi vniuer&longs;aliter&rpar;<emph.end type="italics"/> ide&longs;t, quando vniuer&longs;ale <lb/>
&longs;ubiectum exi&longs;tit quidem, &longs;ed tamen non de ip&longs;o &longs;it demon&longs;tratio, &longs;ed de ali&shy;<lb/>
qua parte ip&longs;ius, v. <!-- REMOVE S-->g. <!-- REMOVE S-->de &longs;pecie aliqua demon&longs;tratur aliquid, quod deberet <lb/>
o&longs;tendi prim&ograve; de ip&longs;o vniuer&longs;ali, cum illi prim&ograve; competat.</s>
        </p>
        <p type="main">
          <s id="s.000940"><arrow.to.target n="marg28"/></s>
        </p>
        <p type="margin">
          <s id="s.000941"><margin.target id="marg28"/>28</s>
        </p>
        <p type="main">
          <s id="s.000942">Ibidem <emph type="italics"/>&lpar;Et proportionale, quod alternatim, &longs;ecundum quod numeri, &amp; &longs;ecun&shy;<lb/>
dum quod line&aelig;, &amp; &longs;ecundum quod &longs;olida, &amp; &longs;ecundum quod tempora: quemad&shy;<lb/>
modum &amp; mon&longs;trabatur aliquando &longs;eor&longs;um, contingens <expan abbr="vtiq;">vtique</expan> de omnibus vnica <lb/>demon&longs;tratione mon&longs;trari; &longs;ed quia non &longs;unt nominatum quidam omnia h&aelig;c vnum, <lb/>
numeri, longitudines, tempora &longs;olida, &amp; &longs;pecie differunt &agrave; &longs;einuicem &longs;eor&longs;um <expan abbr="ac-cipieb&atilde;tur">ac&shy;<lb/>
cipiebantur</expan>. </s>
          <s id="s.000943">nunc autem vniuer aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod line&aelig;, <lb/>aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod hoc, quod vniuer&longs;ale &longs;up&shy;<lb/>
ponunt e&longs;&longs;e&rpar;<emph.end type="italics"/> affert exemplum &longs;ecundi erroris, qui accidit, quando vniuer&longs;a&shy;<lb/>
le exi&longs;tit quidem, &longs;ed tamen e&longs;t innominatum, pro cuius explicatione &longs;cien&shy;


<pb pagenum="51" xlink:href="009/01/051.jpg"/>dum quid &longs;it alterna proportio. </s>
          <s id="s.000944">Alternam igitur proportionem definit Eu&shy;<lb/>
clides definitione 12. quinti, &longs;ic, e&longs;t &longs;umptio antecedentis ad <expan abbr="anteced&etilde;tem">antecedentem</expan>, <lb/>
<figure id="id.009.01.051.1.jpg" place="text" xlink:href="009/01/051/1.jpg"/><lb/>
&amp; con&longs;equentis ad con&longs;equentem. </s>
          <s id="s.000945">Explico, exponantur qua&shy;<lb/>
tuor quantitates proportionales, v.g. <!-- REMOVE S-->vt 6. ad 3. ita &longs;int 4. ad <lb/>
2. &longs;i igitur argumentemur &longs;ic, vt 6. ad 3. ita 4. ad 2. ergo al&shy;<lb/>
ternatim erit, vt 6. ad 4. ita 3. ad 2. &longs;iue dixerimus, vt pri&shy;<lb/>
mum ad &longs;ecundum, ita tertium ad quartum, igitur alterna&shy;<lb/>
tim erit, vt primum ad tertium, ita &longs;ecundum ad quartum: valebit con&longs;e&shy;<lb/>
quentia; qu&aelig; quidem probatur deinde propo&longs;itione 16. quinti de magnitu&shy;<lb/>
dinibus, hoc e&longs;t in vniuer&longs;um de lineis, &longs;uperficiebus, &amp; &longs;olidis. </s>
          <s id="s.000946">quando igi&shy;<lb/>
tur Ari&longs;t. ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita&shy;<lb/>
tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim <lb/>
proportionales, &amp; non mon&longs;tramus vnica demon&longs;tratione de omni quouis <lb/>
proportionali, &longs;ed &longs;eparatim de magnitudinibus in 16. quinti, de numeris <lb/>
in 13. &longs;eptimi, &amp; &longs;eor&longs;um de temporibus in a&longs;tronomia, vel phy&longs;ica; hoc <lb/>
modo non o&longs;tendimus vniuer&longs;aliter de primo &longs;ubiecto, quia talis affectio <lb/>
conuenit &longs;ingulis, non vt numeri, aut magnitudines, aut tempora &longs;unt, &longs;ed <lb/>
&longs;ecundum quandam naturam illis omnibus communem, cui prim&ograve; illa pa&longs;&shy;<lb/>
&longs;io debetur; qu&aelig; quidem natura communis nomine caret, &amp; propterea e&longs;t <lb/>
cau&longs;a erroris.</s>
        </p>
        <p type="main">
          <s id="s.000947"><arrow.to.target n="marg29"/></s>
        </p>
        <p type="margin">
          <s id="s.000948"><margin.target id="marg29"/>29</s>
        </p>
        <p type="main">
          <s id="s.000949"><emph type="italics"/>Nunc autem vniuer&longs;aliter demon&longs;tratur&rpar;<emph.end type="italics"/> nu&longs;quam apud Mathematicos in&shy;<lb/>
uenio hanc demon&longs;trationem vniuer&longs;alem de illo communi omnibus pr&aelig;&shy;<lb/>
dictis, quare dicendum cum Zabarella, illud, nunc, e&longs;&longs;e intelligendum &longs;ic, <lb/>
nunc autem, ide&longs;t, in pr&aelig;&longs;entia autem deberet vniuer&longs;aliter demon&longs;trari, <lb/>
quod tamen cum non fiat, contingit nos decipi putantes vniuer&longs;aliter de&shy;<lb/>
mon&longs;tra&longs;&longs;e. </s>
          <s id="s.000950">vel dicendum i&longs;tud verificari tantum de lineis, &longs;uperficiebus, &amp; <lb/>
&longs;olidis, de quibus &longs;imul in vnica natura communi, qu&aelig; e&longs;t magnitudo, de&shy;<lb/>
mon&longs;tratur in 16. quinti vniuer&longs;aliter. </s>
          <s id="s.000951"><expan abbr="atq;">atque</expan> hoc modo explicatum e&longs;t exem&shy;<lb/>
plum &longs;ecundi erroris, qui verbis illis <emph type="italics"/>&lpar;Vel &longs;it quidem, &longs;ed innominatum &longs;it in <lb/>
rebus &longs;pecie differentibus&rpar;<emph.end type="italics"/> continebatur.</s>
        </p>
        <p type="main">
          <s id="s.000952"><arrow.to.target n="marg30"/></s>
        </p>
        <p type="margin">
          <s id="s.000953"><margin.target id="marg30"/>30</s>
        </p>
        <p type="main">
          <s id="s.000954">Ibidem <emph type="italics"/>&lpar;Propter hoc &longs;i quis mon&longs;trauerit &longs;ingulum triangulum. </s>
          <s id="s.000955">demon&longs;tratio&shy;<lb/>
ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilaterum</expan> &longs;eor&longs;um, <lb/>
&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, ni&longs;i &longs;o&shy;<lb/>
phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs;aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>
triangulum alterum. </s>
          <s id="s.000956">non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omne triangulum, <lb/>
ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>
non nouit&rpar;<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>
lis <emph type="italics"/>&lpar;Quando vel nihil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare&rpar;<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>
vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>
cap. 1. &longs;crip&longs;imus de proprietate illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>
gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>
hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>
tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>
ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>
gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens aut eadem demon&longs;tratione dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52" xlink:href="009/01/052.jpg"/>&longs;eparatim o&longs;tendit, aut vtens diuer&longs;is demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>
tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>
illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>
uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>
non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>
munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>
gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>
gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>
quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numerum, ide&longs;t de vnoquoque, <lb/>
quatenus e&longs;t vnum numero. </s>
          <s id="s.000957">non nouit autem &longs;ecundum &longs;peciem, idest fecun&shy;<lb/>
dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>
ra trianguli. </s>
          <s id="s.000958">hoc autem e&longs;&longs;e exemplum primi erroris manife&longs;t&egrave; conuincitur, <lb/>
tum ex verbis illis, quando nihil &longs;it &longs;uperius, pr&aelig;ter &longs;ingulare, tum ex hu&shy;<lb/>
ius textus verbis illis <emph type="italics"/>&lpar;Singulum triangulum&rpar;<emph.end type="italics"/> &amp; ex illis <emph type="italics"/>&lpar;Ni&longs;i &longs;ecundum nume&shy;<lb/>
rum&rpar;<emph.end type="italics"/> ide&longs;t, ni&longs;i de vno, quod &longs;it vnum numero. </s>
          <s id="s.000959">propterea nos de &longs;ingulari <lb/>
triangulo omi&longs;&longs;a Zabarell&aelig; &longs;ententia explicauimus tandem in confirma&shy;<lb/>tionem no&longs;tr&aelig; expo&longs;itionis in h&aelig;c tria errata illud non omittendum, &longs;atius <lb/>
e&longs;&longs;e dicere, Ari&longs;t. attuli&longs;&longs;e pro tribus erratis tria exempla ordine retrogra&shy;<lb/>
do, qu&agrave;m, quod facit Zabarella, primum e&longs;&longs;e pro tertio, &longs;ecundum pro pri&shy;<lb/>
mo, tertium ver&ograve; pro &longs;ecundo; eo enim modo, Ari&longs;t. confu&longs;ionem nulla ra&shy;<lb/>
tione, im&ograve; contra omnem rationem imponimus.</s>
        </p>
        <p type="main">
          <s id="s.000960"><arrow.to.target n="marg31"/></s>
        </p>
        <p type="margin">
          <s id="s.000961"><margin.target id="marg31"/>31</s>
        </p>
        <p type="main">
          <s id="s.000962">Textu 14. continet quidem qu&aelig;dam mathematica, &longs;ed fer&egrave; eadem cum <lb/>
&longs;uperioribus, qu&aelig; quia tum ex pr&aelig;dictis facile intelligi po&longs;&longs;unt, tum quia <lb/>
ben&egrave; ab expo&longs;itoribus explicantur, ne actum agamus, pr&aelig;termittimus.</s>
        </p>
        <p type="main">
          <s id="s.000963"><arrow.to.target n="marg32"/></s>
        </p>
        <p type="margin">
          <s id="s.000964"><margin.target id="marg32"/>32</s>
        </p>
        <p type="main">
          <s id="s.000965">Tex. 20. <emph type="italics"/>&lpar;Ni&longs;i magnitudines numeri &longs;int&rpar;<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>
feret&aelig;, ita vt cadant &longs;ub numerum, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>
decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s>
          <s id="s.000966">&amp; tunc <lb/>
linea numerus e&longs;t. </s>
          <s id="s.000967">idem de &longs;uperficie, ac &longs;olido intelligendum.</s>
        </p>
        <p type="main">
          <s id="s.000968"><arrow.to.target n="marg33"/></s>
        </p>
        <p type="margin">
          <s id="s.000969"><margin.target id="marg33"/>33</s>
        </p>
        <p type="main">
          <s id="s.000970">Ibidem <emph type="italics"/>&lpar;Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>
e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus&rpar;<emph.end type="italics"/> quo ad verba illa, duo cubi cubus, <lb/>
qu&aelig; ad nos pertinent, vult Ari&longs;t. docere, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones &lpar;per cubos enim intelligit numeros quo&longs;dam <lb/>
&longs;ic dictos, vt paulo po&longs;t o&longs;tendam&rpar; vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>
quod o&longs;tenditur in 4. noni Elem. &longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>
multiplicauerit, productus numerus erit pariter cubus. </s>
          <s id="s.000971">nonnulli latinorum <lb/>
perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>
geometricos, at Euclides definit. </s>
          <s id="s.000972">19. &longs;eptimi, &longs;ic arithmeticum cubum de&shy;<lb/>
finit, cubus numerus e&longs;t, qui &longs;ub tribus numeris &aelig;qualibus continetur, qua&shy;<lb/>
lis e&longs;t. </s>
          <s id="s.000973">8. qui e&longs;t ad in&longs;tar cubi geometrici, &amp; continetur &longs;ub tribus binarijs <lb/>
multiplicatis inuicem, qu&aelig; multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi&shy;<lb/>
<figure id="id.009.01.052.1.jpg" place="text" xlink:href="009/01/052/1.jpg"/><lb/>
narij, 2, 2, 2, primus ducitur in &longs;ecundum, &amp; producitur. <lb/>
</s>
          <s id="s.000974">4. qui e&longs;t numerus quadratus huius figur&aelig;, <figure id="id.009.01.052.2.jpg" place="text" xlink:href="009/01/052/2.jpg"/>, deinde <lb/>
tertius binarius ducitur in pr&aelig;dictum quadratum 4. &amp; pro&shy;<lb/>
ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua&shy;<lb/>
ternarij, vnus &longs;upra alterum, vt in pr&aelig;&longs;enti figura refe&shy;<lb/>
runt cubicam figuram, cuius tam longitudo, quam latitudo,


<pb pagenum="53" xlink:href="009/01/053.jpg"/>&amp; altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna&shy;<lb/>
rijs inuicem modo pr&aelig;dicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/>
<figure id="id.009.01.053.1.jpg" place="text" xlink:href="009/01/053/1.jpg"/><lb/>
qui e&longs;t quadratus. </s>
          <s id="s.000975">quo deinde ducto in tertium ter&shy;<lb/>
narium, producitur 27. qui e&longs;t cubus, &amp; refert figu&shy;<lb/>
ram cubicam hanc. </s>
          <s id="s.000976">Iam ver&ograve; &longs;i cubus 8. multipli&shy;<lb/>
cet cubum 27. procreabitur 216. qui pariter cubus <lb/>
e&longs;t. </s>
          <s id="s.000977"><expan abbr="atq;">atque</expan> hoc &longs;ibi volunt verba illa, &longs;i duo cubi cubus, <lb/>
ide&longs;t, &longs;i duo numeri cubi multiplicentur mutu&ograve;, cu&shy;<lb/>
bus alter producetur; ex quibus videas, quam in&shy;<lb/>
ept&egrave; illi <expan abbr="interpret&etilde;tur">interpretentur</expan> hunc locum, qui dicunt, Ari&shy;<lb/>
&longs;totilem velle dicere non pertinere ad Geometram <lb/>
probare duos cubos geometricos &longs;ibi additos face&shy;<lb/>
re alium cubum, quod erat problema Delphicum de <lb/>
duplatione cubi, nondum inuentum; bis enim i&longs;ti peccant, primo in Logi&shy;<lb/>
cam, quia &longs;ic non tran&longs;iret Geometra de genere in genus, ip&longs;ius enim e&longs;t <lb/>
agere de duplatione cubi; &longs;ecund&ograve; in Mathematicas, cum nondum noue&shy;<lb/>rint arithmeticos cubos; &amp; pr&aelig;terea ignorent duos cubos &longs;ibi additos, non <lb/>
facere alium cubum. </s>
          <s id="s.000978">Quod pr&aelig;terea hoc loco intelligendi &longs;int cubi arith&shy;<lb/>
metici cert&ograve; certius con&longs;tat, ex &longs;equenti 24. textu, vbi &longs;ic dicitur <emph type="italics"/>&lpar;Veluti <lb/>
Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.&rpar;<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.000979"><arrow.to.target n="marg34"/></s>
        </p>
        <p type="margin">
          <s id="s.000980"><margin.target id="marg34"/>34</s>
        </p>
        <p type="main">
          <s id="s.000981">Ibidem <emph type="italics"/>&lpar;<expan abbr="Neq;">Neque</expan> alij &longs;cienti&aelig; quod alterius, ni&longs;i <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ita &longs;e habent inter &longs;e, <lb/>
vt &longs;it alterum &longs;ub altero, vt per&longs;pectiua ad Geometriam, &amp; harmonica ad Arith&shy;<lb/>
meticam&rpar;<emph.end type="italics"/> excipit ab illa regula &lpar;qua prohibetur, quamuis &longs;cientiam in alie&shy;<lb/>
nam falcem immittere&rpar; &longs;cientias &longs;ubalternatas, qu&aelig; propri&egrave; in Mathemati&shy;<lb/>
cis reperiuntur, Per&longs;pectiua enim propri&egrave; &longs;ubalternatur Geometri&aelig;, quia <lb/>
vtitur Demon&longs;trationibus linearibus, quas applicat lineis vi&longs;ualibus, &amp; Mu&shy;<lb/>
&longs;ica &longs;ubalternatur Arithmetic&aelig;, quia ab ip&longs;a mutuatur <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> nu&shy;<lb/>
merorum, quas applicat numeris &longs;onoris. </s>
          <s id="s.000982">v.g. <!-- REMOVE S-->Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>
dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>
tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>
videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/>
<figure id="id.009.01.053.2.jpg" place="text" xlink:href="009/01/053/2.jpg"/><lb/>
per 21. primi Elem. &longs;it enim ma&shy;<lb/>
gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>
culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>
quior ab oculo in D. ductis lineis <lb/>
vi&longs;ualibus C A, C B: D A, D B; ab <lb/>
oculis C, &amp; D, ad extremitates <lb/>
&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>
tioris vi&longs;ionis angulus C, minor <lb/>
angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s>
          <s id="s.000983">Hine <lb/>
per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>
quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>
optica. </s>
          <s id="s.000984">Exemplum &longs;ubalternationis Mu&longs;ic&aelig; &longs;it, <expan abbr="con&longs;on&atilde;tia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/>
vulg&ograve; octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio&shy;<lb/>
rem facere duplam vocis acutioris &longs;umatur chorda A B, &amp; diuidatur bifa&shy;<lb/>riam, &longs;ine in &aelig;qualia in C; tota igitur chorda A B, ad dimidium A C, habet <pb pagenum="54" xlink:href="009/01/054.jpg"/><figure id="id.009.01.054.1.jpg" place="text" xlink:href="009/01/054/1.jpg"/><lb/>
proportionem, quam 2. ad 1. <lb/>
&longs;iue duplam, ergo etiam &longs;o&shy;<lb/>
nus totius chord&aelig; A B, ad <expan abbr="&longs;o-n&utilde;">&longs;o&shy;<lb/>
num</expan> chord&aelig; dimidi&aelig; A C, ha&shy;<lb/>
bebit eandem rationem, <expan abbr="nimir&utilde;">nimirum</expan> quam 2. ad 1. &longs;iue duplam. </s>
          <s id="s.000985">&longs;ed &longs;onus chor&shy;<lb/>
d&aelig; A B, ad &longs;onum chord&aelig; A C, con&longs;onat diapa&longs;on, &longs;eu octauam, ergo in <lb/>
data chorda collocata e&longs;t con&longs;onantia diapa&longs;on, quod oportebat. </s>
          <s id="s.000986">vides me&shy;<lb/>
dium e&longs;&longs;e arithmeticam, conclu&longs;ionem ver&ograve; harmonicam. </s>
          <s id="s.000987">Aliud exemplum <lb/>
Tonus, quod e&longs;t <expan abbr="interuall&utilde;">interuallum</expan> prim&aelig; vocis, Vt, ad &longs;ecundam, R&egrave;, in duo &aelig;qua&shy;<lb/>
lia &longs;emitonia diuidi nequit, ratio e&longs;t Arithmetica, quia proportio &longs;uper&shy;<lb/>
particularis in duo &aelig;qualia arithmetic&egrave; &longs;ecari nequit; at Tonus con&longs;i&longs;tit in <lb/>
ratione &longs;uperparticulari, nemp&egrave; in &longs;e&longs;quioctaua, ergo Tonus bifariam diui&shy;<lb/>
di nequit. </s>
          <s id="s.000988">de&longs;umptum e&longs;t ex Boetio.</s>
        </p>
        <p type="main">
          <s id="s.000989"><arrow.to.target n="marg35"/></s>
        </p>
        <p type="margin">
          <s id="s.000990"><margin.target id="marg35"/>35</s>
        </p>
        <p type="main">
          <s id="s.000991">Tex. 23. <emph type="italics"/>&lpar;Est autem &longs;ic mon&longs;trare, quemadmodum Bry&longs;o quadraturam, &longs;ecun&shy;<lb/>
dum enim commune mon&longs;trant tales rationes&rpar;<emph.end type="italics"/> cum velit o&longs;tendere veram de&shy;<lb/>
mon&longs;trationem con&longs;tare debere ex proprijs, non autem ex communibus; <lb/>
primum affert exemplum demon&longs;trationis cuiu&longs;dam Bry&longs;onis, qu&aelig; ex com&shy;<lb/>
munibus procedat, vt autem ben&egrave; intelligamus, quale&longs;nam &longs;int huiu&longs;modi <lb/>
demon&longs;trationes, qu&aelig; per communia o&longs;tendunt, legenda prius ea &longs;unt, qu&aelig; <lb/>
&longs;crip&longs;imus de quadratura circuli in pr&etail;dicamento relationis. </s>
          <s id="s.000992">Bry&longs;o itaque, <lb/>
vt tradit Alexander, in hunc modum conabatur quadrare <expan abbr="circul&utilde;">circulum</expan>. </s>
          <s id="s.000993">&longs;it qua&shy;<lb/>drandus circulus A B C D, cui circum&longs;cribatur quadratum E F G H. per <lb/>
7 quarti, &amp; alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/>
quid autem &longs;it circum&longs;cribere, &amp; in&longs;cribere figuram circulo, ex definitione <lb/>
<figure id="id.009.01.054.2.jpg" place="text" xlink:href="009/01/054/2.jpg"/><lb/>
3. &amp; 4. eiu&longs;dem libri petatur, quamuis <lb/>
ex in&longs;pectione figur&aelig; <expan abbr="pr&etail;s&etilde;tis">pr&etail;sentis</expan> &longs;atis per&shy;<lb/>
cipi po&longs;&longs;it; deinde aliud <expan abbr="quadrat&utilde;">quadratum</expan> me&shy;<lb/>
dium inter pr&aelig;dicta duo con&longs;tituatur, <lb/>
<expan abbr="&longs;it&qacute;">&longs;itque</expan>; O P Q R. </s>
          <s id="s.000994">Iam &longs;ic o&longs;tendebat i&longs;tud <lb/>
medium quadratum e&longs;&longs;e &aelig;quale circu&shy;<lb/>
lo propo&longs;ito. </s>
          <s id="s.000995"><expan abbr="Qu&aelig;cunq;">Qu&aelig;cunque</expan> &longs;unt, &longs;imul ma&shy;<lb/>
iora eodem, &amp; minora eodem, &longs;unt in&shy;<lb/>
uicem &aelig;qualia, &longs;ed circulus, &amp; quadra&shy;<lb/>
tum medium, &longs;unt ambo maiora qua&shy;<lb/>
drato in&longs;cripto, &amp; ambo minora qua&shy;<lb/>
drato circum&longs;cripto, ergo circulus, &amp; <lb/>
quadratum medium, &longs;unt &aelig;qualia. </s>
          <s id="s.000996">vte&shy;<lb/>
batur, inquit Ari&longs;t pr&etail;dicto principio, <lb/>
etiam numeris, lineis, temporibus, &amp; <lb/>
qualitatibus communi, <expan abbr="neq;">neque</expan> deducto ex natura circuli, aut quadrati, de qui&shy;<lb/>
bus erat demon&longs;tratio. </s>
          <s id="s.000997">pr&aelig;terea aduertendum e&longs;t, illud e&longs;&longs;e fal&longs;um, nam &longs;ex, <lb/>
&amp; quinque, ambo &longs;unt maiores, quam quatuor, &amp; minores, quam &longs;eptem, <lb/>
&amp; tamen non &longs;unt &aelig;quales.</s>
        </p>
        <p type="main">
          <s id="s.000998"><arrow.to.target n="marg36"/></s>
        </p>
        <p type="margin">
          <s id="s.000999"><margin.target id="marg36"/>36</s>
        </p>
        <p type="main">
          <s id="s.001000">In codem textu <emph type="italics"/>&lpar;<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>
&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>
quod illud; vt duobus rectis &aelig;quales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/> <pb pagenum="55" xlink:href="009/01/055.jpg"/><emph type="italics"/>principijs huius&rpar;<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, qu&aelig; non <lb/>
ex communibus, vt pr&aelig;cedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>
affectionem de &longs;ubiecto proprio. </s>
          <s id="s.001001">E&longs;t autem illud exemplum toties decan&shy;<lb/>
tatum de triangulo habente tres angulos &aelig;quales duobus rectis angulis; id&shy;<lb/>
circo oper&aelig;pretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli&shy;<lb/>
dis, qu&aelig; i&longs;tud ex proprijs principijs demon&longs;trat, &amp; quam hoc loco Ari&longs;to&shy;<lb/>
teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. mentem prob&egrave; penetrare poteri&shy;<lb/>
<figure id="id.009.01.055.1.jpg" place="text" xlink:href="009/01/055/1.jpg"/><lb/>
mus. </s>
          <s id="s.001002">&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. <!-- KEEP S--></s>
          <s id="s.001003">Dico ag&shy;<lb/>
gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>
e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>
lis rectis &lpar;vt autem melius intelligas, qu&aelig; <lb/>
&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>
in lib. 1. Priorum &longs;ecto 3. cap. 1.&rpar; produ&shy;<lb/>
catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>
externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>
batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>
facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>
duobus rectis: &amp; quia pariter in prima parte huius propo&longs;. </s>
          <s id="s.001004">32. probatum <lb/>
e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>
tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>
&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>
anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>
&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>
vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>
A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>
dum. </s>
          <s id="s.001005">Medium <expan abbr="itaq;">itaque</expan> huius demon&longs;trationis, &longs;i res ad trutinam Logicam ex&shy;<lb/>
pendatur, e&longs;t, quod partes aggregati <expan abbr="tri&utilde;">trium</expan> <expan abbr="angulor&utilde;">angulorum</expan> A, B, A C B, &longs;unt &aelig;qua&shy;<lb/>
les partibus aggregati <expan abbr="duor&utilde;">duorum</expan>, &amp; ideo <expan abbr="aggregat&utilde;">aggregatum</expan>, aggregato &aelig;qua&shy;<lb/>
le e&longs;t. </s>
          <s id="s.001006">quod medium e&longs;t in genere cau&longs;&aelig; materialis. </s>
          <s id="s.001007">quod ver&ograve; partes illius <lb/>
&longs;int &aelig;quales partibus huius, probatur, per dignitatem <expan abbr="ill&atilde;">illam</expan>, qu&aelig; &longs;unt &aelig;qualia <lb/>
vni tertio, &longs;unt etiam inter &longs;e. </s>
          <s id="s.001008">partes porr&ograve; aggregati trium angulorum <lb/>
erant h&aelig;, anguli A, B, vna; altera ver&ograve; angulus A C B; partes ver&ograve; aggre&shy;<lb/>
gati duorum rectorum erant A C B, A C D, quibus partibus, ill&aelig; &longs;unt &aelig;qua&shy;<lb/>
les, &amp; ideo totum toti &aelig;quale. </s>
          <s id="s.001009">quod medium e&longs;t omnino intrin&longs;ecum, &amp; ex <lb/>
proprijs ip&longs;ius trianguli, &longs;iue ex proprijs angulorum ip&longs;ius, cum &longs;int ip&longs;ius <lb/>
partes. </s>
          <s id="s.001010">quod pariter medium ex parte pa&longs;&longs;ionis, qu&aelig; demon&longs;tratur, e&longs;t ex <lb/>
proprijs, cum &longs;int partes illius materiales. </s>
          <s id="s.001011">per materiam autem oportet <lb/>
hoc loco intelligere materiam intelligibilem, ide&longs;t quantitatem &agrave; qualita&shy;<lb/>tibus ab&longs;tractam, &amp; terminatam, de qua pluribus agemus infra in tractatu <lb/>
de natura mathematicarum. </s>
          <s id="s.001012">Hinc videas eos magnopere decipi, qui pu&shy;<lb/>
tant, hanc demon&longs;trationem e&longs;&longs;e per extrin&longs;eca, e&ograve; quod ad demon&longs;tran&shy;<lb/>
dum producatur linea B C, in D, putantes lineam illam productam C D, <lb/>
e&longs;&longs;e demon&longs;trationis medium; line&aelig; <expan abbr="namq;">namque</expan> huiu&longs;modi, qu&aelig; in demon&longs;tra&shy;<lb/>
tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon&shy;<lb/>
&longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex&shy;<lb/>
cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s>
          <s id="s.001013">Hinc etiam manife&longs;t&egrave; colligas <pb pagenum="56" xlink:href="009/01/056.jpg"/>Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/>
ageometreti negare &longs;olent, &longs;ed audacter aiunt exempla Ari&longs;t. non e&longs;&longs;e vera: <lb/>
<expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quor&utilde;">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/>
illud v&longs;urpari &longs;olet, &amp; debet de exemplis moralibus. </s>
          <s id="s.001014">at vero requiri confor&shy;<lb/>
mitatem exemplorum cum regulis traditis, nemo &longs;an&aelig; mentis dubitabit. <lb/>
</s>
          <s id="s.001015">Verum i&longs;ti confundunt conformitatem cum veritate. </s>
          <s id="s.001016">Veritas exemplo tunc <lb/>
ine&longs;t, quando illud, quod in exemplo narratur, ver&egrave; extitit, vt &longs;i quis in <lb/>
exemplum pudiciti&aelig; afferret hi&longs;toriam Io&longs;ephi, <expan abbr="ver&utilde;">verum</expan> i&longs;tud e&longs;&longs;et exemplum. <lb/>
</s>
          <s id="s.001017">qu&aelig; veritas in exemplis moralibus non &longs;emper e&longs;t nece&longs;&longs;aria, talia exempla <lb/>
&longs;unt &longs;&aelig;p&egrave; parabol&aelig;, &amp; fabul&aelig;, qu&aelig; nunquam extiterunt, v. <!-- REMOVE S-->g. <!-- REMOVE S-->narratur ab <lb/>
Ari&longs;t. de quodam filio, qui patrem crudeliter traxerat, qui po&longs;tea grandior <lb/>
factus, cum filium procrea&longs;&longs;et, ab eodem pariter raptatus e&longs;t ip&longs;e, v&longs;que ad <lb/>
eundem locum, quo ip&longs;e patrem &longs;uum impi&egrave; raptauerat. </s>
          <s id="s.001018">non e&longs;t nece&longs;&longs;e, ta&shy;<lb/>
lem extiti&longs;&longs;e filium, <expan abbr="neq;">neque</expan> patrem. </s>
          <s id="s.001019">Verumtamen &longs;emper conformitas exem&shy;<lb/>
pli cum regulis, &amp; pr&aelig;ceptis, qu&aelig; traduntur nece&longs;&longs;aria e&longs;t, alioquin exem&shy;<lb/>
pla de&longs;truerent id, quod pr&aelig;ceptio con&longs;truit, <expan abbr="illi&qacute;">illique</expan> contraria e&longs;&longs;et, quod om&shy;<lb/>
nino ab&longs;urdum foret. </s>
          <s id="s.001020">non &longs;ecus, ac &longs;i quis vellet alium docere characteres <lb/>
latinos, <expan abbr="illi&qacute;">illique</expan>; barbaros, quos Gothicos vocant in exemplum proponeret. </s>
          <s id="s.001021">re&shy;<lb/>
quiritur igitur &longs;emper in omni exemplo conformitas cum eo, quod doce&shy;<lb/>
tur; in moralibus tamen non &longs;emper requiritur veritas, vti diximus; Alij <lb/>
ver&ograve; dicunt non requiri in exemplis determinatam veritatem, &longs;ed &longs;atis e&longs;&longs;e, <lb/>
&longs;i exemplum verum &longs;it &longs;ecundum opinionem aliquorum: <expan abbr="quor&utilde;">quorum</expan> &longs;ententiam <lb/>
non improbamus. </s>
          <s id="s.001022">Exempla igitur ab Ari&longs;t. pa&longs;&longs;im ex mathematicis allata, <lb/>
congrua, <expan abbr="conformia&qacute;">conformiaque</expan>; omnin&ograve; &longs;unt ip&longs;ius doctrin&aelig;, aliter ip&longs;um perpetu&ograve; <lb/>
mentientem facimus. </s>
          <s id="s.001023">Po&longs;trem&ograve; illud etiam e&longs;t aduertendum, fort&egrave; Ari&longs;t. in <lb/>
pr&aelig;&longs;enti textu &longs;pecta&longs;&longs;e <expan abbr="n&otilde;">non</expan> ad hanc Euclidianam demon&longs;trationem, &longs;ed po&shy;<lb/>
tius ad Pithagoricam. </s>
          <s id="s.001024">Pithagorei enim eam aliter, quamuis per idem me&shy;<lb/>
dium, &longs;cilicet &agrave; cau&longs;a materiali, demon&longs;trabant; con&longs;truebant enim aliter, <lb/>
<expan abbr="neq;">neque</expan> vlla vtebantur diui&longs;ione. </s>
          <s id="s.001025">quod dictum velim propter nonnullos, qui ab <lb/>
huiu&longs;modi diui&longs;ionibus abhorrent, <expan abbr="timent&qacute;">timentque</expan>; ne demon&longs;trationis perfectio&shy;<lb/>
ni per eas plurimum derogetur. </s>
          <s id="s.001026">Pithagoreorum demon&longs;trationem vide <lb/>
apud Clauium in &longs;cholio 32. primi Euclidis, quam ex Eudemo etiam Pro&shy;<lb/>
clus in comm. <!-- REMOVE S-->eiu&longs;dem recitat.</s>
        </p>
        <p type="main">
          <s id="s.001027"><arrow.to.target n="marg37"/></s>
        </p>
        <p type="margin">
          <s id="s.001028"><margin.target id="marg37"/>37</s>
        </p>
        <p type="main">
          <s id="s.001029">Ibidem <emph type="italics"/>&lpar;Sed quemadmod&ubreve;m harmonica per Arithmeticam&rpar;<emph.end type="italics"/> vide &longs;upra tex. <!-- REMOVE S-->20.</s>
        </p>
        <p type="main">
          <s id="s.001030"><arrow.to.target n="marg38"/></s>
        </p>
        <p type="margin">
          <s id="s.001031"><margin.target id="marg38"/>38</s>
        </p>
        <p type="main">
          <s id="s.001032">Ibidem <emph type="italics"/>&lpar;Demon&longs;tratio autem non computatur in aliud genus; ni&longs;i, vt dictum <lb/>e&longs;t geometric&aelig; demon&longs;trationes in Per&longs;pectiuas, aut Mechanicas, &amp; arithmetic&aelig; in <lb/>
harmonicas&rpar;<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiu&aelig;, &amp; Mu&longs;ic&aelig; in tex. <!-- REMOVE S-->20. at&shy;<lb/>
tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t. in&longs;inuat, exem&shy;<lb/>
plum &longs;it illud, quod Archimedes prop. 14. primi Aequep. <!-- REMOVE S-->demon&longs;trat, ni&shy;<lb/>
mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>
line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s>
          <s id="s.001033">&longs;it <lb/>
triangulum A B C, &agrave; cuius angulis A, &amp; B, ducantur du&aelig; rect&aelig; A D, B E, ita <lb/>
vt bifariam &longs;ecent latera A C, B C, in punctis D, &amp; E, &amp; concurrant in F. <lb/>
<!-- KEEP S--></s>
          <s id="s.001034">Dico F, e&longs;&longs;e centrum grauitatis propo&longs;iti trianguli. </s>
          <s id="s.001035">Quoniam enim in 13. <lb/>
Aequep. <!-- REMOVE S-->probauit centrum grauitatis e&longs;&longs;e in ea linea, qu&aelig; ducta ab angulo <lb/>
quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centr&utilde;">centrum</expan> grauitatis.


<pb pagenum="57" xlink:href="009/01/057.jpg"/><figure id="id.009.01.057.1.jpg" place="text" xlink:href="009/01/057/1.jpg"/><lb/>
&longs;ed eadem ratione erit etiam in linea B E, er&shy;<lb/>
go non ni&longs;i in puncto F, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> e&longs;t in vtra&shy;<lb/>
que, quod erat demon&longs;trandum. </s>
          <s id="s.001036">ex quibus ap&shy;<lb/>
paret, qua ratione mechanica conclu&longs;io Geo&shy;<lb/>
metri&aelig; &longs;ubiaceat, dum lineari di&longs;cur&longs;u ip&longs;a <lb/>
demon&longs;tratio perficitur. </s>
          <s id="s.001037">Scias pr&aelig;terea cen&shy;<lb/>
trum grauitatis e&longs;&longs;e tale punctum, ex quo &longs;i &longs;u&shy;<lb/>
&longs;pendatur corpus triangulare vniformis cra&longs;&shy;<lb/>
&longs;itici, manet &longs;emper horizonti parallelum, &longs;i <lb/>
tamen antequam &longs;u&longs;penderetur, iacebat plano horizontis, &aelig;quidi&longs;tans; <lb/>
<expan abbr="neq;">neque</expan> &longs;i &longs;u&longs;pen&longs;um feratur huc illud nutat, &longs;ed &longs;emper in <expan abbr="cod&etilde;">codem</expan> &longs;itu per&longs;euerat.</s>
        </p>
        <p type="main">
          <s id="s.001038"><arrow.to.target n="marg39"/></s>
        </p>
        <p type="margin">
          <s id="s.001039"><margin.target id="marg39"/>39</s>
        </p>
        <p type="main">
          <s id="s.001040">Tex. 24. <emph type="italics"/>&lpar;Veluti Arithmetica quidem quid impar, aut par; aut quadrangu&shy;<lb/>
lum, aut cubus&rpar;<emph.end type="italics"/> cogno&longs;cas hinc cert&ograve; certius quadrangulum, &amp; cubum e&longs;&longs;e <lb/>
&longs;pecies numerorum, &longs;icuti &longs;upra tex. <!-- REMOVE S-->9. &amp; 20. explicauimus, qu&ograve; nunc te vi&shy;<lb/>
ci&longs;&longs;im, vt pr&aelig;&longs;entem locum intelligas, remittimus.</s>
        </p>
        <p type="main">
          <s id="s.001041"><arrow.to.target n="marg40"/></s>
        </p>
        <p type="margin">
          <s id="s.001042"><margin.target id="marg40"/>40</s>
        </p>
        <p type="main">
          <s id="s.001043">Ibidem <emph type="italics"/>&lpar;Geometrica ver&ograve; quid irrationale, aut refrangi, aut concurrere&rpar;<emph.end type="italics"/> per <lb/>
verbum, irrationale, non videtur Ari&longs;t. intellexi&longs;&longs;e proprietatem illam duo&shy;<lb/>
rum linearum incommen&longs;urabilium longitudine, &amp; potentia, quia v&longs;us fui&longs;&shy;<lb/>
&longs;et verbo, <foreign lang="greek">a/orhton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio&shy;<lb/>
ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latin&egrave; redditur improportionale.</s>
        </p>
        <p type="main">
          <s id="s.001044"><arrow.to.target n="marg41"/></s>
        </p>
        <p type="margin">
          <s id="s.001045"><margin.target id="marg41"/>41</s>
        </p>
        <p type="main">
          <s id="s.001046">Per verbum <emph type="italics"/>&lpar;Refrangi&rpar;<emph.end type="italics"/> &longs;eu frangi, intelligit lineam aliquam rectam, non <lb/>in directum tendere, &longs;ed in aliquo puncto frangi, &longs;eu declinari &agrave; rectitudine, <lb/>
ita vt con&longs;tituat angulum.</s>
        </p>
        <p type="main">
          <s id="s.001047">Per verbum <emph type="italics"/>&lpar;Concurrere&rpar;<emph.end type="italics"/> intelligit, non e&longs;&longs;e parallelas, &longs;ed ad idem ali&shy;<lb/>
quod punctum coire, &longs;i protrahantur.</s>
        </p>
        <p type="main">
          <s id="s.001048"><arrow.to.target n="marg42"/></s>
        </p>
        <p type="margin">
          <s id="s.001049"><margin.target id="marg42"/>42</s>
        </p>
        <p type="main">
          <s id="s.001050">Ibidem <emph type="italics"/>&lpar;Et Astrologia &longs;imiliter&rpar;<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t. non iu&shy;<lb/>
diciariam, quamuis &agrave; recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>
dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo&shy;<lb/>
tum, &amp; locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>
&amp; Elementa.</s>
        </p>
        <p type="main">
          <s id="s.001051"><arrow.to.target n="marg43"/></s>
        </p>
        <p type="margin">
          <s id="s.001052"><margin.target id="marg43"/>43</s>
        </p>
        <p type="main">
          <s id="s.001053">Tex. 25. <emph type="italics"/>&lpar;<expan abbr="Neq;">Neque</expan> Geometra fal&longs;a &longs;upponit, quemadmodum quidam a&longs;&longs;eruere di&shy;<lb/>
centes, quod non oportet fal&longs;o vti: Geometram ver&ograve; mentiri dicentem pedalem, non <lb/>
pedalem, aut rectam de&longs;criptam, non rectam <expan abbr="exist&etilde;tem">existentem</expan>: Geometra ver&ograve; nihil con&shy;<lb/>cludit e&ograve;, quod h&aelig;c e&longs;t linea, &longs;ed qu&aelig; per h&aelig;c o&longs;tenduntur&rpar;<emph.end type="italics"/> innuit his verbis eam <lb/>
materiam intelligibilem, qu&aelig; e&longs;t &longs;ubiectum Geometri&aelig;: eam &longs;cilicet, qu&aelig; <lb/>
&longs;ub figuris Geometricis &longs;en&longs;ibilibus, &amp; <expan abbr="plerunq;">plerunque</expan> fal&longs;is latet; nam &longs;&aelig;p&egrave; Geo&shy;<lb/>
metra vtitur linea quadam &longs;en&longs;ibili pro recta, qu&aelig; ver&egrave; nec e&longs;t linea mathe&shy;<lb/>
matica, nec recta; &longs;upponit aliquando talem lineam e&longs;&longs;e pedalem, qu&aelig; ve&shy;<lb/>
r&egrave; non e&longs;t pedalis: Verumtamen non mentitur, quia re&longs;picit ad veram li&shy;<lb/>
neam mathematicam, qu&aelig; &longs;ub illa intelligitur, &amp; qu&aelig; recta concipitur; &amp; <lb/>
quidem h&aelig;c omnia ver&egrave; concipiuntur, quoniam ita e&longs;&longs;e re vera po&longs;&longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.001054"><arrow.to.target n="marg44"/></s>
        </p>
        <p type="margin">
          <s id="s.001055"><margin.target id="marg44"/>44</s>
        </p>
        <p type="main">
          <s id="s.001056">Tex. 28. <emph type="italics"/>&lpar;Coaltern as ver&ograve; coincidere&rpar;<emph.end type="italics"/> per coalternas intelligendas e&longs;&longs;e pa&shy;<lb/>
rallelas lineas, alias, &amp; nunc <expan abbr="quoq;">quoque</expan> monemus.</s>
        </p>
        <p type="main">
          <s id="s.001057"><arrow.to.target n="marg45"/></s>
        </p>
        <p type="margin">
          <s id="s.001058"><margin.target id="marg45"/>45</s>
        </p>
        <p type="main">
          <s id="s.001059">Tex. 29. <emph type="italics"/>&lpar;In Mathematicis ver&ograve; non est &longs;imiliter paralogi&longs;mus, quoniam me&shy;<lb/>
di&ubreve; e&longs;t &longs;emper, quod duplex, de hoc enim omni, &amp; hoc rur&longs;us de alio dicitur omni&rpar;<emph.end type="italics"/><lb/>
aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in


<pb pagenum="58" xlink:href="009/01/058.jpg"/>di&longs;ciplinis, idem tamen apud gr&aelig;cos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci&shy;<lb/>
plin&aelig;; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. <!-- KEEP S--></s>
          <s id="s.001060">Porr&ograve; non <lb/>
e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>
tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>
omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>
primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s>
          <s id="s.001061">H&aelig;c <lb/>
e&longs;t autem pulcherrima mathematicarum commendatio, quippe pr&aelig;clarum <lb/>
e&longs;t &agrave; laudato laudari. </s>
          <s id="s.001062">In mathematicis, inquit, non accidit &longs;imiliter para&shy;<lb/>
logi&longs;mus, ide&longs;t, tam frequenter, quemadmodum in &longs;yllogi&longs;mis dialecticis, <lb/>
quia modus argumentandi mathematicarum e&longs;t perfecti&longs;&longs;imus, quippe in <lb/>
primo modo prim&aelig; figur&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.001063"><arrow.to.target n="marg46"/></s>
        </p>
        <p type="margin">
          <s id="s.001064"><margin.target id="marg46"/>46</s>
        </p>
        <p type="main">
          <s id="s.001065">Eodem tex. <emph type="italics"/>&lpar;Contingit autem quo&longs;dam non &longs;yllogi&longs;tic&egrave; dicere, &amp; quod ex vtri&longs;&shy;<lb/>
que con&longs;equentia accipiunt, quemadmodum &amp; C&aelig;neus facit, quod ignis in multi&shy;<lb/>
plici proportione: etenim ignis celeriter gignitur, vt ait: &amp; h&aelig;c est proportio. </s>
          <s id="s.001066">&longs;ic <lb/>autem non e&longs;t &longs;yllogi&longs;mus, ni&longs;i celerrimam proportio &longs;equatur multiplex: &amp; ignem <lb/>
celerrima in motu proportio&rpar;<emph.end type="italics"/> verba illa &lpar;in multiplici proportione&rpar; gr&aelig;c&egrave; &longs;ic <lb/>
&longs;e habent, <foreign lang="greek">en th&verbar; pollaplasioni analogia&verbar;,</foreign> quod melius redditur latin&egrave; in mul&shy;<lb/>
tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem&shy;<lb/>
admodum in vulgata editione. </s>
          <s id="s.001067">porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>
catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s>
          <s id="s.001068">lib. 5. <lb/>
Elem. ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>
ducunt. </s>
          <s id="s.001069">Proportio igitur multiplex e&longs;t habitudo inter duas quantitates in&shy;<lb/>
&aelig;quales, quarum maior continet minorem, bis, vel ter, vel quater, &amp;c. </s>
          <s id="s.001070">vn&shy;<lb/>
de proportio multiplex habet &longs;ub &longs;e genera infinita, quando enim maior <lb/>
continet minorem bis, dicitur Dupla: quando ter, Tripla: quando quater, <lb/>
Quadrupla: &amp; &longs;ic in infinitum: v. <!-- REMOVE S-->g. <!-- REMOVE S-->2. ad 1. e&longs;t proportio dupla; 3. ad 1. tri&shy;<lb/>
pla; 4. ad 1. quadrupla, &amp;c. </s>
          <s id="s.001071">omnes tamen continentur &longs;ub genere multipli&shy;<lb/>
cis rationis. </s>
          <s id="s.001072">porr&ograve; &longs;i qu&etail;piam proportio ex genere multiplici progrediatur <lb/>
per plures terminos, v. <!-- REMOVE S-->g. <!-- REMOVE S-->proportio quadrupla progrediatur hoc modo, <lb/>
1. 4. 16. 64. 256. &amp;c. </s>
          <s id="s.001073">fit, vt &longs;ub&longs;equentes termini mirum in modum augean&shy;<lb/>
tur. </s>
          <s id="s.001074">hic vides primum ip&longs;am quadruplam rationem in di&longs;po&longs;itis terminis <lb/>
progredi, quia quilibet &longs;equens terminus ad pr&aelig;cedentem e&longs;t quadruplus. <lb/>
</s>
          <s id="s.001075">cernis etiam in paucis terminis, quinque &longs;cilicet magnum factum e&longs;&longs;e incre&shy;<lb/>
mentum, cum <expan abbr="v&longs;q;">v&longs;que</expan> ad 256. excreuerint. </s>
          <s id="s.001076">C&aelig;neus igitur dicens ignem augeri <lb/>
&longs;ecundum multiplicem rationem, vnam ex pr&aelig;dictis intelligebat aliquam, <lb/>
quia qu&aelig;libet illarum magnopere cre&longs;cit, &longs;i propagetur, vt ad 10. quinti <lb/>
definit. </s>
          <s id="s.001077">traditur: &amp; vt paulo ante exemplo licuit per&longs;picere. </s>
          <s id="s.001078">argumentaba&shy;<lb/>
tur igitur C&aelig;neus in hunc modum; quod in multiplici ratione augetur, ce&shy;<lb/>
lerrim&egrave; augetur: ignis celerrim&egrave; augetur, ergo ignis in multiplici ratione <lb/>
augetur, qu&aelig; argumentatio vitio&longs;a e&longs;t, ex duabus quippe affirmatiuis in &longs;e&shy;<lb/>
cunda figura procedens, vt colligitur ex verbis illis tex. <emph type="italics"/>&lpar;Ex viri&longs;que con&longs;e&shy;<lb/>
quentia accipiunt<emph.end type="italics"/>&rpar; ex his mathematica huius locis patere &longs;atis po&longs;&longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.001079"><arrow.to.target n="marg47"/></s>
        </p>
        <p type="margin">
          <s id="s.001080"><margin.target id="marg47"/>47</s>
        </p>
        <p type="main">
          <s id="s.001081">Ibidem &lpar;<emph type="italics"/>Conuertuntur autem magis, qu&aelig;&longs;unt in mathematicis, quoniam nul&shy;<lb/>
lum accidens accipiunt &lpar;in quo quidem ijs pr&aelig;&longs;t&abreve;t, qu&aelig; di&longs;putationibus traduntur&rpar; <lb/>
&longs;ed definitiones<emph.end type="italics"/>&rpar; H&aelig;c e&longs;t altera mathematicarum laus, vnde earum quoque <lb/>
pr&aelig;&longs;tantia elucet, quia &longs;cilicet mathematic&aelig; pro medijs vtuntur definitio&shy;


<pb pagenum="59" xlink:href="009/01/059.jpg"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, qu&aelig; nullo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>
v. <!-- REMOVE S-->g. <!-- REMOVE S-->in prima Euclidis demon&longs;tratione per definitionem &longs;ubiecti probantur <lb/>
tres line&aelig; e&longs;&longs;e &aelig;quales, quia nimirum &longs;int &longs;emidiametri circulorum &aelig;qua&shy;<lb/>
lium, qu&aelig; e&longs;t ip&longs;arum definitio. </s>
          <s id="s.001082">&amp; in 4. primi probantur ba&longs;is, &amp; anguli <lb/>
vnius trianguli &aelig;quales e&longs;&longs;e ba&longs;i, &amp; angulis alterius trianguli per formalem <lb/>
definitionem pa&longs;&longs;ionis, videlicet &aelig;qualitatis, qu&aelig; traditur in octauo axio&shy;<lb/>
mate &longs;ic, qu&aelig; &longs;ibi mutuo congruunt, ea inter &longs;e &longs;unt &aelig;qualia. </s>
          <s id="s.001083">probat igitur <lb/>
Euclides in quarta ba&longs;im, &amp; angulos vnius trianguli e&longs;&longs;e &aelig;qualia ba&longs;i, &amp; an&shy;<lb/>
gulis alterius trianguli, quia o&longs;tendit, quod, &longs;i ba&longs;is illa huic ba&longs;i, &amp; illi an&shy;<lb/>
guli hi&longs;ce angulis &longs;uperponantur, congruunt; ex qua congruentia mutua, <lb/>
qu&aelig; e&longs;t &aelig;qualitatis definitio, infert &aelig;qualitatem ip&longs;arum ba&longs;ium, necnon <lb/>
angulorum. </s>
          <s id="s.001084">eadem deinde &aelig;qualitatis definitione totam demon&longs;trationem <lb/>
concludit, &longs;cilicet totum triangulum toti triangulo &aelig;quale e&longs;&longs;e, quia vnum <lb/>
alteri congruat. </s>
          <s id="s.001085">A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>
terpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>
cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s>
          <s id="s.001086">huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>
Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>
&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. Mathematicas alias omnes natura&shy;<lb/>
les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>
lere. </s>
          <s id="s.001087">a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>
nes ad demon&longs;trandum. </s>
          <s id="s.001088">Reliqua logici expo&longs;itores declarant.</s>
        </p>
        <p type="main">
          <s id="s.001089"><arrow.to.target n="marg48"/></s>
        </p>
        <p type="margin">
          <s id="s.001090"><margin.target id="marg48"/>48</s>
        </p>
        <p type="main">
          <s id="s.001091">Tex. 30. &lpar;<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve;m quod <lb/>
&longs;ph&aelig;rica<emph.end type="italics"/>&rpar; Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>
ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>
fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>
tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>
tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>
quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>
n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>
corpori lumino&longs;o &longs;olet illuminari. </s>
          <s id="s.001092">illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>
eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>
tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>
pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>
in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>
Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s>
          <s id="s.001093">Vt autem <lb/>
huius illuminationis non iniucundam facias experientiam; cape &longs;ph&aelig;ram <lb/>
quampiam &longs;olidam manu, cum qua recede ad medium cubiculi, &amp; pone lu&shy;<lb/>
men &longs;eor&longs;um ad partem aliquam: deinde brachio exten&longs;o oppone &longs;ph&aelig;ram <lb/>
lumini, quo &longs;itu nihil de illuminatione videbis, quamuis dimidium fer&egrave; il&shy;<lb/>
lius illuminetur. </s>
          <s id="s.001094">po&longs;tea conuerte te ip&longs;um ibidem paulatim, ita vt aliquid <lb/>
illuminationis oculo tuo appareat; &amp; videbis partem illam illuminationis, <lb/>
falcat&aelig;, &longs;eu nou&aelig; Lun&aelig; &longs;imilem. </s>
          <s id="s.001095">Deinde adhuc magis te conuerte, &amp; cer&shy;<lb/>
nes illuminationem dimidiat&aelig; Lun&aelig; &longs;imilem: verte adhuc te ip&longs;um donec <lb/>
&longs;it &longs;ph&aelig;ra ita lumini oppo&longs;ita, vt inter ip&longs;am, &amp; lumen oculus tuus &longs;it me&shy;<lb/>
dius; apparebit tunc tota illuminatio, qu&aelig; erit in&longs;tar plenilunij. </s>
          <s id="s.001096">perge ad&shy;


<pb pagenum="60" xlink:href="009/01/060.jpg"/>huc te ip&longs;um conuertere, &amp; videbis paulatim lumen oculo tuo decre&longs;cere <lb/>
non aliter ac in Luna &longs;ene&longs;cente. </s>
          <s id="s.001097"><expan abbr="atq;">atque</expan> hoc e&longs;t &longs;ph&aelig;ric&egrave; illuminari, fierique <lb/>
&longs;ph&aelig;rica illuminationis augmenta. </s>
          <s id="s.001098">cum ergo videamus Lunam eo modo lu&shy;<lb/>
mine augeri, quo &longs;ph&aelig;ra, hinc ip&longs;am <expan abbr="quoq;">quoque</expan> &longs;ph&aelig;ricam e&longs;&longs;e argumentamur.</s>
        </p>
        <p type="main">
          <s id="s.001099"><arrow.to.target n="marg49"/></s>
        </p>
        <p type="margin">
          <s id="s.001100"><margin.target id="marg49"/>49</s>
        </p>
        <p type="main">
          <s id="s.001101">Po&longs;t nonnulla &lpar;<emph type="italics"/>Vt Per&longs;pectiua ad Geometriam, &amp; Mechanica ad Stereome&shy;<lb/>
tricam, &amp; Harmonica ad Arithmeticam, vt Apparentia ad A&longs;trologicam<emph.end type="italics"/>&rpar; &longs;upra <lb/>
tex. <!-- REMOVE S-->20. exempla &longs;ubalternationum Per&longs;pectiu&aelig;, &amp; Mechanic&aelig; cum Geo&shy;<lb/>
metria &longs;unt allata. </s>
          <s id="s.001102">hic primo notandum Stereometriam non e&longs;&longs;e &longs;cientiam <lb/>
di&longs;tinctam &agrave; Geometria, ni&longs;i &longs;icuti partem &agrave; toto: nam cum Geometria <lb/>
con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu&shy;<lb/>dinem, &amp; profunditatem, oritur triplex illius diui&longs;io, de lineis, de &longs;uperfi&shy;<lb/>
ciebus, de &longs;olidis. </s>
          <s id="s.001103">pars igitur, qu&aelig; de &longs;olidis tractat, <expan abbr="partim&qacute;">partimque</expan>; continetur <lb/>
11. 12. 13. 14. &amp; 15. Euclidis, partim aliorum Geometrarum libris, vt li&shy;<lb/>
bro Archim. <!-- REMOVE S-->de Sph&aelig;ra, &amp; Cyl. <!-- REMOVE S-->&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/>
<foreign lang="greek">stereon,</foreign> ide&longs;t &longs;olidum. </s>
          <s id="s.001104">Porr&ograve; cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste&shy;<lb/>
reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>
dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>
chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>
tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s>
          <s id="s.001105">Quod ait Apparen&shy;<lb/>tia ad A&longs;trol. <!-- KEEP S--></s>
          <s id="s.001106">intelligit per Apparentia vulgarem quandam Nautarum, &amp; <lb/>
Agricolarum a&longs;tronomiam, qu&aelig; quodammodo &longs;ubalternatur, &amp; pendet ex <lb/>
&longs;cientia A&longs;trologi&aelig;; indiget enim cognitione ortus, &amp; motus a&longs;trorum, <lb/>
pr&aelig;&longs;ertim Lun&aelig;, Hyadum, Pleiadum, &amp; Canis. </s>
          <s id="s.001107">Reliqua <expan abbr="v&longs;q;">v&longs;que</expan> ad finem ca&shy;<lb/>
pitis optim&egrave; &agrave; Zabarella explicantur, <expan abbr="neq;">neque</expan> ad nos pertinet, cum de Mathe&shy;<lb/>
maticis agant, quatenus ad Logicum &longs;pectant.</s>
        </p>
        <p type="main">
          <s id="s.001108"><arrow.to.target n="marg50"/></s>
        </p>
        <p type="margin">
          <s id="s.001109"><margin.target id="marg50"/>50</s>
        </p>
        <p type="main">
          <s id="s.001110">Po&longs;t nonnulla &lpar;<emph type="italics"/>Hic enim ip&longs;um quidem quod &longs;en&longs;itiuorum e&longs;t &longs;cire, ip&longs;um ve&shy;<lb/>
r&ograve; Propter quid Mathematicorum; hi <expan abbr="namq;">namque</expan> habent cau&longs;arum demon&longs;trationes, <lb/>
&amp;c.<emph.end type="italics"/>&rpar; &longs;en&longs;us e&longs;t in &longs;ubalternatis, &amp; dependentibus di&longs;ciplinis, quas &longs;en&longs;itiuas <lb/>
appellat, quia de rebus &longs;en&longs;ibilibus &longs;unt, vt in Per&longs;pectiua de obiectis vi&longs;ibi&shy;<lb/>
libus, &amp; in Mu&longs;ica de &longs;onis cogno&longs;citur Quod, ide&longs;t effectus: cuius effectus <lb/>
cau&longs;a, &longs;eu Propter quid &longs;citur auxilio Mathematicarum, ide&longs;t, traditur &agrave; <lb/>
&longs;cientijs &longs;ubalternantibus. </s>
          <s id="s.001111">v. <!-- REMOVE S-->g. <!-- REMOVE S-->alicuius effectus in Per&longs;pectiua cau&longs;a inqui&shy;<lb/>ritur, &amp; inuenitur ope Geometri&aelig;, cui illa &longs;ubiacet. </s>
          <s id="s.001112">Hic obiter notandum, <lb/>
Ari&longs;t. fateri manife&longs;t&egrave; Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>
per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s>
        </p>
        <p type="main">
          <s id="s.001113"><arrow.to.target n="marg51"/></s>
        </p>
        <p type="margin">
          <s id="s.001114"><margin.target id="marg51"/>51</s>
        </p>
        <p type="main">
          <s id="s.001115">Et po&longs;tea &lpar;<emph type="italics"/>Se habet autem &amp; ad Per&longs;pectiuam, vt h&aelig;c ad Geometriam, alia ad <lb/>hanc, vt quod e&longs;t de Iride ip&longs;um enim quod Naturalis e&longs;t &longs;cire, ip&longs;um ver&ograve; Prop&shy;<lb/>
ter quid Per&longs;pectiui<emph.end type="italics"/>&rpar; &longs;icut &longs;e habet, inquit, <expan abbr="&longs;ci&etilde;ti&agrave;">&longs;cienti&agrave;</expan> Naturalis de Iride ad Per&shy;<lb/>
&longs;pectiuam, ita Per&longs;pectiua ad Geometriam. </s>
          <s id="s.001116">qua ver&ograve; ratione cau&longs;a Iridis <lb/>
pertineat ad opticam, <expan abbr="atq;">atque</expan> hine tandem ad Geometriam, optim&egrave; patebit <lb/>
in Meteoris, cum ip&longs;ius demon&longs;trationem afferemus.</s>
        </p>
        <p type="main">
          <s id="s.001117"><arrow.to.target n="marg52"/></s>
        </p>
        <p type="margin">
          <s id="s.001118"><margin.target id="marg52"/>52</s>
        </p>
        <p type="main">
          <s id="s.001119">Tex. 37. &lpar;<emph type="italics"/>Vt &aelig;quicruri, &amp; Scaleno hoc, quod e&longs;t duobus rectis &aelig;quales habere <lb/>
&longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>&rpar; quid &longs;it habere tres &aelig;quales duobus rectis <lb/>
&longs;atis explicatum e&longs;t lib. r. </s>
          <s id="s.001120">Priorum &longs;ecto 3. cap. r. </s>
          <s id="s.001121">nunc igitur paraphra&longs;im <lb/>
&longs;olum huius loci dabo. </s>
          <s id="s.001122">Triangulo I&longs;o&longs;celi, &amp; Scaleno convenit pa&longs;&longs;io illa,<lb/>
habere tres angulos &aelig;quales duobus rectis angulis &longs;ecundum aliquod com&shy;


<pb pagenum="61" xlink:href="009/01/061.jpg"/>mune, quia illis competit, quatenus ambo &longs;unt figura qu&aelig;dam, ide&longs;t, qua&shy;<lb/>
tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com&shy;<lb/>
petit habere tres angulos &aelig;quales duobus rectis.</s>
        </p>
        <p type="main">
          <s id="s.001123"><arrow.to.target n="marg53"/></s>
        </p>
        <p type="margin">
          <s id="s.001124"><margin.target id="marg53"/>53</s>
        </p>
        <p type="main">
          <s id="s.001125">Tex. 38. &lpar;<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, hoc autem non idem <lb/>
vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>&rpar; Die&longs;is apud Mu&longs;icos e&longs;t <lb/>
pars Toni. </s>
          <s id="s.001126">Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>
mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s>
          <s id="s.001127">i&longs;tud interuallum <lb/>
diuidunt Mu&longs;ici primum in &longs;emitonia, non tamen &aelig;qualia, &longs;ed vnum maius <lb/>
altero. </s>
          <s id="s.001128">minus iterum in duas partes &aelig;quales &longs;ubdiuidunt, quarum <expan abbr="vtramq;">vtramque</expan> <lb/>
veteres harmonici die&longs;im dixerunt. </s>
          <s id="s.001129">&amp; h&etail;c die&longs;is e&longs;t minima vox ab eis con&shy;<lb/>
&longs;iderata; &amp; qu&aelig; prima cadit &longs;ub &longs;en&longs;um; &amp; propterea veluti &longs;implex prin&shy;<lb/>cipium, &amp; elementum, ex quo alia maiora interualla con&longs;tent; &amp; in quod <lb/>
re&longs;oluuntur. <foreign lang="greek">die/ois</foreign> porr&ograve; gr&aelig;c&egrave; valet inter alia, diui&longs;ionem. </s>
          <s id="s.001130">igitur interual&shy;<lb/>
lum i&longs;tud minimum dictum e&longs;t die&longs;is, quod &longs;it qu&aelig;dam diui&longs;io, &longs;eu &longs;egmen&shy;<lb/>tum Toni &lpar;<emph type="italics"/>Quemadmodum in pondere mina<emph.end type="italics"/>&rpar; qui de ponderibus antiquis tra&shy;<lb/>
ctant, a&longs;&longs;erunt, Minam fui&longs;&longs;e maiorem libra per &longs;emunciam, &aelig;quipondera&shy;<lb/>
bat enim centum drachmis: qu&aelig; refragantur huic loco. </s>
          <s id="s.001131">&longs;ed fort&egrave; <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>
Ari&longs;t. con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>
principium, cum &longs;ex millia minarum in Attico talento continerentur.</s>
        </p>
        <figure id="id.009.01.061.1.jpg" place="text" xlink:href="009/01/061/1.jpg"/>
        <p type="main">
          <s id="s.001132"><arrow.to.target n="marg54"/></s>
        </p>
        <p type="margin">
          <s id="s.001133"><margin.target id="marg54"/>54</s>
        </p>
        <p type="main">
          <s id="s.001134">Tex. 39. <emph type="italics"/>&lpar;Si enim quod duobus rectis ine&longs;t, non in <lb/>
quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>
&longs;cens, &amp;c.&rpar;<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>
bere tres angulos &aelig;quales duobus rectis conuenit <lb/>
&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>
nus triangulus e&longs;t, &amp;c. </s>
          <s id="s.001135">quid &longs;it habere tres &aelig;qua&shy;<lb/>
les duobus rectis, &amp;c. </s>
          <s id="s.001136">fus&egrave; explicatum e&longs;t in lib. 1. <lb/>
Priorum &longs;ecto 3. cap. 1. qu&ograve; te nunc mitto.</s>
        </p>
        <p type="main">
          <s id="s.001137"><arrow.to.target n="marg55"/></s>
        </p>
        <p type="margin">
          <s id="s.001138"><margin.target id="marg55"/>55</s>
        </p>
        <p type="main">
          <s id="s.001139">Po&longs;t pauca <emph type="italics"/>&lpar;Ine&longs;t omni triangulo hoc quod est <lb/>
duos, &amp;c.&rpar;<emph.end type="italics"/> ide&longs;t, h&aelig;c proprietas, qu&aelig; e&longs;t habere <lb/>
duos angulos rectos non actu, &longs;ed per &aelig;quiualen&shy;<lb/>
tiam trium angulorum trianguli. </s>
          <s id="s.001140">Vide qu&aelig; im&shy;<lb/>mediat&egrave; &longs;upra de hac re dixi, &amp; qu&ograve; te remi&longs;i.</s>
        </p>
        <p type="main">
          <s id="s.001141"><arrow.to.target n="marg56"/></s>
        </p>
        <p type="margin">
          <s id="s.001142"><margin.target id="marg56"/>56</s>
        </p>
        <p type="main">
          <s id="s.001143">Eodem tex <emph type="italics"/>&lpar;Quando igitur cogno&longs;cimus, quod <lb/>
quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc deficit, propier quid I&longs;o&longs;celes? </s>
          <s id="s.001144">quoniam trian&shy;<lb/>
gulus: &amp; hoc quoniam figura rectilinea, &amp;c.&rpar;<emph.end type="italics"/> exem&shy;<lb/>
plo geometrico vult o&longs;tendere demon&longs;trationem <lb/>
vniuer&longs;alem e&longs;&longs;e particulari pr&aelig;&longs;tantiorem: e&longs;t <lb/>
autem exemplum de pulcherrima, <expan abbr="atq;">atque</expan> admira&shy;<lb/>
bili proprietate, qu&aelig; omnibus figuris rectilineis <lb/>
conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figur&aelig; rectili&shy;<lb/>ne&aelig; anguli externi omnes &longs;imul &longs;umpti, &longs;unt &aelig;qu<lb/>
les quatuor rectis angulis, qu&aelig; affectio demon&shy;<lb/>
&longs;tratur in &longs;cholio 32. primi Elem. dicuntur autem <lb/>
anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo pr&aelig;&longs;enti anguli externi &longs;unt, B D C,<pb pagenum="62" xlink:href="009/01/062.jpg"/>D F E, F B A, ita vt qu&aelig;libet figura tot angulos externos &longs;ortiatur, quot <lb/>
habet latera; cum exproductis lateribus oriantur. </s>
          <s id="s.001145">Vt autem propo&longs;itio ve&shy;<lb/>
rificetur, &longs;ingula latera ordinatim &longs;unt producenda, hoc e&longs;t, ver&longs;us eandem <lb/>
partem, vt in figuris appo&longs;itis vides. </s>
          <s id="s.001146">Qu&aelig;uis igitur figura rectilinea, &longs;iue <lb/>
trilatera &longs;it, &longs;iue quadrilatera, vel etiam millelatera, &amp; proinde mille quo&shy;<lb/>
que angulos externos habeat, hanc tamen mirabilem proprietatem &lpar;quod <lb/>
vix credi pote&longs;t&rpar; po&longs;&longs;idet, vt omnes illi anguli externi &longs;imul &longs;int &aelig;quales <lb/>
quatuor rectis angulis. </s>
          <s id="s.001147">vnde tres externi anguli trianguli, &amp; quatuor exter&shy;<lb/>
ni quadranguli, &amp; quinque externi <expan abbr="p&etilde;tagoni">pentagoni</expan>, &amp;c. </s>
          <s id="s.001148">&longs;unt &aelig;quales quatuor tan&shy;<lb/>
tum rectis, nec aliter res &longs;e habet in figura millelatera. </s>
          <s id="s.001149">Ex quo fit, vt an&shy;<lb/>guli externi cuiu&longs;uis figur&aelig; &longs;int &aelig;quales angulis omnibus externis alterius <lb/>
cuiu&longs;libet figur&aelig;. </s>
          <s id="s.001150">Ari&longs;t. igitur inquit, quando cogno&longs;cimus, quod quatuor <lb/>
angulis rectis &longs;unt &aelig;quales exteriores omnes anguli alicuius figur&aelig;, quo&shy;<lb/>
niam figura illa e&longs;t triangulum &longs;calenum, adhuc talis cognitio e&longs;t defecti&shy;<lb/>
ua, quia non illi competit illa pa&longs;&longs;io, quia &longs;it triangulum &longs;calenum, neque <lb/>
competit &longs;caleno, quia &longs;it triangulum; &longs;ed his omnibus competit, quia &longs;unt <lb/>
figur&aelig; rectiline&aelig;, cui h&aelig;c proprietas ine&longs;t primo, &amp; vniuer&longs;aliter: qui igi&shy;<lb/>
tur &longs;cit, &longs;calenum habere pr&aelig;dictam affectionem, ex eo, quod &longs;it figura re&shy;<lb/>
ctilinea, perfectius &longs;cit, quia nihil amplius qu&aelig;ri pote&longs;t, quia illa figura re&shy;<lb/>
ctilinea illud vniuer&longs;ale e&longs;t, cui primo competit; reliquis autem per illam. <lb/>
</s>
          <s id="s.001151">qui igitur vniuer&longs;ale &longs;cit, perfectius &longs;cit; quod volebat Ari&longs;t. demon&longs;trare.</s>
        </p>
        <p type="main">
          <s id="s.001152"><arrow.to.target n="marg57"/></s>
        </p>
        <p type="margin">
          <s id="s.001153"><margin.target id="marg57"/>57</s>
        </p>
        <p type="main">
          <s id="s.001154">Eodem tex. <emph type="italics"/>&lpar;Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>
&aelig;quales&rpar;<emph.end type="italics"/> nihil frequentius. </s>
          <s id="s.001155">vide &longs;upra lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001156"><arrow.to.target n="marg58"/></s>
        </p>
        <p type="margin">
          <s id="s.001157"><margin.target id="marg58"/>58</s>
        </p>
        <p type="main">
          <s id="s.001158">Tex. 43. <emph type="italics"/>&lpar;Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/>
&aelig;quales habet angulos&rpar;<emph.end type="italics"/> vide &longs;upra lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001159"><arrow.to.target n="marg59"/></s>
        </p>
        <p type="margin">
          <s id="s.001160"><margin.target id="marg59"/>59</s>
        </p>
        <p type="main">
          <s id="s.001161">Po&longs;t pauca <emph type="italics"/>&lpar;Quare &amp; &longs;i &longs;upra Lunam e&longs;&longs;emus, &amp; videremus obiectam terram, <lb/>
non <expan abbr="vtiq;">vtique</expan> &longs;ciremus cau&longs;am eclyp&longs;is&rpar;<emph.end type="italics"/> loquitur de defectu Lun&aelig;, qui fit, quando <lb/>
terra inter Lunam, &amp; Solem po&longs;ita, impedit, ne lumen Solis feratur in Lu&shy;<lb/>
nam, &longs;ed efficit, vt vmbra ip&longs;ius terr&aelig; eam contegat.</s>
        </p>
        <p type="main">
          <s id="s.001162"><arrow.to.target n="marg60"/></s>
        </p>
        <p type="margin">
          <s id="s.001163"><margin.target id="marg60"/>60</s>
        </p>
        <figure id="id.009.01.062.1.jpg" place="text" xlink:href="009/01/062/1.jpg"/>
        <p type="main">
          <s id="s.001164">Et paulo po&longs;t <emph type="italics"/>&lpar;Quemadmod&ubreve;m &longs;i vi&shy;<lb/>
trum perforatum videremus, &amp; lumen <lb/>
permeans, planum vtique e&longs;&longs;et propter <lb/>
quid comburit&rpar;<emph.end type="italics"/> Ioquitur de ea com&shy;<lb/>
bu&longs;tione, cu&aelig; fit per refractionem <lb/>
media &longs;ph&aelig;ra vitrea. </s>
          <s id="s.001165">de qua Vitel&shy;<lb/>
lio propo&longs;. </s>
          <s id="s.001166">48. decimi libri; non au&shy;<lb/>
tem de ea, qu&aelig; fit per reflexionem <lb/>
ex &longs;peculo concauo quando combu&shy;<lb/>
&longs;tio fit per refractionem, cau&longs;atur &agrave; <lb/>
radijs Solis vitrum permeantibus, <lb/>
in quo ita franguntur, vt egredien&shy;<lb/>
tes &egrave; vitro &longs;imul vniantur, ex qua <lb/>
vnione ita calor intenditur, vt ibi <lb/>
comburat. </s>
          <s id="s.001167">vt in appo&longs;ita figura cer&shy;<lb/>
nere facile e&longs;t; in qua radij &agrave; Sole <lb/>
manentes, &longs;ph&aelig;ram vitream perua&shy;


<pb pagenum="63" xlink:href="009/01/063.jpg"/>dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;&shy;<lb/>
&longs;int, &longs;i quid combu&longs;tibile occurrat, comburere. </s>
          <s id="s.001168">Si igitur, inquit Ari&longs;t. vide&shy;<lb/>
remus illos radios &longs;ic permeare, &amp; refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro&shy;<lb/>
pter quid incendant.<lb/>
<arrow.to.target n="marg61"/></s>
        </p>
        <p type="margin">
          <s id="s.001169"><margin.target id="marg61"/>61</s>
        </p>
        <p type="main">
          <s id="s.001170">Ad finem tex. <!-- REMOVE S-->43. <emph type="italics"/>&lpar;Principia enim duplicia &longs;unt, ex quibus, &amp; circa quod: <lb/>
qu&aelig; quidem igitur, ex quibus, communia &longs;unt: qu&aelig; autem circa quod propria, vt <lb/>
numerus, magnitudo&rpar;<emph.end type="italics"/> nonnulli codices corrupt&egrave; legunt &lpar;vt numerus magni&shy;<lb/>
tudine&rpar; &longs;ed ex gr&aelig;co tex. <!-- REMOVE S-->corrigendi &longs;unt, vti fecimus. </s>
          <s id="s.001171">C&aelig;terum per prin&shy;<lb/>
cipia, ex quibus intelligit Dignitates, quia ex illis di&longs;currimus. </s>
          <s id="s.001172">per princi&shy;<lb/>
pia ver&ograve; circa quod, intelligit Definitiones, quibus, vt apparet apud Eucli&shy;<lb/>
dem, explicatur &longs;ubiectum, circa quod &longs;cientia ver&longs;atur; vt in definitioni&shy;<lb/>
bus primi Elem. docemur, quid &longs;it linea, quid triangulum, quid circulus, <lb/>
quid magnitudines reliqu&aelig;, qu&aelig; &longs;unt materia, circa quam Geometria &longs;pe&shy;<lb/>
culatur. </s>
          <s id="s.001173">In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>
merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>
rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>
metica tractatur.</s>
        </p>
        <p type="main">
          <s id="s.001174"><arrow.to.target n="marg62"/></s>
        </p>
        <p type="margin">
          <s id="s.001175"><margin.target id="marg62"/>62</s>
        </p>
        <p type="main">
          <s id="s.001176">Tex. 44. <emph type="italics"/>&lpar;Commen&longs;urabilem namq; e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t&rpar;<emph.end type="italics"/><lb/>
vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>
lib. 1. Priorum &longs;ecto 1. cap. 23. ait igitur Ari&longs;t. ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>
metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>
qua &longs;unt Logica.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001177"><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001178"><arrow.to.target n="marg63"/></s>
        </p>
        <p type="margin">
          <s id="s.001179"><margin.target id="marg63"/>63</s>
        </p>
        <p type="main">
          <s id="s.001180">Tex. 1. <emph type="italics"/>&lpar;Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>
ram, aut Solem, aut triangulum; aliquid ver&ograve; defectum, &aelig;qualitatem, <lb/>
in&aelig;qualitatem. </s>
          <s id="s.001181">&longs;i in medio, aut non&rpar;<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>
quatenus ad Mathematicum attinet, optim&egrave; declarat. </s>
          <s id="s.001182">In qu&aelig;&shy;<lb/>
&longs;tionibus, &amp; demon&longs;trationibus duo &longs;unt, &longs;ubiectum, &amp; <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan>, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/>
cau&longs;&aelig; exi&longs;tunt, &amp; qu&aelig;runtur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->Luna, terra, Sol, &amp; triangulum &longs;unt &longs;u&shy;<lb/>
biectum in demon&longs;tratione, quorum pr&aelig;dicata &longs;unt, Lun&aelig; quidem, &amp; So&shy;<lb/>
lis, eclyp&longs;is. </s>
          <s id="s.001183">terr&aelig; autem e&longs;&longs;e in medio mundi, quod ab A&longs;tronomis ratione <lb/>
ab eclyp&longs;ibus de&longs;umpta, euidentius, quam ab alio quoquam demon&longs;tratur, <lb/>vt patet ex tractatu de &longs;ph&aelig;ra. </s>
          <s id="s.001184">in quo Zabarella non probatur, qui &longs;olum <lb/>
ait, terram e&longs;&longs;e in medio mundi, &agrave; Phy&longs;icis demon&longs;trari. </s>
          <s id="s.001185"><expan abbr="tri&atilde;gulum">triangulum</expan> autem, <lb/>
&longs;eu angulorum ip&longs;ius <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan> e&longs;t &aelig;qualitas, &amp; in&aelig;qualitas: vt cum in 32. <lb/>
primi Elem. demon&longs;trat Euclides, omne triangulum habere tres angulos <lb/>
&aelig;quales duobus rectis.</s>
        </p>
        <p type="main">
          <s id="s.001186"><arrow.to.target n="marg64"/></s>
        </p>
        <p type="margin">
          <s id="s.001187"><margin.target id="marg64"/>64</s>
        </p>
        <p type="main">
          <s id="s.001188">Ibidem <emph type="italics"/>&lpar;Quid e&longs;t con&longs;onantia? </s>
          <s id="s.001189">ratio numerorum in acuto, &amp; graui, &amp;c&rpar;<emph.end type="italics"/> tan&shy;<lb/>
git breuiter Ari&longs;t. cau&longs;am formalem con&longs;onanti&aelig;, &amp; con&longs;equenter defini&shy;<lb/>
tionem ip&longs;ius. </s>
          <s id="s.001190">definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan&shy;<lb/>
tia e&longs;t compo&longs;itio &longs;oni grauis, &amp; acuti, qu&aelig; &longs;uauiter auribus accidit; &amp; quo&shy;<lb/>
rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>
quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>
vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;cunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64" xlink:href="009/01/064.jpg"/>ex <expan abbr="quinq;">quinque</expan> pr&aelig;dictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnus <lb/>
tantum &longs;onus efficiatur; &longs;onus ille erit concordans, &amp; auribus gratus. </s>
          <s id="s.001191"><expan abbr="atq;">atque</expan> <lb/>
h&aelig;c e&longs;t &longs;ententia pri&longs;corum pr&aelig;&longs;ertim Pythagoreorum, qui propterea di&shy;<lb/>
cebant non licere Mu&longs;ico vltra quaternarium pertran&longs;ire, e&ograve; quod &longs;ol&aelig; pro&shy;<lb/>
portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/>
ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per&shy;<lb/>
<figure id="id.009.01.064.1.jpg" place="text" xlink:href="009/01/064/1.jpg"/><lb/>
cipiamus, accipe exemplum. </s>
          <s id="s.001192">Sint du&aelig; chord&aelig; <lb/>
A, &amp; B, &aelig;qualis cra&longs;&longs;itici, &amp; &aelig;qu&egrave; ten&longs;&aelig;. </s>
          <s id="s.001193">qua&shy;<lb/>
rum A, dupla &longs;it ip&longs;ius B, quia igitur corpora <lb/>
&longs;onantia &longs;unt in dupla proportione, erunt pa&shy;<lb/>
riter eorum &longs;oni in ratione dupla &lpar;vt patet ex <lb/>
principijs harmonic&aelig;&rpar; hoc e&longs;t, <expan abbr="eor&utilde;">eorum</expan> &longs;oni erunt, <lb/>
vt 2. ad 1. quia &longs;cilicet &longs;onus maioris chord&aelig; A, erit duplus ad &longs;onum mi&shy;<lb/>
noris chord&aelig; B. hoc e&longs;t, erit, vt 2. ad 1. &amp; propterea, &longs;i &longs;imul amb&aelig; chord&aelig; <lb/>
pul&longs;entur, &longs;onus, quem ex duobus mixtum edent, con&longs;onans, <expan abbr="atq;">atque</expan> grati&longs;&longs;i&shy;<lb/>
mus auribus no&longs;tris perueniet. </s>
          <s id="s.001194">huiu&longs;modi porr&ograve; con&longs;onantia, qu&aelig; e&longs;t in <lb/>
proportione dupla, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan> omnium &longs;uaui&longs;&longs;ima e&longs;t, &agrave; gr&aelig;cis dicebatur Dia&shy;<lb/>pa&longs;on. </s>
          <s id="s.001195"><expan abbr="atq;">atque</expan> h&aelig;c in pr&aelig;&longs;entia &longs;ufficiant, cum plura de his ad &longs;ectionem pro&shy;<lb/>
blematum 19. qu&aelig; tota e&longs;t de Mu&longs;ica, dicenda &longs;int.</s>
        </p>
        <p type="main">
          <s id="s.001196"><arrow.to.target n="marg65"/></s>
        </p>
        <p type="margin">
          <s id="s.001197"><margin.target id="marg65"/>65</s>
        </p>
        <p type="main">
          <s id="s.001198">Tex. 2. <emph type="italics"/>&lpar;Vt quod omnis triangulus duobus rectis &aelig;quales habet&rpar;<emph.end type="italics"/> vide anno&shy;<lb/>
tata lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001199"><arrow.to.target n="marg66"/></s>
        </p>
        <p type="margin">
          <s id="s.001200"><margin.target id="marg66"/>66</s>
        </p>
        <p type="main">
          <s id="s.001201">Eodem tex. <emph type="italics"/>&lpar;Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>
ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar&rpar;<emph.end type="italics"/> alludit ad de&shy;<lb/>
finitiones 7. Elem. vbi agitur de numeris. </s>
          <s id="s.001202">Qu&aelig; ver&ograve; hoc loco de principijs <lb/>
dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>
Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>
quibus &longs;tatim demon&longs;trationes deriuantur.</s>
        </p>
        <p type="main">
          <s id="s.001203"><arrow.to.target n="marg67"/></s>
        </p>
        <p type="margin">
          <s id="s.001204"><margin.target id="marg67"/>67</s>
        </p>
        <p type="main">
          <s id="s.001205">Et paulo po&longs;t <emph type="italics"/>&lpar;<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>
gura planum&rpar;<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>
lus, cuius definitio e&longs;t inter definitiones primi Elem. 15. &amp; e&longs;t huiu&longs;modi: <lb/>
circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>
pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>
dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>
non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>
&longs;eu plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>
plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>
plurim&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.001206"><arrow.to.target n="marg68"/></s>
        </p>
        <p type="margin">
          <s id="s.001207"><margin.target id="marg68"/>68</s>
        </p>
        <p type="main">
          <s id="s.001208">Ibidem <emph type="italics"/>&lpar;Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>
bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it&rpar;<emph.end type="italics"/> ex dictis lib. 1. Priorum &longs;ecto <lb/>
3. cap. 1. petatur huius loci declaratio.</s>
        </p>
        <p type="main">
          <s id="s.001209"><arrow.to.target n="marg69"/></s>
        </p>
        <p type="margin">
          <s id="s.001210"><margin.target id="marg69"/>69</s>
        </p>
        <p type="main">
          <s id="s.001211">Tex. 7. <emph type="italics"/>&lpar;Quid enim &longs;ignificat triangulum, accipit Geometra&rpar;<emph.end type="italics"/> vt manife&longs;tum <lb/>
e&longs;t in 20. definitione primi Elem.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001212"><arrow.to.target n="marg70"/></s>
        </p>
        <p type="margin">
          <s id="s.001213"><margin.target id="marg70"/>70</s>
        </p>
        <p type="main">
          <s id="s.001214">Ibidem <emph type="italics"/>&lpar;Quod autem &longs;it, monstrat&rpar;<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>
tione</expan> primi Elem. vbi triangulum &aelig;quilaterum con&longs;truit, &amp; po&longs;tea probat <lb/>
illud e&longs;&longs;e triangulum &aelig;quilaterum. </s>
          <s id="s.001215">Certum tamen e&longs;t, Geometram &longs;uppo&shy;<lb/>
nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur,


<pb pagenum="65" xlink:href="009/01/065.jpg"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trui</expan>, <lb/>
&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>
Euclidis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001216"><arrow.to.target n="marg71"/></s>
        </p>
        <p type="margin">
          <s id="s.001217"><margin.target id="marg71"/>71</s>
        </p>
        <p type="main">
          <s id="s.001218">Tex. 11. <emph type="italics"/>&lpar;Manife&longs;tum autem, &amp; &longs;ic, propter quid e&longs;t rectus in &longs;emicirculo&rpar;<emph.end type="italics"/><lb/>
affert exemplum demon&longs;trationis per cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; vti &longs;olet ex <lb/>
Mathematicis petitum, e&longs;t enim apud Euclidem 31. demon&longs;tratio 3. Elem. <lb/>
vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </s>
          <s id="s.001219">Vbi aduertendum e&longs;t <lb/>
propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>
&longs;ecundum innuit hoc loco Ari&longs;t. cui a&longs;cripta e&longs;t figura &longs;imilis huic no&longs;tr&aelig;; <lb/>
in editione Clauiana. </s>
          <s id="s.001220">quod fort&egrave; non ben&egrave; aduertens Iacobus Zabarella, <lb/>
alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi&shy;<lb/>
dere medium Euclidian&aelig; demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/>
tamen nos mox aperiemus. </s>
          <s id="s.001221">per angulum in &longs;emicirculo intelligas eum, qui <lb/>
fit &agrave; lineis ductis ab extremitatibus diametri, &amp; &longs;imul in quoduis punctum <lb/>
<figure id="id.009.01.065.1.jpg" place="text" xlink:href="009/01/065/1.jpg"/><lb/>
circumferenti&aelig; coeuntibus, vt in figura <lb/>
pr&aelig;&longs;enti vides lineas A C, B C, ad C, pun&shy;<lb/>
ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>
A C B, qui dicitur angulus in &longs;emicircu&shy;<lb/>
lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A&shy;<lb/>
C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;an&egrave; mirabilis h&aelig;c &longs;emicirculi <lb/>
proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/>
periph&aelig;ria &longs;umptum fuerit, &longs;emper ta&shy;<lb/>
men angulus A C B, fiat rectus. </s>
          <s id="s.001222">quod Euclides eodem pror&longs;us medio, quod <lb/>
Ari&longs;t. hic innuit, hoc modo demon&longs;trat. </s>
          <s id="s.001223">ducta enim recta D C, &agrave; centro D, <lb/>
ad punctum C, exurgunt duo l&longs;o&longs;celia triangula A D C, C D B, ergo per <lb/>
5. primi, anguli D C A, D A C, &longs;unt &aelig;quales: pariter anguli D C B, D B C, <lb/>
&aelig;quales &longs;unt. </s>
          <s id="s.001224">&amp; quia per 32. primi, anguli D A C, D C A, &longs;imul &longs;unt &aelig;qua&shy;<lb/>
les angulo externo C D B, &amp; inter &longs;e &aelig;quales, erit angulus A C D, dimidium <lb/>
anguli C D B. eadem ratione probatur angulus D C B, e&longs;&longs;e dimidium an&shy;<lb/>
guli C D A. ergo totus angulus A C B, dimidium erit duorum angulorum <lb/>
A D C, C D B, qui per 13. primi, &longs;unt vel recti, vel duobus rectis <expan abbr="&aelig;quiual&etilde;t">&aelig;quiualent</expan>. <lb/>
</s>
          <s id="s.001225">Sequitur igitur, angulum A C B, in &longs;emicirculo e&longs;&longs;e dimidium duorum re&shy;<lb/>
ctorum; &amp; quia omnes recti &longs;unt &aelig;quales, &longs;equitur dimidium duorum re&shy;<lb/>
ctorum, nihil aliud e&longs;&longs;e, quam vnum rectum angulum, ergo angulus in &longs;e&shy;<lb/>
micirculo, cum &longs;it &longs;emi&longs;&longs;is duorum <expan abbr="rector&utilde;">rectorum</expan>, erit vnus rectus angules; quod <lb/>
erat probandum. </s>
          <s id="s.001226">ex quibus vides medium illud, quod Ari&longs;t. a&longs;&longs;ump&longs;it, e&longs;&longs;e <lb/>
omnino idem cum eo, quo Euclides vtitur, &longs;cilicet, e&longs;&longs;e dimidium duorum <lb/>
rectorum, &amp; propterea e&longs;&longs;e rectum: quod etiam medium in toto demon&shy;<lb/>
&longs;trationis decur&longs;u e&longs;t vltimum, &amp; principale, quod proxim&egrave; conclu&longs;ionem <lb/>
attingit, &amp; propterea dici meretur e&longs;&longs;e medium huius demon&longs;trationis. <lb/>
</s>
          <s id="s.001227">C&aelig;terum, quod medium i&longs;tud &longs;it in genere cau&longs;&aelig; materialis, patet ex eo, <lb/>
quod e&longs;t, e&longs;&longs;e dimidium; nam e&longs;&longs;e dimidium, vel e&longs;&longs;e tertiam partem, &amp; &longs;i&shy;<lb/>
milia, nihil aliud e&longs;t, quam e&longs;&longs;e partem; e&longs;&longs;e autem partem e&longs;t e&longs;&longs;e materiam <lb/>
totius, etiam ex &longs;ententia ip&longs;ius Ari&longs;t. ex hac pr&aelig;terea materia conflatur <lb/>
definitio minoris extremi, vel &longs;ubiecti; dum dicitur, angulus in &longs;emicircu&shy;<lb/>
lo e&longs;t dimidium duorum rectorum. </s>
          <s id="s.001228">&longs;yllogi&longs;mus enim reducitur tandem ad <pb pagenum="66" xlink:href="009/01/066.jpg"/>hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir&shy;<lb/>
culo e&longs;t dimidium duorum <expan abbr="rector&utilde;">rectorum</expan>, ergo angulus in &longs;emicirculo e&longs;t rectus. <lb/>
</s>
          <s id="s.001229">vides in minori propo&longs;itione contineri definitionem &longs;ubiecti materialem? <lb/>
</s>
          <s id="s.001230">ade&ograve; vt h&aelig;c &longs;it demon&longs;tratio omnibus numeris ab&longs;oluta per cau&longs;am mate&shy;<lb/>
rialem, vt ben&egrave; &longs;entit Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.001231">Reliqua ad logicum pertinent, etiam&longs;i per cha&shy;<lb/>
racteres more mathematicorum exponantur.</s>
        </p>
        <p type="main">
          <s id="s.001232"><arrow.to.target n="marg72"/></s>
        </p>
        <p type="margin">
          <s id="s.001233"><margin.target id="marg72"/>72</s>
        </p>
        <p type="main">
          <s id="s.001234">Tex. 24. <emph type="italics"/>&lpar;Vt propter quid re&longs;onat? </s>
          <s id="s.001235">aut propter quid apparet? </s>
          <s id="s.001236">aut propter quid <lb/>
Iris? <!-- KEEP S--></s>
          <s id="s.001237">omnia enim h&aelig;c idem problemata &longs;unt genere, omnia enim &longs;unt refractio, &longs;ed <lb/>
&longs;pecie altera&rpar;<emph.end type="italics"/> propter quid re&longs;onat? </s>
          <s id="s.001238">&longs;cilicet echo; propter quid apparet? <lb/>
</s>
          <s id="s.001239">&longs;cilicet imago in &longs;peculo. </s>
          <s id="s.001240">dicit cau&longs;am echo, imaginis in &longs;peculo, &amp; iridis <lb/>
in nubibus e&longs;&longs;e eandem; nimirum refractionem; quamuis tres ill&aelig; refractio&shy;<lb/>
nes, &longs;eu; vt melius loquamur, reflexiones differant &longs;pecie ab inuicem, illa <lb/>
enim e&longs;t repercu&longs;&longs;io vocis; h&aelig;c reflexio &longs;peciei vi&longs;ibilis ex corpore ter&longs;o; <lb/>
i&longs;ta <expan abbr="deniq;">denique</expan> radiorum Solis ex nube rorida in &longs;tato angulo repercu&longs;&longs;us. </s>
          <s id="s.001241">qua <lb/>
ratione autem i&longs;ta omnia fiant, longum e&longs;&longs;et exponere, &amp; ab intelligentia <lb/>
huius loci fort&egrave; alienum. </s>
          <s id="s.001242">Illud tamen non pr&aelig;tereundum, quod &longs;i propri&egrave; <lb/>
cum Per&longs;pectiuis loqui velimus, dicendum e&longs;&longs;e, omnia illa e&longs;&longs;e reflexionem, <lb/>
non refractionem. </s>
          <s id="s.001243">nam reflexio e&longs;t, quando linea vi&longs;ualis, per quam fertur <lb/>&longs;pecies in aliquod corpus ter&longs;um, impingit, ex quo deinde ad oculos refle&shy;<lb/>
ctitur. </s>
          <s id="s.001244">refractio tunc e&longs;t, quando &longs;pecies obiecti vi&longs;ibilis tran&longs;it per media <lb/>
diuer&longs;&aelig; cra&longs;&longs;itiei., vt quando &longs;pecies lapilli per aquam prim&ugrave;m, deinde per <lb/>aerem means ad oculum peruenit; tunc enim linea, per quam &longs;pecies pro&shy;<lb/>
greditur, frangitur in confinio aqu&aelig;, &amp; aeris, ita vt &longs;pecies non per vnicam <lb/>
lineam rectam, &longs;ed per fractam, &longs;eu refractam in confinio illo, oculis tan&shy;<lb/>
dem accidat.</s>
        </p>
        <p type="main">
          <s id="s.001245">In fine textus <emph type="italics"/>&lpar;Quoniam Luna deficit&rpar;<emph.end type="italics"/> non intelligit defectum illum, qui <lb/>
eclyp&longs;is appellatur, &longs;ed ilium, quo paulatim lumen Lun&aelig; minus oculis no&shy;<lb/>
&longs;tris apparet: decre&longs;cente enim Luna &longs;olent humida augeri.</s>
        </p>
        <p type="main">
          <s id="s.001246"><arrow.to.target n="marg73"/></s>
        </p>
        <p type="margin">
          <s id="s.001247"><margin.target id="marg73"/>73</s>
        </p>
        <p type="main">
          <s id="s.001248">Tex. 25. <emph type="italics"/>&lpar;Vt propter quid, &amp; permutatim proportionale? </s>
          <s id="s.001249">&amp; c.<emph.end type="italics"/>&rpar; quod quan&shy;<lb/>
titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>
proportionales explicatum e&longs;t ad tex. <!-- REMOVE S-->13. primi Po&longs;ter. qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>
ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s>
          <s id="s.001250">Illud autem commune propter <lb/>
quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>
e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>
neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>
qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>
portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>
nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>
tionalia.</s>
        </p>
        <p type="main">
          <s id="s.001251"><arrow.to.target n="marg74"/></s>
        </p>
        <p type="margin">
          <s id="s.001252"><margin.target id="marg74"/>74</s>
        </p>
        <p type="main">
          <s id="s.001253">Ibidem &lpar;<emph type="italics"/>Hic quidem forta&longs;&longs;e proportionaliter habere latera, &amp; angulos<emph.end type="italics"/>&rpar; vult <lb/>indicare, in quonam con&longs;i&longs;tat &longs;imilitudo inter duas figuras rectilineas geo&shy;<lb/>
metricas, quam &longs;imilitudinem Euclides definit. </s>
          <s id="s.001254">1. &longs;exti, &longs;ic explicat: &longs;imi&shy;<lb/>
les figur&aelig; rectil&iacute;ne&aelig; &longs;unt; qu&aelig; &amp; angulos &longs;ingulos, &longs;ingulis angulis &aelig;quales <lb/>
habent, <expan abbr="atq;">atque</expan> etiam latera, qu&aelig; circa angulos &aelig;quales &longs;unt proportionalia. <lb/>
</s>
          <s id="s.001255">vt &longs;i duo triangula appo&longs;ita habeant angulos &aelig;quales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. &amp; pr&aelig;terea latera, qu&aelig; &longs;unt <pb pagenum="67" xlink:href="009/01/067.jpg"/><figure id="id.009.01.067.1.jpg" place="text" xlink:href="009/01/067/1.jpg"/><lb/>
circa angulos &aelig;quales, v. <!-- REMOVE S-->g. <!-- REMOVE S-->circa an&shy;<lb/>
gulos A, &amp; D, habeant proportiona&shy;<lb/>
lia, hoc e&longs;t, vt latus A B, ad latus A C; <lb/>
ita &longs;it latus D E, ad latus D F; &amp; &longs;ic de <lb/>
lateribus alijs circa reliquos angulos <lb/>
&aelig;quales; erunt tunc pr&aelig;dicta duo tri&shy;<lb/>
angula &longs;imilia.</s>
        </p>
        <p type="main">
          <s id="s.001256"><arrow.to.target n="marg75"/></s>
        </p>
        <p type="margin">
          <s id="s.001257"><margin.target id="marg75"/>75</s>
        </p>
        <p type="main">
          <s id="s.001258">Ibidem &lpar;<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>&rpar; ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>
gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>
hac re ad tex. <!-- REMOVE S-->39. &longs;ecundi Po&longs;ter. qu&aelig; huic pariter loco &longs;atisfaciunt.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001259"><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.001260"><emph type="italics"/>Ex Primo Libro.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001261"><arrow.to.target n="marg76"/></s>
        </p>
        <p type="margin">
          <s id="s.001262"><margin.target id="marg76"/>76</s>
        </p>
        <p type="main">
          <s id="s.001263">Cap. 13. &lpar;<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>&rpar; vide <lb/>
qu&aelig; de hac re &longs;crip&longs;i lib. 1. Priorum &longs;ecto 1. cap. 23.</s>
        </p>
        <p type="main">
          <s id="s.001264"><arrow.to.target n="marg77"/></s>
        </p>
        <p type="margin">
          <s id="s.001265"><margin.target id="marg77"/>77</s>
        </p>
        <p type="main">
          <s id="s.001266">Eodem cap. &lpar;<emph type="italics"/>Similiter autem &amp; acutum; non enim idem &longs;impliciter <lb/>
in omnibus dicitur: nam vox acuta quidem velox &lpar;&longs;icut dicunt, qui &longs;e&shy;<lb/>cundum numeros harmonici &longs;unt&rpar; angulus autem acutus, qui minor e&longs;t recto; gla&shy;<lb/>
dius ver&ograve;, qui e&longs;t anguli acuti<emph.end type="italics"/>&rpar; affert tres &longs;pecies acuti, aliud dicens e&longs;&longs;e acu&shy;<lb/>
tum, quod e&longs;t in voce acuta; aliud, quod e&longs;t in angulo acuto: aliud denique, <lb/>
quod e&longs;t in gladio acuto horum enim trium acumen diuer&longs;o modo &longs;e habet. <lb/>
</s>
          <s id="s.001267">nam acumen vocis, &amp; &longs;oni ex celeritate motus, qua aer percu&longs;&longs;us impelli&shy;<lb/>
tur; grauitatem autem ex tarditate oriri tradiderunt antiqui Mu&longs;ici om&shy;<lb/>
nes: quamuis non ex &longs;ola celeritate, &amp; tarditate, &longs;ed ex alijs etiam cau&longs;is <lb/>
oriri po&longs;&longs;e voluerint. </s>
          <s id="s.001268">Primus <expan abbr="omni&utilde;">omnium</expan> Architas Tarentinus, vt e&longs;t apud Por&shy;<lb/>
phirium in harmonicis Ptol&aelig;mei, &amp; Zarlinum pag. </s>
          <s id="s.001269">58. complem. </s>
          <s id="s.001270">mu&longs;ica&shy;<lb/>
lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/>
<expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>
ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>
num grauem, vt experientia docet. </s>
          <s id="s.001271">Ptol&aelig;meus deinde lib. 1. cap. 3. Harm. <lb/>
<!-- REMOVE S-->cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>
tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>
berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>
aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>
acutiorem &longs;onum reddet. </s>
          <s id="s.001272">h&aelig;c ille. </s>
          <s id="s.001273">videmus etiam, quod cann&aelig; organo&shy;<lb/>
rum maiores cum plus aeris moueant, &amp; idcirco tardius, &longs;onum grauiorem <lb/>
emittunt, qu&agrave;m cann&aelig; graciliores, qu&aelig; quia parum aeris cient, &amp; ideo ce&shy;<lb/>
lerius, &longs;onum acutum edunt. </s>
          <s id="s.001274">ab hac &longs;ententia po&longs;teriores Mu&longs;ici non recel&longs;<lb/>&longs;erunt, vt videre e&longs;t apud Zarlinum.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001275">In quo po&longs;tea con&longs;i&longs;tat ratio acuti anguli, explicat <expan abbr="induc&etilde;s">inducens</expan> definitionem <lb/>
ip&longs;ius, qu&aelig; e&longs;t inter definitiones primi Elem. huiu&longs;modi, Angulus acutus <lb/>
e&longs;t, qui minor recto e&longs;t. </s>
          <s id="s.001276">Demum explicat, cur nam gladius dicatur acutus, <lb/>
quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>
ficies &longs;imul in acie gladij concurrentes efficiunt.</s>
        </p>
        <pb pagenum="68" xlink:href="009/01/068.jpg"/>
        <p type="main">
          <s id="s.001277"><arrow.to.target n="marg78"/></s>
        </p>
        <p type="margin">
          <s id="s.001278"><margin.target id="marg78"/>78</s>
        </p>
        <p type="main">
          <s id="s.001279">Eodem cap. &lpar;<emph type="italics"/>Rur&longs;um &longs;i eorundem; qu&aelig; &longs;unt &longs;ub eodem nomine diuer&longs;&aelig; diffe&shy;<lb/>
renti&aelig; &longs;unt; vt coloris, qui e&longs;t in corporibus, &amp; in melodijs<emph.end type="italics"/>&rpar; veteres Mu&longs;ici can&shy;<lb/>
tilenas omnes ad tria genera reuocarunt, videlicet Enharmonicum, Chro&shy;<lb/>maticum, &amp; Diatonicum; qu&aelig; di&longs;tinguebantur inuicem ex varia diui&longs;ione <lb/>interuallorum, ex quibus ip&longs;orum Monochordia con&longs;tabant: &longs;iue ex varijs <lb/>
vocum interuallis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->quia in vno continebantur plures toni, vt in Diato&shy;<lb/>
nico; in alio plures die&longs;es, vt in Enharmonico; in tertio ver&ograve; plura &longs;emito&shy;<lb/>
nia, vt in Chromatico: qu&aelig; vox deducitur &agrave; chroma, gr&aelig;co, quod latinis <lb/>
e&longs;t color; quare Chromaticum latin&egrave; redditur coloratum. </s>
          <s id="s.001280">Hic e&longs;t igitur <lb/>
color ille, quem hic Ari&longs;t. innuit. </s>
          <s id="s.001281">quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>
batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>
neribus digno&longs;ceretur. quam con&longs;uetudinem exi&longs;timat Zarlinus cap. 46. &longs;e&shy;<lb/>
cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>
deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>
&longs;unt, colore nigro tinctas e&longs;&longs;e.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001282"><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001283"><arrow.to.target n="marg79"/></s>
        </p>
        <p type="margin">
          <s id="s.001284"><margin.target id="marg79"/>79</s>
        </p>
        <p type="main">
          <s id="s.001285">Cap. 1. loco 10. &lpar;<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>&rpar; nonnulli antiquorum <lb/>
Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo&shy;<lb/>
critus, &amp; Leucippus, &amp; propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade&ograve; paruis, qu&aelig; omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>
quibus plura in libello de line is in&longs;ecabilibus.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001286"><emph type="italics"/>Libro Sexto.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001287"><arrow.to.target n="marg80"/></s>
        </p>
        <p type="margin">
          <s id="s.001288"><margin.target id="marg80"/>80</s>
        </p>
        <p type="main">
          <s id="s.001289">Cap. 2. loco 32. &lpar;<emph type="italics"/>Vt qui lineam definiunt longitudinem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>&rpar; <lb/>&longs;upponimus lectorem intellexi&longs;&longs;e definitiones &longs;altem primi Elem. in&shy;<lb/>
ter quas definitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">eademque</expan>; cum hac Ari&longs;totelis.<!-- KEEP S--></s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001290"><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001291"><arrow.to.target n="marg81"/></s>
        </p>
        <p type="margin">
          <s id="s.001292"><margin.target id="marg81"/>81</s>
        </p>
        <p type="main">
          <s id="s.001293">Cap. 2. loco 41. &lpar;<emph type="italics"/>Videntur autem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob definitionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>
cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>
&longs;tatim manife&longs;tum e&longs;t, quod dicitur, nam eandem ablationem habent loca, &amp; linea, <lb/>
&longs;ive latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>&rpar; mendos&egrave; <lb/>legitur &agrave; nonnullis &lpar;<emph type="italics"/>E&longs;t distem definitio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>&rpar; quos puto de&shy;<lb/>
ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>
nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>
fe&longs;tat. </s>
          <s id="s.001294">Notandum po&longs;tea cum Alexandro &lpar;quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap. de Priori, &amp; alibi&rpar; per verbum &lpar;De&longs;cribi&rpar; &longs;ignificari hoc loco <lb/>
geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibitis de&longs;criptio&shy;<lb/>nibus, &longs;eu figuris demon&longs;trant. </s>
          <s id="s.001295">Vult autem Ari&longs;t. exemplo mathematico <lb/>
o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <expan abbr="argum&etilde;tari">argumentari</expan>, ni&longs;i prius rect&egrave; a&longs;&longs;ignetur <pb pagenum="69" xlink:href="009/01/069.jpg"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>
          <s id="s.001296">Porr&ograve; exemplum mathematicum hic <lb/>
allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro&shy;<lb/>
po&longs;itionem; &longs;i linea ducta fuerit &aelig;quidi&longs;tans lateri vnius plani trianguli, &longs;e&shy;<lb/>cabit &amp; latera, &amp; locum, ide&longs;t &longs;uperficiem illam triangularem &longs;imiliter, ide&longs;t <lb/>
<figure id="id.009.01.069.1.jpg" place="text" xlink:href="009/01/069/1.jpg"/><lb/>
in eadem proportione, vt in triangulo A B C, <lb/>
linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>
&amp; A C, in punctis D, &amp; E, in eadem ratione, <lb/>
in qua etiam fecat totum triangulum, ita vt <lb/>
eadem &longs;it proportio line&aelig; A D, ad D B, &amp; line&aelig; <lb/>
A E, ad E C, qu&aelig; e&longs;t partium totalis trianguli <lb/>A B C, &longs;cilicet qu&aelig; e&longs;t partis A D E, ad partem <lb/>
E D C, fiue ad partem D E B. quod con&longs;tat ex <lb/>
&longs;ecunda 6. Elem. <!-- KEEP S--></s>
          <s id="s.001297">Inquit ergo Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.001298">Si quis <lb/>
vellet hoc demon&longs;trare nondum pr&aelig;mi&longs;&longs;a defi&shy;<lb/>
nitione eorum, qu&aelig; habent eandem rationem, &longs;iue nondum definitione al&shy;<lb/>
lata quantitatum proportionalium, hic difficile id valeret o&longs;tendere: at ve&shy;<lb/>r&ograve; allata prius definitione quantitatum proportionalium facile demon&longs;tra&shy;<lb/>
bit. </s>
          <s id="s.001299">Subdit ver&ograve; Ari&longs;t. dictam definitionem, dicens, tunc quantitates e&longs;&longs;e <lb/>
proportionales, quando habent eandem ablationem, ide&longs;t, eandem diui&longs;io&shy;<lb/>
nem, ide&longs;t, eadem diui&longs;io ne tantum proportionaliter de vna, quantum de <lb/>
altera magnitudine re&longs;ecatur: Quemadmodum etiam Euclides loco cita&shy;<lb/>
to probat, latera illius trianguli, &amp; &longs;uperficiem e&longs;&longs;e &longs;imiliter diui&longs;a, ex quo <lb/>
&longs;equitur e&longs;&longs;e proportionalia. </s>
          <s id="s.001300">Porr&ograve; Euclides definit. </s>
          <s id="s.001301">&longs;eptima 5. paulo ali&shy;<lb/>
ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; eandem habent ratio&shy;<lb/>
nem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;it, vt prima ad &longs;ecundam, ita tertia ad quartam. </s>
          <s id="s.001302">ex quibus <lb/>
quoad Mathematicas &longs;pectat, huic loco &longs;atisfactum &longs;it.</s>
        </p>
        <p type="main">
          <s id="s.001303"><arrow.to.target n="marg82"/></s>
        </p>
        <p type="margin">
          <s id="s.001304"><margin.target id="marg82"/>82</s>
        </p>
        <p type="main">
          <s id="s.001305">Cap. 4. loco 86. <emph type="italics"/>&lpar;Tentandum autem, &amp; ea, in qu&aelig; &longs;&aelig;pi&longs;&longs;im&egrave; incidunt di&longs;puta&shy;<lb/>
tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer&shy;<lb/>
citatum e&longs;&longs;e, &amp; in numeris circa capitales prompt&egrave; &longs;e habere, &amp; multum refert ad <lb/>hoc, &amp; alium numerum cogno&longs;cere multiplicatum&rpar;<emph.end type="italics"/> Elementa vocabant antiqui <lb/>
demon&longs;trationes faciliores, &amp; &longs;impliciores, quales propri&egrave; &longs;unt omnes, qu&aelig; <lb/>
&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele&shy;<lb/>
mentis ab&longs;tru&longs;iores, &amp; difficiliores demon&longs;trationes deducebant. </s>
          <s id="s.001306"><expan abbr="atq;">atque</expan> h&aelig;c <lb/>
e&longs;t ratio, cur Euclides &longs;uos libros elementa nuncupauerit. </s>
          <s id="s.001307">ait igitur curan&shy;<lb/>
dum e&longs;&longs;e horum elementorum cognitionem in promptu habere, quia fre&shy;<lb/>
quens de ip&longs;is incidit di&longs;putatio. </s>
          <s id="s.001308">Per capitales numeros intelligo &longs;implices <lb/>
ab vnitate, <expan abbr="v&longs;q;">v&longs;que</expan> ad nouem inclu&longs;iu&egrave;. </s>
          <s id="s.001309">&amp; quando ait, alium numerum cogno&shy;<lb/>
&longs;cere multiplicatum, &longs;ignificat vtile vald&egrave; e&longs;&longs;e ad quotidianum v&longs;um <lb/>
cogno&longs;cere, quemnam numerum producant numeri capitales, <lb/>
&longs;i ad inuicem multiplicentur, quamuis huiu&longs;modi co&shy;<lb/>
gnitio facilis, ac leuis &longs;it: qua de cau&longs;a vide&shy;<lb/>
mus v&longs;que in hanc diem pueros diu in <lb/>
Abaco memoriter perdi&longs;cen&shy;<lb/>
do detineri.</s>
        </p>
      </chap>
      <chap>
        <pb pagenum="70" xlink:href="009/01/070.jpg"/>
        <p type="head">
          <s id="s.001310"><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001311"><arrow.to.target n="marg83"/></s>
        </p>
        <p type="margin">
          <s id="s.001312"><margin.target id="marg83"/>83</s>
        </p>
        <p type="main">
          <s id="s.001313">Cap. 10. <emph type="italics"/>&lpar;Nam p&longs;eudographi&aelig; non contentio&longs;&aelig; &lpar;&longs;ecundum enim ea, qu&aelig; <lb/>
&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes&rpar; <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>
phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>
Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>
non &longs;ecundum rem, ideo &longs;ophi&longs;ticus&rpar;<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>
exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap. 31. <lb/>
&amp; quo itidem modo Bry&longs;&longs;o lib. 1. Po&longs;ter. tex. <!-- REMOVE S-->23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>
tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>
Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;eudographia <lb/>
autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>
cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>
c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>
cas. </s>
          <s id="s.001314">Qua ratione item Hippocrates ex ijs, qu&aelig; &longs;ub arte Geometri&aelig; &longs;unt, <lb/>
procederet ibi dictum e&longs;t, propter quod non e&longs;t contentio&longs;a, quamuis fallax <lb/>
ip&longs;ius demon&longs;tratio: appellat enim Ari&longs;t illas demon&longs;trationes contentio&shy;<lb/>
&longs;as, qu&aelig; non procedunt ex proprijs illius &longs;cienti&aelig;, in qua fiunt, &longs;ed ex com&shy;<lb/>
munibus alijs &longs;cientijs: captio&longs;as ver&ograve;, &amp; &longs;ophi&longs;ticas, qu&aelig; ex proprijs &longs;cien&shy;<lb/>
ti&aelig;, in qua fiunt, decipiunt. </s>
          <s id="s.001315">At ver&ograve; demon&longs;tratio, &longs;eu p&longs;eudographia Bry&longs;&shy;<lb/>
&longs;onis erat contentio&longs;a, quia ex communibus, &amp; extra Geometriam petitis <lb/>
argumentabatur: quemadmodum ibi explicatum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001316"><arrow.to.target n="marg84"/></s>
        </p>
        <p type="margin">
          <s id="s.001317"><margin.target id="marg84"/>84</s>
        </p>
        <p type="main">
          <s id="s.001318">Eodem cap. <emph type="italics"/>&lpar;Quadratura per lunulas non contentio&longs;a&rpar;<emph.end type="italics"/> inquit Hippocratis <lb/>
tetragoni&longs;mum, de quo in 2. Priorum, qu&aelig; non contentio&longs;a dicitur, quia ex <lb/>
proprijs Geometri&aelig; deducebatur.</s>
        </p>
        <p type="main">
          <s id="s.001319"><arrow.to.target n="marg85"/></s>
        </p>
        <p type="margin">
          <s id="s.001320"><margin.target id="marg85"/>85</s>
        </p>
        <p type="main">
          <s id="s.001321">Ibidem <emph type="italics"/>&lpar;Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>
ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs&rpar;<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>&lpar;&amp; illam qui&shy;<lb/>
dem&rpar;<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s>
          <s id="s.001322">vide 2. Prior cap. 31. &amp; qu&aelig; pau&shy;<lb/>
lo ante in pr&aelig;cedentibus locis diximus.</s>
        </p>
        <p type="main">
          <s id="s.001323"><arrow.to.target n="marg86"/></s>
        </p>
        <p type="margin">
          <s id="s.001324"><margin.target id="marg86"/>86</s>
        </p>
        <p type="main">
          <s id="s.001325">Ibidem <emph type="italics"/>&lpar;Hanc autem ad plures&rpar;<emph.end type="italics"/> intelligit tetragoni&longs;mum Bry&longs;&longs;onis, qui <lb/>
per communia deducebatur. </s>
          <s id="s.001326">lege &longs;uperius dicta in pr&aelig;cedentibus locis hu&shy;<lb/>
ius capituli.</s>
        </p>
        <p type="main">
          <s id="s.001327"><arrow.to.target n="marg87"/></s>
        </p>
        <p type="margin">
          <s id="s.001328"><margin.target id="marg87"/>87</s>
        </p>
        <figure id="id.009.01.070.1.jpg" place="text" xlink:href="009/01/070/1.jpg"/>
        <p type="main">
          <s id="s.001329">Ad finem cap. <emph type="italics"/>&lpar;Aut vt Antiphon quadra&shy;<lb/>
uit&rpar;<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon&shy;<lb/>
tem in orbe quadrando, ac Hippocratem, <lb/>
Ari&longs;t. his verbis videtur &longs;ignificare, ide&longs;t, <lb/>
ip&longs;um, quamuis ex proprijs Geometri&aelig;, <lb/>
fal&longs;is tamen ratiocinatum e&longs;&longs;e. </s>
          <s id="s.001330">C&aelig;terum <lb/>
Antiphontem in hunc modum orbem ad <lb/>
quadrum redigere tenta&longs;&longs;e, tradit Simpli&shy;<lb/>
cius. </s>
          <s id="s.001331">circulo quadrando in&longs;cribebat pri&shy;<lb/>
m&ograve; quadratum A B C D. deinde in &longs;ingu&shy;<lb/>
lis quatuor &longs;egmentis in&longs;cribebat totidem <lb/>trigona &aelig;quilatera, vt patet in ad&longs;cripta <pb pagenum="71" xlink:href="009/01/071.jpg"/>figura. </s>
          <s id="s.001332">po&longs;tea &longs;uper &longs;ingula latera horum triangulorum in reliquis &longs;egmen&shy;<lb/>
tis in&longs;cribebat adhuc triangula &longs;imilia triangulo A I E. alia in&longs;uper trigona <lb/>
&longs;uper latera i&longs;torum con&longs;tituebat, donec ambitus figur&aelig; illius multilater&aelig; <lb/>in circulo delineat&aelig;, circumferenti&aelig; circuli aptaretur. </s>
          <s id="s.001333">quod fieri po&longs;&longs;e ille <lb/>
fals&ograve; contra Geometri&aelig; principia a&longs;&longs;umebat; e&longs;t enim principium Geome&shy;<lb/>
tricum continuum e&longs;&longs;e diui&longs;ibile in infinitum, <expan abbr="neq;">neque</expan> per diui&longs;ionem ab&longs;umi <lb/>po&longs;&longs;e; cui principio aduer&longs;atur, dum putat &longs;e con&longs;umpturum totum circu&shy;<lb/>
lum, diuidendo illud in triangula &longs;emper minora; vel quia putat, lineam <lb/>
curuam con&longs;tare ex minimis lineis rectis. </s>
          <s id="s.001334">Similiter igitur <expan abbr="atq;">atque</expan> Hippocra&shy;<lb/>tes errauit, q&uacute;i pariter in Geometria fallebatur: Antiphon quidem contra <lb/>
principia illius: Hippocrates ver&ograve; a&longs;&longs;umens fal&longs;i quidpiam in Geometria. <lb/>
<!-- KEEP S--></s>
          <s id="s.001335">At Bry&longs;&longs;o, eo quod per communia alijs &longs;cientijs deduceret ratiocinatio&shy;<lb/>
nem propterea p&longs;eudographia Antiphontis non litigio&longs;a quidem, &longs;ed <lb/>
tamen fallax extitit, non enim per communia alijs &longs;cientijs <lb/>
procedat; vnde nec transferri poterat ip&longs;ius fal&longs;a de&shy;<lb/>
&longs;criptio, &longs;eu demon&longs;tratio extra Geometri&aelig; li&shy;<lb/>
mites, quod cau&longs;a e&longs;t contentionis.</s>
        </p>
        <p type="head">
          <s id="s.001336"><emph type="italics"/>Logicorum locorum finis.<emph.end type="italics"/></s>
        </p>
      </chap>
      <pb pagenum="72" xlink:href="009/01/072.jpg"/>
      <chap>
        <p type="head">
          <s id="s.001337">EX PRIMO LIBRO <lb/>
PHYSICORVM.<lb/>
<arrow.to.target n="marg88"/></s>
        </p>
        <p type="margin">
          <s id="s.001338"><margin.target id="marg88"/>88</s>
        </p>
        <p type="main">
          <s id="s.001339">Tex. 11. <emph type="italics"/>&lpar;Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>
principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>
vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>
&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>&rpar; Tetrago&shy;<lb/>
ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>
pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e&shy;<lb/>
ctiones appellat, orbem quadrare tentabat. </s>
          <s id="s.001340">Eius demon&longs;trationem expli&shy;<lb/>
caui ad cap. 31. de Abductione in 2. Priorum, quam inibi videas. </s>
          <s id="s.001341">hoc &longs;olum <lb/>
hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>
dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet &lpar;in&shy;<lb/>
quit Ari&longs;t.&rpar; Geometra illius deceptionem inuenire. </s>
          <s id="s.001342">Tetragoni&longs;mum autem <lb/>
Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>
metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiuiduis, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>
lineis rectis componi: cuius fal&longs;am demon&longs;trationem explicatam inuenies <lb/>
ad cap. 10. primi Elench. <!-- REMOVE S-->po&longs;&longs;umus addere tertiam rationem quia &longs;cilicet <lb/>
Hippocrates non procedebat per communia alijs &longs;cientijs, vt videre e&longs;t ad <lb/>
tex. <!-- REMOVE S-->23. primi Po&longs;ter. cap. 8. vbi ip&longs;ius p&longs;eudographiam expo&longs;ui. Quemad&shy;<lb/>
modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantummodo rationes eas, qu&aelig; &longs;er&shy;<lb/>
uatis Geometricis principijs procedunt; non autem eas, qu&aelig; Geometri&aelig; <lb/>
principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> Parmenidem, ac Me&shy;<lb/>
li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut fallaces eorum rationes <lb/>
coarguere. </s>
          <s id="s.001343">Hoc volebat Ari&longs;toteles inferre.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001344"><emph type="italics"/>Ex Secundo Phy&longs;icorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001345"><arrow.to.target n="marg89"/></s>
        </p>
        <p type="margin">
          <s id="s.001346"><margin.target id="marg89"/>89</s>
        </p>
        <p type="main">
          <s id="s.001347">Tex. 20. &lpar;<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>
e&longs;t phy&longs;ici: Per&longs;pectiua autem mathematicam quidem lineam, &longs;ed non <lb/>
quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>&rpar; quamuis textus hic non pertineat ad Mathe&shy;<lb/>
maticum, libuit tamen illum in ordinem no&longs;trum recen&longs;ere, ope&shy;<lb/>
r&aelig;pretium etenim e&longs;t ea, qu&aelig; in ip&longs;o continentur &agrave; nonnullis recentioribus <lb/>
rect&egrave; intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab&shy;<lb/>
&longs;tineant, ac tandem ex Ari&longs;t. lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>
per&longs;picu&egrave; videant. </s>
          <s id="s.001348">c&aelig;tera, qu&aelig; in pr&aelig;cedentibus locis Ari&longs;t. de Natura Ma&shy;<lb/>
thematicarum habet, &longs;unt pr&aelig;ter no&longs;trum in&longs;titutum.</s>
        </p>
        <p type="main">
          <s id="s.001349"><arrow.to.target n="marg90"/></s>
        </p>
        <p type="margin">
          <s id="s.001350"><margin.target id="marg90"/>90</s>
        </p>
        <p type="main">
          <s id="s.001351">Tex. 28. &lpar;<emph type="italics"/>Alio autem modo, forma, &amp; exemplum: h&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>
quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>
numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>&rpar; vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>
textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. <!-- REMOVE S-->1. cap. primi 2. Po&shy;<lb/>
&longs;ter. <!-- REMOVE S-->&longs;uper verba illa &lpar;<emph type="italics"/>Quid e&longs;t con&longs;onantia?<emph.end type="italics"/>&rpar; vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>
&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>
qu&aelig; &longs;ub his num. </s>
          <s id="s.001352">2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/>
loci intelligentia.</s>
        </p>
        <pb pagenum="73" xlink:href="009/01/073.jpg"/>
        <p type="main">
          <s id="s.001353"><arrow.to.target n="marg91"/></s>
        </p>
        <p type="margin">
          <s id="s.001354"><margin.target id="marg91"/>91</s>
        </p>
        <p type="main">
          <s id="s.001355">Tex. 68. &lpar;<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bilibus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>
alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>&rpar; ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>
mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>
ad definitionem reducant. </s>
          <s id="s.001356">quorum exempla in logicis ex Mathematicis at&shy;<lb/>
tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>
&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>
ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001357"><arrow.to.target n="marg92"/></s>
        </p>
        <p type="margin">
          <s id="s.001358"><margin.target id="marg92"/>92</s>
        </p>
        <p type="main">
          <s id="s.001359">Tex 89. &lpar;<emph type="italics"/>E&longs;t autem nece&longs;&longs;arium in Mathematicis, &amp; in his, qu&aelig; &longs;ecundum <lb/>naturam fiunt qua&longs;i eodem modo; quoniam enim hoc rectum e&longs;t, nece&longs;&longs;e e&longs;t, trian&shy;<lb/>gulum tres angulos habere &aelig;quales duobus rectis; &longs;ed non, &longs;i hoc, illud; &longs;ed &longs;i hoc <lb/>
non e&longs;t, <expan abbr="neq;">neque</expan> rectum e&longs;t.<emph.end type="italics"/>&rpar; cum animaduerterim non parum e&longs;&longs;e di&longs;&longs;en&longs;ionis, &amp; <lb/>
difficultatis in exemplo hoc mathematico explicando, ita vt recentiores <lb/>
quidam textum <expan abbr="h&utilde;c">hunc</expan> pro arbitratu &longs;uo perperam latin&egrave; verterint: ide&ograve; pri&shy;<lb/>
mum ex gr&aelig;cis codicibus interpretationem hanc veram attuli. </s>
          <s id="s.001360">deinde, quia <lb/>
etiam gr&aelig;ci in exemplo mathematico enodando, vel mal&egrave;, vt Simplicius; <lb/>
vel ob&longs;cur&egrave; nimis, vt reliqui; Latini ver&ograve; vel nihil, vel peius mult&ograve; loquun&shy;<lb/>
tur, ide&ograve; &longs;ic ego exponendum cen&longs;ui. </s>
          <s id="s.001361">cum velit Ari&longs;t. o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;eu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>
tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>
&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>
les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>
primo Priorum, &longs;ecto 3. cap. 1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s>
          <s id="s.001362">pro medio autem <lb/>
huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/>
<emph type="italics"/>&lpar;quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>&rpar; vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/>
<figure id="id.009.01.073.1.jpg" place="text" xlink:href="009/01/073/1.jpg"/><lb/>
A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>
ducatur B C, in D; tunc triangulum A B C, <lb/>
habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>
duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>
&longs;it perpendiculare &lpar;quod Ari&longs;t. dicit, cum <expan abbr="re-ct&utilde;">re&shy;<lb/>
ctum</expan> hoc &longs;it&rpar; erunt duo anguli deinceps A C B, <lb/>
A C D, recti, ex definitione line&aelig; perpendicu&shy;<lb/>
laris, cum ergo duo anguli A, &amp; B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int &aelig;quales per <lb/>
32. primi, &amp; reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu&shy;<lb/>
li, &amp; angulus vnus line&aelig; perpendicularis, &amp; ide&ograve; rectus; manife&longs;t&egrave; apparet, <lb/>
tres angulos A, B, A C B, e&longs;&longs;e &aelig;quales nece&longs;&longs;ari&ograve; duobus rectis, ex po&longs;itio&shy;<lb/>
ne illius recti, &longs;iue lateris perpendicularis, quia ex ver&ograve;, verum nece&longs;&longs;ari&ograve; <lb/>
&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>
tres angulos &aelig;quales duobus rectis, nece&longs;&longs;ari&ograve; &longs;equitur illud e&longs;&longs;e rectum, <lb/>ide&longs;t latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>
&longs;equi pote&longs;t ex ver&ograve;, &amp; fals&ograve;. </s>
          <s id="s.001363">valebit tamen h&aelig;c con&longs;equen&shy;<lb/>
tia, &longs;i triangulum non habet hanc proprietatem, ne&shy;<lb/>
que illud rectum e&longs;t, ide&longs;t, <expan abbr="neq;">neque</expan> latus pr&aelig;di&shy;<lb/>ctum erit <expan abbr="perp&etilde;diculare">perpendiculare</expan>, quia fal&longs;um <lb/>non, ni&longs;i ex fal&longs;o &longs;equitur.</s>
        </p>
      </chap>
      <pb pagenum="74" xlink:href="009/01/074.jpg"/>
      <chap>
        <p type="head">
          <s id="s.001364"><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001365"><arrow.to.target n="marg93"/></s>
        </p>
        <p type="margin">
          <s id="s.001366"><margin.target id="marg93"/>93</s>
        </p>
        <p type="main">
          <s id="s.001367">Tex. 26. <emph type="italics"/>&lpar;Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;ura, &amp; <lb/>
ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s>
          <s id="s.001368">&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numeris, circumpo&longs;itis enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidem &longs;emper aliam fieri &longs;pe&shy;<lb/>
ciem, aliquando autem vnam&rpar;<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>
prius, qu&aelig; in cap. de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>
&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>
meris Gnomones Arithmetici. </s>
          <s id="s.001369">Pythagorici enim &lpar;&agrave; quibus i&longs;ta mutuatus <lb/>
e&longs;t Ari&longs;t. numeros impares &longs;olos appellabant Gnomones, e&ograve; quod in for&shy;<lb/>
mam norm&aelig; &aelig;quilater&aelig;, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/>
<figure id="id.009.01.074.1.jpg" place="text" xlink:href="009/01/074/1.jpg"/><lb/>
nimirum in ternario, quinario, &longs;eptenario, &amp; &longs;ic de <lb/>
reliquis imparibus. </s>
          <s id="s.001370">pares autem numeri, quia ne&shy;<lb/>
queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>
non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>
tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>
&longs;ponatur &longs;ic <figure id="id.009.01.074.2.jpg" place="text" xlink:href="009/01/074/2.jpg"/> non refert Gnomonem, quia lateribus in&etail;qualibus con&shy;<lb/>
&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="id.009.01.074.3.jpg" place="text" xlink:href="009/01/074/3.jpg"/> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;&longs;aria e&longs;t. </s>
          <s id="s.001371">Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>
infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>
qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>
parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>
blematic&egrave; probatur in 10. primi Elem. quamuis theorematic&egrave; &longs;it axioma. <lb/>
</s>
          <s id="s.001372">hunc porr&ograve; numerum parem dicebant terminatum e&longs;&longs;e ab impari, quia ori&shy;<lb/>
tur ex diui&longs;ione cuiu&longs;uis rei, qu&aelig; vna &longs;it, &longs;umentes vnitatem pro impari. <lb/>
</s>
          <s id="s.001373">&longs;ignum pr&aelig;terea huius finitatis ab impari, &amp; infinitatis &agrave; pari numero pro&shy;<lb/>
cedentis, aiunt e&longs;&longs;e Gnomones, numeros &longs;cilicet impares: Gnomones enim, <lb/>
ide&longs;t impares numeri vnitati additi, producunt eandem perpetu&ograve; numero&shy;<lb/>
rum formam, videlicet quadratum: at ver&ograve; &egrave; contrari&ograve; numeri pares vni&shy;<lb/>
tati additi, conflant perpetu&ograve; varias numerorum formas: quapropter vi&shy;<lb/>dentur numeri impares e&longs;&longs;e finitatis cau&longs;a; &longs;icut pares ex aduers&ograve; infinitatis <lb/>
principium. </s>
          <s id="s.001374">qu&aelig; vt melius intelligas, declaranda e&longs;t 26. propo&longs;. </s>
          <s id="s.001375">7. Arith&shy;<lb/>
metices lordani, vbi i&longs;tud idem demon&longs;trat, qu&aelig; e&longs;t h&aelig;c. </s>
          <s id="s.001376">&longs;it vnitas, &amp; &longs;uo or&shy;<lb/>
dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. &amp; c. <lb/>
<figure id="id.009.01.074.4.jpg" place="text" xlink:href="009/01/074/4.jpg"/><lb/>
&longs;i igitur vnitati addatur ternarius in Gnomo&shy;<lb/>
nis modum, vt vides in prima figura, produ&shy;<lb/>
cetur quaternarius numerus, qui e&longs;t numerus <lb/>
quadratus &lpar;quid &longs;it quadratus numerus expli&shy;<lb/>
caui in Logicis tex. <!-- REMOVE S-->9. primi Po&longs;ter.&rpar; et&longs;i huic <lb/>
quaternario addatur &longs;equens impar, qui e&longs;t <lb/>quinarius in modum Gnomonis, vt in &longs;ecunda <lb/>
figura, &longs;it numerus nouenarius, qui pariter e&longs;t quadratus. </s>
          <s id="s.001377">et&longs;i huic &longs;imiliter <lb/>addatur &longs;equens impar, nimirum &longs;eptenarius, conflabitur &longs;edenarius, qui <lb/>
numerus pariter quadratus e&longs;t, vt in tertia figura, &amp; hoc modo, &longs;i in infini&shy;


<pb pagenum="75" xlink:href="009/01/075.jpg"/>tum procedatur, numeri &longs;emper quadrati progignentur. </s>
          <s id="s.001378">Vides igitur, qui <lb/>
ratione Gnomonum, &longs;iue imparium additione fiat &longs;emper eadem &longs;pecies, <lb/>
&longs;cilicet quadratus numerus, quod &longs;ignum e&longs;t, inquiunt, imparem numerum <lb/>
non infinitatis, &longs;ed finitatis e&longs;&longs;e auctorem. </s>
          <s id="s.001379">Po&longs;t pr&aelig;dictam 26. propo&longs;itio&shy;<lb/>nem Iordani, &longs;unt aliquot propo&longs;itiones, quarum &longs;umma h&aelig;c e&longs;t: &longs;i pares <lb/>
numeri ab vnitate coaceruentur; coaceruati erunt &longs;emper vari&aelig; form&aelig; nu&shy;<lb/>
merorum. </s>
          <s id="s.001380">qu&aelig; &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/>
hoc modo, 1. 2. 4. 6. &amp;c. </s>
          <s id="s.001381">&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/>
<figure id="id.009.01.075.1.jpg" place="text" xlink:href="009/01/075/1.jpg"/><lb/>
triangularis, vt in prima figura. </s>
          <s id="s.001382">&longs;i huic ternario <lb/>
coaceruetur &longs;equens par, fiet altera &longs;pecies, ni&shy;<lb/>
mirum hexagonus numerus, vt in &longs;ecunda figu&shy;<lb/>
ra. </s>
          <s id="s.001383">cui &longs;i &longs;equens addatur par, &longs;cilicet &longs;enarius, <lb/>
fiet iterum noua numeri forma, v. <!-- REMOVE S-->g. <!-- KEEP S--></s>
          <s id="s.001384">dodecago&shy;<lb/>
nus, vt in tertia figura. </s>
          <s id="s.001385">&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>
form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>
parem infiniti naturam &longs;apere. </s>
          <s id="s.001386">Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>
tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>
Alex. de numeris rectangulis. </s>
          <s id="s.001387"><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s>
        </p>
        <p type="main">
          <s id="s.001388"><arrow.to.target n="marg94"/></s>
        </p>
        <p type="margin">
          <s id="s.001389"><margin.target id="marg94"/>94</s>
        </p>
        <p type="main">
          <s id="s.001390">Tex. 31. <emph type="italics"/>&lpar;Vtuntur etiam Mathematici infinito&rpar;<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>
cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>
finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. <!-- REMOVE S-->71. ip&longs;e Ari&longs;t. <lb/>
exponit. </s>
          <s id="s.001391">alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>
quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>
patet ex 6. po&longs;tulato primi Elem. editionis Clauian&aelig;. </s>
          <s id="s.001392">numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>
geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem. vel demum <lb/>
quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>
po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001393"><arrow.to.target n="marg95"/></s>
        </p>
        <p type="margin">
          <s id="s.001394"><margin.target id="marg95"/>95</s>
        </p>
        <p type="main">
          <s id="s.001395">Tex. 68. &amp; 69. plura de magnitudine, &amp; numero continent; &longs;ed qu&aelig; non <lb/>
indigeant opera no&longs;tra.</s>
        </p>
        <p type="main">
          <s id="s.001396"><arrow.to.target n="marg96"/></s>
        </p>
        <p type="margin">
          <s id="s.001397"><margin.target id="marg96"/>96</s>
        </p>
        <p type="main">
          <s id="s.001398">Tex. 71. <emph type="italics"/>&lpar;Non remouet autem ratio Mathematicos &agrave; contemplatione auferens <lb/>
&longs;ic e&longs;&longs;e infinitum, vt actu &longs;it ver&longs;us augmentum, vt intran&longs;ibile, <expan abbr="ncq;">neque</expan> enim nunc in&shy;<lb/>
digent infinito, <expan abbr="neq;">neque</expan> vtuntur, &longs;ed &longs;olum e&longs;&longs;e <expan abbr="quantumcunqu;">quantumcunque</expan> velint finitam&rpar;<emph.end type="italics"/> ratio <lb/>
phy&longs;ica tollens infinitum actu, non e&longs;t Mathematicis impedimento, quia ip&longs;i <lb/>
non vtuntur infinito actu; quam enim ip&longs;i ducunt lineam infinitam, non e&longs;t <lb/>
ver&egrave; infinita, &longs;ed indefinita, eam enim quantumlibet magnam producunt, vt <lb/>
po&longs;&longs;it ad demon&longs;trandum &longs;ufficere.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001399"><emph type="italics"/>Ex Quarto Phy&longs;icorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001400"><arrow.to.target n="marg97"/></s>
        </p>
        <p type="margin">
          <s id="s.001401"><margin.target id="marg97"/>97</s>
        </p>
        <p type="main">
          <s id="s.001402">Tex. 120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>
&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>
primo Priorum, &longs;ecto primo, cap. 23.</s>
        </p>
      </chap>
      <pb pagenum="76" xlink:href="009/01/076.jpg"/>
      <chap>
        <p type="head">
          <s id="s.001403"><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001404"><arrow.to.target n="marg98"/></s>
        </p>
        <p type="margin">
          <s id="s.001405"><margin.target id="marg98"/>98</s>
        </p>
        <p type="main">
          <s id="s.001406">Tex. 6. <emph type="italics"/>&lpar;Vt media grauis ad vltimam, &amp; acuta ad primam&rpar;<emph.end type="italics"/> alludit ad or&shy;<lb/>
dinem chordarum in mu&longs;icis in&longs;trumentis, vbi media chorda edit &longs;o&shy;<lb/>
num, re&longs;pectu quidem vltim&aelig;, &amp; &longs;uprem&aelig; chord&aelig; grauem: re&longs;pectu ver&ograve; <lb/>
prim&aelig;, &amp; infim&aelig; acutum.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001407"><emph type="italics"/>Ex Octauo Phy&longs;icorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001408"><arrow.to.target n="marg99"/></s>
        </p>
        <p type="margin">
          <s id="s.001409"><margin.target id="marg99"/>99</s>
        </p>
        <p type="main">
          <s id="s.001410">Tex. 15. <emph type="italics"/>&lpar;Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis&rpar;<emph.end type="italics"/><lb/>
lib. 1. Priorum, &longs;ecto 3. cap. 1. huius rei explicationem reperies.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001411"><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001412"><arrow.to.target n="marg100"/></s>
        </p>
        <p type="margin">
          <s id="s.001413"><margin.target id="marg100"/>100</s>
        </p>
        <p type="main">
          <s id="s.001414">Tex. 33. <emph type="italics"/>&lpar;Vt &longs;i quis minimam qu&abreve;dam e&longs;&longs;e dicat magnitudinem, hic enim <lb/>
minimum introducens, maxima <expan abbr="vbiq;">vbique</expan> amoueret mathematicor&ubreve;m&rpar;<emph.end type="italics"/> ide&longs;t, <lb/>
&longs;i quis, vt Democritus po&longs;uerit in magnitudinibus e&longs;&longs;e minima, <lb/>
&longs;eu indiui&longs;ibilia, ex quibus entia mathematica componerentur, <lb/>
hic euerteret maxima mathematicorum, ide&longs;t maxime ip&longs;orum demon&longs;tra&shy;<lb/>
tiones, atque etiam effata euerterentur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->10. primi Elem. qu&aelig; docet <lb/>
quamlibet lineam po&longs;&longs;e diuidi bifariam nulla e&longs;&longs;et, quia linea illa, qu&aelig; con&shy;<lb/>
&longs;taret ex tribus Democriti atomis, nulla ratione bifariam &longs;ecari po&longs;&longs;et. </s>
          <s id="s.001415">pa&shy;<lb/>
riter totus fer&egrave; decimus liber Elem. deceptiuus, &amp; nullus e&longs;&longs;et, &longs;i enim da&shy;<lb/>
rentur ill&aelig; atomi, ex quibus <expan abbr="qu&atilde;titas">quantitas</expan> conflaretur, null&aelig; e&longs;&longs;ent line&aelig; incom&shy;<lb/>
men&longs;urabiles, quandoquidem omnes communi illa, ac indiuidua, commen&shy;<lb/>
&longs;urarentur. </s>
          <s id="s.001416">po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>
minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>
non po&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.001417"><arrow.to.target n="marg101"/></s>
        </p>
        <p type="margin">
          <s id="s.001418"><margin.target id="marg101"/>101</s>
        </p>
        <p type="main">
          <s id="s.001419">Tex. 36. <emph type="italics"/>&lpar;Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; &amp; alia vtrinque <lb/>
infinita, in qua <foreign lang="greek">b</foreign> B; &longs;i <expan abbr="itaq;">itaque</expan> de&longs;cribat circulum linea A G E, circa centrum G, fe-<emph.end type="italics"/><lb/>
<figure id="id.009.01.076.1.jpg" place="text" xlink:href="009/01/076/1.jpg"/><lb/>
<emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali&shy;<lb/>
quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/>
enim tempus, in quo circulariter latum <lb/>
e&longs;t C&oelig;lum finitum e&longs;t, &amp; ablatum igitur, <lb/>quo &longs;ecans ferebatur; erit igitur aliquod <lb/>principium, quo primum linea A G E, li&shy;<lb/>
neam <foreign lang="greek">b</foreign> B, &longs;ecuit. </s>
          <s id="s.001420">&longs;ed impo&longs;&longs;ibile est; non <lb/>
est igitur circulariter verti <expan abbr="infinit&utilde;">infinitum</expan>, quare <lb/>
<expan abbr="neq;">neque</expan> mundum, &longs;i e&longs;&longs;et infinitus&rpar;<emph.end type="italics"/> quamuis <lb/>
textus hic parum &longs;it mathematicus, <lb/>
quia tamen &longs;upponit figuram mathe&shy;<lb/>
maticam, qu&aelig; in codicibus pariter, ac <lb/>
commentarijs de&longs;ideratur, illam pla&shy;<lb/>
cuit apponere. </s>
          <s id="s.001421">in qua quidem, quamuis du&aelig; line&aelig; infinit&aelig; &longs;upponantur, vna <lb/>
ad alteram <expan abbr="t&atilde;tum">tantum</expan> partem in qua E: altera ver&ograve; ad <expan abbr="vtramq;">vtramque</expan> partem <foreign lang="greek">b,</foreign> &amp; B,


<pb pagenum="77" xlink:href="009/01/077.jpg"/>non potuerunt tamen de&longs;cribi, ni&longs;i finit&aelig;; appo&longs;it&aelig; idcirc&ograve; &longs;unt ad partes <lb/>
illas, ad quas deberent e&longs;&longs;e infinit&aelig; lineol&aelig; qu&aelig;dam infinitatem indicantes. <lb/>
</s>
          <s id="s.001422">debemus po&longs;tea, vt mentem Ari&longs;t. percipiamus concipere lineam A G E, <lb/>
moueri circulariter facto centro in G. qu&aelig; quia infinita &longs;upponitur ad par&shy;<lb/>
tem E, &longs;ecabit nece&longs;&longs;ari&ograve; alteram <expan abbr="vtrinq;">vtrinque</expan> infinitam <foreign lang="greek">b</foreign> B, <expan abbr="illam&qacute;">illamque</expan>; nece&longs;&longs;ari&ograve; <lb/>
finito tempore percurret, finito enim tempore tota mundi circulatio per&shy;<lb/>
agitur, &longs;patio videlicet viginti quatuor horarum. </s>
          <s id="s.001423">ex quo Ari&longs;t. infert mun&shy;<lb/>
dum non po&longs;&longs;e e&longs;&longs;e infinit&aelig; magnitudinis; quia &longs;i mundus e&longs;&longs;et infinitus; &amp;. <lb/>
</s>
          <s id="s.001424">du&aelig; line&aelig; infinit&aelig;, quales &longs;unt pr&aelig;dict&aelig; in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte&shy;<lb/>
ra earum A E, intelligatur, alteram <foreign lang="greek">b</foreign> B, manentem in tempore finito, ide&longs;t, <lb/>
in diurna conuer&longs;ione pertran&longs;ibit: fieri autem nequit, vt infinita magni&shy;<lb/>
tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/>
magnitudine pr&aelig;ditum.</s>
        </p>
        <p type="main">
          <s id="s.001425"><arrow.to.target n="marg102"/></s>
        </p>
        <p type="margin">
          <s id="s.001426"><margin.target id="marg102"/>102</s>
        </p>
        <p type="main">
          <s id="s.001427">Tex. 48. <emph type="italics"/>&lpar;Nihil autem refert grauitates, commen&longs;urabiles &longs;int, an incommen&shy;<lb/>&longs;urabiles&rpar;<emph.end type="italics"/> quidnam &longs;it commen&longs;urabilitas, &amp; incommen&longs;urabilitas, expli&shy;<lb/>
catum e&longs;t lib. 1. Priorum, &longs;ecto 1. cap. 23.</s>
        </p>
        <p type="main">
          <s id="s.001428"><arrow.to.target n="marg103"/></s>
        </p>
        <p type="margin">
          <s id="s.001429"><margin.target id="marg103"/>103</s>
        </p>
        <p type="main">
          <s id="s.001430">Tex. 119. <emph type="italics"/>&lpar;Est autem impo&longs;&longs;ibile, &amp; po&longs;&longs;ibile; fal&longs;um, &amp; verum, ex &longs;uppo&longs;itio&shy;<lb/>
ne quidem, dico autem, vt triangulum impo&longs;&longs;ibile e&longs;t duos rectos habere, &longs;i h&aelig;c&rpar;<emph.end type="italics"/><lb/>
ide&longs;t, &longs;i &longs;upponantur fal&longs;a qu&aelig;dam, qu&aelig; &longs;upponi po&longs;&longs;unt, &longs;equetur impo&longs;&longs;i&shy;<lb/>
bile e&longs;&longs;e triangulum habere tres angulos &aelig;quales duobus rectis angulis, vi&shy;<lb/>
de, qu&aelig; &longs;crip&longs;i lib. 1. Priorum, &longs;ecto 3. cap. 1. de hoc, quod e&longs;t, habere tres <lb/>
angulos &aelig;quales duobus rectis. </s>
          <s id="s.001431">v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i in triangulo pag. </s>
          <s id="s.001432">73. producto late&shy;<lb/>
re A C, in D. &longs;i &longs;upponatur externus angulus B C D, non e&longs;&longs;e &aelig;qualis duobus <lb/>internis, &amp; oppo&longs;itis A, &amp; B, nunquam poterimus eo modo, quo Euclides, <lb/>
demon&longs;trare pa&longs;&longs;ionem pr&aelig;dictam de triangulo A B C. huiu&longs;modi impo&longs;&longs;i&shy;<lb/>
bile, cuius oppo&longs;itum non &longs;olum po&longs;&longs;ibile, &longs;ed etiam nece&longs;&longs;arium e&longs;t, vocat <lb/>
Ari&longs;t. impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo&shy;<lb/>
dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an&shy;<lb/>
gulos &aelig;quales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up&shy;<lb/>po&longs;itione, impo&longs;&longs;ibile eua&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.001433"><arrow.to.target n="marg104"/></s>
        </p>
        <p type="margin">
          <s id="s.001434"><margin.target id="marg104"/>104</s>
        </p>
        <p type="main">
          <s id="s.001435">Ibidem <emph type="italics"/>&lpar;Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i h&aelig;c&rpar;<emph.end type="italics"/> vide primo Priorum, <lb/>
&longs;ecto 3. cap. 23. hoc &longs;olum nunc addendum <emph type="italics"/>&lpar;Si h&aelig;c&rpar;<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;upponamus li&shy;<lb/>
neas e&longs;&longs;e compo&longs;itas ex indiui&longs;ibilibus, con&longs;ectarium erit diametrum e&longs;&longs;e <lb/>
commen&longs;urabilem co&longs;t&aelig;, quia indiui&longs;ibile illud, ex quo vtraque linea con&shy;<lb/>
&longs;tat, erit <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> men&longs;ura communis.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001436"><emph type="italics"/>Ex Secundo de C&aelig;lo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001437"><arrow.to.target n="marg105"/></s>
        </p>
        <p type="margin">
          <s id="s.001438"><margin.target id="marg105"/>105</s>
        </p>
        <p type="main">
          <s id="s.001439">Tex. 24. <emph type="italics"/>&lpar;Amplius qui &longs;olida diuidunt in plana, <expan abbr="atq;">atque</expan> ex planis corpora <lb/>
generant, his te&longs;tes fui&longs;&longs;e videntur: &longs;olam enim figurarum &longs;olidarum <lb/>
&longs;ph&aelig;ram non diuidunt, vt non plures &longs;uperficies. </s>
          <s id="s.001440">quam vnam <expan abbr="hab&etilde;um">habentem</expan>. <lb/>
</s>
          <s id="s.001441">diui&longs;io enim in plana non perinde efficitur, vt qui&longs;piam <expan abbr="diuid&etilde;s">diuidens</expan> in par&shy;<lb/>tes diuidat totum, &longs;ed vt in &longs;pecie diuer&longs;a: patet igitur &longs;ph&aelig;ram e&longs;&longs;e &longs;olidarum <lb/>
primam&rpar;<emph.end type="italics"/> qui &longs;olida diuidunt in plana, ea diuidunt <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> numerum &longs;uper&shy;<lb/>ficierum, quibus ambiuntur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->diuidunt cubum in &longs;ex &longs;uperficies, quia <lb/>cubus &longs;ex quadratis planis &longs;uperficiebus continetur: qua ratione nequeunt <pb pagenum="78" xlink:href="009/01/078.jpg"/>&longs;ph&aelig;ram in plana vlla re&longs;oluere, <expan abbr="neq;">neque</expan> in alias plures &longs;uperficies, quia &longs;ph&aelig;&shy;<lb/>
ra ambitur vnica tantum &longs;uperficie &longs;ph&aelig;rica. </s>
          <s id="s.001442">quando ver&ograve; ex planis corpo&shy;<lb/>
ra generant, vt facit Plato in Tim&aelig;o, accip&iacute;unt prim&ograve; triangulum &aelig;quila&shy;<lb/>
terum, &amp; ex quatuor triangulis &aelig;quilateris &longs;imul compactis conficiunt py&shy;<lb/>
ramidem; &amp; hoc modo alia &longs;olida &agrave; pluribus &longs;uperficiebus ambita con&longs;ti&shy;<lb/>
tuunt: verum hac ratione nullo modo po&longs;&longs;unt &longs;ph&aelig;ram componere, quia <lb/>
vnica tantum, <expan abbr="ea&qacute;">eaque</expan>; &longs;ph&aelig;rica &longs;uperficie compr&aelig;henditur: <expan abbr="atq;">atque</expan> hoc pacto i&longs;ti <lb/>
diuidentes, &amp; componentes corpora fidem faciunt, &longs;ph&aelig;ram, cum ex nullis <lb/>
componatur, &longs;olidorum e&longs;&longs;e primam.</s>
        </p>
        <p type="main">
          <s id="s.001443"><arrow.to.target n="marg106"/></s>
        </p>
        <p type="margin">
          <s id="s.001444"><margin.target id="marg106"/>106</s>
        </p>
        <p type="main">
          <s id="s.001445">Tex. 25. <emph type="italics"/>&lpar;Est autem, &amp; &longs;ecundum numerorum ordinem a&longs;&longs;ignantibus, &longs;ic po&shy;<lb/>
nentibus rationabili&longs;&longs;imam, circulum quidem &longs;ecundum vnum; triangulum autem <lb/>
&longs;ecundum dualitatem, quoniam duo recti. </s>
          <s id="s.001446">&longs;i autem &longs;ecundum triangulum, vnum. <lb/>
</s>
          <s id="s.001447">circulus non erit figura&rpar;<emph.end type="italics"/> In ordine figurarum conueniens e&longs;t, inquit, primam <lb/>
facere circulum propter &longs;implici&longs;simam ip&longs;ius naturam, cum vnica, ac per&shy;<lb/>
fecta circulari linea comprehendatur: <expan abbr="Triangul&utilde;">Triangulum</expan> ver&ograve; &longs;ecundam, quoniam <lb/>
duo anguli recti, ide&longs;t, quia triangulum habet tres angulos &aelig;quales duobus <lb/>rectis angulis; quod fus&egrave; explicatum e&longs;t lib. 1. Priorum, &longs;ecto 3. cap. 1. De&shy;<lb/>
mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>
culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s>
        </p>
        <p type="main">
          <s id="s.001448"><arrow.to.target n="marg107"/></s>
        </p>
        <p type="margin">
          <s id="s.001449"><margin.target id="marg107"/>107</s>
        </p>
        <p type="main">
          <s id="s.001450">Tex. 31. <emph type="italics"/>&lpar;At ver&ograve;, quod aqu&aelig; &longs;uperficies talis &longs;it, manife&longs;tum e&longs;t hac &longs;uppo&longs;i&shy;<lb/>
tione &longs;umpta, quod apta natura e&longs;t &longs;emper confluere aqua ad magis concauum: ma&shy;<lb/>
gis autem concauum e&longs;t, quod centro propinquius est. </s>
          <s id="s.001451">ducantur ergo ex centro A,<emph.end type="italics"/><lb/>
<figure id="id.009.01.078.1.jpg" place="text" xlink:href="009/01/078/1.jpg"/><lb/>
<emph type="italics"/>linea A B, &amp; linea A C, &amp; producatur, in qua B C, <lb/>
ducta igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/>
qu&aelig; ex centro. </s>
          <s id="s.001452">magis igitur concauus locus e&longs;t, quare <lb/>
influet aqua, donec <expan abbr="vtiq;">vtique</expan> &aelig;quetur. </s>
          <s id="s.001453">&aelig;qualis e&longs;t autem eis, <lb/>
qu&aelig; ex centro linea A E, quare nece&longs;&longs;e e&longs;t apud eas, qu&aelig; <lb/>
ex centro, e&longs;&longs;e aquam, tunc enim quie&longs;cet. </s>
          <s id="s.001454">linea autem, <lb/>
qu&aelig; eas, qu&aelig; ex centro tangit, circularis e&longs;t, &longs;ph&aelig;rica <lb/>
igitur aqu&aelig; &longs;uperficies e&longs;t, in qua B E C.&rpar;<emph.end type="italics"/> toto hoc <lb/>
textu lineari demon&longs;tratione probat aqu&aelig; manen&shy;<lb/>
tis &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam: qu&aelig; demon&longs;tratio <lb/>
per&longs;picua euadit, &longs;i figura, qu&aelig; in codicibus tam <lb/>
gr&aelig;cis, quam latinis, <expan abbr="atq;">atque</expan> etiam in commentarijs de&longs;ideratur, quemadmo&shy;<lb/>
dum fecimus, re&longs;tituatur. </s>
          <s id="s.001455">&longs;it igitur in pr&aelig;cedenti figura A, centrum mundi, <lb/>
ex quo educantur du&aelig; rect&aelig; line&aelig; &aelig;quales A B, A C, qu&aelig; deinde alia recta <lb/>
B C, coniungantur. </s>
          <s id="s.001456">educatur <expan abbr="quoq;">quoque</expan> recta alia ex centro A, qu&aelig; pertingat <lb/>
ad B C, qu&aelig; ba&longs;is e&longs;t trianguli B A C, &amp; producatur vlterius quantumlibet <lb/>
in E. intelligatur demum circumferentia tran&longs;ire per puncta B, &amp; C, quia <lb/>
ill&aelig; du&aelig; line&aelig; A B, A C, &longs;unt &aelig;quales, qu&aelig; circumferentia alteram A D, qu&aelig; <lb/>
fuit protracta, &longs;ecet in E. <!-- KEEP S--></s>
          <s id="s.001457">Iam &longs;ic argumentatur: aqua natura &longs;ua &longs;emper <lb/>defluit ad locum magis concauum, ide&longs;t, ad loca centro A, terr&aelig; propin&shy;<lb/>
quiora, quale e&longs;&longs;et in figura locus D, re&longs;pectu locorum B, &amp; C, quia A D, <lb/>
linea minor e&longs;t ijs, qu&aelig; ex centro educt&aelig; &longs;unt A B, A C. quapropter aqua <lb/>debet defluere ex B, ad D, vel ex C, ad idem D, donec pertingat ad E. qui <lb/>
locus non e&longs;t decliuior punctis B, &amp; C. quare cum loca B, E, C, qu&aelig; &longs;unt ex&shy;


<pb pagenum="79" xlink:href="009/01/079.jpg"/>trema linearum, &longs;int &aelig;qu&egrave; decliuia, nece&longs;&longs;e e&longs;t aqu&aelig; &longs;uperficiem apud ip&longs;a <lb/>
con&longs;i&longs;tere, tunc enim debet quie&longs;cere, aliter nunquam quie&longs;ceret; &longs;ed vide&shy;<lb/>
mus aquam manentem, &amp; quietam, ergo quie&longs;cit circa puncta B, E, C, &agrave; <lb/>
centro terr&aelig; &aelig;quidi&longs;tantia, per qu&aelig; tran&longs;it linea circularis coniungens illa; <lb/>et&longs;i &longs;uperficies per eiu&longs;modi loca pertran&longs;iret, e&longs;&longs;et &longs;ph&aelig;rica: &longs;ed &longs;uperfi&shy;<lb/>
cies aqu&aelig; tran&longs;it per talia loca, ergo &longs;ph&aelig;rica e&longs;t. </s>
          <s id="s.001458">Huius etiam habes acu&shy;<lb/>
ti&longs;&longs;imam Archimedis demon&longs;trationem initio libelli de ijs, qu&aelig; vehuntur <lb/>
in aqua, quam in &longs;uam &longs;ph&aelig;ram retulit Clauius.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001459"><arrow.to.target n="marg108"/></s>
        </p>
        <p type="margin">
          <s id="s.001460"><margin.target id="marg108"/>108</s>
        </p>
        <p type="main">
          <s id="s.001461">Tex. 46. <emph type="italics"/>&lpar;Reliquum e&longs;t orbes quidem moueri, stellas ver&ograve; quie&longs;cere, &amp; infixas <lb/>
ip&longs;is orbibus ferri; &longs;olum enim &longs;ic nullum ab&longs;urdum accidit. </s>
          <s id="s.001462">celeriorem enim e&longs;&longs;e <lb/>
maioris circuli velocitatem, rationabile e&longs;t circa idem centrum infixis: vt enim in <lb/>
alijs maius corpus velocius fertur propria latione, &longs;ic, &amp; in circularibus: maius <lb/>
enim e&longs;t eorum, qu&aelig; auferuntur ab eis, qu&aelig; ex centro, maioris circuli &longs;egmentum&rpar;<emph.end type="italics"/><lb/>
ex intellectione vltim&aelig; periodi textus totius intelligentia pendet: &longs;it igitur <lb/>
<figure id="id.009.01.079.1.jpg" place="text" xlink:href="009/01/079/1.jpg"/><lb/>
figura pr&aelig;&longs;ens, in qua cum &longs;int duo circuli concen&shy;<lb/>
trici, vnus altero maior, <expan abbr="educt&aelig;&qacute;">educt&aelig;que</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> du&aelig; <lb/>
&longs;emidiametri A D, A E, qu&aelig; <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e&shy;<lb/>
cant, apparet maius e&longs;&longs;e <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> D E, quod &egrave; ma&shy;<lb/>
iori circulo &longs;emidiametri ex <expan abbr="c&etilde;tro">centro</expan> educt&aelig; auferunt, <lb/>
quam &longs;egmentum B C, minoris circuli, quod ei&longs;dem <lb/>&longs;emidiametris intercipitur. </s>
          <s id="s.001463">Verumtamen &longs;i circuli <lb/>
ambo &longs;imul moueantur, maior circulus &aelig;quali tem&shy;<lb/>
pore maius illud &longs;patium D E, &amp; minor minus B C, <lb/>
pertran&longs;ibit: idem igitur de c&oelig;le&longs;tibus orbibus di&shy;<lb/>
cendum, qui quamuis omnes diurnum &longs;imul motum <lb/>
ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tell&aelig; maiori&shy;<lb/>
bus circulis infix&aelig;, <expan abbr="atq;">atque</expan> delat&aelig;, maiori celeritate &longs;uos cur&longs;us peragant, ne&shy;<lb/>
que oportet eas, dum mouentur c&oelig;lum di&longs;&longs;ecare, quod accideret, &longs;i pro&shy;<lb/>prio motu veluti pi&longs;ces per aquam progrederentur.</s>
        </p>
        <p type="main">
          <s id="s.001464">H&aelig;c quidem Ari&longs;t. con&longs;entanea ob&longs;eruationibus veterum A&longs;tronomo&shy;<lb/>
rum; at ver&ograve; illis no&longs;tr&aelig; &aelig;tatis ob&longs;eruationes repugnant; pr&aelig;&longs;ertim ill&aelig;, <lb/>
qu&aelig; fiunt circa &longs;tellas errantes: ex quibus fatendum e&longs;&longs;e videtur, C&oelig;lum, <lb/>
qua parte Planetas continet, liquidum e&longs;&longs;e, ac per illud Planetas proprio <lb/>
motu, ceu pi&longs;ces in aqua progredi. </s>
          <s id="s.001465">Tycho <expan abbr="namq;">namque</expan> Brahe, <expan abbr="alij&qacute;">alijque</expan>; plures exact&egrave; <lb/>
demon&longs;trant Cometas in regione Planetarum e&longs;&longs;e, <expan abbr="eos&qacute;">eosque</expan>; motu quodam in <lb/>
tran&longs;uer&longs;um moueri, quo nece&longs;&longs;ario C&etail;l&uacute; deberent perforare; ijdem o&longs;ten&shy;<lb/>
dunt nonnullos Planetas, Martem pr&aelig;&longs;ertim, ac Venerem modo &longs;upra So&shy;<lb/>
lem, modo infra a&longs;cendere, &amp; de&longs;cendere. </s>
          <s id="s.001466">Idem patet ex ob&longs;eruatione no&shy;<lb/>
ua per nouum Tele&longs;copij i <expan abbr="&longs;trum&etilde;tum">&longs;trumentum</expan> in Venere facta, qu&aelig; lunulata <expan abbr="vtrinq;">vtrinque</expan> <lb/>
&agrave; Sole apparet: quando nimirum e&longs;t in imo epicyclo. </s>
          <s id="s.001467"><expan abbr="iterum&qacute;">iterumque</expan>; rotunda ve&shy;<lb/>
luti Luna plena, cum in &longs;ummo epicyclo ver&longs;atur: qu&aelig; minim&egrave; apparerent, <lb/>
ni&longs;i &longs;upra, ac infra Solem circumiret. </s>
          <s id="s.001468">His rationibus conantur ip&longs;i proba&shy;<lb/>
re C&oelig;lum e&longs;&longs;e liquidum; <expan abbr="atq;">atque</expan> in eo Planetas, veluti aues in aere, permeare: <lb/>quarum &longs;olutio mihi nulla occurrit, alijs forta&longs;&longs;is occurret.</s>
        </p>
        <p type="main">
          <s id="s.001469"><arrow.to.target n="marg109"/></s>
        </p>
        <p type="margin">
          <s id="s.001470"><margin.target id="marg109"/>109</s>
        </p>
        <p type="main">
          <s id="s.001471">Tex. 57. <emph type="italics"/>&lpar;De ordine autem ip&longs;orum, quo quidem modo &longs;ingula di&longs;ponantur, vt <lb/>
qu&aelig;dam &longs;int priora, qu&aelig;dam posteriora, &amp; quomodo &longs;patijs &longs;e &abreve;<expan abbr="habe&atilde;t">habeant</expan> ad inuicem,<emph.end type="italics"/>


<pb pagenum="80" xlink:href="009/01/080.jpg"/><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter&rpar;<emph.end type="italics"/> &longs;umit hoc loco <lb/>
A&longs;trologiam, pro A&longs;tronomia, &longs;i iuxta recentiores loqui velimus. </s>
          <s id="s.001472">Dicit igi&shy;<lb/>
tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, &amp; proportiones magnitu&shy;<lb/>dinum eorundem, cum per naturalis &longs;cienti&aelig; principia &longs;ciri nequeant, ex <lb/>
rationibus A&longs;tronomorum petenda e&longs;&longs;e, apud quos i&longs;ta &longs;ufficienter <expan abbr="demon-&longs;tr&etilde;tur">demon&shy;<lb/>
&longs;trentur</expan>. </s>
          <s id="s.001473">&amp; merit&ograve; quidem h&aelig;c dicuntur; po&longs;teriores enim ab Ari&longs;t. ordines, <lb/>
&longs;itus, ac magnitudines tam c&oelig;lorum, quam &longs;yderum firmis rationibus, <expan abbr="atq;">atque</expan> <lb/>
inuentu peracutis demon&longs;trarunt. </s>
          <s id="s.001474">quorum princeps fuit ptol&aelig;meus; no&longs;tra <lb/>
tamen &aelig;tate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo&shy;<lb/>
re, ac &longs;umptu exantlauit, in nonnullis &agrave; Ptol&aelig;meo, ac reliquis di&longs;&longs;entjt: &longs;tan&shy;<lb/>
dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomi&aelig; peritos in <lb/>
confe&longs;&longs;o e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001475"><arrow.to.target n="marg110"/></s>
        </p>
        <p type="margin">
          <s id="s.001476"><margin.target id="marg110"/>110</s>
        </p>
        <p type="main">
          <s id="s.001477">Tex. <emph type="italics"/>&lpar;Luna autem o&longs;tenditur per ea, qu&aelig; circa vi&longs;um, quod &longs;ph&aelig;rica &longs;it: non <lb/>
enim <expan abbr="vtiq;">vtique</expan> fieret accre&longs;cens, &amp; decre&longs;cens, plurim&ubreve;m quidem alter a ex parte curua, <lb/>
altera concaua, aut <expan abbr="vtrmq;">vtrinque</expan> curua, &longs;emel autem bipartita&rpar;<emph.end type="italics"/> ait per ea, qu&aelig; circa <lb/>
vi&longs;um, ide&longs;t per opticem probari Lunam e&longs;&longs;e &longs;ph&aelig;ricam: &longs;ed con&longs;ule, qu&aelig; <lb/>
primo Po&longs;ter. tex. <!-- REMOVE S-->3. de hac re &longs;crip&longs;i, &amp; plenam etiam huius loci intelligen&shy;<lb/>
tiam a&longs;&longs;equeris, pr&aelig;&longs;ertim &longs;i experimentum ibi traditum inieris.</s>
        </p>
        <p type="main">
          <s id="s.001478"><arrow.to.target n="marg111"/></s>
        </p>
        <p type="margin">
          <s id="s.001479"><margin.target id="marg111"/>111</s>
        </p>
        <p type="main">
          <s id="s.001480">Ibidem <emph type="italics"/>&lpar;Et rur&longs;us per Astrologica, quia <expan abbr="vtiq;">vtique</expan> non e&longs;&longs;ent &longs;olis eclyp&longs;es lunul&aelig; <lb/>&longs;peciem pr&aelig;feferentes. </s>
          <s id="s.001481">Quare &longs;i vnum est tale, palam e&longs;t, quod &amp; alia <expan abbr="vtiq;">vtique</expan> erunt <lb/>
talia&rpar;<emph.end type="italics"/> &longs;icuti <expan abbr="pr&aelig;ced&etilde;s">pr&aelig;cedens</expan> &longs;ph&aelig;ricitatis Lun&aelig; ratio ex Per&longs;pectiua de&longs;umpta e&longs;t, <lb/>
ita pr&aelig;&longs;ens ex A&longs;tronomia, ex e&ograve; enim, quod eclyp&longs;is Solis habeat figuram <lb/>
lunul&aelig;, ide&longs;t, &longs;i in&longs;tar Lun&aelig; falcat&aelig;, probant A&longs;tronomi Lunam e&longs;&longs;e &longs;ph&aelig;ri&shy;<lb/>
cam. </s>
          <s id="s.001482">intellige tamen partem illam Solis, qu&aelig; non eclyp&longs;atur, habere figu&shy;<lb/>
ram lunul&aelig;, pars enim &agrave; Luna obumbrata non videtur, et&longs;i videretur oua&shy;<lb/>lem quandam &longs;peciem, pr&aelig;&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/>
<figure id="id.009.01.080.1.jpg" place="text" xlink:href="009/01/080/1.jpg"/><lb/>
cum Solis defectio ex interpo&longs;itione Lun&aelig; inter nos, &amp; <lb/>
Solem contingat, &amp; Luna &longs;it &longs;ph&aelig;rica, nece&longs;&longs;ari&ograve; &longs;ph&aelig;&shy;<lb/>
ric&egrave;, &amp; circulariter Solem obumbrabit; quare pars illa <lb/>
non obumbrata remanet falcata, &amp; corniculata, vt in <lb/>pr&aelig;&longs;enti figura videre e&longs;t; vbi cernis, Lunam Solem or&shy;<lb/>
biculariter offu&longs;care in linea A D C, partem Solis de&shy;<lb/>
tectam <expan abbr="content&atilde;">contentam</expan> lineis curuis A B C D, e&longs;&longs;e lunularem, <lb/>
&amp; falcatam; cum ergo in hunc modum fiat Solis deli&shy;<lb/>
quium, &longs;ignum certum e&longs;t, Lunam e&longs;&longs;e &longs;ph&aelig;ricam.</s>
        </p>
        <p type="main">
          <s id="s.001483"><arrow.to.target n="marg112"/></s>
        </p>
        <p type="margin">
          <s id="s.001484"><margin.target id="marg112"/>112</s>
        </p>
        <p type="main">
          <s id="s.001485">Tex. 107. <emph type="italics"/>&lpar;Quod autem dubitatur, hoc e&longs;t; videre autem non e&longs;t difficile, &longs;i pa&shy;<lb/>
rum con&longs;iderauerimus, &amp; di&longs;tinxerimus, quonam modo cen&longs;eamus quantamuis ma&shy;<lb/>
gnitudinem grauem ad medium ferri. </s>
          <s id="s.001486">manife&longs;tum enim e&longs;t, quod non quou&longs;que ex&shy;<lb/>
tremum tangat ip&longs;um centrum; &longs;ed maior pars vincat, oportet, <expan abbr="quou&longs;q;">quou&longs;que</expan> &longs;uo medio <lb/>
ip&longs;um medium compr&aelig;hendat; <expan abbr="hucn&longs;q;">hucu&longs;que</expan> enim habet propen&longs;ionem&rpar;<emph.end type="italics"/> &longs;en&longs;us Ari&longs;to&shy;<lb/>
telis e&longs;t, debere nos exi&longs;timare, quod &longs;i qu&aelig;piam grauis magnitudo de&longs;cen&shy;<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;tatim ac ip&longs;ius extremum <lb/>centrum mundi attigent; &longs;ed e&ograve; <expan abbr="v&longs;q;">v&longs;que</expan> de&longs;cen&longs;uram, <expan abbr="quou&longs;q;">quou&longs;que</expan> ip&longs;ius medium, <lb/>mundi medium, &longs;iue centrum a&longs;&longs;equutum &longs;it; maior enim ip&longs;ius pars, in qua <lb/>
&longs;cilicet medium e&longs;t, minorem partem propellit, donec vtrinque &agrave; centro <lb/>
mundi &aelig;qu&egrave; emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81" xlink:href="009/01/081.jpg"/><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i lapis illuc de&longs;cenderet, non quie&longs;ceret &longs;tatim ac <lb/>
prima ip&longs;ius pars ad mundi centrum pertingeret, &longs;ed reliqu&aelig; ip&longs;ius partes <lb/>
adhuc grauitarent, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; vlterius primam partem impellerent, donec lapi&shy;<lb/>dis medium, mundi medio congrueret: quo facto lapis quie&longs;ceret. </s>
          <s id="s.001487">qu&aelig; num <lb/>
vera &longs;int, vt intelligamus, oportet prius pr&aelig;mittere, iuxta Mathematicos <lb/>
duplex e&longs;&longs;e medium, &longs;iue centrum cuiu&longs;uis magnitudinis: aliud enim e&longs;t <lb/>
centrum molis, aliud e&longs;t centrum grauitatis. </s>
          <s id="s.001488">centrum molis e&longs;t illud pun&shy;<lb/>
ctum, &agrave; quo extrema &aelig;quidi&longs;tant: centrum grauitatis e&longs;t punctum illud, &agrave; <lb/>
quo extrema &aelig;que ponderant, &longs;iue &agrave; quo graue &longs;u&longs;pen&longs;um &aelig;qu&egrave; ponderat, <lb/>
&longs;iue in &aelig;quilibrio manet. </s>
          <s id="s.001489">Porr&ograve; in corporibus regularibus, &longs;i vniformia &longs;int <lb/>
idem, &amp; vnum &longs;unt centrum molis, ac centrum grauitatis: vt in &longs;ph&aelig;ra <lb/>plumbea, idem erit <expan abbr="vtrumq;">vtrumque</expan> centrum: &longs;i ver&ograve; difformia &longs;int in grauitate, <lb/>
vt in &longs;ph&aelig;ra partim plumbea, partim lignea, diuer&longs;um erit centrum molis, <lb/>
&agrave; centro grauitatis; illud enim erit in medio &longs;ph&aelig;r&aelig;; centrum ver&ograve; graui&shy;<lb/>
tatis in parte plumbea exi&longs;tet. </s>
          <s id="s.001490">In corporibus deinde irregularibus, etiam&longs;i <lb/>
&longs;int vniformis ponderis, aliud tamen e&longs;&longs;e pote&longs;t centrum molis &agrave; <expan abbr="c&etilde;tro">centro</expan> gra&shy;<lb/>
uitatis, vt in corpore oblongo, cuius alterum extremum &longs;it reliquis parti&shy;<lb/>
bus mult&ograve; maius, vti e&longs;t claua: vbi centrum molis erit in medio longitudi&shy;<lb/>
nis clau&aelig;; centrum ver&ograve; grauitatis, erit propinquius capiti clau&aelig;. </s>
          <s id="s.001491">quando <lb/>
igitur Ari&longs;t. ait, graue de&longs;cen&longs;urum, donec ip&longs;ius medium, &longs;iue centrum, <lb/>
mundi centrum attingat; ben&egrave; dicit, &longs;i de medio grauitatis intelligat; ma&shy;<lb/>
l&egrave; autem &longs;i de medio molis. </s>
          <s id="s.001492">quia grauia omnia ratione centri grauitatis <lb/>
ponderant, <expan abbr="neq;">neque</expan> manent; ni&longs;i ip&longs;um maneat: quare ni&longs;i ip&longs;um <expan abbr="atting&atilde;t">attingant</expan> cen&shy;<lb/>
trum mundi &longs;emper grauitabunt, &amp; mouebuntur. </s>
          <s id="s.001493">Verum enim ver&ograve; ex an&shy;<lb/>
tiquorum monumentis manife&longs;tum e&longs;t, Archimedem, qui mult&ograve; po&longs;t Ari&shy;<lb/>
&longs;totelem floruit, primum omnium de centro grauitatis e&longs;&longs;e philo&longs;ophatum, <lb/>
qua ratione dicendum e&longs;&longs;et, Ari&longs;totelem de centro, molis loquutum e&longs;&longs;e, <lb/>
&amp; perinde non <expan abbr="v&longs;quequaq;">v&longs;quequaque</expan> ver&egrave;.</s>
        </p>
        <p type="main">
          <s id="s.001494"><arrow.to.target n="marg113"/></s>
        </p>
        <p type="margin">
          <s id="s.001495"><margin.target id="marg113"/>113</s>
        </p>
        <p type="main">
          <s id="s.001496">Tex. 109. <emph type="italics"/>&lpar;Pr&aelig;terea <expan abbr="quoq;">quoque</expan> &amp; per ea, qu&aelig; apparent &longs;ecundum &longs;en&longs;um, neque <lb/>
enim Lun&aelig; eclyp&longs;es tales <expan abbr="haber&etilde;t">haberent</expan> deci&longs;iones; nunc enim in ijs, qu&aelig; &longs;ecundum men&shy;<lb/>
&longs;em fiunt, figurationibus, omnes accipit diui&longs;iones: etenim recta fit, &amp; vtrinque <lb/>
curua, &amp; concaua&rpar;<emph.end type="italics"/> probat terram e&longs;&longs;e &longs;ph&aelig;ricam ratione a&longs;tronomica, ex <lb/>
Lun&aelig; eclyp&longs;ibus de&longs;umpta: nam ni&longs;i terra e&longs;&longs;et rotunda, nunquam Luna in <lb/>
eclyp&longs;i haberet tales deci&longs;iones, ide&longs;t non haberet falcatas, aut lunulatas <lb/>partes illas, qu&aelig; in eclyp&longs;i ob&longs;curantur, &amp; qua&longs;i &agrave; Luna re&longs;ecantur. </s>
          <s id="s.001497">quam&shy;<lb/>
uis enim &longs;ingulis men&longs;ibus Luna terminetur modo linea concaua, vt quan&shy;<lb/>
do noua e&longs;t; modo recta, vt quando diuidua e&longs;t: modo vtrinque curua, vt <lb/>cum &agrave; diuidua ad plenilunium tendit. </s>
          <s id="s.001498">quod fu&longs;ius primo Po&longs;ter. tex. <!-- REMOVE S-->30. ex&shy;<lb/>
po&longs;ui. </s>
          <s id="s.001499">in eclyp&longs;ibus tamen &longs;emper curuam habet lineam illam, qu&aelig; partem <lb/>eclyp&longs;atam de&longs;init; vt paulo po&longs;t explicabo. </s>
          <s id="s.001500">Vide precedentem textum 59. <lb/>
&amp; ca, qu&aelig; ibi annotaui, <expan abbr="qu&aelig;q;">qu&aelig;que</expan> tibi propo&longs;ui, &amp; plenam huius loci intelligen&shy;<lb/>
tiam a&longs;&longs;equeris. </s>
          <s id="s.001501">vide etiam, qu&aelig; mox &longs;ubdam circa huius loci reliquum.</s>
        </p>
        <p type="main">
          <s id="s.001502"><arrow.to.target n="marg114"/></s>
        </p>
        <p type="margin">
          <s id="s.001503"><margin.target id="marg114"/>114</s>
        </p>
        <p type="main">
          <s id="s.001504">Ibidem <emph type="italics"/>&lpar;Circa autem eclyp&longs;es, &longs;emper curuam habet termin&abreve;tem lineam: qua&shy;<lb/>re quoniam eclyp&longs;im patitur propter terr&aelig; obiectionem, terr&aelig; <expan abbr="circumfer&etilde;tia">circumferentia</expan> &longs;ph&aelig;&shy;<lb/>
rica exi&longs;tens, figur&aelig; cau&longs;a erit&rpar;<emph.end type="italics"/> probat rotunditatem terr&aelig; ab eclyp&longs;i lunari, <lb/>
ex eo, quod Luna &longs;ph&aelig;ric&egrave; eclyp&longs;etur, quod innuitur illis verbis, &longs;emper


<pb pagenum="82" xlink:href="009/01/082.jpg"/>curuam habet terminantem lineam, linea &longs;cilicet, qu&aelig; terminat partem <lb/>
eclyp&longs;atam &agrave; non eclyp&longs;ata, &longs;emper apparet circularis; cum autem h&aelig;c li&shy;<lb/>
nea &longs;it terminus vmbr&aelig; terr&aelig;, qu&aelig; lumen obumbrat, &longs;ignum <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> e&longs;t <lb/>
vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terr&aelig; obie&shy;<lb/>
ctionem inter ip&longs;am, &amp; Solem, ita, vt vmbra terr&aelig; protendatur <expan abbr="v&longs;q;">v&longs;que</expan> ad Lu&shy;<lb/>
nam, <expan abbr="eam&qacute;">eamque</expan>; in omni eclyp&longs;atione, &longs;iue eclyp&longs;is &longs;it &longs;upra terram, &longs;iue infra, <lb/>
ad quamlibet <expan abbr="deniq;">denique</expan> partem terr&aelig; fiat, orbiculariter eam contegit, &longs;ignum <lb/>
per&longs;picuum e&longs;t terram proijcere quoquouer&longs;us vmbram rotundam, qu&aelig; vt <lb/>
in &longs;ph&aelig;ra o&longs;tenditur, e&longs;t rotunda ad modum coni; cum ergo vmbra terr&aelig; <lb/>
ex quauis parte proijciatur, &longs;it rotunda, cert&ograve; certius colligitur, <expan abbr="terram&qacute;">terramque</expan>; <lb/>
<expan abbr="quoq;">quoque</expan> ip&longs;am rotunda figura pr&aelig;ditam e&longs;&longs;e. </s>
          <s id="s.001505">hanc eandem rationem, &longs;i libue&shy;<lb/>
rit, fu&longs;ius pertractatam videre poteris apud P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra.</s>
        </p>
        <p type="main">
          <s id="s.001506"><arrow.to.target n="marg115"/></s>
        </p>
        <p type="margin">
          <s id="s.001507"><margin.target id="marg115"/>115</s>
        </p>
        <p type="main">
          <s id="s.001508">Tex. <emph type="italics"/>&lpar;Pr&aelig;terea per astrorum apparentiam, non &longs;olum manife&longs;tum e&longs;t, quod re<lb/>tunda, &longs;ed &amp; quod magnitudine non magna &longs;it; paruo enim facto nobis tran&longs;itu ad <lb/>meridiem, &amp; Vr&longs;am, manife&longs;t&egrave; fit alter horizon circulus, ita vt a&longs;tra, qu&aelig; &longs;uper <lb/>caput, magnam habeant mutationem, &amp; non eadem appareant, &amp; ad Vr&longs;am, &amp; ad <lb/>meridiem tran&longs;euntibus, qu&aelig;dam enim in Aegypto quidem stell&aelig; <expan abbr="vid&etilde;tur">videntur</expan>, &amp; cir&shy;<lb/>
ca Cyprum, in ijs autem, qu&aelig; ad Vr&longs;am vergunt regionibus, non <expan abbr="via&etilde;tur">videntur</expan>. </s>
          <s id="s.001509">&amp; a&longs;tro&shy;<lb/>
rum ea, qu&aelig; &longs;emper in ijs, qu&aelig; ad Vr&longs;am vergunt, apparent, in illis locis occidunt. <lb/>
</s>
          <s id="s.001510">Quare non &longs;olum ex his manife&longs;tum e&longs;t rotundam e&longs;&longs;e figuram terr&aelig;, &longs;ed &amp; &longs;ph&aelig;r&aelig; <lb/>
non magn&aelig;: non enim tam celeriter in&longs;igne quippiam faceret, tran&longs;latis nobis ade&ograve; <lb/>
parum&rpar;<emph.end type="italics"/> hic textus ei, qui &longs;ph&aelig;ram mundi audiuerit perfacilis e&longs;t: propte&shy;<lb/>
rea eum breuiter &longs;ic paraphra&longs;tic&egrave; exponam. </s>
          <s id="s.001511">Terram e&longs;&longs;e rotundam, <expan abbr="atq;">atque</expan> <lb/>
re&longs;pectu c&oelig;le&longs;tium corporum non magnam, &longs;ignum e&longs;t, quod facto &agrave; nobis <lb/>
paruo itinere &longs;iue ad meridionalem plagam, &longs;iue ad <expan abbr="&longs;ept&etilde;trionalem">&longs;eptentrionalem</expan> &lpar;quam <lb/>
Vr&longs;am dicit&rpar; magnopere mutatur horizon: quod apparet primo ex varia&shy;<lb/>tione a&longs;trorum, nam qu&aelig; in primo loco &longs;upra no&longs;trum verticem <expan abbr="tr&atilde;&longs;ibant">tran&longs;ibant</expan>, <lb/>
in &longs;ecundo loco non amplius, &longs;ed alia, <expan abbr="atq;">atque</expan> alia valde ab inuicem &longs;eiuncta <lb/>
<figure id="id.009.01.082.1.jpg" place="text" xlink:href="009/01/082/1.jpg"/><lb/>ex facto quamuis paruo itinere tran&longs;eunt. </s>
          <s id="s.001512">&longs;it in <lb/>
pr&aelig;&longs;enti figura terra, vbi A, in qua facta parua <lb/>
mutatione ex loco F, in locum G, fieret magna <lb/>
mutatio <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> ver&longs;icalium B, in C, qu&aelig; mul&shy;<lb/>
tum ab inuicem di&longs;tant. </s>
          <s id="s.001513">&longs;i autem terra e&longs;&longs;et <lb/>
maior, v. <!-- REMOVE S-->g. <!-- REMOVE S-->circulus medius, tunc facta maio&shy;<lb/>
ri mutatione ex D, in E, fieret eadem a&longs;trorum <lb/>
variatio ex B, in C; &longs;ed cum nos experiamur <lb/>fieri magnam a&longs;trorum mutationem, ex parua <lb/>
locorum intercapedine, &longs;ignum e&longs;t magnope&shy;<lb/>
re mutari horizontem, ac proinde terram e&longs;&longs;e <lb/>
rotundam, ac re&longs;pectu c&oelig;le&longs;tium corporum <lb/>
paruam. </s>
          <s id="s.001514">aliud pr&aelig;terea &longs;ignum huius horizontis permutationis e&longs;t, quod <lb/>
&longs;tell&aelig;, qu&aelig; in priori loco &longs;upra horizontem apparebant, mutato paululum <lb/>
loco ad alterutram plagam, &longs;tatim ab&longs;conduntur; ali&aelig; ver&ograve; nou&aelig; <expan abbr="appar&etilde;t">apparent</expan> <lb/>vt in Aegypto, &amp; Cypro, &longs;tella, qu&aelig; dicitur Canobus &longs;upra horizontem <lb/>
a&longs;cendit; qu&aelig; &longs;i paululum Vr&longs;am, &longs;eu &longs;eptentrionem ambulaueris, &longs;tatim <lb/>
latitabit. </s>
          <s id="s.001515">Demum eiu&longs;dem cit&aelig; mutationis finitoris indicium etiam &longs;it,<pb pagenum="83" xlink:href="009/01/083.jpg"/>quod regiones &longs;eptentrionales incolentibus plurima &longs;unt a&longs;tra, qu&aelig; nun&shy;<lb/>quam occidunt, quamuis horizontem leuiter per&longs;tringant, qu&aelig; tamen Cy&shy;<lb/>
prijs, <expan abbr="atq;">atque</expan> Aegyptijs oriuntur, <expan abbr="atq;">atque</expan> occidunt. </s>
          <s id="s.001516">ex quibus &amp; rotunditas, &amp; <lb/>
paruitas terr&aelig; colligi pote&longs;t. </s>
          <s id="s.001517">has ea&longs;dem rationes fu&longs;ius explicatas repe&shy;<lb/>
ries apud P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra.</s>
        </p>
        <p type="main">
          <s id="s.001518"><arrow.to.target n="marg116"/></s>
        </p>
        <p type="margin">
          <s id="s.001519"><margin.target id="marg116"/>116</s>
        </p>
        <p type="main">
          <s id="s.001520">Tex. 111. <emph type="italics"/>&lpar;Quapropter existimantes eum, qui circa Herculeas columnas e&longs;t lo&shy;<lb/>cum coniungi ei, qui circa Indiam, &amp; hoc modo mare vnum e&longs;&longs;e, non admodum <lb/>
incredibilia exi&longs;timare videntur &amp;c.&rpar;<emph.end type="italics"/> exi&longs;timatores ho&longs;ce non perperam exi&shy;<lb/>
&longs;tima&longs;&longs;e apert&egrave; <expan abbr="c&otilde;uincunt">conuincunt</expan> Chri&longs;tophori Columbi, Argonautarum principis <lb/>
nauigationes; quibus nouus orbis repertus e&longs;t, qui inter columnas Hercu&shy;<lb/>
lis, <expan abbr="atq;">atque</expan> orientalem Indiam totus vna <expan abbr="c&utilde;">cum</expan> mari Oceano Atlantico interiacet.</s>
        </p>
        <p type="main">
          <s id="s.001521"><arrow.to.target n="marg117"/></s>
        </p>
        <p type="margin">
          <s id="s.001522"><margin.target id="marg117"/>117</s>
        </p>
        <p type="main">
          <s id="s.001523">Tex. 112. <emph type="italics"/>&lpar;Mathematicorum etiam, qui circumferenti&aelig; magnitudinem ratio&shy;<lb/>cinari tentant, ad 400. dicunt &longs;tadiorum millia, &amp;c.&rpar;<emph.end type="italics"/> quam &longs;ubtilibus rationi&shy;<lb/>
bus inue&longs;tigauerint A&longs;tronomi quantitatem terr&aelig;, optim&egrave;, ac dilucid&egrave; ex&shy;<lb/>
ponitur &agrave; P. <!-- REMOVE S-->Clauio in &longs;ph&aelig;ra: quem &longs;i libet, con&longs;ule, ne inani labore opu&shy;<lb/>
&longs;culum i&longs;tud exere&longs;cat.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001524"><emph type="italics"/>Ex Tertio de C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001525"><arrow.to.target n="marg118"/></s>
        </p>
        <p type="margin">
          <s id="s.001526"><margin.target id="marg118"/>118</s>
        </p>
        <p type="main">
          <s id="s.001527">Tex. 40. <emph type="italics"/>&lpar;Figur&aelig; autem omnes componuntur ex pyramidibus: rectilinea <lb/>quidem ex rectilineis: &longs;ph&aelig;ra ver&ograve; ex octo partibus componitur&rpar;<emph.end type="italics"/> Ale&shy;<lb/>xander exi&longs;timat, Ari&longs;totelem dicere &longs;ph&aelig;ram con&longs;tare ex octo <lb/>
partibus illis, qu&aelig; de&longs;ignantur per tres circulos, quorum duo &longs;e&shy;<lb/>cant &longs;e mutu&ograve; ad angulos rectos, vt in &longs;ph&aelig;ra mundi faciunt duo coluri; <lb/>
tertius ver&ograve; medios illos diuidit &aelig;quidi&longs;tanter &agrave; &longs;ectionibus <expan abbr="illor&utilde;">illorum</expan> mutuis, <lb/>
quemadmodum &aelig;quator in &longs;ph&aelig;ra mundi &longs;ecat duos coluros. </s>
          <s id="s.001528">ex quibus &longs;e&shy;<lb/>
ctionibus tota &longs;ph&aelig;ra in octo partes diuiditur, quibus &longs;ph&aelig;ram componi <lb/>
vult Ari&longs;toteles. <!-- KEEP S--></s>
          <s id="s.001529">aduerte tamen hanc &longs;ph&aelig;r&aelig; compo&longs;itionem nullo modo <lb/>
habere partes actu, cum &longs;ph&aelig;ra &longs;it vnica &longs;implici &longs;uperficie terminata; &longs;ed <lb/>
qu&aelig; tantum &longs;int &agrave; pr&aelig;dictis imaginatis circulis de&longs;ignat&aelig;: at ver&ograve; ali&aelig; fi&shy;<lb/>
gur&aelig;, qu&aelig; pluribus planis terminantur, vt cubus, octaedrum, &amp; &longs;imilia, qu&aelig; <lb/>Ari&longs;t. vocat rectilineas, quia terminantur &longs;uperficiebus rectilineis actu di&shy;<lb/>
&longs;tinctis ab inuicem ex natura &longs;ua, non per no&longs;tram de&longs;ignationem, ide&ograve; re&shy;<lb/>
ct&egrave; dicuntur componi ex pyramidibus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->dicimus cubum componi ex &longs;ex <lb/>
pyramidibus, quia cum habeat &longs;ex ba&longs;es, cogitamus &longs;upra <expan abbr="vnamquamq;">vnamquamque</expan> il&shy;<lb/>
larum &longs;ingulas pyramides erigi, quarum omnium vertices ad idem punctum <lb/>
medium intra cubum imaginatum coeant. </s>
          <s id="s.001530">&amp; &longs;ic de reliquis &longs;olidis. </s>
          <s id="s.001531">qu&aelig; qua <lb/>
ratione re&longs;oluantur in plures pyramides, con&longs;tat ex 10. 11. 12. &amp; 13. Ele&shy;<lb/>
mentorum Euclidis, at ver&ograve; in &longs;ph&aelig;ra nullum reale compo&longs;itionis, aut di&shy;<lb/>
ui&longs;ionis fundamentum reperitur.</s>
        </p>
        <p type="main">
          <s id="s.001532"><arrow.to.target n="marg119"/></s>
        </p>
        <p type="margin">
          <s id="s.001533"><margin.target id="marg119"/>119</s>
        </p>
        <p type="main">
          <s id="s.001534">Tex. <emph type="italics"/>&lpar;Ad h&aelig;c nece&longs;&longs;e e&longs;t non omne corpus e&longs;&longs;e diui&longs;ibile dicere, &longs;ed repugnare <lb/>certi&longs;&longs;imis &longs;cientijs; nam Mathematic&aelig; ip&longs;um quidem intelligibile, accipiunt diui&shy;<lb/>
&longs;ibile&rpar;<emph.end type="italics"/> ip&longs;um intelligibile, ide&longs;t, quantitatem ab&longs;tractam tam continuam, <lb/>quam di&longs;cretam, quam &longs;tatuunt Philo&longs;ophi e&longs;&longs;e &longs;ubiectam materiam ma&shy;<lb/>
thematicarum. </s>
          <s id="s.001535">quam ideo appellant intelligibilem, quia cum &longs;it ab&longs;tracta <lb/>
per intellectum &agrave; &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel&shy;


<pb pagenum="84" xlink:href="009/01/084.jpg"/>lectu perceptibilis. </s>
          <s id="s.001536">Hanc eandem &longs;upponunt e&longs;&longs;e diui&longs;ibilem in infinitum, <lb/>
vt &longs;upra 3. Phy&longs;. textu 31. dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001537"><arrow.to.target n="marg120"/></s>
        </p>
        <p type="margin">
          <s id="s.001538"><margin.target id="marg120"/>120</s>
        </p>
        <p type="main">
          <s id="s.001539">Tex. 66. <emph type="italics"/>&lpar;Omnin&ograve; autem eniti &longs;implicibus corporibus figuras tribuere irratio&shy;<lb/>
nabile e&longs;t. </s>
          <s id="s.001540">prim&ograve; quidem, quia accidit non repleri totum; nam in planis tres figur&aelig; <lb/>
videntur implere locum, Triangulus, Quadratum, &amp; Sexangulus&rpar;<emph.end type="italics"/> per &longs;implicia <lb/>
corpora intelligit quatuor elementa. </s>
          <s id="s.001541">Vult enim probare quatuor elemen&shy;<lb/>
ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au&shy;<lb/>
tem Ari&longs;t. rationem prob&egrave; percipiamus, &longs;ciendum, quod implere totum, <lb/>
&longs;iue locum, ill&aelig; figur&aelig; dicuntur, qu&aelig; &longs;imul &longs;uis angulis in plano quopiam ad <lb/>
vnum, <expan abbr="atq;">atque</expan> idem punctum vnit&aelig; locum illum totum, qui circa punctum il&shy;<lb/>
lud con&longs;i&longs;tit, <expan abbr="c&otilde;tegunt">contegunt</expan>, ita vt nihil vacui inter ip&longs;as relinquatur. </s>
          <s id="s.001542">tales &longs;unt, <lb/>
quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnit&aelig; nihil vacui in <lb/>
pauimento relinquant. </s>
          <s id="s.001543">huiu&longs;modi &longs;unt triangula &aelig;quilatera &lpar;de his enim <lb/>
intelligendus e&longs;t textus&rpar; quadrata, &amp; hexagona, &longs;iue &longs;exilatera regularia; <lb/>
<figure id="id.009.01.084.1.jpg" place="text" xlink:href="009/01/084/1.jpg"/><lb/>
nam &longs;ex triangula &aelig;quilatera &longs;imul iuncta in plano paui&shy;<lb/>
re po&longs;&longs;unt, vt patet in figura pr&aelig;&longs;enti; ratio huius e&longs;t, <lb/>
quia omnes anguli circa idem punctum &lpar;y. </s>
          <s id="s.001544">g. <!-- REMOVE S-->A, in hac <lb/>
figura&rpar; in plano, quotquot fuerint con&longs;tituti, &longs;unt &aelig;qua&shy;<lb/>
les quatuor rectis, ex coroll. </s>
          <s id="s.001545">&longs;ecundo 15. primi Elemen&shy;<lb/>
ti: cum igitur &longs;ex anguli, trianguli &aelig;quilateri <expan abbr="&aelig;quiuale&atilde;t">&aelig;quiualeant</expan> <lb/>
quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/>
A, totum locum circa illud implere po&longs;&longs;unt. </s>
          <s id="s.001546">Quadratum etiam replere lo&shy;<lb/>
<figure id="id.009.01.084.2.jpg" place="text" xlink:href="009/01/084/2.jpg"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;int recti, &longs;i <lb/>
quatuor quadrata ad idem punctum A, copulentur, vt in <lb/>
figura apparet, replebunt eadem de cau&longs;a vacuum.</s>
        </p>
        <p type="main">
          <s id="s.001547">Hexagonum quoque regulare, ide&longs;t &aelig;quilaterum, &amp; <lb/>
&aelig;quiangulum idem pr&aelig;&longs;tare pote&longs;t; cum enim tres angu&shy;<lb/>
li ip&longs;ius &aelig;quiualeant quatuor rectis, &longs;i tria hexagona ad <lb/>
idem punctum A, vt in figura adaptentur, nece&longs;&longs;ari&ograve; ni&shy;<lb/>
hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s>
          <s id="s.001548">pr&aelig;ter has tres <lb/>
<figure id="id.009.01.084.3.jpg" place="text" xlink:href="009/01/084/3.jpg"/><lb/>figuras, nulla alia reperitur, qu&aelig; i&longs;tud efficere po&longs;&shy;<lb/>
&longs;it. </s>
          <s id="s.001549">cuius demon&longs;trationem perfectam videre pote&shy;<lb/>
ris in fine commentarij P. <!-- REMOVE S-->Clauij &longs;uper 4. Elem. nos <lb/>
ea tantum attingimus, qu&aelig; percipi po&longs;&longs;int ab homi&shy;<lb/>
ne vix mathematicis tincto: &longs;ed tamen, qu&aelig; &longs;en&longs;um <lb/>
Ari&longs;totelis patefaciunt. </s>
          <s id="s.001550">Ali&aelig; porr&ograve; figur&aelig; replen&shy;<lb/>
tes locum planum, quibus aliquando Architectores <lb/>
vtuntur, vel &longs;unt irregulares, vel ad pr&aelig;dictas redu&shy;<lb/>
ci po&longs;&longs;unt. </s>
          <s id="s.001551">cum igitur tres tantum ex figuris planis <lb/>
totum repleant, h&aelig; &longs;ol&aelig; poterunt elementis attri&shy;<lb/>
bui, ac propterea non &longs;ufficient, ni&longs;i pro tribus elementis. </s>
          <s id="s.001552">quare quartum <lb/>
<expan abbr="ab&longs;q;">ab&longs;que</expan> figura relinquetur; quod e&longs;t ab&longs;urdum.</s>
        </p>
        <pb pagenum="85" xlink:href="009/01/085.jpg"/>
        <p type="head">
          <s id="s.001553"><emph type="italics"/>Admirabilis qu&aelig;dam A&pgrave;um industria.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001554">C&aelig;terum occa&longs;ione harum figurarum illud hoc loco apponere vi&shy;<lb/>
&longs;um e&longs;t, quod Pappus <expan abbr="Alex&atilde;drinus">Alexandrinus</expan> initio quinti libri collectionum <lb/>
mathematicarum &longs;cribit, De admirabili Apum indu&longs;tria, atque <lb/>
prudentia in con&longs;truendo &longs;uas cellulas figura hexagona regulari. <lb/>
</s>
          <s id="s.001555">cum enim vellent omne vacuum excludere, &amp; pr&aelig;terea capaci&longs;&longs;imam <expan abbr="om-ni&utilde;">om&shy;<lb/>
nium</expan> figuram habere, hexagonam accepere, qu&aelig; inter pr&aelig;dictas tres vtrum&shy;<lb/>
que pr&aelig;&longs;tat, nam &amp; inane omne excludit, &amp; illarum trium capaci&longs;&longs;ima e&longs;t, <lb/>
cum magis ad circularem figuram accedat: vt patet ex tractatu de figuris <lb/>I&longs;operimetris, qui e&longs;t apud Clauium in &longs;ph&aelig;ra, necnon in Geometria pra&shy;<lb/>
ctica. </s>
          <s id="s.001556">hoc ide&ograve; libentius recen&longs;ui, quia animaduerti naturales hi&longs;toriogra&shy;<lb/>
phos omnes latere, vel ip&longs;um Aldobrandum no&longs;trum, qui quamuis indu&shy;<lb/>
&longs;trio&longs;&aelig; Apis in&longs;tar omnia delibauerit, i&longs;tud tamen de Apibus artificium tan&shy;<lb/>
ta &longs;apientia plenum, ne&longs;cio quo modo pr&aelig;termi&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.001557"><arrow.to.target n="marg121"/></s>
        </p>
        <p type="margin">
          <s id="s.001558"><margin.target id="marg121"/>121</s>
        </p>
        <p type="main">
          <s id="s.001559">Ibidem <emph type="italics"/>&lpar;In &longs;olidis ver&ograve; du&aelig; &longs;olum pyramis, &amp; cubus&rpar;<emph.end type="italics"/> ide&longs;t replent locum <lb/>
&longs;olidum. </s>
          <s id="s.001560">nullum reperi, qui in hoc loco explicando non errauerit; nam Gr&aelig;&shy;<lb/>
ci, qui alioqui &longs;olent mathematica prob&egrave; intelligere, hic omnes lap&longs;i &longs;unt, <lb/>
<expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; &amp; Arabes, &amp; Latinos in <expan abbr="e&atilde;dem">eandem</expan> foueam &longs;upra &longs;e mi&longs;er&egrave; traxerunt. <lb/>
</s>
          <s id="s.001561">communis fer&egrave; error omnium fuit, pyramides plures &longs;imul compactas po&longs;&shy;<lb/>
&longs;e replere &longs;olidum locum. </s>
          <s id="s.001562">quod vt melius intelligamus, &longs;ciendum e&longs;t, reple&shy;<lb/>
re locum <expan abbr="&longs;olid&utilde;">&longs;olidum</expan> nihil aliud e&longs;&longs;e, quam &longs;i plura corpora &longs;olida &longs;imul ad idem <lb/>
punctum coaptata, ita con&longs;tipentur, vt totum &longs;patium, quod e&longs;t circa pun&shy;<lb/>
ctum illud omnin&ograve; occupent, hoc e&longs;t, nihil vacui inter ip&longs;a relinquatur: &longs;i&shy;<lb/>
cut enim pr&aelig;dict&aelig; tres figur&aelig; plan&aelig;, de quibus paul&ograve; ante, replent locum <lb/>planum, ide&longs;t &longs;uperficiem; ita cubi replent &longs;olidum, ide&longs;t &longs;oliditatem &longs;imul <lb/>
vniti con&longs;tituunt, ita vt &longs;i octo cubi &longs;imul ad idem punctum <expan abbr="coapt&etilde;tur">coaptentur</expan>, con&shy;<lb/>&longs;tituant corpus &longs;olidum ex octo illius con&longs;tatum, <expan abbr="nihil&qacute;">nihilque</expan>; inane inter ip&longs;os <lb/>
cubos relinquatur. </s>
          <s id="s.001563">&amp; &longs;icuti plan&aelig; ill&aelig; figur&aelig; erant conficiendis pauimentis <lb/>
apt&aelig;, ita &longs;olid&aelig; h&aelig; muris, qui corpora &longs;unt &longs;olida, <expan abbr="con&longs;tru&etilde;dis">con&longs;truendis</expan> idonea &longs;unt. <lb/>
</s>
          <s id="s.001564"><expan abbr="Not&atilde;">Notam</expan> dum pr&aelig;terea, quod per pyramidem debemus intelligere pyramidem <lb/>
regularem, qu&aelig; dicitur etiam Tetraedrum, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;ecunda inter <expan abbr="quinq;">quinque</expan> cor&shy;<lb/>
pora regularia rectilinea, qu&aelig; alias Platonica corpora dicuntur. </s>
          <s id="s.001565"><expan abbr="eorum&qacute;">eorumque</expan>; <lb/>definitiones &longs;unt in 11. Elem. <!-- KEEP S--></s>
          <s id="s.001566">Tetraedrum autem &longs;ic definitur, e&longs;t figura &longs;o&shy;<lb/>
lida &longs;ub quatuor triangulis &aelig;quilateris, <expan abbr="atq;">atque</expan> inuicem &aelig;qualibus contenta: <lb/>
de hac inquam e&longs;t &longs;ermo. </s>
          <s id="s.001567">quia &longs;i liceret intelligere de irregularibus figuris, <lb/>infinit&aelig; reperirentur figur&aelig; tam plan&aelig;, quam &longs;olid&aelig;, qu&aelig; vtrumque locum <lb/>
complerent. </s>
          <s id="s.001568">Aduertendum tandem Ari&longs;t. videri loqui de repletione loci <lb/>
&longs;olidi, quia tran&longs;it &agrave; plan&iuml;s figuris ad &longs;olidas. </s>
          <s id="s.001569">&amp; quia &longs;i h&aelig; du&aelig; pyramis, &amp; <lb/>cubus replent locum &longs;olummodo &longs;ecundum &longs;uas &longs;uperficies, qu&aelig; &longs;unt trian&shy;<lb/>
gulum, &amp; quadratum, iam de his cum proxim&egrave; ante dixi&longs;&longs;et, quid opus fui&longs;&shy;<lb/>
&longs;et idem po&longs;t modum repetere. </s>
          <s id="s.001570">ad h&aelig;c &longs;i in medium &longs;olida h&aelig;c duo profert, <lb/>
<expan abbr="ait&qacute;">aitque</expan>; ip&longs;a replere locum, intelligens, planum, profect&ograve; non loquitur forma&shy;<lb/>liter, ide&longs;t de ip&longs;is, vt &longs;olida &longs;unt. </s>
          <s id="s.001571">Quare Ari&longs;t. videretur &longs;ibi non con&longs;tare, <lb/>
vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s>
          <s id="s.001572">deceptus <pb pagenum="86" xlink:href="009/01/086.jpg"/>fort&egrave; fuit Ari&longs;t. e&ograve; quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi&shy;<lb/>
bus, ver&ugrave;m ill&aelig; non &longs;unt regulares, ide&longs;t <expan abbr="n&otilde;">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten&shy;<lb/>
dam. </s>
          <s id="s.001573">Verum quidem e&longs;t octo cubos &longs;imul adactos &longs;oliditatem conficere, <lb/>
quia ad id nece&longs;&longs;arij &longs;unt octo anguli &longs;olidi, quos octo cubi pr&aelig;bere po&longs;&longs;unt, <lb/>
cum anguli ip&longs;orum &longs;int recti, &amp; &longs;olidi. </s>
          <s id="s.001574">Verum enim ver&ograve; plures pyramides <lb/>
regulares, &longs;iue plura Tetraedra non po&longs;&longs;e replere vacuum, <expan abbr="&longs;olidum&qacute;">&longs;olidumque</expan>; con&shy;<lb/>
&longs;tituere, ex eo patet, quia &longs;i id pr&aelig;&longs;tarent, conflarent nece&longs;&longs;ari&ograve;, vel vnum <lb/>
ex <expan abbr="quinq;">quinque</expan> corporibus regularibus, de quibus in 13. Elemen. <!-- REMOVE S-->vel aliud quod&shy;<lb/>
piam; non aliud, nam, vt patet ex &longs;cholio 13. Elem. non dantur, ni&longs;i illa. <lb/>
</s>
          <s id="s.001575">quinque; <expan abbr="neq;">neque</expan> vllum ex illis, quia diameter huiu&longs;modi corporis, quod com&shy;<lb/>
poneretur ex illis pyramidibus, e&longs;&longs;et dupla lateris eiu&longs;dem, vt patet, quia <lb/>
pyramides ill&aelig; omnes concurrerent ad centrum &longs;ph&aelig;r&aelig; illas omnes com&shy;<lb/>
plectentis, quare latus vnius pyramidis &agrave; &longs;uperficie &longs;ph&aelig;r&aelig; incipiens de&longs;i&shy;<lb/>
neret in centrum, ergo latus i&longs;tud e&longs;&longs;et &longs;emidiameter, quapropter tota dia&shy;<lb/>meter illius &longs;ph&etail;r&aelig;, &amp; con&longs;equenter huius corporis in illa in&longs;cripti, e&longs;&longs;et du&shy;<lb/>
pla lateris eiu&longs;dem figur&aelig; &longs;olid&aelig; in&longs;cript&aelig;, &longs;ed nullo talis proportio diame&shy;<lb/>
tri alicuius ex illis <expan abbr="quinq;">quinque</expan> &longs;olidis regularibus ad latus eiu&longs;dem reperitur, <lb/>
qu&aelig; &longs;it nimirum dupla, vt patet ex vltimis demon&longs;trationibus 13. Elem. ini&shy;<lb/>
tio facto &agrave; 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/>
inter diametrum, &amp; latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani&shy;<lb/>
fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo&shy;<lb/>
do replere locum &longs;olidum. </s>
          <s id="s.001576">cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t. nullo <lb/>
modo po&longs;&longs;e verificari de repletione &longs;olidi per plura Tetraedra, &amp; omnes <lb/>
tamen commentatores auctoritate Ari&longs;t. decepti pro ip&longs;o &longs;tarent, dubius, <lb/>
<expan abbr="anceps&qacute;">ancepsque</expan>; diu h&aelig;&longs;i, neque quid quam mea Minerua a&longs;&longs;erere au&longs;us &longs;um, &longs;ed P. <lb/>
<!-- REMOVE S-->Clauium pr&aelig;ceptorem meum per literas con&longs;ului, qui in hunc modum hu&shy;<lb/>
mani&longs;&longs;im&egrave; re&longs;pondit; cubus implet locum quater &longs;umptus, ad idem enim <lb/>
punctum quatuor cubi coaptantur: &longs;ic etiam pyramis &longs;exies &longs;umpta, &longs;eu &longs;ex <lb/>pyramides ad idem punctum iunct&aelig; ratione &longs;ub&longs;tantium <expan abbr="triangulor&utilde;">triangulorum</expan> &aelig;qui&shy;<lb/>
laterorum. </s>
          <s id="s.001577">Verum hac ratione non videntur implere locum &longs;olidum, fa&shy;<lb/>teor; &longs;ed tamen Ari&longs;t. in eo tex. <!-- REMOVE S-->non loquitur de repletione loci &longs;olidi. </s>
          <s id="s.001578">h&aelig;c <lb/>
ip&longs;e. </s>
          <s id="s.001579">&longs;i igitur libeat Ari&longs;totelem, quod fort&egrave; Clauius intendebat defendere, <lb/>
dicendum e&longs;t cum eo Ari&longs;t non loqui de repletione loci &longs;olidi: <expan abbr="neq;">neque</expan> loqui <lb/>
de cubo, &amp; Tetraedro, quatenus &longs;unt corpora, &longs;ed quatenus habent &longs;uper&shy;<lb/>
ficies, cubus quidem &longs;ex quadratas, Tetraedrum autem quatuor &aelig;quilate&shy;<lb/>
ras &longs;uperficies, qu&aelig; du&aelig; figur&aelig;, vt &longs;upra in hoc textu vidimus, replent lo&shy;<lb/>
cum: <expan abbr="atq;">atque</expan> hoc modo facimus Ari&longs;totelem non formaliter loquentem. </s>
          <s id="s.001580">ex&shy; <lb/>
aduers&ograve; ne videamur magis Ari&longs;t. quam veritatem &longs;equi, videtur dicen&shy;<lb/>
dum, Ari&longs;totilem formaliter locutum e&longs;&longs;e, &amp; vt patet ex rationibus &longs;upra <lb/>
allatis de repletione &longs;olidi e&longs;&longs;e intelligendum, vt etiam intellexerunt omnes <lb/>
huius loci expo&longs;itores; Verumtamen ip&longs;um erra&longs;&longs;e, dum plures pyramides <lb/>
replere &longs;olidum exi&longs;timauit. </s>
          <s id="s.001581">Vtrumuis dixerimus, non tamen Ari&longs;t. ab om&shy;<lb/>ni errore vindicabimus. </s>
          <s id="s.001582">Hoc tamen certum e&longs;t, ex pr&aelig;dictis, Gr&aelig;cos om&shy;<lb/>
nes pariter, ac Latinos, illos &longs;equentes, lapos e&longs;&longs;e, a&longs;&longs;erentes duodecim py&shy;<lb/>
ramides complere &longs;olidum locum, <expan abbr="atq;">atque</expan> Dodecaedrum con&longs;tituere; nam py&shy;<lb/>
ramides Dodecaedron con&longs;tituentes non &longs;unt regulares, ide&longs;t, non &longs;unt Te&shy;


<pb pagenum="87" xlink:href="009/01/087.jpg"/>traedra &lpar;de quibus tamen Ari&longs;t. loquitur&rpar; vt patet ex &longs;upra dictis. </s>
          <s id="s.001583">Indul&shy;<lb/>
geas Lector, &longs;i hoc loco nece&longs;&longs;e fuit in Geometri&aelig; penetralia ingredi: ope&shy;<lb/>
r&aelig;pretium enim e&longs;t aliquando ip&longs;is Mathematicis &longs;atisfacere. </s>
          <s id="s.001584">tu ver&ograve;, &longs;i <lb/>
adeo es mathematicis imbutus, con&longs;ule po&longs;tremas demon&longs;tra. </s>
          <s id="s.001585">13. Elem. &amp; <lb/>
pr&aelig;cipu&egrave; &longs;cholium vltimum, vbi plura de his corporibus &longs;citu digni&longs;&longs;ima, <lb/>
<expan abbr="atq;">atque</expan> huc &longs;pectantia reperies ex his omnibus Mathematica, qu&aelig; no&longs;tr&aelig; &longs;unt <lb/>
partes, per&longs;picu&egrave; &longs;atis expo&longs;uimus.</s>
        </p>
        <p type="main">
          <s id="s.001586">Multo po&longs;t tempore, qu&agrave;m h&aelig;c &longs;crip&longs;eram incidi fort&egrave; in cap. 38. &longs;pecu&shy;<lb/>
lationem 10. Benedicti de placitis Ari&longs;t. <!-- REMOVE S--><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t. hoc loco <lb/>
erroris notari, dum a&longs;&longs;eruit duodecim pyramides replere <expan abbr="loc&utilde;">locum</expan> corporeum, <lb/>
ide&longs;t, vt exponit ip&longs;e, &longs;ex pyramides &longs;uper hexagonam aliquam figuram <lb/>
&longs;uperficialem, &amp; &longs;ex &longs;ub eadem, id pr&aelig;&longs;tarent, cum potius maius vacuum <lb/>
remaneat ad quamlibet partium &longs;upra, &amp; infra, quam plenum. </s>
          <s id="s.001587">h&aelig;c ip&longs;e. </s>
          <s id="s.001588">&longs;ed <lb/>
expo&longs;itio i&longs;ta puerili, ne dum Ari&longs;t. ingenio pror&longs;us indigna e&longs;t: vt propte&shy;<lb/>
rea exi&longs;timem ca&longs;u potius eum Ari&longs;t. rect&egrave; reprehendi&longs;&longs;e, quam ex certa <lb/>
&longs;cientia, cum illius erratum maiori errato conetur corrigere. </s>
          <s id="s.001589">Incidi po&shy;<lb/>
&longs;trem&ograve; in Indicem librorum, quem Maurolyius &longs;u&aelig; Co&longs;mographi&aelig; pr&aelig;po&shy;<lb/>
nit, vbi &longs;ic ait: Demon&longs;tramus autem in libello de figuris planis, <expan abbr="&longs;olidis&qacute;">&longs;olidisque</expan>; <lb/>locum replentibus, cubos per &longs;e, pyramides ver&ograve; cum octaedris compactas <lb/>
dumtaxat implere locum, qua in re Auerroem erra&longs;&longs;e pueriliter manife&longs;tum <lb/>
erit. </s>
          <s id="s.001590">Vides igitur tanti viri auctoritate confirmari no&longs;tram &longs;ententiam, py&shy;<lb/>
ramides videlicet per &longs;e, non replere vacuum. </s>
          <s id="s.001591">cum igitur con&longs;tet vnam tan&shy;<lb/>
tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. &amp; alij plures exi&shy;<lb/>
&longs;timarunt, replere totum &longs;olidum; nulla ratione poterunt <expan abbr="elem&etilde;ta">elementa</expan> quatuor, <lb/>
quatuor diuer&longs;is figuris indui, &longs;ed vnum tantummodo, quare reliqua <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/>
figura remanere nece&longs;&longs;e e&longs;&longs;et: quod e&longs;t omnino inconueniens.</s>
        </p>
        <p type="main">
          <s id="s.001592"><arrow.to.target n="marg122"/></s>
        </p>
        <p type="margin">
          <s id="s.001593"><margin.target id="marg122"/>122</s>
        </p>
        <p type="main">
          <s id="s.001594">Tex. 71 <emph type="italics"/>&lpar;Deinde &longs;i terra e&longs;t cubus &amp;c.&rpar;<emph.end type="italics"/> lege definitiones 11. Elem. qu&aelig; &longs;unt <lb/>admodum faciles, ibi reperies definitiones quinque corporum regularium, <lb/>
quorum figuras Plato elementis tribuebat: qua ver&ograve; id ratione faceret, ha&shy;<lb/>
bes in &longs;ph&aelig;ra Clau. <!-- KEEP S--></s>
          <s id="s.001595">Simpl. <!-- REMOVE S-->etiam hoc loco &longs;atisfacit.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001596"><emph type="italics"/>Ex Quarto de C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001597"><arrow.to.target n="marg123"/></s>
        </p>
        <p type="margin">
          <s id="s.001598"><margin.target id="marg123"/>123</s>
        </p>
        <p type="main">
          <s id="s.001599">Tex. 33. <emph type="italics"/>&lpar;Deinde ad &longs;imiles videtur angulos ignis quidem &longs;ur&longs;um ferri, <lb/>terra autem deor&longs;um, &amp; omnin&ograve; quod grauitatem habet, quare nece&longs;&longs;e <lb/>
est ferri ad medium. </s>
          <s id="s.001600">hoc autem vtrum accidit ad ip&longs;um terr&aelig; medium, <lb/>
an ad vniuer&longs;i, quoniam idem ip&longs;orum &longs;it, alius &longs;ermo e&longs;t&rpar;<emph.end type="italics"/> cum vellet <lb/>
<figure id="id.009.01.087.1.jpg" place="text" xlink:href="009/01/087/1.jpg"/><lb/>
probare Ari&longs;toteles dari <expan abbr="p&utilde;ctum">punctum</expan> quoddam in medio <lb/>
mundi, ad quod grauia de&longs;cendant, &amp; concurrent: <lb/>
&amp; &agrave; quo leuia a&longs;cendat; vtitur, pr&aelig;ter alias, etiam <lb/>
ratione aliqua ex parte mathematica; qu&aelig; e&longs;t huiu&longs;&shy;<lb/>
modi. </s>
          <s id="s.001601">videmus ignem, &amp; c&aelig;tera l&etail;uia a&longs;cendere &agrave; <lb/>
terra &longs;ur&longs;um ad angulos &aelig;quales; &longs;imiliter videmus <lb/>terram, &amp; c&etail;tera grauia de&longs;cendere ad terram deor&shy;<lb/>
&longs;um ad angulos &aelig;quales, quod &longs;ignum e&longs;t omnia i&longs;ta <lb/>
idem mundi medium re&longs;picere: v.g. <!-- REMOVE S-->&longs;it terra in figu&shy;<lb/>
ra pr&aelig;&longs;enti circulus E C D, cuius medium, &longs;ine cen&shy;


<pb pagenum="88" xlink:href="009/01/088.jpg"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, qu&aelig; facit angulos in &longs;u&shy;<lb/>
perficie terr&aelig; &aelig;quales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>eandem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos &aelig;quales de&longs;cendit. </s>
          <s id="s.001602">linea autem, qu&aelig; <lb/>
facit tales angulos tendit ad centrum &longs;ph&aelig;r&aelig; A, vt patet ad &longs;en&longs;um in figu&shy;<lb/>
ra, &amp; probari pote&longs;t geometric&egrave; ex primis tertij Elem. ex quibus patet tam <lb/>
l&aelig;uia, quam grauia, qu&aelig; per talem lineam ferantur, re&longs;picere centrum A, <lb/>
&longs;ph&aelig;r&aelig;. </s>
          <s id="s.001603">Vtrum autem i&longs;tud centrum &longs;it idem cum <expan abbr="c&etilde;tro">centro</expan> totius mundi, alius, <lb/>
inquit, e&longs;t &longs;ermo, hoc e&longs;t, ad a&longs;tronomum pertinet. </s>
          <s id="s.001604">vide igitur hac de re <lb/>
pulchram de&longs;&longs;ertationem apud Clauium in &longs;ph&aelig;ra: qui probat euidenter <lb/>
e&longs;&longs;e vnum, &amp; idem.</s>
        </p>
        <p type="main">
          <s id="s.001605"><arrow.to.target n="marg124"/></s>
        </p>
        <p type="margin">
          <s id="s.001606"><margin.target id="marg124"/>124<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001607"><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap. vlt. </s>
          <s id="s.001608">de C&oelig;lo. <!-- KEEP S--></s>
          <s id="s.001609">cuius loco &igrave;n-<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001610"><arrow.to.target n="marg125"/><lb/>
<arrow.to.target n="marg126"/><lb/>
<emph type="italics"/>terim Lector adeat Di&longs;cur&longs;um Italicum Galil&aelig;i Galil&aelig;i, de his,<emph.end type="italics"/><lb/>
<arrow.to.target n="marg127"/><lb/>
<emph type="italics"/>qu&aelig; in aqua mouentur, ac natant: ubi prop&egrave; finem, plura in hu-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg128"/><lb/>
<emph type="italics"/>ius capitis explicationem affert.<emph.end type="italics"/><lb/>
<arrow.to.target n="marg129"/></s>
        </p>
        <p type="margin">
          <s id="s.001611"><margin.target id="marg125"/>125</s>
        </p>
        <p type="margin">
          <s id="s.001612"><margin.target id="marg126"/>126</s>
        </p>
        <p type="margin">
          <s id="s.001613"><margin.target id="marg127"/>127</s>
        </p>
        <p type="margin">
          <s id="s.001614"><margin.target id="marg128"/>128</s>
        </p>
        <p type="margin">
          <s id="s.001615"><margin.target id="marg129"/>129</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001616"><emph type="italics"/>Ex Lib. 2. de Generatione, &amp; Corruptione.<emph.end type="italics"/><lb/>
<arrow.to.target n="marg130"/><!-- KEEP S--></s>
        </p>
        <p type="margin">
          <s id="s.001617"><margin.target id="marg130"/>130</s>
        </p>
        <p type="main">
          <s id="s.001618">Tex. 56. <emph type="italics"/>&lpar;ldeoqu&eacute; non prima latio cau&longs;a Generationis, &amp; Corruptionis e&longs;t, <lb/>
&longs;ed qu&aelig; &longs;ecundum obliquum circulum, in hac enim &amp; continuum vnum <lb/>
e&longs;t &amp; moueri duobus motibus&rpar;<emph.end type="italics"/> per primam lationem intelligit mo&shy;<lb/>tum primi mobilis, qui &longs;it &longs;uper polis mundi, quo Stell&aelig; omnes <lb/>
ab oriente in occidentem rect&agrave; feruntur. </s>
          <s id="s.001619">per obliquum ver&ograve; circulum in&shy;<lb/>
telligit Zodiacum, qui obliquus e&longs;t, quia poli eius &longs;unt alij &agrave; polis mundi, &amp; <lb/>
quia non tendit rect&agrave; ab ortu ad occa&longs;um, &longs;ed in &longs;ph&aelig;ra mundi tran&longs;uer&shy;<lb/>
&longs;us e&longs;t, &amp; deflectit &agrave; &longs;eptentrione in meridiem, quamuis non rect&agrave;, vt in <lb/>
&longs;ph&aelig;ra explicari &longs;olet. </s>
          <s id="s.001620">motus ergo Planetarum, qui fit &longs;ecundum hunc cir&shy;<lb/>
culum, &amp; ip&longs;e obliquus, &amp; tran&longs;uer&longs;us codem modo erit; ferrentur que per <lb/>
eum &agrave; Borea ad Au&longs;trum, &amp; &egrave; conuer&longs;o; ex quo acce&longs;&longs;u, &amp; rece&longs;&longs;u efficiunt <lb/>
&aelig;&longs;tatem, &amp; hyemem, item generationes, &amp; corruptiones. </s>
          <s id="s.001621">Sol porr&ograve;, &amp; pla&shy;<lb/>
net&aelig;, qui motibus proprijs hunc circulum peragunt, dicuntur moueri duo&shy;<lb/>
bus motibus, &amp; quidem contrarijs: quoniam dum Sol. </s>
          <s id="s.001622">v. <!-- REMOVE S-->g. <!-- REMOVE S-->per Zodiacum <lb/>
graditur motu proprio, interim etiam &agrave; primo mobili fertur ab ortu in oc&shy;<lb/>
ca&longs;um: ex quibus duobus motibus fit vnus tantum Solis motus &longs;piralis, qui <lb/>
mixtus e&longs;t, ide&longs;t, qui fit &agrave; duobus motoribus; vnde re vera Sol non mouetur <lb/>
duobus motibus contrarijs re ip&longs;a di&longs;tinctis; hoc enim impo&longs;&longs;ibile e&longs;t: &longs;ed <lb/>
motu mixto ex duobus, qui &longs;piralis e&longs;t, circa mundum de&longs;cribens &longs;piras ab <lb/>
vno tropico ad alterum: qui, vt dixi, cau&longs;atur &agrave; duobus motoribus, qui &longs;unt <lb/>
Sol ip&longs;e, mouens &longs;e ip&longs;um per Zodiacum: &amp; primum mobile mouens in&longs;u&shy;<lb/>
per ip&longs;um Solem, &amp; Zodiacum ab ortu in occa&longs;um circa mundum.</s>
        </p>
      </chap>
      <pb pagenum="89" xlink:href="009/01/089.jpg"/>
      <chap>
        <p type="head">
          <s id="s.001623"><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001624"><arrow.to.target n="marg131"/></s>
        </p>
        <p type="margin">
          <s id="s.001625"><margin.target id="marg131"/>131</s>
        </p>
        <p type="main">
          <s id="s.001626">Svmma 1. cap. 3. <emph type="italics"/>&lpar;Moles autem terr&aelig; quanta &longs;it ad ambientes magnitudi&shy;<lb/>nes, non immanifestum, iam enim vi&longs;um est per a&longs;trologica theoremata, <lb/>
quod mult&ograve; etiam quibu&longs;dam a&longs;tris est minor&rpar;<emph.end type="italics"/> Quantitas terr&aelig; non &longs;o&shy;<lb/>
lum ab&longs;olut&egrave; con&longs;iderata, ab A&longs;tronomis explorata habetur, vt vi&shy;<lb/>
dere e&longs;t in &longs;ph&aelig;ra Clauij; &longs;ed etiam re&longs;pectiu&egrave; con&longs;iderata, ide&longs;t re&longs;pectu <lb/>
aliorum elementorum, &amp; ip&longs;orum etiam a&longs;trorum; cuius demon&longs;trationes <lb/>
&longs;unt partim in libello Ari&longs;tarchi Samij, de magnitudine, &amp; di&longs;tantia Solis, <lb/>
&amp; Lun&aelig;, partim apud Ptol&aelig;meum in magna Syntaxi, &longs;iue Almage&longs;to: par&shy;<lb/>
tim apud Albategnium de &longs;cientia &longs;tellarum: partim demum apud Ticho&shy;<lb/>
nem Brahe. </s>
          <s id="s.001627">Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>
terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>
in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>
mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>
nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>
riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>
conicam, vt figura refert. </s>
          <s id="s.001628">Cum ergo terra vmbram proijciat turbinatam, <lb/>
nece&longs;&longs;ari&ograve; corpus Solis, quod ip&longs;am illuminat, eadem maior erit: quoti&shy;<lb/>
diana enim experientia docemur, corpore illuminante exi&longs;tente maiore <lb/>
qu&agrave; &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val&shy;<lb/>
de a terra di&longs;tare certum &longs;it, optim&egrave; infertur, eum re&longs;pectu terr&aelig; e&longs;&longs;e maxi&shy;<lb/>
mum: quanto enim du&aelig; line&aelig;, &longs;iue radij B A, B C. &agrave; terra ad partes Solis <lb/>
<figure id="id.009.01.089.1.jpg" place="text" xlink:href="009/01/089/1.jpg"/><lb/>
magis elongantur, tan&shy;<lb/>
to maius corpus <expan abbr="illu-min&atilde;s">illu&shy;<lb/>
minans</expan> intercipiunt. </s>
          <s id="s.001629">ha&shy;<lb/>
ctenus de magnitudine <lb/>
terr&aelig; ad Solem. </s>
          <s id="s.001630">Cum <lb/>
ver&ograve; Luna eclyp&longs;atio&shy;<lb/>
nis tempore, aliquan&shy;<lb/>
do non &longs;olum tota in <lb/>
vmbr&aelig; vertice lateat, <lb/>
ver&ugrave;m etiam <expan abbr="aliqu&atilde;do">aliquando</expan> <lb/>
moram trahat, euidens <lb/>
e&longs;t, eam e&longs;&longs;e mult&ograve; mi&shy;<lb/>
norem illa vmbr&aelig; par&shy;<lb/>
te, in quam immergi&shy;<lb/>
tur; qu&aelig; pars cum &longs;it <lb/>
conic&aelig; vmbr&aelig; media, <lb/>erit mult&ograve; gracilior <lb/>
qu&agrave;m &longs;it ip&longs;a terra. <lb/>
</s>
          <s id="s.001631">Ex quo manife&longs;t&egrave; apparet, Lunam, qu&aelig; illa vmbra minor e&longs;t, e&longs;&longs;e &agrave; fortio&shy;<lb/>
ri mult&ograve; minorem ip&longs;a terre&longs;tri mole. </s>
          <s id="s.001632">Atque h&aelig;c de comparatione terr&aelig; <lb/>
ad Lunam. <!-- KEEP S--></s>
          <s id="s.001633">harum rerum demon&longs;trationes exactiores pertractare non e&longs;t <lb/>
huius loci.</s>
        </p>
        <p type="main">
          <s id="s.001634"><arrow.to.target n="marg132"/></s>
        </p>
        <p type="margin">
          <s id="s.001635"><margin.target id="marg132"/>132</s>
        </p>
        <p type="main">
          <s id="s.001636">Eodem cap. <emph type="italics"/>&lpar;Con&longs;iderantes vtique, qu&aelig; nunc o&longs;tenduntur per Mathematica<emph.end type="italics"/> <pb pagenum="90" xlink:href="009/01/090.jpg"/><emph type="italics"/>&longs;ufficienter, fort&egrave; vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>
e&longs;t putare <expan abbr="vnumquodq;">vnumquodque</expan> eorum qu&aelig; feruntur e&longs;&longs;e paruum magnitudinibus, quia vi&shy;<lb/>detur a&longs;picientibus, hinc nobis &longs;ic&rpar;<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, qu&aelig; <lb/>
pa&longs;&longs;im apud Ari&longs;t. occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;tr&aelig; &aelig;tatis con&longs;iderarent, qui nulla <lb/>
ratione probari po&longs;&longs;e exi&longs;timant, Solem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->terra e&longs;&longs;e centies &longs;exagies &longs;e&shy;<lb/>
xies maiorem; &longs;ed etiam, quod peius e&longs;t, negant e&longs;&longs;e maiorem; ad demon&shy;<lb/>
&longs;trationes autem a&longs;tronomicas dicunt &longs;e exi&longs;timare eas e&longs;&longs;e fallaces; at que <lb/>impo&longs;&longs;ibile e&longs;&longs;e nos res adeo &agrave; nobis di&longs;tantes &longs;ufficienter perue&longs;tigare: <lb/>
quanto &longs;apientius, ac prudentius eorum Magi&longs;ter Ari&longs;t. alibi &longs;&aelig;pius, &longs;ed hoc <lb/>
pr&aelig;cipu&egrave; loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>
i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia pr&aelig;ceptoris a&longs;&longs;equi poterunt.</s>
        </p>
        <p type="main">
          <s id="s.001637"><arrow.to.target n="marg133"/></s>
        </p>
        <p type="margin">
          <s id="s.001638"><margin.target id="marg133"/>133</s>
        </p>
        <p type="main">
          <s id="s.001639">Summa 1. cap. 4. <emph type="italics"/>&lpar;Qu&aelig; igitur astrorum e&longs;t, velox quidem; long&egrave; autem: qu&aelig; <lb/>ver&ograve; Lun&aelig; deor&longs;um quidem, tarda autem: qu&aelig; autem Solis ambo h&aelig;c habet &longs;uffi&shy;<lb/>
cienter&rpar;<emph.end type="italics"/> qu&aelig; igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul &agrave; ter&shy;<lb/>
ra; Lun&aelig; ver&ograve; latio terr&aelig; quidem proxima, tarda tamen: at ver&ograve; Solis la&shy;<lb/>
tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di&shy;<lb/>
&longs;tat, <expan abbr="neq;">neque</expan> tard&egrave; &longs;icut Luna circunfertur. </s>
          <s id="s.001640">exi&longs;timo Ari&longs;t. loqui de motu diur&shy;<lb/>
no, quia &longs;ecundum hunc a&longs;tra inerrantia &longs;unt Sole citatiora, Sol ver&ograve; ip&longs;a <lb/>
Luna citior. </s>
          <s id="s.001641">Verumenimuer&ograve; illud non pr&aelig;tereundum, quod plurium inua&shy;<lb/>
luerit opinio exi&longs;timantium Ari&longs;t. his verbis, Solem &longs;upra Lunam proxim&egrave; <lb/>
colloca&longs;&longs;e; quod tamen ex ip&longs;is nullo pacto deduci pote&longs;t; &longs;ed &longs;olummodo <lb/>
ip&longs;um &longs;upra Lunam colloca&longs;&longs;e. </s>
          <s id="s.001642">quod &longs;i ita &longs;en&longs;i&longs;&longs;et venia dignus haberetur, <lb/>
cum tunc temporis nondum fort&egrave; adinuent&aelig; e&longs;&longs;ent demon&longs;trationes ill&aelig; <lb/>
a&longs;tronomic&aelig;, quibus ordo Planetarum certi&longs;&longs;im&egrave; con&longs;tat, <expan abbr="Sol&qacute;">Solque</expan>; medius in&shy;<lb/>
ter Planetas collocatur. </s>
          <s id="s.001643">At ver&ograve; nulla ratione ferendi &longs;unt <expan abbr="quicunq;">quicunque</expan> no&longs;tra <lb/>
hac tempe&longs;tate non &longs;olum Ari&longs;t. ita &longs;en&longs;i&longs;&longs;e, &longs;ed etiam contra firmi&longs;&longs;imas <lb/>
aftronomorum demon&longs;trationes, quibus ade&ograve; Ari&longs;t. deferebat, vnica, vt pu&shy;<lb/>
tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum &agrave; Luna locum occupare om&shy;<lb/>
ni ope defendunt.</s>
        </p>
        <p type="main">
          <s id="s.001644"><arrow.to.target n="marg134"/></s>
        </p>
        <p type="margin">
          <s id="s.001645"><margin.target id="marg134"/>134</s>
        </p>
        <p type="main">
          <s id="s.001646">Summa 2. cap. 3. <emph type="italics"/>&lpar;Quod accidit circa Mercurij stellam, quia enim modicum <lb/>
<expan abbr="&longs;upera&longs;c&etilde;dis">&longs;upera&longs;cendis</expan>, &longs;&aelig;p&egrave; non apparet, it a vt po&longs;t tempus multum appareat&rpar;<emph.end type="italics"/> quod Mer&shy;<lb/>
curius non ni&longs;i rar&ograve; con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum &agrave; Sole elongatur, <lb/>
&longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s>
          <s id="s.001647">ex quo fit, vt diu fer&egrave; &longs;imul cum So&shy;<lb/>le circumferatur, &amp; propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho&shy;<lb/>
rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t. ait modicum <expan abbr="&longs;upera&longs;c&etilde;dit">&longs;upera&longs;cendit</expan>. <lb/>
</s>
          <s id="s.001648">vnde fit tum propter nimiam Solis vicinitatem, cuius lumine tegitur; tum <lb/>
propter vapores, qui horizonti vt plurimum incumbunt, vt rar&ograve;, &amp; po&longs;t ma&shy;<lb/>
gna temporis interualla con&longs;piciatur. </s>
          <s id="s.001649">non me fugit h&aelig;c omnia ab a&longs;trono&shy;<lb/>
mis per epiciclum excu&longs;ari; &longs;ed ego mediocritati eorum, in quorum gra&shy;<lb/>
tiam h&aelig;c &longs;cribo, con&longs;ultum volo.</s>
        </p>
        <p type="main">
          <s id="s.001650"><arrow.to.target n="marg135"/></s>
        </p>
        <p type="margin">
          <s id="s.001651"><margin.target id="marg135"/>135</s>
        </p>
        <p type="main">
          <s id="s.001652">Eodem cap. <emph type="italics"/>&lpar;Ad au&longs;trum autem quando feratur, copiam quidem habere tal&iacute;s <lb/>humiditatis, &longs;ed quia parua e&longs;t &longs;ectio circuli, qu&aelig; &longs;uper terram, qu&aelig; autem deor&shy;<lb/>
&longs;um multiplex, non po&longs;&longs;e vi&longs;um hominum fractum ferri ad Solem, <expan abbr="neq;">neque</expan> ip&longs;i tropico <lb/>
au&longs;trino appropinquanti; <expan abbr="neq;">neque</expan> in &aelig;&longs;tiuis ver&longs;ionibus exi&longs;tente Sole. <!-- KEEP S--></s>
          <s id="s.001653">quapropter in <lb/>
lis quidem locis neque fieri cometem ip&longs;um. </s>
          <s id="s.001654">quando ver&ograve; ad Boream &longs;ubdefecerit, <lb/>accipere comam, quia magna e&longs;t circunferentia, qu&aelig; e&longs;t &longs;upra horizontem; qu&aelig; au-<emph.end type="italics"/>


<pb pagenum="91" xlink:href="009/01/091.jpg"/><emph type="italics"/>tem e&longs;t &longs;ubtus, pars circuli parua; facil&egrave; enim vi&longs;um hominum pertingere tunc ad <lb/>
Solem&rpar;<emph.end type="italics"/> cur cometa in regione au&longs;trali vltra Solis, <expan abbr="anni&qacute;">annique</expan>; vias con&longs;titutus <lb/>non appareret, cau&longs;am referebat Hippocrates paruitatem circuli, quem <lb/>
motu diurno cometa de&longs;cribebat, ob quam ade&ograve; parum &longs;upra horizontem <lb/>
attolleretur, vt <expan abbr="n&otilde;">non</expan> po&longs;&longs;et vi&longs;us no&longs;ter ab ip&longs;o ad Solem reflecti; quod &longs;ecun&shy;<lb/>
dum ip&longs;um erat nece&longs;&longs;arium ad cometarum apparitionem. </s>
          <s id="s.001655">loquitur igitur <lb/>Hippocrates de circulis, quos diurna conuer&longs;ione cometes circumducit, qui <lb/>
omnin&ograve; &longs;imiles &longs;unt ijs, quos etiam Sol, <expan abbr="reliqua&qacute;">reliquaque</expan>; a&longs;tra eodem motu de &longs;i&shy;<lb/>
gnant. </s>
          <s id="s.001656">qui quidem omnes in no&longs;tra &longs;ph&aelig;ra obliqua ita &longs;e habent, vt ij, qui <lb/>&longs;unt vltra &aelig;quatorem ad Capricorni tropicum, minus &longs;upra horizontem <lb/>extent, qu&agrave;m infra deprimantur, &amp; tanto minus, quanto magis ab &aelig;quato&shy;<lb/>re in au&longs;trum recedunt: contra ver&ograve; faciunt, qui citra &aelig;quatorem ad Can&shy;<lb/>cri conuer&longs;ionem collocantur, quanto enim magis ab &aelig;quatore in boream <lb/>
remouentur, tant&ograve; eorum &longs;ectio, qu&aelig; e&longs;t &longs;upra horizontem, maior e&longs;t ea, <lb/>
qu&aelig; infra horizontem latet. </s>
          <s id="s.001657">qu&aelig; quidem omnia clara &longs;unt adhibita &longs;ph&aelig;ra <lb/>
materiali, quam &longs;i ad tuam poli eleuationem accommodaueris, illic&ograve; vi&shy;<lb/>
debis tropici, Cancri &longs;ectionem, qu&aelig; e&longs;t &longs;upra horizontem multo maiorem <lb/>
ea, qu&aelig; e&longs;t infra. </s>
          <s id="s.001658">oppo&longs;itum ver&ograve; in altero Capricorni tropico, cuius mini&shy;<lb/>
mam portionem &longs;upra, maximam ver&ograve; infra horizontem exi&longs;tere videbis. <lb/>
</s>
          <s id="s.001659">Idem proportionaliter imaginari debes de circulis, quos cometa tam vltra <lb/>
Capricornum, qu&agrave;m citra Cancrum delineat; nam eorum, qui &longs;unt vltra <lb/>
Capricornum ad au&longs;trum minores adhuc &longs;ectiones &longs;upra horizontem exi&shy;<lb/>
&longs;terent, qu&agrave;m opus &longs;it ad cometen &longs;pectandum. </s>
          <s id="s.001660"><expan abbr="At&qacute;ue">Atque</expan> h&aelig;c cau&longs;a e&longs;t ex &longs;en&shy;<lb/>
tentia Hippocr. <!-- REMOVE S-->cur in illa au&longs;trali plaga <expan abbr="n&utilde;quam">nunquam</expan> cometes effulgeat. </s>
          <s id="s.001661">&egrave; con&shy;<lb/>
trario autem, quia ad boream &longs;ectiones ill&aelig; maxim&aelig; &longs;unt, <expan abbr="apt&aelig;&qacute;">apt&aelig;que</expan>; ad refra&shy;<lb/>
ctionem vi&longs;us no&longs;tri v&longs;que ad Solem, idcirc&ograve; in hac mundi parte cometas <lb/>
con&longs;picere &longs;olemus. </s>
          <s id="s.001662">Reliqua Vicomercatus, <expan abbr="atq;">atque</expan> Alexand. <!-- REMOVE S-->optim&egrave; expli&shy;<lb/>
cant, quos tu con&longs;ule, ne actum agatur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001663"><emph type="italics"/>In cap. 4. &longs;umm&aelig; 2. lib. 1. Meteor. <!-- REMOVE S-->de Cometis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001664"><arrow.to.target n="marg136"/></s>
        </p>
        <p type="margin">
          <s id="s.001665"><margin.target id="marg136"/>136</s>
        </p>
        <p type="main">
          <s id="s.001666">In pr&aelig;&longs;enti cap. <!-- REMOVE S-->Ari&longs;t. &longs;uam de Cometis &longs;ententiam exponit: Come&shy;<lb/>
tam nimirum infra Lunam in elementari mundo procreari, &amp; ignitum <lb/>
quoddam Meteoron, ex lenta, pingui, <expan abbr="&longs;icca&qacute;">&longs;iccaque</expan>; materia &agrave; terra in &longs;u&shy;<lb/>
premam aeris regionem attracta, exi&longs;tere; <expan abbr="ibi&qacute;">ibique</expan>; rapti aeris calore, <lb/>
vel elementi ignis &lpar;quod illic e&longs;&longs;e putat&rpar; vicinitate, vel etiam vi a&longs;trorum <lb/>
incendi, <expan abbr="atq;">atque</expan> impelli. </s>
          <s id="s.001667">Han&cacute; porr&ograve; opinionem &amp; &longs;i probabilibus tantum ra&shy;<lb/>
tionibus confirmatam vulg&ograve; tamen <expan abbr="v&longs;q;">v&longs;que</expan> ad hanc diem receptam, cum fal&shy;<lb/>
&longs;am e&longs;&longs;e a&longs;tronomi exi&longs;timent, non erit abs re rationes eas ex &longs;ecundo pro&shy;<lb/>
gymn. </s>
          <s id="s.001668">Tichonis volumine, de&longs;umptas hic breuiter referre, quibus a&longs;trono&shy;<lb/>
mus ille eos &longs;upra Lunam in &aelig;therea regione collocauit: quas quidem ra&shy;<lb/>
tiones ille ex diuturnis ob&longs;eruationibus per exqui&longs;ita organa factis adinue&shy;<lb/>
nit: ea&longs;que Mathematicis linearum, ac numerorum demon&longs;trationibus <lb/>
explicauit.</s>
        </p>
        <p type="main">
          <s id="s.001669">Prima. <!-- KEEP S--></s>
          <s id="s.001670">&longs;ed vt ab auctoritate, in quam obiter incidimus <expan abbr="initi&utilde;">initium</expan> faciamus, <lb/>non e&longs;t exi&longs;timandum nonnullos &longs;olum ex recentioribus id con&longs;tanter a&longs;&longs;e&shy;<pb pagenum="92" xlink:href="009/01/092.jpg"/>uera&longs;&longs;e, &longs;ed &longs;uperiori etiam &aelig;tate id ip&longs;um Hieron. </s>
          <s id="s.001671">Cardan. <!-- REMOVE S-->libro de &longs;ubtili&shy;<lb/>
tate conatus e&longs;t, <expan abbr="neq;">neque</expan> irrito conatu, demon&longs;trare; qui pr&aelig;terea idem cum <lb/>&longs;e ip&longs;o &longs;en&longs;i&longs;&longs;e ait Albumazar. </s>
          <s id="s.001672">quibus etiam ex antiquis Seneca annumeran&shy;<lb/>
dus e&longs;t. </s>
          <s id="s.001673">pr&etail;dicti autem recentiores omnes varijs demon&longs;trationibus ex ac&shy;<lb/>curata ob&longs;eruatione erutis illud cert&ograve; certius confirmare contendunt: <expan abbr="id&qacute;">idque</expan>; <lb/>
non in vno dumtaxat, &longs;ed in <expan abbr="quinq;">quinque</expan> cometis; quorum demon&longs;trationes apud <lb/>
Tychonem partim in progymn. </s>
          <s id="s.001674">partim in epi&longs;t. <!-- REMOVE S-->fu&longs;ius explicatas reperies.</s>
        </p>
        <p type="main">
          <s id="s.001675">2. Quarum poti&longs;&longs;ima illa e&longs;t, qu&aelig; ex parallaxi, &longs;eu a&longs;pectus diuer&longs;itate <lb/>
de&longs;umitur, certi&longs;&longs;imum enim e&longs;t lumen illud e&longs;&longs;e altero &longs;ublimius, quod mi&shy;<lb/>
norem exhibet parallaxim: expertos autem &longs;e e&longs;&longs;e hi omnes, affirmant ho&shy;<lb/>
&longs;ce quinque cometas mult&ograve; minorem pati parallaxim, quam Lunam; im&ograve; <lb/>
quempiam minorem, qu&agrave;m Sol ip&longs;e patiatur, quo po&longs;ito manife&longs;t&egrave; conuin&shy;<lb/>
ceretur eos omnes &longs;upra Lunam in &aelig;therea regione efful&longs;i&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.001676">3. Ratio, qua etiam ante nouas ob&longs;eruationes vti &longs;olebant, de&longs;umitur <lb/>
ex motu comet&aelig; diurno, quo &longs;cilicet oritur, &amp; occidit, quemadmodum c&aelig;&shy;<lb/>
tera &longs;ydera, hoc e&longs;t &longs;patio 24. horarum diurnam conuer&longs;ionem circa totam <lb/>
terram ab&longs;oluit. </s>
          <s id="s.001677">&longs;i igitur comete e&longs;&longs;et in &longs;ublimiori aeris regione, vbi c&aelig;te&shy;<lb/>
ra ignita meteora collocantur, <expan abbr="moueretur&qacute;">mouereturque</expan>; diurno motu circa terram, &longs;e&shy;<lb/>
queretur nece&longs;&longs;ari&ograve; eum tanta velocitate videri &agrave; nobis circumferri, vt po&shy;<lb/>
tius fulgor quidam, &longs;eu radius pertran&longs;iens ab oriente in occidentem appa&shy;<lb/>
reret, quam &longs;tella qu&etail;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni&shy;<lb/>
miam di&longs;tantiam videntur tard&egrave; moueri, quamuis veloci&longs;&longs;im&egrave; moueantur.</s>
        </p>
        <figure id="id.009.01.092.1.jpg" place="text" xlink:href="009/01/092/1.jpg"/>
        <p type="main">
          <s id="s.001678">Quod melius ex &longs;equenti figura <lb/>
<expan abbr="c&otilde;uincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/>
terra, cuius &longs;emidiameter A B. cir&shy;<lb/>
culus ver&ograve; exterior e&longs;t comet&aelig; gy&shy;<lb/>
rus, quem ip&longs;e &longs;patio 24. horarum <lb/>
percurrit, qui &longs;ecundum veram pro&shy;<lb/>
portionem deberet adhuc ip&longs;i terr&aelig; <lb/>
propinquior, ac proinde minor e&longs;&longs;e, <lb/>
iuxta aeris &longs;upremam partem. </s>
          <s id="s.001679">hori&shy;<lb/>
zon e&longs;t recta D C, tangens terram in <lb/>
B, vbi e&longs;t oculus no&longs;ter, qui nihil in&shy;<lb/>
fra ip&longs;am D C, videre pote&longs;t; quare <lb/>
&longs;i cometa 24. horarum totum gyrum <lb/>
D C E, percurrit, non videbitur, ni&longs;i <lb/>
quando percurret portionem D C, <lb/>
&longs;upra horizontem; qu&aelig; quidem por&shy;<lb/>
tio, <expan abbr="neq;">neque</expan> &longs;emihor&aelig; re&longs;ponderet, &longs;i fi&shy;<lb/>
gura iuxta veram proportionem con&longs;trueretur. </s>
          <s id="s.001680">experientia tamen con&longs;tat, <lb/>
cometas videri &longs;upra horizontem tot horis, quot &longs;tell&aelig; fix&aelig;, &longs;ub quibus mo&shy;<lb/>
uentur: non ergo e&longs;t in &longs;upremo aere. </s>
          <s id="s.001681">Quod &longs;i fiat figura, in qua exterior <lb/>
comet&aelig; ambitus ade&ograve; magnus &longs;it, vt ip&longs;ius portio D C, &longs;upra horizontem <lb/>
exi&longs;tens, re&longs;pondeat tempori, quo cometa &longs;upra no&longs;trum pariter horizon&shy;<lb/>
tem &longs;pectatur, ea figura terr&aelig; &longs;emidiametrum A B. toties multiplicabit, vt <lb/>
ip&longs;i Lun&aelig; circuitui proxim&egrave; accedat.</s>
        </p>
        <pb pagenum="93" xlink:href="009/01/093.jpg"/>
        <p type="main">
          <s id="s.001682">Pr&aelig;terea aiunt, quis &longs;an&aelig; mentis dixerit, Meteoron vllum ex materia <lb/>
vaga, ac fluxa con&longs;tans, po&longs;&longs;e tanta pernicitate moueri, vt diurnam con&shy;<lb/>
uer&longs;ionem ab&longs;oluat? </s>
          <s id="s.001683">vnde illi motus i&longs;te? </s>
          <s id="s.001684">pr&aelig;&longs;ertim cum videamus c&aelig;tera <lb/>
ignita meteora e&longs;&longs;e ad modum temporanea, <expan abbr="atq;">atque</expan> euanida.</s>
        </p>
        <p type="main">
          <s id="s.001685">4. Comprobationem nobis &longs;uppeditant ex via, &longs;eu ductus circuli, quem <lb/>
toto durationis tempore proprio cur&longs;u de&longs;ignarunt: pr&aelig;dicti <expan abbr="namq;">namque</expan> quin&shy;<lb/>
que comet&aelig; motu &longs;ibi proprio, quo ab occidente non omnin&ograve; orientem <lb/>
ver&longs;us, &longs;ed ad aquilonem deflectentes ab initio &longs;u&aelig; apparitionis, <expan abbr="v&longs;q;">v&longs;que</expan> ad vl&shy;<lb/>timum finem exqui&longs;iti&longs;&longs;im&egrave; portionem circuli maximi in c&etail;lo de&longs;ignarunt; <lb/>non aliter qu&agrave;m Sol proprio motu per eclypticam in c&oelig;lo mundi &longs;ph&aelig;ram <lb/>
in duo &aelig;qualia diuidentem de&longs;cribit. </s>
          <s id="s.001686">necnon aliter ac Luna &longs;uum iter per <lb/>
circulum maximum c&oelig;lum bifariam diuidentem perficit. </s>
          <s id="s.001687">quapropter co&shy;<lb/>
metas ho&longs;ce <expan abbr="n&otilde;">non</expan> minus quam Sol, vel Luna in ip&longs;o &aelig;there &longs;patiatos e&longs;&longs;e con&shy;<lb/>
tendunt. </s>
          <s id="s.001688">qui enim, aiunt, fieri potui&longs;&longs;et, &longs;i in mundo elementari flagra&longs;&longs;ent, <lb/>
vt tam regulari, <expan abbr="atq;">atque</expan> con&longs;tanti ductu circuli maximi portionem tam exact&egrave; <lb/>
delinea&longs;&longs;ent, quam quidem inter elementa vagum, <expan abbr="atq;">atque</expan> in&longs;tabilem pro ma&shy;<lb/>
teri&aelig; in&longs;tabilitate exercere debui&longs;&longs;ent?</s>
        </p>
        <p type="main">
          <s id="s.001689">5. Adde, quod in maximo hoc circulo de&longs;cribendo, etiam &longs;i in&aelig;quali ve&shy;<lb/>
locitate vi&longs;i &longs;int moueri, in&aelig;qualitatem tamen illam regularem <expan abbr="vbiq;">vbique</expan> &longs;em&shy;<lb/>
per &longs;eruauerunt, in principio quidem velociores, deinde &longs;ucce&longs;&longs;iu&egrave;, &amp; pro&shy;<lb/>
portionaliter velocitatem illam &longs;imili analogia &longs;emper &longs;eruata <expan abbr="inhibuer&utilde;t">inhibuerunt</expan>, <lb/>
nullo igitur pacto inordinatam in&aelig;qualitatem, qua &agrave; tardiore motu &longs;ubito <lb/>
in celeriorem, &amp; rur&longs;us &longs;tatim ab hoc in <expan abbr="ill&utilde;">illum</expan> pro&longs;ilirent exhibuerunt: prout <lb/>
omnia Meteora, qu&aelig; in mundi parte elementari ex flammanti materia ge&shy;<lb/>
nerantur, talem di&longs;parem, <expan abbr="atq;">atque</expan> incon&longs;tantem motum obtinere cernuntur.</s>
        </p>
        <p type="main">
          <s id="s.001690">6. Argumento pr&aelig;terea e&longs;t cometas ho&longs;ce minim&egrave; elementares fui&longs;&longs;e, <lb/>quod hic eorum proprius motus, quo maximo illo tramite ferebantur, nun&shy;<lb/>
quam tantus fuit, vt proprium Lun&aelig; motum, vel tardi&longs;&longs;imum ad&aelig;quauerit, <lb/>
qu&aelig; quidem cum lenti&longs;&longs;ima e&longs;t plus denis gradibus vna die promouetur; <lb/>
cum tamen comet&aelig; initio cum veloci&longs;&longs;imi &longs;unt non multum vltra quinos <lb/>
gradus diurno motu progre&longs;&longs;i &longs;int, vt ob id long&egrave; &longs;upra Lunam cur&longs;um &longs;uum <lb/>
ab&longs;olui&longs;&longs;e manife&longs;t&egrave; comprobari po&longs;&longs;it: quo enim &longs;ydera magis &agrave; terra at&shy;<lb/>
tolluntur, <expan abbr="octau&aelig;&qacute;">octau&aelig;que</expan>; &longs;ph&aelig;r&aelig; propius accedunt, e&ograve; tardioribus proprijs la&shy;<lb/>tionibus proferuntur: ita vt &longs;tell&aelig; i&longs;t&aelig; c&oelig;lo ad&longs;cititi&aelig; &longs;upra Lunam admo&shy;<lb/>
dum euehend&aelig; videantur. </s>
          <s id="s.001691">Quod &longs;i in &longs;uprema aeris regione conflagrarent, <lb/>
qua nam ratione vn&agrave; cum toto c&oelig;lo diurnam conuer&longs;ionem ab&longs;olui&longs;&longs;ent: <lb/>
<expan abbr="neq;">neque</expan> enim putandum e&longs;t &longs;upremum hunc aeris limbum eadem perne citate, <lb/>
qua c&oelig;le&longs;tes orbes, verum minori admodum im&ograve; tardi&longs;&longs;im&egrave; &agrave; diurno mo&shy;<lb/>
tu, &longs;i tamen eo rapitur circumduci.</s>
        </p>
        <p type="main">
          <s id="s.001692">7. Tandem argumentum ex ip&longs;orum duratione de&longs;umatur. </s>
          <s id="s.001693">c&aelig;tera nam&shy;<lb/>
que meteora &longs;tatim <expan abbr="atq;">atque</expan> apparuerint, veluti temporanea pror&longs;us, <expan abbr="atq;">atque</expan> eua&shy;<lb/>
nida extinguuntur: At ver&ograve; comet&aelig; ad men&longs;em aliquando integrum per&shy;<lb/>
&longs;euerant. </s>
          <s id="s.001694">qu&igrave; igitur fieri potuerit, vt in hac corruptibili <expan abbr="m&utilde;di">mundi</expan> parte ex ma&shy;<lb/>teria ade&ograve; fluxa, &amp; vaga, quam illis Ari&longs;toteles &longs;upponit, tandiu perdura&shy;<lb/>
re potui&longs;&longs;ent.</s>
        </p>
        <p type="main">
          <s id="s.001695"><expan abbr="Atq;">Atque</expan> h&aelig; &longs;unt rationes, quibus plurimi a&longs;tronomorum recentiorum, co&shy;


<pb pagenum="94" xlink:href="009/01/094.jpg"/>metas ho&longs;ce motum &aelig;there&aelig; regioni conformem, contr&agrave; quam Ari&longs;t. opi&shy;<lb/>natus e&longs;t, obtinui&longs;&longs;e, manife&longs;tum e&longs;&longs;e volunt; ac proinde eorum locum, &amp; <lb/>
cur&longs;um in c&oelig;le&longs;ti mundi parte extiti&longs;&longs;e, &longs;e comproba&longs;&longs;e exi&longs;timant: qua de <lb/>
re prudentis Lectoris e&longs;to iudicium: <expan abbr="neq;">neque</expan> enim, vt ille cecinit, no&longs;trum e&longs;t, <lb/>
tantas componere lites.</s>
        </p>
        <p type="main">
          <s id="s.001696">Verumenimuer&ograve; Peripatetica omnis &longs;chola reclamat; C&oelig;lum e&longs;t inge&shy;<lb/>nerabile, &amp; incorruptibile, nihil igitur noui c&oelig;lo pote&longs;t accidere. </s>
          <s id="s.001697">&longs;ed age <lb/>
re&longs;pondent, nonne omnium a&longs;tronomorum con&longs;en&longs;u &longs;tell&aelig; tres nou&aelig; no&longs;tro <lb/>
hoc &longs;&aelig;culo in c&oelig;lo toti mundo con&longs;picu&aelig; illuxerunt? </s>
          <s id="s.001698"><expan abbr="eas&qacute;">easque</expan>; in octaua &longs;ph&aelig;&shy;<lb/>ra re&longs;edi&longs;&longs;e con&longs;tans e&longs;t omnium a&longs;&longs;ertio? </s>
          <s id="s.001699">quarum prior anno 1572. in con&shy;<lb/>
&longs;tellatione Ca&longs;&longs;iope&aelig; apparuit. </s>
          <s id="s.001700">Secunda anno 1600. in Cygno, qu&aelig; nec dum <lb/>
extinguitur. </s>
          <s id="s.001701">Tertia anno 1604. inter Sagittarij &longs;tellas vi&longs;a e&longs;t, de quibus vi&shy;<lb/>
de P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra breuiter de illis tractantem: aut &longs;i mauis, &amp; vacat, <lb/>
vide quoad primam primum volumen progymna&longs;matum Tychonis Brahe, <lb/>
vbi etiam aliorum a&longs;tronomorum de eadem certi&longs;&longs;imas commentationes <lb/>
reperies. </s>
          <s id="s.001702">con&longs;ule etiam de reliquis duabus Ioannis Kepleri C&aelig;&longs;are&aelig; Maie&shy;<lb/>
&longs;tatis Mathematici commentaria; &amp; coactus libenter fateberis noui ali&shy;<lb/>
quid c&oelig;lo aduenire po&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.001703">Po&longs;trem&ograve; tandem po&longs;&longs;et qui&longs;piam in hunc <expan abbr="mod&utilde;">modum</expan> opponere: etiam &longs;i con&shy;<lb/>
&longs;tet <expan abbr="quinq;">quinque</expan> cometas c&etail;lo oberra&longs;&longs;e, non propterea dicemus reliquos omnes <lb/>
e&longs;&longs;e pariter c&oelig;le&longs;tes, <expan abbr="nullum&qacute;">nullumque</expan>; proinde &longs;ublunarem. </s>
          <s id="s.001704">Huic memorati A&longs;tro&shy;<lb/>
nomi &longs;ic re&longs;ponderent; id quidem mathematica, &amp; infallibili ratione non <lb/>
colligi, im&ograve; aliquot parum infra Lunam extiti&longs;&longs;e, non omnin&ograve; negandum <lb/>
videri: at ver&ograve; in &longs;uperiori aeris plaga, in tam fluxa, ac in&longs;tabili mundi par&shy;<lb/>
te, cometas vnquam efful&longs;i&longs;&longs;e, nemo &longs;ibi ob allatas rationes merit&ograve; per&longs;ua&shy;<lb/>
dere po&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.001705"><arrow.to.target n="marg137"/></s>
        </p>
        <p type="margin">
          <s id="s.001706"><margin.target id="marg137"/>137</s>
        </p>
        <p type="main">
          <s id="s.001707">Summ&aelig; 2. cap. 5. <emph type="italics"/>&lpar;Ad h&aelig;c autem &longs;i quemadmodum o&longs;tenditur in ijs, qu&aelig; cir&shy;<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t qu&agrave;m terr&aelig;; &amp; di&longs;tan&shy;<lb/>
tia mult&ograve; maior a&longs;trorum ad terram qu&agrave;m So is; &longs;icut Solis ad terram qu&agrave;m Lu&shy;<lb/>
n&aelig;; non <expan abbr="vtiq;">vtique</expan> long&egrave; alicubi &agrave; terra conus, qui &agrave; Sole, conijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbra terr&aelig;, qu&aelig; vocatur nox, erit apud astra; &longs;ed nece&longs;&longs;e Solem omnia a&longs;tra cir&shy;<lb/>
cun&longs;picere, &amp; nulli ip&longs;orum terram ob&longs;istere&rpar;<emph.end type="italics"/> ex dictis &longs;umma 1. cap. 3. huius, <lb/>
&amp; ex figura ibi de&longs;cripta, facil&egrave; e&longs;t intelligere pr&aelig;&longs;entem locum; nam cum <lb/>
Sol &longs;it mult&ograve; maior terra, vt ibi probatur, ac minus di&longs;ter &agrave; terra qu&agrave;m fix&aelig; <lb/>
&longs;tell&aelig;, magis tamen qu&agrave;m Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a&shy;<lb/>
ri&ograve; vmbram terr&aelig;, qu&aelig; nox e&longs;t ip&longs;a, effici turbinatam, &amp; vald&egrave; procul &agrave; ter&shy;<lb/>
ra acumen coni vmbr&aelig; a&longs;cendet, &longs;ed paul&ograve; &longs;upra Lunam conus hic vmbr&aelig; <lb/>
permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il&shy;<lb/>
lis verbis <emph type="italics"/>&lpar;Conijciet radios&rpar;<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t. cum igi&shy;<lb/>
tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>
vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis tenebras offundet. </s>
          <s id="s.001708">quod <lb/>
etiam experientia confirmat, cum nunquam a&longs;tra illa, qu&aelig; Soli opponuntur, <lb/>
<expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; vertex vmbr&aelig; collimat, vllam <expan abbr="pati&atilde;tur">patiantur</expan> eclyp&longs;im. </s>
          <s id="s.001709">quare &longs;ine vllo ter&shy;<lb/>r&aelig; impedimento Sol pote&longs;t affixa omnia &longs;ydera per lu&longs;trare. </s>
          <s id="s.001710">Exactiores ha&shy;<lb/>
rum rerum demon&longs;trationes &longs;unt alterius loci.</s>
        </p>
        <p type="main">
          <s id="s.001711"><arrow.to.target n="marg138"/></s>
        </p>
        <p type="margin">
          <s id="s.001712"><margin.target id="marg138"/>138</s>
        </p>
        <p type="main">
          <s id="s.001713">Eodem cap. <emph type="italics"/>&lpar;Amplius autem e&longs;t tertia qu&aelig;dam opinio de ip&longs;o, dicunt enim<emph.end type="italics"/> <pb pagenum="95" xlink:href="009/01/095.jpg"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut &amp; &longs;tellam comatam; im&shy;<lb/>
po&longs;&longs;ibile autem e&longs;t &amp; hoc, &longs;i enim videns quieuerit &amp; &longs;peculum, &amp; quod videtur <lb/>
omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo&shy;<lb/>
ueatur &longs;peculum, &amp; quod videtur, in eadem quidem di&longs;tantia ad videns, &amp; quie&shy;<lb/>
&longs;cens; ad inuicem autem <expan abbr="neq;">neque</expan> &aelig;qu&egrave; velociter, <expan abbr="neq;">neque</expan> in eadem &longs;emper di&longs;tantia im&shy;<lb/>
po&longs;&longs;ibile eandem imaginem in eadem e&longs;&longs;e parte &longs;peculi. </s>
          <s id="s.001714">Qu&aelig; autem in lactis circu&shy;<lb/>
lo feruntur a&longs;tra, &amp; Sol, ad quem fit reflexio, mouentur manentibus nobis, &amp; &longs;i&shy;<lb/>
militer, &amp; &aelig;qualiter ad nos di&longs;tantia; &agrave; &longs;e ip&longs;is autem non &aelig;qualiter: aliquando <lb/>
enim medijs noctibus Delphin oritur, aliquando ver&ograve; diluculo. </s>
          <s id="s.001715">partes autem lactis <lb/>
e&aelig;dem manent in vnoquoque; atqui non oportebat, &longs;i erat imago, &longs;ed non in ei&longs;dem <lb/>
adhuc e&longs;&longs;et h&aelig;c pa&longs;&longs;io locis&rpar;<emph.end type="italics"/> in his Ari&longs;t. confutat opinionem dicentium Gala&shy;<lb/>
xiam apparere per quandam reflexionem vi&longs;us no&longs;tri ab illa parte c&etail;li, ceu, <lb/>ex quodam &longs;peculo ad Solem: probat autem hoc e&longs;&longs;e impo&longs;&longs;ibile ratione <lb/>
de&longs;umpta ex parte Optices, qu&aelig; dicitur Catoptrica, &longs;iue &longs;pecularia, quia <lb/>
tractat de vi&longs;ione reflexa, qu&aelig; fit mediante &longs;peculo, quam quidem rationem <lb/>
&longs;i vellem mathematic&egrave; explicare, longa nimis, ac pr&aelig;ter in&longs;titutum fieret <lb/>
tractatio. </s>
          <s id="s.001716">Pauca tamen addam, qu&aelig; Ari&longs;totelis <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> &longs;atis per&longs;picuam <lb/>
reddant. </s>
          <s id="s.001717">&longs;i igitur inquit, Galaxia nihil aliud e&longs;&longs;et qu&agrave;m reflexio no&longs;tri vi&longs;us <lb/>
ex illa c&oelig;li parte, in qua ip&longs;a apparet tanquam ex &longs;peculo ad Solem, ita vt <lb/>nihil aliud ip&longs;a e&longs;&longs;et, qu&agrave;m Sol vi&longs;us per reflexionem ex illa c&oelig;li parte tan&shy;<lb/>
quam &longs;peculo; &longs;equeretur eam non &longs;emper in eadem c&oelig;li parte apparere, <lb/>
&longs;ed modo in vna, modo in alia, ita vt &longs;patio vnius anni totum c&oelig;lum perua&shy;<lb/>
garetur: quod tamen non accidit. </s>
          <s id="s.001718">quod autem illud con&longs;equatur manife&shy;<lb/>
&longs;tum e&longs;&longs;e pote&longs;t ex ob&longs;eruatione eorum, qu&aelig; ex &longs;peculis videntur: tunc enim <lb/>
res per &longs;pe culum vi&longs;a in eadem &longs;peculi parte apparet, quando &amp; videns, &amp; <lb/>
&longs;peculum, &amp; obiectum immota manent: quod &longs;i &amp; &longs;peculum, &amp; obiectum ad <lb/>
inuicem accedant, vel recedant, &longs;eruata tamen eadem ab in&longs;pectore di&longs;tan&shy;<lb/>
tia, nullo modo fieri pote&longs;t, vt eadem imago, in eadem &longs;peculi parte &longs;pe&shy;<lb/>
ctanti videatur, ni&longs;i obiectum &longs;peculo per eandem lineam accedat, &longs;ecun&shy;<lb/>
dum quam illi incidebat. </s>
          <s id="s.001719">At ver&ograve; partibus illis lactei circuli, &longs;iue a&longs;tris, qu&aelig; <lb/>
in eo fulgent, Sol perpetu&ograve; accedit, vel recedit, <expan abbr="neq;">neque</expan> per lineam incidenti&aelig; <lb/>
<expan abbr="e&atilde;dem">eandem</expan>, &longs;eruata tamen eadem &agrave; nobis di&longs;tantia, quod quidem inde patet, quia <lb/>
Delphini con&longs;tellatio, qui in ip&longs;o fer&egrave; lacte exi&longs;tit, <expan abbr="aliqu&atilde;do">aliquando</expan> medijs noctibus, <lb/>
aliquando ver&ograve; mane, aliquando etiam ve&longs;peri oritur; quod inde accidit, <lb/>
quia illi Sol mod&ograve; appropinquat, mod&ograve; coniungitur, mod&ograve; ab eo recedit, <lb/>
quare nece&longs;&longs;e e&longs;&longs;et, vt lacteus orbis, non &longs;emper in ij&longs;dem locis, &longs;ed perpe&shy;<lb/>
tu&ograve; in alijs, <expan abbr="atq;">atque</expan> alijs cerneretur, cuius tamen contrarium videmus. </s>
          <s id="s.001720">ex qui&shy;<lb/>
bus con&longs;tat fal&longs;am omnin&ograve; e&longs;&longs;e eorum &longs;ententiam, qui Galaxiam per huiu&longs;&shy;<lb/>modi reflexionem fieri opinabantur. </s>
          <s id="s.001721">Qu&aelig; dicta &longs;unt de &longs;peculo, &amp; obiecto <lb/>
&longs;atius e&longs;t a&longs;&longs;umpto aliquo &longs;peculo experiri, qu&agrave;m ea pluribus ob&longs;curare: qua <lb/>etiam experientia Ari&longs;t. ratio confirmabitur.</s>
        </p>
        <p type="main">
          <s id="s.001722"><arrow.to.target n="marg139"/></s>
        </p>
        <p type="margin">
          <s id="s.001723"><margin.target id="marg139"/>139</s>
        </p>
        <p type="main">
          <s id="s.001724">Ibidem <emph type="italics"/>&lpar;Qu&aelig; autem in lactis cir culo feruntur astra, &amp; Sol, ad quem fit refle&shy;<lb/>xio, mouentur manentibus nobis, &amp; &longs;imiliter, &amp; &aelig;qualiter ad nos di&longs;tantia &agrave; &longs;e <lb/>
ip&longs;is autem non &aelig;qualiter&rpar;<emph.end type="italics"/> qu&aelig; hic ab Ari&longs;totele dicuntur <expan abbr="n&otilde;">non</expan> &longs;unt v&longs;que quaque <lb/>vera propter apog&aelig;um, ac perig&aelig;um Solis, qu&aelig; quidem duo ab omnibus <lb/>
a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apog&aelig;o, maiori multo in&shy;


<pb pagenum="96" xlink:href="009/01/096.jpg"/>teruallo di&longs;tat &agrave; nobis, qu&agrave;m quando e&longs;t in perig&aelig;o, interuallum enim illud <lb/>
con&longs;tat diametris terr&aelig; duobus, &amp; quadraginta, hoc e&longs;t milliarijs 208000. <lb/>
fer&egrave;, ide&longs;t octonis millibus &longs;upra ducenta millia. </s>
          <s id="s.001725">qu&aelig; differentia facit vt Sol <lb/>
manife&longs;t&egrave; appareat nobis minor apog&aelig;us, qu&agrave;m perig&aelig;us. </s>
          <s id="s.001726">Sol pr&aelig;terea &longs;i&shy;<lb/>
militer ip&longs;is inerrantibus &longs;tellis fit tantumdem modo remotior, modo pro&shy;<lb/>
pinquior: &longs;ed fort&egrave; Ari&longs;t. i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>
per&longs;pecta erant.</s>
        </p>
        <p type="main">
          <s id="s.001727"><arrow.to.target n="marg140"/></s>
        </p>
        <p type="margin">
          <s id="s.001728"><margin.target id="marg140"/>140</s>
        </p>
        <p type="main">
          <s id="s.001729">Ibidem <emph type="italics"/>&lpar;Aliquando enim medijs noctibus Delphin oritur&rpar;<emph.end type="italics"/> vt probet, Gala&shy;<lb/>
xiam non &longs;emper &longs;eruare &agrave; Sole di&longs;tantiam eandem, accipit tanquam huius <lb/>
rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no&shy;<lb/>
ctibus oriatur &longs;upra horizontem, aliquando ver&ograve; diluculo; non ide&ograve; tamen <lb/>
putes hanc rationem &longs;upponere Delphinum e&longs;&longs;e in ip&longs;o lacteo circulo, quod <lb/>
tamen verum non e&longs;t, non enim e&longs;t in Galaxia, &longs;ed tamen illi proximus, vt <lb/>
noctu videre e&longs;t in c&oelig;lo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta&shy;<lb/>
men ob id Ari&longs;t. ratio minus valida redditur, cum Delphinus &longs;emper Gala&shy;<lb/>
xi&aelig; eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s>
        </p>
        <p type="main">
          <s id="s.001730"><arrow.to.target n="marg141"/></s>
        </p>
        <p type="margin">
          <s id="s.001731"><margin.target id="marg141"/>141</s>
        </p>
        <p type="main">
          <s id="s.001732">Summ&aelig; 2. cap. 6. Sunt qui velint Ari&longs;t. <!-- REMOVE S-->Galaxiam nihil aliud e&longs;&longs;e, qu&agrave;m <lb/>
quandam refractionem lucis &longs;tellarum illarum, qu&aelig; &longs;unt in &aelig;therea Gala&shy;<lb/>
xia, qu&aelig; inquam refractio fiat circa &longs;upremam aeris regionem ex occur&longs;u <lb/>
exhalationum, qu&aelig; ibi perpetu&ograve; con&longs;eruantur, &amp; vi earumdem &longs;tellarum <lb/>
&longs;ur&longs;um &longs;emper attrahuntur, qu&aelig; refractio fiat ad eum modum, quo halo cir&shy;<lb/>
ca Solem, &amp; Lunam. <!-- KEEP S--></s>
          <s id="s.001733">&amp; quemadmodum halo, &longs;iue area omnibus <expan abbr="vndecunq;">vndecunque</expan> <lb/>
a&longs;picientibus &longs;emper videntur in eodem c&oelig;li loco, hoc e&longs;t &egrave; regione Solis, <lb/>
vel Lun&aelig;; &longs;imiliter Galaxia in aere omnibus <expan abbr="vndecunq;">vndecunque</expan> intuentibus appa&shy;<lb/>
reat in eadem c&oelig;li parte, ide&longs;t ex aduers&ograve; eorumdem &longs;yderum, qu&aelig; c&oelig;le&shy;<lb/>
&longs;tem lacteam viam conficiunt. </s>
          <s id="s.001734">Porr&ograve; qui &longs;ic mentem Ari&longs;t. exponunt, nul&shy;<lb/>
lo modo po&longs;&longs;unt &agrave; Mathematicis redargui per rationem de&longs;umptam &agrave; di&shy;<lb/>
uer&longs;itate a&longs;pectus &lpar;quam po&longs;tea explicabo&rpar; quamuis phy&longs;icis rationibus re&shy;<lb/>
fellantur. </s>
          <s id="s.001735">Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improb&atilde;da">improbanda</expan>, e&ograve; quod <lb/>
Ari&longs;t. &longs;ummum Philo&longs;ophum pueriliter in a&longs;tronomia lap&longs;um fateri cogan&shy;<lb/>
tur. </s>
          <s id="s.001736">Exi&longs;timant hi Galaxiam hanc Ari&longs;totelicam nihil aliud e&longs;&longs;e, qu&agrave;m ip&shy;<lb/>
&longs;as tenues exhalationes in aere &longs;ubuectas, direct&egrave;que infra &longs;tellas illas la&shy;<lb/>
cteum circulum in c&oelig;lo con&longs;tituentes nobis obiectas. </s>
          <s id="s.001737">qui pr&aelig;ter innumera, <lb/>
ac magna ab&longs;urda &egrave; naturali Philo&longs;ophia petita, vnum maximum ex A&longs;tro&shy;<lb/>
nomia, nemp&egrave; ex diuer&longs;itate a&longs;pectus de&longs;umptum, nullo modo vitare po&longs;&shy;<lb/>
&longs;unt; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; huiu&longs;modi, quia &longs;i lacteus hic circulus e&longs;&longs;et in aere, non ab om&shy;<lb/>
nibus, <expan abbr="neq;">neque</expan> ex omni terr&aelig; loco per eadem &longs;ydera commeare cerneretur, &longs;ed <lb/>
&egrave; diuer&longs;is, &amp; pr&aelig;cipu&egrave; ab inuicem valde di&longs;&longs;itis, circa diuer&longs;a a&longs;tra &longs;e &longs;e ocu&shy;<lb/>
lis no&longs;tris obijceret: at te&longs;timonio &longs;en&longs;us con&longs;tat, Galaxiam &longs;emper in eo&shy;<lb/>
dem loco; <expan abbr="eadem&qacute;">eademque</expan>; &agrave; &longs;yderibus fixis di&longs;tantia albicare, erg&ograve; nullo modo <lb/>
viam hanc in aere qua&longs;i pendulam fabricare debemus. </s>
          <s id="s.001738">rationem hanc di&shy;<lb/>
uer&longs;itatis a&longs;pectus a&longs;tronomic&egrave; magis explicatam reperies apud Clauium <lb/>
in &longs;ph&aelig;ra. </s>
          <s id="s.001739">Porr&ograve; h&aelig;c ratio quamuis adeo certa, ac no&longs;tra tempe&longs;tate vul&shy;<lb/>
gata, parum tamen &agrave; nonnullis de rebus Meteorologicis commentaria con&shy;<lb/>
farcinantibus intellecta, minim&egrave; eos ab&longs;terrere potuit, quin pr&aelig;dictam opi&shy;<lb/>
nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="t&atilde;quam">tanquam</expan> veram


<pb pagenum="97" xlink:href="009/01/097.jpg"/>a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>
auxilio Philo&longs;ophiam aggrediuntur.</s>
        </p>
        <p type="main">
          <s id="s.001740"><arrow.to.target n="marg142"/></s>
        </p>
        <p type="margin">
          <s id="s.001741"><margin.target id="marg142"/>142</s>
        </p>
        <p type="main">
          <s id="s.001742">Eodem cap. <emph type="italics"/>&lpar;Ad h&aelig;c autem locus plenus e&longs;t a&longs;tris maximis, &amp; fulgidi&longs;&longs;imis, <lb/>
&amp; adhuc &longs;par&longs;is vocatis&rpar;<emph.end type="italics"/> non &longs;olum viam hanc lacteam a&longs;tris plurimis refer&shy;<lb/>
ti&longs;&longs;imam e&longs;&longs;e videmus, &longs;ed pr&aelig;terea eandem &longs;tellarum admodum feracem <lb/>
appellare licebit, &longs;i quidem &longs;tell&aelig; omnes ill&aelig; nou&aelig;, qu&aelig; no&longs;tra tempe&longs;tate <lb/>
apparuerunt, omnes in hac via exort&aelig; &longs;unt. </s>
          <s id="s.001743">prima enim anno 1572. efful&longs;it <lb/>
in Ca&longs;&longs;iopea; altera anno 1600. in Cygno. </s>
          <s id="s.001744">tertia demum anno 1604. in Sa&shy;<lb/>
gittario, qu&aelig; omnes con&longs;tellationes intra lacteum circulum continentur. <lb/>
</s>
          <s id="s.001745">Veri&longs;&longs;imum pr&aelig;terea e&longs;&longs;e hoc idem confirmatur in&longs;trumenti illius mirabi&shy;<lb/>
lis auxilio, quod &longs;uperiori anno in Belgio excogitatum, &amp; po&longs;tea in Italia <lb/>
&agrave; Galil&aelig;o perfectius <expan abbr="reddit&utilde;">redditum</expan> e&longs;t, <expan abbr="quod&qacute;">quodque</expan>; ip&longs;e primum Italic&egrave; Cannocchiale, <lb/>
Latin&egrave; ver&ograve;, &amp; quidem apt&egrave; &agrave; Gr&aelig;cis mutuato vocabulo alius Tele&longs;copium <lb/>
appellauit: hoc inquam &longs;pecillo adhibito per&longs;picuum &longs;tatim fit non &longs;olum <lb/>
in via lactea innumeras &longs;tellas contineri, verum quid ip&longs;a &longs;it, cert&ograve; certius <lb/>
con&longs;tat; &longs;ed &longs;atius e&longs;t ip&longs;ius Galil&aelig;i verba ex Nuncio &longs;ydereo referre: Quod <lb/>
tertio inquit, loco &agrave; nobis fuit ob&longs;eruatum e&longs;t ip&longs;iu&longs;met lactei circuli e&longs;&longs;en&shy;<lb/>
tia, &longs;en materies, quam Tele&longs;copij beneficio ade&ograve; ad &longs;en&longs;um licet intueri, <lb/>
vt &amp; altercationes omnes, qu&aelig; per tot &longs;&aelig;cula Philo&longs;ophos excruciarunt ab <lb/>
oculata certitudine <expan abbr="dirim&atilde;tur">dirimantur</expan>, <expan abbr="nos&qacute;">nosque</expan>; &agrave; verbo&longs;is di&longs;putationibus liberemur: <lb/>
e&longs;t enim Galaxia nihil aliud, qu&agrave;m innumerarum &longs;tellarum coaceruatim <lb/>
con&longs;itarum congeries, in <expan abbr="qu&atilde;cunq;">quancunque</expan> enim regionem illius &longs;pecillum dirigas, <lb/>&longs;tatim &longs;tellarum ingens frequentia &longs;e &longs;e in con&longs;pectum profert, <expan abbr="quar&utilde;">quarum</expan> com&shy;<lb/>
plures &longs;atis magn&aelig;, ac vald&egrave; con&longs;picu&aelig; videntur; &longs;ed exiguarum multitudo <lb/>
pror&longs;us inexplorabilis e&longs;t. </s>
          <s id="s.001746">h&aelig;c ille.</s>
        </p>
        <p type="main">
          <s id="s.001747"><arrow.to.target n="marg143"/></s>
        </p>
        <p type="margin">
          <s id="s.001748"><margin.target id="marg143"/>143</s>
        </p>
        <p type="main">
          <s id="s.001749">Eodem cap. <emph type="italics"/>&lpar;Con&longs;ideretur autem &amp; circulus, &amp; qu&aelig; &longs;unt in ip&longs;o a&longs;tra ex de&shy;<lb/>
&longs;criptione&rpar;<emph.end type="italics"/> id e&longs;t, con&longs;ideretur Galaxia, &amp; a&longs;tra ip&longs;ius in&longs;piciantur diligenter <lb/>
ex de&longs;criptione alicuius Globi a&longs;tronomici, in quo &longs;olent A&longs;tronomi omnes <lb/>
con&longs;tellationes, ac &longs;tellas &longs;uis locis reddere, <expan abbr="atq;">atque</expan> etiam lacteum ip&longs;um cir&shy;<lb/>
culum graphic&egrave; effingere. </s>
          <s id="s.001750">huiu&longs;modi globum veteres &longs;ph&etail;ram Arat&aelig;am di&shy;<lb/>
cebant ab Arato Poeta gr&aelig;co, qui <expan abbr="c&otilde;&longs;tellationes">con&longs;tellationes</expan> omnes carmine pro&longs;equu&shy;<lb/>
tus e&longs;t, ac proinde globum hunc ordine expo&longs;uit:</s>
        </p>
        <p type="main">
          <s id="s.001751"><arrow.to.target n="marg144"/></s>
        </p>
        <p type="margin">
          <s id="s.001752"><margin.target id="marg144"/>144</s>
        </p>
        <p type="main">
          <s id="s.001753">Eodem cap. <emph type="italics"/>&lpar;Spar&longs;a autem vocata&rpar;<emph.end type="italics"/> put&ograve; &longs;par&longs;a h&aelig;c &longs;ydera illa e&longs;&longs;e, qu&aelig; <lb/>
recentiores informia appellant, e&ograve; quod ad aliorum a&longs;teri&longs;morum formas <lb/>
minim&egrave; reuocentur.</s>
        </p>
        <p type="main">
          <s id="s.001754"><arrow.to.target n="marg145"/></s>
        </p>
        <p type="margin">
          <s id="s.001755"><margin.target id="marg145"/>145</s>
        </p>
        <p type="main">
          <s id="s.001756">Summa 4. cap. 1. <emph type="italics"/>&lpar;In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>fluentes&rpar;<emph.end type="italics"/> rect&egrave; dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t. po&shy;<lb/>
natur in A&longs;ia, cum cert&ograve; certius con&longs;tet, ip&longs;um in Gr&aelig;cia Europ&aelig; regione <lb/>
&longs;itum e&longs;&longs;e. </s>
          <s id="s.001757">fort&egrave; legendum e&longs;t, vt vult Vicomercatus, ex Paropame&longs;&longs;o, non <lb/>
autem ex Parna&longs;&longs;o, quamuis Gr&aelig;ci codices aduer&longs;entur; Paropame&longs;&longs;um <lb/>
<expan abbr="namq;">namque</expan> Plinius, &amp; Strabo in A&longs;ia collocant, <expan abbr="volunt&qacute;">voluntque</expan>; ip&longs;um e&longs;&longs;e iugum quod&shy;<lb/>dam montis Cauca&longs;i: Cauca&longs;um autem &longs;upra Pontum oriri, &amp; <expan abbr="v&longs;q;">v&longs;que</expan> ad Hir&shy;<lb/>
canum, &amp; vltra mare per totam A&longs;iam &longs;e proferre, tradunt veteres Geo&shy;<lb/>
graphi. </s>
          <s id="s.001758">vide The&longs;aurum geographicum Abrahami Ortelij. </s>
          <s id="s.001759">Strabo lib. 15. <lb/>
&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>
orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;&shy;


<pb pagenum="98" xlink:href="009/01/098.jpg"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>
vocant.</s>
        </p>
        <p type="main">
          <s id="s.001760"><arrow.to.target n="marg146"/></s>
        </p>
        <p type="margin">
          <s id="s.001761"><margin.target id="marg146"/>146</s>
        </p>
        <p type="main">
          <s id="s.001762">Ibidem <emph type="italics"/>&lpar;Apparet mare, quod e&longs;t extra&rpar;<emph.end type="italics"/> intelligit illud mare <expan abbr="Ocean&utilde;">Oceanum</expan>, quod <lb/>
Arabiam, ac Per&longs;iam alluit, <expan abbr="Indico&qacute;">Indicoque</expan>; Oceano committitur: <expan abbr="quod&qacute;">quodque</expan>; &agrave; pri&shy;<lb/>
&longs;cis Geographis Rubrum mare appellatur, cuius alterum Rubrum mare, <lb/>
quod inter Africam, &amp; Arabiam &longs;e in&longs;inuat, e&longs;t quidam &longs;inus, quem nunc <lb/>
communiter omnes Rubrum mare appellant. </s>
          <s id="s.001763">de illo inquam merit&ograve; intel&shy;<lb/>
ligit Alexander, non de hoc Aegyptiaco, cum ex a&longs;pectu illius &agrave; monte Pa&shy;<lb/>
ropame&longs;&longs;o, &longs;equatur ip&longs;um e&longs;&longs;e editi&longs;&longs;imum, quod non &longs;equeretur ex altero <lb/>
ob illius propinquitatem. </s>
          <s id="s.001764">Dixit autem mare, quod e&longs;t extra, ide&longs;t extra <lb/>
terram habitatam, ad di&longs;tinctionem maris Mediterranei, quod e&longs;t intra <lb/>
terram habitatam, ac propterea Mediterraneum dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001765"><arrow.to.target n="marg147"/></s>
        </p>
        <p type="margin">
          <s id="s.001766"><margin.target id="marg147"/>147</s>
        </p>
        <p type="main">
          <s id="s.001767">Ibidem <emph type="italics"/>&lpar;Ex hoc igitur fluunt &amp; alij fluuij, &amp; Bactrus, &amp; Choa&longs;pes, &amp; Ara&shy;<lb/>
xes. </s>
          <s id="s.001768">ab hoc autem ab&longs;cinditur Tanais pars exi&longs;tens in Meotidem paludem fluit au&shy;<lb/>
tem, &amp; Indus ex ip&longs;o, omnium fluuiorum fluxio maxima&rpar;<emph.end type="italics"/> h&aelig;c omnia &longs;unt fal&longs;a, <lb/>
&amp; impo&longs;&longs;ibilia; nam cum Bactrus Bactrianam regionem irriget, qu&aelig; e&longs;t vl&shy;<lb/>
tra Per&longs;iam, Choa&longs;pes ver&ograve; Per&longs;iam ip&longs;am, Indus <expan abbr="deniq;">denique</expan> in India oriatur: <lb/>
qu&igrave; fieri pote&longs;t, vt in Regionibus ade&ograve; inuicem di&longs;&longs;itis orti fluuij ab eodem <lb/>
<expan abbr="quoq;">quoque</expan> Paropame&longs;&longs;o monte ortum ducant. </s>
          <s id="s.001769">nec minus fal&longs;um e&longs;t illud de Ta&shy;<lb/>
nai, quod &longs;it qua&longs;i ip&longs;ius Araxis ramus quidam, Tanais enim ex Riph&aelig;is <lb/>
<expan abbr="m&otilde;tibus">montibus</expan> Scythi&aelig; delabitur in Meotidem paludem long&egrave; longius ab Araxi. <lb/>
<!-- KEEP S--></s>
          <s id="s.001770"><expan abbr="eum&qacute;">eumque</expan>; terminum inter Europam, &amp; A&longs;iam Geographi con&longs;tituunt, vnde <lb/>
Diony&longs;ius Afer &longs;ic cecinit:</s>
        </p>
        <p type="main">
          <s id="s.001771"><emph type="italics"/>Europam, <expan abbr="atq;">atque</expan> A&longs;iam Tanais di&longs;terminat amnis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001772">ver&ugrave;m huiu&longs;modi errata Ari&longs;t. <!-- REMOVE S--><expan abbr="atq;">atque</expan> ade&ograve; Geographis illius temporis con&shy;<lb/>
donanda &longs;unt, cum nondum Geographia &longs;atis exculta e&longs;&longs;et.</s>
        </p>
        <p type="head">
          <s id="s.001773"><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001774"><arrow.to.target n="marg148"/></s>
        </p>
        <p type="margin">
          <s id="s.001775"><margin.target id="marg148"/>148</s>
        </p>
        <p type="main">
          <s id="s.001776">Eod. <!-- REMOVE S-->cap. <emph type="italics"/>&lpar;Cauca&longs;us autem maximus mons e&longs;t eorum qui ad ori<expan abbr="&etilde;tem">entem</expan> &aelig;&longs;tiua&shy;<lb/>
lem, &amp; multitudine, &amp; altitudine &longs;igna autem altitudinis quidem, quia <lb/>
videtur &amp; &agrave; vocatis Profundis, &amp; &agrave; nauigantibus in Stagnum in&longs;uper il&shy;<lb/>
lu&longs;trantur &agrave; Sole ip&longs;ius &longs;ummitates, v&longs;que ad tertiam partem nocte, &amp; ab <lb/>
aurora, &amp; iterum a ve&longs;pera&rpar;<emph.end type="italics"/> Cauca&longs;us mons &longs;itus e&longs;t inter mare Euxinum, &amp; <lb/>
Ca&longs;pium, &longs;upra Cholchidem, &amp; Iberiam regiones, vbi polus eleuatur 47. <lb/>
circiter grad. <!-- REMOVE S-->ac re&longs;pectu Gr&aelig;ci&aelig;, &amp; maris Euxini vergit ad eam mundi pla&shy;<lb/>
gam, vnde illis &aelig;&longs;tiuo tempore Sol oritur. </s>
          <s id="s.001777">ait Ari&longs;t. eum e&longs;&longs;e omnium mon&shy;<lb/>
tium illius plag&aelig; alti&longs;&longs;imum, quod probat prim&ograve;, quia admodum &agrave; long&egrave; <lb/>
cernitur, <expan abbr="nimir&utilde;">nimirum</expan> ab illo Euxini loco, qui Profunda vocatur, e&ograve; qu&ograve;d &agrave; Nau&shy;<lb/>
tis nu&longs;quam ibi fundus reperiatur. </s>
          <s id="s.001778">&amp; pr&aelig;terea &agrave; Nauigantibus in Stagnum, <lb/>
&longs;iue in Meotidem paludem, qu&aelig; quidem loca minim&ugrave;m di&longs;tant a Cauca&longs;o <lb/>
560. milliaribus. </s>
          <s id="s.001779">Secund&ograve;, probat il ius altitudinem ex eo, qu&ograve;d &longs;ummi&shy;<lb/>
tates ip&longs;ius <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam partem nocte, &amp; ve&longs;peri &agrave; Sole illu&longs;trentur. </s>
          <s id="s.001780">Lo&shy;<lb/>
cum hunc fus&egrave; pertractat eruditi&longs;&longs;imus Iacobus Mazonius &longs;ectione 3. &amp; 4. <lb/>
de Comparatione Platonis, &amp; Ari&longs;t. quo in opere plurima habet ex Mathe&shy;<lb/>
maticis de&longs;umpta, quibus naturalem Philo&longs;ophiam mirific&egrave; illu&longs;trat, <expan abbr="mani-fe&longs;tum&qacute;">mani&shy;<lb/>
fe&longs;tumque</expan>; reddit, qu&agrave;m nece&longs;&longs;ari&aelig; &longs;int Mathematic&aelig; ad philo&longs;ophic&aelig; veri&shy;


<pb pagenum="99" xlink:href="009/01/099.jpg"/>tatis in&longs;pectionem. </s>
          <s id="s.001781">Is igitur &longs;ect. </s>
          <s id="s.001782">3. cap. 5. de hoc Ari&longs;t. loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>
multis an&longs;am dedit reprehendendi Ari&longs;t. tanquam puerilia effutientem. </s>
          <s id="s.001783">tex&shy;<lb/>
tus <expan abbr="itaq;">itaque</expan> Ari&longs;t. duplicem habet &longs;en&longs;um; alter &agrave; quo non abhorret <expan abbr="Alex&atilde;der">Alexander</expan>; <lb/>
vt tertia illa pars ad montem referatur, qua&longs;i dicat, quod antequam Sol ima <lb/>
montis illu&longs;tret, illuminat illius cacumen <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam montis partem: <lb/>
&longs;ed h&aelig;c Mazonij expo&longs;itio nulla e&longs;t, cuiu&longs;libet enim montis etiam medio&shy;<lb/>
cris altitudinis Sol illu&longs;trat non &longs;olum tertiam partem, &longs;ed &amp; dimidium, &amp; <lb/>
duas tertias, &amp; fer&egrave; totum, antequam ad planam illius ba&longs;im de&longs;cendat. <lb/>
</s>
          <s id="s.001784">Ego &longs;ic exponendum cen&longs;eo, vt Ari&longs;t. dicat, mane, ide&longs;t initio Crepu&longs;culi <lb/>
matutini, &amp; ve&longs;pere, ide&longs;t, in fine Crepu&longs;culi ve&longs;pertini ip&longs;ius tertiam par&shy;<lb/>
tem illuminatam con&longs;pici ab ijs, quorum horizonti tunc incipit, vel de&longs;init <lb/>
Crepu&longs;culum; ex quibus illi nece&longs;&longs;ari&ograve; re&longs;pectu Cauca&longs;i &longs;unt occidentales, <lb/>
qu&igrave; man&egrave; hoc vident, vti &longs;unt ij, qui in Euxino, &longs;eu Ponto, &amp; Meotide naui&shy;<lb/>
gant, vel loca proxima inhabitant: illi ver&ograve;, qui in fine Crepu&longs;culi ve&longs;per&shy;<lb/>
tini hoc cernunt, nece&longs;&longs;ari&ograve; re&longs;pectu Cauca&longs;i erunt orientales. </s>
          <s id="s.001785">Alter huius <lb/>
loci &longs;en&longs;us e&longs;t, ait Mazonius, vt non de tertia montis parte, &longs;ed de tertia <lb/>
noctis portione loquatur, ita vt man&egrave;. </s>
          <s id="s.001786">v. <!-- REMOVE S-->g. <!-- REMOVE S-->initio terti&aelig;, &amp; vltim&aelig; noctis <lb/>
parte, cacumen Cauca&longs;i illuminetur. </s>
          <s id="s.001787">h&aelig;c ille. </s>
          <s id="s.001788">vbi animaduertendum expo&shy;<lb/>
&longs;itionem <expan abbr="h&atilde;c">hanc</expan> par&ugrave;m differre &agrave; no&longs;tra mod&ograve; allata, c&ugrave;m <expan abbr="vtraq;">vtraque</expan> in idem tem&shy;<lb/>
pus recidat; nam &longs;i dixerimus initio Crepu&longs;culi matutini illuminari ter&shy;<lb/>
tiam partem Cauca&longs;i, tempus hoc coincidit cum initio terti&aelig; partis noctis, <lb/>
quantitas enim Crepu&longs;culi in poli eleuatione 47. grad. <!-- REMOVE S-->qualem habet Cau&shy;<lb/>
ca&longs;us, per totam &aelig;&longs;tatem tres horas plus minus continet, vt patet ex tabu&shy;<lb/>
la quantitatis Crepu&longs;culi, qu&aelig; e&longs;t apud Nonium, &amp; apud Clauium in &longs;ph&aelig;&shy;<lb/>
ra vltim&aelig; editionis; qu&aelig; quantitas reperiri geometrico calculo pote&longs;t, vt <lb/>
docent Nonius, Clauius, &amp; Maginus lib. 10. primi mob. </s>
          <s id="s.001789">quod quidem trium <lb/>
circiter horarum tempus e&longs;t tertia fer&egrave; noctis pars in ijs regionibus, quibus <lb/>
polus eleuatur 47. grad. <!-- REMOVE S-->&longs;iue ergo dicamus id contingere initio Crepu&longs;culi, <lb/>
&longs;iue initio terti&aelig; partis noctis, erit idem tempus, trium &longs;cilicet horarum. <lb/>
</s>
          <s id="s.001790">&longs;i ergo, inquit Mazonius, &longs;equamur priorem declarationem, nece&longs;&longs;arium <lb/>
e&longs;t dicere, quod ea tertia pars montis, qu&aelig; initio auror&aelig; Solis lumine per&shy;<lb/>
funditur, &longs;it ea montis altitudo, qua ip&longs;e exuperat illam aeris regionem, <lb/>
vnde Crepu&longs;culum incipit apparere. </s>
          <s id="s.001791">quo po&longs;ito apt&egrave;, ac &longs;agaciter altitudi&shy;<lb/>
nem Cauca&longs;i inue&longs;tigat hoc pacto. </s>
          <s id="s.001792">pr&aelig;mittit autem &longs;eptem propo&longs;itiones <lb/>
apud Mathematicos manife&longs;tas, quas ego mi&longs;&longs;as facio cum non mihi nece&longs;&shy;<lb/>
&longs;ari&aelig; videantur. </s>
          <s id="s.001793">po&longs;tea &longs;ic di&longs;currit; His ergo ita &longs;e habentibus, dico nos in&shy;<lb/>
uenire po&longs;&longs;e viam, qua &longs;altem rudi Minerua, montis altitudinem comper&shy;<lb/>
tam habeamus. </s>
          <s id="s.001794">&longs;i enim in principio Crepu&longs;culi v. <!-- REMOVE S-->g. <!-- REMOVE S-->matutini &lpar;ita enim, vt <lb/>
&longs;upra annotaui intelligendus e&longs;t Ari&longs;t.&rpar; illuminatur tertia pars, nece&longs;&longs;arium <lb/>videtur tertiam illam partem &longs;upra eam regionem collocari, ex qua Cre&shy;<lb/>
pu&longs;culum in planitie apparere incipit, &longs;ed illa regio ex Alhazino, &amp; Vitell. <lb/>
<!-- REMOVE S-->de Crepu&longs;culis milliaribus 52. &agrave; terra recedit, ergo du&aelig; terti&aelig; montis par&shy;<lb/>
tes, qu&aelig; Solem initio auror&aelig; non vident, &longs;unt 52. milliaria ad perpendicu&shy;<lb/>
lum, &amp; tertia alia pars illuminata e&longs;t ad perpendiculum 26. milliaria: ita <lb/>
vt totius montis altitudo perpendicularis &longs;it 78. mill. <!-- REMOVE S-->&longs;ed pap&egrave; in quos acu&shy;


<pb pagenum="100" xlink:href="009/01/100.jpg"/>leos imprudens me conieci? </s>
          <s id="s.001795">rident enim hoc Ari&longs;t. dictum Mathematici, <lb/>
putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s>
          <s id="s.001796">C&aelig;terum ego pro pr&aelig;ceptoris tu&shy;<lb/>tela, dico eum &longs;equutum e&longs;&longs;e famam. </s>
          <s id="s.001797">h&aelig;c Mazonius, quorum nonnulla in&shy;<lb/>
digent con&longs;ideratione cuiu&longs;modi, &longs;unt illa, quando dicit, nece&longs;&longs;arium vi&shy;<lb/>
detur, quod ea pars &longs;upra eam regionem attollatur, vnde Crepu&longs;culum in <lb/>planitie apparere incipit. </s>
          <s id="s.001798">videtur enim his verbis velle dicere, quod quan&shy;<lb/>
do habitantibus planitiem, qu&aelig; e&longs;t ad pedem montis Cauca&longs;i, vel horizon&shy;<lb/>
tem eiu&longs;dem, incipit Crepu&longs;culum, ij&longs;dem etiam tunc tertia montis pars <lb/>
appareat illuminata; in quo &longs;en&longs;u errat po&longs;tea in colligenda montis altitu&shy;<lb/>
dine, quamuis enim verum e&longs;&longs;et partem illuminatam eminere totam &longs;upra <lb/>
52. milliaria, non tamen &longs;equitur ip&longs;am &longs;olam eminere, &longs;ed alia etiam pars <lb/>
eminere pote&longs;t, quod &longs;ic geometric&egrave; demon&longs;trabo. </s>
          <s id="s.001799">de&longs;cribatur enim figura <lb/>
<figure id="id.009.01.100.1.jpg" place="text" xlink:href="009/01/100/1.jpg"/>


<pb pagenum="101" xlink:href="009/01/101.jpg"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>
&amp; Clauius, in qua terr&aelig; globus e&longs;t F L G E, regi&ograve; vaporum, &amp; exhalatio&shy;<lb/>
num M X N T. horizon a&longs;tronomicus O P. phy&longs;icus Q R, tangens terram <lb/>
in puncto F, vbi etiam ponendus e&longs;t huius horizontis habitator, vn&agrave; cum. <lb/>
</s>
          <s id="s.001800">Cauca&longs;o F V. <!-- KEEP S--></s>
          <s id="s.001801">Sol A B C, qui initio Crepu&longs;culi infra horizontem O P, depri&shy;<lb/>
mitur gr. <!-- REMOVE S-->18. vti ab A&longs;tronomis compertum e&longs;t, hoc e&longs;t, arcum D P, e&longs;&longs;e <lb/>
grad. <!-- REMOVE S-->18. radius autem C I K, tangens terram, incipit illuminare halitus, <lb/>
qui &longs;unt ad K, in extremo horizonte &longs;en&longs;ibili F K. quique po&longs;&longs;unt videri ab <lb/>
oculo in F, ide&longs;t ab huius horizontis habitatore. </s>
          <s id="s.001802">C&aelig;ter&ugrave;m pr&aelig;dicti autho&shy;<lb/>
res po&longs;t longam ratiocinationem ex calculo planorum <expan abbr="triangulor&utilde;">triangulorum</expan> tandem <lb/>
o&longs;tendunt in triangulo H F K, latus H K, continere milliaria 3631. ex quo <lb/>detracta H L, &longs;emidiametro terr&aelig;, qu&aelig; e&longs;t milliar. 3579. reliqua L K, &longs;um&shy;<lb/>ma halituum eleuatio relinquatur 52. milliar. </s>
          <s id="s.001803">quibus ab ip&longs;is demon&longs;tra&shy;<lb/>
tis, &longs;i H F, terr&aelig; &longs;emidiameter, qu&aelig; continet milliar. 3579. ponatur &longs;inus <lb/>
totus 100000. &amp; latus F K, ponatur tangens anguli ad H, quem pr&etail;dicti au&shy;<lb/>
thores probant e&longs;&longs;e grad. <!-- REMOVE S-->8. 54. erit F K, tangens partium 15659. fiat igi&shy;<lb/>
tur per 2. pro. </s>
          <s id="s.001804">trjang. </s>
          <s id="s.001805">rectil. </s>
          <s id="s.001806">Clauij;<lb/>
<arrow.to.target n="table4"/></s>
        </p>
        <table>
          <table.target id="table4"/>
          <row>
            <cell>vt H F, &longs;inus totus,</cell>
            <cell>ad milliar.</cell>
            <cell>ita tangens F K,</cell>
            <cell>ad milliar.</cell>
          </row>
          <row>
            <cell>100000.</cell>
            <cell>3579.</cell>
            <cell>15659.</cell>
            <cell>560.</cell>
          </row>
        </table>
        <p type="main">
          <s id="s.001807">&amp; inueniemus per auream regulam latus F K, continere milliar. </s>
          <s id="s.001808">560. quan&shy;<lb/>
ta &longs;cilicet e&longs;t di&longs;tantia ab oculo no&longs;tro ad exhalationes Crepu&longs;culi initium <lb/>
efficientes. </s>
          <s id="s.001809">Con&longs;ideremus iam triangulum F K V, vt ip&longs;ius latus F V, qu&aelig; <lb/>
e&longs;t Cauca&longs;i altitudo, in milliaribus innote&longs;cat. </s>
          <s id="s.001810">iam ip&longs;ius latus F K, inno&shy;<lb/>
tuit, angulus ver&ograve; ad F, e&longs;t rectus; at angulus ad K, &longs;ic manife&longs;tabitur; in <lb/>
quadrilatero F K I H, quatuor anguli &longs;unt &aelig;quales 4. rectis ex 32. primi. </s>
          <s id="s.001811">duo <lb/>
autem F, &amp; I, &longs;unt recti ex 18. 3. ergo reliqui duo H, &amp; K, &aelig;quales erunt duo&shy;<lb/>
bus rectis, quorum alter H, e&longs;t gr. <!-- REMOVE S-->17. 48. vt pr&aelig;diti Mathematici <expan abbr="o&longs;t&etilde;dunt">o&longs;tendunt</expan>, <lb/>
reliquus igitur ad K, erit gr. <!-- REMOVE S-->162. 12. vt compleat duos rectos. </s>
          <s id="s.001812">qui &longs;i detra&shy;<lb/>
hatur &agrave; duobus rectis, qui &longs;unt deinceps ad lineam F K, reliquus angulus <lb/>
F K V, erit gr. <!-- REMOVE S-->17. 48. &longs;i ergo latus F K, notum ponatur &longs;inus totus 100000. <lb/>
latus ver&ograve; F V, tangens anguli noti, erit ip&longs;a 32100. fiat igitur,<lb/>
<arrow.to.target n="table5"/></s>
        </p>
        <table>
          <table.target id="table5"/>
          <row>
            <cell>vt F K, &longs;inus totus,</cell>
            <cell>ad milliar.</cell>
            <cell>ita F V, tangens</cell>
            <cell>ad milliar.</cell>
          </row>
          <row>
            <cell>100000.</cell>
            <cell>560.</cell>
            <cell>32100.</cell>
            <cell>180.</cell>
          </row>
        </table>
        <p type="main">
          <s id="s.001813"><expan abbr="inueniemus&qacute;">inueniemusque</expan>; latus F V, continere milliar. </s>
          <s id="s.001814">180. cuius pars F X, qu&aelig; e&longs;t in&shy;<lb/>
fra habituum altitudinem continet milliar. </s>
          <s id="s.001815">52. quibus detractis ex 180. re&shy;<lb/>
manent 128. pro tota X V, qu&aelig; tota e&longs;t &longs;upra vapores, nondum tamen illu&shy;<lb/>
minata. </s>
          <s id="s.001816">vnde patet Mazonium erra&longs;&longs;e in colligenda hoc modo Cauca&longs;i al&shy;<lb/>
titudine, ex prima Crepu&longs;culi illuminatione in horizonte Cauca&longs;i facta, <lb/>
cum ex pr&aelig;mi&longs;&longs;o calculo con&longs;tet partem montis F V, totam tunc temporis <lb/>
e&longs;&longs;e tenebro&longs;am, quamuis &longs;uperet mult&ograve; regionem vaporum, contr&agrave; qu&agrave;m <lb/>
ip&longs;e putabat, &longs;uperat enim eam milliar. </s>
          <s id="s.001817">128. quare du&aelig; terti&aelig; montis erunt <lb/>
non 52. mill. <!-- REMOVE S-->vt ip&longs;e ait, &longs;ed mill. <!-- REMOVE S-->180. &amp; proinde tota altitudo erit mill. <!-- REMOVE S-->270. <lb/>
quod &longs;an&egrave; ridiculum e&longs;t, cum nullius montis altitudo &longs;e&longs;quimilliare tran&shy;<lb/>
&longs;cendat. </s>
          <s id="s.001818">Quod &longs;i &longs;equamur alteram expo&longs;itionem, vt nimirum Ari&longs;tot. <!-- REMOVE S-->lo&shy;<lb/>
quatur non de tertia montis parte, &longs;ed noctis, ita vt dicat, circa initium <lb/>
terti&aelig; partis noctis apicem montis illu&longs;trari, altitudo eius erit tantum&shy;


<pb pagenum="102" xlink:href="009/01/102.jpg"/>modo 180. quot continet latus F V. vt vidimus, qu&aelig; quamuis illa minor &longs;it, <lb/>
adhuc tamen ab&longs;urda e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.001819">Si ver&ograve; dixerimus Ari&longs;t. intelligere h&aelig;c omnia, non re&longs;pectu horizontis <lb/>
Cauca&longs;i, &longs;ed alterius, cuius habitator in principio &longs;ui Crepu&longs;culi tertiam <lb/>
Cauca&longs;i partem iam illu&longs;tratam videat, vti accideret &longs;i Cauca&longs;us &longs;tatuere&shy;<lb/>
tur in L K, vbi incipit Crepu&longs;culum habitanti in F. tunc e&longs;&longs;et altitudo tanta, <lb/>
quanta colligit Mazonius, &longs;i tamen Ari&longs;t. intelligatur de tertia montis par&shy;<lb/>
te; e&longs;t enim L K, altitudo habituum 52. mill. <!-- REMOVE S-->&amp; du&aelig; terti&aelig; montis, quare <lb/>
totus mons erit 78. &longs;i autem intelligatur circa tertiam noctis partem, mon&shy;<lb/>tis apicem illuminatum videri ab habitatore F, &longs;ic altitudo eius erit tan&shy;<lb/>
tummodo 52. mill. <!-- REMOVE S-->qu&aelig; tamen adhuc omnem veritatem nimium &longs;uperat. <lb/>
</s>
          <s id="s.001820">Cum ergo hinc inde &longs;equantur ab&longs;urda, putat Mazonium excu&longs;andum e&longs;&longs;e <lb/>
Ari&longs;tot. dicendo eum &longs;equutum e&longs;&longs;e famam, <expan abbr="loquutum&qacute;">loquutumque</expan>; e&longs;&longs;e populariter. <lb/>
</s>
          <s id="s.001821">Verumenimuer&ograve; &longs;apientiores iudicent num rect&egrave; philo&longs;ophus, cuius e&longs;t re&shy;<lb/>
condita, <expan abbr="atq;">atque</expan> abdita docere, excu&longs;etur, &longs;i dicatur, eum, popularem famam <lb/>
&longs;equutum e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.001822">Tandem monendus mihi Lector e&longs;t, in demon&longs;tratione Magini, qu&aelig; e&longs;t <lb/>
apud Mazonium &longs;ect. </s>
          <s id="s.001823">4. citati operis; a&longs;&longs;umi radium Solis tangentem terr&aelig; <lb/>
globum, qui cum horizonte faciat angulum gr. <!-- REMOVE S-->18. quod fal&longs;um e&longs;t, &longs;olus <lb/>
enim radius centralis, qui &agrave; centro Solis ad centrum terr&aelig; ducitur talem <lb/>
facit angulum, <expan abbr="atq;">atque</expan> hac de cau&longs;a ip&longs;e colligit altitudinem no&longs;tra maiorem; <lb/>
no&longs;tra e&longs;t 270. mill. <!-- REMOVE S-->&longs;ua ver&ograve; 276. vbi etiam, &longs;icut &amp; nos a&longs;&longs;umit horizon&shy;<lb/>
tem Cauca&longs;i.</s>
        </p>
        <p type="main">
          <s id="s.001824">Aduertendum tandem Mazonium admodum aduer&longs;antia loquutum e&longs;&longs;e, <lb/>
&longs;ect. </s>
          <s id="s.001825">enim 3. demon&longs;tratin&egrave; concludit altitudinem 76. mill. <!-- REMOVE S-->&longs;ect. </s>
          <s id="s.001826">ver&ograve; 4. &longs;i&shy;<lb/>
mul <expan abbr="c&utilde;">cum</expan> Magino demon&longs;tratiu&egrave; pariter colligit altitudinem eiu&longs;dem 276. m. <lb/>
</s>
          <s id="s.001827">qu&aelig; nimis ab inuicem di&longs;crepant, cum tamen <expan abbr="vtrobiq;">vtrobique</expan> demon&longs;tret, &amp; ve&shy;<lb/>
ritas &longs;it vna. </s>
          <s id="s.001828">At ver&ograve; cau&longs;a huius di&longs;crepanti&aelig; e&longs;t, qu&ograve;d &longs;ect. </s>
          <s id="s.001829">3. accipit Cre&shy;<lb/>
pu&longs;culum non horizontis Cauca&longs;i, &longs;ed illius, in cuius extremitate orientali, <lb/>
vbi incipit Crepu&longs;culum, Cauca&longs;us &longs;itus &longs;it, <expan abbr="di&longs;tet&qacute;">di&longs;tetque</expan>; ab habitatore 560. m. <lb/>
</s>
          <s id="s.001830">vt &longs;upra o&longs;tendimus. </s>
          <s id="s.001831">&longs;ect. </s>
          <s id="s.001832">ver&ograve; 4. accipit horizontem ip&longs;ius Cauca&longs;i, vt ex <lb/>
figura illic de&longs;cripta videre e&longs;t. </s>
          <s id="s.001833">ex hac igitur horizontum varia &longs;uppo&longs;itio&shy;<lb/>
ne, varia etiam altitudo colligitur, quamuis <expan abbr="vtrobiq;">vtrobique</expan> ex <expan abbr="vtraq;">vtraque</expan> &longs;uppo&longs;itio&shy;<lb/>
ne <expan abbr="vtramq;">vtramque</expan> altitudinem rect&egrave; concludat. </s>
          <s id="s.001834"><expan abbr="Atq;">Atque</expan> h&aelig;c de Cauca&longs;o &longs;ufficiant.</s>
        </p>
        <p type="main">
          <s id="s.001835"><arrow.to.target n="marg149"/></s>
        </p>
        <p type="margin">
          <s id="s.001836"><margin.target id="marg149"/>149</s>
        </p>
        <p type="main">
          <s id="s.001837">Eodem cap. <emph type="italics"/>&lpar;Ex Pyreneo autem, hic autem est mons ad occidentem &aelig;quino&shy;<lb/>ctialem in Gallia, fluunt i&longs;ter, &amp; Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au&shy;<lb/>tem per totam Europam in Pontum Euxinum&rpar;<emph.end type="italics"/> Ari&longs;t. fort&egrave; &longs;equutus e&longs;t Herodo&shy;<lb/>tum, qui fals&ograve; tradit I&longs;trum, &longs;ine Dannbium ex Pyreneis defluere, nam Iu&shy;<lb/>
ce clarius con&longs;tat ip&longs;um ex ijs Alpibus, qu&aelig; Heluetiorum montes dicuntur, <lb/>
prop&egrave; Ba&longs;ileam ex Adula monte ortum ducere. </s>
          <s id="s.001838"><expan abbr="neq;">neque</expan> verum e&longs;t Tarte&longs;&longs;um, <lb/>
quem &amp; B&oelig;tim alij nominant ex Pyreneis de&longs;cendere. </s>
          <s id="s.001839">Tarte&longs;&longs;um hunc Ma&shy;<lb/>
ginus putat e&longs;&longs;e Tagum, cui fauet vocabulorum quali&longs;cunque &longs;imilitudo. <lb/>
</s>
          <s id="s.001840">extra tamen columnas Herculis qui&longs;quis &longs;it in Oceanum occidentale illa&shy;<lb/>
bitur. </s>
          <s id="s.001841">Igno&longs;cenda &longs;unt i&longs;ta Ari&longs;t. tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s>
        </p>
        <p type="main">
          <s id="s.001842"><arrow.to.target n="marg150"/></s>
        </p>
        <p type="margin">
          <s id="s.001843"><margin.target id="marg150"/>150</s>
        </p>
        <p type="main">
          <s id="s.001844">Ad finem eiu&longs;dem cap. <emph type="italics"/>&lpar;Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>
quidam fluuius, &amp; iterum egreditur &longs;ecundum alium locum&rpar;<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> &amp; hoc <pb pagenum="103" xlink:href="009/01/103.jpg"/>Ari&longs;t. vt &longs;uperiora, ob Geographi&aelig; illius &longs;eculi imperfectionem, nu&longs;quam <lb/>
enim in tota Liguria quidpiam tale reperitur.</s>
        </p>
        <p type="head">
          <s id="s.001845"><emph type="italics"/>De Terr&aelig; rotunditate.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001846"><arrow.to.target n="marg151"/></s>
        </p>
        <p type="margin">
          <s id="s.001847"><margin.target id="marg151"/>151</s>
        </p>
        <p type="main">
          <s id="s.001848">Svmma 4. cap. 2. quod e&longs;t de permutatione, &amp; vici&longs;&longs;itudine aquarum, <lb/>
&amp; continentis. </s>
          <s id="s.001849">Pergratum Lectori fore exi&longs;timaui, nec alienum ab <lb/>
in&longs;tituto, &longs;i occa&longs;ione huius permutationis maris, ac terr&aelig;, rem ex&shy;<lb/>po&longs;uero &longs;citu digni&longs;&longs;imam, quam pridem ob&longs;eruare c&oelig;pi, ac in dies <lb/>
ob&longs;eruo, pr&aelig;&longs;ertim cum nullus pr&aelig;teritorum &longs;criptorum, quod &longs;ciam, eam <lb/>
literis mandauerit: Terr&aelig; &longs;cilicet totius molem paulatim reduci ad perfe&shy;<lb/>
ctam &longs;ph&aelig;ricitatem, ita vt aliquando nece&longs;&longs;e &longs;it futurum ip&longs;am &agrave; mari inun&shy;<lb/>
dari, <expan abbr="atq;">atque</expan> omnin&ograve; inhabitabilem reddi. </s>
          <s id="s.001850">Primum igitur illud ex &longs;acris lite&shy;<lb/>
ris &longs;tatuendum, orbem terr&aelig; in &longs;uo primordio fui&longs;&longs;e ab opifice rerum om&shy;<lb/>
nium, figura &longs;ph&aelig;rica donatum, hoc e&longs;t <expan abbr="ab&longs;q;">ab&longs;que</expan> montium eminentijs, atque <lb/>
vallium depre&longs;&longs;ionibus. </s>
          <s id="s.001851">quod patet ex eo, quia <expan abbr="t&utilde;c">tunc</expan> tota Mari obtegebatur, <lb/>
ita vt minim&egrave; apta e&longs;&longs;et animantibus ad inhabitandum. </s>
          <s id="s.001852">redditam ver&ograve; ha&shy;<lb/>
bitabilem, cum ip&longs;ius conditor <expan abbr="qu&atilde;dam">quandam</expan> ip&longs;ius partem humiliorem, &amp; quan&shy;<lb/>
dam eminentiorem effeci&longs;&longs;et; transferendo nimirum maximam terr&aelig; por&shy;<lb/>
tionem ex vno loco in alium, vnde illic maris concauitas, i&longs;tic ver&ograve; mon&shy;<lb/>
tium &longs;ublimitas emer&longs;it. </s>
          <s id="s.001853">quo facto aqu&aelig; omnes in loca illa decliuiora &longs;ua <lb/>
&longs;pont&egrave; rece&longs;&longs;erunt, qu&aelig; aquarum congregatio Mare appellatum e&longs;t. </s>
          <s id="s.001854">Hine <lb/>
nonnulli auctores graui&longs;&longs;imi a&longs;&longs;erere non dubitarunt, montes <expan abbr="c&otilde;flatos">conflatos</expan> fui&longs;&shy;<lb/>
&longs;e ex terra illa, qu&aelig; locum illum occupabat, quem po&longs;tea maria inua&longs;erunt. <lb/>
</s>
          <s id="s.001855">qu&aelig; cum ita &longs;int. </s>
          <s id="s.001856">&longs;equitur terram <expan abbr="n&utilde;c">nunc</expan> e&longs;&longs;e extra naturalem &longs;uam figuram, &amp; <lb/>
propterea in quodam &longs;tatu violento, <expan abbr="viol&etilde;tum">violentum</expan> autem <expan abbr="null&utilde;">nullum</expan> <expan abbr="perpetu&utilde;">perpetuum</expan>. </s>
          <s id="s.001857">pr&aelig;&shy;<lb/>
terea cum terra &longs;it grauior qu&agrave;m aqua, nulla ratione deberent terr&aelig; partes <lb/>
&longs;uperiores a qu&aelig; &longs;uperficiem &longs;uperare, cuius tamen <expan abbr="contrari&utilde;">contrarium</expan> accidit, nam <lb/>
&longs;uperficies ip&longs;a terr&aelig;, &amp; mult&ograve; magis <expan abbr="m&otilde;tana">montana</expan> loca &longs;uperficiem maris cuiu&longs;&shy;<lb/>
uis non parum &longs;uperant; qu&aelig; altera violentia terr&aelig;, &amp; aqu&aelig; ine&longs;t, &amp; ide&ograve; <lb/>
minim&egrave; mirum e&longs;t, im&ograve; <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> natur&aelig; vald&egrave; conueniens terram redire ad <lb/>
pri&longs;tinam, ac primigeniam figuram, ex qua con&longs;ectarium erit aquam <expan abbr="quoq;">quoque</expan> <lb/>
&longs;uam pariter illam &longs;ibi prim&aelig;uam recuperaturam e&longs;&longs;e figuram. </s>
          <s id="s.001858">cau&longs;am au&shy;<lb/>
tem re&longs;tauratricem huius terren&aelig; <expan abbr="rot&utilde;ditatis">rotunditatis</expan> e&longs;&longs;e aquas tum pluuiales, tum <lb/>
fluuiales iamdi&ugrave; ob&longs;eruauimus, vt ex &longs;equentibus ob&longs;eruationibus patebit.</s>
        </p>
        <p type="main">
          <s id="s.001859">Prim&ograve;, videmus flumina quotidie montium radices corrodere, ac qua&longs;i <lb/>
&longs;uffodere, ita vt pa&longs;&longs;im ex hoc, vel illo monte magnas faciant ruinas, ac pr&etail;&shy;<lb/>
cipitia, <expan abbr="atq;">atque</expan> hinc inde pr&aelig;rupti appareant montes, vt merit&ograve; legamus apud <lb/>Iob cap. 14. alluuione paulatim terra con&longs;umitur. </s>
          <s id="s.001860">humum porr&ograve; illam ex <lb/>
montibus delap&longs;am &longs;emper ad loca humiliora fluuij &longs;ecum detrahunt. </s>
          <s id="s.001861">Ex <lb/>
continua etiam hac inter montes corro&longs;ione facta manife&longs;t&egrave; apparet, flumi&shy;<lb/>
num alueos in montanis mod&ograve; e&longs;&longs;e humiliores qu&agrave;m olim, quamuis contra&shy;<lb/>rium accidat alueis fluuiorum per plana decurrentium, qui mod&ograve; altiores <lb/>
&longs;unt <expan abbr="qu&atilde;">quam</expan> exordio mundi, vt paul&ograve; po&longs;t <expan abbr="o&longs;t&etilde;dam">o&longs;tendam</expan>. </s>
          <s id="s.001862">Illud autem liquid&ograve; apparet <lb/>
ex &longs;ignis, &longs;eu &longs;ymbolis, &longs;eu ex &longs;imilitudine terr&aelig;, aut lapidis, qu&aelig; in alti&longs;&longs;imis <lb/>
fluminum ripis hinc inde pa&longs;&longs;im <expan abbr="vid&etilde;tur">videntur</expan>, qu&aelig; indicio &longs;unt montes illos iam <pb pagenum="104" xlink:href="009/01/104.jpg"/>olim fui&longs;&longs;e continuos, <expan abbr="atq;">atque</expan> vnam, <expan abbr="eandem&qacute;">eandemque</expan>; terram <expan abbr="contin&etilde;tem">continentem</expan>, antequam <lb/>
flumen eos ab inuicem &longs;epararet; <expan abbr="flumen&qacute;">flumenque</expan>; ip&longs;um olim altius, vbi &longs;unt &longs;igna <lb/>
illa ambula&longs;&longs;e; quemadmodum in Pyramo Cilici&aelig; amne ob&longs;eruauit Strabo, <lb/>
dum libro 12. de illius ripis h&aelig;c tradit, mira pr&aelig;terea e&longs;t montis c&aelig;&longs;ura, <lb/>
per quam alueus ducitur; nam quemadmodum in petris per medium &longs;ci&longs;&longs;is <lb/>
contingit, alterius partis depre&longs;&longs;ioribus ita conuenire alterius partis emi&shy;<lb/>
nentias, vt coniungi po&longs;&longs;int: &longs;ic videre e&longs;t imminentes flumini petras vtrin&shy;<lb/>
que fer&egrave; <expan abbr="v&longs;q;">v&longs;que</expan> ad montis &longs;umma pertendentes duorum, triumu&egrave; iugerum <lb/>
&longs;patio concauitates qua&longs;dam eminentijs oppo&longs;itas habere. </s>
          <s id="s.001863">h&aelig;c Strabo de <lb/>
vno, quod nos in pluribus ob&longs;eruauimus. </s>
          <s id="s.001864">Pr&etail;terea videmus quotidie pluuias <lb/>
aquas, idem quantum po&longs;&longs;unt efficere, &longs;uperficies montium, eorum maxi&shy;<lb/>
m&egrave;, qui coluntur, perpetu&ograve; ab&longs;umentes, <expan abbr="atq;">atque</expan> ad loca conuallium deducen&shy;<lb/>
tes. </s>
          <s id="s.001865">hinc videre e&longs;t, montes c&aelig;teris duriores, vt &longs;unt lapido&longs;i, c&aelig;teris altio&shy;<lb/>
res reman&longs;i&longs;&longs;e; quippe qui magis &amp; pluuijs, &amp; fluuialibus aquis &longs;ua duritie <lb/>
ob&longs;titerunt. </s>
          <s id="s.001866">idem montani incol&aelig; omnes confirmant, qui omnes aiunt &longs;ibi <lb/>
hanc montium demolitionem iampridem innotui&longs;&longs;e, ex eo quod nonnulli <lb/>
montes olim &longs;ibi impedimento erant, ne arcem, turremu&egrave; in vlteriore mon&shy;<lb/>
te &longs;itam con&longs;picerent, quam deinde plures po&longs;t annos intermedio monte <lb/>
depre&longs;&longs;o, commod&egrave; videbant. </s>
          <s id="s.001867">Ad h&aelig;c; antiqua in montium verticibus con&shy;<lb/>
&longs;tituta &aelig;deficia, propterea intercidunt, quia terra hinc, &amp; inde ab aquis <lb/>paulatim con&longs;umpta, <expan abbr="deor&longs;um&qacute;">deor&longs;umque</expan>; delap&longs;a, fundamenta ip&longs;orum nuda prim&ograve; <lb/>
relinquit; deind&eacute; terra etiam ip&longs;a, qua fundamenta innitebatur &longs;en&longs;im de&shy;<lb/>
lap&longs;a, ip&longs;a <expan abbr="quoq;">quoque</expan> fundamenta vn&agrave; cum toto &aelig;deficio nece&longs;&longs;e e&longs;t collabi, hu&shy;<lb/>
ius &longs;igna infinita propemodum videri po&longs;&longs;unt; vnum tamen, quod toti orbi <lb/>con&longs;picuum e&longs;t, non ommittam; Capitolium videlicet Romanum, cuius <lb/>
modo fundamenta tota extant, qu&aelig; olim alt&egrave; &longs;ub terram de&longs;cendebant. </s>
          <s id="s.001868">vi&shy;<lb/>
de pulcherrimam hac de re tractationem apud Georgium Agricolam lib. 3. <lb/>
cap. 1. qui amplius addit illud, quod &amp; mihi maxim&egrave; probatur; flumina ni&shy;<lb/>
mirum producere montes, <expan abbr="colles&qacute;">collesque</expan>; hoc modo; vult enim initio mundi non <lb/>
extiti&longs;&longs;e tot particulares montes ab inuicem di&longs;cretos, &longs;ed fui&longs;&longs;e perpetua <lb/>
qu&aelig;dam terr&aelig; iuga eminentia quidem, &longs;ed non tot vallibus di&longs;&longs;ecta: v. <!-- REMOVE S-->g. <lb/>
<!-- REMOVE S-->mons no&longs;ter Apenninus erat iugum, &longs;iue dor&longs;um quoddam terr&aelig; eminens <lb/>
quidem, &longs;ed nullis vallibus in tot particulares colles, aut montes di&longs;&longs;ectum; <lb/>
&longs;ed po&longs;tquam flumina &agrave; &longs;ummitate ip&longs;ius deor&longs;um fluere c&oelig;perunt; paula&shy;<lb/>
tim corrodentes humum in dies magis, ac magis effecerunt valles, <expan abbr="atq;">atque</expan> hac <lb/>
ratione in colles, <expan abbr="montes&qacute;">montesque</expan>; plurimos totus Apenninus diui&longs;us e&longs;t. </s>
          <s id="s.001869">h&aelig;c de <lb/>
montibus &longs;ufficiant, nunc ad plana de&longs;cendamus.</s>
        </p>
        <p type="main">
          <s id="s.001870">Contrarium igitur omnin&ograve; accidere videmus in planis, quoniam e&aelig;dem <lb/>
aqu&aelig;, qu&aelig; ex montibus quotidie terram &longs;ecum deducunt, eam ad humilio&shy;<lb/>
ra loca, vt &longs;unt plana, &amp; campe&longs;tria, &longs;iue ibi &longs;int maria, &longs;iue arida, compor&shy;<lb/>
tant, <expan abbr="eam&qacute;">eamque</expan>; ibidem deponunt. </s>
          <s id="s.001871">hinc videmus antiqua &aelig;deficia in planis locis <lb/>
ex&longs;tructa, e&longs;&longs;e iam pen&egrave; tota &longs;epulta, contra quam in montanis, cuius exem&shy;<lb/>
plum habes etiam Rom&aelig; prop&egrave; ip&longs;um Capitolium, in Arcu triumphali Sep&shy;<lb/>
timij, qui iam fer&egrave; totus ruino&longs;a vndique terra obruitur. </s>
          <s id="s.001872">&longs;ic Pantheon. </s>
          <s id="s.001873">&longs;ic <lb/>
etiam templa Epi&longs;copalia, qu&aelig; <expan abbr="plerunq;">plerunque</expan> &longs;atis peruetu&longs;ta &longs;unt, admodum <lb/>
infra terram con&longs;piciuntur. </s>
          <s id="s.001874">Idem affirmant c&oelig;mentarij, &amp; architectores <pb pagenum="105" xlink:href="009/01/105.jpg"/>omnes, quibus <expan abbr="vbiq;">vbique</expan> terrarum, dum in planis &aelig;deficiorum fundamenta ex&shy;<lb/>
canant, occurrit prim&ograve; terra qu&aelig;dam, quam ip&longs;i motam appellant, qu&aelig; li&shy;<lb/>
gnis, ruderibus, ferramentis, numi&longs;matis, &longs;epulturis, <expan abbr="varijs&qacute;">varijsque</expan>; rebus per&shy;<lb/>
mixta e&longs;t; qua eruta, reperitur terra alia, quam nunquam fui&longs;&longs;e motam, ap&shy;<lb/>
paret, ex eo quod &longs;olida, ac ben&egrave; compacta &longs;it, neque vllis externis rebus, <lb/>
pr&aelig;&longs;ertim artificiatis admixta, terra illa, quam motam dicunt, variam va&shy;<lb/>
rijs in locis &longs;ortita e&longs;t altitudinem, prout aqu&aelig; plurimum, vel minimum <lb/>
montan&aelig; terr&aelig; huc, vel illuc comportarunt: alicubi vt hic Parm&aelig; erit &longs;ex <lb/>
vlnarum, alibi viginti, vt Mutin&aelig;; alibi triginta, vt Rom&aelig;, nonnullis in lo&shy;<lb/>
cis. </s>
          <s id="s.001875">Comprobatur tandem h&aelig;c no&longs;tra ob&longs;eruatio ex arte illa, qua per ea&longs;&shy;<lb/>
dem fluuiales aquas &longs;olent, tam loca depre&longs;&longs;iora per aggerationem paula&shy;<lb/>
tim replere, <expan abbr="atq;">atque</expan> eleuare: qu&agrave;m etiam altiora per aquarum earumdem cor&shy;<lb/>
ro&longs;ionem deprimere. </s>
          <s id="s.001876">qua in arte exercitati&longs;&longs;imum P. <!-- REMOVE S-->Augu&longs;tinum Spernac&shy;<lb/>
ciatum no&longs;tr&aelig; Societatis videmus modo de mandato Summi Pontificis Pa&shy;<lb/>
dum, ac Renum Bononien&longs;em ob aggerationem &longs;tagnantes in mari emitte&shy;<lb/>
re; cui totus hic no&longs;ter di&longs;cur&longs;us maxim&egrave; probatur. </s>
          <s id="s.001877">Ex quibus omnibus &longs;e&shy;<lb/>
quitur &longs;uperficiem terr&aelig; tam montium, quam planorum quotidie variari. <lb/>
</s>
          <s id="s.001878">illam nimirum deprimi, hanc attolli. </s>
          <s id="s.001879">vnde aliud maximum notandum &longs;e&shy;<lb/>
quitur, videlicet hac tempe&longs;tate non e&longs;&longs;e eandem agrorum &longs;uperficiem, qu&aelig; <lb/>
erat antiquitus, cum in montanis agris &longs;it mult&ograve; humilior, in campe&longs;tribus <lb/>
ver&ograve; altior, qu&agrave;m antiqua illa, ac primigenia; quapropter mirum videri <lb/>
non debet, &longs;i quorumdam locorum ade&ograve; immutata natura e&longs;t, vt qu&aelig; olim <lb/>
genero&longs;a vina ferebant, vel quouis alio e&longs;&longs;ent pr&aelig;dita munere, ade&ograve; dege&shy;<lb/>
nerauerint, vt &amp; vina, &amp; alia nullius mod&ograve; valoris, vel in parua copia pro&shy;<lb/>
ferant. </s>
          <s id="s.001880">Quod ver&ograve; ad marium aggerationem &longs;pectat, dicimus ij&longs;dem aquis <lb/>magnam arenarum copiam perpetu&ograve; importantibus, fieri aggerationem, <lb/>
hoc e&longs;t littora quotidie magis cre&longs;cere, &longs;eu in mare ingredi, &amp; con&longs;equen&shy;<lb/>
ter mare recedere. </s>
          <s id="s.001881">quod prim&ograve; Ari&longs;t. te&longs;timonio in hoc cap. comprobatur, <lb/>
cum quo pariter &longs;entiunt veteres Geographi, &amp; Hi&longs;torici omnes. </s>
          <s id="s.001882">Ari&longs;t. igi&shy;<lb/>
tur in comprobationem huius adducit prim&ograve; magnam Aegypti aggeratio&shy;<lb/>
nem; pars enim illa Aegypti, qu&aelig; Delta, <expan abbr="Nili&qacute;">Nilique</expan>; donum appellatur ab He&shy;<lb/>
rodoto, ex arenis, &amp; limo, ex Aethyopi&aelig; montibus &longs;imul cum Nilo in mare <lb/>
delabentibus, e&longs;t conflata, <expan abbr="atq;">atque</expan> antiquo littori addita, cui locum paulatim <lb/>
mare ce&longs;&longs;it; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; propterea donum Nili appellata, quod ab ip&longs;o illuc are&shy;<lb/>
nas importante &longs;it facta. </s>
          <s id="s.001883">&longs;ecundum, Ari&longs;t. exemplum e&longs;t Ammonia Regio, <lb/>
cuius humiliora loca. </s>
          <s id="s.001884">f. </s>
          <s id="s.001885">maritima, palam e&longs;t, inquit, quod aggeratione facta, <lb/>
fiunt &longs;tagna, &amp; continens: &longs;uccedente autem tempore, &longs;tagnans aqua ob <lb/>
nouam aggerationem de&longs;iccata e&longs;t, &amp; iam annihilata. </s>
          <s id="s.001886">tertium e&longs;t Meotidis <lb/>
Paludis; At ver&ograve;, ait, &amp; qu&aelig; &longs;unt circa Meotidem Paludem creuerunt allu&shy;<lb/>
uione fluuiorum tantum, vt mult&ograve; minores magnitudine naues, nunc innare <lb/>
po&longs;&longs;int, qu&agrave;m anno ab hinc &longs;exage&longs;imo. </s>
          <s id="s.001887">quare ex hoc facil&egrave; e&longs;t ratiocinari, <lb/>
quod &amp; prim&ograve;, vt multa &longs;tagnorum, ita &amp; hoc opus e&longs;t fluuiorum, &amp; tan&shy;<lb/>
dem nece&longs;&longs;e e&longs;t totum fieri &longs;iccum. </s>
          <s id="s.001888"><expan abbr="quart&utilde;">quartum</expan> e&longs;t illi Bo&longs;phorus Tracius; quod <lb/>
vn&agrave; cum pr&aelig;cedentibus &longs;atius e&longs;t apud ip&longs;um, vel potius apud eius expo&longs;i&shy;<lb/>
torem Vicomercatum videre, vt breuitati con&longs;ulatur. </s>
          <s id="s.001889">Accedit &amp; Plinij te&shy;<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;ed <pb pagenum="106" xlink:href="009/01/106.jpg"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraci&aelig; portu 10. millia pa&longs;&longs;uum; ab <lb/>
Athenarum ver&ograve; <expan abbr="quinq;">quinque</expan> millia, &amp; alijs in locis plus minu&longs;u&egrave; rece&longs;&longs;i&longs;&longs;e &longs;cri&shy;<lb/>
bit. </s>
          <s id="s.001890">Huc facit locus quidam Strabonis ex lib. 12. de Pyramo Cilici&aelig; fluuio: <lb/>
&longs;ic; montes ver&ograve; egre&longs;&longs;us tantum limum in mare deducit, partim ex Ca&shy;<lb/>taonia, partim ex Cilici&aelig; campis, vt huiu&longs;modi de eo oraculum feratur;</s>
        </p>
        <p type="main">
          <s id="s.001891"><emph type="italics"/>Tempus erit rapidis olim cum Pyramus vndis <lb/>In &longs;acram veniet conge&longs;to litore, Cyprum:<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001892">hic enim fluuius &egrave; regione Cypri in&longs;ul&aelig; in mari influit, &amp;c. </s>
          <s id="s.001893">h&aelig;c Strabo.</s>
        </p>
        <p type="main">
          <s id="s.001894">Ver&ugrave;m recentiora non de&longs;unt exempla. </s>
          <s id="s.001895">Rauenna olim erat in extremo <lb/>
littore &longs;ita, nunc paulatim aggeratione aucto litore, mare multum ab ea <lb/>
rece&longs;&longs;it. </s>
          <s id="s.001896">Patauium pariter, vt fertur mare alluebat, quod modo 25. pa&longs;&longs;uum <lb/>
millibus ab eo di&longs;tat. </s>
          <s id="s.001897">A&aelig;&longs;tuarium ip&longs;um Venetum, ob arenas &agrave; varijs flu&shy;<lb/>
minibus in ip&longs;um immi&longs;&longs;as ade&ograve; fundum extulit, vt vix amplius nauigatio&shy;<lb/>
ni &longs;it aptum, <expan abbr="periculam&qacute;">periculamque</expan>; &longs;it ne Venetiarum mirabilis locus, ex maritimo <lb/>
fiat terre&longs;tris. </s>
          <s id="s.001898">demum exemplum &longs;it Bononien&longs;ium Renus, qui quamuis exi&shy;<lb/>
guus &longs;it torrens, paucis tamen annis Padum ip&longs;um, in quem immi&longs;&longs;us fue&shy;<lb/>
rat arena ita repleuit, vt &amp; &longs;ibi, &amp; Pado magno vicinorum agrorum damno <lb/>
viam in mare ob&longs;truxerit. </s>
          <s id="s.001899">Cum igitur mare ob hanc ad aggerationem co&shy;<lb/>
gatur &longs;e quotidie magis recipere, <expan abbr="fiat&qacute;">fiatque</expan>; propterea alueus ip&longs;ius angu&longs;tior, <lb/>
<expan abbr="atq;">atque</expan> elatior, nece&longs;&longs;e e&longs;t etiam ip&longs;am quoque maris aquam quotidie magis <lb/>
coangu&longs;tari, <expan abbr="atq;">atque</expan> attolli, &amp; aliquando futurum, vt exundare incipiat. </s>
          <s id="s.001900">quod <lb/>
iam <expan abbr="pleri&longs;q;">pleri&longs;que</expan> in locis accidit, vt in littore Baltico, Danico, &amp; Hollandico, <lb/>
quibus in locis &longs;unt hac tempe&longs;tate extructi pr&aelig;longi, ac pr&aelig;alti aggeres <lb/>
contra maritimas innundationes: quibus antiquitus minim&egrave; fui&longs;&longs;e opus hi&shy;<lb/>
&longs;toricorum, ac <expan abbr="Geographor&utilde;">Geographorum</expan> &longs;ilentium comprobat. </s>
          <s id="s.001901">Hoc igitur modo ter&shy;<lb/>
ra, qua montes, <expan abbr="colles&qacute;">collesque</expan>; con&longs;tant paulatim ab aquis in maris concauitates <lb/>
deportata, cau&longs;a e&longs;t, vt mare &longs;en&longs;im modo hac, modo illac, terr&aelig; &longs;uperfi&shy;<lb/>
ciei &longs;uperfundatur, <expan abbr="terra&qacute;">terraque</expan>; iterum, quemadmodum exordio mundi inhabi&shy;<lb/>tabilis reddatur: quod tunc maxim&egrave; accidet cum aqu&aelig; tam fluuiales, qu&agrave;m <lb/>
pluui&aelig;, &longs;uper faciem terr&aelig; perpetu&ograve; di&longs;currentes, totam illam montanam <lb/>
terram in pri&longs;tinum locum, vbi ab initio fuerat, <expan abbr="vnde&qacute;">vndeque</expan>; &longs;ublata fuit, re&longs;ti&shy;<lb/>
tuerint; tunc terra erit iterum rotunda, &amp; &longs;ph&aelig;rica, hoc e&longs;t &longs;u&aelig; primigeni&aelig; <lb/>
iterum figur&aelig; re&longs;tituetur: quapropter mare etiam rur&longs;us &longs;icut initio mundi <lb/>
totam terr&aelig; faciem <expan abbr="circumquaq;">circumquaque</expan> innundabit, quod probare volebam.</s>
        </p>
        <p type="main">
          <s id="s.001902"><emph type="italics"/>Tantum &aelig;ui mutare potest long&aelig;ua vetu&longs;tas.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001903">Hinc nonnulla colligi po&longs;&longs;unt non minus notatu, ac &longs;citu, qu&agrave;m pr&aelig;ceden&shy;<lb/>
tia digni&longs;&longs;ima, quibus Ethnicorum Philo&longs;ophorum error redarguatur, &longs;ides <lb/>
ver&ograve; no&longs;tra magis roboretur: mundum nimirum ab &aelig;terno neutiquam ex&shy;<lb/>
titi&longs;&longs;e, vel &longs;altem terram ab &aelig;terno non fui&longs;&longs;e hac figura pr&aelig;ditam, qua nunc <lb/>videmus, nec mundum perpetu&ograve; duraturum. </s>
          <s id="s.001904">nam &longs;i h&aelig;c montuo&longs;a illi figu&shy;<lb/>
ra ab &aelig;terno ine&longs;&longs;et, iampridem tota illa montium tubero&longs;itas fui&longs;&longs;et ab <lb/>
aquis ex&aelig;&longs;a, &amp; con&longs;umpta: <expan abbr="neq;">neque</expan> &aelig;terna erit, quia &longs;ucce&longs;&longs;u temporis, vt pro&shy;<lb/>
bauimus, reducetur ad rotunditatem, <expan abbr="atq;">atque</expan> &agrave; mari innundabitur, &amp; idcirc&ograve; <lb/>
inhabitabilis, vnde nece&longs;&longs;ari&ograve; mortalium genus interibit. </s>
          <s id="s.001905">Quapropter ni&longs;i <lb/>
igne illo, quem &longs;acr&aelig; liter&aelig; innuunt catacly&longs;mus ille pr&aelig;ueniatur, aqua <lb/>
mundus interiturus e&longs;&longs;et. </s>
          <s id="s.001906">&longs;ed de his hactenus.</s>
        </p>
        <pb pagenum="107" xlink:href="009/01/107.jpg"/>
        <p type="main">
          <s id="s.001907">Quoad magnum illud Diluuium, quod Ari&longs;t. hoc capite exi&longs;timat po&longs;t <lb/>
multa &longs;ecula reuolui, hoc veritati e&longs;&longs;e con&longs;entaneum argumento &longs;unt, ac <lb/>
pariter admirationi varia <expan abbr="c&otilde;chiliorum">conchiliorum</expan> genera, qu&aelig; t&ugrave;m in Apennino mon&shy;<lb/>
te, t&ugrave;m in Alpibus ob&longs;eruaui; <expan abbr="&Igrave;dem&qacute;">&Igrave;demque</expan>; in alijs mundi partibus inueniri pu&shy;<lb/>
to; pr&aelig;&longs;ertim in tam immen&longs;a copia, <expan abbr="atq;">atque</expan> intra vi&longs;cera montium colloca&shy;<lb/>ta, qu&aelig; nulla vis humana illuc contuli&longs;&longs;et, ni&longs;i temporibus catacly&longs;mi ebul&shy;<lb/>
lientibus aquis maris &longs;uper terram facta fui&longs;&longs;et h&aelig;c varia rerum maritima&shy;<lb/>
rum cum terre&longs;tribus commixtio: qu&aelig; quidem optim&egrave; ex Pomponio Mela <lb/>
comprobantur, qui libro 1. de Numidia &longs;ic narrat: interius, &amp; long&egrave; &longs;atis <lb/>
&agrave; litore, &longs;i fides res capit, mirum admodum, &longs;pin&aelig; pi&longs;cium, <expan abbr="Muric&utilde;">Muricum</expan>, <expan abbr="O&longs;treo-rum&qacute;">O&longs;treo&shy;<lb/>
rumque</expan>; fragmenta, &longs;axi atritu, vti &longs;olent fluctibus, &amp; non differentia mari&shy;<lb/>
nis, infix&aelig; cautibus anchor&aelig;, <expan abbr="alia&qacute;">aliaque</expan>; huiu&longs;modi &longs;igna, &amp; ve&longs;tigia effu&longs;i olim <lb/>
<expan abbr="v&longs;q;">v&longs;que</expan> ad ea loca pelagi, in campis nihil alentibus e&longs;&longs;e inuenirique narrantur. <lb/>
</s>
          <s id="s.001908">neque locus ille Ouid. <!-- REMOVE S-->Met. <!-- REMOVE S-->15. extra rem:</s>
        </p>
        <p type="main">
          <s id="s.001909"><emph type="italics"/>Vidi ego, quod fuerat olim &longs;olidi&longs;&longs;ima petra <lb/>E&longs;&longs;e fretum, vidi factas ex &aelig;quore terras: <lb/>
Et procul &agrave; Pelago conch&aelig; iacuere marin&aelig;, <lb/>
Et vetus inuenta e&longs;t in montibus anchora &longs;ummis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001910">Nos autem Chri&longs;tiani ad Noemi Diluuium i&longs;ta referre debemus.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.001911"><emph type="italics"/>Ex Secundo Meteororum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001912"><arrow.to.target n="marg152"/></s>
        </p>
        <p type="margin">
          <s id="s.001913"><margin.target id="marg152"/>152</s>
        </p>
        <p type="main">
          <s id="s.001914">Cap. 1. ait multa e&longs;&longs;e maria, qu&aelig; ad inuicem non communicant. <lb/>
</s>
          <s id="s.001915">Eorum rubrum mare vnum e&longs;&longs;e; quod cum Oceano <expan abbr="Atl&atilde;tico">Atlantico</expan>, qui <lb/>
e&longs;t extra Herculeum fretum ad occidentem parum videtur com&shy;<lb/>
mi&longs;ceri &longs;iue Ari&longs;t. pro Rubro mari intelligat Oceanum illum, qui <lb/>
Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>
interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>
vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s>
          <s id="s.001916">&longs;ed merit&ograve; hoc <lb/>
Ari&longs;tot. condonandum, cum tunc temporis nondum tota Africa e&longs;&longs;et cert&ograve; <lb/>
circumlu&longs;trata, <expan abbr="neq;">neque</expan> iter ab Hi&longs;pania ad Indos maritimum, adeo nunc fre&shy;<lb/>
quens, patefactum e&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.001917"><arrow.to.target n="marg153"/></s>
        </p>
        <p type="margin">
          <s id="s.001918"><margin.target id="marg153"/>153</s>
        </p>
        <p type="main">
          <s id="s.001919">Summ&aelig; 2. cap. 2. <emph type="italics"/>&lpar;Quapropter &amp; circa Orionis ortum maxim&egrave; fit tranquilli&shy;<lb/>
tas&rpar;<emph.end type="italics"/> quando Medici, Philo&longs;ophi, Poet&aelig;, ac reliqui auctores loquuntur de <lb/>
ortu a&longs;trorum fixorum, aut con&longs;tellationum, qu&aelig; &longs;unt in firmamento, vti <lb/>
e&longs;t Orion &lpar;&amp; Canis, de quo po&longs;tea&rpar; intelligunt &longs;emper de ortu ip&longs;orum, qui <lb/>
fit matutino tempore, quando &longs;cilicet vel &longs;imul cum Sole, vel paul&ograve; ante <lb/>
Solem emergunt, ita vt videantur &agrave; nobis; qui ortus dicitur Co&longs;micus, tunc <lb/>
propri&egrave;, quando &longs;imul a&longs;trum cum Sole oritur; quando autem incipit appa&shy;<lb/>rere mane ante Solem, dicitur ortus Heliacus. </s>
          <s id="s.001920">i. </s>
          <s id="s.001921">&longs;olaris, quia oritur quodam&shy;<lb/>
modo ex radijs Solis, &longs;ub quibus antea latebat. </s>
          <s id="s.001922">A&longs;tra ver&ograve; inerrantia, &amp; <lb/>
planet&aelig; Sole tardiores oriuntur <expan abbr="vtroq;">vtroque</expan> modo. </s>
          <s id="s.001923">nam c&ugrave;m ip&longs;a Sol, quippe il&shy;<lb/>
lis velocior primum a&longs;&longs;equitur, ea &longs;uo lumine obtegit, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; hic occa&longs;us eo&shy;<lb/>
rum heliacus: cum ver&ograve; eadem pr&aelig;terierit, ac po&longs;t &longs;e reliquerit fit, vt mo&shy;<lb/>
tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliac&egrave; <lb/>oriantur: &amp; cum quotidie magis Sol ab illis recedat, ip&longs;aque magis &agrave; Sole <pb pagenum="108" xlink:href="009/01/108.jpg"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, &amp; citius mane au&shy;<lb/>
te Solem videantur. </s>
          <s id="s.001924"><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; tanto in dies citius, vt deinde media etiam nocte <lb/>
oriantur; tum ante mediam noctem po&longs;tea paul&ograve; ante occa&longs;um Solis. <!-- KEEP S--></s>
          <s id="s.001925">de&shy;<lb/>
mum cum fuerint Soli oppo&longs;ita, occidente Sole oriantur, qui ortus dicitur <lb/>
Ve&longs;pertinus, vel Acronicus. </s>
          <s id="s.001926">po&longs;tea oriuntur &longs;emper in die ante Solis occa&shy;<lb/>
&longs;um, donec Sol ip&longs;a iterum a&longs;&longs;equatur, <expan abbr="ea&qacute;">eaque</expan>; radijs &longs;uis offu&longs;cet, quod e&longs;t he&shy;<lb/>
liac&egrave; occidere; &amp; mox cum ip&longs;o Sole occumbant, quod Acronic&egrave; e&longs;t occi&shy;<lb/>
dere. </s>
          <s id="s.001927">Totum porr&ograve; illud tempus, quo per diem oriuntur, non eorum ortui, <lb/>
&longs;ed occa&longs;ui deputatur, e&ograve; quod non cernuntur oriri, vt &longs;equenti loco expli&shy;<lb/>
cabitur. </s>
          <s id="s.001928">Qu&aelig; omnia adhibito Globo a&longs;tronomico, in quo con&longs;tellationes <lb/>
omnes depict&aelig; &longs;unt, <expan abbr="eo&qacute;">eoque</expan>; ad tui poli eleuationem con&longs;tituto, appo&longs;itoque <lb/>
Sole &longs;uo loco in Zodiaco, qui paulatim per Zodiacum orientem ver&longs;us gra&shy;<lb/>diatur, &amp; interim diurno motu globus conuertatur, ad &longs;en&longs;um manife&longs;ta <lb/>
apparebunt. </s>
          <s id="s.001929">In &longs;umma auctores intelligunt de ortu, qui mane fit ante So&shy;<lb/>
lem, quia tunc primum po&longs;t diuturnas latebras incipit apparere. </s>
          <s id="s.001930"><expan abbr="n&otilde;">non</expan> autem <lb/>
intelligunt de ortu Acronico, quia ante hunc ortum videbatur noctu, <expan abbr="itaq;">itaque</expan> <lb/>
ortu Acronico non fit noua apparitio; ideo de hoc non intelligunt. </s>
          <s id="s.001931">fit au&shy;<lb/>
tem ortus hic Orionis, heliacus, &amp; matutinus, de quo Ari&longs;t. hoc loco, &amp; alij <lb/>
auctores, no&longs;tra hac tempe&longs;tate paul&ograve; ante Solis ingre&longs;&longs;um in Cancrum, &longs;i&shy;<lb/>
ue ante &longs;ol&longs;titium &aelig;&longs;tiuum circa 22. Iunij.<!-- REMOVE S--><arrow.to.target n="marg154"/></s>
        </p>
        <p type="margin">
          <s id="s.001932"><margin.target id="marg154"/>154</s>
        </p>
        <p type="main">
          <s id="s.001933">Eodem cap. <emph type="italics"/>&lpar;Incertus autem, &amp; mole&longs;tus Orion e&longs;&longs;e videtur &amp; occumbens, &amp; <lb/>
oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, &amp; ortus, a&longs;tate, aut hye&shy;<lb/>
me, &amp; propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas&rpar;<emph.end type="italics"/> hoc loco Vico&shy;<lb/>
mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem&shy;<lb/>
pore, Sole Scorpionem ob&longs;idente docet, quod &amp; verba Ari&longs;t. clar&egrave; &longs;ignifi&shy;<lb/>
cant, cum dicat ortum ip&longs;ius fieri &aelig;&longs;tate; in tran&longs;mutatione ver&ograve; temporis, <lb/>
videlicet in autumno fieri occa&longs;um. </s>
          <s id="s.001934">Porr&ograve; occa&longs;us hic fieri incipit primum <lb/>
mane oriente Sole, <expan abbr="dicitur&qacute;">diciturque</expan>; occa&longs;us co&longs;micus, quia dum Sol e&longs;t in oriente, <lb/>
Orion e&longs;t in occidente, &amp; infra orizontem cadit: deinde paul&ograve; ante Solis or&shy;<lb/>
tum, &longs;ed tamen nocturno tempore, ita vt occa&longs;us eius videri po&longs;&longs;it, donec <lb/>
occidat parum po&longs;t Solis occa&longs;um, &amp; tandem cum Sole ip&longs;o heliac&egrave; euane&shy;<lb/>
&longs;cat. </s>
          <s id="s.001935">Scriptores autem fer&egrave; &longs;emper cum loquuntur de occa&longs;u inerrantium <lb/>
&longs;yderum, de eo, qui noctu videatur, intelligunt: &longs;icuti ortum intelligunt <lb/>
eum, qui noctu fit, <expan abbr="noctu&qacute;">noctuque</expan>; videtur. </s>
          <s id="s.001936">affixa <expan abbr="namq;">namque</expan> &longs;ydera per &longs;ex ferm&egrave; men&shy;<lb/>
&longs;es noctu oriuntur, <expan abbr="oriri&qacute;">oririque</expan>; ea con&longs;picimus, &amp; propterea totum illud tem&shy;<lb/>
pus, ortui ip&longs;orum deputamus: Reliquum ver&ograve; <expan abbr="t&etilde;pus">tempus</expan>, quo per diem oriun&shy;<lb/>
tur, &amp; idcirc&ograve; ortus illorum minim&egrave; apparet, nulla ratione ortui debuit <lb/>
a&longs;cribi: totum ver&ograve; tempus, quo noctu occidunt, &amp; occidere cernuntur, oc&shy;<lb/>
ca&longs;ui illorum merit&ograve; attribuitur. </s>
          <s id="s.001937">&amp; <expan abbr="quemadmod&utilde;">quemadmodum</expan> temporis illius initium, <lb/>
quo primo de nocte apparere incipiunt, dicitur ab&longs;olut&egrave; ortus cuiu&longs;uis &longs;y&shy;<lb/>
deris; &longs;ic etiam initium temporis illius, quo primum per noctem ea occide&shy;<lb/>
re videmus, &longs;impliciter occa&longs;um appellamus.</s>
        </p>
        <p type="main">
          <s id="s.001938"><arrow.to.target n="marg155"/></s>
        </p>
        <p type="margin">
          <s id="s.001939"><margin.target id="marg155"/>155</s>
        </p>
        <p type="main">
          <s id="s.001940">Eodem cap. <emph type="italics"/>&lpar;Ete&longs;i&aelig; autem flant post ver&longs;iones, &amp; Canis ortum&rpar;<emph.end type="italics"/> per ver&longs;io&shy;<lb/>
nes intelligit tropicos, quod &amp; tropici etymon confirmat, <expan abbr="c&utilde;">cum</expan> tropicus idem <lb/>
valeat, ac conuer&longs;iuus. </s>
          <s id="s.001941">circa Canis ortum eadem &longs;unt notanda, qu&aelig; &longs;upra <lb/>de ortu Orionis annotaui; intelligit enim eum Canis ortum, qui mane fiat <pb pagenum="109" xlink:href="009/01/109.jpg"/>primum paul&ograve; ante Solis ortum, cum &longs;cilicet incipit apparere.</s>
        </p>
        <p type="main">
          <s id="s.001942">Cum porr&ograve; in c&etail;lo &longs;it Canis maior, &amp; Canis minor, qui &amp; Procyon, ide&longs;t <lb/>
Anticanis dicitur, exi&longs;timo Canem maiorem e&longs;&longs;e eum, qui vulg&ograve; Canicula <lb/>
nominatur, <expan abbr="&longs;olet&qacute;">&longs;oletque</expan>; vehementes, ac noxios calores excitare. </s>
          <s id="s.001943">de quo etiam <lb/>
put&ograve; Ari&longs;t. intelligere. </s>
          <s id="s.001944">eius porr&ograve; ortus in no&longs;tra poli eleuatione quadra&shy;<lb/>
ginta quinque graduum, circa diem tertium Augu&longs;ti contingit, Sole autem <lb/>
10. gradum Leonis occupante. </s>
          <s id="s.001945">Ex Magini tabulis ante ephemerides.</s>
        </p>
        <p type="main">
          <s id="s.001946"><arrow.to.target n="marg156"/></s>
        </p>
        <p type="margin">
          <s id="s.001947"><margin.target id="marg156"/>156</s>
        </p>
        <p type="main">
          <s id="s.001948">Eodem cap. <emph type="italics"/>&lpar;Duobus enim exi&longs;tentibus &longs;egmentis habitabilis regionis: vno <lb/>
quidem ad &longs;uperiorem polum, qui no&longs;ter e&longs;t; altero ad alterum, &amp; ad meridiem: <lb/>
<expan abbr="ea&qacute;">eaque</expan>, tympani &longs;peciem habeant, talem enim figuram terr&aelig; excidunt ex centro ip&longs;ius <lb/>duct&aelig; line&aelig;, &amp; faciunt duos conos, hunc quidem habentem ba&longs;im tropicum, alte&shy;<lb/>
rum autem habentem ba&longs;im circulum &longs;emper manifestum, verticem autem in me&shy;<lb/>
dio terr&aelig;. </s>
          <s id="s.001949">eodem autem modo ad inferiorem polum alij duo coni terr&aelig; &longs;egmenta fa&shy;<lb/>
ciunt&rpar;<emph.end type="italics"/> vt ben&egrave; duas ha&longs;ce terr&aelig; portiones, quas &longs;olas habitabiles putat Ari&shy;<lb/>
&longs;tot. concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/>
<figure id="id.009.01.109.1.jpg" place="text" xlink:href="009/01/109/1.jpg"/><lb/>
Maior circulus &longs;it c&oelig;lum, in quo polus L, articus; M, antarticus, ille eleua&shy;<lb/>
tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te ver&ograve; totidem infra <lb/>
depre&longs;&longs;us. </s>
          <s id="s.001950"><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110" xlink:href="009/01/110.jpg"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>
X O, Capricorni, vt vides in figura. </s>
          <s id="s.001951">Terra &longs;it A B C H G F E D Z K. &agrave; cu&shy;<lb/>
ius centro Z, educantur primo du&aelig; line&aelig; rect&aelig; Z R, Z S. ad circulum &longs;em&shy;<lb/>
per apparentium maximum, qu&aelig; in terra tran&longs;eant per puncta B, K. &amp; iun&shy;<lb/>
gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap&shy;<lb/>
parens S R, vertex autem Z, in centro terr&aelig;, vt ait Ari&longs;tot. <!-- KEEP S--></s>
          <s id="s.001952">educantur nunc <lb/>
du&aelig; ali&aelig; rect&aelig; ad tropicum Cancri Z T, Z Q, qu&aelig; in terra faciant puncta <lb/>
I, C, <expan abbr="iungatur&qacute;">iungaturque</expan>; recta I C; hic pariter vides conum alterum T Q Z, cuius ba&shy;<lb/>
&longs;is e&longs;t circulus Cancri, vertex ver&ograve; centrum terr&aelig; Z. con&longs;idera iam figuram <lb/>
B K I C, inter duas rectas B K, I C, &amp; duos circuli terr&aelig; arcus contentam; <lb/>
hanc Ari&longs;t. appellat tympanum vnum terr&aelig; habitabile, quod e&longs;t ad Vr&longs;am, <lb/>
ide&longs;t in &longs;eptentrionali plaga, in qua &longs;umus nos: qu&aelig; quidem portio &longs;i con&longs;i&shy;<lb/>
deretur vt &longs;olida, &amp; &agrave; reliqua terra pr&aelig;ci&longs;a, erit corpus rotundum, <expan abbr="vtrinq;">vtrinque</expan> <lb/>
tamen duobus planis circulis ad in&longs;tar tympani terminatum: Ductis dein&shy;<lb/>
de &longs;imiliter alijs quattuor lineis &agrave; centro Z, ver&longs;us polum antarticum fit al&shy;<lb/>
terum tympanum H D E G, au&longs;tralis terr&aelig; habitabilis, vt in figura manife&shy;<lb/>
&longs;tum e&longs;t. </s>
          <s id="s.001953">fui&longs;&longs;e autem huiu&longs;modi habitabilis terr&aelig; &longs;egmenta figur&aelig; tympa&shy;<lb/>
ni &longs;imilia, optim&egrave; declarant veteres figur&aelig; geographic&aelig; Ptol&etail;mei, &amp; patet <lb/>
etiam ex longitudine, &amp; latitudine, vt ben&egrave; ait Ari&longs;t. quas Geographi por&shy;<lb/>
tioni terr&aelig; habitabili attribuebant, longitudinem enim dixerunt eius di&shy;<lb/>
men&longs;ionem ab occa&longs;u ad ortum: latitudinem autem &agrave; &longs;eptentrione in meri&shy;<lb/>
diem, e&ograve; qu&ograve;d illa mult&ograve; hac longior e&longs;&longs;et. </s>
          <s id="s.001954">Ex quibus apparet habitatam <lb/>
fui&longs;&longs;e veluti Zonam, terram ab occa&longs;u ad ortum pr&aelig;cingentem. </s>
          <s id="s.001955">qu&aelig; Zona <lb/>
&longs;i &longs;umatur cum &longs;oliditate, quam ambit, ab Ari&longs;t. tympano a&longs;&longs;imilatur.</s>
        </p>
        <p type="main">
          <s id="s.001956"><arrow.to.target n="marg157"/></s>
        </p>
        <p type="margin">
          <s id="s.001957"><margin.target id="marg157"/>157</s>
        </p>
        <p type="main">
          <s id="s.001958">Eodem cap. <emph type="italics"/>&lpar;H&aelig; autem habitari &longs;ol&aelig; po&longs;&longs;ibiles: &amp; <expan abbr="neq;">neque</expan> vltra ver&longs;iones; vm&shy;<lb/>
bra enim non <expan abbr="vtiq;">vtique</expan> e&longs;&longs;et ad Vr&longs;am: nunc autem inhabitabilia prius fiunt loca, qu&agrave;m <lb/>
&longs;ubdeficiat, aut permutetur vmbra ad meridiem. </s>
          <s id="s.001959">Qu&aelig; autem &longs;ub Vr&longs;a, &egrave; frigore <lb/>
inhabitabilia&rpar;<emph.end type="italics"/> quod ait vltra ver&longs;iones, ide&longs;t intra tropicos in ip&longs;a &longs;cilicet <lb/>
Zona torrida, non po&longs;&longs;e habitari, fal&longs;um e&longs;&longs;e o&longs;tendunt plurim&aelig; regiones <lb/>
tam veteris, quam noui orbis, &longs;uperiori &longs;eculo patefact&aelig;, in quibus magna <lb/>
in am&oelig;nitate, ac fertilitate, <expan abbr="&longs;ummis&qacute;">&longs;ummisque</expan>; delicijs viuitur. </s>
          <s id="s.001960">Quoad vmbram il&shy;<lb/>
lam, intellige meridianam. </s>
          <s id="s.001961">i. </s>
          <s id="s.001962">quam Sole circa meridiem exi&longs;tente, nos qui <lb/>
Boreales &longs;umus, &longs;emper ad <expan abbr="&longs;ept&etilde;trionem">&longs;eptentrionem</expan> proijcimus. </s>
          <s id="s.001963">Quod &longs;i ad meridiem <lb/>
perrexerimus, occurret inhabitabilis &lpar;vt fals&ograve; putat&rpar; terra, prius quam. <lb/>
</s>
          <s id="s.001964">vmbra meridiana in Boream vergens deficiat. </s>
          <s id="s.001965">qu&aelig; &longs;igna &longs;unt no&longs;tram habi&shy;<lb/>
tationem e&longs;&longs;e citra Zonam torridam, in Boreali parte. </s>
          <s id="s.001966">Qu&aelig; autem &longs;ub Vr&shy;<lb/>
&longs;a, ide&longs;t &longs;ub polo arctico, ob nimium frigus inho&longs;pita omnin&ograve; habetur, nam</s>
        </p>
        <p type="main">
          <s id="s.001967"><emph type="italics"/>Quod latus mundi nebul&aelig;, <expan abbr="malus&qacute;">malusque</expan>; <lb/>
Iupiter vrget.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.001968">Verumtamen, qu&aelig; &longs;ub <expan abbr="vtroq;">vtroque</expan> polo partes &longs;unt adhuc incognit&aelig; manent.</s>
        </p>
        <p type="main">
          <s id="s.001969"><arrow.to.target n="marg158"/></s>
        </p>
        <p type="margin">
          <s id="s.001970"><margin.target id="marg158"/>158</s>
        </p>
        <p type="main">
          <s id="s.001971">Eodem cap: <emph type="italics"/>&lpar;Fertur autem, &amp; corona &longs;ecundam hunc locum, videtur enim &longs;u&shy;<lb/>per caput e&longs;&longs;e nobis, cum fuerit &longs;ecundum meridianum&rpar;<emph.end type="italics"/> con&longs;tellatio videlicet, <lb/>
qu&aelig; corona Ariadn&aelig; dicitur, h&aelig;c cum in c&oelig;lo manife&longs;t&egrave; &longs;it Borealis, <expan abbr="no-&longs;tro&qacute;">no&shy;<lb/>
&longs;troque</expan>; vertici noctu, quando meridianum pertran&longs;it, incumbat: clar&egrave; indi&shy;<lb/>
cat nos <expan abbr="quoq;">quoque</expan> e&longs;&longs;e Boreales.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.001972"><arrow.to.target n="marg159"/></s>
        </p>
        <p type="margin">
          <s id="s.001973"><margin.target id="marg159"/>159</s>
        </p>
        <p type="main">
          <s id="s.001974">Eodem cap. <emph type="italics"/>&lpar;Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus habita-<emph.end type="italics"/>


<pb pagenum="111" xlink:href="009/01/111.jpg"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter &aelig;&longs;tum&rpar;<emph.end type="italics"/><lb/>
illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam fer&egrave; <lb/>
torridam Zonam, &amp; quidem alicubi percommod&egrave; habitari, cuius cau&longs;&aelig; &longs;unt <lb/>
quatuor, qu&aelig; ip&longs;um latuerunt. </s>
          <s id="s.001975">prima <expan abbr="ea&qacute;">eaque</expan>; toti Zon&aelig; torrid&aelig; communis, <lb/>
e&longs;t perpetuum &aelig;quinoctium, quo Sol tantum &longs;upra, quantum infra terram <lb/>
immoratur. </s>
          <s id="s.001976">accedit, qu&ograve;d Sol nocturno tempore maxim&egrave; ad imum c&oelig;li fe&shy;<lb/>
ratur, <expan abbr="plurimum&qacute;">plurimumque</expan>; ab horizonte, <expan abbr="&longs;upero&qacute;">&longs;uperoque</expan>; hemi&longs;pherio recedat. </s>
          <s id="s.001977">atque ob <lb/>
hanc &longs;olam rationem Campanus in &longs;ua &longs;ph&aelig;ra Zonam hanc putat maxim&egrave; <lb/>
e&longs;&longs;e habitabilem: quamuis h&aelig;c &longs;ola cau&longs;a, vt quotidiana docet experientia, <lb/>
non &longs;ufficiat. </s>
          <s id="s.001978">&longs;ecunda &longs;unt pluui&aelig;, qu&aelig; alicubi quotidie &longs;tata hora decidunt. <lb/>
</s>
          <s id="s.001979">tertia venti, qui veluti flabella qu&aelig;dam aerem agitant. </s>
          <s id="s.001980">quarta pr&aelig;alti mon&shy;<lb/>
tes perpetuis niuibus ob&longs;iti. </s>
          <s id="s.001981">qu&aelig; quatuor torridam hanc pa&longs;&longs;im refrigerant, <lb/>
atque habitabilem reddunt.</s>
        </p>
        <p type="main">
          <s id="s.001982"><arrow.to.target n="marg160"/></s>
        </p>
        <p type="margin">
          <s id="s.001983"><margin.target id="marg160"/>160.a</s>
        </p>
        <p type="main">
          <s id="s.001984">Summ&aelig; 2. cap. 3. de <expan abbr="v&etilde;tis">ventis</expan> <emph type="italics"/>&lpar;Oportet autem de &longs;itu &longs;imul rationes ex de&longs;criptio <lb/>
ne con&longs;iderare&rpar;<emph.end type="italics"/> ide&longs;t rationes ventorum ex de&longs;criptione, ide&longs;t in figura ali&shy;<lb/>
qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t. figuras, im&ograve; demon&longs;tratio&shy;<lb/>
nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>
monuimus.</s>
        </p>
        <p type="main">
          <s id="s.001985"><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, &amp; <lb/>
rotundus&rpar;<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>
referret,</s>
        </p>
        <figure id="id.009.01.111.1.jpg" place="text" xlink:href="009/01/111/1.jpg"/>
        <pb pagenum="112" xlink:href="009/01/112.jpg"/>
        <p type="main">
          <s id="s.001986"><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, qu&aelig; nobis habitatur; qu&aelig; <lb/>
eodem modo diuidi poterit&rpar;<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter&shy;<lb/>
r&aelig; habitat&aelig; partem, qu&aelig; quamuis rotunda non &longs;it, poterit tamen, ac &longs;i ro&shy;<lb/>
tunda e&longs;&longs;et in figura circulari repre&longs;entari, <expan abbr="atq;">atque</expan> in plures partes eo modo, <lb/>
quo circulus &longs;ecatur, &longs;ecari.</s>
        </p>
        <p type="main">
          <s id="s.001987"><emph type="italics"/>Supponatur autem prim&ograve; contraria &longs;ecundum locum, e&longs;&longs;e plurimum di&longs;tantia <lb/>
&longs;ecundum locum; &longs;icut &longs;ecundum &longs;peciem contraria, plurimum di&longs;tant &longs;ecundum <lb/>
&longs;peciem. </s>
          <s id="s.001988">plurimum autem di&longs;tant &longs;ecundum locum, qu&aelig; per diametrum opponuntur, <lb/>
&longs;it igitur vbi A, occidens &aelig;quinoctionalis, contrarius autem huic locus vltimus B, <lb/>
ortus &aelig;quinoctionalis&rpar;<emph.end type="italics"/> ide&longs;t in &longs;equenti figura ducta diametro B A. in altera <lb/>
ip&longs;ius extremitate vbi A. &longs;it occa&longs;us &aelig;quinoctialis, qui fit Sole exi&longs;tente in <lb/>
alterutro &aelig;quinoctio; huic igitur per diametrum opponatur ortus &aelig;quino&shy;<lb/>
ctialis in B. qui pariter contingit tempore &aelig;quinoctiorum: linea autem B A, <lb/>
refert ip&longs;um &aelig;quatorem.</s>
        </p>
        <p type="main">
          <s id="s.001989"><emph type="italics"/>Alia autem diameter hanc perpendiculariter &longs;ecet, cuius punctum illud, in quo <lb/>
G, &longs;it Vr&longs;a: huic autem contrarium ex oppo&longs;ito illud, in quo H, meridies&rpar;<emph.end type="italics"/> h&aelig;c dia&shy;<lb/>
meter erit ip&longs;a linea meridiana. </s>
          <s id="s.001990">pro Vr&longs;a ver&ograve; intelligit &longs;eptentrionem, <lb/>
quod ibi &longs;it Vr&longs;&aelig; con&longs;tellatio.</s>
        </p>
        <p type="main">
          <s id="s.001991"><emph type="italics"/>Id autem, in quo F, ortus &aelig;&longs;tiualis; in quo ver&ograve; E, occidens &aelig;&longs;tiualis&rpar;<emph.end type="italics"/> qu&aelig; duo <lb/>
puncta iunguntur linea F E, qu&aelig; refert &longs;ectionem tropici, Cancri cum ho&shy;<lb/>
rizonte: ortus enim, &amp; occa&longs;us &aelig;&longs;tiualis contingunt Sole Cancri tropicum <lb/>
percurrente.</s>
        </p>
        <p type="main">
          <s id="s.001992"><emph type="italics"/>Id autem, in quo D, oriens hyemalis; vbi ver&ograve; C, occidens hyemalis&rpar;<emph.end type="italics"/> linea au&shy;<lb/>
tem D C, erit &longs;ectio tropici Capricorni, &amp; horizontis; Sole enim hunc tro&shy;<lb/>
picum attingente ortus, &amp; occa&longs;us hybernus fiunt.</s>
        </p>
        <p type="main">
          <s id="s.001993"><emph type="italics"/>Ab F, autem ducatur diameter ad C, &amp; &agrave; D, ad E. quoniam igitur plurimum <lb/>
di&longs;tantia &longs;ecundum locum, contraria &longs;unt &longs;ecundum locum: plurimum autem di&shy;<lb/>
stantia, qu&aelig; &longs;ecundum diametrum; nece&longs;&longs;arium e&longs;t, &amp; flatuum hos inuicem con&shy;<lb/>
trarios e&longs;&longs;e, <expan abbr="quicunq;">quicunque</expan> &longs;ecundum diametrum exi&longs;tunt. </s>
          <s id="s.001994">vocantur autem &longs;ecundum po&shy;<lb/>
&longs;itionem locorum venti &longs;ic; Zephyrus quidem ab A, hoc enim e&longs;t occidens &aelig;quino&shy;<lb/>
ctialis. </s>
          <s id="s.001995">Boreas autem, &amp; Aparetias &agrave; G. hic enim Vr&longs;a, contrarius autem huic <lb/>
Notus ab H. <!-- KEEP S--></s>
          <s id="s.001996">Meridies enim e&longs;t hic, &agrave; quo flat, &amp; H, ip&longs;i G, contrarium e&longs;t; &longs;ecun&shy;<lb/>
dum enim diametrum &longs;unt. </s>
          <s id="s.001997">Ab F, autem C&aelig;cias; hic enim oriens &aelig;&longs;tiuus e&longs;t; cui <lb/>
contrarius est, non qui flat ab E, &longs;ed qui &agrave; C. Libs, i&longs;te enim ab occidente hyemali <lb/>
flat; <expan abbr="est&qacute;">estque</expan>, illi contrarius, quia &longs;ecundum diametrum illi opponitur. </s>
          <s id="s.001998">Qui ver&ograve; &agrave; D, <lb/>
Eurus, i&longs;te enim ab horiente hyberno flat, vicinus existens Noto, vnde &amp; &longs;&aelig;p&egrave; Eu&shy;<lb/>
ronoti flare dicuntur: <expan abbr="c&otilde;trarius">contrarius</expan> autem huic, non qui &agrave; C. Libs, &longs;ed qui ab E, quem <lb/>
vocant, hi quidem Arge&longs;ten, hi autem Olympium, alij ver&ograve; Scironem; iste enim ab <lb/>
occidente &aelig;&longs;tiuo flat, &amp; &longs;ecundum diametrum ip&longs;i &longs;olus opponitur. </s>
          <s id="s.001999">Venti igitur, qui <lb/>
&longs;ecundum diametrum po&longs;iti &longs;unt, &amp; quibus alij aduer&longs;antur, ij &longs;unt. </s>
          <s id="s.002000">Alij autem <lb/>
&longs;unt, &longs;ecundum quos non &longs;unt contrarij venti, ab I, quem vocant Tra&longs;ciam, qui me&shy;<lb/>dius e&longs;t inter Argesten, &amp; Apparitiam, &agrave; K, autem, quem vocant Me&longs;en, Medius <lb/>
enim e&longs;t C&aelig;ci&aelig;, &amp; Apareti&aelig;. </s>
          <s id="s.002001">Diameter autem K I, iuxta circulum &longs;emper con&longs;pi&shy;<lb/>
cuum e&longs;&longs;e &longs;olet, non tamen exact&egrave;&rpar;<emph.end type="italics"/> ide&longs;t linea K I, &longs;olet in horizonte referre <lb/>
diametrum circuli omnium &longs;emper apparentium maximi, eo quod &longs;it fer&egrave; <lb/>&longs;ub diametro illius, in qualibet enim &longs;ph&aelig;ra obliqua, ide&longs;t, in qua polus ele&shy;<pb pagenum="113" xlink:href="009/01/113.jpg"/>uatur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma&shy;<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, &amp; interuallo v&longs;que <lb/>
ad horizontem, circa ip&longs;um polum: hunc appellant &longs;emper apparentium, <lb/>
maximum, quia intra hunc alios quamplurimos concipiunt circa eundem <lb/>
polum, quorum minores &longs;emper &longs;unt polo propinquiores. </s>
          <s id="s.002002">huius igitur dia&shy;<lb/>
metrum vult Ari&longs;t. per lineam, qu&aelig; &agrave; K, in I, duceretur &lpar;quamuis non exa&shy;<lb/>
ct&egrave;&rpar; repre&longs;entari.</s>
        </p>
        <p type="main">
          <s id="s.002003"><emph type="italics"/>Contrarij autem non &longs;unt his &longs;tatibus, <expan abbr="neq;">neque</expan> ip&longs;i Me&longs;e, &longs;piraret enim <expan abbr="vtiq;">vtique</expan> aliquis <lb/>
ab eo, in quo M. hoc enim illi e&longs;t &longs;ecundum diametrum; <expan abbr="neq;">neque</expan> Trafci&aelig; ab N, enim, <lb/>
quod punctum per diametrum aduer&longs;um illi e&longs;t, &longs;piraret. </s>
          <s id="s.002004">Ni&longs;i ab eo veniat, qui ta&shy;<lb/>
men non long&egrave; progreditur ventus quidam, quem accol&aelig; Ph&aelig;niciam vocant. </s>
          <s id="s.002005">maxi&shy;<lb/>
m&egrave; igitur pr&aelig;cipui, &amp; definiti venti hi &longs;unt: <expan abbr="hoc&qacute;">hocque</expan>, modo di&longs;po&longs;iti&rpar;<emph.end type="italics"/> &longs;upradicta por&shy;<lb/>
r&ograve; omnia ex &longs;equenti figura optim&egrave; poterunt intelligi, quam diligenti ope&shy;<lb/>
ra ad mentem Ari&longs;t. ex gr&aelig;cis codicibus re&longs;tituere conatus &longs;um, cum ani&shy;<lb/>maduerterem figuras vald&egrave; deprauatas pa&longs;&longs;im apud <expan abbr="c&otilde;mentatores">commentatores</expan> reperiri. <lb/>
</s>
          <s id="s.002006">Porr&ograve; ad literam M, in figura &longs;crip&longs;i ventum Libonotum, quem Ari&longs;t. qui&shy;<lb/>
dem non ponit propter ip&longs;ius paruitatem; im&ograve; apert&egrave; dicit Hele&longs;pontum <lb/>
non habere contrarium: &longs;ed feci, vt completum ventorum numerum, quem <lb/>
alij tradunt, haberemus.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002007"><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002008"><arrow.to.target n="marg161"/></s>
        </p>
        <p type="margin">
          <s id="s.002009"><margin.target id="marg161"/>160.b</s>
        </p>
        <p type="main">
          <s id="s.002010">Antequam textuum explicationem aggrediar, illud animaduerten-<lb/>
dum e&longs;t, <expan abbr="vbicunq;">vbicunque</expan> interpretatio antiqua vtitur verbis, refractio, <lb/>
&amp; refrangere; ibi Vicomercatum in &longs;ua interpretatione merit&ograve;, <lb/>
&amp; propri&egrave; v&longs;um e&longs;&longs;e verbis; reflexio, &amp; reflecti: differunt enim <lb/>
vald&egrave; apud Opticos refractio, &amp; reflexio, vt etiam refrangere, &amp; reflectere. <lb/>
</s>
          <s id="s.002011">propterea optim&egrave; hoc loco Olympiodorus di&longs;tinguit inter <foreign lang="greek">anaklasin, kai <lb/>diaklasin,</foreign> reflexionem, &amp; refractionem. </s>
          <s id="s.002012">Reflexio enim fit ex repercu&longs;&longs;o, vt <lb/>
quando lumen Solis incidens in aliquod &longs;peculum, inde re&longs;ilit in oppo&longs;itum <lb/>
parietem, illud re&longs;ilire e&longs;t propri&egrave; per&longs;pectiuis reflecti, vnde reflexio. </s>
          <s id="s.002013">Re&shy;<lb/>
fractio autem fit ex tran&longs;pectu: vt quando lapis, qui e&longs;t in aqua, emittit <lb/>
fuam &longs;peciem ad oculum, qui e&longs;t in aere, tunc enim, quia &longs;pecies lapidis re&shy;<lb/>
pre&longs;entatiua non tendit recta ad oculum, &longs;ed in confinio aqu&aelig;, &amp; aeris fran&shy;<lb/>
gitur, dicitur fieri refractio, &amp; refrangi, in refractione igitur requiruntur <lb/>duo media, per qu&aelig; fiat vi&longs;io, qu&aelig; &longs;int diuer&longs;&aelig; den&longs;itatis, vt &longs;unt aqua, &amp; <lb/>
aer: vapor, exhalatio, &amp; aer: vitrum, &amp; aer, &amp;c. </s>
          <s id="s.002014">quando igitur videmus <lb/>
Solem, aut Lunam per vapores, aut exhalationes fit refractio, quia den&longs;ior <lb/>
e&longs;t vapor, &amp; exhalatio, quam aer.</s>
        </p>
        <p type="main">
          <s id="s.002015">Notandum etiam Aream, de qua mox dicam explicari po&longs;&longs;e tam per re&shy;<lb/>
flexionem, qu&agrave;m per refractionem: per reflexionem, quia &longs;upponunt Philo&shy;<lb/>&longs;ophi e&longs;&longs;e in acre rorido innumera &longs;pecula parua inuicem vald&egrave; proxima, <lb/>ide&longs;t guttulas, per quas reflectatur ad oculum no&longs;trum &longs;pecies &longs;yderis. </s>
          <s id="s.002016">per <lb/>refractionem ver&ograve;, vt vult Vitellio, quia &longs;umit totum illum aerem humi&shy;<lb/>
dum magis den&longs;um e&longs;&longs;e aere paro, qui e&longs;t circa oculos no&longs;tros, &amp; hoc modo <lb/>con&longs;tituit diuer&longs;a media in den&longs;itate, per quam fiat vi&longs;io; corpus inquam <pb pagenum="114" xlink:href="009/01/114.jpg"/>illud humidum den&longs;ius, &amp; aerem deinde circa oculum rarius. </s>
          <s id="s.002017">Vicomerca&shy;<lb/>
tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex pr&aelig;di&shy;<lb/>ctis videtur reprehendendus.</s>
        </p>
        <p type="main">
          <s id="s.002018"><arrow.to.target n="marg162"/></s>
        </p>
        <p type="margin">
          <s id="s.002019"><margin.target id="marg162"/>161</s>
        </p>
        <p type="main">
          <s id="s.002020">Summ&aelig; 2. cap. 2. De Are&aelig; figura <emph type="italics"/>&lpar;Refrangitur autem &agrave; con&longs;i&longs;tente caligine <lb/>
circa Solem, aut Lunam vi&longs;us; quapropter non ex oppo&longs;ito &longs;icut iris, apparet. </s>
          <s id="s.002021"><expan abbr="Vn-diq;">Vn&shy;<lb/>
dique</expan> autem &longs;imiliter refracto, nece&longs;&longs;e e&longs;t circulum e&longs;&longs;e, aut circuli partem. </s>
          <s id="s.002022">ab co&shy;<lb/>
dem enim &longs;igno ad idem &longs;ignum &aelig;quales frangentur &longs;uper circuli lineam &longs;emper. </s>
          <s id="s.002023">&longs;it <emph.end type="italics"/><lb/>
<figure id="id.009.01.114.1.jpg" place="text" xlink:href="009/01/114/1.jpg"/><lb/>
<emph type="italics"/>enim &agrave; puncto, in quo A, ad B, fracta, &amp; ea, qu&aelig; est <lb/>
A C B, &amp; qu&aelig; A F B, &amp; qu&aelig; A D B, &aelig;quales autem <lb/>&amp; h&aelig; A C, A F, A D, inuicem. </s>
          <s id="s.002024">&amp; qu&aelig; ad B, inui&shy;<lb/>
cem &longs;cilicet C B, E B, D B. &amp; protrahatur A E B, <lb/>
quare trianguli &aelig;quales, etenim &longs;uper &aelig;qualem, qu&aelig; <lb/>
e&longs;t A E B, ducantur autem <expan abbr="perp&etilde;diculares">perpendiculares</expan> ad A E B, <lb/>
ex angulis; &agrave; C, quidem, qu&aelig; e&longs;t C E; ab F, autem, <lb/>
qu&aelig; e&longs;t F E; &agrave; D, autem, qu&aelig; e&longs;t D E, &aelig;quales itaque <lb/>h&aelig;, in &aelig;qualibus enim tri&abreve;ngulis, &amp; in vno plano om&shy;<lb/>nes, ad rectum enim omnes ei, qu&aelig; e&longs;t A E B. &amp; ad <lb/>
vnum punctum E, copulantur, circulus igitur erit <lb/>
de&longs;cripta, centrum autem E. &longs;it autem B, quidem Sol, <lb/>
A, autem vi&longs;us, qu&aelig; autem e&longs;t circa C D F, circun&shy;<lb/>
ferentia nubes, &agrave; qua refrangitur vi&longs;us ad Solem&rpar;<emph.end type="italics"/><lb/>
quia &longs;uppono Aream, &longs;iue Halonem fieri per re&shy;<lb/>
fractionem, vt vult etiam Vitellio, propterea <lb/>
<expan abbr="pr&aelig;mitt&etilde;dum">pr&aelig;mittendum</expan> e&longs;t principium quoddam, quo tra&shy;<lb/>
ctatio de refractione innititur; e&longs;t autem huiu&longs;&shy;<lb/>
modi; ea, qu&aelig; <expan abbr="vid&etilde;tur">videntur</expan> per refractionem, &longs;iue &longs;ub <lb/>
aliquo refractionis angulo, manentibus nobis &amp; <lb/>
a&longs;tro, &amp; medio ij&longs;dem in locis, non po&longs;&longs;unt vide&shy;<lb/>
ri &longs;ub diuer&longs;o angulo &agrave; priori, nec per con&longs;e<expan abbr="qu&etilde;s">quens</expan> <lb/>
alibi apparere. </s>
          <s id="s.002025">v. <!-- REMOVE S-->g. <!-- REMOVE S-->Sol &lpar;vt in pr&aelig;&longs;enti figura&rpar; <lb/>
videatur ab oculo A, media nube C D F, &longs;ub an&shy;<lb/>
gulo refractionis B C A, vel B F A, &amp; alijs &longs;imilibus angulis in eadem nube; <lb/>
manente igitur oculo A, &amp; a&longs;tro B, necnon nube C D E. eodem in loco, im&shy;<lb/>
po&longs;&longs;ibile e&longs;t Solem videri ab eodem oculo &longs;ub diuer&longs;o angulo &agrave; priori, nec <lb/>
con&longs;equenter alibi apparere, quam in B. <!-- KEEP S--></s>
          <s id="s.002026">Nunc ad textus declarationem, in <lb/>
quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>
uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>
in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>
con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>
etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>
gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>
ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s>
          <s id="s.002027">Sed iam textum Ari&longs;t. <lb/>qui geometricam huius rei continet demon&longs;trationem, explicemus. </s>
          <s id="s.002028">Suppo&shy;<lb/>
nit igitur prim&ograve; Ari&longs;t. lineas vi&longs;uales &agrave; &longs;ydere B, ad oculos no&longs;tros A, per <lb/>
nubem roridam C D F, procedentes, in nube con&longs;imiliter refrangi, ide&longs;t <expan abbr="vn-diq;">vn&shy;<lb/>
dique</expan> circa Solem, Lunamu&egrave; facere angulos refractionis &aelig;quales. </s>
          <s id="s.002029">quod etiam <pb pagenum="115" xlink:href="009/01/115.jpg"/>patet ex 48. 10. Vitellionis; vt in figura, in qua &longs;ydus B, oculus A, nubes <lb/>
C D F, radij vi&longs;uales tres refracti in nube &longs;int B C A, B D A, B E A, facien&shy;<lb/>
tes con&longs;imilem refractionem, ide&longs;t angulos refractos B C A, B D A, B E A, <lb/>
&aelig;quales in punctis C, D, F: <expan abbr="atq;">atque</expan> hoc e&longs;t con&longs;imilem facere refractionem. <lb/>
</s>
          <s id="s.002030">Supponit &longs;ecund&ograve; lineas &agrave; &longs;ydere ad nubem, v&longs;que exten&longs;as e&longs;&longs;e &aelig;quales, vt <lb/>
&longs;unt B C, B D, B F: &longs;imiliter reliquas tres &agrave; nube ad vi&longs;um A. pares e&longs;&longs;e C A, <lb/>
D A, F A. his &longs;uppo&longs;itis, &longs;i deinde protrahatur recta A B, ab oculo ad &longs;ydus, <lb/>exurgunt tria triangula omnin&ograve; &aelig;qualia, &amp; &longs;imilia, cum duo latera vnius <lb/>
&longs;int &aelig;qualia duobus alterius <expan abbr="vtrunq;">vtrunque</expan> vtrique, &amp; angulus angulo, &amp; pr&aelig;terea <lb/>
ba&longs;is &longs;it communis; ide&ograve; per quartam primi &longs;unt omnin&ograve; &aelig;qualia. </s>
          <s id="s.002031">ducan&shy;<lb/>
tur nunc ex angulis C, D, F, tres perpendiculares ad rectam A B, qu&aelig; &longs;int <lb/>
C E, D E, F E, in figura; qu&aelig; tres nece&longs;&longs;ari&ograve; erunt &aelig;quales, cum &longs;int duct&aelig; <lb/>
ab angulis &aelig;qualibus &aelig;qualium triangulorum ad communem ba&longs;im, &amp; di&shy;<lb/>
uident nece&longs;&longs;ari&ograve; ba&longs;im in eodem puncto E, cum diuidant triangula &aelig;qua&shy;<lb/>
lia proportionaliter; <expan abbr="erunt&qacute;">eruntque</expan>; propterea h&aelig; tres rect&aelig; in eodem plano, quod <lb/>
in nube concipitur ex 5. 11. Quare &longs;i concipiamus &longs;uperficiem, &longs;iue planum <lb/>
delineari circa E, ad interuallum linearum &aelig;qualium C E, D E, F E, de&shy;<lb/>
&longs;criptus erit circulus per 9. tertij, cuius circumferentia C D F. <!-- KEEP S--></s>
          <s id="s.002032">Ex quibus <lb/>
patet tria illa puncta C, D, E, per qu&aelig; Sol tran&longs;paret e&longs;&longs;e in orbem di&longs;po&longs;i&shy;<lb/>
ta. </s>
          <s id="s.002033">cau&longs;a igitur rotunditatis Are&aelig;, e&longs;t &longs;imilitudo angulorum refractionis, <lb/>
quibus Sol tran&longs;paret: vel ideo rotunda e&longs;t, quia &longs;imiles anguli nece&longs;&longs;ari&ograve; <lb/>
in orbem con&longs;tituuntur, vt o&longs;ten&longs;um e&longs;t. </s>
          <s id="s.002034">Eadem ratione omnia alia puncta <lb/>
eiu&longs;dem <expan abbr="circ&utilde;ferenti&aelig;">circunferenti&aelig;</expan> &longs;unt puncta, per qu&aelig; Sol videtur refract&egrave;; &amp; hoc mo&shy;<lb/>
do ad &longs;imilitudinem trium linearum A C B, A D B, A F B, refractarum, in&shy;<lb/>
finit&aelig; <expan abbr="vndiq;">vndique</expan> intelligend&aelig; &longs;unt, quarum ali&aelig; refrangantur in circunferentia <lb/>
pr&aelig;dicta, ali&aelig; ver&ograve; in alia periph&aelig;ria maiori, ali&aelig; etiam in minori, ita vt <lb/>
ex tota nube fiant refractiones circulares plurim&aelig;, ex quibus in nube area <lb/>
con&longs;tituatur. </s>
          <s id="s.002035"><expan abbr="Atq;">Atque</expan> h&aelig;c cur Halonis figura orbicularis videatur, rationem <lb/>
reddunt, <expan abbr="vna&qacute;">vnaque</expan>; textui lucem afferunt.</s>
        </p>
        <p type="head">
          <s id="s.002036"><emph type="italics"/>Summ&aelig; 2. cap. 4. De Iridis figura.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002037"><arrow.to.target n="marg163"/></s>
        </p>
        <p type="margin">
          <s id="s.002038"><margin.target id="marg163"/>162</s>
        </p>
        <p type="main">
          <s id="s.002039"><emph type="italics"/>Qvod autem <expan abbr="neq;">neque</expan> circulum po&longs;&longs;ibile &longs;it fieri Iridis, <expan abbr="neq;">neque</expan> maiorem &longs;emicir&shy;<lb/>
culo portionem, &amp; de alijs accidentibus circa ip&longs;am, ex de&longs;criptione <lb/>
erit con&longs;iderantibus manife&longs;tum&rpar;<emph.end type="italics"/> In Logicis &longs;&aelig;pius monui Ari&longs;t. per <lb/>
de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>
etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri&shy;<lb/>
ptionem appellat, Iridis figur&aelig; accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>
circularis, nunquam tamen circulus integer, im&ograve; <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>
maior, &longs;ed tamen &longs;emicirculo minor.</s>
        </p>
        <p type="main">
          <s id="s.002040"><arrow.to.target n="marg164"/></s>
        </p>
        <p type="margin">
          <s id="s.002041"><margin.target id="marg164"/>163</s>
        </p>
        <p type="main">
          <s id="s.002042">Ibidem <emph type="italics"/>&lpar;Hemi&longs;ph&aelig;rio enim exi&longs;tente &longs;uper horizontis circulum in quo A. cen&shy;<lb/>
tro autem K, alio autem quodam oriente puncto, in quo G, &longs;i line&aelig;, qu&aelig; &agrave; K, &longs;ecun&shy;<lb/>
dum conum excidentes faciant velut axem lineam in qua G K, &amp; &agrave; K. ad M, co&shy;<lb/>
pulat&aelig; refrangantur ab hemi&longs;ph&aelig;rio ad G, &longs;uper maiorem angulum, circuli circun&shy;<lb/>
ferentiam incident line&aelig;, qu&aelig; &agrave; K, &amp; &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/>
fiat, &longs;emicirculus ab <expan abbr="horiz&otilde;te">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s>
          <s id="s.002043">&longs;i autem &longs;upra, minor<emph.end type="italics"/> <pb pagenum="116" xlink:href="009/01/116.jpg"/><figure id="id.009.01.116.1.jpg" place="text" xlink:href="009/01/116/1.jpg"/><lb/>
<emph type="italics"/>&longs;emper &longs;emicirculo, minus autem, <lb/>
cum in meridie fuerit a&longs;trum&rpar;<emph.end type="italics"/> quod <lb/>
&longs;upra monui, iterum moneo, <expan abbr="re-tin&etilde;dam">re&shy;<lb/>
tinendam</expan> vocem reflexionis, <expan abbr="qu&atilde;-uis">quam&shy;<lb/>
uis</expan> in antiqua tran&longs;latione lega&shy;<lb/>
tur refractio, e&longs;t enim apud om&shy;<lb/>
nes in confe&longs;&longs;o Iridem fieri per <lb/>
reflexionem. </s>
          <s id="s.002044">E&longs;t igitur in &longs;upe&shy;<lb/>
riori figura, quam textui, vt par <lb/>
erat re&longs;titui, horizon G K O. cuius centrum K. in quo e&longs;t vi&longs;us no&longs;ter, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; <lb/>
hemi&longs;ph&aelig;rium no&longs;trum in arcu G A M O, repr&aelig;&longs;entatum, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; nubes rori&shy;<lb/>
da, in qua Iris appareat, vbi M, quod punctum M, nubem referens, in figu&shy;<lb/>
ra ponitur in hemi&longs;ph&aelig;rij ambitu, quod c&oelig;lum repr&aelig;&longs;entat, cum tamen <lb/>nubes parum &agrave; terra &longs;ubuehatur; id enim ad demon&longs;trationem fer&egrave; perinde <lb/>
e&longs;t. </s>
          <s id="s.002045">in oriente G, &longs;it a&longs;trum. </s>
          <s id="s.002046">&longs;i erg&ograve; line&aelig; vi&longs;uales &agrave; K, ad M, nubem tenden&shy;<lb/>
tes reflectantur &longs;uper maiorem angulum M K G, ad G, erit reflexarum vna <lb/>
veluti M G. <!-- KEEP S--></s>
          <s id="s.002047">Porro omnes line&aelig; vi&longs;uales, qu&aelig; ad nubem M, incidunt, nece&longs;&shy;<lb/>
&longs;ari&ograve;, vt probabo, cadent in ambitum circularem. </s>
          <s id="s.002048">debemus enim innume&shy;<lb/>ras lineas imaginari &agrave; K, in coni figuram excidentes, cuius vertex &longs;it in K, <lb/>
&amp; axis G K O, quas omnes repr&aelig;&longs;entat vna K M, <expan abbr="melius&qacute;">meliusque</expan>; repr&aelig;&longs;entabit, fi <lb/>
cogitemus axem G K O, circa polos G, O, manentes circumuolui, <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; <lb/>
lineam K M, circumducere. </s>
          <s id="s.002049">in hac etiam giratione linea K M, tran&longs;ibit per <lb/>
omnes illas lineas, quas imaginabamur; <expan abbr="de&longs;cribet&qacute;">de&longs;cribetque</expan>; conum, quem ill&aelig; con&shy;<lb/>
formare debebant. </s>
          <s id="s.002050">In pr&aelig;dicta autem axis volutatione, extremum M, li&shy;<lb/>
ne&aelig; K M, nece&longs;&longs;ari&ograve; de&longs;cribit circulum, qui e&longs;t circulus Iridis, &amp; e&longs;t ba&longs;is <lb/>
memorati coni.</s>
        </p>
        <p type="main">
          <s id="s.002051">Si igitur oriente, vel occidente a&longs;tro fiat iris, Iris erit &longs;emicirculus, ide&longs;t <lb/>
illa &longs;emi&longs;&longs;is circuli pr&etail;dicti &lpar;quem horizon bifariam diuidit&rpar; qu&aelig; &longs;upra ter&shy;<lb/>
ram extabit. </s>
          <s id="s.002052">&longs;i autem a&longs;trum eleuatum &longs;upra horizontem fuerit, quando fit <lb/>
iris, erit &longs;emper arcus Iridis &longs;emicirculo minor; <expan abbr="tunc&qacute;">tuncque</expan>; minimus <expan abbr="c&utilde;">cum</expan> a&longs;trum <lb/>
<expan abbr="meridian&utilde;">meridianum</expan> <expan abbr="circul&utilde;">circulum</expan> occupauerit. </s>
          <s id="s.002053">h&etail;c tria &longs;unt, qu&aelig; deinceps <expan abbr="prob&atilde;da">probanda</expan> recipit.</s>
        </p>
        <p type="main">
          <s id="s.002054"><arrow.to.target n="marg165"/></s>
        </p>
        <p type="margin">
          <s id="s.002055"><margin.target id="marg165"/>264</s>
        </p>
        <figure id="id.009.01.116.2.jpg" place="text" xlink:href="009/01/116/2.jpg"/>
        <p type="main">
          <s id="s.002056">Ibidem <emph type="italics"/>&lpar;Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri&shy;<lb/>
mum vbi G, &amp; refracta &longs;it K M, <lb/>
ad G, &amp; planum erectum &longs;it in quo <lb/>
A, &agrave; triangulo in quo G K M, cir&shy;<lb/>
culus igitur erit &longs;ectio &longs;ph&aelig;r&aelig;, qui <lb/>
maximus &longs;it in quo A, differet enim <lb/>nihil &longs;i quod<expan abbr="c&ubreve;q;">c&ubreve;que</expan> eorum, qu&aelig; &longs;uper <lb/>
G K, &longs;ecundum triangul&ubreve; K M G, <lb/>
erectum fuerit planum. </s>
          <s id="s.002057">line&aelig; igitur <lb/>ab ijs, qu&aelig; G, K, duct&aelig; in hac ratio&shy;<lb/>ne non con&longs;tituentur ad aliud, &amp; <lb/>
aliud punctum, qu&agrave;m &longs;emicirculi <lb/>
in quo A. <!-- KEEP S--></s>
          <s id="s.002058">Quoniam enim puncta <lb/>
G, K, data &longs;unt, &amp; qu&aelig; K M, vtique data erit; &amp; qu&aelig; M G, ad M K; datam igi&shy;<lb/>
tur circunferentiam tanget M, fit <expan abbr="itaq;">itaque</expan> h&aelig;c in qua M N, quare &longs;ectio circunferen-<emph.end type="italics"/>


<pb pagenum="117" xlink:href="009/01/117.jpg"/><emph type="italics"/>tiarum data e&longs;t. </s>
          <s id="s.002059">apud autem aliud punctum, quam ip&longs;ius M N, circunferenti&aelig;, ab <lb/>
ij&longs;dem punctis, eadem ratio in eodem plano non con&longs;i&longs;tit&rpar;<emph.end type="italics"/> eorum omnium, qu&aelig; <lb/>
demon&longs;tranda &longs;unt, pr&aelig;mittenda &longs;unt duo nece&longs;&longs;aria fundamenta. </s>
          <s id="s.002060">Primum <lb/>
e&longs;t; ea, qu&aelig; videmus per reflexionem &longs;ub quopiam angulo, manentibus no&shy;<lb/>
bis &longs;peculo, &amp; obiecto ij&longs;dem in locis, non po&longs;&longs;unt videri &longs;ub alio diuer&longs;o <lb/>
angulo, nec alibi con&longs;equenter apparere. </s>
          <s id="s.002061">v. <!-- REMOVE S-->g. <!-- REMOVE S-->in &longs;uperiori figura, quam <lb/>
textui re&longs;tituimus exi&longs;tente Sole in G, oculo in K, &amp; nube in M. ex qua ra&shy;<lb/>dius Solis G M, reflectatur ad vi&longs;um in K, per <expan abbr="line&atilde;">lineam</expan> M K, &longs;ub angulo G M K, <lb/>
impo&longs;&longs;ibile e&longs;t manentibus illis, vt dixi, videri Solem in nube M, &longs;ub diuer&shy;<lb/>
&longs;o angulo &agrave; priori, nec alibi apparere. </s>
          <s id="s.002062">Alterum e&longs;t apud Opticos vulga&shy;<lb/>
tum; ea &longs;cilicet, qu&aelig; per reflexionem &lpar;de quorum numero e&longs;t Iris&rpar; viden&shy;<lb/>
tur, videri, tunc &longs;olum, quando angulus incidenti&aelig; fuerit &aelig;qualis angulo <lb/>
reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura &lpar;&longs;i fieri <lb/>
<figure id="id.009.01.117.1.jpg" place="text" xlink:href="009/01/117/1.jpg"/><lb/>
pote&longs;t&rpar; vtitur. </s>
          <s id="s.002063">v. <!-- REMOVE S-->g. <!-- REMOVE S-->in figura pr&aelig;&longs;enti &longs;it &longs;pe&shy;<lb/>
culum C D E, obiectum A, oculus B, linea in&shy;<lb/>
cidenti&aelig; e&longs;t A D, &amp; angulus pariter inciden&shy;<lb/>
ti&aelig; e&longs;t A D C. linea ver&ograve; D B, e&longs;t linea refle&shy;<lb/>
xionis, &amp; angulus pariter reflexionis e&longs;t B D&shy;<lb/>
E, qui duo anguli ni&longs;i fuerint &aelig;quales, nun&shy;<lb/>
quam videbitur obiectum A, ab oculo B, hinc <lb/>
e&longs;t, quod aliquando po&longs;ito &longs;peculo, obiectum <lb/>
quamuis illi aduer&longs;um, &agrave; nobis pariter ante <lb/>
&longs;peculum con&longs;titutis, videri nequit, quia &longs;ci&shy;<lb/>
licet in tali po&longs;itione &longs;peculi, obiecti, &amp; no&longs;tri, nulla linea incidenti&aelig;, ide&longs;t, <lb/>
qu&aelig; ab obiecto in &longs;peculum tendit, facere pote&longs;t angulum cum &longs;peculo, qui <lb/>
dicitur angulus incidenti&aelig;, &aelig;qualem angulo illi, quem facit linea eadem re&shy;<lb/>flexa &agrave; &longs;peculo ad oculum, quem dicunt angulum reflexionis. </s>
          <s id="s.002064">Cum ergo in <lb/>
Iride videamus colorem Solis per reflexionem, tunc &longs;olum apparebit Iris, <lb/>
quando Sol, nubes, &amp; oculus fuerint in ea con&longs;titutione, qua radius <expan abbr="incid&etilde;s">incidens</expan> <lb/>
nubi, &amp; radius &agrave; nube repercu&longs;&longs;us faciant pares angulos. </s>
          <s id="s.002065">Et quia quando <lb/>nubes ro&longs;cida perpendiculariter opponitur Soli, &amp; nobis, po&longs;&longs;unt fieri pr&aelig;&shy;<lb/>
dicti anguli &aelig;quales non in vno loco nubis, &longs;ed in pluribus, con&longs;titutis ta&shy;<lb/>
men in circuli periph&aelig;ria, hinc fit, quod Solis color reflectatur ex pluribus <lb/>
locis in orbem con&longs;titutis, qu&aelig; reflexio e&longs;t ip&longs;ius Iridis arcus. </s>
          <s id="s.002066">ex Vitellion <lb/>
63. 10. Totam autem figur&aelig; Iridis demon&longs;trationem &longs;ic breuiter puto ad&shy;<lb/>
inuentam e&longs;&longs;e. </s>
          <s id="s.002067">cum Sol in Iride videatur in orbem, <expan abbr="atq;">atque</expan> con&longs;imiliter, ne ce&longs;&shy;<lb/>
&longs;e e&longs;t id prouenire ex angulis reflexionum con&longs;imilibus, &longs;iue &aelig;qualibus: di&longs;&shy;<lb/>
&longs;imiles enim anguli, di&longs;&longs;imilem <expan abbr="vtiq;">vtique</expan> efficiunt Solis <expan abbr="appar&etilde;tiam">apparentiam</expan>. </s>
          <s id="s.002068">atqui con&shy;<lb/>
&longs;imiles anguli, &longs;iue &aelig;quales, non ni&longs;i in orbem po&longs;&longs;unt con&longs;titui; igitur an&shy;<lb/>
gulorum &aelig;qualitas cau&longs;a erit rotundationis arcus. </s>
          <s id="s.002069">h&etail;c e&longs;t &longs;umma totius di&shy;<lb/>
&longs;cur&longs;us, quem pluribus, &amp; nimis ob&longs;cur&egrave; Ari&longs;t. explicat.</s>
        </p>
        <p type="main">
          <s id="s.002070">Inquit igitur Ari&longs;t. &longs;it enim in oriente, &amp;c. </s>
          <s id="s.002071">vbi aggreditur probare vnum <lb/>
ex tribus illis, qu&aelig; &longs;upra propo&longs;uit, nimirum tunc Iridem e&longs;&longs;e &longs;emicircu&shy;<lb/>
lum, quando a&longs;trum fuerit in oriente, &longs;iue in horizonte, vbi G. &longs;i igitur per <lb/>
triangulum G M K, intelligamus <expan abbr="plan&utilde;">planum</expan> exten&longs;um, in quo A, in figura, adeo <lb/>
magnum, vt totum &longs;ecet hemi&longs;ph&aelig;rium, faciet in &longs;uperficie hemi&longs;ph&aelig;rij &longs;e&shy;


<pb pagenum="118" xlink:href="009/01/118.jpg"/>ctionem, qu&aelig; erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e&shy;<lb/>
cans hemi&longs;ph&aelig;rium, tran&longs;eat per <expan abbr="centr&utilde;">centrum</expan> ip&longs;ius, qu&aelig; &longs;ectio, &longs;iue circuli por&shy;<lb/>tio repr&aelig;&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M&shy; <lb/>
R O. nihil autem refert quodcunque intelligas planum &longs;uper axem G K O, <lb/>
tran&longs;iens &longs;iue per triangulum G K M, &longs;iue per aliud illi &longs;imile. </s>
          <s id="s.002072">Pr&aelig;mitten&shy;<lb/>
dum pr&aelig;terea non po&longs;&longs;e in &longs;emicirculo &longs;uperiori, quod e&longs;t planum, &amp; &longs;ectio <lb/>
trianguli G K M, poni alias duas lineas. </s>
          <s id="s.002073">v. <!-- REMOVE S-->g. <!-- REMOVE S-->G R, K R, ad aliud punctum, <lb/>
vti e&longs;t R, qu&aelig; habeant eandem inuicem proportionem, quam habent prio&shy;<lb/>
res du&aelig; G M, K M, quod probatur, quia &longs;i &longs;int vt G M, ad K M, ita G R, ad <lb/>
K R, cum G R, &longs;it centro K, propinquior quam G M, erit etiam eadem G R, <lb/>
longior ip&longs;a G M, per 15. 3. &amp; tamen deberet e&longs;&longs;e &aelig;qualis illi; quemadmo&shy;<lb/>
dum K M, e&longs;t &aelig;qualis alteri K R; nequeunt autem du&aelig; line&aelig; in&aelig;quales inui&shy;<lb/>
cem, habere eandem rationem ad duas inuicem &aelig;quales: ergo non habent <lb/>
eandem rationem G M, &amp; K M, quam habent G R, &amp; K R. quod &longs;i punctum <lb/>
R, &longs;umatur &longs;upra M, erit &longs;imilis <expan abbr="dem&otilde;&longs;tratio">demon&longs;tratio</expan>, &longs;i liter&aelig; M, &amp; R, loca permu&shy;<lb/>
tent. </s>
          <s id="s.002074">his po&longs;itis, ait <emph type="italics"/>&lpar;Quoniam enim G, K, puncta data &longs;unt, &amp; c.&rpar;<emph.end type="italics"/> ide&longs;t data <lb/>
&longs;unt po&longs;itione, cum notum &longs;it vbi &longs;int. </s>
          <s id="s.002075">G, enim e&longs;t in ortu. </s>
          <s id="s.002076">K, ver&ograve; in centro <lb/>horizontis, &longs;equitur, quod etiam linea G K, cuius ip&longs;a &longs;unt extrema, data <lb/>
&longs;it, &amp; po&longs;itione, &amp; magnitudine, per 26. Datorum Euclidis. <!-- KEEP S--></s>
          <s id="s.002077">eadem quoque <lb/>
ratione data erit K M, linea; &longs;iue quia e&longs;t &aelig;qualis ip&longs;i G K, &longs;iue quia per <lb/>
a&longs;trolabium po&longs;&longs;umus ip&longs;ius longitudinem, &amp; po&longs;itionem inue&longs;tigare; qua&shy;<lb/>
re &amp; punctum M, datum erit per 27. Datorum, quare &amp; linea G M, data <lb/>
erit quoad &longs;itum, &amp; magnitudinem per 26. Datorum. <!-- KEEP S--></s>
          <s id="s.002078">Quare per primam <lb/>
Datorum erit data proportio linearum G M, M K, punctum <expan abbr="itaq;">itaque</expan> M, tanget <lb/>
ambitum datum, qui ba&longs;is e&longs;t coni, quem linea K M, de&longs;cribit in reuolutio&shy;<lb/>
ne axis G K O, &longs;uper polis G, O. cum enim data &longs;it K M, po&longs;itu, &amp; magni&shy;<lb/>
tudine, <expan abbr="ea&qacute;">eaque</expan>; &longs;it latus pr&aelig;dicti coni, &longs;equitur periph&aelig;riam, vel ambitum ba&shy;<lb/>
&longs;is coni e&longs;&longs;e datum per &longs;imilem definitionem 5. definitioni Datorum. <!-- KEEP S--></s>
          <s id="s.002079">&longs;it <expan abbr="au-t&etilde;">au&shy;<lb/>
tem</expan> ambitus ille in figura &longs;equenti notatus literis L M N. qui ambitus L M N, <lb/>
non e&longs;t <expan abbr="concipi&etilde;dus">concipiendus</expan> in eodem plano &longs;emicirculi G A N O, quemadmodum <lb/>
fals&ograve; pingitur in figura; &longs;ed debemus ip&longs;um concipere tanquam erectum ad <lb/>
angulos rectos cum pr&aelig;dicto &longs;emicirculo, necnon cum horizonte G K O. <lb/>
<!-- KEEP S--></s>
          <s id="s.002080">Iam &longs;i <expan abbr="tri&atilde;gulum">triangulum</expan> G M K, prioris figur&aelig; circumuoluatur circa axem G K O, <lb/>
punctum ip&longs;ius M, de&longs;cribit pr&aelig;dictum ambitum L M N. hunc ambitum <lb/>inquit Ari&longs;tot. <!-- REMOVE S-->linea K M, attinget, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/>
<figure id="id.009.01.118.1.jpg" place="text" xlink:href="009/01/118/1.jpg"/><lb/>
Erit pr&aelig;terea &longs;ectio circunferentiarum ho&shy;<lb/>rizontis, &amp; huius ambitus data, cuius extre&shy;<lb/>
ma puncta e&longs;&longs;ent L, &amp; N. &longs;i enim <expan abbr="c&otilde;cipiamus">concipiamus</expan> <lb/>
in figura non &longs;olum horizontis diametrum <lb/>
G K O, &longs;ed etiam circunferentiam &lpar;in qua <lb/>
circunferentia e&longs;&longs;ent duo illa puncta L, &amp; N, <lb/>vt in pr&aelig;&longs;enti de&longs;criptione melius intellige&shy;<lb/>
tur, in qua horizon G N O L, &amp; ambitus <lb/>
pr&aelig;dictus e&longs;t L M N, qui debet intelligi ele&shy;<lb/>
uatus &longs;upra horizontem perpendiculariter&rpar; <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119" xlink:href="009/01/119.jpg"/>linea N P L, cuius extrema puncta &longs;unt L, N, qu&aelig; data erunt, cum &longs;int ex&shy;<lb/>
trema line&aelig; K M, circumlat&aelig;; &amp; quemadmodum dabatur &longs;uperius punctum <lb/>
M. eadem ratione ex Datis, dabitur punctum N, &amp; L. quare etiam &longs;ectio <lb/>
N P L, qu&aelig; inter data puncta continetur, data erit ex 26. Datorum.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002081">Illud nunc in memoriam <expan abbr="reuoc&atilde;dum">reuocandum</expan>, quod paul&ograve; ante probaui, nimirum <lb/>
proportionem linearum G M, K M, non po&longs;&longs;e &longs;eruari in alijs lineis, qu&aelig; &longs;int <lb/>
in eodem plano trianguli G M K, &longs;i ducantur ab ij&longs;dem punctis G, K. pote&longs;t <lb/>
tamen &longs;eruari in alijs duabus, qu&aelig; cadant in pr&aelig;dictum ambitum, &longs;iue <expan abbr="cir-cunfer&etilde;tiam">cir&shy;<lb/>
cunferentiam</expan> L M N, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; &longs;int in alio plano, <expan abbr="qu&atilde;">quam</expan> in plano trianguli G M K, <lb/>
quod tamen tran&longs;eat per axem G K O, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vnum ex planis illis, de quibus <lb/>
&longs;upra dictum e&longs;t. </s>
          <s id="s.002082">Verumenimuer&ograve; ad quid probatio h&aelig;c? </s>
          <s id="s.002083">non po&longs;&longs;e duas <lb/>
alias lineas in eodem plano, &amp;c.? exi&longs;timo Ari&longs;t. idcirc&ograve; hoc proba&longs;&longs;e, quia <lb/>
&longs;i ali&aelig; du&aelig; line&aelig; habentes eandem rationem, po&longs;&longs;ent collocari in eodem <lb/>
plano; e&longs;&longs;ent <expan abbr="permut&atilde;do">permutando</expan> ill&aelig; du&aelig; &lpar;in priori figura&rpar; G R, R K. <expan abbr="vtraq;">vtraque</expan> <expan abbr="vtriq;">vtrique</expan> <lb/>
&aelig;quales prioribus G M, M K, per quas videtur Iris, cum enim K R, &longs;it &aelig;qua&shy;<lb/>
lis ip&longs;i K M, erit, &amp; G M, &aelig;qualis ip&longs;i G R, per 7. 5. &amp; in eius &longs;cholio. </s>
          <s id="s.002084">qua&shy;<lb/>
re natura ageret tam per lineas breui&longs;&longs;imas <expan abbr="ag&etilde;do">agendo</expan> per has, quam per illas, <lb/>
<expan abbr="hoc&qacute;">hocque</expan>; pacto per has etiam Iris videri po&longs;&longs;et. </s>
          <s id="s.002085">cum erg&ograve; con&longs;tet non po&longs;&longs;e has <lb/>
e&longs;&longs;e prioribus proportionales, &longs;ed maiorem, vel minorem, alteram illarum, <lb/>
qu&agrave;m &longs;it G M, &longs;equitur, quod non faciunt angulum &aelig;qualem angulo G M K, <lb/>
&longs;ub quo videtur Iris, <expan abbr="nimir&utilde;">nimirum</expan> angulum G R K, qui &longs;it &aelig;qualis angulo G M K; <lb/>
habet enim Iris hunc angulum determinatum, ita vt &longs;ub maiori, vel mino&shy;<lb/>
ri videri nequeat; ex 10. Bapti&longs;ta Porta. </s>
          <s id="s.002086">&longs;i autem punctum R, e&longs;&longs;et infra M, <lb/>
angulus G R K, e&longs;&longs;et minor angulo Iridis G M K, &longs;i ver&ograve; &longs;upra e&longs;&longs;et maior <lb/>
eodem, quod vel ad &longs;en&longs;um patere pote&longs;t in quouis circulo, <expan abbr="id&qacute;">idque</expan>; &longs;ufficiat, ne <lb/>
longior euadat h&aelig;c tractatio. </s>
          <s id="s.002087">Fort&egrave; etiam addi pote&longs;t, quod alibi exi&longs;ten&shy;<lb/>
te puncto R, qu&agrave;m in M, non po&longs;&longs;ent anguli incidenti&aelig;, &amp; reflexionis e&longs;&longs;e <lb/>
&aelig;quales, qu&aelig; cau&longs;a e&longs;&longs;et cur &longs;ub alio angulo, quam pr&aelig;dicto G M K, Iris <lb/>
non appareret.</s>
        </p>
        <p type="main">
          <s id="s.002088">Pr&aelig;dicta omnia &longs;unt &longs;ecundum Ari&longs;tot. di&longs;cur&longs;um, &amp; figurationem dicta, <lb/>
nam &longs;ecundum veritatem po&longs;&longs;unt in eadem nube con&longs;titui plures anguli <lb/>
&aelig;quales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alter&utilde;">alterum</expan>; vt in figura pr&aelig;&shy;<lb/>
<figure id="id.009.01.119.1.jpg" place="text" xlink:href="009/01/119/1.jpg"/><lb/>
&longs;enti, &longs;i nubes e&longs;&longs;et vbi B D. <lb/>
oculus in C, Sol in A. e&longs;&longs;ent <lb/>
duo anguli A B C, A D C, &aelig;&shy;<lb/>
quales per 33. 3. qui tamen <lb/>
non &longs;unt in gyrum con&longs;tituti, <lb/>
po&longs;&longs;et igitur, per <expan abbr="illor&utilde;">illorum</expan> vtrun&shy;<lb/>
que Sol Iridem efficere. </s>
          <s id="s.002089">atque <lb/>
animaduer&longs;io h&etail;c videtur ma&shy;<lb/>
gni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;&longs;e, ad Iridis <expan abbr="de-mon&longs;tration&etilde;">de&shy;<lb/>
mon&longs;trationem</expan> con&longs;tituendam: <lb/>
cum hinc v&longs;itat&aelig; demon&longs;tra&shy;<lb/>
tiones infringatur. </s>
          <s id="s.002090">Fort&egrave; confugiendum e&longs;t ad illud, quod Maurolycus, &amp; <lb/>
10. Bapti&longs;ta Porta ob&longs;eruarunt; debere <expan abbr="nimir&utilde;">nimirum</expan> di&longs;tantiam ab oculo ad cen&shy;<lb/>
trum Iridis e&longs;&longs;e &aelig;qualem altitudini, &longs;iue &longs;emidiametro Iridis. </s>
          <s id="s.002091">Ita vt non &longs;o&shy;


<pb pagenum="120" xlink:href="009/01/120.jpg"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="qu&atilde;ta">quanta</expan> requi&shy;<lb/>
ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s>
          <s id="s.002092">h&aelig;c &agrave; <lb/>
nemine hactenus animaduer&longs;a placuit addere, vt ex ijs demon&longs;tratio Iridis <lb/>
omnibus numeris aliquando ab&longs;olui po&longs;&longs;it, quod infra &lpar;ni fallor, fauente <lb/>
Deo&rpar; pr&aelig;&longs;tabimus.<lb/>
<arrow.to.target n="marg166"/></s>
        </p>
        <p type="margin">
          <s id="s.002093"><margin.target id="marg166"/>165</s>
        </p>
        <p type="main">
          <s id="s.002094">Ibidem <emph type="italics"/>&lpar;Extraponatur igitur qu&aelig;dam linea, qu&aelig; D B, &amp; &longs;eindatur vt M G, ad <lb/>
M K, &longs;ic qu&aelig; D, ad B, maior autem qu&aelig; M G, ea qu&agrave;m M K, quoniam &longs;uper ma&shy;<lb/>
iorem angulum reflexio coni, maiori enim angulo &longs;ubtenditur trianguli M K G. <lb/>
<!-- KEEP S--></s>
          <s id="s.002095">Maior igitur e&longs;t &amp; ip&longs;a D, ip&longs;a B. addatur igitur ad eam, qu&aelig; B, ea in qua F, vt <lb/>
&longs;it quod D, ad B, qu&aelig; B F, ad D. <!-- KEEP S--></s>
          <s id="s.002096">Deinde quod F, ad K G, qu&aelig; B, ad aliam fiat, <lb/>
qu&aelig; K P. &amp; &agrave; P, ad M, copuletur qu&aelig; P M, erit igitur P. polus circuli, ad quem <lb/>
line&aelig;, qu&aelig; &agrave; K, incidunt&rpar;<emph.end type="italics"/> <expan abbr="hucu&longs;q;">hucu&longs;que</expan> o&longs;tendit lineas vi&longs;uales cadere ad M, pun&shy;<lb/>
ctum in Iridis periph&aelig;riam, pergit deinceps inue&longs;tigare polum, &amp; po&longs;tea <lb/>
centrum eiu&longs;dem ambitus, vtraque autem exi&longs;tere in horizonte reperit, vt <lb/>
hinc inferat Iridis portionem illam, qu&aelig; oriente Sole &longs;upra horizontem ap&shy;<lb/>
paret, e&longs;&longs;e &longs;emicirculum, vt propo&longs;uerat. </s>
          <s id="s.002097">Differt autem polus circuli &agrave; cen&shy;<lb/>
tro eiu&longs;dem circuli. </s>
          <s id="s.002098">polus e&longs;t punctum extra planum circuli, ex quo tamen <lb/>
vt <expan abbr="c&etilde;tro">centro</expan> adhibito circino circuli periph&aelig;ria de&longs;cribi pote&longs;t; &longs;ic polus &aelig;qua&shy;<lb/>
toris e&longs;t idem, qui polus mundi: <expan abbr="centr&utilde;">centrum</expan> ver&ograve; e&longs;t in plano &longs;ui cir culi, &longs;ic cen&shy;<lb/>
trum &aelig;quatoris e&longs;t idem cum centro mundi, cum &aelig;quator per illud incedat.</s>
        </p>
        <p type="main">
          <s id="s.002099">Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t. cum data &longs;it proportio linearum K M, &amp; M G, in &longs;upe&shy;<lb/>
riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex&shy;<lb/>
<figure id="id.009.01.120.1.jpg" place="text" xlink:href="009/01/120/1.jpg"/><lb/>
ponatur alia linea recta B D. qu&aelig; diui&shy;<lb/>
datur in partes B, &amp; D. proportionales <lb/>
cum lineis K M, G M, per 10. 6. cum <lb/>
ergo K M, &longs;it minor qu&agrave;m G M, per 19. <lb/>
primi, quia in triangulo G M K, oppo&shy;<lb/>
nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor qu&agrave;m D, addatur iam ip&longs;i B. linea <lb/>
nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, &amp; D, per 11. 6. <lb/>
hoc ordine, vt F B, ad D. ita D, ad B. <!-- KEEP S--></s>
          <s id="s.002100">Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>
B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>
gatur recta P M. <!-- KEEP S--></s>
          <s id="s.002101">Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>
ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/>
in &longs;equentibus.</s>
        </p>
        <p type="main">
          <s id="s.002102"><arrow.to.target n="marg167"/></s>
        </p>
        <p type="margin">
          <s id="s.002103"><margin.target id="marg167"/>166</s>
        </p>
        <p type="main">
          <s id="s.002104">Ibidem <emph type="italics"/>&lpar;Erit etiam, quod qu&aelig; F, ad K G. &amp; qu&aelig; B, ad K P. &amp; qu&aelig; D, ad P M. <lb/>non enim &longs;it, &longs;ed aut ad minorem, aut ad maiorem ea, qu&aelig; P M, nihil enim differet. <lb/>
</s>
          <s id="s.002105">&longs;it enim ad P R. eandem ergo rationem G K, &amp; K P, &amp; P R, inuicem habebunt, <lb/>
quam qu&aelig; F, B, D: qu&aelig; autem F, B, D, proportionales crant, quod quidem D, ad <lb/>
B. qu&aelig; F B, ad D: quare quod qu&aelig; P G, ad P R, qu&aelig; P R, ad eam, qu&aelig; P K. &longs;i igi&shy;<lb/>
tur ab ijs, qu&aelig; K G, qu&aelig; G R, &amp; K R, ad R, coniungantur, coniunct&aelig; h&aelig; eandem <lb/>
habebunt rationem, quam qu&aelig; G P, ad eam, qu&aelig; P R, circa eundem enim angulum <lb/>
P, proportion aliter, &amp; qu&aelig; trianguli G P R, &amp; eius, qui K R P. quare &amp; qu&aelig; G R, <lb/>
ad eam qu&aelig; K R, eandem rationem habebit, quam &amp; qu&aelig; G P, ad eam qu&aelig; P R, <lb/>
habet autem &amp; qu&aelig; M G, ad M K, eam rationem, quam qu&aelig; D, ad eam qu&aelig; B, <lb/>quare amb&aelig; &agrave; punctis G K, non &longs;olum ad circunferentiam M N, con&longs;tituentur ean&shy;<lb/>dem habentes rationem, &longs;ed &amp; alibi, quod quidem impo&longs;&longs;ibile&rpar;<emph.end type="italics"/> incipit, vt dixi,


<pb pagenum="121" xlink:href="009/01/121.jpg"/>probare P, e&longs;&longs;e polum pr&aelig;dicti ambitus, &longs;ic. </s>
          <s id="s.002106">Prim&ograve; enim &longs;ciendum in pr&aelig;&shy;<lb/>
mi&longs;&longs;a con&longs;tructione e&longs;&longs;e, vt F, ad G K, &amp; B, ad K P, ita D, ad P M. nam &longs;i non <lb/>
&longs;it eadem ratio D, ad P M, cum alijs pr&aelig;dictis, erit eadem ratio eiu&longs;dem D, <lb/>ad aliam maiorem, vel minorem ip&longs;a P M. &longs;it ad minorem P R. nihil enim <lb/>
refert &longs;iue dixeris habere eandem rationem ad minorem, &longs;iue ad maiorem, <lb/>
ergo permutando erunt G K, K P, P R, proportionales cum F, B, D. &longs;ed li&shy;<lb/>
ne&aelig; F, B, D, erant proportionales <expan abbr="compon&etilde;do">componendo</expan> hoc modo, vt F B, ad D, ita <lb/>
D, ad B: quare &longs;imiliter erunt vt G P, ad P R, ita P R, ad P K. per 18. 5. &longs;i igi&shy;<lb/>
tur &agrave; punctis G, &amp; K, figur&aelig; nu. </s>
          <s id="s.002107">164. <expan abbr="iung&atilde;tur">iungantur</expan> line&aelig; ad R, qu&aelig; &longs;int G R, K R, <lb/>
erit vt G R, ad K R, ita G P, ad P R. quia orta <expan abbr="s&utilde;t">sunt</expan> duo <expan abbr="tri&atilde;gula">triangula</expan> G P R, K P R, <lb/>
qu&aelig; habent eundem angulum ad P. &amp; latera proportionalia circa dictum <lb/>
angulum. </s>
          <s id="s.002108">e&longs;t etiam vt G P, ad P R, in maiori triangulo, ita P R, ad K P, in <lb/>
minori, ex con&longs;tructione, quare per 6. 6. erunt illa duo triangula &aelig;quian&shy;<lb/>
gula; erg&ograve; per 4. 6. erunt latera circum &aelig;quales angulos proportionalia; <lb/>
quare erit vt G P, ad P R. ita G R, ad R K: erat autem vt K M, ad G M, ita <lb/>
B, ad D. &amp; ita etiam G P, ad P R; erg&ograve; per 11. 5. vt K M, ad M G. ita K R, <lb/>
ad R G, intra eandem circunferentiam, &amp; in eodem plano: quod e&longs;&longs;e im&shy;<lb/>
po&longs;&longs;ibile &longs;upra o&longs;tendimus, hoc autem impo&longs;&longs;ibile, &longs;equitur &longs;i neges e&longs;&longs;e vt <lb/>
F, ad G K; &amp; B, ad K P, ita D, ad P M.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002109"><arrow.to.target n="marg168"/></s>
        </p>
        <p type="margin">
          <s id="s.002110"><margin.target id="marg168"/>167</s>
        </p>
        <p type="main">
          <s id="s.002111">Ibidem <emph type="italics"/>&lpar;Quoni&abreve;m igitur qu&aelig; D, <expan abbr="neq;">neque</expan> ad minorem ea, qu&aelig; P M, <expan abbr="neq;">neque</expan> ad maiorem <lb/>&lpar;&longs;imiliter enim demon&longs;trabimus&rpar; palam e&longs;t, quod ad ip&longs;am <expan abbr="vtiq;">vtique</expan> erit, in qua P M, <lb/>
quare erit, quod qu&aelig; M P, ad P K, qu&aelig; P G, ad M P. <!-- KEEP S--></s>
          <s id="s.002112">Si igitur eo in quo P, polo <lb/>vtens, di&longs;tantia autem ea, in qua P M, circulus de&longs;cribatur, omnes angulos attin&shy;<lb/>
get, quos reflex&aelig; faciunt, qu&aelig; &agrave; K, G. &longs;i autem non, &longs;imiliter o&longs;tendentur eandem <lb/>
babere rationem, qu&aelig; alibi, quam in &longs;emicirculo con&longs;tituuntur; quod quidem erat <lb/>
impo&longs;&longs;ibile&rpar;<emph.end type="italics"/> quoniam igitur, inquit, linea D, <expan abbr="neq;">neque</expan> ad minorem, <expan abbr="neq;">neque</expan> ad ma&shy;<lb/>
iorem quam P M, habet eam rationem, qu&aelig; e&longs;t ip&longs;ius F, ad G K, aut ip&longs;ius <lb/>
B, ad K P. &longs;imiliter enim demon&longs;tratur ab&longs;urdum &longs;equi. </s>
          <s id="s.002113">pal&agrave;m e&longs;t, quoniam <lb/>
erit D, ad P M, vt pr&aelig;dict&aelig; ad pr&aelig;dictas: quare componendo, &amp; permu&shy;<lb/>
tando, erunt tandem vt G P, ad P M, ita P M, ad P K, &amp; ita G M, ad M K, <lb/>
a&longs;&longs;ump&longs;imus enim in con&longs;tructione e&longs;&longs;e G M, ad M K, ita F B, ad D, &amp; D, ad <lb/>
B. quare cum &longs;it vt G M, ad M K, ita F B, ad D. &amp; G P, ad P M. &amp; P M, ad <lb/>
K P; erunt per 11. 5. vt G M, ad M K. ita G P, ad P M. &amp; P M, ad P K. &longs;i quis <lb/>
igitur vtens puncto P, tanquam polo, &amp; interuallo P M, circulum de&longs;cribat, <lb/>
omnes angulos reflexionis attinget, quos faciunt line&aelig; product&aelig; &agrave; K, &amp; re&shy;<lb/>
flex&aelig; ab M, ad G. harum enim infinitam multitudinem debemus imaginari <lb/>
&agrave; K, ad infinita puncta M, produci in ambitu illo con&longs;tituta, <expan abbr="re&longs;lecti&qacute;">reflectique</expan>; ad G. <lb/>
&longs;i enim non attingat omnes illos angulos, &longs;equitur, vt &longs;upra, in eodem &longs;emi&shy;<lb/>
circulo <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan> po&longs;&longs;e duas alias rectas proportionales prioribus G M, M K, <lb/>
quod e&longs;t impo&longs;&longs;ibile. </s>
          <s id="s.002114">Porr&ograve; &longs;ub angulo G M K, linearum G M, M K, Iris <lb/>
apparet: quare apparebit etiam &longs;ub alijs omnibus, qu&aelig; &agrave; punctis G K, duci <lb/>
po&longs;&longs;unt ad extremum line&aelig; P M, quia erunt in eadem ratione cum illis; cum <lb/>
non de&longs;inant in eundem <expan abbr="&longs;emicircul&utilde;">&longs;emicirculum</expan>, &longs;ed in ambitum Iridis M N, in quo M, <lb/>
punctum imaginamur circumduci. </s>
          <s id="s.002115">Ex quibus pater P, e&longs;&longs;e polum Iridis, ex <lb/>
quo per puncta M, vbi &longs;it reflexio, de&longs;cribitur arcus attingens omnes Iridis <lb/>
reflexiones.</s>
        </p>
        <pb pagenum="122" xlink:href="009/01/122.jpg"/>
        <p type="main">
          <s id="s.002116"><arrow.to.target n="marg169"/></s>
        </p>
        <p type="margin">
          <s id="s.002117"><margin.target id="marg169"/>168</s>
        </p>
        <p type="main">
          <s id="s.002118">Ibidem <emph type="italics"/>&lpar;Si igitur circumducas &longs;emicircul&ubreve;m, in quo A, circa diametrum in qua <lb/>
G K P, que &agrave; G, K, reflex&aelig; ad id in quo M; in omnibus planis &longs;imiliter &longs;e habebunt, <lb/>&amp; &aelig;qualem facient angulum, qui K M G, &amp; quem etiam facient angulum, qu&aelig; <lb/>
K P, &amp; P M, &longs;uper eam, qu&aelig; G P, &longs;emper &aelig;qualis erit. </s>
          <s id="s.002119">Trianguli igitur &longs;uper eam, <lb/>
qu&aelig; G P, &aelig;quales ei, qui G M P. con&longs;i&longs;tunt. </s>
          <s id="s.002120">horum autem perpendiculares ad idem <lb/>
&longs;ignum cadent eius, qu&aelig; G P, &amp; &aelig;quales erunt, cadunt ad <foreign lang="greek">w,</foreign> centrum erg&ograve; circuli <lb/>
<foreign lang="greek">w</foreign> &longs;emicirculus autem, qui circa M N, ab&longs;ectus e&longs;t ab horizonte&rpar;<emph.end type="italics"/> hac vltima <lb/>
textus parte concludit Iridis portionem &longs;upra horizontem a&longs;tro <expan abbr="ori&etilde;te">oriente</expan> exi&shy;<lb/>
&longs;tentem e&longs;&longs;e &longs;emicirculum, hoc modo; &longs;i igitur imaginatione circumducas <lb/>
&longs;emicirculum, in quo A, circa diametrum horizontis G K P, in hac circum&shy;<lb/>
uolutione du&aelig; line&aelig; G M, M K, in omnibus planis con&longs;titui po&longs;&longs;ibilibus cir&shy;<lb/>
ca pr&aelig;dictam diametrum, qu&aelig; &longs;upra etiam fieri &agrave; triangulis infinitis dixi&shy;<lb/>
mus, &longs;ucce&longs;&longs;iu&egrave; erunt; &longs;iue percurrent &longs;imiliter omnia illa plana, &amp; facient <lb/>
vbique angulum Iridis K M G, eundem: pariter du&aelig; line&aelig; K P, P M, facient <lb/>
vndique eundem angulum K P M. quare omnia triangula in predictis planis <lb/>
imaginata, &amp; <expan abbr="c&otilde;&longs;tituta">con&longs;tituta</expan> &longs;uper linea G P, &longs;imilia ip&longs;i G M P, &amp; &aelig;qualia erunt; <lb/>
&longs;i igitur ab angulis ip&longs;orum, in quibus M, duct&aelig; &longs;int perpendiculares ad la&shy;<lb/>
tus G P, omnes cadent in idem punctum <foreign lang="greek">w,</foreign> vt in figura; <expan abbr="quar&utilde;">quarum</expan> vna erit M <foreign lang="greek">w,</foreign><lb/>
qu&aelig; tamen c&aelig;teras omnes repre&longs;entabit, <expan abbr="eis&qacute;">eisque</expan>; omnibus in volutatione axis <lb/>
G K <foreign lang="greek">w,</foreign> coincidit; erunt autem omnes &aelig;quales, quandoquidem &longs;unt trian&shy;<lb/>
gulorum &aelig;qualium. </s>
          <s id="s.002121"><expan abbr="erunt&qacute;">eruntque</expan>; in eodem eiu&longs;dem circuli plano, &amp; punctum <foreign lang="greek">w,</foreign><lb/>
erit centrum ip&longs;ius. </s>
          <s id="s.002122">&longs;imilia dicta &longs;unt in Halone. </s>
          <s id="s.002123">Cum erg&ograve; ip&longs;ius centrum <lb/>
<foreign lang="greek">w</foreign>, &longs;it in diametro horizontis G K <foreign lang="greek">w</foreign> P O, manife&longs;tum fit portionem eius, qu&aelig; <lb/>
&longs;upra horizontem eminet, e&longs;&longs;e &longs;emicirculum, qui in figura notatur lineis <lb/>
L M N. <!-- KEEP S--></s>
          <s id="s.002124">Atque hoc accidit Sole, vel Luna in horizonte exi&longs;tentibus; quod <lb/>
erat primo loco demon&longs;trandum.</s>
        </p>
        <p type="main">
          <s id="s.002125">Porr&ograve; &longs;ciendum po&longs;&longs;e nos breuius polum pr&aelig;dictum inuenire, &longs;i nimirum <lb/>
<figure id="id.009.01.122.1.jpg" place="text" xlink:href="009/01/122/1.jpg"/><lb/>
ad M, ducatur M P, faciens angulum K P M, &aelig;qua&shy;<lb/>
lem angulo G M K, per 23. primi, erunt enim duo <lb/>
triangula <expan abbr="&aelig;qui&atilde;gula">&aelig;quiangula</expan> G P M, K P M, angulus enim <lb/>
P, e&longs;t communis, angulus ver&ograve; M K P, e&longs;t &aelig;qualis <lb/>
duobus G, &amp; G M K, per 32. primi, ergo etiam <lb/>
duobus ad M, &longs;iue toti G M P, &amp; reliquus K M P, <lb/>
reliquo, quare per 4.6. latera circa angulos &aelig;qua&shy;<lb/>
les proportionalia erunt, &amp; omologa G M, ad M K, ita G P, ad P M, qu&aelig; <lb/>&aelig;qualibus angulis &longs;ubtenduntur. </s>
          <s id="s.002126"><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habebant etiam <lb/>
triangula Ari&longs;t. in figura, de qua paul&ograve; ante dicebam. </s>
          <s id="s.002127">Verba illa <emph type="italics"/>&lpar;Qu&aelig; ali&shy;<lb/>bi quam in &longs;emicirculo constituuntur&rpar;<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/>
tran&longs;lata, nam Gr&aelig;c&egrave; &longs;ic, <foreign lang="greek">ai alloqi toῡ hmikoklnou/ sunistamenai,</foreign> transferenda <lb/>
e&longs;&longs;ent, qu&aelig; in alio circuli loco concurrunt.</s>
        </p>
        <p type="main">
          <s id="s.002128"><arrow.to.target n="marg170"/></s>
        </p>
        <p type="margin">
          <s id="s.002129"><margin.target id="marg170"/>169</s>
        </p>
        <p type="main">
          <s id="s.002130">Ibidem <emph type="italics"/>&lpar;Iterum &longs;it horizon quidem in quo A C. oriatur autem &longs;upra hunc G, <lb/>
axis autem &longs;it nunc in quo G P. <!-- KEEP S--></s>
          <s id="s.002131">Alia igitur omnia &longs;imiliter o&longs;tendentur vt &amp; prius. <lb/>
</s>
          <s id="s.002132">Polus autem circuli, in quo P, erit &longs;ub horizonte eo, in quo A C, eleuato puncto, <lb/>
in quo G. in eadem autem &amp; polus, &amp; centrum circuli, &amp; terminantis nunc ortum, <lb/>
e&longs;t enim i&longs;te, in quo G P. <!-- KEEP S--></s>
          <s id="s.002133">Quoniam autem &longs;upra diametrum, qu&aelig; A C, quod K G, <lb/>
centrum vtique erit &longs;ub horizonte priori eius, in quo A C, in linea K P, in quo <foreign lang="greek">w,</foreign><emph.end type="italics"/>


<pb pagenum="123" xlink:href="009/01/123.jpg"/><figure id="id.009.01.123.1.jpg" place="text" xlink:href="009/01/123/1.jpg"/><lb/>
<emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir&shy;<lb/>
culo, in qua S T, &lpar;nam Q S T, &longs;emicir&shy;<lb/>
culus est, nunc autem inter&longs;ectus e&longs;t ab <lb/>
horizonte A C; <expan abbr="itaq;">itaque</expan> Q S, di&longs;parens erit&rpar; <lb/>
eleuato ip&longs;o Sole&rpar;<emph.end type="italics"/> demon&longs;trat propo&longs;i&shy;<lb/>
tionem &longs;ecundam nimirum Sole &longs;upra <lb/>horizontem eleuato, ambitum Iridis <lb/>
e&longs;&longs;e minorem circuli portionem, &longs;iue <lb/>
&longs;emicirculo minorem. </s>
          <s id="s.002134">&longs;it igitur in fi&shy;<lb/>
gura &longs;uperiori, quam textui <expan abbr="c&otilde;gruen-tem">congruen&shy;<lb/>
tem</expan> re&longs;tituimus, linea A C, horizon&shy;<lb/>
talis, &longs;upra quam Sol &longs;it eleuatus in <lb/>
circulo altitudinis in loco G, axis au&shy;<lb/>
rem coni, quem reflex&egrave; faciunt &longs;it <lb/>
G K <foreign lang="greek">w</foreign> P. alia igitur omnia, qu&aelig; &longs;upra exi&longs;tente in ortu a&longs;tro o&longs;ten&longs;a &longs;unt, hic <lb/>
pariter o&longs;tendi po&longs;&longs;unt, &longs;cilicet Iridem fieri tantum per lineas proportiona&shy;<lb/>
les, &amp; &aelig;quales lineis G M, M K, quia Iris videri nequit, ni&longs;i in tali, ac deter&shy;<lb/>
minata reflexione, &amp; angulo, vt initio &longs;uppo&longs;ui; &amp; quia line&aelig; illis propor&shy;<lb/>
tionales non po&longs;&longs;unt alibi con&longs;titui, quam in ambitu circulari, &amp; in diuer&longs;is <lb/>
planis, &longs;equitur, vt &longs;upra Iridem e&longs;&longs;e circularem M N L; <expan abbr="eius&qacute;">eiusque</expan>; polum P, &amp; <lb/>
centrum <foreign lang="greek">w,</foreign> inueniemus &longs;imiliter in axe G K <foreign lang="greek">w</foreign> P, &amp; quia axis hic &longs;ecat hori&shy;<lb/>
zontem in K, in hac vltima figura propter eleuationem Solis &longs;upra A C, in <lb/>
G, &longs;equitur partem axis, in qua <foreign lang="greek">w,</foreign> &amp; P, exi&longs;tunt, infra horizontem deprimi. <lb/>
</s>
          <s id="s.002135">&amp; quia &lpar;vt pater ex 64. 10. Vitell.&rpar; &amp; P, polus, &amp; centrum <foreign lang="greek">w,</foreign> Iridis, &amp; cen&shy;<lb/>trum K, circuli horizontis, cuius &longs;cilicet diameter e&longs;&longs;et A K S, &amp; Sol, &longs;unt <lb/>
in eadem linea G K <foreign lang="greek">w</foreign> P, &longs;i centrum Iridis <foreign lang="greek">w,</foreign> &longs;it infra horizontem, patet mi&shy;<lb/>
norem circuli portionem, quam &longs;it &longs;emicirculus &longs;upra horizontem eminere, <lb/>
in qua po&longs;ui literas S L T, nam Q S L T R, e&longs;t &longs;emicirculus, cuius pars con&shy;<lb/>
tenta inter duos arcus Q S, &amp; T R, e&longs;t infra horizontem. </s>
          <s id="s.002136">debemus autem <lb/>
hunc &longs;emicirculum, &amp; hanc portionem ip&longs;ius S L T, extantem &longs;upra hori&shy;<lb/>
zontem imaginari erectam e&longs;&longs;e, vt planum ip&longs;ius circuli faciat angulos re&shy;<lb/>
ctos &longs;iue &longs;it perpendiculare cum axe G K P; &amp; <expan abbr="circul&utilde;">circulum</expan> altitudinis A G M N, <lb/>
modo fungi vice horizontis. </s>
          <s id="s.002137">&longs;ic enim &longs;ola portio S L T, appareret nobis, <expan abbr="e&longs;-&longs;et&qacute;">e&longs;&shy;<lb/>
&longs;etque</expan>; rationabiliter con&longs;tituta. </s>
          <s id="s.002138">Ex quibus 2. Ari&longs;t. propo&longs;itio manife&longs;ta e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002139"><arrow.to.target n="marg171"/></s>
        </p>
        <p type="margin">
          <s id="s.002140"><margin.target id="marg171"/>180</s>
        </p>
        <p type="main">
          <s id="s.002141">Ibidem <emph type="italics"/>&lpar;Minima autem cum in meridie, quanto enim &longs;uperius G, tanto infe&shy;<lb/>
rius &amp; polus, &amp; centrum circuli erit&rpar;<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi&shy;<lb/>
rum Sole exi&longs;tente in meridie minimam <expan abbr="omni&utilde;">omnium</expan> e&longs;&longs;e Iridis arcus portionem: <lb/>
ratio autem e&longs;t, quia tunc G, &longs;iue Sol, e&longs;t alti&longs;&longs;imus &longs;upra horizontem, &amp; <lb/>
con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir&shy;<lb/>
culi Iridis portio ab&longs;condetur, &amp; proinde minima apparebit, quod erat vl&shy;<lb/>
timo <expan abbr="dem&otilde;&longs;trandum">demon&longs;trandum</expan>. </s>
          <s id="s.002142">Non me latet has Ari&longs;t. figurationes e&longs;&longs;e apud Olym&shy;<lb/>
piodorum nonnullis obiectionibus obnoxias, &longs;ed cum facil&egrave; dilui po&longs;&longs;int, &amp; <lb/>
etiam &longs;i non diluantur, &longs;aluetur tamen veritas Ari&longs;totelic&aelig; demon&longs;tratio&shy;<lb/>
nis, breuitati &longs;tudens, con&longs;ult&ograve; eas pr&aelig;termitto.</s>
        </p>
        <p type="main">
          <s id="s.002143">Aduertendum pr&aelig;terea Vicomercatum inordinat&egrave; citare librum Dato&shy;<lb/>
rum Euclidis, &amp; <expan abbr="quandoq;">quandoque</expan> etiam mal&egrave; citare Euclidem ip&longs;um. </s>
          <s id="s.002144">peius ver&ograve; <pb pagenum="124" xlink:href="009/01/124.jpg"/>faciunt ij, qui has demon&longs;trationes <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla libri Datorum mentione ex&shy;<lb/>
plicare conantur, cum manife&longs;t&egrave; illo innitantur.</s>
        </p>
        <p type="main">
          <s id="s.002145">C&aelig;terum &longs;i quis breues, ac dilucidas harum rerum demon&longs;trationes re&shy;<lb/>
quirat, is legat 74. 75. 76. propo&longs;itiones 10. Vitell. <!-- REMOVE S-->vel &longs;equentem no&longs;tram <lb/>
de Iride additionem. </s>
          <s id="s.002146">ego enim longiorem hanc, <expan abbr="atq;">atque</expan> impeditam Ari&longs;t. tra&shy;<lb/>
ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e&shy;<lb/>
quutus &longs;um.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002147"><arrow.to.target n="marg172"/></s>
        </p>
        <p type="margin">
          <s id="s.002148"><margin.target id="marg172"/>181</s>
        </p>
        <p type="main">
          <s id="s.002149">Ibidem <emph type="italics"/>&lpar;Quod autem in minoribus quidem diebus ijs, qui po&longs;t &aelig;quinoctium au&shy;<lb/>
tumnale <expan abbr="c&otilde;tingit">contingit</expan> &longs;emper fieri Iridem: in longioribus aurem diebus ijs qui ab &aelig;qui&shy;<lb/>noctio altero, ad &aelig;quinoctium alterum circa meridiem non fit Iris, cau&longs;a est, quia <lb/>
qu&aelig; ad Vr&longs;am &longs;ectiones omnes maiores &longs;unt &longs;emicirculo, &amp; &longs;emper ad maiores quod <lb/>
autem e&longs;t occultum, paruum: qu&aelig; autem ad &aelig;quatoris meridiem &longs;ectiones, qu&aelig; qui&shy;<lb/>
dem &longs;upra &longs;ectio, parua; qu&aelig; autem &longs;ub terra magna, &amp; &longs;emper maiores, qu&aelig; lon&shy;<lb/>
gius. </s>
          <s id="s.002150">quare in ijs, qui ad &aelig;&longs;tiuas ver&longs;iones diebus propter magnitudinem &longs;ectionis, <lb/>
antequam veniat G, ad medium &longs;ectionis, infra iam p&oelig;nitus fit P; propterea quod <lb/>
long&egrave; di&longs;tat &agrave; terra meridies propter magnitudinem &longs;ectionis. </s>
          <s id="s.002151">In ijs autem diebus, <lb/>qui ad hyemales ver&longs;iones, quia non mult&ubreve;μ &longs;unt &longs;upra terram &longs;ectiones circulorum, <lb/>
contrarium nece&longs;&longs;arium fieri, modicum enim eleuato in quo G, in meridie fit Sol&rpar;<emph.end type="italics"/><lb/>
qu&aelig;rit cur po&longs;t &aelig;quinoctium autumnale v&longs;que ad vernum, hoc e&longs;t hyemali <lb/>
tempore, Iris appareat etiam Sole meridiem occupante: reliquo autem <lb/>
tempore &aelig;&longs;tiuo, quod e&longs;t ab &aelig;quinoctio verno ad autumnale appareat tan&shy;<lb/>
tum Sole vel in ortu, aut occa&longs;u exi&longs;tente, vel parum &longs;upra terram &longs;ublato. <lb/>
</s>
          <s id="s.002152">cau&longs;a autem huius refert in &longs;ectiones parallelorum circulorum, quos Sol <lb/>
diurno motu inter <expan abbr="vtrunq;">vtrunque</expan> <expan abbr="tropic&utilde;">tropicum</expan> de&longs;cribit: nam &longs;ectiones parallelorum, <lb/>
qui &longs;unt ad Vr&longs;am, ide&longs;t in parte &longs;ph&aelig;r&aelig; Boreali, qui omnes &longs;unt inter &aelig;qua&shy;<lb/>
torem, &amp; tropicum Cancri; &longs;ectiones inquam horum circulorum, qu&aelig; &longs;unt <lb/>
&longs;upra horizontem, maiores &longs;unt &longs;ectionibus infra horizontem depre&longs;&longs;is, &amp; <lb/>&longs;emper e&ograve; maiores, qu&ograve; propiores &longs;unt Cancro, ita vt magna vald&egrave; &longs;it ea <lb/>
portio, qu&aelig; e&longs;t &longs;upra terram, exigua ver&ograve; admodum, qu&aelig; infra &lpar;intelligan&shy;<lb/>
tur h&aelig;c in &longs;ph&aelig;ra obliqua, cuius polus eleuetur grad. <!-- REMOVE S-->45. circiter&rpar; quare <lb/>
quando a&longs;trum G, con&longs;cenderit meridiem, ade&ograve; P, polus Iridis, &amp; etiam <foreign lang="greek">w,</foreign><lb/>
centrum eius infra terram deprimitur, vt aut nihil, aut in&longs;en&longs;ibile quid de <lb/>
Iridis ambitu &longs;upra terram eleuari po&longs;&longs;it, contrarium accidit in parallelis <lb/>
meridionalibus, quia eorum &longs;ectiones &longs;uperiores &longs;unt &longs;emper inferioribus <lb/>
minores, quapropter etiam &longs;i a&longs;trum ad meridiem eleuetur, parum tamen <lb/>
attollitur, &amp; con&longs;equenter centrum <foreign lang="greek">w,</foreign> Iridis parum infra horizontem <lb/>
de&longs;cendit, ac propterea etiam in meridie pars ip&longs;ius &longs;atis ma&shy;<lb/>
gna con&longs;picitur. </s>
          <s id="s.002153">qu&aelig; omnia adhibita &longs;ph&aelig;ra materia&shy;<lb/>
li, eaque a&longs;tronomic&egrave; ad &longs;uam eleuationem <lb/>
accommodata, nullo negotio li&shy;<lb/>
cebit intueri.</s>
        </p>
        <pb pagenum="125" xlink:href="009/01/125.jpg"/>
        <p type="head">
          <s id="s.002154"><emph type="italics"/>Additio de Iride.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002155">Cvm &longs;uperior Ari&longs;tot. de Iride tractatio ob&longs;cura, ac tricis pluribus <lb/>
impedita eua&longs;erit, <expan abbr="cum&qacute;">cumque</expan>; aliorum etiam demon&longs;trationes aliqua <lb/>ex parte vacillent, vi&longs;um e&longs;t breuiter expeditam, <expan abbr="atq;">atque</expan> ab&longs;olutam <lb/>
ip&longs;ius apponere demon&longs;trationem. </s>
          <s id="s.002156">Cum igitur in c&oelig;le&longs;ti arcu <lb/>
duo poti&longs;&longs;imum &longs;int, qu&aelig; &longs;ui admiratione <expan abbr="Philo&longs;ophor&utilde;">Philo&longs;ophorum</expan> animos in &longs;ui con&shy;<lb/>
templationem alliciant, colores, &longs;cilicet, &amp; figura: nos mirabilem illam co&shy;<lb/>
lorum triadem, tanquam alienam, phy&longs;icis relinquentes, de figura ip&longs;ius iu&shy;<lb/>
re mathematico di&longs;&longs;eremus: rotunditatis &longs;cilicet Iridis cau&longs;am opticis ra&shy;<lb/>
tionibus venabimur, cur aliquando &longs;emicirculus, aliquando &longs;emicirculo mi&shy;<lb/>
nor appareat. </s>
          <s id="s.002157">vt igitur ordine procedamus.</s>
        </p>
        <p type="main">
          <s id="s.002158">Primo loco aduertendum e&longs;t tria ad Iridis vi&longs;ionem e&longs;&longs;e nece&longs;&longs;aria, So&shy;<lb/>
lem, oculum, &amp; nubem tenuem, ac ro&longs;cidam, qu&aelig; &longs;cilicet minutis guttulis <lb/>
iam &longs;cateat; hac enim ratione guttul&aelig; ill&aelig; innumera erunt veluti parua <lb/>
&longs;pecula, qu&aelig; lumen Solis ob paruitatem imperfecto quodam modo repre&shy;<lb/>
&longs;entare po&longs;&longs;int, ex tali enim repre&longs;entatione Iris apparet. </s>
          <s id="s.002159">qu&aelig; tria debent <lb/>
e&longs;&longs;e ita di&longs;po&longs;ita, vt Sol, oculus, &amp; centrum Iridis &longs;int in eadem recta linea <lb/>
con&longs;tituta, <expan abbr="oculus&qacute;">oculusque</expan>; medium locum, inter Solem, &amp; Iridis <expan abbr="c&etilde;trum">centrum</expan> obtineat, <lb/>
vt in prima figura videre e&longs;t, in qua Sol vbi A, oculus in C. nubes ver&ograve; <lb/>
G H L E, in qua apparet Iris in arcu E B F, quem debemus concipere e&longs;&longs;e <lb/>
in rece&longs;&longs;u, vt pictores aiunt, depictum. </s>
          <s id="s.002160">i. </s>
          <s id="s.002161">non in hoc &longs;itu, &amp; ouali figura, &longs;ed <lb/>
<figure id="id.009.01.125.1.jpg" place="text" xlink:href="009/01/125/1.jpg"/><lb/>
e&longs;&longs;e perfect&egrave; &longs;emicircularem, <expan abbr="habere&qacute;">habereque</expan>; talem po&longs;itionem, vt pars ip&longs;ius B F, <lb/>
&longs;it citra chartam eleuata, <expan abbr="ip&longs;i&qacute;">ip&longs;ique</expan>; perpendicularis, pars ver&ograve; E B, vltra pagi&shy;


<pb pagenum="126" xlink:href="009/01/126.jpg"/>nam rect&agrave; recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>
linea horizontali A C L, in quo &longs;itu oculo C, totus ex oppo&longs;ito direct&egrave; &longs;pe&shy;<lb/>
ctaretur, non aliter ac Iridem ip&longs;am con&longs;picere &longs;olemus. </s>
          <s id="s.002162">Quod autem ne&shy;<lb/>
ce&longs;&longs;aria &longs;it nubes ro&longs;cida, pulcherrima hac experientia <expan abbr="c&otilde;probatur">comprobatur</expan>: &longs;i enim <lb/>
in Sole po&longs;iti ore aquam efflantes leui a&longs;pergine aerem Soli, ac nobis ad&shy;<lb/>
uer&longs;um irroremus, actutum Iridis arcum guttulis illis, quamuis volitanti&shy;<lb/>bus inh&aelig;rentem &longs;umma voluptate &longs;pectabimus. </s>
          <s id="s.002163">Quod pr&aelig;terea oculus no&shy;<lb/>
&longs;ter, cum Iridem videmus, medius &longs;it inter Solem, &amp; Iridis centrum, expe&shy;<lb/>
rimento diuturno, manife&longs;tum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002164">Secund&ograve;, notandum e&longs;t, arcum per reflexionem fieri: quod quidem pri&shy;<lb/>
mo eadem experientia, qua pr&aelig;cedens conclu&longs;io confirmatur: deinde, quia <lb/>
Iridem &longs;emper in oppo&longs;ita Soli, ac nobis parte <expan abbr="c&otilde;&longs;picimus">con&longs;picimus</expan>; quemadmodum <lb/>
in eadem figura o&longs;tenditur, quod aliter qu&agrave;m per reflexionem fieri nequit.</s>
        </p>
        <p type="main">
          <s id="s.002165">Terti&ograve;, &longs;ciendum e&longs;t ex Maurolyco, &amp; 10. Bapti&longs;ta Porta, tantam e&longs;&longs;e di&shy;<lb/>
&longs;tantiam C D, ab oculo ad centrum arcus, quanta e&longs;t altitudo, &longs;eu &longs;emidia&shy;<lb/>
meter D B, ob&longs;eruarunt enim ip&longs;i angulos D C B, &amp; C B D, e&longs;&longs;e &longs;emirectos, <lb/>
&amp; proinde &aelig;quales, &amp; con&longs;equenter duo latera C D, D B, trianguli C D B, <lb/>
per 6. 1. &aelig;qualia &longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.002166">Quart&ograve;, con&longs;iderandum e&longs;t lineas A B, A D, ob maximam Solis ab Iride <lb/>
di&longs;tantiam in&longs;en&longs;ibiliter differre; &amp; ide&ograve; &longs;upponi po&longs;&longs;unt &aelig;quidi&longs;tantes, <lb/>
quare angulus A B C, qui &aelig;qualis e&longs;t alterno B C D, &longs;umi pote&longs;t ab&longs;que vllo <lb/>
errore pro &longs;emirecto. </s>
          <s id="s.002167">hic autem angulus A B C, dicitur angulus reflexionis <lb/>
Iridis, &longs;ub tali enim reflexione lumen Solis occurrens nubi in B, reflectitur <lb/>
ad oculum C.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002168">Quint&ograve;, &longs;equitur ex pr&aelig;dictis arcum videri &longs;emper &longs;ub &longs;tato, ac determi&shy;<lb/>
nato reflexionis angulo, &longs;cilicet &longs;ub &longs;emirecto, <expan abbr="neq;">neque</expan> po&longs;&longs;e per alium videri. <lb/>
</s>
          <s id="s.002169">quod etiam probari pote&longs;t ex Ari&longs;t. quia nimirum videmus arcum apparere <lb/>
con&longs;imiliter in ambitu circulari, erg&ograve; nece&longs;&longs;ari&ograve; apparebit <expan abbr="vbiq;">vbique</expan> in toto il&shy;<lb/>
lo ambitu per con&longs;imilem reflexionem, &longs;iue per &aelig;quales reflexionis angulos, <lb/>
pro quibus omnibus vnus cernitur in figura angulus A B C.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002170">Sext&ograve;, ad Iridis vi&longs;ionem, pr&aelig;ter ea, requiri aeris rorantis multiplica&shy;<lb/>
tionem; &longs;icuti enim nebulam videre nequimus, ni&longs;i aer exhalatione illa in&shy;<lb/>
fectus multus &longs;it ante oculum no&longs;trum: &longs;ic etiam exi&longs;timo ad Iridis appari&shy;<lb/>
tionem, opus e&longs;&longs;e plurima nube rore&longs;cente, vt ex multiplicatione guttula&shy;<lb/>
rum, quarum ali&aelig; po&longs;t alias &longs;int, totus tandem Iris appareat. </s>
          <s id="s.002171">quia pauc&aelig; <lb/>
guttul&aelig;, etiam &longs;i qu&aelig;libet illarum aliquid Iridis efficeret, ob paruitatem <lb/>
tamen illarum, nulla arcus figura &longs;pectaretur. </s>
          <s id="s.002172">Quod &longs;i ante oculum pluri&shy;<lb/>
m&aelig; &longs;int in toto aere ali&aelig; po&longs;t alias, tunc &longs;e mutu&ograve; iuuantes, obiectum &longs;atis <lb/>&longs;en&longs;ibile, quod Iris e&longs;t, efficere po&longs;&longs;unt. </s>
          <s id="s.002173">Adde, quod etiam ex tali guttula&shy;<lb/>
rum multiplicatione, aer opacatur, qu&aelig; opacatio plurimum iuuat ad Iri&shy;<lb/>
dem &longs;pectandam.</s>
        </p>
        <p type="main">
          <s id="s.002174">Septim&ograve;, Iridis rotundationis cau&longs;am ex pr&aelig;mi&longs;&longs;is con&longs;tare poti&longs;&longs;imum <lb/>
ex duabus. </s>
          <s id="s.002175">prim&ograve;, ex angulo reflexionis determinato, qui videlicet &longs;it fer&egrave; <lb/>
&longs;emirectus. </s>
          <s id="s.002176">&longs;ecund&ograve;, ex paribus di&longs;tantijs C D, D B, huiu&longs;modi enim plures <lb/>
anguli, qui ad Iridem &longs;unt nece&longs;&longs;arij &lpar;debent enim &longs;ingul&aelig; Iridis partes &longs;ub <lb/>
huiu&longs;modi angulo repre&longs;entari&rpar; non po&longs;&longs;unt aliter qu&agrave;m in gyrum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>,


<pb pagenum="127" xlink:href="009/01/127.jpg"/>quem gyrum optim&egrave; concipiemus, &longs;i imaginemur triangulum A B C, cir&shy;<lb/>
cumuerti circa lineam horizontalem A C L, fixam, tanquam circa axem. </s>
          <s id="s.002177">in <lb/>
hac enim conuer&longs;ione angulus Iridis B, de&longs;cribet circulum, qui erit Iris, &amp; <lb/>pertran&longs;ibit omnes angulos, qui in tali Solis, oculi, ac nubis &longs;itu, arcum ef&shy;<lb/>
ficere &longs;unt idonei.</s>
        </p>
        <p type="main">
          <s id="s.002178">Sed contra pr&aelig;dicta de angulo Iridis determinato eadem nobis obijcies, <lb/>
qu&aelig; nos &longs;upra ad finem numeri 164. Ari&longs;t. &amp; alijs obiecimus, plures <expan abbr="nimi-r&utilde;">nimi&shy;<lb/>
rum</expan> po&longs;&longs;e con&longs;titui angulos &aelig;quales angulo Iridis B, in plano trianguli A B C, <lb/>
qui non &longs;int in eodem orbe con&longs;tituti, in quo &longs;unt omnes anguli B. <!-- KEEP S--></s>
          <s id="s.002179">Iridem <lb/>
reflectentes, <expan abbr="quiq;">quique</expan> reflexionem faciant ad eundem oculum C, vnde &longs;equitur <lb/>
pr&aelig;dictam Iridis altitudinem non e&longs;&longs;e, vti diximus, determinatam, cum <lb/>
po&longs;&longs;it angulus B, alios &longs;ibi &aelig;quales tam &longs;upra, qu&agrave;m infra habere, qua ra&shy;<lb/>
tione deberet etiam Iris, &amp; altius, &amp; inferius apparere.</s>
        </p>
        <p type="main">
          <s id="s.002180">Huic dubitationi re&longs;pondeo, quod quamuis huiu&longs;modi plures anguli <lb/>
&aelig;quales fiant, non tamen Iridis generationi ob&longs;tant, quinim&ograve; ad eam vald&egrave; <lb/>
nece&longs;&longs;arij &longs;unt; <expan abbr="c&utilde;">cum</expan> enim omnes &longs;int in <expan abbr="circunfer&etilde;tia">circunferentia</expan> circuli A C D B, quar&shy;<lb/>
t&aelig; figur&aelig; num. </s>
          <s id="s.002181">164. qu&aelig; modo in&longs;picienda e&longs;t, vt &longs;unt in ea anguli A D C, <lb/>
A B C; qu&aelig; circunferentia ob &longs;ui circuli immen&longs;itatem ad &longs;en&longs;um e&longs;t in&longs;tar <lb/>
line&aelig; rect&aelig;, fit vt omnes illi anguli t&agrave;m qui &longs;upra B, qu&agrave;m qui infra &longs;unt, <lb/>
&longs;int quoad &longs;en&longs;um in eadem recta C D B, ante vi&longs;um proten&longs;a, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; Iris, qui <lb/>
apparet in D, &amp; in B, &amp;c. </s>
          <s id="s.002182">ob medij rorantis multiplicationem vnam <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> <lb/>
oculo Iridem repre&longs;entet. </s>
          <s id="s.002183">locus tamen, in quo apparet, &amp; vbi e&longs;t angulus <lb/>
B, qui propri&egrave; Iridis appellatur, e&longs;t in tanta di&longs;tantia &agrave; centro arcus, quan&shy;<lb/>
ta e&longs;t ab eodem centro ad oculum, vt &longs;upra dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002184">Quod ver&ograve; alibi extra circunferentiam illius circuli, poni nequeat angu&shy;<lb/>lus &aelig;qualis angulo B, pr&aelig;&longs;entis figur&aelig;, qui reflectat ad C. patet &longs;ic, &longs;it enim <lb/>
angulus A N O, &longs;emirectas, &amp; ide&ograve; &aelig;qualis angulo B, erunt ergo B C, N O, <lb/>
parallel&aelig;, quare non concurrent amb&aelig; ad C, &longs;ed altera ad E, altera ver&ograve; ad <lb/>
O, qu&aelig; propterea oculo in O, po&longs;ito Iridem efficeret, non autem oculo C: <lb/>
<expan abbr="&longs;ic&qacute;">&longs;icque</expan>; oculus C, &amp; oculus O, viderent diuer&longs;os arcus. </s>
          <s id="s.002185">eodem modo o&longs;tendi <lb/>
pote&longs;t, <expan abbr="neq;">neque</expan> in &longs;uperiori parte nubis vbi P, con&longs;titui po&longs;&longs;e angulum &aelig;qualem <lb/>
angulo B, qui oculo C, Iridem valeat o&longs;tendere. </s>
          <s id="s.002186">Ex quibus &longs;atis patefacta <lb/>
e&longs;t cau&longs;a rotunditatis arcus, angulus &longs;cilicet determinatus cum di&longs;tantia&shy;<lb/>
rum C D, D B, paritate, necnon cum medij rorantis &longs;ufficienti multiplica&shy;<lb/>
tione. </s>
          <s id="s.002187">Ex his etiam Iridis definitio in hunc modum concinnari pote&longs;t, Iris <lb/>
e&longs;t arcus multicolor in nube rorida, ex radiorum Solis, aut Lun&aelig; reflexio&shy;<lb/>ne &longs;ub &longs;tatuto angulo effulgens.</s>
        </p>
        <p type="main">
          <s id="s.002188">Octauo loco Problemata nonnulla re&longs;oluemus.</s>
        </p>
        <pb pagenum="128" xlink:href="009/01/128.jpg"/>
        <p type="head">
          <s id="s.002189"><emph type="italics"/>Problema Primum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002190">Cur oriente, aut occumbente Sole, Iris &longs;emicirculus e&longs;t?</s>
        </p>
        <p type="main">
          <s id="s.002191">Cau&longs;a huius h&aelig;c e&longs;t; &longs;upra enim dictum e&longs;t, in omni Iridis appari&shy;<lb/>
tione tria h&aelig;c, Solem, oculum, &amp; Iridis centrum e&longs;&longs;e in eadem re&shy;<lb/>
cta linea, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in linea A C D, pr&aelig;cedentis figur&aelig;, cum igitur Sol <lb/>
tam oriens, quam occidens &longs;it in horizonte, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in A, horizontis <lb/>
puncto, &longs;imiliter oculus &longs;it in C, horizontis centro, con&longs;ectarium e&longs;t, cen&shy;<lb/>
trum etiam Iridis D, e&longs;&longs;e pariter in horizontis &longs;uperficie, quare &longs;ecabitur <lb/>
ab horizonte per centrum, vnde etiam &longs;equitur ip&longs;ius Iridis portionem <lb/>
E B F, qu&aelig; &longs;upra horizontem extat e&longs;&longs;e &longs;emicirculum. </s>
          <s id="s.002192">Quod &longs;i horizon non <lb/>
ob&longs;taret, <expan abbr="integr&utilde;">integrum</expan> Iris compleret orbem, <expan abbr="cerneretur&qacute;">cernereturque</expan>; toto ambitu B F M E.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.002193">An <expan abbr="quando&qacute;">quandoque</expan>; maior &longs;emicirculo appareat?</s>
        </p>
        <p type="head">
          <s id="s.002194"><emph type="italics"/>Problema Secundum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002195">Maior quidem, im&ograve; etiam integer circulus, &longs;ed ab oculo in &longs;ummitate <lb/>
montis con&longs;tituto, <expan abbr="Sole&qacute;">Soleque</expan>; iam multum eleuato videri pote&longs;t, vt in <lb/>
hac &longs;ecunda figura cernitur, vbi euecto Sole ad locum E, &longs;upra horizontem <lb/>
<figure id="id.009.01.128.1.jpg" place="text" xlink:href="009/01/128/1.jpg"/><lb/>
A B, poterit oculus in vertice montis C, po&longs;itus Iridem F G H I, comple&shy;<lb/>
tam videre, quia infra lineam E C D, in qua exi&longs;tunt Sol, oculus, &amp; Iridis <lb/>
centrum, nihil e&longs;t ad partes D, vbi nubes irrorat, quod Iridis apparitioni <lb/>
&longs;it impedimento.</s>
        </p>
        <pb pagenum="129" xlink:href="009/01/129.jpg"/>
        <p type="head">
          <s id="s.002196">Cur quanto Sol altior e&longs;t, tanto inferior, <expan abbr="tanto&qacute;">tantoque</expan>; &longs;emicir&shy;<lb/>
culo minor appareat Iris?<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.002197"><emph type="italics"/>Problema Tertium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002198">Qvia eleuato Sole ad E, vt in hac tertia figura, nece&longs;&longs;ario centrum Iri&shy;<lb/>
dis D, infra horizontem A B, deprimetur, cum in eadem recta E C D. <lb/>
<figure id="id.009.01.129.1.jpg" place="text" xlink:href="009/01/129/1.jpg"/><lb/>
Sol E, oculus C, <expan abbr="centr&utilde;&qacute;">centrumque</expan>; Iridis D, exi&longs;tant: vnde nece&longs;&longs;ari&ograve; &longs;equitur Iridis <lb/>
portionem F G H, &longs;upra horizontem extantem, &longs;emicirculo minorem e&longs;&longs;e.</s>
        </p>
        <p type="head">
          <s id="s.002199">Cur Iris in&longs;equentes fugit, fugientes ver&ograve; in&longs;equitur?</s>
        </p>
        <p type="head">
          <s id="s.002200"><emph type="italics"/>Problema Quartum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002201">Pvlcherrimum i&longs;tud ph&aelig;nomenon primus omnium Philippus Mend&aelig;us <lb/>
Platonis di&longs;cipulus, ob&longs;eruauit; Cuius ratio e&longs;t, quia arcus non ni&longs;i &longs;ub <lb/>determinato angulo, di&longs;tantijs etiam illis paribus, ac tandem idonea a&longs;per&shy;<lb/>
gino&longs;&aelig; nubis multiplicatione &longs;pectatur; quapropter &longs;i quis per aerem to&shy;<lb/>
tum <expan abbr="vndiq;">vndique</expan> ro&longs;cidum inambulet, <expan abbr="vbicunq;">vbicunque</expan> illi anguli, <expan abbr="ill&aelig;&qacute;">ill&aelig;que</expan>; conditiones af&shy;<lb/>
fuerint Iris apparebit: quod &longs;i in aperta planitie obequitans arcu con&longs;pe&shy;<lb/>
cto, additis equo calcaribus citatum cur&longs;um ad eum direxerit, fugientem <lb/>
ante &longs;e Iridem &longs;umma cum iucunditate mirabitur.</s>
        </p>
        <p type="main">
          <s id="s.002202">Ex dictis pr&etail;tere a patet, &longs;impliciter nimis eos hallucinari, qui exi&longs;timant <lb/>
in plana, aut concaua nubis &longs;uperficie Iridem tantummodo apparere po&longs;&longs;e.</s>
        </p>
        <pb pagenum="130" xlink:href="009/01/130.jpg"/>
        <p type="head">
          <s id="s.002203">Cur lunares Irides fiunt rariores?</s>
        </p>
        <p type="head">
          <s id="s.002204"><emph type="italics"/>Problema Quintum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002205">Qvoniam iuxta plenilunia tantum, cum &longs;cilicet Luna plurimo lumine <lb/>
abundat, quod Iridem efficere debet, contingunt: pr&aelig;terea quia cum <lb/>
lunare lumen debile &longs;it, ni&longs;i ali&aelig; cau&longs;&aelig; perfect&aelig; admodum concur&shy;<lb/>
rant, quod rar&ograve; accidit, Iris nullo modo effulgere valet. </s>
          <s id="s.002206">Hactenus de Iri&shy;<lb/>
dis figura &longs;it &longs;atis.</s>
        </p>
        <p type="head">
          <s id="s.002207"><emph type="italics"/>Summa 2. cap. 5. De Parelio.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002208"><arrow.to.target n="marg173"/></s>
        </p>
        <p type="margin">
          <s id="s.002209"><margin.target id="marg173"/>182</s>
        </p>
        <p type="main">
          <s id="s.002210">Textus <emph type="italics"/>&lpar;Fiunt autem vt diximus, &amp; Virg&aelig;, &amp; Parelia in ortu, &amp; oc&shy;<lb/>
ca&longs;u, &amp; nec &longs;upra Solem, nec infra, &longs;ed ex lateribus, nec prop&egrave; admo&shy;<lb/>
dum, nec procul omnin&ograve;. </s>
          <s id="s.002211">propinquam enim concretionem Sol di&longs;&longs;oluit: <lb/>
&longs;i autem procul ab&longs;it, a&longs;pectus non reflectetur, &longs;i enim &agrave; paruo &longs;peculo <lb/>
procul protenditur imbecillus fit. </s>
          <s id="s.002212">quare, &amp; Coron&aelig; &egrave; regione Solis non fiunt. </s>
          <s id="s.002213">&longs;i igi&shy;<lb/>
tur &longs;upra fuerit, &amp; proxima; eam Sol di&longs;&longs;oluet: &longs;i ver&ograve; procul a&longs;pectus minor <lb/>quam vt reflecti po&longs;&longs;it in Solem non incidet; &agrave; latere autem fieri pote&longs;t, vt &longs;pecu&shy;<lb/>
lum ita distet &agrave; Sole, vt non &longs;oluatur, &amp; a&longs;pectus totus ad eum perueniat, eo quod <lb/>
ad terram dum fertur, qua&longs;i per immen&longs;um feratur, peruenire nequeat. </s>
          <s id="s.002214">&longs;ub Sole <lb/>
ver&ograve; non fit, quia cum ad terram propius acce&longs;&longs;erit &agrave; Sole di&longs;&longs;oluitur, cum medium <lb/>
c&oelig;li tenuerit a&longs;pectus di&longs;trahitur. </s>
          <s id="s.002215">omnin&ograve; ne &agrave; latere quidem, Sole medium c&oelig;li <lb/>tenente, efficitur, quia a&longs;pectus &longs;ub terram non fertur, quare exiguus ad &longs;peculum <lb/>producitur, &amp; qui reflectitur pror&longs;us imbecillis redditur&rpar;<emph.end type="italics"/> ibi <emph type="italics"/>&lpar;propinquam enim <lb/>
concretionem Sol di&longs;&longs;oluit&rpar;<emph.end type="italics"/> rationes, quas affert circa Parelia videntur &lpar;auda&shy;<lb/>
cter loquar&rpar; admodum debiles. </s>
          <s id="s.002216">pr&aelig;&longs;ens ea e&longs;t, vt Parelium non fiat prop&egrave; <lb/>
Solem, quia illa nubis concretio, qu&aelig; Parelio nece&longs;&longs;aria e&longs;t, nequit adeo So&shy;<lb/>
li propinqua e&longs;&longs;e, quia nimirum Sol ob propinquitatem eam di&longs;&longs;olueret; &longs;ed <lb/>
quis non videt eam nubem, quam vulg&ograve; exi&longs;timamus e&longs;&longs;e Soli propinquam, <lb/>
&longs;eu qua&longs;i inter nos, &amp; Solem tantum, im&ograve; etiam minus aliquando &agrave; Sole ve&shy;<lb/>
r&egrave; di&longs;tare, qu&agrave;m alia, qu&agrave;m vulg&ograve; remotiorem &agrave; Sole putabimus? </s>
          <s id="s.002217">pr&aelig;te&shy;<lb/>
rea omnes nubes no&longs;tri horizontis re vera &aelig;quidi&longs;tare &agrave; Sole certum e&longs;t, ob <lb/>
maximam enim Solis di&longs;tantiam totus no&longs;ter horizon phy&longs;icus e&longs;t in&longs;en&longs;i&shy;<lb/>
bilis quantitatis ad Solem, &amp; vnius puncti vicem gerit.</s>
        </p>
        <p type="main">
          <s id="s.002218">Ibi ver&ograve; <emph type="italics"/>&lpar;Si autem procul ab&longs;it, &amp;c.&rpar;<emph.end type="italics"/> reddit rationem, cur parelium non <lb/>
appareat in nube &agrave; Sole valde remota &longs;ecundum vulgarem &aelig;&longs;timationem, <lb/>
vnde vulgarem etiam rationem affert, ait enim, nubem illam e&longs;&longs;e veluti &longs;pe&shy;<lb/>
culum Solis repre&longs;entatiuum, &longs;peculum autem t&agrave;m long&egrave; &agrave; Sole po&longs;itum, <lb/>
reddi debile, &amp; proptere&aacute; non po&longs;&longs;e Solis imaginem referre: Ver&ugrave;m ratio <lb/>
h&aelig;c nulla e&longs;&longs;e videtur, quis enim ignorat non propterea e&longs;&longs;e remotius &agrave; So&shy;<lb/>
le, quamuis maiorem habere videatur &agrave; Sole lateralem di&longs;tantiam, vt pau&shy;<lb/>
l&ograve; ante dixi? </s>
          <s id="s.002219">Eandem rationem illi dubitationi accommodat, cur <expan abbr="neq;">neque</expan> vi&shy;<lb/>
deatur &longs;upra Solem, quamuis non ei quadret, pote&longs;t enim aliqua nubes vi&shy;


<pb pagenum="131" xlink:href="009/01/131.jpg"/>deri &longs;upra Solem, qu&aelig; tamen remotior &longs;it &agrave; Sole, quam illa, in qua Parelium <lb/>
gignitur. </s>
          <s id="s.002220">Ait po&longs;tea <emph type="italics"/>&lpar;A latere autem, &amp;c.&rpar;<emph.end type="italics"/> cur appareat in nube fatis Soli <lb/>
&agrave; latere vicina, in di&longs;tantiam &agrave; Sole refert: &longs;ed qu&aelig; dudum dicta &longs;unt, i&longs;tud <lb/>
<expan abbr="quoq;">quoque</expan> refellunt. </s>
          <s id="s.002221">Verba illa <emph type="italics"/>&lpar;Eo quod ad terram dum fertur qua&longs;i per immen&longs;um <lb/>
feratur, peruenire nequeat&rpar;<emph.end type="italics"/> videntur alieno loco dicta; &longs;imilia pr&aelig;cedentibus <lb/>
&longs;unt reliqua, pr&aelig;&longs;ertim qu&aelig; ibi <emph type="italics"/>&lpar;Sub Sole ver&ograve; non fit, quia cum ad terram pro&shy;<lb/>
pius acce&longs;&longs;erit&rpar;<emph.end type="italics"/> cur non videatur infra Solem, rationem quandam, qu&aelig; fort&egrave; <lb/>
inanis e&longs;t reddit; nunquid enim non po&longs;&longs;umus tam infra Solem, qu&agrave;m &longs;upra <lb/>
ita &longs;peculum accommodare, vt Solem no&longs;tris vi&longs;ibus remittat? </s>
          <s id="s.002222">huic cert&egrave; <lb/>
Optice tota repugnat. </s>
          <s id="s.002223">Cum igitur Mathematica ratione h&aelig; rationes non <lb/>
con&longs;i&longs;tant, alias alij excogitent. </s>
          <s id="s.002224">Mirum tamen e&longs;t, omnes, quos viderim <lb/>
commentatores, eas tanquam optimas admittere.</s>
        </p>
        <p type="head">
          <s id="s.002225"><emph type="italics"/>In quarto Meteororum nihil Mathematicum occurrit.<emph.end type="italics"/></s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002226"><emph type="italics"/>EX LIB. PRIMO DE ANIMA.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002227"><arrow.to.target n="marg174"/></s>
        </p>
        <p type="margin">
          <s id="s.002228"><margin.target id="marg174"/>183</s>
        </p>
        <p type="main">
          <s id="s.002229">Tex. 11. <emph type="italics"/>&lpar;Videtur autem non &longs;olum ip&longs;um quid e&longs;t cogno&longs;cere vtile e&longs;&longs;e <lb/>
ad cogno&longs;cendas cau&longs;as accidentium &longs;ub&longs;tantijs: &longs;icut in Mathemati&shy;<lb/>cis quid rectum, &amp; quid obliquum, aut quid linea, &amp; planum, ad co&shy;<lb/>gno&longs;cendum quot rectis, trianguli anguli &longs;unt &aelig;quales&rpar;<emph.end type="italics"/> quid &longs;it <expan abbr="vnum-quodq;">vnum&shy;<lb/>
quodque</expan> ex pr&aelig;dictis patet tum ex definitionibus primi Elem. tum ex com&shy;<lb/>
mentarijs ip&longs;arum; quamuis autem ibi non definiatur <expan abbr="rect&utilde;">rectum</expan>, nec obliquum <lb/>
in genere, definitur tamen linea recta, &amp; obliqua, &amp; plana &longs;uperficies, &longs;iue <lb/>
planum, ex quibus facil&egrave; definitio recti, &amp; obliqui colligi pote&longs;t: qu&aelig; defi&shy;<lb/>
nitiones nece&longs;&longs;ari&aelig; &longs;unt ad cogno&longs;cendum quot rectis angulis &aelig;quales &longs;int <lb/>tres anguli cuiu&longs;uis trianguli. </s>
          <s id="s.002230">vide qu&aelig; de hac &aelig;qualitate &longs;crip&longs;i lib, primo <lb/>
Priorum, &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002231"><arrow.to.target n="marg175"/></s>
        </p>
        <p type="margin">
          <s id="s.002232"><margin.target id="marg175"/>184</s>
        </p>
        <p type="main">
          <s id="s.002233">Tex. 13. <emph type="italics"/>&lpar;Si igitur e&longs;t aliqua anim&aelig; operatio, aut pa&longs;&longs;io propria, continget vti&shy;<lb/>
que ip&longs;am &longs;eparari: &longs;i ver&ograve; nulla e&longs;t propria ip&longs;ius non vtique erit &longs;eparabilis. </s>
          <s id="s.002234">&longs;ed <lb/>
&longs;icut recto in quantum rectum multa accidunt, vt tangere &aelig;neam &longs;ph&aelig;ram &longs;ecun&shy;<lb/>
dum punctum, non tamen tanget hoc, rectum ip&longs;um &longs;eparatum: in&longs;eparabile enim, <lb/>
&longs;i quidem cum corpore quodam &longs;emper e&longs;t&rpar;<emph.end type="italics"/> Propo&longs;itio 2. tertij Elem. &pacute;robat li&shy;<lb/>
<figure id="id.009.01.131.1.jpg" place="text" xlink:href="009/01/131/1.jpg"/><lb/>
neam rectam, duo qu&aelig;libet puncta <expan abbr="qu&atilde;tumuis">quantumuis</expan> pro&shy;<lb/>
pinqua in circuli ambitu a&longs;&longs;umpta coniungentem <lb/>
cadere intra circulum. </s>
          <s id="s.002235">v. <!-- REMOVE S-->g. <!-- REMOVE S-->puncta A B, quantum&shy;<lb/>uis &longs;ibi inuicem propinqua unerint, attamen &longs;i line a <lb/>
A B, ea coniungat, ip&longs;a cadet intra circulum, &amp; <lb/>
veluti chorda &longs;ubtendet arcum A B, quantulum&shy;<lb/>
cunque. </s>
          <s id="s.002236">ex qua demon&longs;tratione colligitur in corol&shy;<lb/>
lario eius lineam rectam tangentem circulum ip&shy;<lb/>
&longs;um in vnico puncto tangere. </s>
          <s id="s.002237">v. <!-- REMOVE S-->g. <!-- REMOVE S-->rectam C D, tan&shy;<lb/>
gere circulum in puncto E. &longs;i enim dixeris tangere <lb/>
in duobus admodum propinquis, vt in E F, tunc non erit amplius tangens, <lb/>
&longs;ed &longs;ecans, quia vt modo dixi, pars line&aelig; rect&aelig;, qu&aelig; <expan abbr="c&otilde;iungeret">coniungeret</expan> puncta E F,


<pb pagenum="132" xlink:href="009/01/132.jpg"/>intra circulum per &longs;ecundam pr&aelig;allegatam caderet, quod e&longs;t ab&longs;urdum, <lb/>
quia contra hypothe&longs;im, cum &longs;upponamus illam &longs;ol&ugrave;m tangere, non autem <lb/>
&longs;ecare circulum. </s>
          <s id="s.002238">Ex hac Euclidis doctrina Theodo&longs;ius primo &longs;ph&aelig;ricorum, <lb/>
propo&longs;itione 3. probat planum, &longs;iue &longs;uperficiem planam tangere &longs;ph&aelig;ram <lb/>
in vnico puncto, vt hoc loco innuit Philo&longs;ophus. <!-- KEEP S--></s>
          <s id="s.002239">probat autem hac fer&egrave; ra&shy;<lb/>
<figure id="id.009.01.132.1.jpg" place="text" xlink:href="009/01/132/1.jpg"/><lb/>
tione. </s>
          <s id="s.002240">&longs;it &longs;ph&aelig;ra A B C, qu&aelig; tangat quodpiam planum <lb/>
in duobus punctis A, B, &longs;i fieri pote&longs;t. </s>
          <s id="s.002241">per qu&aelig; duo pun&shy;<lb/>
cta intelligatur ducta recta linea A B, intelligatur <expan abbr="eti&atilde;">etiam</expan> <lb/>
circulus A B C, qui &longs;ecet &longs;ph&aelig;ram per centrum C. &amp; <lb/>
per puncta A, B, ergo ex demon&longs;tratis ab Euclide li&shy;<lb/>
nea A B, qu&aelig; coniungit puncta A B, cadet intra pr&aelig;di&shy;<lb/>
ctum circulum; &longs;ed linea h&aelig;c e&longs;t in plano tangente ex <lb/>
&longs;uppo&longs;itione, circulus ver&ograve; in &longs;ph&aelig;ra; erg&ograve; cum linea <lb/>
cadat intra circulum, cadet etiam nece&longs;&longs;ari&ograve; planum <lb/>
in quo e&longs;t linea, &amp; cum linea cadat intra circulum, cadet etiam nece&longs;&longs;ari&ograve; <lb/>
intra &longs;ph&aelig;ram; <expan abbr="idem&qacute;">idemque</expan>; faciet planum, quod eam nece&longs;&longs;ari&ograve; &longs;equatur, erg&ograve; <lb/>
planum &longs;ecat &longs;ph&aelig;ram, non autem tangit, quod e&longs;t ab&longs;urdum, quia contra <lb/>
hypothe&longs;im, &longs;upponunt autem Mathematici, entia h&aelig;c mathematica e&longs;&longs;e <lb/>
perfecta, qualia in &longs;ublunaribus fort&egrave; non reperiuntur; &aelig;nea enim &longs;ph&aelig;ra <lb/>
nulla erit perfect&egrave; rotunda, vel planum aliquod perfect&egrave; complanatum, vt <lb/>
ip&longs;i &longs;upponunt, e&ograve; quod materi&aelig; imperfectio, ac ruditas id nequaquam pa&shy;<lb/>
tiatur. </s>
          <s id="s.002242">quare cum huiu&longs;modi entia non reperiantur ab&longs;tracta ab impura hac <lb/>
materia, nullum erit inquit Ari&longs;t. ab&longs;tractum planum, quod po&longs;&longs;it mathe&shy;<lb/>
matic&egrave;, <expan abbr="atq;">atque</expan> ade&ograve; in vnico puncto mathematico &longs;ph&aelig;ram tangere. </s>
          <s id="s.002243"><expan abbr="hucu&longs;q;">hucu&longs;que</expan> <lb/>
nece&longs;&longs;aria &longs;unt mathematica ad huius loci <expan abbr="intelligenti&atilde;">intelligentiam</expan>. </s>
          <s id="s.002244">ex quibus ea etiam, <lb/>
qu&aelig; ad phy&longs;icum &longs;pectant manife&longs;ta fiunt, nimirum &longs;icut entia mathemati&shy;<lb/>
ca &agrave; materia non exi&longs;tunt &longs;eparata, quia &longs;ic nullam haberent operationem; <lb/>
ita etiam anima, &longs;i nullam habet propriam operationem non exi&longs;tet &agrave; cor&shy;<lb/>
pore &longs;eparata.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002245"><emph type="italics"/>Ex Secundo de Anima.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002246"><arrow.to.target n="marg176"/></s>
        </p>
        <p type="margin">
          <s id="s.002247"><margin.target id="marg176"/>185</s>
        </p>
        <p type="main">
          <s id="s.002248">Tex. 12. <emph type="italics"/>&lpar;Non enim &longs;olum ip&longs;um, quod &longs;it, oportet definitiuam rationem <lb/>o&longs;tendere, &longs;icut plures definitionum dicunt, &longs;ed &amp; cau&longs;am ine&longs;&longs;e, &amp; ap&shy;<lb/>
parere. </s>
          <s id="s.002249">nunc autem, vt conclu&longs;iones rationes definitionum &longs;unt, vt quid <lb/>
tetragoni&longs;mus? </s>
          <s id="s.002250">&aelig;quale altera parte longiori rectangulum &aelig;quilaterum <lb/>
e&longs;&longs;e, talis autem definitio ratio conclu&longs;ionis. </s>
          <s id="s.002251">dicens autem, quod tetragoni&longs;mus e&longs;t <lb/>
medij inuentio rei cau&longs;am dicit&rpar;<emph.end type="italics"/> aggre&longs;&longs;urus Ari&longs;t. anim&aelig; definitionem pr&aelig;&shy;<lb/>
mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, qu&aelig; explicat &longs;olum rei <lb/>
e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram ver&ograve;, qu&aelig; pr&aelig;te&shy;<lb/>
rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram&shy;<lb/>
que autem exemplo Geometrico explicat.</s>
        </p>
        <p type="main">
          <s id="s.002252">In cap. igitur de relatione plura &longs;crip&longs;i de tetragoni&longs;mo, &longs;eu quadratio&shy;<lb/>
ne circuli, qu&aelig; huc &longs;pectant. </s>
          <s id="s.002253">propterea nunc tantum propria huius loci <expan abbr="de-clar&atilde;da">de&shy;<lb/>
claranda</expan> re&longs;tant. </s>
          <s id="s.002254">loquitur igitur hic Philo&longs;ophus non de quadratione circuli,<pb pagenum="133" xlink:href="009/01/133.jpg"/>&longs;ed figur&aelig; rectiline&aelig; illius, qu&aelig; dicitur Altera parte longior, qualis e&longs;t pr&aelig;&shy;<lb/>
&longs;ens figura A B C D, cuius quadrand&aelig; ratio e&longs;t huiu&longs;modi. </s>
          <s id="s.002255">per 13. 6. inue&shy;<lb/>
<figure id="id.009.01.133.1.jpg" place="text" xlink:href="009/01/133/1.jpg"/><lb/>
niatur recta linea media proportionalis inter <lb/>
duo latera figur&aelig; A B, B C, <expan abbr="ea&qacute;">eaque</expan>; &longs;it B D, in &longs;e&shy;<lb/>
quenti figura. </s>
          <s id="s.002256">e&longs;&longs;e autem mediam proportio&shy;<lb/>
nalem nihil aliud e&longs;t quam ita e&longs;&longs;e A B, ad B D, <lb/>
&longs;icut B D, ad B C. <expan abbr="dicitur&qacute;">diciturque</expan>; media proportio&shy;<lb/>
nalis, quia in hac habitudine medium locum obtinet. </s>
          <s id="s.002257">quadratum autem li&shy;<lb/>
ne&aelig; B D, &aelig;quale e&longs;t rectangulo dato A B C D, per 17.6. Inuentio porr&ograve; hu&shy;<lb/>
ius medi&aelig; proportionalis, quia facilis e&longs;t, &amp; &longs;citu iucunda, eam &longs;ic habeto. <lb/>
<figure id="id.009.01.133.2.jpg" place="text" xlink:href="009/01/133/2.jpg"/><lb/>
accipe duo latera A B, &amp; B C, <expan abbr="quadr&atilde;di">quadrandi</expan> rectan&shy;<lb/>
guli, <expan abbr="ea&qacute;">eaque</expan>; in directum con&longs;titue, vt vnicam re&shy;<lb/>
ctam con&longs;tituant A C, vt apparet in figura; de&shy;<lb/>
inde diui&longs;a tota A C, bifariam in E, facto cen&shy;<lb/>
tro in E, de&longs;cribe &longs;emicirculum &longs;uper lineam <lb/>
A C, demum &agrave; puncto B, in quo duo latera con&shy;<lb/>
iunguntur, erigatur linea perpendicularis <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>
ad periph&aelig;riam, qu&aelig; &longs;it B D. h&aelig;c enim B D, e&longs;t media proportionalis inter <lb/>
latera A B, B D, quam nimirum habitudinem habet A B, ad B D, eam quo&shy;<lb/>
que obtinet B D, ad B C. <!-- KEEP S--></s>
          <s id="s.002258">Quadratum igitur huius B D, hoc e&longs;t quadratum, <lb/>cuius quatuor latera &longs;int &aelig;qualia line&aelig; B D, quale e&longs;t pr&aelig;&longs;ens, &aelig;quale erit <lb/>
<figure id="id.009.01.133.3.jpg" place="text" xlink:href="009/01/133/3.jpg"/><lb/>
dato &longs;uperiori rectangulo A B C D, <expan abbr="atq;">atque</expan> hoc modo per&shy;<lb/>
acta erit quadratio, &longs;eu tetragoni&longs;mus dati quadrilateri <lb/>
A B C D. <!-- KEEP S--></s>
          <s id="s.002259">Vides igitur, qua ratione quadratum con&longs;ti&shy;<lb/>
tuatur &aelig;quale dato quadrilatero; &amp; qua rationem inuen&shy;<lb/>
tio illius medi&aelig; proportionalis &longs;it cau&longs;a quadratur&aelig; re&shy;<lb/>
ctanguli, &amp; proinde &longs;i quis dicat quadrationem hanc e&longs;&longs;e <lb/>
effectionem rectanguli &aelig;quilateri, ide&longs;t quadrati, &aelig;qualis dato quadrilate&shy;<lb/>
ro, hic definitionem formalem &longs;olum afferet: qu&aelig; definitio, vt dixit in Lo&shy;<lb/>
gicis, e&longs;t in&longs;tar conclu&longs;ionis. </s>
          <s id="s.002260">&longs;i quis ver&ograve; dicat tetragoni&longs;mum hunc quadri&shy;<lb/>
lateri dati e&longs;&longs;e medi&aelig; pr&aelig;dict&aelig; inuentionem cau&longs;alem afferet definitionem, <lb/>
cum rei cau&longs;am dicat. </s>
          <s id="s.002261">Aduerte 10. Grammaticum immerit&ograve; accu&longs;are Ale&shy;<lb/>
xandrum, quod dicat quadrationem hanc per inuentionem medi&aelig; propor&shy;<lb/>
tionalis tradi in 2. Elem. nam ver&egrave; in 14. 2. traditur talis inuentio, quam&shy;<lb/>uis enim ibi nulla fiat expre&longs;&longs;a mentio huiu&longs;modi medi&aelig;, in ip&longs;a tamen ea <lb/>
reperitur, ac per eam figur&aelig; rectiline&aelig; quadrantur: quod patet ex figura <lb/>
14. pr&aelig;dict&aelig;, qu&aelig; eadem e&longs;t cum figura 13. 6. qua docemur pr&aelig;dictam in&shy;<lb/>
uentionem.</s>
        </p>
        <p type="main">
          <s id="s.002262"><arrow.to.target n="marg177"/></s>
        </p>
        <p type="margin">
          <s id="s.002263"><margin.target id="marg177"/>186</s>
        </p>
        <p type="main">
          <s id="s.002264">Tex. 86. <emph type="italics"/>&lpar;Acutum mouet &longs;en&longs;um in tempore pauco mult&ugrave;m: graue autem in <lb/>multo par&ugrave;m; non igitur velox e&longs;t acutum, graue autem tardum, ed &longs;it illius qui&shy;<lb/>
dem propter velocitatem motus huiu&longs;modi, huius autem propter tarditatem&rpar;<emph.end type="italics"/> vide <lb/>
qu&aelig; de hac re primo topic. </s>
          <s id="s.002265">cap. 13. dicta &longs;unt, illa enim omnia in hunc lo&shy;<lb/>
cum quadrant. </s>
          <s id="s.002266">Verum occurrit illa dubitatio; quod cum Ari&longs;t. ibi dicat <lb/>
<emph type="italics"/>&lpar;Vox acuta quidem velox&rpar;<emph.end type="italics"/> hic autem <emph type="italics"/>&lpar;Non igitur velox e&longs;t acutum<emph.end type="italics"/>&rpar; repugnan&shy;<lb/>
tia dicere videtur. </s>
          <s id="s.002267">cui dubitationi &longs;ic occurrendum; vt dicamus ibi Philo&shy;<lb/>&longs;ophum dicere vocem acutam e&longs;&longs;e velocem, quatenus acumen vocis oritur <pb pagenum="134" xlink:href="009/01/134.jpg"/>ex velocitate motus aerem impellentis. </s>
          <s id="s.002268">hic ver&ograve; di&longs;tinguere acutum &agrave; ve&shy;<lb/>
loci, tanquam effectum &agrave; cau&longs;a.</s>
        </p>
        <p type="main">
          <s id="s.002269"><arrow.to.target n="marg178"/></s>
        </p>
        <p type="margin">
          <s id="s.002270"><margin.target id="marg178"/>187</s>
        </p>
        <p type="main">
          <s id="s.002271">Tex. 159. <emph type="italics"/>&lpar;Apparent autem, &amp; fal&longs;a, de quibus &longs;imul exi&longs;timationem veram <lb/>habet, vt apparet &longs;ol vnius pedis, per&longs;ua&longs;um autem e&longs;t, eum maiorem e&longs;&longs;e habitata&rpar;<emph.end type="italics"/><lb/>
habitata, ide&longs;t terra habitata. </s>
          <s id="s.002272">Vide, qu&aelig; cap. 3. &longs;umm&aelig; 1. primi Meteor. <lb/>
<!-- KEEP S--></s>
          <s id="s.002273">Item capite 5. &longs;umm&aelig; 2. de Solis magnitudine &longs;crip&longs;i, ea enim huic loco <lb/>
abund&egrave; &longs;atisfaciunt.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002274"><emph type="italics"/>Ex Tertio de Anima.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002275"><arrow.to.target n="marg179"/></s>
        </p>
        <p type="margin">
          <s id="s.002276"><margin.target id="marg179"/>188</s>
        </p>
        <p type="main">
          <s id="s.002277">Tex. 21. <emph type="italics"/>&lpar;Vt incommen&longs;urabile, &amp; diameter&rpar;<emph.end type="italics"/> vide, qu&aelig; de incom&shy;<lb/>
men&longs;uratione diametri, &amp; co&longs;t&aelig; &longs;cripta &longs;unt lib. 1. Priorum, cap. <lb/>
23. vnde &longs;atis huic loco fieri pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002278"><arrow.to.target n="marg180"/></s>
        </p>
        <p type="margin">
          <s id="s.002279"><margin.target id="marg180"/>189</s>
        </p>
        <p type="main">
          <s id="s.002280">Tex 25. <emph type="italics"/>&lpar;Punctum autem, &amp; omnis diui&longs;io, &amp; &longs;ic indiui&longs;ibile mon&shy;<lb/>&longs;tratur &longs;icut priuatio&rpar;<emph.end type="italics"/> punctum enim cum &longs;it terminus line&aelig;, e&longs;t negatio vl&shy;<lb/>
terioris line&aelig; <emph type="italics"/>&lpar;Et omnis diui&longs;io&rpar;<emph.end type="italics"/> innuit his verbis pr&aelig;ter punctum, lineam <lb/>
etiam, &amp; &longs;uperficiem, nam quemadmodum punctus oritur ex diui&longs;ione li&shy;<lb/>
ne&aelig;, ita linea ex diui&longs;ione &longs;uperficiei, &amp; &longs;uperficies ex diui&longs;ione corporis. <lb/>
</s>
          <s id="s.002281">&amp; quamuis punctum, linea, &longs;uperficies, &longs;int indiui&longs;ibilia, mon&longs;trantur ta&shy;<lb/>
men quatenus &longs;unt priuationes, &longs;eu negationes, illud vlterioris line&aelig;, i&longs;ta <lb/>
vlterioris &longs;uperficiei, h&aelig;c tandem vlterioris corporis.</s>
        </p>
        <p type="main">
          <s id="s.002282"><arrow.to.target n="marg181"/></s>
        </p>
        <p type="margin">
          <s id="s.002283"><margin.target id="marg181"/>190</s>
        </p>
        <p type="main">
          <s id="s.002284">Tex. 32. <emph type="italics"/>&lpar;Sit igitur vt A, quidem album, ad B, quod nigrum; &longs;ic C, ad D; qua&shy;<lb/>
re &amp; permutatim&rpar;<emph.end type="italics"/> ide&longs;t, quare &amp; permutando &lpar;vt aiunt Geometr&aelig;&rpar; erit vt <lb/>
A, ad C, ita B, ad D, hunc argumentandi modum &agrave; permutata proportio&shy;<lb/>
ne explicaui in primo Po&longs;ter. cap. 5. tex. <!-- REMOVE S-->13. dicitur etiam alterna ratio; <lb/>
&amp; definitur ab Euclide definitione 12, 5.<!-- KEEP S--></s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002285"><emph type="italics"/>Ex Libro de Sen&longs;u.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002286"><arrow.to.target n="marg182"/></s>
        </p>
        <p type="margin">
          <s id="s.002287"><margin.target id="marg182"/>191</s>
        </p>
        <p type="main">
          <s id="s.002288">Cap, 6. <emph type="italics"/>&lpar;Et qui in Die&longs;i &longs;onus latet, quamuis continuum exi&longs;tentem audit <lb/>omnem cantum, di&longs;tantia enim eius ad extremos &longs;onos latet&rpar;<emph.end type="italics"/> quid &longs;it <lb/>
Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. tex. <!-- REMOVE S-->38. cum <lb/>
autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>
mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>
tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>
ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latet inter extrema illius.</s>
        </p>
        <p type="main">
          <s id="s.002289"><arrow.to.target n="marg183"/></s>
        </p>
        <p type="margin">
          <s id="s.002290"><margin.target id="marg183"/>192</s>
        </p>
        <p type="main">
          <s id="s.002291">Cap. 8. <emph type="italics"/>&lpar;<expan abbr="Vnumquodq;">Vnumquodque</expan> magis e&longs;t &longs;entire &longs;implex exi&longs;tens, qu&agrave;m mixtum, velut <lb/>
vinum non temperatum, qu&agrave;m temperatum; &amp; mel, &amp; colorem, &amp; neten &longs;olam. <lb/>
</s>
          <s id="s.002292">qu&agrave;m in diapa&longs;on, quia ob&longs;curant &longs;e inuicem&rpar;<emph.end type="italics"/> nete apud veteres mu&longs;icos erat <lb/>
in mu&longs;icis in&longs;trumentis omnium chordarum acuti&longs;&longs;ima, cuiu&longs;modi apud <lb/>
nos e&longs;t, quam vulg&ograve; canto appellant. </s>
          <s id="s.002293">Hypate ver&ograve; erat chorda omnium <lb/>
graui&longs;&longs;ima, qualis e&longs;t ea, quam modo Ba&longs;&longs;o vocant. </s>
          <s id="s.002294">h&aelig; du&aelig; &longs;imul pul&longs;at&aelig; <lb/>edebant con&longs;onantiam, qu&aelig; Diapa&longs;on dicitur, &amp; vulg&ograve; octaua. </s>
          <s id="s.002295">ex quibus <lb/>
&longs;en&longs;us verberum Ari&longs;t. manife&longs;tus e&longs;t.</s>
        </p>
        <pb pagenum="135" xlink:href="009/01/135.jpg"/>
        <p type="main">
          <s id="s.002296"><arrow.to.target n="marg184"/></s>
        </p>
        <p type="margin">
          <s id="s.002297"><margin.target id="marg184"/>193</s>
        </p>
        <p type="main">
          <s id="s.002298">Eodem cap. <emph type="italics"/>&lpar;Velut Diapa&longs;on, &amp; Diapente&rpar;<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>
&longs;on, explicaui in primo Po&longs;ter. tex. <!-- REMOVE S-->1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/>
<figure id="id.009.01.135.1.jpg" place="text" xlink:href="009/01/135/1.jpg"/><lb/>
bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>
3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s>
          <s id="s.002299">v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;int du&aelig; <lb/>chord&aelig; &aelig;qualis cra&longs;&longs;itiei, <expan abbr="atq;">atque</expan> &aelig;qu&egrave; ten&longs;&aelig;: vna <lb/>
tamen habeat ad alteram proportionem &longs;e&longs;&shy;<lb/>
quialteram, vt in figura apparet; &longs;i &longs;imul pul&shy;<lb/>
&longs;entur, edent con&longs;onantiam Diapente. <!-- KEEP S--></s>
          <s id="s.002300">vulg&ograve; autem quinta.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002301"><emph type="italics"/>Ex Libro de Memoria, &amp; remini&longs;centia.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002302"><arrow.to.target n="marg185"/></s>
        </p>
        <p type="margin">
          <s id="s.002303"><margin.target id="marg185"/>194</s>
        </p>
        <p type="main">
          <s id="s.002304">Cap. 1. <emph type="italics"/>&lpar;Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales&rpar;<emph.end type="italics"/> ide&longs;t <lb/>
&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>
les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>
          <s id="s.002305">lege annotata primo <lb/>
Po&longs;ter. &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002306"><arrow.to.target n="marg186"/></s>
        </p>
        <p type="margin">
          <s id="s.002307"><margin.target id="marg186"/>195</s>
        </p>
        <p type="main">
          <s id="s.002308">Cap. 3. <emph type="italics"/>&lpar;Sunt facil&egrave; remini&longs;cibilia, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> habent ordinationem aliquam, <lb/>
vt mathemata&rpar;<emph.end type="italics"/> h&etail;c Philo&longs;ophus dicens &longs;pectabat ad mirabilem illam, ac per&shy;<lb/>
petuam de mon&longs;trationum connexionem, qua Geometr&aelig; omnes, &amp; pr&aelig;ci&shy;<lb/>
pu&egrave; Euclides opera &longs;ua ab initio ad finem v&longs;que, diuino plan&egrave; ingenij acu&shy;<lb/>
mine deduxerunt.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002309"><emph type="italics"/>Ex Libro de Somnijs.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002310"><arrow.to.target n="marg187"/></s>
        </p>
        <p type="margin">
          <s id="s.002311"><margin.target id="marg187"/>196</s>
        </p>
        <p type="main">
          <s id="s.002312">Cap. 2. <emph type="italics"/>&lpar;Cur autem fallimur, cau&longs;a e&longs;t, quoniam non &longs;olum cum &longs;en&longs;ibile <lb/>
mouetur apparent qu&aelig;libet, &longs;ed etiam cum &longs;en&longs;us ip&longs;e mouetur, &longs;i eodem <lb/>
modo moueatur, quemadmodum &agrave; &longs;en&longs;ibili. </s>
          <s id="s.002313">dico autem velut terra vi&shy;<lb/>
detur nauigantibus moueri, dummodo vi&longs;us ab alio&rpar;<emph.end type="italics"/> reddit rationem, <lb/>
cur nauigantibus videatur terra ip&longs;a moueri, ac retrocedere, non autem <lb/>ip&longs;i nauigantes, quin potius ip&longs;i &longs;ibi &longs;tare videantur. </s>
          <s id="s.002314">cau&longs;am igitur eam e&longs;&shy;<lb/>
&longs;e ait, quia ex motu nauis, terra ip&longs;a manente, accidit, vt eodem modo im&shy;<lb/>
mutetur &longs;en&longs;us vi&longs;us, ac &longs;i terra ip&longs;a moueretur, vi&longs;us ver&ograve; quie&longs;ceret. <lb/>
</s>
          <s id="s.002315">At cur eodem modo afficitur &longs;en&longs;us? </s>
          <s id="s.002316">Per&longs;pectiui rationem e&longs;&longs;e dicunt, quia <lb/>
ea, qu&aelig; circa oculum &longs;unt, vt nauis, &amp; ea, qu&aelig; in naui &longs;unt, non mutant &longs;i&shy;<lb/>
tum re&longs;pectu oculi, quemadmodum facerent, &longs;i nos ip&longs;i &longs;ine naui progrede&shy;<lb/>
remur. </s>
          <s id="s.002317">arbores autem, &amp; reliqua, qu&aelig; in terra &longs;unt, variant &longs;itum re&longs;pectu <lb/>
oculi, non &longs;ecus, ac &longs;i ip&longs;&aelig; arbores retro deferrentur. </s>
          <s id="s.002318">propterea igitur vi&longs;us <lb/>
tunc arbores remeare iudicat, quia qu&aelig; circa oculum &longs;unt re&longs;pectu ip&longs;ius <lb/>
oculi non mouentur, &longs;iue non variant &longs;itum ad ip&longs;um; ex variatione enim <lb/>
&longs;itus rei re&longs;pectu oculi, percipimus cuiu&longs;uis rei localem motum.</s>
        </p>
        <p type="main">
          <s id="s.002319"><arrow.to.target n="marg188"/></s>
        </p>
        <p type="margin">
          <s id="s.002320"><margin.target id="marg188"/>197</s>
        </p>
        <p type="main">
          <s id="s.002321">Cap. 3. <emph type="italics"/>&lpar;Quemadmodum igitur, &longs;i quem lateat &longs;uppo&longs;itus oculo digitus, non <lb/>&longs;olum apparebit, &longs;ed etiam putabitur duo, quod e&longs;t vnum. </s>
          <s id="s.002322">Si ver&ograve; non lateat appa&shy;<lb/>
rebit quidem, non putabitur tamen&rpar;<emph.end type="italics"/> e&longs;t h&aelig;c optica deceptio, qu&aelig; tunc accidit, <lb/>
cum aliquod obiectum intuentes, interim digito alterum oculum &longs;ur&longs;um <lb/>
pellimus, ita vt oculi propterea varient &longs;itum re&longs;pectu obiecti, &longs;iue non eo&shy;


<pb pagenum="136" xlink:href="009/01/136.jpg"/>dem &longs;itu vterque obiectum intueatur, hoc e&longs;t, vt optici aiunt, axes vi&longs;uales <lb/>
non amplius concurrunt &longs;imul in rem vi&longs;am. </s>
          <s id="s.002323">Vnde &longs;equitur &longs;peciem rei in&shy;<lb/>
tentionalem oculis vario &longs;itu affectis imprimi, ac proinde eam eundem &longs;i&shy;<lb/>
tum in vtroque oculo minim&egrave; obtinere, &longs;ed ea, qu&aelig; oculo &agrave; &longs;uo naturali <lb/>&longs;tatu dimoto accidit ab altera alterius oculi differt; quapropter vario <lb/>etiam modo, duplici nimirum, obiectum repre&longs;entant. </s>
          <s id="s.002324">atque h&aelig;c <lb/>
ip&longs;a cau&longs;a e&longs;t, cur illud, quod vnum tantum e&longs;t, duo tamen <lb/>
emoto oculorum altero, videatur. </s>
          <s id="s.002325">Vide Alhaze&shy;<lb/>
num lib. 3. propo&longs;it. </s>
          <s id="s.002326">11. &amp; 12. &amp; infra <lb/>
Problem. 7. &longs;ectionis 31.</s>
        </p>
      </chap>
      <pb pagenum="137" xlink:href="009/01/137.jpg"/>
      <chap>
        <p type="head">
          <s id="s.002327">EX PRIMO <lb/>
METAPHYSICAE.</s>
        </p>
        <p type="main">
          <s id="s.002328"><arrow.to.target n="marg189"/></s>
        </p>
        <p type="margin">
          <s id="s.002329"><margin.target id="marg189"/>198</s>
        </p>
        <p type="main">
          <s id="s.002330">Capite 1. <emph type="italics"/>&lpar;Circa Aegyptum Mathematic&aelig; artes constitut&aelig; &longs;unt; illic <lb/>
enim gens Sacerdotum vacare permittitur&rpar;<emph.end type="italics"/> Notanda maxim&egrave; no&shy;<lb/>
bilis Mathematicarum origo, cum ab Aegyptiorum Sacerdoti&shy;<lb/>
bus te&longs;te Philo&longs;opho fuerint adinuent&aelig;, quibus occa&longs;ionem pr&aelig;&shy;<lb/>
buit anniuer&longs;aria agrorum ob Nili innundationem, diui&longs;io: cum enim iam <lb/>
perplures dimetiendorum agrorum rationes repert&aelig; fui&longs;&longs;ent, Sacerdotes <lb/>ip&longs;i, quibus per otium licebat, illarum praxium demon&longs;trationes c&oelig;perunt <lb/>
perue&longs;tigare, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; paulatim po&longs;tea Geometria amplius exculta adoleuit; <lb/>
qu&aelig; deinde ij&longs;dem ad res a&longs;tronomicas per&longs;crutandas <expan abbr="adium&etilde;to">adiumento</expan> fuit, <expan abbr="hac&qacute;">hacque</expan>; <lb/>
ratione reliquas etiam in mathematicas inciderunt.</s>
        </p>
        <p type="main">
          <s id="s.002331"><arrow.to.target n="marg190"/></s>
        </p>
        <p type="margin">
          <s id="s.002332"><margin.target id="marg190"/>199</s>
        </p>
        <p type="main">
          <s id="s.002333">Cap. 2. <emph type="italics"/>&lpar;Sicut de pr&aelig;&longs;tigio&longs;is, qu&aelig; per &longs;e mouentur, illi qui nondum &longs;peculati <lb/>
&longs;unt cau&longs;am<emph.end type="italics"/>&rpar; verbis illis &lpar;<emph type="italics"/>Qu&aelig; per &longs;emouentur<emph.end type="italics"/>&rpar; vnica dictio <expan abbr="Gr&aelig;care&longs;p&otilde;det">Gr&aelig;ca re&longs;pondet</expan>, <lb/>
Automata. <!-- KEEP S--></s>
          <s id="s.002334">erant autem Automata apud veteres Gr&etail;cos machin&aelig; qu&etail;dam, <lb/>
qu&aelig; &agrave; Mathematicis Mechanic&aelig; artis occultis quibu&longs;dam ingenijs, ea arte <lb/>
con&longs;truebantur, vt &agrave; &longs;eip&longs;is de loco ad locum, ac &longs;i viu&aelig; e&longs;&longs;ent &longs;pont&egrave; pro&shy;<lb/>grederentur; vnde, &amp; automata, qua&longs;i &longs;pontanea dicebantur. </s>
          <s id="s.002335">Extat adhuc <lb/>
de huiu&longs;modi machinis liber Heronis Alexandrini, quem nuper ex gr&aelig;co <lb/>
latinum reddidit docti&longs;&longs;imus Abbas Gua&longs;tallenfis. </s>
          <s id="s.002336">de huiu&longs;modi artificio&longs;is <lb/>
operibus, quibus &longs;&aelig;p&egrave; pri&longs;ci ita admirationi fuere, vt pr&aelig;&longs;tigia qu&aelig;dam ar&shy;<lb/>
tificium ignorantibus, viderentur, intelligit hoc loco Ari&longs;t.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002337"><arrow.to.target n="marg191"/></s>
        </p>
        <p type="margin">
          <s id="s.002338"><margin.target id="marg191"/>200</s>
        </p>
        <p type="main">
          <s id="s.002339">Cap. 3. &lpar;<emph type="italics"/>Aut de &longs;ol&longs;titijs<emph.end type="italics"/>&rpar; quid &longs;ol&longs;titium, cur dicatur &longs;ol&longs;titium, &amp; cur Sol <lb/>
in <expan abbr="vtroq;">vtroque</expan> topico, quoad dierum incrementum, ac decrementum, &amp; quoad <lb/>
eleuationem eius, aut depre&longs;&longs;ionem meridianam, videatur moras trahere, <lb/>
quamuis no&longs;trum &longs;it explicare, ob rei tamen facilitatem omittantur. </s>
          <s id="s.002340">Hoc <lb/>
tantum &longs;cias velim &longs;ol&longs;titiorum cau&longs;am e&longs;&longs;e Zodiaci ad Tropicos longio&shy;<lb/>
rem adh&aelig;&longs;ionem, ide&longs;t, qu&ograve;d Zodiacus prop&egrave; contactum tropicorum ab ijs <lb/>
parum recedat, cum ergo Sol motu proprio &longs;emper per Zodiacum inam&shy;<lb/>
bulet, fit vt ip&longs;e <expan abbr="quoq;">quoque</expan> pariter modicum &agrave; tropicis remoueatur, im&ograve; pluri&shy;<lb/>
mum &longs;ecus illos incedat, ita vt eo tempore, quo ad eos paulatim accedit, <lb/>
aut ab eis paulatim recedit, qua&longs;i &longs;tare, &longs;iue quie&longs;cere apud eo&longs;dem videa&shy;<lb/>
tur: <expan abbr="atq;">atque</expan> hinc etiam quantitas <expan abbr="dier&utilde;">dierum</expan>, ac noctium videatur fer&egrave; nihil variari; <lb/>&amp; noua eleuatio, aut depre&longs;&longs;io Solis &longs;upra horizontem nulla fer&egrave; appareat.</s>
        </p>
        <p type="main">
          <s id="s.002341"><arrow.to.target n="marg192"/></s>
        </p>
        <p type="margin">
          <s id="s.002342"><margin.target id="marg192"/>201</s>
        </p>
        <p type="main">
          <s id="s.002343">Ibidem &lpar;<emph type="italics"/>Aut de diametri incommen&longs;urabilitate, admirabile enim omnibus vi&shy;<lb/>
detur, &longs;i quid, cum non &longs;it minimum non men&longs;uretur, decet autem in contrarium, <lb/>&amp; in melius &longs;ecundum prouerbium con&longs;umare, quemadmod&ubreve;m in his fit, cum di&longs;cant, <lb/>nihil enim magis vir Geometricus admiraretur, qu&agrave;m &longs;i diameter commen&longs;urabi&shy;<lb/>lis fieret<emph.end type="italics"/>&rpar; vide qu&aelig; de hac commen&longs;urabilitate &longs;crip&longs;i lib. 1. Priorum, &longs;ect. </s>
          <s id="s.002344">1. <lb/>
cap. 1. Videtur inquit mirum &agrave; principio Geometriam aggredienti diame&shy;<lb/>
trum, &amp; latus eiu&longs;dem quadrati non commen&longs;urari, cum in neutro eorum <lb/>
detur minimum, &longs;eu indiui&longs;ibile, videtur enim omne diui&longs;ibile po&longs;&longs;e men&longs;u&shy;


<pb pagenum="138" xlink:href="009/01/138.jpg"/>rari. </s>
          <s id="s.002345">po&longs;tea tamen cum in Geometria ver&longs;atus fuerit, maxim&egrave; admirare&shy;<lb/>
tur, &longs;i audiret diametrum e&longs;&longs;e lateri commen&longs;urabilem.</s>
        </p>
        <p type="main">
          <s id="s.002346"><arrow.to.target n="marg193"/></s>
        </p>
        <p type="margin">
          <s id="s.002347"><margin.target id="marg193"/>202</s>
        </p>
        <p type="main">
          <s id="s.002348">Summa 2. cap. 3. &lpar;<emph type="italics"/>Pythagorici primi Mathematicis operam dedere, h&aelig;c pr&aelig;po&shy;<lb/>
nebant, &amp; in cis enutriti, eorum principia, entium <expan abbr="quoq;">quoque</expan> cunctorum putant e&longs;&longs;e <lb/>
principia<emph.end type="italics"/>&rpar; vtinam no&longs;trates Philo&longs;ophi Pythagoricos imitarentur; enimue&shy;<lb/>
r&ograve; mult&ograve; melius &amp; &longs;ibi, &amp; Philo&longs;ophi&aelig; con&longs;ulerent. </s>
          <s id="s.002349">At ver&ograve; non &longs;ine ma&shy;<lb/>
gno artium, <expan abbr="atq;">atque</expan> di&longs;ciplinarum omnium di&longs;pendio &agrave; plurimis hac tempe&shy;<lb/>
&longs;tate de&longs;pectui habentur; &longs;ed quid mirum cum quas &longs;cientiarum omnium <lb/>alumni Pythagorei omnibus &longs;cientijs anteferebant; eas no&longs;tri &longs;eculi quam&shy; <lb/>
plures omnibus alijs facultatibus po&longs;thabeant.</s>
        </p>
        <p type="main">
          <s id="s.002350"><arrow.to.target n="marg194"/></s>
        </p>
        <p type="margin">
          <s id="s.002351"><margin.target id="marg194"/>203</s>
        </p>
        <p type="main">
          <s id="s.002352">Tex. 47. &lpar;<emph type="italics"/>Qui Geometriam di&longs;cit aliqua pr&aelig;&longs;cire contingit<emph.end type="italics"/>&rpar; ide&longs;t definitio&shy;<lb/>
nes, po&longs;tulata, axiomata, qu&aelig; &longs;unt tria principiorum genera, ex quibus to&shy;<lb/>
ta Geometria deducitur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002353"><emph type="italics"/>Ex Secundo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002354"><arrow.to.target n="marg195"/></s>
        </p>
        <p type="margin">
          <s id="s.002355"><margin.target id="marg195"/>204</s>
        </p>
        <p type="main">
          <s id="s.002356">Tex. 14. &lpar;<emph type="italics"/>Quantam ver&ograve; vim con&longs;uetudo habeat, leges declarant, in qui&shy;<lb/>
bus fabulo&longs;a, ac puerilia plus po&longs;&longs;unt propter con&longs;uetudinem, qu&agrave;m &longs;i <lb/>
ea cogno&longs;ceremus<emph.end type="italics"/>&rpar; per leges intelligit cantilenas illas, quas vete&shy;<lb/>
res Mu&longs;ici leges appellabant, e&ograve; qu&ograve;d eas &longs;olas, c&aelig;teris abroga&shy;<lb/>
tis liceret lata lege decantari. </s>
          <s id="s.002357">Vide declarationem problematis 15. &amp; 28. <lb/>
&longs;ect. </s>
          <s id="s.002358">19. <expan abbr="problemat&utilde;">problematum</expan> vbi <expan abbr="tanqu&atilde;">tanquam</expan> in proprio loco i&longs;ta fu&longs;ius pertractabuntur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002359"><emph type="italics"/>Ex Tertio Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002360"><arrow.to.target n="marg196"/></s>
        </p>
        <p type="margin">
          <s id="s.002361"><margin.target id="marg196"/>205</s>
        </p>
        <p type="main">
          <s id="s.002362">Tex. 3. Verba huius textus, cum &longs;atis per&longs;picua &longs;int, ac parum ma&shy;<lb/>
thematicis indigeant, omittenda duxi. </s>
          <s id="s.002363">Quod ad mathematicas <lb/>
attinet, ait, eas non demon&longs;trare, nec per cau&longs;am finalem, nec <lb/>
per efficientem &lpar;quod intelligendum e&longs;t de Mathematicis puris, <lb/>
&amp; &longs;peculatiuis nam mathematic&aelig; practic&aelig; reliquas etiam cau&longs;as, efficien&shy;<lb/>
tem, &amp; finalem nece&longs;&longs;ari&ograve; habere debent, quapropter &longs;ophi&longs;ta quidam no&shy;<lb/>
mine Ari&longs;tippus, eas irridebat, <expan abbr="atq;">atque</expan> adeo illiberalibus, ac &longs;edentarijs arti&shy;<lb/>
bus po&longs;thabebat, qu&aelig; cau&longs;am efficientem, quia &longs;cilicet operantur, &amp; fina&shy;<lb/>
lem &longs;cilicet qu&aelig;&longs;tum &longs;ibi proponunt. </s>
          <s id="s.002364">fuit autem i&longs;te ex Plutarcho, &amp; Laer&shy;<lb/>
tio primus, qui pacto pretio doceret, <expan abbr="philo&longs;ophiam&qacute;">philo&longs;ophiamque</expan>; faceret qu&aelig;&longs;tuo&longs;am: <lb/>
<expan abbr="ideo&qacute;">ideoque</expan>; mathematicas paruipendebat, qu&ograve;d neglecta cau&longs;a efficiente, nihil <lb/>
efficerent; &amp; finali, nihil lucrarentur. </s>
          <s id="s.002365">videas igitur quales &longs;int pulcherrima&shy;<lb/>
rum facultatum contemptores, ij nimirum, qui philo&longs;ophi&aelig;, aut lucri, aut <lb/>
ambitionis cau&longs;a dant operam. </s>
          <s id="s.002366">Quod autem Mathematic&aelig; nihil efficiant, <lb/>
<expan abbr="nihil&qacute;">nihilque</expan>; lucrentur, ne videamur vtile paruifacere, e&longs;t omnin&ograve; fal&longs;um: &longs;unt <lb/>
enim plures mathematic&aelig; practic&aelig;, qu&aelig; innumera, <expan abbr="atq;">atque</expan> <expan abbr="admir&atilde;da">admiranda</expan> efficiunt <lb/>
opera, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; magnos qu&aelig;&longs;tus quotidie faciunt. </s>
          <s id="s.002367">huiu&longs;modi &longs;unt Geometria <lb/>
practica, qua men&longs;urationes omnes vel &longs;olo vi&longs;u perficiuntur. </s>
          <s id="s.002368">Arithmeti&shy;<lb/>
ca, cuius v&longs;us qu&agrave;m lat&egrave; patet? </s>
          <s id="s.002369">Mu&longs;ica practica, qua quotidie ip&longs;i oblecta&shy;


<pb pagenum="139" xlink:href="009/01/139.jpg"/>mur; <expan abbr="Deo&qacute;">Deoque</expan>; Optimo Maximo laudes debitas concinimus. </s>
          <s id="s.002370">Mechanica pra&shy;<lb/>
ctica, cuius ope ingentia pondera, vel exigua vi, <expan abbr="inuita&qacute;">inuitaque</expan>; natura &longs;u&longs;q; <expan abbr="de&qacute;">deque</expan>; <lb/>
commouentur. </s>
          <s id="s.002371">Per&longs;pectiua, qu&aelig; Pictoribus, &amp; Architectoribus adeo in&longs;er&shy;<lb/>
uit, vt <expan abbr="ab&longs;q;">ab&longs;que</expan> ea nihil ferm&egrave; audeant. </s>
          <s id="s.002372">A&longs;tronomia tandem, &longs;i in praxim de&shy;<lb/>
ducatur, ex vna &longs;olum eclyp&longs;ium pr&aelig;dictione, quantam vniuer&longs;o orbi ad&shy;<lb/>
mirationem parit? </s>
          <s id="s.002373">mitto hanc &longs;olam dierum, men&longs;ium, &amp; annorum di&longs;tri&shy;<lb/>
butionem, ac temporum emendationem exhibere, rem ade&ograve; Reipublic&aelig; <lb/>
Chri&longs;tian&aelig; nece&longs;&longs;ariam.</s>
        </p>
        <p type="main">
          <s id="s.002374"><arrow.to.target n="marg197"/></s>
        </p>
        <p type="margin">
          <s id="s.002375"><margin.target id="marg197"/>206</s>
        </p>
        <p type="main">
          <s id="s.002376">Eodem tex. <!-- REMOVE S-->3. &lpar;<emph type="italics"/>Item &amp; in c&aelig;teris tunc &longs;cire vnumquodque arbitramur torum, <lb/>
quorum &longs;unt demonstrationes, cum quid e&longs;t &longs;ciamus, vt puta quid tetragoni&longs;mus, <lb/>
qu&ograve;d inuentio medi&aelig;<emph.end type="italics"/>&rpar; eadem reperies &longs;uperius in &longs;ecundo de Anima, tex. <!-- REMOVE S-->12. <lb/>
fu&longs;ius explicata.</s>
        </p>
        <p type="main">
          <s id="s.002377"><arrow.to.target n="marg198"/></s>
        </p>
        <p type="margin">
          <s id="s.002378"><margin.target id="marg198"/>207</s>
        </p>
        <p type="main">
          <s id="s.002379">Tex. 8. &lpar;<emph type="italics"/>Si enim in hoc differret &longs;olum Geometria &agrave; Geod&aelig;&longs;ia, quod h&aelig;c quidem <lb/>
eorum e&longs;t, qu&aelig; &longs;entimus, illa ver&ograve; non &longs;en&longs;ibilium e&longs;t<emph.end type="italics"/>&rpar; Geod&aelig;&longs;ia e&longs;t pars Geo&shy;<lb/>
metri&aelig; practic&aelig;, ea &longs;cilicet, qu&aelig; circa diui&longs;ionem &longs;uperficierum ver&longs;atur. <lb/>
</s>
          <s id="s.002380">audi Pedia&longs;mum de men&longs;uratione: Terr&aelig; inquit men&longs;uratio in duas partes <lb/>
diuiditur, Geometriam &longs;cilicet, &amp; Geod&aelig;&longs;iam: Are&aelig; <expan abbr="namq;">namque</expan> &longs;ecundum ar&shy;<lb/>
tem men&longs;uratio, &amp; terr&aelig; men&longs;uratio e&longs;t, &amp; merit&ograve; Geometria vocatur. <lb/>
</s>
          <s id="s.002381">Vnius ver&ograve;, &amp; eiu&longs;dem are&aelig;, &longs;eu loci diui&longs;io inter diuer&longs;as per&longs;onas, parti&shy;<lb/>
tio qu&aelig;dam e&longs;t terr&aelig;, &amp; iure optimo Geod&aelig;&longs;ia appellatur. </s>
          <s id="s.002382">h&aelig;c ille. </s>
          <s id="s.002383">dicitur <lb/>
autem Geod&aelig;&longs;ia &agrave; <foreign lang="greek">gea</foreign>, terra, &amp; <foreign lang="greek">da/iw</foreign>, diuido. </s>
          <s id="s.002384">Vocabulum tamen i&longs;tud Geo&shy;<lb/>
d&aelig;&longs;i&aelig; fuit po&longs;tea ad latiorem tran&longs;latum &longs;ignificationem: extat enim Geo&shy;<lb/>
d&aelig;&longs;ia Heronis Mechanici antiqui &longs;criptoris, quampridem Baroccius lati&shy;<lb/>
nitate donauit, qu&aelig; quidem ars e&longs;t eadem cum Geometria practica, cum <lb/>non &longs;olum diui&longs;iones, &longs;ed men&longs;urationes omnes etiam per dioptricam fa&shy;<lb/>
cultatem, &longs;eu per lineas vi&longs;uales doceat inue&longs;tigare.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002385"><emph type="italics"/>Ex Quarto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002386"><arrow.to.target n="marg199"/></s>
        </p>
        <p type="margin">
          <s id="s.002387"><margin.target id="marg199"/>208</s>
        </p>
        <p type="main">
          <s id="s.002388">Tex. 4. <emph type="italics"/>&lpar;Philo&longs;ophus <expan abbr="namq;">namque</expan> e&longs;t, vt ille, qui Mathematicus dicitur, &amp; <lb/>h&aelig;c enim habet partes: ac prima qu&aelig;dam, &amp; &longs;ecunda &longs;cientia e&longs;t: c&aelig; <lb/>
ter&aelig; <expan abbr="quoq;">quoque</expan> con&longs;equenter in mathematibus<emph.end type="italics"/>&rpar; inter mathematicas pri&shy;<lb/>
m&aelig; &longs;cienti&aelig; &longs;unt Geometria, &amp; Arithmetica, quia ip&longs;&aelig; &agrave; c&aelig;teris <lb/>
nulla ratione dependent; im&ograve; c&aelig;ter&aelig; ip&longs;is innituntur, qu&aelig; &longs;ecund&aelig; hoc lo&shy;<lb/>
co appellantur, h&aelig; &longs;unt Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia. <!-- KEEP S--></s>
          <s id="s.002389">illas <lb/>
duas recentiores &longs;ubalternantes, has ver&ograve; &longs;ecundas &longs;ubalternatas vocant. <lb/>
</s>
          <s id="s.002390">Exempla &longs;ubalternationum varia attuli in Logicis tex. <!-- REMOVE S-->20. &amp; 23. primi Po&shy;<lb/>
&longs;ter. <!-- REMOVE S-->vbi clar&egrave; licet intueri quid &longs;it &longs;ubalternatio, vnde etiam pr&aelig;&longs;ens lo&shy;<lb/>
cus illu&longs;tratur.</s>
        </p>
        <p type="main">
          <s id="s.002391"><arrow.to.target n="marg200"/></s>
        </p>
        <p type="margin">
          <s id="s.002392"><margin.target id="marg200"/>209</s>
        </p>
        <p type="main">
          <s id="s.002393">Tex. 28. &lpar;<emph type="italics"/>Vti diametrum commen&longs;urabilem e&longs;&longs;e<emph.end type="italics"/>&rpar; legenda &longs;unt ea, qu&aelig; libro <lb/>
primo Priorum, &longs;ecto 1. cap. 23. de hac commen&longs;urabilitate, &amp; incommen&shy;<lb/>
&longs;urabilitate tractata &longs;unt.</s>
        </p>
      </chap>
      <pb pagenum="140" xlink:href="009/01/140.jpg"/>
      <chap>
        <p type="head">
          <s id="s.002394"><emph type="italics"/>Ex Quinto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002395"><arrow.to.target n="marg201"/></s>
        </p>
        <p type="margin">
          <s id="s.002396"><margin.target id="marg201"/>210</s>
        </p>
        <p type="main">
          <s id="s.002397">Tex. 2. &lpar;<emph type="italics"/>Alia ver&ograve; cau&longs;a e&longs;t forma, &amp; exemplar: h&aelig;c autem e&longs;t ratio ip&shy;<lb/>&longs;ius quid erat e&longs;&longs;e, &amp; horum genera, vt ip&longs;ius Diapa&longs;on duo ad vnum, <lb/>&amp; &longs;impliciter numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>&rpar; affert exem&shy;<lb/>
plum cau&longs;&aelig; formalis ex Mu&longs;ica petitum; <expan abbr="ait&qacute;">aitque</expan>; cau&longs;am formalem <lb/>
illius con&longs;onanti&aelig;, qu&aelig; Diapa&longs;on dicitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; omnium perfecti&longs;&longs;ima, e&longs;&longs;e <lb/>
duplam proportionem, ide&longs;t, qu&aelig; e&longs;t inter duo, &amp; vnum, id, quod omnes <lb/>
Mu&longs;ici <expan abbr="fat&etilde;tur">fatentur</expan>. </s>
          <s id="s.002398">quod vt inelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. ad tex. <!-- REMOVE S-->1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap. 8. Amplius inquit cau&longs;am <lb/>
formalem genericam eiu&longs;dem Diapa&longs;on e&longs;&longs;e numerum, &amp; partes numeri, <lb/>
&longs;ub numero enim continentur &amp; duo, &amp; vnum. </s>
          <s id="s.002399">Occurrit hoc loco vnum <lb/>
magnopere notandum, videlicet tam con&longs;onantias, quam di&longs;&longs;onantias ha&shy;<lb/>
bere proportiones numerorum, hoc tamen di&longs;crimine, quod con&longs;onanti&aelig; <lb/>
habent &longs;ol&ugrave;m proportiones numerorum eorum, qui quaternario continen&shy;<lb/>
tur, ex veterum pr&aelig;&longs;ertim Pythagoreorum &longs;ententia, qui propterea vltra <lb/>
quaternarium progredi vetabant. </s>
          <s id="s.002400">Recentiores tamen u&longs;que ad &longs;enarium <lb/>
procedunt, quippe, qui omnes vocum con&longs;onantias admittunt, qu&aelig; pro&shy;<lb/>
portionibus numerorum &longs;enario contentorum pr&aelig;dit&aelig; &longs;int. </s>
          <s id="s.002401">Di&longs;&longs;onanti&aelig; <lb/>ver&ograve; &longs;ecundum pri&longs;cos habent proportiones numerorum extra quaterna&shy;<lb/>
rium progredientium, iuxta no&longs;tros autem extra &longs;enarium. </s>
          <s id="s.002402">qua de re pluri&shy;<lb/>
bus Zarlinus colloquio 2. definit. </s>
          <s id="s.002403">3.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002404"><arrow.to.target n="marg202"/></s>
        </p>
        <p type="margin">
          <s id="s.002405"><margin.target id="marg202"/>211</s>
        </p>
        <p type="main">
          <s id="s.002406">Tex. 3. <emph type="italics"/>&lpar;Partes <expan abbr="quoq;">quoque</expan> totius<emph.end type="italics"/>&rpar; ide&longs;t &longs;unt materia; loquitur enim de cau&longs;a <lb/>
materiali. </s>
          <s id="s.002407">libuit locum hunc annotare in gratiam Geometricarum demon&shy;<lb/>
&longs;trationum, quorum media &longs;&aelig;p&egrave; &longs;unt ex cau&longs;a materiali &longs;umpta, quod ta&shy;<lb/>
men non ita ab omnibus ob&longs;eruatur, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim probant affectio&shy;<lb/>
nem quampiam de aliquo &longs;ubiecto, ex eo, quod &longs;ubiectum illud &longs;it, vel di&shy;<lb/>
midium alicuius, vel duplum, vel reliquum, vel tertia pars, &amp; his &longs;imilia, <lb/>
erit talis ratio in genere cau&longs;&aelig; materialis. </s>
          <s id="s.002408"><expan abbr="neq;">neque</expan> e&longs;t cur recentiores quidam, <lb/>naturalibus &longs;cientijs a&longs;&longs;ueti, negent huiu&longs;modi materiam veram e&longs;&longs;e mate&shy;<lb/>riam, ac proinde neque, Geometricas demon&longs;trationes veras e&longs;&longs;e demon&longs;tra&shy;<lb/>
tiones; dicendum enim talem quidem materiam non e&longs;&longs;e veram materiam <lb/>
phy&longs;icam, &amp; proinde illas demon&longs;trationes <expan abbr="n&otilde;">non</expan> e&longs;&longs;e veras naturales demon&shy;<lb/>&longs;trationes, e&longs;&longs;e tamen veram materiam intelligibilem, qu&aelig; Geometri&aelig; &longs;u&shy;<lb/>
bijcitur, &amp; proinde demon&longs;trationes illas veras e&longs;&longs;e demon&longs;trationes Geo&shy;<lb/>
metricas; id quod Ari&longs;t. &longs;&aelig;pius in libris Po&longs;ter, apert&egrave; &longs;ignificat, tum a&longs;&longs;er&shy;<lb/>
tionibus, tum exemplis quamplurimis. </s>
          <s id="s.002409">Quapropter cauendum e&longs;t illis, ne <lb/>
ingrati animi notam incurrant, dum pulcherrimam artem re&longs;olutoriam, <lb/>
quam Ari&longs;t. &agrave; Mathematicis acceptam omnibus &longs;cientijs accommodauit <lb/>
&lpar;vt initio Priorum o&longs;ten&longs;um e&longs;t&rpar; eam ip&longs;i ita alijs facultatibus adaptent, vt <lb/>
Mathematicis ip&longs;is, ex quibus orta, &amp; &longs;ub quibus adoleuit, pulla ratione <lb/>conuenire po&longs;&longs;it. </s>
          <s id="s.002410">De hac materia fu&longs;ius infra in additamento de natura Ma&shy;<lb/>
thematicarum.</s>
        </p>
        <p type="main">
          <s id="s.002411"><arrow.to.target n="marg203"/></s>
        </p>
        <p type="margin">
          <s id="s.002412"><margin.target id="marg203"/>212</s>
        </p>
        <p type="main">
          <s id="s.002413">Tex. 3. &lpar;<emph type="italics"/>Et ip&longs;ius Diapa&longs;on duplum, &amp; numerus<emph.end type="italics"/>&rpar; &longs;cilicet cau&longs;&aelig; formales <lb/>
&longs;unt, quemadmodum &longs;upra tex. <!-- REMOVE S-->2. huius cap. explicatum e&longs;t.</s>
        </p>
        <pb pagenum="141" xlink:href="009/01/141.jpg"/>
        <p type="main">
          <s id="s.002414"><arrow.to.target n="marg204"/></s>
        </p>
        <p type="margin">
          <s id="s.002415"><margin.target id="marg204"/>213</s>
        </p>
        <p type="main">
          <s id="s.002416">Tex. 4. &lpar;<emph type="italics"/>Similiter autem figurationum <expan abbr="quoq;">quoque</expan> elementa dicuntur, ac &longs;impliciter <lb/>demon&longs;trationum prim&aelig; enim demon&longs;trationes, qu&aelig; in pluribus demonstrationibus <lb/>
in&longs;unt, h&aelig;c elementa demon&longs;trationum dicuntur<emph.end type="italics"/>&rpar; verbo &lpar;<emph type="italics"/>Figurationum<emph.end type="italics"/>&rpar; &longs;iue <expan abbr="de-&longs;cription&utilde;">de&shy;<lb/>
&longs;criptionum</expan>, Ari&longs;t, intelligere demon&longs;trationes Geometricas, &longs;&aelig;pius dictum <lb/>
e&longs;t, pr&aelig;&longs;ertim in Logicis, &amp; ex hoc loco pariter confirmatur. </s>
          <s id="s.002417">Ex hoc por&shy;<lb/>
r&ograve; loco illud innote&longs;cit dignum, quod pr&aelig;cipu&egrave; &agrave; Mathematico non igno&shy;<lb/>
retur, qu&aelig; nam &longs;int demon&longs;trationes ill&aelig;, qu&aelig; nomine <expan abbr="elementor&utilde;">elementorum</expan> debeant <lb/>appellari, necnon cau&longs;a cur Euclides &longs;uum opus elementa nuncupauerit, <lb/>
&longs;unt enim ill&aelig;, qu&aelig; in pluribus demon&longs;trationibus in&longs;unt, ide&longs;t, qu&aelig; &longs;&aelig;pius <lb/>
in alijs demon&longs;trationibus citantur, vti &longs;unt pr&aelig;cipu&egrave; &longs;ex priores libri Eu&shy;<lb/>
clidis: <expan abbr="atq;">atque</expan> hac ratione elementa appellantur.</s>
        </p>
        <p type="main">
          <s id="s.002418"><arrow.to.target n="marg205"/></s>
        </p>
        <p type="margin">
          <s id="s.002419"><margin.target id="marg205"/>214</s>
        </p>
        <p type="main">
          <s id="s.002420">Tex. 12. <emph type="italics"/>&lpar;Principium <expan abbr="itaq;">itaque</expan> &longs;cibilis, circa <expan abbr="vnumquodq;">vnumquodque</expan> ip&longs;um vnum, non e&longs;t au&shy;<lb/>tem idem in cunctis generibus vnum, &longs;ed hic quidem die&longs;is, hic ver&ograve; vocalis, aut <lb/>
muta&rpar;<emph.end type="italics"/> ide&longs;t, in Mu&longs;ica quidem principium omnium, &amp; elementum e&longs;t die&shy;<lb/>
&longs;is, qu&aelig; e&longs;t minima vox, aut &longs;onus, qui &longs;ub Mu&longs;ici con&longs;iderationem cadat. <lb/>
</s>
          <s id="s.002421">Porr&ograve; ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. de die&longs;i plura &longs;unt dicta.</s>
        </p>
        <p type="main">
          <s id="s.002422"><arrow.to.target n="marg206"/></s>
        </p>
        <p type="margin">
          <s id="s.002423"><margin.target id="marg206"/>215</s>
        </p>
        <p type="main">
          <s id="s.002424">Tex. 17. <emph type="italics"/>&lpar;Veluti diametrum commen&longs;urabilem e&longs;&longs;e impo&longs;&longs;ibile est&rpar;<emph.end type="italics"/> huius expo&shy;<lb/>
&longs;itionem inuenies 1. Priorum, &longs;ecto 1. cap. 23.</s>
        </p>
        <figure id="id.009.01.141.1.jpg" place="text" xlink:href="009/01/141/1.jpg"/>
        <p type="main">
          <s id="s.002425"><arrow.to.target n="marg207"/></s>
        </p>
        <p type="margin">
          <s id="s.002426"><margin.target id="marg207"/>216</s>
        </p>
        <p type="main">
          <s id="s.002427">Tex. eodem <emph type="italics"/>&lpar;Metaphoric&egrave; autem, qu&aelig; in Geometria po&shy;<lb/>
tentia dicitur&rpar;<emph.end type="italics"/> potentiam vnius line&aelig; appellant Geometr&aelig; <lb/>
quadratum illius, ide&longs;t quadratum &longs;uper ip&longs;am con&longs;tru&shy;<lb/>
ctum. </s>
          <s id="s.002428">v. <!-- REMOVE S-->g. <!-- REMOVE S-->quadratum in quo C, dicitur potentia line&aelig; <lb/>
D B, quia &longs;uper illam con&longs;tructum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002429"><arrow.to.target n="marg208"/></s>
        </p>
        <p type="margin">
          <s id="s.002430"><margin.target id="marg208"/>217</s>
        </p>
        <p type="main">
          <s id="s.002431">Tex. 34. &lpar;<emph type="italics"/>Quemadmodum dicitur diametrum e&longs;&longs;e commen&longs;urabilem<emph.end type="italics"/>&rpar; vide an&shy;<lb/>notata 1. Priorum, &longs;ecto 1. cap. 23.</s>
        </p>
        <p type="main">
          <s id="s.002432"><arrow.to.target n="marg209"/></s>
        </p>
        <p type="margin">
          <s id="s.002433"><margin.target id="marg209"/>218</s>
        </p>
        <p type="main">
          <s id="s.002434">Tex. 35. &lpar;<emph type="italics"/>Vt triangulo duos rectos habere<emph.end type="italics"/>&rpar; ide&longs;t affectio trianguli e&longs;t habe&shy;<lb/>
re tres angulos &aelig;quales duobus rectis angulis. </s>
          <s id="s.002435">Vide declarationem huius <lb/>lib. primo Priorum, &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002436"><emph type="italics"/>Ex Sexto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002437"><arrow.to.target n="marg210"/></s>
        </p>
        <p type="margin">
          <s id="s.002438"><margin.target id="marg210"/>219</s>
        </p>
        <p type="main">
          <s id="s.002439">Tex. 1. &lpar;<emph type="italics"/>Mathematicorum quoque principia, elementa, &amp; cau&longs;&aelig; &longs;unt<emph.end type="italics"/>&rpar; <lb/>
notanda &longs;unt h&aelig;c aduer&longs;us quo&longs;dam, qui negant in Mathemati&shy;<lb/>
cis cau&longs;as reperiri, vt hinc <expan abbr="quoq;">quoque</expan> illis &longs;cientiam auferant. </s>
          <s id="s.002440">enim&shy;<lb/>
uer&ograve; apert&egrave; patet eos falli ex toto hoc Ari&longs;t. di&longs;cur&longs;u.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002441"><emph type="italics"/>Ex Nono Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002442"><arrow.to.target n="marg211"/></s>
        </p>
        <p type="margin">
          <s id="s.002443"><margin.target id="marg211"/>220</s>
        </p>
        <p type="main">
          <s id="s.002444"><emph type="italics"/>Vt &longs;i quis dicat diametrum po&longs;&longs;e commen&longs;urari, non tamen commen&longs;u&shy;<lb/>
rabitur<emph.end type="italics"/>&rpar; &amp; paul&ograve; infra &lpar;<emph type="italics"/>Commen&longs;urari enim impo&longs;&longs;ibile e&longs;t<emph.end type="italics"/>&rpar; expo&longs;i&shy;<lb/>
tionem horum reperies 1. Priorum, &longs;ecto 1. cap. 23.</s>
        </p>
        <p type="main">
          <s id="s.002445"><arrow.to.target n="marg212"/></s>
        </p>
        <p type="margin">
          <s id="s.002446"><margin.target id="marg212"/>221</s>
        </p>
        <p type="main">
          <s id="s.002447">Tex. 20. &lpar;<emph type="italics"/>De&longs;criptiones <expan abbr="quoq;">quoque</expan> actu inueniuntur, diuidentes nanque <lb/>inuenirent, quod &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife&longs;t&egrave; e&longs;&longs;ent, nunc autem in&longs;unt potentia, cur <lb/>
triangulus duo recti? </s>
          <s id="s.002448">quia qui circa vnum punctum anguli duobus rectis &aelig;quales<emph.end type="italics"/> <pb pagenum="142" xlink:href="009/01/142.jpg"/><emph type="italics"/>&longs;unt, &longs;i igitur qu&aelig; ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>&rpar; per de&longs;cri&shy;<lb/>
ptiones, vel figurationes, vel de&longs;ignationes intelligendas e&longs;&longs;e demon&longs;tra&shy;<lb/>
tiones Geometricas &longs;&aelig;pius &longs;upra dictum e&longs;t, &amp; pariter ex hoc loco com&shy;<lb/>
probatur. </s>
          <s id="s.002449">Dicit igitur, quod demon&longs;trationes &longs;uas Geometr&aelig; inueniunt, <lb/>
reducendo ad actum ea, qu&aelig; erant in potentia, diuidentes enim educunt in <lb/>actum, figuras, angulos, lineas, &amp; c&aelig;tera huiu&longs;modi, qu&aelig; prius &longs;ol&ugrave;m erat <lb/>
in potentia, ex quibus po&longs;tea &longs;uas demon&longs;trationes perficiunt &lpar;<emph type="italics"/>Cur triangu&shy;<lb/>
lus duo recti<emph.end type="italics"/>&rpar; affert exemplum eius, quod proxim&egrave; dixerat, &longs;cilicet Geome&shy;<lb/>
tras demon&longs;trare producendo ad actum entia qu&aelig;dam Mathematica, quod <lb/>
exemplum, vt intelligas ijs opus habes, qu&aelig; primo Priorum, &longs;ecto 3. cap. 1. <lb/>
con&longs;cripta &longs;unt &lpar;<emph type="italics"/>Cur triangulus duo recti?<emph.end type="italics"/>&rpar; ide&longs;t, cur triangulus habet tres <lb/>
angulos &aelig;quales duobus rectis angulis &lpar;<emph type="italics"/>Quia qui circa vnum punctum anguli <lb/>
duobus rectis angulis &aelig;quales &longs;unt<emph.end type="italics"/>&rpar; ni&longs;i hoc dictum ad bonum trahatur &longs;en&longs;um, <lb/>
<figure id="id.009.01.142.1.jpg" place="text" xlink:href="009/01/142/1.jpg"/><lb/>
fal&longs;um e&longs;t, nam omnes anguli, qui circa vnum <lb/>
punctum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->A, &longs;unt con&longs;tituti, &aelig;quales &longs;unt <lb/>
non duobus, vt e&longs;t in textu, &longs;ed quatuor rectis, <lb/>
vt patet ex corollario 2. 15. primi Elem. quot&shy;<lb/>
quot enim anguli con&longs;tituantur ad punctum A, <lb/>
omnes &longs;imul erunt &aelig;quales quatuor rectis, quos <lb/>
faciunt pr&aelig;&longs;entes line&aelig; B C, D E. vniuer&longs;i enim <lb/>
illi congruent his quatuor rectis: &longs;ed Ari&longs;t. &longs;en&shy;<lb/>
&longs;us e&longs;t omnes angulos ad ea&longs;dem partes con&longs;ti&shy;<lb/>
tutos, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad partes &longs;uperiores line&aelig; B C, e&longs;&longs;e <lb/>
&aelig;quales duobus rectis B A D, D A C, vt o&longs;tenditur in 13. primi, necnon <lb/>
etiam patere pote&longs;t ex corollario 2. 15. eiu&longs;dem. </s>
          <s id="s.002450">tales &longs;unt quatuor anguli <lb/>
ad &longs;uperiores partes line&aelig; B C, &amp; ad punctum A, con&longs;tituti, qui, vt patet, <lb/>
<figure id="id.009.01.142.2.jpg" place="text" xlink:href="009/01/142/2.jpg"/><lb/>
&longs;unt &aelig;quales duobus rectis B A D, D A C, <lb/>
tales etiam &longs;unt in hac &longs;ecunda figura tres <lb/>
anguli B C A, A C D, D C E, qui quidem <lb/>
&aelig;quales &longs;unt duobus rectis angulis. </s>
          <s id="s.002451">hoc <lb/>
&longs;en&longs;i&longs;&longs;e Ari&longs;t. patet ex demon&longs;tratione 32. <lb/>
primi, qu&aelig; demon&longs;trat <expan abbr="memorat&atilde;">memoratam</expan> ab Ari&shy;<lb/>
&longs;tot. trianguli affectionem, &amp; ad quam <lb/>
propterea ip&longs;e &longs;pectabat, cuius figura e&longs;t <lb/>
eadem cum hac &longs;ecunda, in qua Euclides o&longs;tendit pr&aelig;dictos tres angulos <lb/>
&aelig;quari duobus rectis. </s>
          <s id="s.002452">&longs;ubdit po&longs;tea, &longs;i igitur linea C D, qu&aelig; ad latus A B, <lb/>
parallela e&longs;t in potentia, educeretur in actum, videnti mox e&longs;&longs;et manife&longs;tum <lb/>
tres angulos trianguli A B C, e&longs;&longs;e pares duobus rectis. </s>
          <s id="s.002453">ducta enim C D, pa&shy;<lb/>
rallela lateri B A, apparet &longs;tatim angulus A, &aelig;qualis angulo A C D, &amp; an&shy;<lb/>
gulus B, angulo D C E; cum reliquus ver&ograve; <expan abbr="tri&atilde;guli">trianguli</expan> angulus B C A, &longs;it apud <lb/>pr&aelig;dictos duos ad idem punctum C, con&longs;titutus; <expan abbr="atq;">atque</expan> omnes hi tres duobus <lb/>rectis &aelig;quentur, mox in&longs;picienti talem figurationem manife&longs;tum fit tres an&shy;<lb/>gulos illius trianguli e&longs;&longs;e duobus rectis &aelig;quales.</s>
        </p>
        <p type="main">
          <s id="s.002454"><arrow.to.target n="marg213"/></s>
        </p>
        <p type="margin">
          <s id="s.002455"><margin.target id="marg213"/>222</s>
        </p>
        <p type="main">
          <s id="s.002456">Ibidem &lpar;<emph type="italics"/>Cur in &longs;emicirculo vniuer&longs;aliter rectus? </s>
          <s id="s.002457">quia &longs;i tres &aelig;quales, &amp; qu&aelig; <lb/>
ba&longs;is e&longs;t duo, &amp; qu&aelig; ex medio &longs;upra stat recta, videnti manifestum erit ei, qui illud <lb/>
&longs;ciat<emph.end type="italics"/>&rpar; In 2. Po&longs;ter. tex. <!-- REMOVE S-->11. inuenies huius loci expo&longs;itionem. </s>
          <s id="s.002458">nunc &longs;ol&ugrave;m <pb pagenum="143" xlink:href="009/01/143.jpg"/><figure id="id.009.01.143.1.jpg" place="text" xlink:href="009/01/143/1.jpg"/><lb/>
h&aelig;c addenda &longs;unt. </s>
          <s id="s.002459">Re&longs;pondet Ari&longs;t. qu&aelig;&shy;<lb/>
&longs;ito pr&etail;cedenti, cur &longs;cilicet angulus in &longs;e&shy;<lb/>
micirculo &longs;it rectus, qualis e&longs;t in figura <lb/>
angulus A C B, <expan abbr="dicit&qacute;">dicitque</expan>; cau&longs;am e&longs;&longs;e, quia <lb/>
in figura tres line&aelig; &longs;unt &aelig;quales, du&aelig; ni&shy;<lb/>
mirum, in quas ba&longs;is B A, diuiditur, qu&aelig; <lb/>
&longs;unt B D, D A, &amp; tertia, qu&aelig; ex medio <lb/>
ba&longs;is erigitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; D C, cum omnes &longs;int <lb/>&longs;emidiametri eiu&longs;dem circuli. </s>
          <s id="s.002460">educta <expan abbr="itaq;">itaque</expan> linea D C, de potentia in actum, <lb/>
&longs;i cuipiam trium harum linearum &aelig;qualitas innote&longs;cat, continu&ograve; ei etiam <lb/>
manife&longs;tum erit angulum A C B, in &longs;emicirculo, e&longs;&longs;e rectum. </s>
          <s id="s.002461">quia &longs;tatim ap&shy;<lb/>
parent duo i&longs;o&longs;celia B D C, A D C, quorum anguli ad ba&longs;es B C, A C, &longs;unt <lb/>
&aelig;quales inuicem; &amp; anguli duo ad D, &longs;unt dupli duorum <expan abbr="angulor&utilde;">angulorum</expan> A C D, <lb/>
D C B, ex quibus conflatur totus angulus A C B, ergo duo anguli ad D, &longs;unt <lb/>
dupli anguli B C A, &longs;ed duo anguli ad D, &longs;unt &aelig;quales duobus rectis, ergo <lb/>
duo recti &longs;unt dupli anguli A C B, ergo angulus B C A, e&longs;t dimidium duo&shy;<lb/>
rum rectorum. </s>
          <s id="s.002462">cum autem omnes recti &longs;int &aelig;quales, con&longs;ectarium e&longs;t dimi&shy;<lb/>
dium duorum rectorum e&longs;&longs;e angulum rectum. </s>
          <s id="s.002463">patet igitur, qua ratione ex <lb/>
ductu linearum pr&aelig;dictarum actu, manife&longs;tum fiat angulum in &longs;emicirculo <lb/>
A C B, e&longs;&longs;e rectum. </s>
          <s id="s.002464">ne mireris &longs;i vulgatam tran&longs;lationem antiquam non <lb/>
&longs;um &longs;equutus, indigebat enim correctione, quam iuxta gr&aelig;cum exem&shy;<lb/>
plar adhibui.</s>
        </p>
        <p type="main">
          <s id="s.002465"><arrow.to.target n="marg214"/></s>
        </p>
        <p type="margin">
          <s id="s.002466"><margin.target id="marg214"/>223</s>
        </p>
        <p type="main">
          <s id="s.002467">Tex. 22. &lpar;<emph type="italics"/>Vt puta &longs;i triangulum non putet mutari, non opinabitur modo duos <lb/>
rectos habere, modo non, mutaretur enim<emph.end type="italics"/>&rpar; quia nimirum huius habemus &longs;cien&shy;<lb/>
tiam per demon&longs;trationem 32. primi Elementorum. <!-- KEEP S--></s>
          <s id="s.002468">quomodo autem tri&shy;<lb/>
angulus habeat duos rectos, ide&longs;t tres angulos &aelig;quales duobus rectis angu&shy;<lb/>
lis, explicatum e&longs;t primo Priorum, &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002469"><arrow.to.target n="marg215"/></s>
        </p>
        <p type="margin">
          <s id="s.002470"><margin.target id="marg215"/>224</s>
        </p>
        <p type="main">
          <s id="s.002471">Ibidem &lpar;<emph type="italics"/>Verum aliquid quidem, aliquid ver&ograve; non, vt puta parem numerum <lb/>
primum nullum e&longs;&longs;e; aut quo&longs;dam quidem, quo&longs;dam ver&ograve; non<emph.end type="italics"/>&rpar; definitione 11. <lb/>
7. Elem. &longs;ic numerus ille, qui &agrave; Mathematicis dicitur primus, definitur, pri&shy;<lb/>
mus numerus e&longs;t, quem vnitas &longs;ola metitur, vnde patet inter numeros pa&shy;<lb/>
res &longs;olum binarium e&longs;&longs;e primum, cum ip&longs;um &longs;ola vnitas bis replicata men&shy;<lb/>
&longs;uraret. </s>
          <s id="s.002472">quaternarium autem, &longs;enarium, &amp;c. </s>
          <s id="s.002473">pares, non e&longs;&longs;e primos, cum <lb/>
eos non &longs;ola vnitas, &longs;ed alius numerus metiatur: quaternarium enim bina&shy;<lb/>
rius bis replicatus men&longs;urat: &longs;enarium men&longs;urat &amp; binarius, &amp; ternarius: <lb/>
quare verum erit exi&longs;timare inter pares numeros aliquos e&longs;&longs;e primos, ide&longs;t <lb/>
binarium, aliquos ver&ograve; non, ide&longs;t c&aelig;teros pares vltra binarium.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002474"><emph type="italics"/>Ex Decimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002475"><arrow.to.target n="marg216"/></s>
        </p>
        <p type="margin">
          <s id="s.002476"><margin.target id="marg216"/>225</s>
        </p>
        <p type="main">
          <s id="s.002477">Tex. 4. &lpar;<emph type="italics"/>Ac etiam motum &longs;implici, &amp; veloci&longs;&longs;imo motu men&longs;urant, mi&shy;<lb/>
nimum enim tempus hic habet. </s>
          <s id="s.002478">quapropter in A&longs;trologia tale vn&ubreve;m prin&shy;<lb/>
cipium, &amp; men&longs;ura e&longs;t. </s>
          <s id="s.002479">motum enim &aelig;qualem, &amp; veloci&longs;&longs;im&ubreve;m c&oelig;li &longs;up&shy;<lb/>ponunt, ad quem c&aelig;teros iudicant<emph.end type="italics"/>&rpar; intelligit motum diurnum, quam <lb/>primo c&oelig;lo, &longs;eu mobili a&longs;cribunt, hic enim veloci&longs;&longs;imus e&longs;t omnium reli&shy;<pb pagenum="144" xlink:href="009/01/144.jpg"/>quorum c&oelig;le&longs;tium motuum, ac &longs;implici&longs;&longs;imus, &amp; vald&egrave; vniformis, ac regu&shy;<lb/>
laris, &amp; propterea minimum habet tempus, ide&longs;t tempus vnius diei natura&shy;<lb/>
lis, quo tempore totum primum mobile circulationem integram perficit. <lb/>
</s>
          <s id="s.002480">per minimum tempus, po&longs;&longs;unt etiam intelligi partes diei, qu&aelig; &longs;unt hor&aelig;, &amp; <lb/>
horarum partes. </s>
          <s id="s.002481">con&longs;iderant hunc motum in circulo &aelig;qu&agrave;toris, quia &aelig;qua&shy;<lb/>tor motu primi mobilis, &longs;eu diurno vniformiter, ae maxim&egrave; regulariter <lb/>
mouetur: hac de cau&longs;a hunc motum tanquam reliquorum men&longs;uram, ac <lb/>
normam merit&ograve; a&longs;&longs;ump&longs;erunt.</s>
        </p>
        <p type="main">
          <s id="s.002482"><arrow.to.target n="marg217"/></s>
        </p>
        <p type="margin">
          <s id="s.002483"><margin.target id="marg217"/>226</s>
        </p>
        <p type="main">
          <s id="s.002484">Ibidem <emph type="italics"/>&lpar;Et in Mu&longs;ica Die&longs;is primus &longs;en&longs;ibilis &longs;onus, quia minimum&rpar;<emph.end type="italics"/> ide&longs;t mi&shy;<lb/>
nimum interuallum, quod &agrave; Mu&longs;icis con&longs;ideretur, e&longs;t men&longs;ura maiorum in&shy;<lb/>
teruallorum. </s>
          <s id="s.002485">ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. &longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s>
        </p>
        <p type="main">
          <s id="s.002486"><arrow.to.target n="marg218"/></s>
        </p>
        <p type="margin">
          <s id="s.002487"><margin.target id="marg218"/>227</s>
        </p>
        <p type="main">
          <s id="s.002488">Eodem tex. <!-- REMOVE S-->&longs;ed cap. 3. <emph type="italics"/>&lpar;Nox &longs;emper autem men&longs;ura numero vnum e&longs;t, verum <lb/>aliquando plura, vt puta die&longs;es du&aelig;, non quidem &longs;ecundum auditum, &longs;ed in ratio&shy;<lb/>
nibus, &amp; voces plures, quibus men&longs;uramus, &amp; diameter duobus men&longs;uratur, &amp; la&shy;<lb/>
tus, &amp; omnes magnitudines&rpar;<emph.end type="italics"/> ita corrigenda e&longs;t antiqua tran&longs;latio. </s>
          <s id="s.002489">quid die&longs;is <lb/>
dictum &longs;it ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. quando autem ait <emph type="italics"/>&lpar;Vt puta du&aelig; die&longs;es&rpar;<emph.end type="italics"/><lb/>
ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>
qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>
cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>
intellectum excogitatis, quando ait <emph type="italics"/>&lpar;Et voces plures quibus men&longs;uramus&rpar;<emph.end type="italics"/><lb/>
quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>
tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantum &longs;pecie. Ait <emph type="italics"/>&lpar;Et dia&shy;<lb/>
meter duobus men&longs;uratur&rpar;<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->duobus &longs;emidiametris: vel duobus pedibus. <lb/>
</s>
          <s id="s.002490">&amp; latus pariter quadrati, duobus. </s>
          <s id="s.002491">v. <!-- REMOVE S-->g. <!-- REMOVE S-->pedibus mensuratur; eode<expan abbr="m&qacute;">mque</expan>; mo&shy;<lb/>do reliqu&aelig; omnes magnitudines po&longs;&longs;unt ab eadem men&longs;ura &longs;&aelig;pius replica&shy;<lb/>
ta men&longs;urari.</s>
        </p>
        <p type="main">
          <s id="s.002492"><arrow.to.target n="marg219"/></s>
        </p>
        <p type="margin">
          <s id="s.002493"><margin.target id="marg219"/>228</s>
        </p>
        <p type="main">
          <s id="s.002494">Eodem tex. <emph type="italics"/>&lpar;Semper autem men&longs;ura eiu&longs;dem generis e&longs;t, magnitudinum nam&shy;<lb/>que magnitudo, &amp; &longs;ecundum vnumquodque, longitudinis longitudo<emph.end type="italics"/>&rpar; ex his ratio <lb/>
manife&longs;ta apparet, cur Geometr&aelig; practici men&longs;urent longitudines per ali&shy;<lb/>
quam longitudinem, vt puta per vlnam, digitum, vnciam, &amp;c. </s>
          <s id="s.002495">&longs;uperficies <lb/>
etiam per aliquam &longs;uperficiem, &longs;ed qu&aelig; &longs;it quadrata, vt puta per vlnam qua&shy;<lb/>
dratam, palmum quadratum, &amp;c. </s>
          <s id="s.002496">corpora <expan abbr="quoq;">quoque</expan> per corpus, quod tamen <lb/>
&longs;it cubus, vt per vlnam cubicam, palmum cubicum, vnciam cubicam, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.002497"><arrow.to.target n="marg220"/></s>
        </p>
        <p type="margin">
          <s id="s.002498"><margin.target id="marg220"/>229</s>
        </p>
        <p type="main">
          <s id="s.002499">Tex. 11. <emph type="italics"/>&lpar;Similia ver&ograve; &longs;i cum non &longs;int eadem &longs;impliciter, nec &longs;ecundum &longs;ub&longs;tan&shy;<lb/>tiam &longs;ubiectam indifferentia &longs;ecundum formam eadem &longs;it: quemadmodum quadra&shy;<lb/>tum maius minori &longs;imile e&longs;t, &amp; line&aelig; in&aelig;quales, h&aelig; enim &longs;imiles quidem, ver&ubreve;m non <lb/>
c&aelig;dem &longs;impliciter &longs;unt&rpar;<emph.end type="italics"/> Prima definitio &longs;exti definit &longs;imiles figuras eas e&longs;&longs;e, <lb/>
qu&aelig; &longs;unt &aelig;quiangul&aelig; inuicem, &amp; qu&aelig; habent latera proportionalia circa <lb/>
&aelig;quales angulos. </s>
          <s id="s.002500">cum erg&ograve; quadratum maius, &amp; minus &longs;int &aelig;quiangula, <lb/>
quia habent omnes angulos rectos; &amp; pr&aelig;terea habeant latera circa &aelig;qua&shy;<lb/>
les angulos proportionalia, &longs;icut enim latera maioris quadrati circa vnum <lb/>
angulum rectum &longs;unt in proportione &aelig;qualitatis; ita <expan abbr="quoq;">quoque</expan> latera minoris <lb/>
circa vnum angulum rectum &longs;unt illis proportionalia, cum &longs;int inuicem pa&shy;<lb/>
riter in proportione &aelig;qualitatis, erunt nece&longs;&longs;ari&ograve; &longs;imilia h&aelig;c duo quadrata. <lb/>
</s>
          <s id="s.002501">du&aelig; etiam, exempli gratia, line&aelig; rect&aelig; &longs;unt inuicem &longs;imiles, quamuis vna <lb/>
&longs;it maior altera.</s>
        </p>
        <pb pagenum="145" xlink:href="009/01/145.jpg"/>
        <p type="main">
          <s id="s.002502"><arrow.to.target n="marg221"/></s>
        </p>
        <p type="margin">
          <s id="s.002503"><margin.target id="marg221"/>230</s>
        </p>
        <p type="main">
          <s id="s.002504">Eodem tex. <emph type="italics"/>&lpar;Tertium &longs;icut illa, qu&aelig; in Mathematicis&rpar;<emph.end type="italics"/> tertium &longs;cilicet mo&shy;<lb/>
dum diuer&longs;i, ponit in entibus Mathematicis, &longs;icut enim po&longs;uit idem e&longs;&longs;e in <lb/>
Mathematicis, quando du&aelig; figur&aelig; &longs;unt &longs;imiles, &amp; &aelig;quales: ita ex oppo&longs;ito <lb/>
diuer&longs;um erit in Mathematicis, quando du&aelig; figur&aelig; fuerint di&longs;&longs;imiles, &amp; in&shy;<lb/>
&aelig;quales, <expan abbr="dicentur&qacute;">dicenturque</expan>; diuer&longs;&aelig;, in quo con&longs;i&longs;tat &longs;imilitudo figurarum dictum <lb/>
e&longs;t in pr&aelig;cedenti expo&longs;itione.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002505"><emph type="italics"/>Ex Vndecimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002506"><arrow.to.target n="marg222"/></s>
        </p>
        <p type="margin">
          <s id="s.002507"><margin.target id="marg222"/>231</s>
        </p>
        <p type="main">
          <s id="s.002508">Svmma r. </s>
          <s id="s.002509">cap. 2. <emph type="italics"/>&lpar;Si quis ver&ograve; lineas, aut qu&aelig; has &longs;equuntur, dico autem <lb/>
primas &longs;uperficies principia e&longs;&longs;e ponat. </s>
          <s id="s.002510">h&aelig;c non &longs;unt &longs;ub&longs;tanti&aelig; &longs;eparabiles, <lb/>
ver&ugrave;m &longs;ectiones, &amp; diui&longs;iones, ill&aelig; quidem in &longs;uperficierum, h&aelig;c ver&ograve; cor&shy;<lb/>
porum, puncta ver&ograve; linearum &longs;unt, &amp; etiam ip&longs;arum earumdem termini; <lb/>
h&aelig;c autem omnia in alijs &longs;unt, &amp; nihil &longs;eparabile e&longs;t&rpar;<emph.end type="italics"/> ait puncta oriri ex &longs;ectio&shy;<lb/>
ne line&aelig;, quamuis &longs;int etiam termini illius; lineas ver&ograve; oriri ex diui&longs;ione <lb/>
&longs;uperficierum, quamuis &longs;int etiam termini illarum. </s>
          <s id="s.002511">&longs;uperficies <expan abbr="quoq;">quoque</expan> oriri <lb/>
ex diui&longs;ione corporum, quamuis &longs;int etiam termini, illorum. </s>
          <s id="s.002512">H&aelig;c placuit <lb/>
annotare propter <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan> conuenientiam <expan abbr="c&utilde;">cum</expan> ijs, qu&aelig; &agrave; Geometris traduntur.</s>
        </p>
        <p type="main">
          <s id="s.002513"><arrow.to.target n="marg223"/></s>
        </p>
        <p type="margin">
          <s id="s.002514"><margin.target id="marg223"/>232</s>
        </p>
        <p type="main">
          <s id="s.002515">Summa 3. cap. 2. <emph type="italics"/>&lpar;Vt puta &longs;ub Cane fiat frigus&rpar;<emph.end type="italics"/> ide&longs;t &longs;ub ortum Canis c&oelig;&shy;<lb/>
l&aelig;&longs;tis, &longs;eu Canicul&aelig;. <!-- KEEP S--></s>
          <s id="s.002516">Vide qu&aelig; libro &longs;ecundo Meteororum, &longs;umma 2. cap. 2. <lb/>
de hac &longs;tella &longs;crip&longs;imus.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002517"><emph type="italics"/>Ex Duodecimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002518"><arrow.to.target n="marg224"/></s>
        </p>
        <p type="margin">
          <s id="s.002519"><margin.target id="marg224"/>233</s>
        </p>
        <p type="main">
          <s id="s.002520">Tex. 44. <emph type="italics"/>&lpar;Pluralitatem ver&ograve; lationum ex peculiari&longs;&longs;ima Philo&longs;ophia <lb/>
Mathematicarum &longs;cientiarum, videlicet ex A&longs;tronomia con&longs;iderandum <lb/>
est: h&aelig;c enim de &longs;ub&longs;tantia &longs;en&longs;ibili quidem, ac &longs;empiterna &longs;peculatur&rpar;<emph.end type="italics"/><lb/>
pluralitatem nimirum c&oelig;le&longs;tium motuum petendam e&longs;&longs;e a&longs;&longs;erit <lb/>
ex pr&aelig;cipua totius Philo&longs;ophi&aelig; parte, quam ait e&longs;&longs;e A&longs;tronomiam. </s>
          <s id="s.002521">dignum <lb/>
porr&ograve; con&longs;ideratione e&longs;t, quanti faciat Ari&longs;t. Mathematicas di&longs;ciplinas, ac <lb/>
pr&aelig;cipu&egrave; &longs;yderalem &longs;cientiam.</s>
        </p>
        <p type="main">
          <s id="s.002522"><arrow.to.target n="marg225"/></s>
        </p>
        <p type="margin">
          <s id="s.002523"><margin.target id="marg225"/>234</s>
        </p>
        <p type="main">
          <s id="s.002524">Tex. 45. <emph type="italics"/>&lpar;Eudoxus igitur Solis, &amp; Lun&aelig; lationem po&longs;uit fieri &agrave; tribus orbibus, <lb/>quorum primus quidem e&longs;&longs;et, qui inerrantium &longs;tellarum; &longs;ecundus ver&ograve; &longs;ecundum <lb/>
id, quod per medium Zodiacum; tertius tandem, &longs;ecundum quem qui in latitudine <lb/>
Zodiaci obliquatur. </s>
          <s id="s.002525">in maiori autem latitudine obliquari eum &longs;ecundum quem Lu&shy;<lb/>na, qu&agrave;m eum &longs;ecundum quem Sol fertur&rpar;<emph.end type="italics"/> Eudoxi tempore nondum &longs;atis ex&shy;<lb/>
culta fuerat A&longs;tronomia, vt propterea minim&egrave; mirandum &longs;it, eum hoc lo&shy;<lb/>
co imperfecta admodum circa c&etail;le&longs;tia tradere. </s>
          <s id="s.002526">omittit enim in Sole orbem <lb/>
motum augis conficientem; necnon duos eccentricos, qui &longs;olis anomaliam, <lb/>
<expan abbr="atq;">atque</expan> eccentricitatis variationem excu&longs;ant. </s>
          <s id="s.002527">attribuit pr&aelig;terea Soli motum <lb/>
quendam in latitudinem, quod fal&longs;um e&longs;t omnin&ograve;, cum Sol perpetu&ograve; direct&egrave; <lb/>
&longs;ub eclyptica incedat. </s>
          <s id="s.002528">In Luna pariter plures nece&longs;&longs;arios illi orbes ad motus <lb/>
ip&longs;ius &longs;aluandos pr&aelig;termittit. </s>
          <s id="s.002529">Ex &longs;ententia tamen Tychonis Brahe hos or&shy;<lb/>
bes, ac circulos tanquam ab inuicem di&longs;tinctos abrogare debemus.</s>
        </p>
        <pb pagenum="146" xlink:href="009/01/146.jpg"/>
        <p type="main">
          <s id="s.002530"><arrow.to.target n="marg226"/></s>
        </p>
        <p type="margin">
          <s id="s.002531"><margin.target id="marg226"/>235</s>
        </p>
        <p type="main">
          <s id="s.002532">Tex. 46. <emph type="italics"/>&lpar;Errantium ver&ograve; &longs;tellarum <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> in quatuor &longs;ph&aelig;ris, quarum <lb/>primam quidem, &amp; &longs;ecundam eandem illis e&longs;&longs;e: etenim, qu&aelig; fixarum e&longs;t eam illam <lb/>e&longs;&longs;e, qu&aelig; omnes fert: at eam, qu&aelig; &longs;ub ip&longs;a ordinata e&longs;t, ac qu&aelig; &longs;ecundum Zodiacum <lb/>
lationem habet, communem omnibus e&longs;&longs;e. </s>
          <s id="s.002533">Terti&aelig; ver&ograve; omnium polos in eo, quod <lb/>
per medium Zodiacum e&longs;t. </s>
          <s id="s.002534">Quart&aelig; autem lationem &longs;ecundum eum, qui obliquatus <lb/>ad medium eius e&longs;t; e&longs;&longs;e ver&ograve; terti&aelig; &longs;ph&aelig;r&aelig; polos aliarum quidem proprios, Veneris <lb/>
autem, &amp; Mercurij eo&longs;dem&rpar;<emph.end type="italics"/> pergit tradere theoriam reliquorum errantium <lb/>
<expan abbr="quinq;">quinque</expan> &longs;yderum, &longs;ecundum mentem Eudoxi, qui propri&egrave; Planet&aelig; dicuntur: <lb/>
Sol autem, &amp; Luna hoc nomine non e&longs;t complexus, eo quod ip&longs;a mereantur <lb/>
potius duo mundi luminaria appellari, qu&agrave;m cum c&etail;teris &longs;tellis in ordinem <lb/>
redigi. </s>
          <s id="s.002535">Reliquis igitur <expan abbr="quinq;">quinque</expan> erronibus &longs;ingulis quatuor &longs;ph&aelig;ris attribue&shy;<lb/>
bat, quarum prima, &amp; &longs;ecunda eodem modo &longs;e habebant, ac in Sole, &amp; Lu&shy;<lb/>
na, etenim octaua &longs;ph&aelig;ra, &longs;eu firmamentum, quod affixa &longs;ibi &longs;ydera differt <lb/>
communicabat, &longs;ecundum ip&longs;um reliquis inferioribus &longs;ph&aelig;ris motum &longs;uum <lb/>
peculiarem, videlicet diurnum, quo ab oriente in occidentem tota c&etail;li ma&shy;<lb/>
china conuertebatur. </s>
          <s id="s.002536">fecundam eam facit, qu&aelig; Planetas omnes &longs;ecundum <lb/>
Zodiaci longitudinem ab occidente in <expan abbr="ori&etilde;tem">orientem</expan> vehebat, qu&aelig; pariter eodem <lb/>
modo &longs;e habet in &longs;ingulis. </s>
          <s id="s.002537">Tertiam ver&ograve; eam confinxit, cuius poli e&longs;&longs;ent in <lb/>
eclyptica, in quibus cita, ab eclyptica vltr&ograve;, <expan abbr="citro&qacute;">citroque</expan>; dilataretur. </s>
          <s id="s.002538">Quartam <lb/>
demum po&longs;uit, qu&aelig; tertiam bifariam &longs;ecaret, <expan abbr="eam&qacute;">eamque</expan>; tali motu cieret, ne ab <lb/>
eclyptica plus iu&longs;to ver&longs;us mundi polos exorbitaret. </s>
          <s id="s.002539">porr&ograve; in reliquis vo&shy;<lb/>
luit polos tertij orbis e&longs;&longs;e peculiares, Veneri autem, &amp; Mercurio eo&longs;dem <lb/>
e&longs;&longs;e, ide&longs;t e&longs;&longs;e in eadem linea. </s>
          <s id="s.002540">Ex mente igitur Eudoxi c&oelig;le&longs;tes orbes in <lb/>
vniuer&longs;um 27. numerantur, in Sole &longs;imul, ac Luna 6. in reliquis quinque er&shy;<lb/>
rantibus 20. <expan abbr="atq;">atque</expan> octau&aelig; &longs;ph&aelig;r&aelig; 1. Non me later, has Eudoxi po&longs;itiones, <lb/>
ob ratas po&longs;teriorum a&longs;tronomorum ob&longs;eruationes non &longs;ub&longs;i&longs;tere. </s>
          <s id="s.002541">at ver&ograve; <lb/>
hic non ip&longs;ius placita, &longs;ed pr&aelig;cipu&egrave; textus intelligentiam per&longs;equor.</s>
        </p>
        <p type="main">
          <s id="s.002542"><arrow.to.target n="marg227"/></s>
        </p>
        <p type="margin">
          <s id="s.002543"><margin.target id="marg227"/>236</s>
        </p>
        <p type="main">
          <s id="s.002544">Tex. 47. <emph type="italics"/>&lpar;At Calippus &longs;itum quidem &longs;ph&aelig;rarum eundem Eudoxo ponebat, hoc <lb/>
e&longs;t di&longs;tantiarum ordinem. </s>
          <s id="s.002545">pluralitatem autem &longs;tell&aelig; quidem Iouis, ac Saturni ean&shy;<lb/>
dem illi attribuebat. </s>
          <s id="s.002546">Solis ver&ograve;, &amp; Lun&aelig; duas adhuc putabat &longs;ph&aelig;ras addendas <lb/>e&longs;&longs;e, &longs;i quis eorum, qu&aelig; &longs;en&longs;ibiliter apparent, cau&longs;as a&longs;&longs;ignare debeat. </s>
          <s id="s.002547">C&aelig;teris ve&shy;<lb/>
r&ograve; errantium vnicuique vnam. </s>
          <s id="s.002548">nece&longs;&longs;e ver&ograve; e&longs;&longs;e, &longs;i debent omnes &longs;imul po&longs;it&aelig;, qu&aelig; <lb/>
apparent reddere, &longs;ecundam <expan abbr="vnamquamq;">vnamquamque</expan> errantium alteras &longs;ph&aelig;ras vna paucio&shy;<lb/>
res e&longs;&longs;e, qu&aelig; reuoluant, &amp; ad idem po&longs;itione &longs;emper primam eius astri &longs;ph&aelig;ram, <lb/>
quod inferius ordinatum e&longs;t, con&longs;tituant. </s>
          <s id="s.002549">hoc enim modo &longs;ol&ugrave;m contingit errantium <lb/>
lationem omnia facere. </s>
          <s id="s.002550">C&ugrave;m igitur, in quibus ip&longs;a quidem feruntur &longs;ph&aelig;ris, h&aelig; <lb/>quidem octo, b&aelig; ver&ograve; <expan abbr="vigintiquinq;">vigintiquinque</expan> &longs;int. </s>
          <s id="s.002551">horum &longs;ane non oportet illas &longs;olas reuo&shy;<lb/>lui, in quibus fertur, quod infim&egrave; ordinatum e&longs;t. </s>
          <s id="s.002552">qu&aelig; quidem duarum &longs;ph&aelig;rarum <lb/>
primas reuoluant, &longs;ex erunt. </s>
          <s id="s.002553">qu&aelig; ver&ograve; po&longs;teriorum quatuor, &longs;exdecim. </s>
          <s id="s.002554">cunctarum <lb/>
ver&ograve; numerus, t&ugrave;m earum qu&aelig; ferunt, t&ugrave;m qu&aelig; reuoluunt eas, quinquaginta quin&shy;<lb/>
que. </s>
          <s id="s.002555">qu&ograve;d &longs;i Lun&aelig;, &amp; Soli, non addat aliquis quos diximus motus, omnes &longs;ph&aelig;r&aelig; <lb/>
erunt &longs;eptem, &amp; quadraginta. </s>
          <s id="s.002556">pluralitas <expan abbr="itaq;">itaque</expan> &longs;ph&aelig;rarum tanta &longs;it&rpar;<emph.end type="italics"/> textum hunc <lb/>
per paraphra&longs;im &longs;ic explico; Calippus igitur eundem quidem ordinem, at&shy;<lb/>
que di&longs;tantiam &longs;ph&aelig;rarum cum Eudoxo ponebat: <expan abbr="eandem&qacute;">eandemque</expan>; pluralitatem <lb/>orbium mouentium Saturnum, ac Iouem; quatuor <expan abbr="nimir&utilde;">nimirum</expan> <expan abbr="vnicuiq;">vnicuique</expan> eorum. <lb/>
</s>
          <s id="s.002557">&longs;ed putabat &longs;oli duas addendas, ac Lun&aelig; &longs;imiliter, &longs;i quis eorum <expan abbr="appar&etilde;tias">apparentias</expan> <pb pagenum="147" xlink:href="009/01/147.jpg"/>&longs;aluare vellet. </s>
          <s id="s.002558">c&aelig;teris ver&ograve; errantium, Marti, Veneri, &amp; Mercurio <expan abbr="vnicuiq;">vnicuique</expan> <lb/>
vnam. </s>
          <s id="s.002559">nece&longs;&longs;e pr&aelig;terea exi&longs;timabat e&longs;&longs;e, vt pr&aelig;dict&aelig; omnes &longs;ph&aelig;r&aelig; &longs;imul <lb/>
apparentias omnes excu&longs;arent, addendas e&longs;&longs;e alias &longs;ingulis planetis toti&shy;<lb/>
dem &longs;ph&aelig;ras vna minus, quas Reuoluentes appellabat; ita vt qui quatuor <lb/>Mouentes &longs;ph&aelig;ras habui&longs;&longs;et, tribus pr&aelig;terea reuoluentibus opus haberet: <lb/>
qu&aelig; &longs;ph&aelig;r&aelig; reuoluentes id pr&aelig;&longs;tabant, vt qua&longs;i priores Mouentes ita in of&shy;<lb/>
ficio continerent, vt priori po&longs;itioni a&longs;trum, quod interiori orbi affigebur <lb/>
&longs;uo tempore re&longs;tituerent, vt Alexander exponit. </s>
          <s id="s.002560">hoc enim &longs;olummodo po&longs;&shy;<lb/>
&longs;ibile putabat omnes errantium lationes nos imitari po&longs;&longs;e. </s>
          <s id="s.002561">Cum igitur mo&shy;<lb/>
uentes &longs;ph&aelig;r&aelig; ill&aelig; quidem Saturni, ac Iouis &longs;int octo; reliquorum ver&ograve; vi&shy;<lb/>
gintiquinque, nam reliqui Planet&aelig; <expan abbr="quinq;">quinque</expan> &longs;inguli &longs;ph&aelig;ras <expan abbr="quinq;">quinque</expan> mouentes <lb/>
habent, qu&aelig; omnes &longs;imul numerum <expan abbr="vigintiquinq;">vigintiquinque</expan> explent: quarum omnium <lb/>
&longs;ol&aelig; inferiores, quibus a&longs;trum affixum volebat, non indigebant reuoluente, <lb/>
&longs;equitur duorum &longs;uperiorum Saturni, &amp; Iouis, quorum octo erant mouen&shy;<lb/>
tes, &longs;ex debere e&longs;&longs;e reuoluentes. </s>
          <s id="s.002562">Inferiorum ver&ograve; quatuor planetarum re&shy;<lb/>
uoluentes erunt &longs;exdecim: &longs;ed hoc loco Ari&longs;t. memoria fallit, deberet enim <lb/>
dicere, reliquorum <expan abbr="quinq;">quinque</expan> planetarum reuoluentes erunt vigint&igrave;, &longs;unt enim <lb/>
planet&aelig; &longs;eptem, quorum Saturno, ac Ioui &longs;upremis &longs;ex reuoluentes attri&shy;<lb/>buit habita ratione &longs;ph&aelig;rarum mouentium; reliquis igitur <expan abbr="quinq;">quinque</expan> planetis <lb/>
habita ratione &longs;uorum orbium mouentium, 25. cum &longs;inguli habeant <expan abbr="quinq;">quinque</expan> <lb/>mouentes, habebunt ex pr&aelig;&longs;cripto Calippi &longs;inguli 4. reuoluentes; ac pro&shy;<lb/>
inde 20. in vniuer&longs;um erunt reuoluentes. </s>
          <s id="s.002563">Omnium igitur &longs;ph&aelig;rarum tam <lb/>
mouentium, qu&agrave;m reuoluentium &longs;ummam ait, &longs;ed perperam, e&longs;&longs;e quinqua&shy;<lb/>ginta quinque; cum enim mouentes Saturni, &amp; Iouis &longs;int 8. reliquorum au&shy;<lb/>
tem 25. reuoluentes ver&ograve; Saturni, &amp; Iouis &longs;int 6. reliquorum autem, vt ip&shy;<lb/>
&longs;e memoria fal&longs;us ponit, &longs;exdecim, conflant quidem &longs;ummam pr&aelig;dictam, <lb/>
&longs;ed illi in memoria reuocandus e&longs;t, planeta ille, quem oblitus e&longs;t, cuius &longs;unt <lb/>
quatuor reuoluentes, qui prioribus additi &longs;ph&aelig;rarum errantium numerum <lb/>
quinquaginta nouem con&longs;tituent: quibus etiam addenda e&longs;t octaua &longs;ph&aelig;ra, <lb/>
&longs;eu firmamentum, quod inerrantium &longs;edes e&longs;t, non enim &longs;olum errantium, <lb/>
&longs;ed omnium c&oelig;le&longs;tium orbium numerum inue&longs;tigare volebat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; e&longs;&longs;ent <lb/>
omnes &longs;ecundum Calippum &longs;ph&etail;r&aelig; &longs;exaginta. </s>
          <s id="s.002564">Quod &longs;i Lun&aelig;, &amp; Soli non ad&shy;<lb/>
dantur &longs;ingulis duo mouentes, vt facit Calippus, <expan abbr="neq;">neque</expan> con&longs;equenter quatuor <lb/>
illis debiti reuoluentes non erunt omnes, 55. ver&ugrave;m, detractis octo pr&aelig;di&shy;<lb/>
ctis, erunt tantum 47. &longs;eu vt melius loquatur non erunt in vniuer&longs;um, 60. &longs;ed <lb/>
52. tantum. </s>
          <s id="s.002565">Hactenus de numero c&oelig;lorum.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002566"><emph type="italics"/>Ex Decimotertio Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002567"><arrow.to.target n="marg228"/></s>
        </p>
        <p type="margin">
          <s id="s.002568"><margin.target id="marg228"/>237</s>
        </p>
        <p type="main">
          <s id="s.002569">Svmma 1. cap. 3. <emph type="italics"/>&lpar;Qui dicunt Mathematicas &longs;cientias nihil de bono, vel <lb/>
pulchro dicere, fal&longs;um dicunt. </s>
          <s id="s.002570">dicunt. </s>
          <s id="s.002571">n. </s>
          <s id="s.002572">&amp; maxim&egrave; <expan abbr="o&longs;t&etilde;dunt">o&longs;tendunt</expan>. </s>
          <s id="s.002573">nam &amp; &longs;i non <lb/>
nominant, quia tamen opera, &amp; rationes ostendunt, non ne dicunt de eis? <lb/>
</s>
          <s id="s.002574">pulchra <expan abbr="namq;">namque</expan> maxim&egrave; &longs;pecies &longs;unt, ordo, commen&longs;uratio, &amp; definit&ubreve;, qu&aelig; <lb/>
maxim&egrave; &agrave; Mathematicis &longs;cientijs o&longs;tenduntur, &amp;c.&rpar;<emph.end type="italics"/> placuit h&aelig;c in Mathemati&shy;<lb/>
carum commendationem, ac defen&longs;ionem apponere, cum non de&longs;int hac <lb/>no&longs;tra tempe&longs;tate ageometreti complures, qui eas libenter &longs;ugillare &longs;olent.</s>
        </p>
      </chap>
      <pb pagenum="148" xlink:href="009/01/148.jpg"/>
      <chap>
        <p type="head">
          <s id="s.002575"><emph type="italics"/>IN MECHANICAS QV&AElig;STIONES.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002576">Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>
plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. <!-- REMOVE S-->Ari&longs;t. <lb/>
&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>
&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/>
</s>
          <s id="s.002577">E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>
tus, ac deprauatus, vt nullo modo emendari queat.</s>
        </p>
        <p type="head">
          <s id="s.002578"><emph type="italics"/>Caput Primum.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002579">Qu&aelig; &longs;it artis Mechanic&aelig; facultas.</s>
        </p>
        <p type="main">
          <s id="s.002580"><arrow.to.target n="marg229"/></s>
        </p>
        <p type="margin">
          <s id="s.002581"><margin.target id="marg229"/>238</s>
        </p>
        <p type="main">
          <s id="s.002582">Eorum, qu&aelig; miraculo &longs;unt, alia quidem natura contingunt, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; ea, <lb/>
quorum ignorantur cau&longs;&aelig;: alia ver&ograve; &longs;unt, qu&aelig; pr&aelig;ter naturam per <lb/>
artificium aliquod ad hominum vtilitatem perficiuntur, in multis <lb/>
<expan abbr="namq;">namque</expan> natura ei, quod nobis v&longs;ui e&longs;&longs;e pote&longs;t, contrarium facit, quod <lb/>
inde oritur, quia natura eundem &longs;emper, ac &longs;implicem &longs;eruat modum: quod <lb/>
autem nobis vtile e&longs;t, plurimas &longs;ubit varietates. </s>
          <s id="s.002583">quando igitur quippiam <lb/>
pr&aelig;ter naturam facere opportuerit, illud, quod faciendum e&longs;t, difficultate <lb/>
&longs;ua nos remoratur, <expan abbr="arte&qacute;">arteque</expan>; propterea indigemus. </s>
          <s id="s.002584">quamobrem eam artis <lb/>
partem, qu&aelig; huiu&longs;modi &longs;uccurrit difficultatibus, Mechanicam appellamus. <lb/>
</s>
          <s id="s.002585">C&aelig;ter&ugrave;m optim&egrave; Antiphon Poeta in hunc modum cecinit;</s>
        </p>
        <p type="head">
          <s id="s.002586"><emph type="italics"/>Arte &longs;uperamus ea, in quibus &agrave; natura vincimur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002587">Quemadmodum accidit, cum minora &longs;uperant maiora, &amp; qu&aelig;cunque exi&shy;<lb/>
guam vim habentia, magna tamen mouent pondera, &amp; omnia fer&egrave; illa, qu&aelig; <lb/>
&longs;ub ea cadunt problemata, qu&aelig; mechanica nuncupari <expan abbr="&longs;ol&etilde;t">&longs;olent</expan>. </s>
          <s id="s.002588">&longs;unt autem h&aelig;c <lb/>
<expan abbr="neq;">neque</expan> naturalibus omnin&ograve; qu&aelig;&longs;tionibus eadem, <expan abbr="neq;">neque</expan> &longs;eiugata valde: ver&ugrave;m <lb/>
mathematicarum contemplationum, <expan abbr="naturaliumq;">naturaliumque</expan> communia. </s>
          <s id="s.002589">Po&longs;tea in <lb/>
gr&aelig;cis codicibus h&aelig;c &longs;equuntur &lpar;<foreign lang="greek">to\ men ga\r w= di/a twn maqhmatikw=n dhlon: to<lb/>de peri\ o&lpar;/, di\a tw=n fusikw=n</foreign>&rpar; ide&longs;t, &longs;i quidem quomodo &longs;int, &longs;eu qua ratione <lb/>
exi&longs;tant, manife&longs;tum e&longs;t per Mathematica: illud ver&ograve; circa quod ver&longs;antur, <lb/>
hoc e&longs;t obiectum, de quo pertractant Mechanic&aelig; qu&aelig;&longs;tiones per &longs;cientias <lb/>
phy&longs;icas habetur, ide&longs;t res naturalis e&longs;t; e&longs;t enim pondus, &amp; vis, aut poten&shy;<lb/>
tia pondus ip&longs;um mouens, quatenus quanta &longs;unt; &longs;iue dixeris e&longs;t quantitas <lb/>
ponderum, <expan abbr="atq;">atque</expan> potentiarum. </s>
          <s id="s.002590">Mathematic&aelig; enim medi&aelig;, de quorum nu&shy;<lb/>
mero e&longs;t facultas Mechanica, con&longs;iderant quantitatem rei alicuius <lb/>
determinat&aelig;, &longs;ic A&longs;tronomia circa c&oelig;le&longs;tium corporum, <expan abbr="mo-tuum&qacute;">mo&shy;<lb/>
tuumque</expan>; quantitates, Per&longs;pectiua circa linearum vi&longs;ua&shy;<lb/>
lium; Mu&longs;ica circa &longs;onorum quantitates ver&shy;<lb/>
&longs;antur. </s>
          <s id="s.002591">qu&aelig; placuit annotare, vt &longs;cien&shy;<lb/>
ti&aelig; huius naturam per&longs;pectam <lb/>
haberemus.</s>
        </p>
        <pb pagenum="149" xlink:href="009/01/149.jpg"/>
        <p type="head">
          <s id="s.002592">De dignitatibus, <expan abbr="admirandis&qacute;">admirandisque</expan>; Circuli proprietatibus.</s>
        </p>
        <p type="head">
          <s id="s.002593"><emph type="italics"/>Cap. Secundum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002594"><arrow.to.target n="marg230"/></s>
        </p>
        <p type="margin">
          <s id="s.002595"><margin.target id="marg230"/>239</s>
        </p>
        <p type="main">
          <s id="s.002596">Cvm vellet Ari&longs;t. mirabilium effectuum, quos in Mechanicis admi&shy;<lb/>
ramur, cau&longs;am referre in circulum: merit&ograve; ante omnia de admi&shy;<lb/>
randa ip&longs;ius circuli natura di&longs;&longs;erit, quo minus mirum deinde vi&shy;<lb/>deatur pr&aelig;dictas mirabiles operationes ex ip&longs;o procedere. </s>
          <s id="s.002597">quan&shy;<lb/>
doquidem exadmiranda cau&longs;a admirabiles effectus prodire debeant. </s>
          <s id="s.002598">qua&shy;<lb/>lia &longs;unt ea, qu&aelig; circa vectem, cum magna <expan abbr="omni&utilde;">omnium</expan> admiratione contingunt. <lb/>
</s>
          <s id="s.002599">videmus enim exiguam pror&longs;us vim ingens pondus, quod <expan abbr="ab&longs;q;">ab&longs;que</expan> vecte mini&shy;<lb/>
m&egrave; mouere po&longs;&longs;et, addito etiam ip&longs;ius vectis pondere, facil&egrave; <expan abbr="quocunq;">quocunque</expan> vo&shy;<lb/>
luerit propellere. </s>
          <s id="s.002600">quod quidem auditu ab&longs;urdum foret, ni&longs;i vi&longs;u con&longs;taret. <lb/>
</s>
          <s id="s.002601">omnium autem huiu&longs;modi cau&longs;&aelig; principium circulus obtinet: &amp; hoc qui&shy;<lb/>
dem merit&ograve;, ex admirabili enim, quippiam mirandum accidere rationi <lb/>omnin&ograve; con&longs;entaneum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002602">Prim&ograve; igitur maxim&egrave; admirandum e&longs;t contraria &longs;imul fieri, aut exi&longs;tere:<lb/>
circulus tamen ex contrarijs e&longs;t con&longs;titutus, oritur enim circulus ex com&shy;<lb/>moto, &amp; manente, qu&aelig; quidem naturaliter &longs;unt inuicem contraria. </s>
          <s id="s.002603">&longs;it au&shy;<lb/>
tem circulus ex commoto, &amp; manente, quia oritur ex circumuolutione <lb/>
vnius rect&aelig; line&aelig;, cuius alterum extremum fixum manet, alterum ver&ograve; cir&shy;<lb/>
cumagitur; quamobrem i&longs;th&aelig;c cernentes minus admirari <expan abbr="c&otilde;uenit">conuenit</expan> reliquas, <lb/>
qu&aelig; in ip&longs;o &longs;unt contrarietates. </s>
          <s id="s.002604">cuiu&longs;modi e&longs;t h&aelig;c, quod cum linea, qu&aelig; cir&shy;<lb/>
culi orbem complectitur, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; circunferentia appellatur, nullam habeat <lb/>
latitudinem, ei tamen contraria quodammodo in&longs;unt, concauum &longs;cilicet, <lb/>
&amp; curuum; qu&aelig; quidem eo modo &longs;unt contraria, quo etiam magnum, &amp; pa&shy;<lb/>
ruum, horum enim medium e&longs;t &aelig;quale; illorum ver&ograve; rectum. </s>
          <s id="s.002605">&amp; &longs;icuti quan&shy;<lb/>
do magnum, &amp; paruum inuicem commutantur, ita vt quod magnum e&longs;t fiat <lb/>
paruum, quod ver&ograve; paruum fiat magnum, nece&longs;&longs;e e&longs;t, vt perueniant ad <lb/>
&aelig;quale priu&longs;quam ad extremum alterutrum; ita linea curua antequam fiat <lb/>
concaua, debet prius fieri recta: &amp; ex concaua, vt tran&longs;eat ad conuexam, <lb/>
&amp; circularem, debet &longs;imiliter prius e&longs;&longs;e recta.</s>
        </p>
        <p type="main">
          <s id="s.002606">Alterum contrarium, quod circulo ine&longs;t, e&longs;t &longs;imul <expan abbr="c&otilde;trarijs">contrarijs</expan> motibus mo&shy;<lb/>neri: &longs;imul enim ad anteriorem mouetur locum, &amp; ad po&longs;teriorem. </s>
          <s id="s.002607">&amp; eo&shy;<lb/>
dem modo linea illa, qu&aelig; ex vno extremo manens, ex altero ver&ograve; circum&shy;<lb/>lata circulum de&longs;cribit, &longs;e habet; contraria enim &longs;imul continet, primum <lb/>
&longs;cilicet, &amp; extremum. </s>
          <s id="s.002608">Ex quo enim primo loco circumagi incipit ad eun&shy;<lb/>
dem rur&longs;us po&longs;trem&ograve; reuertitur, ita, vt primum ip&longs;ius, &amp; po&longs;tremum idem <lb/>
&longs;int; quapropter, vt prius dicebamus non e&longs;t inconueniens, ip&longs;um circulum <lb/>
miraculorum omnium e&longs;&longs;e principium. </s>
          <s id="s.002609">Admiranda igitur ea, qu&aelig; circa li&shy;<lb/>bram fiunt, ad circulum <expan abbr="t&atilde;quam">tanquam</expan> cau&longs;am referuntur, qu&aelig; ver&ograve; circa vectem <lb/>
ad ip&longs;am libram: alia autem fer&egrave; omnia, qu&aelig; circa mechanicas contingunt <lb/>
motiones, ad vectem reducuntur.</s>
        </p>
        <p type="main">
          <s id="s.002610">Pr&aelig;ter pr&aelig;dicta aliud tandem mirum ip&longs;i ine&longs;t, quia nimirum cum innu&shy;<lb/>
mera &longs;int puncta in vna <expan abbr="eadem&qacute;">eademque</expan>; linea, qu&aelig; &longs;emidiameter e&longs;t, omnia tamen <pb pagenum="150" xlink:href="009/01/150.jpg"/>quando &longs;emidiameter circa centrum mouetur, quamuis cum ip&longs;a mouean&shy;<lb/>tur, in&aelig;quali velocitate mouentur; Nam punctum illud &longs;emper velocius <lb/>
mouetur, quod remotius e&longs;t &agrave; centro circuli, &longs;eu &agrave; manente &longs;emidiametri <lb/>
termino, &amp; proinde illud tardius, quod centro proximius e&longs;t. </s>
          <s id="s.002611"><expan abbr="Atq;">Atque</expan> ex hac <lb/>
mira circuli proprietate, <expan abbr="pleraq;">pleraque</expan> miraculorum accidunt circuli motioni&shy;<lb/>
bus, vt in &longs;equentibus qu&aelig;&longs;tionibus manife&longs;tum erit.</s>
        </p>
        <p type="main">
          <s id="s.002612">Quoniam autem &longs;ecundum contrarias &longs;imul motiones mouetur circulus, <lb/>
&amp; alterum quidem diametri extremum vbi A, in figura pr&aelig;&longs;enti antror&longs;um <lb/>
<figure id="id.009.01.150.1.jpg" place="text" xlink:href="009/01/150/1.jpg"/><lb/>
mouetur; alterum ver&ograve; vbi B, retror&shy;<lb/>
&longs;um, efficiunt nonnulli, vt ab vnica mo&shy;<lb/>
tione multi contrari&ograve; &longs;imul mouean&shy;<lb/>
tur denticulati circuli: vt &longs;unt ij, quos <lb/>
in locis proponunt &longs;acris, quorum alij <lb/>
&longs;unt &aelig;nei, alij ferrei. </s>
          <s id="s.002613">&longs;i enim circulus <lb/>
A B, alterum circulum C D, contige&shy;<lb/>
rit, mota diametro A B, ita vt A, an&shy;<lb/>
tror&longs;um eat, commouebit alteram dia&shy;<lb/>
metrum C D, ita vt C, retror&longs;um, hoc e&longs;t in contrarium ip&longs;i A, veniat, in <lb/>
contrarium igitur mouebitur &longs;ecundus circulus C D, ad circulum A B, &amp; <lb/>
rur&longs;us circulus E F. in contrarium ip&longs;i C D, commouebitur ab ip&longs;o C D, ob <lb/>
eandem rationem. </s>
          <s id="s.002614">eodem etiam modo &longs;i plures fuerint, idem facient vno <lb/>
&longs;olo tanquam primo motore <expan abbr="c&otilde;moto">commoto</expan>. </s>
          <s id="s.002615">hanc igitur circuli naturam animad&shy;<lb/>
uertentes Architecti, in&longs;trumentum artificios&egrave; <expan abbr="fabric&atilde;t">fabricant</expan>, motus principium <lb/>
occultantes, vt machin&aelig; &longs;ol&ugrave; manife&longs;tum &longs;it illud, quod admirationem <lb/>
parit, cau&longs;a ver&ograve; lateat: quod genus machinarum Automata dicebantur, <lb/>
quia &longs;pont&egrave; &agrave; &longs;e ip&longs;is mouebantur.</s>
        </p>
        <p type="main">
          <s id="s.002616">In primis igitur, qu&aelig; circa libram accidunt, dubitare faciunt, quamnam <lb/>
ob cau&longs;am maiores libr&aelig; minoribus &longs;int exactiores: huius autem rei prin&shy;<lb/>
cipium e&longs;t illud, quod &longs;upra innuimus, quod &longs;cilicet, qu&aelig; &agrave; centro plus di&shy;<lb/>
&longs;tat linea, &longs;iue qu&aelig; longior e&longs;t, eadem vi commota citius fertur, quam illa, <lb/>
qu&aelig; minus &agrave; centro di&longs;tat, &longs;eu qu&aelig; minor e&longs;t. </s>
          <s id="s.002617">Porr&ograve; citius bifariam dicitur; <lb/>
&longs;iue enim in minori tempore &aelig;quale pertran&longs;it &longs;patium: &longs;iue in &aelig;quali tem&shy;<lb/>
pore, maius conficit interuallum; citius feci&longs;&longs;e dicitur. </s>
          <s id="s.002618">&longs;i autem du&aelig; line&aelig; <lb/>
circa idem centrum moueantur vna maior, &amp; altera minor in &aelig;quali tem&shy;<lb/>
pore; maior maiorem circulum de&longs;cribet, quam minor; quia circulus &agrave; ma&shy;<lb/>iori de&longs;criptus, alterum &agrave; minori delineatum circumpleρetur, <expan abbr="atq;">atque</expan> intra &longs;e <lb/>
continebit; maius autem e&longs;t continens, qu&agrave;m <expan abbr="cont&etilde;tum">contentum</expan>. </s>
          <s id="s.002619">horum autem cau&shy;<lb/>
&longs;a, quoniam qu&aelig; circulum de&longs;cribit linea, duabus fertur lationibus, qu&aelig; nul&shy;<lb/>
lam inuicem obtinent analogiam: quod antequam probemus, &longs;ciendum <lb/>
e&longs;t, quod, quidquid duobus motibus inuicem proportionatis, mouetur, ne&shy;<lb/>ce&longs;&longs;e e&longs;t, quod motu ex illis mixto progrediatur per lineam rectam, qu&aelig; dia&shy;<lb/>
meter e&longs;t quadrilateri, cuius latera habeant illam proportionem, quam <lb/>
duo illi motus. </s>
          <s id="s.002620">&longs;it enim in figura proportio lateris A B, ad latus A C, quam <lb/>
ctiam habent duo motus, &longs;ecundum quos latum quodpiam feratur, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; la&shy;<lb/>
tum illud A, &amp; feratur motu vno ver&longs;us B, per lineam A B, altero ver&ograve; mo&shy;<lb/>
tu feratur ver&longs;us C. quod fiet &longs;i cogitemus latus A B, <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan> ver&longs;us M C,


<pb pagenum="151" xlink:href="009/01/151.jpg"/><figure id="id.009.01.151.1.jpg" place="text" xlink:href="009/01/151/1.jpg"/><lb/>ip&longs;i &aelig;quidi&longs;tanter, dum punctum A, mouetur <lb/>
ad B. his duabus lationibus A, latum. </s>
          <s id="s.002621">nece&longs;&longs;a&shy;<lb/>ri&ograve; motu mixto progredietur per diametrum <lb/>
A M, quod &longs;ic probari pote&longs;t; &longs;it iam A, mo&shy;<lb/>
tum primo motu <expan abbr="v&longs;q;">v&longs;que</expan> ad D, linea ver&ograve; ex &longs;e&shy;<lb/>
cundo motu &longs;it in G F E, quo motu punctum <lb/>
A, quod erat in D, <expan abbr="tract&utilde;">tractum</expan> erit in F. quod pun&shy;<lb/>
ctum e&longs;t in diametro A M, quoniam enim mo&shy;<lb/>
uetur duobus motibus, cum lineis A B, A C, proportionalibus, motus au&shy;<lb/>
tem <expan abbr="hucu&longs;q;">hucu&longs;que</expan> &longs;unt A D, A E, qu&aelig; debent e&longs;&longs;e proportionales, cum A B, A C <lb/>
compleatur rectangulum A D F E, erunt &longs;imiliter proportionalia F E, D E, <lb/>
cum &longs;int &aelig;qualia duobus D A, A E, quare per 26. 6. cum quadrilaterum <lb/>
paruum A D F E, &longs;it &longs;imile toti A B M C, erit A M, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> diameter, erg&ograve; <lb/>
punctum F, in quo e&longs;t A, e&longs;t in diametro A M. eodem modo, de quouis pun&shy;<lb/>
cto in linea A B, ad quod A, perueniat, probabitur ab altero motu de&longs;cen&shy;<lb/>
di&longs;&longs;e v&longs;que ad diametrum. </s>
          <s id="s.002622">&longs;emper erg&ograve; latum A, per rectam A M, diame&shy;<lb/>
trum quadrilateri, cum illis motibus proportionalibus progreditur, quod <lb/>
probandum erat. </s>
          <s id="s.002623">&egrave; conuers&ograve; manife&longs;tum etiam e&longs;t, quod &longs;i quid &longs;ecundum <lb/>
diametrum duabus fertur lationibus, eas lationes e&longs;&longs;e proportionales late&shy;<lb/>
ribus quadrilateri, cuius e&longs;t illa diameter, &longs;i enim ill&aelig; lationes non &longs;unt la&shy;<lb/>
teribus proportionales, latum illud non feretur &longs;ecundum diametrum il&shy;<lb/>
lam, &longs;ed &longs;ecundum aliam alterius quadrilateri.</s>
        </p>
        <p type="main">
          <s id="s.002624">Quod &longs;i quid duabus lationibus nullam habentibus proportionem per&shy;<lb/>
petu&ograve; ferratur, impo&longs;&longs;ibile e&longs;t ip&longs;um motu mixto lineam rectam de&longs;cribere. <lb/>
</s>
          <s id="s.002625">&longs;i enim dixeris illud po&longs;&longs;e de&longs;cribere rectam lineam, tunc circa rectam il&shy;<lb/>
lam tanquam diametrum de&longs;cribam quadrilaterum, &amp; po&longs;tea o&longs;tendam, vt <lb/>
proxim&egrave; o&longs;ten&longs;um e&longs;t, illud latum e&longs;&longs;e &longs;ecundum laterum illius proportio&shy;<lb/>
nem, quare impo&longs;&longs;ibile e&longs;t id, quod mouetur duabus lationibus nullam in&shy;<lb/>
uicem rationem habentibus, ferri per lineam rectam: quapropter <expan abbr="dic&etilde;dum">dicendum</expan> <lb/>
e&longs;t hoc modo <expan abbr="lat&utilde;">latum</expan>, nece&longs;&longs;ari&ograve; ferri circulariter, &longs;iue per lineam circularem. <lb/>
</s>
          <s id="s.002626">Quod autem ea, qu&aelig; de&longs;cribit circulum linea, dum altero eius manente <lb/>
extremo circumagitur, duabus &longs;imul feratur lationibus, ex quibus motus <lb/>
orbicularis oriatur, manife&longs;tum e&longs;t ex &longs;uperioribus, quia &amp; antror&longs;um, &amp; <lb/>
retror&longs;um impellitur; t&ugrave;m etiam, quia &longs;i rect&agrave; tenderet recta <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> cir&shy;<lb/>
<figure id="id.009.01.151.2.jpg" place="text" xlink:href="009/01/151/2.jpg"/><lb/>
culum, nunquam ad diametri perpendiculum <lb/>
perueniret, &longs;ed tamen peruenit, ita vt &longs;it ip&longs;a <lb/>
&agrave; centro perpendicularis diametro. </s>
          <s id="s.002627">&longs;it circuli <lb/>
figura A B C D, in qua extremum diametri <lb/>
B, feratur ad alterum extremum vbi D, per <lb/>
ip&longs;ius diametri B D, circumuolutionem circa <lb/>
centrum F, nece&longs;&longs;e e&longs;t aliquando B, perueniat <lb/>
ad C. &longs;i igitur B, feretur duabus lationibus <lb/>
aliquo modo proportionatis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->vt e&longs;t pro&shy;<lb/>
portio lateris B E, ad E C, latus, &longs;equeretur <lb/>
ex demon&longs;tratis ip&longs;um B, ferri per <expan abbr="rect&atilde;">rectam</expan> B C, <lb/>qu&aelig; diameter e&longs;&longs;et quadrilateri B E C G. &longs;ed <pb pagenum="152" xlink:href="009/01/152.jpg"/>quia in nulla proportione fertur, propterea per circularem lineam B E C, <lb/>
progreditur ad C, ita vt ip&longs;a diameter B D, in po&longs;itione A C, fiat perpendi&shy;<lb/>
cularis priori diametro B D. ex quibus &longs;equitur eam moueri duobus moti&shy;<lb/>
bus nullam rationem habentibus; quod erat intentum.</s>
        </p>
        <p type="main">
          <s id="s.002628">Hoc modo Ari&longs;t. probare conatur, lineam circulum de&longs;cribentem, dua&shy;<lb/>bus ferri lationibus, qu&aelig; nullam habeant analogiam: Ver&ugrave;m, vt liber&egrave; fa&shy;<lb/>
tear nullo modo mihi videtur intentum a&longs;&longs;equi, nam <expan abbr="neq;">neque</expan> ex dictis pater, <lb/>
ip&longs;am duobus motibus ferri, quibus opus e&longs;&longs;et: neque patet eos &lpar;quamuis <lb/>
concedantur&rpar; nullam inuicem habere analogiam: qui enim fieri pote&longs;t, vt <lb/>
duo motus reperiantur, qu&igrave; nulla &longs;e mutu&ograve; habitudine re&longs;piciant? </s>
          <s id="s.002629">Pr&aelig;te&shy;<lb/>
rea &longs;i B, ferretur illis motibus, non &longs;equitur debere moueri per lineam cir&shy;<lb/>
cularem, cum pr&aelig;ter lineam rectam &longs;int plures curu&aelig;, qu&aelig; tamen non &longs;unt <lb/>
circulares, vt &longs;unt &longs;ectiones parabolic&aelig;, &amp; line&aelig; &longs;pirales. </s>
          <s id="s.002630">Deinde pergit.</s>
        </p>
        <p type="main">
          <s id="s.002631"><arrow.to.target n="marg231"/></s>
        </p>
        <p type="margin">
          <s id="s.002632"><margin.target id="marg231"/>241</s>
        </p>
        <p type="main">
          <s id="s.002633">Vt autem cau&longs;a appareat, cur ea, qu&aelig; &agrave; centro longior e&longs;t linea velocius <lb/>
moueatur, &longs;iue quod in eadem &longs;emidiametro remotiora puncta &agrave; <expan abbr="c&etilde;tro">centro</expan> ve&shy;<lb/>
locius moueantur, vt &longs;upra dictum e&longs;t, &longs;ciendum e&longs;t, Quod &longs;i duo mouean&shy;<lb/>
tur ab eadem potentia, quorum vnum &agrave; quopiam alio mouente plus repel&shy;<lb/>
latur &agrave; motu priori, alterum ver&ograve; minus, rationi <expan abbr="c&otilde;&longs;entaneum">con&longs;entaneum</expan> e&longs;&longs;e, tardius <lb/>
moueri id, quod plus, eo quod minus impeditur; quod videtur accidere <lb/>
maiori, &amp; minori illarum, qu&aelig; &agrave; centro egre&longs;&longs;&aelig; circulos delineant. </s>
          <s id="s.002634">quoniam <lb/>
enim propius e&longs;t manenti eius, qu&aelig; minor e&longs;t extremum, qu&agrave;m extremum <lb/>
maioris, propterea plus &agrave; centro, cui propius e&longs;t, retrahitur &agrave; priori mo&shy;<lb/>
tu, <expan abbr="hinc&qacute;">hincque</expan>; motus eius tardior redditur, ide&longs;t, quia centro propius e&longs;t; hinc <lb/>
fit, vt extremum illud de&longs;cribat lineam circularem quidem, &longs;ed tamen <lb/>
curuiorem quam de&longs;cribat extremum longioris line&aelig;, qu&aelig; circulum minus <lb/>
curuum, &longs;eu magis ad rectam lineam accedentem delineat. </s>
          <s id="s.002635">omni quidem <lb/>
igitur line&aelig; circulum de&longs;cribenti i&longs;tud accidit, vt duobus feratur motioni&shy;<lb/>
bus; vna quidem, qu&aelig; illi naturalis, ac &longs;ecundum circunferentiam, qua re&shy;<lb/>
ct&agrave; tenderet ni&longs;i impediretur: altera ver&ograve;, qu&aelig; illi innaturalis, qua in tran&longs;&shy;<lb/>
uer&longs;um agitur, &longs;eu &longs;ecus centrum, ob quam cogitur in gyrum duci, minor <lb/>
autem linea &longs;ecundum hanc motionem innaturalem plus fertur, qu&agrave;m ma&shy;<lb/>
ior, ide&longs;t plus ip&longs;ius progre&longs;&longs;io inflectitur in orbem; quia enim e&longs;t centro <lb/>
<figure id="id.009.01.152.1.jpg" place="text" xlink:href="009/01/152/1.jpg"/><lb/>
vicinior, quod quodammodo retra&shy;<lb/>
hit &agrave; motu naturali, propterea ma&shy;<lb/>
gis vincitur, qu&agrave;m remotior. </s>
          <s id="s.002636">Quod <lb/>
ex his erit <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan>. </s>
          <s id="s.002637">&longs;it circulus vbi <lb/>
B C E D, &amp; alter in eo minor, vbi <lb/>
N M O P, circa idem centrum A. &amp; <lb/>
proijciantur diametri in magno qui&shy;<lb/>
dem C D, B E, in minori ver&ograve; M O, <lb/>
N P. &amp; altera parte longius quadri&shy;<lb/>
laterum compleatur D K R C. &longs;i igi&shy;<lb/>
tur &longs;emidiameter A B, circumacta <lb/>
de&longs;cribit circulum maiorem, reuer&shy;<lb/>
titur tandem ad locum B A, vnde di&shy;<lb/>
gre&longs;&longs;a e&longs;t. </s>
          <s id="s.002638">&longs;imiliter M A, circumuoluta <pb pagenum="153" xlink:href="009/01/153.jpg"/>redibit ad priorem po&longs;itionem in M A. <!-- KEEP S--></s>
          <s id="s.002639">Tardius autem fertur M A, qu&agrave;m <lb/>
B A, vt dictum e&longs;t, quia maior illi fit retractio &agrave; recta progre&longs;&longs;ione. </s>
          <s id="s.002640">Sit igi&shy;<lb/>
tur linea A B, mota v&longs;que ad locum A L F, &amp; &agrave; puncto L, ducatur L Q, per&shy;<lb/>
pendicularis ip&longs;i A B, in minori circulo. </s>
          <s id="s.002641">&amp; rur&longs;us ducatur L S, parallela ei&shy;<lb/>
dem A B, &amp; &agrave; puncto S, in maiori circulo ducatur S T, perpendicularis ei&shy;<lb/>
dem B A, necnon F X. erunt igitur S T, L Q, latera rectanguli T L, &aelig;qualia <lb/>
per 34. primi. </s>
          <s id="s.002642">erit po&longs;tea B T, minor quam M Q, quia &aelig;quales rect&aelig; S T, <lb/>
L Q, duct&aelig; &agrave; circunferentia ad diametrum perpendiculares in circulis in&shy;<lb/>
&aelig;qualibus, ea qu&aelig; e&longs;t in maiori circulo minorem re&longs;ecat diametri portio&shy;<lb/>
nem, qu&agrave;m qu&aelig; in minori.</s>
        </p>
        <p type="main">
          <s id="s.002643">In quanto autem tempore ip&longs;a A L, lata e&longs;t per circunferentiam M L, in <lb/>
tanto temporis &longs;patio in maiori circulo B, extremum ip&longs;ius B A, latum erit <lb/>per maiorem arcum qu&agrave;m &longs;it B S; iam con&longs;iderandum e&longs;t motus vtriu&longs;que <lb/>
line&aelig; in hoc ca&longs;u &aelig;quales e&longs;&longs;e, &longs;unt enim de&longs;cripti per lineas &aelig;quales T S, <lb/>
Q L, qu&aelig; &longs;unt rect&aelig;; tam enim linea B A, qu&agrave;m M A, naturali motu recta <lb/>
tenderet, vt dictum e&longs;t, <expan abbr="peragra&longs;&longs;et&qacute;">peragra&longs;&longs;etque</expan>; illa rectam T S: h&aelig;c ver&ograve; rectam Q L. <lb/>
<!-- KEEP S--></s>
          <s id="s.002644">Verum lationes innaturales &longs;unt impares, latio enim B T, breuior e&longs;t M <expan abbr="q.">que</expan> <lb/>
quantitate autem B T, retracta e&longs;t B A, &agrave; motu &longs;ibi naturali, &amp; recto: quan&shy;<lb/>
titate ver&ograve; M Q, retracta e&longs;t M A, vnde apparet motu hoc violento magis <lb/>
retractam e&longs;&longs;e minorem M A, qu&agrave;m maiorem B A, quod erat primo de&shy;<lb/>
clarandum.</s>
        </p>
        <p type="main">
          <s id="s.002645">Quod autem ob id A B, maior c&etail;lerius mota &longs;it motu naturali, qu&agrave;m mi&shy;<lb/>
nor M A, pal&agrave;m fiet. </s>
          <s id="s.002646">quia enim oportet <expan abbr="vtramq;">vtramque</expan> lineam maiorem, &amp; mi&shy;<lb/>
norem eadem vi motam, confeci&longs;&longs;e binos illos motus proportionales, ide&longs;t <lb/>
ita &longs;e debet habere motus naturalis maioris ad motum innaturalem eiu&longs;&shy;<lb/>
dem, quemadmodum &longs;e habet motus naturalis minoris ad motum innatu&shy;<lb/>
ralem eiu&longs;dem: Oportet ergo, vt &longs;i A B, &amp; A M, &longs;unt eadem vi commot&aelig;, <lb/>
vt &longs;it eadem ratio T S, ad Q L, qu&aelig; e&longs;t B T, ad M Q, non e&longs;t autem, vt o&longs;ten&shy;<lb/>
&longs;um e&longs;t; ergo linea A B, eadem vi commota, ac M A, conficit plu&longs;quam <lb/>
B S, &longs;ed nece&longs;&longs;ari&ograve; peruenit ad F. hoc enim in puncto erunt pr&aelig;dicti motus <lb/>
proportionales, vt oportet, erit enim motus naturalis in maiori perpendi&shy;<lb/>
cularis F X, &amp; innaturalis B X, in minori ver&ograve; naturalis L Q, innaturalis <lb/>
M <expan abbr="q.">que</expan> quod &longs;i ducantur rect&egrave; B F, M L, apparebunt duo triangula &aelig;quian&shy;<lb/>
gula B X F, M Q L, &amp; erunt per 4. 6. vt F X, ad B X. ita L Q, ad M Q, &amp; <lb/>
permutando erunt etiam vt F X, ad L Q, ita B X, ad M <expan abbr="q.">que</expan> ide&longs;t, vt motus <lb/>
naturalis ad naturalem, ita innaturalis ad innaturalem. </s>
          <s id="s.002647">In alio autem lo&shy;<lb/>
co pr&aelig;ter F, non erunt e&aelig;dem proportiones.</s>
        </p>
        <p type="main">
          <s id="s.002648">Ex quibus patere &longs;atis pote&longs;t, cur A B, longior &agrave; centro velocius mouea&shy;<lb/>
tur qu&agrave;m minor M A, &longs;eu cur puncta eiu&longs;dem B A, velocius vertuntur, quo <lb/>
longius ab&longs;unt &agrave; centro A, ide&longs;t maiorem arcum B F, peractum e&longs;&longs;e &agrave; B, <lb/>
qu&agrave;m &longs;it arcus M L, peractus ab M, quod erat o&longs;tendendum.</s>
        </p>
        <p type="main">
          <s id="s.002649">Atque hic e&longs;t di&longs;cur&longs;us ille Ari&longs;t. quo putat &longs;e cau&longs;am aperui&longs;&longs;e, cur lon&shy;<lb/>
gior &longs;emidiameter velocius moueatur: quod num rect&egrave; attigerit, non puto <lb/>
oper&aelig;pretium e&longs;&longs;e hoc loco di&longs;cutere, pr&aelig;&longs;ertim cum ad naturalem Philo&shy;<lb/>
&longs;ophum &longs;pectet.</s>
        </p>
        <p type="main">
          <s id="s.002650">Mihi tamen maxim&egrave; con&longs;iderandum videtur hoc ip&longs;um quod a&longs;&longs;eruit, &amp; <pb pagenum="154" xlink:href="009/01/154.jpg"/>ex &longs;e patet, remotiores &longs;cilicet partes diametrorum &agrave; centro velocius mo&shy;<lb/>
ueri, qu&agrave;m viciniores; ex hac enim maiori velocitate &longs;equitur maiore etiam <lb/>
vi moueri, vnde &amp; potenti&aelig; mouenti in extremo eius vis augebitur, &amp; plus <lb/>
poterit quam &longs;ola &longs;ine vecte, e&longs;t enim vectis du&aelig; &longs;emidiametri altera alte&shy;<lb/>
ram longior; ex quibus fort&egrave; apparet vnde vectis vires oriantur.</s>
        </p>
        <p type="main">
          <s id="s.002651">His igitur tanquam huius Mechanic&aelig; facultatis principijs po&longs;itis, ad va&shy;<lb/>
rias Qu&aelig;&longs;tiones di&longs;cutiendas accedit.</s>
        </p>
        <p type="head">
          <s id="s.002652"><emph type="italics"/>QV&AElig;STIO PRIMA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002653"><emph type="italics"/>De Libra.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002654"><arrow.to.target n="marg232"/></s>
        </p>
        <p type="margin">
          <s id="s.002655"><margin.target id="marg232"/>242</s>
        </p>
        <p type="main">
          <s id="s.002656">Cvr autem maiores libr&aelig; minoribus &longs;int exactiores, pal&agrave;m e&longs;t ex <lb/>
pr&aelig;mi&longs;&longs;is principijs. </s>
          <s id="s.002657">con&longs;iderare enim oportet, quod in motu li&shy;<lb/>
br&aelig; de&longs;cribitur quidam circulus, cuius diameter &longs;unt ip&longs;a libr&aelig; <lb/>brachia, centrum ver&ograve; e&longs;t &longs;partum, &longs;iue trutina; hoc enim pun&shy;<lb/>
ctum in motu libr&aelig; manet: duo ver&ograve; brachia &longs;unt veluti du&aelig; &longs;emidiametri <lb/>
<figure id="id.009.01.154.1.jpg" place="text" xlink:href="009/01/154/1.jpg"/><lb/>
&agrave; centro exeuntes, vt in figura cerne&shy;<lb/>
re e&longs;t, in qua centrum, &longs;iue &longs;partum <lb/>
e&longs;t vbi C, reliqua &longs;unt manife&longs;ta. </s>
          <s id="s.002658">In <lb/>
eadem porr&ograve; figura libra maior &longs;it <lb/>
A B. minor ver&ograve; circa idem &longs;partum <lb/>
C, &longs;it F G. <!-- KEEP S--></s>
          <s id="s.002659">Iam vt pr&aelig;mi&longs;&longs;um e&longs;t, ea&shy;<lb/>
dem vi, vel eodem onere in lance B, <lb/>
po&longs;ito, mouebitur velocius brachium <lb/>
libr&aelig; maioris, qu&agrave;m minoris &longs;it ma&shy;<lb/>
ior tran&longs;lata ad <expan abbr="loc&utilde;">locum</expan> D E, erg&ograve; com&shy;<lb/>
mota e&longs;t per arcum B E, vel A D. <!-- KEEP S--></s>
          <s id="s.002660">Minor autem libra acta e&longs;&longs;et per mino&shy;<lb/>
rem arcum G I, vel F H, melius autem apparet arcus B E, maior, quam mi&shy;<lb/>
nor G I, <expan abbr="atq;">atque</expan> hoc e&longs;t, qu&ograve;d maiores libras exactiores facit. </s>
          <s id="s.002661"><expan abbr="hinc&qacute;">hincque</expan>; etiam e&longs;t, <lb/>
qu&ograve;d nonnulla pondera in minimis libris ade&ograve; paruam brachiorum aper&shy;<lb/>
tionem faciant, vt &aelig;gr&egrave; percipi po&longs;&longs;it; in magnis ver&ograve; propter brachiorum <lb/>
longitudinem vald&egrave; &longs;en&longs;ibilem efficiant. </s>
          <s id="s.002662">qu&aelig;dam ver&ograve; ben&egrave;, &amp; in magnis, <lb/>
&amp; in paruis apparent, &longs;ed tamen &longs;emper melius in magnis ob dictam ratio&shy;<lb/>
nem. </s>
          <s id="s.002663">Quamobrem machinantur ij, qui purpuram vendunt, vt pendendo <lb/>
defraudent, tum in medio libr&aelig; non ponentes &longs;partum, vt hoc modo bra&shy;<lb/>
chium ex vna parte longius factum facilius moueatur, &amp; proinde &agrave; minori <lb/>
purpur&aelig; pondere; tum etiam <expan abbr="plumb&utilde;">plumbum</expan> in lancem illam infundentes inquam <lb/>
merces imponitur, vel partem illam lancis, quam magis grauitare cu&shy;<lb/>
piunt ex ligno radici proximo, vel ex nodo&longs;o facientes: lignum <lb/>
enim, quod radici proximum e&longs;t, graue admodum e&longs;t, <lb/>
quemadmodum etiam nodus; quia nodus e&longs;t, <lb/>
qu&aelig;dam radix. </s>
          <s id="s.002664"><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t huius pri&shy;<lb/>
m&aelig; qu&aelig;&longs;tionis paraphra&longs;is.</s>
        </p>
        <pb pagenum="155" xlink:href="009/01/155.jpg"/>
        <p type="head">
          <s id="s.002665"><emph type="italics"/>QV&AElig;STIO SECVNDA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002666"><emph type="italics"/>De Libra<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002667"><arrow.to.target n="marg233"/></s>
        </p>
        <p type="margin">
          <s id="s.002668"><margin.target id="marg233"/>243</s>
        </p>
        <p type="main">
          <s id="s.002669"><emph type="italics"/>Cvr &longs;i quidem &longs;ur&longs;um fuerit &longs;partum, quando deor&longs;um lato pondere, qui&longs;&shy;<lb/>
piam id amouet, rur&longs;um a&longs;cendit libra? </s>
          <s id="s.002670">Si autem deor&longs;um constitutum <lb/>
fuerit, non a&longs;cendit, &longs;ed manet? </s>
          <s id="s.002671">An quia &longs;ur&longs;um &longs;parto quidem exi&longs;ten&shy;<lb/>
te plus libr&aelig; extra perpendiculum fit, &longs;partum enim e&longs;t perpendiculum, <lb/>
quare nece&longs;&longs;e est deor&longs;um ferri id, quod plus est, donec a&longs;cendat, qu&aelig; bifariam li&shy;<lb/>bram diuidit ad ip&longs;um perpendicul&ubreve;m, cum onus incumbat ad libr&aelig; partem tractam.<emph.end type="italics"/><lb/>
<figure id="id.009.01.155.1.jpg" place="text" xlink:href="009/01/155/1.jpg"/><lb/>
<emph type="italics"/>&longs;it libra vbi recta B C, &longs;partum autem <lb/>
A D: hoc igitur &longs;ur&longs;um erecto, perpendi&shy;<lb/>
culum erit vbi A D M. &longs;i igitur in ip&longs;o B, <lb/>
ponatur onus, B, quidem de&longs;cendet vbi E; <lb/>
C, autem a&longs;cendat vbi H, quamobrem ea, <lb/>
qu&aelig; bifariam libram &longs;ecat, prim&ograve; quidem <lb/>
erit D M, ip&longs;ius perpendiculi; incumben&shy;<lb/>
te autem onere erit D G, quare libr&aelig; ip&shy;<lb/>
&longs;ius vbi E H, quod extra A M, perpendi&shy;<lb/>
culum e&longs;t, vbi e&longs;t D D H, maius e&longs;t dimidio. </s>
          <s id="s.002672">&longs;i igitur amoueatur onus ab ip&longs;o E, ne&shy;<lb/>
ce&longs;&longs;e e&longs;t H, deor&longs;um ferri, minus enim e&longs;t ip&longs;um E D. &longs;i quidem igitur &longs;ur&longs;um ha&shy;<lb/>
buerit &longs;partum, propter hoc a&longs;cendit libra. </s>
          <s id="s.002673">&longs;i autem deor&longs;um fuerit, id quod &longs;ub&shy;<lb/>
stat, contrarium facit; plus enim dimidio fit libr&aelig;, qu&aelig; deor&longs;um e&longs;t, pars, qu&agrave;m <lb/>
quod perpendiculum &longs;ecet; quapropter non a&longs;cendit, pars enim eleuata leuior e&longs;t.<emph.end type="italics"/><lb/>
<figure id="id.009.01.155.2.jpg" place="text" xlink:href="009/01/155/2.jpg"/><lb/>
<emph type="italics"/>&longs;it libra vbi N G, perpendiculum autem <lb/>
K L M, bifariam igitur &longs;ecatur N G. im&shy;<lb/>
po&longs;ito autem onere in ip&longs;o N, erit quidem <lb/>
N, vbi O, ip&longs;um autem G, vbi R; K L, au&shy;<lb/>
tem vbi K P, quare maius e&longs;t L P O, qu&agrave;m <lb/>
L R, ip&longs;o P L. <!-- KEEP S--></s>
          <s id="s.002674">Ablato igitur onere, ne&shy;<lb/>
ce&longs;&longs;e e&longs;t manere; incumbit enim, ceu onus <lb/>
exce&longs;&longs;us medietatis in quo P L.&rpar;<emph.end type="italics"/> Aduer&shy;<lb/>
te textum gr&aelig;cum e&longs;&longs;e mendo&longs;um, la&shy;<lb/>
tinum vero mendo&longs;i&longs;&longs;imum. </s>
          <s id="s.002675">Ego partim ex certa rei intelligentia, vti vi&shy;<lb/>
des re&longs;titui. </s>
          <s id="s.002676"><expan abbr="Idem&qacute;">Idemque</expan>; circa figuras pr&aelig;&longs;titi. </s>
          <s id="s.002677">Porr&ograve; quoniam Piccolomineus, <lb/>
&amp; &longs;i plurimum, vt ip&longs;e fatetur, in&longs;udauerit, non tamen &longs;olutionem huius <lb/>
qu&aelig;&longs;tionis e&longs;t a&longs;&longs;ecutus, eam tibi ex Mechanicis Guidibaldi tradam. </s>
          <s id="s.002678">Ari&longs;t. <lb/>
igitur ponit duas libr&aelig; &longs;pecies, &longs;iue potius duas eiu&longs;dem libr&aelig; po&longs;itiones, <lb/>vnam, qu&aelig; habet &longs;partum, &longs;iue perpendiculum &longs;upra; alteram, qu&aelig; infra. <lb/>
<figure id="id.009.01.155.3.jpg" place="text" xlink:href="009/01/155/3.jpg"/><lb/>
vt in pr&aelig;&longs;enti figura, &longs;it libra B C, cuius <lb/>
&longs;partum, &longs;iue perpendiculum A D, &longs;it &longs;ur&shy;<lb/>
&longs;um, ita vt in puncto A, &longs;it affixum perpen&shy;<lb/>
diculum, &amp; circa idem punctum A, tan&shy;<lb/>
quam circa centrum tota libra circum&shy;<lb/>
uertatur. </s>
          <s id="s.002679">h&aelig;c e&longs;t prima libr&aelig; collocatio. </s>
          <s id="s.002680">&longs;it deinde libra B C, cuius &longs;partum, <lb/>
&longs;iue perpendiculum A D, &longs;it deor&longs;um, vt in altera figura, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; circa pun&shy;


<pb pagenum="156" xlink:href="009/01/156.jpg"/><figure id="id.009.01.156.1.jpg" place="text" xlink:href="009/01/156/1.jpg"/><lb/>
ctum A, tanquam circa <expan abbr="centr&utilde;">centrum</expan>, aut axem <lb/>
ita fixum, vt ip&longs;i libr&aelig; conuer&longs;io innita&shy;<lb/>
tur, qu&aelig; e&longs;t altera libr&aelig; po&longs;itio. </s>
          <s id="s.002681">Qu&aelig;rit <lb/>
igitur, cur &longs;i in libra &longs;ur&longs;um <expan abbr="hab&etilde;te">habente</expan> per&shy;<lb/>
pendiculum, &amp; centrum, ponatur ex vna <lb/>
parte onus quodpiam, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in parte B, vt in prima textus figura factum e&longs;t, <lb/>
libra de primo &longs;itu B C, mouetur ad &longs;itum E H, &longs;ed tamen ablato pondere <lb/>
reuertitur &longs;ua &longs;pont&egrave; ad pri&longs;tinum &longs;itum B C. &longs;i autem in libra, cuius per&shy;<lb/>
pendiculum, ac centrum deor&longs;um &longs;it, vt in &longs;ecunda figura textus, pondus <lb/>
imponatur, ip&longs;a quidem &agrave; &longs;itu B C, ad &longs;itum O R, transferretur; verumta&shy;<lb/>
men ablato onere, <expan abbr="n&otilde;">non</expan> amplius ad priorem po&longs;itionem, vti prior, reuertitur.</s>
        </p>
        <p type="main">
          <s id="s.002682">Huic qu&aelig;&longs;tioni, vt re&longs;pondeat, tacit&egrave; &longs;upponit omne graue tendere de&shy;<lb/>
or&longs;um, hoc pacto, vt centrum grauitatis ip&longs;ius tendat per lineam rectam <lb/>
ad mundi centrum ab ip&longs;o grauitatis centro protractam, quam lineam Di&shy;<lb/>
rectionis Recentiores appellant. </s>
          <s id="s.002683">&longs;ciendum autem centrum grauitatis e&longs;&longs;e <lb/>
punctum quoddam in quolibet graui, ex quo &longs;i graue illud &longs;u&longs;pendatur, &longs;em&shy;<lb/>
per manet in &aelig;quilibrio, nec vnquam po&longs;itionem re&longs;pectu &longs;uarum partium <lb/>
mutat, quamuis ita &longs;u&longs;pen&longs;um huc illuc transferatur. </s>
          <s id="s.002684">Ita Pappus Alexan&shy;<lb/>
drinus initio octaui libri Mathematicarum collectionum. </s>
          <s id="s.002685">Totius igitur li&shy;<lb/>
br&aelig; ab&longs;que onere centrum grauitatis e&longs;&longs;et circa punctum D, quod e&longs;&longs;et di&shy;<lb/>
&longs;tinctum &agrave; centro circumuolutionis A. quod grauitatis centrum, &longs;emper <lb/>
quantum fieri pote&longs;t, &longs;i nihil ob&longs;tet, centro mundi appropinquat; &amp; propte&shy;<lb/>
rea facit, vt prior libra &longs;ine onere &longs;u&longs;pen&longs;a in A, in &aelig;quilibrio, atque hori&shy;<lb/>
zonti parallela permaneat, &longs;tante enim D, centro mundi maxim&egrave; propin&shy;<lb/>
quo, &longs;iue in loco humillimo, erit inter punctum A, &amp; centrum mundi, ac <lb/>
con&longs;equenter in linea directionis. </s>
          <s id="s.002686">qu&aelig; linea directionis in prima figura <lb/>
textus e&longs;&longs;et eadem cum perpendiculo A D M, manente libra &longs;ine pondere <lb/>
horizonti parallela; in <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> autem figura textus coincideret pariter cum <lb/>
perpendiculo K L M, antequam libra ob impo&longs;itum onus ab &aelig;quilibrio di&shy;<lb/>
moueretur. </s>
          <s id="s.002687">per hanc enim lineam centrum grauitatis libr&aelig;, quod e&longs;t prop&egrave; <lb/>
puncta D, &amp; L, tenderet ad mundi centrum, &longs;i libra liber&egrave; ad centrum mun&shy;<lb/>
di dilaberetur. </s>
          <s id="s.002688">his pr&aelig;mi&longs;&longs;is &longs;ic qu&aelig;&longs;tioni &longs;atisfacit, &amp; prim&ograve; prim&aelig; parti, <lb/>
quando nimirum &longs;partum &longs;upern&egrave; collocatum e&longs;t. </s>
          <s id="s.002689">Ratio igitur, cur tunc li&shy;<lb/>
bra amoto pondere ad horizontis &aelig;quilibrium reuertatur e&longs;t, quia pondus <lb/>
libr&aelig; impo&longs;itum in altera tantum libr&aelig; parte, grauitando impellit libram <lb/>
ad alium &longs;itum E H, ita vt maior pars libr&aelig; con&longs;tituatur ex altera parte li&shy;<lb/>ne&aelig; directionis prioris A D M, in qua etiam parte exi&longs;tit centrum grauita&shy;<lb/>
tis libr&aelig; ip&longs;ius, e&longs;t enim circa D, quod centrum vi ponderis incumbentis in <lb/>
E, cogitur paul&ugrave;m a&longs;cendere, <expan abbr="atq;">atque</expan> contra ip&longs;ius naturalem inclinationem &agrave; <lb/>
mundi centro recedere, vt &longs;i in libra B C, appendatur onus in B, vt in pri&shy;<lb/>
ma textus figura; B, de&longs;cendet ad E, &amp; C, a&longs;cendet ad H, &amp; centrum graui&shy;<lb/>tatis D, paul&ugrave;m a&longs;cendet &agrave; centro mundi, &amp; linea A D M, qu&aelig; libram bi&shy;<lb/>
fariam &longs;ecabat modo tran&longs;lato perpendiculo in A D G, non amplius cam <lb/>
bifariam &longs;ecabit; &longs;ed libr&aelig; E H, maior pars erit vltra perpendiculum A D&shy;<lb/>
M, qu&aelig; maior pars e&longs;t D D H.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002690">Si igitur nunc onus amoueatur libr&aelig; E H, centrum grauitatis, quod e&longs;t <pb pagenum="157" xlink:href="009/01/157.jpg"/>ad D, remanet vltra priorem Directionis lineam; &amp; quia pondus non am&shy;<lb/>
plius illi &aelig; que ponderat, grauitabit, &amp; quia libra c&ugrave;m affixa &longs;it ad A, nequit <lb/>
deor&longs;um recta tendere, circumferretur circa A, trahente ip&longs;am grauitatis <lb/>
centro, cum nihil ob&longs;it, donec iterum perpendiculum A D G, priori &longs;itui <lb/>
A D M, congruat: hac enim ratione centrum grauitatis, quantum pote&longs;t, <lb/>
iuxta naturam &longs;uam de&longs;cendet, <expan abbr="libra&qacute;">libraque</expan>; ad pri&longs;tinum &aelig;quilibrij B C, &longs;itum <lb/>
re&longs;tituetur. </s>
          <s id="s.002691">Si autem deor&longs;um fuerit &longs;partum in &longs;ecunda figura textus, im&shy;<lb/>
po&longs;ito pondere contrarium accidit, quia maior pars libr&aelig;, &amp; in qua cen&shy;<lb/>
trum grauitatis e&longs;t, in tali motu de&longs;cendit: altera autem pars minor, ac l&aelig;&shy;<lb/>
uior &longs;ur&longs;um tollitur. </s>
          <s id="s.002692">&amp; quia graue natura &longs;ua nequit a&longs;cendere, propterea <lb/>
ablato pondere non reuertitur ad &aelig;quilibrium B C, cum centrum grauita&shy;<lb/>
tis a&longs;cendere ne queat, quod tunc oporteret.</s>
        </p>
        <p type="main">
          <s id="s.002693">Sit libra N G, in &longs;ecunda figura, cuius perpendiculum, <expan abbr="&longs;imul&qacute;">&longs;imulque</expan>; directio&shy;<lb/>nis linea &longs;it K L M, qu&aelig; libram in prima po&longs;itione diuidit bifariam; impo&longs;i&shy;<lb/>
to autem onere in N. N, trahetur ad O, &amp; G, ad R, &amp; K L, vbi K P. quare <lb/>
maior e&longs;t O L, in quo <expan abbr="centr&utilde;">centrum</expan> grauitatis, &amp; propterea grauior qu&agrave;m &longs;it L R: <lb/>
&longs;uperat enim O L, ip&longs;am L R, exce&longs;&longs;u dupl&aelig; P L, quod facil&egrave; apparet &longs;i po&shy;<lb/>
natur tota O R, 10. &amp; dimidia O P, &amp; O R, 5. &amp; P L, ponatur 2. erit enim <lb/>
tunc O L, 7. &amp; L R, 3. qu&aelig; hanc &longs;uperat 4. duplo &longs;cilicet ip&longs;ius P L, 2. qua&shy;<lb/>
re ne&longs;cio cur Ari&longs;t. dicat, ip&longs;am O L, &longs;uperare ip&longs;am L R, &longs;ol&ugrave;m quantitate <lb/>
P L. <!-- KEEP S--></s>
          <s id="s.002694">Quapropter etiam &longs;i onus auferatur, nece&longs;&longs;e e&longs;t ibi libram manere, <lb/>
quia maior, &amp; grauior ip&longs;ius pars deor&longs;um e&longs;t, nec pote&longs;t natura &longs;ua l&aelig;ui&shy;<lb/>
tare, vel a&longs;cendere, vt oporteret, &longs;i ad pri&longs;tinum &longs;itum N G, re&longs;titui debe&shy;<lb/>
ret. </s>
          <s id="s.002695">remanebit igitur in O R.</s>
        </p>
        <p type="main">
          <s id="s.002696">Ex his, qu&aelig;&longs;tionis &longs;olutionem, textus explicationem, ac re&longs;titutio&shy;<lb/>
nem habeto.</s>
        </p>
        <p type="main">
          <s id="s.002697">Aduertendum quoad &longs;ecundam libram, ne &longs;imul cum 10. Bapti&longs;ta Bene&shy;<lb/>
dicto in libro &longs;peculationum immerit&ograve; Ari&longs;t. erroris arguamus: ip&longs;e enim, <lb/>
quia libram hanc non agnouit, au&longs;us e&longs;t affirmare, Ari&longs;tot. hoc loco fal&longs;um <lb/>pror&longs;us dixi&longs;&longs;e, cum dixit libram &longs;parto infim&egrave; collocato, non redire ad <lb/>
pri&longs;tinam po&longs;itionem.</s>
        </p>
        <p type="head">
          <s id="s.002698"><emph type="italics"/>QV&AElig;STIO TERTIA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002699"><emph type="italics"/>De Vecte.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002700"><arrow.to.target n="marg234"/></s>
        </p>
        <p type="margin">
          <s id="s.002701"><margin.target id="marg234"/>244</s>
        </p>
        <p type="main">
          <s id="s.002702">Cvm textus tam gr&aelig;ci, qu&agrave;m latini mendis &longs;cateant, <expan abbr="neq;">neque</expan> hi textus <lb/>
maioris &longs;int momenti, eos per paraphra&longs;im explicabo, in qua ta&shy;<lb/>
men totus textus continebitur, <expan abbr="atq;">atque</expan> emendabitur. </s>
          <s id="s.002703">Cur exigu&aelig; <lb/>
vires &lpar;quemadmodum &agrave; principio dictum e&longs;t&rpar; adhibito vecte, ma&shy;<lb/>
iora mouent pondera, quam <expan abbr="ab&longs;q;">ab&longs;que</expan> vecte? </s>
          <s id="s.002704">contrarium enim videtur debere <lb/>
fieri, nam mouenti additur grauitas vectis, &amp; ide&ograve; pondus augetur, erg&ograve; <lb/>
difficilius ip&longs;um cum vecte, qu&agrave;m &longs;ine eo mouere deberet.</s>
        </p>
        <p type="main">
          <s id="s.002705">Vectis porr&ograve; e&longs;t in&longs;trumentum oblongum, quo ad &longs;ubleuandum graue <lb/>
quodpiam vtuntur opifices, quod innititur cuidam fulcimento, quod gr&aelig;c&egrave; <lb/>hypomoclion dicitur: hypomoclion autem oneri leuando, quantum fieri <pb pagenum="158" xlink:href="009/01/158.jpg"/>pote&longs;t proximum e&longs;&longs;e debet, vt vectis pars longior &longs;it ad partes potenti&aelig; <lb/>
mouentis. </s>
          <s id="s.002706">vt plurimum ver&ograve; fulcimentum e&longs;t inter pondus, &amp; potentiam: <lb/>
aliquando etiam e&longs;t ex altero vectis extremo, ita vt onus &longs;it inter fulturam, <lb/>
&amp; potentiam; aliquando potentia e&longs;t inter vtrunque, vnde tres vectis &longs;pe&shy;<lb/>
cies exi&longs;tunt. </s>
          <s id="s.002707">vt in &longs;ubiectis figuris apparet. </s>
          <s id="s.002708">In prima, vectis e&longs;t A B, fultu&shy;<lb/>
<figure id="id.009.01.158.1.jpg" place="text" xlink:href="009/01/158/1.jpg"/><lb/>
ra E, onus C. potentia autem &longs;eu vis, <lb/>
&longs;eu aliud pondus <expan abbr="mou&etilde;s">mouens</expan> &longs;it vbi D. qu&aelig; <lb/>
deor&longs;um in D, pr&aelig;mens eleuabit &longs;ur&shy;<lb/>
&longs;um ex altera parte onus C. &amp; vectis <lb/>
circa fulturam E, tanquam centrum <lb/>
conuertetur. </s>
          <s id="s.002709">In altera figura pondus <lb/>
e&longs;t inter fulturam, &amp; potentiam, ful&shy;<lb/>
tura autem in altera extremitate, vt <lb/>
patet in figura, hic autem potentia <lb/>
non pr&aelig;mit deor&longs;um in D: &longs;ed &longs;ur&longs;um <lb/>
vectem eleuando pondus C, attollitur. <lb/>
</s>
          <s id="s.002710">In tertia tandem figura potentia, e&longs;t <lb/>
inter vtrunque, e&longs;t enim in D, ibique <lb/>
&longs;ur&longs;um vrget. </s>
          <s id="s.002711">verum tamen e&longs;t hunc vectem artificibus e&longs;&longs;e inutilem, quip&shy;<lb/>
pe qui nullo modo iuuet potentiam, im&ograve; ver&ograve; pondus ip&longs;um grauius reddit: <lb/>
<expan abbr="neq;">neque</expan> hoc genere in his Mechanicis indigemus.</s>
        </p>
        <p type="main">
          <s id="s.002712">Re&longs;pondet igitur dubitationi, dicens rationem huius incrementi poten&shy;<lb/>
ti&aelig; motricis, quod fit a&longs;&longs;umpto vecte fort&egrave; inde oriri, quod vectis &longs;it qu&aelig;&shy;<lb/>
dam libra, cuius alterum brachium &longs;it altero longius; in prima autem qu&aelig;&shy;<lb/>
&longs;tione explicatum e&longs;t, cur libra maior, maiorem vim habeat, eam ad cir&shy;<lb/>
culum reducendo; vectis autem fit libra, hypomoclion enim e&longs;t loco &longs;parti, <lb/>
tam enim &longs;partum, quam hypomoclion veluti centra manent. </s>
          <s id="s.002713">quoniam ve&shy;<lb/>
r&ograve; ab eodem pondere, c&etail;lerius, &longs;iue maiori vi mouetur linea, quant&ograve; lon&shy;<lb/>
gior &agrave; centro fuerit, vt dictum e&longs;t de admiranda circuli natura; hinc fit, vt <lb/>
cum du&aelig; &longs;int in vecte potenti&aelig;, &longs;iue duo pondera, mouens, &amp; motum, illud <lb/>
facilius ac maiore vi moueat, &longs;iue vires ex vecte acquirat, quod longiorem <lb/>
vectis partem pre&longs;&longs;erit. </s>
          <s id="s.002714">quemadmodum igitur pars vectis longior, qu&aelig; &longs;pe&shy;<lb/>
ctabat ad mouentem potentiam, &longs;uperat minorem partem, in qua e&longs;t mo&shy;<lb/>
tum; ita etiam maius e&longs;t pondus <expan abbr="mot&utilde;">motum</expan>, qu&agrave;m mouens. </s>
          <s id="s.002715">&longs;emper autem quan&shy;<lb/>
to ab hypomoclio magis di&longs;tabit potentia, tant&ograve; facilius mouebit, cuius <lb/>
cau&longs;a &longs;upra reddita e&longs;t, quoniam nimirum, qu&aelig; plus &agrave; centro elongatur ma&shy;<lb/>
iorem de&longs;cribit circulum, qui magis ad lineam rectam accedit: quare ab <lb/>
eadem potentia adhibito vecte, tant&ograve; facilius pars vectis mouens dimoue&shy;<lb/>
bitur, quant&ograve; magis &agrave; fulcimento di&longs;tabit. </s>
          <s id="s.002716">Exempli gratia &longs;it in &longs;uperiori <lb/>
prima figura vectis A B, pondus C, mouens D, hypomoclion E, in qua pr&aelig;&shy;<lb/>
dicta poteris contemplari. </s>
          <s id="s.002717">vltima illa textus verba <emph type="italics"/>&lpar;Quod autem vbi D, mo&shy;<lb/>
uens, vbi F, motum autem vbi C, pondus in G,&rpar;<emph.end type="italics"/> videntur &longs;uperuacanea, atque <lb/>
mendos&egrave; addita.</s>
        </p>
        <p type="main">
          <s id="s.002718">In hac qu&aelig;&longs;tione re&longs;pexit Ari&longs;t. &longs;ol&ugrave;m ad primam vectis &longs;peciem. </s>
          <s id="s.002719">Illud <lb/>
demum, quod dixit eandem habere rationem potentiam ad pondus, qu&agrave;m <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;im&egrave; ab Archimede <pb pagenum="159" xlink:href="009/01/159.jpg"/>propo&longs;itione 6. &amp; 7. de &aelig;queponderantibus: &amp; no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam&shy;<lb/>
uis modo, &amp; vnica demon&longs;tratione &agrave; Guido Vbaldo in &longs;uis Mechanicis pro&shy;<lb/>
po&longs;itione 1. de Vecte, qu&aelig; e&longs;t huiu&longs;modi; Potentia &longs;u&longs;tinens pondus vecti <lb/>
appen&longs;um, eandem ad ip&longs;um pondus proportionem habet, quam vectis di&shy;<lb/>
&longs;tantia inter fulcimentum, ac ponderis &longs;u&longs;pen&longs;ionem, ad di&longs;tantiam, &agrave; fulci&shy;<lb/>
mento ad potentiam interiectam. </s>
          <s id="s.002720">quod de omni vecte ab eo demon&longs;tratur, <lb/>
cuius propo&longs;itionis &longs;en&longs;us e&longs;t hic; in &longs;uperiori prima figura &longs;i pars vectis <lb/>
E B, fuerit, v.g. <!-- REMOVE S-->quadrupla partis A E; etiam pondus C, erit quadruplo ma&shy;<lb/>
ius pondere, &longs;eu vi in D, qu&aelig; ip &longs;um C, ope vectis &longs;u&longs;tinet. </s>
          <s id="s.002721">quod etiam trans&shy;<lb/>
ferre debes ad &longs;ecundam figuram.</s>
        </p>
        <p type="head">
          <s id="s.002722"><emph type="italics"/>QV&AElig;STIO QVARTA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002723"><emph type="italics"/>De Remo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002724"><arrow.to.target n="marg235"/></s>
        </p>
        <p type="margin">
          <s id="s.002725"><margin.target id="marg235"/>245</s>
        </p>
        <p type="main">
          <s id="s.002726">EI, qui &longs;uperiora intellexerit &longs;atis clara videtur. </s>
          <s id="s.002727">Illud tamen non <lb/>
omittendum, &longs;cilicet dicendum potius Remum e&longs;&longs;e vectem &longs;ecundi <lb/>
generis, qu&agrave;m primi, quod fort&egrave; Ari&longs;t. non animaduertit, nec Pic&shy;<lb/>
colomineus, nam mare e&longs;t hypomoclion, re&longs;pectu enim nauis non <lb/>
mouetur, &longs;ed manet, &longs;calmus autem &longs;imul cum tota naui e&longs;t pondus motum; <lb/>
ver&egrave; enim nauis ip&longs;a mouetur. </s>
          <s id="s.002728">mouens e&longs;t ip&longs;e remex. </s>
          <s id="s.002729">Reliqua in textu <lb/>
&longs;unt clara.</s>
        </p>
        <p type="head">
          <s id="s.002730"><emph type="italics"/>QV&AElig;STIO QVINTA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002731"><emph type="italics"/>De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002732"><arrow.to.target n="marg236"/></s>
        </p>
        <p type="margin">
          <s id="s.002733"><margin.target id="marg236"/>246</s>
        </p>
        <p type="main">
          <s id="s.002734">Qvemadmodum in pr&aelig;cedenti qu&aelig;&longs;tione Ari&longs;t. vectem &longs;ecundi ge&shy;<lb/>
neris ad &longs;olutionem non adhibuit, vt par erat, &amp; propterea ob&longs;cu&shy;<lb/>rior eua&longs;it, ita etiam in pr&aelig;&longs;enti, qu&etail;&longs;tionem ad vectem primi ge&shy;<lb/>
neris reducit, qu&aelig; ad alterum reducend&agrave; erat: <expan abbr="atq;">atque</expan> hinc ob&longs;curi&shy;<lb/>
tas, atque prolixitas &longs;olutionis manauit. </s>
          <s id="s.002735">E&longs;t enim propri&egrave; Temo, &longs;iue gu&shy;<lb/>
bernaculum nauis, vectis &longs;ecundi generis, vt mox explicabo, e&longs;t enim temo <lb/>
<figure id="id.009.01.159.1.jpg" place="text" xlink:href="009/01/159/1.jpg"/><lb/>
in&longs;trumentum in extrema nanis par&shy;<lb/>te, &longs;eu puppi affixum, vt in figura pre&shy;<lb/>
&longs;enti vides tabellam, in qua B C D, <lb/>
cuius manubrium A B, intra nauim <lb/>
recipitur, qu&aelig; tabella, &longs;eu temo in <lb/>
duobus cardinibus, vbi C, &amp; D, cir&shy;<lb/>
cumuertitur &agrave; Nauis gubernatore, <lb/>
manubrium vbi A, tractante; ex qua <lb/>
conuer&longs;ione nauigium, qu&ograve; vult ip&longs;e <lb/>
gubernator facil&egrave; dirigit, ip&longs;umque <lb/>
nauigium huc illuc quamuis ade&ograve; magnum ip&longs;e &longs;olus impellit, &amp; agitat. </s>
          <s id="s.002736">e&longs;t <lb/>
enim temo vectis, cuius auxilio vires mirum in modum augentur, nam to&shy;<lb/>
ta A B, e&longs;t ip&longs;a Vectis longitudo, cuius hypomoclion e&longs;t mare, cui contra&shy;


<pb pagenum="160" xlink:href="009/01/160.jpg"/>nititur tabella B E; onus autem e&longs;t puppis, quod onus pr&aelig;&longs;ertim in cardini&shy;<lb/>
bus C D, mouenti re&longs;i&longs;tit, &amp; quod pr&aelig;cipu&egrave; mouere gubernator intendit. <lb/>
</s>
          <s id="s.002737">cum igitur motum onus &longs;it intra vectis extrema, hypomoclion in extremo <lb/>
ad B E, vbi in motu temonis tabella mare vrget, quod minim&egrave; cedit, <expan abbr="ip&longs;a&qacute;">ip&longs;aque</expan>; <lb/>
in hoc motu fer&egrave; maneat, &amp; fiat qua&longs;i centrum, circa quod totus temo cir&shy;<lb/>
cumducitur, patet temonem e&longs;&longs;e vectem &longs;ecund&aelig; &longs;peciei, vt dicebam. </s>
          <s id="s.002738">quod <lb/>
etiam hinc patere pote&longs;t, quia temo e&longs;t veluti remus, cuius &longs;calmus &longs;int car&shy;<lb/>
dines C, D. &longs;icut ergo remus e&longs;t vectis &longs;ecundi generis, cuius pondus e&longs;t <lb/>&longs;calmus, &amp; mare hypomoclion; ita temo erit vectis eiu&longs;dem generis, cuius <lb/>
pondus erit vbi cardines, fultura ver&ograve; mare.</s>
        </p>
        <p type="main">
          <s id="s.002739">Qu&aelig;rit igitur Ari&longs;t. vnde nam tantas vires paruus nauis temo guberna&shy;<lb/>
tori &longs;uggerat, <expan abbr="re&longs;pondet&qacute;">re&longs;pondetque</expan>; propterea id contingere, quod temo vectis na&shy;<lb/>
turam obtineat, cuius inquit onus e&longs;t mare, melius autem, vt dixi, dixi&longs;&longs;et <lb/>
onus e&longs;&longs;e nauim, mare autem hypomoclion, mouens autem e&longs;t gubernator. <lb/>
</s>
          <s id="s.002740">Differunt autem remus, &amp; temo, quamuis <expan abbr="vterq;">vterque</expan> &longs;it vectis, quoniam remus <lb/>
&longs;ecundum latitudinem nauis, &longs;eu ad latera nauis mari obnititur. </s>
          <s id="s.002741">temo au&shy;<lb/>
tem in directum fer&egrave; nauigij con&longs;titutus mare &longs;cindit. </s>
          <s id="s.002742">hinc fit, vt remus ad <lb/>
nauem antror&longs;um rect&agrave; agitandam, gubernaculum ver&ograve; ad eam in latera, <lb/>&amp; obliqu&egrave; contorquendam idoneum &longs;it. </s>
          <s id="s.002743">quoniam enim mare e&longs;t hypomo&shy;<lb/>
clion, fit vt dum gubernator mouet an&longs;am temonis in A, &longs;eu ad dextram, <lb/>
&longs;eu ad &longs;ini&longs;tram &longs;ecum ad eandem partem trahat nauigium, quod temoni <lb/>
e&longs;t connexum; ad <expan abbr="c&otilde;trariam">contrariam</expan> tamen partem trahit ei, &longs;ecundum quam mare <lb/>
impingit. </s>
          <s id="s.002744"><expan abbr="atq;">atque</expan> hoc pacto remus antror&longs;um, temo ver&ograve; obliqu&egrave; nauim agit.</s>
        </p>
        <p type="main">
          <s id="s.002745">Po&longs;th&aelig;c &longs;equuntur huiu&longs;modi verba <emph type="italics"/>&lpar;In extremo autem, &amp; non in medio <lb/>
iacet, quoniam <expan abbr="mou&etilde;ti">mouenti</expan> facillimum est ab extremo motum mouere: prima enim pars <lb/>celerrim&egrave; fertur, quoniam quemadmodum in ijs, qu&aelig; feruntur in fine deficit latio, <lb/>
&longs;ic ip&longs;ius continui in fine imbecili&longs;&longs;ima e&longs;t latio, imbecili&longs;&longs;ima autem ad <expan abbr="expell&etilde;dum">expellendum</expan> <lb/>est facilis, propter h&aelig;c igitur in puppi gubernaculum ponitur&rpar;<emph.end type="italics"/> quorum &longs;en&longs;us <lb/>
videtur difficilis, <expan abbr="neq;">neque</expan> gr&aelig;cus textus excu&longs;andus e&longs;t, ben&egrave; enim tran&longs;lata <lb/>
&longs;unt. </s>
          <s id="s.002746">Piccolomin&aelig;us quidem plura qu&agrave;m Ari&longs;t. fatur, &longs;ed non clariora. </s>
          <s id="s.002747">dif&shy;<lb/>
ficultas e&longs;t in verbis illis <emph type="italics"/>&lpar;Prima enim pars celerrim&egrave; fertur&rpar;<emph.end type="italics"/> &amp; in illis <emph type="italics"/>&lpar;Sic ip&shy;<lb/>&longs;ius continui in fine imbecili&longs;&longs;ima e&longs;t latio&rpar;<emph.end type="italics"/> videtur velle dicere, quod quando <lb/>
continuum aliquod proiectum fertur per aera, pars ip&longs;ius anterior ea e&longs;t, <lb/>
qu&aelig; pr&aelig; c&aelig;teris partibus principaliter mouetur, &amp; ad cuius motum reliqu&aelig; <lb/>po&longs;teriores tanquam &longs;ub&longs;equentes moueantur; qua&longs;i dicat tota vis lationis <lb/>
e&longs;t in anteriori parte: &longs;iue ip&longs;i impetus maior ine&longs;t: videmus enim proiecta, <lb/>
quorum vna pars e&longs;t c&aelig;teris grauior, quia ei parti melius imprimitur mo&shy;<lb/>
tus, eam etiam fieri anteriorem in latione, quamuis initio fuerit po&longs;terior. <lb/>
</s>
          <s id="s.002748">&longs;ic etiam quando graue fertur deor&longs;um, dicimus ip&longs;um ferri &longs;ecundum cen&shy;<lb/>
trum grauitatis ip&longs;ius, <expan abbr="ibi&qacute;">ibique</expan>; maiorem vim grauitandi exi&longs;tere, &longs;ic in proie&shy;<lb/>
ctis partem anteriorem dicere po&longs;&longs;umus e&longs;&longs;e, &longs;ecundum quam totum conti&shy;<lb/>
nuum fertur: <expan abbr="ibi&qacute;">ibique</expan>; totum e&longs;&longs;e impetum lationis, &amp; propterea etiam maio&shy;<lb/>
ri impetu, <expan abbr="atq;">atque</expan> celerrim&egrave; ferri: &amp; <expan abbr="con&longs;equ&etilde;ter">con&longs;equenter</expan> partem po&longs;teriorem, quam&shy;<lb/>
uis priorem &aelig;qua velocitate con&longs;equatur, non tamen tanto impetu, cum ip&shy;<lb/>&longs;a ad alterius impetum moueatur, &amp; propterea latio ip&longs;ius e&longs;t admodum <lb/>
imbecillis.</s>
        </p>
        <pb pagenum="161" xlink:href="009/01/161.jpg"/>
        <p type="main">
          <s id="s.002749">Si quis &longs;agittam per aerem latam &agrave; &longs;uo motu vellet deflectere, eam faci&shy;<lb/>
lius in po&longs;teriore parte &agrave; &longs;uo cur&longs;u deuiaret, qu&agrave;m in anteriore. </s>
          <s id="s.002750">hunc con&shy;<lb/>
cinui corporis motum continuo proiectorum motui a&longs;&longs;imilat: quemadmo&shy;<lb/>
dum enim motus proiectorum in fine debilior lente&longs;cit: &longs;ic totum conti&shy;<lb/>
nuum in po&longs;trema parte &longs;egnius impellitur. </s>
          <s id="s.002751">Quia igitur nauis e&longs;t <expan abbr="c&otilde;tinuum">continuum</expan>, <lb/>
quod vi remorum recta antror&longs;um fertur, &amp; propterea maiore vi prora, <lb/>
qu&agrave;m puppis, facilius e&longs;t &agrave; &longs;uo directo cur&longs;u nauem deflectere, eam in pup&shy;<lb/>
pi, qu&agrave;m in prora commouendo. </s>
          <s id="s.002752">hac igitur de cau&longs;a, gubernaculum puppi <lb/>
affigitur. </s>
          <s id="s.002753">qu&aelig; quidem ratio, &amp; quantum valeat, &amp; an naui quadret, &amp; num <lb/>
ben&egrave; &longs;it explicata, phy&longs;icorum e&longs;t iudicare.</s>
        </p>
        <p type="main">
          <s id="s.002754">Ego tamen aliam huius rationem video, quia nimirum &longs;i temo in priori <lb/>
parte e&longs;&longs;et, quando &agrave; rectitudine ip&longs;ius nauis ad dextram, aut ad &longs;ini&longs;tram <lb/>e&longs;&longs;et inclinandus, tunc quia aqua in vnam tantum ip&longs;ius partem, &longs;eu faciem <lb/>
tota impingeret, in eam &longs;cilicet, qu&aelig; antror&longs;um re&longs;piceret, eam aqua re&shy;<lb/>
tror&longs;um &longs;imul cum tota naui auerteret, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; totam nauim inuerteret, ita <lb/>
vt prora, cui adh&aelig;reret temo extrema fieret. </s>
          <s id="s.002755">impetus igitur aqu&aelig;, &amp; naui&shy;<lb/>
gij temonati, cogit temonem e&longs;&longs;e po&longs;tremum non primum, nec medium. <lb/>
</s>
          <s id="s.002756"><expan abbr="atq;">atque</expan> hinc oritur nece&longs;&longs;itas <expan abbr="e&utilde;">eum</expan> po&longs;teriori parti affigendi. </s>
          <s id="s.002757">&longs;ubdit po&longs;tea aliam <lb/>
eiu&longs;dem rationem, quia nimirum parua motione facta in puppi multo ma&shy;<lb/>
ius interuallum cogitur mutare prora; nam idem angulus, quo eius line&aelig; <lb/>
&longs;unt longiores, e&ograve; maiorem &longs;ubten&longs;am &longs;ibi lineam re&longs;picit, quod facil&egrave; in <lb/>
<figure id="id.009.01.161.1.jpg" place="text" xlink:href="009/01/161/1.jpg"/><lb/>
ad&longs;cripta figura intueri licet; in qua du&aelig; <lb/>
line&aelig; A B, A C, continent angulum A, cui <lb/>
angulo &longs;ubtenduntur tres line&aelig; parallel&aelig; <lb/>
F G, D E, B C, quarum B C, maxima e&longs;t, <lb/>
quia ibi maiores, &longs;iue remotiores &longs;unt ab <lb/>
angulo A, du&aelig; rect&aelig; A B, A C, ip&longs;um con&shy;<lb/>
tinentes, quod Geometric&egrave; per 4. 6. pro&shy;<lb/>
bari pote&longs;t. </s>
          <s id="s.002758">&longs;ic etiam facta motione, vel <lb/>
parua in puppi, tota nauis transfertur ad <lb/>
alium &longs;itum, ita vt prora multum ali&ograve; transferatur, quod non accideret, &longs;i <lb/>
eadem motio fieret ad medium nauigij. </s>
          <s id="s.002759">propterea igitur apti&longs;&longs;im&egrave; puppi <lb/>
gubernaculum connectitur.</s>
        </p>
        <p type="main">
          <s id="s.002760"><arrow.to.target n="marg237"/></s>
        </p>
        <p type="margin">
          <s id="s.002761"><margin.target id="marg237"/>247</s>
        </p>
        <p type="main">
          <s id="s.002762">Ex ij&longs;dem etiam rationibus mathematicis patet, cur magis antror&longs;um <lb/>
procedit nauigium, qu&agrave;m remi ip&longs;ius palmula retror&longs;um: eadem enim ma&shy;<lb/>
gnitudo, ij&longs;dem mota viribus in aere plus, qu&agrave;m in aqua progreditur. <lb/>
</s>
          <s id="s.002763">Sit igitur A B, remus, G, ver&ograve; &longs;calmus. </s>
          <s id="s.002764">A, autem in nauigio &longs;it remi initium. <lb/>
</s>
          <s id="s.002765">B, ver&ograve; in mari palmula. </s>
          <s id="s.002766">&longs;i igitur A, vbi D, transferatur, per totum &longs;pa&shy;<lb/>
tium A D, non permeabit tantumdem &longs;patij B, <expan abbr="v&longs;q;">v&longs;que</expan> ad E. <!-- KEEP S--></s>
          <s id="s.002767">B E, enim ponitur <lb/>
&aelig;qualis ip&longs;i A D, &longs;ed minus interuallum propter re&longs;i&longs;tentiam aqu&aelig; ex &longs;up&shy;<lb/>
po&longs;itione percurret, quale e&longs;t B F, quod minus e&longs;t qu&agrave;m A D, quare etiam li&shy;<lb/>
nea B G, abbreuiabitur, <expan abbr="erit&qacute;">eritque</expan>; veluti F Y, qu&aelig; etiam erit minor ip&longs;a D G, <lb/>qu&aelig; facta e&longs;t D Y, propter duo &longs;imilia triangula D Y A, B Y F, &longs;imilia au&shy;<lb/>
tem triangula &longs;unt ea, quorum anguli vnius &longs;unt &aelig;quales angulis alterius, <lb/>
quo po&longs;ito &longs;unt etiam latera vnius proportionalia lateribus alterius, vt pa&shy;<lb/>
tet ex prima definitione 6. necnon ex quarta eiu&longs;dem demon&longs;tratione. </s>
          <s id="s.002768">h&aelig;c <pb pagenum="162" xlink:href="009/01/162.jpg"/><figure id="id.009.01.162.1.jpg" place="text" xlink:href="009/01/162/1.jpg"/><lb/>
quidem duo triangula &longs;unt &longs;imi&shy;<lb/>
lia, &amp; rect&egrave; concluditur F Y, mi&shy;<lb/>
nus e&longs;&longs;e qu&agrave;m D Y, &longs;ed tamen <lb/>
non videntur i&longs;ta propo&longs;itum <lb/>
o&longs;tendere, quod erat, plus nauim <lb/>
procedere, qu&agrave;m palmulam re&shy;<lb/>
trocedere. </s>
          <s id="s.002769">Fateor quidem tex&shy;<lb/>
tum hunc e&longs;&longs;e ob&longs;curi&longs;&longs;imum, <lb/>
<expan abbr="id&qacute;">idque</expan>; propterea fort&egrave; quia e&longs;t admodum corruptus, pr&aelig;&longs;ertim circa chara&shy;<lb/>
cteres, qui corrigendi &longs;unt vti nos facimus. </s>
          <s id="s.002770">ne&longs;cio qua ratione Piccolomi&shy;<lb/>
neus videatur &longs;ibi locum hunc explica&longs;&longs;e. </s>
          <s id="s.002771">For&longs;itan addenda &longs;unt nonnulla <lb/>
hoc pacto; cum initio remigationis ponamus remum in &longs;itu A B, in fine ve&shy;<lb/>
r&ograve; prim&aelig; impul&longs;ionis in D F, &longs;calmum ver&ograve; circa medium remi in G, pri&shy;<lb/>
mo; vltimo erit etiam circa medium D F, vbi H, quare &longs;calmus tran&longs;latus <lb/>
e&longs;t &agrave; G, ad H, <expan abbr="tota&qacute;">totaque</expan>; G H, perficit, quam deberet Ari&longs;tot. vt &longs;ibi con&longs;taret <lb/>
probare e&longs;&longs;e maiorem ip&longs;a B F, quam palmula obiuit, &amp; con&longs;equenter pro&shy;<lb/>
ba&longs;&longs;et nauigium plus proce&longs;&longs;i&longs;&longs;e, qu&agrave;m palmula rece&longs;&longs;erit: quod propo&longs;ue&shy;<lb/>
rat. </s>
          <s id="s.002772">Verum hoc non demon&longs;trat; <expan abbr="neq;">neque</expan> ex pr&aelig;mi&longs;&longs;is deduci pote&longs;t. </s>
          <s id="s.002773">po&longs;tea <lb/>
&longs;ubdit <emph type="italics"/>&lpar;Stans autem erit medium vbi e&longs;t G, in contrarium enim ip&longs;i, qu<foreign lang="greek"/>od in mari <lb/>e&longs;t, extremo B, procedit, vbi extremum in nauigio e&longs;t A, non procederet autem <lb/>vbi est D, ni&longs;i commoueretur nauigi&ubreve;m, &amp; e&ograve; transferretur vbi e&longs;t remi principium&rpar;<emph.end type="italics"/><lb/>
vbi in textu mendos&egrave; legitur C, pro G.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002774">Sen&longs;us porr&ograve; horum verborum e&longs;t hic; &longs;i remus circa &longs;calmum G, verte&shy;<lb/>
retur, &amp; tamen nauis ab eo non propelleretur, &longs;ed &longs;taret, tunc medium na&shy;<lb/>
uis maneret vbi G, per motum enim remi impellitur in contrarias partes <lb/>
ip&longs;i palmul&aelig; B, qu&aelig; e&longs;t in mari, quia &longs;equitur motum alterius extremi A, <lb/>
manubrij &longs;cilicet remi, qui e&longs;t in naui: quod autem nauigium &agrave; remo mo&shy;<lb/>
neatur, &longs;ignum e&longs;t, quia manubrium A, non procederet vbi e&longs;t D, ni&longs;i pari&shy;<lb/>
ter cum remo nauigium illor&longs;um con&longs;equeretur. </s>
          <s id="s.002775">H&aelig;c quidem Ari&longs;t. circa <lb/>
motum nauigij imperfect&egrave; admodum ni&longs;i textus corruptionem cau&longs;etur, di&shy;<lb/>
xi&longs;&longs;e videatur. </s>
          <s id="s.002776">Quapropter oper&aelig;pretium me facturum exi&longs;timo, &longs;i Petri <lb/>
Nonij acuti&longs;&longs;imi Mathematici, &longs;ubtili&longs;&longs;imas, <expan abbr="&longs;citu&qacute;">&longs;cituque</expan>; digni&longs;&longs;imas in pr&aelig;&longs;ens <lb/>problema annotationes hoc loco de&longs;crip&longs;ero, ex quibus perfect&egrave;, ac ma&shy;<lb/>
thematic&egrave; toti huic qu&aelig;&longs;tioni fit &longs;atis, qu&aelig; &longs;ic &longs;e habent.</s>
        </p>
        <p type="head">
          <s id="s.002777"><emph type="italics"/>In Problema Mechanicum Arist. de motu Nauigij <lb/>
ex remis, annotatio Petri Nonij.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002778">Cvm olim di&longs;cipulis no&longs;tris mechanicas Ari&longs;t. qu&aelig;&longs;tiones interpre&shy;<lb/>
taremur, nonnulla circa problema illud annotauimus, cur magis <lb/>
procedat nauigium, quam remi palmula in contrarium. </s>
          <s id="s.002779">Ari&longs;tot. <lb/>
enim ratiocinatio ob&longs;cura e&longs;t; quam nos tamen, vt aliquid lucis <lb/>
haberet, ad hunc modum explicauimus; &amp; propter materi&aelig; &longs;imilitudinem <lb/>
hi&longs;ce no&longs;tris libris de nauigandi ratione adiunximus. </s>
          <s id="s.002780">Supponit autem ip&longs;e <lb/>
auctor remi palmulam retrocedere, quoties nauigium in anteriora progre&shy;


<pb pagenum="163" xlink:href="009/01/163.jpg"/>ditur, <expan abbr="locum&qacute;">locumque</expan>; &longs;calmi, &longs;uper quo circulari motu remus vertitur, in medio <lb/>
ip&longs;ius remi po&longs;itum e&longs;&longs;e, vt &longs;cilicet tantum di&longs;tet &agrave; manubrio, quantum &agrave; <lb/>
palmula. </s>
          <s id="s.002781">Du&aelig; <expan abbr="itaq;">itaque</expan> rect&aelig; line&aelig; ponantur &aelig;quales A B, &amp; D E, qu&aelig; quidem <lb/>
in C, puncto medio &longs;e inuicem &longs;ecent, &amp; connectantur A B, &amp; D E: remus <lb/>
autem in initio vnius remigationis po&longs;itionem habeat rectam lineam A B, <lb/>
<expan abbr="&longs;it&qacute;">&longs;itque</expan>; A, manubrium; B, palmula; C, ver&ograve; &longs;calmus. </s>
          <s id="s.002782">Cum igitur A, remi ca&shy;<lb/>
put in fine ip&longs;ius remigationis e&ograve; tran&longs;latum fuerit D, non erit B, vbi E; &longs;i <lb/>
<figure id="id.009.01.163.1.jpg" place="text" xlink:href="009/01/163/1.jpg"/><lb/>
enim ibi fuerit; remus igitur po&longs;itionem <lb/>
habebit rectam lineam D E; &amp; quoniam <lb/>
contrapo&longs;iti anguli, qui ad C, &aelig;quales &longs;unt, <lb/>
&amp; duo latera A C, &amp; D C, trianguli A D C, <lb/>
duobus lateribus B C, &amp; C E, trianguli B&shy;<lb/>
E C, &aelig;qualia etiam &longs;unt: reliqui igitur an&shy;<lb/>
guli, <expan abbr="atq;">atque</expan> ba&longs;es ip&longs;orum <expan abbr="tri&atilde;gulorum">triangulorum</expan> &aelig;qua&shy;<lb/>
les erunt per 4. propo&longs;itionem primi libri <lb/>
Euclidis, &amp; propterea tantum &longs;patium per&shy;<lb/>
curret B, quantum A: &longs;calmus ver&ograve; C, im&shy;<lb/>
motus omnin&ograve; erit: &amp; nauigium idcirc&ograve;, in <lb/>
quo ip&longs;e &longs;calmus, immotum etiam erit con&shy;<lb/>
tra hypothe&longs;im. </s>
          <s id="s.002783">&longs;upponitur enim in que&longs;tio&shy;<lb/>
ne, quod nauigium illa remigatione in anteriora moueatur, remi ver&ograve; pal&shy;<lb/>
mula retrocedat. </s>
          <s id="s.002784">Scalmus porr&ograve; quamquam circularis remi motus expers <lb/>
&longs;it; motu tamen nauigij commouetur. </s>
          <s id="s.002785">Remus igitur po&longs;itionem habeat in <lb/>fine ip&longs;ius remigationis rectam lineam D Z, qu&aelig; quidem rectam A B, &longs;ecet <lb/>
in T, inter B, &amp; C; rectam ver&ograve; B E, in Z. <!-- KEEP S--></s>
          <s id="s.002786">Et quoniam duo coalterni anguli <lb/>
C A D, &amp; C B E, &aelig;quales <expan abbr="o&longs;t&etilde;&longs;i">o&longs;ten&longs;i</expan> &longs;unt, &amp; angulus A T D, contrapo&longs;ito B T Z, <lb/>
&aelig;qualis e&longs;t: duo igitur triangula A T D, &amp; B Z T, &aelig;quiangula erunt per 32. <lb/>
primi, &amp; communem &longs;ententiam. </s>
          <s id="s.002787">Similia <expan abbr="itaq;">itaque</expan> erunt ip&longs;a triangula, <expan abbr="late-ra&qacute;">late&shy;<lb/>
raque</expan>; habebunt proportionalia per 4. 6. &longs;icut A T, ad B T, ita D A, ad B Z. <lb/>
<!-- KEEP S--></s>
          <s id="s.002788">Maior e&longs;t autem A T, qu&agrave;m B T: maior igitur D A, qu&agrave;m B Z, quod etiam <lb/>
per <expan abbr="c&otilde;munem">communem</expan> <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> neglecta <expan abbr="triangulor&utilde;">triangulorum</expan> &longs;imilitudine concludi pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.002789">Maius <expan abbr="itaq;">itaque</expan> &longs;patium decurrit manubrium, qu&agrave;m remi palmula, <expan abbr="atq;">atque</expan> illuc <lb/>
tran&longs;uehetur nauigium, qu&ograve; remi capulus deportatus fuerit: nauigium igi&shy;<lb/>
tur in diuer&longs;a procedens, plus &longs;patij, qu&agrave;m remi palmula tran&longs;mittet. </s>
          <s id="s.002790">Vti&shy;<lb/>
mur aurem tralatione, <expan abbr="atq;">atque</expan> demon&longs;trationis figura Victoris Fau&longs;ti. </s>
          <s id="s.002791">Aduer&shy;<lb/>
tendum e&longs;t tamen, quod cum remus po&longs;itionem habuerit D Z, remi palmu&shy;<lb/>
la erit infra Z. <!-- KEEP S--></s>
          <s id="s.002792">Nam quoniam <expan abbr="tri&atilde;guli">trianguli</expan> A D C, duo latera A C, &amp; D C, &aelig;qua&shy;<lb/>lia po&longs;ita &longs;unt: duo igitur anguli, qui ad D, &amp; A, &aelig;quales erunt: angulus <lb/>
igitur A D T, angulo D A T, maior erit: &amp; idcirc&ograve; latus A T, trianguli A&shy;<lb/>
T D, latere D T, maius erit per 19. primi. </s>
          <s id="s.002793">A&aelig;qualis porr&ograve; o&longs;ten&longs;us e&longs;t an&shy;<lb/>
guius B Z T, angulo A D T, pr&aelig;terea angulus D A T; angulo T B Z, &aelig;qua&shy;<lb/>
lis: angulus igitur B Z T, angulo T B Z, maior erit, &amp; propterea latus B T, <lb/>
trianguli B T Z, latere T Z, maius erit: tota igitur recta linea A B, tota <lb/>
D Z, maior erit: &amp; idcirc&ograve; cum remus po&longs;itionem habuerit rectam lineam <lb/>
D Z palmula erit vltra Z. <!-- KEEP S--></s>
          <s id="s.002794">E&longs;to igitur in K, &amp; connectantur rect&aelig; line&aelig; B D, <lb/>&amp; B K: &longs;patium igitur decur&longs;um ab ip&longs;a palmula non erit B Z, &longs;ed B K: quod <pb pagenum="164" xlink:href="009/01/164.jpg"/>quidem minus etiam o&longs;tendemus e&longs;&longs;e ip&longs;o D A. <!-- KEEP S--></s>
          <s id="s.002795">Nam quoniam duo latera <lb/>
B D, &amp; D K, trianguli B D K, duobus lateribus B D, &amp; D E, <expan abbr="tri&atilde;guli">trianguli</expan> B E D, <lb/>&aelig;qualia &longs;unt, &longs;ed minor e&longs;t angulus B D K, angulo B D E: minor igitur erit <lb/>
ba&longs;is B K, ba&longs;e B E, per 24. primi, quod demon&longs;trandum erat</s>
        </p>
        <p type="main">
          <s id="s.002796">Pr&aelig;terea, quod Ari&longs;t. ratiocinando &longs;umit tantum &longs;patium conficere na&shy;<lb/>
uigium, quantum remi manubrium, ambiguum e&longs;t. </s>
          <s id="s.002797">Nam remi manubrium <lb/>
duabus fertur motionibus: vna propria, <expan abbr="circulari&qacute;">circularique</expan>; &longs;uper &longs;calmo: altera <lb/>
ver&ograve;, qua vn&agrave; fertur cum ip&longs;o nauigio. </s>
          <s id="s.002798">&longs;patium igitur, quod omnin&ograve; decur&shy;<lb/>&longs;um e&longs;t &agrave; remi manubrio, eo quod &agrave; nauigio confectum e&longs;t, maius erit. </s>
          <s id="s.002799">At <lb/>
&longs;i paria &longs;patia decur&longs;a e&longs;&longs;e intelligat &agrave; remi manubrio motu proprio, &amp; &agrave; <lb/>
nauigio, <expan abbr="neq;">neque</expan> hoc difficultate caret. </s>
          <s id="s.002800">Nam nauigium interdum maius &longs;pa&shy;<lb/>
tium percurret, interdum minus, iuxta remigum vires, &amp; prout mari remi <lb/>
palmula immer&longs;a fuerit: remi ver&ograve; manubrium tamet&longs;i ab exiguis viribus <lb/>
moueatur haud minorem tamen ambitum de&longs;cribet, qu&agrave;m &longs;i &agrave; multo ma&shy;<lb/>
iore virtute moueretur. </s>
          <s id="s.002801">Quapropter, vt huiu&longs;modi Ari&longs;t. &longs;ententiam exa&shy;<lb/>minaremus, Theoremata, qu&aelig; &longs;equuntur, demon&longs;trauimus.</s>
        </p>
        <p type="head">
          <s id="s.002802"><emph type="italics"/>PROPOSITIO PRIMA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002803">Si Remiges nauigium mouere po&longs;&longs;unt, maius &longs;emper &longs;pa&shy;<lb/>
tium remi manubrium percurrit, qu&agrave;m nauigium.</s>
        </p>
        <p type="main">
          <s id="s.002804">Sit enim remus A C, manubrium A, &longs;calmus B, qui propter nauigij <lb/>motum &longs;patium percurrat &agrave; B, in D, in quo loco ip&longs;e remus A C, &longs;i&shy;<lb/>
<figure id="id.009.01.164.1.jpg" place="text" xlink:href="009/01/164/1.jpg"/><lb/>
tum rectitudinis habeat E F. <!-- KEEP S--></s>
          <s id="s.002805">Spatium <lb/>itaque, quod A, conficit, curua linea <lb/>
&longs;it A E, cui recta linea re&longs;pondeat A Z, in re&shy;<lb/>ctam E F, perpendicularis. </s>
          <s id="s.002806">Nauigium ver&ograve; <lb/>idem &longs;patium conficiet, quod &longs;calmus B: aio <lb/>
igitur ip&longs;am A Z, rectam lineam, recta B D, <lb/>
maiorem e&longs;&longs;e. </s>
          <s id="s.002807">&longs;ecet enim recta A C, rectam <lb/>
E F, in G: &aelig;quiangula &longs;unt igitur bina trian&shy;<lb/>
gula A G Z, &amp; B G D, quapropter &longs;icut A G, <lb/>
ad B G, &longs;ie A Z, ad B D, per. </s>
          <s id="s.002808">4. 6. libri Eucli&shy;<lb/>dis: maior e&longs;t autem A G, ip&longs;a B G, &amp; maior <lb/>
igitur erit A Z, quam B D. &amp; proinde maius <lb/>
&longs;patium remi manubrium percurrit, quam <lb/>
nauigium, quod demon&longs;trandum erat.</s>
        </p>
        <p type="main">
          <s id="s.002809">Quod &longs;i &agrave; puncto B, rectam lineam vtrinque <lb/>
ducamus H K, ad remi men&longs;uram, rectos facientem angulos cum B D, <expan abbr="re-ctam&qacute;">re&shy;<lb/>
ctamque</expan>; A Z, &longs;ecantem in I, manife&longs;t&egrave; intelligemus ip&longs;am rectam A Z, con&shy;<lb/>
&longs;tare ex A I, &amp; I Z, quarum prior re&longs;pondet curu&aelig; A H, qu&aelig; motu proprio <lb/>
manubrij de&longs;cripta e&longs;t; po&longs;terior ver&ograve; &aelig;qualis e&longs;t rect&aelig; B D, qu&aelig; motu na&shy;<lb/>
uigij decur&longs;a e&longs;t.</s>
        </p>
        <pb pagenum="165" xlink:href="009/01/165.jpg"/>
        <p type="head">
          <s id="s.002810"><emph type="italics"/>PROPOSITIO SECVNDA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002811">Si remi manubrium motu proprio, &amp; nauigium, &aelig;qualia <lb/>
&longs;patia pertran&longs;ierint, fieri non poterit, vt palmula mo&shy;<lb/>
ueatur: &longs;ed veluti centrum immota manebit.</s>
        </p>
        <p type="main">
          <s id="s.002812">Esto iterum remus A C, manubrium A, &longs;calmus B: tantum autem &longs;pa&shy;<lb/>
tium conficiat nauigium; quantum motu proprio A. Dico, quod C, <lb/>
remi palmula immota manebit. </s>
          <s id="s.002813">Nam &longs;i a loco &longs;uo dimota fuerit: <lb/>
&longs;patium igitur permeet C D, ad po&longs;teriora: quo quidem decur&longs;o, <lb/>remus A C, po&longs;itionem rectitudinis habeat F D, &longs;calmus <expan abbr="itaq;">itaque</expan> B, tran&longs;latus <lb/>
erit in G. <!-- KEEP S--></s>
          <s id="s.002814">Excitetur autem &agrave; puncto B, in <expan abbr="vtramq;">vtramque</expan> partem linea E B R, ad <lb/>
<figure id="id.009.01.165.1.jpg" place="text" xlink:href="009/01/165/1.jpg"/><lb/>
rectos angulos &longs;uper B G, &amp; &agrave; <expan abbr="p&utilde;cto">puncto</expan> A, recta A H, <lb/>
&longs;uper D F: itemque &agrave; puncto E, recta C E, &longs;uper <lb/>
E R; ip&longs;arum ver&ograve; rectarum linearum E R, &amp; <lb/>
A H, &longs;ectio &longs;it in K, &longs;ed C F., &amp; D F, &longs;it in Z, &amp; quo&shy;<lb/>
niam A K, id &longs;patium e&longs;t, quod motu proprio re&shy;<lb/>
mi manubrium permeauit, curuilineo enim re&shy;<lb/>
&longs;pondeat A R, recta autem B G, id &longs;patium e&longs;t, <lb/>
quod nauigium confecit: ip&longs;&aelig; igitur rect&aelig; line&aelig; <lb/>
H K, &amp; B G, &aelig;quales erunt. </s>
          <s id="s.002815">Atqui in duobus &aelig;qui&shy;<lb/>
angulis triangulis E B C, &amp; B A K, vel per 26. <lb/>
propo&longs;itionem primi Euclidis, vel 4. 6. &aelig;quales <lb/>
e&longs;&longs;e concludes A K, &amp; E C, rectas lineas: quapro&shy;<lb/>
pter &aelig;qualis erit E C, rect&aelig; B G, per communem <lb/>
&longs;ententiam: eidem autem B G, &aelig;qualis e&longs;t E Z, <lb/>
in parallelogrammo, per 34. propo&longs;itionem ip&shy;<lb/>
&longs;ius primi libri: &aelig;qualis igitur erit recta E Z, re&shy;<lb/>
ct&aelig; E C, pars toti, quod e&longs;t impo&longs;&longs;ibile. </s>
          <s id="s.002816">Et pro&shy;<lb/>
pterea immota manebit palmula C, quod erat &agrave; <lb/>
nobis o&longs;tendendum.</s>
        </p>
        <p type="head">
          <s id="s.002817"><emph type="italics"/>PROPOSITIO TERTIA.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.002818">Si remi manubrium motu proprio duplum confecerit &longs;pa&shy;<lb/>
tium, qu&agrave;m nauigium, tantum prouehetur ea remiga&shy;<lb/>
tione nauigium, quantum palmula retroce&longs;&longs;erit.</s>
        </p>
        <p type="main">
          <s id="s.002819">Remus enim incipiente motu po&longs;itionem habeat A C, de&longs;inente <lb/>
ver&ograve; rectitudinis &longs;itum F G. &longs;calmus igitur B, propter nauigij <lb/>motum, &longs;patium conficiet B D. <!-- KEEP S--></s>
          <s id="s.002820">Excitetur &agrave; puncto B, in <expan abbr="vtramq;">vtramque</expan> <lb/>
partem perpendicularis E Z, in quam veniant a punctis A, &amp; C, <lb/>ad rectos angulos rect&aelig; line&aelig; A E, &amp; C Z: &longs;patium autem A E, &agrave; manubrio <pb pagenum="166" xlink:href="009/01/166.jpg"/><figure id="id.009.01.166.1.jpg" place="text" xlink:href="009/01/166/1.jpg"/><lb/>
decur&longs;um motu proprio &longs;patij B D, duplum <lb/>
&longs;it: recta ver&ograve; linea C H, curu&aelig; re&longs;pondeat <lb/>
C G, qu&aelig; &agrave; remi palmula de&longs;cripta e&longs;t. </s>
          <s id="s.002821">Di&shy;<lb/>
co ip&longs;as rectas lineas B D, &amp; C H, &aelig;quales <lb/>
e&longs;&longs;e. </s>
          <s id="s.002822">Nam in duobus triangulis B A E, &amp; <lb/>
C B Z, du&aelig; rect&aelig; line&aelig; A E, &amp; C Z, &aelig;qua&shy;<lb/>
les &longs;unt. </s>
          <s id="s.002823">In parallelogrammo autem B H, <lb/>
du&aelig; B D, &amp; H Z, &aelig;quales, atqui recta A E, <lb/>
dupla e&longs;t rect&aelig; B D, per hypothe&longs;im; dupla <lb/>
e&longs;t igitur, &amp; C Z, rect&aelig; H Z, quapropter <lb/>
C H, &amp; H Z, &aelig;quales erunt, Du&aelig; igitur <lb/>
C H, &amp; B D, &aelig;quales per communem &longs;en&shy;<lb/>
tentiam.</s>
        </p>
        <p type="main">
          <s id="s.002824">Et quia nauigium tantum &longs;patium de&shy;<lb/>
currit &longs;emper, quantum &longs;calmus: &longs;i igitur <lb/>
remi manubrium motu proprio duplum <lb/>
confecerit &longs;patium, qu&agrave;m nauigium, tan&shy;<lb/>
tum prouehetur nauigium, quantum pal&shy;<lb/>
mula retroce&longs;&longs;erit, quod demon&longs;trandum <lb/>
erat.</s>
        </p>
        <p type="head">
          <s id="s.002825"><emph type="italics"/>PROPOSITIO QVARTA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002826">Si nauigium minus &longs;patium decurrat, qu&agrave;m remi manu&shy;<lb/>
brium, &longs;ed &longs;upra dimidium, magis prouehetur, qu&agrave;m pal&shy;<lb/>
mula retrocedat; &longs;i ver&ograve; citra dimidium, minus.</s>
        </p>
        <p type="main">
          <s id="s.002827">In de&longs;cripta enim figura ponatur B D, minor quam A E, &longs;ed eius dimi&shy;<lb/>
dio maior. </s>
          <s id="s.002828">Dico, quod ip&longs;a B D, maior e&longs;t qu&agrave;m C H. <!-- KEEP S--></s>
          <s id="s.002829">Nam B D, &amp; <lb/>
H Z, &aelig;quales &longs;unt: Ad h&aelig;c A E, &amp; C Z, &aelig;quales &longs;unt rect&aelig; line&aelig;; ma&shy;<lb/>
ior igitur erit H Z, dimidio ip&longs;ius A E: quapropter reliqua C H, mi&shy;<lb/>
nor dimidio erit eiu&longs;dem A E, &amp; minor igitur erit C H, qu&agrave;m B D. <!-- KEEP S--></s>
          <s id="s.002830">Spa&shy;<lb/>
tium autem B D, id e&longs;t, quod nauigium conficit, &longs;patium ver&ograve; C H, remi <lb/>
palmula in contrarium decurrit; idcirc&ograve; prior pars Theorematis vera e&longs;t. <lb/>
</s>
          <s id="s.002831">Po&longs;terior autem &longs;imiliter o&longs;tendetur. </s>
          <s id="s.002832">&longs;i enim B D, minor e&longs;t dimidio ip&longs;ius <lb/>
A E: minor igitur erit, &amp; H Z, dimidio eiu&longs;dem A E; &amp; quoniam A E, &amp; <lb/>
C Z, &aelig;quales &longs;unt: reliqua igitur C H, dimidio eiu&longs;dem A E, maior erit: &amp; <lb/>
proinde minor erit B D, qu&agrave;m C H. <!-- KEEP S--></s>
          <s id="s.002833">Nauigium igitur minus &longs;patium de&shy;<lb/>
curret in anteriora, quam remi palmula in contrarium, quod demon&longs;tran&shy;<lb/>
dum &longs;u&longs;cepimus.</s>
        </p>
        <p type="head">
          <s id="s.002834"><emph type="italics"/>Corollarium.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002835">Ex hac, &amp; pr&aelig;cedenti infertur, quod &longs;i remi manubrium motu proprio <lb/>
maius &longs;patium decurrat, qu&agrave;m nauigium, &longs;iue id &longs;it duplum, &longs;iue mi&shy;


<pb pagenum="167" xlink:href="009/01/167.jpg"/>nus duplo, &longs;iue maius duplo, &longs;patium, quod nauigium interim decurrit ad <lb/>
anteriora, &amp; quod palmula remi in contrarium &longs;imul iuncta, ei quod ip&longs;um <lb/>
remi manubrium motu proprio conficit, &aelig;qualia erunt. </s>
          <s id="s.002836">&longs;emper enim B D, <lb/>
&aelig;qualis e&longs;t H Z: tota ver&ograve; C Z, qu&aelig; &aelig;qualis e&longs;t A E, ex &longs;uis partibus C H, <lb/>
&amp; H Z, con&longs;tabit.</s>
        </p>
        <p type="head">
          <s id="s.002837"><emph type="italics"/>Propo&longs;itionis conuer&longs;io.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002838">Si nauigium longius progrediatur, qu&agrave;m remi palmula re&shy;<lb/>
trocedat, &longs;patium conficiet plu&longs;quam dimidium eius, <lb/>
quod motu proprio remi manubrium decurrit: <lb/>
&longs;i minus, citra dimidium.</s>
        </p>
        <p type="head">
          <s id="s.002839"><emph type="italics"/>Huius demon&longs;tratio ex &longs;upradictis facil&egrave; colligi poterit.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002840"><emph type="italics"/>PROPOSITIO QVINTA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002841">Si celerius feratur nauigium, qu&agrave;m remi manubrium, mo&shy;<lb/>
uebitur palmula in vlteriora, <expan abbr="nil&qacute;">nilque</expan>; vnquam retroce&shy;<lb/>
det, <expan abbr="id&qacute;">idque</expan>; &longs;patium decurret, quo nauigij motus <lb/>
motum manubrij &longs;uperat.</s>
        </p>
        <p type="main">
          <s id="s.002842">Habeat enim remus incipiente motu po&longs;itionem A C: de&longs;inente <lb/>
<figure id="id.009.01.167.1.jpg" place="text" xlink:href="009/01/167/1.jpg"/><lb/>
ver&ograve; <expan abbr="&longs;it&utilde;">&longs;itum</expan> rectitudinis F G. &longs;cal&shy;<lb/>
mus igitur B, propter nauigij <lb/>
motum tran&longs;latus, erit in D, &longs;it <lb/>
<expan abbr="itaq;">itaque</expan> &longs;patium B D, maius qu&agrave;m A H, &agrave; re&shy;<lb/>
mi manubrio motu proprio decur&longs;um: &longs;ic <lb/>
enim celerius dicetur ferri <expan abbr="nauigi&utilde;">nauigium</expan>, qu&agrave;m <lb/>
manubrium. </s>
          <s id="s.002843">Dico, qu&ograve;d palmula C, in <lb/>
vlteriora mouebitur. </s>
          <s id="s.002844">Nam cum &longs;calmus <lb/>
B, prouectus fuerit in D: tran&longs;lata erit ip&shy;<lb/>&longs;a palmula C, vbi G, in rectitudinis &longs;itu, <lb/>
<expan abbr="&longs;patium&qacute;">&longs;patiumque</expan>; conficiet C G, curuilineum, cui <lb/>
re&longs;pondet C K: mouebitur igitur palmula <lb/>
in vlteriora. </s>
          <s id="s.002845">Nihil autem vnquam retro&shy;<lb/>
cedere, o&longs;tendetur in hunc modum. </s>
          <s id="s.002846">eadem <lb/>
enim celeritate mouentur A, in H, &amp; C, <lb/>
ver&longs;us I, circa &longs;calmum. </s>
          <s id="s.002847">Atqui per hypo&shy;<lb/>
the&longs;im celerius fertur nauigium, quam A. <lb/>
in H, celerius igitur ip&longs;um nauigium fer&shy;<lb/>tur, qu&agrave;m C, ver&longs;us I. &longs;ed mouetur idem <pb pagenum="168" xlink:href="009/01/168.jpg"/>C. ip&longs;a nauigij celeritate ver&longs;us K; celerius igitur ferretur C, ad K, quam <lb/>
ad I, quapropter nihil vnquam retrocedet ip&longs;um C, im&ograve; ver&ograve; in vlteriora <lb/>
progredietur, <expan abbr="&longs;patium&qacute;">&longs;patiumque</expan>; decurret C K, quod quidem relinquitur detracto <lb/>
I C, ex I K. &longs;i enim remi palmula tota ip&longs;a nauigij celeritate moueretur, vl&shy;<lb/>
tra K, progrederetur, cum B, perueniret ad D: &longs;ed retrahitur interim, pro&shy;<lb/>
pter eum motum, qui fit circa B. <!-- KEEP S--></s>
          <s id="s.002848">Sic igitur palmul&aelig; celeritate, qu&aelig; &agrave; mo&shy;<lb/>
tu nauigij prouenit retardata, decur&longs;um &longs;patium erit C K. <!-- KEEP S--></s>
          <s id="s.002849">Videtur autem <lb/>
&longs;olo remorum impul&longs;u hoc fieri non po&longs;&longs;e, &longs;ed alia in&longs;uper virtute impel&shy;<lb/>
lente opus e&longs;&longs;e, vt venti, vel aqu&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.002850">Ex his Theorematis liquet, inquit Nonius, qu&agrave;m incerta interroget Ari&shy;<lb/>
&longs;toteles, &amp; qu&agrave;m in&longs;cit&egrave; re&longs;pondeat. </s>
          <s id="s.002851">Nam non continu&ograve; &longs;i nauigium in an&shy;<lb/>teriora mouetur, remi palmula retrocedet; neque etiam &longs;i retrocedat, mi&shy;<lb/>
nus &longs;pat&igrave;um tran&longs;mittit in contrarium, qu&agrave;m nauigium progrediatur. </s>
          <s id="s.002852">De&shy;<lb/>
mon&longs;trant hoc &longs;ecunda, &amp; tertia propo&longs;itio. </s>
          <s id="s.002853">Remi ver&ograve; manubrium motu <lb/>
proprio, qui circa &longs;calmum fit, &amp; vn&agrave; cum nauigij motu maius &longs;patium con&shy;<lb/>
ficit qu&agrave;m nauigium. </s>
          <s id="s.002854">&longs;olo autem proprio motu, &longs;i contingat tantum &longs;pa&shy;<lb/>
tium conficere, quantum nauigium, fieri non poterit, vt palmula mouea&shy;<lb/>
tur. </s>
          <s id="s.002855">fru&longs;tra igitur conatur in vniuer&longs;um demon&longs;trare remi manubrium ma&shy;<lb/>
ius &longs;patium decurrere, qu&agrave;m palmulam in contrarium. </s>
          <s id="s.002856">Pr&aelig;terea quando <lb/>
nauigium <expan abbr="l&otilde;gius">longius</expan> progreditur, qu&agrave;m remi palmula regrediatur, minus &longs;pa&shy;<lb/>
tium decurrit, quam manubrium: igitur hon &aelig;quale. </s>
          <s id="s.002857">Et proinde con&longs;tat <lb/>
neque veritatem in propo&longs;ito, neque demon&longs;trationem in ijs, qu&aelig; conge&shy;<lb/>
rit, reperiri.</s>
        </p>
        <p type="main">
          <s id="s.002858">Huiu&longs;que Petrus Nonius:</s>
        </p>
        <p type="main">
          <s id="s.002859">Reliqua huius textus vtinam quemadmodum &longs;unt clara, ita etiam vera <lb/>
e&longs;&longs;ent: &longs;ed quia qu&aelig; modo dixit de remo, eadem temoni applicat propte&shy;<lb/>
rea ij&longs;dem etiam obnoxia &longs;unt difficultatibus.</s>
        </p>
        <p type="head">
          <s id="s.002860"><emph type="italics"/>QV&AElig;STIO SEXTA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002861"><emph type="italics"/>De Antenna.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002862"><arrow.to.target n="marg238"/></s>
        </p>
        <p type="margin">
          <s id="s.002863"><margin.target id="marg238"/>248</s>
        </p>
        <p type="main">
          <s id="s.002864">Qv&aelig;rit cur quanto Antenna &longs;ublimior fuerit, ij&longs;dem velis, &amp; vento <lb/>
eodem celerius ferantur nauigia. </s>
          <s id="s.002865">Re&longs;pondet inde id prouenire, <lb/>
quia malus, &longs;iue arbor nauis in huiu&longs;modi ventorum impul&longs;u ve&shy;<lb/>
ctis euadit, cuius auxilio idem ventus, qui mouens e&longs;t, maiorem <lb/>
vim acquirit, quanto longior fuerit pars vectis, qu&aelig; inter hypomoclion, &amp; <lb/>
vim mouentem intercipitur: quando autem altior fuerit antenna, tunc ea <lb/>
vectis pars longior euadit, &amp; propterea accidit, vt vires ventorum augean&shy;<lb/>
tur. </s>
          <s id="s.002866">&longs;ed i&longs;ta melius in figura in&longs;piciamus. </s>
          <s id="s.002867">&longs;it nauis A B, cuius arbor C D E, <lb/>
antenna F C G, velum F G H, vectis e&longs;t arbor, cuius fultura e&longs;t in E, extre&shy;<lb/>
mo mali in fundo nauis, onus autem in D, vbi malus exit &egrave; carina. </s>
          <s id="s.002868">mouens <lb/>
potentia e&longs;t ventus, qui mouet in antenna F C G. quanto igitur &longs;ublimior <lb/>
e&longs;t antenna, tanto longior euadit vectis E C, <expan abbr="tanto&qacute;">tantoque</expan>; maiores fiunt venti <lb/>
vires. </s>
          <s id="s.002869">dixi autem onus e&longs;&longs;e in D, quia &longs;i nauis vento ob&longs;i&longs;teret, ip&longs;a inuerte&shy;<lb/>retur hac ratione, vt puppis A, eleuata, prora B, demergeretur, manente <pb pagenum="169" xlink:href="009/01/169.jpg"/><figure id="id.009.01.169.1.jpg" place="text" xlink:href="009/01/169/1.jpg"/><lb/>
veluti centro parte E. quia ve&shy;<lb/>
r&ograve; ob maris liquiditatem na&shy;<lb/>uis minim&egrave; ob&longs;i&longs;tit, &longs;ed facil&egrave; <lb/>
cedens &agrave; ventis vrgetur, hinc <lb/>
fit, vt merit&ograve; dixerim pondus <lb/>
nauis e&longs;&longs;e ad D, fulcimentum <lb/>
ver&ograve; ad E.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002870">Qu&aelig;&longs;tio &longs;eptima, &amp; &longs;atis per <lb/>
&longs;e clara e&longs;t; <expan abbr="neq;">neque</expan> Mathemati&shy;<lb/>
ci e&longs;t eam exponere.</s>
        </p>
        <p type="head">
          <s id="s.002871"><emph type="italics"/>QV&AElig;STIO OCTAVA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002872"><emph type="italics"/>De Rota.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.002873">Cur ex figurarum genere qu&aelig;cunque rotund&aelig; &longs;unt, &amp; cir&shy;<lb/>
culares facilius mouentur?</s>
        </p>
        <p type="main">
          <s id="s.002874"><arrow.to.target n="marg239"/></s>
        </p>
        <p type="margin">
          <s id="s.002875"><margin.target id="marg239"/>249</s>
        </p>
        <p type="main">
          <s id="s.002876">Tribus autem modis circulum rotari contingit; aut enim &longs;ecun&shy;<lb/>
dum ap&longs;idem, &longs;iue curuaturam centro &longs;imul moto, quemadmo&shy;<lb/>
dum plau&longs;trorum rot&aelig; vertuntur: aut circa manentem axem, <lb/>
tanquam centrum veluti rotul&aelig; ill&aelig;, ex quibus trochlea compo&shy;<lb/>
nitur; vel quibus ad puteos vtimur, qu&aelig; quidem rect&aelig; ad horizontem &longs;o&shy;<lb/>
lent con&longs;titui. </s>
          <s id="s.002877">aut quem ad modum rota figuli, qu&aelig; pariter circa <expan abbr="man&etilde;s">manens</expan> cen&shy;<lb/>
trum gyratur, &longs;ed qua&longs;i pro&longs;trata horizonti &aelig;quidi&longs;tans collocata e&longs;t. </s>
          <s id="s.002878">Qu&aelig; <lb/>
igitur primo modo mouentur, fort&egrave; facilius quam figur&aelig; rectiline&aelig;, vt &longs;unt <lb/>
triangulares, quadrat&aelig;, pentagon&aelig;, &amp;c. </s>
          <s id="s.002879">mouentur, quia circulares figur&aelig; <lb/>
parua &longs;ui parte, &amp; qua&longs;i in puncto planum, &longs;eu pauimentum contingunt, vn&shy;<lb/>
de fit, vt <expan abbr="neq;">neque</expan> offen&longs;ent, <expan abbr="neq;">neque</expan> impingant; cuius cau&longs;a e&longs;t, quia &agrave; terra &longs;emo&shy;<lb/>
tus e&longs;t angulus, ide&longs;t tali angulo planum contingunt, vt ab eo &longs;tatim rot&aelig; <lb/>
curuatura &agrave; terra eleuari incipiat, &amp; propterea parum terr&aelig; h&aelig;reat: in fi&shy;<lb/>
guris ver&ograve; rectilineis, in quadrata. </s>
          <s id="s.002880">v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;ecus accidit, quia ab angulo ad an&shy;<lb/>
gulum linea recta tenditur, vnde in ip&longs;ius volutatione po&longs;t contactum vnius <lb/>
anguli tota recta linea &longs;equens, plano adaptabitur, &amp; non &longs;emouebitur &longs;ta&shy;<lb/>
tim in altum, &amp; ide&ograve; multum offen&longs;abit, &amp; impinget, <expan abbr="tarde&qacute;">tardeque</expan>; idcirc&ograve; mo&shy;<lb/>
uebitur. </s>
          <s id="s.002881">Pr&aelig;terea circulares etiam, &longs;i cui obuiam fiunt corpori, illud &longs;imi&shy;<lb/>liter &longs;ecundum pu&longs;illum tangunt: rectiline&aelig; ver&ograve; figur&aelig;, rectitudine &longs;ua <lb/>
plani multum contingerent. </s>
          <s id="s.002882">Ad h&aelig;c motor mouens huiu&longs;modi rotas, eas <lb/>
mouet, qu&ograve; nutant: nam quando rota erecta e&longs;t &longs;uper pauimentum, dia&shy;<lb/>meter ip&longs;ius, qu&aelig; &agrave; contactu pauimenti ad angulos rectos, ad &longs;upremum <pb pagenum="170" xlink:href="009/01/170.jpg"/>rot&aelig; perducitur totum rot&aelig; pondus in duas &aelig;quas partes diuidit, ita vt ta&shy;<lb/>
le pondus in &aelig;quilibrio con&longs;tituatur, cum ex vna parte tantum &longs;it, quantum <lb/>
ex altera; ex quo fit, vt vel exigua vis ip&longs;am impellere valeat: quando enim <lb/>
duo &aelig;qualia pondera &longs;unt in &aelig;quilibrio, quelibet vis pote&longs;t ea ab &aelig;quilibrio <lb/>
dimouere. </s>
          <s id="s.002883">quando po&longs;tea rota e&longs;t in motu, vel cum primum ei motus fuerit <lb/>
&agrave; motore inditus, &longs;emper nutat ad partes illas, ad quas primum fuit incita&shy;<lb/>
ta per impre&longs;&longs;am motionem, quapropter nullo negotio ad ea&longs;dem partes, <lb/>
&longs;eu antror&longs;um mouetur; qu&ograve; enim <expan abbr="vnumquodq;">vnumquodque</expan> vergit, illuc facillim&egrave; fer&shy;<lb/>
tur: quemadmodum &egrave; contrario difficillimum e&longs;t in contrariam nutus &longs;ui <lb/>
partem vnumquodque pellere. </s>
          <s id="s.002884">Huc etiam pertinet, quod nonnulli dicunt, <lb/>
circuli nimirum periph&aelig;riam perenni ver&longs;ari motu, <expan abbr="atq;">atque</expan> hinc facilius mo&shy;<lb/>
ueri. </s>
          <s id="s.002885">&longs;icuti etiam dicunt, quod manentia propterea manent, quia contrani&shy;<lb/>
tuntur, &amp; ob&longs;i&longs;tunt mouenti: quod fort&egrave; dicebant propter maximam circu&shy;<lb/>li ad motum aptitudinem. </s>
          <s id="s.002886">&amp; quia &longs;icut diameter ad diametrum, ita maio&shy;<lb/>
ris circuli periph&aelig;ria ad minoris periph&aelig;riam &lpar;vt po&longs;tea o&longs;tendam&rpar; &amp; quia <lb/>
quo <expan abbr="l&otilde;gior">longior</expan> diameter e&longs;t, e&ograve; facilius, vt initio probaui, mouetur, fit vt etiam <lb/>
periph&aelig;ria maioris facilius, qu&agrave;m minoris moueatur, &longs;iue dixeris, quod an&shy;<lb/>
gulus maioris circuli ad angulum minoris nutum quendam habet; &amp; quia <lb/>
facilius mouetur angulus maioris, qu&agrave;m minoris, fit, vt maior rota adhi&shy;<lb/>
beatur ad minorem mouendam: &amp; quia intra maiorem infinit&aelig; circa idem <lb/>
centrum concipi po&longs;&longs;unt, hinc fit, vt rot&aelig; maiores facilius moueantur, &amp; <lb/>
mot&aelig; moueant c&aelig;teras intra &longs;e contentas. </s>
          <s id="s.002887">quod dictum e&longs;t de nutu anguli <lb/>
maioris circuli ad angulum minoris ex appo&longs;ita figura facil&egrave; patebit, vbi <lb/>
<figure id="id.009.01.170.1.jpg" place="text" xlink:href="009/01/170/1.jpg"/><lb/>
pro minore angulo intelligendus e&longs;t arcus C B, <lb/>
pro maiore autem arcus D E, quorum <expan abbr="vterq;">vterque</expan> vo&shy;<lb/>
catur angulus, quoniam angulo A, qui e&longs;t in cen&shy;<lb/>
tro opponuntur. </s>
          <s id="s.002888">Atque h&aelig;c &longs;ufficiant de ijs, qu&aelig; <lb/>primo modo mouentur.</s>
        </p>
        <p type="main">
          <s id="s.002889">Nunc ad ea, qu&aelig; reliquis duobus modis cieri <lb/>
&longs;olent, qu&aelig; &longs;cilicet non mouentur &longs;ecundum ap&longs;i&shy;<lb/>
dem, &longs;ed aut iuxta planitiem, ide&longs;t, qu&aelig; &aelig;quidi&shy;<lb/>&longs;tanter pauimento collo<expan abbr="c&atilde;tur">cantur</expan>, vt rot&aelig; figulorum, <lb/>
aut qu&aelig; in loco &agrave; terra eleuato, vt troclearum or&shy;<lb/>
biculi. </s>
          <s id="s.002890">rot&aelig; h&aelig; facilius ip&longs;&aelig;, &amp; ea etiam, qu&aelig; ip&longs;is annectuntur commouen&shy;<lb/>
tur, quam &longs;i rectilinea figura con&longs;tarent; non quia parua &longs;ui portione vel <lb/>
tangant planum, vel offen&longs;ent, &longs;ed ob aliam inclinationem, de qua initio <lb/>
huius operis ante qu&aelig;&longs;tiones dictum e&longs;t, vbi diximus circulum duas incli&shy;<lb/>
nationes ad motum obtinere, &longs;ecundum quas &agrave; motore mouetur; vna e&longs;t, <lb/>
quam diximus naturalem, qua &longs;olet cieri &longs;ecundum periph&aelig;riam, motor <lb/>
enim &longs;emper mouet circulum in periph&aelig;ria, &amp; &longs;ecundum hanc inclinatio&shy;<lb/>
nem extremum diametri rect&agrave;, non circulariter moueretur: hanc inclina&shy;<lb/>
tionem fort&egrave; habet &agrave; materia grauitante, &amp; in ip&longs;o circulo con&longs;tituta in <lb/>
&aelig;quilibrio: qu&aelig; autem in &aelig;quilibrio, facillim&egrave; cedunt; &amp; qui talia mouent, <lb/>
qua&longs;i prius mota mouent, &amp; ide&ograve; facillim&egrave;. </s>
          <s id="s.002891">Secundum igitur inclinatio&shy;<lb/>
nem hanc, qu&aelig; in obliquum e&longs;t, ide&longs;t, qu&aelig; &longs;ecundum circunferentiam &longs;it, <lb/>
ip&longs;am rotam mouens facillim&egrave; mouet. </s>
          <s id="s.002892">altera latio e&longs;t, &longs;ecundum quam cir&shy;


<pb pagenum="171" xlink:href="009/01/171.jpg"/>culus &agrave; &longs;eip&longs;o &longs;ecundum diametrum mouetur, ide&longs;t circa &longs;uum centrum re&shy;<lb/>
trahit continu&ograve; extrema diametri; ne recta &longs;ecundum naturalem lationem <lb/>
ferantur, &longs;ed in orbem circulariter circa centrum gyrentur. </s>
          <s id="s.002893">h&aelig;c Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.002894">Re&shy;<lb/>
&longs;tat vt &longs;atisfaciam promi&longs;&longs;is.</s>
        </p>
        <p type="main">
          <s id="s.002895">Dictum e&longs;t ab Ari&longs;t. in textu <emph type="italics"/>&lpar;Sicut diameter ad diametrum, ita maior circu&shy;<lb/>
lus ad maiorem&rpar;<emph.end type="italics"/> qu&aelig; verba intelligenda e&longs;&longs;e non de circulis, &longs;ed de periph&aelig;&shy;<lb/>
rijs, vti expo&longs;ui, manife&longs;tum e&longs;t ex 11. propo&longs;it. </s>
          <s id="s.002896">5. Pappi Alexandrini, qu&aelig; <lb/>
talis e&longs;t: Circulorum circunferenti&aelig; inter &longs;e &longs;unt vt diametri. </s>
          <s id="s.002897">quam etiam <lb/>
Pater Clauius demon&longs;trat propo&longs;. </s>
          <s id="s.002898">2. lib. 8. &amp; propo&longs;. </s>
          <s id="s.002899">1. lib. 4. Geom. <!-- REMOVE S-->pract. <lb/>
<!-- REMOVE S-->&longs;i autem de ip&longs;is circulis intelligerentur fal&longs;a e&longs;&longs;ent, non enim e&longs;t circulus <lb/>
ad circulum, vt diameter ad diametrum; &longs;ed circuli &longs;unt inter &longs;e, quemad&shy;<lb/>
modum &agrave; diametris ip&longs;orum quadrata per &longs;ecundam 12. Elem. quadrata <lb/>
autem &longs;unt inter &longs;e in duplicata ratione laterum per 20. 6. <expan abbr="eiusq;">eiusque</expan> corolla&shy;<lb/>
rium; hoc e&longs;t &longs;i fiat, vt latus maioris quadrati ad latus minoris, ita latus mi&shy;<lb/>
noris ad aliam tertiam lineam, erit quadratum maius ad minus, vt latus <lb/>
ip&longs;ius ad tertiam illam lineam; non autem vt ad latus minoris. </s>
          <s id="s.002900">cum ergo <lb/>
circulus &longs;it ad circulum, vt quadratum diametri ad quadratum diametri, <lb/>
&amp; quadrata non <expan abbr="habe&atilde;t">habeant</expan> rationem laterum, &longs;eu diametrorum pr&aelig;dictorum, <lb/>
&longs;ed illorum duplicatam, <expan abbr="neq;">neque</expan> circuli inuicem illam habere poterunt.</s>
        </p>
        <p type="main">
          <s id="s.002901">Illud demum non ignorandum, quod Guidus Vbaldus propo&longs;it. </s>
          <s id="s.002902">1. de Tro&shy;<lb/>
chlea, demon&longs;trat, quod nimirum potentia &longs;u&longs;tinens pondus per rotulam, <lb/>
cui funis &longs;upern&aelig; fuerit circumductus, qualis ea e&longs;t, qua ad hauriendam ex <lb/>
puteis aquam vtimur, talis inquam potentia e&longs;t &aelig;qualis ponderi; cuius ra&shy;<lb/>
tio e&longs;t, quia tunc trochlea fit vectis, cuius fulcimentum e&longs;t in medio vectis, <lb/>
pondus ver&ograve;, &amp; potentia in extremitatibus &longs;unt, &amp; &aelig;quidi&longs;tant ab hypomo&shy;<lb/>
clio, &amp; propterea cum &longs;it eadem proportio ponderis ad potentiam, qu&aelig; di&shy;<lb/>
&longs;tanti&aelig; ad di&longs;tantiam, vt &longs;upra qu&etail;&longs;t. </s>
          <s id="s.002903">3. probatum e&longs;t ex Archimede, &amp; Gui&shy;<lb/>
do Vbaldo, di&longs;tanti&aelig; autem &longs;int &aelig;quales, erunt etiam pondus, &amp; potentia <lb/>
&aelig;qualia, ide&longs;t, &longs;i pondus e&longs;&longs;et vnius libr&aelig;, &longs;u&longs;tineretur &agrave; tanta vi, <expan abbr="qu&atilde;ta">quanta</expan> opus <lb/>
e&longs;t ad libram vnam &longs;u&longs;tinendam, &amp; non amplius. </s>
          <s id="s.002904">vt autem clar&egrave; appareat <lb/>
vectis in trochlea, &amp; hypomoclion, &amp; &aelig;quales di&longs;tanti&aelig;, &longs;it figura, in qua <lb/>
<figure id="id.009.01.171.1.jpg" place="text" xlink:href="009/01/171/1.jpg"/><lb/>
pondus D, ductario funi D C B E, alligatum. </s>
          <s id="s.002905">poten&shy;<lb/>
tia <expan abbr="&longs;u&longs;tin&etilde;s">&longs;u&longs;tinens</expan> E. axis autem erit diameter rotul&aelig; B A C, <lb/>
nam potentia premit rotulam in B, &amp; pondus in C, &amp; <lb/>
cum rotula &longs;u&longs;tineatur in A, &agrave; &longs;u&longs;pen&longs;orio F A. erit <lb/>
punctum A, hypomoclion, quia in motu vectis eua&shy;<lb/>
dit centrum, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; punctum manens. </s>
          <s id="s.002906">&aelig;quales autem <lb/>
di&longs;tanti&aelig; <expan abbr="vtrinq;">vtrinque</expan> ab hypomoclio &longs;unt B A, A C, &longs;unt <lb/>
enim ex centro eodem. </s>
          <s id="s.002907">ex quibus manife&longs;tum e&longs;t hu&shy;<lb/>
iu&longs;modi rotulam nullam vim mouenti addere, &longs;ed &longs;o&shy;<lb/>
lum illud pr&aelig;&longs;tat, vt omne tollat impedimentum, <lb/>
quemadmodum ait Ari&longs;t. manife&longs;tum etiam e&longs;t ma&shy;<lb/>
iorem vim quamlibet, quam &longs;it ea, qu&aelig; &longs;u&longs;tinet, po&longs;&longs;e <lb/>
idem pondus &longs;ur&longs;um mouere. </s>
          <s id="s.002908">h&aelig;c &amp; pr&aelig;&longs;enti loco, &amp; <lb/>
&longs;equentibus lucem afferre po&longs;&longs;unt.</s>
        </p>
        <pb pagenum="172" xlink:href="009/01/172.jpg"/>
        <p type="head">
          <s id="s.002909"><emph type="italics"/>QV&AElig;STIO NONA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002910"><emph type="italics"/>De Trochleis, &amp; Scytalis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002911"><arrow.to.target n="marg240"/></s>
        </p>
        <p type="margin">
          <s id="s.002912"><margin.target id="marg240"/>250</s>
        </p>
        <p type="main">
          <s id="s.002913"><emph type="italics"/>Cvr ea, qu&aelig; per maiores circulos tollantur, &amp; trahuntur facilius, &amp; ci&shy;<lb/>
tius mouentur? </s>
          <s id="s.002914">veluti per maiores trochleas, qu&agrave;m per minores, &amp; &longs;cy&shy;<lb/>
talas &longs;imiliter? </s>
          <s id="s.002915">An quanto maior fuerit illa, qu&aelig; &agrave; centro e&longs;t, in &aelig;quali <lb/>
temporis &longs;patio maius &longs;patium conficit? </s>
          <s id="s.002916">quamobrem &aelig;qual&igrave; inexi&longs;tente <lb/>
onere, idem faciet, &longs;icuti diximus maiores libras minoribus exactiores e&longs;&longs;e; &longs;par&shy;<lb/>
tum enim in illis centrum e&longs;t: partes ver&ograve; libr&aelig; vtrinque &agrave; &longs;parto &longs;unt veluti line&aelig; <lb/>
ex centro&rpar;<emph.end type="italics"/> Cum textus huius qu&aelig;&longs;tionis fatis clarus &longs;it, pr&aelig;&longs;ertim &longs;i prius <lb/>
legantur, qu&aelig; dicta &longs;unt de libra in prima qu&aelig;&longs;t. </s>
          <s id="s.002917">&amp; qu&aelig; de rota, &amp; trochlea <lb/>
in proxima pr&aelig;cedenti, &agrave; paraphra&longs;i ip&longs;ius &longs;uper&longs;edebo. </s>
          <s id="s.002918">Illud tamen, quod <lb/>
magis nece&longs;&longs;arium e&longs;t, non omittam, vt &longs;cilicet difficultatibus quibu&longs;dam <lb/>
occurram. </s>
          <s id="s.002919">Et primo, quod Ari&longs;t. ait, ea qu&aelig; per maiores circulos veluti <lb/>
trochleas, &longs;eu rotulas trahuntur, facilius trahi, qu&agrave;m ea, qu&aelig; per minores, <lb/>
non videtur ex omni parte verom. </s>
          <s id="s.002920">nam &longs;icuti in <expan abbr="pr&aelig;ced&etilde;ti">pr&aelig;cedenti</expan> qu&aelig;&longs;tione o&longs;ten&shy;<lb/>
&longs;um e&longs;t ex Guido Vbaldo, trochlea &longs;implex, &longs;iue rotula illa &longs;triata, cui funis <lb/>
&longs;upern&egrave; inditur, vt in &longs;uperiori figura; nullas addit vires potenti&aelig;, quia re&shy;<lb/>
ducitur ad vectem, cuius fultura &longs;it in medio ip&longs;ius. </s>
          <s id="s.002921">&longs;iue igitur rotula illa <lb/>
magna fuerit, &longs;iue parua, &longs;emper in talem vectem re&longs;oluetur, &amp; propterea, <lb/>
vt etiam experientia con&longs;tat eodem labore aquam hauriunt, &longs;iue rotula illa <lb/>
magna fuerit, &longs;ine parua. </s>
          <s id="s.002922">nec minus vera videtur re&longs;pon&longs;io, cum ait <emph type="italics"/>&lpar;An quia <lb/>
quanto maior fuerit illa, qu&aelig; &agrave; centro e&longs;t, in &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> maius mouetur &longs;patium&rpar;<emph.end type="italics"/><lb/>
qu&aelig; quidem vera &longs;unt, &longs;i intelligantur hoc modo, nimirum, quod quando <lb/>
plures <expan abbr="circul&longs;conc&etilde;trici">circuli concentrici</expan>, <expan abbr="atq;">atque</expan> inuicem connexi fuerint, ita vt vnus &longs;ine alijs <lb/>
moueri nequeat, tunc quanto maior fuerit diameter, &amp; con&longs;equenter cir&shy;<lb/>
cunferentia, tanto velocius mouebitur. </s>
          <s id="s.002923">&longs;i autem intelligantur de duobus <lb/>
circulis ab inuicem &longs;eparatis, quorum vnus <expan abbr="ab&longs;q;">ab&longs;que</expan> altero moueri pote&longs;t, vt &longs;ie <lb/>
quando vtimur modo rotula magna, modo parua ad aquam hauriendam <lb/>
non videntur vera, in quo &longs;en&longs;u manife&longs;t&egrave; loquitur Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.002924">Quapropter vt &longs;in&shy;<lb/>
cer&egrave; loquar, nunc ne&longs;cio, qua ratione Ari&longs;t ab errore excu&longs;are valeam, alijs <lb/>
fort&egrave; occurret.</s>
        </p>
        <p type="main">
          <s id="s.002925">Secundo loco videndum quid &longs;int &longs;cyntal&aelig;. </s>
          <s id="s.002926">Vt autem con&longs;tat ex &longs;equenti <lb/>
qu&aelig;&longs;tione 11. &longs;cyntala erat in&longs;trumentum quoddam vectorium, quod ro&shy;<lb/>
tas, &longs;icut currus, aliter tamen factas, habebat, porr&ograve; <foreign lang="greek">skutalh\,</foreign> ide&longs;t &longs;cytala <lb/>
inter alia &longs;ignificat <expan abbr="bacul&utilde;">baculum</expan>, &longs;iue lignum oblongum, ac teres, qualia ea &longs;unt, <lb/>
quibus vtimur in &longs;ucculis, vulg&ograve; Na&longs;pe; &amp; in axe in peritrochio, vt videre <lb/>
e&longs;t apud <expan abbr="Guid&utilde;">Guidum</expan> Vbaldum. </s>
          <s id="s.002927">hinc factum e&longs;t, vt apud Lac&aelig;demonios &longs;cytala <lb/>
&longs;ignificaret quoddam genus epi&longs;tol&aelig;, quam &longs;cytalem laconicam dicebant, <lb/>
quia in charta in&longs;tar zon&aelig; oblonga, &amp; circa &longs;cytalam, hoc e&longs;t circa bacillum <lb/>quendam &longs;piratim circumuoluta exarabatur; ita vt ver&longs;us &longs;criptur&aelig; &longs;ecun&shy;<lb/>dum &longs;urculi longitudinem ducerentur, ex quo fiebat, vt per iuncturas mem&shy;<lb/>
bran&aelig;, liter&aelig;, ac verba procederent, membranam hanc ex &longs;cytala reuolu&shy;<lb/>
tam, &amp; aliter complicatam Imperatori mittebant, re&longs;olutio autem mem&shy;


<pb pagenum="173" xlink:href="009/01/173.jpg"/>bran&aelig; literas truncas, atque mutilas reddebat; cum partim continerentur <lb/>
citra iuncturas, partim vltra: e&aelig;qu&egrave; partes, qu&aelig; &longs;imul fuerant &longs;cript&aelig;, &amp; <lb/>continuat&aelig;, po&longs;t re&longs;olutionem erant ab inuicem valde di&longs;&longs;it&aelig;. </s>
          <s id="s.002928">quapropter <lb/>
Imperator commenti totius con&longs;cius, eandem membranam &longs;cytali alteri <lb/>
priori omnin&ograve; &longs;imili, <expan abbr="&aelig;quali&qacute;">&aelig;qualique</expan>; eodem modo, quo prius circumponebat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>
iunctur&aelig; priores redibant, qu&aelig; literas, ac verba mutila, &amp; imperfecta in <lb/>
integrum re&longs;tituebant, vt facil&egrave; legi po&longs;&longs;ent. </s>
          <s id="s.002929">hoc illi vtebantur &longs;ecreto, cum <lb/>
literas ad Imperatores &longs;uos mi&longs;&longs;as, ho&longs;tibus occultas e&longs;&longs;e volebant.</s>
        </p>
        <p type="main">
          <s id="s.002930">Ex quibus conijcere licet &longs;cytalam fui&longs;&longs;e lignum oblongum, &amp; teres, &longs;iue <lb/>
vt Geometr&aelig; dicunt, Cylindrum; in cuius tamen extremitatibus e&longs;&longs;ent <lb/>
margines duo aliquantulum prominentes, ceu bin&aelig; rot&aelig;, cum ip&longs;o tamen <lb/>
continu&aelig;, &amp; connex&aelig;, vt cum ip&longs;o &longs;imul conuoluerentur; non tamen tan&shy;<lb/>
<figure id="id.009.01.173.1.jpg" place="text" xlink:href="009/01/173/1.jpg"/><lb/>
quam circa axem. </s>
          <s id="s.002931">cuius hanc accipe fi&shy;<lb/>
guram. </s>
          <s id="s.002932">Qu&aelig;rit igitur Ari&longs;t. cur huiu&longs;&shy;<lb/>
modi &longs;cytal&aelig; facilius moueantur, quo <lb/>
maiores ip&longs;arum &longs;unt rot&aelig;. </s>
          <s id="s.002933">Cui qu&aelig;&shy;<lb/>
&longs;tioni &longs;imul, ij&longs;demque verbis, quibus <lb/>
qu&aelig;&longs;tioni de maioribus rotulis re&longs;pondet, &longs;ed non &longs;atisfacit ob eandem ra&shy;<lb/>
tionem, quam ibi attuli. </s>
          <s id="s.002934">Crediderim tamen maiores &longs;cytalas, &amp; maiores <lb/>
curruum rotas, &amp; alia id generis, qu&aelig; volutantur, ita vt motu progre&longs;&longs;iuo <lb/>
mutent locum, facilius moueri, &longs;ed ob aliam cau&longs;am, quia nimirum maio&shy;<lb/>
res rot&aelig; minus &longs;i quid obuiam fiat, offen&longs;ant, quia &longs;ua magnitudine quem&shy;<lb/>
libet obicem facil&egrave; &longs;uperare po&longs;&longs;unt; cuius cau&longs;a e&longs;t angulus <expan abbr="acuti&longs;&longs;im&utilde;s">acuti&longs;&longs;imus</expan>, <lb/>
quem cum terra facit; at ver&ograve; exigu&aelig; rot&aelig;, &longs;i cui maiori ob&longs;taculo obuia&shy;<lb/>
rint, ip&longs;um nequeunt &longs;uperare, aut &longs;upera&longs;cendere, quia angulum cum ter&shy;<lb/>
ra faciunt in&longs;to maiorem, vnde facil&egrave; ip&longs;orum cur&longs;us inhibetur, <expan abbr="ip&longs;&aelig;&qacute;">ip&longs;&aelig;que</expan>; pro&shy;<lb/>
pterea pr&aelig; maioribus tardiores euadunt. </s>
          <s id="s.002935">Atque h&aelig;c in hanc qu&aelig;&longs;tionem <lb/>
dicta &longs;ufficiant.</s>
        </p>
        <p type="head">
          <s id="s.002936"><emph type="italics"/>QV&AElig;STIO DECIMA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002937"><emph type="italics"/>De libra vacua, &amp; alijs &longs;imilibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002938"><arrow.to.target n="marg241"/></s>
        </p>
        <p type="margin">
          <s id="s.002939"><margin.target id="marg241"/>251</s>
        </p>
        <p type="main">
          <s id="s.002940">Cvr libr&aelig;, qu&aelig; omni incumbente pondere &longs;unt vacu&aelig; ab impo&longs;ito <lb/>
pondere facilius mouentur, qu&agrave;m &longs;i quopiam inexi&longs;tente pondere <lb/>
aliud rur&longs;us onus &longs;uperaddatur. </s>
          <s id="s.002941">&longs;imiliter etiam rota, &amp; huiu&longs;modi <lb/>
quippiam, quod grauius quidem e&longs;t, difficilius commouetur qu&agrave;m <lb/>
l&aelig;ue, v. <!-- REMOVE S-->g. <!-- REMOVE S-->rota ferrea difficilius, qu&agrave;m lignea. </s>
          <s id="s.002942">&longs;imiliter qu&aelig; maiora &longs;unt, <lb/>
etiam &longs;i ex eadem materia con&longs;tent difficilius mouentur qu&agrave;m minora, vt <lb/>
rota maior ferrea, qu&agrave;m minor etiam ferrea. </s>
          <s id="s.002943">Habet h&aelig;c qu&aelig;&longs;tio tres par&shy;<lb/>
tes, quibus Ari&longs;t. re&longs;pondet dicens, quod graue e&longs;t &aelig;gr&egrave; moneri non &longs;olum <lb/>contra nutum &longs;uum, ide&longs;t &longs;ur&longs;um, &longs;ed etiam in obliquum, &longs;eu ad latera, quia <lb/>
grauia deor&longs;um <expan abbr="nut&atilde;t">nutant</expan>, non &longs;ur&longs;um, nec in tran&longs;uer&longs;um: ideo libr&aelig; cum one&shy;<lb/>re, quia &longs;unt grauiores, &amp; rota ferrea qu&agrave;m lignea, &amp; ferrea etiam maior, <lb/>
qu&agrave;m minor grauior e&longs;t, ide&ograve; difficilius agitatur.</s>
        </p>
        <p type="main">
          <s id="s.002944">Contra quam re&longs;pon&longs;ionem &longs;ic fort&egrave; obijcies; in pr&aelig;cedenti enim qu&aelig;&shy;


<pb pagenum="174" xlink:href="009/01/174.jpg"/>&longs;tione dictum e&longs;t ab Ari&longs;t. maiores trochleas, &amp; &longs;cytalas, minoribus facilius <lb/>
commoueri, hic autem dicit maiorem rotam difficilius qu&agrave;m minorem mo&shy;<lb/>
ueri. </s>
          <s id="s.002945">Hanc obiectionem Piccolomineus di&longs;&longs;imula&longs;&longs;e videtur, cui ego, inge&shy;<lb/>
nu&egrave; fateor, me &longs;atisfacere ne&longs;cire, vt enim in pr&aelig;cedenti annotaui, nulla <lb/>
mihi ratio Ari&longs;t. excu&longs;andi occurrit, alijs fort&egrave; occurret. </s>
          <s id="s.002946">In pr&aelig;&longs;enti au&shy;<lb/>
tem ben&egrave; quidem re&longs;pondet, &longs;ed tamen intimam rei cau&longs;am non attingit.</s>
        </p>
        <p type="main">
          <s id="s.002947">Sciendum igitur e&longs;t id, quod Guidus Vbaldus in tractatu de libra pluri&shy;<lb/>
bus demon&longs;trauit: quod &longs;i quoduis graue &longs;u&longs;pendatur pror&longs;us in <expan abbr="c&etilde;tro">centro</expan> gra&shy;<lb/>
uitatis, ita vt in perfecto &longs;it &aelig;quilibrio, tunc &longs;iue magnum, &longs;iue paruum, <lb/>
&longs;iue graue, grauiu&longs;u&egrave; fuerit, &agrave; quauis exigua vi poterit ab &aelig;quilibrio dimo&shy;<lb/>
ueri. </s>
          <s id="s.002948">cur ergo in libris, &amp; rotis grauioribus, aut maioribus <expan abbr="experi&etilde;tia">experientia</expan> con&shy;<lb/>
trarium o&longs;tendit? </s>
          <s id="s.002949">ratio e&longs;t, quia h&aelig;c omnia communiter non collocantur, <lb/>
ita vt circa centrum &longs;uum, quod etiam centrum grauitatis e&longs;t, conuerti <lb/>
po&longs;&longs;int: verum aptantur circa axem, &amp; quidem iu&longs;to maiorem, laxiu&longs;que <lb/>
circa ip&longs;um conuertuntur, vnde fit, vt ip&longs;a ob in&longs;itam grauitatem premant <lb/>
axem in &longs;uperiori parte, vnde quando ab aliquo gyrantur, non propri&egrave; gy&shy;<lb/>
rant, &longs;ed in &longs;uperiori axis parte h&aelig;rentes ip&longs;um atterunt; ex qua attritione <lb/>
fit, vt retardentur, <expan abbr="id&qacute;">idque</expan>; e&ograve; magis, quo grauiora magis premunt; h&aelig;rent, <lb/>
<expan abbr="difficilius&qacute;">difficiliusque</expan>; propterea raptantur potius, qu&agrave;m gyrentur.</s>
        </p>
        <p type="main">
          <s id="s.002950">Ex his, &amp; textus, &amp; ratio Ari&longs;totelis &longs;atis clara redduntur.</s>
        </p>
        <p type="head">
          <s id="s.002951"><emph type="italics"/>QV&AElig;STIO VNDECIMA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002952"><emph type="italics"/>De Scytala, &amp; Curru.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002953"><arrow.to.target n="marg242"/></s>
        </p>
        <p type="margin">
          <s id="s.002954"><margin.target id="marg242"/>252</s>
        </p>
        <p type="main">
          <s id="s.002955">Cvr &longs;uper &longs;cytalas facilius portantur onera qu&agrave;m &longs;uper currus, cum <lb/>
tamen currus magnas habeant rotas, &longs;cytal&aelig; ver&ograve; pu&longs;illas?</s>
        </p>
        <p type="main">
          <s id="s.002956">Quidnam &longs;cytala e&longs;&longs;et explicatum e&longs;t in 9. qu&aelig;&longs;t. </s>
          <s id="s.002957">Quo autem <lb/>
modo per &longs;cytalas onera <expan abbr="port&etilde;tur">portentur</expan>, &longs;ic, accipe: exi&longs;timo binas &longs;cy&shy;<lb/>
talas inuicem &aelig;quidi&longs;tantes, &amp; aliquantulum &longs;emotas inuicem &longs;ic di&longs;poni, <lb/>
vt efficiant in&longs;trumentum vectorium currus in&longs;tar, &amp; fort&egrave; veteres vteban&shy;<lb/>
tur his &longs;cytalis eo modo, quo nunc architectores vtuntur duobus illis lignis <lb/>
longis, ac rotundis, qu&aelig; vulg&ograve; dicuntur Ruccioli.</s>
        </p>
        <p type="main">
          <s id="s.002958">Re&longs;pondet igitur id accidere, quia rot&aelig; &longs;cytalarum &longs;imul &longs;unt cum &longs;uo <lb/>axe compact&aelig;, ita vt &longs;imul cum ip&longs;o rotentur: rot&aelig; autem curruum, quia <lb/>
&longs;eiunct&aelig; &longs;unt ab earum axe, ita vt &longs;ine illius rotatione ip&longs;&aelig; voluantur, fit vt <lb/>ill&aelig; firmius incedant, nec huc, <expan abbr="illuc&qacute;">illucque</expan>; nutent, veluti rot&aelig; plau&longs;tri: <expan abbr="neq;">neque</expan> ill&aelig; <lb/>
ad ip&longs;um axem offen&longs;ent, quemadmodum i&longs;t&aelig;. </s>
          <s id="s.002959">addit aliam rationem, quia <lb/>
currus nimia oneris grauitate premens rotas ip&longs;as fer&egrave; &longs;i&longs;tit, quod &longs;cytalis <lb/>
non accidit, cum rot&aelig; ip&longs;arum vnum, &amp; idem cum &longs;uo &longs;int axe. </s>
          <s id="s.002960">qu&aelig; ratio <lb/>
quantum valeat, ne&longs;cio, nam quamuis rot&aelig; &longs;cytalarum non premantur ab <lb/>
axe, premitur tamen axis ip&longs;arum ab onere, &agrave; quo &longs;imiliter &longs;i&longs;ti debe&shy;<lb/>
rent &longs;cytal&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.002961">Crediderim ego facilius portari magna onera per &longs;cytalas, propter ip&longs;a&shy;<lb/>
rum firmitatem, currus enim <expan abbr="ip&longs;orumq;">ip&longs;orumque</expan> rot&aelig; &longs;unt mult&ograve; debiliores, neque <lb/>
maioribus oneribus &longs;ufficiunt. </s>
          <s id="s.002962">Concludit po&longs;tea qu&aelig;&longs;tionem dicens, quia <pb pagenum="175" xlink:href="009/01/175.jpg"/>igitur &longs;cytal&aelig; ab ip&longs;o onere non ita premuntur quin moueri melius po&longs;&longs;int <lb/>
qu&agrave;m currus, im&ograve; ab ip&longs;o onere iam commoto, ip&longs;&aelig; quoque incitentur, &amp; <lb/>
pr&aelig;terea &agrave; potentia per planum infern&egrave;, ben&egrave; &longs;ub&longs;tratum, &amp; complanatum <lb/>
trahantur, fit, vt qua&longs;i in duobus locis ip&longs;arum rot&aelig; impellantur ab onere <lb/>
&longs;upra, &amp; &agrave; potentia infra; &longs;icque facilius quam currus ingentia pr&aelig;&longs;ertim <lb/>
onera vehunt.</s>
        </p>
        <p type="head">
          <s id="s.002963"><emph type="italics"/>De Funda.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002964"><emph type="italics"/>QV&AElig;STIO DVODECIMA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002965">Non videtur declaratione indigere.</s>
        </p>
        <p type="head">
          <s id="s.002966"><emph type="italics"/>QV&AElig;STIO DECIMATERTIA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002967"><emph type="italics"/>De Iugo, &amp; Succula.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002968"><arrow.to.target n="marg243"/></s>
        </p>
        <p type="margin">
          <s id="s.002969"><margin.target id="marg243"/>253</s>
        </p>
        <p type="main">
          <s id="s.002970">Declarandum prius quid &longs;it hoc loco iugum: e&longs;t igitur iugum li&shy;<lb/>
gnum illud cylindricum, quod vulg&ograve; dicitur Subbio. </s>
          <s id="s.002971">quorum bi&shy;<lb/>
na ponuntur in ea machina textoria, quam vulg&ograve; dicunt Telaio, <lb/>
qua&longs;i telarium, eo quod in ip&longs;a tel&aelig; texantur. </s>
          <s id="s.002972">alteri autem iugo <lb/>
conuoluitur &longs;tamen: alteri ver&ograve; contexta iam tela &longs;ubinde cum opus e&longs;t cir&shy;<lb/>
cumponitur: qu&aelig; duo textores faciunt ip&longs;a iuga conuertendo. </s>
          <s id="s.002973">qu&aelig; vt faci&shy;<lb/>
lius conuertant, iugis vtrinque in&longs;erunt per bina foramina binos collopes. <lb/>
</s>
          <s id="s.002974">qui collopes &longs;unt duo ligna oblonga &longs;atis gracilia vnius vln&aelig; fer&egrave; in longi&shy;<lb/>
tudinem; quibus <expan abbr="appr&aelig;h&etilde;&longs;is">appr&aelig;hen&longs;is</expan>, <expan abbr="motis&qacute;">motisque</expan>; iugum facil&egrave; ver&longs;atur. </s>
          <s id="s.002975">quanto autem <lb/>
collopes &longs;unt longiores, facilius iugum circumagitur. </s>
          <s id="s.002976">cuius cau&longs;a e&longs;t, quia <lb/>
collops ad vectem reducitur, cuius fultura e&longs;t circa medium iugi, pondus <lb/>
ver&ograve; e&longs;t extima iugi &longs;uperficies &egrave; qua tel&aelig;, aut &longs;taminis pondus pendet: in <lb/>
altera ver&ograve; extremitate collopis, qu&aelig; extra iugum multum prominet, e&longs;t <lb/>
potentia: ibi enim textoris manus premit, vel trahit. </s>
          <s id="s.002977">quando erg&ograve; longior <lb/>
e&longs;t collops, ea pars, qu&aelig; e&longs;t inter fulturam, &amp; vim, augetur; altera non mu&shy;<lb/>
tata; quia &longs;emper inter fulturam, &longs;eu centrum iugi, &amp; vltimam iugi &longs;uper&shy;<lb/>ficiem continetur; quanto autem illa hanc &longs;uperat, tantum virium po&shy;<lb/>
tenti&aelig; addi.</s>
        </p>
        <p type="main">
          <s id="s.002978">Secund&ograve;, videndum quid &longs;it &longs;uccula: hanc vulg&ograve; Na&longs;pa appellant, ni fal&shy;<lb/>
lor &agrave; verbo gr&aelig;co <foreign lang="greek">a&rpar;gaspa/w,</foreign> oriunda, quod &longs;ur&longs;um extrahere &longs;ignificat. </s>
          <s id="s.002979">cum <lb/>
quo, &amp; voce, &amp; &longs;ignificatione conuenit; e&longs;t enim in&longs;trumentum, quo &longs;&aelig;pius <lb/>
architectores in extrahendis &longs;ur&longs;um ruderibus effo&longs;&longs;is vtuntur. </s>
          <s id="s.002980">e&longs;t autem <lb/>compago qu&aelig;dam cylindrica non admodum longa, cui ex vna parte poti&longs;&shy;<lb/>
&longs;imum prominent plures collopes non mobiles, vt in iugo, verum &longs;tabiles, <lb/>
ac cum ip&longs;a &longs;uccula compacti, quibus manu appr&aelig;hen&longs;is &longs;uccula &longs;upra bi&shy;<lb/>
nos polos ver&longs;atur, <expan abbr="ei&qacute;">eique</expan>; interim ductarius funis circumuoluitur, &longs;ecumque <lb/>
&longs;ur&longs;um pondus educit. </s>
          <s id="s.002981">cuius imaginem <expan abbr="qualcmcunq;">qualemcunque</expan> in&longs;pice. </s>
          <s id="s.002982">qu&aelig;rit igitur, <lb/>cur quanto gracilius fuerit corpus &longs;uccul&aelig; A B, tanto facilius vertitur. <lb/>
</s>
          <s id="s.002983">Ratio e&longs;t, quia collops, quemadmodum etiam iugum, reducitur ad vectem,


<pb pagenum="176" xlink:href="009/01/176.jpg"/><figure id="id.009.01.176.1.jpg" place="text" xlink:href="009/01/176/1.jpg"/><lb/>
cuius hypomoclion e&longs;t in medio <lb/>
&longs;uccul&aelig;, &longs;iue in axe ip&longs;ius &longs;uccul&aelig;; <lb/>
potentia ver&ograve; e&longs;t in &longs;ummitatibus <lb/>
collopum, vt in C, E, F, D, pon&shy;<lb/>
dus ver&ograve; e&longs;t vbi funis ductarius <lb/>
cum onere pendet &egrave; &longs;uccula in &longs;u&shy;<lb/>
perficie nimirum, vt vbi L, quare <lb/>
pars vectis inter axim, &amp; &longs;uperfi&shy;<lb/>
ciem &longs;uccul&aelig; eadem e&longs;t, qu&aelig; inter <lb/>
hypomoclium, &amp; pondus. </s>
          <s id="s.002984">quanto <lb/>
igitur &longs;uccul&aelig; corpus gracilius fuerit, tanto h&aelig;c pars minuetur; &amp; con&longs;e&shy;<lb/>
quenter altera inter hypomoclium, &amp; potentiam productior euadet: eaque <lb/>
propter facilius &agrave; motore ver&longs;abitur.</s>
        </p>
        <p type="head">
          <s id="s.002985"><emph type="italics"/>De ligno ad genu fracto.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002986"><emph type="italics"/>QV&AElig;STIO DECIMAQVARTA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002987">Satis per&longs;e clara videtur.</s>
        </p>
        <p type="head">
          <s id="s.002988"><emph type="italics"/>QV&AElig;STIO DECIMAQVINTA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002989"><emph type="italics"/>De Vmbilicis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002990"><arrow.to.target n="marg244"/></s>
        </p>
        <p type="margin">
          <s id="s.002991"><margin.target id="marg244"/>254</s>
        </p>
        <p type="main">
          <s id="s.002992">Notandum prim&ograve;, qu&aelig; Gr&aelig;cis <foreign lang="greek">*krokai,</foreign> ide&longs;t Croc&aelig; dicuntur, Latinis <lb/>
Vmbilicos appellari; de his enim loquitur Cic. <!-- REMOVE S-->2. de Oratore, vbi <lb/>
&longs;ic, non audeo dicere de talibus viris, &longs;ed tamen ita narrare &longs;ole&shy;<lb/>
bat Sceuola, conchas, eos, &amp; vmbilicos ad Caietam, &amp; ad Lucri&shy;<lb/>
num legere con&longs;ueui&longs;&longs;e. </s>
          <s id="s.002993">hos autem vmbilicos exponunt Grammatici e&longs;&longs;e <lb/>
lapillos paruos, acrotundos, polito&longs;que, de quibus etiam Ari&longs;t. loquitur. <lb/>
</s>
          <s id="s.002994">Quare decipitur Piccolomineus dum negat, nos harum crocarum latinum <lb/>
nomen habere. </s>
          <s id="s.002995">C&aelig;ter&ugrave;m, &amp; qu&aelig;&longs;tio, &amp; re&longs;pon&longs;io, ex &longs;uperioribus &longs;atis <lb/>
per&longs;picua e&longs;&longs;e videntur.</s>
        </p>
        <p type="head">
          <s id="s.002996"><emph type="italics"/>QV&AElig;STIO DECIMASEXTA<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.002997"><emph type="italics"/>De ligno oblongo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002998"><arrow.to.target n="marg245"/></s>
        </p>
        <p type="margin">
          <s id="s.002999"><margin.target id="marg245"/>255</s>
        </p>
        <p type="main">
          <s id="s.003000">Ex appo&longs;ita figura totus huius problematis textus, alioquin &longs;atis cla&shy;<lb/>
rus patebit. </s>
          <s id="s.003001">&longs;int duo ligna oblonga, vnum altero longius, &amp; cra&longs;&longs;ius. <lb/>
</s>
          <s id="s.003002">in eleuatione maioris, fulcimentum e&longs;t in B, vbi manus altera fer&egrave; <lb/>
manens appr&aelig;hendit; in C, ver&ograve;, vbi altera manus mouens premit <lb/>
e&longs;t potentia, &longs;iue maius onus. </s>
          <s id="s.003003">in A, ver&ograve; onus ip&longs;ius ligni, deor&longs;um tendens <lb/>
premit, quod nunc e&longs;t in&longs;tar potenti&aelig; motricis, quare A, &amp; C, &longs;unt &longs;ibi in&shy;<lb/>
uicem, &amp; potenti&aelig;, &amp; pondera. </s>
          <s id="s.003004">In minori autem ligno, onus ligni in D,


<pb pagenum="177" xlink:href="009/01/177.jpg"/><figure id="id.009.01.177.1.jpg" place="text" xlink:href="009/01/177/1.jpg"/><lb/>
fultura manus in E, potentia alterius ma&shy;<lb/>nus in F. iam inquit Ari&longs;t. maius lignum <lb/>
A B C, magis flectitur, quamuis cra&longs;&longs;ius <lb/>&longs;it, qu&agrave;m lignum D E F, quod e&longs;t tenuius, <lb/>
&longs;ed mult&ograve; breuius; quia in maiori onus <lb/>
ip&longs;ius ligni, quod circa A, deor&longs;um pre&shy;<lb/>
mit <expan abbr="l&otilde;gius">longius</expan> di&longs;tat ab hypomoclio B, qu&agrave;m <lb/>
in minori ligno. </s>
          <s id="s.003005">Ex quo &longs;equitur iuxta <lb/>
ip&longs;ius principia, vt onus A, facilius lignum mouere, aut inflectere <lb/>
po&longs;&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.003006">C&aelig;ter&ugrave;m exi&longs;timo, quod &longs;i maioris ligni longitudo ad eiu&longs;dem <lb/>
cra&longs;&longs;itiem haberet <expan abbr="e&atilde;dem">eandem</expan> proportionem, qu&agrave;m minoris longitudo ad eiu&longs;&shy;<lb/>
dem cra&longs;&longs;itiem, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <expan abbr="vtrumq;">vtrumque</expan> e&longs;&longs;et ab hypomoclio in eadem ratione diui&shy;<lb/>
&longs;um, fore, vt <expan abbr="vtrunq;">vtrunque</expan> eodem modo inflecteretur, quia haberent pondera <lb/>
eandem rationem ad di&longs;tantias ab hypomoclio, oportet igitur vt &longs;int non <lb/>
analoga, &longs;ed aloga, vt eis pr&aelig;&longs;ens problema Ari&longs;totelis vn&agrave; cum eiu&longs;dem <lb/>
&longs;olutione competat.</s>
        </p>
        <p type="head">
          <s id="s.003007"><emph type="italics"/>QV&AElig;STIO XVII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003008"><emph type="italics"/>De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003009"><arrow.to.target n="marg246"/></s>
        </p>
        <p type="margin">
          <s id="s.003010"><margin.target id="marg246"/>256</s>
        </p>
        <p type="main">
          <s id="s.003011">Cvr paruo cuneo magna finduntur onera, &amp; corporum moles, <expan abbr="adeoq;">adeoque</expan> <lb/>
valida fit impre&longs;&longs;io? </s>
          <s id="s.003012">fort&egrave;, quia cuneus duobus vectibus &longs;ibi inui&shy;<lb/>
cem oppo&longs;itis con&longs;tat; quorum vterque, &amp; potentiam mouentem, <lb/>
&amp; hypomoclion, &amp; <expan abbr="p&otilde;dus">pondus</expan> habet. </s>
          <s id="s.003013">hypomoclion autem illud ip&longs;um <lb/>
e&longs;&longs;e ait, quod cuneo diuellitur; hoc autem dicit Ari&longs;tot. quia non agnouit <lb/>
alium, pr&aelig;ter primi generis vectem, vt &longs;upra etiam dixi.</s>
        </p>
        <p type="main">
          <s id="s.003014">Verum &longs;atius e&longs;t cum Guido Vbaldo reducere cuneum ad duos &longs;ecundi <lb/>
generis vectes, quorum fultura &longs;it in cunei apice extremo, pondus ver&ograve; in&shy;<lb/>
tra vectem, ea nimirum pars ligni, que &agrave; cuneo vrgetur, ac diuellitur. </s>
          <s id="s.003015">cuneo <lb/>
pr&aelig;terea vires adduntur ex valida mallei percu&longs;&longs;ione; malleus autem ip&longs;e <lb/>
magna vi percutit, quia motus mouet, &longs;eu quia mouens malleum, mouet <lb/>
ip&longs;um etiam dum e&longs;t in ip&longs;a latione, vnde ip&longs;a lationis celeritate malleus <lb/>
fit valentior: <expan abbr="hoc&qacute;">hocque</expan>; modo paruos cunei vectes maiores con&longs;equuntur vires, <lb/>
<figure id="id.009.01.177.2.jpg" place="text" xlink:href="009/01/177/2.jpg"/><lb/>
qu&agrave;m ip&longs;a vectium magnitudo po&longs;tulet. <lb/>
</s>
          <s id="s.003016">&longs;it cuneus A B C. lignum autem &longs;cinden&shy;<lb/>
dum D E F G, <expan abbr="vectes&qacute;">vectesque</expan> duo &longs;int A C, &amp; <lb/>
B C, quorum commune hypomoclion e&longs;t <lb/>
in C, onus autem vectis B C, e&longs;t pars li&shy;<lb/>
gni G, h&aelig;c enim ip&longs;i contranititur, <expan abbr="atq;">atque</expan> <lb/>
ab eo expellitur. </s>
          <s id="s.003017">potentia ver&ograve; mouens <lb/>
vectem e&longs;t in malleo, dum &longs;uperius latus <lb/>
cunei A B, percutit. </s>
          <s id="s.003018">alter huic auer&longs;us <lb/>
vectis e&longs;t latus A C, cuius fultura e&longs;t C, <lb/>eadem cum priori, onus propul&longs;atum D,<pb pagenum="178" xlink:href="009/01/178.jpg"/>potentia cum altero communis e&longs;t in latere A B, &agrave; malleo valid&egrave; percu&longs;&longs;o. <lb/>
</s>
          <s id="s.003019">cunei igitur virtus partim ex vectibus, partim ex percu&longs;&longs;ione con&longs;tat.</s>
        </p>
        <p type="head">
          <s id="s.003020"><emph type="italics"/>QV&AElig;STIO XVIII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003021"><emph type="italics"/>De Trochlea.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003022"><arrow.to.target n="marg247"/></s>
        </p>
        <p type="margin">
          <s id="s.003023"><margin.target id="marg247"/>257</s>
        </p>
        <p type="main">
          <s id="s.003024">Hvius qu&aelig;&longs;tionis &longs;en&longs;us, ac verba optim&egrave; intelligentur ex &longs;equen&shy;<lb/>
tibus. </s>
          <s id="s.003025">Trochlea, vt patet ex &longs;uperioribus Ari&longs;t. e&longs;t orbiculus in <lb/>
periph&aelig;ria &longs;triatus, vna cum toto loculumento, cui in&longs;eritur: <lb/>
cuius imaginem ad 8. qu&aelig;&longs;t. </s>
          <s id="s.003026">exhibui. </s>
          <s id="s.003027">Apud Architectores ver&ograve; <lb/>
trochlea con&longs;tat &longs;altem ex duobus pr&aelig;dictis loculamentis, in quibus &longs;unt <lb/>
orbiculi; &amp; vnus orbiculus e&longs;t &longs;upern&egrave; collocatus, alter ver&ograve; infern&egrave;, vt pa&shy;<lb/>
tebit in &longs;equenti figuratione: quod <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> nunc vulg&ograve; dicitur Taglia, <lb/>
&agrave; nonnullis dicitur etiam Rechamo. </s>
          <s id="s.003028">Auxilio huius in&longs;trumenti machinato&shy;<lb/>
res parua vi attollunt ingentia pondera. </s>
          <s id="s.003029">communiter autem con&longs;tat ex plu&shy;<lb/>
<figure id="id.009.01.178.1.jpg" place="text" xlink:href="009/01/178/1.jpg"/><lb/>
ribus orbiculis, qui partim &longs;uperiori loculamento, <lb/>partim inferiori inditi &longs;unt, per quos orbiculos cer&shy;<lb/>
ta lege circumductus e&longs;t ductarius funis, qui deinde <lb/>
in &longs;ui po&longs;trema parte &agrave; potentia tractus omnes illos <lb/>
orbiculos, per quos tran&longs;it circumuoluens inferius <lb/>
loculamentum, cui appen&longs;um e&longs;t pondus, vn&agrave; cum <lb/>pondere attollit. </s>
          <s id="s.003030">figuram &longs;implicis trochle&aelig;, con&shy;<lb/>
&longs;tantis &longs;cilicet ex duobus tantum orbiculis, facilita&shy;<lb/>
tis cau&longs;a exhibebo, in hac enim melius apparebit, <lb/>
qua ratione trochlea ad vectem reducatur. </s>
          <s id="s.003031">vnde, &amp; <lb/>
Ari&longs;t. &longs;en&longs;um, quamuis ob&longs;curi&longs;&longs;imum, ac proinde <lb/>
problematis &longs;olutionem optim&egrave; percipere licebit. <lb/>
</s>
          <s id="s.003032">Sit igitur orbiculus &longs;uperior A, qui in pegmate I K&shy;<lb/>
L D, voluatur circa axem G, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; pegma i&longs;tud &longs;upe&shy;<lb/>
rius fixum, &amp; immobile &agrave; clauo H, pendens. </s>
          <s id="s.003033">Infe&shy;<lb/>
rior orbiculus B, in loculamento O P Q R, circa <lb/>
axem B, conuoluatur: &longs;itque funis ductarius circa <lb/>
hos orbiculos hoc modo circumductus. </s>
          <s id="s.003034">primo ca&shy;<lb/>
put funis religetur clauo D, in &longs;uperiori pegmate <lb/>
infixo, hinc demi&longs;&longs;us &longs;ubtus inferiorem rotulam per <lb/>
ip&longs;ius &longs;triam de&longs;cendat per puncta L S, a&longs;cendatque <lb/>
po&longs;tea per M E N, ad &longs;uperiorem rotulam, &longs;upra <lb/>
quam a&longs;cendat per punctum T, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; ad V, &amp; <lb/>
inde demittatur ad <expan abbr="pot&etilde;tiam">potentiam</expan> F. Iam &longs;i quepiam po&shy;<lb/>
tentia in F, traxerit funem F V, deor&longs;um, interim <lb/>
partes T, N, E, M, &longs;ur&longs;um attrahentur, &amp; locula&shy;<lb/>
mentum inferius &longs;imul cum appen&longs;o pondere eleua&shy;<lb/>
bitur, manente tamen interim fune prope D, vbi <lb/>
clauo D, e&longs;t religatus, &amp; immobilis. </s>
          <s id="s.003035">&longs;ed vbinam hic <lb/>
vectis? </s>
          <s id="s.003036">con&longs;idera diametrum M L, inferioris orbiculi, h&aelig;c enim ea e&longs;t, qu&aelig; <pb pagenum="179" xlink:href="009/01/179.jpg"/>vectem gerit. </s>
          <s id="s.003037">huius enim extrema L M, &agrave; fune tanguntur, &amp; ab eius medio <lb/>B, onus pendet, &amp; grauitat; &amp; quia funis in M, &longs;ur&longs;um trahitur, <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; ex <lb/>parte illa &longs;ur&longs;um elenat diametrum L M, erit potentia mouens, &amp; eleuans <lb/>
in M. pondus ver&ograve; intra vectem ad B, medium vectis; quare fulcimentum <lb/>
erit in reliquo extremo L, vbi funis &longs;u&longs;tinet loculamentum, &amp; vbi diameter, <lb/>
&longs;eu vectis innititur. </s>
          <s id="s.003038">quare diameter h&aelig;c e&longs;t vectis &longs;ecundi generis expo&longs;iti. <lb/>
</s>
          <s id="s.003039">aduerte pr&aelig;terea vectem hunc e&longs;&longs;e mobilem, &longs;imul cum <expan abbr="fulcim&etilde;to">fulcimento</expan>, quia dum <lb/>
ex parte M, &longs;ur&longs;um tollitur &longs;imul cum toto orbiculo, ac loculamento, &longs;ub&shy;<lb/>
&longs;equitur etiam alterum extremum L, quod fune fulcitur, &amp; in ip&longs;o fune &longs;ur&shy;<lb/>&longs;um ver&longs;us D, a&longs;cendit; &amp; hoc modo inferius tignum cum onere tandem ad <lb/>
&longs;uperius tignum &longs;ublatum erit. </s>
          <s id="s.003040">hinc verum dixi&longs;&longs;e Ari&longs;t. con&longs;tat, trochleam <lb/>
&longs;cilicet idem e&longs;&longs;e, ac vectem. </s>
          <s id="s.003041">quod tamen de &longs;olo inferiori orbiculo intelli&shy;<lb/>
gi debet, &longs;uperior enim rotula quamuis vectis fiat, non tamen vires vllas <lb/>
potenti&aelig; tribuit, cum eius hypomoclion &longs;it in medio, quemadmodum &longs;upra <lb/>
ad 8. qu&aelig;&longs;t. </s>
          <s id="s.003042">expo&longs;ui. </s>
          <s id="s.003043">Inferior igitur ille e&longs;t, qui mouenti maximo e&longs;t adiu&shy;<lb/>
mento. </s>
          <s id="s.003044">quod &longs;i &longs;cire aueas quantum iuuet, re&longs;pondeo ip&longs;um vires potenti&aelig; <lb/>
duplicare; adeo vt &longs;i quatuor. </s>
          <s id="s.003045">v. <!-- REMOVE S-->g. <!-- REMOVE S-->homines erant nece&longs;&longs;arij ad pondus tol&shy;<lb/>
lendum, auxilio huius &longs;implicis trochle&aelig; duo tantum &longs;ufficiant. </s>
          <s id="s.003046">quod &longs;i ad&shy;<lb/>
dantur duo alij orbiculi, vnus &longs;uperior, alter inferior, rur&longs;us vires duplica&shy;<lb/>
buntur, <expan abbr="erit&qacute;">eritque</expan>; vnus <expan abbr="t&atilde;tum">tantum</expan> homo nece&longs;&longs;arius. </s>
          <s id="s.003047">quod &longs;i plures ali&aelig; rotul&aelig; tam <lb/>&longs;upern&egrave;, qu&agrave;m infern&egrave; addantur, vt &longs;olet in maioribus trochleis, quas ve&shy;<lb/>
teres Poly&longs;pa&longs;tos, ide&longs;t multum trahentes dixerunt, augebuntur vires in in&shy;<lb/>
finitum. </s>
          <s id="s.003048">quod dixi de virium duplicatione con&longs;tat ex 6. &amp; 7. propo&longs;itione <lb/>
Archimedis de Aequip. <!-- KEEP S--></s>
          <s id="s.003049">quia enim in vecte no&longs;tro L M, dupla e&longs;t proportio <lb/>
inter L M, &amp; L B, eadem etiam proportio erit inter pondus, &amp; potentiam, <lb/>
quare pondus C, duplum erit potenti&aelig; in M, hoc e&longs;t &agrave; minore potentia &longs;ibi <lb/>
&longs;ubdupla &longs;u&longs;tinebitur: &amp; &agrave; quauis adhuc <expan abbr="quantumcunq;">quantumcunque</expan> maiore eleuabitur.</s>
        </p>
        <p type="main">
          <s id="s.003050">Qui plura de trochlea de&longs;iderat, adeat Guidi Vbaldi, Mechanica, cuius <lb/>
auxilio fateor me verum &longs;en&longs;um harum Mechanicarum Ari&longs;t. &amp; pr&aelig;&longs;ertim <lb/>
huius loci enuclea&longs;&longs;e. </s>
          <s id="s.003051">qu&aelig; &longs;i cum Piccolominei expo&longs;itione contuleris, vide&shy;<lb/>
bis eum nequaquam cognoui&longs;&longs;e, vbi nam vectis in trochlea lateret, eumque <lb/>
tam &longs;uperiorem, qu&agrave;m inferiorem <expan abbr="rotul&atilde;">rotulam</expan> &aelig;qu&egrave; vectem facere; in quo etiam <lb/>
Io. <!-- REMOVE S-->Bapti&longs;ta Benedictus pariter erra&longs;&longs;e videtur in &longs;uis &longs;peculationibus, cum <lb/>
inferiores tantummodo vice vectium fungantur, vt probatum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.003052"><expan abbr="Atq;">Atque</expan> ex his &longs;atis mihi videtur textus, ac &longs;en&longs;us Ari&longs;t. illu&longs;trari.</s>
        </p>
        <p type="head">
          <s id="s.003053"><emph type="italics"/>QV&AElig;STIO XVIIII.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.003054"><emph type="italics"/>De Securi.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003055"><arrow.to.target n="marg248"/></s>
        </p>
        <p type="margin">
          <s id="s.003056"><margin.target id="marg248"/>258</s>
        </p>
        <p type="main">
          <s id="s.003057">Partim ex &longs;e, partim ex dictis in 17. qu&aelig;&longs;t. </s>
          <s id="s.003058">&longs;atis clara e&longs;t. </s>
          <s id="s.003059">placet au&shy;<lb/>
tem his, qu&aelig; de cuneo, &amp; &longs;ecuri dicta &longs;unt, nonnulla ex Guido Vbal&shy;<lb/>
do loco corollarij adijcere, videlicet. </s>
          <s id="s.003060">Ad huiu&longs;modi facultatis in&shy;<lb/>&longs;trumentum ea <expan abbr="quoq;">quoque</expan> omnia commod&egrave; referri po&longs;&longs;unt, qu&aelig; percu&longs;&shy;<lb/>
&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, perforant, <expan abbr="huiu&longs;modi&qacute;">huiu&longs;modique</expan>; alia obeunt <lb/>
munera; vt en&longs;es, gladij, mucrones, &longs;ecures, terebr&aelig;, &amp; &longs;imilia: &longs;erra <expan abbr="quoq;">quoque</expan> <lb/>
ad hoc reducitur, dentes enim percutiunt, <expan abbr="cunei&qacute;">cuneique</expan>; in&longs;tar exi&longs;tunt.</s>
        </p>
        <pb pagenum="180" xlink:href="009/01/180.jpg"/>
        <p type="head">
          <s id="s.003061"><emph type="italics"/>Additio de veteri Securi, &amp; Bipenne.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003062">Libet etiam huic tractationi de &longs;ecuri nonnulla addere, qu&aelig; olim oc&shy;<lb/>
ca&longs;ione ex Proclo accepta in tenebris diu delite&longs;centia in lucem re&shy;<lb/>
&longs;tituimus, &longs;unt autem h&aelig;c. </s>
          <s id="s.003063">Prim&ograve;, antiqu&aelig; &longs;ecuris, necnon bipen&shy;<lb/>
nis figuram re&longs;tituam. </s>
          <s id="s.003064">Secund&ograve;, o&longs;tendam angulum &longs;ecuris, qui <lb/>
curuilineus e&longs;t, &aelig;qualem e&longs;&longs;e angulo trianguli &aelig;quilateri, qui rectilineus e&longs;t. <lb/>
</s>
          <s id="s.003065">Proclus igitur in comm. <!-- REMOVE S-->23. primi Euclidis, &longs;ic ait: o&longs;ten&longs;um fuit ab anti&shy;<lb/>
quis, &longs;cilicet Geometris, quod angulus figur&aelig; illius, qu&aelig; &longs;ecuri &longs;imilis e&longs;t, <lb/>
&aelig;qualis e&longs;t angulo rectilineo, quippe qui duabus tertijs anguli recti &aelig;qualis <lb/>
e&longs;t. </s>
          <s id="s.003066">hanc anguli &longs;ecuris affectionem, cum nec ille, nec alij, quod &longs;ciam de&shy;<lb/>
mon&longs;trent, ego paul&ograve; po&longs;t demon&longs;trabo. </s>
          <s id="s.003067">deinde &longs;ubdit; fit autem huiu&longs;mo&shy;<lb/>
di &longs;ecuralis figura, qu&aelig; pelecoides vocatur duobus circulis per centra &longs;e <lb/>
mutu&ograve; &longs;ecantibus. </s>
          <s id="s.003068">h&aelig;c Proclus. <!-- KEEP S--></s>
          <s id="s.003069">Ex his autem po&longs;tremis verbis de&longs;criptio&shy;<lb/>
nem antiqu&aelig; &longs;ecuris, &longs;ic puto eruendam. </s>
          <s id="s.003070">Ducatur primo recta A C, qu&aelig; <lb/>
<figure id="id.009.01.180.1.jpg" place="text" xlink:href="009/01/180/1.jpg"/><lb/>
erit in&longs;tar manubrij &longs;ecuris. </s>
          <s id="s.003071">de&shy;<lb/>
inde ex centro C, interuallo. </s>
          <s id="s.003072">v. <!-- REMOVE S-->g. <lb/>
C B, de&longs;cribatur circulus B F; &longs;i&shy;<lb/>
militer eodem interuallo B D, ex <lb/>
centro D, de&longs;cribatur circulus <lb/>
B E; tandem ex B, centro, atque <lb/>
eodem interuallo ducatur alius <lb/>
circulus D E F C, qui priores duos &longs;ecabit in punctis E F. <expan abbr="c&otilde;&longs;ideremus">con&longs;ideremus</expan> iam, <lb/>
reliquis circulorum partibus ommi&longs;&longs;is, curuilineam figuram B E F, quam <lb/>
e&longs;&longs;e veteris &longs;ecuris formam ex <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan> Proclinon e&longs;t dubitandum, cum cir&shy;<lb/>
culis &longs;e mutu&ograve; per centra &longs;ecantibus con&longs;tituatur, vt vult ip&longs;e, &amp; pr&aelig;terea <lb/>
habeat angulos E F, tantos, quantos ip&longs;e tradit, vt mox patebit; linea au&shy;<lb/>
tem A B C, &longs;ecuris manubrium refert.</s>
        </p>
        <p type="main">
          <s id="s.003073">Quod autem tam angulus E, qu&agrave;m angulus F, &longs;int &aelig;quales duabus tertijs <lb/>vnius anguli recti, &longs;iue quod idem e&longs;t angulo trianguli &aelig;quilateri, manife&shy;<lb/>&longs;tum erit hoc modo. </s>
          <s id="s.003074">De&longs;cribatur iterum &longs;ecuralis figura pr&aelig;dicto modo, <lb/>
&longs;<expan abbr="itq;">itque</expan> ea A B C. ducantur pr&aelig;terea ad &longs;ingulos angulos tres rect&aelig; A B, B C, <lb/>C A, qu&aelig; con&longs;tituunt triangulum &aelig;quilaterum A B C, tria enim ip&longs;ius late&shy;<lb/>
<figure id="id.009.01.180.2.jpg" place="text" xlink:href="009/01/180/2.jpg"/><lb/>
ra &longs;ubtendunt tres arcus &aelig;quales A B, B C, C A, <lb/>
&longs;unt enim tres &longs;extantes &aelig;qualium circulorum, <lb/>
ut facil&egrave; colligi pote&longs;t ex 15. 4. ex quo etiam &longs;e&shy;<lb/>quitur tres illas circulorum portiones, quas re&shy;<lb/>
ct&egrave; cum &longs;uis arcubus con&longs;tituunt e&longs;&longs;e inuicem <lb/>&aelig;quales, &amp; &longs;imiles portiones nimirum A B E, <lb/>
B C D, C A F. hinc pr&etail;terea &longs;equitur angulos ip&shy;<lb/>
&longs;arum e&longs;&longs;e inuicem &aelig;quales, angulos, v.g. <!-- REMOVE S-->A B E, <lb/>C B D, mixtos e&longs;&longs;e &aelig;quales, quod facil&egrave; e&longs;t per imaginariam &longs;uperpo&longs;itio&shy;<lb/>
nem demon&longs;trare. </s>
          <s id="s.003075">cum igitur pr&aelig;dicti duo anguli &longs;int &aelig;quales, &longs;itque inter <lb/>eos medius alius angulus E B C, qui pariter mixtus e&longs;t, &longs;i ip&longs;e addatur tam <lb/>angulo C B D, qu&agrave;m angulo A B E, inuicem &aelig;qualibus, erunt duo anguli <pb pagenum="181" xlink:href="009/01/181.jpg"/>A B C, rectilineus, &amp; E B D, curuilineus &aelig;quales. </s>
          <s id="s.003076">ille autem e&longs;t angulus <lb/>
&aelig;quilateri, qui &aelig;qualis e&longs;t duabus tertijs vnius recti ex corollario 32. primi. <lb/>
</s>
          <s id="s.003077">hic ver&ograve; e&longs;t angulus &longs;ecuris. </s>
          <s id="s.003078">e&longs;t igitur angulus &longs;ecuris &aelig;qualis duabus ter&shy;<lb/>
tijs vnius recti, vt ait Proclus, quod demon&longs;trandum erat. </s>
          <s id="s.003079">quod etiam ma&shy;<lb/>nife&longs;tum &longs;ignum e&longs;t &longs;ecuris figuram a me re&longs;titutam e&longs;&longs;e illam veterem, de <lb/>
qua idem Proclus loquitur.</s>
        </p>
        <p type="main">
          <s id="s.003080">Re&longs;tat, vt de antiqu&aelig; bipennis etiam figura di&longs;&longs;eramus; qu&aelig; nihil aliud <lb/>
erat, qu&agrave;m duplex &longs;ecuris, &longs;iue &longs;ecuris anceps, qualis e&longs;t pr&aelig;&longs;ens figura, vt <lb/>
<figure id="id.009.01.181.1.jpg" place="text" xlink:href="009/01/181/1.jpg"/><lb/>
propterea etiam &longs;&aelig;pius <expan abbr="bip&etilde;nis">bipennis</expan> ip&shy;<lb/>
&longs;a &longs;ecuris appelletur. </s>
          <s id="s.003081">dicitur enim <lb/>
bipennis, qua&longs;i binis pinnis, qu&aelig; &longs;e&shy;<lb/>
cures erant, con&longs;tet, vt &amp; Gr&aelig;cis <lb/>
<foreign lang="greek">dipteros</foreign> dicebatur. </s>
          <s id="s.003082">te&longs;te etiam No&shy;<lb/>
nio, illud bipenne e&longs;t, quod <expan abbr="vtrinq;">vtrinque</expan> <lb/>
acutum e&longs;t. </s>
          <s id="s.003083">collegi autem <expan abbr="vtcunq;">vtcunque</expan> <lb/>
hanc bipennis figuram ex Simmi&aelig; <lb/>
peruetufti poet&aelig; gr&aelig;ci <expan abbr="epigr&atilde;mate">epigrammate</expan>, quod Simmi&aelig; &longs;ecuris appellatur. </s>
          <s id="s.003084">quod <lb/>
epigramma carminibus loco linearum con&longs;tat, qu&aelig; in &longs;ecuris formam con&shy;<lb/>
&longs;tituta &longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.003085">Sciendum namque e&longs;t Simmiam, poeticam hanc &longs;ecurim concinna&longs;&longs;e in <lb/>
gratiam Epei illius, qui equum Troianum ligneum fuerat architectatus, vt <lb/>
e&longs;t apud Virg. <!-- KEEP S--></s>
          <s id="s.003086">Et ip&longs;e doli fabricator Epeus. <!-- KEEP S--></s>
          <s id="s.003087">qui cum &longs;oluendi voti cau&longs;a <lb/>
vellet &longs;ecurim, &longs;iue bipennem, qua in equi Durij molitione v&longs;us fuerat, Mi&shy;<lb/>
neru&aelig; De&aelig;, quod &longs;ibi in eo opere faciendo auxilio fui&longs;&longs;et, dedicare, <expan abbr="eam&qacute;">eamque</expan>; <lb/>
vt Ari&longs;t. in libello de admirandis audit. </s>
          <s id="s.003088">num. </s>
          <s id="s.003089">104. narrat, in templo gr&aelig;&shy;<lb/>
c&aelig; Mineru&aelig;, quod erat in Gargaria Itali&aelig; Regione prop&egrave; Metapontum, <lb/>
&longs;u&longs;pendere, a pr&aelig;fato Simmia qu&aelig;&longs;iuit, vt epigrammate aliquo dedicatio&shy;<lb/>
nem hanc &longs;uam complecteretur. </s>
          <s id="s.003090">qui vt illi morem gereret ingenio&longs;&aelig; illius <lb/>
bipennis dedicationem, vt melius imitaretur, &longs;ecuri hac carminum com&shy;<lb/>
plexus e&longs;t. </s>
          <s id="s.003091">qu&aelig; dedicatio, &longs;iue epigramma, quod adhuc extat, deinceps &longs;e&shy;<lb/>
curis Simmi&aelig; vocitata e&longs;t; ex qua figura bipennis illius, equi Durij fabrica&shy;<lb/>
tricis nobis adhuc magna cum voluptate innotuit. </s>
          <s id="s.003092">Porr&ograve; gratum, <expan abbr="atq;">atque</expan> ad <lb/>
ea, qu&aelig; diximus intelligenda vtile Lectori fore arbitrati &longs;umus, ip&longs;am Sim&shy;<lb/>
mi&aelig; bipennem ex operibus Theocriti, quibus addi &longs;olet, huc referre; quam <lb/>
P. <!-- REMOVE S-->Ricardus E&longs;ius de no&longs;tra Societate lingu&aelig; gr&aelig;c&aelig; periti&longs;&longs;imus, in hunc <lb/>
modum tran&longs;tulit. </s>
          <s id="s.003093">hoc autem ordine legenda e&longs;t: lectio &agrave; manubrio <lb/>
incipiat, deinde legatur carmen; forti&longs;&longs;im&aelig; De&aelig;, quod &longs;ub&longs;e&shy;<lb/>
quatur; dedit Epeus, &amp; &longs;ic in orbem lectio, <expan abbr="v&longs;q;">v&longs;que</expan> ad me&shy;<lb/>
dium circumducatur. </s>
          <s id="s.003094">h&aelig;c &longs;unt, qu&aelig; pr&aelig;&longs;ertim <lb/>
in gratiam eorum, qui &longs;uaui&longs;&longs;imo an&shy;<lb/>
tiquitatis &longs;tudio tenentur, la&shy;<lb/>
tere nolui.</s>
        </p>
        <pb pagenum="182" xlink:href="009/01/182.jpg"/>
        <p type="head">
          <s id="s.003095"><emph type="italics"/>Simmi&aelig; Rhodij <lb/>
Bipennis.<emph.end type="italics"/></s>
        </p>
        <figure id="id.009.01.182.1.jpg" place="text" xlink:href="009/01/182/1.jpg"/>
        <pb pagenum="183" xlink:href="009/01/183.jpg"/>
        <p type="head">
          <s id="s.003096"><emph type="italics"/>QV&AElig;STIO XX.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003097"><emph type="italics"/>De Statera.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003098"><arrow.to.target n="marg249"/></s>
        </p>
        <p type="margin">
          <s id="s.003099"><margin.target id="marg249"/>259</s>
        </p>
        <p type="main">
          <s id="s.003100">Antequam ad textus explicationem accedamus, con&longs;ultius e&longs;&longs;e iu&shy;<lb/>
dico veteris &longs;tater&aelig; figuram, atque de&longs;criptionem pr&aelig;mittere, <lb/>
qu&agrave;m ex hoc Ari&longs;t. loco, magna mihi licuit cum delectatione col&shy;<lb/>
ligere: quod etiam antiquitatis &longs;tudio&longs;is pergratum fore non du&shy;<lb/>
bito: <expan abbr="atq;">atque</expan> hinc etiam ineptas, <expan abbr="atq;">atque</expan> ad &longs;cititias textus huius figuras tanquam <lb/>
adulterinas reijcere; <expan abbr="in&qacute;">inque</expan>; earum locum veras re&longs;tituere licebit. </s>
          <s id="s.003101">erat igitur <lb/>
<figure id="id.009.01.183.1.jpg" place="text" xlink:href="009/01/183/1.jpg"/><lb/>
&longs;tatera, quantum ex Ari&longs;t. conijcio <lb/>
primum ha&longs;ta oblonga, qualis e&longs;t in <lb/>
pr&aelig;&longs;enti figura A B, ex cuius altero <lb/>
extremo B, pendebat appendicu&shy;<lb/>
lum, quod propri&egrave; &aelig;quipondium <lb/>
dicitur: ex altera ver&ograve; extremitate <lb/>
A, lanx vna pendebat; in qua carnes, ali&aelig;u&egrave; merces ponderabantur: in me&shy;<lb/>
dia <expan abbr="deniq;">denique</expan> ha&longs;ta paribus interuallis plures trutin&aelig;, ex quibus &longs;ingulis modo <lb/>
hac, modo illa, prout pondus emptoris po&longs;tulabat &longs;u&longs;pendebatur, <expan abbr="atq;">atque</expan> in&shy;<lb/>
terim tantum mercis lanci imponebatur, donec &aelig;quipondio pr&aelig;pondera&shy;<lb/>
ret in &aelig;quilibrio. </s>
          <s id="s.003102">&longs;ingul&aelig; autem trutin&aelig; ad aliquod determinatum pondus <lb/>
trutinandum, erant con&longs;titut&aelig;, v. <!-- REMOVE S-->g. <!-- REMOVE S-->vna ad &longs;ex libras, altera ad octo, &amp;c. <lb/>
</s>
          <s id="s.003103">quam diui&longs;ionem, ac fabricam &longs;tater&aelig; non e&longs;t difficil&egrave; exhibere, cum ex Ar&shy;<lb/>
chimede propo&longs;. </s>
          <s id="s.003104">6. &amp; 7. de &aelig;quip. </s>
          <s id="s.003105">eadem &longs;it proportio inter pondus mer&shy;<lb/>
cis, &amp; pondus &aelig;quipondij, qu&aelig; e&longs;t permutatim inter di&longs;tantias vtrinque ab <lb/>
a&longs;&longs;umpta trutina, qu&aelig; in trutinando hypomoclij vicem gerit: nam &longs;tatera <lb/>
reducitur ad vectem; pondus erit &aelig;quipondium; &amp; merces in lance erit po&shy;<lb/>
tentia mouens: &longs;unt autem in tota &longs;tater&aelig; ha&longs;ta trutin&aelig; plures, hoc enim <lb/>
modo tota fit vniformis quoad pondus. </s>
          <s id="s.003106">&aelig;quipondium pr&aelig;terea debet ha&shy;<lb/>
bere tantum pondus, quantum e&longs;t in nuda lance, vt &longs;ic tota &longs;tatera &longs;it per &longs;e <lb/>
&longs;ola &aelig;quilibrabilis: &amp; pr&aelig;terea debet habere pondus &longs;tatum, a c legitimum, <lb/>
v. <!-- REMOVE S-->g. <!-- REMOVE S-->vnius libr&aelig;, aut duarum, aut trium, prout magis <expan abbr="trutin&atilde;d&aelig;">trutinand&aelig;</expan> merci ido&shy;<lb/>
neum erit, &amp; hoc erit proprium &aelig;quipondij pondus. </s>
          <s id="s.003107">vt autem ex &longs;ingulis <lb/>
trutinis &longs;ingula pondera ponderentur. </s>
          <s id="s.003108">&longs;ingulis nota aliqua &longs;culpenda e&longs;t, vt <lb/>
facil&egrave; mercatores merces ponderent, quod hac ratione fieri pote&longs;t. </s>
          <s id="s.003109">pona&shy;<lb/>
mus &aelig;quipondium e&longs;&longs;e 12. librarum. </s>
          <s id="s.003110">dico, quod trutina C, dabit in lance <lb/>
pondus mercis 12. librarum, &longs;i ex ea fiat &aelig;quilibrium, e&longs;t enim vt A C, ad <lb/>
C B, ita permutatim &aelig;quipondium 12. ad mercem; &longs;ed A C, ip&longs;i C B, e&longs;t <lb/>
&aelig;qualis, erg&ograve; etiam &aelig;quipondium 12. erit merci &aelig;quale, hoc e&longs;t vtrunque <lb/>
erit, 12. librarum.</s>
        </p>
        <p type="main">
          <s id="s.003111">Similiter &longs;i fieret &aelig;quilibrium ex trutina D, e&longs;&longs;et vt A D, 3. ad B D, 9. <lb/>
ita 12. ad 36. tandem trutina E, &aelig;quilibrante, e&longs;&longs;et vt A E, 9. ad E B, 3. ita <lb/>
12. ad 4. Si igitur trutina C, notetur 12. numero, trutina D, num. </s>
          <s id="s.003112">36. tru&shy;<lb/>
tina E, num. </s>
          <s id="s.003113">4. &amp; idem de c&aelig;teris: &longs;tatim facil&egrave; erit quodlibet pondus per <lb/>
huiu&longs;modi &longs;tateram exhibere. </s>
          <s id="s.003114">Vnde videas contrario ab illis modo in no&shy;


<pb pagenum="184" xlink:href="009/01/184.jpg"/>&longs;tris &longs;tateris &aelig;quipondium totam ha&longs;tam percurrere; in illis ver&ograve; manent&egrave; <lb/>
&aelig;quipondio trutinam quodammodo per ha&longs;tam moueri.</s>
        </p>
        <p type="main">
          <s id="s.003115">His pr&aelig;mi&longs;&longs;is ad textus paraphra&longs;im veniamus.</s>
        </p>
        <p type="main">
          <s id="s.003116">Cur &longs;tatera, qua carnes ponderantur, paruo appendiculo magna truti&shy;<lb/>
nat onera, cum alioquin tota &longs;tatera nihil aliud &longs;it, qu&agrave;m dimidiata libra, <lb/>
vbi enim onus mercis imponitur vna lanx pendet, quam vnicam &longs;tatera ha&shy;<lb/>
bet; in altera autem parte, vbi libra habet alteram lancem, &longs;tatera nullam <lb/>
habet, &longs;ed &longs;ola &longs;ine lance e&longs;t. </s>
          <s id="s.003117">Cau&longs;a igitur e&longs;t, quia &longs;tatera &longs;imul, &amp; libra e&longs;t, <lb/>
&amp; vectis. </s>
          <s id="s.003118">libra e&longs;t, quia &longs;partorum, &longs;iue trutinarum qu&aelig;libet fit veluti cen&shy;<lb/>
trum libr&aelig;, <expan abbr="in&qacute;">inque</expan>; altera parte e&longs;t lanx; in altera ver&ograve; loco lancis ip&longs;um &aelig;qui&shy;<lb/>
pondium, quod libr&aelig; incumbit, <expan abbr="fungitur&qacute;">fungiturque</expan>; vice alterius lancis, cui &longs;it onus <lb/>
impo&longs;itum; manife&longs;tum enim e&longs;t, quod &aelig;quipondium &longs;tater&aelig; tantumdem <lb/>
trahit oneris, quantum e&longs;t illud, quod in altera lance e&longs;t. </s>
          <s id="s.003119">eapropter &longs;tatera <lb/>
quodammodo tot libras in &longs;e continet, quot trutinas: quarum vna qu&aelig;que <lb/>
cum &longs;it intra appendiculum, &amp; lancem, apta e&longs;t e&longs;&longs;e medium, &longs;eu centrum <lb/>
&longs;tater&aelig;, <expan abbr="atq;">atque</expan> adeo etiam libr&aelig;; qu&aelig; vnam quidem lancem habeat ex vna <lb/>
parte, ex altera ver&ograve; pro lance &aelig;quipondium. </s>
          <s id="s.003120">&longs;tatera ver&ograve; dicitur, quate&shy;<lb/>
nus ex vna parte habet non lancem, &longs;ed perpendiculum. </s>
          <s id="s.003121">&longs;ed hoc nihil e&longs;t <lb/>
aliud qu&agrave;m e&longs;&longs;e plures in vna libras; Cur autem &longs;parta, qu&aelig; lanci, &longs;iue ap&shy;<lb/>
pen&longs;o oneri proximiora &longs;unt, maiora &longs;ubleuent onera, cau&longs;a e&longs;t vectis natu&shy;<lb/>
ra, qu&aelig; &longs;tater&aelig; ine&longs;t. </s>
          <s id="s.003122">e&longs;t enim &longs;tatera vectis, quamuis quodammodo inuer&shy;<lb/>&longs;us, e&longs;t enim ip&longs;ius fulcimentum trutina ip&longs;a &longs;upern&egrave; collocata, pondus ve&shy;<lb/>r&ograve; leuandum e&longs;t ip&longs;a merx, potentia ver&ograve; appendiculum. </s>
          <s id="s.003123">quant&ograve; autem pro&shy;<lb/>
ductior fuerit pars vectis &agrave; fulcimento ad potentiam, tanto facilius poten&shy;<lb/>
tia mouet, vt in pr&aelig;&longs;entia accidit. </s>
          <s id="s.003124">mouet autem <expan abbr="v&longs;q;">v&longs;que</expan> ad &aelig;quilibrium; <expan abbr="hoc&qacute;">hocque</expan>; <lb/>
modo pars illa productior &longs;tater&aelig;, qu&aelig; vergit ad &aelig;quipondium, facit, vt <lb/>
onus &longs;tater&aelig; impo&longs;itum facil&egrave; trutinetur.</s>
        </p>
        <p type="head">
          <s id="s.003125"><emph type="italics"/>QV&AElig;STIO XXI.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003126"><emph type="italics"/>De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003127"><arrow.to.target n="marg250"/></s>
        </p>
        <p type="margin">
          <s id="s.003128"><margin.target id="marg250"/>260</s>
        </p>
        <p type="main">
          <s id="s.003129">Cvr Medici facilius dentes extrahunt dentiforcipis onere adiecto, <lb/>
qu&agrave;m &longs;i &longs;ola manu vtantur? </s>
          <s id="s.003130">fort&egrave;, quia ex manu facilius dens ela&shy;<lb/>
bitur propter &longs;ui ip&longs;ius lubricitatem, qu&agrave;m ex forcipe. </s>
          <s id="s.003131">Vel etiam, <lb/>
quia digiti propter carnis mollitiem cedentem nequeunt dentem <lb/>firmiter circumplecti; ferrum ver&ograve;, cum vndique durum &aelig;que &longs;it, nec ce&shy;<lb/>dens, melius dentem comprehendit. </s>
          <s id="s.003132">Aut tandem, quia forceps h&aelig;c duos <lb/>
in &longs;e continet contrarios vectes; quorum, vnum tantum e&longs;t hypomoclion, <lb/>
<figure id="id.009.01.184.1.jpg" place="text" xlink:href="009/01/184/1.jpg"/><lb/>eorum &longs;cilicet connexio; Virtute igitur <lb/>
vectis arctius dentem per&longs;tringunt, <expan abbr="atq;">atque</expan> <lb/>
ade&ograve; obtinent, <expan abbr="atq;">atque</expan> hinc etiam facilius <lb/>
commouent. </s>
          <s id="s.003133">&longs;it dentiforcipis figura, ex&shy;<lb/>
po&longs;ita, cuius alterum extremum, vbi &longs;unt <lb/>
A, B, e&longs;t illud, quod binis &longs;emicirculis <lb/>
concurrentibus dentem arct&egrave; <expan abbr="c&otilde;&longs;tringit">con&longs;tringit</expan>,


<pb pagenum="185" xlink:href="009/01/185.jpg"/>&amp; commouet. </s>
          <s id="s.003134">Vectis vnus e&longs;t A G D, alter B G C, communis fultura e&longs;t G, <lb/>
vbi e&longs;t ip&longs;orum decu&longs;&longs;ata connexio; dens loco ponderis e&longs;t; vtroque igitur <lb/>
C, &amp; D, tanquam manubrijs vectium dentem Medici compr&aelig;hendentes ip&shy;<lb/>
&longs;um facil&egrave; commouent: quando autem commotus fuerit, facilius manu, <lb/>
qu&agrave;m in&longs;trumento extrahitur.</s>
        </p>
        <p type="head">
          <s id="s.003135"><emph type="italics"/>QV&AElig;STIO XXII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003136"><emph type="italics"/>De Instrumento Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003137"><arrow.to.target n="marg251"/></s>
        </p>
        <p type="margin">
          <s id="s.003138"><margin.target id="marg251"/>261</s>
        </p>
        <p type="main">
          <s id="s.003139">Tempore Ari&longs;t. vt colligitur ex hac qu&aelig;&longs;tione, ad frangendas nu&shy;<lb/>
ces peculiare in&longs;trumentum ligneum adhibeant, quod erat in&longs;tar <lb/>
forcipis, ita tamen concinnatum, vt non ad &longs;cindendum, nec ad <lb/>
extrahendum, &longs;ed ad frangendum per <expan abbr="c&otilde;pre&longs;&longs;ionem">compre&longs;&longs;ionem</expan> e&longs;&longs;et aptum. <lb/>
</s>
          <s id="s.003140">cuius hanc qualemcumque figuram in&longs;pice. </s>
          <s id="s.003141">cuius latus inferius A D, fort&egrave; <lb/>
alicui fulcimento in plano horizontis, fixum h&aelig;rebat: alterum ver&ograve; A C, <lb/>
manu tractabatur, vt &longs;ic expedit&aelig; nucium plurima quantitas breui po&longs;&longs;et <lb/>
confringi. </s>
          <s id="s.003142">Credibile e&longs;t nucifragam hanc ad capita F E, habui&longs;&longs;e aliquod <lb/>
impedimentum, ne omnin&ograve; con&longs;tringeretur, vt nuces <expan abbr="franger&etilde;tur">frangerentur</expan> quidem, <lb/>
non autem comminuerentur. </s>
          <s id="s.003143">Cur igitur nuces <expan abbr="ab&longs;q;">ab&longs;que</expan> ictu facil&egrave; confringun&shy;<lb/>
tur hi&longs;ce in&longs;trumentis, qu&aelig; ad eum fiunt v&longs;um? </s>
          <s id="s.003144">contrarium <expan abbr="namq;">namque</expan> accidere <lb/>
deberet, vtentes enim pr&aelig;dictis in&longs;trumentis, omnibus illis viribus de&longs;ti&shy;<lb/>
tuuntur, quas motio, ac violentia percu&longs;&longs;ionis afferre &longs;olent. </s>
          <s id="s.003145">pr&aelig;terea cur <lb/>
ligneo vtuntur, ac proinde leui? </s>
          <s id="s.003146">non ne aptius e&longs;&longs;et durum, <expan abbr="atq;">atque</expan> pondero&shy;<lb/>
&longs;um veluti ferreum?</s>
        </p>
        <p type="main">
          <s id="s.003147">His re&longs;pondendum e&longs;t, nucifragum i&longs;tud in&longs;trumentum reduci ad binos <lb/>
vectes, quemadmodum etiam dentiforcipem. </s>
          <s id="s.003148">nux igitur hoc modo duplici <lb/>
vecte comprimitur. </s>
          <s id="s.003149">vecte autem facil&egrave; onera qu&aelig;libet <expan abbr="obui&atilde;tia">obuiantia</expan> diuelluntur. <lb/>
</s>
          <s id="s.003150">qui duo vectes vnicum habent hypomoclion ip&longs;am &longs;cilicet connexionem <lb/>
<figure id="id.009.01.185.1.jpg" place="text" xlink:href="009/01/185/1.jpg"/><lb/>
A. vectes &longs;unt bin&aelig; in&longs;trumenti ha&longs;t&aelig;, F A D, <lb/>
E A C. <expan abbr="dilat&atilde;do">dilatando</expan> igitur extrema C D, deducun&shy;<lb/>
tur etiam alia extrema F, E, &amp; impo&longs;ita nuce in <lb/>
hiatu K, qu&aelig;uis potentia con&longs;tringendo C, D, <lb/>
con&longs;tringet &longs;imul F, E, <expan abbr="ip&longs;am&qacute;">ip&longs;amque</expan>; nucem confrin&shy;<lb/>
get. </s>
          <s id="s.003151">quod igitur cum percu&longs;&longs;ione feci&longs;&longs;et pon&shy;<lb/>
dus mallei, id valentiori vectium virtute efficiunt F A D, E A C. quanto au&shy;<lb/>
tem locus nucis K, propinquior fuerit hypomoclio A, tanto celerius <lb/>
confringitur, quia partes vectium A C, A D, tunc &agrave; centro <lb/>
A, productiores fiunt, ide&longs;t mult&ograve; maiores fiunt, <lb/>
qu&agrave;m &longs;int di&longs;tanti&aelig; inter nucem, &amp; cen&shy;<lb/>
trum A, quod maxim&egrave; poten&shy;<lb/>
tiam iuuat.</s>
        </p>
        <p type="main">
          <s id="s.003152">Ex quibus pr&aelig;&longs;enti qu&aelig;&longs;tioni &longs;atisfactum videtur.</s>
        </p>
        <pb pagenum="186" xlink:href="009/01/186.jpg"/>
        <p type="head">
          <s id="s.003153"><emph type="italics"/>QV&AElig;STIO XXIII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003154"><emph type="italics"/>De Rhombo.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003155"><arrow.to.target n="marg252"/></s>
        </p>
        <p type="margin">
          <s id="s.003156"><margin.target id="marg252"/>262</s>
        </p>
        <p type="main">
          <s id="s.003157">Rhombus ex definitione 23. primi Elem. e&longs;t figura &aelig;quilatera qui&shy;<lb/>
<figure id="id.009.01.186.1.jpg" place="text" xlink:href="009/01/186/1.jpg"/><lb/>
dem, &longs;ed non &aelig;quiangula, habet enim <lb/>
binos oppo&longs;itos angulos acutos, &amp; alies <lb/>
binos oppo&longs;itos obtu&longs;os, talis e&longs;t pr&aelig;&shy;<lb/>
&longs;ens figura A B D C. <!-- KEEP S--></s>
          <s id="s.003158">In pr&aelig;&longs;enti porr&ograve; qu&aelig;&longs;tione <lb/>
&longs;upponitur punctum A, quod e&longs;t vnum extremum <lb/>
in rhombo moueri &longs;uper latus A B, ver&longs;us B, &amp; &longs;i&shy;<lb/>
militer interim &aelig;qua velocitate moueri alterum <lb/>extremum B, &longs;uper idem latus A B, ver&longs;us A, &amp; in&shy;<lb/>
terim dum h&aelig;c duo puncta hoc modo &longs;ibi obuiam <lb/>
procedunt, moueri latus totum A B, eadem ve&shy;<lb/>
locitate, ver&longs;us latus C D, ita vt &longs;emper ip&longs;i C D, <lb/>&aelig;quidi&longs;ter, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; per latera A C, B D, quo&shy;<lb/>
u&longs;que ip&longs;i C D, congruat.</s>
        </p>
        <p type="main">
          <s id="s.003159">Horum igitur trium motuum quemadmodum <lb/>
&aelig;qu&aelig; &longs;unt celeritates, ita etiam &longs;patia, quibus peraguntur, nam puncta duo <lb/>
mouentur in latere A B, ip&longs;um ver&ograve; A B, mouetur in lateribus A C, &amp; B D, <lb/>
qu&aelig; cum priori A B, &longs;unt &aelig;qualia.</s>
        </p>
        <p type="main">
          <s id="s.003160">Aduertendum pr&aelig;terea, quod hac ratione duo puncta A, &amp; B, duabus la&shy;<lb/>
tionibus mouebuntur, &longs;i quidem proprio motu <expan abbr="mou&etilde;tur">mouentur</expan> in ip&longs;o latere A B, <lb/>
&amp; quia latus A B, per quod ip&longs;a incedunt eodem tempore mouetur ver&longs;us <lb/>
C D, &longs;equitur, quod etiam ip&longs;a hoc eodem motu ferantur. </s>
          <s id="s.003161">erit igitur ip&longs;o&shy;<lb/>
rum motus ex his duobus mixtus; &amp; quidem ip&longs;ius A, latio erit per longio&shy;<lb/>
rem diametrum A D; ip&longs;ius ver&ograve; B, per breuiorem B C. <!-- KEEP S--></s>
          <s id="s.003162">Quare cum pun&shy;<lb/>
ctum A, peruenerit ad D, etiam punctum B, eadem c&etail;leritate acce&longs;&longs;erit ad <lb/>
C. maius autem e&longs;t &longs;patium A D, quod confecit A, quam &longs;patium B C, con&shy;<lb/>
fectum a C. <!-- KEEP S--></s>
          <s id="s.003163">Qu&aelig;rit igitur prim&ograve;, cur c&ugrave;m A, &amp; B, mota &longs;int &aelig;quali celeri&shy;<lb/>tate in vtra que latione, vnum tamen maiorem lineam, qu&agrave;m alterum per&shy;<lb/>
tran&longs;iuit? </s>
          <s id="s.003164">Qu&aelig;rit &longs;ecund&ograve;, cur punctum B, confecit lineam B C, qu&aelig; mi&shy;<lb/>
nor e&longs;t quam ip&longs;um latus A C, quod in &longs;uo motu conficit latus A B, quando <lb/>
ad D C, acce&longs;&longs;it. </s>
          <s id="s.003165">&amp; tamen B, duplici fertur latione; A B, ver&ograve; vnica; vtrun&shy;<lb/>
que autem in &aelig;quali velocitate? </s>
          <s id="s.003166">Quod autem punctus A, motu illo de&longs;cri&shy;<lb/>
bat lineam A D, punctus ver&ograve; B. lineam B C, manife&longs;tum erit hoc modo. </s>
          <s id="s.003167">&longs;it <lb/>
v. <!-- REMOVE S-->g. <!-- REMOVE S-->punctum A, motu proprio delatum, <expan abbr="v&longs;q;">v&longs;que</expan> ad punctum E, medium late&shy;<lb/>
ris A B, erit interim totum latus A B, tran&longs;latum vbi e&longs;t F G, hoc e&longs;t, ad &longs;ui <lb/>
itineris dimidium, quia horum motus ponuntur &aelig;quales: hoc autem motu <lb/>
ip&longs;um punctum A, erit nece&longs;&longs;ari&ograve; in K, hoc e&longs;t in linea A D, vt dicebamus. <lb/>
</s>
          <s id="s.003168">Similiter in fine <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> motus, A, erit in B, proprio motu, &longs;ed alieno in D, <lb/>
extremo &longs;cilicet line&aelig; A D. &longs;imili ratione o&longs;tendi pote&longs;t de ip&longs;o B, qui cum <lb/>
&aelig;qua velocitate moueatur, ac punctum A, quando A erit in E; B, pariter <lb/>
illi occurret in E, proprio motu: &longs;ed alieno &agrave; latere B A, proueniente erit


<pb pagenum="187" xlink:href="009/01/187.jpg"/>in K, vbi etiam ob alterum motum erit A: erit igitur B, in linea B C, vt vo&shy;<lb/>
lebamus. </s>
          <s id="s.003169">&agrave; quo po&longs;tea di&longs;cedens ver&longs;us C, motu pariter compo&longs;ito &longs;i&longs;titur <lb/>
tandem in C, extremo line&aelig; pariter B C. eodem ergo tempore duo rhombi <lb/>
extrema puncta &aelig;qu&egrave; velocia, &longs;ecundum <expan abbr="vtramq;">vtramque</expan> lationem mota, interual&shy;<lb/>
la nequaquam &aelig;qualia confecerunt, &longs;ed A, maius, nimirum A D; B, ver&ograve; <lb/>
minus nimirum B C.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003170">Ex quibus etiam &longs;ecund&aelig; qu&aelig;&longs;tionis explicatio, &amp; dubitandi ratio pate&shy;<lb/>
bit: nam cum in rhombo duo &longs;int obtu&longs;i anguli B, &amp; C, &amp; duo acuti A, &amp; D, <lb/>
punctus ille, qui ab obtu&longs;o angulo B, recedit, fertur duabus lationibus inui&shy;<lb/>
cem fer&egrave; contrarijs, propria enim tendit &longs;ur&longs;um ad A, aliena ver&ograve; deor&longs;um <lb/>
trahitur ver&longs;us D; cau&longs;a huius contrarietatis &longs;unt line&aelig; D B, B A, obtu&longs;um <lb/>
angulum continentes, qu&aelig; &agrave; pr&aelig;dicto angulo in contrarias partes &longs;eparan&shy;<lb/>
tur: per has autem lineas fiunt pr&aelig;dicti motus, vnde ip&longs;i quoque contrarij <lb/>
&longs;int nece&longs;&longs;e e&longs;t: &amp; propterea &longs;e mutu&ograve; impediunt: <expan abbr="atq;">atque</expan> hinc nece&longs;&longs;e e&longs;t pun&shy;<lb/>ctum B, motu compo&longs;ito hinc inhibito minus interuallum B C, pertran&longs;ire. <lb/>
</s>
          <s id="s.003171">At ver&ograve; punctum A, quia ab acuto angulo de&longs;cendit, <expan abbr="vtraq;">vtraque</expan> latione fertur <lb/>
deor&longs;um, qu&aelig; lationes &longs;e mutu&ograve; iuuant, <expan abbr="faciunt&qacute;">faciuntque</expan>; vt A, maius, quamuis eo&shy;<lb/>
dem tempore, &amp; eadem celeritate peragret &longs;patium A D. nam punctum A, <lb/>
&longs;ua &longs;pont&egrave; <expan abbr="de&longs;c&etilde;dit">de&longs;cendit</expan> per latus A B, &amp; ab ip&longs;o latere A B, quod fertur ad C D, <lb/>
pariter deor&longs;um vehitur. </s>
          <s id="s.003172">nihil igitur mirum fit, &longs;i A, maius <expan abbr="interuall&utilde;">interuallum</expan> A D, <lb/>
quam B C, percurrat. </s>
          <s id="s.003173">cau&longs;a ver&ograve; huius motuum concordi&aelig; e&longs;t angulus acu&shy;<lb/>
tus A, ob quem latera rhombi magis inuicem approximantur, redduntque <lb/>
longiorem A D, qu&agrave;m B C: &egrave; contrari&ograve; autem, quo obtu&longs;iores &longs;unt anguli <lb/>
B, C, minorem faciunt ip&longs;am B C, latera enim &longs;emper magis ad rectam li&shy;<lb/>
neam accedunt; donec tandem omni angulo euane&longs;cente in directum con&shy;<lb/>
&longs;tituantur; quo ca&longs;u congruerent cum linea A D, <expan abbr="rhombus&qacute;">rhombusque</expan>; ip&longs;e amplius <lb/>
nullus e&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.003174">Ex his igitur &longs;equitur, quod punctum A, ab angulo A, acuto di&longs;cedens, <lb/>
duobus feratur motibus &longs;imilibus ad eandem partem tendentibus, &amp; qu&ograve; <lb/>
acutiores &longs;unt anguli, e&ograve; magis tendent ad eandem partem; &amp; melius &longs;e <lb/>mutu&ograve; iuuabunt. </s>
          <s id="s.003175">B, autem vice ver&longs;a, quoniam quanto obtu&longs;ior e&longs;t angulus <lb/>
B, tanto magis latera illius diuaricantur; du&aelig; etiam motiones, quibus B, <lb/>
progreditur in diuer&longs;as partes tendent; fiunt enim per illa latera; &amp; tanto <lb/>
etiam magis &longs;ibi contrari&aelig; erunt; <expan abbr="magis&qacute;">magisque</expan>; &longs;ibi mutu&ograve; impedimento erunt. <lb/>
</s>
          <s id="s.003176">&amp; propterea punctum B, minus interuallum, quale e&longs;t B C, percurret, quan&shy;<lb/>
do A, maius A D, percurrit.</s>
        </p>
        <p type="main">
          <s id="s.003177">Ad &longs;ecundam ver&ograve; qu&aelig;&longs;tionis partem, re&longs;pondeo con&longs;iderandum e&longs;&longs;e <lb/>
latus B A, moueri vnico motu ad D C, quare &agrave; nullo impedi&shy;<lb/>
tur, vnde nihil mirum videri debet, qu&ograve;d ip&longs;um vnica <lb/>
latione maius conficiat &longs;pacium qu&agrave;m B, quod <lb/>
quamuis duplici pellatur motu, vnus <lb/>
tamen ab altero inhibetur.</s>
        </p>
        <pb pagenum="188" xlink:href="009/01/188.jpg"/>
        <p type="head">
          <s id="s.003178"><emph type="italics"/>QV&AElig;STIO XXIIII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003179"><emph type="italics"/>De duobus circulis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003180"><arrow.to.target n="marg253"/></s>
        </p>
        <p type="margin">
          <s id="s.003181"><margin.target id="marg253"/>263</s>
        </p>
        <p type="main">
          <s id="s.003182">Vnde e&longs;t, quod &longs;i duo circuli, vnus altero maior, circa idem cen&shy;<lb/>
trum po&longs;iti, volutentur, ita vt etiam centrum feratur, eo &longs;cilicet <lb/>
modo, quo plau&longs;trorum rot&aelig; &longs;olent, &longs;ecundum &aelig;qualem lineam <lb/>
conuoluuntur, &longs;iue &aelig;quale &longs;patium conficiunt: &longs;i ver&ograve; &longs;eor&longs;um <lb/>
&longs;eparati quilibet eodem modo volutetur, non &aelig;quale <expan abbr="&longs;pati&utilde;">&longs;patium</expan> pertran&longs;ibunt, <lb/>
&longs;ed maior maiorem lineam, qu&agrave;m minor; <expan abbr="id&qacute;">idque</expan>; ea proportione, quam inui&shy;<lb/>
cem eorum circunferenti&aelig; obtinent, cum in hac veluti rot&aelig; conuolutione, <lb/>
circunferentia tota &longs;ucce&longs;&longs;iu&egrave; decur&longs;o &longs;patio adaptetur, ita vt tanta &longs;it de&shy;<lb/>
cur&longs;a linea, quanta e&longs;t rot&aelig; circunferentia? </s>
          <s id="s.003183">Quin etiam eodem exi&longs;tente <lb/>
<expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> centro, aliquando confectum &longs;patium ab <expan abbr="vtroq;">vtroque</expan> tantum e&longs;t, quan&shy;<lb/>
tum minor circulus &longs;olus, &longs;ecundum &longs;uam periph&aelig;riam reuolutus perfeci&longs;&shy;<lb/>
&longs;et; <expan abbr="quando&qacute;">quandoque</expan>; ver&ograve; quantum maior &longs;olus ab&longs;olui&longs;&longs;et. </s>
          <s id="s.003184">Quod autem maior <lb/>
&longs;olus in &longs;ua reuolutione maiorem lineam de&longs;cribat, manife&longs;tum e&longs;t hinc, <lb/>
quia &longs;en&longs;u patet maiorem circunferentiam in maiori circulo &longs;ubtendere <lb/>
angulum, qui fit &agrave; diametris in centro; minorem ver&ograve; circunferentiam <lb/>
&longs;ubtendere eundem angulum in minori orbe, vt etiam in 8. qu&aelig;&longs;t. </s>
          <s id="s.003185"><expan abbr="dict&utilde;">dictum</expan> e&longs;t: <lb/>
eandem igitur, vt proxim&egrave; dixi habebunt etiam proportionem ill&aelig; line&aelig;, <lb/>
qu&aelig; &agrave; &longs;ingulis &longs;eor&longs;um orbibus reuolutis de&longs;ignabuntur. </s>
          <s id="s.003186">Quod pr&aelig;terea &longs;e&shy;<lb/>
cundum &aelig;qualem conuoluuntur, quando circa idem po&longs;iti fuerint centrum, <lb/>
manife&longs;tum e&longs;t, ita tamen, vt aliquando amb&aelig; &aelig;quales &longs;int ei, &longs;ecundum <lb/>
quam &longs;olus maior conuolueretur; aliquando ver&ograve; &longs;ecundum quam minor. <lb/>
<figure id="id.009.01.188.1.jpg" place="text" xlink:href="009/01/188/1.jpg"/><lb/>
&longs;it enim circulus maior quidem vbi <lb/>
D F C, minor ver&ograve; vbi E G B, <expan abbr="vtriq;">vtrique</expan> <lb/>
autem centrum A, linea, &longs;ecundum <lb/>
quam quadrans F C, maioris per &longs;e <lb/>
rotaretur, &longs;it F L. linea ver&ograve;, &longs;ecun&shy;<lb/>
dum quam <expan abbr="quadr&atilde;s">quadrans</expan> G B, minoris &longs;e&shy;<lb/>
iuncti &agrave; maiori, volutaretur &longs;it G K, <lb/>
qu&aelig; &aelig;qualis e&longs;t dicto quadranti G B, <lb/>
&longs;icut etiam F I, &aelig;qualis e&longs;t quadran&shy;<lb/>
ti F C. &longs;i quis igitur impellat mino&shy;<lb/>
rem orbem mouens &longs;imul commune <lb/>
centrum A, cui maior e&longs;t circumpo&shy;<lb/>
&longs;itus, donec diameter A B, perpendicularis &longs;it line&aelig; G K, in puncto K. tunc <lb/>
pariter diameter maioris A C, erit perpendicularis line&aelig; F L, in puncto L. <lb/>
<!-- KEEP S--></s>
          <s id="s.003187">G K, autem, &amp; F L, nece&longs;&longs;ari&ograve; erunt &aelig;quales per 34. primi, &aelig;quales igitur <lb/>
lineas hoc modo peragrarunt in&aelig;quales circunferenti&aelig;, &longs;iue quadrantes <lb/>
G B, F C. &longs;i autem quadrantes hoc pr&aelig;&longs;tant, manife&longs;tum e&longs;t, quod &amp; toti <lb/>
ambitus idem efficiunt, quare quando tota periph&aelig;ria G B E G, fuerit re&shy;<lb/>
uoluta etiam tota F C D F, &longs;uum orbem <expan abbr="complet&utilde;">completum</expan> habebit. </s>
          <s id="s.003188">&longs;imiliter &longs;i ma&shy;<lb/>iorem quis mouerit, cui minor &longs;it annexus eodem exi&longs;tente centro, &longs;imul ac <pb pagenum="189" xlink:href="009/01/189.jpg"/>diameter A C, erit perpendicularis ad F I, in puncto I, erit etiam A B, per&shy;<lb/>
pendicularis ip&longs;i G M, in M; &longs;unt autem G M, &amp; F I, &aelig;quales, quare quan&shy;<lb/>
do F C, quadrans maioris pertran&longs;iuerit rectam F C, etiam C B, quadrans <lb/>
minoris tran&longs;actam habebit illi parem G M. hoc autem accidit nulla inter&shy;<lb/>
cedente mora in vllo ip&longs;orum: quando enim mouetur maior, nihil ce&longs;&longs;at <lb/>
minor: &amp; quando minor agitur, maior nunquam quie&longs;cit. </s>
          <s id="s.003189">quod &longs;i hoc acci&shy;<lb/>
dit quart&aelig; parti circulorum, idem, &amp; totis accidit periph&aelig;rijs. </s>
          <s id="s.003190">vbi in&longs;uper <lb/>
illud etiam mirum, centrum nimirum ip&longs;orum eadem celeritate motum, <lb/>ac vnica &longs;emper exi&longs;tenti latione, modo maius, modo minus &longs;patium per&shy;<lb/>
ficere; idem ver&ograve; eadem velocitate latum, &aelig;quale &longs;emper deberet interual&shy;<lb/>
lum tran&longs;ilire. </s>
          <s id="s.003191">&amp; tamen in pr&aelig;&longs;entia vtrouis modo moueas eadem pernici&shy;<lb/>
tate, mod&ograve; maius, mod&ograve; minus &longs;patium pertran&longs;ibit.</s>
        </p>
        <p type="main">
          <s id="s.003192">Huius qu&aelig;&longs;tionis enodand&aelig; cau&longs;a, &longs;upponendum prim&ograve; e&longs;t, quod eadem, <lb/>
&longs;eu &aelig;qualis potentia, hanc quidem magnitudinem tardius, illam ver&ograve; citius <lb/>
mouere pote&longs;t. </s>
          <s id="s.003193">&longs;i enim fuerit quippiam, quod &agrave; &longs;eip&longs;o moueri minim&egrave; ap&shy;<lb/>
tum &longs;it; &amp; aliud, quod &agrave; &longs;e ip&longs;o moueri aptum &longs;it; qui hoc &longs;imul cum illo <lb/>
coniunctum mouerit, tardius mouebit, qu&agrave;m &longs;i ip&longs;um &longs;olum moueret. </s>
          <s id="s.003194">&amp; &longs;i <lb/>
quid moueatur, quod aptum &longs;it ex &longs;e moueri, verumtamen in eo motu nihil <lb/>
ex &longs;e moueatur, perinde e&longs;t, ac &longs;i minim&egrave; aptum &longs;it ad motum, &amp; proinde <lb/>
tardius mouebitur; nec fieri poterit, vt plu&longs;quam mouens moueatur, cum <lb/>
nihil innata motione vtatur. </s>
          <s id="s.003195">Si quis igitur minorem circulum, quem mo&shy;<lb/>
do B, appello, mouerit &longs;upra &longs;uam circunferentiam, cui annexus &longs;it maior, <lb/>
quem modo appello A, &longs;ic quidem maior mouebitur, non autem ex &longs;e, &longs;ed <lb/>
&longs;olum quatenus &agrave; minori feretur, vnde tantum pertran&longs;ibit de recta F L, <lb/>
quantum &agrave; minori fuerit impul&longs;us; tantum autem e&longs;t impul&longs;us, quantum <lb/>
minor e&longs;t motus; quare &aelig;qualem cum illo viam confecit. </s>
          <s id="s.003196">&longs;i igitur minor fe&shy;<lb/>
cit pedalem G K, maior confecit etiam pedalem F L, quia maior nihil de <lb/>
proprio motu addidit, &longs;ed &longs;olum motione minoris e&longs;t tran&longs;latus. </s>
          <s id="s.003197">&longs;imiliter <lb/>
&longs;i quis rotet maiorem &longs;upra &longs;uam circunferentiam annexo minori, tantum <lb/>
minor mouebitur, quantum &agrave; maiori deportabitur, quia nihil ex &longs;e impel&shy;<lb/>
litur. </s>
          <s id="s.003198">Verum &longs;i &longs;eor&longs;um ambo ex &longs;e &longs;ecundum &longs;uos ambitus moueantur, &longs;iue <lb/>
cit&ograve;, &longs;iue tard&egrave;, eadem etiam velocitate perficiant integram &longs;u&aelig; periph&aelig;&shy;<lb/>
ri&aelig; volutationem, maior maius, minor ver&ograve; minus conficiet &longs;patium.</s>
        </p>
        <p type="main">
          <s id="s.003199">Sed fort&egrave; augebitur difficultas con&longs;ideranti, quod pr&aelig;dicti circuli &longs;unt <lb/>
circa idem centrum, &amp; circa illud mouentur. </s>
          <s id="s.003200">moueri autem circulum cir&shy;<lb/>
ca &longs;uum centrum, e&longs;t moueri &longs;ecundum &longs;uum naturalem motum, ad quem <lb/>
circuli ex &longs;e &longs;unt apti. </s>
          <s id="s.003201">&longs;i ver&ograve; vnus moueretur circa &longs;uum centrum, alter ve&shy;<lb/>
r&ograve; non, vt quando alter alteri non e&longs;t circa idem centrum compactus, &amp; ab <lb/>
altero mouetur, vbi manife&longs;t&egrave; apparet, quod fertur omnin&ograve; ab illo, &amp; in il&shy;<lb/>
la latione non circumuertitur circa proprium centrum, quare tunc minim&egrave; <lb/>
mirum e&longs;t, &longs;i <expan abbr="neq;">neque</expan> plus, <expan abbr="neq;">neque</expan> minus &longs;patium conficiat, qu&agrave;m ab altero de&shy;<lb/>
portetur, cui quoquo modo adiacet, aut appen&longs;us e&longs;t extra illius centrum.</s>
        </p>
        <p type="main">
          <s id="s.003202">Huic obiectioni <expan abbr="re&longs;pond&etilde;dum">re&longs;pondendum</expan> e&longs;t, quod quamuis pr&aelig;dicti orbes &longs;int con&shy;<lb/>
centrici, nihilominus non mouentur ambo &longs;uamet motione, &longs;ed ille, qui ab <lb/>
alio fertur mouetur &longs;ecundum motionem illam, tanquam &longs;i nullam ad eam <lb/>haberet aptitudinem; quamuis enim po&longs;&longs;it moueri circa centrum illud A,<pb pagenum="190" xlink:href="009/01/190.jpg"/>propria natura, in pr&aelig;&longs;enti tamen ca&longs;u minim&egrave; vtitur illa aptitudine; &amp; <lb/>
propterea motus debet moueri, quantum mouens, nec plus, nec minus.</s>
        </p>
        <p type="main">
          <s id="s.003203">Qu&ograve;d autem &longs;pectat ad id, quod initio dicebatur de eodem centro, &amp; de <lb/>
mouente eadem velocitate, &amp; de &aelig;quali ab in&aelig;qualibus orbibus pertran&longs;i&shy;<lb/>ta linea, &longs;ube&longs;t huic dubitationi paralogi&longs;mus: quamuis enim &longs;it idem am&shy;<lb/>
borum centrum, e&longs;t tamen vnius centrum per &longs;e in motione, alteri ver&ograve; per <lb/>
accidens, veluti per accidens e&longs;t eundem virum e&longs;&longs;e mu&longs;icum, &amp; album. </s>
          <s id="s.003204">ille <lb/>
enim circulus, qui mouet alterum, obtinet illud centrum per &longs;e, &amp; ex natu&shy;<lb/>
ra &longs;ua; alter ver&ograve;, qui mouetur, habet illud idem per accidens, quia non <lb/>
vtitur illo tanquam centro. </s>
          <s id="s.003205">non igitur circa idem &longs;impliciter centrum fit <lb/>
horum motus, &longs;ed alio modo vnus, alio modo alter, vnde &amp; reliquis dubi&shy;<lb/>
tationibus facil&egrave; &longs;atisfiet.</s>
        </p>
        <p type="head">
          <s id="s.003206"><emph type="italics"/>QV&AElig;STIO XXV.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003207"><emph type="italics"/>De Lecto<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003208"><arrow.to.target n="marg254"/></s>
        </p>
        <p type="margin">
          <s id="s.003209"><margin.target id="marg254"/>264</s>
        </p>
        <p type="main">
          <s id="s.003210">Cvr lectulorum &longs;pondas faciunt &longs;ecundum duplam proportionem, <lb/>
hoc e&longs;t longiorem &longs;pondam duplo longiorem, qu&agrave;m &longs;it altera: il&shy;<lb/>
lam enim &longs;ex pedum, vel paul&ograve; plus, hanc ver&ograve; trium? </s>
          <s id="s.003211">pr&aelig;terea <lb/>
cur re&longs;tes, quibus culcitr&aelig; &longs;u&longs;tinentur non extendunt per diame&shy;<lb/>
trum, &longs;ed per tran&longs;uer&longs;um?</s>
        </p>
        <p type="main">
          <s id="s.003212">Ad primum re&longs;pondetur ide&ograve; facere &longs;pondas in dupla ratione, vt &longs;int hu&shy;<lb/>
mano corpori proportionat&aelig;, &longs;ic enim lecti longitudinem habebunt qua&shy;<lb/>
tuor cubitorum, latitudinem ver&ograve; duorum, in tali enim &longs;patio commo&shy;<lb/>
d&egrave; cubamus.</s>
        </p>
        <p type="main">
          <s id="s.003213">Ad &longs;ecundum ver&ograve; dicendum extendi illos funes non per diametrum, &longs;ed <lb/>
ex oppo&longs;ito, quia hoc modo ligna ip&longs;ius lecti minus di&longs;trahuntur: facil&egrave; <lb/>
enim ex natura &longs;ua ligna h&aelig;c ab inuicem &longs;ecundum longum &longs;eparantur; ar&shy;<lb/>
ctius autem ductis funibus per tran&longs;uer&longs;um, qu&agrave;m per diametrum inuicem <lb/>
con&longs;tringuntur: pr&aelig;terea, quia &longs;ic etiam funes minus laborant, cum &longs;int eo&shy;<lb/>rum ductus breuiores; &amp; quia debent &longs;u&longs;tinere onus &longs;tragulorum, <expan abbr="atq;">atque</expan> cul&shy;<lb/>
c&igrave;trarum, &longs;ic cert&egrave; ex hoc onere minus laborabunt &longs;i tran&longs;uer&longs;im, qu&agrave;m &longs;i <lb/>
diametraliter &longs;ubtendantur.</s>
        </p>
        <p type="main">
          <s id="s.003214">Tertia demum ratio e&longs;t, quia hac ratione minus re&longs;tium ab&longs;umitur, qu&aelig; <lb/>
<figure id="id.009.01.190.1.jpg" place="text" xlink:href="009/01/190/1.jpg"/><lb/>vt ben&egrave; intelligatur, de&longs;criba&shy;<lb/>
tur lectuli figura A F G K, &amp; <lb/>
bifariam diuidatur latus F G, <lb/>
in B. &amp; quia tota F G, dupla <lb/>
e&longs;t ip&longs;ius A F, erit dimidium <lb/>
F B, &aelig;quale ip&longs;i A F. &amp; propte&shy;<lb/>
rea tot erunt foramina, quibus <lb/>
funes immittuntur in F B, quot <lb/>
in A F. <expan abbr="ext&etilde;dunt">extendunt</expan> autem funem <lb/>
hoc modo incipiunt ab A, &amp; <lb/>
ducunt ad B, po&longs;tea per C, re&shy;


<pb pagenum="191" xlink:href="009/01/191.jpg"/>uertuntur ad D; hinc flectunt per H, v&longs;que ad E, &amp; per G, angulum iterum <lb/>
de&longs;cendunt ad M, &agrave; quo recta tendunt in F, hinc per 2. deducunt ad 3. &agrave; quo <lb/>
foramine, per foramen 4. reflexum faciunt ad 5. &agrave; quo iterum per B, de&longs;cen&shy;<lb/>
dunt ad angulum K, <expan abbr="ibi&qacute;">ibique</expan>; alterum funis extremum de&longs;init: <expan abbr="hoc&qacute;">hocque</expan>; modo duo <lb/>
anguli A, &amp; K, re&longs;tis habent capita, &amp; re&longs;tes exten&longs;&aelig; &longs;unt non diametrali&shy;<lb/>
ter, &longs;ed tran&longs;uer&longs;im.</s>
        </p>
        <p type="main">
          <s id="s.003215">Notandum autem, quod re&longs;tes &aelig;quales &longs;unt cum &longs;uis curuaturis. </s>
          <s id="s.003216">v. <!-- REMOVE S-->g. <!-- REMOVE S-->re&shy;<lb/>
&longs;tis A B, cum &longs;ua curuatura B C, &aelig;qualis e&longs;t re&longs;ti C D, vn&agrave; cum eius curua&shy;<lb/>
tura D H, &amp; ali&aelig; eodem modo &longs;e habent, quia eadem demon&longs;tratio omni&shy;<lb/>
bus accommodari pote&longs;t: quia enim figura A B G M, parallelogrammum <lb/>
e&longs;t, &aelig;qualia enim &longs;unt latera B G, A M, &amp; quot foramina &longs;unt in vno, tot <lb/>
etiam &longs;unt in altero, <expan abbr="ea&qacute;">eaque</expan>; inuicem &aelig;quidi&longs;tant, &longs;equitur omnes re&longs;tes e&longs;&longs;e <lb/>
parallelas, &amp; &aelig;quales, per 33, primi. </s>
          <s id="s.003217">ex qua etiam &longs;equitur pr&aelig;dictas cu&shy;<lb/>
ruaturas, B C, D H, E G, e&longs;&longs;e &aelig;quales. </s>
          <s id="s.003218">quare manife&longs;tum e&longs;t in dimidio le&shy;<lb/>
ctulo tot e&longs;&longs;e re&longs;tes &aelig;quales re&longs;ti A B, quot &longs;unt foramina in dimidio latere <lb/>
B G, vel in dimidio F B, hoc e&longs;t e&longs;&longs;e quatuor. </s>
          <s id="s.003219">porr&ograve; oportet quantitatem <lb/>
harum omnium re&longs;tium per&longs;crutari, vt eam cum quantitate re&longs;tium diame&shy;<lb/>
traliter exten&longs;arum conferamus, quod geometric&egrave; hoc modo a&longs;&longs;eque mur: <lb/>
triangulum enim B G K, rectangulum e&longs;t, erg&ograve; per 47. primi, quadrata la&shy;<lb/>terum B G, G K, &aelig;qualia &longs;unt quadrato line&aelig; B K: latus B G, e&longs;t trium pe&shy;<lb/>
dum, quemadmodum etiam latus G K quadratus autem numerus ternarij <lb/>
e&longs;t 9. ergo duo quadrati numeri 9. &longs;iue 18. &aelig;quales &longs;unt quadrato line&aelig; B K, <lb/>
erg&ograve; linea B K, e&longs;t radix quadrata numeri 18. qu&aelig; radix non pote&longs;t exact&egrave; <lb/>
in numeris repr&aelig;&longs;entari, e&longs;t enim, vt aiunt, radix &longs;urda. </s>
          <s id="s.003220">verumtamen per <lb/>
radicum extractionem, <expan abbr="atq;">atque</expan> approximationem ea poni pote&longs;t e&longs;&longs;e 41/4. ide&longs;t <lb/>
quatuor pedum cum vna quarta. </s>
          <s id="s.003221">cum igitur in toto lecto &longs;int huiu&longs;modi <lb/>
octo re&longs;tes, erit omnium &longs;umma pedum 34. fer&egrave;. </s>
          <s id="s.003222">&longs;i autem &longs;eeundum diame&shy;<lb/>
trum extendantur re&longs;tes, vti factum e&longs;t in lectulo A B C D, neutiquam re&shy;<lb/>
&longs;tes omnes &longs;imul &longs;uperiori quantitati ad&aelig;quabuntur, &longs;ed illam long&egrave; &longs;upe&shy;<lb/>
<figure id="id.009.01.191.1.jpg" place="text" xlink:href="009/01/191/1.jpg"/><lb/>
rabunt. </s>
          <s id="s.003223">Sit igitur lectus A B&shy;<lb/>
C D, in quo diametraliter du&shy;<lb/>
ct&aelig; &longs;int re&longs;tes B D, E H, &amp; re&shy;<lb/>
liqu&aelig;, vt in figura. </s>
          <s id="s.003224">har&ucirc;m quan&shy;<lb/>
titas &longs;i per 47. primi, &amp; per ra&shy;<lb/>
dicis quadrat&aelig; extractionem <lb/>
inueniatur, erit &longs;umma earum <lb/>
pedum quadraginta cum dimi&shy;<lb/>
dio; qu&aelig; quantitas pr&aelig;cedenti <lb/>
maior e&longs;t &longs;ex pedibus cum di&shy;<lb/>
midio.</s>
        </p>
        <p type="main">
          <s id="s.003225"><expan abbr="Atq;">Atque</expan> hic e&longs;t &longs;en&longs;us Ari&longs;t. quamuis tex. <!-- REMOVE S-->ip&longs;ius propter nimiam tam in gr&aelig;&shy;<lb/>
cis, qu&agrave;m in latinis codicibus corruptionem, totus re&longs;titui nequiuerit.</s>
        </p>
        <pb pagenum="192" xlink:href="009/01/192.jpg"/>
        <p type="head">
          <s id="s.003226"><emph type="italics"/>QV&AElig;STIO XXVI.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003227"><emph type="italics"/>De ligno humeris gestato.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003228"><arrow.to.target n="marg255"/></s>
        </p>
        <p type="margin">
          <s id="s.003229"><margin.target id="marg255"/>265</s>
        </p>
        <p type="main">
          <s id="s.003230">Cvr difficilius e&longs;t <expan abbr="l&otilde;ga">longa</expan> ligna ab extremo &longs;uper humeros ferre, qu&agrave;m <lb/>
&longs;ecundum medium, c&ugrave;m tamen <expan abbr="vtroq;">vtroque</expan> modo &longs;it &longs;emper idem pon&shy;<lb/>
dus? </s>
          <s id="s.003231">An quia dum fertur lignum &longs;uper humeros ab altero extre&shy;<lb/>mo, alterum extremum vibratur, &amp; agitatur, qu&aelig; agitatio ip&longs;ius <lb/>
lationem impedit? </s>
          <s id="s.003232">An quia licet nihil inflectatur ob agitationem, <expan abbr="neq;">neque</expan> ma&shy;<lb/>
gnam habeat longitudinem, difficilius tamen ab extremo fertur, quoniam <lb/>
facilius ex medio eleuatur, qu&agrave;m ab extremo, &amp; quia latio e&longs;t qua&longs;i qu&aelig;&shy;<lb/>
dam continua eleuatio, propterea etiam difficilius &longs;ic portatur? </s>
          <s id="s.003233">cau&longs;a au&shy;<lb/>
tem cur facilius ex medio eleuetur e&longs;t, quia hoc modo totum lignum fit ve&shy;<lb/>
ctis, cuius hypomoclion e&longs;t in medio, vbi is, qui eleuat, tenet aut fert: ex&shy;<lb/>
trema autem &longs;ibi mutu&ograve; <expan abbr="&aelig;queponder&atilde;t">&aelig;queponderant</expan>, ita vt <expan abbr="ab&longs;q;">ab&longs;que</expan> vllo alio auxilio, &acirc; tan&shy;<lb/>
ta vi, quantum e&longs;t totum ligni pondus &longs;u&longs;tineatur; quod &longs;i ab extremo ele&shy;<lb/>
uetur non &longs;ufficit amplius pr&aelig;dicta vis, &longs;ed opus erit maiori, quia non &longs;o&shy;<lb/>lum oportebit illud eleuare, &longs;ed pr&aelig;terea etiam illud in &aelig;quilibrio con&longs;ti&shy;<lb/>
tuere, &amp; con&longs;eruare. </s>
          <s id="s.003234">pondus enim totius ligni vergit fer&egrave; ad alteram ligni <lb/>medietatem, qu&aelig; ab hypomoclio productior euadit, quapropter ad onus <lb/>
i&longs;tud &aelig;quilibrandum, opus e&longs;t alia potentia in altero extremo. </s>
          <s id="s.003235">&longs;it lignum <lb/>
<figure id="id.009.01.192.1.jpg" place="text" xlink:href="009/01/192/1.jpg"/><lb/>
A B, &longs;u&longs;pen&longs;um ex medio C. <lb/>
hoc modo lignum ponderi&shy;<lb/>
bus libratum &longs;uis manet in <lb/>
&aelig;quilibrio, pote&longs;tque &agrave; &longs;ola <lb/>
potentia illud eleuante etiam deferri: quia A, &amp; B, extrema &longs;e mutu&ograve; &longs;u&longs;ti&shy;<lb/>
<figure id="id.009.01.192.2.jpg" place="text" xlink:href="009/01/192/2.jpg"/><lb/>
nent. </s>
          <s id="s.003236">quod &longs;i non ex medio eleuaretur, <lb/>
&longs;ed ab extremo, vt in &longs;ecunda figura, <lb/>
eleuans potentia ex C, &aelig;qualis oportet, <lb/>
vt &longs;it pr&aelig;cedenti; &longs;ed pr&aelig;terea opus e&longs;t <lb/>
alia vi, qu&aelig; in B, &aelig;quiponderet alteri <lb/>
extremo A, quod magis grauitat, quo ab C, longius fuerit; &amp; hoc modo in <lb/>
&aelig;quilibrio con&longs;titutum, &amp; con&longs;eruatum poterit non &longs;olum eleuari, &longs;ed <lb/>
etiam circumferri.</s>
        </p>
        <p type="head">
          <s id="s.003237"><emph type="italics"/>QV&AElig;STIO XXVII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003238"><emph type="italics"/>De Gestatis &longs;uper humerum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003239"><arrow.to.target n="marg256"/></s>
        </p>
        <p type="margin">
          <s id="s.003240"><margin.target id="marg256"/>266</s>
        </p>
        <p type="main">
          <s id="s.003241">Cvr &longs;i vald&egrave; procerum &longs;uerit idem pondus difficilius &longs;uper humeros <lb/>
ge&longs;tatur, etiam &longs;i ex medio illud feratur, qu&agrave;m &longs;i breuius &longs;it? </s>
          <s id="s.003242">quod <lb/>
enim dudum dictum e&longs;t cau&longs;a non e&longs;t, &longs;ed vibratio, &amp; &longs;uccu&longs;&longs;atio <lb/>
ligni nunc e&longs;t: quando enim ab humero productius fuerit, magis <lb/>
vibrantur extrema, quam ob rem contingit portantem difficilius ge&longs;tare. <lb/>
</s>
          <s id="s.003243">vibrationis autem cau&longs;a e&longs;t, quoniam ab eadem vi mouente magis extrema <pb pagenum="193" xlink:href="009/01/193.jpg"/>huc illuc transferuntur, quanto procerius fuerit lignum, quia tunc maior <lb/>
fit di&longs;tanti&agrave; &agrave; centro, &longs;eu hypomoclio, quod modo e&longs;t humerus ip&longs;e. </s>
          <s id="s.003244">&longs;it vt <lb/>
in prima pr&aelig;cedentis qu&aelig;&longs;tionis figura, humerus vbi A. di&longs;tanti&aelig; autem ab <lb/>
ip&longs;o centro &longs;unt A B, A C, quod autem maior di&longs;tantia; faciliorem reddat <lb/>
motum o&longs;ten&longs;um e&longs;t initio huius operis.</s>
        </p>
        <p type="head">
          <s id="s.003245"><emph type="italics"/>QV&AElig;STIO XXVIII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003246"><emph type="italics"/>De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003247"><arrow.to.target n="marg257"/></s>
        </p>
        <p type="margin">
          <s id="s.003248"><margin.target id="marg257"/>267</s>
        </p>
        <p type="main">
          <s id="s.003249">In&longs;trumentum i&longs;tud, quod gr&aelig;ca voce Leonicus interpres Celonia vo&shy;<lb/>
cat, latinis dicitur Tolleno, &agrave; tollendo; quod etiam manife&longs;tum e&longs;t <lb/>
ex Fe&longs;to, qui ait, Tolleno e&longs;t genus machin&aelig;, quo hauritur aqua in al&shy;<lb/>
teram partem pr&aelig;grauante pondere; qu&aelig; tollenonis de&longs;criptio om&shy;<lb/>
nin&ograve; machin&aelig; pr&aelig;&longs;entis qu&aelig;&longs;tionis competit. </s>
          <s id="s.003250">Hi&longs;pani Telonam fort&egrave; a tol&shy;<lb/>
lenone nuncupant. </s>
          <s id="s.003251">E&longs;t autem tolleno <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> hauriend&aelig; &egrave; puteo aqu&aelig; <lb/>
idoneum, quo ru&longs;tici pa&longs;&longs;im vtuntur: <expan abbr="id&qacute;">idque</expan>; iuxta puteos &longs;tabile, ac firmum <lb/>
con&longs;truunt, quale &agrave; figura &longs;equenti refertur. </s>
          <s id="s.003252">vbi puteus F, tolleno con&longs;tat <lb/>
<figure id="id.009.01.193.1.jpg" place="text" xlink:href="009/01/193/1.jpg"/><lb/>
erecto tigno D C, &amp; tran&longs;&shy;<lb/>
uer&longs;a ha&longs;ta A C B, vn&agrave; cum <lb/>
fune B E, &amp; hydria E. ap&shy;<lb/>
ponitur pr&aelig;terea onus &longs;a&shy;<lb/>
tis graue ad <expan abbr="part&etilde;">partem</expan> A, quale <lb/>
e&longs;t G. ha&longs;ta porr&ograve; A B, ve&shy;<lb/>
luti vectis circa <expan abbr="p&utilde;ctum">punctum</expan> C, <lb/>
tanquam hypomoclion, <lb/>
<expan abbr="&longs;us&qacute;">&longs;usque</expan>; <expan abbr="de&qacute;">deque</expan>; agitur, &agrave; poten&shy;<lb/>
tia funem B E, trahente. <lb/>
</s>
          <s id="s.003253">&longs;ed iam textus exponatur.</s>
        </p>
        <p type="main">
          <s id="s.003254">Cur iuxta puteos tolle&shy;<lb/>
nones faciunt eo, quo vi&shy;<lb/>
&longs;untur modo, ligno enim <lb/>
tran&longs;uer&longs;o A B, adiungunt <lb/>
onus plumbi G, cum alio&shy;<lb/>
quin vas ip&longs;um E, &amp; vacuum, &amp; plenum pondus habeat: cur inquam, vt fa&shy;<lb/>
cilius moueant tollenonem, tollenonis oneri onus addunt G? </s>
          <s id="s.003255">An quoniam <lb/>
c&ugrave;m opus hauriendi diuidatur in duo, in intingendi nimirum, &amp; &longs;ur&longs;um tra&shy;<lb/>
hendi tempora: accidit quidem <expan abbr="ab&longs;q;">ab&longs;que</expan> plumbi onere facilius intingere, quia <lb/>
tunc vas e&longs;t vacuum: at ver&ograve; &longs;ur&longs;um vas deinde plenum trahere, laborio&shy;<lb/>
&longs;ius erit. </s>
          <s id="s.003256">&longs;i ver&ograve; addatur onus G, tunc quidem paul&ograve; difficilius intingemus, <lb/>
&longs;ed tamen vas plenum po&longs;tea mult&ograve; facilius, quod opus, &amp; labor e&longs;t, &longs;ur&longs;um <lb/>
educemus: oper&aelig;pretium igitur e&longs;t, onus illud plumbi, aut lapidis adiun&shy;<lb/>
gere in extremo A, quia &longs;ic pondus illud tanquam qu&aelig;dam potentia vecte <lb/>
A B, vtens &longs;ur&longs;um hydriam plenam rapiet, <expan abbr="hac&qacute;">hacque</expan>; ratione nos labore leua&shy;<lb/>
bit, <expan abbr="totum&qacute;">totumque</expan>; hauriendi opus demi&longs;&longs;ione, <expan abbr="atq;">atque</expan> eleuatione <expan abbr="con&longs;t&atilde;s">con&longs;tans</expan>, alleuabit,</s>
        </p>
        <pb pagenum="194" xlink:href="009/01/194.jpg"/>
        <p type="head">
          <s id="s.003257"><emph type="italics"/>QV&AElig;STIO XXVIIII.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003258"><emph type="italics"/>De onere phalanga gestato.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003259"><arrow.to.target n="marg258"/></s>
        </p>
        <p type="margin">
          <s id="s.003260"><margin.target id="marg258"/>268</s>
        </p>
        <p type="main">
          <s id="s.003261">Cvr quando &longs;uper ligno, aut huiu&longs;modi quopiam duo portauerint <lb/>
homines &aelig;quale pondus, non &longs;imiliter grauantur, ni&longs;i quando pon&shy;<lb/>
dus in medio eorum fuerit; &longs;ed magis ille premitur, cui onus vici&shy;<lb/>
nius fuerit? </s>
          <s id="s.003262">An quia lignum illud vectis efficitur, cuius hypomo&shy;<lb/>
clion e&longs;t vbi pondus ge&longs;tatum &longs;u&longs;penditur; ge&longs;tantium autem oneri proxi&shy;<lb/>
mior gerit vicem illius, quod vecte mouetur, remotior ver&ograve; e&longs;t potentia <lb/>
vecte mouens. </s>
          <s id="s.003263">quanto igitur plus di&longs;tat ab hypomoclio, &longs;eu ge&longs;tato ponde&shy;<lb/>
re, tanto facilius mouet, hoc e&longs;t, alterum magis deor&longs;um premit, contra&shy;<lb/>
nitente nimirum ge&longs;tato onere <expan abbr="t&atilde;quam">tanquam</expan> hypomoclio. </s>
          <s id="s.003264">&longs;i autem in medio fue&shy;<lb/>
rit pondus, nihilo magis alter ge&longs;tantium fit id, quod vecte mouetur, qu&agrave;m <lb/>
alter; <expan abbr="neq;">neque</expan> magis mouet: &longs;ed eodem modo alter alteri fit pondus.</s>
        </p>
        <p type="main">
          <s id="s.003265">C&aelig;terum &longs;ciendum huiu&longs;modi lignum, quo tran&longs;uer&longs;o onera <expan abbr="deport&atilde;tur">deportantur</expan> <lb/>
dici &agrave; latinis phalangam, vnde etiam verbum phalangare deducitur, quod <lb/>
huiu&longs;modi ge&longs;tationem &longs;ignificat; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; Vitruuio v&longs;itatum, &amp; Afranio, qui <lb/>
ait, capream vnam &longs;emilaceram quaterni &longs;imul phalangabant.</s>
        </p>
        <p type="head">
          <s id="s.003266"><emph type="italics"/>QV&AElig;STIO XXX.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.003267"><emph type="italics"/>De &longs;urgente &agrave; &longs;e&szlig;ione.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003268"><arrow.to.target n="marg259"/></s>
        </p>
        <p type="margin">
          <s id="s.003269"><margin.target id="marg259"/>269</s>
        </p>
        <p type="main">
          <s id="s.003270">Cvm &longs;edemus, pr&aelig;cipu&egrave; &longs;i commod&egrave; &longs;edeamus, &longs;olemus duos angu&shy;<lb/>
los rectos facere, vnum quidem, quem facit thorax cum femore; <lb/>
alterum quem facit femur cum crure, vt in figura thorax &longs;it A B, <lb/>
<figure id="id.009.01.194.1.jpg" place="text" xlink:href="009/01/194/1.jpg"/><lb/>
femur B C, crus C D, anguli duo recti &longs;unt B, <lb/>
&amp; C. <!-- KEEP S--></s>
          <s id="s.003271">Qu&aelig;rit igitur, cur quando &longs;urgere volumus angu&shy;<lb/>
los ho&longs;ce rectos in acutos commutamus, nam crus re&shy;<lb/>
trahimus &longs;ub femur ad acutum angulum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad po&longs;itio&shy;<lb/>
nem C F. <expan abbr="fit&qacute;">fitque</expan>; acutus angulus B C F. &longs;imiliter thoracem <lb/>
femori aptamus ad acutum angulum E B C, alioquin &longs;ur&shy;<lb/>
gere non valemus? </s>
          <s id="s.003272">An quia id, quod &aelig;quale e&longs;t, quietis <lb/>
<expan abbr="vbiq;">vbique</expan> e&longs;t cau&longs;a, rectus autem angulus e&longs;t angulus &aelig;quali&shy;<lb/>
tatis, <expan abbr="atq;">atque</expan> &longs;tationis? </s>
          <s id="s.003273"><expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> enim angulis rectis con&shy;<lb/>
&longs;tant, vt quadratum, vt cubus, quieti, ac &longs;tationi &longs;unt <lb/>idonea, vt propterea Pytagorei dicerent terram e&longs;&longs;e cubicam, propter ip&shy;<lb/>
&longs;ius immobilitatem. </s>
          <s id="s.003274">e&longs;t autem angulus rectus, angulus &aelig;qualitatis, quia <lb/>
omnes anguli recti &longs;unt inuicem &aelig;quales, vel quia linea illa, qu&aelig; angulum <lb/>
rectum facit e&longs;t perpendicularis alteri line&aelig;, cui incumbit, <expan abbr="&aelig;qualiter&qacute;">&aelig;qualiterque</expan>; in <lb/>
<expan abbr="vtramq;">vtramque</expan> partem inclinata e&longs;t: quapropter fit, vt qu&aelig;cunque con&longs;tituta &longs;int <lb/>&longs;uper &longs;uperficiem terr&aelig; ad angulos rectos non cadant, &longs;ed recta maneant. <lb/>
</s>
          <s id="s.003275">pariter <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ad angulos rectos pauimento incumbunt, non &longs;olum, quia <lb/>cum illo faciant angulos rectos, &longs;ed etiam, quia &longs;imul faciunt cum &longs;uperficie <pb pagenum="195" xlink:href="009/01/195.jpg"/>terr&aelig; perpendiculum. </s>
          <s id="s.003276">An quia qui &longs;urgit fit rectus; rectus autem manens, <lb/>oportet, vt &longs;it &longs;uperficiei terr&aelig; perpendicularis. </s>
          <s id="s.003277">debet igitur e&longs;&longs;e &longs;ecundum <lb/>
eandem rectitudinem, ide&longs;t caput &longs;upra thoracem, thorax ver&ograve; &longs;upra femo&shy;<lb/>
ra, femora ver&ograve; &longs;upra crura in eadem rectitudine, qu&aelig; horizonti perpendi&shy;<lb/>
culariter in&longs;i&longs;tat: quando autem &longs;edemus thorax, &amp; crura, non &longs;unt in ea&shy;<lb/>
dem linea horizonti perpendiculariter erecta, quapropter nece&longs;&longs;e e&longs;t pedes <lb/>
retrahere, caput autem reclinare, vt &longs;ic in eadem recta linea horizonti per&shy;<lb/>
pendiculariter con&longs;tituantur, <expan abbr="hoc&qacute;">hocque</expan>; modo a&longs;&longs;urgere erit po&longs;&longs;ibile.</s>
        </p>
        <p type="main">
          <s id="s.003278"><arrow.to.target n="marg260"/></s>
        </p>
        <p type="margin">
          <s id="s.003279"><margin.target id="marg260"/>270</s>
        </p>
        <p type="main">
          <s id="s.003280">Reliqu&aelig; qu&aelig;&longs;tiones ad Phy&longs;icum &longs;pectant. </s>
          <s id="s.003281">In 33. aperit propriam &longs;en&shy;<lb/>
tentiam de motu proiectorum.</s>
        </p>
        <p type="main">
          <s id="s.003282">In 35. &amp; vltima de vortice quamuis videatur mathematicam &longs;apere, e&longs;t <lb/>
tamen phy&longs;ica. </s>
          <s id="s.003283">Eius autem re&longs;olutiones tres ab Ari&longs;t. allatas, fal&longs;as e&longs;&longs;e <lb/>
&longs;u&longs;picor; experientia enim docet, quod &longs;i quippiam ponatur &longs;upra rotam <lb/>
figuli, id non ad centrum, &longs;ed extra rotam proijcitur. </s>
          <s id="s.003284">&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip&longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>
gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>
illa ad centrum per plures conuolutiones deducantur. </s>
          <s id="s.003285">C&aelig;terum &longs;i quis ve&shy;<lb/>
lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/>
traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>
de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>
grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>
ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003286"><emph type="italics"/>IN LIBELLVM DE MVNDO <lb/>
AD ALEXANDRVM.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003287">Cvm plures libellum hunc Ari&longs;t. attribuant, cogor loca ip&longs;ius ma&shy;<lb/>
thematica ex in&longs;tituto exponere.</s>
        </p>
        <p type="main">
          <s id="s.003288"><arrow.to.target n="marg261"/></s>
        </p>
        <p type="margin">
          <s id="s.003289"><margin.target id="marg261"/>271</s>
        </p>
        <p type="main">
          <s id="s.003290">In 2. cap. recen&longs;et Planetarum ordinem, iuxta antiqui&longs;&longs;imorum <lb/>
A&longs;tronomorum traditiones, qui ob paucas, <expan abbr="eas&qacute;">easque</expan>; imperfectas ob&shy;<lb/>&longs;eruationes multa ignorarunt, <expan abbr="atq;">atque</expan> in multis, &amp; pr&aelig;cipu&egrave; in ordine Plane&shy;<lb/>
tarum &longs;tatuendo, fal&longs;i &longs;unt: A&longs;tronomi enim po&longs;teriores, &amp; maxim&egrave; Ptol&aelig;&shy;<lb/>
meus, vn&agrave; cum recentioribus no&longs;tri &longs;eculi alium ordinem exactioribus ob&shy;<lb/>
&longs;eruationibus, <expan abbr="atq;">atque</expan> demon&longs;trationibus a&longs;truentes vetu&longs;ti&longs;&longs;imorum illorum <lb/>
errores patefecerunt. </s>
          <s id="s.003291">E&longs;t autem verus ordo, vt Luna &longs;it omnium terris pro&shy;<lb/>
xima, deinde Mercurius, t&ugrave;m Venus, po&longs;tea Sol, Mars, Iupiter, <expan abbr="Saturnus&qacute;">Saturnusque</expan>; <lb/>
&agrave; terris alti&longs;&longs;imus, quos omnes &longs;tellarum affixarum &longs;ph&aelig;ra, qu&aelig; etiam fir&shy;<lb/>
mamentum dicitur, complectitur. </s>
          <s id="s.003292">non me latet huius no&longs;tri &longs;eculi di&shy;<lb/>
ligenti&longs;&longs;imos a&longs;tronomos nouam mundani &longs;y&longs;tematis hy&shy;<lb/>
pothe&longs;im inducere; &longs;ed ea pr&aelig;dicto Planctarum <lb/>
ordini parum, aut nihil repugnat.</s>
        </p>
        <pb pagenum="196" xlink:href="009/01/196.jpg"/>
        <p type="head">
          <s id="s.003293"><emph type="italics"/>De &aelig;stu Maris.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003294"><arrow.to.target n="marg262"/></s>
        </p>
        <p type="margin">
          <s id="s.003295"><margin.target id="marg262"/>272</s>
        </p>
        <p type="main">
          <s id="s.003296">In 3. cap. <emph type="italics"/>&lpar;Aiunt etiam multos &aelig;stus vndarumqu&eacute; &longs;ublationes fiatis quibu&longs;&shy;<lb/>dam temporibus cum Luna circumagi&rpar;<emph.end type="italics"/> Perpaucis maris fluxum, &amp; reflu&shy;<lb/>xum attingit, qui quia ex motu pr&aelig;cipu&egrave; Lun&aelig; pendet, non videtur <lb/>
alienum hoc loco eum fu&longs;ius explicare, <expan abbr="atq;">atque</expan> nonnullis difficultatibus <lb/>occurrere, quibus recentiores nonnulli nimis implicantur. </s>
          <s id="s.003297">Ae&longs;tus maris <lb/>
e&longs;t qu&aelig;dam maris ebullitio, ob quam vt &longs;olet in ebullientibus aquis, mare <lb/>
intume&longs;cit: fiunt autem in toto mundo duobus tantum in locis ex hoc &aelig;&longs;tu <lb/>
tumores duo, quorum vnus &longs;emper direct&egrave; Lun&aelig; &longs;ubiacet, alter ver&ograve; in <lb/>
auer&longs;a terr&aelig; parte, &longs;iue huic antipoda, &amp; diametraliter oppo&longs;ita.</s>
        </p>
        <p type="main">
          <s id="s.003298">Ex his Marium tumoribus fit vt aqu&aelig;, qu&aelig; natur&aelig; &longs;ua decliuiora petunt, <lb/>qua&longs;i exundantes ad littora fluant. </s>
          <s id="s.003299">atque hic aquarum cur&longs;us fluxus maris <lb/>
appellatur. </s>
          <s id="s.003300">decre&longs;cente deinde maris &aelig;&longs;tu, &amp; tumore ex rece&longs;&longs;u Lun&aelig;, aqu&aelig; <lb/>
iterum ad medium mare refluunt: <expan abbr="atq;">atque</expan> hic maris refluxus dicitur. </s>
          <s id="s.003301">Cum au&shy;<lb/>
tem in toto die &longs;int 24. hor&aelig; &amp; &longs;emper &longs;int &longs;imul in mundo duo &aelig;&longs;tus, &amp; tu&shy;<lb/>
mores, fit vt &longs;int pariter &longs;emper in mundo duo fluxus, qui tumores illos co&shy;<lb/>
mitantur; necnon duo refluxus, qui eo&longs;dem &longs;ub&longs;equantur; hinc fit vt <expan abbr="vni-cuiq;">vni&shy;<lb/>
cuique</expan> illorum &longs;ex her&aelig; <expan abbr="conueni&atilde;t">conueniant</expan>, &longs;ex fluxui, &longs;ex refluxui, qui &longs;ub Luna fiunt; <lb/>
&longs;ex ver&ograve; fluxui, &amp; &longs;ex tandem refluxui Lun&aelig; auer&longs;is, qu&aelig; totam Lun&aelig; circa <lb/>
mundum periodum 25. horarum expleant. </s>
          <s id="s.003302">Cau&longs;am autem cur mare hoc <lb/>
modo &longs;tatis horis, paul&ograve; tamen &longs;erius ob Lun&aelig; tardiorem ortum &longs;emper <lb/>
cre&longs;cat, &amp; decre&longs;cat antiqui omnes in Lunam retulerunt, vt primus omnium <lb/>
Ari&longs;t. hoc loco, deinde Strabo, Pomponius Mela, Plinius, Solinus, &amp; alij <lb/>
plures idem &longs;en&longs;erunt. </s>
          <s id="s.003303">Lunam &longs;cilicet eam habere vim in mare, vt pars il&shy;<lb/>la, qu&aelig; Lun&aelig; &longs;ubiacet, &longs;iue quam Luna radijs ferit, &aelig;&longs;tuet, &amp; turgeat; non <lb/>
aliter pars maris huic antipoda, &amp; auer&longs;a, quamuis tota terr&aelig; moles inter <lb/>
<figure id="id.009.01.196.1.jpg" place="text" xlink:href="009/01/196/1.jpg"/><lb/>
ip&longs;am, &amp; Lunam interpona&shy;<lb/>
tur, &aelig;&longs;tuat, fluxumque, ac re&shy;<lb/>
fluxum quamuis priori mi&shy;<lb/>
norem, efficit. </s>
          <s id="s.003304">qu&aelig; omnia <lb/>
melius in figura cernentur; <lb/>
vbi infra Lunam vides tumo&shy;<lb/>
rem A, ex quo fluxus deriua&shy;<lb/>
tur. </s>
          <s id="s.003305">&amp; in parte huic auer&longs;a <lb/>
tumorem B, ex quo alter flu&shy;<lb/>
xus deriuatur. </s>
          <s id="s.003306">&amp; quia in alijs <lb/>
duobus mundi lateribus non <lb/>
<expan abbr="fi&utilde;t">fiunt</expan> huiu&longs;modi tumores, im&ograve; <lb/>
mare ob refrigerationem <lb/>
&longs;ub&longs;idet, ibi fiunt duo reflu&shy;<lb/>
xus C, &amp; D, ita vt &longs;emper &longs;int <lb/>
in mari pr&aelig;&longs;ertim Oceano <lb/>
quatuor pr&aelig;dicti effectus, qui <lb/>
&longs;imul, vt ait hic Ari&longs;t. &amp; ex&shy;


<pb pagenum="197" xlink:href="009/01/197.jpg"/>perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s>
          <s id="s.003307">hoc e&longs;t <lb/>
&longs;i Luna, qu&aelig; modo e&longs;t in &longs;uperiori parte meridionali, venerit ad locum E, <lb/>occidentalem, eam fluxus A, &longs;ub&longs;equitur, <expan abbr="vergit&qacute;">vergitque</expan>; tumorem &longs;uum ad occi&shy;<lb/>
dentem E, vnde, &amp; fluxus B, promouebitur ad orientem, ita vt punctum F, <lb/>
orientalem a&longs;piciat.</s>
        </p>
        <p type="main">
          <s id="s.003308">Alij pr&aelig;terea duo refluxus eadem proportione promoti erunt, vbi prius <lb/>
erant fluxus: qu&aelig; <expan abbr="con&longs;equ&etilde;tia">con&longs;equentia</expan> ad Lunam perpetua, manife&longs;tum e&longs;t, &longs;ignum, <lb/>ho&longs;ce fluxus, ac refluxus non aliunde qu&agrave;m &agrave; Luna manare. </s>
          <s id="s.003309">quod adhuc ma&shy;<lb/>
nife&longs;tius erit, &longs;i con&longs;ideremus, quod quanto tardius quotidie Luna oritur, <lb/>
tanto etiam maris &aelig;&longs;tus tardius incipit. </s>
          <s id="s.003310">Porr&ograve; vt appareat hanc e&longs;&longs;e vete&shy;<lb/>
rum &longs;ententiam libet hic attexere qu&aelig;dam ex lib. 3. Strabonis, qu&aelig; ip&longs;e ex <lb/>
Po&longs;&longs;idonio acceperat. </s>
          <s id="s.003311">&longs;ic. </s>
          <s id="s.003312">Oceani ver&ograve; motum ait, &longs;cilicet Po&longs;&longs;idonius, &longs;y&shy;<lb/>
deris &longs;ubire circuitum, quendam quidem diurnum, quendam men&longs;truum, <lb/>
quendam annuum, vt Lun&aelig; etiam contingit. </s>
          <s id="s.003313">quo etiam tempore i&longs;ta &longs;uper <lb/>
horizontem a&longs;cenderit, mare terram a&longs;cendere incipit, &longs;en&longs;u te&longs;te, <expan abbr="quou&longs;q;">quou&longs;que</expan> <lb/>
ad c&oelig;li medium Luna con&longs;cenderit. </s>
          <s id="s.003314">Vbi ver&ograve; declinare &longs;ydus ip&longs;um c&oelig;&shy;<lb/>
perit, &longs;en&longs;im rur&longs;us &agrave; terra pelagus ad medium mare reuertitur, donec ad <lb/>occidentis punctum Luna de&longs;cenderit. </s>
          <s id="s.003315">deinde tanto eadem incon&longs;tantia <lb/>tempore manet, quanto Luna ad ip&longs;um occa&longs;um coniungitur, &amp; adhuc tan&shy;<lb/>to magis, quanto &longs;ub terram mota, &longs;ignum ab horizonte di&longs;tet. </s>
          <s id="s.003316">po&longs;tea rur&shy;<lb/>&longs;us mare a&longs;cendere, quou&longs;que &longs;ub tellurem in medio c&oelig;li &longs;it Luna, deinde <lb/>
mare &agrave; littore regredi quoad iterum Luna in orientem procedat, ac &longs;upra <lb/>horizontem eleuetur, con&longs;i&longs;tere ver&ograve; v&longs;que quo &longs;ignum &longs;upra terram eleue&shy;<lb/>
tur, &amp; rur&longs;us terras mare a&longs;cendere. </s>
          <s id="s.003317">Hanc diurnam e&longs;&longs;e circuitionem a&longs;&longs;e&shy;<lb/>
rit Po&longs;&longs;idonius, men&longs;truam ver&ograve;, &amp;c. </s>
          <s id="s.003318">vbi pergit explicare, qua ratione, ma&shy;<lb/>ria etiam alijs motibus men&longs;truo. </s>
          <s id="s.003319">&longs;cilicet, &amp; annuo cieantur, iuxta Lun&aelig; <lb/>
periodos men&longs;truam, &amp; annuam. </s>
          <s id="s.003320">Eadem omnin&ograve; habet Plinius, &amp; alij ve&shy;<lb/>
teres omnes, quos tu con&longs;ulere poteris vnde mirum videri debeat, cur re&shy;<lb/>
centiores plurimi, <expan abbr="neq;">neque</expan> veterum auctoritate, <expan abbr="neq;">neque</expan> ratione, aut experientia <lb/>
nixi, hanc maris affectionem, &agrave; Luna effici negarint.</s>
        </p>
        <p type="main">
          <s id="s.003321">Verum ip&longs;i duabus poti&longs;&longs;imum rationibus id negant.</s>
        </p>
        <p type="main">
          <s id="s.003322">Prima e&longs;t, quod vario admodum tempore, &amp; modo in diuer&longs;is fiant ma&shy;<lb/>
ribus, &amp; in nonnullis nihil horum &aelig;&longs;tuum appareat.</s>
        </p>
        <p type="main">
          <s id="s.003323">Huic re&longs;pondendum e&longs;t, id ex varia marium di&longs;po&longs;itione, tum etiam va&shy;<lb/>rio &longs;itu, quo Lunam a&longs;piciunt prouenire. </s>
          <s id="s.003324">hoc modo videmus vario tempo&shy;<lb/>
re, &amp; modo, in toto orbe effici dies, ac noctes, &aelig;&longs;tatem, &amp; hyemem; &amp; ta&shy;<lb/>
men certum e&longs;t Solem i&longs;ta omnia efficere. </s>
          <s id="s.003325">Sed melius etiam huic dubita&shy;<lb/>
tioni occurremus certa quadam, <expan abbr="atq;">atque</expan> omnin&ograve; explorata experientia ex ar&shy;<lb/>
te Nautica de&longs;umpta. </s>
          <s id="s.003326">libri enim nautici ab&longs;que vlla dubitatione Lun&aelig; h&aelig;c <lb/>omnia ver&egrave; a&longs;cribunt, dum qua&longs;dam regulas tradunt, eas tamen pro varijs <lb/>maribus varias, quibus per &aelig;tatem Lun&aelig;, &amp; &longs;itum ip&longs;ius &longs;upra horizontem <lb/>
illius maris cert&ograve; certius horam fluxus; &amp; refluxus, im&ograve; eorum etiam ma&shy;<lb/>gnitudinem pr&aelig;no&longs;cunt, ac pr&aelig;dicunt. </s>
          <s id="s.003327">huiu&longs;modi librum vidi ego Parm&aelig;, <lb/>
manu &longs;criptum, auctore Augu&longs;tino C&aelig;&longs;areo, quem ille olim Sereni&longs;s. <!-- REMOVE S-->Duci <lb/>
Octauio dono dederat. </s>
          <s id="s.003328">quod &longs;i hi &aelig;&longs;tus &agrave; Luna minim&egrave; penderent, nulla ra&shy;<lb/>tione regul&aelig; ill&aelig; effici potui&longs;&longs;ent, quibus per &aelig;tatem ip&longs;ius, ac &longs;itum &longs;upra <lb/>
horizontem eos pr&aelig;dicere tuto valerent.</s>
        </p>
        <pb pagenum="198" xlink:href="009/01/198.jpg"/>
        <p type="main">
          <s id="s.003329">Secunda ver&ograve; ratio, qu&aelig; maxim&egrave; eos torquet e&longs;t quanam ratione &agrave; Luna <lb/>
effici po&longs;&longs;it &longs;ecundus refluxus B, prim&ograve; oppo&longs;itus, cum tota terr&aelig; moles in&shy;<lb/>
teriecta ob&longs;tare videatur.</s>
        </p>
        <p type="main">
          <s id="s.003330">Verum huic difficultati optim&egrave; ex opticis &longs;atisfacere po&longs;&longs;umus, fi dixe&shy;<lb/>
rimus, &aelig;&longs;tum illum effici quidem &agrave; Luna, &amp; Sole, &longs;ed tamen per lumen ex <lb/>
&longs;yderibus ad partem illam auer&longs;am reflexum; quod vt melius explicetur, &amp; <lb/>
confirmetur. </s>
          <s id="s.003331">Illud prim&ograve; &longs;ciendum non &longs;olam Lunam, verum etiam Solem <lb/>ad &aelig;&longs;tum maris ciendum concurrere, quamuis primas in hoc Lun&aelig; conce&shy;<lb/>
dat; experientia enim con&longs;tat maiorem fieri fluxum, quando Sol, &amp; Luna <lb/>
&longs;imul &longs;unt coniuncta, vt in nouilunio accidit, quia lumina, &amp; eorum virtu&shy;<lb/>
tes vnit&aelig; fortius eandem maris partem directis radijs percellunt. </s>
          <s id="s.003332">&longs;imiliter <lb/>
maior fit, quando luminaria &longs;unt oppo&longs;ita, vt in plenilunio contingit, quia <lb/>
tunc radij vnius directi, a&longs;&longs;ociantur cum reflexis alterius radijs, <expan abbr="hoc&qacute;">hocque</expan>; mo&shy;<lb/>
do duplicati ea&longs;dem terr&aelig; partes, &amp; direct&egrave;, &amp; reflex&egrave; feriunt, vt melius in <lb/>
&longs;equenti figura patebit.</s>
        </p>
        <p type="main">
          <s id="s.003333">Secund&ograve; pr&aelig;mittendum e&longs;t, lumen Solis, &amp; Lun&aelig; reflecti ex den&longs;is, ac per&shy;<lb/>politis corporibus, vti &longs;unt omnia &longs;ydera.</s>
        </p>
        <p type="main">
          <s id="s.003334">Terti&ograve;, ex opticis a&longs;&longs;umendum, &longs;i corpora plurima &longs;ph&aelig;rica lumen re&shy;<lb/>flectentia fuerint in circulari ambitu con&longs;tituta, quemadmodum &longs;unt &longs;tell&aelig; <lb/>
affix&aelig; in ambitu firmamenti collocat&aelig;, reflectere <expan abbr="plurim&utilde;">plurimum</expan> lumen ad vnum, <lb/>
&amp; idem punctum, quod &longs;it inter lumen, &amp; ambitum illum; quod a&longs;&longs;umptum <lb/>
manife&longs;tum e&longs;t ex Iride, vbi ex plurimis &longs;ph&aelig;ricis guttulis lumen Solis re&shy;<lb/>
flectitur ad oculum; quamuis geometric&egrave;, &amp; quidem facil&egrave; &agrave; Per&longs;pectiuo <lb/>
demon&longs;trari po&longs;&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.003335">Quart&ograve;, ex opticis, dato corpore lumino&longs;o, &amp; &longs;ph&aelig;rico reflectente, &amp; <lb/>
puncto quouis, ad quod po&longs;&longs;it reflecti lumen, pote&longs;t inueniri in &longs;ph&aelig;ra refle&shy;<lb/>
ctente punctum reflexionis.</s>
        </p>
        <p type="main">
          <s id="s.003336">Quint&ograve;, quanto radij perpendiculariores incidunt, tanto maiorem <lb/>
vim habere.</s>
        </p>
        <p type="main">
          <s id="s.003337">Sit erg&ograve; Sol, &amp; Luna &longs;imul, vt in figura <expan abbr="&longs;it&qacute;">&longs;itque</expan>; octau&aelig; &longs;ph&aelig;r&aelig; portio A B C, <lb/>
cum innumeris in ea affixis &longs;yderibus. </s>
          <s id="s.003338">e&longs;&longs;e autem totum c&oelig;lum &longs;tellis pen&egrave; <lb/>
infinitis, ac con&longs;tipatis refertum &longs;en&longs;ui palam fit, adhibito nouo illo, ac mi&shy;<lb/>
rabili Tele&longs;copij inuento.</s>
        </p>
        <p type="main">
          <s id="s.003339">Iam, vt patet ex 39.5. Alhazeni, ex &longs;ingulis &longs;tellis Solis, ac Lun&aelig; lumen <lb/>
reflecti pote&longs;t &lpar;ni&longs;i quid ob&longs;tet&rpar; ad partem terr&aelig; D, luminaribus auer&longs;am, <lb/>
vt quarto loco &longs;uppo&longs;ui. </s>
          <s id="s.003340">&amp; pr&aelig;terea ex &longs;tellis circa B, po&longs;itis radij Solis re&shy;<lb/>
percuti po&longs;&longs;unt ad eandem terr&aelig; partem D, perpendiculares, qui pr&aelig; c&aelig;te&shy;<lb/>
ris maximam vim obtinent. </s>
          <s id="s.003341">quemadmodum line&aelig; in figura reflex&aelig; <expan abbr="vtcunq;">vtcunque</expan> <lb/>
o&longs;tendunt, ide&ograve; a&longs;&longs;erendum e&longs;t eos, &aelig;&longs;tum D, excitare pr&aelig;cipu&egrave; po&longs;&longs;e, <expan abbr="neq;">neque</expan> <lb/>
terr&aelig; quantitas Solis luci obe&longs;t, cum con&longs;tet vmbram terr&aelig; parum &longs;upra <lb/>
Lun&aelig; c&oelig;lum produci. </s>
          <s id="s.003342">pote&longs;t tamen Lun&aelig; e&longs;&longs;e impedimento quoad hos ra&shy;<lb/>
dios perpendiculares; &longs;ed tamen alios minus perpendiculares, &longs;eu parum <lb/>
obliquos nullo modo impedire pote&longs;t, quo minus ad D, re&longs;iliant. </s>
          <s id="s.003343">qui quam&shy;<lb/>
uis &longs;int minus qu&agrave;m perpendiculares efficaces, obtinent tamen non modi&shy;<lb/>
cam vim. </s>
          <s id="s.003344">Ex &longs;tellis igitur circa A, &amp; C, reflecti pote&longs;t ex quarto fundamen&shy;<lb/>
to lumen <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> luminaris ad D, quod &longs;atis e&longs;t efficax, c&ugrave;m fer&egrave; perpendi&shy;


<pb pagenum="199" xlink:href="009/01/199.jpg"/><figure id="id.009.01.199.1.jpg" place="text" xlink:href="009/01/199/1.jpg"/><lb/>
culariter terr&aelig; D, incidat. </s>
          <s id="s.003345">quamuis autem ex &longs;tellis F, E, lumen aliquod ad <lb/>
D, tran&longs;mittatur, tamen cum obliqu&egrave; admodum illi accidat, nihil pen&egrave; ef&shy;<lb/>
ficere valet. </s>
          <s id="s.003346">Verumenimuer&ograve; qui&longs;piam in hunc modum obijciet: hac ra&shy;<lb/>
tione deberet fieri etiam &aelig;&longs;tus in terr&aelig; lateribus H, I, quando quidem etiam <lb/>
illuc lumen ex quarto fundamento reflecti pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.003347">Cui &longs;ic re&longs;pondendum, po&longs;&longs;e quidem aliquod lumen illuc re&longs;ilire, &longs;ed ta&shy;<lb/>
men exiguum admodum, &amp; proinde nullius pen&egrave; roboris, quod experientia <lb/>
de&longs;umpta ex illuminatione Lun&aelig; comprobari pote&longs;t; videmus enim, quod <lb/>
quanto Luna magis Soli opponitur, &amp; proinde &longs;uam illuminationem magis <lb/>
ver&longs;us terram obuertit, vt in plenilunio, tanto maiorem eam vim habere <lb/>
&aelig;&longs;tus excitandi. </s>
          <s id="s.003348">multo ver&ograve; minorem, quando e&longs;t in a&longs;pectu Solis quadrato, <lb/>
quia dimidiam tantum &longs;ui illuminationem nobis reflectit. </s>
          <s id="s.003349">Idem proportio&shy;<lb/>
naliter de &longs;tellis dicendum, qu&aelig; enim luminari maxim&egrave; opponuntur, vt qu&aelig; <lb/>
&longs;unt circa B, ill&aelig; totam illuminationem terr&aelig; o&longs;tendunt, vnde, &amp; efficacio&shy;<lb/>
res &longs;unt. </s>
          <s id="s.003350">c&aelig;ter&aelig;, quo magis ab illis di&longs;tant minus de &longs;ua illuminatione ter&shy;<lb/>
r&aelig;, &longs;eu mari <expan abbr="obuert&utilde;t">obuertunt</expan>, &amp; proinde minus efficiunt. </s>
          <s id="s.003351">vnde fit, vt quamuis non&shy;<lb/>
nulli radij etiam perpendiculares ad terr&aelig; latera H, I, referri po&longs;&longs;int, tamen <lb/>
quia pauciores &longs;unt, qu&agrave;m alibi, propterea nullam ibi &aelig;&longs;tus <expan abbr="prouoc&atilde;di">prouocandi</expan> vim <lb/>
obtinent. </s>
          <s id="s.003352">&longs;ydera porr&ograve; illa, qu&aelig; &longs;upra Solem exi&longs;tunt, etiam &longs;i ip&longs;orum illu&shy;


<pb pagenum="200" xlink:href="009/01/200.jpg"/>minatio tota ad terras vergat, tamen in lateribus terr&aelig; pr&aelig;dictis nihil ef&shy;<lb/>
ficiunt, quia in illa vel obliqu&egrave; admodum radij incidunt, vel ea tantummo&shy;<lb/>
do tangunt. </s>
          <s id="s.003353">Verum illuminatione &longs;ua ea&longs;dem maris partes, qu&aelig; &longs;unt ad G, <lb/>
vn&agrave; cum Sole, ac Luna percellunt.</s>
        </p>
        <p type="main">
          <s id="s.003354">Ex quibus apparet duas tantum orbis terr&aelig; partes totis, ac plenis a&longs;tro&shy;<lb/>rum luminibus impeti, in quibus &longs;cilicet duo oppo&longs;iti &aelig;&longs;tus ebulliunt.</s>
        </p>
        <p type="main">
          <s id="s.003355">Idem po&longs;&longs;umus hoc modo confirmare, quia cum totum firmamentum &longs;it <lb/>
innumeris pen&egrave; &longs;yderibus &longs;tipatum, loco concaui, ac &longs;ph&aelig;ri&ccedil;i &longs;peculi ha&shy;<lb/>
beri pote&longs;t, &amp; proinde illius in&longs;tar amborum luminarium lumen reflectere; <lb/>
qua ratione patet omnem fer&egrave; ad partes pr&aelig;dictas D, emitti reflexionem.</s>
        </p>
        <p type="main">
          <s id="s.003356">His rationibus manife&longs;tum e&longs;&longs;e patet pr&aelig;dictum &aelig;&longs;tus tumorem lumina&shy;<lb/>
ribus auer&longs;um, <expan abbr="atq;">atque</expan> antipodum ex pr&aelig;dicta reflexione exurgere.</s>
        </p>
        <p type="main">
          <s id="s.003357">Po&longs;&longs;et etiam qui&longs;piam &longs;ic opponere, &longs;i illuc pr&aelig;dicta luminum reflexio <lb/>
pertineret, non &longs;olum illam aquarum ebullitionem efficeret, verum etiam <lb/>
lucem aliquam e&ograve;dem afferret, quod tamen &longs;en&longs;u minim&egrave; apparet. </s>
          <s id="s.003358">cui &longs;ic <lb/>
re&longs;pondendum videtur, nece&longs;&longs;arium non e&longs;&longs;e, vt reflexio illa, qu&aelig; hoc modo <lb/>
mare afficit tanta &longs;it, vt etiam illud luce &longs;olito maiori afficiat; quod <expan abbr="expe-ri&etilde;tia">expe&shy;<lb/>
rientia</expan> con&longs;tat in alijs c&etail;li influxibus: qu&agrave;m &longs;&aelig;p&egrave; enim Luna nubilo&longs;o etiam <lb/>tempore, fluxum, ac refluxum priorem parit, cum tamen nullam tunc lu&shy;<lb/>
cem nobis afferat? </s>
          <s id="s.003359">quamuis enim lumen &longs;tellarum &longs;uperficiem maris non <lb/>
attingat, attingit tamen &longs;uperficiem vaporum, exhalationum, ac nubium, <lb/>
qu&aelig; terram in &longs;ph&aelig;r&aelig; modum ambiunt, ac parum &agrave; terra <expan abbr="circumquaq;">circumquaque</expan> at&shy;<lb/>
tolluntur: quem exhalationum ambitum deinde luminarium virtus facil&egrave; <lb/>
penetrare pote&longs;t. </s>
          <s id="s.003360">Nullum pr&aelig;terea lumen apparet, quia lumen reflexum <lb/>
pr&aelig;&longs;ertim ex conuexis corporibus, vt &longs;unt &longs;tell&aelig;, valde debile e&longs;t, quia <expan abbr="con-uex&utilde;">con&shy;<lb/>
uexum</expan> illud reflectendo non vnit, &longs;ed di&longs;gregat, contra quam facit concauum.</s>
        </p>
        <p type="main">
          <s id="s.003361">Tandem qu&aelig;rere quis po&longs;&longs;et, cur &aelig;&longs;tus hic &longs;ecundus minor &longs;it priori. </s>
          <s id="s.003362">Cui <lb/>
re&longs;pondendum, quia ille &agrave; directis radijs, hic ver&ograve; &agrave; reflexis progignitur: <lb/>
radios autem reflexos debiliores e&longs;&longs;e directis optici docent, <expan abbr="atq;">atque</expan> experien&shy;<lb/>
tia confirmat.</s>
        </p>
        <p type="main">
          <s id="s.003363">Porr&ograve; quando luminaria &longs;unt oppo&longs;ita, vt &longs;i Luna e&longs;&longs;et in B, Sol ver&ograve; in K, <lb/>
tunc maximus fit <expan abbr="vterq;">vterque</expan> fluxus, quia radij directi <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> vniuntur cum ra&shy;<lb/>
dijs reflexis alterius; ita vt <expan abbr="vterq;">vterque</expan> &aelig;&longs;tus fiat, &amp; per radium reflexum, &amp; per <lb/>
directum &longs;imul, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;&longs;tus, qui Lun&aelig; &longs;ubiacet fit per radium Lun&aelig; directum, <lb/>
&amp; quia Sol e&longs;t in oppo&longs;itione cum Luna, &longs;it vt ip&longs;ius radij reflectantur, &amp; <lb/>
vniantur cum directis Lun&aelig; ad eundem tumorem excitandum. </s>
          <s id="s.003364">&longs;imiliter in&shy;<lb/>
fra Solem direct&egrave; alius fit &agrave; directis ip&longs;ius radijs; &amp; quia Luna ei opponitur <lb/>
lumen eius ad <expan abbr="v&longs;q;">v&longs;que</expan> &longs;ydera pertinens reuertitur, <expan abbr="vna&qacute;">vnaque</expan>; cum directa Solis lu&shy;<lb/>
ce ad eundem efficiendum concurrit.</s>
        </p>
        <p type="main">
          <s id="s.003365">Exi&longs;tentibus demum luminaribus circa quadratum a&longs;pectum, vt &longs;i Luna <lb/>
e&longs;&longs;et in F, Sole exi&longs;tente in K. exiguus, ac pen&egrave; nullus fit fluxus, quia eorum <lb/>
vires non &longs;unt vnit&aelig;, c&ugrave;m radij nec incidentes, nec reflexi vniantur im&ograve; vi&shy;<lb/>res eorum &longs;eparat&aelig; maria in contrarias partes di&longs;trahunt, vnde fit, vt neu&shy;<lb/>
tro alteri concedente, apud neutrum victoria con&longs;tet.</s>
        </p>
        <p type="main">
          <s id="s.003366"><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t mea de &aelig;&longs;tu maris per reflexionem &longs;ententia. </s>
          <s id="s.003367">quam iamdiu <lb/>
inuentam, <expan abbr="atq;">atque</expan> auditoribus meis &longs;&aelig;pius explicatam, reperi tandem non &longs;ine <pb pagenum="201" xlink:href="009/01/201.jpg"/>gaudio fui&longs;&longs;e etiam &longs;ubtili&longs;&longs;imi Scoti opinionem, quam ip&longs;e breuiter in pri&shy;<lb/>
mum &longs;ent. </s>
          <s id="s.003368">de creatione mundi tantummodo &longs;ine vlla expo&longs;itione, <expan abbr="atq;">atque</expan> con&shy;<lb/>
firmatione proponit. </s>
          <s id="s.003369">in eadem pror&longs;us &longs;ententia e&longs;t Rogerius Bachon inter <lb/>
Opticos probati&longs;&longs;imus, cap. 5. de Speculis Mathematicis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003370">Aliorum demum opinationes, &longs;iue Angelo cuidam, &longs;iue virtuti totam <lb/>
terram peruadenti hunc &aelig;&longs;tum a&longs;cribentium, non e&longs;t meum refellere, cum <lb/>
non phy&longs;icum, &longs;ed mathematicum agere in&longs;tituerim.</s>
        </p>
        <p type="main">
          <s id="s.003371"><arrow.to.target n="marg263"/></s>
        </p>
        <p type="margin">
          <s id="s.003372"><margin.target id="marg263"/>273</s>
        </p>
        <p type="main">
          <s id="s.003373">Cap. 7. <emph type="italics"/>&lpar;Quod Imagunculas animatas e&longs;&longs;e, &amp;c.&rpar;<emph.end type="italics"/> huiu&longs;modi imagines, &amp; <lb/>
&longs;tatuas, qu&aelig; &longs;pont&egrave; mouebantur Gr&aelig;ci appellarunt Automata, ide&longs;t &longs;pon&shy;<lb/>
tanea, cuiu&longs;modi &longs;unt automata Heronis, Alexandrini, qu&aelig; adhuc extant.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003374"><emph type="italics"/>IN LIBELLVM <lb/>
De admirandis auditionibus.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003375"><arrow.to.target n="marg264"/></s>
        </p>
        <p type="margin">
          <s id="s.003376"><margin.target id="marg264"/>274</s>
        </p>
        <p type="main">
          <s id="s.003377">Nvmero 82. Qu&aelig; de illa in&longs;ula extra Herculis columnas &longs;ita narrat, <lb/>
eam putant recentiores Geographi, &amp; quidem merit&ograve; nouo orbi <lb/>
conuenire.</s>
        </p>
        <p type="main">
          <s id="s.003378"><arrow.to.target n="marg265"/></s>
        </p>
        <p type="margin">
          <s id="s.003379"><margin.target id="marg265"/>275</s>
        </p>
        <p type="main">
          <s id="s.003380">Numero 100. Qu&aelig; de I&longs;tro, &longs;iue Dannubio tradit, eum &longs;cilicet <lb/>
e&longs;&longs;e bifidum, <expan abbr="altero&qacute;">alteroque</expan>; ramo in Pontum, altero ver&ograve; in Mediterraneum ex&shy;<lb/>
onerari: &longs;unt contra omnes recentiores Geographos; apparet tamen eam <lb/>
fui&longs;&longs;e veterum nonnullorum opinionem, quos <expan abbr="&longs;e&qacute;uutus">&longs;equutus</expan> Ari&longs;t. deceptus e&longs;t, <lb/>
&agrave; quibus etiam mult&ograve; po&longs;t fal&longs;i &longs;unt Diodorus, Pomponius, &amp; Solinus, qui <lb/>
I&longs;trum I&longs;tri&aelig; Prouinc&igrave;&aelig; fluuium faciunt, quem ex I&longs;tro Germani&aelig; veluti ra&shy;<lb/>
mum contra omnem veritatem deriuant. </s>
          <s id="s.003381">Ver&ugrave;m hoc illis condonandum <lb/>
pr&aelig;&longs;ertim antiquioribus, cum tunc temporis Geographia parum e&longs;&longs;et <lb/>
exculta.</s>
        </p>
        <p type="main">
          <s id="s.003382">Primus Strabo hanc fal&longs;itatem libro 1. redarguit, &amp; po&longs;t ip&longs;um Plinius <lb/>
I&longs;trum i&longs;tum fabulo&longs;um appellat.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003383"><emph type="italics"/>IN LIBELLVM <lb/>
De lineis in&longs;ecabilibus, &longs;iue indiuiduis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003384"><arrow.to.target n="marg266"/></s>
        </p>
        <p type="margin">
          <s id="s.003385"><margin.target id="marg266"/>276</s>
        </p>
        <p type="main">
          <s id="s.003386">Di&longs;putat libellus hic &longs;an&egrave; acuti&longs;&longs;imus, Vtrum quantitas con&longs;tet ex <lb/>
indiui&longs;ibilibus, quam qu&etail;&longs;tionem recentiores agitant in Phy&longs;icis <lb/>
tractatione de Quantitate; <expan abbr="atq;">atque</expan> hinc nonnulla &longs;umunt argumen&shy;<lb/>
ta: plura &longs;umpturi ni&longs;i operis ob&longs;curitas, &amp; mathematicarum, <lb/>
ignoratio hactenus ob&longs;titi&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.003387">Sciendum igitur primo loco, nos po&longs;&longs;e duo indiui&longs;ibilium genera in quan&shy;<lb/>
titate concipere. </s>
          <s id="s.003388">primum eorum, qu&aelig; ver&egrave; indiuidua &longs;unt, <expan abbr="nullas&qacute;">nullasque</expan>; habent <lb/>partes, &longs;iue nullo modo &longs;unt quanta; cuiu&longs;modi e&longs;t <expan abbr="punct&utilde;">punctum</expan> mathematicum.</s>
        </p>
        <p type="main">
          <s id="s.003389">Alterum quorumdam indiui&longs;ibilium quidem, &longs;ed tamen quantorum cu&shy;<lb/>
iu&longs;modi e&longs;&longs;ent, qu&aelig;dam ade&ograve; minim&aelig; line&aelig;, qu&aelig; omnem effugiant diui&longs;io&shy;<lb/>nem: ex quibus antiqui opinabantur lineas totales, ac diuiduas componi. <lb/>
</s>
          <s id="s.003390">atque de hoc &longs;ecundo indiuiduorum, quantorum genere videtur opu&longs;culum <pb pagenum="202" xlink:href="009/01/202.jpg"/>i&longs;tud di&longs;&longs;erere. </s>
          <s id="s.003391">&amp; quia partim rationibus phy&longs;icis, partim geometricis vti&shy;<lb/>
tur, ide&ograve; nec omnin&ograve; phy&longs;icus nec omnin&ograve; mathematicus e&longs;t. </s>
          <s id="s.003392">Ego igitur, <lb/>qu&aelig; mathematica &longs;unt, ex in&longs;tituto exponere aggrediar.</s>
        </p>
        <p type="main">
          <s id="s.003393">Ad intelligentiam igitur huius operis nece&longs;&longs;arium e&longs;t noui&longs;&longs;e, qu&aelig; nam <lb/>
&longs;int quantitates commen&longs;urabiles, &amp; qu&aelig; in commen&longs;urabiles. </s>
          <s id="s.003394">qu&aelig; prima, <lb/>
&amp; &longs;ecunda definitione 10. Elem. explicantur; <expan abbr="ego&qacute;">egoque</expan>; eas primo Priorum oc&shy;<lb/>
ca&longs;ione a&longs;ymetri&aelig; diametri cum co&longs;ta &longs;atis expo&longs;ui: vtrumuis locum vide&shy;<lb/>
ris pr&aelig;&longs;enti nece&longs;&longs;itati con&longs;ultum erit.</s>
        </p>
        <p type="main">
          <s id="s.003395"><arrow.to.target n="marg267"/></s>
        </p>
        <p type="margin">
          <s id="s.003396"><margin.target id="marg267"/>277</s>
        </p>
        <p type="main">
          <s id="s.003397">Primus locus Mathematicus e&longs;t hic <emph type="italics"/>&lpar;Po&longs;trem&ograve; ex ijs, qu&aelig; tradunt Mathe&shy;<lb/>
maticis imbuti di&longs;ciplinis, quiuis lineam aliquam in&longs;ecabilem e&longs;&longs;e concedet. </s>
          <s id="s.003398">nam <lb/>
&longs;i, vt aiunt, ill&aelig; commen&longs;urabiles &longs;unt line&aelig;, qu&aelig; eadem men&longs;ura dimetiri queunt, <lb/>&amp; nihil impedit, quin omnes commen&longs;urabiles re ip&longs;a dimetiantur, extabit profe&shy;<lb/>
ct&ograve; longitudo aliqua, qua omnes commen&longs;urabuntur; qu&aelig; nece&longs;&longs;ario erit indiuidua, <lb/>
nam &longs;i dicatur e&longs;&longs;e diuidua, huius <expan abbr="quoq;">quoque</expan> men&longs;ur&aelig; partes, men&longs;uram aliquam com&shy;<lb/>
munem habebunt, partes enim toti commen&longs;urabiles &longs;unt ita, vt portio partis il&shy;<lb/>
lius, qu&aelig; dimidium totius fuerat, efficiatur dupla alterius; quoniam autem hoc <lb/>
fieri nequit, atoma debet e&longs;&longs;e men&longs;ura h&aelig;c communis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003399"><emph type="italics"/>Eodem modo, &amp; qu&aelig; &longs;imul ab ip&longs;a men&longs;ura commen&longs;urat&aelig;, tanquam omnes ex <lb/>
ea men&longs;ura compo&longs;it&aelig; &longs;unt line&aelig;, veluti ex atomis conflantur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003400">Affert rationem quandam ex Mathematicis, qua nonnulli probabant ex&shy;<lb/>
tare lineas atomas, ex quibus c&aelig;ter&aelig; line&aelig; tanquam partibus con&longs;tarent: <lb/>
ac proinde negabant lineas e&longs;&longs;e in infinitum diuiduas, &longs;eu quamlibet lineam <lb/>
&longs;ecari po&longs;&longs;e, &longs;ed a&longs;&longs;erebant <expan abbr="diuid&etilde;do">diuidendo</expan>, tandem ad indiuiduas <expan abbr="deueniend&utilde;">deueniendum</expan> e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.003401">Pr&aelig;mi&longs;&longs;a igitur, vt monui commen&longs;urabilium, &amp; incommen&longs;urabilium <lb/>
linearum cognitione in hunc modum, &amp; textum Ari&longs;tot. &amp; rationem ip&longs;o&shy;<lb/>
rum exponam.</s>
        </p>
        <p type="main">
          <s id="s.003402">Mathematici o&longs;tendunt extare lineas commen&longs;urabiles, qu&aelig; &longs;cilicet ea&shy;<lb/>
dem communi men&longs;ura men&longs;urantur: at nihil impedit quin omnes <expan abbr="c&otilde;men-&longs;urabiles">commen&shy;<lb/>
&longs;urabiles</expan> re ip&longs;a men&longs;urentur, debet erg&ograve; extare vna aliqua longitudo, qua <lb/>
omnes commen&longs;urabiles dimetiamur. </s>
          <s id="s.003403">hanc autem nece&longs;&longs;e e&longs;t e&longs;&longs;e atomam, <lb/>
nam &longs;i diuidua &longs;tatuatur, poterit &longs;emper &longs;ecari, &amp; &longs;ub&longs;ecari bifariam, qua&shy;<lb/>
re cum partes huiu&longs;modi &longs;int toti commen&longs;urabiles, &longs;equetur aliam exi&longs;tere <lb/>
men&longs;uram, qua omnes h&aelig; partes, &amp; proinde tota linea commen&longs;urentur. <lb/>
</s>
          <s id="s.003404">Ver&ugrave;m hoc fieri nequit, nam hoc pacto non e&longs;&longs;et vna tantum longitudo om&shy;<lb/>
nium commen&longs;urabilium linearum communis men&longs;ura, ver&ugrave;m plures, &amp; <lb/>
plures in infinitum, quod e&longs;t contra Mathematicorum placita. </s>
          <s id="s.003405">dicendum, <lb/>
itaque, communem illam omnium men&longs;uram e&longs;&longs;e omnis diui&longs;ionis exper&shy;<lb/>
tem; &amp; propterea etiam lineas omnes commen&longs;urabiles ex atomis lineis <lb/>
componi, qu&aelig; nimirum pr&aelig;dict&aelig; communi men&longs;ur&aelig; &aelig;quales &longs;int. </s>
          <s id="s.003406"><expan abbr="atq;">atque</expan> h&aelig;c <lb/>
e&longs;t illarum prima argumentatio.</s>
        </p>
        <p type="main">
          <s id="s.003407"><arrow.to.target n="marg268"/></s>
        </p>
        <p type="margin">
          <s id="s.003408"><margin.target id="marg268"/>278</s>
        </p>
        <p type="main">
          <s id="s.003409">Secundus locus <emph type="italics"/>&lpar;Idem etiam contingit in figuris planis, qu&aelig; &agrave; lineis rationa&shy;<lb/>
libus procreantur: nam omnes huiu&longs;modi figur&aelig; erunt etiam inuicem commen&longs;ura&shy;<lb/>
biles, quare <expan abbr="&emacr;adem">eadem</expan> ratione, qua in lineis proxim&egrave; v&longs;i &longs;umus, &longs;equetur earum com&shy;<lb/>
munem men&longs;uram e&longs;&longs;e pariter indiuiduam.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003410">Sciendum e&longs;t omnes lineas <expan abbr="c&otilde;men&longs;urabiles">commen&longs;urabiles</expan> longitudine, e&longs;&longs;e etiam com&shy;<lb/>
men&longs;urabiles &lpar;vt aiunt Geometr&aelig;&rpar; potentia, ide&longs;t &longs;ecundum quadrata ea&shy;


<pb pagenum="203" xlink:href="009/01/203.jpg"/>rum, &longs;iue dicas quadrata <expan abbr="quoq;">quoque</expan> earum e&longs;&longs;e commen&longs;urabilia, v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea dua&shy;<lb/>
<figure id="id.009.01.203.1.jpg" place="text" xlink:href="009/01/203/1.jpg"/><lb/>
rum vnciarum, &amp; linea trium vnciarum &longs;unt <lb/>
commen&longs;urabiles longitudine, &amp; potentia, <lb/>
quia potentia line&aelig; duarum vnciarum, &longs;iue <lb/>
<expan abbr="quadrat&utilde;">quadratum</expan>, e&longs;t quatuor vnciarum &longs;uperficia&shy;<lb/>
lium: &amp; quadratum line&aelig; trium vnciarum, <lb/>
e&longs;t nouem vnciarum quadratarum, vt patet <lb/>
in figuris, quorum quadratorum communis <lb/>
men&longs;ura e&longs;t vncia vna quadrata. </s>
          <s id="s.003411">atque hanc <lb/>
illi nullo modo diuidi po&longs;&longs;e contendebant.</s>
        </p>
        <p type="main">
          <s id="s.003412"><arrow.to.target n="marg269"/></s>
        </p>
        <p type="margin">
          <s id="s.003413"><margin.target id="marg269"/>279</s>
        </p>
        <p type="main">
          <s id="s.003414">Tertius locus <emph type="italics"/>&lpar;Pr&aelig;terea &longs;i quis communem &longs;tatam, ac determinatam men&longs;u&shy;<lb/>ram faciat diuiduam, non erit amplius in rerum natura linea vlla rationalis, aut <lb/>
irrationalis, re&longs;pectu expo&longs;it&aelig;, ac determinat&aelig; line&aelig;; neque aliarum vlla erit, de <lb/>
quibus modo dictum e&longs;t, veluti quam Apotomen vocant ex duobus nominibus. </s>
          <s id="s.003415">Ve&shy;<lb/>
r&ugrave;m neque &longs;ecundum &longs;e aliquam definitam naturam habebunt, &longs;ed collat&aelig; &longs;ibi ip&longs;is <lb/>
tam rationales, qu&agrave;m irrationales erunt omnes.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003416">H&aelig;c e&longs;t alia eorumdem ratio ad idem comprobandum: quam, vt ben&egrave; <lb/>
percipiamus, nonnulla prius ex definitionibus 10. Elem. &longs;unt explicanda: <lb/>
vt qu&aelig; nam &longs;int line&aelig; rationales, qu&aelig; irrationales, qu&aelig; ex binis nomini&shy;<lb/>
bus, qu&aelig; Apotom&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.003417">Propo&longs;ita igitur linea quapiam, v. <!-- REMOVE S-->g. <!-- REMOVE S-->trium palmorum qualis e&longs;t linea A, <lb/>
po&longs;&longs;unt inueniri quamplurim&aelig; line&aelig;, quarum ali&aelig; &longs;int illi longitudine com&shy;<lb/>
<figure id="id.009.01.203.2.jpg" place="text" xlink:href="009/01/203/2.jpg"/><lb/>
men&longs;urabiles, &longs;iue qu&aelig; cum expo&longs;ita A, ha&shy;<lb/>
beant communem men&longs;uram. </s>
          <s id="s.003418">v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea B, <lb/>
<expan abbr="quinq;">quinque</expan> palmorum e&longs;t commen&longs;urabilis line&aelig; <lb/>
A, quia vtramque communis men&longs;ura vnius <lb/>
palmi metitur: ali&aelig; ver&ograve; &longs;int eidem A, lon&shy;<lb/>
gitudine incommen&longs;urabiles, qualis e&longs;&longs;et diameter C D, quadrati line&aelig; A, <lb/>
qu&aelig; e&longs;t cum latere A, incommen&longs;urabilis ex vltima 10.</s>
        </p>
        <figure id="id.009.01.203.3.jpg" place="text" xlink:href="009/01/203/3.jpg"/>
        <p type="main">
          <s id="s.003419">C&aelig;terum lineam prim&ograve; expo&longs;itam, vt e&longs;t in pr&aelig;&shy;<lb/>
&longs;entia A, quod e&longs;&longs;et not&aelig; quantitatis, Gr&aelig;ci appella&shy;<lb/>
runt <foreign lang="greek">*rh/thn,</foreign> ide&longs;t rationalem, quemadmodum Latini <lb/>
eam appellant.</s>
        </p>
        <p type="main">
          <s id="s.003420">Linearum autem longitudine <expan abbr="incomm&etilde;&longs;urabilium">incommen&longs;urabilium</expan> <lb/>
cum expo&longs;ita rationali A, ali&aelig; &longs;unt, qu&aelig; tamen &longs;unt <lb/>
commen&longs;urabiles eidem potentia, ide&longs;t con&longs;tituunt <lb/>
quadrata, qu&aelig; &longs;unt commen&longs;urabilia quadrato ra&shy;<lb/>
tionali A, vt linea C D, cum &longs;it diameter quadrati li&shy;<lb/>
ne&aelig; A, quadratum exhibet, quod e&longs;t duplum quadrati line&aelig; A, ex 47. primi, <lb/>
quadratum autem line&aelig; A, e&longs;t nouem, igitur quadratum eius duplum erit <lb/>
octodecim, quadratum &longs;cilicet line&aelig; C D. octodecim autem, &amp; nouem &longs;unt <lb/>
<expan abbr="c&otilde;men&longs;urabilia">commen&longs;urabilia</expan> communi vnitatis men&longs;ura, huiu&longs;modi line&aelig; dicuntur com&shy;<lb/>men&longs;urabiles potentia tantum, potentia. </s>
          <s id="s.003421">n. </s>
          <s id="s.003422">line&aelig; dicuntur <expan abbr="quadrat&utilde;">quadratum</expan> illius.</s>
        </p>
        <p type="main">
          <s id="s.003423">Qu&aelig; igitur rationali propo&longs;it&aelig; &longs;unt commen&longs;urabiles aliquo modo, &longs;iue <lb/>
longitudine, &amp; potentia &lpar;<expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> enim commen&longs;urabilis e&longs;t longitudine, <lb/>
e&longs;t etiam potentia&rpar; &longs;iue potentia &longs;ol&ugrave;m, rationales ip&longs;&aelig; quoque dicuntur.


<pb pagenum="204" xlink:href="009/01/204.jpg"/><figure id="id.009.01.204.1.jpg" place="text" xlink:href="009/01/204/1.jpg"/><lb/>
Ali&aelig; ver&ograve; &lpar;quarum permult&aelig; in decimo reperiun&shy;<lb/>
tur&rpar; qu&aelig; nec longitudine, nec potentia illi &longs;unt <lb/>
commen&longs;urabiles, irrationales appellantur, qua&shy;<lb/>
lis e&longs;&longs;et media proportionalis E F, inter duas A, <lb/>
&amp; C D, in pr&aelig;&longs;enti figura ex 11. 10.</s>
        </p>
        <p type="main">
          <s id="s.003424">Sciendum pr&aelig;terea ex 37. 10. &amp; &longs;equentibus, <lb/>
quod ex duabus lineis rationalibus re&longs;pectu rationalis expo&longs;it&aelig;. </s>
          <s id="s.003425">v. <!-- REMOVE S-->g. <!-- REMOVE S-->A, com&shy;<lb/>
men&longs;urabilibus inuicem tantum potentia, componitur linea, qu&aelig; cum ea&shy;<lb/>
<figure id="id.009.01.204.2.jpg" place="text" xlink:href="009/01/204/2.jpg"/><lb/>
dem expo&longs;ita e&longs;t irrationalis, <expan abbr="vocatur&qacute;">vocaturque</expan>; ex <lb/>
duobus nominibus, &longs;iue Binomium, vt &longs;i ex <lb/>
latere A, &amp; diametro C D, componatur li&shy;<lb/>
nea A C D, erit irrationalis cum rationali <lb/>
A, <expan abbr="dicetur&qacute;">diceturque</expan>; binomium. </s>
          <s id="s.003426">Amplius ex 74. 10. &amp; &longs;equentibus, &longs;i pr&aelig;dictum <lb/>
minus nomen, &longs;iue minor linea A, detrahatur ex maiori nomine C D, vt re&shy;<lb/>
linquatur B D linea, erit ip&longs;a reliqua B D, irrationalis, quam po&longs;tea appel&shy;<lb/>
lant Apotomen, &longs;iue latin&egrave; Re&longs;iduum.</s>
        </p>
        <p type="main">
          <s id="s.003427">Po&longs;trem&ograve;, &amp; hoc non ignorandum ex 43. 10. lineam, &longs;iue <expan abbr="binomi&utilde;">binomium</expan> A C D, <lb/>
non po&longs;&longs;e diuidi in alio puncto, pr&aelig;ter C, in duas lineas, qu&aelig; &longs;int rationales <lb/>
expo&longs;it&aelig;, &amp; potentia tantum inuicem commen&longs;urabiles.</s>
        </p>
        <p type="main">
          <s id="s.003428">His pr&aelig;mi&longs;&longs;is textum, ac rationem illorum explicabo in hunc modum.</s>
        </p>
        <p type="main">
          <s id="s.003429">Si quis faciat diuiduam lineam illam, qu&aelig; e&longs;t communis <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> omnium <lb/>
commen&longs;urabilium, &longs;equetur hoc ab&longs;urdum contra demon&longs;trationes 10. <lb/>
quod nulla erit amplius linea rationalis, nec irrationalis, quia &longs;i communis <lb/>
men&longs;ura diuidatur, tolletur ea de rerum natura; vnde non erit amplius in&shy;<lb/>
ter lineas &longs;ymetria vlla, quare neque vll&aelig; erunt rationales, e&longs;&longs;e enim ratio&shy;<lb/>
nale oritur ex commen&longs;urabilitate. </s>
          <s id="s.003430">quare <expan abbr="neq;">neque</expan> extabit illa rationalis expo&shy;<lb/>
&longs;ita, ad quam c&aelig;ter&aelig; relat&aelig; dicuntur rationales, vel irrationales: quapro&shy;<lb/>
pter etiam irrationales null&aelig; erunt, <expan abbr="neq;">neque</expan> vlla alia erit ex pr&aelig;dictis, veluti <lb/>
nec irrationalis illa, quam vocant Apotomen ex Binomio, &longs;iue ex duobus <lb/>
nominibus, de qua Euclides propo&longs;. </s>
          <s id="s.003431">74. 10. &amp; &longs;equentibus pertractat.</s>
        </p>
        <p type="main">
          <s id="s.003432">Notandum in ver&longs;u illo <emph type="italics"/>&lpar;Apotomen ex duobus nominibus compo&longs;itam&rpar;<emph.end type="italics"/> vni&shy;<lb/>
ca voce illa <emph type="italics"/>&lpar;Compo&longs;itam&rpar;<emph.end type="italics"/> addita ab Interprete Iatino, qu&aelig; non extat in tex. <lb/>
<!-- REMOVE S-->gr&aelig;co, magnum Ari&longs;toteli imponi erratum, cum hac ratione dicat apoto&shy;<lb/>
men ex duobus nominibus e&longs;&longs;e compo&longs;itam, quod fal&longs;i&longs;&longs;imum e&longs;t. </s>
          <s id="s.003433">Apotome <lb/>
enim, vt &longs;upra dictum e&longs;t, ne dum ex duobus nominibus con&longs;tat, verum ip&shy;<lb/>
&longs;a e&longs;t re&longs;iduum line&aelig; maioris, &longs;i minor ab ip&longs;a detrahatur. </s>
          <s id="s.003434">Verumenimuero <lb/>
vox illa <emph type="italics"/>&lpar;Compo&longs;itam&rpar;<emph.end type="italics"/> in nullo codice reperitur, quare pro arbitrio, atque <lb/>
ex Geometri&aelig; in&longs;citia addita, tolli debet, ne tant&aelig; in&longs;citi&aelig; Ari&longs;t. ip&longs;e re&shy;<lb/>
darguatur. </s>
          <s id="s.003435">h&aelig;c in hunc locum &longs;ufficiant.</s>
        </p>
        <p type="main">
          <s id="s.003436"><arrow.to.target n="marg270"/></s>
        </p>
        <p type="margin">
          <s id="s.003437"><margin.target id="marg270"/>280</s>
        </p>
        <p type="main">
          <s id="s.003438">Quartus locus <emph type="italics"/>&lpar;Quod ver&ograve; de commen&longs;urabilibus lineis po&longs;trem&ograve; dicunt, om&shy;<lb/>nes vna quadam, &amp; eadem men&longs;ura oportere men&longs;urari, fal&longs;um e&longs;t admodum, &amp; <lb/>
nequaquam Mathematicorum &longs;uppo&longs;itionibus concordat. </s>
          <s id="s.003439">non enim ita &longs;upponunt <lb/>
Geometr&aelig;, <expan abbr="neq;">neque</expan> vtile ip&longs;is i&longs;tud foret, im&ograve; potius aduer&longs;aretur, lineas omnes com&shy;<lb/>men&longs;urabiles e&longs;&longs;e, &amp; omnium commen&longs;urabilium linearum communem men&longs;uram <lb/>
exi&longs;timare. </s>
          <s id="s.003440">quamobrem ridiculum e&longs;t eos, qui dicunt &longs;e demonstrare ex Geometra&shy;<lb/>
rum decretis, &amp; ex quibus Mathematici docent in contentio&longs;am pariter, ac falla&shy;<emph.end type="italics"/>


<pb pagenum="205" xlink:href="009/01/205.jpg"/><emph type="italics"/>cem diuertere argumentationem, pr&aelig;&longs;ertim tam inualidam. </s>
          <s id="s.003441">nam multis modis im&shy;<lb/>becillis e&longs;t eiu&longs;modi ratio, &amp; quouis modo licet euitare, ne aut inu&longs;itata dicere, aut <lb/>
argui videamur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003442">Refellit hoc loco &longs;uperiores rationes in tribus locis pr&aelig;mi&longs;&longs;is allatas, <lb/>
quibus nonnulli probabant quantitatem ex indiuiduis con&longs;tare, &amp; proinde <lb/>
concedenda e&longs;&longs;e qu&aelig;dam Quanta, omnin&ograve; atoma; &longs;ic igitur inquit. </s>
          <s id="s.003443">Quod <lb/>ver&ograve; de commen&longs;urabilibus lineis dicunt, omnes videlicet vnica quadam, <lb/>
<expan abbr="eadem&qacute;">eademque</expan>; determinata men&longs;ura men&longs;urari oportere, fal&longs;um omnin&ograve; e&longs;t, &amp; <lb/>
contra mathematicorum dogmata, non enim Geometr&aelig; hoc a&longs;&longs;erunt, c&ugrave;m <lb/>ip&longs;orum demon&longs;trationibus aduer&longs;etur; &longs;ed <expan abbr="tant&utilde;">tantum</expan> dicunt omnes lineas, qu&aelig; <lb/>
ad inuicem &longs;unt commen&longs;urabiles, commen&longs;urari, vna <expan abbr="eadem&qacute;">eademque</expan>; men&longs;ura, <lb/>
<figure id="id.009.01.205.1.jpg" place="text" xlink:href="009/01/205/1.jpg"/><lb/>
&longs;ed non tamen vnica, ide&longs;t non vnica, ac determi&shy;<lb/>
nata. </s>
          <s id="s.003444">po&longs;&longs;unt enim e&longs;&longs;e plures <expan abbr="e&aelig;dem&qacute;">e&aelig;demque</expan>; men&longs;ur&aelig; <lb/>
communes plurium quantitatum commen&longs;ura&shy;<lb/>
bilium, vt pr&aelig;&longs;entium trium linearum 4. 6. 8. <lb/>
communis <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> e&longs;t linea 2. binarius enim tres <lb/>
numeros 4.6. &amp; 8. men&longs;urat. </s>
          <s id="s.003445">&amp; &longs;i linea 2. bifariam <lb/>
&longs;ecetur, erit dimidium eius linea 1. qu&aelig; pariter <lb/>
erit communis men&longs;ura trium pr&aelig;dictarum li&shy;<lb/>
nearum, c&ucirc;m vnitas &longs;it omnium numerorum communis men&longs;ura. ben&egrave; ve&shy;<lb/>
rum e&longs;t, quod Geometr&aelig;, quando &longs;impliciter loquuntur de huiu&longs;modi com&shy;<lb/>
muni men&longs;ura, intelligunt de ea, qu&aelig; inter omnes e&longs;t maxima: vt in pr&aelig;di&shy;<lb/>
ctis tribus lineis maxima earum communis men&longs;ura e&longs;t linea 2. <expan abbr="Atq;">Atque</expan> hoc &longs;i&shy;<lb/>
bi volunt Geometr&aelig;, ex quibus totus hic textus intelligi pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.003446"><arrow.to.target n="marg271"/></s>
        </p>
        <p type="margin">
          <s id="s.003447"><margin.target id="marg271"/>281</s>
        </p>
        <p type="main">
          <s id="s.003448">Quintus locus <emph type="italics"/>&lpar;Ob rect&aelig; ver&ograve; line&aelig; motum in &longs;emicirculum, quam nece&longs;&longs;e e&longs;t <lb/>
in rectum ita diuidere, vt infinit&aelig; circunferenti&aelig;, &amp; interualla totidem inuenian&shy;<lb/>
tur&rpar;<emph.end type="italics"/> Interpres latinus &longs;ic vertit <emph type="italics"/>&lpar;Ob rect&aelig; ver&ograve; line&aelig; motum in &longs;emicirculum <lb/>
diuiduas non credere, &amp;c.&rpar;<emph.end type="italics"/> vbi verba illa <emph type="italics"/>&lpar;Diuiduas non credere&rpar;<emph.end type="italics"/> pro arbitrio, <lb/>
ac &longs;ine ratione, im&ograve; contra rationem addidit: tum quia in Gr&aelig;co textu non <lb/>
extant, tum quia &longs;en&longs;us totius &longs;ententi&aelig; is e&longs;t, vt potius debui&longs;&longs;et affirmati&shy;<lb/>
u&egrave; dicere <emph type="italics"/>&lpar;Diuiduas credere&rpar;<emph.end type="italics"/> nam Ari&longs;toteles videtur &longs;ic <expan abbr="argum&etilde;tari">argumentari</expan>, quan&shy;<lb/>
<figure id="id.009.01.205.2.jpg" place="text" xlink:href="009/01/205/2.jpg"/><lb/>
do recta linea A B, vt in appo&longs;ita figura mo&shy;<lb/>
uetur intrando in &longs;emicirculum C A D B, ita <lb/>
vt prim&ograve; &longs;it in &longs;itu A B, &longs;ecund&ograve; in E F, terti&ograve; <lb/>
in G H, &amp; &longs;imiliter in alijs omnibus &longs;emicir&shy;<lb/>
culi locis, nece&longs;&longs;ari&ograve; accidit, vt infinit&aelig; peri&shy;<lb/>
ph&etail;ri&aelig;, quales <expan abbr="s&utilde;t">sunt</expan> A B, E A B F, G E A B F H, <lb/>
cadant inter infinitas partes line&aelig; ingredien&shy;<lb/>
tis, vt &longs;unt A B, E F, G H, <expan abbr="atq;">atque</expan> tam tota recta <lb/>
ingrediens, qu&agrave;m totus &longs;emicirculus, diuidatur in partes infinitas, ita vt <lb/>
nulla pars line&aelig; rect&aelig;, <expan abbr="neq;">neque</expan> vlla &longs;emicirculi &longs;uper&longs;it, qu&aelig; &longs;e &longs;e mutu&ograve; non <lb/>
diuidantur, erg&ograve; nihil tam in linea, qu&agrave;m in &longs;emicirculo remanet, quod non <lb/>
&longs;ecetur: tota igitur linea recta, &amp; periph&aelig;ria illa diuidua e&longs;t, quam ob rem <lb/>
nullo modo con&longs;tare pote&longs;t ex indiuiduis, ex quibus manife&longs;tum e&longs;t perpe&shy;<lb/>
ram additamentum illud factum e&longs;&longs;e, &amp; &longs;imul ratio, &amp; textus Ari&longs;t. eadem <lb/>
opera patefacta &longs;unt.</s>
        </p>
        <pb pagenum="206" xlink:href="009/01/206.jpg"/>
        <p type="main">
          <s id="s.003449"><arrow.to.target n="marg272"/></s>
        </p>
        <p type="margin">
          <s id="s.003450"><margin.target id="marg272"/>282</s>
        </p>
        <p type="main">
          <s id="s.003451">Sextus locus <emph type="italics"/>&lpar;Rur&longs;us <expan abbr="quoq;">quoque</expan> facil&egrave; per&longs;uaderi pote&longs;t ex mota duorurm circulo&shy; <lb/>rum &aelig;qualium, nam qui&longs;quis horum moueatur, oportet per maiorem &longs;emicirculum <lb/>moueri, &amp; qu&aelig;cunque alia huiu&longs;modi constituta &longs;unt de lineis, fieri non po&longs;&longs;e, vt <lb/>
talis vllus motus peragatur, quin prius omnibus, &amp; &longs;ingulis interiectis occurrat. <lb/>
</s>
          <s id="s.003452">Atque h&aelig;c Mathematicorum &longs;cita, mult&ograve; magis ab omnibus conce&longs;&longs;a &longs;unt, qu&agrave;m <lb/>
illorum dicta.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003453">H&aelig;c e&longs;t alia ratio, qua probat totam circuli periph&aelig;riam e&longs;&longs;e diuiduam. <lb/>
<figure id="id.009.01.206.1.jpg" place="text" xlink:href="009/01/206/1.jpg"/><lb/>
&longs;int enim duo circuli &aelig;quales primum in eo&shy;<lb/>
dem loco, <expan abbr="vocentur&qacute;">vocenturque</expan>; A, &amp; B, deinde circu&shy;<lb/>
lus B, moueatur, &amp; di&longs;cedat &agrave; circulo A, ma&shy;<lb/>
nente; &longs;tatim <expan abbr="namq;">namque</expan> pars egre&longs;&longs;a E F G, erit <lb/>
maior &longs;emicirculo, &amp; &longs;emper fiet maior, ac <lb/>
maior. </s>
          <s id="s.003454"><expan abbr="atq;">atque</expan> in tali motu omnes partes egre&shy;<lb/>
dientis circuli &longs;ecantur ab omnibus partibus <lb/>
circuli manentis. </s>
          <s id="s.003455">vnde patet nihil e&longs;&longs;e in eo&shy;<lb/>
rum periph&aelig;rijs, quod non diuidatur. </s>
          <s id="s.003456">nul&shy;<lb/>
lum igitur in eis e&longs;t indiuiduum. </s>
          <s id="s.003457">falluntur igitur aduer&longs;arij.</s>
        </p>
        <p type="main">
          <s id="s.003458"><arrow.to.target n="marg273"/></s>
        </p>
        <p type="margin">
          <s id="s.003459"><margin.target id="marg273"/>283</s>
        </p>
        <p type="main">
          <s id="s.003460">Septimus locus <emph type="italics"/>&lpar;Quamuis autem ex confutatis nuper rationibus appareat, ne&shy;<lb/>
que probabile, neque nece&longs;&longs;arium e&longs;&longs;e lineas vllas indiuiduas extare, tamen ex ijs <lb/>etiam, qu&aelig; deinceps &longs;ubiungam, mult&ograve; magis per&longs;picuum euadet. </s>
          <s id="s.003461">&amp; prim&ograve; quidem <lb/>
per ea, qu&aelig; Mathematici demon&longs;trant, at que addi&longs;cenda proponunt, qu&aelig; mutare <lb/>
non decet, ni&longs;t probabiliores rationes habeamus. </s>
          <s id="s.003462">Nam neque line&aelig;, neque rect&aelig; li&shy;<lb/>
ne&aelig; definitio cum in&longs;ecabili linea con&longs;entit, vt qu&aelig; nec inter duo puncta exten&longs;a <lb/>&longs;it, nec medium vllam habeat.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003463">Idem, &longs;ed paul&ograve; mutatis verbis po&longs;tea repetit, qu&aelig; fort&egrave; ab aliquo per <lb/>
errorem addita &longs;unt. </s>
          <s id="s.003464">Verumenimuer&ograve; maxim&egrave; con&longs;iderandum e&longs;t, quan&shy;<lb/>
tum hoc loco Ari&longs;t. Mathematicis demon&longs;trationibus tribuat: quod dixe&shy;<lb/>
rim propter recentiores quo&longs;dam, qui e&ograve; audaci&aelig; deuenerunt, vt Euclidis <lb/>
firmi&longs;&longs;imas, <expan abbr="atq;">atque</expan> Ari&longs;tot. te&longs;timonio, <expan abbr="veterum&qacute;">veterumque</expan>; Philo&longs;ophorum omnium <lb/>
comprobatas, negare non verentur Demon&longs;trationes.</s>
        </p>
        <p type="main">
          <s id="s.003465">C&aelig;ter&ugrave;m Ari&longs;t. iterum opinionem <expan abbr="a&longs;&longs;er&etilde;tium">a&longs;&longs;erentium</expan> lineas in&longs;ecabiles hoc mo&shy;<lb/>
do confutat: nam &longs;i inquit, lineam illam, quam vocant in&longs;ecabilem, e&longs;t non <lb/>
&longs;olum linea, &longs;ed etiam linea recta, illi conueniret rect&aelig; line&aelig; definitio, &longs;ed <lb/>
nullo modo pote&longs;t ci conuenire, erg&ograve; tollend&aelig; &longs;unt de rerum natura huiu&longs;&shy;<lb/>
modi line&aelig;. </s>
          <s id="s.003466">Porr&ograve; definitio line&aelig; e&longs;t, vt &longs;it longitudo latitudinis expers, &amp; <lb/>
&longs;i recta &longs;it ex &aelig;quo &longs;ua interiacet puncta extrema, erg&ograve; ip&longs;a linea media erit <lb/>
inter duo indiuidua extrema puncta; at ver&ograve; linea, quam ip&longs;i volunt e&longs;&longs;e <lb/>
indiuiduum quoddam, qua ratione medium erit inter alia duo indiuidua? <lb/>
</s>
          <s id="s.003467">ip&longs;i enim <expan abbr="vid&etilde;tur">videntur</expan> velle i&longs;tam lineam non habere medium vllum, &longs;i enim con&shy;<lb/>cederent habere medium, iam po&longs;&longs;et in medio &longs;ecari, quod ip&longs;i nequaquam <lb/>
concederent: patet igitur definitionem line&aelig; minim&egrave; illi conuenire, &amp; pro&shy;<lb/>
pterea <expan abbr="neq;">neque</expan> e&longs;&longs;e inter lineas enumerandam.</s>
        </p>
        <p type="main">
          <s id="s.003468"><arrow.to.target n="marg274"/></s>
        </p>
        <p type="margin">
          <s id="s.003469"><margin.target id="marg274"/>284</s>
        </p>
        <p type="main">
          <s id="s.003470">Octauus locus <emph type="italics"/>&lpar;Deinde omnes line&aelig; commen&longs;urabiles erunt: nam omnes ab in&shy;<lb/>
diuiduis lineis dimetientur, qu&aelig;qu&eacute;; longitudine, qu&aelig;qu&eacute;; potentia &longs;unt commen&longs;urabi&shy;<lb/>
les. </s>
          <s id="s.003471">indiuidu&aelig; autem line&aelig; &longs;ibi ip&longs;is commen&longs;urabiles &longs;unt longitudine, cum inter &longs;e <lb/>
fiat &aelig;quales; quare potentia quoque, quod &longs;i hoc e&longs;t, diuiduum erit quadratum.<emph.end type="italics"/></s>
        </p>
        <pb pagenum="207" xlink:href="009/01/207.jpg"/>
        <p type="main">
          <s id="s.003472">Pergit adhuc nouis rationibus aduer&longs;arios refellere, dicens, &longs;i extarent <lb/>
huiu&longs;modi indiuidu&aelig; line&aelig;, &longs;equeretur omnes omnin&ograve; lineas e&longs;&longs;e commen&shy;<lb/>
&longs;urabiles, quod e&longs;t contra demon&longs;trata in 10. Elem. quia cum omnes line&aelig; <lb/>
<expan abbr="con&longs;t&etilde;t">con&longs;tent</expan> per ip&longs;os ex lineis atomis, i&longs;t&aelig; atom&aelig; e&longs;&longs;ent omnium linearum com&shy;<lb/>
munes men&longs;ur&aelig;, vnde &amp; ill&aelig;, qu&aelig; dicuntur potentia tantum commen&longs;ura&shy;<lb/>
biles, vt &longs;upra explicaui, erunt etiam commen&longs;urabiles longitudine. </s>
          <s id="s.003473">indiui&shy;<lb/>
du&aelig; ver&ograve; ip&longs;&aelig;, cum &longs;int inuicem &aelig;quales, erunt ip&longs;&aelig; <expan abbr="quoq;">quoque</expan> commen&longs;urabi&shy;<lb/>
les longitudine, quare &amp; potentia, omnes enim longitudine commen&longs;ura&shy;<lb/>
biles, &longs;unt etiam potentia commen&longs;urabiles, ex 9. 10. vnde &longs;equitur qua&shy;<lb/>
drata earum omnia e&longs;&longs;e <expan abbr="quoq;">quoque</expan> commen&longs;urabilia: <expan abbr="atq;">atque</expan> hinc con&longs;equitur, in&shy;<lb/>
quit, ea e&longs;&longs;e <expan abbr="quoq;">quoque</expan> diuidua &lpar;quam con&longs;ecutionem probat infra num. </s>
          <s id="s.003474">290.&rpar; <lb/>
vnde &longs;equeretur ip&longs;am <expan abbr="quoq;">quoque</expan> lineam latus quadrati po&longs;&longs;e diuidi, non igitur <lb/>
ponenda erat indiuidua.</s>
        </p>
        <p type="main">
          <s id="s.003475"><arrow.to.target n="marg275"/></s>
        </p>
        <p type="margin">
          <s id="s.003476"><margin.target id="marg275"/>285</s>
        </p>
        <p type="main">
          <s id="s.003477">Nonus Iocus, cuius latinam interpretationem, cum admodum e&longs;&longs;et de&shy;<lb/>
prauata ex gr&aelig;co textu, in hunc modum correxi <emph type="italics"/>&lpar;Pr&aelig;terea c&ugrave;m circa maio&shy;<lb/>rem latitudinem facit applicata, &aelig;quale ei, quod ab indiuidua, &amp; pedali copulatis <lb/>
circa bipedalem, minorem faciet latitudinem, qu&agrave;m &longs;it indiuidua: erit minus, quod <lb/>
circa indiuiduam&rpar;<emph.end type="italics"/> ide&longs;t c&ugrave;m minor linea applicata cum maiore, latitudinem <lb/>
<figure id="id.009.01.207.1.jpg" place="text" xlink:href="009/01/207/1.jpg"/><lb/>
faciat. </s>
          <s id="s.003478">v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea minor A B, applicata cum ma&shy;<lb/>
iori B C, vt in figura, ita vt contineant figuram <lb/>
A B C D. <!-- KEEP S--></s>
          <s id="s.003479">Minor A B, facit latitudinem figur&aelig;, <lb/>
maior ver&ograve; B C, facit longitudinem. </s>
          <s id="s.003480">Iam cum <lb/>
aduer&longs;arij velint extare huiu&longs;modi lineas ato&shy;<lb/>
mas, con&longs;tituatur figura &longs;ub vna ex illis, qu&aelig; &longs;it v. <!-- REMOVE S-->g. <!-- REMOVE S-->A B, &amp; altera maiori, <lb/>
qu&aelig; &longs;it pedalis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->B C, vt in pr&aelig;cedenti figura, &longs;umatur deinde linea bi&shy;<lb/>
<figure id="id.009.01.207.2.jpg" place="text" xlink:href="009/01/207/2.jpg"/><lb/>
pedalis E F, cui per 45. primi ap&shy;<lb/>
plicetur &longs;patium E F G H, &aelig;quale <lb/>
&longs;patio &longs;uperiori A B C D, nece&longs;&longs;a&shy;<lb/>
ri&ograve; latitudo E H, huius &longs;ecund&aelig; fi&shy;<lb/>
gur&aelig; minor erit qu&agrave;m latitudo il&shy;<lb/>lius, hoc e&longs;t minor, qu&agrave;m &longs;it indiuidua A B, quod e&longs;t ab&longs;urdum. </s>
          <s id="s.003481">vel dicere <lb/>
oportet <expan abbr="&longs;pati&utilde;">&longs;patium</expan> circa indiuiduam A B, e&longs;&longs;e minus qu&agrave;m i&longs;tud po&longs;terius, quod <lb/>
e&longs;t contra con&longs;tructionem, &amp; propterea pariter inconueniens, non igitur <lb/>
huiu&longs;modi line&aelig; &longs;unt ponend&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.003482"><arrow.to.target n="marg276"/></s>
        </p>
        <p type="margin">
          <s id="s.003483"><margin.target id="marg276"/>286</s>
        </p>
        <p type="main">
          <s id="s.003484">Decimus locus <emph type="italics"/>&lpar;Cum ex tribus datis lineis triangulus componatur, ex tribus <lb/>
<expan abbr="quoq;">quoque</expan> indiuiduis lineis componi poterit. </s>
          <s id="s.003485">in omni autem &aelig;quilatero perpendicularis <lb/>in mediam ba&longs;im incidit, quare, &amp; in medium indiuidu&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003486">Ex 22. primi Elem. ex tribus datis lineis, quarum qu&aelig;libet du&aelig; &longs;int, re&shy;<lb/>
liqua maiores pote&longs;t con&longs;titui triangulum: poterit igitur ex tribus indiui&shy;<lb/>
<figure id="id.009.01.207.3.jpg" place="text" xlink:href="009/01/207/3.jpg"/><lb/>
duis con&longs;titui <expan abbr="tri&atilde;gulum">triangulum</expan>, <expan abbr="illud&qacute;">illudque</expan>; &aelig;quilaterum, cum omnes in&shy;<lb/>
diuidu&aelig; line&aelig; &longs;int &aelig;quales. </s>
          <s id="s.003487">&longs;it igitur ex eis triangulum A B C, <lb/>
&longs;i igitur ab angulo A, ducatur perpendicularis A D, ad ba&longs;im <lb/>
B C, eam bifariam &longs;ecabit ex &longs;cholio 26. primi, erit igitur li&shy;<lb/>
nea B C, &longs;ecabilis, contra quam aduer&longs;arij opinantur.</s>
        </p>
        <p type="main">
          <s id="s.003488"><arrow.to.target n="marg277"/></s>
        </p>
        <p type="margin">
          <s id="s.003489"><margin.target id="marg277"/>287</s>
        </p>
        <p type="main">
          <s id="s.003490">Vndecimus locus <emph type="italics"/>&lpar;Si quadratum ex quatuor indiuiduis con&longs;tituatur diametro <lb/>
protracta, &amp; perpendiculari ducta, quadrati co&longs;ta potentia <expan abbr="perp&etilde;dicularem">perpendicularem</expan>, diame-<emph.end type="italics"/>


<pb pagenum="208" xlink:href="009/01/208.jpg"/><emph type="italics"/>trumqu&eacute; mediam &aelig;quat: quare non erit minima. </s>
          <s id="s.003491">neque duplum erit &longs;patium &agrave; diame&shy;<lb/>
tro con&longs;urgens illius, quod ab indiuidua procreatur: nans &aelig;quali ablato, reliquum <lb/>erit minus indiuidua, nam &longs;i &aelig;qualis, diameter quadruplum de&longs;criberet, &amp;c.&rpar; <emph.end type="italics"/><lb/>
<figure id="id.009.01.208.1.jpg" place="text" xlink:href="009/01/208/1.jpg"/><lb/>
ide&longs;t &longs;i per 46 primi quadratum. </s>
          <s id="s.003492">v.g. <!-- REMOVE S-->A B C D, ex qua&shy;<lb/>
tuor in&longs;ecabilibus componatur, cuius diametro B C, <lb/>
perpendicularis A E, in&longs;i&longs;tat, erit per 47. primi qua&shy;<lb/>
dratum line&aelig; A B, &aelig;quale quadratis <expan abbr="linear&utilde;">linearum</expan> A E, E B, <lb/>
quare tam E B, qu&agrave;m A E, minores erunt ip&longs;a A B; <lb/>
quare ip&longs;a non erit minima cum &longs;it indiuidua, quod e&longs;t <lb/>
ab&longs;urdum. </s>
          <s id="s.003493">Pr&aelig;terea ex &longs;cholio 47. primi, quadratum <lb/>
C B F G, diametri C B, duplum e&longs;t quadrati A B C D, <lb/>
erg&ograve; diameter C B, maior qu&agrave;m A B. <!-- KEEP S--></s>
          <s id="s.003494">Auferatur igitur ab ip&longs;a, C B, &aelig;qua&shy;<lb/>
lis ip&longs;i A B, qu&aelig; igitur reliqua erit, vel erit &aelig;qualis ip&longs;i A B, vel minor. </s>
          <s id="s.003495">non <lb/>
&aelig;qualis, quia tunc diameter dupla e&longs;&longs;et lateris A B, &amp; quadratum diametri <lb/>
quadruplum foret quadrati lateris A B. ex &longs;cholio 4. &longs;ecundi, quod ab&longs;ur&shy;<lb/>
dum e&longs;t, repugnat enim 47. primi. </s>
          <s id="s.003496">nec minor, quia hoc modo exi&longs;teret linea <lb/>
qu&aelig;dam minor minima, &longs;cilicet atoma, quod pariter e&longs;t inconueniens.</s>
        </p>
        <p type="main">
          <s id="s.003497"><arrow.to.target n="marg278"/></s>
        </p>
        <p type="margin">
          <s id="s.003498"><margin.target id="marg278"/>288</s>
        </p>
        <p type="main">
          <s id="s.003499">Duodecimus locus <emph type="italics"/>&lpar;Amplius &longs;i qu&aelig;uis linea pr&aelig;ter in&longs;ectilem in partes diui&shy; <lb/>
di pote&longs;t, t&ugrave;m &aelig;quales, t&ugrave;m in&aelig;quales, &longs;eindatur linea in tria fru&longs;ta, qu&aelig; non con&shy;<lb/>
&longs;tet ex tribus atomis, &longs;ed vniuer&longs;aliter ex imparibus numero atomis, &longs;ic diui&longs;a erit <lb/>
linea indiuidua. </s>
          <s id="s.003500">&longs;imiliter autem &longs;i in duo diuidatur linea, qu&aelig; ex imparibus <expan abbr="c&otilde;&longs;tat">con&longs;tat</expan>&rpar;<emph.end type="italics"/><lb/>
hoc e&longs;t detur linea qu&aelig;piam ab aduer&longs;ario ex lineis indiuiduis numer&ograve; im&shy;<lb/>
paribus, con&longs;tans. </s>
          <s id="s.003501">v. <!-- REMOVE S-->g. <!-- REMOVE S-->ex quinque; h&aelig;c diuidi pote&longs;t in tres &aelig;quas partes <lb/>
per 10.6. Si igitur diuidatur in tria &aelig;qualia, nece&longs;&longs;ari&ograve; tres ex atomis illam <lb/>
integrantibus erunt di&longs;&longs;ect&aelig;, nam tertia qu&aelig;libet pars continebit indiui&shy;<lb/>
duam vnam cum duabus tertijs alterius partibus. </s>
          <s id="s.003502">idem accidet &longs;i bifariam <lb/>
per 10. primi, &longs;ecetur qu&aelig;uis ex imparibus numero atomis conflata.</s>
        </p>
        <p type="main">
          <s id="s.003503"><arrow.to.target n="marg279"/></s>
        </p>
        <p type="margin">
          <s id="s.003504"><margin.target id="marg279"/>289</s>
        </p>
        <p type="main">
          <s id="s.003505">Decimustertius locus <emph type="italics"/>&lpar;Quod &longs;i bifariam quidem non omnis linea finditur, &longs;ed <lb/>
qu&aelig; &longs;olum ex paribus conflata &longs;it. </s>
          <s id="s.003506">&longs;i iam in duas partes diui&longs;a, in <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> diuidi <lb/>
pote&longs;t diuideretur, &longs;ic <expan abbr="quoq;">quoque</expan> in&longs;ectilis linea diuideretur, quando ex paribus compo&shy;<lb/>
&longs;ita, per in&aelig;qualia &longs;cinderetur&rpar;<emph.end type="italics"/> ide&longs;t, quod &longs;i dixerit aduer&longs;arius, non omnem <lb/>
lineam bifariam diuidi po&longs;&longs;e, &longs;ed eam &longs;ol&ugrave;m, qu&aelig; ex numero paribus atomis <lb/>
con&longs;titerit: ea igitur diuidatur primo bifariam. </s>
          <s id="s.003507">deinde iterum diuidatur <lb/>
quomodocunque, ide&longs;t &amp; bifariam, &amp; non bifariam, nam hoc etiam pacto <lb/>
indiuidua diuidetur, quod e&longs;t inconueniens.</s>
        </p>
        <p type="main">
          <s id="s.003508"><arrow.to.target n="marg280"/></s>
        </p>
        <p type="margin">
          <s id="s.003509"><margin.target id="marg280"/>290</s>
        </p>
        <p type="main">
          <s id="s.003510">Decimusquartus locus <emph type="italics"/>&lpar;Amplius non e&longs;&longs;et cuiu&longs;uis line&aelig; quadratum: habe&shy;<lb/>
ret enim longitudinem, &amp; latitudinem; <expan abbr="atq;">atque</expan> idcirc&ograve; diui&longs;ibile erit, cum illa quidem <lb/>aliquid, h&aelig;c autem aliquid aliud; quod &longs;i quadratum diuiduum e&longs;t, &amp; linea, vnde <lb/>
procreatur, diuidua erit&rpar;<emph.end type="italics"/> po&longs;&longs;e &longs;uper quamuis datam lineam quadratum de&shy;<lb/>
&longs;cribi patet ex 46. primi, quadratum igitur de&longs;criptum ab indiuidua, cum <lb/>
&longs;it &longs;uperficies, latitudinem, ac longitudinem habebit, qu&aelig; diuer&longs;&aelig; &longs;unt di&shy;<lb/>
men&longs;iones. </s>
          <s id="s.003511">poterit erg&ograve; &longs;ecundum <expan abbr="vtramq;">vtramque</expan> diuidi; ex qua diui&longs;ione nece&longs;&shy;<lb/>
&longs;ari&ograve; latera ip&longs;ius, hoc e&longs;t line&aelig;, quas indiuiduas illi ponunt diuidentur, <lb/>quod e&longs;t inconueniens, non igitur indiuidu&aelig; erunt.</s>
        </p>
        <p type="main">
          <s id="s.003512"><arrow.to.target n="marg281"/></s>
        </p>
        <p type="margin">
          <s id="s.003513"><margin.target id="marg281"/>291</s>
        </p>
        <p type="main">
          <s id="s.003514">Decimusquintus locus <emph type="italics"/>&lpar;Adhuc etiam, vt linea &longs;ic, &amp; &longs;uperficies, &amp; corpus <lb/>erit impartibile: vno quippe indiuiduo exi&longs;tente, c&aelig;tera <expan abbr="quoq;">quoque</expan> con&longs;equentur, quia<emph.end type="italics"/> <pb pagenum="209" xlink:href="009/01/209.jpg"/><emph type="italics"/>vnum per aliud diuiditur, at corpus indiuiduum non e&longs;t, cum in &longs;e latitudinem, &amp; <lb/>
profunditatem contineat: quare nec linea pote&longs;t e&longs;&longs;e atoma. </s>
          <s id="s.003515">corpus &longs;iquidem in &longs;u&shy;<lb/>perficies, &longs;uperficies ver&ograve; in lineas &longs;oluitur&rpar;<emph.end type="italics"/> hoc e&longs;t: pr&aelig;terea, quemadmodum <lb/>linea per aduer&longs;arium extat indiuidua, &longs;ic &amp; &longs;uperficies ab eadem linea de&shy;<lb/>
&longs;cripta erit atoma, &amp; corpus ab hac &longs;uperficie de&longs;criptum erit impartibile. <lb/>
</s>
          <s id="s.003516">Sciendum enim, quod ex motu puncti de&longs;cribitur linea: ex motu line&aelig; de&shy;<lb/>
&longs;cribitur &longs;uperficies: ex motu tandem &longs;uperficiei corpus ortum habet, vt &longs;o&shy;<lb/>
let in horum definitionibus explicari.</s>
        </p>
        <p type="main">
          <s id="s.003517">Si igitur horum vnum nemp&egrave; linea &longs;it atoma, &amp; reliqua, qu&aelig; ab ip&longs;a ma&shy;<lb/>
nant erunt indiui&longs;a, quia corpus diuiditur per &longs;uperficiem, &amp; &longs;uperficies <lb/>
per lineam, ide&longs;t ad diui&longs;ionem corporis nece&longs;&longs;e e&longs;t diuidi &longs;uperficiem, &amp; ad <lb/>
&longs;uperficiei diui&longs;ionem diuidi lineam, qu&aelig; ip&longs;am terminat. </s>
          <s id="s.003518">At cum omne <lb/>
corpus latitudinem, &amp; profunditatem habeat, nullum poterit extare cor&shy;<lb/>
pus, quod diuidi nequeat; quare neque illud, quod ab atoma linea oriretur. <lb/>
</s>
          <s id="s.003519">Quare nec linea illa corporis procreatrix erit indiuidua; corpus &longs;iquidem <lb/>
in &longs;uperficies, &amp; &longs;uperficies in lineas quodammodo re&longs;oluitur: &amp; ex diui&shy;<lb/>
&longs;ione &longs;olidi &longs;uperficies &longs;ecari debet, &amp; demum &longs;uperficiei, &longs;ectionem line&aelig; <lb/>
&longs;ectio &longs;ub&longs;equitur. </s>
          <s id="s.003520">Tollend&aelig; igitur &longs;unt de rerum natura line&aelig; atom&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.003521"><arrow.to.target n="marg282"/></s>
        </p>
        <p type="margin">
          <s id="s.003522"><margin.target id="marg282"/>292</s>
        </p>
        <p type="main">
          <s id="s.003523">Decimus&longs;extus locus <emph type="italics"/>&lpar;Quin etiam orbis circunferentia rectam lineam pluri&shy;<lb/>
bus tanget punctis, punctus enim contactus, quiqu&eacute; e&longs;t in circulo, quiqu&eacute; e&longs;t in recta, <lb/>
&longs;e &longs;e mutu&ograve; tangunt. </s>
          <s id="s.003524">quod &longs;i hoc fieri nequit, <expan abbr="neq;">neque</expan> punctus punctum tangere valet: <lb/>
quod &longs;i &longs;e tangere nequeunt, <expan abbr="neq;">neque</expan> linea punctis con&longs;tare pote&longs;t, nam neque punctum <lb/>
tangere nece&longs;&longs;arium e&longs;t.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003525">In 2. 3. &amp; corollario eius demon&longs;tratur circuli peripheriam tangere re&shy;<lb/>
ctam lineam in vnico puncto. </s>
          <s id="s.003526">iam &longs;i linea con&longs;taret ex punctis indiuiduis <lb/>
tanquam partibus, po&longs;&longs;et circulus <expan abbr="t&atilde;gere">tangere</expan> rectam lineam in duobus punctis. <lb/>
<figure id="id.009.01.209.1.jpg" place="text" xlink:href="009/01/209/1.jpg"/><lb/>
Sit circulus, cuius centrum A, tangens lineam <lb/>
rectam B C, con&longs;tantem ex punctis, quorum vnus <lb/>
&longs;it in extremo D, line&aelig; B D, alterum ver&ograve; in E, <lb/>
principio line&aelig; E C, circulus A, tangere poterit <lb/>
in F, termino communi vtriu&longs;que line&aelig;, hocque <lb/>
modo tanget <expan abbr="vtrunq;">vtrunque</expan> punctum D, &amp; E, quod e&longs;t <lb/>
impo&longs;&longs;ibile per 2. 3. &longs;equitur igitur <expan abbr="neq;">neque</expan> illa duo puncta D, E, &longs;e mutu&ograve; tan&shy;<lb/>
gere, &amp; eadem ratione nulla alia <expan abbr="p&utilde;cta">puncta</expan> eiu&longs;dem line&aelig;, ex quibus manife&longs;tum <lb/>
e&longs;t, impo&longs;&longs;ibile e&longs;&longs;e, lineam ex huiu&longs;modi punctis con&longs;tare po&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.003527">Reliqua huius opu&longs;culi, quamuis Mathematica alicui videri po&longs;&longs;int, <lb/>
non tamen &longs;unt, non enim linearibus indigent demon&longs;trationi&shy;<lb/>
bus, <expan abbr="neq;">neque</expan> ex Geometri&aelig; principijs procedunt. </s>
          <s id="s.003528">ad Phy&longs;i&shy;<lb/>
cum igitur pertinebunt, cuius e&longs;t di&longs;putare, num <lb/>
indiuidua exi&longs;tant, &amp; quomodo in quanti&shy;<lb/>
tate, <expan abbr="id&qacute;">idque</expan>; rationibus aliunde, qu&agrave;m <lb/>
ex Geometria deductis.</s>
        </p>
        <pb pagenum="210" xlink:href="009/01/210.jpg"/>
        <p type="head">
          <s id="s.003529"><emph type="italics"/>In Librum de Propriet. <!-- REMOVE S-->Elementorum.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003530">Libellum de cau&longs;is proprietatum Elementorum, quamuis nonnulla <lb/>
mathematica loca contineat, tamen, quia cert&ograve; con&longs;tat ex ijs, <lb/>
qu&aelig; in eo de Secta Arabum, de Sclauis, de Dalmatis, qui multis <lb/>
po&longs;t Ari&longs;totelem &longs;&aelig;culis floruerunt, auctorem alium e&longs;&longs;e ab Ari&longs;to&shy;<lb/>
tele con&longs;ult&ograve; &amp; merit&ograve; omi&longs;i.</s>
        </p>
        <p type="head">
          <s id="s.003531"><emph type="italics"/>In Librum de Cau&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003532">Alterum de cau&longs;is libellum pariter pr&aelig;termi&longs;i, cum is vocibus Arabi&shy;<lb/>cam barbariem redolentibus &longs;cateat: phra&longs;is pr&aelig;terea, &amp; qu&etail;dam <lb/>de Deo dicta, plan&egrave; indicant authorem non e&longs;&longs;e Ari&longs;totelem; &longs;ed potius <lb/>
Arabem quempiam.</s>
        </p>
      </chap>
      <pb pagenum="211" xlink:href="009/01/211.jpg"/>
      <chap>
        <p type="head">
          <s id="s.003533">EX LIBRO NONO <lb/>
DE HIST. ANIMALIVM</s>
        </p>
        <p type="head">
          <s id="s.003534"><emph type="italics"/>Araneorum industri&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003535"><arrow.to.target n="marg283"/></s>
        </p>
        <p type="margin">
          <s id="s.003536"><margin.target id="marg283"/>293</s>
        </p>
        <p type="main">
          <s id="s.003537">Cap. 39. <emph type="italics"/>&lpar;Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>
tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor&shy;<lb/>
pore, veluti cortice; aut more eorum animalium, qu&aelig; &longs;uos villos iacu&shy;<lb/>
lantur, vt hystricis&rpar;<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;it <lb/>animum meum illa cupido, vt &longs;cilicet cert&ograve; &longs;cirem, num iure, an iniuria <lb/>
Ari&longs;t. Democritum hoc loco reijceret, Araneum fila ab intrin&longs;eco emitte&shy;<lb/>
re a&longs;&longs;erentem: quapropter ad magi&longs;tram rerum experientiam confugi, ac&shy;<lb/>
cepto manu bacillo Araneum quendam ex ijs, qui circulares telas, quas <lb/>
<expan abbr="n&otilde;nulli">nonnulli</expan>, &amp; quidem apt&egrave; labyrinthos appellant, ingenio <expan abbr="vtiq;">vtique</expan> mathematico <lb/>contexunt, &longs;ic adij, vt Araneus pro arbitrio &longs;uper bacillum liber&egrave; inambu&shy;<lb/>
laret, dum ip&longs;e interim curio&longs;ius illum ob&longs;eruarem, quanam videlicet ex <lb/>
parte filum foras ederet; cum ecce tibi Araneus experienti mihi vltr&ograve; fa&shy;<lb/>
uens &longs;e &longs;e ex baculo demi&longs;it, ita tamen, vt ex filo &longs;uo in aere &longs;u&longs;pen&longs;us re&shy;<lb/>
maneret. </s>
          <s id="s.003538">cum primum ob&longs;eruo ip&longs;um inuer&longs;um, hoc e&longs;t capite deor&longs;um, &amp; <lb/>
ventre &longs;ur&longs;um pendere. </s>
          <s id="s.003539">vt autem acutius cernerem, eum opac&aelig; cuidam rei <lb/>
oppo&longs;ui, ne pr&aelig; nimia luce tenui&longs;&longs;imum aranei filum aciem oculorum effu&shy;<lb/>
geret; quo facto in temperata luce illa, clari&longs;&longs;im&egrave; videbam filum ex &longs;ece&longs;&longs;u <lb/>
aranei prodire. </s>
          <s id="s.003540"><expan abbr="Araneum&qacute;">Araneumque</expan>; vno pede filum illud retinere, ne amplius exi&shy;<lb/>
ret, <expan abbr="longius&qacute;">longiusque</expan>; fieret, qu&agrave;m &longs;uo con&longs;ilio par e&longs;&longs;et. </s>
          <s id="s.003541">coegi deinde ip&longs;um a&longs;cen&shy;<lb/>
dere, &amp; de&longs;cendere &longs;&aelig;pius, donec cert&ograve; certius, mihi con&longs;titi&longs;&longs;et filum illud <lb/>
non ab extrin&longs;eco, vt hoc loco Ari&longs;t. affirmat, &longs;ed ab intrin&longs;eco quippe ex <lb/>
&longs;ece&longs;&longs;u prodire, ac proinde veri&longs;&longs;imam e&longs;&longs;e quamuis ab Ari&longs;t. reiectam De&shy;<lb/>
mocriti &longs;ententiam. </s>
          <s id="s.003542">cum Ari&longs;t. pariter errauit Vly&longs;&longs;es Aldobrandus in &longs;uo <lb/>
de in&longs;ectis pulcherrimo, <expan abbr="atq;">atque</expan> docti&longs;&longs;imo Opere.</s>
        </p>
        <p type="main">
          <s id="s.003543">Verumenimuer&ograve; opportun&egrave; accidit, vt huius dubitationis &longs;olutio, aliam <lb/>
mihi alterius qu&aelig;&longs;tionis, iam olim &longs;ummis votis expetitam afferret expli&shy;<lb/>
cationem. </s>
          <s id="s.003544">ea e&longs;t huiu&longs;modi. </s>
          <s id="s.003545">&longs;&aelig;pius fueram expertus, Araneos quo&longs;dam e&longs;&shy;<lb/>
&longs;e, qui ex vno loco ad alium omnin&ograve; &longs;ibi inacce&longs;&longs;ibilem, tran&longs;eant, &longs;iue quod <lb/>
idem e&longs;t, ex eo loco, ad illum fila deducant, vt ex vna arbore ad aliam; <lb/>
quamuis inter <expan abbr="vtramq;">vtramque</expan> aut aqu&aelig;, aut den&longs;i&longs;&longs;ima &longs;pineta, ac &longs;epes interpo&shy;<lb/>
nantur. </s>
          <s id="s.003546">quod maxim&egrave; mane &aelig;quitantes experimur, dum nobis fila per vias <lb/>
tran&longs;uer&longs;a, oculis, atque vultui obuiantia adh&aelig;rent. </s>
          <s id="s.003547">Qua ratione id Ara&shy;<lb/>neus perficeret, neminem, qui literis manda&longs;&longs;et, reperi, ne ip&longs;um quidem. <lb/>
</s>
          <s id="s.003548">Vly&longs;&longs;em Aldobrandum, qui in hac eruditorum pal&aelig;&longs;tra, maiores no&longs;tros <lb/>
omnes videtur &longs;upera&longs;&longs;e. </s>
          <s id="s.003549">Phy&longs;iologi &agrave; me hac de re interrogati, varij va&shy;<lb/>ria, nec con&longs;entientia re&longs;pondebant. </s>
          <s id="s.003550">Alij aiebant Araneum &longs;e demittere, <lb/>
ac &longs;u&longs;pendere ex vna arbore, &amp; deinde ad aliam &agrave; vento perferri, at ego his <lb/>
minim&egrave; a&longs;&longs;entiebar, quia m Araneo nullum e&longs;&longs;et naturale in&longs;trumentum,


<pb pagenum="212" xlink:href="009/01/212.jpg"/>veluti velum, in quod ventus po&longs;&longs;it impingere. </s>
          <s id="s.003551">Alij Araneum ex vna arbo&shy;<lb/>
re de&longs;cendere, &amp; po&longs;tea alteram con&longs;cendere, interim emi&longs;&longs;um retro filum <lb/>
raptando, ac deinde &longs;ur&longs;um attrahendo attollere, ac pr&aelig;tendere: &longs;ed ho&shy;<lb/>
rum re&longs;pon&longs;ionum ob plurima impedimenta, qu&aelig; tenui&longs;&longs;imum filum &longs;&aelig;pius <lb/>
&longs;cidi&longs;&longs;ent, &longs;ubridens refellebam. </s>
          <s id="s.003552">Alij ver&ograve; aiebant Araneum qualitate qua&shy;<lb/>
dam pr&aelig;ditum e&longs;&longs;e, qua ip&longs;e per aera, non &longs;ecus, ac per aquam pi&longs;ces, &amp; <lb/>
per aerem volucres, ambulare po&longs;&longs;et. </s>
          <s id="s.003553">Verum opinatio i&longs;ta, ne ri&longs;u quidem <lb/>
digna videbatur. </s>
          <s id="s.003554">Huius igitur qu&aelig;&longs;iti &longs;olutionem, quam omnes ad hanc <lb/>
<expan abbr="v&longs;q;">v&longs;que</expan> diem latui&longs;&longs;e put&ograve;, <expan abbr="quam&qacute;">quamque</expan>; omnibus grati&longs;&longs;imam fore cognoui tibi lo&shy;<lb/>
co auctarij initio promi&longs;&longs;i, nunc per&longs;oluam. </s>
          <s id="s.003555">accidit erg&ograve;, vt dicebam, vt <lb/>
dum Araneus fug&aelig; cupidus ex bacillo in temperat&aelig; lucis loco, nimirum &egrave; <lb/>
regione alicuius opaci penderet, vt cernerem ex filo illo, ex quo &longs;u&longs;pende&shy;<lb/>
batur plura alia fila hinc inde alternatim prodire, quemadmodum ex alter&shy;<lb/>
nis arundinum nodis folia ena&longs;ci &longs;olent. </s>
          <s id="s.003556">qu&aelig; fila, innata l&aelig;uitate, per ae&shy;<lb/>
rem quoquo ver&longs;us ceu natantia diffundebantur. </s>
          <s id="s.003557">factum e&longs;t autem, vt eo&shy;<lb/>
rum vnum quendam arboris cuiu&longs;dam ramum attingeret, <expan abbr="ei&qacute;">eique</expan>; &longs;tatim adh&aelig;&shy;<lb/>
reret; quod illic&ograve; Araneus optim&egrave; per&longs;en&longs;it, quippe quod filum illud vi&longs;ce&shy;<lb/>
ribus eius ex altero capite affigeretur, atque per filum illud, alijs ommi&longs;&longs;is, <lb/>&longs;ubit&ograve;, vti egregius funambulus accurrit, &longs;ed tamen pedibus &longs;ur&longs;um, dor&longs;o <lb/>
autem deor&longs;um, non &longs;upra filum, &longs;ed infra ad ramum illum &longs;e contulit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>
me ho&longs;tem &longs;uum fuga &longs;&aelig;pius elu&longs;it. </s>
          <s id="s.003558">Ex qua repetita &longs;&aelig;pius ob&longs;eruatione lu&shy;<lb/>
ce clarius comperi Araneum non &longs;implex filum, &longs;ed ramo&longs;um, ac multiplex <lb/>
emittere, <expan abbr="atq;">atque</expan> aliquando ex &longs;ece&longs;&longs;u etiam ip&longs;o duo &longs;imul eijcere, <expan abbr="alter&utilde;">alterum</expan> quo <lb/>
<figure id="id.009.01.212.1.jpg" place="text" xlink:href="009/01/212/1.jpg"/><lb/>
&longs;u&longs;pendatur, alterum <lb/>
ver&ograve;, quod &longs;orte hac, <lb/>
<expan abbr="atq;">atque</expan> illac volitans, ali&shy;<lb/>
cui rei occurrat, <expan abbr="atq;">atque</expan> <lb/>
h&aelig;reat, per quod po&shy;<lb/>
&longs;tea ip&longs;e incedens, ad <lb/>
locum &longs;ibi prius inac&shy;<lb/>
ce&longs;&longs;um, aditum parat. <lb/>
</s>
          <s id="s.003559">qua inre fures eos per&shy;<lb/>
bell&egrave; imitatur, qui <lb/>&longs;cholas ex funibus con&shy;<lb/>
textas, ac hamis fer&shy;<lb/>
reis munitas, ad fene&shy;<lb/>
&longs;tras proijciunt, vt per <lb/>eas ibi affixas con&longs;cen&shy;<lb/>
dere queant. </s>
          <s id="s.003560">qu&aelig; om&shy;<lb/>
nia ex appo&longs;ita figura <lb/>
melius percipies, vbi <lb/>
ex &longs;ini&longs;tra arbore pen&shy;<lb/>
det Araneus A, ex filo <lb/>
B A, ex quo tanquam <lb/>
rami alia fila C G, D H, <lb/>
E I, M O, F L, alter&shy;


<pb pagenum="213" xlink:href="009/01/213.jpg"/>natim prodeunt, ac per aerem hinc inde volitant. </s>
          <s id="s.003561">Si erg&ograve; filum E I, dextr&aelig; <lb/>
arbori occurrerit, <expan abbr="ei&qacute;">eique</expan>; h&aelig;&longs;erit, vt in figura, illic&ograve; Araneus huius rei con&shy;<lb/>
&longs;cius per filum A E I, a&longs;cendit, <expan abbr="&longs;e&qacute;">&longs;eque</expan>; ad prius inacce&longs;&longs;am &longs;ibi dextram arbo&shy;<lb/>
rem transfert; <expan abbr="atq;">atque</expan> deinde inter <expan abbr="vtramq;">vtramque</expan> ducto iam filo vno, pote&longs;t vltr&ograve;, <lb/>
<expan abbr="citro&qacute;">citroque</expan>; means, &longs;uam etiam circularem, ac labyrinthiacam telam in mu&longs;ca&shy;<lb/>
rum capturam contexere; quales aliquando inter duas arbores admira&shy;<lb/>
ri &longs;olemus.</s>
        </p>
        <p type="main">
          <s id="s.003562">Qu&aelig;res fort&egrave;, num Araneus filum intus tanquam in glomo, vel &longs;pira con&shy;<lb/>
uolutum contineat? </s>
          <s id="s.003563">dicam, quod non &longs;ine experientia conijcio, exi&longs;timo <lb/>
Araneum non continere intra &longs;e filum vllum, verum humorem quendam <lb/>
vi&longs;co&longs;um, qui in tenui&longs;&longs;ima fila &longs;it ductilis; quemadmodum videmus acci&shy;<lb/>
dere gummi, qu&aelig; di&longs;rupta exhibet lentorem quendam, qui &longs;olo attritu ita <lb/>
digitis h&aelig;ret, vt amoto &longs;en&longs;im digito, filum tenue, &amp; oblongum vald&egrave; de&shy;<lb/>
ducatur, hoc inde conijcio, quia aliquando cum ventrem Araneorum &longs;ecui&longs;&shy;<lb/>
&longs;em nullum intus filum, &longs;ed &longs;olus humor quidam lentus apparuit.</s>
        </p>
        <p type="main">
          <s id="s.003564">C&ugrave;m ex paruulis hi&longs;ce meis ob&longs;eruationibus circa animalculum i&longs;tud <lb/>
vnum tam pr&aelig;clara cognoui&longs;&longs;em, qu&aelig; nullus ad hanc <expan abbr="v&longs;q;">v&longs;que</expan> diem, quod &longs;ciam <lb/>
ob&longs;erua&longs;&longs;et; animaduerti lati&longs;&longs;imum patere campum ad animalium hi&longs;to&shy;<lb/>
riam ampliandam, &longs;i ij, qui huic pulcherrim&aelig; cognitioni dant operam, non <lb/>
ijs &longs;olum, qu&aelig; ab alijs per&longs;cripta &longs;unt contenti e&longs;&longs;ent, ver&ugrave;m etiam certi&longs;&shy;<lb/>
&longs;imis, <expan abbr="atq;">atque</expan> explorati&longs;&longs;imis experientijs ea coniungerent.</s>
        </p>
        <p type="main">
          <s id="s.003565">Atque h&aelig;c de Araneo &longs;atis.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003566"><emph type="italics"/>De ince&longs;&longs;u animalium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003567"><arrow.to.target n="marg284"/></s>
        </p>
        <p type="margin">
          <s id="s.003568"><margin.target id="marg284"/>294</s>
        </p>
        <p type="main">
          <s id="s.003569">Cap. 7. <emph type="italics"/>&lpar;Etenim habentia pedes, quoniam &longs;uper <expan abbr="vtrumq;">vtrumque</expan> oppo&longs;itorum cru&shy;<lb/>
rum vici&longs;&longs;im &longs;tant, pondusqu&eacute; &longs;ustinent, nece&longs;&longs;e habent altero progredien&shy;<lb/>
te, inflectere alterum; &aelig;qualia namque longitudine nata &longs;unt habere op&shy;<lb/>
po&longs;ita membra. </s>
          <s id="s.003570">&amp; quod ponderi &longs;ub&longs;tat rectum e&longs;&longs;e oportet, vt perpen&shy;<lb/>
diculum ad terram. </s>
          <s id="s.003571">quando autem progreditur, fit hypotenu&longs;a, valens manentem <lb/>
magnitudinem, &amp; eam, qu&aelig; interiacet. </s>
          <s id="s.003572">quoniam autem &aelig;qualia &longs;unt membra, ne&shy;<lb/>
ce&longs;&longs;e e&longs;t inflecti id, quod manet, aut in poplite, aut in conflexione&rpar;<emph.end type="italics"/> Vult probare <lb/>
in gre&longs;&longs;u nece&longs;&longs;ariam e&longs;&longs;e aliquam flexionem membrorum. </s>
          <s id="s.003573">verum prius <lb/>
&longs;ciendum, quod lineam hypotenu&longs;am, quemadmodum etiam Athen&aelig;us lib. <lb/>
<!-- REMOVE S-->10. te&longs;tatur, eam appellant geometr&aelig;, qu&aelig; in triangulo rectangulo recto <lb/>
angulo &longs;ubtenditur, vnde &amp; denominata e&longs;t hypotenu&longs;a, ide&longs;t &longs;ubten&longs;a, vt <lb/>
<figure id="id.009.01.213.1.jpg" place="text" xlink:href="009/01/213/1.jpg"/><lb/>
in triangulo A B C, cuius angulus B, rectus &longs;it, recta <lb/>
A C, angulo recto B, &longs;ubten&longs;a, hypotenu&longs;a dicitur. <lb/>
</s>
          <s id="s.003574">Ari&longs;t. igitur ait, quod antequam animal ambulare in&shy;<lb/>
cipiat, dum &longs;cilicet manet, habet crura, qu&aelig; manent <lb/>
recta, &longs;iue perpendicularia horizonti, cum autem in&shy;<lb/>
cipit progredi nece&longs;&longs;e e&longs;t <expan abbr="vtr&utilde;q;">vtrunque</expan> crus inclinari ad ho&shy;<lb/>
rizontem. </s>
          <s id="s.003575">nam primum crus in ingre&longs;&longs;u prolatum fit <lb/>
hypotenu&longs;a, quia &longs;cilicet &longs;ubtendit angulum rectum, <lb/>
quem facit alterum crus adhuc quie&longs;cens, cum hori&shy;


<pb pagenum="214" xlink:href="009/01/214.jpg"/>zonte; vt in &longs;uperiori triangulo, &longs;i concipiamus crura fui&longs;&longs;e duo latera A B, <lb/>
A D, qu&aelig; manente animali, fui&longs;&longs;ent ambo &longs;imul in &longs;itu A B, perpendicula&shy;<lb/>
ria horizonti; incipiens autem animal ambulare, proferat primo crus A D, <lb/>
A D, fiet hypotenu&longs;a trianguli A B C, &amp; quia crus hoc A D, factum hypo&shy;<lb/>tenu&longs;a &aelig;quale e&longs;t alteri manenti A B, nequit totius ver&aelig; hypotenu&longs;&aelig; A C, <lb/>officio fungi, qu&aelig; &aelig;quiualet toti A D, &amp; pr&aelig;terea interiacenti D C, vt ea au&shy;<lb/>
<figure id="id.009.01.214.1.jpg" place="text" xlink:href="009/01/214/1.jpg"/><lb/>tem hypotenu&longs;a debet e&longs;&longs;e maior, quia opponitur <lb/>
maiori angulo nimirum recto B, quam latus A B, <lb/>
quod angulo acuto C, opponitur per 19. primi, &amp; <lb/>
propterea ni&longs;i alterum &longs;ub&longs;equens crus A B, incli&shy;<lb/>
netur, vt in &longs;ecunda figura, non pote&longs;t hypotenu&longs;a <lb/>
A D, terram attingere, <expan abbr="atq;">atque</expan> hac de cau&longs;a nece&longs;&longs;e <lb/>
e&longs;t, vt initio gre&longs;&longs;us <expan abbr="vtrumq;">vtrumque</expan> crus, quod prius per&shy;<lb/>
pendiculare erat, inclinetur; inclinato igitur crure <lb/>
A B, antror&longs;um tunc prolatum crus A C, terram <lb/>
contingit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; factus e&longs;t primus gre&longs;&longs;us B C.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003576"><arrow.to.target n="marg285"/></s>
        </p>
        <p type="margin">
          <s id="s.003577"><margin.target id="marg285"/>295</s>
        </p>
        <p type="main">
          <s id="s.003578">Eodem loco <emph type="italics"/>&lpar;Signum autem, quod hoc ita &longs;e habet illud est. </s>
          <s id="s.003579">&longs;i quis enim iuxta <lb/>
parietem per terram ambulet, qu&aelig; de&longs;ignatur linea non e&longs;t recta, &longs;ed obtorta, quo&shy;<lb/>
niam minorem quidem flectentis fieri de&longs;criptam nece&longs;&longs;e e&longs;t; &longs;tantis autem, &amp; ere&shy;<lb/>
cti maiorem&rpar;<emph.end type="italics"/> Vt probet, quod animal in gradiendo modo attollitur, modo <lb/>
deprimitur, &longs;ignum hoc affert, quia &longs;i quis &longs;ecus parietem per terram am&shy;<lb/>
bulet, linea quam vertex capitis in pariete de&longs;ignat non e&longs;t recta, &longs;eb obtor&shy;<lb/>
ta: qu&aelig; linea optim&egrave; de&longs;ignatur, &longs;i ambulantis vmbra in pariete apparens <lb/>
&longs;imul, cum ip&longs;o in pariete ambulet; videmus enim vmbram illam modo al&shy;<lb/>
tiorem fieri, modo breuiorem; quod &longs;ignum e&longs;t ambulantem modo incli&shy;<lb/>
nari, quando &longs;cilicet crus alterum profert, &longs;eu crura dilatat; modo erigi, <lb/>cum crus &longs;ub&longs;equens pr&aelig;cedenti coniungit, tune enim incedens fit horizon&shy;<lb/>
ti perpendicularis.</s>
        </p>
        <p type="main">
          <s id="s.003580"><arrow.to.target n="marg286"/></s>
        </p>
        <p type="margin">
          <s id="s.003581"><margin.target id="marg286"/>296</s>
        </p>
        <p type="main">
          <s id="s.003582">Eodem cap. <emph type="italics"/>&lpar;Quoniam autem fiat ad rectum, vel concidet recto minore effe&shy;<lb/>
cto, vel non progredietur: &longs;i enim altero crure recto progreditur alterum, maius <lb/>
erit cum &longs;it &aelig;quale: hoc <expan abbr="nanq;">nanque</expan> poterit, &amp; id, quod quie&longs;cit, &amp; ip&longs;am hypotenu&shy;<lb/>
&longs;am, nece&longs;&longs;e igitur e&longs;t, &amp; inflectere id, quod procurrit, &amp; inflexum &longs;imul alterum <lb/>
extendere, membra enim triangulorum &aelig;quilaterorum efficiuntur, <expan abbr="caput&qacute;">caputque</expan>, fit infe&shy;<lb/>
rius, vbi perpendiculum fuerit, in quo firmatum e&longs;t&rpar;<emph.end type="italics"/> H&aelig;c &longs;unt fer&egrave; eadem cum <lb/>
ijs, qu&aelig; in primo huius capitis loco dicta &longs;unt. </s>
          <s id="s.003583">proinde ea cum duabus illis <lb/>
triangulorum figuris repetenda &longs;unt, vt breuius qu&aelig; nunc re&longs;tant explicen&shy;<lb/>
tur. </s>
          <s id="s.003584">quoniam igitur animal antequam gradiatur, maxim&egrave; homo, &longs;tat hori&shy;<lb/>
zonti perpendicularis, nece&longs;&longs;e e&longs;t ad progrediendum, vt fiat aliqua mem&shy;<lb/>
brorum inflexio, &longs;i enim homo &longs;ine vlla &longs;ui corporis flexura inclinet &longs;e ad <lb/>
horizontem, ita vt cum horizonte faciat ex anteriori parte. </s>
          <s id="s.003585">v. <!-- REMOVE S-->g. <!-- REMOVE S-->angulum <lb/>
recto minorem, &longs;iue acutum, vel concidet, vel non poterit progredi; &longs;i enim <lb/>
alterum crus pr&aelig;mitteretur, altero manente perpendiculari, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; progre&shy;<lb/>
deretur qui&longs;piam, &longs;equeretur crus prolatum, quale e&longs;t A D, iu priori trian&shy;<lb/>
gulo, debere fieri maius altero crure A B, manente, quia fieret tota hypo&shy;<lb/>
tenu&longs;a A C, &longs;ie enim terram attingeret; at non pote&longs;t fieri illo maius, quia <lb/>
e&longs;t illi &aelig;quale, erg&ograve; hac ratione ince&longs;&longs;us fieri nequit. </s>
          <s id="s.003586">nece&longs;&longs;e igitur refle&shy;


<pb pagenum="215" xlink:href="009/01/215.jpg"/>ctere <expan abbr="vtrumq;">vtrumque</expan> crus non &longs;olum ad horizontem, &longs;ed etiam circa aliquam cor&shy;<lb/>
poris flexuram, vel nodum, vt circa genu, aut alia. </s>
          <s id="s.003587">crura enim in gre&longs;&longs;u fiunt <lb/>
latera &longs;uperiora trianguli i&longs;o&longs;celis, vt in &longs;ecunda figura patuit, cuius ba&longs;is <lb/>
e&longs;t pa&longs;&longs;us. </s>
          <s id="s.003588">&amp; tunc caput ambulantis fit inferius, qu&agrave;m antequam gradere&shy;<lb/>
<figure id="id.009.01.215.1.jpg" place="text" xlink:href="009/01/215/1.jpg"/><lb/>
tur; quia tunc ambo crura erant horizonti perpen&shy;<lb/>
dicularia. </s>
          <s id="s.003589">quando autem caput fuerit in linea <expan abbr="per-p&etilde;diculari">per&shy;<lb/>
pendiculari</expan> trianguli i&longs;o&longs;celis, tunc erit inferius qu&agrave;m <lb/>
alibi, vt in pr&etail;&longs;enti figura, linea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> trian&shy;<lb/>
guli huius i&longs;o&longs;celis e&longs;t linea A E, quia ba&longs;i B C, per&shy;<lb/>
pendicularis incidit; quando igitur caput ambulan&shy;<lb/>
tis. </s>
          <s id="s.003590">v. <!-- REMOVE S-->g. <!-- REMOVE S-->D, fuerit in hac linea, <expan abbr="t&utilde;c">tunc</expan> erit inferius qu&agrave;m <lb/>
in quauis alia gre&longs;&longs;us parte: quia tunc crura A B, <lb/>
A C, &longs;unt maxim&egrave; diuaricata, &amp; proinde angulus A, <lb/>
&amp; &longs;imul punctum D, maxim&egrave; demi&longs;&longs;a.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003591"><emph type="italics"/>De motu animalium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003592"><arrow.to.target n="marg287"/></s>
        </p>
        <p type="margin">
          <s id="s.003593"><margin.target id="marg287"/>297</s>
        </p>
        <p type="main">
          <s id="s.003594">Cap. 1. <emph type="italics"/>&lpar;Primum quidem in animalibus: oportet enim &longs;i moueatur aliqua <lb/>particularum quie&longs;cere aliquam, &amp; propter hoc, &amp; flexus animalibus <lb/>in&longs;unt: tanquam enim centro vtuntur flexibus &amp; fit tota pars, in qua <lb/>
e&longs;t flexus &amp; vna, &amp; du&aelig;; &amp; recta, &amp; flexa, qu&aelig; permutatur potentia, <lb/>
&amp; actu, propter flexum. </s>
          <s id="s.003595">cum autem flectitur, &amp; mouetur, hoc quidem &longs;ignum mo-<emph.end type="italics"/><lb/>
<figure id="id.009.01.215.2.jpg" place="text" xlink:href="009/01/215/2.jpg"/><lb/>
<emph type="italics"/>vetur, illud autem manet in flexibus, quemadmodum <expan abbr="vtiq;">vtique</expan> &longs;i dia&shy;<lb/>
metri, qu&aelig; quidem A D, maneat, qu&aelig; cutem B, moueatur, &amp; <lb/>
fiat A C, &longs;ed hic quidem videtur, &longs;ecundum omnem modum in&shy;<lb/>
diui&longs;ibile e&longs;&longs;e centrum. </s>
          <s id="s.003596">etenim moueri, vt aiunt, fingunt in ip&longs;is, <lb/>
non enim mouetur mathematicorum aliquid.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003597">Intendit probare nece&longs;&longs;e e&longs;&longs;e ad motum animalium, vt <lb/>
vna pars quie&longs;cat, dum altera mouetur. </s>
          <s id="s.003598">propter hoc enim inquit flexus ani&shy;<lb/>
malibus in&longs;unt, vbi in gr&aelig;co pro voce flexus legitur <foreign lang="greek">kampth,</foreign> quod &longs;ignifi&shy;<lb/>
cat nodum, articulum, &amp; <expan abbr="deniq;">denique</expan> locum ip&longs;um, vbi fit membri flexura, tan&shy;<lb/>
quam enim centro quodam vtuntur flexibus, ide&longs;t nodis, &longs;eu iunctur&aelig; &longs;unt <lb/>
in motu membrorum in&longs;tar centri. </s>
          <s id="s.003599">v. <!-- REMOVE S-->g. <!-- REMOVE S-->nodus cubiti fit centrum, cum bra&shy;<lb/>
chij parte, qu&aelig; e&longs;t inter humerum, &amp; cubitum manente, reliquum brachij <lb/>
circumducimus; &longs;ic manente genu tanquam centro, crus huc illud agita&shy;<lb/>
mus, &amp; fit tota pars. </s>
          <s id="s.003600">v. <!-- REMOVE S-->g. <!-- REMOVE S-->totum brachium, in quo e&longs;t cubiti iunctura, &amp; vna <lb/>
tota pars, quando manet rectum; &amp; du&aelig; <expan abbr="qu&atilde;do">quando</expan> in flexura cubiti brachium <lb/>inflectitur; &amp; fit tota h&aelig;c longitudo recta prius, po&longs;tea flexa: qu&aelig; propter <lb/>
flexuram modo vna e&longs;t actu, &longs;ed du&aelig; potentia. </s>
          <s id="s.003601">modo du&aelig; in actu, &longs;ed vna in <lb/>
potentia. </s>
          <s id="s.003602">cum autem flectitur, &amp; mouetur brachium, vnum quidem &longs;ignum, <lb/>
&longs;iue punctum, quod e&longs;t extremum partis manentis, manet; alterum ver&ograve; &longs;i&shy;<lb/>
gnum, &longs;iue punctum, quod e&longs;t extremum partis mot&aelig; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; alteri &longs;igno con&shy;<lb/>
tiguum mouetur &longs;imul cum tota parte mota. </s>
          <s id="s.003603">quemadmodum, &longs;i diametri <lb/>
&longs;uperioris figur&aelig;, pars D A, maneat, pars autem A B, moueatur ad A C, <lb/>
erit huius flexur&aelig; centrum A, quod vt extremum line&aelig; D A, manentis, ma&shy;


<pb pagenum="216" xlink:href="009/01/216.jpg"/>net: vt ver&ograve; extremum mot&aelig; A B, mouetur. </s>
          <s id="s.003604">quamuis in mathematicis h&aelig;c <lb/>
quidem duorum centrorum di&longs;tinctio nulla &longs;it, quia centrum mathemati&shy;<lb/>
cum omnin&ograve; indiuiduum e&longs;t: neque in mathematicis e&longs;t propri&egrave; motus, <lb/>
quamuis enim aliquando Mathematici dicant, &longs;i linea, vel &longs;i punctum mo&shy;<lb/>
ueretur, vel moueatur, &amp; &longs;imilia, huiu&longs;modi tamen motus &longs;unt rebus ma&shy;<lb/>
thematicis extrin&longs;eci, nec quatenus hoc modo mouentur con&longs;iderantur: <lb/>
patet igitur, qua ratione Ari&longs;tot. partem manentem in motu nece&longs;&longs;ariam <lb/>
e&longs;&longs;e velit.</s>
        </p>
        <p type="main">
          <s id="s.003605"><arrow.to.target n="marg288"/></s>
        </p>
        <p type="margin">
          <s id="s.003606"><margin.target id="marg288"/>298 a</s>
        </p>
        <p type="main">
          <s id="s.003607">Cap. 5. <emph type="italics"/>&lpar;Quemadmodum autem &longs;pontanea mouentur paruo motu facto&rpar;<emph.end type="italics"/> Spon&shy;<lb/>
tanea i&longs;ta erant machin&aelig;, qu&aelig; &agrave; &longs;eip&longs;is mouebantur, quas Gr&aelig;ci automata <lb/>dixerunt, cuiu&longs;modi &longs;unt Automata Heronis Alexandrini, qu&aelig; adhuc <expan abbr="ext&atilde;t">extant</expan>.</s>
        </p>
        <p type="main">
          <s id="s.003608">Cap. 8. E&longs;t ibi quoddam triangulum cum elementis more geometrarum <lb/>
depictum, vnde locus ille videri po&longs;&longs;it mathematicus, verumtamen nullo <lb/>
modo geometri&aelig; auxilio indiget.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003609"><emph type="italics"/>De generatione animalium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003610"><arrow.to.target n="marg289"/></s>
        </p>
        <p type="margin">
          <s id="s.003611"><margin.target id="marg289"/>298.b</s>
        </p>
        <p type="main">
          <s id="s.003612">Lib. 2. cap. 1. <emph type="italics"/>&lpar;Sitqu&eacute; perinde ac admirabilia illa &longs;pontanea&rpar;<emph.end type="italics"/> Intelligit ma&shy;<lb/>
chinas illas miro artificio confictas, qu&aelig; &agrave; &longs;e ip&longs;is intrin&longs;eco prin&shy;<lb/>
cipio mouebantur, quas Gr&aelig;ci veteres Automata, ide&longs;t &longs;pontanea, <lb/>
vel &longs;pontina, vt vertit Interpres vocabant, cuiu&longs;modi &longs;unt Auto&shy;<lb/>
mata Heronis Alexandrini, qu&aelig; adhuc extant gr&aelig;ca, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; ab Abbate Gua&shy;<lb/>
&longs;tallen&longs;i in Italicum &longs;unt conuer&longs;a. </s>
          <s id="s.003613">Automata hodie &longs;unt Horologia, qu&aelig; ex <lb/>
multis dentatis rotis Germani con&longs;truunt.</s>
        </p>
        <p type="main">
          <s id="s.003614"><arrow.to.target n="marg290"/></s>
        </p>
        <p type="margin">
          <s id="s.003615"><margin.target id="marg290"/>299</s>
        </p>
        <p type="main">
          <s id="s.003616">Lib. 2. cap. 4. <emph type="italics"/>&lpar;Nam &amp; triangula figura duobus rectis &aelig;quale &longs;emper habet&rpar;<emph.end type="italics"/><lb/>
vide qu&aelig; de hac re &longs;crip&longs;i lib. 1. Priorum, &longs;ecto 3. cap. 1.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003617"><arrow.to.target n="marg291"/></s>
        </p>
        <p type="margin">
          <s id="s.003618"><margin.target id="marg291"/>300</s>
        </p>
        <p type="main">
          <s id="s.003619">Ibidem <emph type="italics"/>&lpar;Et diametrum incommen&longs;urabilem e&longs;&longs;e cum co&longs;ta &longs;empiternum e&longs;t: at&shy;<lb/>
tamen cau&longs;a eorum aliqua &amp; demon&longs;tratio e&longs;t.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003620">Qu&aelig; libro 1. Priorum, &longs;ecto 1. cap. 23. de hac re annotata &longs;unt, abund&egrave; <lb/>
huic etiam loco &longs;atisfaciunt.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003621"><emph type="italics"/>In Ethica, &longs;eu Moralia ad Nicomachum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003622"><arrow.to.target n="marg292"/></s>
        </p>
        <p type="margin">
          <s id="s.003623"><margin.target id="marg292"/>301</s>
        </p>
        <p type="main">
          <s id="s.003624">Lib. 1. cap. 7. <emph type="italics"/>&lpar;Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/>
<expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>
ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat&rpar;<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/>
confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/>
<figure id="id.009.01.216.1.jpg" place="text" xlink:href="009/01/216/1.jpg"/><lb/>
qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>
&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>
ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>
ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>
conficiunt. </s>
          <s id="s.003625">Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>
gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>
pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s>
          <s id="s.003626">10. primi,


<pb pagenum="217" xlink:href="009/01/217.jpg"/>vt in figura, vbi linea A B, in&longs;i&longs;tens alteri D C, perpendiculariter, ide&longs;t ita <lb/>
vt faciat angulos hinc inde &aelig;qualis A B D, A B C, pr&aelig;dictos inquam duos <lb/>
angulos con&longs;iderat e. </s>
          <s id="s.003627">&longs;e rectos. </s>
          <s id="s.003628">contemplatur pr&aelig;terea Geometra omnes <lb/>
angulos rectos e&longs;&longs;e inter &longs;e &aelig;quales, vt in 12. axiomate primi Elem. ponitur, <lb/>
&amp; &longs;imilia plura alia, quorum con&longs;iderationem Faber omnin&ograve; negligit.</s>
        </p>
        <p type="main">
          <s id="s.003629"><arrow.to.target n="marg293"/></s>
        </p>
        <p type="margin">
          <s id="s.003630"><margin.target id="marg293"/>302</s>
        </p>
        <p type="main">
          <s id="s.003631">Libro 2. capite 6. <emph type="italics"/>&lpar;Id quod &longs;ecundum Arithmeticam rationem medium e&longs;t&rpar;<emph.end type="italics"/><lb/>
Arithmetica ratio, fiue proportio ea e&longs;t, cuius termini cre&longs;cunt per &aelig;qua&shy;<lb/>
les exce&longs;&longs;us, vt 2. 6. 10. 14. horum enim terminorum exce&longs;&longs;us &aelig;quales &longs;unt, <lb/>
cum &longs;int omnes quaternarij. </s>
          <s id="s.003632">&longs;imiliter inter hos terminos 3. 6. 9. 12. e&longs;t arith&shy;<lb/>
metica analogia, c&ugrave;m omnes ternario numero &longs;uperent pr&aelig;cedentes, &amp; &agrave; <lb/>
&longs;equentibus &longs;uperentur. </s>
          <s id="s.003633">Porr&ograve; apud Mathematicos tria &longs;unt genera pro&shy;<lb/>
portionum, &longs;iue medietatum, Arithmetica quam modo &longs;uppo&longs;ui; Geome&shy;<lb/>
trica, &amp; Harmonica, quas inferius oblata occa&longs;ione opportunius explicabo.</s>
        </p>
        <figure id="id.009.01.217.1.jpg" place="text" xlink:href="009/01/217/1.jpg"/>
        <p type="main">
          <s id="s.003634"><arrow.to.target n="marg294"/></s>
        </p>
        <p type="margin">
          <s id="s.003635"><margin.target id="marg294"/>303</s>
        </p>
        <p type="main">
          <s id="s.003636">Lib. 2. cap. 9. <emph type="italics"/>&lpar;Vt circuli medium deprehendere non <lb/>
cuiu&longs;libet, &longs;ed <expan abbr="&longs;ci&etilde;tis">&longs;cientis</expan> &longs;olummodo e&longs;t&rpar;<emph.end type="italics"/> Reperire medium, <lb/>
&longs;iue centrum dati circuli docet Euclides propo&longs;itio&shy;<lb/>
ne prima 3. hoc modo. </s>
          <s id="s.003637">in dato circulo ducatur vt&shy;<lb/>
cunque recta B C, qu&aelig; per 10. primi diuidatur bifa&shy;<lb/>
riam in F, &amp; per F, ducatur <expan abbr="perp&etilde;dicularis">perpendicularis</expan> A E F D, <lb/>
qu&aelig; &longs;ecetur bifariam in E, <expan abbr="erit&qacute;">eritque</expan>; punctum E, non &longs;o&shy;<lb/>
lum ip&longs;ius line&aelig; medium; &longs;ed etiam totius circuli <lb/>centrum, quemadmodum ibi demon&longs;trat Euclides.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003638"><arrow.to.target n="marg295"/></s>
        </p>
        <p type="margin">
          <s id="s.003639"><margin.target id="marg295"/>304</s>
        </p>
        <p type="main">
          <s id="s.003640">Lib. 3. cap. 3. <emph type="italics"/>&lpar;De &aelig;ternis autem nemo con&longs;ultat, vt <lb/>
de mundo, aut diametro, &amp; latere, quod nulla inter &longs;e <lb/>
&aelig;quabilitate conueniant&rpar;<emph.end type="italics"/> Qua ratione diameter, &amp; latus eiu&longs;dem quadrati <lb/>nulla &aelig;quabilitate, ide&longs;t nulla communi men&longs;ura inter &longs;e conueniant, fus&egrave; <lb/>
explicatum e&longs;t libro Priorum, &longs;ecto 1. cap. 23.</s>
        </p>
        <p type="main">
          <s id="s.003641"><arrow.to.target n="marg296"/></s>
        </p>
        <p type="margin">
          <s id="s.003642"><margin.target id="marg296"/>305</s>
        </p>
        <p type="main">
          <s id="s.003643">Eodem cap. <emph type="italics"/>&lpar;Qui enim con&longs;ultat qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, <lb/>
quemadmodum de&longs;ignationes&rpar;<emph.end type="italics"/> Per de&longs;ignationes Ari&longs;t. intelligere geometri&shy;<lb/>
cas demon&longs;trationes &longs;&aelig;pius dictum e&longs;t in logicis textibus, quod pariter ex <lb/>
hoc loco confirmatur. </s>
          <s id="s.003644">quando autem ait <emph type="italics"/>&lpar;Re&longs;oluere pr&aelig;dicto modo, quemad&shy;<lb/>
modum de&longs;ignationes&rpar;<emph.end type="italics"/> innuit re&longs;olutionem geometricam, de qua abund&egrave; di&shy;<lb/>
ctum e&longs;t in explicatione tituli librorum Re&longs;olutoriorum; quam expo&longs;ui, ni&shy;<lb/>
hil aliud e&longs;&longs;e, quam medij inqui&longs;itionem ad id, quod propo&longs;itum fuerit de&shy;</s>
        </p>
        <p type="main">
          <s id="s.003645"><arrow.to.target n="marg297"/><lb/>
mon&longs;trandum. </s>
          <s id="s.003646">veram autem, <expan abbr="atq;">atque</expan> germanam fui&longs;&longs;e huiu&longs;modi explicatio&shy;<lb/>nem, hoc loco Ari&longs;t. ip&longs;e confirmat, cum hanc re&longs;olutionem dicat e&longs;&longs;e &longs;imi&shy;<lb/>
lem con&longs;ultationi, &longs;iue inqui&longs;itioni mediorum ad finem in rebus practicis <lb/>con&longs;equendum; ip&longs;a ver&ograve; e&longs;t inqui&longs;itio mediorum ad id, quod in rebus &longs;pe&shy;<lb/>
culatiuis propo&longs;itum e&longs;t, demon&longs;trandum. </s>
          <s id="s.003647">con&longs;ultatio igitur e&longs;t in rebus <lb/>
practicis, quod in &longs;peculatiuis e&longs;t re&longs;olutio.<lb/>
<arrow.to.target n="marg298"/></s>
        </p>
        <p type="margin">
          <s id="s.003648"><margin.target id="marg297"/>306</s>
        </p>
        <p type="margin">
          <s id="s.003649"><margin.target id="marg298"/>307</s>
        </p>
        <p type="main">
          <s id="s.003650">Lib. 5. cap. 3. <emph type="italics"/>&lpar;Quod enim proportione con&longs;tat, id non tam vnitario numero, <lb/>
qu&agrave;m numero in vniuer&longs;um proprium e&longs;t&rpar;<emph.end type="italics"/> Per vnitarium numerum intelligitur <lb/>numerus ex vnitatibus ab&longs;tractis conφlatus, ide&longs;t, cuius vnitates non &longs;int res <lb/>
phy&longs;ic&aelig;, &longs;ed &agrave; naturalibus ab&longs;tract&aelig;, qualis con&longs;iderat Arithmeticus: omni <lb/>tamen numero &longs;iue ab&longs;tracto, &longs;iue non, conuenit proportiones &longs;u&longs;cipere, <lb/>
id e&longs;t &amp; numero, &amp; rebus numeratis.</s>
        </p>
        <pb pagenum="218" xlink:href="009/01/218.jpg"/>
        <p type="main">
          <s id="s.003651"><arrow.to.target n="marg299"/></s>
        </p>
        <p type="margin">
          <s id="s.003652"><margin.target id="marg299"/>308</s>
        </p>
        <p type="main">
          <s id="s.003653">Ibidem <emph type="italics"/>&lpar;N im proportio &aelig;qualitas e&longs;t rationum&rpar;<emph.end type="italics"/> Per proportionem hoc lo&shy;<lb/>
co intelligenda e&longs;t illa, quam nunc appellant proportionalitatem, qu&aelig; e&longs;t <lb/>
duarum rationum, &longs;eu proportionum &longs;imilitudo, &longs;iue &aelig;qualitas, vt manife&shy;<lb/>
&longs;tum e&longs;t ex 4. definit. </s>
          <s id="s.003654">5. Elem. v. <!-- REMOVE S-->g. <!-- REMOVE S-->cum &longs;it eadem ratio 9. ad 6. qu&aelig; e&longs;t 6. ad <lb/>
4. propterea h&aelig;c rationum &longs;imilitudo, vel &aelig;qualitas dicitur ip&longs;a proportio, <lb/>
&longs;eu di&longs;tinctionis gratia Proportionalitas.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003655"><arrow.to.target n="marg300"/></s>
        </p>
        <p type="margin">
          <s id="s.003656"><margin.target id="marg300"/>309</s>
        </p>
        <p type="main">
          <s id="s.003657">Ibidem <emph type="italics"/>&lpar;In quatuorqu&eacute; minimis reperitur, di&longs;iunctam &longs;an&egrave; in quatuor con&longs;istere <lb/>per&longs;picuum e&longs;t: &longs;ed &amp; continentem nihilominus, vno enim h&aelig;c perinde, aψ duobus <lb/>vtitur, bi&longs;que id accipit in hunc modum, qualis primi re&longs;pectus e&longs;t ad &longs;ecundum, <lb/>talis &longs;ecundi ad tertium; bis enim hic, &longs;ecundum dictum e&longs;t, quare &longs;i &longs;ecundum bis <lb/>
po&longs;itum &longs;it, quatuor erunt ea, qu&aelig; con&longs;tant proportione&rpar;<emph.end type="italics"/> Qu&aelig; hic ab Ari&longs;tot. di&shy;<lb/>
cuntur de&longs;umpta &longs;unt, partim ex definit. </s>
          <s id="s.003658">6. 5. partim ex 9. definit. </s>
          <s id="s.003659">eiu&longs;dem. <lb/>
</s>
          <s id="s.003660">breuiter autem &longs;ic &longs;e habent. </s>
          <s id="s.003661">Ad con&longs;tituendam proportionalitatem ne&shy;<lb/>
ce&longs;&longs;arij &longs;unt omnin&ograve; quatuor termini, quod quidem primum per&longs;picuum <lb/>e&longs;t in ea proportionalitate, quam Di&longs;iunctam vocant, qu&aelig; e&longs;t huiu&longs;modi, <lb/>
vt 9. ad 6. ita 3. ad 2. deinde <expan abbr="ver&utilde;">verum</expan> e&longs;t etiam in ea, quam continuam dicunt, <lb/>
qu&aelig; talis e&longs;t, vt 9. ad 6. ita 6. ad 4. qu&aelig; in tribus quidem terminis 9. 6. 4. <lb/>con&longs;i&longs;tit, &longs;ed tamen, quia medius 6. <expan abbr="vtrumq;">vtrumque</expan> re&longs;picit extremum, ide&ograve; vices <lb/>
duorum gerit, ac proinde e&longs;t, ac &longs;i hoc modo termini di&longs;ponantur 9. 6. 6. 4. <lb/>
vbi 6. bis ponitur, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; quatuor huius etiam proportionalitatis termini. <lb/>
</s>
          <s id="s.003662">hinc Ari&longs;t. textum &longs;atis intelligere poteris.</s>
        </p>
        <p type="main">
          <s id="s.003663"><arrow.to.target n="marg301"/></s>
        </p>
        <p type="margin">
          <s id="s.003664"><margin.target id="marg301"/>310</s>
        </p>
        <p type="main">
          <s id="s.003665">Eodem cap. <emph type="italics"/>&lpar;Sicut igitur primus terminus &longs;e habebit ad &longs;ecundum, ita tertius <lb/>
ad quartum; igitur etiam alterna vice, &longs;icut primus ad tertium, ita &longs;ecundus ad <lb/>
quartum. </s>
          <s id="s.003666">quare etiam totum ad totum, quod di&longs;tributio binatim copulat. </s>
          <s id="s.003667">qu&aelig; &longs;i <lb/>
etiam ita compo&longs;ita fuerint, iust&egrave; copulat&rpar;<emph.end type="italics"/> Accipit Ari&longs;t. illum argumentandi <lb/>
modum, quem Geometr&aelig; alternam rationem vocant, <expan abbr="qu&agrave;m&qacute;">qu&agrave;mque</expan>; definit. </s>
          <s id="s.003668">12. <lb/>
5. exponunt, vt eam rebus ip&longs;is accommodet, <expan abbr="atq;">atque</expan> in praxim deducat; e&longs;t <lb/>
autem huiu&longs;modi, &longs;int primum quatuor termini proportionales, ide&longs;t, vt <lb/>
primus ad &longs;ecundum, ita tertius ad quartum. </s>
          <s id="s.003669">v. <!-- REMOVE S-->g. <!-- REMOVE S-->vt 9. ad 6. ita 3. ad 2. <lb/>
valet con&longs;equentia h&aelig;c, erg&ograve; etiam alternatim erit, vt primus ad tertium, <lb/>
ita &longs;ecundus ad quartum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in allato exemplo, ita erit 9. ad 3. vt 6. ad 2. <lb/>
quam &longs;equelam e&longs;&longs;e validam probat deinde Euclides propo&longs;it. </s>
          <s id="s.003670">16. 5. hinc <lb/>
aliam deducit con&longs;equentiam, quam Euclides propo&longs;it. </s>
          <s id="s.003671">12. 5. demon&longs;trat, <lb/>
dum ait, quare etiam totum ad totum erit. </s>
          <s id="s.003672">v. <!-- REMOVE S-->g. <!-- REMOVE S-->quia conclu&longs;um e&longs;t ita e&longs;&longs;e <lb/>
9. ad 3. quemadmodum 6. ad 2. ita etiam erit totum ad totum, ide&longs;t ita <lb/>
etiam erunt antecedentes termini &longs;imul ad con&longs;equentes &longs;imul, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ita erit <lb/>
etiam totum 15. quod e&longs;t totum ex antecedentibus terminis 9. &amp; 6. ad to&shy;<lb/>
tum 5. conflatum ex con&longs;equentibus terminis 3. &amp; 2. In &longs;umma igitur &longs;i fue&shy;<lb/>
rit vt 9. ad 3. ita 6. ad 2. ita etiam erit 15. ad 5. quod verum e&longs;&longs;e apparet in <lb/>
his numeris, cum tam 9. ad 3. qu&agrave; 6. ad 2. &amp; 15. ad 5. habeant triplam <lb/>
proportionem.</s>
        </p>
        <p type="main">
          <s id="s.003673">Horum exemplum in rebus practicis &longs;it hoc: &longs;it vt Plato ad Proclum, ita <lb/>
mille aurei ad quingentos aureos, erg&ograve; alternatim ita erit Plato ad 1000. <lb/>
aureos, &longs;icuti Proclus ad 500. quare ita etiam totum erit ad totum, &longs;cilicet <lb/>
Plato, &amp; Proclus &longs;imul ad 1000. &amp; 500. &longs;imul, qu&aelig; duo tota, di&longs;tributio mo&shy;<lb/>ralis, ac practica diuidit, &amp; binatim copulat, hoc modo dicens, vt Plato ad <pb pagenum="219" xlink:href="009/01/219.jpg"/>Proclum, ita 1000. ad 500, &amp; po&longs;tea, vt Plato ad 1000. ita Proclus ad 500. <lb/>
iuxta <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> merita, &amp; quidem i&longs;ta e&longs;t huiu&longs;modi moralis di&longs;tributio, cum <lb/>
modis argumentandi ab Euclide comprobatis, nitatur.</s>
        </p>
        <p type="main">
          <s id="s.003674"><arrow.to.target n="marg302"/></s>
        </p>
        <p type="margin">
          <s id="s.003675"><margin.target id="marg302"/>311</s>
        </p>
        <p type="main">
          <s id="s.003676">Ibidem <emph type="italics"/>&lpar;Hanc ver&ograve; proportionalitatem Mathematici Geometricam vocant: <lb/>
propterea quod in Geometrica euenit, vt eandem totum ad totum rationem habeat, <lb/>
quam habet alterutrum, ad alterutrum&rpar;<emph.end type="italics"/> ide&longs;t, hanc duarum Geometricarum <lb/>
rationum &longs;imilitudinem Mathematici proportionalitatem Geometricam <lb/>
appellant, propterea quod in hac duarum rationum geometricarum &longs;imili&shy;<lb/>
tudine accidit, vt &longs;it totum ad totum, quemadmodum etiam partes toto&shy;<lb/>
rum, vt &longs;upra explicatum e&longs;t; quod non accidit in duarum proportionum <lb/>
arithmeticarum &longs;imilitudine; &longs;i enim ponamus has duas rationes arithme&shy;<lb/>
ticas &longs;imiles, vt 10. ad 8. ita 6. ad 4. qu&aelig; &longs;unt &longs;imiles, propter &longs;imiles exce&longs;&shy;<lb/>
&longs;us primorum, &amp; &longs;ecundorum terminorum, cum <expan abbr="vbiq;">vbique</expan> exce&longs;&longs;us &longs;it binarij. <lb/>
</s>
          <s id="s.003677">non erit tamen totum 16. ad totum 12. in eadem ratione cum diui&longs;is ter&shy;<lb/>
minis, cum ibi &longs;it exce&longs;&longs;us binarij, hic ver&ograve; quaternarij. </s>
          <s id="s.003678">h&aelig;c videtur e&longs;&longs;e <lb/>
Ari&longs;t. ratio; quam adhuc melius declara&longs;&longs;e libet. </s>
          <s id="s.003679">Geometrica igitur pro&shy;<lb/>
portionalitas ita dicta e&longs;t, quia qu&aelig;libet proportio pote&longs;t in materia Geo&shy;<lb/>
metrica, lineis, &longs;uperficiebus, &amp; corporibus continuari in quatuor termi&shy;<lb/>
nis, ita vt proportionalitas, &longs;eu &longs;imilitudo rationum exurgat, quod in nu&shy;<lb/>meris fieri &longs;emper nequit, cum plures &longs;int proportiones, qu&aelig; numeris ex&shy;<lb/>
primi nequeunt, vt &longs;unt e&aelig;, quas irrationales appellant, cuiu&longs;modi e&longs;t inter <lb/>
diametrum, &amp; co&longs;tam eiu&longs;dem quadrati, cuius nec proportio, nec propor&shy;<lb/>
tionalitas in numeris reperiri pote&longs;t, qu&aelig; tamen in lineis, &longs;uperficiebus, ac <lb/>
corporibus e&longs;&longs;e po&longs;&longs;unt: e&longs;t enim vt diameter vnius quadrati ad latus eiu&longs;&shy;<lb/>
dem, ita idem latus ad aliam lineam inuentam per 11. 6. vel vt diameter ad <lb/>
co&longs;tam, ita qu&aelig;libet alia linea ad aliam inuentam, per 12. 6. omnis igitur <lb/>
proportionalitas rebus Geometricis ine&longs;&longs;e pote&longs;t; non autem numeris, in <lb/>
quibus &longs;olum po&longs;&longs;unt e&longs;&longs;e rationes rationales, &longs;eu <expan abbr="rer&utilde;">rerum</expan> commen&longs;urabilium; <lb/>
latius igitur patet Geometrica h&aelig;c &longs;imilitudo, qu&agrave;m Arithmetica, c&ugrave;m <lb/>
Geometrica complectatur tam rationales, qu&agrave;m irrationales. </s>
          <s id="s.003680">merit&ograve; igi&shy;<lb/>
tur talis proportionalitas appellari debuit &agrave; rebus Geometricis, in quibus <lb/>
&longs;emper reperitur, non autem ab Arithmeticis, cum quibus &longs;&aelig;pius reperiri <lb/>
nequit. </s>
          <s id="s.003681">Vide Campanum in explicatione definitionis 3. 5. Elemen.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003682"><arrow.to.target n="marg303"/></s>
        </p>
        <p type="margin">
          <s id="s.003683"><margin.target id="marg303"/>312</s>
        </p>
        <p type="main">
          <s id="s.003684">Ibidem <emph type="italics"/>&lpar;Non e&longs;t autem continens h&aelig;c proportio: non enim vnus, &amp; idem ter&shy;<lb/>
minus efficitur, &amp; cui, &amp; quod&rpar;<emph.end type="italics"/> ide&longs;t, h&aelig;c proportionalitas contracta ad res <lb/>
practicas, non e&longs;t continens, ide&longs;t, qu&aelig; con&longs;i&longs;tat in tribus tantum terminis, <lb/>
quorum medius e&longs;t, ad quem refertur primus, &amp; is qui refertur ad ter&shy;<lb/>
tium; &longs;ed e&longs;t di&longs;iuncta, quia con&longs;tat &longs;emper quatuor terminis, quorum duo <lb/>
&longs;unt per&longs;on&aelig; aliqu&aelig;, reliqui ver&ograve; duo &longs;unt res, qu&aelig; per&longs;onis debentur, vt &longs;i <lb/>
&longs;int Plato, &amp; Proclus, quibus iuxta meritorum quantitatem debeant diuidi <lb/>
1500. aurei, debent diuidi aurei in duas partes, qu&aelig; habeant eam propor&shy;<lb/>
tionem, quam habet Plato ad Proclum. </s>
          <s id="s.003685">quod &longs;i Plato duplum m&etail;ruit qu&agrave;m <lb/>
Proclus, erit vt Plato ad Proclum, ita 1000. ad 500.</s>
        </p>
        <p type="main">
          <s id="s.003686">Ex quibus patet hanc analogiam in rebus agendis non ni&longs;i in quatuor <lb/>
terminis con&longs;i&longs;tere po&longs;&longs;e, &amp; ideo non e&longs;&longs;e continuam, &longs;ed di&longs;iunctam, vt vo&shy;<lb/>
lebat Ari&longs;tot.<!-- KEEP S--></s>
        </p>
        <pb pagenum="220" xlink:href="009/01/220.jpg"/>
        <p type="main">
          <s id="s.003687"><arrow.to.target n="marg304"/></s>
        </p>
        <p type="margin">
          <s id="s.003688"><margin.target id="marg304"/>313</s>
        </p>
        <p type="main">
          <s id="s.003689">Lib. 5. cap. 6. <emph type="italics"/>&lpar;Atque id vel proportione vel numero&rpar;<emph.end type="italics"/> ide&longs;t, vel proportio&shy;<lb/>
nalitate Geometrica, vel Arithmetica; qu&aelig; autem &longs;it proportionalitas <lb/>
Geometrica, dictum e&longs;t paul&ograve; ante in prioribus locis Mathematicis huius <lb/>
quinti libri; qu&aelig; ver&ograve; &longs;it proportionalitas Arithmetica dictum e&longs;t &longs;uperius <lb/>
lib. 2. cap. 6. Verum h&aelig;c Arithmetica proportionalitas, merit&ograve; ab Ari&longs;tot. <lb/>
hic contradi&longs;tincta e&longs;t &agrave; proportionalitate Geometrica: quia Arithmetica <lb/>
h&aelig;c analogia attenditur &longs;olum, iuxta eundem exce&longs;&longs;um numerorum, non, <lb/>
autem iuxta proportionem, &longs;eu habitudinem terminorum ad inuicem, quod <lb/>
maxim&egrave; in Geometrica &longs;pectatur. </s>
          <s id="s.003690">propterea Mathematici <expan abbr="c&etilde;&longs;ent">cen&longs;ent</expan> eam vo&shy;<lb/>
candam e&longs;&longs;e potius medietatem Arithmeticam, quam proportionalita&shy;<lb/>
tem, cum quibus nunc Ari&longs;t. con&longs;entit.</s>
        </p>
        <p type="main">
          <s id="s.003691"><arrow.to.target n="marg305"/></s>
        </p>
        <p type="margin">
          <s id="s.003692"><margin.target id="marg305"/>314</s>
        </p>
        <p type="main">
          <s id="s.003693">Lib. 6. cap. 5. <emph type="italics"/>&lpar;Verbi cau&longs;a triangulum tres angulos duobus rectis &aelig;quales ha&shy;<lb/>bere, vel non habere&rpar;<emph.end type="italics"/> lib. 1. Priorum, &longs;ecto 3. cap. 1. fus&egrave; hanc trianguli affe&shy;<lb/>
ctionem expo&longs;ui.</s>
        </p>
        <p type="main">
          <s id="s.003694"><arrow.to.target n="marg306"/></s>
        </p>
        <p type="margin">
          <s id="s.003695"><margin.target id="marg306"/>315</s>
        </p>
        <p type="main">
          <s id="s.003696">Lib. 6. cap. 8. <emph type="italics"/>&lpar;Nam illud etiam con&longs;ideratione dignum videtur. </s>
          <s id="s.003697">quid &longs;it, quod <lb/>
puer fieri Mathematicus pote&longs;t, &longs;apiens autem naturalis non pote&longs;t. </s>
          <s id="s.003698">An quia illa <lb/>
per ab&longs;tractionem &longs;unt, horum autem principia ab experientia &longs;umuntur&rpar;<emph.end type="italics"/> Ex hoc <lb/>
loco manife&longs;t&egrave; apparet Ari&longs;t. exi&longs;timare principia Mathematica nullo mo&shy;<lb/>
do nobis per experientiam innote&longs;cere, quod nonnulli negant.</s>
        </p>
        <p type="main">
          <s id="s.003699"><arrow.to.target n="marg307"/></s>
        </p>
        <p type="margin">
          <s id="s.003700"><margin.target id="marg307"/>316</s>
        </p>
        <p type="main">
          <s id="s.003701">Lib. 7. cap. 8. <emph type="italics"/>&lpar;In actionibus autem principium illud e&longs;t, cuius cau&longs;a res fit, <lb/>
&longs;icut in Mathematicis &longs;uppo&longs;itiones; nam neque illic ratio e&longs;t, qu&aelig; doctrinam tra&shy;<lb/>
dat principiorum, neque hic<emph.end type="italics"/>&rpar; Suppo&longs;itionum, &longs;iue principiorum Mathemati&shy;<lb/>
corum tria &longs;unt genera, definitiones, po&longs;tulata, axiomata, qu&aelig; in ip&longs;o primi <lb/>
Elementorum ve&longs;tibulo proponuntur: &longs;olaque terminorum explicatione <lb/>
<expan abbr="ab&longs;q;">ab&longs;que</expan> vllo di&longs;cur&longs;u, addi&longs;cuntur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003702"><emph type="italics"/>Ex primo Libro Magnorum Moralium.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003703"><arrow.to.target n="marg308"/></s>
        </p>
        <p type="margin">
          <s id="s.003704"><margin.target id="marg308"/>317</s>
        </p>
        <p type="main">
          <s id="s.003705">Cap. 1. &lpar;<emph type="italics"/>Nec enim lu&longs;titia e&longs;t numerus pariter par<emph.end type="italics"/>&rpar; vt &longs;cilicet dicebat <lb/>
Pythagoras. </s>
          <s id="s.003706">Porr&ograve; definit. </s>
          <s id="s.003707">8. 7. &longs;ic habetur: Pariter par nume&shy;<lb/>
rus e&longs;t, quem par numerus per numerum parem, ide&longs;t paribus vi&shy;<lb/>
cibus, metitur, cuiu&longs;modi e&longs;t numerus 24. quem numerus 6. me&shy;<lb/>
titur per numerum parem, nimirum per 4. quia &longs;cilicet numerus 6. paribus <lb/>
vicibus, quippe per 4. &longs;iue quater ip&longs;um numerum 24. men&longs;urat, quia to&shy;<lb/>
ties in ip&longs;o ad&aelig;quat&egrave; continetur.</s>
        </p>
        <p type="main">
          <s id="s.003708"><arrow.to.target n="marg309"/></s>
        </p>
        <p type="margin">
          <s id="s.003709"><margin.target id="marg309"/>318</s>
        </p>
        <p type="main">
          <s id="s.003710">Cap. 2. &lpar;<emph type="italics"/>Ab&longs;urdum enim &longs;it, volenti o&longs;tendere triangulum duobus rectis &aelig;qua&shy;<lb/>les habere angulos, &longs;umere principium huiu&longs;modi, anima immortalis est<emph.end type="italics"/>&rpar; Repete, <lb/>
qu&aelig; de hac trianguli proprietate fus&egrave; &longs;crip&longs;i lib. 1. Priorum, &longs;ect. </s>
          <s id="s.003711">3. cap. 1. <lb/>
quam affectionem debet Geometra demon&longs;trare ex Geometri&aelig; principijs, <lb/>
quemadmodum facit Euclides in 32. primi, non autem ex principijs extrin&shy;<lb/>
&longs;ecis, vt quod anima &longs;it immortalis.</s>
        </p>
        <p type="main">
          <s id="s.003712"><arrow.to.target n="marg310"/></s>
        </p>
        <p type="margin">
          <s id="s.003713"><margin.target id="marg310"/>319</s>
        </p>
        <p type="main">
          <s id="s.003714">Cap. 10. <emph type="italics"/>&lpar;Vt enim habuerint principia, ita, qu&aelig; de principijs ortum ducunt, <lb/>
Per&longs;picu&egrave; autem licet hoc in Geometria magis intueri, vbi cum aliqua &longs;ump&longs;eris <lb/>
principia, vt ea habuerint, ita etiam, qu&aelig; ip&longs;a con&longs;equuntur: velut &longs;i triangulum <lb/>
duobus rectis &aelig;quales habet angulos, quadratum <expan abbr="quoq;">quoque</expan> quatuor angulis rectis ha-<emph.end type="italics"/>


<pb pagenum="221" xlink:href="009/01/221.jpg"/><emph type="italics"/>beat nece&longs;&longs;e e&longs;t. </s>
          <s id="s.003715">&amp; &longs;i triangulum &longs;ecus, ita etiam, &amp; quadratum commutabitur, <lb/>
ex altera parte enim ei re&longs;pondet. </s>
          <s id="s.003716">&amp; &longs;i quadratum quatuor angulis rectis &aelig;quales, <lb/>
non habuerit angulos ne quidem triangulum duobus rectis habebit &aelig;quales&rpar;<emph.end type="italics"/> Hanc <lb/>
trianguli affectionem, habere &longs;cilicet, &longs;uos tres angulos &aelig;quales duobus re&shy;<lb/>
ctis angulis abund&egrave; explicaui libro 1. Priorum, &longs;ecto 3. cap. 1. quam Eucli&shy;<lb/>
des propo&longs;it. </s>
          <s id="s.003717">32. primi demon&longs;trauit, ex qua demon&longs;tratione, tanquam ex <lb/>
Geometrico principio &longs;equitur omne <expan abbr="quoq;">quoque</expan> quadrangulum habere quatuor <lb/>
angulos &aelig;quales quatuor rectis angulis; omne <expan abbr="namq;">namque</expan> quadrangulum e&longs;t po&shy;<lb/>
tentia duo triangula, cum diuidatur ducta ip&longs;ius diametro in duo <expan abbr="tr&igrave;&atilde;gula">tr&igrave;angula</expan>. <lb/>
</s>
          <s id="s.003718">quod &longs;i triangulus proprietatem illam non haberet, <expan abbr="neq;">neque</expan> h&aelig;c quadrangulo <lb/>
conueniret. </s>
          <s id="s.003719">&amp; &longs;i quadrangulum non haberet quatuor angulos &aelig;quales qua&shy;<lb/>
tuor rectis angulis, neque triangulum habere po&longs;&longs;et tres angulos &aelig;qua&shy;<lb/>
les duobus rectis, cum nihil &longs;it aliud triangulum, qu&agrave;m dimidiatum qua&shy;<lb/>
drangulum.</s>
        </p>
        <p type="main">
          <s id="s.003720"><arrow.to.target n="marg311"/></s>
        </p>
        <p type="margin">
          <s id="s.003721"><margin.target id="marg311"/>320</s>
        </p>
        <p type="main">
          <s id="s.003722">Cap. 16. <emph type="italics"/>&lpar;In Geometria &longs;i quidem cum quis dixerit quadrangul&ubreve;m quatuor rectis <lb/>&aelig;quales habere, &amp; percunctatur propter quid, occurrit, quia etiam triangul&ubreve;m duo&shy;<lb/>
bus rectis &aelig;quales habet. </s>
          <s id="s.003723">in his igitur ex determinato &longs;ibi principio propter quid <lb/>
a&longs;&longs;ump&longs;erunt&rpar;<emph.end type="italics"/> Lege, qu&aelig; proxim&egrave; in pr&aelig;cedenti loco expo&longs;ui, ea enim om&shy;<lb/>
nia huc etiam pertinent. </s>
          <s id="s.003724">hoc &longs;olum addendum ad illorum verborum &lpar;<emph type="italics"/>Ex de&shy;<lb/>
terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>&rpar; intelligentiam, ide&longs;t ex vna <lb/>
conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rect&egrave; <lb/>
fieri Ari&longs;t. in primo Po&longs;ter. docet.</s>
        </p>
        <p type="main">
          <s id="s.003725"><arrow.to.target n="marg312"/></s>
        </p>
        <p type="margin">
          <s id="s.003726"><margin.target id="marg312"/>321</s>
        </p>
        <p type="main">
          <s id="s.003727">Cap. 31. &lpar;<emph type="italics"/>A qui proportionale in quatuor nihilominus perficitur: nam quem&shy;<lb/>
admodum A, ad B, ita C, ad D.<emph.end type="italics"/>&rpar; ide&longs;t proportionalitas in quatuor terminis <lb/>
con&longs;i&longs;tit, quemadmodum pluribus &longs;upra lib. 5. cap. 3. Ethycorum explica&shy;<lb/>
tum e&longs;t: qu&ograve; nunc Lectorem ablego.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003728"><emph type="italics"/>Ex primo Libro Moralium Eudemiorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003729"><arrow.to.target n="marg313"/></s>
        </p>
        <p type="margin">
          <s id="s.003730"><margin.target id="marg313"/>322</s>
        </p>
        <p type="main">
          <s id="s.003731">Cap. 5 &lpar;<emph type="italics"/>Vt &longs;i duplum multiplicium primum est, non licet multiplex com&shy;<lb/>
muniter pr&aelig;dicatum &longs;eparari, quippe, quod duplo prius e&longs;t<emph.end type="italics"/>&rpar; Inter pro&shy;<lb/>
portionum genera vnum e&longs;t, quod dicitur multiplex, quod &longs;ub &longs;e <lb/>
infinitas &longs;pecies continet, vt Duplum, Triplum, Quadruplum, &amp; c. <lb/>
<!-- REMOVE S-->in infinitum. </s>
          <s id="s.003732">vbi vides, cur Ari&longs;t. dixerit duplum e&longs;&longs;e primum inter multi&shy;<lb/>
plicia, cum ver&egrave; naturali ordine numerorum ip&longs;i primus debeatur locus. <lb/>
</s>
          <s id="s.003733">Vides etiam cur non liceat, Multiplex ip&longs;um genus commune pr&aelig;dicatum <lb/>
omnibus &longs;peciebus veluti Id&aelig;am &longs;eparari; tunc enim ait, ip&longs;um mul&shy;<lb/>
tiplex ab&longs;tractum e&longs;&longs;et prius ordine ip&longs;o primo multiplici, &longs;ci&shy;<lb/>
licet duplo; &amp; Duplum non e&longs;&longs;et primum inter mul&shy;<lb/>
tiplicia, qu&aelig; <expan abbr="vtraq;">vtraque</expan> &longs;unt ab&longs;urda; non igitur <lb/>
illud tanquam Id&aelig;am licet &longs;epa&shy;<lb/>
ratum ponere.</s>
        </p>
      </chap>
      <pb pagenum="222" xlink:href="009/01/222.jpg"/>
      <chap>
        <p type="head">
          <s id="s.003734"><emph type="italics"/>Ex Secundo Moralium Eudem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003735"><arrow.to.target n="marg314"/></s>
        </p>
        <p type="margin">
          <s id="s.003736"><margin.target id="marg314"/>323</s>
        </p>
        <p type="main">
          <s id="s.003737">Cap. 7. <emph type="italics"/>&lpar;Nam &longs;i habenti trigono duos rectos, nece&longs;&longs;e e&longs;t tetragonum qua&shy;<lb/>
tuor rectis con&longs;tare, manife&longs;tum e&longs;t, quod trigonus duos rectos habens <lb/>
cau&longs;a eius exi&longs;tat. </s>
          <s id="s.003738">Ver&ugrave;m &longs;i quid in trigono mutaris, nece&longs;&longs;arium e&longs;t, &amp; <lb/>
in tetragono mutes, vt &longs;i tres habuerunt, &longs;ex; &amp; &longs;i quatuor, octo; &longs;in <lb/>
ver&ograve; non mutes, vt illud, ita hoc <expan abbr="quoq;">quoque</expan> habeat nece&longs;&longs;e e&longs;t&rpar;<emph.end type="italics"/> Lege prius, qu&aelig; &longs;upra <lb/>
lib. 1. Magnor. <!-- REMOVE S-->moral. </s>
          <s id="s.003739">cap. 10. &longs;crip&longs;i, ex quibus po&longs;tea &longs;ic locum hunc in&shy;<lb/>
terpretaberis, &longs;i triangulum habet tres angulos &aelig;quales duobus rectis an&shy;<lb/>
gulis, nece&longs;&longs;e e&longs;t quodcunque quadrilaterum habere &longs;uos quatuor angulos <lb/>
&aelig;quales quatuor rectis, quia omne quadrangulum continet duo triangula; <lb/>
&amp; &longs;i natura trianguli fuerit immutata ita, vt habeat tres angulos &aelig;quales <lb/>
non duobus, &longs;ed tribus rectis, tunc nece&longs;&longs;e erit tetragonum <expan abbr="quoq;">quoque</expan> mutatum <lb/>
e&longs;&longs;e, quia nece&longs;&longs;ari&ograve; habebit &longs;uos angulos &aelig;quales non quatuor tantum re&shy;<lb/>
ctis, &longs;ed &longs;ex: pariter &longs;i triangulum habeat tres angulos quatuor rectis pa&shy;<lb/>
res, quadrangulum &longs;uos habebit angulos, octo rectis &aelig;quiualentes. </s>
          <s id="s.003740">His igi&shy;<lb/>
tur ex Geometria &longs;atisfactum &longs;it.</s>
        </p>
        <p type="main">
          <s id="s.003741"><arrow.to.target n="marg315"/></s>
        </p>
        <p type="margin">
          <s id="s.003742"><margin.target id="marg315"/>324</s>
        </p>
        <p type="main">
          <s id="s.003743">Cap. 10. <emph type="italics"/>&lpar;Multa ver&ograve; opinione concipiunt, qu&aelig; penes nos non &longs;unt, vt diame&shy;<lb/>
trum commen&longs;urabilem e&longs;&longs;e&rpar;<emph.end type="italics"/> Qu&aelig; lib. 1. Priorum, &longs;ecto 3. cap. 23. de a&longs;yme&shy;<lb/>
tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati allata &longs;unt, &longs;atis huic etiam loco <lb/>
facere po&longs;&longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.003744"><arrow.to.target n="marg316"/></s>
        </p>
        <p type="margin">
          <s id="s.003745"><margin.target id="marg316"/>325</s>
        </p>
        <p type="main">
          <s id="s.003746">Eodem cap. <emph type="italics"/>&lpar;Quapropter non deremotis apud Indos, nec de circuli quadratu&shy;<lb/>
ra deliberamus: nam illa ad nos non &longs;pectant, hoc ver&ograve; fieri nequit&rpar;<emph.end type="italics"/> Quid &longs;it cir&shy;<lb/>
culi quadratio, &amp; qua ratione eam antiqui inue&longs;tigauerint in Pr&aelig;dicamen&shy;<lb/>
to Relationis, &amp; alibi in Logicis, pluribus explicatum e&longs;t. </s>
          <s id="s.003747">An ver&ograve; po&longs;&longs;i&shy;<lb/>
bilis &longs;it circuli quadratura, re&longs;pondendum e&longs;t cum di&longs;tinctione, nam theo&shy;<lb/>
rematic&egrave; quidem facta e&longs;t ab Archimede, cum ip&longs;e probauerit circulum, <lb/>
quemuis &aelig;qualem e&longs;&longs;e triangulo, cuius vnum latus circa angulum rectum <lb/>&longs;it circuli &longs;emidiameter, alterum ver&ograve; circunferentia. </s>
          <s id="s.003748">Problematic&egrave; ver&ograve;, <lb/>
ide&longs;t, vt opere ip&longs;o efficiamus <expan abbr="tri&atilde;gulum">triangulum</expan> illud, nondum &agrave; quoquam rit&egrave; per&shy;<lb/>
actum e&longs;t: &amp; propterea problema hoc difficile admodum cen&longs;endum e&longs;t, <lb/>
pr&aelig;&longs;ertim cum tota Geometrarum antiquitas, <expan abbr="atq;">atque</expan> po&longs;teritas in ip&longs;um fru&shy;<lb/>
&longs;tra <expan abbr="hucu&longs;q;">hucu&longs;que</expan> in&longs;udauerit, <expan abbr="atq;">atque</expan> ade&ograve; etiam moraliter impo&longs;&longs;ibile exi&longs;timan&shy;<lb/>
dum e&longs;t. </s>
          <s id="s.003749">quo &longs;en&longs;u locutum e&longs;&longs;e Ari&longs;t. hoc loco crediderim, dum ait, illud <lb/>
fieri non po&longs;&longs;e. </s>
          <s id="s.003750">ab&longs;olut&egrave; tamen a&longs;&longs;erere non debemus e&longs;&longs;e impo&longs;&longs;ibilem, cum <lb/>
nulla id demon&longs;tratione certum &longs;it, im&ograve; ego &longs;impliciter, vt aiunt, credo e&longs;&shy;<lb/>
&longs;e po&longs;&longs;ibilem, cum alia theoremata, <expan abbr="atq;">atque</expan> problemata &lpar;quale e&longs;t pytagoreum <lb/>
illud celebre, quod 47. locum in primo Elemen. <!-- REMOVE S-->occupat, &amp; pro cuius adin&shy;<lb/>uentione Pythagoras Mu&longs;is Hecatombas &longs;acrificauit&rpar; olim fuerint di&ugrave; &agrave; <lb/>
multis inca&longs;&longs;um qu&aelig;&longs;ita, <expan abbr="atq;">atque</expan> impo&longs;&longs;ibilia habita, qu&aelig; po&longs;tea tandem re&shy;<lb/>
perta &longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.003751"><arrow.to.target n="marg317"/></s>
        </p>
        <p type="margin">
          <s id="s.003752"><margin.target id="marg317"/>326</s>
        </p>
        <p type="main">
          <s id="s.003753">Cap. 12. &lpar;<emph type="italics"/>Si triangulo duo recti, nece&longs;&longs;um e&longs;t hoc con&longs;equi<emph.end type="italics"/>&rpar; ide&longs;t, &longs;i triangu&shy;<lb/>
lum habet tres angulos &aelig;quales duobus rectis, nece&longs;&longs;e e&longs;t con&longs;equi, vt &longs;upe&shy;<lb/>
rius &longs;epius dixit, quod quadrilaterum habeat quatuor angulos &aelig;quales qua&shy;<lb/>
tuor rectis, lib. 1. Magn. <!-- REMOVE S-->moral. </s>
          <s id="s.003754">cap. 10. &longs;atis de hac re dictum e&longs;t.</s>
        </p>
      </chap>
      <pb pagenum="223" xlink:href="009/01/223.jpg"/>
      <chap>
        <p type="head">
          <s id="s.003755"><emph type="italics"/>Ex Septimo Moralium Eudem.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003756"><arrow.to.target n="marg318"/></s>
        </p>
        <p type="margin">
          <s id="s.003757"><margin.target id="marg318"/>327</s>
        </p>
        <p type="main">
          <s id="s.003758">Cap. 12. &lpar;<emph type="italics"/>luxtaqu&eacute; diametrum iungit<emph.end type="italics"/>&rpar; ide&longs;t diametraliter opponit, qu&aelig; <lb/>
e&longs;t omnium maxima oppo&longs;itio, ita vt qu&aelig; diametraliter oppo&longs;ita <lb/>
&longs;unt, amplius di&longs;tare nequeant, quia diameter e&longs;t maxima om&shy;<lb/>
nium di&longs;tantia, &longs;iue fit diameter quadrilater&aelig; figur&aelig;, &longs;iue circuli.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003759"><emph type="italics"/>Ex Libro 3. Politicorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003760"><arrow.to.target n="marg319"/></s>
        </p>
        <p type="margin">
          <s id="s.003761"><margin.target id="marg319"/>328</s>
        </p>
        <p type="main">
          <s id="s.003762">Cap. 2. &lpar;<emph type="italics"/>Ceu harmoniam earumdem vocem aliam e&longs;&longs;e dicimus, &amp; mod&ograve; <lb/>
Doricam, mod&ograve; Phrygiam vocitamus<emph.end type="italics"/>&rpar; Harmonias Doricam, &amp; Phry&shy;<lb/>
giam veteres Mu&longs;ici, vt Ari&longs;toxenes, Euclides, Ptol&aelig;meus vocant <lb/>
Tonos, &amp; Modos, Dorium &longs;cilicet, &amp; Phrygium. </s>
          <s id="s.003763">per mu&longs;icum au&shy;<lb/>
tem modum intelligebant quandam vocum con&longs;titutionem, &longs;eu rithmum, <lb/>
quem nos hodie vulg&ograve; ariam vocamus, vt doct&egrave; explicat Io&longs;ephus Zarlinus <lb/>
in 4. parte In&longs;titut. <!-- REMOVE S-->Mu&longs;icalium, necnon in lib. 6. &longs;upplem. </s>
          <s id="s.003764">Denominati au&shy;<lb/>
tem fuerunt pr&aelig;dicti, <expan abbr="alij&qacute;">alijque</expan>; plures modi &agrave; nationibus illis, apud quas ma&shy;<lb/>
xim&egrave; in v&longs;u erant, vt Dorius &agrave; Dorien&longs;ibus; Phrygius &agrave; Phrygijs; Lydius &agrave; <lb/>
Lydijs. </s>
          <s id="s.003765">Porr&ograve; pr&aelig;ter pr&aelig;dictos modos alij plures &agrave; veteribus Mu&longs;icis com&shy;<lb/>
memorantur; vari&egrave; tamen, alij enim tres, alij &longs;eptem, alij quindecim, vel <lb/>
&longs;eptemdecim etiam connumerarunt; Tres tamen pr&aelig;cipui, &amp; ad quos reli&shy;<lb/>
qui reuocabantur, fuerunt Dorius, Phrygius, &amp; Lydius. </s>
          <s id="s.003766">quorum h&aelig; fuerunt <lb/>
proprietates. </s>
          <s id="s.003767">Dorius erat grauis, &longs;euerus, &amp; bellico&longs;us. </s>
          <s id="s.003768">vnde pri&longs;ci exi&longs;ti&shy;<lb/>
marunt ip&longs;um in hominum animos prudentiam, ca&longs;titatem, <expan abbr="atq;">atque</expan> virtutem <lb/>
inducere. </s>
          <s id="s.003769">Phrygius ver&ograve; erat hilaris, l&aelig;tus, placidus, ac propterea fe&longs;tis, <lb/>
&amp; choreis idoneus. </s>
          <s id="s.003770">vnde prouerbium illud vetus ortum habuit, &agrave; Dorio ad <lb/>
Phrygium, ide&longs;t &agrave; rebus alti&longs;&longs;imis, &amp; &longs;erijs ad humiles, &amp; iucundas. </s>
          <s id="s.003771">Hos <lb/>
ambos &longs;olos Plato, &amp; Ari&longs;t. in Rempublicam admi&longs;erunt. </s>
          <s id="s.003772">Lydius demum <lb/>
modus erat horribilis, m&oelig;&longs;tus, ac tri&longs;tis, <expan abbr="ideo&qacute;">ideoque</expan>; lamentationibus, ac la&shy;<lb/>
crymis aptus. </s>
          <s id="s.003773">Hoc in funeribus mortuos lamentantes vtebantur, ita vt pre&shy;<lb/>
&longs;entibus lacrymas cierent, <expan abbr="vita&qacute;">vitaque</expan>; functos lacrymis pro&longs;equerentur.</s>
        </p>
        <p type="main">
          <s id="s.003774">Recentiores Mu&longs;ici &longs;uos modos vocant Tonos, in quibus vtinam anti&shy;<lb/>
quos imitarentur, illi enim &longs;uis rithmis, modi&longs;u&egrave; auditorum animos varijs <lb/>
pro illorum varietate motibus mir&egrave; afficiebant: &longs;ed no&longs;tri, rithmos in &longs;uis <lb/>
cantilenis negligunt, nec illis cur&aelig; e&longs;t, vt per rithmos hominum affectiones <lb/>
percellant, cum tamen Plato a&longs;&longs;erat Mu&longs;ici officium e&longs;&longs;e rithmos adinueni&shy;<lb/>
re; pr&aelig;terea quod animis ciendis vald&egrave; ob&longs;tat, cantilen&aelig; verba, ac &longs;en&longs;um <lb/>pror&longs;us per &longs;uos, quos vocant, contrapunctos, omnin&ograve; offu&longs;cant, vt nihil <lb/>
pr&aelig;ter magnum quendam vocum &longs;trepitum concordem exaudiatur: <expan abbr="qui&qacute;">quique</expan>; <lb/>
rithmis imitari hominum mores deberent, mimicis quibu&longs;dam adinuentis <lb/>
id pr&aelig;&longs;tare conantur.</s>
        </p>
        <p type="main">
          <s id="s.003775">Ver&ugrave;m hac de re legantur eruditi&longs;&longs;imi Dialogi de Mu&longs;ica Vincentij Ga&shy;<lb/>
lil&aelig;i, cuius pr&aelig;cipuas rationes in fine huius operis, &amp; chronologi&aelig; videre <lb/>
poteris. </s>
          <s id="s.003776">C&aelig;terum, qui plura de modis tam antiquis, qu&agrave;m nouis de&longs;iderat,


<pb pagenum="224" xlink:href="009/01/224.jpg"/>con&longs;ulat Io&longs;ephum Zarlinum in 4. parte In&longs;titutionum Mu&longs;icalium, necnon <lb/>
lib. 6. &longs;upplemen. <!-- REMOVE S-->virum vatia eruditione refertum, <expan abbr="de&qacute;">deque</expan>; Mu&longs;ica in primis <lb/>
optim&egrave; meritum.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003777"><emph type="italics"/>Ex Quarto Politicorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003778"><arrow.to.target n="marg320"/></s>
        </p>
        <p type="margin">
          <s id="s.003779"><margin.target id="marg320"/>329</s>
        </p>
        <p type="main">
          <s id="s.003780">Cap. 3. &lpar;<emph type="italics"/>Eodemqu&eacute; modo in harmonijs, vt quidam tradunt: nam &amp; in illis <lb/>
po&longs;uerunt duas &longs;pecies, vnam Doricam, alteram Phrygiam: c&aelig;teras <lb/>
ver&ograve; omnes vel ad Doricam, vel ad Phrygiam referri.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003781">Vide proxim&egrave; in pr&aelig;cedenti loco dicta, qu&aelig; omnia ita etiam <lb/>
huic loco quadrant, vt pr&aelig;terea nihil de&longs;ideretur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003782"><emph type="italics"/>Ex Quinto Politicorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003783"><arrow.to.target n="marg321"/></s>
        </p>
        <p type="margin">
          <s id="s.003784"><margin.target id="marg321"/>330.a</s>
        </p>
        <p type="main">
          <s id="s.003785">Cap. 1. &lpar;<emph type="italics"/>Quare opus e&longs;t partim arithmetica &aelig;quitate vti, partim ea, qu&aelig; <lb/>
e&longs;t &longs;ecundum dignitatem.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003786">Arithmeticam medietatem &longs;upra explicaui lib. 2. cap. 6. Ethi&shy;<lb/>
corum. </s>
          <s id="s.003787">per eam deinde, qu&aelig; e&longs;t &longs;ecundum dignitatem, intelligit <lb/>
Geometricam, quam &longs;upra lib. 5. cap. 3. Ethicorum expo&longs;ui. </s>
          <s id="s.003788">vtimur enim <lb/>
ea, quando opus e&longs;t di&longs;tribuere pr&aelig;mia non omnibus &aelig;qualiter, &longs;ed habita <lb/>
ratione meritorum vniu&longs;cuiu&longs;que. </s>
          <s id="s.003789">quando autem non &longs;ecundum per&longs;ona&shy;<lb/>
rum dignitatem, &longs;ed omnibus &aelig;qualiter fit di&longs;tributio, illa dicitur Arithme&shy;<lb/>
tica proportionalitas, quia &longs;eruat eandem <expan abbr="vbiq;">vbique</expan> differentiam terminorum.</s>
        </p>
        <p type="main">
          <s id="s.003790"><arrow.to.target n="marg322"/></s>
        </p>
        <p type="margin">
          <s id="s.003791"><margin.target id="marg322"/>330.b</s>
        </p>
        <p type="main">
          <s id="s.003792">Cap. 12. &amp; vlt. &lpar;<emph type="italics"/>In Republica ver&ograve; Platonis Socrates de mutationibus loqui&shy;<lb/>
tur, nec tamen rect&egrave;. </s>
          <s id="s.003793">illius enim Reip. <!-- REMOVE S-->qu&aelig; e&longs;t optima, <expan abbr="atq;">atque</expan> prima, mutatio nulla <lb/>
propria a&longs;&longs;ignatur. </s>
          <s id="s.003794">inquit enim cau&longs;am e&longs;&longs;e mutationis, quia &longs;ic natura compara&shy;<lb/>
tum &longs;it, vt nihil permaneat, &longs;ed in ambitu quodam temporis, mutationem recipiat. <lb/>
</s>
          <s id="s.003795">e&longs;&longs;e ver&ograve; principium horum, inquit, quor&ubreve;m &longs;e&longs;quitertia radix quinario iuncta, duas <lb/>
exhibet harmonias. </s>
          <s id="s.003796">inquiens quando numerus huius diagrammatis efficiatur &longs;oli&shy;<lb/>
dus<emph.end type="italics"/>&rpar; Quoad textus interpretationem, nonnulli pro &lpar;&longs;e&longs;quitertia radix&rpar; ver&shy;<lb/>
tunt &lpar;&longs;e&longs;quitertius cubus&rpar; &longs;ed qua id ratione ignoro. </s>
          <s id="s.003797">gr&aelig;cum verbum e&longs;t <lb/>
<foreign lang="greek">puqmh\n,</foreign> quod fundamentum, latus, &amp; radicem &longs;ignificat, non autem cubum. <lb/>
</s>
          <s id="s.003798">pr&aelig;terea &longs;en&longs;ui radix, non autem cubus quadrare pote&longs;t. </s>
          <s id="s.003799">Porr&ograve; &longs;ciendum <lb/>
Ari&longs;t. locum hunc ex Platonis lib. 8. de Rep. <!-- REMOVE S-->accepi&longs;&longs;e, loco Mathematico <lb/>
ob&longs;curi&longs;&longs;imo, vbi ille de Reip. <!-- REMOVE S-->&longs;eu Gubernation is mutatione, ac duratione <lb/>
pertractat. </s>
          <s id="s.003800">qu&igrave; locus ade&ograve; &longs;emper ob&longs;curus habitus e&longs;t, vt Cicero ip&longs;e cum <lb/>
rem p&oelig;nitus ob&longs;curam &longs;ignificare vellet, dicere &longs;olitus e&longs;&longs;et, numero Plato&shy;<lb/>
nis ob&longs;curius. </s>
          <s id="s.003801">quam ob cau&longs;am Theon Smyrn&aelig;us, qui Mathematica Plato&shy;<lb/>
nis loca commentarijs illu&longs;trauit, hi&longs;ce tenebris lucem nullam afferre au&longs;us <lb/>
e&longs;t, ver&ugrave;m eas di&longs;&longs;imulans caut&egrave; declinauit. </s>
          <s id="s.003802">c&ugrave;m igitur pr&aelig;&longs;ens Ari&longs;t. locus <lb/>&longs;it illius Platonici particula qu&aelig;dam, quid mirum, &longs;i non minori ob&longs;curita&shy;<lb/>
te, ac difficultate impeditus &longs;it? </s>
          <s id="s.003803">vnde etiam &longs;equitor huius explicationem, <lb/>
ab illius explicatione petendam e&longs;&longs;e. </s>
          <s id="s.003804">Locum illum Platonis fu&longs;i &longs;im&egrave; expli&shy;<lb/>
cat Mar&longs;ilius Ficinus to 2. operum &longs;uorum pag. </s>
          <s id="s.003805">1413. vbi pag. </s>
          <s id="s.003806">1421. cap. 12.


<pb pagenum="225" xlink:href="009/01/225.jpg"/>illius commentarij prop&egrave; finem pr&aelig;&longs;ens Ari&longs;t. locus ex pr&aelig;mi&longs;&longs;is ab eo bre&shy;<lb/>
uiter, ac dilucid&egrave; declaratur. </s>
          <s id="s.003807">qu&aelig; explanatio, quoniam mihi pr&aelig; c&aelig;teris ar&shy;<lb/>
ridet, eam hoc loco, explicatiorem tamen, referam. </s>
          <s id="s.003808">Illud autem pr&aelig;&longs;cien&shy;<lb/>
dum e&longs;t, h&aelig;c qu&aelig; a Socrate lib. 8. de Repub. <!-- REMOVE S-->recen&longs;entur, confingi &agrave; Mu&longs;is, <lb/>
tanquam oraculum quoddam ob&longs;curi&longs;&longs;imum effata; quo arcana qu&aelig;dam <lb/>
my&longs;teria de Rerump. <!-- REMOVE S-->durationibus, ac mutationibus continerentur.</s>
        </p>
        <p type="main">
          <s id="s.003809">Aiebat igitur Socrates, Mu&longs;arum &longs;piritu afflatus, optimam Politiam, op&shy;<lb/>
timis &longs;cilicet legibus, ac moribus con&longs;titutam, &longs;ua natura omnin&ograve; immu&shy;<lb/>
tabilem, <expan abbr="atq;">atque</expan> ade&ograve; diuturnam per &longs;e fore. </s>
          <s id="s.003810">Verumtamen mutationi obno&shy;<lb/>xiam e&longs;&longs;e, quoniam &longs;ie natura comparatum e&longs;t, vt cuncta, qu&aelig; natur&aelig; &longs;inu <lb/>
continentur, certa quadam annorum, vel &longs;&aelig;culorum periodo exacta, mu&shy;<lb/>
tationem &longs;ubire fatali lege, cogantur. </s>
          <s id="s.003811">tunc autem harum vice&longs;&longs;itudinum <lb/>
principium contingere, fatidic&aelig; Mu&longs;&aelig; &longs;ignificare voluerunt, c&ugrave;m is anno&shy;<lb/>
rum, vel &longs;&aelig;culorum numerus ab illius Reip. <!-- REMOVE S-->exordio elap&longs;us fuerit, qui &longs;it <lb/>
numerus &longs;olidus, &amp; cubus, eius numeri, in quo optima Reipub. <!-- REMOVE S-->con&longs;titutio <lb/>
con&longs;i&longs;tit. </s>
          <s id="s.003812">hic porr&ograve; numerus, in quo Reip. <!-- REMOVE S-->perfectio &longs;tatuitur, e&longs;t Duodena&shy;<lb/>
rius, quem multis in locis, varias ob rationes extulit Plato, pr&aelig;cipu&egrave; ver&ograve;, <lb/>
quoniam in &longs;e ip&longs;o duas continet harmonias, &longs;iue duas proportiones har&shy;<lb/>
monicas, qu&aelig; &longs;imul iunct&aelig;, perfecti&longs;&longs;imam omnium conflant harmoniam, <lb/>
qu&aelig; Diapa&longs;on dicitur. </s>
          <s id="s.003813">du&aelig; autem ill&aelig; rationes harmonic&aelig; &longs;unt Se&longs;quiter&shy;<lb/>
tia, &amp; Se&longs;quialtera. </s>
          <s id="s.003814">Se&longs;quitertia reperitur prim&ograve; inter hos numeros 4. 3. <lb/>
c&ugrave;m enim ea inter duas voces, aut &longs;onos reperitur, ij edunt harmoniam, <lb/>
&longs;eu con&longs;onantiam illam, qu&aelig; Diate&longs;&longs;aron appellatur. </s>
          <s id="s.003815">&longs;imul autem ijdem ad&shy;<lb/>
diti efficiunt 7. qui numerus propterea in textu dicitur radix Epitrite, &longs;iue <lb/>
Se&longs;quitertia, quoniam vt vidimus <expan abbr="c&otilde;ponitur">componitur</expan> ex numeris 4. 3. Se&longs;quitertiam <lb/>
rationem habentibus. </s>
          <s id="s.003816">Se&longs;quialtera ver&ograve; ratio reperitur prim&ograve; inter hos <lb/>
numeros 3. 2. c&ugrave;m enim duo &longs;oni in earum fuerint ratione &longs;uauem edent <lb/>
<expan abbr="con&longs;on&atilde;tiam">con&longs;onantiam</expan>, qu&aelig; Diapente nominatur; &longs;imul autem ijdem compo&longs;iti Qui&shy;<lb/>
narium efficiunt; cui quinario &longs;e&longs;quitertia radix adiuncta, qu&aelig; e&longs;t 7. Duo&shy;<lb/>
denarium componunt: qui propterea duas exhibet harmonias. </s>
          <s id="s.003817">Pr&aelig;terea <lb/>
h&aelig; du&aelig; harmoni&aelig; &longs;imul copulat&aelig; conflant &longs;uaui&longs;&longs;imam Diapa&longs;on con&longs;onan&shy;<lb/>
tiam, nam iunct&aelig; &longs;imul pr&aelig;dict&aelig; du&aelig; rationes &longs;e&longs;quialtera, &amp; &longs;e&longs;quitertia, <lb/>
eo modo quo tradunt Mu&longs;ici, hoc &longs;cilicet modo 4. 3. 2. oritur inter extre&shy;<lb/>
mos numeros dupla ratio, qu&aelig; ip&longs;ius Diapa&longs;on e&longs;t forma. </s>
          <s id="s.003818">nam ratio 4.ad 3. <lb/>
e&longs;t &longs;e&longs;quitertia; ratio 3. ad 2. e&longs;t &longs;e&longs;quialtera; ratio ver&ograve; 4. ad 2. qu&aelig; ex il&shy;<lb/>
lis componitur, e&longs;t dupla. </s>
          <s id="s.003819">qu&ograve;d &longs;i duo &longs;oni duplam hanc rationem nacti fue&shy;<lb/>rint, con&longs;onantiam Diapa&longs;on &longs;uaui&longs;&longs;imam re&longs;onabunt. </s>
          <s id="s.003820">C&ugrave;m igitur nume&shy;<lb/>
rus 12. harmonias ha&longs;ce complectatur, per eum Mu&longs;&aelig; optimum Reip. <!-- REMOVE S-->ini&shy;<lb/>
tium, ac &longs;tatum &longs;ignificare voluerunt. </s>
          <s id="s.003821">Verumenimuer&ograve; cum numerus hu&shy;<lb/>
ius diagrammatis, ide&longs;t huiu&longs;cemodi conditionis, qui e&longs;t 12. factus fuerit <lb/>
&longs;olidus, hoc e&longs;t, quando Re&longs;p. ben&egrave; con&longs;tituta ad eam annorum, vel &longs;&aelig;culo&shy;<lb/>
rum periodum peruenerit, qui &longs;it numerus &longs;olidus numeri 12. tunc fatali <lb/>
ordine, mutationem pati incipiet, atque in peius, c&ugrave;m optimi mutatio &longs;it <lb/>
pe&longs;sima, prolabi. </s>
          <s id="s.003822">porr&ograve; numerus &longs;olidus ip&longs;ius 12. e&longs;t 1728. vti mox expli&shy;<lb/>
cabo. </s>
          <s id="s.003823">vult igitur Socrates ibi my&longs;tic&egrave; &longs;ignificare po&longs;t tot annorum, aut &longs;&aelig;&shy;<lb/>
culorum numerum Remp. <!-- REMOVE S-->omnem quamuis optimam, in deterius prolap&longs;u&shy;<pb pagenum="226" xlink:href="009/01/226.jpg"/>ram, c&ugrave;m enim ad &longs;ummam perfectionem peruenerit, qu&aelig; in numero &longs;oli&shy;<lb/>
do, &amp; cubico &longs;ignificatur, &longs;i vlterius progre&longs;sura &longs;it, nece&longs;&longs;ari&ograve; &longs;ummam <lb/>
perfectionem pr&aelig;teribit, ac derelinquet. </s>
          <s id="s.003824">Qu&ograve;d autem numerus 1728. &longs;it <lb/>
numerus &longs;olidus, &amp; cubus ip&longs;ius Duodenarij &longs;ic pal&agrave;m fiet, &longs;i tamen prius, <lb/>
ea repetiueris, qu&aelig; &longs;upra in primo Po&longs;ter. num. </s>
          <s id="s.003825">33. marginali, de numero <lb/>
Quadrato, &amp; Cubo dicta &longs;unt: e&longs;t autem cubus numerus is, qui ex gemina&shy;<lb/>
to ductu alicuius numeri in &longs;e ip&longs;um, producitur. </s>
          <s id="s.003826">multiplica igitur prim&ograve; <lb/>
12. in 12. &amp; producetur numerus 144. qui quadratus, &amp; planus e&longs;t. </s>
          <s id="s.003827">rur&longs;us <lb/>
duc 12. in hunc 144. <expan abbr="producetur&qacute;">produceturque</expan>; numerus 1728. qu&igrave; cubus, ac proinde <lb/>
&longs;olidus e&longs;t, vt loco citato explicauimus. </s>
          <s id="s.003828"><expan abbr="Atq;">Atque</expan> h&aelig;c Socratici huius my&longs;terij <lb/>
explicatio &longs;ufficiat.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.003829"><emph type="italics"/>Ex Octauo Politicorum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003830"><arrow.to.target n="marg323"/></s>
        </p>
        <p type="margin">
          <s id="s.003831"><margin.target id="marg323"/>331</s>
        </p>
        <p type="main">
          <s id="s.003832">Cap. 5. &lpar;<emph type="italics"/>Mu&longs;icam ver&ograve; omnes fatemur e&longs;&longs;e ex iucundi&longs;&longs;imis, &longs;iue nuda &longs;it, <lb/>
&longs;iue cum melodia<emph.end type="italics"/>&rpar; Quamuis latina interpretatio pro melodia, di&shy;<lb/>
cat, modulatione, Gr&etail;cus tamen textus habet <foreign lang="greek">meta melwdias,</foreign> ide&longs;t <lb/>
<expan abbr="c&utilde;">cum</expan> melodia. </s>
          <s id="s.003833">per Mu&longs;icam nudam, forte Ari&longs;toteles intelligit eam, <lb/>
qu&aelig; &longs;olis &longs;onis <expan abbr="ab&longs;q;">ab&longs;que</expan> oratione con&longs;tat; per melodiam ver&ograve; intelligit eam, <lb/>
quam Io&longs;ephus Zarlinus in 2. parte &longs;uarum In&longs;titutionum Mu&longs;icalium defi&shy;<lb/>
nit, qu&aelig; e&longs;t concentus plurium vocum harmonicus cum rithmo, &amp; oratio&shy;<lb/>
ne, ide&longs;t, qua canitur oratio aliqua &longs;ub aliquo rithmo, aut modo, &longs;iue vt <lb/>nunc loquimur, conqualchearia.</s>
        </p>
        <p type="main">
          <s id="s.003834">Ex quibus liquet no&longs;tros contrapunti&longs;tas toto c&oelig;lo aberrare, dum &longs;uas <lb/>
cantilenas, ab&longs;que vlla verborum intelligentia, atque ab&longs;que vllo rithmo <lb/>
di&longs;perdunt.</s>
        </p>
        <p type="main">
          <s id="s.003835"><arrow.to.target n="marg324"/></s>
        </p>
        <p type="margin">
          <s id="s.003836"><margin.target id="marg324"/>332</s>
        </p>
        <p type="main">
          <s id="s.003837">Eodem capite prop&egrave; finem meminit harmoni&aelig; Lydi&aelig;, Mixt&aelig;, Doric&aelig;, <lb/>
Phrygi&aelig;. </s>
          <s id="s.003838">de quibus &longs;upra 3. lib. <!-- REMOVE S-->Polit. <!-- REMOVE S-->cap. 2. tractaui, <expan abbr="earum&qacute;">earumque</expan>; proprieta&shy;<lb/>
tes, quas hic Ari&longs;t. recen&longs;et ibi connumeraui.</s>
        </p>
        <p type="main">
          <s id="s.003839"><arrow.to.target n="marg325"/></s>
        </p>
        <p type="margin">
          <s id="s.003840"><margin.target id="marg325"/>333</s>
        </p>
        <p type="main">
          <s id="s.003841">Ibidem meminit etiam Rithmorum, &amp; Harmonie. </s>
          <s id="s.003842">Quid Rithmus dictum <lb/>
e&longs;t &longs;uperius lib. 3. Politic. <!-- REMOVE S-->e&longs;&longs;e quem nunc vulg&ograve; ariam cantores, ac tibici&shy;<lb/>
nes appellant.</s>
        </p>
        <p type="main">
          <s id="s.003843">Harmonia e&longs;t plurium vocum ex acuto, &amp; graui concors modulatio.</s>
        </p>
        <p type="main">
          <s id="s.003844">Ver&ugrave;m de his fu&longs;ius in Problematibus Mu&longs;icis, &longs;ect. </s>
          <s id="s.003845">19.</s>
        </p>
        <p type="main">
          <s id="s.003846"><arrow.to.target n="marg326"/></s>
        </p>
        <p type="margin">
          <s id="s.003847"><margin.target id="marg326"/>334</s>
        </p>
        <p type="main">
          <s id="s.003848">Cap. 7 &lpar;<emph type="italics"/>Con&longs;iderandum vtrum omnibus vtendum &longs;it harmonijs, &amp; rithmis<emph.end type="italics"/>&rpar; <lb/>
Vide qu&aelig; &longs;upra lib. 3. Politic. <!-- REMOVE S-->cap. 2. annotaui.</s>
        </p>
        <p type="head">
          <s id="s.003849"><emph type="italics"/>In Oeconomicis nihil Mathematicum reperi.<emph.end type="italics"/></s>
        </p>
      </chap>
      <pb pagenum="227" xlink:href="009/01/227.jpg"/>
      <chap>
        <p type="head">
          <s id="s.003850"><emph type="italics"/>EX PROBLEMATIBVS ARIST.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.003851"><emph type="italics"/>Ex Sectione Prima.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003852"><arrow.to.target n="marg327"/></s>
        </p>
        <p type="margin">
          <s id="s.003853"><margin.target id="marg327"/>335</s>
        </p>
        <p type="main">
          <s id="s.003854">Sectione 1. num. </s>
          <s id="s.003855">3. <emph type="italics"/>&lpar;Quemadmodum tempora, ita &longs;yderum ortus, Orionis <lb/>
Arcturi, Virgiliarum, Canicul&aelig;, qui flatus, imbresqu&eacute; excitant, qui &longs;ereni&shy;<lb/>
tates, frigora, tepore&longs;u&egrave; &longs;olent afferre&rpar;<emph.end type="italics"/> Intelligit de ortu co&longs;mico, qui <lb/>
fit, quando a&longs;trum &longs;imul cum Sole oritur: quem ortum abund&egrave; in 2. <lb/>
Meter. <!-- REMOVE S-->&longs;umma 2. cap. 2. explicatum inuenies. </s>
          <s id="s.003856">Vt autem intelligas, qu&aelig;nam <lb/>
&longs;int Orionis, Arcturi, Virgiliarum, &amp; Canicul&aelig; con&longs;tellationes, &amp; in qua <lb/>
c&oelig;li parte &longs;int collocat&aelig;, &longs;atius e&longs;t globum aliquem a&longs;tronomicum, in quo <lb/>
a&longs;teri&longs;mi omnes clar&egrave; depicti &longs;int, intueri, qu&agrave;m hoc loco pluribus verbis <lb/>
rem per &longs;e claram, ob&longs;curare. </s>
          <s id="s.003857">De Orione plura dicta &longs;unt 2. Meter. <!-- REMOVE S-->pr&aelig;&shy;<lb/>
&longs;ertim quo tempore oriatur. </s>
          <s id="s.003858">Arcturus ver&ograve;, &longs;iue Bootes, prim&aelig; magnitu&shy;<lb/>
dinis &longs;tella, mane vn&agrave; c&ugrave;m Sole in no&longs;tro climate ex Magini Tabulis, circa <lb/>
28. diem Septembris oritur. </s>
          <s id="s.003859">De Virgilijs tamen illud exi&longs;timo <expan abbr="aduert&etilde;dum">aduertendum</expan>, <lb/>quod in Tauri a&longs;teri&longs;mo, du&aelig; ali&aelig; partiales con&longs;tellationes continentur; in <lb/>
capite enim ip&longs;ius, &longs;unt ill&aelig;, qu&aelig; &amp; Hiades, &amp; Atlantides, &amp; Succul&aelig; nuncu&shy;<lb/>
pantur. </s>
          <s id="s.003860">in dor&longs;o autem &longs;unt ill&aelig;, qu&aelig; Pleiades, &amp; Virgili&aelig; &longs;unt appellat&aelig;,</s>
        </p>
        <p type="main">
          <s id="s.003861"><emph type="italics"/>Qu&aelig; &longs;eptem dici, &longs;ex tamen e&longs;&longs;e &longs;olent.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003862">Vt cecinit Ouidius, quandoquidem &longs;eptima fer&egrave; nunquam apparet. </s>
          <s id="s.003863">has vul&shy;<lb/>
gus Gallinellam vocat. </s>
          <s id="s.003864">quod &longs;i eas per Tele&longs;copium in&longs;piciamus, mirum di&shy;<lb/>
ctu, ea&longs;dem plures e&longs;&longs;e, qu&agrave;m quadraginta &longs;tellas minimas clar&egrave; videbimus, <lb/>
vt optim&egrave; primus omnium Galil&aelig;us ob&longs;eruauit. </s>
          <s id="s.003865">Porr&ograve; con&longs;tellatio Tauri in <lb/>
no&longs;tris regionibus oriri cum Sole, incipit vno circiter &longs;e&longs;quimen&longs;e po&longs;t ver&shy;<lb/>
num &aelig;quinoctium. </s>
          <s id="s.003866">De Canicula &longs;atis dixi in 2. Meteor. <!-- REMOVE S-->&longs;umma 2. cap. 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.003867"><arrow.to.target n="marg328"/></s>
        </p>
        <p type="margin">
          <s id="s.003868"><margin.target id="marg328"/>336</s>
        </p>
        <p type="main">
          <s id="s.003869">Eadem &longs;ect. </s>
          <s id="s.003870">num. </s>
          <s id="s.003871">17. <emph type="italics"/>&lpar;Cur &agrave; Virgiliarum occa&longs;u ad Fauonij v&longs;que flatus, bi <lb/>poti&longs;&longs;imum pereant, qui morbo longo laborant, &amp; &longs;enes, quam iuuenes potius?&rpar; <emph.end type="italics"/><lb/>
Lege, qu&aelig; &longs;crip&longs;i de occa&longs;u &longs;yderum lib. 2. Meteor. <!-- REMOVE S-->&longs;umma 2. cap. 2. dein&shy;<lb/>
de, qu&aelig; in &longs;uperiore proxim&egrave; loco de Virgilijs: quibus h&aelig;c pauca <expan abbr="add&atilde;tur">addantur</expan>. <lb/>
</s>
          <s id="s.003872">cum intelligat de co&longs;mico Virgiliarum occa&longs;u, qui noctu apparet, <expan abbr="incipit&qacute;">incipitque</expan>; <lb/>
tunc primum, quando oriente Sole, ip&longs;e occumbunt, nece&longs;&longs;e e&longs;t occa&longs;um <lb/>
hunc incipere po&longs;t autumnale <expan abbr="&aelig;quinocti&utilde;">&aelig;quinoctium</expan> fer&egrave; &longs;e&longs;quimen&longs;e in no&longs;tris regio&shy;<lb/>
nibus; cum enim Virgili&aelig; &longs;int in Tauro, nece&longs;&longs;e e&longs;t occidente Tauro initio <lb/>
dixi, vt Sol &longs;it in oppo&longs;ito &longs;igno, videlicet in Scorpione; in quo a&longs;teri&longs;mo <lb/>
Sol reperitur po&longs;t pr&aelig;dictum &aelig;quinoctium vno fer&egrave; men&longs;e cum dimidio. </s>
          <s id="s.003873">de <lb/>
hac re plura Plinius lib. 18. cap. 31.</s>
        </p>
        <p type="head">
          <s id="s.003874"><emph type="italics"/>Ex Sectione 15.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003875"><arrow.to.target n="marg329"/></s>
        </p>
        <p type="margin">
          <s id="s.003876"><margin.target id="marg329"/>337</s>
        </p>
        <p type="main">
          <s id="s.003877">Nvm. <!-- REMOVE S-->1. <emph type="italics"/>&lpar;Cur linea ab angulo ad angulum ducta, &longs;ola ex omnibus, qu&aelig; fi&shy;<lb/>guras rectilineas bifariam &longs;ecant, diameter vocata e&longs;t? </s>
          <s id="s.003878">An quod dia&shy;<lb/>
meter, vt nomen ip&longs;um de&longs;ignat, duas in partes figuram &aelig;qu&egrave; dimetien&shy;<lb/>do diuidit, nihil dimen&longs;&aelig; figur&aelig; defiruens? </s>
          <s id="s.003879">igitur h&aelig;c, qu&aelig; per commi&longs;&shy;<lb/>&longs;uras, hoc est, per angulos figuram diuidit, appellanda e&longs;t diameter, quoniam h&aelig;c<emph.end type="italics"/> <pb pagenum="228" xlink:href="009/01/228.jpg"/><emph type="italics"/>figuram non de&longs;truit, quamuis diuidat. </s>
          <s id="s.003880">quemadmodum faciunt; qui va&longs;a militaria <lb/>
partiuntur. </s>
          <s id="s.003881">At c&aelig;ter&aelig; line&aelig;, qu&aelig; per lineas compo&longs;itam figuram &longs;ecant, eam cor&shy;<lb/>rumpunt: committitur enim rectilinea figura in angulis, vel &longs;ecundum angulos&rpar;<emph.end type="italics"/><lb/>
Vt rect&egrave; problema hoc percipiamus, proponenda e&longs;t figura rectilinea, &amp; <lb/>vna ex ijs, qu&aelig; parallelogramma dicuntur, vt &longs;unt Quadratum, Quadrila&shy;<lb/>
<figure id="id.009.01.228.1.jpg" place="text" xlink:href="009/01/228/1.jpg"/><lb/>
terum, Rhombus, Rhomboides, cuiu&longs;mo&shy;<lb/>
di e&longs;t pr&aelig;&longs;ens, aliter verba Ari&longs;t. illi non <lb/>
&longs;emper quadrarent, quia illarum diameter <lb/>
illas &longs;emper bifariam non &longs;e caret. </s>
          <s id="s.003882">quemad&shy;<lb/>
modum videre e&longs;t in trapezio. </s>
          <s id="s.003883">&amp; pentagono <lb/>
etiam &aelig;quilatero. </s>
          <s id="s.003884">Qu&aelig;rit igitur, cur ex om&shy;<lb/>
nibus lineis, qu&aelig; quadrilaterum A B C D, <lb/>
bifariam diuidunt, quales &longs;unt E F, G H, &amp; <lb/>
D B. &longs;ola D B, qu&aelig; ab angulo ad angulum <lb/>
ducta e&longs;t, m&oelig;ruit appellari diameter. </s>
          <s id="s.003885">Re&longs;pondet autem, eam fort&egrave; appel&shy;<lb/>
lationem hanc pr&aelig; c&aelig;teris inde promerui&longs;&longs;e, qu&ograve;d, quamuis ali&aelig; omnes <lb/>
&aelig;qu&egrave; parallelogrammum dimetiantur, &longs;ola tamen ip&longs;a D B, ip&longs;um non de&shy;<lb/>
&longs;truit, nec &longs;cindit, c&ugrave;m ei nouam aliquam diui&longs;ionem non inferat, &longs;ed id per <lb/>
angulos &longs;ecet, vbi prius laterum commi&longs;&longs;ur&aelig; <expan abbr="er&atilde;t">erant</expan>: reliqu&aelig; ver&ograve; omnes no&shy;<lb/>
uas figur&aelig; &longs;ectiones inferunt, c&ugrave;m eius latera in punctis E, F, G, H, <expan abbr="diuid&atilde;t">diuidant</expan>, <lb/>
vbi nulla prius erat diui&longs;io; quapropter ip&longs;am quodammodo de&longs;truunt, <lb/>
<expan abbr="atq;">atque</expan> corrumpunt. </s>
          <s id="s.003886">Aduert&egrave; vulgatam ver&longs;ionem latinam hanc <emph type="italics"/>&lpar;Angulis enim <lb/>
constant, qu&aelig; rectis lineis continentur&rpar;<emph.end type="italics"/> mal&egrave; gr&aelig;co textui <foreign lang="greek">sugkeintai gar to\ <lb/>
euqugrammon kata\ tas gwni/as,</foreign> re&longs;pondere, qui &longs;ic latin&egrave; reddendus e&longs;t: com&shy;<lb/>
ponitur enim rectilineum iuxta angulos; qu&aelig; interpretatio vera e&longs;t, quia <lb/>
anguli &longs;unt laterum commi&longs;&longs;ur&aelig;, vt dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.003887"><arrow.to.target n="marg330"/></s>
        </p>
        <p type="margin">
          <s id="s.003888"><margin.target id="marg330"/>338</s>
        </p>
        <p type="main">
          <s id="s.003889">Eadem &longs;ect. </s>
          <s id="s.003890">num. </s>
          <s id="s.003891">2. <emph type="italics"/>&lpar;cur diameter ita e&longs;t appellata? </s>
          <s id="s.003892">Vtrum quoniam &longs;ola bi&shy;<lb/>
partit&ograve; figuram diuidat? </s>
          <s id="s.003893">An quod &longs;ola figuram &longs;ecat per partes, &longs;iue membra, qui&shy;<lb/>
bus in flexa coarctatur, c&ugrave;m c&aelig;ter&aelig; per latera diuidant?&rpar;<emph.end type="italics"/> pr&aelig;&longs;entis problematis <lb/>expo&longs;itio petatur ex pr&aelig;cedentis expo&longs;itione.</s>
        </p>
        <p type="main">
          <s id="s.003894"><arrow.to.target n="marg331"/></s>
        </p>
        <p type="margin">
          <s id="s.003895"><margin.target id="marg331"/>339</s>
        </p>
        <p type="main">
          <s id="s.003896">In problemate 3. <emph type="italics"/>&lpar;Cur homines omnes tam Gr&aelig;ci, qu&agrave;m Barbari ad decem <lb/>
<expan abbr="v&longs;q;">v&longs;que</expan> numerare con&longs;ueuere, &amp; c. <!-- KEEP S--></s>
          <s id="s.003897">Vtrum quod denarius numerus perfectus &longs;it: con&shy;<lb/>tinet enim omnia numerorum genera. </s>
          <s id="s.003898">vt par, impar, quadratum, quadrantale, lon&shy;<lb/>
gum, planum, primum, compo&longs;itum&rpar;<emph.end type="italics"/> Cur omnes nationes miro quodam con&shy;<lb/>
&longs;en&longs;u &longs;uos numeros in denas, veluti in gradus quo&longs;dam diuidant, Ari&longs;toteles <lb/>
cau&longs;am indagaturus, re&longs;pondet prim&ograve; id fort&egrave; accidi&longs;&longs;e ob denarij numeri <lb/>perfectionem: cuius perfectionis hoc e&longs;t indicium, quod denarius contineat <lb/>
omnes numerorum &longs;pecies. </s>
          <s id="s.003899">qu&aelig; quidem omnes numerorum &longs;pecies in defi&shy;<lb/>
nitionibus 7. Elem. exponuntur, quas con&longs;ulere debes. </s>
          <s id="s.003900">in denario numero <lb/>
contineri numeros pares, ac impares, per &longs;e patet. </s>
          <s id="s.003901">continetur etiam in eo <lb/>
quadratus numerus, im&ograve; duo quadrati numeri, nam, &amp; quaternarius e&longs;t <lb/>
numerus quadratus, quippe qui ex ductu binarij in binarium producatur: <lb/>
item nouenarius e&longs;t quadratus, quippe qui ex multiplicatione ternarij in <lb/>
ternarium gignitur. </s>
          <s id="s.003902">Porr&ograve; pro quadrantali numero intelligendus e&longs;t nume&shy;<lb/>
rus cubus, erat. </s>
          <s id="s.003903">n. </s>
          <s id="s.003904">quadratal apud Romanos vas cubic&aelig; figur&aelig;: im&ograve; in gr&aelig;&shy;<lb/>
co textu voci huic quadrantali, re&longs;pondet <foreign lang="greek">kubos,</foreign> ide&longs;t, cubus. </s>
          <s id="s.003905">vnde apud la&shy;<pb pagenum="229" xlink:href="009/01/229.jpg"/>tinos quadrantal pro cubo &longs;olet v&longs;urpari. </s>
          <s id="s.003906">in denario autem <expan abbr="c&otilde;tinetur">continetur</expan> etiam <lb/>
hic numerus, e&longs;t enim octonarius numerus cubus, fit enim ex binario ter in <lb/>
&longs;e ip&longs;um multiplicato, hoc modo; duo bis faciunt quatuor: rur&longs;us duo qua&shy;<lb/>
ter faciunt octo; quem ex definitione numeri cubi, con&longs;tat e&longs;&longs;e cubum. </s>
          <s id="s.003907">qua <lb/>
ratione deinde reliqui numeri, longus, planus, primus, compo&longs;itus, in de&shy;<lb/>
nario exi&longs;tant, facil&egrave; e&longs;t cogno&longs;cere, dummodo eorum definitiones tenean&shy;<lb/>
tur, qu&aelig; initio 7. Elem. traduntur.</s>
        </p>
        <p type="main">
          <s id="s.003908"><arrow.to.target n="marg332"/></s>
        </p>
        <p type="margin">
          <s id="s.003909"><margin.target id="marg332"/>340</s>
        </p>
        <p type="main">
          <s id="s.003910">Ibidem <emph type="italics"/>&lpar;An quod denarius fons, <expan abbr="atq;">atque</expan> principium e&longs;t, quippe qui ex vno, duo&shy;<lb/>
bus, tribus, &amp; quatuor con&longs;tet&rpar;<emph.end type="italics"/> Aliam denarij dignitatem a&longs;&longs;ignat, quam ex <lb/>Plutarcho lib. 1. cap. 3. de Placitis Philo&longs;ophorum, optim&egrave; po&longs;&longs;umus intel&shy;<lb/>
ligere: vbi &longs;ic ait: Pythagorei aiebant denarium e&longs;&longs;e Naturam, quoniam <lb/>
omnes gentes <expan abbr="v&longs;q;">v&longs;que</expan> ad decem natura duce numerabant. </s>
          <s id="s.003911">tum etiam, quia ex <lb/>
quaternario con&longs;tabat, ide&longs;t, ex his quatuor numeris 1. 2. 3. 4. qui &longs;imul ad&shy;<lb/>
diti faciunt decem: quaternarium enim Pythagorei multis de cau&longs;is, quas <lb/>
apud Petrum Bungum de my&longs;terijs numerorum videre poteris, ade&ograve; extol&shy;<lb/>
lebant, vt dicerent ex quaternario naturalia, omnia con&longs;tare, vt quaterni&shy;<lb/>
tati omnia accepta referrent. </s>
          <s id="s.003912">vnde etiam per ip&longs;um conceptis his ver&longs;ibus <lb/>
iurare &longs;olebant,</s>
        </p>
        <p type="main">
          <s id="s.003913"><emph type="italics"/>Iuro per omnipotentem anim&aelig;, qui Tetrada no&longs;tr&aelig; <lb/>
Perpetuos fontes natur&aelig; infudit habentem.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003914">Pr&etail;cipua ver&ograve; cau&longs;a, cur tantopere Pythagorei quaternitatem celebrarint, <lb/>
refertur &agrave; Mar&longs;ilio Ficino cap. 24. compendij in Tymeum, his verbis: ex <lb/>
quatuor elementis, geometrica, &amp; harmonica ratione coniunctis inuicem, <lb/>
vniuer&longs;um Mundum compo&longs;itum Pythagorei omnes exi&longs;timant: con&longs;onan&shy;<lb/>tiam horum in c&oelig;lo &longs;emper e&longs;&longs;e perfectam, &longs;ub c&oelig;lo autem aliquando di&longs;&shy;<lb/>
&longs;onantem. </s>
          <s id="s.003915">volebant erg&ograve; totum mundum, tam &aelig;thereum, qu&agrave;m elementa&shy;<lb/>
rem, con&longs;tare ex quatuor elementis; &amp; ide&ograve; ex quaternario omnia con&longs;ta&shy;<lb/>
re dicebant. </s>
          <s id="s.003916">hac de cau&longs;a Pythagorei in mu&longs;icis con&longs;onantijs, vltra quater&shy;<lb/>
narium progredi vetabant; hoc e&longs;t nullam admittebant con&longs;onantiam, qu&aelig; <lb/>
numeris quaternario <expan abbr="cont&etilde;tis">contentis</expan> non exprimeretur, idcirc&ograve; &longs;upra quadruplam <lb/>
non a&longs;cendebant. </s>
          <s id="s.003917">Ver&ugrave;m inter alias quaternitatis dignitates hanc maximi <lb/>
faciebant, quod denarius ex ip&longs;a, vti modo dictum e&longs;t, componeretur; cu&shy;<lb/>
ius excellentiam in ip&longs;um proinde denarium transfundebant, dicebantque <lb/>
denarium e&longs;&longs;e numerum perfectum, &amp; aliorum numerorum fontem, atque <lb/>
principium. </s>
          <s id="s.003918">quemadmodum natura ip&longs;a quaternario <expan abbr="c&otilde;&longs;tans">con&longs;tans</expan>, erat omnium <lb/>
rerum origo. </s>
          <s id="s.003919">Ex quibus manife&longs;tum e&longs;t Ari&longs;t. <!-- REMOVE S-->Problema hoc, <expan abbr="atq;">atque</expan> eius &longs;o&shy;<lb/>
lutionem ex Pythagoreorum philo&longs;ophia accepi&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.003920"><arrow.to.target n="marg333"/></s>
        </p>
        <p type="margin">
          <s id="s.003921"><margin.target id="marg333"/>341</s>
        </p>
        <p type="main">
          <s id="s.003922">Ibidem <emph type="italics"/>&lpar;An quia corpora, qu&aelig; feruntur numero nouenario continentur&rpar;<emph.end type="italics"/> Puto <lb/>
h&aelig;c nouem corpora, qu&aelig; mouentur, e&longs;&longs;e c&oelig;los, primum &longs;cilicet Mobile, <lb/>
Firmamentum, &amp; &longs;eptem Planetarum orbes: quibus &longs;i addas &longs;ph&aelig;ram ele&shy;<lb/>
mentarem, habebis denarium corporum perfecti&longs;&longs;imum, ex quo tota Mun&shy;<lb/>
di machina componitur.</s>
        </p>
        <p type="main">
          <s id="s.003923"><arrow.to.target n="marg334"/></s>
        </p>
        <p type="margin">
          <s id="s.003924"><margin.target id="marg334"/>342</s>
        </p>
        <p type="main">
          <s id="s.003925">Ibidem <emph type="italics"/>&lpar;An quod decem proportionibus, quatuor cubales numeri con&longs;umun&shy;<lb/>
tur, &egrave; quibus numeris vniuer&longs;um con&longs;tare Pythagoreis placet?&rpar;<emph.end type="italics"/> Aliam denarij <lb/>perfectionem affert, quam ex 8. 9. Elem. <!-- REMOVE S-->comprobare, <expan abbr="atq;">atque</expan> intelligere po&longs;&shy;<lb/>
&longs;umus. </s>
          <s id="s.003926">e&longs;t autem 8. 9. Elem. propo&longs;itio h&aelig;c: &longs;i decem numeri in eadem pro&shy;


<pb pagenum="230" xlink:href="009/01/230.jpg"/>portione progrediantur ab vnitate incipientes, erunt ex illis quatuor cubi, <lb/>
v.g. <!-- REMOVE S-->in &longs;erie dupl&aelig; proportionis progrediantur hi decem termini: 1. 2. 4. 8. <lb/>
16. 32. 64. 128. 256. 512. ex his decem numeris &longs;unt quatuor cubi, nimi&shy;<lb/>
rum hi 1. 8. 64. 512. numerus cubus e&longs;t, qui fit ex tribus &aelig;qualibus numeris <lb/>
in &longs;e multiplicatis. </s>
          <s id="s.003927">&longs;ic vnitas e&longs;t cubus, quia fit ex vnitatibus tribus in &longs;e du&shy;<lb/>
ctis, nam 1. in 1. facit 1. &amp; rur&longs;us i&longs;tud 1. in 1. facit 1. &longs;ic etiam 8. e&longs;t cubus, <lb/>
quia fit ex tribus his numeris &aelig;qualibus 2. 2. 2. inuicem ductis hoc modo, <lb/>
2. in 2. facit 4. rur&longs;us 4. in 2. facit 8. qui e&longs;t cubus. </s>
          <s id="s.003928">&longs;ic 64. fit ex tribus hi&longs;ce <lb/>
4. 4. 4. pariter. </s>
          <s id="s.003929">512. fit ex tribus his 8. 8. 8. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; propterea cubus. </s>
          <s id="s.003930">&longs;imiliter <lb/>
&longs;i alia progre&longs;&longs;io in&longs;tituatur v&longs;que ad decem terminos, erunt in ea quatuor <lb/>
cubi, eodem ordine, quo in &longs;uperiori progre&longs;&longs;ione, ide&longs;t primo loco, 4.7. &amp; <lb/>
10. v.g. <!-- REMOVE S-->&longs;it tripla progre&longs;&longs;io h&aelig;c 1. 3. 9. 27. 81. 243. 729. 2182. 6546. 19638. <lb/>
quatuor cubi erunt hi 1. 27. 729. 19638. quorum latera cubica, &longs;unt hi nu&shy;<lb/>
meri 1. 3. 9. 27.</s>
        </p>
        <p type="main">
          <s id="s.003931">Po&longs;tquam huius loci explicationem ex allegata Euclidiana demon&longs;tratio&shy;<lb/>
ne attuli&longs;&longs;em, incidi in Petri Apponen&longs;is horum problematum commenta&shy;<lb/>
ria, qui aliam &agrave; &longs;e confictam expo&longs;itionem affert, <expan abbr="ait&qacute;">aitque</expan>; &longs;e per quatuor inte&shy;<lb/>
gros annos labora&longs;&longs;e, antequam eam inuenire, <expan abbr="locum&qacute;">locumque</expan>; hunc intelligere <lb/>
po&longs;&longs;et. </s>
          <s id="s.003932">e&longs;t autem h&aelig;c; Denarius componitur ex quaternario, ide&longs;t ex qua&shy;<lb/>
tuor primis numeris cubis, &longs;cilicet 1. 9. 27. 64. qui &longs;unt cubi, &amp; &longs;imul additi <lb/>
con&longs;tituunt decem denas, ide&longs;t <expan abbr="c&etilde;tum">centum</expan>. </s>
          <s id="s.003933">qu&aelig; cum nulli Mathematic&aelig; demon&shy;<lb/>&longs;trationi innitatur, nec vniuer&longs;alis &longs;it, ex &longs;e apparet, qu&agrave;m &longs;it <expan abbr="comm&etilde;titia">commentitia</expan>, <lb/>
&amp; ab Ari&longs;t. mente aliena. </s>
          <s id="s.003934">Enim uer&ograve; me antea ip&longs;ius commentarijs carui&longs;&shy;<lb/>
&longs;e gaui&longs;us &longs;um, quibus ni&longs;i carui&longs;&longs;em, veritate ip&longs;a carui&longs;&longs;em, acquieui&longs;&longs;em <lb/>
enim illius fictioni, qu&aelig; <expan abbr="vtcunq;">vtcunque</expan> videtur quadrare, <expan abbr="hoc&qacute;">hocque</expan>; pacto veritatis in&shy;<lb/>quirend&aelig; occa&longs;io &longs;ublata fui&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.003935"><arrow.to.target n="marg335"/></s>
        </p>
        <p type="margin">
          <s id="s.003936"><margin.target id="marg335"/>343</s>
        </p>
        <p type="main">
          <s id="s.003937">Ibidem <emph type="italics"/>&lpar;An quod omnes homines digitis decem lege naturali creantur? </s>
          <s id="s.003938">it aque <lb/>&longs;ui numeri qua&longs;i calculos adipi&longs;centes hac eadem multitudine, c&aelig;tera <expan abbr="quoq;">quoque</expan> nume&shy;<lb/>
rant&rpar;<emph.end type="italics"/> h&aelig;c Ari&longs;t. ratio confirmatur ex recentiorum relationibus de populis <lb/>
Bra&longs;ili&aelig;, qui cum per &longs;ummam barbariem, in omni rerum ignoratione ver&shy;<lb/>
&longs;arentur, ex digitis tamen, <expan abbr="vtcunq;">vtcunque</expan> numerabant. </s>
          <s id="s.003939"><expan abbr="cum&qacute;">cumque</expan>; vellent &longs;ignificare <lb/>
quinque dicebant, manum vnam: cum ver&ograve; decem dicebant, manus duas: <lb/>
cum viginti dicebant, manus, &amp; pedes. </s>
          <s id="s.003940">&amp; &longs;imiliter in alijs. </s>
          <s id="s.003941">non tamen hac <lb/>
ratione long&egrave; progrediebantur.</s>
        </p>
        <p type="main">
          <s id="s.003942"><arrow.to.target n="marg336"/></s>
        </p>
        <p type="margin">
          <s id="s.003943"><margin.target id="marg336"/>344</s>
        </p>
        <p type="main">
          <s id="s.003944">In 4. problema. </s>
          <s id="s.003945">quoniam textus huius problematis, tam apud gr&aelig;cos, <lb/>
qu&agrave;m latinos mendo&longs;us apparet, eum propterea per &longs;equentem paraphra&shy;<lb/>
&longs;im exponam, qua &amp; intelligi, &amp; re&longs;titui etiam poterit. </s>
          <s id="s.003946">Qu&aelig;&longs;tio autem e&longs;t <lb/>
de in&aelig;quali incremento, ac decremento vmbrarum Solis, qu&aelig; propri&egrave; de <lb/>
vmbris in plano horizontali proiectis, quas rectas vmbras appellant intel&shy;<lb/>ligenda e&longs;t: h&aelig; enim in&aelig;qualiter cre&longs;cunt, &amp; decre&longs;cunt, &longs;i quidem mane <lb/>
plurimum, po&longs;tea parum, tandem nihil fer&egrave; circa meridiem minuuntur, po&shy;<lb/>
&longs;itis tamen &aelig;qualibus temporibus. </s>
          <s id="s.003947">Qu&aelig;rit igitur Ari&longs;t. cur cum Sol eodem <lb/>
vigore feratur, non idem tamen incrementum, decrementumu&egrave; vmbrarum <lb/>
exultet? </s>
          <s id="s.003948">pro cuius intelligentia, ac &longs;olutione in&longs;picienda e&longs;t figura &longs;equens: <lb/>
in qua &longs;emicirculus, &longs;iue arcus A B C, &longs;it is, per quem Sol incedit, dum ele&shy;<lb/>
uatur &longs;upra horizontem H I; &amp; quia Sol vniformiter &longs;candit hunc arcum,


<pb pagenum="231" xlink:href="009/01/231.jpg"/><figure id="id.009.01.231.1.jpg" place="text" xlink:href="009/01/231/1.jpg"/><lb/>
&longs;int duo arcus &aelig;quales A B, B C. <lb/>
in plano autem horizontis ere&shy;<lb/>
ctum &longs;it corpus G D, quod &agrave; So&shy;<lb/>
le con&longs;piciatur, &longs;iue illuminetur. <lb/>
</s>
          <s id="s.003949"><expan abbr="&longs;it&qacute;">&longs;itque</expan>; primum Sol in A. radius ip&shy;<lb/>
&longs;ius per verticem D, tran&longs;iliens <lb/>
erit A D I; vmbra ver&ograve; erit G I. <lb/>
<!-- KEEP S--></s>
          <s id="s.003950">Sole deinde in B, exi&longs;tente, erit <lb/>
radius B D E, &amp; vmbra G E. <!-- KEEP S--></s>
          <s id="s.003951">So&shy;<lb/>
le tandem in C. <expan abbr="radio&qacute;">radioque</expan>; C D F. <lb/>
vmbra erit G F. <!-- KEEP S--></s>
          <s id="s.003952">Dicit erg&ograve; Ari&longs;t. quod cum anguli A D B, B D C, &longs;int ex <lb/>
&aelig;qualibus arcubus A B, B C. ad centrum D, con&longs;tituti, erunt &aelig;quales, qua&shy;<lb/>
re erunt etiam &aelig;quales alij duo anguli illis ad verticem oppo&longs;iti, per 15. <lb/>
primi, qui &longs;unt contenti in triangulo G D I. quod <expan abbr="tri&atilde;">tria</expan>ngulum fit &agrave; radio pri&shy;<lb/>
mo D I, re con&longs;pecta &agrave; Sole G D, &amp; vmbra G I. anguli inquam F D E, E D I, <lb/>
qui &longs;unt ad verticem pr&aelig;dictis angulis, erunt, &amp; ip&longs;i &aelig;quales inuicem.</s>
        </p>
        <p type="main">
          <s id="s.003953">Supponit pr&aelig;terea pro certo radium D I, qui c&aelig;teris longius prolabitur, <lb/>
e&longs;&longs;e maiorem propinquiore D E. <expan abbr="ip&longs;um&qacute;">ip&longs;umque</expan>; D E, maiorem e&longs;&longs;e reliquo radio <lb/>
D F. oportet autem <expan abbr="radi&utilde;">radium</expan> B E, terminari in puncto E, quod &longs;it citra radium <lb/>
D I. &amp; radium D F, de&longs;inere in F, citra radium D E, aliter &longs;equitur lineam <lb/>
rectam B E, vel C F, &longs;ecare lineam recta A I, in pluribus punctis, qu&agrave;m vno <lb/>
D. quod e&longs;t impo&longs;&longs;ibile. </s>
          <s id="s.003954">c&ugrave;m erg&ograve; totus angulus F D I, diuidatur &agrave; linea <lb/>
D E, in duos angulos &aelig;quales F D E, E D I. <expan abbr="&longs;it&qacute;">&longs;itque</expan>; latus D I, maius latere D F. <lb/>erit ex &longs;cholio 19. primi Elemen. <!-- REMOVE S-->linea E I, maior, quam F E, qu&aelig; &longs;unt du&aelig; <lb/>
in&aelig;quales vmbr&aelig;, qu&aelig; tamen re&longs;pondent &aelig;qualibus arcubus A B, B C. &longs;imi&shy;<lb/>
liter vmbra F E, maior e&longs;&longs;e probaretur &longs;equenti qualibet vmbra, qu&aelig; tamen <lb/>
ex arcu &aelig;quali procederet. </s>
          <s id="s.003955">&amp; &longs;ic deinceps v&longs;quequ&ograve; Sol e&longs;&longs;et in meridie, vbi <lb/>
vmbra e&longs;&longs;et omnium minima.</s>
        </p>
        <p type="main">
          <s id="s.003956">Atque ex his patet, cur quamuis Sol vniformiter in c&oelig;lo moueatur, vm&shy;<lb/>
brarum tamen incrementa, &longs;int di&longs;paria, nec vniformia. </s>
          <s id="s.003957">eadem intelligen&shy;<lb/>
da &longs;unt de vmbrarum decrementis promeridianis Sole ad occa&longs;um labente: <lb/>
tunc enim, vt ille cecinit.</s>
        </p>
        <p type="main">
          <s id="s.003958"><emph type="italics"/>Maioresqu&eacute; cadunt altis de montibus vmbr&aelig;.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003959">Aduerte verba illa &lpar;<emph type="italics"/>Angulus D E, maior, quam E F, angulo D G, est<emph.end type="italics"/>&rpar; e&longs;&longs;e <lb/>
mendo&longs;a, etiam in gr&aelig;co textu; vnde, &amp; mal&egrave; in latinum tran&longs;lata: <expan abbr="neq;">neque</expan> in <lb/>
gr&aelig;co e&longs;t vox, angulus: aliter Ari&longs;t. qu&aelig;&longs;tioni non &longs;atisfaceret. </s>
          <s id="s.003960">quare di&shy;<lb/>
cendum, &amp; interpretandum videtur, quemadmodum &agrave; me factum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.003961"><arrow.to.target n="marg337"/></s>
        </p>
        <p type="margin">
          <s id="s.003962"><margin.target id="marg337"/>345</s>
        </p>
        <p type="main">
          <s id="s.003963">In 5. problema. </s>
          <s id="s.003964">Difficile admodum e&longs;t problema i&longs;tud, &amp; cuius &longs;olutio&shy;<lb/>
nem nullus veterum, quod &longs;ciam, perfect&egrave; attigit: quamuis Vitellio nu. </s>
          <s id="s.003965">39. <lb/>
lib. 2. hoc idem proponat, ac &longs;oluere contendat: Ver&ugrave;m nec Ari&longs;t. nec Vi&shy;<lb/>
tellio intellectui &longs;atisfaciunt mathematico: probabilia tamen afferunt. </s>
          <s id="s.003966">op&shy;<lb/>tim&egrave; hae de re Maurolicus, in &longs;uis Po&longs;thumis, nuper editis Photi&longs;mis, &amp; Ke&shy;<lb/>
plerus, in paralip. </s>
          <s id="s.003967">ad Vitell. <!-- KEEP S--></s>
          <s id="s.003968">Sen&longs;um Ari&longs;t. ac textum pariter per paraphra&shy;<lb/>
&longs;im exponam, ita tamen, vt eius textus ex hac paraphra&longs;i omnin&ograve; clarus <lb/>
euadat. </s>
          <s id="s.003969">Qu&aelig;rit igitur; cur lumen Solis ingrediens per quadrangularia, &longs;eu <lb/>triangularia foramina, vel etiam per rimulas, c&ugrave;m po&longs;tea recipiatur in pla&shy;<pb pagenum="232" xlink:href="009/01/232.jpg"/>no &longs;atis ab illo foramine remoto, vt in pariete, vel pauimento, non recipi&shy;<lb/>
tur in eadem figura, per quam ingre&longs;&longs;um e&longs;t; quamuis. </s>
          <s id="s.003970">n. </s>
          <s id="s.003971">foramen &longs;it angulo&shy;<lb/>
&longs;um, illuminatio tamen in oppo&longs;ito plano facta e&longs;t &longs;emper circularis, &longs;i pla&shy;<lb/>
num &longs;it &longs;atis remotum, &amp; radio Solis direct&egrave;, &longs;eu perpendiculariter obie&shy;<lb/>
ctum: &longs;i enim non &longs;it perpendiculariter, &longs;ed obliqu&egrave;, tunc illuminationes <lb/>apparent non omnino circulares, &longs;ed ouales; quemadmodum quotidie ac&shy;<lb/>
cidere videmus in pauimentis, vbi omnes fer&egrave; huiu&longs;modi illuminationes <lb/>
ellip&longs;es &longs;unt, quamuis Sol per angulo&longs;a foramina ingrediatur. </s>
          <s id="s.003972">qu&aelig; ellip&longs;es &longs;i <lb/>
in plano Solis radio <expan abbr="perp&etilde;diculariter">perpendiculariter</expan> obiecto recipiantur, perfecti euadunt <lb/>
orbes. </s>
          <s id="s.003973">hoc etiam, inquit Ari&longs;t, in cratibus patet; crates enim ill&aelig; habebant <lb/>
foramina angulo&longs;a, atque oblonga, fiunt enim crates ex virgis decu&longs;&longs;atis, <lb/>
quorum foramina &longs;unt quadrilatera, per qu&aelig; Sol ingrediens, non tamen <lb/>
recipit angulo&longs;am figuram, &longs;ed in debita remotione rotundatur. </s>
          <s id="s.003974">Re&longs;pon&shy;<lb/>
det propo&longs;it&aelig; qu&aelig;&longs;tioni dicens; radijs Solis fort&egrave; illud accidere, quod &amp; ra&shy;<lb/>
dijs vi&longs;ualibus, qui ab oculo ad rem con&longs;pectam producuntur: ij enim in <lb/>
turbinis, &longs;eu coni figuram aguntur, cuius apex e&longs;t in oculo, ba&longs;is autem e&longs;t <lb/>
in re vi&longs;a: &amp; quamuis res vi&longs;a &longs;it angulo&longs;a, vt triangula, vel quadrangula, <lb/>
tamen &longs;i &agrave; long&egrave; con&longs;piciatur, circularis apparet; vnde &amp; figura vi&longs;ualium <lb/>
radiorum, qu&aelig; in proximum obiectum incidens ba&longs;im angulo&longs;am, remoto, <lb/>
quantum &longs;atis e&longs;t, obiecto, ba&longs;im habebit orbicularem. </s>
          <s id="s.003975">eodem igitur modo <lb/>
de Solis radijs exi&longs;timare debemus: qui quamuis per angulo&longs;a foramina in&shy;<lb/>
trent, tamen, &longs;i in remoto obiecto recipiantur, figuram circularem &longs;ortien&shy;<lb/>
tur: quod &longs;i non &longs;atis remoto plano occurrant, angulo&longs;am etiam figuram <lb/>
pro foraminis qualitate efficient: &amp; quidem eo foramini &longs;imiliorem, quo ei <lb/>
propior erit coni lumino&longs;i ba&longs;is. </s>
          <s id="s.003976">vel aliter etiam <expan abbr="re&longs;pond&etilde;dum">re&longs;pondendum</expan> e&longs;t, hoc mo&shy;<lb/>
do; figura Solis, qu&aelig; orbicularis e&longs;t, vndique lineis rectis, &longs;eu radijs, quos <lb/>
emittit, circundata e&longs;t, qui radij cum intrent per foramina lineis <expan abbr="quoq;">quoque</expan> re&shy;<lb/>
ctis contenta, accidunt lateribus figur&aelig; foraminis, &amp; propterea cum rect&aelig; <lb/>
line&aelig; lineis rectis applicentur, deberent hi radij in figuram rectilineam con&shy;<lb/>
formari; quod &amp; faciunt, vt patet in cratium fene&longs;tellis, vbi &longs;i radij po&longs;t in&shy;<lb/>
gre&longs;&longs;um &longs;tatim in plano quopiam recipiantur, figuram efficiunt fene&longs;tell&aelig; &longs;i&shy;<lb/>
milem. </s>
          <s id="s.003977">quod &longs;i in plano, &longs;atis remoto, de&longs;inant, non amplius angulo&longs;am, <lb/>
&longs;ed circularem illuminationem efficient. </s>
          <s id="s.003978">Cuius cau&longs;a e&longs;t, quia, vt initio di&shy;<lb/>
xi, eodem modo lumen, &longs;eu radij Solis producuntur, quo etiam radij vi&shy;<lb/>
&longs;uales, quod inde patere pote&longs;t, quia per&longs;pectiui eadem de <expan abbr="vtri&longs;q;">vtri&longs;que</expan> &amp; &longs;uppo&shy;<lb/>
nunt, &amp; o&longs;tendunt. </s>
          <s id="s.003979">quemadmodum igitur quando oculi no&longs;tri a&longs;pectus ad <lb/>
figuram rectilineam, &amp; angulo&longs;am, qu&aelig; propinqua &longs;it directus, eam angu&shy;<lb/>lo&longs;am iudicat, vt re vera e&longs;t, quam deinde long&egrave; &longs;emotam oualem, aut cir&shy;<lb/>
cularem exi&longs;timat; propterea quod radij vi&longs;uales ad extremitates laterum <lb/>
figur&aelig;, &longs;iue angulos ip&longs;ius proten&longs;i euane&longs;cunt, quia imbecilli admodum <lb/>
&longs;unt; &longs;unt autem imbecilli, quia, <expan abbr="c&utilde;">cum</expan> tendant ad angulos, qu&aelig; minim&aelig; partes <lb/>
&longs;unt obiecti, &amp; quidem long&egrave; &longs;emoti, fit, vt ij anguli &longs;ub angulo ade&ograve; paruo <lb/>ad oculum veniant, vt &longs;ub eo vi&longs;io fieri nequeat; idcirc&ograve; c&ugrave;m anguli cerni <lb/>
nequeant, obiectum &longs;ub circulari figura apparebit. </s>
          <s id="s.003980">&longs;ed quantum lateris re&shy;<lb/>
cti vi&longs;i in turbine vi&longs;uali continetur, ac &longs;ub angulo vi&longs;ioni idoneo ad ocu&shy;<lb/>
lum defertur, id tantum in vi&longs;um agere pote&longs;t. </s>
          <s id="s.003981">Reliquum, quod e&longs;t in an&shy;<pb pagenum="233" xlink:href="009/01/233.jpg"/>gulis ob dictam rationem non pote&longs;t, quia radij vi&longs;uales, vt dictum e&longs;t, in&shy;<lb/>
di&longs;creti &longs;unt, &amp; confu&longs;i. </s>
          <s id="s.003982"><expan abbr="neq;">neque</expan> hoc mirum, c&ugrave;m multa videre nullo pacto po&longs;&shy;<lb/>
&longs;imus, quamuis no&longs;tro attingantur a&longs;pectu, vt ea, qu&aelig; &longs;unt in tenebris, cui <lb/>
&longs;imile accidit, cum quadratum &agrave; long&egrave; vi&longs;um videtur habere plurimos an&shy;<lb/>gulos; atq; ade&ograve; ad rotunditatem, &longs;i remoueatur adhuc, accedere, vt etiam <lb/>
circulus videatur. </s>
          <s id="s.003983">C&ugrave;m enim, vt &longs;upra dixi, a&longs;pectus in turbinis modum <lb/>
procedat quoties figura con&longs;pecta vlterius &longs;epo&longs;ita e&longs;t, radij vi&longs;uales, qui ad <lb/>
angulos tendant, quoniam &amp; imbecilli, &amp; pauci &longs;unt, ob dictam cau&longs;am rem <lb/>
a&longs;&longs;equi nequeunt: qui autem in mediam partem concurrunt, hi per&longs;i&longs;tere <lb/>po&longs;&longs;unt, vtpot&egrave;, conferti, &amp; validi: erg&ograve; cum figura prop&egrave; e&longs;t, anguli <expan abbr="quoq;">quoque</expan> <lb/>
a&longs;pici po&longs;&longs;unt, aucta di&longs;tantia non po&longs;&longs;unt. </s>
          <s id="s.003984">hac etiam de cau&longs;a linea circu&shy;<lb/>
laris vald&egrave; di&longs;tans, &amp; in &longs;itu, quo conuexum ad oculum rect&agrave; vergat: &amp; in <lb/>
Luna die octauo, quando dimidia e&longs;t linea illa, qu&aelig; illuminatam partem &agrave; <lb/>
non illuminata diuidit, recta videtur, quamuis circularis &longs;it, e&longs;t enim in <lb/>
&longs;ph&aelig;rico corpore de&longs;ignata. </s>
          <s id="s.003985">quando enim circunferentia prop&egrave; e&longs;t, vi&longs;us <lb/>
di&longs;cernere valet quanto pars altera, parte altera, &longs;it propior; vnde rotun&shy;<lb/>
ditas apparet: at c&ugrave;m procul abe&longs;t rect&egrave; &longs;entire nequit, &longs;ed &aelig;qualem par&shy;<lb/>
tium &longs;itum cernere &longs;ibi videtur, <expan abbr="eam&qacute;">eamque</expan>; propterea rectam iudicat. </s>
          <s id="s.003986">h&aelig;c igi&shy;<lb/>
tur, qu&aelig; accidere vi&longs;ui certum e&longs;t, eadem &longs;imiliter radijs Solis conuenire <lb/>
par e&longs;t credere. </s>
          <s id="s.003987">ex quibus iam patere pote&longs;t, cur lumen Solis per quadrila&shy;<lb/>
teras figuras profluens illuminationem rotundam reddat.</s>
        </p>
        <p type="head">
          <s id="s.003988"><emph type="italics"/>De Lucis Figuratione.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.003989"><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t &longs;olutio admirandi huius effectus ab Ari&longs;t. allata, qu&aelig; <lb/>
quoniam non paucas habet difficultates, aliam ex Maurolyco de&shy;<lb/>
&longs;umptam, qu&aelig; &longs;atis demon&longs;tratiua e&longs;t, afferam.</s>
        </p>
        <p type="main">
          <s id="s.003990">Prim&ograve; igitur illud Per&longs;pectiuus principium &longs;tatuendum e&longs;t, ex <lb/>
quolibet corporis lucidi puncto, ad quodlibet medij punctum, lumen rectis <lb/>
lineis quoquouer&longs;us emicare, ita vt lumen &agrave; quouis puncto lucidi, tanquam <lb/>
&agrave; centro <expan abbr="circumquaq;">circumquaque</expan> effu&longs;um in modum &longs;ph&aelig;r&aelig; diffundatur.</s>
        </p>
        <p type="main">
          <s id="s.003991">Secund&ograve;, qu&ograve; magis duorum vicinorum circulorum peripheri&aelig; augen&shy;<lb/>
tur, e&ograve; magis ad vnius circuli &longs;imilitudinem accedere; vt in hac figura cer&shy;<lb/>
<figure id="id.009.01.233.1.jpg" place="text" xlink:href="009/01/233/1.jpg"/><lb/>
nere licet, vbi &longs;unt prim&ograve; duo parui <lb/>
circuli circa centra A, &amp; B, de&longs;cripti, <lb/>
quorum circunferenti&aelig; cre&longs;cant <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>
ad circunferentias C D, &amp; E F, quo in&shy;<lb/>
cremento po&longs;ito, &longs;tatim vel ad &longs;en&longs;um <lb/>
manife&longs;tum e&longs;t, has duas maiores pe&shy;<lb/>ripherias, magis referre vnius circuli <lb/>
&longs;imilitudinem, qu&agrave;m referant duo pa&shy;<lb/>
rui circelli. </s>
          <s id="s.003992">quod &longs;i e&longs;&longs;ent tres circelli, <lb/>
qui augerentur, magis adhuc vnicum <lb/>
circulum imitarentur; <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; deinceps, <lb/>qu&ograve; plures e&ograve; perfectius: &amp; qu&ograve; magis <pb pagenum="234" xlink:href="009/01/234.jpg"/>etiam augentur e&ograve; perfectius. </s>
          <s id="s.003993"><expan abbr="propterea&qacute;">proptereaque</expan>; poterunt aliquando exact&egrave; cir&shy;<lb/>
culum qu&ograve; ad &longs;en&longs;um imitari. </s>
          <s id="s.003994">quod de circulis dictum e&longs;t, intelligi etiam de&shy;<lb/>
bet de omnibus alijs figuris eiu&longs;dem &longs;peciei, vt de duabus ellip&longs;ibus, aut <lb/>
de duobus triangulis, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.003995">Terti&ograve;, lumen Solis per foramen tam <expan abbr="exigu&utilde;">exiguum</expan>, quod &longs;it in&longs;tar puncti tran&longs;&shy;<lb/>
mi&longs;&longs;um, <expan abbr="figur&atilde;">figuram</expan> Solis rotundam videlicet, quamuis conuer&longs;am referre; quod <lb/>
<figure id="id.009.01.234.1.jpg" place="text" xlink:href="009/01/234/1.jpg"/><lb/>
hac de&longs;criptione patefiet. </s>
          <s id="s.003996">&longs;it Sol vbi A B, fora&shy;<lb/>
men in&longs;tar puncti vbi E. illuminatio, in planum <lb/>
radio Solis perpendiculariter obiectum, &longs;it C I D. <lb/>
aio eam e&longs;&longs;e in&longs;tar Solis rotundam, inuer&longs;am ta&shy;<lb/>
men. </s>
          <s id="s.003997">nam &longs;i ab omnibus punctis &longs;olaris periphe&shy;<lb/>
ri&aelig; radij per vnicum punctum E, rect&agrave; transfe&shy;<lb/>
rantur ad planum rect&agrave; obiectum, vbi C D, con&shy;<lb/>
flabunt duas conicas &longs;uperficies A E B, C E D, <lb/>
ba&longs;es habentes circulos A B, C D, verticem ver&ograve; <lb/>
eundem E. <!-- KEEP S--></s>
          <s id="s.003998">C&ugrave;m igitur illuminatio C D, &longs;it ve&shy;<lb/>
luti &longs;ectio lumino&longs;i coni C E D, qu&aelig; perpendicu&shy;<lb/>
lariter eum &longs;ecat, ex Apollonij conicis circulus <lb/>
erit, ac proinde Solis figuram imitabitur. </s>
          <s id="s.003999">erit <lb/>
tamen inuer&longs;a, quia cum, vt dictum e&longs;t in prima <lb/>
pr&aelig;notatione, radij rectis lineis ferantur, pun&shy;<lb/>
ctum A, &longs;ini&longs;trum, repre&longs;entabitur in D, parte <lb/>
dextra. </s>
          <s id="s.004000">B, ver&ograve; dexterum apparebit in C, parte <lb/>
&longs;ini&longs;tra, &amp; H, in anteriore parte Solis, feretur in <lb/>
I, punctum illuminationis po&longs;terius: <expan abbr="atq;">atque</expan> eodem <lb/>
modo reliqua puncta in contrarias partes trans&shy;<lb/>
ferentur. </s>
          <s id="s.004001">Quod &longs;i planum terminans conum ra&shy;<lb/>
dio&longs;um non illi &longs;it perpendiculare, &longs;ed obliquum, <lb/>
vti e&longs;t G F, &longs;ectionem faciet ellipticam ex eodem <lb/>
Apollonio, <expan abbr="ideo&qacute;">ideoque</expan>; Solis il luminatio, quod pluri&shy;<lb/>
m&ugrave;m accidit, oualis apparet. </s>
          <s id="s.004002">Quod dictum e&longs;t de Solis illuminatione, in&shy;<lb/>telligi etiam debet de alijs quibu&longs;uis lucidis, vel coloratis luce perfu&longs;is, qu&aelig; <lb/>&longs;uas &longs;pecies emittunt, cuiu&longs;uis &longs;int figur&aelig;, eodem enim modo o&longs;tendemus <lb/>
eorum illuminationes, &longs;eu &longs;pecies debere figuram ip&longs;orum primitiuam re&shy;<lb/>
ferre, quamuis inuer&longs;am.</s>
        </p>
        <p type="main">
          <s id="s.004003">Quart&ograve;, dico, Cau&longs;am huius apparenti&aelig; primariam e&longs;&longs;e ip&longs;am Solis ro&shy;<lb/>tunditatem, qu&aelig; per &longs;ingula foraminis cuiu&longs;uis puncta in oppo&longs;itum planum <lb/>
&longs;e &longs;e transfundit. </s>
          <s id="s.004004">quod enim nuper de vnico puncto o&longs;ten&longs;um e&longs;t, idem intel&shy;<lb/>
ligendum e&longs;t de &longs;ingulis foraminis punctis, per &longs;ingula enim puncta &longs;ingul&aelig; <lb/>
illuminationes rotund&aelig; in aduer&longs;um planum tran&longs;mittuntur, qu&aelig; qu&ograve; lon&shy;<lb/>
gius &agrave; foramine proce&longs;&longs;erint, c&ograve; perfectiorem rotunditatem a&longs;&longs;equentur, ob <lb/>
eam cau&longs;am, qu&agrave;m in &longs;ecunda pr&aelig;notatione innuimus. </s>
          <s id="s.004005">qu&aelig; vt explicatius <lb/>
tractentur, neu&egrave; in hac Solis luce c&aelig;cutiamus, linearem demon&longs;trationem <lb/>
afferemus. </s>
          <s id="s.004006">&longs;it &longs;olare corpus A B, foramen ver&ograve; <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> figur&aelig;, veluti ri&shy;<lb/>
mula C D, per quam Solis &longs;plendor illap&longs;us oppo&longs;itum planum, in quo F E, <lb/>
collu&longs;tret. </s>
          <s id="s.004007">iam ex infinitis punctis rimul&aelig; C D, &longs;atis erit extrema duo C, D,


<pb pagenum="235" xlink:href="009/01/235.jpg"/>con&longs;iderare. </s>
          <s id="s.004008">per punctum igitur D, ducantur radij A D E, B D K. per pun&shy;<lb/>
ctum ver&ograve; C, ducantur alij A C H, B C F, qui c&ugrave;m ab extremitatibus Solis <lb/>
profluant, reliquos omnes radios intra &longs;e continebunt. </s>
          <s id="s.004009">ex tertia igitur pr&etail;&shy;<lb/>
notatione per punctum C, procedit rotunda illuminatio, cuius diameter <lb/>
<figure id="id.009.01.235.1.jpg" place="text" xlink:href="009/01/235/1.jpg"/><lb/>
F H, &longs;imiliter per punctum D, illuminatio <lb/>
rotunda emanat, cuius diameter K E, &amp; pa&shy;<lb/>
riter ex omnibus alijs rimul&aelig; punctis ro&shy;<lb/>
tundi &longs;plendores in &longs;uperficiem, vbi F E, <lb/>
tran&longs;mittuntur. </s>
          <s id="s.004010">Iam dicimus has duas illu&shy;<lb/>
minationes ex pr&aelig;notatis &longs;ecundo loco, <lb/>
qu&agrave;m longius planum F E, &agrave; foramine de&shy;<lb/>
&longs;titerit, vt &longs;i e&longs;&longs;et in L M, ad vnius circuli <lb/>
rotunditatem magis accedere, vt apparet <lb/>
in plano L M, vbi maiores fact&aelig; &longs;unt illumi&shy;<lb/>
nationes, &amp; ide&ograve; magis ad vnam circula&shy;<lb/>
rem accedunt. </s>
          <s id="s.004011"><expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> eft enim, qu&ograve; lon&shy;<lb/>
gius radij C F, C H, producti fuerint, e&ograve; <lb/>
maiorem fore <expan abbr="diametr&utilde;">diametrum</expan> illuminationis F H. <lb/>
euadet enim L O, &amp; &longs;imiliter ex productio&shy;<lb/>
ne radiorum D K, D E, diameter alterius <lb/>
illuminationis K E, augebitur, &amp; fiet N M. <lb/>
&amp; con&longs;equenter du&aelig; ip&longs;arum peripheri&aelig; &longs;i&shy;<lb/>
mul maiores fient, ac proinde ad vnius cir&shy;<lb/>
culi &longs;imilitudinem ex <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> notatione per&shy;<lb/>
uenient. </s>
          <s id="s.004012">&amp; quamuis ex radiorum produ&shy;<lb/>
ctione augeantur non &longs;olum pr&aelig;dict&aelig; dia&shy;<lb/>
metri illuminationum, &longs;ed etiam earum <lb/>
differenti&aelig; F K, &amp; H E; h&aelig; tamen differen&shy;<lb/>
ti&aelig; re&longs;pectu illorum nihil, quod &longs;en&longs;ibile &longs;it <lb/>
augentur; quod inde oritur, quia angulus F C H, maior e&longs;t angulo F B K, <lb/>
per 16. primi Elem. &amp; ide&ograve; crura F C, H C, magis dilatata &longs;unt qu&agrave;m cru&shy;<lb/>
ra F B, K B, &amp; ide&ograve; &longs;i producantur, mult&ograve; magis cre&longs;cit F H, dum euadit <lb/>
M N, qu&agrave;m F K, dum euadit M O. eodem modo magis cre&longs;cit K E, dum fit <lb/>
O L, qu&agrave;m H E, dum fit K L. quare ex &longs;ecunda notatione earum periphe&shy;<lb/>
ri&aelig; ad vnius orbis figuram tandem concurrere videbuntur. </s>
          <s id="s.004013">mult&ograve; autem <lb/>
euidentius ad rotunditatem accederent, &longs;i tertia illuminatio per tertium <lb/>
aliquod punctum tran&longs;iens, &longs;ic perueniret; &amp; quo plures, e&ograve; etiam perfectius, <lb/>
omnes enim rotund&aelig; e&longs;&longs;ent, &amp; ex radiorum proce&longs;&longs;u augerentur, atque ad <lb/>
vnius orbis formam &longs;e &longs;e reciperent.</s>
        </p>
        <p type="main">
          <s id="s.004014">H&aelig; porr&ograve;, qu&aelig; Geometric&egrave; comprobata &longs;unt, libet etiam iucunda qua&shy;<lb/>
dam experientia confirmare; fiant igitur in fene&longs;tra quapiam duo, vel tria <lb/>
parua admodum foramina, inuicem proxima, per qu&aelig; totidem illumina&shy;<lb/>
tiones ad obiectam chartam transferantur, h&aelig; admota foramini charta <lb/>
paru&aelig;, ac &longs;ibi mutu&ograve; parum incumbentes apparebunt, &amp; proinde vnicum <lb/>
circulum non pr&aelig;&longs;eferent; qu&ograve; autem longius charta remouebitur, e&ograve; ma&shy;<lb/>
iores fient, ac &longs;ibi mutu&ograve; magis incumbentes, ac idcirc&ograve; in vnum fer&egrave; cir&shy;


<pb pagenum="236" xlink:href="009/01/236.jpg"/>culum coale&longs;cent. </s>
          <s id="s.004015">nunquam tamen ad geometricam rotunditatem perue&shy;<lb/>
nient, quamuis illam &longs;en&longs;ui obijciant.</s>
        </p>
        <p type="main">
          <s id="s.004016">Aliter Ioannes Keplerus totam hanc demon&longs;trationem in&longs;tituit, quem tu <lb/>
in &longs;uis ad Vitellionem Paralipom. <!-- REMOVE S-->con&longs;ule. </s>
          <s id="s.004017">eius tantum experientiam non <lb/>
iniucundam, qua i&longs;tud probat, non grauabor referre. </s>
          <s id="s.004018">cap. igitur &longs;ecundo <lb/>
de Figuratione lucis h&aelig;c habet: librum in &longs;ublimi locaui, qui e&longs;&longs;et loco lu&shy;<lb/>
centis corporis, hunc inter &amp; pauimentum figebatur tabella foramine mul&shy;<lb/>tangulo. </s>
          <s id="s.004019">filum deinde ex vno libri angulo per foramen in pauimentum de&shy;<lb/>
mi&longs;&longs;um, ita incidebat in pauimento, vt terminos foraminis raderet, cuius <lb/>
ve&longs;tigia creta imitabar; qua ratione creabatur figura in pauimento &longs;imilis <lb/>
foramini. </s>
          <s id="s.004020">Idem accidebat, annexo filo ex altero, tertio, quarto libri angu&shy;<lb/>
lo, <expan abbr="adeo&qacute;">adeoque</expan>; ex infinitis marginum punctis. </s>
          <s id="s.004021"><expan abbr="Itaq;">Itaque</expan> infinitarum in pauimento <lb/>
figurarum foraminis exilium &longs;eries adumbrabat magnam, &amp; quadrangulam <lb/>
libri figuram. </s>
          <s id="s.004022">hic primus e&longs;t in hoc labore &longs;ucce&longs;&longs;us. </s>
          <s id="s.004023">h&aelig;c ille; ex quibus po&shy;<lb/>
&longs;tea &longs;uam demon&longs;trationem adornauit. </s>
          <s id="s.004024">His igitur per&longs;picu&egrave; demon&longs;tratis <lb/>
facil&egrave; erit nonnulla corollaria inde contexere.</s>
        </p>
        <p type="main">
          <s id="s.004025">Primum, &longs;i ad planum F E, radius perpendiculariter incidat, illuminatio <lb/>
erit circulus, &longs;i ver&ograve; obliqu&egrave; ellip&longs;is, vt in tertio loco vidimus. </s>
          <s id="s.004026">c&ugrave;m igitur <lb/>
pauimentis, ac parietibus h&aelig; illuminationes, vt plurimum obliqu&egrave; acci&shy;<lb/>
dant, ide&ograve; fer&egrave; &longs;emper ouales apparent.</s>
        </p>
        <p type="main">
          <s id="s.004027">Secundum, quod quidem magni momenti e&longs;t, e&longs;t enim, vti &longs;cientiam de&shy;<lb/>
cet, vniuer&longs;ale, quod enim o&longs;ten&longs;um e&longs;t de Sole, eodem modo o&longs;tendi pote&longs;t <lb/>
de quouis lucido, &amp; de quouis corpore illuminato &longs;uam &longs;peciem diffunden&shy;<lb/>
te. </s>
          <s id="s.004028">&longs;imili enim modo demon&longs;trare po&longs;&longs;umus cur Sol eclyp&longs;im patiens, illu&shy;<lb/>
minationem pariter eclyp&longs;atam efficiat, &amp; inuer&longs;am. </s>
          <s id="s.004029">eadem e&longs;t ratio de <lb/>
Lun&aelig; illuminationibus.</s>
        </p>
        <p type="main">
          <s id="s.004030">Tertium, &amp; quidem &longs;citu digni&longs;&longs;imum <expan abbr="quodq;">quodque</expan> hactenus doctorum viro&shy;<lb/>
rum ingenia latuit, rationem reddere hinc po&longs;&longs;umus, cur &longs;i fene&longs;tris omni&shy;<lb/>
bus ob&longs;eratis, conclaue ob&longs;curum reddatur, tenui tant&ugrave;m relicto forami&shy;<lb/>
ne, per quod externo lumini aditus patent, form&aelig; externarum rerum pro&shy;<lb/>
pri&aelig;, quamuis inuer&longs;&aelig;, in oppo&longs;ito plano, appareant. </s>
          <s id="s.004031">eadem &longs;cilicet de cau&shy;<lb/>
&longs;a, qua &amp; Solis imago propria, <expan abbr="quoni&atilde;">quoniam</expan> videlicet per &longs;ingula foraminis pun&shy;<lb/>
cta, vt tertio loco patuit, <expan abbr="vnaqu&aelig;q;">vnaqu&aelig;que</expan> res, &longs;eu lucida, &longs;eu illuminata tant&ugrave;m <lb/>
&longs;it, per &longs;ingula foraminis puncta, &longs;ingulas proprias emittit imagines, qu&aelig; <lb/>
omnes po&longs;tea in vnam ex iu&longs;ta di&longs;tantia coale&longs;cunt. </s>
          <s id="s.004032"><expan abbr="atq;">atque</expan> eadem ratione in&shy;<lb/>uertuntur. </s>
          <s id="s.004033">ob quam etiam rationem &longs;olares macul&aelig; in Solis &longs;plendoribus, <lb/>
non eodem &longs;itu quem in Solis di&longs;co obtinent, &longs;ed inuer&longs;o &longs;pectantur. </s>
          <s id="s.004034">atque <lb/>
h&aelig;c pro in&longs;tituto dicta &longs;ufficiant.</s>
        </p>
        <p type="main">
          <s id="s.004035"><arrow.to.target n="marg338"/></s>
        </p>
        <p type="margin">
          <s id="s.004036"><margin.target id="marg338"/>346</s>
        </p>
        <p type="main">
          <s id="s.004037">In 6. Problema. </s>
          <s id="s.004038">quoniam vulgata interpretatio videtur mendo&longs;a, cum in <lb/>
multis textui gr&aelig;co non con&longs;entiat, eam &longs;ic emendatam accipe <emph type="italics"/>&lpar;Cur Lun&aelig; <lb/>
&longs;ph&aelig;rica exi&longs;tente, rectam cum &longs;emiplena e&longs;t, cernimus? </s>
          <s id="s.004039">An quoniam eodem in <lb/>
plano a&longs;pectus noster ver&longs;atur, vt circuli ambitus, quem Lun&aelig; Solingruens facit, <lb/>quod c&ugrave;m accidit, Sol recta linea videtur; cum enim quid &longs;uum a&longs;pectum &longs;ph&aelig;r&aelig; <lb/>
admouerit, orbem videre nece&longs;&longs;e &longs;it; Luna autem &longs;ph&aelig;rica &longs;it, eamqu&eacute; Sol a&longs;piciat; <lb/>orbis profect&ograve; id e&longs;&longs;e debet, quod &agrave; Sole efficitur. </s>
          <s id="s.004040">Hic erg&ograve; cum &egrave; regione &longs;e nobis <lb/>
pr&aelig;bet, totus videtur, &amp; &longs;ic plenilunium apparet, c&ugrave;m autem mutatur propter<emph.end type="italics"/> <pb pagenum="237" xlink:href="009/01/237.jpg"/><emph type="italics"/>Solis di&longs;ce&longs;&longs;um peripheria eius a&longs;pici pote&longs;t, ita vt recta appareat. </s>
          <s id="s.004041">altera ver&ograve; pars <lb/>
circularis, quoniam ex aduers&ograve; no&longs;tri a&longs;pectus hemi&longs;ph&aelig;rium e&longs;t; talis ver&ograve; appa&shy;<lb/>ret &longs;emicirculus. </s>
          <s id="s.004042">&longs;emper enim Luna a&longs;pectui nostro oppo&longs;ita e&longs;t, &longs;ed quando Sol in&shy;<lb/>
cubuerit, non videtur, &amp; repletur post diem octauum &longs;ecundum dimidium; quo&shy;<lb/>niam paulatim Sol euadens, orbem nobis facit inclinatiorem; ita ver&ograve; circulus ad <lb/>
oculum no&longs;trum di&longs;po&longs;itus, &longs;imilis videtur &longs;ectioni conic&aelig;. </s>
          <s id="s.004043">lunaris ver&ograve; apparet <lb/>
iam Sole amoto; c&ugrave;m enim ad extrema puncta peruenerit, iuxta qu&aelig; dimidiata <lb/>
apparet, circulus fit Solis, &amp; Solis circunferentia videtur; non enim amplius in <lb/>
directum vi&longs;ui iacet, &longs;ed pr&aelig;terit. </s>
          <s id="s.004044">quo facto, &amp; per eadem puncta ducto circulo, ne&shy;<lb/>
ce&longs;&longs;e e&longs;t lunularem apparere: pars enim aliqua circuli &longs;tatim a&longs;pectui patet, priori &egrave; <lb/>
contra exi&longs;tente, ita vt de &longs;plendido re&longs;ecetur. </s>
          <s id="s.004045">tum etiam extrema <expan abbr="man&etilde;t">manent</expan> in eodem, <lb/>
vt oporteat lunularem apparere magis, &amp; minus, &longs;ecundum Solis motum. </s>
          <s id="s.004046">per&shy;<lb/>
moto enim Sole, &amp; circulus, &longs;ecundum quem con&longs;picitur, reuertitur ad eadem <lb/>
puncta. </s>
          <s id="s.004047">&longs;ecundum enim infinitas inclinationes accidit inclinari: &longs;i quidem maxi&shy;<lb/>
mi circuli per eadem puncta duci po&longs;&longs;unt infiniti&rpar;<emph.end type="italics"/> Vt rect&egrave; textum hunc intel&shy;<lb/>
ligas, lege prius, qu&aelig; de Lun&aelig; illuminatione lib. 1. Po&longs;t. <!-- REMOVE S-->tex. <!-- REMOVE S-->30. dicta &longs;unt. <lb/>
</s>
          <s id="s.004048">&amp; ante omnia experire in pila aliqua lumini lucern&aelig;, aut candel&aelig; obiecta, <lb/>
&amp; circumlata, omnes illius &longs;pher&aelig; illuminationes, vt ibi docui. </s>
          <s id="s.004049">videbis enim <lb/>
qua ratione linea illa, qu&aelig; confinium e&longs;t partis illuminat&aelig;, &amp; partis ob&longs;cu&shy;<lb/>
r&aelig;, aliquando videatur lunularis, aliquando oualis, aliquando recta linea, <lb/>
quorum rationem Ari&longs;t. in pr&aelig;&longs;enti problemate inquirit. </s>
          <s id="s.004050">lege pr&aelig;terea, &longs;i <lb/>
plenam huius rei cognitionem de&longs;ideras, propo&longs;it. </s>
          <s id="s.004051">74. 75. 76. 77. libri 4. <lb/>Vitellionis, vbi h&aelig;c omnia exact&egrave;, &amp; non leui brachio, vt hic fit ab Ari&longs;tot. <lb/>
<!-- REMOVE S-->demon&longs;trantur. </s>
          <s id="s.004052">Interim tamen huius loci explicationem hanc accipe. </s>
          <s id="s.004053">Cur <lb/>
c&ugrave;m Luna &longs;emiplena e&longs;t, linea illa, qu&aelig; terminus e&longs;t partis illuminat&aelig;, &amp; <lb/>
partis ob&longs;cur&aelig;, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; Lunam bifariam diuidit, videtur linea recta, c&ugrave;m ta&shy;<lb/>
men non &longs;it; c&ugrave;m enim fit in globo&longs;a &longs;uperficie Lun&aelig;, nece&longs;&longs;ari&ograve; circularis <lb/>
<figure id="id.009.01.237.1.jpg" place="text" xlink:href="009/01/237/1.jpg"/><lb/>
e&longs;t? </s>
          <s id="s.004054">vt autem rem hanc melius intelli&shy;<lb/>
gamus, pr&aelig;&longs;ens figura illuminationis <lb/>
Lun&aelig; in&longs;picienda e&longs;t: vbi oculus no&longs;ter <lb/>
e&longs;t in centro mundi A; vnde varias Lu&shy;<lb/>
n&aelig; illuminationes a&longs;picit: &egrave; quibus <lb/>
octo tantum, in figura &longs;unt depict&aelig;: in <lb/>
quibus videre e&longs;t Lun&aelig; &longs;emper dimi&shy;<lb/>
dium illud, &longs;iue hemi&longs;ph&aelig;rium, quod <lb/>
Solem a&longs;picit, e&longs;&longs;e illuminatum, cuius <lb/>
terminus, &longs;iue ba&longs;is e&longs;t linea K L, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; <lb/>confinium illu&longs;trat&aelig; partis, &amp; opac&aelig;. <lb/>
</s>
          <s id="s.004055">qu&aelig; linea &longs;emper in Luna e&longs;t circula&shy;<lb/>
ris, cum &longs;it in &longs;ph&etail;rico corpore: quan&shy;<lb/>
do tamen Luna videtur &longs;emiplena, vt <lb/>
<expan abbr="qu&atilde;do">quando</expan> e&longs;t in D, vel in K. h&aelig;c linea K L, <lb/>
videtur recta. </s>
          <s id="s.004056">ratio huius e&longs;t, quia exi&shy;<lb/>
&longs;tente Luna &longs;emiplena, circulus K D L, <lb/>
qui e&longs;t ba&longs;is illuminationis &longs;olaris, e&longs;t in eodem plano cum oculo A, &longs;iue in <lb/>eadem rectitudine, vt apparet in figura, vbi, fi linea K D L, &longs;umatur loco <pb pagenum="238" xlink:href="009/01/238.jpg"/>diametri pr&aelig;dicti circuli, &amp; produci intelligatur ver&longs;us oculum A, per ip&shy;<lb/>&longs;um tran&longs;ilit; quo in &longs;itu, &longs;i circulus oculo &longs;ubijciatur, non planam ip&longs;ius <lb/>
&longs;uperficiem, &longs;ed circunferentiam <expan abbr="tant&utilde;">tantum</expan> a&longs;picit, <expan abbr="fit&qacute;">fitque</expan>; vt non lineam curuam, <lb/>
&longs;ed rectam videre videatur, vt in pr&aelig;cedenti problemate diximus, &amp; Per&shy;<lb/>
&longs;pectiui demon&longs;trant, &amp; Vitellio lib. 4. propo&longs;it. </s>
          <s id="s.004057">5. &amp; propo&longs;it. </s>
          <s id="s.004058">50.</s>
        </p>
        <p type="main">
          <s id="s.004059">Quidquid porr&ograve; &longs;ph&aelig;ram a&longs;pexerit, nece&longs;&longs;ari&ograve; ita illam a&longs;picit, vt quod <lb/>
de ip&longs;a videt, &longs;it orbiculare, cum erg&ograve; Sol Lunam a&longs;piciat, &longs;iue illuminet, <lb/>
debet illuminatio illa e&longs;&longs;e orbicularis, hoc e&longs;t habere orbicularem ba&longs;im, vt <lb/>
in figura patet, in qua Sol a&longs;piciens Lunam, quamuis in diuer&longs;is locis po&longs;i&shy;<lb/>
tam, eius tamen &longs;emper dimidium illu&longs;trat, cuius dimidij ba&longs;is e&longs;t circula&shy;<lb/>
ris, <expan abbr="repre&longs;entatur&qacute;">repre&longs;entaturque</expan>; in lineis K B L, K C L, K D L, &amp; c&etail;teris &longs;imilibus, quan&shy;<lb/>
do igitur Luna e&longs;t in tali po&longs;itione, vt totus ille orbis illuminationis oculis <lb/>
no&longs;tris in A, po&longs;itis obijciatur, totus vna cum tota illuminatione con&longs;pici&shy;<lb/>
tur, vt accidit, quando Luna e&longs;t in F. <expan abbr="tunc&qacute;">tuncque</expan>; e&longs;t oppo&longs;ita diametraliter So&shy;<lb/>
li, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; Plenilunium. <!-- KEEP S--></s>
          <s id="s.004060">C&ugrave;m autem Luna vetus mutatur in nouam, receden&shy;<lb/>
do &agrave; Sole, vt quando tran&longs;it &agrave; B, in C, tunc <expan abbr="circ&utilde;ferentia">circunferentia</expan> K B L, pr&aelig;dicti or&shy;<lb/>
bis, qu&aelig; Luna in B, exi&longs;tente, videri non poterat, incipit videri quando fue&shy;<lb/>
rit in C. <expan abbr="cernitur&qacute;">cerniturque</expan>; pars illius illuminationis circa punctum L, qu&aelig; videtur <lb/>
falcata; qu&aelig; pars recedente adhuc magis Luna &agrave; Sole, &longs;emper augetur, ide&longs;t <lb/>
&longs;emper maior illuminationis pars cernitur: ita vt c&ugrave;m fuerit in D, &longs;emiple&shy;<lb/>
na appareat, &amp; linea K D L, qu&aelig; ibi orbicularis e&longs;t, oculo in A, videtur re&shy;<lb/>
ct&agrave;, ob cau&longs;am &longs;uperius dictam; tunc igitur lumen Lun&aelig; ex vna parte vide&shy;<lb/>
tur terminari linea recta, ex altera circulari, ita vt figura luminis &longs;it &longs;emi&shy;<lb/>
circulus. </s>
          <s id="s.004061">Porr&ograve; Luna &longs;emper ex &longs;e oculis no&longs;tris opponitur, quamuis non <lb/>
&longs;emper cernatur, vt accidit in Nouilunio, quando &longs;cilicet Luna e&longs;t infra <lb/>Solem in B, quia cum Sol &longs;it &longs;upra ip&longs;am, illuminat hemi&longs;ph&aelig;rium eius &longs;u&shy;<lb/>
perius, quod oculo in A, e&longs;t auer&longs;um; &amp; ide&ograve; videri nequit; po&longs;tea paula&shy;<lb/>
tim recidendo &agrave; Sole, incipit hemi&longs;ph&aelig;rium illu&longs;tratum ad oculum A, ver&shy;<lb/>
gere, &amp; ideo con&longs;pici, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; primo apparet lunularis, &longs;eu falcata, deinde mi&shy;<lb/>
nus, ac minus falcata, quia linea interior falcis minus curuatur, &amp; &longs;ectio&shy;<lb/>
nem conicam, quam oualem dicunt, refert: deinde magis ad rectitudinem <lb/>
accedit, ita vt circa octauum diem, &longs;eu circa primum Lun&aelig; quadrantem, <lb/>linea illa videatur recta, Luna autem dixotomos, &longs;eu dimidiata; vbi enim <lb/>
circunferentia illuminationis Solis, ad puncta deuenit vltima, per qu&aelig; Lu&shy;<lb/>
na bifariam diuiditur, apparet tantum oculo circunferentia illius, &amp; nullo <lb/>
modo ip&longs;um circuli planum, qui ba&longs;is e&longs;t: &longs;ed, vt &longs;upra etiam dictum e&longs;t, <lb/>
planum eius productum &longs;ecaret oculum in A, exi&longs;tentem, &amp; &longs;tatim ab hoc <lb/>
&longs;itu mutatur, &amp; pr&aelig;terit, quod c&ugrave;m fit, nece&longs;&longs;e e&longs;t, vt pr&aelig;dictus circulus per <lb/>&longs;umma puncta K L, de&longs;ignatus, non amplius recta linea, &longs;ed curua, &amp; lunu&shy;<lb/>
laris appareat, quia aliquo modo planum pr&aelig;dicti circuli ad oculos incli&shy;<lb/>
natur, priori tamen circunferentia ex aduers&ograve; oculorum, vt dictum e&longs;t, exi&shy;<lb/>
&longs;tente, <expan abbr="atq;">atque</expan> hoc modo ex inclinatione ba&longs;is ad oculum aliquid lucis amplius <lb/>
re&longs;ecatur, ide&longs;t ab oculo cernitur. </s>
          <s id="s.004062">tum etiam extrema huius circunferenti&aelig; <lb/>in codem per&longs;i&longs;tunt, ide&longs;t in ei&longs;dem punctis, &amp; propterea linea illa magis, <lb/>&amp; minus incuruatur pro Solis remotione; ita vt tandem reuertatur ad ea&shy;<lb/>
dem puncta. </s>
          <s id="s.004063">fieri enim pote&longs;t, vt infinitas inclinationes &longs;u&longs;cipiat, &longs;i quidem <pb pagenum="239" xlink:href="009/01/239.jpg"/>per eadem duo extrema puncta K, L, duci po&longs;&longs;unt infiniti circuli maximi. <lb/>
</s>
          <s id="s.004064"><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t Ari&longs;totelis &longs;ententia, non &longs;ine ingrata tautologia, tandem <expan abbr="vt-cunq;">vt&shy;<lb/>
cunque</expan> expre&longs;&longs;a.</s>
        </p>
        <p type="main">
          <s id="s.004065"><arrow.to.target n="marg339"/></s>
        </p>
        <p type="margin">
          <s id="s.004066"><margin.target id="marg339"/>347</s>
        </p>
        <p type="main">
          <s id="s.004067">In 7. problema <emph type="italics"/>&lpar;Cur Sol, &amp; Luna plana e&longs;&longs;e videntur, c&ugrave;m tamen &longs;ph&aelig;rica <lb/>
&longs;int? </s>
          <s id="s.004068">An, vt ea omnia, quorum quodnam plus, minu&longs;u&egrave;, di&longs;tet, incertum &longs;it, &aelig;qu&egrave; <lb/>
po&longs;ita e&longs;&longs;e videntur? </s>
          <s id="s.004069">&longs;ic etiam res, quamuis vna, c&ugrave;m plures tamen habeat partes, <lb/>
ni&longs;i varius color ad&longs;it, partes ill&aelig; omnes, ex &aelig;quo collocatas videri nece&longs;&longs;e e&longs;t: quod <lb/>
autem ex &aelig;quo videtur, nece&longs;&longs;arium etiam e&longs;t &aelig;quabile, ac planum apparere&rpar;<emph.end type="italics"/><lb/>
Qu&aelig;&longs;tionem hanc demon&longs;tratiu&egrave; pertractat Vitellio lib. 4. propo&longs;it. </s>
          <s id="s.004070">65. Eu&shy;<lb/>
clides etiam theor. </s>
          <s id="s.004071">25. optices. </s>
          <s id="s.004072">c&aelig;ter&ugrave;m textus &longs;atis clarus videtur: vbi au&shy;<lb/>
tem ait <emph type="italics"/>&lpar;ni&longs;i varius color ad&longs;it&rpar;<emph.end type="italics"/> hoc ait, quia nonnulli colores &longs;unt, qui fa&shy;<lb/>
ciunt, vt obiecta appareant prominentiora, &amp; proinde propinquiora; ta&shy;<lb/>
les &longs;unt colores, qui pr&aelig; c&aelig;teris Iucidiores &longs;unt: alij ver&ograve; &longs;unt, qui obiecta <lb/>
deprimunt, &amp; proinde remouent; cuiu&longs;modi &longs;unt colores omnes tenebri&shy;<lb/>
co&longs;i. </s>
          <s id="s.004073">po&longs;ito igitur in re vi&longs;a eodem colore, partes illius ob magnam di&longs;tan&shy;<lb/>
tiam <expan abbr="vid&etilde;tur">videntur</expan> &aelig;qualiter &agrave; vi&longs;u di&longs;tare, &amp; ideo res plana apparet. </s>
          <s id="s.004074">quia, quam&shy;<lb/>
uis di&longs;tanti&aelig; ill&aelig; partium ab oculo ab inuicem differant, tamen parum dif&shy;<lb/>
ferunt, idcirc&ograve; eas &longs;en&longs;us iudicat &aelig;quales, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; &aelig;qualiter iudicamus di&longs;tare <lb/>
partes remoti&longs;&longs;im&aelig; &longs;ph&aelig;r&aelig;, quamuis pars illa, cui linea vi&longs;ualis perpendi&shy;<lb/>
culariter accidit, &longs;it propinquior; &longs;iue illa, qu&aelig; e&longs;t in medio hemiph&aelig;rij vi&longs;i: <lb/>
partes autem, qu&aelig; &longs;unt circa ba&longs;im dicti hemi&longs;ph&aelig;rij &longs;int remotiores. </s>
          <s id="s.004075">reli&shy;<lb/>
qua ex &longs;e manife&longs;ta &longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.004076"><arrow.to.target n="marg340"/></s>
        </p>
        <p type="margin">
          <s id="s.004077"><margin.target id="marg340"/>348</s>
        </p>
        <p type="main">
          <s id="s.004078">In 8. problema <emph type="italics"/>&lpar;Cur Sol oriens, <expan abbr="etq;">etque</expan> occidens vmbras efficit longas; efferens <lb/>
&longs;e, minores: obtinens c&oelig;li medium minimas? </s>
          <s id="s.004079">An quod oriens primo vmbram ter&shy;<lb/>
r&aelig; &aelig;quidi&longs;tantem reddit, ac infinitam p&etail;n&egrave; protrahit, deinde longam, &amp; po&longs;tea mi&shy;<lb/>
norem &longs;ubinde? </s>
          <s id="s.004080">quia linea recta, qu&aelig; de &longs;uperiori puncto elicitur, interius cadit.<emph.end type="italics"/><lb/>
<figure id="id.009.01.239.1.jpg" place="text" xlink:href="009/01/239/1.jpg"/><lb/>
<emph type="italics"/>&longs;it Gnomon A B. Sol, vbi C, &amp; vbi D. <lb/>
radius igitur ex C, prefici&longs;cens, e&longs;t C F, <lb/>&amp; exterius procedit, qu&agrave;m radius D E. <lb/>
e&longs;t autem vmbra B E, Sole &longs;ublimiori <lb/>
exi&longs;tente: vmbra ver&ograve; B F, Sole humi&shy;<lb/>
liori. </s>
          <s id="s.004081">erg&ograve; qu&ograve; Sol altior fuerit, e&ograve; mi&shy;<lb/>
nor vmbra erit, minimaqu&eacute; tunc erit, cum <lb/>
Sol &longs;uper caput no&longs;trum ver&longs;abitur&rpar;<emph.end type="italics"/><lb/>
Problema pr&aelig;&longs;ens e&longs;t idem <expan abbr="c&utilde;">cum</expan> quar&shy;<lb/>
to huius &longs;ectionis: eadem igitur ex&shy;<lb/>
po&longs;itio <expan abbr="vtriq;">vtrique</expan> in&longs;eruiat. </s>
          <s id="s.004082">hoc &longs;olum addendum e&longs;t, Gnomonem apud gr&aelig;cos <lb/>
inter c&aelig;tera &longs;ignificare &longs;tylum &longs;olaris horologij: in quo &longs;en&longs;u hoc loco po&shy;<lb/>
nitur. </s>
          <s id="s.004083">&longs;ignificat pr&aelig;terea amu&longs;&longs;im, &longs;eu normam, qu&aelig; nihil aliud e&longs;t, quam <lb/>
quidam angulus rectus materialis: &amp; quoniam &longs;tylus horologij figitur ad <lb/>
angulos rectos in plano horizontali, propterea ip&longs;e <expan abbr="quoq;">quoque</expan> Gnomon appel&shy;<lb/>
latus e&longs;t: im&ograve; <expan abbr="pleriq;">plerique</expan> amu&longs;&longs;im quandam horologijs pr&aelig;&longs;ertim viatorijs, lo&shy;<lb/>
co &longs;tyli accommodant.</s>
        </p>
        <p type="main">
          <s id="s.004084"><arrow.to.target n="marg341"/></s>
        </p>
        <p type="margin">
          <s id="s.004085"><margin.target id="marg341"/>349</s>
        </p>
        <p type="main">
          <s id="s.004086">In 9. <emph type="italics"/>&lpar;Cur vmbr&aelig; Lun&aelig; maiores, quam Solis &longs;unt c&ugrave;m eodem proueniant per&shy;<lb/>
pendiculo? </s>
          <s id="s.004087">An quod Sol &longs;uperior, quam Luna e&longs;t? </s>
          <s id="s.004088"><expan abbr="itaq;">itaque</expan> nece&longs;&longs;e e&longs;t radium &agrave; &longs;upe&shy;<lb/>
riore procedentem intus cadere. </s>
          <s id="s.004089">&longs;it Gnomon A D, Luna B Sol C, Lun&aelig; radius B F.<emph.end type="italics"/>


<pb pagenum="240" xlink:href="009/01/240.jpg"/><figure id="id.009.01.240.1.jpg" place="text" xlink:href="009/01/240/1.jpg"/><lb/>
<emph type="italics"/>erg&ograve; vmbra Lun&aelig; D F, Solis radius <lb/>
C E; vmbra igitur nece&longs;&longs;ari&ograve; minor <lb/>
e&longs;t, e&longs;t enim D E.&rpar;<emph.end type="italics"/> de hac re vide <lb/>
Spheram P. Clauij, cap. de Ordine <lb/>
c&oelig;lorum, vnde huius textus expo&shy;<lb/>
&longs;itionem in hunc modum licebit af&shy;<lb/>
ferre. </s>
          <s id="s.004090">Quando igitur Ari&longs;t. qu&aelig;rit, <lb/>
cur Luna maiores proijciat vm&shy;<lb/>
bras, qua Sol, debet &longs;upponere So&shy;<lb/>
lem, &amp; Lunam e&longs;&longs;e in eadem altitu&shy;<lb/>
dine &longs;upra horizontem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->e&longs;&longs;e <expan abbr="vtrunq;">vtrunque</expan> in eadem linea recta C D, ducta &agrave; <lb/>
centro mundi ad Solem; &longs;ic enim habebunt eandem ambo eleuationem &longs;u&shy;<lb/>
pra horizontem G H, vt factum e&longs;t in figura: aliter Sol etiam faciet vmbras <lb/>
Lun&aelig; vmbris modo longiores, modo breuiores. </s>
          <s id="s.004091">cur igitur, inquit, exi&longs;tente <lb/>
<expan abbr="vtroq;">vtroque</expan> in eadem altitudine, &longs;iue in eadem recta C D. vmbr&aelig; lunares fact&aelig; &agrave; <lb/>
Gnomone D A, &longs;unt vmbris &longs;olaribus longiores?</s>
        </p>
        <p type="main">
          <s id="s.004092">Re&longs;pondet id fort&egrave; accidere, quia Sol mult&ograve; remotior &longs;it &agrave; centro mun&shy;<lb/>
di D, qu&agrave;m Luna. <!-- KEEP S--></s>
          <s id="s.004093">vnde quamuis &aelig;qu&egrave; &longs;upra horizontem &longs;int eleuata, cum <lb/>
ambo &longs;int in linea C D. tamen propter Lun&aelig; propinquitatem ad centrum <lb/>
mundi, fit vt magnitudo &longs;tyli D A, re&longs;pectu Lun&aelig; &longs;it vald&egrave; &longs;en&longs;ibilis, qu&aelig; ta&shy;<lb/>
men collata <expan abbr="c&utilde;">cum</expan> Sole &agrave; terra remoti&longs;&longs;imo nullius euadit &longs;en&longs;ibilitatis; <expan abbr="idem&qacute;">idemque</expan>; <lb/>
e&longs;t punctum D, ac punctum A. ex quo fit, vt radius Lun&aelig; B F, cadat extra <lb/>
radium Solis C E: <expan abbr="hinc&qacute;">hincque</expan>; rur&longs;us nece&longs;&longs;e e&longs;t vmbram Solis D E, minorem e&longs;&shy;<lb/>
&longs;e vmbra Lun&aelig; D F. <!-- KEEP S--></s>
          <s id="s.004094">Quod &longs;i concipiamus Lunam magis &agrave; terris di&longs;tantem, <lb/>
<expan abbr="Soli&qacute;">Solique</expan>; propinquiorem, vt in puncto R, tunc amborum radij &longs;imul fer&egrave; co&shy;<lb/>
incident: <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; &aelig;quales fer&egrave; vmbr&aelig; <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> erunt.</s>
        </p>
        <p type="main">
          <s id="s.004095">Huius rei facil&egrave; experientiam facere poteris, &longs;i per quadrantem Solis al&shy;<lb/>
titudine notata, &longs;imul etiam ip&longs;ius vmbram ex quopiam magno Gnomone <lb/>
proiectam ob&longs;eruaueris: deinde eadem Lun&aelig; &longs;plendentis altitudine per cal&shy;<lb/>
culum ob&longs;eruata vmbram lunarem eiu&longs;dem Gnomonis cum vmbra &longs;olari <lb/>
contuleris: inuenies enim lunarem &longs;olari longiorem.</s>
        </p>
        <p type="main">
          <s id="s.004096"><arrow.to.target n="marg342"/></s>
        </p>
        <p type="margin">
          <s id="s.004097"><margin.target id="marg342"/>350</s>
        </p>
        <p type="main">
          <s id="s.004098">In 10. problem. <emph type="italics"/>&lpar;Propter quid in Solis eclyp&longs;ibus, &longs;i quis &longs;pectet per cribrum, <lb/>aut per folium, veluti platani, vel alterius latifolij, vel per digitos altera manu <lb/>
&longs;uper alteram coniungens &longs;plendores, qui in terra fiunt &longs;unt lunul&aelig;? </s>
          <s id="s.004099">An quod &longs;icu&shy;<lb/>ti lux per foramen angulo&longs;um &longs;plendens, turbo, &amp; conus fit: cau&longs;a ver&ograve;, quia duo <lb/>
efficiuntur coni, vnus &agrave; Sole ad foramen, &amp; alter hinc ad terram, qui &longs;imul <expan abbr="hab&etilde;t">habent</expan> <lb/>
vertices. </s>
          <s id="s.004100">quando igitur &longs;ic &longs;e habet; &amp; &longs;uperiori parte circulari detrahitur, erunt <lb/>
&egrave; contrari&ograve; lucis lunul&aelig; in terra; ex peripheria enim lunulari procedunt radij. </s>
          <s id="s.004101">qu&aelig; <lb/>
autem in digitis, aut cribris, veluti foramina fiunt, manife&longs;tius id faciunt, qu&agrave;m <lb/>
magna foramina. </s>
          <s id="s.004102">A Luna autem hoc non fit, <expan abbr="neq;">neque</expan> ip&longs;a deficiente, <expan abbr="neq;">neque</expan> cre&longs;cente, <lb/>
<expan abbr="neq;">neque</expan> decre&longs;cente, quia &longs;plendores extremitatum eius non &longs;unt manife&longs;ti, &amp; certi. <lb/>
</s>
          <s id="s.004103">&longs;ed in medio poti&longs;&longs;imum <expan abbr="&longs;pl&etilde;det">&longs;plendet</expan>. </s>
          <s id="s.004104">lunula autem falcata exiguam habet latitudinem&rpar;<emph.end type="italics"/><lb/>
Vt rect&egrave;, atque non &longs;ine delectatione problema pr&aelig;&longs;ens intelligas, lege ea, <lb/>
qu&aelig; in additione ad problema 5. huius &longs;ectionis &longs;crip&longs;imus de Figuratione <lb/>
lucis: deinde oper&aelig;pretium erit audire, quid dicat Gemma Fri&longs;ius in tra&shy;<lb/>ctatu de Radij a&longs;tronomici &longs;tructura, cap. 18. vbi loquitur de Solis deliquij <pb pagenum="241" xlink:href="009/01/241.jpg"/>dimen&longs;ione, his verbis, extat, inquit, alius modus dimeti&eacute;nd&aelig; &longs;olaris eclyp&shy;<lb/>
&longs;is, omnium facillimus, ac certi&longs;&longs;imus, cuius nos admonuit Era&longs;mus Rei&shy;<lb/>
noldus in comm. <!-- REMOVE S-->in Theoricas Peurbarhij. </s>
          <s id="s.004105">tempore igitur &longs;olaris defectus, <lb/>
intra parietes v&longs;piam, clau&longs;is omnibus fene&longs;tris, admittatur Solis radius, <lb/>
per angu&longs;tum foramen rotundum; <expan abbr="excipiatur&qacute;">excipiaturque</expan>; radius hic in plana tabella, <lb/>
vbi certo quantum Sol defecerit ad vnguem, licet videre, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla intui&shy;<lb/>tus mole&longs;tia, ac tam perfect&egrave;, atque fi in c&oelig;lo coram ade&longs;&longs;es&rpar; h&aelig;c ille, licet <lb/>
autem videre, quia illuminatio in tabella excepta, qu&aelig; alias &longs;olet e&longs;&longs;e cir&shy;<lb/>
cularis, erit tempore eclyp&longs;is ip&longs;a pariter cum Sole defectiua, <expan abbr="atq;">atque</expan> in&longs;tar fal&shy;<lb/>
cat&aelig; lunul&aelig;. </s>
          <s id="s.004106">deinde &longs;ubdit; verum hoc omnin&ograve; &longs;cire nece&longs;&longs;arium e&longs;t, con&shy;<lb/>
trario modo apparere defectum illum in tabula per radios Solis, qu&agrave;m in <lb/>
c&oelig;lo contingit: hoc e&longs;t, &longs;i in c&oelig;lo &longs;uperior pars deliquium patiatur, in ra&shy;<lb/>
dijs apparebit inferior deficere, vt ratio exigit optica&rpar; <expan abbr="hucu&longs;q;">hucu&longs;que</expan> Gemma Fri&shy;<lb/>
&longs;ius; ex quo etiam placuit accipere totius huius <expan abbr="experi&etilde;ti&aelig;">experienti&aelig;</expan> figuram, quam <lb/>
<figure id="id.009.01.241.1.jpg" place="text" xlink:href="009/01/241/1.jpg"/><lb/>
ip&longs;e <expan abbr="cuiu&longs;d&atilde;">cuiu&longs;dam</expan> eclyp&longs;is an&shy;<lb/>
ni 1544. apponit. </s>
          <s id="s.004107">e&longs;t au&shy;<lb/>
tem h&aelig;c. </s>
          <s id="s.004108">in qua Sol <expan abbr="de-fici&etilde;s">de&shy;<lb/>
ficiens</expan> e&longs;t A B C. pars in&shy;<lb/>
ferior B D P C, ip&longs;a e&longs;t <lb/>
lumine priuata; &longs;uperior <lb/>
B A P D, &longs;plendens, qu&aelig; <lb/>
&longs;imilis e&longs;t falcat&aelig; lunu&shy;<lb/>
l&aelig;. </s>
          <s id="s.004109">radij Solis <expan abbr="ingredi&utilde;-tur">ingrediun&shy;<lb/>
tur</expan> in cubiculum per fo&shy;<lb/>
ramen E. <expan abbr="excipiuntur&qacute;">excipiunturque</expan>; <lb/>
in tabella K M N O, fo&shy;<lb/>
ramini, &longs;eu radio Solis <lb/>
<expan abbr="perp&etilde;diculariter">perpendiculariter</expan> oppo&shy;<lb/>
&longs;ita: in qua propterea <lb/>
apparet Solis illuminatio, non vt alias circularis, &longs;ed manca, ac defectiua, <lb/>
lunul&aelig; in&longs;tar: <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; G H I L, qu&aelig; inuer&longs;o modo &longs;e habet, ac in c&oelig;lo, quem&shy;<lb/>
admodum figura o&longs;tendit: cuius cau&longs;a e&longs;t, quia radij Solis A E, D E, C E, <lb/>
po&longs;t foraminis ingre&longs;&longs;um commutantur, quia &longs;e mutu&ograve; &longs;ecant, vnde qui &longs;u&shy;<lb/>
periores erant, fiunt inferiores intra foramen, &amp; in tabella; &longs;ic radius A E, <lb/>
omnibus &longs;uperior, po&longs;t ingre&longs;&longs;um fit omnibus inferior; e&longs;t enim E H, <expan abbr="de&longs;i-nit&qacute;">de&longs;i&shy;<lb/>
nitque</expan>; in puncto H, omnium illuminationis infimo. </s>
          <s id="s.004110">reliqua autem pars cir&shy;<lb/>
culi illuminationis G L I F, deficit, quia pars Solis B D P C, qu&aelig; ip&longs;am illu&shy;<lb/>&longs;trare &longs;olet, propter eclyp&longs;im nullos per foramen E, immittit radios. </s>
          <s id="s.004111">Ve&shy;<lb/>
rum eclyp&longs;is tempore, etiam &longs;i huiu&longs;modi illuminationes intra cubiculum <lb/>
non ob&longs;eruentur, &longs;ed foris, manife&longs;t&egrave; omnes apparent, non &longs;ecus, ac ip&longs;e &longs;ol <lb/>
defectiu&aelig;: tales &longs;&ugrave;nt omnes, qu&aelig; per qu&aelig;libet foramina, in quolibet paui&shy;<lb/>mento, aut oppo&longs;ito pariete apparent: de quibus etiam Ari&longs;tot. in pr&aelig;&longs;enti <lb/>
problemate loquitur. </s>
          <s id="s.004112">ex his facil&egrave; e&longs;t verborum Ari&longs;t. &longs;en&longs;um a&longs;&longs;equi. </s>
          <s id="s.004113">Qu&aelig;&shy;<lb/>
rit igitur, cur tempore &longs;olaris deliquij, &longs;i Solis illuminationes per cribri fo&shy;<lb/>
ramina, aut inter alicuius arboris folia, ex ijs, qu&aelig; lata habent folia, aut <lb/>
inter manuum decu&longs;&longs;atos digitos, ingredientes, atque in terra apparentes,


<pb pagenum="242" xlink:href="009/01/242.jpg"/>&longs;pectemus, eas falcatas, ac lunulatas, videamus; non autem, vt &longs;olemus, <lb/>
rotundas. </s>
          <s id="s.004114">Re&longs;pondet, id fort&egrave; accidere, quia lux per foramen intrans, fit <lb/>
conus natura &longs;ua, vt in 5. problemate pr&etail;cedenti, explicatum e&longs;t. </s>
          <s id="s.004115">&amp; in pr&aelig;&shy;<lb/>
&longs;enti figura conus lucis intrantis per foramen E, figuratur &agrave; lineis E F, E H, <lb/>
quibus &longs;imiles alias plurimas debemus concipere ab E, ad circularem ba&shy;<lb/>
&longs;im F G L I, qu&aelig; turbinem perfectum efficiunt. </s>
          <s id="s.004116">alius pr&aelig;terea conus e&longs;t &agrave; fo&shy;<lb/>
ramine ad Solem, cuius ba&longs;is e&longs;t A B C P, circulus Solis: &amp; continetur &longs;ub <lb/>
infinitis radijs, quorum duo &longs;unt A E, C E; <expan abbr="vter&qacute;">vterque</expan>; autem habet verticem ad <lb/>
E, quia igitur plures radij &longs;uperioris coni deficiunt, ide&ograve; etiam in inferiori <lb/>
deficient: <expan abbr="erit&qacute;">eritque</expan>; &longs;itus eorum inuer&longs;us ob radiorum inter&longs;ectionem ad pun&shy;<lb/>
ctum E, <expan abbr="erit&qacute;">eritque</expan>; &longs;plendor in tabella apparens lunulatus, quia ex parte Solis <lb/>
pariter lunulata producitur. </s>
          <s id="s.004117">c&aelig;tera &longs;atis &longs;unt per &longs;e clara.</s>
        </p>
        <p type="head">
          <s id="s.004118"><emph type="italics"/>Ex Sectione 16.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.004119"><arrow.to.target n="marg343"/></s>
        </p>
        <p type="margin">
          <s id="s.004120"><margin.target id="marg343"/>351</s>
        </p>
        <p type="main">
          <s id="s.004121">In 1. problema <emph type="italics"/>&lpar;Cur ba&longs;es bullarum in aquis &longs;unt alb&aelig;; &amp; &longs;i in Sole ponan&shy;<lb/>
tur, non faciunt vmbram; &longs;ed bull&aelig; reliquum vmbram facit, ba&longs;is ver&ograve; non <lb/>
facit, &longs;ed circulariter &agrave; Sole illuminatur. </s>
          <s id="s.004122">quod ver&ograve; mirabilius e&longs;t, quod <expan abbr="neq;">neque</expan> <lb/>
&longs;i quodpiam lignum in aquam inferatur in Sole, h&aelig;c &longs;ub aqua diuiduntur. <lb/>
</s>
          <s id="s.004123">An non fit vmbra, &longs;ed &agrave; Sole di&longs;&longs;ipatur vmbra? </s>
          <s id="s.004124">fi igitur vmbra est non in&longs;pectum, <lb/>&amp; &agrave; Sole circulariter in&longs;picitur moles: hoc ver&ograve; impo&longs;&longs;ibile e&longs;&longs;e o&longs;tenditur in Op&shy;<lb/>
ticis. </s>
          <s id="s.004125"><expan abbr="neq;">neque</expan> enim minimum, &agrave; maximo totum con&longs;pici pote&longs;t&rpar;<emph.end type="italics"/> C&ugrave;m ex ip&longs;ius textus <lb/>verbis &longs;atis per&longs;picu&egrave; appareat, quid proponatur, reliqua &longs;ic breuiter ex&shy;<lb/>
ponam. </s>
          <s id="s.004126">quod igitur de ligno ait, exi&longs;timo hoc modo <expan abbr="accipiend&utilde;">accipiendum</expan>, vt lignum <lb/>
illud in aqua ponatur &longs;ub bulla, ita vt vmbra bull&aelig; cadat &longs;uper ip&longs;um, <expan abbr="t&utilde;c&qacute;">tuncque</expan>; <lb/>
vmbra illius &longs;imiliter apparebit defectiua, quia ba&longs;is illuminatio ip&longs;am ex <lb/>
parte de&longs;truet. </s>
          <s id="s.004127">Re&longs;pondet, An non fit vmbra, &longs;ed &agrave; Sole vmbra fugatur? <lb/>
</s>
          <s id="s.004128">qu&aelig; verba &longs;ubob&longs;cura &longs;unt; <expan abbr="neq;">neque</expan> re&longs;pon&longs;io videtur allata ad &longs;oluendum pro&shy;<lb/>
blema, &longs;ed ad eum magis confirmandum. </s>
          <s id="s.004129">deinde ait: &longs;i igitur nihil aliud e&longs;t <lb/>
vmbra, quam id, quod non a&longs;picitur &agrave; Sole, &amp; &agrave; Sole tamen videamus illu&shy;<lb/>
minari totam bull&aelig; ba&longs;im circulariter, nece&longs;&longs;e e&longs;t totam etiam bullam <expan abbr="vn-diq;">vn&shy;<lb/>
dique</expan> &agrave; Sole illuminari, &amp; con&longs;pici, quod tamen impo&longs;&longs;ibile e&longs;&longs;e demon&longs;tra&shy;<lb/>
tur ab opticis: ip&longs;i enim demon&longs;trant, nullum corpus, quantumuis mini&shy;<lb/>
mum, totum po&longs;&longs;e circum&longs;pici &agrave; quamuis maximo illuminante. </s>
          <s id="s.004130">quod qui&shy;<lb/>
dem antiquitus demon&longs;trauit Ari&longs;tarchus Samius in libello de di&longs;tantijs So&shy;<lb/>
<figure id="id.009.01.242.1.jpg" place="text" xlink:href="009/01/242/1.jpg"/><lb/>
lis, &amp; Lun&aelig;: &amp; <lb/>
po&longs;tea Vitellio <lb/>
lib. 2. propo&longs;. </s>
          <s id="s.004131">27. <lb/>
&amp; ex figura pr&aelig;&shy;<lb/>
&longs;enti facil&egrave; e&longs;t id <lb/>
intelligere: <expan abbr="&itilde;">i</expan>n qua <lb/>
&longs;it Sol &longs;ph&aelig;ra A, <lb/>
illuminans &longs;ph&aelig;&shy;<lb/>
rulam B, extre&shy;<lb/>
mi radij DF, EF.


<pb pagenum="243" xlink:href="009/01/243.jpg"/>vmbra erit igitur G F H, ad partes C, Soli auer&longs;as. </s>
          <s id="s.004132">quas nunquam Sol, etiam <lb/>
&longs;i &longs;ph&aelig;ra B, arenul&aelig; vnius grano minor fuerit poterit illu&longs;trare. </s>
          <s id="s.004133">qu&aelig; quidem <lb/>
non &longs;oluunt qu&aelig;&longs;tionem, &longs;ed eam difficiliorem reddunt. </s>
          <s id="s.004134">Quapropter non <lb/>
videtur Ari&longs;t. volui&longs;&longs;e hoc di&longs;cutere, &longs;ed &longs;olum tanquam mirum quodam <lb/>
proponere. </s>
          <s id="s.004135">quod &longs;i quid mutire liceat, vbi tantus philo&longs;ophus admirabun&shy;<lb/>dus obmute&longs;cit, dixerim propterea ba&longs;im bull&aelig; non adumbrari ab vmbra <lb/>
ip&longs;ius bull&aelig;, quia cum bulla &longs;it &longs;ph&aelig;rica, &amp; tran&longs;parens, Solis lumen eam <lb/>
peruadit, <expan abbr="atq;">atque</expan> ex &longs;uperficie concaua ad illius ba&longs;im partim reflectitur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>
eam illuminat. </s>
          <s id="s.004136">quamuis enim &longs;it diaphana, non tamen omnin&ograve; tran&longs;parens <lb/>
e&longs;t, cum aqua &longs;it aere cra&longs;&longs;ior: bulla autem e&longs;t ex aqua. </s>
          <s id="s.004137">&longs;uperficiem autem <lb/>
bull&aelig; concauam id efficere debere, patet ex concaua figura, qu&aelig; maxim&egrave; <lb/>
reflexioni e&longs;t apta.</s>
        </p>
        <p type="main">
          <s id="s.004138"><arrow.to.target n="marg344"/></s>
        </p>
        <p type="margin">
          <s id="s.004139"><margin.target id="marg344"/>352</s>
        </p>
        <p type="main">
          <s id="s.004140">In 3. problem. <emph type="italics"/>&lpar;Cur in magnitudinibus, qu&aelig; pondere &longs;unt in&aelig;quali, accidit, vt <lb/>
&longs;i partem moueas l&aelig;uiorem, circunferatur, quod iacitur; vt in talis fieri opplum&shy;<lb/>
batis videmus&rpar;<emph.end type="italics"/> Ari&longs;totelis tempore tales tali opplumbati erant in v&longs;u, qui <lb/>
exemplo pr&aelig;&longs;enti que&longs;tioni e&longs;&longs;e po&longs;&longs;ent: Aptius nunc exemplum de&longs;umi po&shy;<lb/>
te&longs;t ex bacillo aliquo, cuius altera extremitas &longs;it c&aelig;teris partibus mult&ograve; <lb/>
grauior, qui &longs;i per aerem manibus eiaculatur, &longs;olet, dum per aerem fertur, <lb/>
circumuerti.</s>
        </p>
        <p type="main">
          <s id="s.004141"><arrow.to.target n="marg345"/></s>
        </p>
        <p type="margin">
          <s id="s.004142"><margin.target id="marg345"/>353</s>
        </p>
        <p type="main">
          <s id="s.004143">Ibidem <emph type="italics"/>&lpar;Sin autem alterum altero fertur c&aelig;lerius, circulo ferri nece&longs;&longs;e e&longs;t, c&ugrave;m <lb/>
in hoc &longs;olo figur&aelig; genere efficiatur, vt puncta eadem &longs;ubalterna, lineas in&aelig;quales <lb/>po&longs;&longs;int eodem tempore permeare&rpar;<emph.end type="italics"/> Quando, inquit, duo puncta in eadem magni&shy;<lb/>
tudine po&longs;ita mouentur ad motum illius, &amp; tamen non &aelig;qualiter progre&shy;<lb/>
diuntur, &longs;ignum e&longs;t, illam magnitudinem moueri circulariter, &amp; proinde <lb/>
vel e&longs;&longs;e circulum, vel &longs;altem circuli in modum conuerti; cum in &longs;olo orbi&shy;<lb/>
culari motu contingat, vt duo puncta in&aelig;qualiter a centro remota, po&longs;&longs;int <lb/>
in&aelig;quales lineas eodem tempore permeare, punctum enim, quod <expan abbr="c&etilde;tro">centro</expan> pro&shy;<lb/>
pinquius e&longs;t, breuiorem de&longs;cribit lineam, quod autem remotius, maiorem.</s>
        </p>
        <p type="main">
          <s id="s.004144"><arrow.to.target n="marg346"/></s>
        </p>
        <p type="margin">
          <s id="s.004145"><margin.target id="marg346"/>354</s>
        </p>
        <p type="main">
          <s id="s.004146">In 4. problem. </s>
          <s id="s.004147">&longs;atis e&longs;&longs;e exi&longs;timo per paraphra&longs;im pr&aelig;&longs;ens problema ex&shy;<lb/>
ponere, ex qua tamen, vbi opus fuerit, textus corrigatur. </s>
          <s id="s.004148">Cur ea, qu&aelig; in <lb/>
terram cadunt, <expan abbr="atq;">atque</expan> re&longs;iliunt angulos ad planitiem, faciunt &longs;imiles vtraque <lb/>
<figure id="id.009.01.243.1.jpg" place="text" xlink:href="009/01/243/1.jpg"/><lb/>
ex parte, qua planum tetigerint? </s>
          <s id="s.004149">v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>
corpus quodpiam cadat ex puncto D, per <lb/>
lineam D C, &longs;uper planum A B, ex puncto <lb/>
C, vbi c&aelig;ciderat, re&longs;ilit per lineam C E, <lb/>
ita vt faciat duos angulos &aelig;quales vtrin&shy;<lb/>
que ad punctum. </s>
          <s id="s.004150">C, angulum &longs;cilicet in&shy;<lb/>
cidenti&aelig; D C B, &amp; angulum reflexionis <lb/>
E C A? </s>
          <s id="s.004151">An quod omnia i&longs;ta, natura qui&shy;<lb/>
dem &longs;ua feruntur per rectam lineam, vi&shy;<lb/>
demus enim grauia omnia deor&longs;um re&shy;<lb/>
ct&agrave; tendere; &longs;i autem aliquod impedi&shy;<lb/>
mentum occurrat, vt fit, quando plano <lb/>
terr&aelig; occurrunt, tunc lineam illam, quam infra terram facerent <expan abbr="eundem&qacute;">eundemque</expan>; <lb/>
angulum, quem infra <expan abbr="plan&utilde;">planum</expan> facerent, &longs;upra faciunt, v. <!-- REMOVE S-->g. <!-- REMOVE S-->mobile per lineam <lb/>D C, cadens, ni&longs;i ob&longs;titi&longs;&longs;et planum A B, tetendi&longs;&longs;et per lineam rectam <pb pagenum="244" xlink:href="009/01/244.jpg"/>D C G, <expan abbr="feci&longs;&longs;et&qacute;">feci&longs;&longs;etque</expan>; propterea angulum A C G, infra planum, &aelig;qualem angulo <lb/>
D C B, quo ceciderat. </s>
          <s id="s.004152">cum igitur nequeat pr&aelig;dictum angulum infra pla&shy;<lb/>
num conficere, par eft, vt eum re&longs;iliendo &longs;upra planum efficiat; propterea <lb/>
re&longs;ilit per lineam C E; qu&aelig; <expan abbr="angul&utilde;">angulum</expan> A C E, &longs;upra cum plano con&longs;tituit &aelig;qua&shy;<lb/>
lem angulo A C G, infra, &amp; proinde &aelig;qualem <expan abbr="eti&atilde;">etiam</expan> angulo incidenti&aelig; D C B. <lb/>
<!-- KEEP S--></s>
          <s id="s.004153">Duobus porr&ograve; modis grauia &longs;uper terr&aelig; planitiem cadunt; aut enim per&shy;<lb/>
pendiculariter, &amp; fecundum mundi diametrum decidunt; aut obliqu&egrave;, &longs;eu <lb/>
in latera. </s>
          <s id="s.004154">qu&aelig; igitur primo modo de&longs;cendunt, ide&longs;t perpendiculariter, &longs;eu <lb/>
qu&aelig; angulos rectos cum plano faciunt, ea etiam re&longs;iliunt perpendiculariter, <lb/>&longs;eu ad angulos rectos, &amp; ideo nece&longs;&longs;ari&ograve; per eandem lineam, qua decide&shy;<lb/>
rant, repercutiuntur; cuius cau&longs;a e&longs;&longs;e pote&longs;t, quia diameter &longs;cilicet mundi, <lb/>
per quam delap&longs;a &longs;unt, ea bifariam diuidit, vt in figura, graue E, per D C, <lb/>
<figure id="id.009.01.244.1.jpg" place="text" xlink:href="009/01/244/1.jpg"/><lb/>
plano A B, perpendicularem de&longs;cendat; <lb/>
qu&aelig; <expan abbr="perp&etilde;dicularis">perpendicularis</expan> coincidit cum mun&shy;<lb/>
di diametro, perpendicula enim omnia <lb/>
ad mundi centrum tendunt; graue igi&shy;<lb/>
tur E, dum puncto C, alliditur, diuidi&shy;<lb/>
tur bifariam, &agrave; diametro mundi D C: <lb/>
vnde &amp; in &aelig;quilibrio con&longs;tituitur, ita vt <lb/>
nulla &longs;it maior ratio, cur ad partem <lb/>
vnam, qu&agrave;m ad alteram re&longs;ultet, &amp; ideo <lb/>
<expan abbr="conueni&etilde;s">conueniens</expan> e&longs;t, ip&longs;um per eandem lineam <lb/>
D C, reuerti; &longs;ic enim faciet etiam an&shy;<lb/>
gulos incidenti&aelig;, &amp; reflexionis &aelig;quales. <lb/>
</s>
          <s id="s.004155">qu&aelig; ver&ograve; &longs;ecundo modo decidunt, ide&longs;t <lb/>
obliqu&egrave;, &amp; &longs;ecundum latera: quoniam non &longs;ecundum perpendiculum, &longs;ed <lb/>
ex puncto extra perpendiculum po&longs;ito, planum feriunt, accidit vt &agrave; puncto <lb/>
incidenti&aelig; C, vt in priori figura, in contrariam partem repul&longs;a re&longs;ulcent; <lb/>de&longs;cenderant enim ex D, &amp; in contrariam partem, &longs;cilicet ad E, prioris fi&shy;<lb/>
gur&aelig; reflectuntur. </s>
          <s id="s.004156">qu&ograve;d &longs;i huiu&longs;modi grauia &longs;int rotunda, facilius in contra&shy;<lb/>
rias partes exurgunt, propter ip&longs;orum figuram motui, ac re&longs;ultationi ap&shy;<lb/>ti&longs;&longs;imam; &longs;iue moueantur, ita vt centrum eorum etiam locum permutet, <lb/>
&longs;iue ita vt quie&longs;cat. </s>
          <s id="s.004157">qu&aelig; ver&ograve; non &longs;unt rotunda, &longs;ed rectilinea, idem faciunt, <lb/>
quoniam perpendiculum ip&longs;orum, ide&longs;t linea, per quam deberent perpen&shy;<lb/>
diculariter re&longs;ultare ob impul&longs;um eliditur, &amp; flectitur ad altiorem partem, <lb/>
vbi nimirum e&longs;t linea C E, in priori figura, ita vt &agrave; perpendiculo quodam&shy;<lb/>
modo deflectantur. </s>
          <s id="s.004158">quemadmodum ij, quorum pars altera inferior, v. <!-- REMOVE S-->g. <!-- REMOVE S-->al&shy;<lb/>
terum crus ab&longs;cinditur, qui coguntur &agrave; rectitudine priori in alteram par&shy;<lb/>
tem, vel etiam retror&longs;um cadere: quando, vt dixi, eorum perpendiculum, <lb/>
quod perpendiculariter eleuatum e&longs;t, &amp; &longs;ecundum quod corpus ip&longs;um de&shy;<lb/>
beret &aelig;quari, &longs;eu in &aelig;quilubrio con&longs;titui, antror&longs;um pellitur. </s>
          <s id="s.004159">Porr&ograve; in his, <lb/>
qu&aelig; ob grauitatem de&longs;cendunt; deor&longs;um, &amp; retror&longs;um, opponuntur; deor&shy;<lb/>
&longs;um enim e&longs;t pars, qu&aelig; ad terram, anterior ver&ograve; ea pars e&longs;t, qu&aelig; &longs;ur&longs;um, &longs;eu <lb/>
retror&longs;um, vergit. </s>
          <s id="s.004160">quod igitur in his grauibus, &longs;iue rotundis, &longs;iue rectilineis <lb/>
e&longs;t ca&longs;us ex vna parte, idem pr&aelig;&longs;tat ex oppo&longs;ita parte latio, qua re&longs;urgunt, <lb/>ide&longs;t ad angulos pares fit ca&longs;us, &amp; latio: propterea neutra eorum ad rectum <pb pagenum="245" xlink:href="009/01/245.jpg"/>angulum repercutiuntur, <expan abbr="neq;">neque</expan> &longs;ecundum perpendicularem, quia perpendi&shy;<lb/>
culum eductum ex puncto ca&longs;us diuidit ea bifariam. </s>
          <s id="s.004161">fieri autem nequit, vt <lb/>
ad idem <expan abbr="punct&utilde;">punctum</expan> C, plani A B. plura perpendicula erigantur ex 13. 11. Elem. <lb/>
&lpar;vt in &longs;ecunda figura, &longs;ola linea C D, perpendicularis e&longs;&longs;e pote&longs;t ad idem, <lb/>
punctum C,&rpar; quibus perpendiculis grauia <expan abbr="diuid&atilde;tur">diuidantur</expan> bifariam, <expan abbr="atq;">atque</expan> in &aelig;qui&shy;<lb/>
librio con&longs;tituantur: quod tamen &longs;equeretur, &longs;i linea reflexionis eorum, qu&aelig; <lb/>
obliqu&egrave; cadunt, e&longs;&longs;et perpendicularis, ab hac enim diuiderentur bifariam, <lb/>
&amp; pr&aelig;terea etiam ab alia, qu&aelig; perpendicularis ver&egrave; e&longs;t: &amp; pr&aelig;terea etiam <lb/>
&agrave; priori linea incidenti&aelig;, qu&aelig; pariter e&longs;&longs;et perpendicularis, cum &longs;imiliter <lb/>
cadat, <expan abbr="atq;">atque</expan> reflexa, <expan abbr="diuider&etilde;tur">diuiderentur</expan> bipartit&ograve;. </s>
          <s id="s.004162">Quod ab&longs;urdum e&longs;t. </s>
          <s id="s.004163">&longs;ed c&ugrave;m ad&shy;<lb/>
uer&longs;am quidem in partem <expan abbr="fer&atilde;tur">ferantur</expan>, &amp; non ad angulum rectum, reliquum e&longs;t, <lb/>
vt ad acutum angulum re&longs;iliant, ex altera puncti incidenti&aelig; parte, quia an&shy;<lb/>
gulus rectus e&longs;t terminus, intra quem omnes anguli aduer&longs;i <expan abbr="contin&etilde;tur">continentur</expan>, qua&shy;<lb/>
les &longs;unt in prima figura ij, quorum vnum angulum incidenti&aelig;, alterum re&shy;<lb/>
flexionis appellant.</s>
        </p>
        <p type="main">
          <s id="s.004164">Notandum quoad ver&longs;ionem latinam Theodori Gaz&aelig;, quod vbi &longs;unt ver&shy;<lb/>
ba illa <emph type="italics"/>&lpar;Aut colei violantur&rpar;<emph.end type="italics"/> in gr&aelig;co e&longs;t, <foreign lang="greek">kolutrous u&rpar;farpazousi.</foreign> quorum ver&shy;<lb/>borum paraphra&longs;im omi&longs;i, quia the&longs;auri, aut lexica gr&aelig;ca nullam huius ver&shy;<lb/>
bi notionem afferunt, qu&aelig; huic loco quadret, dicunt enim ex Athen&aelig;o <foreign lang="greek">tous <lb/>koluqrous</foreign>, &longs;ignificare ficus maturas: Suidas ver&ograve; ait e&longs;&longs;e quoddam plant&aelig; ge&shy;<lb/>
nus: quorum neutrum ad rem facit. </s>
          <s id="s.004165">propterea vel textus corruptus e&longs;t, vel <lb/>
metaphoric&egrave; v&longs;us e&longs;t Ari&longs;t. hoc verbo, cuius metaphor&aelig; mod&ograve; intelligen&shy;<lb/>
tiam non habemus.</s>
        </p>
        <p type="main">
          <s id="s.004166"><arrow.to.target n="marg347"/></s>
        </p>
        <p type="margin">
          <s id="s.004167"><margin.target id="marg347"/>355</s>
        </p>
        <p type="main">
          <s id="s.004168">In 5. problem. <emph type="italics"/>&lpar;Cur Cylinder propul&longs;us fertur in directum, &longs;uisqu&eacute; terminanti&shy;<lb/>
bus orbibus lineas rectas de&longs;cribit, turbo ver&ograve; &longs;uo manente murone circunfertur, <lb/>
at que in &longs;uo terminante orbe orbem de&longs;cribit? </s>
          <s id="s.004169">&amp;c.&rpar;<emph.end type="italics"/> Ad huius textus intelligen&shy;<lb/>
tiam fatis e&longs;t no&longs;&longs;e, quid Cylindrus, &amp; quid Conus, &longs;iue turbo &longs;it. </s>
          <s id="s.004170">conum igi&shy;<lb/>
tur ex definitione 8. 11. &longs;ic po&longs;&longs;umus de&longs;cribere, e&longs;&longs;e corpus ex vna parte <lb/>acuminatum, ex altera ver&ograve; planum, quod planum dicitur ba&longs;is coni, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; <lb/>
circulus: vulg&ograve; appellatur Pyramis rotunda. </s>
          <s id="s.004171">Cylindrum ver&ograve; ex definit. </s>
          <s id="s.004172">21. <lb/>
eiu&longs;dem 11. &longs;ic po&longs;&longs;umus explicare: e&longs;&longs;e corpus rotundum <expan abbr="oblong&utilde;">oblongum</expan>, &aelig;qua&shy;<lb/>
lis vtrinque cra&longs;&longs;itiei, cuius du&aelig; ba&longs;es &longs;unt circuii: <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti fru&longs;tum co&shy;<lb/>
lumn&aelig;. </s>
          <s id="s.004173">his cognitis poteris nullo negotio totius problematis &longs;olutionem <lb/>
ex textu Ari&longs;t. percipere.</s>
        </p>
        <p type="main">
          <s id="s.004174"><arrow.to.target n="marg348"/></s>
        </p>
        <p type="margin">
          <s id="s.004175"><margin.target id="marg348"/>356</s>
        </p>
        <p type="main">
          <s id="s.004176">In 6. probl. <emph type="italics"/>&lpar;Cur voluminum &longs;ectio plana, &amp; recta, &longs;i quidem fuerit ba&longs;i volu&shy;<lb/>minis &aelig;quidi&longs;tans, explicata lineam rectam o&longs;tendit: &longs;i ver&ograve; fuerit ba&longs;i inclinata, <lb/>tortuo&longs;am? </s>
          <s id="s.004177">An quia accidit, vt circulis illius &longs;ectionis in eodem plano existenti&shy;<lb/>
bus, hanc quidem &longs;ectionem non adiacentem e&longs;&longs;e. </s>
          <s id="s.004178">&longs;ed hic quidem pius, illic ver&ograve; mi&shy;<lb/>
nus ab eadem distare. </s>
          <s id="s.004179">Ita vt explicato volumine circuli quidem ij, qui in eodem, <lb/>&longs;unt plano, &amp; principium habent in eodem plano, ex &longs;e ip&longs;is euolutis faci&ecaron;t rectam <lb/>
lineam: e&longs;t enim facta recta ex circulis, qui &longs;unt in eodem plano; ita vt etiam re&shy;<lb/>
cta exi&longs;tat in plano. </s>
          <s id="s.004180">At ver&ograve; obliqu&aelig; illius &longs;ectionis linea explicata, non exi&longs;tens <lb/>prim&aelig; &aelig;quidi&longs;tans, &longs;ed hic quidem plus, illic ver&ograve; minus ab ea recedens, propterea <lb/>quod etiam ip&longs;a &longs;ectio ita &longs;e habeat ad eandem non εrit in eodem plano: <expan abbr="itaq;">itaque</expan> <expan abbr="neq;">neque</expan> <lb/>
recta, <expan abbr="neq;">neque</expan> enim eiu&longs;dem rect&aelig; pars in vno plano, pars ver&ograve; alia in alio plano e&longs;&longs;e <lb/>
pote&longs;t&rpar;<emph.end type="italics"/> &longs;i Theodorus Gaza loco horum verborum <emph type="italics"/>&lpar;Cur &longs;ectio chartarum, &longs;iue <emph.end type="italics"/>e <pb pagenum="246" xlink:href="009/01/246.jpg"/><emph type="italics"/>papyri&rpar;<emph.end type="italics"/> ver&longs;i&longs;&longs;et; cur voluminum &longs;ectio, quemadmodum ego feci, quod, &amp; <lb/>
facere debebat, iuxta <expan abbr="gr&aelig;cor&utilde;">gr&aelig;corum</expan> <expan abbr="verbor&utilde;">verborum</expan> notionem, <foreign lang="greek">*dia ti/ tw=n bibli/wn h\ tomh</foreign>, <lb/>
locum hunc non &longs;olum non ob&longs;cura&longs;&longs;et, verum etiam clarum omnin&ograve; red&shy;<lb/>
didi&longs;&longs;et, e&longs;t enim Problema de &longs;ectione voluminis papyracei, quibus vete&shy;<lb/>
res illi &longs;cribebant. </s>
          <s id="s.004181">quapropter optim&egrave; intelliges textum hunc, &longs;i huiu&longs;modi <lb/>
volumen bis &longs;ecueris, primo quidem &longs;ectione ba&longs;i voluminis parallela; &longs;e&shy;<lb/>
cundo ver&ograve; &longs;ectione tran&longs;uer&longs;ali, &longs;eu obliqua ad ba&longs;im: nam explicata pri&shy;<lb/>
ma &longs;ectione apparebit eam e&longs;&longs;e lineam rectam: euoluta ver&ograve; <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> &longs;ectio&shy;<lb/>ne apparebit eam e&longs;&longs;e tortuo&longs;am, &amp; flexuo&longs;am; Ari&longs;t. <!-- REMOVE S-->reddens rationem, <lb/>
cur h&aelig;c &longs;it tortuo&longs;a, ait id e&longs;&longs;e, quia &longs;ectione obliqua exi&longs;tente, ide&longs;t ex vna <lb/>
parte depre&longs;&longs;iori, &amp; ex altera altiori, &longs;equitur, quod circuli, qui ex tali &longs;e&shy;<lb/>
ctione oriuntur non remanent in eodem plano, dum euoluuntur; quare <expan abbr="neq;">neque</expan> <lb/>
linea, ex qua illi circuli con&longs;tant, poterit e&longs;&longs;e in eodem plano, &amp; ideo <expan abbr="neq;">neque</expan> <lb/>
recta e&longs;&longs;e poterit, quia fieri nequit, vt eiu&longs;dem line&aelig; pars &longs;it in plano vno, <lb/>
pars ver&ograve; in altero; quod o&longs;tenditur in prima 11. Elem. qu&aelig; e&longs;t h&aelig;c; rect&aelig; <lb/>
line&aelig; pars qu&aelig;dam non e&longs;t in &longs;ubiecto plano, pars ver&ograve; in &longs;ublimi.</s>
        </p>
        <p type="main">
          <s id="s.004182"><arrow.to.target n="marg349"/></s>
        </p>
        <p type="margin">
          <s id="s.004183"><margin.target id="marg349"/>357</s>
        </p>
        <p type="main">
          <s id="s.004184">In 12. problem. </s>
          <s id="s.004185">quod e&longs;t idem cum tertio &longs;uperiori, videnda &longs;unt, qu&aelig; ibi <lb/>
annotaui, hic tamen aliter &longs;oluitur, &longs;ed tanta facilitate, vt nihil pr&aelig;te&shy;<lb/>
rea opus &longs;it.</s>
        </p>
        <p type="main">
          <s id="s.004186"><arrow.to.target n="marg350"/></s>
        </p>
        <p type="margin">
          <s id="s.004187"><margin.target id="marg350"/>358</s>
        </p>
        <p type="main">
          <s id="s.004188">In 13. probl. </s>
          <s id="s.004189">quod e&longs;t idem cum quarto pr&aelig;cedenti, repetenda e&longs;t illius. <lb/>
</s>
          <s id="s.004190">explicatio, vt huic in&longs;eruiat. </s>
          <s id="s.004191">Ari&longs;t. autem pulchr&egrave;, &amp; apt&egrave; a&longs;&longs;imilat refle&shy;<lb/>
xionem corporum reflexioni radiorum vi&longs;ualium ex &longs;peculis; vbi, vt docent <lb/>
Per&longs;pectiui, radius vi&longs;ualis &longs;peculo incidens, facit &longs;emper angulum &aelig;qua&shy;<lb/>
lem ei, quem facit radius reflexus; e&longs;t enim apud eos axioma, angulus in&shy;<lb/>
cidenti&aelig; &aelig;qualis e&longs;t angulo reflexionis.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.004192"><emph type="italics"/>SECTIO XIX.<!-- KEEP S--></s>
          <lb/>
          <s id="s.004193">De Mu&longs;ica.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004194"><arrow.to.target n="marg351"/></s>
        </p>
        <p type="margin">
          <s id="s.004195"><margin.target id="marg351"/>359</s>
        </p>
        <p type="main">
          <s id="s.004196">Problema primum ex &longs;e clarum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004197">In 2. problema. </s>
          <s id="s.004198">In verba illa <emph type="italics"/>&lpar;Sed quemadmodum linea bipedalis non <emph.end type="italics"/><lb/>
<figure id="id.009.01.246.1.jpg" place="text" xlink:href="009/01/246/1.jpg"/><lb/>
<emph type="italics"/>duplum, &longs;ed quadruplum quoddam de&longs;cribit, <lb/>
&longs;ic, &amp;c.&rpar;<emph.end type="italics"/> ide&longs;t, quemadmodum linea bi&shy;<lb/>
pedalis, qu&aelig; quamuis &longs;it dupla line&aelig; pedalis non <lb/>
tamen de&longs;cribit quadratum duplum quadrati il&shy;<lb/>
lius, &longs;ed quadruplum: vt probatur in &longs;cholio 4. <lb/>
2. Elem. &amp; videre e&longs;t in hac figura, vbi linea A B, <lb/>
e&longs;t dupla line&aelig; A C. quadratum ver&ograve; line&aelig; A B, <lb/>
&longs;cilicet quadratum A B D E, e&longs;t <expan abbr="quadrupl&utilde;">quadruplum</expan> qua&shy;<lb/>
drati line&aelig; A C, quadrati nimirum A C F G. re&shy;<lb/>
liqua huius textus manife&longs;ta &longs;unt</s>
        </p>
        <p type="main">
          <s id="s.004199">Scias Lector, me nullum, horum de Mu&longs;ica Problematum &lpar;quemadmo&shy;<lb/>
dum &amp; in pluribus alijs mathematicis locis accidit&rpar; vidi&longs;&longs;e expo&longs;itorem, <lb/>
pr&aelig;ter vnum Petrum Aponentem, quem tamen tanquam omnin&ograve; his rebus <lb/>
elucidandis ineptum, reieci.</s>
        </p>
        <pb pagenum="247" xlink:href="009/01/247.jpg"/>
        <p type="main">
          <s id="s.004200">Vt autem c&aelig;tera problemata rect&egrave;, ac facil&egrave; &longs;oluantur, oper&aelig;pretium <lb/>
e&longs;t, ortum, ac generationem totius Mu&longs;ic&aelig; breuiter pr&aelig;mittere; natura <lb/>
enim ip&longs;ius rit&egrave; per&longs;pecta, ea deinde, qu&aelig; ip&longs;am con&longs;equuntur nullo nego&shy;<lb/>
tio percipi po&longs;&longs;unt.</s>
        </p>
        <p type="main">
          <s id="s.004201">Prim&ograve; igitur &longs;ciendum e&longs;t, duplicem nos po&longs;&longs;e con&longs;iderare in voce, &longs;ono&shy;<lb/>
u&egrave; varietatem. </s>
          <s id="s.004202">prima e&longs;t, qua eadem vox, aut &longs;onus modo maior, modo mi&shy;<lb/>
nor efficitur, vt quando eadem chorda lent&egrave; pul&longs;ata &longs;onum edit exiguum; <lb/>
vehementer ver&ograve; percu&longs;&longs;a, maiorem emittit &longs;onum. </s>
          <s id="s.004203">huiu&longs;modi vocem ap&shy;<lb/>
pellant Mu&longs;ici continuam. </s>
          <s id="s.004204">Philo&longs;ophi fort&egrave; eam vocarent vocis exten&longs;io&shy;<lb/>
nem. </s>
          <s id="s.004205">&longs;ecunda vocis differentia, aut varietas e&longs;t, cum ab vna voce ad aliam <lb/>
tran&longs;imus, vt cum &agrave; graui ad acutiorem a&longs;cendimus, vel contra, ab acuta <lb/>
ad grauem de&longs;cendimus, ita vt h&aelig;c &longs;it mutatio ab vna voce ad aliam, hanc <lb/>
harmonici di&longs;cretam vocem dicunt. </s>
          <s id="s.004206">quam fort&egrave; Philo&longs;ophi ex varia vocis <lb/>
inten&longs;ione prouenire iure dixerint. </s>
          <s id="s.004207">Hanc porr&ograve; di&longs;cretam vocem, altera <lb/>
omi&longs;&longs;a, con&longs;iderant Mu&longs;ici. <!-- KEEP S--></s>
          <s id="s.004208">qua ratione autem, &amp; in quot, qua&longs;u&egrave; voces eam <lb/>
diui&longs;erint antiqui, paucis accipe.</s>
        </p>
        <p type="main">
          <s id="s.004209">Cape duas chordas &aelig;reas, ex ijs &longs;cilicet, quas in cytharis adhibere <expan abbr="&longs;ol&etilde;t">&longs;olent</expan>; <lb/>nam qu&aelig; ex inte&longs;tinis ouium fiunt, vt plurimum aut fal&longs;&aelig; &longs;unt, aut aeris mu&shy;<lb/>
tationi obnoxi&aelig;. </s>
          <s id="s.004210">&longs;int h&aelig; du&aelig; chord&aelig; &aelig;quales omnin&ograve;, atque &aelig;qu&egrave; inten&longs;&aelig;, <lb/>
<figure id="id.009.01.247.1.jpg" place="text" xlink:href="009/01/247/1.jpg"/><lb/>
ita vt &longs;int vni&longs;on&aelig;, hoc e&longs;t, vna <expan abbr="tan-t&utilde;">tan&shy;<lb/>
tum</expan> vox &longs;it. </s>
          <s id="s.004211">quamuis du&aelig; fides. </s>
          <s id="s.004212">opor&shy;<lb/>
tet autem, vt &longs;int &longs;uper regula ali&shy;<lb/>
qua lignea oblonga, &amp; perpolita, <lb/>
collocat&aelig;, <expan abbr="quemadmod&utilde;">quemadmodum</expan> &longs;uper ma&shy;<lb/>
nubrio alicuius mu&longs;ici in&longs;trumenti. <lb/>
</s>
          <s id="s.004213">hanc regulam veteres appellant regulam harmonicam, vel etiam mono&shy;<lb/>
chordium; quo in&longs;trumento omnes con&longs;onantias, ac <expan abbr="di&longs;&longs;on&atilde;tias">di&longs;&longs;onantias</expan>, <expan abbr="atq;">atque</expan> etiam <lb/>
interualla mu&longs;ica experiebantur. </s>
          <s id="s.004214">altera iam ex illis diuidatur bifariam in <lb/>
E. deinde &longs;ub puncto E, pone quem vulg&ograve; Tactum dicunt, veteres autem, <lb/>
hemi&longs;ph&aelig;rium &agrave; figura denominabant, erat autem in&longs;tar vnius Tacti mobi&shy;<lb/>
lis: &longs;uppo&longs;ito igitur in E, Tacto, preme ibi chordam, ita vt altera tantum <lb/>
ip&longs;ius medietas, v. <!-- REMOVE S-->g. <!-- REMOVE S-->E D, tota pul&longs;ari, atque re&longs;onare po&longs;&longs;it; pul&longs;a igitur <lb/>
chordam vtranque &longs;imul, &longs;cilicet totam A B, &amp; dimidiam E D, ita vt &longs;imul <lb/>
re&longs;onent. </s>
          <s id="s.004215">&amp; audies &longs;uaui&longs;&longs;imam omnium con&longs;on&egrave;ntiam, ex &longs;ono totius A B, <lb/>
&amp; &longs;ono dimidi&aelig; E D, conflatam. </s>
          <s id="s.004216">hunc veteres Diapa&longs;on, ide&longs;t per omnes <lb/>
&longs;ubaudi, chordas appellabant, quia in <expan abbr="antiquor&utilde;">antiquorum</expan> mu&longs;icis in&longs;trumentis chor&shy;<lb/>
d&aelig; du&aelig; omnium extrem&aelig;, ide&longs;t graui&longs;&longs;ima, &amp; acuti&longs;&longs;ima omnium fidium, <lb/>
con&longs;onantiam hanc continebant: ita vt &agrave; graui&longs;&longs;ima omnium facto tran&longs;itu <lb/>
per omnes chordas ad omnium &longs;upremam, &amp; acuti&longs;&longs;iman, con&longs;onantiam <lb/>
hanc &longs;uaui&longs;&longs;imam exaudirent. </s>
          <s id="s.004217">appellatur etiam Dupla ratione proportio&shy;<lb/>nis vnius vocis ad alteram, vox enim chord&aelig; A B, e&longs;t duplo maior, aut gra&shy;<lb/>
uior voce dimidi&aelig; E D. quemadmodum enim corpora &longs;ononantia &longs;e habent <lb/>
ad inuicem, ita &longs;e &longs;oni eorum. </s>
          <s id="s.004218">chorda autem A B, dupla e&longs;t chord&aelig; E D. <lb/>nunc eam vulgus Octauam appellat, eo quod &agrave; prima voce, <expan abbr="ea&qacute;">eaque</expan>; graui&longs;&longs;i&shy;<lb/>
ma, qu&aelig; Vt dicitur, <expan abbr="v&longs;q;">v&longs;que</expan> ad eam vocem, qu&aelig; ei in con&longs;onantia diapa&longs;on re&shy;<lb/>
&longs;pondent, &longs;unt h&aelig; octo voces, Vt, Re, Mi, Fa, Sol, Re, Mi, Fa. <!-- KEEP S--></s>
          <s id="s.004219">ex quibus <pb pagenum="248" xlink:href="009/01/248.jpg"/>prima, Vt, &amp; vltima, Fa, qu&aelig; octaua e&longs;t, con&longs;onantiam diapa&longs;on, aut du&shy;<lb/>
plam, aut octauam reddunt.</s>
        </p>
        <p type="main">
          <s id="s.004220">Rur&longs;us eadem chorda C D, diuidatur in tres partes &aelig;quales in punctis <lb/>
<figure id="id.009.01.248.1.jpg" place="text" xlink:href="009/01/248/1.jpg"/><lb/>
F, G. <!-- KEEP S--></s>
          <s id="s.004221">F D igitur erit du&aelig; ter&shy;<lb/>
ti&aelig; tam totius C D, qu&agrave;m to&shy;<lb/>
tius A B. ponatur iam tactus <lb/>
in F, <expan abbr="percuti&atilde;tur&qacute;">percutianturque</expan>; &longs;imul A B, <lb/>
&amp; F D; audietur con&longs;onantia <lb/>
&longs;uauis admodum, &amp; perfecta <lb/>
quidem, &longs;ed <expan abbr="n&otilde;">non</expan> tamen, vt Dia&shy;<lb/>
pa&longs;on. <!-- KEEP S--></s>
          <s id="s.004222">hanc pri&longs;ci Diapente dixerunt, ide&longs;t per <expan abbr="quinq;">quinque</expan> &longs;ubaudi chordas, e&ograve; <lb/>
quod prima, &amp; quinta chorda, hanc con&longs;onarent. </s>
          <s id="s.004223">&longs;ecundum proportionem <lb/>
ver&ograve; dicitur &longs;e&longs;quialtera, quoniam chorda A B, ad chordam F D, e&longs;t &longs;e&longs;qui&shy;<lb/>
altera, &amp; con&longs;equenter etiam earum &longs;oni erunt in eadem ratione. </s>
          <s id="s.004224">&longs;e&longs;quial&shy;<lb/>
tera autem proportio e&longs;t, quando maior quantitas A B, continet minorem <lb/>
F D, &longs;emel,&amp; adhuc dimidium ip&longs;ius. </s>
          <s id="s.004225">vulg&ograve; quinta, quia ex prima voce, Vt, <lb/>
&amp; quinta, Sol, con&longs;tat.</s>
        </p>
        <p type="main">
          <s id="s.004226">Eadem iterum chorda in quatuor &aelig;quas partes &longs;ecetur in punctis H, E, I, <lb/>
<figure id="id.009.01.248.2.jpg" place="text" xlink:href="009/01/248/2.jpg"/><lb/>
ita vt chorda H D, &longs;it tres quart&aelig; <lb/>
totius A D. facto deinde tactu in <lb/>
H, pul&longs;entur &longs;imul A B, H D, &amp; au&shy;<lb/>
dietur con&longs;onantia quidem, &longs;ed <lb/>
duabus pr&aelig;cedentibus imperfe&shy;<lb/>
ctior. </s>
          <s id="s.004227">h&aelig;c antiquitus Diate&longs;&longs;aron, <lb/>
ide&longs;t per quatuor, &longs;ubaudi chor&shy;<lb/>
das, aut voces, &longs;imili ratione, qua &longs;uperiores dicta fuit. </s>
          <s id="s.004228">re&longs;pectu autem pro&shy;<lb/>
portionis chordarum, ac &longs;onorum dicitur &longs;e&longs;quitertia, quia maior A B, mi&shy;<lb/>
norem H D, &longs;emel, &amp; adhuc tertiam ip&longs;ius partem continet. </s>
          <s id="s.004229">vulg&ograve; nunc di&shy;<lb/>
citur, quarta, quid inter primam vocem, Vt, &amp; quartam, Fa, reperiatur. <lb/>
</s>
          <s id="s.004230">Iam ver&ograve; &longs;i in eadem chorda C D, ponantur puncta H, &amp; F, vt in pr&aelig;cedenti <lb/>
figura, &amp; &longs;imul du&aelig; chord&aelig; H D, &amp; F D, hoc e&longs;t tres quart&aelig;, &amp; du&aelig; terti&aelig;, <lb/>
arithmeticis rationibus comparentur, reperiemus maiorem H D, ad mi&shy;<lb/>
norem F D, proportionem habere &longs;e&longs;quioctauam, &amp; &longs;onum maioris H D, <lb/>
ad minorem F D, eandem habebit rationem, hoc e&longs;t, vt nouis vocabulis <lb/>
vtamur inter Fa, &amp; Sol, e&longs;&longs;e &longs;e&longs;quioctauam proportionem; &longs;i autem &longs;imul <lb/>
hi duo &longs;oni exaudiantur di&longs;&longs;onantiam auribus facient. </s>
          <s id="s.004231">di&longs;tantiam porr&ograve; <lb/>hanc inter voces Fa, Sol, &longs;iue inter chordas H D, F D, &longs;iue inter duo inter&shy;<lb/>
ualla H D, F D, harmonici, quorum ratio e&longs;&longs;et &longs;e&longs;quioctaua Tonum appel&shy;<lb/>
larunt. </s>
          <s id="s.004232">Diui&longs;erunt po&longs;tea totam C D, in nouem partem &aelig;quales, quarum <lb/>
prima &longs;it in puncto K, diui&longs;a, ita vt tota C D, ad reliquam K D, qu&aelig; conti&shy;<lb/>
net octo partes ex illis, habeat rationem &longs;e&longs;quioctauam, hoc pariter inter&shy;<lb/>uallum Toni erit, cuius primum &longs;onum, ide&longs;t totius C D, nunc dicunt, Vt, <lb/>
&longs;ecundum ver&ograve; &longs;onum reliqu&aelig; chord&aelig; K D, dicunt, Re Reliquam po&longs;tea <lb/>
K D, &longs;imiliter in nouem partes diui&longs;erunt, cuius prima pars &longs;it in puncto L, <lb/>
notata. </s>
          <s id="s.004233">&amp; eadem ratione inter chordam K D, &amp; chordam L D, <expan abbr="earum&qacute;">earumque</expan>; &longs;o&shy;<lb/>
nos erit &longs;e&longs;quioctaua proportio. </s>
          <s id="s.004234">&longs;onum chord&aelig; L D, nunc appellant, Mi.


<pb pagenum="249" xlink:href="009/01/249.jpg"/>Interuallum ver&ograve;, quod inter chordam L D, &amp; chordam H D, remanet, non <lb/>
habet proportionem &longs;e&longs;quioctauam, &longs;ed dimidio fer&egrave; minorem, &amp; propte&shy;<lb/>
rea huiu&longs;modi interuallum &longs;emitonium, &amp; etiam die&longs;is, &longs;iue diui&longs;io, appel&shy;<lb/>
latur. </s>
          <s id="s.004235">Interuallum ver&ograve; illud, quod inter puncta F, &amp; E, remanet, diui&longs;e&shy;<lb/>
runt eodem modo, quo diui&longs;um fuit &longs;patium inter C, &amp; H, &amp; repercerunt <lb/>
ea&longs;dem iterum voces; &longs;int diui&longs;iones ill&aelig; punctis M, &amp; N, notat&aelig;; &amp; pari&shy;<lb/>
ter hic etiam inter N, &amp; E, &longs;iue inter Mi, &amp; Fa, e&longs;t alterum &longs;emitonium. <lb/>
</s>
          <s id="s.004236">&longs;unt igitur h&aelig; octo voces, Vt, Re, Mi, Fa, Sol, Re, Mi, Fa, qu&aelig; totam Dia&shy;<lb/>
pa&longs;on componunt, vt enim &longs;upra dictum e&longs;t inter Vt, &amp; Fa, <expan abbr="vltim&utilde;">vltimum</expan>, e&longs;t con&shy;<lb/>
&longs;onantia diapa&longs;on, &longs;iue dicamus inter chordam C D, vel A B, &amp; chordam <lb/>
E D. ex interuallis autem,qu&aelig; &longs;unt inter voces, duo &longs;unt &longs;emitonia, &longs;cilicet <lb/>
vnum inter Mi, &amp; Fa, notatum literis L, H. &amp; alterum inter vltima Mi, &amp; <lb/>
Fa, &longs;ignatum notis N, E. reliqua <expan abbr="quinq;">quinque</expan> interualla &longs;unt integri toni. </s>
          <s id="s.004237">Aduer&shy;<lb/>
tendum pr&aelig;terea e&longs;t, ab Vt, <expan abbr="v&longs;q;">v&longs;que</expan> ad primum Sol, e&longs;&longs;e con&longs;onantiam Dia&shy;<lb/>
pente, qu&aelig; continet tria interualla toniaca, &amp; vnum &longs;emitonium; in vni&shy;<lb/>
uer&longs;um tamen &longs;unt <expan abbr="quinq;">quinque</expan> voces, Vt, Re, Mi, Fa, Sol.</s>
        </p>
        <p type="main">
          <s id="s.004238">Notandum etiam, quod &agrave; Sol, <expan abbr="v&longs;q;">v&longs;que</expan> ad vltimum Fa, &longs;unt quatuor voces, <lb/>
Sol, Re, Mi, Fa,qu&aelig; omnin&ograve; &longs;imiles &longs;unt primis quatuor, Vt, Re, Mi Fa. <!-- KEEP S--></s>
          <s id="s.004239">h&aelig; <lb/>
tamen &longs;unt grauiores, ill&aelig; ver&ograve; acutiores, &amp; quemadmodum ab Vt, ad pri&shy;<lb/>
mum Fa, e&longs;t Diate&longs;&longs;aron, ita etiam &agrave; Sol, <expan abbr="v&longs;q;">v&longs;que</expan> ad vltimum Fa, e&longs;t altera Dia&shy;<lb/>
te&longs;&longs;aron. </s>
          <s id="s.004240">Ex quibus vltim&ograve; notandum &longs;equitur, duas con&longs;onantias Diate&longs;&shy;<lb/>
&longs;aron, &amp; Diapente totam con&longs;tituere Diapa&longs;on: &longs;iue Diapa&longs;on diuidi in <lb/>
vnam Diate&longs;&longs;aron, &amp; vnam Diapente; nam ab Vt, ad Sol, e&longs;t Diapente; &agrave; <lb/>
Sol, ver&ograve; in Fa, po&longs;tremum, e&longs;t Diate&longs;&longs;aron. <!-- KEEP S--></s>
          <s id="s.004241">quod etiam aliter con&longs;tabit, &longs;i <lb/>
dicamus ab Vt, ad primum Fa, e&longs;&longs;e Diate&longs;&longs;aron, vt patet ex chord&aelig; diui&longs;io&shy;<lb/>
ne: ex Fa, autem prim&ograve; ad vltimum Fa, e&longs;&longs;e Diapente: vt manife&longs;tum e&longs;t <lb/>
ex quatuor ip&longs;ius interuallis, quorum tria &longs;unt Toni, reliquum ver&ograve; &longs;emito&shy;<lb/>
nium, qu&aelig; etiam erant in altera Diapente inter Vt, &amp; Sol, contenta.</s>
        </p>
        <p type="main">
          <s id="s.004242">Nunc rur&longs;us fiat tactus in I, e&longs;t autem I D, quarta pars totius C D. per&shy;<lb/>
cutiantur &longs;imul A B, &amp; I D; <expan abbr="edetur&qacute;">edeturque</expan>; &longs;uaui&longs;&longs;ima con&longs;onantia Di&longs;diapa&longs;on <lb/>
appellata, propterea quod ex duabus Diapa&longs;on con&longs;tet; quarum prima e&longs;t <lb/>
inter A B, &longs;iue C D, &amp; E D: &longs;ecunda ver&ograve; inter ip&longs;am E D, &amp; I D. harum <lb/>
enim proportio dupla e&longs;t, &longs;icuti illarum. </s>
          <s id="s.004243">proportio huius e&longs;t quadrupla, vt <lb/>
ex diui&longs;ione con&longs;tat; vulg&ograve; dicitur decimaquinta, quia &agrave; primo Vt, <expan abbr="v&longs;q;">v&longs;que</expan> ad <lb/>
hanc vocem,qu&aelig; etiam Fa, nominatur, e&longs;&longs;ent quindecim voces, &longs;i interual&shy;<lb/>
lum E I, eo modo diuideretur, quo diui&longs;um e&longs;t primum C E.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004244">Po&longs;trem&ograve; &longs;it G D, tertia pars totius C D, <expan abbr="fiat&qacute;">fiatque</expan>; in G, tactus, pul&longs;entur &longs;i&shy;<lb/>mul A B, G D. audietur &longs;uauis con&longs;onantia, qu&aelig; Diapa&longs;ondiapente nomi&shy;<lb/>
natur, quod con&longs;tet ex vna Diapa&longs;on contenta interuallo C E, &longs;iue duabus <lb/>
chordis C D, E D, &amp; vna Diapente contenta interuallo E G, &longs;iue chordis <lb/>
E D, G D; nam chorda E D, ad chordam G D, &longs;e&longs;quialtera e&longs;t; qu&aelig; propor&shy;<lb/>
tio naturam ip&longs;ius diapente con&longs;tituit huius con&longs;onanti&aelig; proportio e&longs;t tri&shy;<lb/>
pla, e&longs;t enim chorda A B, vel C D, tripla ip&longs;ius G D. vulg&ograve; dicitur duode&shy;<lb/>cima, c&ograve; quod inter Vt, &amp; Sol, notatum litera G, &longs;int duodecim voces, &longs;i in&shy;<lb/>
teruallum E O, &longs;uas recipiat diui&longs;iones. </s>
          <s id="s.004245">ex quibus omnibus manife&longs;tum e&longs;t <lb/>
auris experimento, e&longs;&longs;e omnin&ograve; quinque con&longs;onantias, tres &longs;implices Dia&shy;


<pb pagenum="250" xlink:href="009/01/250.jpg"/>pa&longs;on, Diapente, Diate&longs;&longs;aron; duas ver&ograve; compo&longs;itas, Di&longs;diapa&longs;on, &amp; Dia&shy;<lb/>
pa&longs;ondiapente.</s>
        </p>
        <p type="main">
          <s id="s.004246">Illud po&longs;trem&ograve; loco non ignorandum, aliter has voces Vt, Re, &amp;c. </s>
          <s id="s.004247">vete&shy;<lb/>
res illos Gr&aelig;cos denomina&longs;&longs;e, nam primam, ide&longs;t graui&longs;&longs;imam vocem, &longs;iue <lb/>
chordam, quam mod&ograve; Vt, dicunt, eam ip&longs;i Hypaten vocarunt, &amp; reliquas <lb/>
ordine &longs;equenti.</s>
        </p>
        <figure id="id.009.01.250.1.jpg" place="text" xlink:href="009/01/250/1.jpg"/>
        <p type="main">
          <s id="s.004248">Vt, Hypate &mdash; ide&longs;t Principalis.</s>
        </p>
        <p type="main">
          <s id="s.004249">Re, Parhypate &mdash;&mdash; Po&longs;tprincipalis.</s>
        </p>
        <p type="main">
          <s id="s.004250">Mi, Lychanos &mdash;&mdash; Index.</s>
        </p>
        <p type="main">
          <s id="s.004251">Fa, Me&longs;e &mdash;&mdash;&mdash;&mdash; Media.</s>
        </p>
        <p type="main">
          <s id="s.004252">Sol, Parame&longs;e &mdash;&mdash; Po&longs;tmedia.</s>
        </p>
        <p type="main">
          <s id="s.004253">Re, Trite&mdash;&mdash;&mdash;&mdash; Tertia.</s>
        </p>
        <p type="main">
          <s id="s.004254">Mi, Paranete &mdash;&mdash; Antepenultima.</s>
        </p>
        <p type="main">
          <s id="s.004255">Fa, Nete &mdash;&mdash;&mdash;&mdash; Vltima, vel &longs;uprema.</s>
        </p>
        <p type="main">
          <s id="s.004256">His paucis ex magno Mu&longs;ic&aelig; Campo decerptis problematum declara&shy;<lb/>
tionem &longs;atis in&longs;tructi aggrediamur.</s>
        </p>
        <p type="main">
          <s id="s.004257"><arrow.to.target n="marg352"/></s>
        </p>
        <p type="margin">
          <s id="s.004258"><margin.target id="marg352"/>360</s>
        </p>
        <p type="main">
          <s id="s.004259">Problema 3. <emph type="italics"/>&lpar;Cur maxim&egrave; in cantando Parhypatem, vox rumpi non minus &longs;o&shy;<lb/>
leat, quam in Nete, &longs;upremisqu&eacute; quamquam c&ugrave;m interuallo ampliori? </s>
          <s id="s.004260">An quod eius <lb/>
cantus &amp; perdifficilis est, &amp; cantandi primordium obtinet? </s>
          <s id="s.004261">difficilis autem pro&shy;<lb/>
pter inten&longs;ionem, &amp; compre&longs;&longs;ionem vocis e&longs;t, quibus in rebus e&longs;t labor, &amp; difficul&shy;<lb/>
tas: corrumpi autem qu&aelig;qu&eacute; maxim&egrave; &longs;olent, quoties labore acrius opprimuntur&rpar;<emph.end type="italics"/><lb/>
Qu&aelig;rit Ari&longs;t. cur qui eam vocem cantant, qu&aelig; Parhypate dicitur, non mi&shy;<lb/>
nus defatigetur, <expan abbr="vocem&qacute;">vocemque</expan>; perdat, quam qui Neten, aut aliam ex acutiori&shy;<lb/>
bus vocibus, ip&longs;i Nete proximam, vt Paranetem. </s>
          <s id="s.004262">ratio dubitandi e&longs;t, quia <lb/>
Parhypate e&longs;t vox grauis, &amp; qu&aelig; paruo interuallo di&longs;tat &agrave; graui&longs;&longs;ima om&shy;<lb/>
nium Hypate: at ver&ograve; Nete, <expan abbr="ali&aelig;&qacute;">ali&aelig;que</expan>; illi viciniores &longs;unt acuti&longs;&longs;im&aelig;, <expan abbr="magnis&qacute;">magnisque</expan>; <lb/>
ab Hypate di&longs;tant interuallis. </s>
          <s id="s.004263">Re&longs;pondet, id accidere ob difficultatem, qu&aelig; <lb/>
in eius cantu reperitur; qu&aelig; difficultas laborem infert, labor autem vocem <lb/>
<expan abbr="corr&utilde;pit">corrumpit</expan>. </s>
          <s id="s.004264">&longs;ed vnde h&aelig;c difficultas? </s>
          <s id="s.004265">re&longs;pondet inde prouenire, quia h&aelig;c vox <lb/>
cantandi principium e&longs;t. </s>
          <s id="s.004266">vbi per cantandi principium puto ip&longs;um intellige&shy;<lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>
<figure id="id.009.01.250.2.jpg" place="text" xlink:href="009/01/250/2.jpg"/><lb/>
re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>
Po&longs;ter. cap. 38. die&longs;is h&etail;c, &longs;iue &longs;emitonium dicitur <lb/>
principium cantus, quia minimum e&longs;t omnium in&shy;<lb/>
teruallorum, qu&aelig; voce po&longs;&longs;int exprimi: <expan abbr="atq;">atque</expan> ex eo <lb/>
alia interualla con&longs;tant, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti illorum ele&shy;<lb/>
mentum. </s>
          <s id="s.004267">vide illius loci explanationem. </s>
          <s id="s.004268">Iam ve&shy;<lb/>
r&ograve; difficile admodum e&longs;&longs;e cantare per &longs;emitonia, <lb/>
per&longs;picuum e&longs;t cantoribus, quod oporteat, vt ait <lb/>
Ari&longs;t. vocem, quantum opus e&longs;t, intendere, &longs;imul <lb/>
ac comprimere, ne &longs;cilicet in maius iu&longs;to inter&shy;<lb/>
uallum erumpat.</s>
        </p>
        <p type="main">
          <s id="s.004269">Verum dubitabis, cur Ari&longs;t. ponat &longs;emitonium <lb/>
ab Hypate ad Parhypatem, c&ugrave;m &longs;uperius <expan abbr="dict&utilde;">dictum</expan> &longs;it, <lb/>&longs;emitonium e&longs;&longs;e tantummodo inter Mi, &amp; Fa, ide&longs;t <lb/>
inter Lychanon, &amp; Me&longs;en. <!-- KEEP S--></s>
          <s id="s.004270">Scias igitur alios aliter <lb/>
<expan abbr="interuallor&utilde;">interuallorum</expan> ordinem feci&longs;&longs;e: inter quos Lychaon <pb pagenum="251" xlink:href="009/01/251.jpg"/>antiqui&longs;&longs;imus Mu&longs;icus &longs;ic ea di&longs;po&longs;uit; vt in pr&aelig;&longs;enti ordine, vbi, vt vides <lb/>
inter hypatem, &amp; perhypatem, e&longs;t &longs;emitonij interuallum. </s>
          <s id="s.004271">ad hunc Lichaonis <lb/>igitur ordinem videtur Ari&longs;t. re&longs;pexi&longs;&longs;e. </s>
          <s id="s.004272">ego ver&ograve; &longs;uperius communiorem <lb/>
viam, nec ade&ograve; antiquam &longs;equutus &longs;um. <!-- KEEP S--></s>
          <s id="s.004273">ex Boethio, &amp; Zarlino.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004274"><arrow.to.target n="marg353"/></s>
        </p>
        <p type="margin">
          <s id="s.004275"><margin.target id="marg353"/>361</s>
        </p>
        <p type="main">
          <s id="s.004276">Probl. 4. <emph type="italics"/>&lpar;S&eacute;d cur h&aelig;c difficile, hypate facil&egrave; cantatur, cum non ni&longs;i die&longs;i di&shy;<lb/>
&longs;crepent? </s>
          <s id="s.004277">An quod hypate remi&longs;&longs;ior e&longs;t, <expan abbr="atq;">atque</expan> etiam l&aelig;uius &agrave; con&longs;titutione a&longs;cendi&shy;<lb/>
tur? </s>
          <s id="s.004278">h&aelig;c eadem cau&longs;a est, cur ad vnam cantari videantur, qu&aelig; ad hanc parane&shy;<lb/>
temqu&eacute; cantantur. </s>
          <s id="s.004279">agendum enim e&longs;t, cum intentione, conditionequ&eacute; moribus idonea <lb/>pro voluntate. </s>
          <s id="s.004280">qu&aelig; ver&ograve; cau&longs;a e&longs;t, vt cum con&longs;onantia &longs;it?&rpar;<emph.end type="italics"/> Ide&longs;t, cur parhypa&shy;<lb/>
te, de qua in pr&aelig;cedenti problemate dictum e&longs;t, difficilius canitur, quam <lb/>
hypate, c&ugrave;m tamen ab inuicem di&longs;tent non ni&longs;i &longs;emitonij interuallo? </s>
          <s id="s.004281">for&longs;i&shy;<lb/>
tan id accidit, quia hypate e&longs;t remi&longs;&longs;ior, c&ugrave;m &longs;it omnium graui&longs;&longs;ima, hoc <lb/>
e&longs;t, non e&longs;t opus in ea decantanda, ita vocem intendere, quemadmodum in <lb/>
parhypate, qu&aelig; acutior e&longs;t. </s>
          <s id="s.004282">reliqua huius loci verba exi&longs;timo e&longs;&longs;e admodum <lb/>
mendo&longs;a tam gr&aelig;c&egrave;, qu&agrave;m latin&egrave;, c&ugrave;m nonnulla in eis &longs;int, qu&aelig; nullo pacto <lb/>
ad rem faciunt, pr&aelig;&longs;ertim extrema &longs;ententia. </s>
          <s id="s.004283">&amp; con&longs;ultius e&longs;&longs;e exi&longs;timo fa&shy;<lb/>
teri me ea non intelligere, quam ea violenter huc, <expan abbr="atq;">atque</expan> illuc diducere.</s>
        </p>
        <p type="main">
          <s id="s.004284"><arrow.to.target n="marg354"/></s>
        </p>
        <p type="margin">
          <s id="s.004285"><margin.target id="marg354"/>362</s>
        </p>
        <p type="main">
          <s id="s.004286">Probl. 5. <emph type="italics"/>&lpar;Cur &longs;uauius cantilenam, quam nouimus, audire &longs;olemus, quam eam, <lb/>
quam ignoramus? </s>
          <s id="s.004287">Vtrum, quia c&ugrave;m quod cantatur, agno&longs;cimus, tunc magis ma&shy;<lb/>
nife&longs;tus e&longs;t, qui veluti &longs;copum a&longs;&longs;equitur. </s>
          <s id="s.004288">id autem contemplatu &longs;uaue e&longs;t. </s>
          <s id="s.004289">An quia <lb/>
di&longs;cere &longs;eu intelligere &longs;uaue e&longs;t, cuius ratio e&longs;t, quia hoc quidem ver&longs;atur in acci&shy;<lb/>
pienda &longs;cientia, illud ver&ograve; in vtenda. </s>
          <s id="s.004290">pr&aelig;terea &longs;olitum in&longs;olito &longs;uauius e&longs;t?&rpar;<emph.end type="italics"/> Vbi <lb/>
Theodorus Gaza po&longs;uerat, calcem re&longs;titui ex gr&aelig;co textu, &longs;copum, vt res <lb/>
ip&longs;a etiam po&longs;tulabat. </s>
          <s id="s.004291">Porr&ograve; tres affert rationes, cur &longs;uauius &longs;it notam <lb/>
iam cantilenam au&longs;cultare, qu&agrave;m ignotam. </s>
          <s id="s.004292">prima e&longs;t, quia, c&ugrave;m cogno&longs;ci&shy;<lb/>
mus, quod cantatur, tunc &longs;copus, ac finis, in quem cantor, ac tota tendit <lb/>
cantilena manife&longs;tus e&longs;t, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; eam melius percipimus; quia dum ip&longs;am au&shy;<lb/>
dimus, &longs;copum etiam ip&longs;ius, cuius contemplatio iucunda e&longs;t, contempla&shy;<lb/>
mur. </s>
          <s id="s.004293">quemadmodum iucundius e&longs;t &longs;pectare currentem canem, &amp; iam cap&shy;<lb/>tantem feram, &longs;i &longs;imul feram etiam ip&longs;am, qu&aelig; &longs;copus ip&longs;ius e&longs;t, quam &longs;i fe&shy;<lb/>
ram minim&egrave; videamus. </s>
          <s id="s.004294">&longs;ecunda e&longs;t, quia ip&longs;um di&longs;cere, ac intelligere dele&shy;<lb/>
ctabile e&longs;t, &amp; huius quidem ratio manife&longs;ta e&longs;t tam in accipienda, qu&agrave;m in <lb/>
vtenda &longs;cientia: dum igitur cantilenam <expan abbr="prim&utilde;">primum</expan> audimus, quam prius igno&shy;<lb/>
rabamus, &longs;cientiam illius tantum accipimus; dum autem notam au&longs;culta&shy;<lb/>
mus, non &longs;olum ip&longs;am, &longs;ed ip&longs;ius etiam &longs;copum contemplantes, ea perfect&egrave; <lb/>
vtimur. </s>
          <s id="s.004295">tertia ratio e&longs;t, quia res &longs;olit&aelig; plerumque, quam in&longs;olit&aelig; iucundio&shy;<lb/>
res exi&longs;tunt.</s>
        </p>
        <p type="main">
          <s id="s.004296">Probl. 6. &amp; per &longs;e &longs;atis clarum e&longs;t; &amp; ad harmonicam non &longs;pectat.</s>
        </p>
        <p type="main">
          <s id="s.004297"><arrow.to.target n="marg355"/></s>
        </p>
        <p type="margin">
          <s id="s.004298"><margin.target id="marg355"/>363</s>
        </p>
        <p type="main">
          <s id="s.004299">Probl. 7. <emph type="italics"/>&lpar;Cur veteres cum &longs;eptem fidibus concentus di&longs;ponerent, hypaten, non <lb/>
neten relinquebant? </s>
          <s id="s.004300">An fals&ograve; id dicitur &lpar;earum enim <expan abbr="vtramq;">vtramque</expan> &longs;eruarunt; &longs;ed tri&shy;<lb/>
ten adimere &longs;olebant&rpar; An non? </s>
          <s id="s.004301">&longs;ed quia grauior &longs;onum pote&longs;t acutioris. </s>
          <s id="s.004302">erg&ograve; hypa&shy;<lb/>
te magis antiphonum, quam nete reddebat; nam vt acutum vim de&longs;iderat plenio&shy;<lb/>
rem, &longs;ic graue exprimi facilius pote&longs;t&rpar;<emph.end type="italics"/> Propter quid, inquit, antiqui&longs;&longs;imi Mu&shy;<lb/>&longs;icorum c&ugrave;m ex &longs;eptem tantum chordis mu&longs;ica in&longs;trumenta <expan abbr="componer&etilde;t">componerent</expan>, <lb/>
neten non hypat&egrave;n omittebant? </s>
          <s id="s.004303">&longs;upra octo voces, &longs;eu chordas recen&longs;ui, <expan abbr="ra-tionem&qacute;">ra&shy;<lb/>
tionemque</expan>; ip&longs;arum, vn&agrave; cum antiquis appellationibus explicaui, quarum <pb pagenum="252" xlink:href="009/01/252.jpg"/><figure id="id.009.01.252.1.jpg" place="text" xlink:href="009/01/252/1.jpg"/><lb/>
prima e&longs;t hypate, vltima ver&ograve; note, quibus re&shy;<lb/>
petitis facil&egrave; e&longs;t intelligere, quod re&longs;pondet <lb/>
Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.004304">Re&longs;pondet enim id non omnin&ograve; verum <lb/>
cen&longs;eri debere, nam vtramque quidem hypa&shy;<lb/>
tem, &longs;cilicet &amp; neten a&longs;&longs;umebant; triten ver&ograve; <lb/>
<expan abbr="omitteb&atilde;t">omittebant</expan>. </s>
          <s id="s.004305">quibus verbis ordinem, quem Ter&shy;<lb/>
pander inuexit, in&longs;inuare videtur, nam vt ait <lb/>
Pau&longs;anias in Lachonicis, Timoth&aelig;us quatuor <lb/>
chordas, antiquis &longs;eptem chordis &agrave; Terpan&shy;<lb/>
dro ordinatis addidit, quarum &longs;eptem chor&shy;<lb/>
darum hic erat ordo, &amp; nomenclatura, &amp; in&shy;<lb/>
terualla; &egrave; quibus triten ademptam videre e&longs;t, <lb/>
vt Ari&longs;t. innuit.</s>
        </p>
        <p type="main">
          <s id="s.004306">Subdit po&longs;tea aliam rationem dicens; fort&egrave; &longs;atius e&longs;&longs;e dicere neten qui&shy;<lb/>
dem antiquitus fui&longs;&longs;e pr&aelig;termi&longs;&longs;am, relicta hypate, co quod hypate, cum <lb/>
di&longs;tet per octauam, &longs;eu per Diapa&longs;on &agrave; Nete, erat illius Antiphonum, ide&longs;t, <lb/>
erat vox eiu&longs;dem natur&aelig;, &amp; fer&egrave; eadem cum ea. </s>
          <s id="s.004307">&longs;ciendum. </s>
          <s id="s.004308">n. </s>
          <s id="s.004309">Mu&longs;icos docere <lb/>
voces omnes <expan abbr="v&longs;q;">v&longs;que</expan> ad &longs;eptem e&longs;&longs;e ab inuicem differentes, &amp; diuer&longs;&aelig; natur&aelig; <lb/>c&ugrave;m autem ad octauam ventum e&longs;t, tunc redire voces iterum eiu&longs;dem na&shy;<lb/>
tur&aelig;, &amp; fer&egrave; e&aelig;dem cum pr&aelig;cedentibus: ita vt octaua &longs;it eadem cum pri&shy;<lb/>
ma, &amp; nona cum &longs;ecunda, &amp; decima cum tertia, &amp; &longs;ic de reliquis, qu&aelig; om&shy;<lb/>
nes di&longs;tant per octonarium, &longs;ine &longs;unt octau&aelig;. </s>
          <s id="s.004310"><expan abbr="dicebantur&qacute;">dicebanturque</expan>; huiu&longs;modi voces <lb/>
Antiphon&aelig;, qua&longs;i contra&longs;onantes, vel vici&longs;&longs;im &longs;onantes &lpar;vide infra annota&shy;<lb/>
ta in 14. Probl.&rpar; quarum vox grauior, c&ugrave;m dupla &longs;it, acutioris edit &longs;onum, <lb/>
qui duplus e&longs;t &longs;oni acutioris, &longs;iue qui bis in &longs;e continet <expan abbr="&longs;on&utilde;">&longs;onum</expan> acutioris. </s>
          <s id="s.004311">Qua&shy;<lb/>
re relicta hypate, &amp; dempta nete, quarum illa e&longs;t huius dupla, nihil fer&egrave; ad&shy;<lb/>
emptum fui&longs;&longs;e videbatur, c&ugrave;m &longs;onus nete contineretur in &longs;ono hypates. </s>
          <s id="s.004312">hac <lb/>
igitur de cau&longs;a veteres illi netem potius, quam hypatem omi&longs;erunt. </s>
          <s id="s.004313">pr&aelig;te&shy;<lb/>
rea dici pote&longs;t, eos hypatem potius retinui&longs;&longs;e, quia c&ugrave;m remi&longs;&longs;ior &longs;it, fa&shy;<lb/>
cilius cantatur; Nete autem c&ugrave;m acuti&longs;&longs;ima &longs;it maiore vi, vt cantetur, <lb/>
opus habet.</s>
        </p>
        <p type="main">
          <s id="s.004314"><arrow.to.target n="marg356"/></s>
        </p>
        <p type="margin">
          <s id="s.004315"><margin.target id="marg356"/>364</s>
        </p>
        <p type="main">
          <s id="s.004316">Probl. 8. <emph type="italics"/>&lpar;Cur grauis &longs;onum pote&longs;t acut&aelig;? </s>
          <s id="s.004317">An quia maius e&longs;t; etenim quemad&shy;<lb/>
modum graue obtu&longs;o, &longs;ic acutum acuto angulo &longs;imile e&longs;t&rpar;<emph.end type="italics"/> Ex intelligentia pr&aelig;&shy;<lb/>cedentis problematis, pr&aelig;&longs;ens fatis fer&egrave; clarum e&longs;t: im&ograve; ex illo ortum i&longs;tud <lb/>
e&longs;&longs;e videtur. </s>
          <s id="s.004318">qu&aelig;rit, cur vox grauior po&longs;&longs;it vocem acutiorem, &longs;iu&egrave; illi &aelig;qui&shy;<lb/>
ualeat, vt dictum e&longs;t, in pr&aelig;cedenti de Antiphonis. </s>
          <s id="s.004319">cau&longs;a e&longs;t, inquit, quia <lb/>grauis maior e&longs;t, qu&agrave;m acuta; grauis enim oritur &agrave; maiori corpore, vt &agrave; <lb/>
chorda maiori, vt &longs;uperius apparuit; vel &agrave; maiori canna, vt patet in Orga&shy;<lb/>
nis. </s>
          <s id="s.004320">voces autem, &amp; &longs;oni eandem habent cum corporibus &longs;onantibus pro&shy;<lb/>
portionem. </s>
          <s id="s.004321">quare grauis &longs;onus maior e&longs;t acuto; <expan abbr="c&utilde;">cum</expan> igitur maior &longs;it, eum in <lb/>
&longs;e continebit, <expan abbr="eum&qacute;">eumque</expan>; poterit. </s>
          <s id="s.004322">e&longs;t enim grauis &longs;onus &longs;imilis angulo obtu&longs;o, &amp; <lb/>
acutus &longs;onus &longs;imilis acuto angulo: obtu&longs;us autem angulus maior e&longs;t acuto, <lb/>
<expan abbr="eum&qacute;">eumque</expan>; in &longs;e continet. </s>
          <s id="s.004323"><expan abbr="eum&qacute;">eumque</expan>; propterea pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004324"><arrow.to.target n="marg357"/></s>
        </p>
        <p type="margin">
          <s id="s.004325"><margin.target id="marg357"/>365</s>
        </p>
        <p type="main">
          <s id="s.004326">Probl. 9. <emph type="italics"/>&lpar;Cur &longs;olitarias cantilenas &longs;uauius audire &longs;olemus, &longs;i ad tybiam, aut <lb/>ad lyram vnam cantatur, c&ugrave;m tamen ad fides, canticumqu&eacute; idem, modo <expan abbr="vtroq;">vtroque</expan> per&shy;<lb/>
agatur? </s>
          <s id="s.004327">nam &longs;i idem ita amplius fit, plus ad plures tibias, <expan abbr="atq;">atque</expan> etiam &longs;uauius e&longs;&longs;e<emph.end type="italics"/> <pb pagenum="253" xlink:href="009/01/253.jpg"/><emph type="italics"/>oportet? </s>
          <s id="s.004328">An quoniam manife&longs;tior e&longs;t &longs;copus eius, c&ugrave;m ad vnam lyram, vel tibiam <lb/>
cantatur? </s>
          <s id="s.004329">ad plures ver&ograve; &longs;uauitas &longs;eruari non pote&longs;t, c&ugrave;m cantilena offu&longs;cetur, te&shy;<lb/>
taqu&eacute; pen&egrave; deleatur&rpar;<emph.end type="italics"/> Cur &longs;olitari&aelig; cantilen&aelig; &lpar;quas Gr&aelig;ci Monodias appella&shy;<lb/>
bant, &amp; ab vna tantum per&longs;ona cantabantur&rpar; &longs;uauiores &longs;unt, &longs;i ad lyram <lb/>
vnam, vel ad tibiam vnam, quam &longs;i ad plures lyras, aut tibias accinantur; <lb/>c&ugrave;m tamen vtroque modo, ide&longs;t tam ad lyram, qu&agrave;m ad tibiam, &amp; tam ad <lb/>
vnam, qu&agrave;m ad plures idem canticum per&longs;onetur. </s>
          <s id="s.004330">&amp; c&ugrave;m idem canticum <lb/>
ad plures lyras, aut tibias decantatum in maius exere&longs;cat, deberet etiam <lb/>
&longs;uauius auribus accidere. </s>
          <s id="s.004331">Re&longs;pondet fort&egrave; monodiam iucundiorem e&longs;&longs;e ad <lb/>vnum in&longs;trumentum, quia ip&longs;ius &longs;copus tunc manife&longs;tior e&longs;t: pluribus au&shy;<lb/>
tem adhibitis in&longs;trumentis &longs;uauitas &longs;eruari nequit, c&ugrave;m cantilena tot &longs;onis <lb/>
offu&longs;cetur, ac tota pen&egrave; obruatur. </s>
          <s id="s.004332">Verumenimuer&ograve; vtinam recentiores Mu&shy;<lb/>
&longs;ic&aelig; contrapunti&longs;t&aelig;, i&longs;ta, qu&aelig; hoc loco ab Ari&longs;t tradita &longs;unt rit&egrave; animad&shy;<lb/>
uertent. </s>
          <s id="s.004333">non <expan abbr="vtiq;">vtique</expan> tanta verborum, <expan abbr="atq;">atque</expan> rithmorum confu&longs;ione, <expan abbr="atq;">atque</expan> pluri&shy;<lb/>
morum in&longs;trumentorum &longs;trepitu gauderent: ex quibus eorum cantilena ita <lb/>
offu&longs;catur, vt nulla omnin&ograve; reddatur; <expan abbr="&longs;olus&qacute;">&longs;olusque</expan>; &longs;trepitus quidam ingens aures <lb/>
obtundat; quem modum non &longs;ine huius &aelig;tatis dedecore, futura &longs;ecula non <lb/>
&longs;ine irri&longs;ione mirabuntur: non aliter, ac nos &longs;emipri&longs;c&aelig; &aelig;tatis architectu&shy;<lb/>
ram, &amp; &longs;culpturam irridere &longs;olemus.</s>
        </p>
        <p type="main">
          <s id="s.004334"><arrow.to.target n="marg358"/></s>
        </p>
        <p type="margin">
          <s id="s.004335"><margin.target id="marg358"/>366</s>
        </p>
        <p type="main">
          <s id="s.004336">Probl. 10. &longs;atis clarum ex &longs;e. </s>
          <s id="s.004337">illud &longs;olum notatione dignum e&longs;t, Teretiza&shy;<lb/>
re, quod e&longs;t canere, vt modo aiunt, non verba, &longs;ed notas, fui&longs;&longs;e idem, quod <lb/>nunc &longs;olmifationem, aut lalagen decantare.</s>
        </p>
        <p type="main">
          <s id="s.004338"><arrow.to.target n="marg359"/></s>
        </p>
        <p type="margin">
          <s id="s.004339"><margin.target id="marg359"/>367</s>
        </p>
        <p type="main">
          <s id="s.004340">Probl. 11. <emph type="italics"/>&lpar;Cur vox, aut &longs;onus de&longs;inens acutoir fit? </s>
          <s id="s.004341">An quia minor, vt qu&aelig; fa&shy;<lb/>
cta &longs;it imbecillior?&rpar;<emph.end type="italics"/> lege qu&aelig; in probl. </s>
          <s id="s.004342">8. annotata &longs;unt, &amp; huic quoque &longs;atis&shy;<lb/>
factum erit.</s>
        </p>
        <p type="main">
          <s id="s.004343"><arrow.to.target n="marg360"/></s>
        </p>
        <p type="margin">
          <s id="s.004344"><margin.target id="marg360"/>368</s>
        </p>
        <p type="main">
          <s id="s.004345">Probl. 12. <emph type="italics"/>&lpar;Quamobrem qu&aelig; grauior &egrave; fidibus eft &longs;emper modulationem, aut <lb/>
cantilenam &longs;u&longs;cipit: nam &longs;i oporteat canere parame&longs;en c&ugrave;m &longs;ola me&longs;e, nihilominus <lb/>
medium gignetur: &longs;i ver&ograve; me&longs;en, nece&longs;&longs;arium ambo, &longs;ola non gignitur? </s>
          <s id="s.004346">An quia <lb/>
graue magnum e&longs;t, itaque validius: &amp; in magno paruum ine&longs;i. </s>
          <s id="s.004347">&amp; per interceptio&shy;<lb/>
nem du&aelig; net&aelig; ex hypate fiunt&rpar;<emph.end type="italics"/> Vt facil&egrave; pr&aelig;&longs;ens problema intelligatur, ha&shy;<lb/>
bendus e&longs;t ob oculos ordo antiquarum chordarum, quem &longs;upra ante pro&shy;<lb/>
blema tertium expo&longs;ui. </s>
          <s id="s.004348">Qu&aelig;rit cur fidicines &longs;olerent modulationem tam <lb/>
cum cautu, qu&agrave;m &longs;ine cantu &agrave; graui&longs;&longs;ima omnium chordarum exordiri:<lb/>
ide&longs;t primam omnium graui&longs;&longs;imam chordam pul&longs;are; vt ip&longs;a reliquis acu&shy;<lb/>
tioribus, qua&longs;i dux pr&aelig;iret, quam reliqu&aelig; &longs;equerentur: &amp; &longs;i oporteat cane&shy;<lb/>
re parame&longs;en vn&agrave; c&ugrave;m me&longs;e, qu&aelig; grauior e&longs;t, gignitur, non &longs;onus parame&shy;<lb/>
&longs;es, &longs;ed ip&longs;ius me&longs;es redditur. </s>
          <s id="s.004349">&longs;i ver&ograve; oporteat canere me&longs;en, id non pote&longs;t <lb/>
fieri per &longs;olam parame&longs;en, &longs;ed <expan abbr="vtraq;">vtraque</expan> nece&longs;&longs;aria e&longs;t, vel &longs;altem ip&longs;a me&longs;e. <lb/>
</s>
          <s id="s.004350">Ratio huius, inquit, e&longs;t, quia quod graue e&longs;t, magnum e&longs;t, &amp; proinde acuto <lb/>
etiam validius. </s>
          <s id="s.004351">pr&aelig;terea in magno etiam paruum ine&longs;t: grauior igitur vox <lb/>
maior e&longs;t, ac validior, qu&agrave;m acuta, vt &longs;uperius explicatum e&longs;t; merit&ograve; igi&shy;<lb/>
tur &longs;onus grauior pr&etail;ire debet, <expan abbr="atq;">atque</expan> ad modulationem alios prouocare, c&ugrave;m <lb/>
reliquas &longs;ecum tanquam partes proprias naturaliter trahat. </s>
          <s id="s.004352">quando autem <lb/>
parame&longs;e, ac me&longs;e &longs;imul canuntur, tunc me&longs;e &longs;ola videtur exaudiri; quia <lb/>
c&ugrave;m ip&longs;a grauior &longs;it, qu&agrave;m parame&longs;e, erit etiam ip&longs;a maior, ac validior, &amp; <lb/>propterea &longs;onus parame&longs;es in &longs;ono me&longs;es euane&longs;cit, &longs;iue &longs;uperuacaneus e&longs;t,<pb pagenum="254" xlink:href="009/01/254.jpg"/>At ver&ograve; &longs;ola parame&longs;e nequit pr&aelig;ter proprium &longs;onum, etiam &longs;onum me&longs;es <lb/>
efficere; quia c&ugrave;m parame&longs;e &longs;it acutior, qu&agrave;m me&longs;e, vt patet ex pr&aelig;ceden&shy;<lb/>
tibus, erit etiam ip&longs;a minor, ac imbecillior: idcirc&ograve; ad &longs;onum me&longs;es effi&shy;<lb/>
ciendum, aut me&longs;e cum parame&longs;e, aut &longs;altem &longs;ola me&longs;e nece&longs;&longs;aria e&longs;t. </s>
          <s id="s.004353">qu&ograve;d <lb/>
autem grauior &longs;onus &longs;it acuto maior, hinc patet, quia du&aelig; net&aelig; in hypate <lb/>
continentur; &longs;i enim &longs;onus hypates bifariam diuidatur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i flatus ex ali&shy;<lb/>
qua graui&longs;&longs;ima canna exiens ita intercipiatur, vt medius tantum per can&shy;<lb/>
nam effletur, fit &longs;onus ex hypate nete, ex dimidio nimirum flatu hypates fit <lb/>
nete; idem patet in chordis, quia dimidium alicuius chord&aelig;, vt &longs;upra pa&shy;<lb/>
tuit, ad totam, e&longs;t nete ad hypatem. </s>
          <s id="s.004354">du&aelig; igitur nete in hypate continentur <lb/>
<emph type="italics"/>&lpar;Cantilenam &longs;u&longs;cipit&rpar;<emph.end type="italics"/> ide&longs;t &longs;oliti erant ad grauiorem vocem canere. </s>
          <s id="s.004355">hic e&longs;t <lb/>
fort&egrave; &longs;en&longs;us Ari&longs;totelis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004356"><arrow.to.target n="marg361"/></s>
        </p>
        <p type="margin">
          <s id="s.004357"><margin.target id="marg361"/>369</s>
        </p>
        <p type="main">
          <s id="s.004358">Problema 13. <emph type="italics"/>&lpar;Cur in con&longs;onantia Diapa&longs;on graue quidem acuti antiphonum <lb/>
accipi potest; grauis ver&ograve; acutum non pote&longs;t? </s>
          <s id="s.004359">An maxim&egrave;, quia in vtroque mo&shy;<lb/>
dus <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> contentus est? </s>
          <s id="s.004360">Sed &longs;i minus, cert&egrave; in graui acutum e&longs;t, maius enim <lb/>
graue e&longs;t&rpar;<emph.end type="italics"/> Cur inquit, ex duobus &longs;onis, qui Diapa&longs;on efficiant, grauis qui&shy;<lb/>
dem habet in &longs;e Antiphonum acuti, ide&longs;t, in &longs;e continet etiam acutum: at <lb/>
ver&ograve; acutus non habet antiphonum grauis, ide&longs;t non continet in &longs;e grauem. <lb/>
</s>
          <s id="s.004361">Ratio e&longs;t, inquit, quia in <expan abbr="vtraq;">vtraque</expan> continetur &longs;onus, &longs;eu modus <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> qua&shy;<lb/>
tenus voces huius con&longs;onanti&aelig; &longs;unt eiu&longs;dem natur&aelig;, vt in 7. Probl. dictum <lb/>
e&longs;t. </s>
          <s id="s.004362">Sed melius e&longs;t Dicere, quia in graui tanquam in magno acutum veluti <lb/>
paruum includitur, vt paul&ograve; ante fu&longs;ius explicatum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004363"><arrow.to.target n="marg362"/></s>
        </p>
        <p type="margin">
          <s id="s.004364"><margin.target id="marg362"/>370</s>
        </p>
        <p type="main">
          <s id="s.004365">Problema 14. <emph type="italics"/>&lpar;Cur Antiphon&ubreve;m con&longs;onanti&aelig; Diapa&longs;on ita latitat, vt vni&longs;onum <lb/>
e&longs;&longs;e videatur, veluti in Punico, aut homine? </s>
          <s id="s.004366">Qu&aelig; <expan abbr="namq;">namque</expan> po&longs;ita in acutis &longs;unt, non <lb/>
vni&longs;ona, &longs;ed ex proportione &longs;ibi Diapa&longs;on concinentia re&longs;pondent? </s>
          <s id="s.004367">An modus pro&shy;<lb/>
portionis facit, vt &longs;onus qua&longs;i <expan abbr="id&etilde;">idem</expan> e&longs;&longs;e appareat? </s>
          <s id="s.004368">Proportio. </s>
          <s id="s.004369">n. </s>
          <s id="s.004370">in &longs;onis &aelig;qualitas e&longs;t; <lb/>
a quale autem omne ad vnitatem <expan abbr="refer&etilde;dum">referendum</expan> e&longs;t. </s>
          <s id="s.004371">hoc idem in fi&longs;tolis etiam euenit, vt <lb/>
falli aures po&longs;&longs;int&rpar;<emph.end type="italics"/> Qu&aelig;nam &longs;int voces Antiphon&aelig; in 7. Probl. dictum e&longs;t. </s>
          <s id="s.004372">quod <lb/>
ad textum attinet pro verbo, atropo, quod in Gaz&aelig; translatione legitur, <lb/>
repo&longs;ui, Homine, Gr&aelig;c&egrave; enim e&longs;t, <foreign lang="greek">anqrwpw&verbar;,</foreign> ex quo fort&egrave; mendos&egrave; factum <lb/>
e&longs;t illud, atropo. </s>
          <s id="s.004373">quod quid &longs;ibi velit, nu&longs;quam reperitur: Verbum pr&aelig;te&shy;<lb/>
rea Punicum, puto &longs;ignificare in&longs;trumentum aliquod mu&longs;icum Ph&etail;nicibus <lb/>
v&longs;itatum, vel ab eis repertum, Gr&aelig;c&egrave; enim legitur in <foreign lang="greek">foi/nikw&verbar;</foreign>. His pr&aelig;mi&longs;&shy;<lb/>
&longs;is, qu&aelig;ritur, cur Antiphonum, ide&longs;t vocum corri&longs;pondentia in Diapa&longs;on <lb/>
ita latitat, vt non du&aelig; voces differentes, &longs;ed du&aelig; vni&longs;on&aelig;, fiue vni&longs;onum <lb/>
videatur? </s>
          <s id="s.004374">vt manife&longs;t&egrave; audire e&longs;t in in&longs;trumento Punico, &amp; in humana voce? <lb/>
</s>
          <s id="s.004375">Dubitationis cau&longs;a e&longs;t, quia voces acut&aelig; nullo modo cum grauioribus &longs;ibi <lb/>
Antiphonis vni&longs;on&aelig; &longs;unt, &longs;ed per octo voces ab illis in acutum di&longs;tant.</s>
        </p>
        <p type="main">
          <s id="s.004376">Re&longs;pondet modum proportionis, ide&longs;t duplam proportionem, qu&aelig; inter <lb/>
huiu&longs;modi voces reperitur in cau&longs;a e&longs;&longs;e, vt voces ill&aelig; videantur vni&longs;on&aelig;. </s>
          <s id="s.004377">e&longs;t <lb/>
enim proportio dupla &lpar;qu&aelig; forma ip&longs;ius Diapa&longs;on e&longs;t&rpar; &longs;implici&longs;sima, &amp; pri&shy;<lb/>
ma inter omnes mu&longs;icales proportiones. </s>
          <s id="s.004378">dupla enim proportio e&longs;t omnium <lb/>
prima, ac &longs;implici&longs;&longs;ima, reliqu&aelig; enim, vt &longs;unt tripla, &longs;elquialtera, &longs;e&longs;qui&shy;<lb/>
tertia, &amp; huiu&longs;modi ali&aelig;, &longs;unt ip&longs;a compo&longs;itiores. </s>
          <s id="s.004379">In dupla enim propor&shy;<lb/>
tione altera quantitas diuiditur tantum bifariam, vt &longs;uperius patuit: diui&longs;io <lb/>porr&ograve; bifariam, &longs;iue in partes &aelig;quales e&longs;t prima <expan abbr="omni&utilde;">omnium</expan>, quia magis ad vni&shy;


<pb pagenum="255" xlink:href="009/01/255.jpg"/><expan abbr="tate&etilde;">tatem</expan>, siue ad indiui&longs;um, &amp; ad &aelig;quale accedit, c&ugrave;m in partes &aelig;quas diuidat: <lb/>
&amp; c&ugrave;m ad eam opus &longs;it unica tantum diuisione. </s>
          <s id="s.004380">In alijs proportionalibus, vt <lb/>
in tripla, opus e&longs;t duabus diui&longs;ionibus, vt supra patuit: &longs;imiliter in alijs, &longs;e&longs;&shy;<lb/>
quialtera, &longs;e&longs;quitertia, opus e&longs;t pluribus diui&longs;ionibus: c&ugrave;m igitur ip&longs;a pr&aelig;&shy;<lb/>c&aelig;teris magis ad &aelig;qualitatem, &amp; vnitatem accedat, facit,vt voces ip&longs;ius <lb/>videantur fer&egrave; &aelig;quales, hoc e&longs;t fer&egrave; e&aelig;dem, &amp; vni&longs;on&aelig;, &amp; eiu&longs;dem natur&aelig;: <lb/>id, quod etiam in  &longs;i&longs;stolis ade&ograve; verum e&longs;t, vt aliquando aures decipiant, c&ugrave;m <lb/>nimirum aures iudicent duas fi&longs;stulas e&longs;&longs;e aut vnam tantum, aut duas vni&shy;<lb/>
&longs;onas, qu&aelig; tamen re vera &longs;unt in con&longs;onantia Diapa&longs;on.<arrow.to.target n="marg363a"/></s>
        </p>
        <p type="margin">
          <s id="s.004381"><margin.target id="marg363a"/>371</s>
        </p>
        <p type="main">
          <s id="s.004382">Probl. 15 &lpar;Cur genus cantilen&aelig;, quod lex apellatum e&longs;t non per anti&longs;trophos <lb/>
olim agebatur, c&ugrave;m tamen c&aelig;teris chorici canticis anti&longs;trophi v&longs;us non dee&longs;&longs;et? <lb/>
</s>
          <s id="s.004383">An quod olim leges &agrave; certatoribus, &amp; pugilibus agebantur, qui c&ugrave;m iam egregi&egrave; <lb/>
imitari, <expan abbr="valenterq&qacute;">valenterque</expan>; pertendere po&longs;&longs;ent, cantum prolixum, ac varium efficiebant <lb/>
<expan abbr="itaq&qacute;">itaque</expan> vt verba, ita etiam moduli, <expan abbr="numeriq&qacute;">numerique</expan> vari&egrave; &longs;ubinde imitationem in&longs;equeban&shy;<lb/>
tur; imitari <expan abbr="namq&qacute;">namque</expan> modulamine potius, quam vocabulis nece&longs;&longs;e e&longs;t. </s>
          <s id="s.004384">Quamobrem <lb/>
dithryambi etiam po&longs;teaquam imitari coeperunt, anti&longs;trophis amplius non vtuntur <lb/>
quamquam plurimum ante vterentur. </s>
          <s id="s.004385">Cuius rei cau&longs;a e&longs;t, quod olim homines li&shy;<lb/>
beri, atque ingenui &longs;olebant ip&longs;i tripudiare, atque choreas ducere: &iuml;taque multos <lb/>
e&longs;&longs;e, qui certatorio cantu fungi po&longs;&longs;ent, erat difficile: quapropter illis in more fue&shy;<lb/>
rat, vt modulos enharmonios cantarent. </s>
          <s id="s.004386">Vnus enim crebr&ograve; cantilenam mutare, <lb/>
<expan abbr="variamq&qacute;">variamque</expan>, contexere facilius pote&longs;t, qu&agrave;m multi; &amp; certator, qu&agrave;m qui mores con&shy;<lb/>
&longs;eruat: quocirca &longs;implicius illi modulari debuerant. </s>
          <s id="s.004387">Anti&longs;trophus autem simplex <lb/>
e&longs;t, e&longs;t enim numerus, &amp; ab vno men&longs;uratur: h&aelig;c eadem causa e&longs;t, cur in &longs;cena nul&shy;<lb/>
li &longs;int anti&longs;trophi: in choro ver&ograve; maxim&egrave;. </s>
          <s id="s.004388">Hi&longs;trio namque &longs;imul &amp; certator, &amp; <lb/>
imitator e&longs;t: chorus ver&ograve; minus imitatur&rpar; </s>
          <s id="s.004389">Cur cantilen&aelig; qu&aelig;dam antiquitus <lb/>
leges apellarentur, infra Probl. 28. explicabitur. </s>
          <s id="s.004390">Anti&longs;trophon hoc loco <lb/>
&longs;umitur pro &longs;tropha, &longs;troph&aelig; autem nihil aliud &longs;unt, qu&agrave;m Odarum partes <lb/>
ill&aelig; &longs;ibi numer&ograve;, &amp; genere carminum con&longs;imiles, ex quibus tota ode <expan abbr="co&ntilde;">con&longs;tat</expan>. <lb/>
 </s>
          <s id="s.004391">Dithryambi erant hymni in honorem Bacchi decantari &longs;oliti. </s>
          <s id="s.004392">Tandem, vt <lb/>
intelligamus quidnam e&longs;&longs;ent modi enharmonij, sciendum e&longs;t veteres illos <lb/>
Mu&longs;icos tria totius mu&longs;ic&aelig; genera feci&longs;&longs;e, <expan abbr="Diatonicu&utilde;">Diatonicum</expan>, Chromaticum, Enhar&shy;<lb/>
monicum. </s>
          <s id="s.004393">qu&aelig; genera ab invicem di&longs;tinguebantur, &longs;ecundum variam Te&shy;<lb/>
trachordorum <expan abbr="co&ntilde;">con&longs;titutionem</expan>; ex tetrachordis enim totam &longs;eriem, &longs;eu Mo&shy;<lb/>
nochordium, &longs;eu regulam harmonicam componebant. </s>
          <s id="s.004394">Erat autem tetra&shy;<lb/>
chordum intervallum Diate&longs;&longs;aron, con&longs;tans ex quatuor chordis, &longs;eu voci&shy;<lb/>
bus, vt, re, mi, fa; <expan abbr="quaru&utilde;">quarum</expan> vocum interualla vnius tetrachordi generis, vnius, <lb/>
differebant ab interuallis alterius tetrachordi alterius generis, v.g. in ge&shy;<lb/>nere Diatonico erat huiu&longs;modi tetra chordium, cuius primum interualllum <lb/>
<figure id="id.009.01.255.1.jpg" place="text" xlink:href="009/01/255/1.jpg"/>erat &longs;emitonium, reliqua ver&ograve; duo erant to&shy;<lb/>
ni.  </s>
          <s id="s.004395">&amp; &agrave; prima voce Hypate, ad vltimam Me&shy;<lb/>
&longs;en, erat con&longs;onantia Diate&longs;&longs;eron huic tetra&shy;<lb/>
chordo addebant aliud &longs;imile, mediante tono <lb/>
vno inter vtrunque: ita vt ex duobus confla&shy;<lb/>
retur tota diapa&longs;on &agrave; gravi hypate, ad &longs;upre&shy;<lb/>
mam Neten. </s>
          <s id="s.004396">his interuallis, ac tetrachordis <lb/>in genere Diatonico cantabatur. Genus ver&ograve; <pb pagenum="256" xlink:href="009/01/256.jpg"/><figure id="id.009.01.256.1.jpg" place="text" xlink:href="009/01/256/1.jpg"/><lb/>
<expan abbr="chromatic&utilde;">chromaticum</expan> inter chordas &longs;ui tetrachor&shy;<lb/>
di <expan abbr="&longs;equ&etilde;tia">&longs;equentia</expan> interualla &longs;eruabat. </s>
          <s id="s.004397"><expan abbr="trihemi-toni&utilde;">trihemi&shy;<lb/>
tonium</expan> autem interuallum ex tribus &longs;emi&shy;<lb/>
tonijs con&longs;tabat, &longs;eu ex vno toto, &amp; vno <lb/>
&longs;emitonio ex duobus huiu&longs;modi tetra&shy;<lb/>
chordis &longs;uum monochordium, &longs;eu &longs;uas <lb/>
octo voces, &longs;eu &longs;uam Diapa&longs;on genus <lb/>
chromaticum componebat. </s>
          <s id="s.004398">Enharmo&shy;<lb/>
nicum tandem genus tetrachordo vtebatur, cuius interualla erant ea, qu&aelig; <lb/>
&longs;equuntur.</s>
        </p>
        <figure id="id.009.01.256.2.jpg" place="text" xlink:href="009/01/256/2.jpg"/>
        <p type="main">
          <s id="s.004399">Erat hic etiam inter hypate, &amp; Me&longs;e Diate&longs;&longs;aron; huic aliud tetrachor&shy;<lb/>
dum pariter addebatur, vt in alijs generibus, ex quibus tota Diapa&longs;on <expan abbr="c&otilde;-flabatur">con&shy;<lb/>
flabatur</expan>. </s>
          <s id="s.004400">Huiu&longs;cemodi igitur tetrachordis <expan abbr="vnumquodq;">vnumquodque</expan> genus &longs;uum &longs;y&longs;te&shy;<lb/>
ma, &longs;iue <expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> Diapa&longs;on componebat, <expan abbr="add&etilde;do">addendo</expan> priori tetrachordo <lb/>
aliud <expan abbr="tetrachord&utilde;">tetrachordum</expan>, ita vt Me&longs;e vltima chorda primi tetrachordi, c&ugrave;m Nete <lb/>
vltima &longs;ecundi tetrachordi Diapente re&longs;onaret; prima ver&ograve; hypate, c&ugrave;m <lb/>
vltima Nete Diapa&longs;on efficerent, vt &longs;uperius in &longs;erie Lychaonis videre e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004401">Ex quibus patet quinam e&longs;&longs;ent enharmonij moduli, &longs;iue interualla, qui&shy;<lb/>
bus enharmonium genus decantaretur. </s>
          <s id="s.004402">Sciendum pr&aelig;terea ex lib. 3. Mu&longs;i&shy;<lb/>
corum Ptol. <!-- REMOVE S-->modulos enharmonios fui&longs;&longs;e graues, &amp; &longs;eueros, vt idcirco Do&shy;<lb/>
rien&longs;es, quorum modi grauitate, ac &longs;eueritate pr&aelig;diti erant, ip&longs;is maxim&egrave; <lb/>
delectarentur. </s>
          <s id="s.004403">Vnde etiam patere pote&longs;t enharmonios modos minim&egrave; cer&shy;<lb/>tatorijs canticis idoneos fui&longs;&longs;e. </s>
          <s id="s.004404">His pr&aelig;mi&longs;&longs;is, &longs;ic textum facil&egrave; exponere <lb/>
e&longs;t: cur cantilen&aelig; genus illud, quod lex appellatur, non per anti&longs;trophos, <lb/>
&longs;eu &longs;trophas olim agebatur, c&ugrave;m tamen c&aelig;teris chor&etail;arum, ac chori can&shy;<lb/>
ticis anti&longs;trophi, &longs;eu &longs;troph&aelig; non dee&longs;&longs;ent. </s>
          <s id="s.004405">Ratio huius for&longs;itan h&aelig;c e&longs;t; <lb/>
quia v&longs;us anti&longs;trophorum, &longs;eu &longs;tropharum eundem &longs;emper modum per to&shy;<lb/>
tam cantilenam &longs;eruat, c&ugrave;m cantilena con&longs;tet ex pluribus &longs;trophis &longs;ibi &longs;i&shy;<lb/>
milibus: quapropter &longs;tropharum v&longs;us maxim&egrave; ei conuenit, qui <expan abbr="eund&etilde;">eundem</expan> &longs;em&shy;<lb/>
per morem in cantando retinet, &egrave; contra ver&ograve; ei, qui varios mores, <expan abbr="vari&utilde;&qacute;">variunque</expan>; <lb/>
<expan abbr="cant&utilde;">cantum</expan> &longs;tudet efficere minim&egrave; quadrat: talis enim non indiget &longs;tatutis &longs;tro&shy;<lb/>
phis, nec rithmis, vt &longs;unt od&aelig;, &longs;ed potius carmine libero, vt &longs;unt heroica <lb/>
poemata hexametris ver&longs;ibus contexta. </s>
          <s id="s.004406">quia igitur olim certatores, ac pu&shy;<lb/>
giles, qui viribus pollebant, <expan abbr="qui&qacute;">quique</expan>; egregi&egrave; varios mores imitabantur; c&ugrave;m <lb/>
cantum varium, ac prolixum, intentum, ac remi&longs;&longs;um efficere valerent, hu&shy;<lb/>
iu&longs;modi leges decantabant, propterea nullis &longs;trophis vtebantur, vt &longs;cilicet <lb/>
facilius in omnes partes po&longs;&longs;et vox, &amp; cantus excurrere. </s>
          <s id="s.004407"><expan abbr="Itaq;">Itaque</expan> vt verba, ita <lb/>etiam modulos, ac numeros, prout imitatio requirebat, &longs;ubinde varios red&shy;<lb/>
debant; modulatione enim melius, quam verbis ip&longs;is imitatio perficitur.


<pb pagenum="257" xlink:href="009/01/257.jpg"/>hac eadem de cau&longs;a hymni Dithyrambici, po&longs;tquam ad imitationem adhi&shy;<lb/>
beri c&oelig;perunt, vt liberius imitationi in&longs;eruirent, &longs;trophis, quibus antea, <lb/>plurimum abundabant, priuati &longs;unt. </s>
          <s id="s.004408">cur autem olim &longs;trophas habuerint, <lb/>
quibus modo carent, cau&longs;a e&longs;t, quia olim nobiles viri &longs;olebant ip&longs;i choros, <lb/>
<expan abbr="choreas&qacute;">choreasque</expan>; adire, <expan abbr="atq;">atque</expan> in ip&longs;is tripudiare, ac canere; chori autem, &amp; chore&aelig; <lb/>
&longs;trophas &longs;emper habuerunt, in choris enim eundem &longs;emper morem, ac mo&shy;<lb/>
dum, rithmumu&egrave; con&longs;eruant; quapropter difficile erat inuenire multos, qui <lb/>
certatorio, ac vario &longs;emper cantu, <expan abbr="varia&qacute;">variaque</expan>; imitatione decantarent: talis <lb/>
enim cantus &longs;trophas reijcit: eadem de cau&longs;a modulos enharmonios vte&shy;<lb/>
bantur in &longs;uis canticis, quippe qui graues, ac &longs;eueri erant, <expan abbr="neq;">neque</expan> idonei va&shy;<lb/>
rijs rationibus, ac moribus. </s>
          <s id="s.004409">vnus enim, vt accidit in cantu certatorio can&shy;<lb/>
tilenam facilius pro libito in omnes partes immutare pote&longs;t, qu&agrave;m multi, <lb/>
vt &longs;olent e&longs;&longs;e in choro. </s>
          <s id="s.004410">&amp; certator etiam facilius id pr&aelig;&longs;tat, quam qui eun&shy;<lb/>
dem &longs;emper morem, ac modum retinet, quocirca &longs;implicius, quod fit per <lb/>
&longs;trophas illi, qui in choris <expan abbr="caneb&atilde;t">canebant</expan>, modulari debuerant; &longs;tropha enim &longs;im&shy;<lb/>
plex e&longs;t, <expan abbr="vno&qacute;">vnoque</expan>; tempore, ac men&longs;ura &longs;emper eadem men&longs;uratur. </s>
          <s id="s.004411">h&aelig;c eadem <lb/>cau&longs;a e&longs;t, cur in &longs;cena nullus, vbi vari&aelig; imitationes aguntur, in choro ver&ograve;, <lb/>
vbi &longs;emper eodem tenore proceditur, plurimus &longs;tropharum v&longs;us &longs;it: Hi&longs;trio <lb/>
namque, qu&igrave; in &longs;cena agit, &amp; certator, &amp; imitator &longs;imul e&longs;t; chorus autem <lb/>
minus imitatur, hoc e&longs;t &longs;implici, <expan abbr="atq;">atque</expan> vniformi &longs;emper imitatione procedit.</s>
        </p>
        <p type="main">
          <s id="s.004412"><arrow.to.target n="marg363"/></s>
        </p>
        <p type="margin">
          <s id="s.004413"><margin.target id="marg363"/>372</s>
        </p>
        <p type="main">
          <s id="s.004414">Probl. 16. <emph type="italics"/>&lpar;Qua de cau&longs;a Antiphonum &longs;uauius est &longs;ymphono? </s>
          <s id="s.004415">An quia in an&shy;<lb/>tiphono manife&longs;tior est ip&longs;a con&longs;onantia, qu&agrave;m e&ugrave;m ad &longs;ymphoniam cantatur: ne&shy;<lb/>ce&longs;&longs;e enim e&longs;t in &longs;ymphonia alteram vocem alteri vni&longs;onam e&longs;&longs;e; ita vt du&aelig; in ean&shy;<lb/>
dem coale&longs;centes altera alteram offu&longs;care po&longs;&longs;it&rpar;<emph.end type="italics"/> Per antiphonum intelligit nunc <lb/>
Ari&longs;t. con&longs;onantiam ex vocibus <expan abbr="differ&etilde;tibus">differentibus</expan> conflatam, cuiu&longs;modi e&longs;t Dia&shy;<lb/>
pa&longs;on, Diapente, &amp; Diate&longs;&longs;aron: per &longs;ymphonum intelligit con&longs;onantiam <lb/>
ex vocibus eiu&longs;dem inten&longs;ionis, &longs;iue ex vni&longs;onis. </s>
          <s id="s.004416">non me latet aliter Mu&longs;i&shy;<lb/>
cos antiphonas, &longs;ymphonas, ac homophonas accipere. </s>
          <s id="s.004417">vide Prol&aelig;m. <!-- REMOVE S-->lib. 1. <lb/>
cap. 7. harm. </s>
          <s id="s.004418">&longs;ed hoc loco ita accipiendas e&longs;&longs;e, vti dixi, manife&longs;tum e&longs;t ex <lb/>
Ari&longs;t. contextu. </s>
          <s id="s.004419">Ait igitur &longs;uauiorem e&longs;&longs;e antiphonarum con&longs;onantiam, <lb/>
quam vni&longs;onarum; quia ibi con&longs;onantia melius percipitur; nam in vocibus <lb/>vni&longs;onis, vox alteri voci con&longs;onans, eundem cum illa edit &longs;onum, ita vt du&aelig; <lb/>
in vnam, <expan abbr="eandem&qacute;">eandemque</expan>; pror&longs;us coale&longs;cant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; altera alteram offu&longs;cet, vnde <lb/>
con&longs;onantia, qu&aelig; ex pluribus con&longs;tare debet, non percipitur.</s>
        </p>
        <p type="main">
          <s id="s.004420"><arrow.to.target n="marg364"/></s>
        </p>
        <p type="margin">
          <s id="s.004421"><margin.target id="marg364"/>373</s>
        </p>
        <p type="main">
          <s id="s.004422">Probl. 17. <emph type="italics"/>&lpar;Cur &longs;ola Diapa&longs;on con&longs;onantia cantatur? </s>
          <s id="s.004423">&longs;ecundum hanc enim, &amp; <lb/>
nullam aliam magadare &longs;olent. </s>
          <s id="s.004424">An quod h&aelig;c &longs;ola ex fidibus inuicem antiphonis <lb/>
con&longs;tat? </s>
          <s id="s.004425">in antiphonis autem etiam&longs;i alteram tantum canis, idem efficies, voces <lb/>enim vtriu&longs;que chord&aelig; vna &longs;ola continet. </s>
          <s id="s.004426">ita vt in hac con&longs;onantia, quamuis vox <lb/>
vna tantum cantetur, tota tamen con&longs;onantia quodammodo canitur. </s>
          <s id="s.004427">ita vt in hac <lb/>
&longs;ymphonia, &amp; vnica voce canente, &amp; duabus, exurgat quodammodo harmonia. <lb/>
</s>
          <s id="s.004428">vel vna decantante, altera ver&ograve; per tibiam &longs;onante, veluti vnam amb&aelig;, con&longs;tituunt. <lb/>
</s>
          <s id="s.004429">propterea in &longs;ola Diapa&longs;on canere &longs;olemus, quoniam, inquam, voces antiphon&aelig; <lb/>
vnius, eiu&longs;demqu&eacute; chord&aelig; vocem obtinent&rpar;<emph.end type="italics"/> Sciendum prim&ograve; apud veteres v&longs;ui <lb/>
fui&longs;&longs;e in&longs;trumentum quoddam mu&longs;icum, quod Magadis, &amp; Magas appella&shy;<lb/>
batur, ad quod &longs;uas cantilenas canere &longs;olebant, <expan abbr="atq;">atque</expan> hoc erat <foreign lang="greek">magadi/zein</foreign><lb/>
magadi&longs;&longs;are. </s>
          <s id="s.004430">Erat autem vnius chord&aelig; tantum, vel vnius vocis, &longs;i fort&egrave; fue&shy;


<pb pagenum="258" xlink:href="009/01/258.jpg"/>rit tibia, ide&longs;t, quod vnicam vocem, &amp; non plures &longs;imul ederet, quemad&shy;<lb/>
modum refert Zarlinus; quamuis varias voces &longs;ucce&longs;&longs;iu&egrave; po&longs;&longs;et edere. </s>
          <s id="s.004431">hoc <lb/>
enim pacto ad ip&longs;um canentes, Diapa&longs;on cum ip&longs;o facil&egrave; effeci&longs;&longs;ent. </s>
          <s id="s.004432">Notan&shy;<lb/>
dum pr&aelig;terea Ari&longs;t. &longs;umere in textu Antiphonum pro &longs;ola Diapa&longs;on. <!-- KEEP S--></s>
          <s id="s.004433">Qu&aelig;&shy;<lb/>
rit igitur, cur canentes &longs;oliti &longs;int per &longs;olam Diapa&longs;on con&longs;onantiam cane&shy;<lb/>
re, quod probat ex v&longs;u Magadis, quod vulg&ograve; ad cantum adhibere &longs;olebant, <lb/>
c&ugrave;m eo enim omnes in Diapa&longs;on conueniebant. </s>
          <s id="s.004434">Cau&longs;am huius in identita&shy;<lb/>
tem, vt aiunt, <expan abbr="voc&utilde;">vocum</expan>, ex quibus Diapa&longs;on con&longs;tat, refert. </s>
          <s id="s.004435">quamuis enim non <lb/>
&longs;int vni&longs;on&aelig; du&aelig; voces octauam con&longs;tituentes, &longs;unt tamen eiu&longs;dem natur&aelig;, <lb/>
&amp; acutior, vt &longs;upra dictum e&longs;t, re&longs;pectu grauioris e&longs;t eadem cum graui, in <lb/>
acutiori vocum ordine, qua&longs;i renata. </s>
          <s id="s.004436">ob quam ade&ograve; perfectam duorum vo&shy;<lb/>
cum &longs;imilitudinem fit, vt illarum altera cantata, aut &longs;onata, altera natura&shy;<lb/>
liter ad illius pr&aelig;&longs;entiam excitetur, &amp; decantetur: vnde huiu&longs;modi voces <lb/>
mutuam obtinent altera alterius vim. </s>
          <s id="s.004437">Hinc fit, vt pa&longs;&longs;im in agris, ac pra&shy;<lb/>
tis ip&longs;i me&longs;&longs;ores, <expan abbr="atq;">atque</expan> pa&longs;tores naturalia quadam harum vocum &longs;imilitudi&shy;<lb/>
ne prouocati, &longs;olam Diapa&longs;on con&longs;onantiam &longs;uauiter &longs;imul canentes, &longs;uos <lb/>
labores f&oelig;liciter fallant.</s>
        </p>
        <p type="main">
          <s id="s.004438"><arrow.to.target n="marg365"/></s>
        </p>
        <p type="margin">
          <s id="s.004439"><margin.target id="marg365"/>374</s>
        </p>
        <p type="main">
          <s id="s.004440">Probl. 18. <emph type="italics"/>&lpar;Sed cur Solis Antiphonis vocibus hoc ine&longs;t? </s>
          <s id="s.004441">An quod &longs;ole pari in&shy;<lb/>
teruallo di&longs;tant &agrave; Me&longs;e. </s>
          <s id="s.004442">Medietas igitur &longs;imilitudinem quandam tonorum efficit, <lb/>
vt &longs;en&longs;us aurium dicat, quod eadem, &amp; quod amb&aelig; extrem&aelig;&rpar;<emph.end type="italics"/> Qu&aelig;rit cau&longs;am <lb/>
tant&aelig; &longs;imilitudinis inter voces Diapa&longs;on con&longs;tituentes, de qua &longs;imilitudi&shy;<lb/>
ne <expan abbr="dict&utilde;">dictum</expan> e&longs;t in pr&aelig;cedenti problemate: ait igitur fort&egrave; hanc &longs;imilitudinem <lb/>
inde prouenire, quod <expan abbr="vtra&qacute;">vtraque</expan>; illarum <expan abbr="duar&utilde;">duarum</expan> vocum, qu&aelig; Diapa&longs;on efficiunt, <lb/>
&aelig;quidi&longs;tat &agrave; Me&longs;e, &longs;eu Media: grauis deor&longs;um, acuta ver&ograve; &longs;ur&longs;um: quare <lb/>
tot gradus grauitatis grauis obtinebit, quot acuta acuminis, igitur &longs;imilli&shy;<lb/>
m&aelig; erunt, &amp; propterea auditus iudicat vnam e&longs;&longs;e, qu&aelig; quidem ratio iuxta <lb/>
ordinem <expan abbr="Terp&atilde;dri">Terpandri</expan>, &amp; antiquorum illius &aelig;ui nullam habet <expan abbr="difficultat&etilde;">difficultatem</expan>, c&ugrave;m <lb/>
&longs;eptem tantum fidibus, quarum media Me&longs;e erat totum <expan abbr="Monochordi&utilde;">Monochordium</expan> con&shy;<lb/>
&longs;tituerent. </s>
          <s id="s.004443">At ver&ograve; in ordine Lychaonis, &amp; po&longs;teriorum, qui octo chordas <lb/>
a&longs;&longs;umebant, aliter re &longs;e haberet.</s>
        </p>
        <p type="main">
          <s id="s.004444"><arrow.to.target n="marg366"/></s>
        </p>
        <p type="margin">
          <s id="s.004445"><margin.target id="marg366"/>375</s>
        </p>
        <p type="main">
          <s id="s.004446">Probl. 19. <emph type="italics"/>&lpar;Cur non canunt Diapente, &amp; Diate&longs;&longs;aron in Antiphonis? </s>
          <s id="s.004447">An quod <lb/>
non eadem con&longs;onandi ratio ijs ine&longs;t, qu&aelig; in Diapa&longs;on: in qua vox grauis eundem <lb/>
habet in grauitate modum, quem acuta in acumine: ita vt, &amp; eadem vox quidem, <lb/>
&amp; &longs;imul diuer&longs;a oriatur. </s>
          <s id="s.004448">At per&ograve; in Diapente, &amp; Diate&longs;&longs;aron non ita est, quam&shy;<lb/>
obrem &longs;onus vocis oppo&longs;it&aelig; non apparet; non enim e&longs;t idem&rpar;<emph.end type="italics"/> Cur in quotidia&shy;<lb/>
nis cantilenis, in quibus voces non vni&longs;on&aelig;, &longs;ed diuer&longs;&aelig;, &longs;eu antiphon&aelig; ad&shy;<lb/>
hibentur, non vtuntur vocibus Diapente, aut Diate&longs;&longs;aron re&longs;onantibus, &longs;ed <lb/>
tantum, vt antea dictum e&longs;t, Diapa&longs;on. <!-- KEEP S--></s>
          <s id="s.004449">Ratio, inquit, e&longs;t, quia inter voces <lb/>
illarum non e&longs;t tanta &longs;imilitudo, quanta in vocibus Diapa&longs;on con&longs;onanti&aelig;, <lb/>
in qua vox grauis tanta e&longs;t in grauitate, quanta acuta in acumine; &amp; proin&shy;<lb/>
de non ita naturaliter, ac facil&egrave; &longs;e produnt, &amp; canuntur, quemadmodum <lb/>
Diapa&longs;on, vbi vox altera alteram ob naturalem &longs;imilitudinem prouocat.</s>
        </p>
        <p type="main">
          <s id="s.004450"><arrow.to.target n="marg367"/></s>
        </p>
        <p type="margin">
          <s id="s.004451"><margin.target id="marg367"/>376</s>
        </p>
        <p type="main">
          <s id="s.004452">Probl. 20. <emph type="italics"/>&lpar;Cur &longs;i quis, mota Me&longs;e, alijs quamuis omnibus chordis ben&egrave; con&shy;<lb/>
&longs;onantibus, in&longs;trumento vtatur, non &longs;ol&ubreve; cum ad Me&longs;es &longs;on&ubreve; peruenerit, &longs;ed etiam <lb/>
in reliqua melodia, aures anget, modumque <expan abbr="inc&otilde;innum">incom<gap/>innum</expan> efficient: &longs;i ver&ograve; Lycha&shy;<lb/>
nos, aut alia qu&aelig;piam mota fuerit, tunc di&longs;crimen, aut inc<expan abbr="&otilde;">on</expan>cinnitas &longs;olum appare-<emph.end type="italics"/>


<pb pagenum="259" xlink:href="009/01/259.jpg"/><emph type="italics"/>bit, c&ugrave;m ip&longs;am, quis pul&longs;auerit? </s>
          <s id="s.004453">An non ratione id optima accidit? </s>
          <s id="s.004454">quandoqui&shy;<lb/>
dem optima <expan abbr="qu&aelig;q;">qu&aelig;que</expan> melodi&aelig; gratia &longs;&aelig;p&egrave; Me&longs;e vtuntur: omne&longs;que probi Poet&aelig; cre&shy;<lb/>
br&ograve; ad me&longs;en veniunt: &amp; &longs;i ab ea di&longs;ce&longs;&longs;erint, ad eam &longs;tatim reuertuntur: nec vllam <lb/>
aliam toties repetunt. </s>
          <s id="s.004455">quemadmodum igitur demptis ex oratione quibu&longs;dam con&shy;<lb/>
iunctionibus &lpar;veluti <foreign lang="greek">te\, &amp; h&rpar;/</foreign>&rpar; non e&longs;t amplius &longs;ermo gr&aelig;cus; alijs ver&ograve; detractis <lb/>nihil &longs;ermoni detrahitur; e&ograve;, quod illis vti &longs;&aelig;p&egrave; nece&longs;&longs;e e&longs;t, his ver&ograve; perrar&ograve;. </s>
          <s id="s.004456">&longs;ic <lb/>etiam &longs;onus me&longs;es e&longs;t veluti aliorum &longs;onorum coniunctio, maximeque pulchrior&ubreve;; <lb/>
propterea eius &longs;onus &longs;&aelig;pi&longs;&longs;im&egrave; a&longs;&longs;umi &longs;olet&rpar;<emph.end type="italics"/> Si quis ea, qu&aelig; initio dicta &longs;unt, pro&shy;<lb/>
b&egrave; tenuerit, facil&egrave; ad huius problematis intelligentiam perueniet; per me&shy;<lb/>
&longs;en motam intellige de &longs;uo &longs;ibi conuente &longs;tatu <expan abbr="dimot&atilde;">dimotam</expan>, &amp; ide&ograve; ab alijs chor<lb/>
dis di&longs;&longs;onantem. </s>
          <s id="s.004457">Idem qu&aelig;rit Probl. 38.</s>
        </p>
        <p type="main">
          <s id="s.004458"><arrow.to.target n="marg368"/></s>
        </p>
        <p type="margin">
          <s id="s.004459"><margin.target id="marg368"/>377</s>
        </p>
        <p type="main">
          <s id="s.004460">Probl. 21. <emph type="italics"/>&lpar;Cur qui grauius c&abreve;ntant, &longs;i ab&longs;onant deprehendi facilius po&longs;&longs;unt, qu&abreve;, <lb/>
qui cantant acutius: nec ver&ograve; &longs;ecus in rithmis accidit. </s>
          <s id="s.004461">euidentiores enim, qui pec&shy;<lb/>
cant in grauiori. </s>
          <s id="s.004462">Vtrum, qu&ograve;d plus temporis graue obtinet? </s>
          <s id="s.004463">plus autem plenius &agrave; <lb/>&longs;en&longs;u auri&ubreve;m percipi pote&longs;t. </s>
          <s id="s.004464">Vel quia illud in ampliori tempore agitur, &amp; ide&ograve; am&shy;<lb/>
pliorem etiam &longs;ui &longs;en&longs;ationem exhibet. </s>
          <s id="s.004465">Velox autem, &amp; acut&ubreve; facil&egrave; ob &longs;uam ve&shy;<lb/>
locitatem latitat&rpar;<emph.end type="italics"/> Quid e&longs;&longs;et rithmus explicabitur in problemate 27. <expan abbr="&longs;equ&etilde;-ti">&longs;equen&shy;<lb/>
ti</expan> ait: <emph type="italics"/>&lpar;Velox autem, &amp; acutum&rpar;<emph.end type="italics"/> Cur vox acuta &longs;it velox, <expan abbr="dict&utilde;">dictum</expan> e&longs;t in 1. Top. <lb/>
<!-- REMOVE S-->cap. 13. reliqua &longs;unt &longs;atis clara.</s>
        </p>
        <p type="main">
          <s id="s.004466">Probl. 22. ex &longs;e manife&longs;tum e&longs;t: atque idem cum &longs;equenti num. </s>
          <s id="s.004467">46.</s>
        </p>
        <p type="main">
          <s id="s.004468"><arrow.to.target n="marg369"/></s>
        </p>
        <p type="margin">
          <s id="s.004469"><margin.target id="marg369"/>378</s>
        </p>
        <p type="main">
          <s id="s.004470">Probl. 23. <emph type="italics"/>&lpar;Cur Nete duplo acutior e&longs;t hypate? </s>
          <s id="s.004471">An primum, quod cum ner&shy;<lb/>
uus parte &longs;ui dimidia, &amp; totus &longs;imul pul&longs;atur, Diapa&longs;on concinentia exultat: quod <lb/>
pariter in fi&longs;tulis apparet, &longs;onus enim, qui per medium foramen emergit Diapa&longs;on <lb/>
cum eo re&longs;onat, qui per totam fi&longs;tulam exit. </s>
          <s id="s.004472">In c&aelig;teris etiam duplo interuallo Dia&shy;<lb/>
pa&longs;on continetur, nam, &amp; qui tibias perforant, it a eas o&longs;&longs;umunt. </s>
          <s id="s.004473">&amp; qui fi&longs;tulas apt&egrave; <lb/>elaborant, &longs;umitatem extremam t&abreve;ntum hypates circumlinunt: netem ver&ograve; ad <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>
dimidium obturant. </s>
          <s id="s.004474">&amp; in Triquetris P&longs;alterijs, nerui, quorum alter &longs;it alterius <lb/>
longitudine duplus, &aelig;qu&egrave; intenti Diapa&longs;on reddunt. </s>
          <s id="s.004475">Diapente ver&ograve; &longs;e&longs;quialtera <lb/>
proportione; Diate&longs;&longs;aron autem &longs;e&longs;quitertio interuallo continetur&rpar;<emph.end type="italics"/> Ex ijs, qu&aelig; <lb/>
initio huius tractationis de Monochordij diui&longs;ione, <expan abbr="de&qacute;">deque</expan>; Diapa&longs;on, <expan abbr="Diap&etilde;-te">Diapen&shy;<lb/>
te</expan>, Diate&longs;&longs;aron con&longs;onantiarum ordine, ac proportione dicta &longs;unt, per&longs;pi&shy;<lb/>
cua omnino redduntur omnia, qu&aelig; hic qu&aelig;runtur, &amp; redduntur. </s>
          <s id="s.004476">Illud no&shy;<lb/>
tandum Triquetrum P&longs;alterium in&longs;trumentum mu&longs;icum fui&longs;&longs;e, &agrave; triangula&shy;<lb/>
ri figura denominatum, no&longs;tr&aelig; for&longs;an Harp&aelig;, per&longs;imile: in quo fides e&longs;&longs;ent <lb/>
eo modo di&longs;po&longs;it&aelig;, ac intent&aelig;, vt in Harpa.</s>
        </p>
        <p type="main">
          <s id="s.004477"><arrow.to.target n="marg370"/></s>
        </p>
        <p type="margin">
          <s id="s.004478"><margin.target id="marg370"/>379</s>
        </p>
        <p type="main">
          <s id="s.004479">Probl. 24. <emph type="italics"/>&lpar;Cur &longs;i quis p&longs;allens netem pul&longs;atam apprehenderit, &longs;olam Hypa&shy;<lb/>
tem re&longs;onare videbitur? </s>
          <s id="s.004480">An quod tinnitus huius maxim&egrave; connaturalis e&longs;t &longs;ono il&shy;<lb/>
lius, illique con&longs;onus. </s>
          <s id="s.004481">quia igitur cum &longs;uo con&longs;imili augetur, hoc ce&longs;&longs;ante, ille &longs;o&shy;<lb/>
lus apparet &longs;oni ver&ograve; alij propter paruitatem euane&longs;cunt&rpar;<emph.end type="italics"/> Cur &longs;i quis dum p&longs;al&shy;<lb/>
terium pul&longs;atur, neten pul&longs;atam &longs;onantem manu apprehenderit, ita vt &longs;o&shy;<lb/>num ip&longs;ius interpellet, &longs;onus ille intermortuus, ac dimidiatus, videbitur &longs;o&shy;<lb/>nus hypates, &amp; non alterius chord&aelig;, quia, vt dictum e&longs;t, hypates, &amp; nete, <lb/>
Diapa&longs;on re&longs;onant; cuius con&longs;onanti&aelig; voces &longs;unt eiu&longs;dem natur&aelig;, aut val&shy;<lb/>
d&egrave; <expan abbr="connatur&atilde;les">connaturales</expan>; im&ograve; &longs;onus hypates duplus e&longs;t &longs;oni netes. </s>
          <s id="s.004482">Interpellato igi&shy;<lb/>
tur acutioris &longs;ono, reliquus qui ip&longs;i ade&ograve; &longs;imilis e&longs;t merit&ograve; videbitur hypa&shy;<lb/>tes: &longs;oni ver&ograve; aliarum chordarum ob ip&longs;orum paruitatem, quia nimirum <pb pagenum="260" xlink:href="009/01/260.jpg"/>minores, quam &longs;ub dupli illius &longs;unt, omnin&ograve; euane&longs;cunt. </s>
          <s id="s.004483">Hic e&longs;t &longs;en&longs;us he&shy;<lb/>
rum verborum; vtrum autem allata ratio &longs;it bona, aliorum e&longs;to iudicium. <lb/>
</s>
          <s id="s.004484">Idem qu&aelig;rit num. </s>
          <s id="s.004485">43.</s>
        </p>
        <p type="main">
          <s id="s.004486"><arrow.to.target n="marg371"/></s>
        </p>
        <p type="margin">
          <s id="s.004487"><margin.target id="marg371"/>380</s>
        </p>
        <p type="main">
          <s id="s.004488">Probl. 25. <emph type="italics"/>&lpar;Cur in harmonijs chorda illa, qu&aelig; dicitur Me&longs;e, &longs;eu media, &longs;ic ap&shy;<lb/>pellata e&longs;t? </s>
          <s id="s.004489">cum inter octo nullum medium &longs;it? </s>
          <s id="s.004490">An quoniam olim harmoni&aelig; &longs;ep&shy;<lb/>
tem fidibus con&longs;tabant, qui numerus medium habet&rpar;<emph.end type="italics"/> Ex ordine chordarum Li&shy;<lb/>
chaonis, &amp; <expan abbr="Terp&atilde;dri">Terpandri</expan>, quorum alter &longs;eptem, alter ver&ograve; octo chordis mono&shy;<lb/>
chordium conflabat, vt &longs;upra recen&longs;ui, huic loco abund&egrave; &longs;atisfieri pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004491">Probl. 26. &longs;atis ex &longs;e clarum e&longs;t, <expan abbr="atq;">atque</expan> idem cum num. </s>
          <s id="s.004492">47.</s>
        </p>
        <p type="main">
          <s id="s.004493"><arrow.to.target n="marg372"/></s>
        </p>
        <p type="margin">
          <s id="s.004494"><margin.target id="marg372"/>381</s>
        </p>
        <p type="main">
          <s id="s.004495">Probl. 27. <emph type="italics"/>&lpar;Cur inter omnia, qu&aelig; &longs;ub &longs;en&longs;us cadunt, &longs;ola audibilia mores obti&shy;<lb/>
nent? </s>
          <s id="s.004496">quamuis &longs;ine &longs;ermone aliquid modulemur, mores tamen pr&aelig; &longs;e ip&longs;a modula&shy;<lb/>
tio fert, &longs;ed nec color, nec odor, nec &longs;apor id habet. </s>
          <s id="s.004497">An quia motum non &longs;ol&ubreve; eum <lb/>obtinet, quo ip&longs;e &longs;trepitus aures mouet &lpar;talis enim motio reliquis etiam &longs;en&longs;ibus <lb/>
ine&longs;t, nam, &amp; color mouet vi&longs;um&rpar; &longs;ed illum etiam quem po&longs;t pr&aelig;dictum, <expan abbr="&longs;ub&longs;equ&etilde;-tem">&longs;ub&longs;equen&shy;<lb/>
tem</expan> percipimus: hic. </s>
          <s id="s.004498">n. </s>
          <s id="s.004499">&longs;imilitudinem habet, &amp; in rithmis, &amp; in &longs;onorum grauium, <lb/>
&amp; acutorum ordine: non autem in eorum mixtione; quod in alijs &longs;en&longs;ibilibus non <lb/>
e&longs;t. </s>
          <s id="s.004500">porr&ograve; motus ip&longs;i practici &longs;unt, praxis autem morum index est&rpar;<emph.end type="italics"/> Mores obti&shy;<lb/>
nere, aut pr&aelig;&longs;eferre nihil aliud e&longs;t, qu&agrave;m mores illius referre, &amp; in mentem <lb/>
reuocare, &agrave; quo talis motus, aut &longs;onus prouenire &longs;olet, qui &longs;onus mores il&shy;<lb/>
los refert. </s>
          <s id="s.004501">propterea videmus cantilenas nonnullas turpes mores reddere, <lb/>
vt la&longs;ciuiam, procacitatem, leuitatem, quia &agrave; natura <expan abbr="homin&utilde;">hominum</expan> turpium, vt <lb/>
la&longs;ciuorum profici&longs;ci <expan abbr="&longs;ol&etilde;t">&longs;olent</expan>, <expan abbr="eos&qacute;">eosque</expan>; decent. </s>
          <s id="s.004502">alij <expan abbr="c&atilde;tus">cantus</expan> ex oppo&longs;ito bonos mo&shy;<lb/>res referunt, vt grauitatem, temperantiam, &aelig;&longs;titatem; qui quidem ex pro&shy;<lb/>
borum hominum natura prodire &longs;olent, <expan abbr="eos&qacute;">eosque</expan>; decent. </s>
          <s id="s.004503">Illud in prophanis <lb/>
canticis, i&longs;tud ver&ograve; in Eccle&longs;ia&longs;ticis quotidie experimur; cur autem Audi&shy;<lb/>
bilia pr&aelig; c&aelig;t&eacute;ris mores referant, cau&longs;am Ari&longs;t. refert in motum illum, qui <lb/>
in &longs;onis, &amp; vocibus percipitur. </s>
          <s id="s.004504"><expan abbr="neq;">neque</expan> hic motus e&longs;t is, quo &longs;onus aures immu&shy;<lb/>
tat, hoc enim commune e&longs;t omnibus &longs;en&longs;orijs, vt &agrave; &longs;uis obiectis immuten&shy;<lb/>tur, &amp; afficiantur: &longs;ed is e&longs;t, qui pr&aelig;dictam aurium immutationem &longs;ub&longs;e&shy;<lb/>
quitur, <expan abbr="intellectu&qacute;">intellectuque</expan>; percipitur, v.g. <!-- REMOVE S-->quando audimus cantilenam, &longs;onus ip&shy;<lb/>
&longs;e prim&ograve; aures ferit, <expan abbr="eas&qacute;">easque</expan>; afficit; deinde percipimus vocis ip&longs;ius motum, <lb/>&amp; qua&longs;i cur&longs;um, quo &agrave; graui in acutum, &amp; &egrave; c&oacute;ntra, aliquando celeriter, ali&shy;<lb/>
quando tard&egrave; vario modulamine mouetur. </s>
          <s id="s.004505">huiu&longs;modi motus habet in &longs;e <lb/>morum &longs;imilitudinem; hac igitur de cau&longs;a audibilia mores referunt. </s>
          <s id="s.004506">Vide <lb/>
infra probl. </s>
          <s id="s.004507">39.</s>
        </p>
        <p type="main">
          <s id="s.004508">Iam explicandum e&longs;t breuiter, quid &longs;it rithmus, quem Latini numerum <lb/>
dicunt partim ex Platone, partim ex Ari&longs;t. <!-- KEEP S--></s>
          <s id="s.004509">Plato lib. 2. de leg. <!-- REMOVE S-->&longs;ic. </s>
          <s id="s.004510">alia qui&shy;<lb/>
dem animalia non habent &longs;en&longs;ationem ordinationis, &amp; inordinationis mo&shy;<lb/>
tuum, quibus rithmus, &amp; harmonia nomen e&longs;t. </s>
          <s id="s.004511">Ari&longs;t. infra probl. </s>
          <s id="s.004512">38. &longs;ic. <lb/>
</s>
          <s id="s.004513">rithmo ver&ograve; gaudemus, quia habet numerum manife&longs;tum, ordinatum, ra&shy;<lb/>
tumque: vnde &amp; nos ordinat&egrave; mouet. </s>
          <s id="s.004514">Ex quibus patet, rithmum e&longs;&longs;e cer&shy;<lb/>tam, ac &longs;tatam periodum aliquot interuallerum &longs;ibi &longs;ucced&eacute;ntium in quouis <lb/>
motu in determinata men&longs;ura temporis. </s>
          <s id="s.004515">qu&aelig; periodus &longs;olet &longs;&aelig;pius recur&shy;<lb/>
rere, aut repeti. </s>
          <s id="s.004516">dictum e&longs;t in quouis motu, quia in choreis pedum pul&longs;a&shy;<lb/>
tione, ac motu, rithmi complures efficiuntur, quos chore&aelig; magi&longs;tri <expan abbr="doc&etilde;t">docent</expan>, <lb/>
qualis e&longs;t is, quem vulg&ograve; <expan abbr="dic&utilde;t">dicunt</expan> Gagliarda. </s>
          <s id="s.004517">Digitorum etiam motu, &amp; mal&shy;


<pb pagenum="261" xlink:href="009/01/261.jpg"/>leorum ictibus pote&longs;t rithmus fieri: <expan abbr="atq;">atque</expan> ade&ograve; c&aelig;teris omnibus, qu&aelig; in &longs;uo <lb/>
motu certis interuallis mouentur; ita vt etiam pi&longs;tores ip&longs;i machina &longs;ua il&shy;<lb/>
la, qua ma&longs;&longs;am &longs;ubigunt, rithmum quendam efficere &longs;oleant. </s>
          <s id="s.004518">His porr&ograve; mo&shy;<lb/>
tus &longs;i in vocibus, ac &longs;onis mu&longs;icis, &longs;eu in cantilenis exi&longs;tat, pr&aelig;cipu&egrave; rithmus <lb/>
dicitur, quod &longs;i concinnus &longs;it, &amp; elegans aures &longs;uauiter mulcet, <expan abbr="animum&qacute;">animumque</expan>; <lb/>
in varias pa&longs;&longs;iones inducit: rithmum hunc, qui in cantilenis e&longs;t, vulg&ograve; can&shy;<lb/>
tores appellant Ariam. <!-- KEEP S--></s>
          <s id="s.004519">Vnde qui intelligit, quid &longs;int Ari&aelig;, qu&aelig; pa&longs;&longs;im can&shy;<lb/>tantur, ac &longs;onantur, facil&egrave; etiam quid &longs;it rithmus, intelliget. </s>
          <s id="s.004520">Hic igitur <lb/>
rithmus miram habet in &longs;e morum &longs;imilitudinem, qu&aelig; con&longs;i&longs;tit in motu <lb/>
rithmi, &longs;eu in ordine interuallorum apti&longs;&longs;imo, per qu&aelig; vox a&longs;cendit, &amp; de&shy;<lb/>
&longs;cendit: nullo autem modo con&longs;i&longs;tit in mixtione &longs;onorum grauium, &amp; acu&shy;<lb/>
torum; ex hac enim mixtione non rithmus, &longs;ed con&longs;onantia exurgit. </s>
          <s id="s.004521">mo&shy;<lb/>
tus autem omnis fit per aliquam actionem, actio ver&ograve; omnis e&longs;t morum il&shy;<lb/>
lius, cuius e&longs;t actio manife&longs;tatrix. </s>
          <s id="s.004522">ex quibus patet, cur in cantilenis rithmi&shy;<lb/>
cis mores appareant, non autem in c&aelig;teris &longs;en&longs;uum obiectis.</s>
        </p>
        <p type="main">
          <s id="s.004523"><arrow.to.target n="marg373"/></s>
        </p>
        <p type="margin">
          <s id="s.004524"><margin.target id="marg373"/>382</s>
        </p>
        <p type="main">
          <s id="s.004525">Problema 28. <emph type="italics"/>&lpar;Cur pler&aelig;que cantilen&aelig; leges appellantur? </s>
          <s id="s.004526">An quod homines <lb/>
priusqu&eacute;, literas &longs;cirent, leges cantabant, ne eas obliuione traderent, quod etiam <lb/>no&longs;tra &aelig;tate Agathyr&longs;is in more e&longs;t. </s>
          <s id="s.004527">erg&ograve; primas po&longs;teriorum cantilenarum, eodem <lb/>
appellauerunt nomine, quo omnes &longs;uperiores vocantur&rpar;<emph.end type="italics"/> Agathyr&longs;i populi &agrave; Pli&shy;<lb/>
nio, &amp; Pomponio Mela &longs;upra paludem Meotidem inter Scythicas nationes <lb/>
numerantur. </s>
          <s id="s.004528">cur autem cantilen&aelig; nonnull&aelig; leges dicerentur, pr&aelig;ter ratio&shy;<lb/>nem hic ab Ari&longs;tot. allatam, aliam Plutarchus de Mu&longs;ica affert, vbi &longs;ic ait: <lb/>
Non enim antiquitus pro libidine cuiu&longs;que, vti nunc, licebat fidibus canere, <lb/>
nec rithmos, <expan abbr="concentus&qacute;">concentusque</expan>; transferre; in ip&longs;is <expan abbr="namq;">namque</expan> legibus accommoda&shy;<lb/>
tam cuique tentionem tuebantur, cuius rei cau&longs;a id nominis inditum erat; <lb/>
leges enim &longs;unt vocat&aelig; quoniam pr&aelig;&longs;criptum, qua&longs;i lege, <expan abbr="cautum&qacute;">cautumque</expan>; erat, ne <lb/>
quis pro qualibet, vnam &longs;peciem, <expan abbr="formam&qacute;">formamque</expan>; tentionis lege &longs;ancitam, tran&longs;&shy;<lb/>
grederetur. </s>
          <s id="s.004529">h&aelig;c ille. </s>
          <s id="s.004530">fubdit po&longs;tea alias fui&longs;&longs;e &longs;imiles illis harmonijs, quas <lb/>
nunc &longs;onatas dicimus, fui&longs;&longs;e tamen &longs;tatas, ac determinatas numero, quibus <lb/>
&longs;olis vti liceret.</s>
        </p>
        <p type="main">
          <s id="s.004531">Probl. 29. Idem e&longs;t cum pr&aelig;cedenti 27. eadem igitur <expan abbr="quoq;">quoque</expan> &longs;it explicatio.</s>
        </p>
        <p type="main">
          <s id="s.004532"><arrow.to.target n="marg374"/></s>
        </p>
        <p type="margin">
          <s id="s.004533"><margin.target id="marg374"/>383</s>
        </p>
        <p type="main">
          <s id="s.004534">Probl. 30. <emph type="italics"/>&lpar;Cur <expan abbr="neq;">neque</expan> hypodorium, <expan abbr="neq;">neque</expan> hypophrygium est in trag&oelig;diarum obo&shy;<lb/>
ro? </s>
          <s id="s.004535">An quia non habet anti&longs;trophon, vtpot&egrave; qu&aelig; &longs;cenica &longs;unt, imitationiqu&eacute;, accom&shy;<lb/>
modata&rpar;<emph.end type="italics"/> huc pertinent ea, qu&aelig; ad cap. 2. lib. 3. Polit. <!-- REMOVE S-->&longs;crip&longs;i, de tonis, Do&shy;<lb/>
rio, Phrygio, Lydio. </s>
          <s id="s.004536">quibus nunc h&aelig;c addo, ex Boetio lib. 4. tonus, &longs;en mo&shy;<lb/>
dus erat qu&aelig;dam cantus con&longs;titutio, ab hypate <expan abbr="v&longs;q;">v&longs;que</expan> ad netem, proprio rith&shy;<lb/>
mo modificata: ita vt modos Dorius alium rithmum, &agrave; Phrygio, &amp; reliquis <lb/>
di&longs;crepantem haberet. </s>
          <s id="s.004537">quilibet preterea modus &longs;uam certam &longs;edem in Mo&shy;<lb/>
nochordio obtinebat, vnde &longs;equebatur vnum e&longs;&longs;e reliquis omnibus <lb/>
grauiorem, alium e&longs;&longs;e omnium acuti&longs;&longs;imum, reliquos ver&ograve; in&shy;<lb/>
termedios, alijs grauiores fui&longs;&longs;e, vt in &longs;equenti figura, <lb/>
in qua, tanquam in tabella, omnia, qu&aelig; de hi&longs;ce <lb/>
modis dici &longs;olent, per&longs;picu&egrave; licet <lb/>intueri.</s>
        </p>
        <pb pagenum="262" xlink:href="009/01/262.jpg"/>
        <p type="head">
          <figure id="id.009.01.262.1.jpg" place="text" xlink:href="009/01/262/1.jpg"/>
          <s id="s.004538"><emph type="italics"/>ORDO ANTIQVORVM MODORVM.<emph.end type="italics"/><lb/>
<arrow.to.target n="table6"/></s>
        </p>
        <table>
          <table.target id="table6"/>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>T.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>S.</cell>
            <cell>S.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell/>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos</cell>
            <cell>Parhypate</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
          </row>
          <row>
            <cell/>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos.</cell>
            <cell>Parhypat.</cell>
            <cell>Hypate.</cell>
          </row>
          <row>
            <cell/>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
          </row>
          <row>
            <cell>Nete.</cell>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos.</cell>
            <cell>Parhypat.</cell>
            <cell>Hypatc.</cell>
            <cell>Pro&longs;lamb.</cell>
          </row>
          <row>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>&mdash; &mdash;</cell>
          </row>
          <row>
            <cell>Paranete.</cell>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos</cell>
            <cell>Parhypat.</cell>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Hypermix</cell>
          </row>
          <row>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell>tolydius.</cell>
          </row>
          <row>
            <cell>Trite.</cell>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos.</cell>
            <cell>Parhypat.</cell>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Mixtolyd.</cell>
            <cell/>
          </row>
          <row>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Me&longs;e.</cell>
            <cell>Lychanos.</cell>
            <cell>Parhypat.</cell>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Lydius.</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Lychanos</cell>
            <cell>Parhypat.</cell>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Phrygius.</cell>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>S.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Parhypate</cell>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Dorius.</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>T.</cell>
            <cell>T.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Hypate.</cell>
            <cell>Pro&longs;lamb.</cell>
            <cell>Hypolyd.</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>T.</cell>
            <cell>&mdash; &mdash;</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Pro&longs;lamb.</cell>
            <cell>Hypophry</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>&mdash; &mdash;</cell>
            <cell>gius.</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>Hypodor.</cell>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
            <cell/>
          </row>
        </table>
        <pb pagenum="263" xlink:href="009/01/263.jpg"/>
        <p type="main">
          <s id="s.004539">In qua apparet Hypodorium fui&longs;&longs;e omnium <expan abbr="graui&longs;&longs;im&utilde;">graui&longs;&longs;imum</expan>, quo acutior erat <lb/>tono vno Hypophrygius; &longs;ic reliqui pr&aelig;cedentibus erant vel tono, vel &longs;e&shy;<lb/>
mitonio acutiores. </s>
          <s id="s.004540">liter&aelig; T, &amp; S, &longs;ignificant Tonos, &amp; Semitonia, quibus <lb/>
voces &longs;ingulorum modorum di&longs;tabant. </s>
          <s id="s.004541">ex quibus etiam apparet vario or&shy;<lb/>
dine interualla vnius Modi &longs;e habui&longs;&longs;e, <expan abbr="atq;">atque</expan> in alio. </s>
          <s id="s.004542">pr&aelig;terea <expan abbr="vnumquemq;">vnumquemque</expan> <lb/>
modum vnius Diapa&longs;on con&longs;titutionem habui&longs;&longs;e. </s>
          <s id="s.004543">tres illi Hypodorius, Hy&shy;<lb/>
pophrygius, Hypolydius, ita &longs;unt appellati, quod collocati e&longs;&longs;ent infra Do&shy;<lb/>
rium, Phrygium, Lydium per vnum Tetrachordum, vt patet in figura. </s>
          <s id="s.004544">&longs;ed <lb/>
vt adhuc melius hanc rem intelligamus, dicendum e&longs;t cum Zarlino lib. 4. <lb/>
In&longs;tit. <!-- KEEP S--></s>
          <s id="s.004545">Modos fui&longs;&longs;e varias &longs;pecies cantilenarum proprios rithmos haben&shy;<lb/>
tes, certo ordine, ac certo carmine, <expan abbr="certo&qacute;">certoque</expan>; etiam in&longs;trumento decantari <lb/>
&longs;olitas: denominabantur autem Dori&aelig;, Phrygi&aelig;, &amp;c. </s>
          <s id="s.004546">ab illis &longs;cilicet natio&shy;<lb/>nibus, apud quas magis e&longs;&longs;ent in v&longs;u. </s>
          <s id="s.004547">huiu&longs;modi modos nos hodie Arias ap&shy;<lb/>
pellamus, <expan abbr="eas&qacute;">easque</expan>; pariter &agrave; varijs nationibus denominamus, vt quas dicimus <lb/>
Spagnolettam, France&longs;cam, Gr&aelig;cam, Neapolitanam, Siculam, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.004548">De qualitatibus horum modorum plura veteres, ac Zarlinus ip&longs;e citato <lb/>
loco: <expan abbr="nos&qacute;">nosque</expan>; nonnulla &longs;upra in Politicis diximus. </s>
          <s id="s.004549">Quod ad hunc locum &longs;pe&shy;<lb/>
ctat, videndum quales e&longs;&longs;ent Hypodorius, &amp; Hypophrygius: quod Ari&longs;t. ip&shy;<lb/>
&longs;e infra Problem. 49. docet, ait enim, modum hypophrygium animos Lym&shy;<lb/>
phatis, &longs;imiles reddere, <expan abbr="cogere&qacute;">cogereque</expan>; debacchari: Hypodorium ver&ograve; e&longs;&longs;e mo&shy;<lb/>
dum magnificum, con&longs;tantem, grauemque. </s>
          <s id="s.004550"><expan abbr="vtrumq;">vtrumque</expan> autem fui&longs;&longs;e vari&aelig; imi&shy;<lb/>
tationi aptum, <expan abbr="ideo&qacute;">ideoque</expan>; carui&longs;&longs;e &longs;trophis: qu&aelig; ad eandem &longs;emper imitatio&shy;<lb/>
nem, <expan abbr="eundem&qacute;">eundemque</expan>; morem tendunt: vt &longs;upra Probl. 15. explicaui. </s>
          <s id="s.004551">ex quibus <lb/>
intelligere po&longs;&longs;umus Problema pr&aelig;&longs;ens; modus &longs;cilicet Hypodorius, &amp; Hy&shy;<lb/>
pophrygius &agrave; choro Trag&oelig;diarum arcebantur, quia carebant anti&longs;trophis, <lb/>
quibus chorus gaudebat; chorus enim non imitabatur varios mores, <expan abbr="va-rios&qacute;">va&shy;<lb/>
riosque</expan>; hominum affectus, &longs;ed eodem &longs;eruato affectu per ea&longs;dem &longs;trophas ad <lb/>
finem <expan abbr="v&longs;q;">v&longs;que</expan> perueniebat. </s>
          <s id="s.004552">erant autem pr&aelig;dicti duo modi &longs;cenis idonei, quia <lb/>
in &longs;cena varios mores, affectus, &amp; animi pa&longs;&longs;iones imitabantur, <expan abbr="atq;">atque</expan> ad eo&longs;&shy;<lb/>
dem vari&egrave; auditorum animos impellebant; ad quod peragendum ip&longs;i erant <lb/>
idonei te&longs;te Ari&longs;t. citato loco. </s>
          <s id="s.004553">c&ugrave;m pr&aelig;&longs;ertim anti&longs;trophis carerent, qu&aelig; ob&shy;<lb/>
&longs;i&longs;tere vari&aelig;, ac multiplici imitationi poterant. </s>
          <s id="s.004554">&longs;i plura de modis, aut tonis <lb/>
de&longs;ideras, con&longs;ule Ptol&aelig;m. <!-- REMOVE S-->lib. 2. harm. </s>
          <s id="s.004555">Boetium lib. 4. Io&longs;ephum Zarli&shy;<lb/>
num lib. 4. In&longs;tit. <!-- REMOVE S-->&amp; lib. 6. Supplem. <!-- REMOVE S-->mu&longs;icorum.</s>
        </p>
        <p type="main">
          <s id="s.004556">Illud nunc occurrit maxim&egrave; notandam. </s>
          <s id="s.004557">Veteres non &longs;olum in choris, &longs;ed <lb/>in ip&longs;a &longs;cena etiam cantare, aut &longs;onorare &longs;olitos fui&longs;&longs;e, quod manife&longs;t&egrave; ap&shy;<lb/>
paret ex problemate 75. ex 30. pr&aelig;&longs;enti, necnon ex 31. &amp; 49. &longs;equentibus.</s>
        </p>
        <p type="main">
          <s id="s.004558"><arrow.to.target n="marg375"/></s>
        </p>
        <p type="margin">
          <s id="s.004559"><margin.target id="marg375"/>384</s>
        </p>
        <p type="main">
          <s id="s.004560">Probl. 31. <emph type="italics"/>&lpar;Cur Phrynicus, c&aelig;teriqu&eacute;, illius &aelig;tatis Mu&longs;ici magis Melop&aelig;i er&abreve;t? <lb/>
</s>
          <s id="s.004561">An quoniam tunc temporis in trag&aelig;dijs carmine contextis maior erat <expan abbr="c&amacr;tilenarum">cantilenarum</expan> <lb/>
v&longs;us&rpar;<emph.end type="italics"/> Apud Suidam inter plures Phrynicos, vnus recen&longs;etur patria Athe&shy;<lb/>nien&longs;is, &amp; Poeta Tragicus, qui circa Olympiadem 67. floruit: quem puto <lb/>hunc e&longs;&longs;e, de quo in hoc problemate agitur. </s>
          <s id="s.004562">hic enim Poeta Tragicus quo&shy;<lb/>que erat, vt apparet ex illis verbis &lpar;in trag&oelig;dijs carmine contextis&rpar; quod <lb/>
autem &longs;imul Mu&longs;icus e&longs;&longs;et, non videtur dubium; antiquitus enim, vt rect&egrave; <lb/>
etiam Zarlinus ob&longs;eruabit, ijdem erant Poet&aelig;, &amp; Mu&longs;ici, quod optim&egrave; ex <lb/>
Plutarco d&eacute; mu&longs;ica confirmatur, vbi plures connumerat antiquos Mu&longs;icos,


<pb pagenum="264" xlink:href="009/01/264.jpg"/>qu&igrave; &longs;imul Poet&etail; extiterunt, &longs;ic ait; Ste&longs;ichorus, &amp; veteres alij <expan abbr="Poetar&utilde;">Poetarum</expan>, qui <lb/>
carmina adhibitis modulis condidere. </s>
          <s id="s.004563">&longs;ed quid erat Melop&aelig;ia? </s>
          <s id="s.004564">ex Ari&longs;to&shy;<lb/>
xeno, <expan abbr="atq;">atque</expan> Euclide; Melop&aelig;ia e&longs;t v&longs;us harmonic&aelig; tractationi &longs;ubiectorum, <lb/>
ad decorum propo&longs;iti argumenti. </s>
          <s id="s.004565">ex qua definitione patet Melop&aelig;um eum <lb/>
fui&longs;&longs;e, quem modo vocant Compo&longs;itorem. </s>
          <s id="s.004566">dicitur Melop&aelig;ia, qua&longs;i cantus <lb/>
effectrix. </s>
          <s id="s.004567">is igitur erat Melop&aelig;us, qui res &longs;ubiectas harmonic&aelig; &longs;cienti&aelig;, vt <lb/>
&longs;unt &longs;onus, interualla, genera, modi, con&longs;onanti&aelig;, di&longs;&longs;onanti&aelig; rit&egrave; in v&longs;um <lb/>
vocabat: vnde cantilenas humana oratione con&longs;tructas ad decorum, ide&longs;t <lb/>
pro rei argumento conuenientibus rythmis modulabatur. </s>
          <s id="s.004568">Antiquitus igi&shy;<lb/>
tur Melop&aelig;i&aelig; magis &longs;tudebant, qu&agrave;m Ari&longs;t. tempe&longs;tate, quia tunc tempo&shy;<lb/>
ris magis erant in trag&aelig;dijs cantilen&aelig; in v&longs;u, quam po&longs;tea.</s>
        </p>
        <p type="main">
          <s id="s.004569"><arrow.to.target n="marg376"/></s>
        </p>
        <p type="margin">
          <s id="s.004570"><margin.target id="marg376"/>385</s>
        </p>
        <p type="main">
          <s id="s.004571">Probl. 32. <emph type="italics"/>&lpar;Cur Diapa&longs;on con&longs;onantiam dicimus, non ratione numeri Diao&shy;<lb/>cto, vti Diate&longs;&longs;aron, &amp; Diapente? </s>
          <s id="s.004572">An quod antiquitus non pluribus, qu&agrave;m &longs;ep&shy;<lb/>
tem vterentur numeris? </s>
          <s id="s.004573">Deinde Terpander trit&egrave; exempta, Neten adiunxit, eiusqu&eacute; <lb/>temporibus con&longs;onantia h&aelig;c dicta e&longs;t Diapa&longs;on, non Diaocto: quippe qu&aelig; &longs;eptem <lb/>non octo con&longs;taret&rpar;<emph.end type="italics"/> Lege, qu&aelig; &longs;upra ad 7. problem. </s>
          <s id="s.004574">&longs;unt annotata de ordine <lb/>
chordarum, quem Terpander induxit. </s>
          <s id="s.004575">Septem nimirum chordas <expan abbr="c&otilde;&longs;tituit">con&longs;tituit</expan>, <lb/>
inter quas Trite de&longs;iderabatur, vt ibi explicaui. </s>
          <s id="s.004576">quare Terpander non im&shy;<lb/>mutauit numerum chordarum antiquum, &longs;ed tantummodo Neten cum Tri<lb/>
te commutauit. </s>
          <s id="s.004577">Tempore igitur Terpandri cum &longs;eptem e&longs;&longs;ent <expan abbr="tant&utilde;">tantum</expan> chor&shy;<lb/>
d&aelig; in p&longs;alterijs, etiam&longs;i prima cum vltima con&longs;onantiam Diapa&longs;on re&longs;ona&shy;<lb/>
ret, non tamen potuit h&aelig;c con&longs;onantia appellari Diaocto. </s>
          <s id="s.004578">Boetius lib. 1. <lb/>
cap. 20. Mu&longs;ic&aelig;, pr&aelig;dicta a&longs;&longs;erit de Terpandro. </s>
          <s id="s.004579">Suidas ait <expan abbr="Terpandr&utilde;">Terpandrum</expan> fui&longs;&longs;e <lb/>
<expan abbr="Lesbi&utilde;">Lesbium</expan>, &amp; Poetam Lyricum, qui primus lyram ex &longs;eptem chordis fecit, c&ugrave;m <lb/>
prius &agrave; Mercurio ex quatuor tantum con&longs;tructa fui&longs;&longs;et. </s>
          <s id="s.004580">C&aelig;terum ip&longs;a Dia&shy;<lb/>
pa&longs;on &longs;ic dicta e&longs;t, qua&longs;i per omnes, quia &agrave; prima chorda per omnes a&longs;cen&shy;<lb/>
dendo ad vltimam perueniebatur, cum qua prima Diapa&longs;on re&longs;onabat. </s>
          <s id="s.004581">vel <lb/>
quia intra Diapa&longs;on reliqu&aelig; omnes con&longs;onanti&aelig; concinentur, qu&aelig; dicuntur <lb/>
prim&aelig;: qu&aelig; enim &longs;upra Diapa&longs;on &longs;unt, e&aelig;dem &longs;unt cum pr&aelig;dictis, &longs;iue eiu&longs;&shy;<lb/>
dem natur&aelig;; &longs;ed qu&aelig; repetuntur, vt &longs;upra &longs;&aelig;pe dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004582"><arrow.to.target n="marg377"/></s>
        </p>
        <p type="margin">
          <s id="s.004583"><margin.target id="marg377"/>386</s>
        </p>
        <p type="main">
          <s id="s.004584">Probl. 33. <emph type="italics"/>&lpar;Cur aptius de acuto in graue canitur, quam de graue in acutum? <lb/>
</s>
          <s id="s.004585">Vtrum, quod ita fit, vt &agrave; &longs;uo inchoetur principio? </s>
          <s id="s.004586">neruus enim, qui medius, &amp; dux <lb/>
e&longs;t &longs;ecundi tetrachordi, acuti&longs;&longs;imus est. </s>
          <s id="s.004587">illo autem modo non &agrave; principio, &longs;ed &agrave; fine <lb/>
exordiretur. </s>
          <s id="s.004588">An quod graue genero&longs;ius, &amp; &longs;onantius ab acuto oriri pote&longs;t&rpar;<emph.end type="italics"/> Na&shy;<lb/>
turale e&longs;t omnibus, c&ugrave;m canere incipiunt, ab acuto incipere; cum autem <lb/>
de&longs;inunt, in graui de&longs;inere: quod &longs;i quis <expan abbr="contrari&utilde;">contrarium</expan> faciat, inept&egrave; agere &aelig;&longs;ti&shy;<lb/>
mabitur? </s>
          <s id="s.004589">Huius qu&aelig;ritur cau&longs;a. </s>
          <s id="s.004590">Vbi explicandum quid &longs;it tetrachordum. <lb/>
</s>
          <s id="s.004591">Tetrachordum igitur erat &longs;y&longs;tema, vel <expan abbr="c&otilde;&longs;titutio">con&longs;titutio</expan> quatuor chordarum, qui&shy;<lb/>
bus Diate&longs;&longs;aron con&longs;tabat. </s>
          <s id="s.004592">in maximo autem &longs;y&longs;temate, quod erat duarum <lb/>
Diapa&longs;on, &longs;iue Di&longs;diapa&longs;on, erant plura tetrachorda. </s>
          <s id="s.004593">horum primum illud <lb/>
erat, quod in parte graui&longs;&longs;ima <expan abbr="collocat&utilde;">collocatum</expan> erat, cuius h&aelig; erant chord&aelig;, Hy&shy;<lb/>
pate, Parhypate, Lychanos, Me&longs;e. </s>
          <s id="s.004594">&longs;i igitur in&longs;trumentum habuerit tantum <lb/>duo tetrachorda, neruus medius crit ip&longs;a Me&longs;e, qu&aelig; e&longs;t acuti&longs;&longs;ima primi te&shy;<lb/>
trachordi, e&longs;t pr&aelig;terea h&aelig;c Me&longs;e veluti dux reliquarum chordarum, nam, <lb/>
vt dictum e&longs;t in Probl. 20. e&longs;t in medio carum vti dux; &longs;&aelig;pi&longs;&longs;im&egrave; omnium <lb/>pul&longs;atur: ca &longs;ola ab alijs di&longs;&longs;onante, reliqu&aelig; omnes videntur di&longs;&longs;onare. </s>
          <s id="s.004595">c&ugrave;m <pb pagenum="265" xlink:href="009/01/265.jpg"/>igitur alijs pr&aelig;&longs;tet <expan abbr="&longs;it&qacute;">&longs;itque</expan>; &longs;ui tetrachordi acuti&longs;&longs;ima, <expan abbr="c&otilde;uenienter">conuenienter</expan> natura du&shy;<lb/>
ce fit, vt ab acuta voce cantum exordiamur. </s>
          <s id="s.004596">ide&longs;t &longs;icut in tetrachoreo prin&shy;<lb/>
cipalis e&longs;t acuta, &longs;iue principium tetrachordi e&longs;t acutum, ita etiam princi&shy;<lb/>
pium cantus debet e&longs;&longs;e acutum. </s>
          <s id="s.004597">Quod &longs;i &agrave; graui cantandi principium fa&shy;<lb/>
ceremus, &agrave; fine potius, qu&agrave;m &agrave; principio contra natur&aelig; ordinem <expan abbr="principi&utilde;">principium</expan> <lb/>
faceremus. </s>
          <s id="s.004598">Theodorus Gaza vertit, primi tetrachordi, verum in vulgatis, <lb/>
atque correctis codicibus gr&aelig;cis legitur, <foreign lang="greek">para/tetraxordou,</foreign> quod non pri&shy;<lb/>
mum, &longs;ed potius &longs;ub&longs;equens tetrachordum, &longs;ignificare videtur. </s>
          <s id="s.004599">vtrumuis le&shy;<lb/>
gamus, explicatio allata &longs;ufficere pote&longs;t. </s>
          <s id="s.004600">Subdit po&longs;tea aliam re&longs;pon&longs;io&shy;<lb/>
nem, quod nimirum hoc modo grauis vox cantilenam claudens, quando ex <lb/>
acuto quodammodo orta e&longs;t, genero&longs;ior, <expan abbr="atq;">atque</expan> &longs;onantior euadit.</s>
        </p>
        <p type="main">
          <s id="s.004601"><arrow.to.target n="marg378"/></s>
        </p>
        <p type="margin">
          <s id="s.004602"><margin.target id="marg378"/>387</s>
        </p>
        <p type="main">
          <s id="s.004603">Probl. 34. <emph type="italics"/>&lpar;Cur bis Diapente, aut bis Diate&longs;&longs;aron <expan abbr="c&otilde;&longs;onantia">con&longs;onantia</expan> <expan abbr="c&otilde;poni">componi</expan> non pote&longs;t, <lb/>
bis <expan abbr="a&utilde;t">autem</expan> Diapa&longs;on pote&longs;t? </s>
          <s id="s.004604">An, qu&ograve;d bis Diapente, non bis Diate&longs;&longs;aron e&longs;t: &longs;ed Dia&shy;<lb/>
te&longs;&longs;aron, &amp; Diapente in vn&abreve; Diapa&longs;on concurrunt&rpar;<emph.end type="italics"/> Quamuis textus <expan abbr="aliquantul&utilde;">aliquantulum</expan> <lb/>
<expan abbr="&etilde;t">et</expan> gr&aelig;cus corruptus &longs;it, verumtamen &longs;en&longs;um Ari&longs;t. ex &longs;equentibus percipie&shy;<lb/>
mus. </s>
          <s id="s.004605">Pro intelligentia igitur huius problematis placet hic de&longs;cribere <expan abbr="dem&otilde;-&longs;trationem">demon&shy;<lb/>
&longs;trationem</expan> 16. lib. 3. docti&longs;&longs;imi Fabri &longs;tapulentis, qua ip&longs;e ve&longs;tigijs <expan abbr="antiquo-r&utilde;">antiquo&shy;<lb/>
rum</expan> inh&aelig;rens optim&egrave; pr&aelig;&longs;enti qu&aelig;&longs;tioni &longs;atisfacit. </s>
          <s id="s.004606">e&longs;t <expan abbr="a&utilde;t">aut</expan> huiu&longs;modi: Bi&longs;dia&shy;<lb/>
te&longs;&longs;aron, aut bis <expan abbr="Diap&etilde;te">Diapente</expan> <expan abbr="null&atilde;">nullam</expan> con&longs;onantiam <expan abbr="c&otilde;ponere">componere</expan> pote&longs;t, omnis <expan abbr="namq;">namque</expan> <lb/>
con&longs;onantia, aut in proportione multiplici, aut in &longs;uperparticulari collo&shy;<lb/>
canda e&longs;t, ex Pythagoreorum, <expan abbr="aliorum&qacute;">aliorumque</expan>; Mu&longs;icorum traditione; &longs;ed &longs;i du&aelig; <lb/>
Diate&longs;&longs;aron, aut du&aelig; Diapente componantur, <expan abbr="neq;">neque</expan> multiplicem, neque &longs;u&shy;<lb/>
perarticularem creant rationem, erg&ograve; addit&aelig; nullam efficere valent <expan abbr="c&otilde;&longs;o-nantiam">con&longs;o&shy;<lb/>
nantiam</expan>. </s>
          <s id="s.004607">duas Diapentes nullam facere rationem multiplicem, aut &longs;uper&shy;<lb/>
particularem patet ex numeris earum rationem continentibus &longs;imul addi&shy;<lb/>
tis, eo modo, quo Mu&longs;ici &longs;olent addere. </s>
          <s id="s.004608">ratio Diapentes e&longs;t &longs;e&longs;quialtera, &longs;i <lb/>
ergo du&aelig; &longs;e&longs;quialter&aelig; &longs;imul continuentur, vt in his numeris. </s>
          <s id="s.004609">9. 6. 4. ratio <lb/>
primi 9 ad vltimum 4. erit compo&longs;ita ex duabus &longs;e&longs;quialteris; ratio autem <lb/>
9. &amp; 4. <expan abbr="neq;">neque</expan> e&longs;t multiplex, <expan abbr="neq;">neque</expan> &longs;uperarticularis, vt oporteret, &longs;ed e&longs;t multi&shy;<lb/>
plex &longs;uperparticularis, qu&aelig; ad con&longs;onantiam inepta e&longs;t. </s>
          <s id="s.004610">propterea igitur <lb/>
du&aelig; Diapent&aelig; addit&aelig; nullam faciunt con&longs;onantiam. </s>
          <s id="s.004611">quod pr&aelig;terea expe&shy;<lb/>
rientia ip&longs;a manife&longs;tat. </s>
          <s id="s.004612">&longs;ed cur proprio multiplex, &amp; &longs;uperarticularis &longs;unt <lb/>
harmonic&aelig;; multiplex ver&ograve; &longs;uperarticularis, aut qu&aelig;libet alia non? </s>
          <s id="s.004613">fort&egrave; <lb/>
quia in illis maior &longs;eruatur integritas, qu&aelig; perfectio e&longs;t: in c&aelig;teris ver&ograve; mi&shy;<lb/>
nor integritas, qu&aelig; imperfectio e&longs;t. </s>
          <s id="s.004614">quod melius in &longs;equenti problem. </s>
          <s id="s.004615">ex&shy;<lb/>
plicabitur. </s>
          <s id="s.004616">&longs;imiliter duas Diate&longs;&longs;aron nullam facere <expan abbr="ration&etilde;">rationem</expan> con&longs;onantem, <lb/>
patet ex numeris illarum additis: eorum proportio e&longs;t &longs;e&longs;quitertia, <expan abbr="add&atilde;-tur">addan&shy;<lb/>
tur</expan>; erg&ograve; du&aelig; &longs;e&longs;quiterti&aelig;, vt in his numeris 16. 12. 9. ratio primi 16. ad <lb/>
extremum 9. nec multiplex, nec &longs;uperparticularis e&longs;t, vt oporteret: erg&ograve; <lb/>
nullam con&longs;onantiam efficient. </s>
          <s id="s.004617">At ver&ograve;, &longs;i vna Diate&longs;&longs;aron, &amp; vna Dia&shy;<lb/>pente, componantur, efficiunt Diapa&longs;on; quia ip&longs;arum rationes addit&aelig; du&shy;<lb/>
plam, qu&aelig; e&longs;t ratio Diapa&longs;on, efficiunt: dupla autem e&longs;t multiplex. </s>
          <s id="s.004618"><expan abbr="pon&atilde;-tur">ponan&shy;<lb/>
tur</expan> hi tres numeri 6. 4. 3. proportio primi 6. &amp; &longs;ecundi 4. e&longs;t &longs;e&longs;quialtera, <lb/>
pro Diapente. <!-- KEEP S--></s>
          <s id="s.004619">proportio &longs;ecundi 4. &amp; 3. e&longs;t &longs;e&longs;quitertia pro Diate&longs;&longs;aron. <lb/>
<!-- KEEP S--></s>
          <s id="s.004620">Iam proportio inter primum 6. &amp; vltimum 3. e&longs;t dupla: qu&aelig; e&longs;t ratio ip&longs;ius <lb/>
perfecti&longs;&longs;im&aelig; con&longs;onanti&aelig; Diapa&longs;on. <!-- KEEP S--></s>
          <s id="s.004621">Ex quibus Ari&longs;t. &longs;ententia manife&longs;ta <pb pagenum="266" xlink:href="009/01/266.jpg"/>e&longs;t. </s>
          <s id="s.004622">idem qu&aelig;rit etiam problemate 42. H&aelig;c de ratione multiplici, &amp; &longs;uper&shy;<lb/>
particulari dicta &longs;unt ex veterum &longs;ententia: recentiores enim mu&longs;ic&aelig; de&shy;<lb/>
prauatores plures alias rationes perperam inter harmonicas intru&longs;erunt.</s>
        </p>
        <p type="main">
          <s id="s.004623"><arrow.to.target n="marg379"/></s>
        </p>
        <p type="margin">
          <s id="s.004624"><margin.target id="marg379"/>388</s>
        </p>
        <p type="main">
          <s id="s.004625">Probl. 35. <emph type="italics"/>&lpar;Cur Diapa&longs;on con&longs;onantia omnium pulcherrima e&longs;t? </s>
          <s id="s.004626">An quod <lb/>
integris terminis huius proportiones continentur: c&aelig;terarum autem non integris? <lb/>
</s>
          <s id="s.004627">c&ugrave;m enim Nete dupla ad hypaten &longs;it, quocunque in genere Nete duo tenuerit, hy&shy;<lb/>
pate vnum habebit; &amp; vbi hypate duo, Nete quatuor re&longs;onabit, &amp; ita deinceps. <lb/>
</s>
          <s id="s.004628">At ver&ograve; eadem Nete me&longs;es &longs;e&longs;quialtera e&longs;t: proportio <expan abbr="namq;">namque</expan> &longs;e&longs;quialtera, qua <expan abbr="c&otilde;-&longs;onantia">con&shy;<lb/>
&longs;onantia</expan> diapente concluditur, non integris numeris po&longs;ita e&longs;t: maior enim mino&shy;<lb/>
rem intra &longs;e continet totum, &amp; partem eius dimidiam. </s>
          <s id="s.004629">quamobrem non integri <lb/>
c&ugrave;m integris comparantur, &longs;ed partes &longs;uper&longs;unt. </s>
          <s id="s.004630">Con&longs;onantia quoque Diate&longs;&longs;a&shy;<lb/>ron proportione &longs;e&longs;quitertia continetur, qu&aelig; terminis con&longs;tat, quorum maior mi&shy;<lb/>
norem totum continet, &amp; in&longs;uper tertiam eius partem. </s>
          <s id="s.004631">An quod ex amba&shy;<lb/>
bus con&longs;i&longs;tit, perfecti&longs;&longs;ima e&longs;t? </s>
          <s id="s.004632">&amp; quoniam modulandi men&longs;uram h&aelig;c tenet, meri&shy;<lb/>
t&ograve; omnium eleganti&longs;&longs;ima&rpar;<emph.end type="italics"/> Proportio con&longs;onanti&aelig; Diapa&longs;on e&longs;t &longs;icuti 2. ad 1. <lb/>
vbi vides vtrunque terminum e&longs;&longs;e integrum, quia maior minorem bis inte&shy;<lb/>
gr&egrave; continet. </s>
          <s id="s.004633">proportio ver&ograve; con&longs;onanti&aelig; Diapente, e&longs;t &longs;icuti 3. ad 2. vbi <lb/>
maior terminus minorem non integr&egrave; continet, &longs;ed &longs;emel, &amp; adhuc <expan abbr="dimidi&utilde;">dimidium</expan> <lb/>
illius. </s>
          <s id="s.004634">proportio <expan abbr="deni&qacute;">denique</expan>; Diate&longs;&longs;aron e&longs;t &longs;icuti 4. ad 3. vbi maior <expan abbr="minor&etilde;">minorem</expan> non <lb/>
integr&egrave; continet, &longs;ed &longs;emel, &amp; adhuc tertiam ip&longs;ius partem: breuiter deno&shy;<lb/>
minationes <expan abbr="har&utilde;">harum</expan> <expan abbr="proportion&utilde;">proportionum</expan> &longs;unt hi, 2/1. 1 1/2. 1 1/3. vbi vides, <expan abbr="prim&utilde;">primum</expan>, qui e&longs;t <lb/>
Diapa&longs;on con&longs;tare ex integris numeris. </s>
          <s id="s.004635">&longs;ecundum ver&ograve;, &amp; tertium, qui &longs;unt <lb/>
Diapente, &amp; Diate&longs;&longs;aron exintegro cum fractione. </s>
          <s id="s.004636">maior autem perfectio <lb/>
e&longs;t integritas, quam fractio, aut diui&longs;io. </s>
          <s id="s.004637">propterea perfectior reliquis e&longs;t <lb/>
con&longs;onantia Diapa&longs;on: &amp; Diapente adhuc perfectior, quam Diate&longs;&longs;aron, <lb/>
quia illius numeri minorem habent fractionem, quam huius. </s>
          <s id="s.004638">Aliter re&longs;pon&shy;<lb/>
det po&longs;tea dicens, Diapa&longs;on perfectam e&longs;&longs;e ade&ograve; con&longs;onantiam; quoniam <lb/>ex duabus Diapente, &amp; Diate&longs;&longs;aron con&longs;tat, vt &longs;upra ex diui&longs;ione mono&shy;<lb/>
chordij, &amp; in pr&aelig;cedenti etiam problemate patuit. </s>
          <s id="s.004639">qu&aelig; ratio, quantum va&shy;<lb/>
leat, alij viderint. </s>
          <s id="s.004640">Re&longs;pondet tandem Diapa&longs;on ide&ograve; perfecti&longs;&longs;imam e&longs;&longs;e, <lb/>
quia ip&longs;a &longs;it modulandi men&longs;ura, ide&longs;t, quia intra terminos huius <expan abbr="con&longs;on&atilde;-ti&aelig;">con&longs;onan&shy;<lb/>
ti&aelig;</expan> omnes ali&aelig; &longs;implices con&longs;onanti&aelig; continentur, vt &longs;upra initio explica&shy;<lb/>
ui. </s>
          <s id="s.004641">merit&ograve; igitur omnium eleganti&longs;&longs;ima e&longs;t. </s>
          <s id="s.004642">In gr&aelig;co textu &longs;uper&longs;unt <expan abbr="n&omacr;-nulla">non&shy;<lb/>
nulla</expan>, qu&aelig; merit&ograve; Gaza omi&longs;it, cum nullo pacto c&ugrave;m pr&aelig;cedentibus coh&aelig;&shy;<lb/>
reant. </s>
          <s id="s.004643">Verba illa <emph type="italics"/>&lpar;Cum enim nete ad hypatem dupla &longs;it, quocunque in genere <lb/>duo tenuerit, hypate vn&ubreve;μ habebit &amp;c.&rpar;<emph.end type="italics"/> Videntur <foreign lang="greek">nsterog prwteron&middot;</foreign> cum debui&longs;&shy;<lb/>
&longs;et dicere, hypatem duplam e&longs;&longs;e ip&longs;ius netes, vt &longs;upra patuit ex diui&longs;ione <lb/>
regul&aelig; harmonic&aelig;. </s>
          <s id="s.004644">Fort&egrave; vult dicere neten e&longs;&longs;e dupl&ograve; acutiorem, <expan abbr="qu&atilde;">quam</expan> hy&shy;<lb/>
pate: vel fuit memori&aelig; lap&longs;us. </s>
          <s id="s.004645">quod ait <emph type="italics"/>&lpar;At ver&ograve; eadem nete Me&longs;es &longs;e&longs;qui&shy;<lb/>
altera e&longs;t&rpar;<emph.end type="italics"/> vult dicere Me&longs;en ad neten habere &longs;e&longs;quialteram proportionem, <lb/>
quamuis inuers&egrave; loquatur: qua ratione ver&ograve; Me&longs;e ad netem &longs;e&longs;quialtera <lb/>
&longs;it, ex diui&longs;ione monochordij initio tradita &longs;atis patere pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004646"><arrow.to.target n="marg380"/></s>
        </p>
        <p type="margin">
          <s id="s.004647"><margin.target id="marg380"/>389</s>
        </p>
        <p type="main">
          <s id="s.004648">Probl. 36. <emph type="italics"/>&lpar;Cur &longs;i neruus medius ex &longs;uo intentionis modo dimotus fuerit, c&aelig;te&shy;<lb/>
ris <expan abbr="quoq;">quoque</expan> omnes nerui, &longs;onos di&longs;&longs;onos reddent: &longs;ed &longs;i, immoto illo manente, ali&shy;<lb/>
quis ex c&aelig;teris dimotus fuerit, &longs;olus hic, qui modo &longs;uo caruerit, aberrabit? </s>
          <s id="s.004649">An, <lb/>quod ratio concinendi, aptaneruorum omnium intentione continetur, qu&aelig; non ni&longs;<emph.end type="italics"/>i <pb pagenum="267" xlink:href="009/01/267.jpg"/><emph type="italics"/>per habitudinem quandam ad Me&longs;en, &longs;eu ad Medium, <expan abbr="accommod&amacr;da">accommodanda</expan> omnibus e&longs;t, <lb/>
ordoqu&eacute;, ratione illius di&longs;poni &longs;ingulis debet? </s>
          <s id="s.004650">ergo &longs;ublata concinendi cau&longs;a, <expan abbr="conc&emacr;-tus">concen&shy;<lb/>
tus</expan> &aelig;qu&egrave; cu&longs;todiri pr&aelig;terεa nequit. </s>
          <s id="s.004651">Veruntamen Me&longs;e &longs;ibi con&longs;tante, &longs;i quis alius <lb/>
di&longs;creparit, merit&ograve; illius &longs;ola pars dee&longs;t: c&aelig;teri <expan abbr="uamq;">νamque</expan> omnes modum &longs;u&aelig; <expan abbr="concin&etilde;-ti&aelig;">concinen&shy;<lb/>
ti&aelig;</expan> &longs;eruant integrum&rpar; &lpar;Neruus medius&rpar;<emph.end type="italics"/> ide&longs;t, Me&longs;e, &longs;ic appellata, quod me&shy;<lb/>
dia e&longs;&longs;et. <emph type="italics"/>&lpar;Qu&aelig; non ni&longs;i per habitudinem quandam ad Me&longs;en&rpar;<emph.end type="italics"/> hypate cum Me&shy;<lb/>
&longs;e con&longs;onabat Diate&longs;&longs;aron: nete cum eadem Me&longs;e con&longs;onabat Diapente, <lb/>
qu&aelig; &longs;unt du&aelig; pr&aelig;cipu&aelig; con&longs;onanti&aelig;, Diapa&longs;on integrantes; ergo &longs;ublata <lb/>
Me&longs;e de &longs;uo &longs;tatu, illas pariter tolli nece&longs;&longs;e e&longs;t. </s>
          <s id="s.004652">eandem qu&aelig;&longs;tionem &longs;upra <lb/>
Probl. 20. pertractauit, qu&agrave;m nunc reui&longs;ere con&longs;ultum erit.</s>
        </p>
        <p type="main">
          <s id="s.004653"><arrow.to.target n="marg381"/></s>
        </p>
        <p type="margin">
          <s id="s.004654"><margin.target id="marg381"/>390</s>
        </p>
        <p type="main">
          <s id="s.004655">Probl. 37. <emph type="italics"/>&lpar;Cur existente vocum acumine, &longs;ecundum paruum: grauitate au&shy;<lb/>
tem &longs;ecundum multum<emph.end type="italics"/> &lpar;<emph type="italics"/>quod enim graue e&longs;t, ob va&longs;titatem graue e&longs;t: quod ver&ograve; <lb/>
acutum ob paruitatem<emph.end type="italics"/>&rpar; <emph type="italics"/>difficilius e&longs;t acutas voces canere, qu&agrave;m graues; &amp; pauci <lb/>
&longs;unt, qui &longs;uperna cantare valeant; &amp; leges orthi&aelig;, &amp; acut&aelig; cantu difficiles &longs;unt, <lb/>
quod &longs;int vald&egrave; inten&longs;&aelig;. </s>
          <s id="s.004656">Quamquam facilius &longs;it mouere exiguum, quam <expan abbr="magn&utilde;">magnum</expan>: <lb/>
idem <expan abbr="itaq;">itaque</expan> in aere deberet accidere. </s>
          <s id="s.004657">An quia non idem e&longs;t e&longs;&longs;e acut&aelig; vocis &agrave; natu&shy;<lb/>
r&aelig;, <expan abbr="atq;">atque</expan> <expan abbr="acut&utilde;">acutum</expan> canere: ver&ugrave;m naturaliter imbecilla omnia acut&aelig; &longs;unt vocis; prop&shy;<lb/>
terea ectici &longs;unt acut&aelig; vocis, quia parum aeris non multum ciere po&longs;&longs;unt: paucus <lb/>ver&ograve; velociter fertur; in cantu ver&ograve; acutum canere &longs;ignum e&longs;t roboris, quod enim <lb/>
vald&egrave; <expan abbr="f&emacr;rtur">fertur</expan>, velociter fertur: &amp; difficil&egrave; e&longs;t alta canere, at grauia &longs;unt humilia&rpar;<emph.end type="italics"/><lb/>
Vt intelligas pr&etail;&longs;ens Problema, lege, qu&aelig; lib. 1. Top. <!-- REMOVE S-->c. <!-- REMOVE S-->3. &longs;crip&longs;i. </s>
          <s id="s.004658">Leges Or&shy;<lb/>
thi&aelig;, erant cantilen&aelig; &lpar;vt &longs;upra probl. </s>
          <s id="s.004659">28. patuit&rpar; inten&longs;a admodum, <expan abbr="alta&qacute;">altaque</expan>; <lb/>
voce decantari &longs;olit&aelig;, vnde, &amp; Orthi&aelig; &longs;unt dict&aelig;; de quibus vide Herodo&shy;<lb/>
tum lib. <!-- REMOVE S-->I. &amp; Agell. <!-- REMOVE S-->lib. 16. Plutarchus <expan abbr="quoq;">quoque</expan> de mu&longs;ica &longs;&aelig;p&egrave; meminit Or&shy;<lb/>
thi&aelig; legis.</s>
        </p>
        <p type="main">
          <s id="s.004660">Difficilius deberet e&longs;&longs;e canere graue, qu&agrave;m <expan abbr="acut&utilde;">acutum</expan>, quia graue e&longs;t in mul&shy;<lb/>
to, &amp; acutum in paruo, vt patet in cannis. </s>
          <s id="s.004661">canna enim grauis e&longs;t maior, &amp; <lb/>
ideo plus aeris mouet. </s>
          <s id="s.004662">chorda etiam grauior, e&longs;t maior, erg&ograve; etiam plus <lb/>
aeris impellit; idem in c&aelig;teris. </s>
          <s id="s.004663">facilius tamen e&longs;t graue, quam acutum: <lb/>
pr&aelig;terea imbecilla, vt Ectici, mulieres, pueri, vocem habent naturaliter <lb/>
acutam, erg&ograve; facilius deberet e&longs;&longs;e acutum canere, c&ugrave;m exigua vis id pr&aelig;&shy;<lb/>
&longs;tare videatur? </s>
          <s id="s.004664">Re&longs;pondet aliud e&longs;&longs;e canere acutum, &amp; aliud &agrave; natura ha&shy;<lb/>
bere vocem acutam. </s>
          <s id="s.004665">qui enim cantat acutum, oportet, vt valid&egrave; vocem in&shy;<lb/>
tendat exten&longs;iu&egrave;, <expan abbr="atq;">atque</expan> inten&longs;iu&egrave;, ide&longs;t opus e&longs;t acumine, &amp; vociferatione, <lb/>
quam debiles edere nequeunt; quia quamuis vocem <expan abbr="habe&atilde;t">habeant</expan> acutam, tamen <lb/>
paruam habent. </s>
          <s id="s.004666"><expan abbr="Neq;">Neque</expan> difficile e&longs;t canere graue, quia a natura e&longs;t habere ar&shy;<lb/>
teriam magnam, &amp; ideo multum aeris ciere, &amp; proinde canere, qu&aelig; enim <lb/>
naturaliter fiunt, facil&egrave; fiunt.</s>
        </p>
        <p type="main">
          <s id="s.004667">Obijces, Ari&longs;t. in Probl. 26. &amp; 47. dixi&longs;&longs;e contrarium, &longs;cilicet facilius <lb/>
e&longs;&longs;e canere acutum, quam graue, ibi enim re&longs;pondet: vtrum, quod facilius <lb/>
acutum, quam graue cantatur? </s>
          <s id="s.004668">Re&longs;pondeo prim&ugrave;m, Ari&longs;t. ibi non a&longs;&longs;ere&shy;<lb/>
re, &longs;ed dubitanter loqui. </s>
          <s id="s.004669">&longs;ecund&ograve;, h&aelig;c ab eo dicta e&longs;&longs;e problematic&egrave;, ide&longs;t <lb/>
non con&longs;equenter, &longs;ed qu&aelig; po&longs;&longs;int in <expan abbr="vtramq;">vtramque</expan> partem di&longs;putari.</s>
        </p>
        <p type="main">
          <s id="s.004670"><arrow.to.target n="marg382"/></s>
        </p>
        <p type="margin">
          <s id="s.004671"><margin.target id="marg382"/>391</s>
        </p>
        <p type="main">
          <s id="s.004672">Probl. 38. <emph type="italics"/>&lpar;Cur rithmo, modulo, cantico, &amp; omnin&ograve; &longs;ymphonijs gaudent om&shy;<lb/>
nes? </s>
          <s id="s.004673">An quia motibus naturalibus naturaliter gaudemus. </s>
          <s id="s.004674">iudicium, quod infantes <lb/>nuper editi, ip&longs;is delectantur. </s>
          <s id="s.004675">ob con&longs;uetudinem ver&ograve; canticorum modis gaudemus.<emph.end type="italics"/>


<pb pagenum="268" xlink:href="009/01/268.jpg"/><emph type="italics"/>rithmo autem gaudemus, quod habeat numerum ratum, &amp; ordinatum, &amp; quod <lb/>
nos ordinat&egrave; moueat. </s>
          <s id="s.004676">magis enim proprium natur&aelig; e&longs;t ordinatus motus, quam in&shy;<lb/>
ordinatus: &amp; ide&ograve; magis etiam &longs;ecundum naturam e&longs;t. </s>
          <s id="s.004677">argumentum, quod c&ugrave;m la&shy;<lb/>
boramus, &amp; bibimus, &amp; comedimus ordinat&egrave;, naturam, viresqu&eacute; no&longs;tras, &amp; &longs;erua&shy;<lb/>
mus, &amp; augemus: c&ugrave;m ver&ograve; inordinat&egrave; eam corrumpimus, &amp; dimouemus. </s>
          <s id="s.004678">morbi <lb/>
enim dimotiones &longs;unt naturalis con&longs;titutionis corporis. </s>
          <s id="s.004679">con&longs;onantia ver&ograve; l&aelig;tamur, <lb/>
quod &longs;it mixtio qu&etail;dam contrariorum, proportionem habentium ad inuicem. </s>
          <s id="s.004680">&longs;i qui&shy;<lb/>
dem proportio ordo e&longs;t, qui natur&agrave; quidem &longs;uauis est. </s>
          <s id="s.004681">mixtum ver&ograve; omne &longs;uauius <lb/>
e&longs;t immixto. </s>
          <s id="s.004682">pr&aelig;&longs;ertim &longs;i c&ugrave;m &longs;en&longs;ibile &longs;it, &aelig;qu&egrave; <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> extremi vim retineat, in <lb/>
con&longs;onantia porr&ograve; proportio e&longs;t&rpar;<emph.end type="italics"/> Quid rithmus &longs;it, &longs;upra num. </s>
          <s id="s.004683">27. explicaui. <lb/>
</s>
          <s id="s.004684">&longs;ed optim&egrave; ex hoc loco elicitur rithmum e&longs;&longs;e certam quandam in aliquo <lb/>
motu periodum, &longs;cilicet determinatorum ictuum, &amp; temporum. </s>
          <s id="s.004685">Sympho&shy;<lb/>
niam, Mu&longs;ici dicunt e&longs;&longs;e plurium &longs;onorum conuenientium mixtionem, &longs;e&shy;<lb/>
cundum aliquem canendi modum. </s>
          <s id="s.004686">quod ait, pueri nuper editi ip&longs;is delecta&shy;<lb/>
ri &longs;olent. </s>
          <s id="s.004687">patet hoc modo; &longs;olo rithmo l&aelig;tantur, quando incunabulum or&shy;<lb/>
dinat&egrave; agitatur: modis mu&longs;icis, c&ugrave;m illis cantilena qu&aelig;piam etiam &longs;olita&shy;<lb/>
ria, vti e&longs;t Nenia accinitur: &longs;ymphonia tandem, quando mu&longs;ico aliquo in&shy;<lb/>&longs;trumento addita etiam humana voce concinnitur. </s>
          <s id="s.004688">reliqua per &longs;e patent.</s>
        </p>
        <p type="main">
          <s id="s.004689"><arrow.to.target n="marg383"/></s>
        </p>
        <p type="margin">
          <s id="s.004690"><margin.target id="marg383"/>392</s>
        </p>
        <p type="main">
          <s id="s.004691">Probl. 39. <emph type="italics"/>&lpar;Cur &longs;uauius e&longs;t &longs;ymphonum, qu&agrave;m vni&longs;onum? </s>
          <s id="s.004692">An quod antipho&shy;<lb/>
num ip&longs;um quoque <expan abbr="con&longs;on&atilde;">con&longs;onam</expan> e&longs;t per Diapa&longs;on, quippe c&ugrave;m ex pueris, virisqu&eacute; fiat an&shy;<lb/>
tiphonum, qui ita inter &longs;e vocibus distant, vt Nete, &amp; Hypate. </s>
          <s id="s.004693">omnis autem &longs;ym&shy;<lb/>
phonia &longs;eno &longs;implici &longs;uauior e&longs;t, cur autem ita dictum e&longs;t: quarum &longs;uaui&longs;&longs;ima est <lb/>
Diapa&longs;on: Vni&longs;onum autem &longs;implicem &longs;onum habet&rpar;<emph.end type="italics"/> Cur &longs;uauior e&longs;t con&longs;onan&shy;<lb/>tia, qu&aelig; oritur ex vocibus &longs;ymphonis, ide&longs;t, diuer&longs;is, quam qu&aelig; ij&longs;dem &longs;iue <lb/>
vni&longs;onis? </s>
          <s id="s.004694">An quia talis con&longs;onantia magis ad naturam Diapa&longs;on accedit; <lb/>
im&ograve; Diapa&longs;on ip&longs;a vna e&longs;t ex &longs;ymphonis; ip&longs;a autem fit ex puerorum, ac vi&shy;<lb/>
rorum vocibus, qu&aelig; inuicem di&longs;tant, vt Nete, &amp; Hypate, ide&longs;t in dupla ra&shy;<lb/>
tione; omnis autem con&longs;onantia &longs;uauior e&longs;t &longs;ono &longs;implici: at ver&ograve; &longs;ympho&shy;<lb/>
num continet diuer&longs;os &longs;onos: vni&longs;onum autem quamuis plures contineat, <lb/>
tamen propter earum nimiam &longs;imilitudinem, perinde ac vna &longs;implex vox, <lb/>
re&longs;pectu illius reputatur. </s>
          <s id="s.004695">non me latet aliter exponi voces &longs;ymphonon, &amp; <lb/>
omophon &agrave; Ptol&aelig;m. <!-- KEEP S--></s>
          <s id="s.004696">primo harm. </s>
          <s id="s.004697">cap. 7. &amp; alijs: &longs;ed illa Ari&longs;tot. &longs;ententi&aelig; <lb/>
minim&egrave; quadrant. </s>
          <s id="s.004698">Probl. 16. &longs;uperius e&longs;t fer&egrave; idem cum hoc.</s>
        </p>
        <p type="main">
          <s id="s.004699"><arrow.to.target n="marg384"/></s>
        </p>
        <p type="margin">
          <s id="s.004700"><margin.target id="marg384"/>393</s>
        </p>
        <p type="main">
          <s id="s.004701">Probl. 40. <emph type="italics"/>&lpar;Cur in &longs;ola Diapa&longs;on con&longs;onantia magadari &longs;olitum e&longs;t? </s>
          <s id="s.004702">An quia, <lb/>
vt pedes carminum proportionem, aut &aelig;qualis ad &aelig;qualem, aut duo ad vnum, aut <lb/>aliam aliquam obtinent; ita &longs;oni, quibus con&longs;onantia confiat, motus rationem in&shy;<lb/>
ter &longs;e aliquam &longs;eruant. </s>
          <s id="s.004703">c&aelig;terarum igitur <expan abbr="con&longs;on&amacr;tiarum">con&longs;onantiarum</expan> alterius quidem fines &longs;unt <lb/>
imperfecti, c&ugrave;m finiant ad dimidium. </s>
          <s id="s.004704">propterea nequeunt e&longs;&longs;e eiu&longs;dem facultatis. <lb/>
</s>
          <s id="s.004705">eumqu&eacute; &longs;int di&longs;pares, di&longs;crepantia illa &longs;en&longs;ui occurrit; quemadmodum in choris in <lb/>
ip&longs;o fine alium maiori voce abundare accidit. </s>
          <s id="s.004706">Pr&aelig;terea ip&longs;i hypate accidit, vt eun&shy;<lb/>dem finem habeat periodorum in &longs;onis c&ugrave;m nete: vltimus enim &agrave; nete ictus ceris <lb/>
factus hypate e&longs;t. </s>
          <s id="s.004707">quod c&ugrave;m finiant in idem, quamuis non idem fecerint, euenit, vt <lb/>
opus ab&longs;olui vnum, communequ&eacute; po&longs;&longs;it, vt eis accidit, qui &longs;ub extremam cantilenam <lb/>
pul&longs;ant; nam etiam&longs;i prius non &longs;onuerint, tamen qu&ograve;d in idem de&longs;ierint hoc extre&shy;<lb/>
mo magis delectent, quam contri&longs;tauerint ante finem di&longs;crepantijs. </s>
          <s id="s.004708">quoniam igitur <lb/>in Diapa&longs;on, quod commune exultat cum differentijs &longs;uaui&longs;&longs;imum e&longs;t; magadari <emph.end type="italics"/> <pb pagenum="269" xlink:href="009/01/269.jpg"/><emph type="italics"/>autem ex contrarijs vocibus con&longs;i&longs;tat, propterea in Diapa&longs;on magadari &longs;ol&ecaron;&rpar;<emph.end type="italics"/> Hic <lb/>
repetenda &longs;unt, qu&aelig; probl. </s>
          <s id="s.004709">17. annotaui, vbi quid Magadis, &amp; Magadari <lb/>
explicatum e&longs;t. </s>
          <s id="s.004710">repetenda &longs;unt pariter, qu&aelig; in 35. probl. </s>
          <s id="s.004711">de pr&aelig;&longs;tantia con&shy;<lb/>
&longs;onanti&aelig; Diapa&longs;on &longs;unt dicta. </s>
          <s id="s.004712">verba illa <emph type="italics"/>&lpar;Cum finiat ad dimidiam&rpar;<emph.end type="italics"/> <expan abbr="intellig&emacr;-da">intelligen&shy;<lb/>
da</expan> &longs;unt de Diapente, cuius rationis termini &longs;unt 1 1/2. qui ad dimidium fi&shy;<lb/>niunt; po&longs;tea videtur aliquid addendum pro Diate&longs;&longs;aron, cuius <expan abbr="nimir&umacr;">nimirum</expan> ter&shy;<lb/>
mini &longs;unt 1 1/3. qui ad vnam tertiam finiunt; nequeunt igitur horum termi&shy;<lb/>
norum con&longs;onanti&aelig; Diapente, &amp; Diate&longs;&longs;aron, e&longs;&longs;e eiu&longs;dem facultatis cum <lb/>
Diapa&longs;on, cuius rationis termini &longs;unt integri, vt 2. ad 1. verba illa <emph type="italics"/>&lpar;Pr&aelig;te&shy;<lb/>rea ip&longs;i hypati accidit, &amp; c.&rpar;<emph.end type="italics"/> vt intelligantur, vide problem. </s>
          <s id="s.004713">24. cum &longs;ua ex&shy;<lb/>
plicatione.</s>
        </p>
        <p type="main">
          <s id="s.004714"><arrow.to.target n="marg385"/></s>
        </p>
        <p type="margin">
          <s id="s.004715"><margin.target id="marg385"/>394</s>
        </p>
        <p type="main">
          <s id="s.004716">Probl. 41. <emph type="italics"/>&lpar;Cur &longs;uauius cantum audimus, quem &longs;cimus, quam quem ignora&shy;<lb/>
mus? </s>
          <s id="s.004717">Vtrum, quoniam cum <expan abbr="cantilen&atilde;">cantilenam</expan> agno&longs;cimus, manife&longs;tior e&longs;t, qui veluti &longs;co&shy;<lb/>
pum, a&longs;&longs;equatur. </s>
          <s id="s.004718">cogno&longs;centium autem &longs;peculatio &longs;uauis e&longs;t. </s>
          <s id="s.004719">An quia accidit, vt <lb/>
auditor vn&agrave; cum cantore afficiatur, qui notam cantat cantilenam, nam tunc audi&shy;<lb/>
tor illi qua&longs;i &longs;uccinit. </s>
          <s id="s.004720">Solet autem qui&longs;que alacriter canere, ni&longs;i ob aliquam nece&longs;&shy;<lb/>
&longs;itatem id faciat&rpar;<emph.end type="italics"/> Lege problem. </s>
          <s id="s.004721">5. eiu&longs;que explicationem, <expan abbr="erit&qacute;">eritque</expan> huic etiam <lb/>
&longs;atisfactum.</s>
        </p>
        <p type="main">
          <s id="s.004722"><arrow.to.target n="marg386"/></s>
        </p>
        <p type="margin">
          <s id="s.004723"><margin.target id="marg386"/>395</s>
        </p>
        <p type="main">
          <s id="s.004724">Probl. 42. <emph type="italics"/>&lpar;Cur nec bis Diapente, nec bis Diate&longs;&longs;aron con&longs;onant, &longs;ed bis Dia&shy;<lb/>
pa&longs;on. <!-- KEEP S--></s>
          <s id="s.004725">An quod Diapente con&longs;onantia est in proportione &longs;e&longs;quialtera? </s>
          <s id="s.004726">quod &longs;i tres <lb/>
&longs;e&longs;quialteri, aut &longs;e&longs;quitertij numeri ordine di&longs;ponantur, extremi <expan abbr="null&atilde;">nullam</expan> inuicem pro&shy;<lb/>
portionem habebunt, <expan abbr="neq;">neque</expan> enim multiplices, <expan abbr="neq;">neque</expan> &longs;uperparticulares erunt: At con&shy;<lb/>&longs;onantia Diapa&longs;on, quoniam in dupla ratione con&longs;i&longs;tit, qua duplicata, quadruplam <lb/>
extremi rationem obtinebunt. </s>
          <s id="s.004727">Itaque cum con&longs;onantia ex &longs;onis con&longs;iet proportio&shy;<lb/>
nem, habentibus, <expan abbr="proportionem&qacute;">proportionemque</expan>; habeant ij, qui interuallo bis Diapa&longs;on compo&shy;<lb/>
nuntur; minim&egrave; autem, ij, qui bis Diate&longs;&longs;aron, aut bis Diapente interuallis conti&shy;<lb/>
nentur; idcirco &longs;oni bis Diapa&longs;on con&longs;oni &longs;unt, c&aelig;teri ver&ograve; <expan abbr="nequaqu&atilde;">nequaquam</expan> ob pr&aelig;dicta&rpar;<emph.end type="italics"/><lb/>
Qu&aelig; dicta &longs;unt ad probl. </s>
          <s id="s.004728">34. &amp; 35. totum fer&egrave; hunc locum illu&longs;trant. </s>
          <s id="s.004729">C&aelig;&shy;<lb/>
terum <expan abbr="qu&atilde;do">quando</expan> Mu&longs;ici volunt duas &longs;e&longs;quialteras ratione &longs;imul addere, di&longs;po&shy;<lb/>
nunt ordine tres numeros habentes inuicem &longs;e&longs;quialteram rationem, vt &longs;e&shy;<lb/>
quentes 9. 6. 4. quam deinde habent rationem extremi 9. &amp; 4. eam dicunt <lb/>
<expan abbr="compo&longs;it&atilde;">compo&longs;itam</expan> ex duabus &longs;e&longs;quialteris: qu&aelig; quidem e&longs;t dupla &longs;e&longs;quiquarta, qu&aelig; <lb/>
con&longs;onanti&aelig; faciend&aelig; inepta e&longs;t; &longs;iue qu&aelig; non e&longs;t con&longs;onantia harmonica; <lb/>
vnde Mu&longs;ici dicunt eo&longs;dem numero nullam habere rationem, ide&longs;t harmo&shy;<lb/>
nicam, cum omnis harmonica &longs;it, aut multiplex, aut &longs;uperparticularis, vn&shy;<lb/>de patet cur bis Diapente nullam pariat con&longs;onantiam. </s>
          <s id="s.004730">Similiter, du&aelig; ra&shy;<lb/>tiones &longs;e&longs;quiterti&aelig;, 16. 12. 9. addit&aelig; efficiunt rationem, qu&aelig; e&longs;t inter 16. &amp; <lb/>
9. qu&aelig; non e&longs;t harmonica, quia neque multiplex, neque &longs;uperpendicularis <lb/>
e&longs;t; ideo apud Mu&longs;icos nulla e&longs;t; quamuis re vera ab Arithmeticis dicatur, <lb/>
&amp; &longs;it &longs;uperpartiens, &amp; in &longs;pecie &longs;uperquintupartiens nonas. </s>
          <s id="s.004731">Du&aelig; ver&ograve; du&shy;<lb/>
pl&aelig;, vti 4. 2. 1. eo modo conflant rationem inter 4. &amp; 1. qu&aelig; multiplex e&longs;t, <lb/>&amp; quadrupla dicitur, ide&ograve; harmonica e&longs;t portio: vnde patet ratio, cur du&aelig; <lb/>
Diapa&longs;on con&longs;onant. </s>
          <s id="s.004732">talis autem con&longs;onantia appellatur Di&longs;diapa&longs;on, cu&shy;<lb/>
ius forma e&longs;t in ratione quadrupla.</s>
        </p>
        <p type="main">
          <s id="s.004733"><arrow.to.target n="marg387"/></s>
        </p>
        <p type="margin">
          <s id="s.004734"><margin.target id="marg387"/>396</s>
        </p>
        <p type="main">
          <s id="s.004735">Probl. 43. <emph type="italics"/>&lpar;Cur &longs;i quis <expan abbr="p&longs;all&etilde;s">p&longs;allens</expan> neten appreh&ecaron;dat, &longs;ola hypate &longs;ub&longs;onare videtur? <lb/>
</s>
          <s id="s.004736">An <expan abbr="quoni&atilde;">quoniam</expan> nete de&longs;inens &amp; elangue&longs;cens euadit hypate; <expan abbr="indici&utilde;">indicium</expan>, qu&ograve;d po&longs;t hypaten <emph.end type="italics"/>-<pb pagenum="270" xlink:href="009/01/270.jpg"/><emph type="italics"/>neten canore apti&longs;&longs;im&egrave; licet. </s>
          <s id="s.004737">qua&longs;i. </s>
          <s id="s.004738">n. </s>
          <s id="s.004739">cantus illius, &longs;it etiam huius &longs;imilitudinem ex <lb/>
illa capiunt. </s>
          <s id="s.004740">c&ugrave;m <expan abbr="a&utilde;t">aut</expan> Echo eius cantus quidam &longs;it &lpar;e&longs;t. </s>
          <s id="s.004741">n. </s>
          <s id="s.004742">tactus vocis netes de&longs;inen&shy;<lb/>
tis&rpar; &longs;onus idem exi&longs;tens &longs;ono hypates, merit&ograve; ob &longs;imilitudinem nete videtur moue&shy;<lb/>
re hypaten. </s>
          <s id="s.004743">&longs;cimus enim neten appr&aelig;hen&longs;am non moueri; videntes ver&ograve; hypatem <lb/>
non appr&aelig;hen&longs;am, &amp; &longs;onitum ip&longs;ius audientes, ip&longs;am &longs;onare credimus. </s>
          <s id="s.004744">quod qui&shy;<lb/>
dem in multis nobis accidit, in quibus <expan abbr="neq;">neque</expan> ratione, <expan abbr="neq;">neque</expan> &longs;en&longs;u po&longs;&longs;umus certi ali&shy;<lb/>
quid videre. </s>
          <s id="s.004745">Pr&aelig;terea &longs;i nete maxim&egrave; intenta percutiatur, accidit iugum tremere, <lb/>
nihil igitur mirum. </s>
          <s id="s.004746">ip&longs;o commoto, omnes chordas &longs;imul commoueri, nec ab&longs;urdum <lb/>
eas &longs;onum facere. </s>
          <s id="s.004747">&longs;onus quidem netes, &amp; de&longs;inens, &amp; incipiens alienus e&longs;t &agrave; c&aelig;te&shy;<lb/>ris: de&longs;inens tamen idem c&ugrave;m hypate: quo addito propri&aelig; ip&longs;ius motioni, illius to&shy;<lb/>
tum videri, nihil ab&longs;urdi. </s>
          <s id="s.004748">e&longs;t ver&ograve; maior, quam communis reliquarum chordarum <lb/>&longs;onus, quod ill&aelig; quidem, qua&longs;i &agrave; nete, propul&longs;&aelig; molliter &longs;onant: nete ver&ograve; totis vi&shy;<lb/>
ribus, omnium quippe vehementi&longs;&longs;ima. </s>
          <s id="s.004749">it aque &longs;ecundarius eius &longs;onus &longs;uperior reli&shy;<lb/>
quis erit; pr&aelig;&longs;ertim c&ugrave;m l&aelig;ui&longs;&longs;imo motu moueantur&rpar;<emph.end type="italics"/> Idem qu&aelig;&longs;iuit num. </s>
          <s id="s.004750">24. qu&aelig; <lb/>
ibi dicta &longs;unt, huc etiam pertinent. </s>
          <s id="s.004751">quibus repetitis melius &longs;equentem pa&shy;<lb/>
raphra&longs;im percipies. </s>
          <s id="s.004752">Verum ante omnia antiqu&aelig; lyr&aelig; ex antiquis monu&shy;<lb/>
mentis figuram oculis &longs;ubijciam.</s>
        </p>
        <figure id="id.009.01.270.1.jpg" place="text" xlink:href="009/01/270/1.jpg"/>
        <p type="main">
          <s id="s.004753">Porr&ograve;, vt tradit Vincentius Galil&aelig;us in &longs;uis Dialogis, erat eius figura, <lb/>
qua&longs;i ex caprino capite con&longs;tructa, cuius duo brachia erant capr&aelig; cornua; <lb/>
inferior pars cranium, qu&aelig; tota ba&longs;i complanat&aelig; ita &longs;uperponebatur, vt in <lb/>
quouis po&longs;ita plano recta con&longs;i&longs;teret, <expan abbr="neq;">neque</expan> vt ge&longs;taretur, opus erat. </s>
          <s id="s.004754">chord&aelig; <lb/>
ip&longs;ius, qu&aelig; e&longs;&longs;ent, &amp; qua ratione e&longs;&longs;ent collocat&aelig;, in figura apparet; quot <lb/>
autem fuerint, pro temporum varietate determinandum e&longs;t, nam primo 4. <lb/>
deinde 7. demum 8. fuerunt, &amp; plures etiam. </s>
          <s id="s.004755">Iugum autem, cuius cau&longs;a fi&shy;<lb/>
guram appo&longs;ui, erat &longs;upernum illud tran&longs;uer&longs;arium, cui fides annecteban&shy;<lb/>
tur, vt idem Vincentius a&longs;&longs;erit. </s>
          <s id="s.004756">nunc ad textum.</s>
        </p>
        <pb pagenum="271" xlink:href="009/01/271.jpg"/>
        <p type="main">
          <s id="s.004757">Cur &longs;i quis neten c&aelig;teris intactis, percu&longs;&longs;am, ac &longs;onantem manu compre&shy;<lb/>
hendat, ac &longs;i&longs;tat, videbitur audire hypaten? </s>
          <s id="s.004758">primo re&longs;pondet, id accidere, <lb/>
quia &longs;onus ille extremus, quo nete ce&longs;&longs;at, euadit &longs;onus ip&longs;ius hypates. </s>
          <s id="s.004759">pro&shy;<lb/>
pterea igitur <expan abbr="t&utilde;c">tunc</expan> exi&longs;timamus audire hypatem. </s>
          <s id="s.004760">cuius rei indicium e&longs;t, quod <lb/>
qui cantant hypaten, facil&egrave; ad neten cantandam tran&longs;eunt; c&ugrave;m enim can&shy;<lb/>
tus hypates, &longs;it etiam cantus netes, &amp; veluti illius echo, facil&egrave; e&longs;t ex hypa&shy;<lb/>
te &longs;imilitudinem netes accipere. </s>
          <s id="s.004761">pr&aelig;terea in hoc decipimur, quia cum au&shy;<lb/>
diamus &longs;onum hypates, <expan abbr="eam&qacute;">eamque</expan>; minim&egrave; tentam videamus, quemadmodum <lb/>
neten videmus, eam &longs;onare merit&ograve; credimus; quod quidem in multis acci&shy;<lb/>
dit, vbi nec ratio, nec &longs;en&longs;us attingit, &longs;ic in &longs;cena aliquando putamus quem&shy;<lb/>
piam tuba &longs;onare, quod eam ori ip&longs;ius admotam videamus, c&ugrave;m tamen <lb/>
alius po&longs;t &longs;cenam lateat, qui tuba &longs;onet. </s>
          <s id="s.004762">&longs;imile accidit in nete, &amp; hypate. <lb/>
</s>
          <s id="s.004763">terti&ograve; re&longs;pondet, quod quando quis neten percutit, qu&aelig; omnium inten&longs;i&longs;&longs;i&shy;<lb/>
ma e&longs;t, accidit, vt iugum, cui illa nectitur, moueatur, tremetque, ex quo <lb/>
tremore fit, vt reliqu&aelig; omnes chord&aelig; moueantur, ac tremant, &amp; proinde <lb/>
&longs;onum edant. </s>
          <s id="s.004764">c&ugrave;m autem &longs;onus netis, &amp; incipiens, &amp; de&longs;inens &longs;it fer&egrave; idem <lb/>
cum &longs;ono hypates, accidit in hoc ca&longs;u, vt &longs;onus de&longs;inentis netis, vniatur <lb/>
cum &longs;ono hypates, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; manife&longs;t&egrave; totus ille &longs;onus hypates e&longs;&longs;e videatur. <lb/>
</s>
          <s id="s.004765">c&aelig;ter&aelig; ver&ograve; chord&aelig; non audiuntur ob eorum &longs;onorum paruitatem, qui ide&ograve; <lb/>
exigui &longs;unt, quia excitati &longs;unt ab impul&longs;u, &amp; motu iugi, qui exiguus erat. <lb/>
</s>
          <s id="s.004766">&longs;onus autem netes illis omnibus &longs;uperior e&longs;t, &amp; quia ip&longs;a prim&ograve; percu&longs;&longs;a e&longs;t, <lb/>
&amp; quia inten&longs;i&longs;&longs;ima e&longs;t, &amp; celerrim&egrave; mouetur.</s>
        </p>
        <p type="main">
          <s id="s.004767"><arrow.to.target n="marg388"/></s>
        </p>
        <p type="margin">
          <s id="s.004768"><margin.target id="marg388"/>397</s>
        </p>
        <p type="main">
          <s id="s.004769">Probl. 44. <emph type="italics"/>&lpar;Cur &longs;uauius &longs;olitariam cantilenam audimus, c&ugrave;m ad tibiam, quam <lb/>
c&ugrave;m ad lyram cantatur? </s>
          <s id="s.004770">An quod omne &longs;uaue, quod <expan abbr="mixi&utilde;">mixtum</expan> est cum &longs;uauiori, &longs;ua&shy;<lb/>
uius redditur? </s>
          <s id="s.004771">Atqui tibia, quam lyra &longs;uauior e&longs;t: erg&ograve; cantilena tibi&aelig; admixta <lb/>
&longs;uauior erit, quam lyr&aelig;. </s>
          <s id="s.004772">quoniam omne mixtum, immixto &longs;uauius, modo quis &longs;en&shy;<lb/>
&longs;um amborum percipiat. </s>
          <s id="s.004773">Vinum enim oximele &longs;uauius e&longs;t, quoniam qu&aelig; natura <lb/>permi&longs;cet, long&egrave; melius temperantur, quam qu&aelig; &agrave; nobis mi&longs;centur. </s>
          <s id="s.004774">Vinum enim <lb/>
ex acuto, &amp; dulci &longs;apore mixtum e&longs;t. </s>
          <s id="s.004775">Idem manifestant mala punica, qu&aelig; vino&longs;a <lb/>
appellantur. </s>
          <s id="s.004776">Enimuer&ograve; cantilena, &amp; tibia inuicem mi&longs;centur, ob &longs;imilitudinem, <lb/>
&longs;piritu enim <expan abbr="vtraq;">vtraque</expan> perficitur. </s>
          <s id="s.004777">&longs;onus autem lyr&aelig;, quoniam non &longs;piritu &longs;it, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan> mi&shy;<lb/>
nus &longs;en&longs;ibilis, quam tibi&aelig;, minus voci immi&longs;cetur: quare &longs;en&longs;ui di&longs;crimen inferens, <lb/>
minus &longs;uauis e&longs;t; quemadmodum de &longs;aporibus dictum e&longs;t. </s>
          <s id="s.004778">Adde, quod tibia &longs;oni&shy;<lb/>
tu &longs;uo, &amp; human&aelig; vocis &longs;imilitudine, <expan abbr="pleros&qacute;">plerosque</expan> cantilen&aelig; errores occultare pote&longs;t. <lb/>
</s>
          <s id="s.004779">Sonus autem lyr&aelig; c&ugrave;m exiguus, <expan abbr="atq;">atque</expan> voci immixtus, <expan abbr="ideoq;">ideoque</expan> manife&longs;tus per &longs;e, ma&shy;<lb/>
nife&longs;tum cantilen&aelig; errorem, qua&longs;t appo&longs;ita regula facit. </s>
          <s id="s.004780">c&ugrave;m ver&ograve; multa in can&shy;<lb/>
tando peccentur, quod ex <expan abbr="vtri&longs;q;">vtri&longs;que</expan> compo&longs;itum e&longs;t, nece&longs;&longs;ari&ograve; peius e&longs;t&rpar;<emph.end type="italics"/> &longs;atis ex &longs;e <lb/>
clarum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004781"><arrow.to.target n="marg389"/></s>
        </p>
        <p type="margin">
          <s id="s.004782"><margin.target id="marg389"/>398</s>
        </p>
        <p type="main">
          <s id="s.004783">Probl. 45. <emph type="italics"/>&lpar;Cur neruum illum, quem Me&longs;en, &longs;eu medium dicimus, &longs;ic appella&shy;<lb/>
mus; c&ugrave;m inter &longs;eptem, non autem inter octo &longs;it <expan abbr="medi&utilde;">medium</expan>? </s>
          <s id="s.004784">An quod olim harmoni&aelig; <lb/>
&longs;eptem neruis con&longs;tabant, quorum medium e&longs;t. </s>
          <s id="s.004785">Pr&aelig;terea eorum, qu&aelig; inter qu&aelig;uis <lb/>
extrema continentur illud &longs;olum, quod medium e&longs;t, principium ctiam quoddam e&longs;t: <lb/>
quod enim in medio eorum e&longs;t, qu&aelig; in aliquo interuallo ad vtrumuis extremorum <lb/>
vergunt; illud &longs;olum, &amp; <expan abbr="medi&utilde;">medium</expan>, &amp; principium est. </s>
          <s id="s.004786">c&ugrave;m igitur in harmoni&aelig; inter&shy;<lb/>
uillo extrema &longs;int hypate, &amp; nete, <expan abbr="his&qacute;">hisque</expan> interiaceant reliqui &longs;oni, quorum is, qui <lb/>
Me&longs;e dicitur, e&longs;t etiam principium, quippe <expan abbr="principi&utilde;">principium</expan> alterius tetrachordi, idcirc&ograve;<emph.end type="italics"/> <pb pagenum="272" xlink:href="009/01/272.jpg"/><emph type="italics"/>merit&ograve; Me&longs;e, &longs;eu medius dictus e&longs;t. </s>
          <s id="s.004787">principium enim, &amp; medium vnum &longs;olum e&longs;&longs;e <lb/>
potuit eorum, qu&aelig; inter extrema aliqua continentur&rpar;<emph.end type="italics"/> Idem qu&aelig;&longs;iuit &longs;upra num, <lb/>
25. vide igitur, qu&aelig; ibi annotaui. </s>
          <s id="s.004788">vide pr&aelig;terea, qu&aelig; nu. 35. de Tetrachor&shy;<lb/>
dis dicta &longs;unt, vbi cur Me&longs;e &longs;it dux, &amp; principium primi tetrachordi appa&shy;<lb/>
rebit. </s>
          <s id="s.004789">Qu&aelig;&longs;tioni autem re&longs;pondet duplici modo. </s>
          <s id="s.004790">prim&ograve;, quemadmodum <lb/>
etiam in 25. &longs;ecund&ograve;, re&longs;pondet idcirc&ograve; Me&longs;en ita e&longs;&longs;e appellatam, quod in&shy;<lb/>
ter eos &longs;onos inter extrema contentos rationem principij haberet, &longs;olent <lb/>
enim ea, qu&aelig; inter extrema aliqua &longs;unt <expan abbr="c&aelig;teror&utilde;">c&aelig;terorum</expan> principia, e&longs;&longs;e <expan abbr="eti&atilde;">etiam</expan> media.</s>
        </p>
        <p type="main">
          <s id="s.004791">Probl. 46. e&longs;t idem cum &longs;uperiori 22. <expan abbr="vtrumq;">vtrumque</expan> autem ex &longs;e ita manife&longs;tum <lb/>
e&longs;t, vt <expan abbr="ab&longs;q;">ab&longs;que</expan> harmonica facultate prob&egrave; intelligatur.</s>
        </p>
        <p type="main">
          <s id="s.004792">Probl. 47. idem cum 26. in quibus ait, facilius e&longs;&longs;e canere acutum, qu&agrave;m <lb/>
graue: in 37. ver&ograve; contrarium: difficilius e&longs;&longs;e cantare acutum, qu&agrave;m gra&shy;<lb/>
ue. </s>
          <s id="s.004793">&longs;ibi conciliabitur, &longs;i dixeris, h&aelig;c dicta e&longs;&longs;e problematic&egrave;.</s>
        </p>
        <p type="main">
          <s id="s.004794"><arrow.to.target n="marg390"/></s>
        </p>
        <p type="margin">
          <s id="s.004795"><margin.target id="marg390"/>399</s>
        </p>
        <p type="main">
          <s id="s.004796">Probl. 48. <emph type="italics"/>&lpar;Cur veteres c&ugrave;m &longs;eptem neruis concentus facerent, hypaten, non <lb/>
neten reliquerunt? </s>
          <s id="s.004797">An non hypate, &longs;ed nunc <expan abbr="vocat&atilde;">vocatam</expan> paraneten, toniqu&eacute; interuallum <lb/>
ab&longs;tulerunt, vltima ver&ograve; Acutiden&longs;i pro Me&longs;e vtebantur propterea ip&longs;am Me&longs;en <lb/>
appellarunt. </s>
          <s id="s.004798">An quod &longs;uperioris Tetrachordi finis <expan abbr="principi&utilde;">principium</expan> erat inferioris, &amp; me&shy;<lb/>
dium extremorum habebat &longs;ecundum &longs;oni proportionem&rpar;<emph.end type="italics"/> Idem qu&aelig;&longs;iuit &longs;upra <lb/>
num. </s>
          <s id="s.004799">7. vide igitur, qu&aelig; ibi expo&longs;ui; hoc loco qu&aelig;rendum re&longs;tat, quid &longs;it <lb/>
illud Acutiden&longs;um. </s>
          <s id="s.004800">pro qua re vide Ari&longs;toxenum lib. 3. &amp; Euclidem in I&longs;a&shy;<lb/>
goge ad Mu&longs;icam: Zarlinum tandem lib. 2. &longs;upplem. </s>
          <s id="s.004801">&amp; 5. qu&aelig; res, quamuis <lb/>
plura dicant, adhuc ob antiquitatem non &longs;atis intelliguntur. </s>
          <s id="s.004802">Quid e&longs;&longs;et Den&shy;<lb/>
&longs;um, exponit &longs;ic Euclides: Den&longs;um e&longs;t certa trium &longs;onorum, vel duorum <lb/>
interuallorum ex ijs, qui Diate&longs;&longs;aron componunt di&longs;po&longs;itio talis, vt inter&shy;<lb/>
uallum, quod con&longs;tituunt h&aelig; tres voces, vel h&aelig;c duo interualla, &longs;it maius <lb/>
reliquo interuallo ip&longs;ius Diate&longs;&longs;aron. <!-- KEEP S--></s>
          <s id="s.004803">ponit pr&aelig;terea &longs;onorum alios e&longs;&longs;e <lb/>
Grauiden&longs;os, alios Medioden&longs;os, alios Acutiden&longs;os. </s>
          <s id="s.004804">quibus con&longs;onant, qu&aelig; <lb/>
Ari&longs;toxenus ait, dum ait den&longs;um fui&longs;&longs;e illam partem Diate&longs;&longs;aron, in qua <lb/>
erant duo toni; &longs;ic enim reliquum, quod erat <expan abbr="&longs;emitoni&utilde;">&longs;emitonium</expan> mult&ograve; minus erat. <lb/>
</s>
          <s id="s.004805">erant autem vari&aelig; Diate&longs;&longs;aron diui&longs;iones pro Generum varietate. </s>
          <s id="s.004806">Antiqui <lb/>
igitur &longs;ecundum aliquam eorum diui&longs;ionem, qu&aelig; den&longs;um in parte acuta po&shy;<lb/>
nebat vltimam chordam illius den&longs;i, qu&aelig; pariter vltima erat illius Tetra&shy;<lb/>
chordi, &longs;iue Diate&longs;&longs;aron pro media vtebantur, <expan abbr="eam&qacute;">eamque</expan>; idcirc&ograve; Me&longs;en appel&shy;<lb/>
larunt. </s>
          <s id="s.004807">qu&aelig; de Tetrachordis &longs;ubdit clara &longs;unt ex dictis num. </s>
          <s id="s.004808">33.</s>
        </p>
        <p type="main">
          <s id="s.004809">Per &longs;uperius Tetrachordum intelligere debemus Acutius, &longs;ic enim finis <lb/>
illius erit principium inferioris, ide&longs;t grauioris Tetrachordi; vult enim <lb/>
Ari&longs;t. vt &longs;upra non &longs;emel vi&longs;um e&longs;t, acutiorem &longs;onum Tetrachordi e&longs;&longs;e illius <lb/>
principium. </s>
          <s id="s.004810">vide pr&aelig;&longs;ertim num. </s>
          <s id="s.004811">45. Antiqui igitur Paraneten omittentes, <lb/>
aliam, qu&aelig; vltima erat in parte den&longs;a Tetrachordi, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; principium pri&shy;<lb/>
mi, &amp; finis &longs;ecundi erat, pro Me&longs;e vtebantur, ex quibus qu&aelig;&longs;tioni vtcunque <lb/>
inuolut&egrave; &longs;atis re&longs;pondet.</s>
        </p>
        <p type="main">
          <s id="s.004812"><arrow.to.target n="marg391"/></s>
        </p>
        <p type="margin">
          <s id="s.004813"><margin.target id="marg391"/>400</s>
        </p>
        <p type="main">
          <s id="s.004814">Probl. 49. <emph type="italics"/>&lpar;Cur Trag&oelig;diarum choris, <expan abbr="neq;">neque</expan> &longs;ubdorio, <expan abbr="neq;">neque</expan> &longs;ubphrygio cantandi <lb/>
genere, vti mos e&longs;t? </s>
          <s id="s.004815">An quod modul&ubreve;m pr&aelig;&longs;tare h&aelig; harmoni&aelig; nequeunt, quo choris <lb/>
vald&egrave; opus e&longs;t; mores habet hypophrygius practicos &lpar;<expan abbr="quamobr&etilde;">quamobrem</expan> in Gerione excur&shy;<lb/>&longs;us, &amp; armatio ip&longs;o perficiunter&rpar; Subdorius ver&ograve; magnificus, constans, <expan abbr="gram&longs;q;">graui&longs;que</expan> <lb/>e&longs;t, quocirca omnium harmoniarum maxim&egrave; cythar&aelig; conuenit. </s>
          <s id="s.004816">&longs;ed h&aelig;c ambo, vt<emph.end type="italics"/> <pb pagenum="273" xlink:href="009/01/273.jpg"/><emph type="italics"/>choris minim&egrave; congruunt, &longs;ic &longs;cenis &longs;unt magis dome&longs;tica; etenim &longs;cena Heroum <lb/>
facta, dictaqu&eacute; &longs;imulat. </s>
          <s id="s.004817">Veterum autem duces &longs;oli Heroes fuerunt. </s>
          <s id="s.004818">populi ver&ograve; erant <lb/>
Homines, ex quibus chorus con&longs;tat. </s>
          <s id="s.004819">quapropter choro competunt mores flebiles, &amp; <lb/>&aelig;quales, &amp; moduli; h&aelig;c enim humana &longs;unt. </s>
          <s id="s.004820">qu&aelig;qu&eacute; harmoni&aelig; c&aelig;ter&aelig; ali&aelig; non ha&shy;<lb/>
bent. </s>
          <s id="s.004821">minim&egrave; ver&ograve; hypophrygius, qui lymphaticus, <expan abbr="atq;">atque</expan> bacchicus e&longs;t. </s>
          <s id="s.004822">At mixto&shy; <lb/>
lydius illa pr&aelig;&longs;tare pote&longs;t; propterea eo aliquo modo afficimur. </s>
          <s id="s.004823">magis autem debi&shy;<lb/>
les afficiuntur, qu&agrave;m fortes, quapropter ille choris conuenit. </s>
          <s id="s.004824">Hypodorio ver&ograve;, &amp; <lb/>
hypophrygio agimus, qui choro non conueniunt; est enim chorus, veluti curator <lb/>
quidam otio&longs;us, ijs &longs;olum beneuolentiam pr&aelig;bens, quibus ade&longs;t&rpar;<emph.end type="italics"/> lege Probl. 30. <lb/>
vbi idem qu&aelig;&longs;iuit. </s>
          <s id="s.004825">lege pr&aelig;terea, qu&aelig; ad num. </s>
          <s id="s.004826">15. annotaui: ex quibus lo&shy;<lb/>
cum hunc intelliges. </s>
          <s id="s.004827">quod ait <emph type="italics"/>&lpar;In Gerione excur&longs;us, &amp; armatio&rpar;<emph.end type="italics"/> exi&longs;timo, <lb/>
Gerionem hunc Trag&oelig;diam fui&longs;&longs;e illam, quam Suidas in Nicomacho inter <lb/>
Nicomachi Alexandrini Tragici Trag&oelig;dias recen&longs;et. </s>
          <s id="s.004828">excur&longs;us ver&ograve;, &amp; ar&shy;<lb/>
matio erant partes, quibus con&longs;tabat Trag&oelig;dia, quemadmodum no&longs;tr&aelig; in <lb/>
<expan abbr="quinq;">quinque</expan> actus diuiduntur. </s>
          <s id="s.004829">vide Zarlinum cap. 5. prim&aelig; partis In&longs;tit. <!-- REMOVE S-->vbi tra&shy;<lb/>
dit fabulam quandam Delonam dictam, qu&aelig; in modum Trag&oelig;di&aelig; habeba&shy;<lb/>
tur, fui&longs;&longs;e diui&longs;am in 5. partes, Explorationem, Prouocationem, Iambicum, <lb/>
Spondeum, &amp; Ouationem, aut Saltationem.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004830"><arrow.to.target n="marg392"/></s>
        </p>
        <p type="margin">
          <s id="s.004831"><margin.target id="marg392"/>401</s>
        </p>
        <p type="main">
          <s id="s.004832">Probl. 50. <emph type="italics"/>&lpar;Cur in &longs;onis grauioribus &longs;ymphonia mollior euadit? </s>
          <s id="s.004833">An quod mo&shy;<lb/>
dulatus cantus &longs;ua quidem natura mollis e&longs;t, &amp; quietus: &longs;ed admixti numeri, &longs;eu <lb/>
rithmi ratione a&longs;perior redditur, &amp; mouentior. </s>
          <s id="s.004834">c&ugrave;m igitur &longs;onus granis, mollis, &amp; <lb/>quietus &longs;it; &longs;onus autem acutus mouens, &amp; irritans; omnin&ograve; &longs;equitur admixito&shy;<lb/>
ne eiu&longs;dem numeri grauiorem cantum debere e&longs;&longs;e <expan abbr="quoq;">quoque</expan> molliorem; e&longs;t enim modu&shy;<lb/>
latus cantus ex ijs, qu&aelig; mollia &longs;unt&rpar;<emph.end type="italics"/> &longs;oni grauiores natura molliores &longs;unt, ide&longs;t, <lb/>
molles mores reddunt, &longs;eu molles, <expan abbr="eff&oelig;minatos&qacute;">eff&oelig;minatosque</expan>; decent magis, qu&agrave;m &longs;o&shy;<lb/>
ni acuti: moduli pr&aelig;terea, &longs;iue cantilen&aelig; modulat&aelig;, aut rithmi, molles na&shy;<lb/>
tura &longs;unt, vt &longs;uperius num. </s>
          <s id="s.004835">38. explicatum e&longs;t: &longs;i igitur vtrique &amp; graui, &amp; <lb/>
acuto addatur numerus, nece&longs;&longs;ari&ograve; graue mollius euadet.</s>
        </p>
        <p type="main">
          <s id="s.004836"><arrow.to.target n="marg393"/></s>
        </p>
        <p type="margin">
          <s id="s.004837"><margin.target id="marg393"/>402</s>
        </p>
        <p type="main">
          <s id="s.004838">Probl. 51. <emph type="italics"/>&lpar;Cur &aelig;qualium, &amp; &longs;imilium doliorum, &longs;i vnum &longs;it inane; alterum <lb/>
ver&ograve; dimidiatum tinnitus eorum Diapa&longs;on re&longs;onabunt? </s>
          <s id="s.004839">An quoniam &longs;onus dimi&shy;<lb/>
diati cum &longs;ono vacui duplam habent inuicem proportionem: quid enim in i&longs;tis po&shy;<lb/>
tius, qu&agrave;m in fi&longs;tulis res euariat? </s>
          <s id="s.004840">motum <expan abbr="namq;">namque</expan> e&ubreve;ndem acutiorem putamus, quem <lb/>
velociorem. </s>
          <s id="s.004841">in maioribus ver&ograve; aer tardius occurrit, vt in duplis dupl&ograve;, &amp; c&aelig;teris <lb/>
&longs;ecundum proportionem. </s>
          <s id="s.004842">in vtris etiam, duplus c&ugrave;m dimidio Diapa&longs;on con&longs;onat&rpar;<emph.end type="italics"/><lb/>
qu&aelig; initio dixi in diui&longs;ione monochordij, &amp; alibi, &longs;ed pr&aelig;&longs;ertim in Probl. 23. <lb/>
locum hunc abund&egrave; declarant. </s>
          <s id="s.004843">Vbicunque enim corpus &longs;onans duplum e&longs;t <lb/>
alterius corporis &longs;onantis, &longs;iue &longs;int chord&aelig;, &longs;iue fi&longs;tul&aelig;, &longs;iue dolia, &longs;iue vtres, <lb/>
re&longs;onant Diapa&longs;on, cuius forma con&longs;i&longs;tit in proportione dupla, qu&aelig; in hu&shy;<lb/>
iu&longs;modi corporum &longs;onis reperitur.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.004844"><emph type="italics"/>Ex Sectione 23.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.004845"><arrow.to.target n="marg394"/></s>
        </p>
        <p type="margin">
          <s id="s.004846"><margin.target id="marg394"/>403</s>
        </p>
        <p type="main">
          <s id="s.004847">Problema 2. <emph type="italics"/>&lpar;Cur nauigia onu&longs;tiora in portu, qu&agrave;m in alto e&longs;&longs;e videntur? </s>
          <s id="s.004848">c&aelig;&shy;<lb/>
lerius enim de alto in terram veniunt, qu&agrave;m de terra in altum prouehantur? <lb/>
</s>
          <s id="s.004849">An quod plus aqu&aelig;, qu&agrave;m minus reniti validius pote&longs;t? </s>
          <s id="s.004850">parua enim oppre&longs;&longs;a onere<emph.end type="italics"/> <pb pagenum="274" xlink:href="009/01/274.jpg"/><emph type="italics"/>cedit, vt demergi nece&longs;&longs;e &longs;it: multa &egrave; contrari&ograve; repellit, ac &longs;ustinet. </s>
          <s id="s.004851">vis enim ea <lb/>
e&longs;t aqu&aelig;. </s>
          <s id="s.004852">vt &longs;ur&longs;um ver&longs;us compellat inferius; erg&ograve;, vt in portu maris par&ugrave;m, &longs;ic <lb/>
mult&ugrave;m in alto e&longs;t: <expan abbr="itaq;">itaque</expan> plus oneris conuehi in portu videbitur, etiam mouebitur <lb/>&aelig;grius, quia magis immergitur, &amp; aqua minus reniti pote&longs;t: at ver&ograve; in alto res <lb/>contra v&longs;u venit&rpar;<emph.end type="italics"/> &longs;en&longs;us verborum Ari&longs;t. &longs;atis per&longs;picuus e&longs;t, res tamen &longs;unt <lb/>
magis expendend&aelig;. </s>
          <s id="s.004853">prim&ograve; <expan abbr="namq;">namque</expan> maxim&egrave; ambigo de experientia ip&longs;a, qu&aelig; <lb/>
huic qu&aelig;&longs;tioni &longs;ubijcitur, &longs;i enim vera &longs;unt ea, qu&aelig; ab A&longs;tronomis afferun&shy;<lb/>tur, vt maris &longs;ph&aelig;ricitatem a&longs;&longs;erant, fal&longs;a nece&longs;&longs;ari&ograve; erit experientia h&aelig;c: <lb/>
aiunt autem ip&longs;i pari velocitate nauigia &egrave; portu in altum euehi, <expan abbr="atq;">atque</expan> ex al&shy;<lb/>to in portum appellant; quod &longs;ignum manife&longs;tum e&longs;t, &longs;uperficiem maris <expan abbr="ex-tim&atilde;">ex&shy;<lb/>
timam</expan> &aelig;qu&egrave; <expan abbr="vndiq;">vndique</expan> &agrave; centro mundi di&longs;tare, ac proinde omnin&ograve; <expan abbr="&longs;ph&aelig;ric&atilde;">&longs;ph&aelig;ricam</expan> e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.004854">Illud po&longs;tea, quod pro &longs;olutione Problematis affert, dum ait, nauim ma&shy;<lb/>
gis in portu, qu&agrave;m in alto demergi &lpar;quoniam plus aqu&aelig;, valeat magis, qu&agrave;m <lb/>
minus, nauigij onus &longs;u&longs;tinere, parua enim aqua oppre&longs;&longs;a onere c&aelig;dit faci&shy;<lb/>lius, qu&agrave;m multa&rpar; non paruam habet difficultatem. </s>
          <s id="s.004855">refragantur enim ma&shy;<lb/>
ximorum <expan abbr="Matnematicor&utilde;">Mathematicorum</expan> demon&longs;trationes. </s>
          <s id="s.004856">Archimedes enim demon&longs;t. </s>
          <s id="s.004857">5. <lb/>
lib. 1. de ijs, qu&aelig; vehuntur in aqua acuti&longs;&longs;im&egrave; demon&longs;trat; &longs;olidarum ma&shy;<lb/>
gnitudinum humido l&aelig;uiorum, in humidum e&ograve; <expan abbr="v&longs;q;">v&longs;que</expan> demergi, vt tanta moles <lb/>
humidi, quanta e&longs;t partis demer&longs;&aelig;, eandem quam tota magnitudo, graui&shy;<lb/>
tatem habeat. </s>
          <s id="s.004858">quod idem Galil&aelig;us Galil&aelig;us, in Italico Di&longs;cur&longs;u de rebus, <lb/>
qu&aelig; aqu&aelig; innatunt, &longs;ubtiliter <expan abbr="c&otilde;probauit">comprobauit</expan>, vt videre e&longs;t apud ip&longs;um pag. </s>
          <s id="s.004859">14. <lb/>
qu&aelig; cum certa &longs;int, &longs;equitur nece&longs;&longs;ari&ograve; fal&longs;um e&longs;&longs;e, maiorem aqu&aelig; copiam <lb/>
alti&ugrave;s nauim qu&agrave;m minorem, extollere. </s>
          <s id="s.004860">dummodo tamen aqua <expan abbr="vtrobiq;">vtrobique</expan> &longs;it <lb/>
eiu&longs;dem grauitatis. </s>
          <s id="s.004861">quare Galil&aelig;us pag. </s>
          <s id="s.004862">17. &longs;ic orationem claudit: valeant <lb/>
inquit, eorum fals&egrave; opiniones, qui exi&longs;timant nauigium facilius &agrave; magna <lb/>
aqu&aelig; copia &longs;u&longs;tineri, qu&agrave;m &agrave; parua: quod Ari&longs;t. &longs;ect. </s>
          <s id="s.004863">23. probl. </s>
          <s id="s.004864">2. credidit: <lb/>cum contr&agrave; verum &longs;it, nauim &aelig;qu&egrave; facil&egrave; in oceano, <expan abbr="atq;">atque</expan> in decem doliorum <lb/>
aqua innatare, ac &longs;u&longs;tineri h&aelig;c ille.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.004865"><emph type="italics"/>Ex Sectione 30.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.004866"><arrow.to.target n="marg395"/></s>
        </p>
        <p type="margin">
          <s id="s.004867"><margin.target id="marg395"/>404</s>
        </p>
        <p type="main">
          <s id="s.004868">Ad 6 Probl. <emph type="italics"/>&lpar;Cur nihil in eo delectamur, quod triangulum duobus rectis pa&shy;<lb/>
res angulos internos habere &longs;pectamus&rpar;<emph.end type="italics"/> vide qu&aelig; lib. 1. Priorum, &longs;ecto <lb/>
3. cap. 3. de hac trianguli proprietate annotaui, cuius etiam &longs;&aelig;pius Ari&longs;t. <lb/>
meminit, nunquam tamen verbum illud, internos, pr&aelig;terquam hic, addi&shy;<lb/>
dit; vt autem ben&egrave; intelligas quinam &longs;int hi anguli interni, &amp; qui externi, <lb/>
&amp; quod etiam rectis externi &aelig;quiualeat, lege qu&aelig; ad tex. <!-- REMOVE S-->39. primi Po&longs;ter, <lb/>
&longs;unt annotata.</s>
        </p>
      </chap>
      <chap>
        <p type="head">
          <s id="s.004869"><emph type="italics"/>Ex Sectione 31.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.004870">Eorum, qu&aelig; ad oculos pertinent,</s>
        </p>
        <p type="main">
          <s id="s.004871"><arrow.to.target n="marg396"/></s>
        </p>
        <p type="margin">
          <s id="s.004872"><margin.target id="marg396"/>405</s>
        </p>
        <p type="main">
          <s id="s.004873">Probl. 7. <emph type="italics"/>&lpar;Quam ob cau&longs;am <expan abbr="vtrunq;">vtrunque</expan> a&longs;pectum &longs;imul diuertere de&longs;tror&longs;um, &amp; <lb/>
&longs;ini&longs;tror&longs;um, &amp; ad nares demittere valemus, &amp; alterum ad dextram, &amp; ad <lb/>
&longs;ini&longs;tram, &longs;imul ver&ograve; vnum dextror&longs;um, alterum &longs;ini&longs;tror&longs;um nequimus; &longs;imiliter <lb/>
<expan abbr="neq;">neque</expan> deor&longs;um, <expan abbr="neq;">neque</expan> &longs;ur&longs;um. </s>
          <s id="s.004874">&longs;imul ver&ograve; ad idem po&longs;&longs;umus, &longs;eparatim ver&ograve; nequa-<emph.end type="italics"/>


<pb pagenum="275" xlink:href="009/01/275.jpg"/><emph type="italics"/>quam? </s>
          <s id="s.004875">An quia quamuis &longs;int duo a&longs;pectus, ex vnico tamen principio eodem modo <lb/>
dependent? </s>
          <s id="s.004876"><expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> autem ita &longs;e habent, quoties alterum extrem&ubreve;μ mouetur, ne&shy;<lb/>ce&longs;&longs;e est alterum con&longs;equi ad idem; alterius enim extremum e&longs;t alterius extremi <lb/>
principium. </s>
          <s id="s.004877">&longs;i igitur res vna nequit, &longs;imul in contraria moueri; nec a&longs;pectus pote&shy;<lb/>
runt: c&ugrave;m ita accidat, vt extrema in partes aduer&longs;as moueantur, &longs;i quidem alter <lb/>
&longs;ur&longs;um, alter deor&longs;um moueatur, initiumqu&eacute; &longs;equi alterum a&longs;pectum; quod impo&longs;&longs;i&shy;<lb/>
bile. </s>
          <s id="s.004878">Oculorum ver&ograve; limitas inde oritur, quia oculorum globi principio continen&shy;<lb/>
tur, quo &amp; &longs;ur&longs;um, &amp; deor&longs;um, &amp; ad latera conuerti po&longs;&longs;int. </s>
          <s id="s.004879">c&ugrave;m igitur ita &longs;int <lb/>
collocati, vt &longs;itu inuicem &longs;imili re&longs;pondeant, <expan abbr="atq;">atque</expan> &longs;int in medio &longs;e &longs;e mouendi &longs;ur&shy;<lb/>
&longs;um, deor&longs;um, &amp; ad latera, eodemqu&eacute; in puncto vi&longs;um habeant, tali &longs;itu pr&aelig;cipu&egrave; <lb/>
ab inuicem &longs;unt inuariabiles. </s>
          <s id="s.004880">qui ver&ograve; in eodem puncto pupillas habent, limi non <lb/>&longs;unt, &longs;ed tamen ab inuicem differ&ubreve;νt: nam alijs nigri aliquid occultatur, &amp; &longs;ur&longs;um <lb/>proijciunt alba, veluti &longs;ternutaturi. </s>
          <s id="s.004881">alijs in angul&ubreve;μ oculi exteriorem, nigr&ubreve;μ vergit, <lb/>
&longs;icuti furio&longs;is: alijs in interiorem ad nares, vt per&longs;onis tragicis, &amp; &longs;eueris, qui &longs;unt <lb/>
contuitu graui. </s>
          <s id="s.004882">Quibus ver&ograve; &longs;itu di&longs;&longs;imili globi &longs;unt po&longs;iti, &longs;ed eodem puncto &longs;tant <lb/>
pupill&aelig;: aut quibus &longs;itus &longs;imilis e&longs;t, &longs;ed non idem punctum pupillarum hi nece&longs;&longs;ari&ograve; <lb/>
limi &longs;unt. </s>
          <s id="s.004883">propterea toru&egrave; a&longs;piciunt, &amp; oculos contrahunt; conantur enim in eun&shy;<lb/>
dem habitum collocare globum, alterum firmum continentes, alter&ubreve; ver&ograve; agitan&shy;<lb/>
tes. </s>
          <s id="s.004884">nece&longs;&longs;ari&ograve; enim limus e&longs;t, cui non eodem de puncto vi&longs;us prodeunt, quippe qui <lb/>
dimotum contuendi principium, perinde ac ille, cui &longs;uppre&longs;&longs;o oculo res vna gemi&shy;<lb/>
nata videtur. </s>
          <s id="s.004885">erg&ograve; &longs;i oculus &longs;ur&longs;um dimotus e&longs;t, terminus in&longs;piciendi deor&longs;um e&longs;t: <lb/>
&longs;ed &longs;i oculus deor&longs;um lap&longs;us e&longs;t, terminus &longs;ur&longs;um. </s>
          <s id="s.004886">Vno ver&ograve; oculo &agrave; &longs;itu &longs;uo di&shy;<lb/>
moto, moueri quidem res vi&longs;a &longs;ur&longs;um, deor&longs;umu&egrave; ob id videtur, quia &amp; pupilla: <lb/>&longs;ed geminata nunquam apparebit, ni&longs;i duo &longs;int vi&longs;us, qui contorqueantur. </s>
          <s id="s.004887">talis ap&shy;<lb/>
paret limo <foreign lang="greek">eterofqalmw&verbar;,</foreign> &longs;eu &longs;traboni, vt duplicata illi videatur. </s>
          <s id="s.004888">propter po&longs;itio&shy;<lb/>nem ver&ograve; id fit, quia &longs;cilicet oculus &longs;uo medio non &longs;it constitutus&rpar;<emph.end type="italics"/> Qu&aelig;cunque ab <lb/>
Ari&longs;t. hoc loco l&aelig;uiter attinguntur, exact&egrave; ab opticis Alhazeno, &amp; Vitell. <lb/>
<!-- REMOVE S-->pertractantur. </s>
          <s id="s.004889">vide propo&longs;. </s>
          <s id="s.004890">26. lib. 3. Vitell. <!-- REMOVE S-->qu&aelig; e&longs;t h&aelig;c. </s>
          <s id="s.004891">Vno oculo moto <lb/>
nece&longs;&longs;e e&longs;t alium eidem conformiter moueri.</s>
        </p>
        <p type="main">
          <s id="s.004892">Quando ait <emph type="italics"/>&lpar;Et alterum ad dextram, &amp; ad &longs;ini&longs;tram&rpar;<emph.end type="italics"/> &longs;ignificat nos po&longs;&longs;e <lb/>
mouere alterum oculum, altero manente, quoquouer&longs;us: quod non video <lb/>
quomodo verum &longs;it, alij fort&egrave; videbunt.</s>
        </p>
        <p type="main">
          <s id="s.004893">Quando ait <emph type="italics"/>&lpar;<expan abbr="Atq;">Atque</expan> &longs;int in medio mouendi &longs;e &longs;e&rpar;<emph.end type="italics"/> per medium mouendi intel&shy;<lb/>
ligit Ari&longs;t. punctum, quod concipitur e&longs;&longs;e in medio inter &longs;ur&longs;um, &amp; deor&shy;<lb/>
&longs;um; necnon inter dextrum, &amp; &longs;ini&longs;trum oculorum in naturali po&longs;itione <lb/>
manentium.</s>
        </p>
        <p type="main">
          <s id="s.004894">Quando ait <emph type="italics"/>&lpar;Eodemque in puncto vi&longs;um habent&rpar;<emph.end type="italics"/> &amp; <emph type="italics"/>&lpar;Quiver&ograve; in eodem pun&shy;<lb/>
cto pupillas habent&rpar;<emph.end type="italics"/> per idem <expan abbr="p&utilde;ctum">punctum</expan> intelligo illud, quod in vno oculorum <lb/>
habet eandem po&longs;itionem cum altero puncto alterius oculi, &longs;ic duo oculi <lb/>
habebunt pupillas in codem puncto, quando eas habebunt con&longs;imiliter lo&shy;<lb/>
catas, &amp; habebunt eandem in <expan abbr="vtroq;">vtroque</expan> oculo po&longs;itionem.</s>
        </p>
        <p type="main">
          <s id="s.004895">Quando ait <emph type="italics"/>&lpar;Dimotum contuendi principi&ubreve;m habet<emph.end type="italics"/>&rpar; ide&longs;t, locum pupill&aelig; non <lb/>
habet in eodem &longs;itu, in quo oporteret, ide&longs;t non habet con&longs;imilem &longs;itum re&shy;<lb/>
&longs;pectu &longs;ur&longs;um, &amp; deor&longs;um, dextror&longs;um, &amp; &longs;ini&longs;tror&longs;um, alteri pupill&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.004896">Quando ait <emph type="italics"/>&lpar;Perinde vt ille, cui res vna geminari oculo &longs;uppre&longs;&longs;o videtur&rpar;<emph.end type="italics"/> vt <lb/>rectius ea, qu&aelig; hoc loco ab Ari&longs;t. dicuntur, percipi po&longs;&longs;int, explicandum <pb pagenum="276" xlink:href="009/01/276.jpg"/>prius exi&longs;timo, cur quamuis geminatos oculos habeamus, res tamen vnic&aelig; <lb/>
non &longs;olent geminat&aelig; videri, dummodo oculi &agrave; naturali &longs;uo &longs;itu non luxen&shy;<lb/>
tur, quod etiam &agrave; Vitell. <!-- REMOVE S-->propo&longs;it. </s>
          <s id="s.004897">28. &amp; 46. lib. 3. pertractatur: quamuis <lb/>
commentum illud Vitell. <!-- REMOVE S-->&amp; Alaz. <!-- REMOVE S-->non placeat de neruorum opticorum <lb/>
vnione, e&ograve; quod Anatomici refragentur.</s>
        </p>
        <p type="main">
          <s id="s.004898">Dicendum igitur, quod c&ugrave;m anima vna &longs;it, &amp; obiectum etiam &longs;it vnum, <lb/>
&amp; c&ugrave;m <expan abbr="vter&qacute;">vterque</expan>; oculus habeat con&longs;imilem omnin&ograve; &longs;itum, &longs;it etiam, vt &longs;pecies <lb/>obiecti repre&longs;entatiua eodem modo in <expan abbr="vtroq;">vtroque</expan> oculo &longs;ituetur, ob quem con&shy;<lb/>
&longs;imilem &longs;itum, tum oculi, tum &longs;peciei &longs;it, vt anima vtatur duobus oculis, <lb/>tanquam vno oculo, &amp; duabus &longs;peciebus tanquam vna &longs;pecie: &longs;i enim alter <lb/>
oculus alteri oculo imponeretur, e&longs;&longs;ent omnin&ograve; partes vnius congruentes <lb/>
partibus alterius, &amp; &longs;pecies vnius oculi congrueret, &amp; vniretur p&oelig;nitus <lb/>
cum altera alterius, &longs;ecundum &longs;ingulas earum partes con&longs;imiles. </s>
          <s id="s.004899">vt autem <lb/>
&longs;pecies &longs;ituentur con&longs;imiliter in vtroque oculo nece&longs;&longs;e e&longs;t, vt <expan abbr="vter&qacute;">vterque</expan>; oculus <lb/>
eodem modo a&longs;piciat <expan abbr="obiect&utilde;">obiectum</expan>; quod tunc &longs;it, quando axes vi&longs;uales vtriu&longs;q; <lb/>
oculi vniuntur in obiecto. </s>
          <s id="s.004900">axis porr&ograve; vi&longs;ualis e&longs;t linea ab obiecto tendens ad <lb/>
centrum oculi, qu&aelig; tamen tran&longs;eat per centra corne&aelig;, vue&aelig;, &amp; pupill&aelig;. </s>
          <s id="s.004901">tunc <lb/>
partes &longs;pecierum erunt omnin&ograve; con&longs;imiliter collocat&aelig; in <expan abbr="vtroq;">vtroque</expan> vi&longs;u: ita <lb/>
vt pars &longs;peciei, qu&aelig; dextra e&longs;t in vno, &longs;it etiam dextra in altero. </s>
          <s id="s.004902">Intelligo <lb/>
eandem partem re&longs;pectu obiecti, qu&aelig; refert eandem obiecti partem. </s>
          <s id="s.004903">quem&shy;<lb/>
admodum igitur nec duabus auribus audimus duas voces, nec duabus nari&shy;<lb/>
bus geminos odores, nec duplici manu duplicatas res tactas: ita anima, <lb/>
&longs;eruatis, qu&aelig; nuper dixi, duobus vi&longs;ibus res vnam vnic&egrave; videre debet.</s>
        </p>
        <p type="main">
          <s id="s.004904">Hinc facilius cogno&longs;cemus, qua de cau&longs;a res vi&longs;a aliquando geminetur. <lb/>
</s>
          <s id="s.004905">quoties enim &longs;pecies eiu&longs;dem obiecti in altero oculorum habet alium &longs;itum, <lb/>
qu&agrave;m in altero, geminatio accidit, quia non habet con&longs;imilem &longs;itum, &amp; &longs;i <lb/>
vna alteri &longs;upponeretur, non re&longs;ponderent partes vnius dexter&aelig;, v. <!-- REMOVE S-->g. <!-- REMOVE S-->par&shy;<lb/>
tibus dextris alterius; vnde non identificarentur; nec qu&aelig; e&longs;&longs;ent in eadem <lb/>
parti oculi repre&longs;entarent eandem obiecti partem; &amp; propterea oculi non <lb/>
e&longs;&longs;ent quodammodo vnus oculus, c&ugrave;m alter ab altero diuer&longs;imod&egrave; &agrave; &longs;pecie <lb/>
informaretur. </s>
          <s id="s.004906">vt autem &longs;pecies <expan abbr="vtrumq;">vtrumque</expan> oculum con&longs;imiliter <expan abbr="inform&etilde;t">informent</expan>, ne&shy;<lb/>
<figure id="id.009.01.276.1.jpg" place="text" xlink:href="009/01/276/1.jpg"/><lb/>
ce&longs;&longs;e e&longs;t, vt axes vi&longs;uales, quales <lb/>
&longs;unt in appo&longs;ita figura, C B, D B, <lb/>
ab oculis C, D, ad obiectum B, <lb/>ducti, in ip&longs;o obiecto B. im&ograve; in <lb/>
eodem ip&longs;ius puncto vniantur: <lb/>
quoties. </s>
          <s id="s.004907">n. </s>
          <s id="s.004908">res vi&longs;a <expan abbr="n&otilde;">non</expan> e&longs;t in con&shy;<lb/>
cur&longs;u axium, vt e&longs;t res A. tunc <lb/>
di&longs;&longs;imiliter &longs;peciem ad oculos <lb/>
mittit, nam &longs;pecies puncti A, in oculo D, erit ad &longs;ini&longs;tram centri pupill&aelig;; <lb/>
in oculo ver&ograve; C, erit ad dextram.</s>
        </p>
        <p type="main">
          <s id="s.004909">Quando pariter alterum oculorum digito &longs;ur&longs;um, aut deor&longs;um compri&shy;<lb/>
mimus, fit, vt ille aliquantulum &agrave; loco &longs;uo naturali, &amp; con&longs;imili &longs;itui alte&shy;<lb/>
rius dimoueatur; quare nece&longs;&longs;e, vt axis ip&longs;ius &longs;imiliter ad motum oculi di&shy;<lb/>
moueatur, nec amplius concurrat cum altero axe, in eodem obiecti puncto, <lb/>
in quod alter <expan abbr="t&etilde;det">tendet</expan>, vel <expan abbr="&etilde;t">et</expan> in <expan abbr="alter&utilde;">alterum</expan> <expan abbr="obiect&utilde;">obiectum</expan>. </s>
          <s id="s.004910">vide Vitell. <!-- REMOVE S-->prop. 103. &amp; 104. li. </s>
          <s id="s.004911">4.<!-- KEEP S--></s>
        </p>
        <pb pagenum="277" xlink:href="009/01/277.jpg"/>
        <p type="main">
          <s id="s.004912">Quando ait <emph type="italics"/>&lpar;Si oculus &longs;ur&longs;um dimotus e&longs;t, terminus in&longs;piciendi deor&longs;um est&rpar;<emph.end type="italics"/><lb/>Per terminum in&longs;piciendi intelligo rem illam, qu&aelig; prius videbatur, &amp; po&longs;t <lb/>
oculi dimotionem infra axem vi&longs;ualem remanet.</s>
        </p>
        <p type="main">
          <s id="s.004913">Quando ait <emph type="italics"/>&lpar;Sed geminata nunquam apparebit, ni&longs;i duo &longs;int vi&longs;us, qui contor&shy;<lb/>
queantur&rpar;<emph.end type="italics"/> ni&longs;i duplex &longs;it con&longs;pectus, ide&longs;t, ni&longs;i oculus vnus ab altero diffe&shy;<lb/>renter &longs;ituetur, &longs;ic enim &longs;peciem diuers&egrave; re&longs;piciunt, non videbitur res du&shy;<lb/>
plicata.</s>
        </p>
        <p type="main">
          <s id="s.004914">Quando ait <emph type="italics"/>&lpar;Tali apparet limo, &longs;eu &longs;traboni&rpar;<emph.end type="italics"/> gr&aelig;c&egrave; ait <foreign lang="greek">eterofqslmw</foreign>, quod <lb/>
propri&egrave; &longs;ignificat eum, quem Latini Lu&longs;cum dicunt, qui vnius <expan abbr="tant&utilde;">tantum</expan> e&longs;t ocu&shy;<lb/>
li. </s>
          <s id="s.004915">videtur tamen v&longs;urpa&longs;&longs;e illud pro limo, &longs;eu &longs;trabone, vt Gaza etiam ac&shy;<lb/>
cipit, &longs;ecus enim non po&longs;&longs;et illi res geminari, c&ugrave;m ad id nece&longs;&longs;arij &longs;int duo <lb/>
oculi, vt modo dixerat.</s>
        </p>
        <p type="main">
          <s id="s.004916">Quando ait <emph type="italics"/>&lpar;Propter po&longs;itionem ver&ograve; id fit&rpar;<emph.end type="italics"/> ex paul&ograve; ante dictis po&longs;&longs;unt <lb/>
intelligi. </s>
          <s id="s.004917">verumtamen, &amp; illud addam; Duplicis con&longs;pectus, vel gemina&shy;<lb/>tionis cau&longs;a e&longs;&longs;e pote&longs;t, vel diuer&longs;us oculorum &longs;itus, vel etiam &longs;itus &longs;pecie&shy;<lb/>
rum diuer&longs;us, vt quando obiectum e&longs;t intra concur&longs;ionem axium, vt in <expan abbr="pr&aelig;-ced&etilde;ti">pr&aelig;&shy;<lb/>
cedenti</expan> figura, vbi etiam&longs;i oculi naturalem <expan abbr="&longs;it&utilde;">&longs;itum</expan> con&longs;eruent, res geminabitur.</s>
        </p>
        <p type="main">
          <s id="s.004918"><arrow.to.target n="marg397"/></s>
        </p>
        <p type="margin">
          <s id="s.004919"><margin.target id="marg397"/>406</s>
        </p>
        <p type="main">
          <s id="s.004920">Probl. 11. <emph type="italics"/>&lpar;Cur di&longs;tractis oculis res vna du&aelig; apparent? </s>
          <s id="s.004921">An quod radij <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/>
oculi ad idem <expan abbr="p&utilde;ctum">punctum</expan> non concurrunt? </s>
          <s id="s.004922">qua&longs;i erg&ograve; duo videat, bis idem videre ani&shy;<lb/>
ma exi&longs;timat &longs;imile e&longs;t in permutatis digitis, vnum' enim duo apparet, tanquam bis <lb/>
tactum<emph.end type="italics"/>&rpar; Pr&aelig;&longs;ens Problema ex dictis in pr&aelig;cedenti problemate &longs;atis clarum <lb/>
euadit: im&ograve; illa ex his vici&longs;&longs;im confirmantur.</s>
        </p>
        <p type="main">
          <s id="s.004923">Quando ait &lpar;<emph type="italics"/>Radij <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> oculi ad idem punctum non concurrunt<emph.end type="italics"/>&rpar; intelligit <lb/>
de axibus vi&longs;ualibus, quos in &longs;uperiori declaratos habes.</s>
        </p>
        <p type="main">
          <s id="s.004924">Quando ait &lpar;<emph type="italics"/>Simile e&longs;t in permutatis digitis<emph.end type="italics"/>&rpar; vt pulcherrimum i&longs;tud experi&shy;<lb/>mentum, quo res vna tacta, du&aelig; videntur, experiaris oportet, vt globulum <lb/>
quempiam duobus proximis digitis eiu&longs;dem manus tangas, ita vt vnus al&shy;<lb/>
terum decu&longs;&longs;et, &longs;iue tran&longs;cendat, vel ei conuoluatur, ita vt extremitates di&shy;<lb/>
gitorum permutent loca, vel vt extremum vnius &longs;it, vbi deberet e&longs;&longs;e extre&shy;<lb/>
mum alterius; deinde globulum inter <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> digiti extrema locatum, &longs;imul <lb/>
tangant, tunc enim exi&longs;timabis te duos globulos tangere.</s>
        </p>
        <p type="main">
          <s id="s.004925"><arrow.to.target n="marg398"/></s>
        </p>
        <p type="margin">
          <s id="s.004926"><margin.target id="marg398"/>407</s>
        </p>
        <p type="main">
          <s id="s.004927">Probl. 17. <emph type="italics"/>&lpar;Cur res vna non videtur geminari, &longs;i oculum in latera contorquent? <lb/>
An quia con&longs;piciendi <expan abbr="principi&utilde;">principium</expan> ab eadem linea &longs;umendum e&longs;t. </s>
          <s id="s.004928">duo autem videntur, <lb/>quando illud &longs;ur&longs;um, aut deor&longs;um mutatur; in latus ver&ograve; nihil refert, ni&longs;i &longs;imul <lb/>
&longs;ur&longs;um, aut deor&longs;um&rpar;<emph.end type="italics"/> quod pr&aelig;&longs;enti problemate proponitur, non videtur <expan abbr="v&longs;-quequaq;">v&longs;&shy;<lb/>
quequaque</expan> verum, expertus enim &longs;um, moto etiam in latus oculo, res vi&longs;as, <lb/>
quamuis magna cum difficultate, geminari. </s>
          <s id="s.004929">per lineam illam, &agrave; qua princi&shy;<lb/>
pium &longs;umitur con&longs;piciendi, intelligit lineam rectam tran&longs;euntem per cen&shy;<lb/>
tra <expan abbr="vcriu&longs;q;">vtriu&longs;que</expan> pupill&aelig;. </s>
          <s id="s.004930">quod autem ait nihil referri, &longs;i oculus in latus, &longs;iue ad <lb/>
pr&aelig;dictam lineam luxetur, fal&longs;um omnin&ograve; puto ex dictis &longs;upra ad Probl. 7. <lb/>hoc enim modo alter oculus di&longs;&longs;imiliter ab altero collocatur, vnde nece&longs;&longs;e <lb/>
e&longs;t <expan abbr="c&otilde;&longs;equi">con&longs;equi</expan> geminationem &longs;ecus ac &longs;i &longs;ur&longs;um, aut deor&longs;um <expan abbr="alter&utilde;">alterum</expan> luxaueris.</s>
        </p>
        <p type="main">
          <s id="s.004931"><arrow.to.target n="marg399"/></s>
        </p>
        <p type="margin">
          <s id="s.004932"><margin.target id="marg399"/>408</s>
        </p>
        <p type="main">
          <s id="s.004933">Probl 21. <emph type="italics"/>&lpar;Cur alia quidem ambobus oculis potius in&longs;picimus; rectitudinem <lb/>
ver&ograve;, qu&aelig; e&longs;t in ver&longs;ibus, vnum oculum literis admouentes potius con&longs;picimus? <lb/>
</s>
          <s id="s.004934">An quia ver&longs;us quidem coincidentes quemadmodum tradunt Optici, perturbatio&shy;<lb/>nem quandam afferunt; quando ver&ograve; vnico vi&longs;u in&longs;picimus, &longs;ecundum vnicam re-<emph.end type="italics"/>


<pb pagenum="278" xlink:href="009/01/278.jpg"/><emph type="italics"/>ctam vi&longs;ualem lineam in&longs;picimus, qua tanquam recta regula melius ver&longs;uum re&shy;<lb/>ctitudinem digno&longs;cimus; rectum enim recto dijudicatur.&rpar;<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.004935">Quando ait <emph type="italics"/>&lpar;V num oculum literis admouentes&rpar;<emph.end type="italics"/> quando volumus in&longs;picere <lb/>
num rectus &longs;it &longs;criptur&aelig; alicuius ver&longs;us, oculum alterum altero clau&longs;o, prin&shy;<lb/>
cipio, aut extremo illius ver&longs;us admouemus, vt hoc modo &longs;ecundum longi&shy;<lb/>
tudinem, non autem &egrave; regione illum intueamur, &longs;ic enim linea vi&longs;ualis re&shy;<lb/>
cta, qua&longs;i linea <expan abbr="qu&aelig;d&atilde;">qu&aelig;dam</expan> materialis rectitudini ver&longs;us coaptata,ill&atilde; examinat.</s>
        </p>
        <p type="main">
          <s id="s.004936">Libet his opticis Problematibus, auctarij loco, tractationem quandam <lb/>
de Oculi pupilla, c&ugrave;m &longs;it eiu&longs;dem argumenti, apponere, in qua nonnulla <lb/>
&longs;citu digna, <expan abbr="atq;">atque</expan> iucunda, ac nuper ob&longs;eruata traduntur.</s>
        </p>
        <p type="head">
          <s id="s.004937"><emph type="italics"/>De humani Oculi Pupilla.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004938">Vt ea, qu&aelig; dicenda &longs;unt, facilius percipi po&longs;&longs;int, nece&longs;&longs;e e&longs;t breuiter <lb/>
oculi fabricam, in qua mirum totius natur&aelig; Opificis artificium elu&shy;<lb/>
cet, auxilio &longs;equentium figurarum pr&aelig;mittere.</s>
        </p>
        <figure id="id.009.01.278.1.jpg" place="text" xlink:href="009/01/278/1.jpg"/>
        <p type="main">
          <s id="s.004939">A B C, cornea. </s>
          <s id="s.004940">&longs;patium A B, e&longs;t propri&egrave; corne&aelig; pars tran&longs;lucida.</s>
        </p>
        <p type="main">
          <s id="s.004941">E G F, vuea. </s>
          <s id="s.004942">H I, pupilla, &longs;eu foramen vue&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.004943">L M N O P, aranea, qu&aelig; medium orbiculum M N Q, ambit.</s>
        </p>
        <p type="main">
          <s id="s.004944">Referat erg&ograve; prima h&aelig;c figura humanum oculum, &longs;eu potius oculi &longs;e&shy;<lb/>
ctionem, qui nimirum di&longs;&longs;ectus &longs;it ab anteriori, <expan abbr="v&longs;q;">v&longs;que</expan> ad po&longs;teriorem partem <lb/>
in duas &aelig;quas partes. </s>
          <s id="s.004945">qua &longs;ectione appareant omnes tunic&aelig;, &amp; humores,ex <lb/>
quibus ille conflatur. </s>
          <s id="s.004946">con&longs;tat autem &longs;ecundum Anatomicos ex tribus tuni&shy;<lb/>
cis, <expan abbr="totidem&qacute;">totidemque</expan>; humoribus. </s>
          <s id="s.004947">verum figuram explicemus. </s>
          <s id="s.004948">Pedunculus ille C, <lb/>
neruus e&longs;t opticus &egrave; cerebro manans, ex quo tanquam ex radice totus ena&shy;<lb/>
&longs;citur oculus.</s>
        </p>
        <p type="main">
          <s id="s.004949">Exteriori illa circunferentia A B C, &longs;ignificatur membrana totum ocu&shy;<lb/>
lum complectens, qu&aelig; cornea propter duritiem appellatur. </s>
          <s id="s.004950">cuius pars pun&shy;<lb/>
ctis A, B, terminata, in&longs;tar Latern&aelig; cornu, pellucida e&longs;t. </s>
          <s id="s.004951">hanc vulg&ograve; lucem <lb/>
oculi, Medici Iridem maiorem appellant.</s>
        </p>
        <p type="main">
          <s id="s.004952">Media illa, &amp; imperfecta peripheria E H I F G, vuea ab acini vu&aelig; nigr&aelig; <lb/>
&longs;imilitudine nuncupatur; e&longs;t enim plurimum nigra. </s>
          <s id="s.004953">h&aelig;c vbi ad partem cor&shy;<lb/>
ne&aelig; tran&longs;lucidam A B, peruenit, eam qua&longs;i fugiens intra oculum &longs;ub&longs;idit,


<pb pagenum="279" xlink:href="009/01/279.jpg"/>&amp; tendens per loca E H I F, ip&longs;i corne&aelig;, veluti <expan abbr="infundibul&utilde;">infundibulum</expan> quoddam &longs;uppo&shy;<lb/>
nitur. </s>
          <s id="s.004954">hinc <expan abbr="alior&utilde;">aliorum</expan> anatomicorum figuras corrigere licebit, in quibus mem&shy;<lb/>
brana E H I E, <expan abbr="tanqu&atilde;">tanquam</expan> plana &longs;uperficies ip&longs;i corne&aelig; &longs;upponitur.n&otilde; e&longs;t tamen <lb/>
hac parte tota integra, nam, vt ait Plinius, medium eius fene&longs;trauit Pupilla. <lb/>
<!-- KEEP S--></s>
          <s id="s.004955">ea e&longs;t paruum foramen rotundum inter puncta H, I.porr&ograve; &longs;i liceat <expan abbr="h&atilde;c">hanc</expan> vue&etail; <lb/>partem E, H, I, F, &egrave; direct&ograve; integram a&longs;picere, &longs;imilis videbitur huic cir&shy;<lb/>
culo &longs;ecund&aelig; figur&aelig; A B C; in cuius medio circulus G H I, foramen e&longs;t, cui <lb/>tum Iridi minori, tum Pupill&aelig; nomen e&longs;t; qu&aelig; no&longs;tri e&longs;t materia &longs;ermonis: <lb/>
res quidem exigua, &longs;ed plan&egrave; admirabilis: tantillo enim foramine, maria, <lb/>
montes, innumera animalia, ac plantas graphic&egrave;, <expan abbr="atq;">atque</expan> ade&ograve; locis di&longs;tincta <lb/>
animus no&longs;ter in&longs;picit; im&ograve;, vt cecinit Manilius.</s>
        </p>
        <p type="main">
          <s id="s.004956"><emph type="italics"/>Paruula &longs;ic magnum perui&longs;it pupula C&oelig;lum.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.004957">Sic olim admirationi fuit Homeri Ilias, exiguis ade&ograve; litoris con&longs;cripta, vt <lb/>
vnius nucis cortice clauderetur.</s>
        </p>
        <p type="main">
          <s id="s.004958">Superficies huius membran&aelig; E H I F, exterior, qu&aelig; &longs;cilicet corneam re&shy;<lb/>
&longs;picit, in homine varia e&longs;t, c&aelig;&longs;ia, glauca, &longs;ubalbida, nigra. </s>
          <s id="s.004959">Excipiendi &longs;unt <lb/>
&agrave; c&aelig;teris Sinarum gentes, qu&aelig;, vt po&longs;trem&ograve; perlatum e&longs;t &agrave; no&longs;tris PP. &longs;unt <lb/>
omnes &longs;pectandi nigris oculis. </s>
          <s id="s.004960">Tartari etiam omnes virides habent oculos. <lb/>
</s>
          <s id="s.004961"><expan abbr="vtri&qacute;">vtrique</expan>; &longs;cilicet tales habent oculos, qu&ograve;d tales habeant vueas. </s>
          <s id="s.004962">ex hac enim <lb/>
varius oculorum color: quippe qui non in exteriori &longs;uperficie corne&aelig;, qu&aelig; <lb/>
omnin&ograve; diaphana e&longs;t, &amp; propterea excolor, &longs;ed vue&aelig; in&longs;idet. </s>
          <s id="s.004963">In nocturnis <lb/>
tamen animalibus lucida e&longs;t; <expan abbr="atq;">atque</expan> hinc lux illa, cuius ope, circumfu&longs;us aer <lb/>
ade&ograve; illu&longs;tratur, vt noctu videre queant. </s>
          <s id="s.004964">&longs;i qui etiam <expan abbr="homin&utilde;">hominum</expan> noctu videant, <lb/>
ij flaua, ac lucida vuea, vt ob&longs;eruaui, pr&aelig;diti &longs;unt: &amp; ide&ograve; interdi&ugrave; maiorem <lb/>
Iridem flauum o&longs;tendunt. </s>
          <s id="s.004965">&longs;uperficies tandem illius, qu&aelig; oculi interiora con&shy;<lb/>
&longs;picit, nigerrimo colore, qu&igrave; vel <expan abbr="Anatomicor&utilde;">Anatomicorum</expan> digitos inficiat, intincta e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.004966">Tertia tandem, qu&aelig; per P L M N O, incedit Aranea dicitur, e&longs;t enim in&shy;<lb/>
&longs;tar arane&aelig; tenui&longs;&longs;ima, pr&aelig;&longs;ertim, qu&agrave; vu&aelig; E H I F, &longs;upponitur. </s>
          <s id="s.004967">h&aelig;c pr&aelig;te&shy;<lb/>rea globuli M K I N Q, anteriorem partem M H I N, circumue&longs;tit, qui in <lb/>
ea affixus, non &longs;ecus ac Araneus in &longs;u&aelig; arane&aelig; centro, immobilis h&aelig;ret. <lb/>
</s>
          <s id="s.004968">h&aelig;c de tunicis.</s>
        </p>
        <p type="main">
          <s id="s.004969">Reliqui &longs;unt humores tres, quibus oculus repleatur; po&longs;terius i&longs;tud &longs;pa&shy;<lb/>tium P L Q O, humori vitreo ob vitri &longs;imilitudinem dicto, natura attri&shy;<lb/>
buit: anteriorem oculi &longs;edem inter corneam, &amp; vueam, humor aqueus oc&shy;<lb/>
cupauit, &longs;ic dictus, quod &longs;it natura limpidi&longs;&longs;imus; quippe qui primus ingre&shy;<lb/>
dientia rerum &longs;imulacra excipiat. </s>
          <s id="s.004970">medium locum, pr&aelig;dictum &longs;cilicet glo&shy;<lb/>
bulum, quem aranea complectitur, humor chri&longs;tallinus &longs;ibi vindicauit. </s>
          <s id="s.004971">hic <lb/>
qu&agrave; corneam &longs;pectat &longs;ph&aelig;ric&aelig; e&longs;t figur&aelig;, atque ex hac parte foramen H I, <lb/>
vue&aelig;, &longs;eu pupillam ob&longs;idet, vt aduentantibus rerum &longs;imulacris &longs;it obuius, <lb/>
<expan abbr="ea&qacute;">eaque</expan>; &longs;i&longs;tat, vnde factum e&longs;t illi <expan abbr="quoq;">quoque</expan> pupill&aelig; nomen. </s>
          <s id="s.004972">Huic <expan abbr="quoq;">quoque</expan> Aranea &longs;i&shy;<lb/>
mul, &amp; vuea tenui&longs;&longs;imis fibris in orbem connectuntur; qu&aelig; connexio non in <lb/>
ora pupill&aelig; extrema, &longs;ed circa ip&longs;am, vt in circulo D E F, &longs;ecund&aelig; figur&aelig;: <lb/>
qui fibrarum circulus apparet etiam in vuea, e&longs;t enim veluti &longs;utura qu&aelig;dam <lb/>
circularis circa pupillam, non long&egrave; tamen ab ip&longs;a. </s>
          <s id="s.004973">porr&ograve; iunctura h&aelig;c <lb/>
ade&ograve; fortis e&longs;t, vt non &longs;ine aliqua vi vuea, &amp; aranea inde &agrave; chri&longs;tallino di&shy;<lb/>
uellantur. </s>
          <s id="s.004974">H&aelig;c de oculi fabrica nunc &longs;ufficiant.</s>
        </p>
      </chap>
      <pb pagenum="280" xlink:href="009/01/280.jpg"/>
      <chap>
        <p type="head">
          <s id="s.004975"><emph type="italics"/>PROBLEMATA NONNVLLA <lb/>
De Oculi Pupilla.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.004976">1. Cvr ei Pupill&aelig; nomen inditum e&longs;t? </s>
          <s id="s.004977">Admiratione &longs;an&egrave; non caret <lb/>apud pr&aelig;cipuas linguas, miro quodam con&longs;en&longs;u, idem etymon <lb/>
obtinere: &longs;cilicet denominatam e&longs;&longs;e ab imaguncula illa, qu&aelig; <lb/>
veluti parua puppa, &longs;eu pupula, &longs;eu pupilla, qualis in figura <lb/>
&longs;pectatur, perpetu&ograve; in paruo hoc vu&aelig; circello &longs;pectatur. </s>
          <s id="s.004978">propter hanc igitur <lb/>
puppam Hebr&aelig;i circellum G B I, Bath, ide&longs;t filiolam, Gr&aelig;ci <foreign lang="greek">korhn</foreign>, ide&longs;t puel&shy;<lb/>
lam, Latini demum pupillam cognominarunt.</s>
        </p>
        <p type="main">
          <s id="s.004979">2. Atqui vnde imaguncula h&aelig;c, qu&aelig; in oculis no&longs;tris perpetu&ograve; &longs;pectatur? <lb/>
</s>
          <s id="s.004980">&longs;cilicet ob ter&longs;itiem, &amp; &longs;ph&aelig;ricitatem cornea e&longs;t in&longs;tar <expan abbr="c&otilde;uexi">conuexi</expan> &longs;peculi, quod <lb/>
&longs;pectanti imaginem reddat, quam erg&ograve; videmus in aliorum oculis puppam, <lb/>
no&longs;tra e&longs;t imago, qu&aelig; propterea tamen parua e&longs;t, quoniam oculus &longs;peculum <lb/>
paruum, ac conuexum &longs;imul e&longs;t, cuius e&longs;t imagines rebus ip&longs;is mult&ograve; mino&shy;<lb/>
res reflectere. </s>
          <s id="s.004981">vt in tractatu de Speculis optici demon&longs;trant.</s>
        </p>
        <p type="main">
          <s id="s.004982">3. C&ugrave;m tota cornea, qu&aelig; Iris maior e&longs;t, &longs;it &aelig;qu&egrave; tor&longs;a, ac perpolita, cur <lb/>
non &aelig;qu&egrave; tota hanc pupulam o&longs;tendit? </s>
          <s id="s.004983">&longs;ed &egrave; regione minoris Iridis fer&egrave; tan&shy;<lb/>
tum? </s>
          <s id="s.004984">cau&longs;a e&longs;t in promptu, quia nimirum &longs;peculum debet e&longs;&longs;e omnis colo&shy;<lb/>
ris expers, ne colores &longs;peculi coloribus imaginum mi&longs;ceantur; tali&longs;que e&longs;t <lb/>
Iris minor,qu&aelig; etiam&longs;i videatur nigra, non tamen ver&egrave; colorata e&longs;t, vt mox <lb/>
o&longs;tendam: at ver&ograve; maiori Iridi colores vue&aelig; &longs;ub&longs;unt, qui ne &longs;peculi officio <lb/>
fungatur, &longs;unt impedimento. </s>
          <s id="s.004985">e&longs;t pr&aelig;terea Iris minor admodum opacata, <lb/>
qu&aelig; altera conditio, maxim&egrave; &longs;peculo nece&longs;&longs;aria e&longs;t: illa enim nigredo Iri&shy;<lb/>
dis minoris, &longs;eu pupill&aelig;, non nigredo, &longs;ed opacitas e&longs;t, vt dicetur po&longs;tea.</s>
        </p>
        <p type="main">
          <s id="s.004986">4. C&ugrave;m iam <expan abbr="c&otilde;&longs;tet">con&longs;tet</expan> foramini vu&aelig; G H I, &agrave; pupilla in ip&longs;o ver&longs;ante nomen <lb/>
inditum e&longs;&longs;e; nec non vnde &longs;it ea pupilla, &amp; cur tam parua; qu&aelig;ritur iam, <lb/>
quid &longs;it pupilla, &longs;eu Iris minor, an &longs;cilicet &longs;it foramen illud vue&aelig;, an potius <lb/>
chri&longs;tallinus humor, qui in illud intruditur, <expan abbr="vacuum&qacute;">vacuumque</expan>; illius replet? </s>
          <s id="s.004987">Re&shy;<lb/>
&longs;pondeo, Ari&longs;t. humorem ip&longs;um <expan abbr="chri&longs;tallin&utilde;">chri&longs;tallinum</expan> appella&longs;&longs;e pupillam: Galenum<lb/>
tum chri&longs;tallinum, tum foramen ip&longs;um: apt&egrave; tamen <expan abbr="vtrumq;">vtrumque</expan> dici exi&longs;timo. <lb/>
</s>
          <s id="s.004988">Chri&longs;tallinum quidem &amp; quia replet vacuum illud, <expan abbr="atq;">atque</expan> &egrave; regione illius pu&shy;<lb/>
pill&aelig; imaguncula &longs;pectatur. </s>
          <s id="s.004989">foramen ver&ograve;, quia terminos illius rotunditatis <lb/>
circum&longs;cribat. </s>
          <s id="s.004990">vnde aptius fort&egrave; dixeris, vtrumque, chri&longs;tallinum &longs;cilicet, <lb/>
&amp; foramen veluti partes ad totam pupillam con&longs;tituendam e&longs;&longs;e nece&longs;&longs;aria: <lb/>
ita vt nihil aliud ip&longs;a &longs;it, qu&agrave;m &longs;uperficies illa chri&longs;tallini; qu&aelig; vue&aelig; fora&shy;<lb/>
mine continetur.</s>
        </p>
        <p type="main">
          <s id="s.004991">5. Cur in omnibus hominibus nigra videtur? </s>
          <s id="s.004992">cum tamen nigri nihil ibi <lb/>
e&longs;&longs;e ex anotomia con&longs;tet: im&ograve; ibi chri&longs;tallinus e&longs;t omnin&ograve; pelluidus; &amp; vl&shy;<lb/>
tra, <expan abbr="citra&qacute;">citraque</expan>; alij duo humores, vitreus, &amp; aqueus, &aelig;qu&egrave; tran&longs;parentes, <expan abbr="atq;">atque</expan> <lb/>
omnis nigredinis expertes. </s>
          <s id="s.004993">vnde igitur nigredo illa? </s>
          <s id="s.004994">Dicendum e&longs;t nigre&shy;<lb/>
dinem hanc non e&longs;&longs;e veram, &longs;ed apparentem, <expan abbr="eam&qacute;">eamque</expan>; ex interna oculi opa&shy;<lb/>
citate; opacitatem ver&ograve; ex foraminis paruitate, qu&aelig; lumen non admittat, <lb/>prouenire: quotidiana enim nos docet experientia fene&longs;tellas, &amp; huiu&longs;modi <pb pagenum="281" xlink:href="009/01/281.jpg"/>alia foramina, qu&aelig; intus non &longs;int illuminata, &longs;ed tenebro&longs;a, nigra quamuis <lb/>
minim&egrave; &longs;int, apparere. </s>
          <s id="s.004995">Idem pr&aelig;terea mihi ex anatome manife&longs;t&egrave; patuit, <lb/>
c&ugrave;m enim per &longs;ectionem ca&longs;u quodam pupilla oculi, quem &longs;ecabam, facta <lb/>
fui&longs;&longs;et aliquanto mior, illic&ograve; nigredine omni exuta, alba vi&longs;a e&longs;t; quia &longs;ci&shy;<lb/>
licet patuit lumini aditus, quod internam oculi opacitatem fugauit. </s>
          <s id="s.004996">pro&shy;<lb/>
pterea in bobus, &amp; capris, quia magna, &amp; oblonga e&longs;t, qu&aelig; multum lucis <lb/>
admittat, aloa &longs;imiliter, non vt in nobis nigra con&longs;picitur.</s>
        </p>
        <p type="main">
          <s id="s.004997">6. Cur in clari&longs;&longs;ima luce Solis pupilla omnin&ograve; euane&longs;cit? </s>
          <s id="s.004998">ex dictis in pr&aelig;&shy;<lb/>
cedenti problemate, huic <expan abbr="quoq;">quoque</expan> &longs;atisfieri pote&longs;t. </s>
          <s id="s.004999">c&ugrave;m enim clari&longs;&longs;imo lumi&shy;<lb/>ni obijcitur, fit, vt oculi interiora illu&longs;trentur; vnde fugatis tenebris, &amp; om&shy;<lb/>
ni opacitate, etiam nigredo illa nulla &longs;it.</s>
        </p>
        <p type="main">
          <s id="s.005000">7. Po&longs;&longs;umus ne dum in oculos alterius intuemur, quanta &longs;it re vera, co&shy;<lb/>
gno&longs;cere? </s>
          <s id="s.005001">exi&longs;timo certam ip&longs;ius quantitatem oculos no&longs;tros omnin&ograve; late&shy;<lb/>
re: videtur enim per refractionem, c&ugrave;m &longs;it infra humorem aqueum aere <lb/>den&longs;iorem, at qu&aelig; refract&egrave; videntur ex medio den&longs;iore, ea maiora, qu&agrave;m <lb/>
&longs;int, apparere, demon&longs;trant Per&longs;pectiui. </s>
          <s id="s.005002">attamen c&ugrave;m in luce &longs;atis tempe&shy;<lb/>
rata ver&longs;amur, &longs;i oculum direct&egrave;, vt minor fiat refractio, &longs;pectemus, ip&longs;am <lb/>
non mult&ograve; ver&ograve; maiorem &longs;pectabimus.</s>
        </p>
        <p type="main">
          <s id="s.005003">8. Sed vnde nam illud mirum illi accidit, vt modo maior, modo minor <lb/>
nullo ferm&egrave; tempore interpo&longs;ito, euadat; &amp; aliquando ad tantam magni&shy;<lb/>
tudinem exere&longs;cat, vt totam for&egrave; maiorem Iridem occupet; vt &longs;i in &longs;ecun&shy;<lb/>
da figura foramen B G I, <expan abbr="v&longs;q;">v&longs;que</expan> ad circulum L M N O, dilataretur? </s>
          <s id="s.005004">Antiquio&shy;<lb/>
res, vt Galenus, c&ugrave;m ob&longs;erua&longs;&longs;ent eam, mult&ograve; maiorem e&longs;&longs;e noctu, quam <lb/>
interdi&ugrave;, id &longs;olummodo ratione noctis, &amp; diei contingere, <expan abbr="atq;">atque</expan> foramen il&shy;<lb/>
lud ver&egrave; augeri, &amp; minui exi&longs;timarunt. </s>
          <s id="s.005005">&longs;u&longs;pen&longs;um tamen Galenum reddit, <lb/>
nulla huius motus organa reperiri, qua propter ad &longs;piritus animales confu&shy;<lb/>
git, <expan abbr="eis&qacute;">eisque</expan>; huius augmenti, &amp; decrementi cau&longs;am attribuit: eiu&longs;dem &longs;enten&shy;<lb/>
ti&aelig; e&longs;t 10. Bapti&longs;ta Porta, inter huius &aelig;tatis Per&longs;pectiuos celebris. </s>
          <s id="s.005006">Hiero&shy;<lb/>
nymus ab Aquapendente ab antiquioribus in eo di&longs;&longs;entit, quod cau&longs;am hu&shy;<lb/>
ius referat non in &longs;piritus, &longs;ed in proprietatem quandam ip&longs;ius vue&aelig; natu&shy;<lb/>
ralem. </s>
          <s id="s.005007">Porr&ograve; cum ego &longs;ententias horum mente ver&longs;arem opportun&egrave; acci&shy;<lb/>
dit, vt vel ip&longs;o meridie c&ugrave;m quodam in loco &longs;atis opaco colloquerer, <expan abbr="atq;">atque</expan> <lb/>
eo illius capitis &longs;itu, vt oculi illius in multa e&longs;&longs;ent opacitate, c&ugrave;m ecce tibi <lb/>
pupillas illius, magna cum admiratione, ade&ograve; magnas con&longs;pexi, vt totam <lb/>
fer&egrave; maiorem Iridem ad&aelig;quarent; illic&ograve; hominem in claram lucem, atque <lb/>
Solem deduxi; <expan abbr="atq;">atque</expan> ecce tibi repent&egrave; e&aelig;dem pupill&aelig; minim&aelig; fact&aelig; &longs;unt. <lb/>
</s>
          <s id="s.005008">eandem &longs;ubinde experientiam &longs;excenties ob&longs;eruaui, vnde duo notatu di&shy;<lb/>
gna innotuerunt.</s>
        </p>
        <p type="main">
          <s id="s.005009">Primum e&longs;t: Maiores no&longs;tros hallucinatos e&longs;&longs;e c&ugrave;m nocte tantummodo <lb/>
magnas, per diem ver&ograve; paruas fieri pupillas opinati &longs;unt: Verum id ratio&shy;<lb/>
ne lucis, &amp; tenebrarum quouis tempore accidere patuit. </s>
          <s id="s.005010">vnde etiam in ob&shy;<lb/>
&longs;curi&longs;&longs;ima nocte admota oculis accen&longs;a candella, minuantur; amota &longs;tatim <lb/>
augeantur. </s>
          <s id="s.005011">hinc accidit, pupillam hanc, Medicum quendam &aelig;tate no&longs;tra <lb/>
celebrem fefelli&longs;&longs;e, qu&igrave; dum &aelig;grotum quendam in cubiculo &longs;atis tenebro&longs;o, <lb/>
<expan abbr="oculis&qacute;">oculisque</expan>; laborantem curaret, animaduertit illius pupillas e&longs;&longs;e iu&longs;to maio&shy;<lb/>
res, quapropter plurima illi medicamenta pro pupillarum re&longs;trictione ad&shy;


<pb pagenum="282" xlink:href="009/01/282.jpg"/>hibuit; &longs;ed omnia tamen irrita; cui ad mota luce, &longs;tatim &longs;unt imminut&aelig;: <lb/>
nec tamen &aelig;ger conualuit. </s>
          <s id="s.005012">erat &longs;cilicet apparentia, non veritas.</s>
        </p>
        <p type="main">
          <s id="s.005013">Secundum hoc modo patuit. </s>
          <s id="s.005014">C&etail;peram <expan abbr="namq;">namque</expan> pariter de principali qu&aelig;&shy;<lb/>
&longs;tione ambigere circa &longs;ententiam eorundem, num &longs;cilicet ver&egrave; pupill&aelig; mo&shy;<lb/>
d&ograve; dilatarentur, mod&ograve; con&longs;tringerentur; an potius aliqua &longs;it, qu&aelig; eos fe&shy;<lb/>
fellerit apparentia. </s>
          <s id="s.005015"><expan abbr="atq;">atque</expan> tandem po&longs;t diuturnam ob&longs;eruationem, po&longs;t <expan abbr="plu-rimor&utilde;">plu&shy;<lb/>
rimorum</expan> oculorum di&longs;&longs;ectionem, tut&ograve; au&longs;us &longs;um prim&ograve; a&longs;&longs;erere, pupillas ve&shy;<lb/>
r&egrave; nec augeri, nec minui, &longs;ed meram illam e&longs;&longs;e apparentiam, quod &longs;equen&shy;<lb/>
tibus rationibus comprobabam.</s>
        </p>
        <p type="main">
          <s id="s.005016">Prim&ograve;, &longs;i ver&egrave; tunc cum ferm&egrave; maiorem totam Iridem occupant, relicta <lb/>
tantummodo gracili in orbem armilla, dilatarentur, tunc nece&longs;&longs;ari&ograve; con&shy;<lb/>
nexio vue&aelig; cum aranea &longs;cinderetur, c&ugrave;m tunc pupill&aelig; gyrum D E F, illius <lb/>
connexionis ve&longs;tigium tran&longs;cendant; ac pr&aelig;terea tenui&longs;&longs;im&aelig; ill&aelig; fibr&aelig;, qui&shy;<lb/>
bus con&longs;uitur, frangerentur, <expan abbr="&longs;tatim&qacute;">&longs;tatimque</expan>; iterum nemine auctore re&longs;arcirentur. <lb/>
</s>
          <s id="s.005017">quod nec &longs;ine oculi detrimento, nec &longs;ine &longs;en&longs;u doloris aliquo fieri po&longs;&longs;e, quis <lb/>
dicat? </s>
          <s id="s.005018">qu&aelig; omnia nullo modo con&longs;equuntur.</s>
        </p>
        <p type="main">
          <s id="s.005019">Secund&ograve;, nulla extant huius organa motus, quod plures Anatomicos, <lb/>
<expan abbr="atq;">atque</expan> Galenum ip&longs;um dubios reddit.</s>
        </p>
        <p type="main">
          <s id="s.005020">Terti&ograve;, Medici omnes volunt eos, qui angu&longs;tiori &longs;unt pupilla, acie ocu&shy;<lb/>
lorum plus valere, qu&agrave;m qui &longs;unt latiori; &longs;i erg&ograve; i&longs;ta e&longs;&longs;et vera con&longs;trictio, <lb/>
&amp; dilatatio, accideret nos eodem p&etail;n&egrave; temporis momento, mod&ograve; acutius, <lb/>mod&ograve; hebetius videre: im&ograve; in temperata luce, vbi maior apparet, minus, <lb/>
quam in clari&longs;&longs;ima luce, &amp; Sole, vbi minima apparet, videremus. </s>
          <s id="s.005021">quibus <lb/>
quotidiana refragatur experientia.</s>
        </p>
        <p type="main">
          <s id="s.005022">Quart&ograve;, plura obiecta compr&aelig;henderet oculus in opacitate, qu&agrave;m in cla&shy;<lb/>
ritate, &amp; Sole: omnia enim illa videmus, qu&aelig; intra pyramidem vi&longs;ualem <lb/>
continentur, qu&aelig; e&ograve; capacior, &amp; latior e&longs;t, qu&ograve; pupilla maior e&longs;t: habet <lb/>
<expan abbr="namq;">namque</expan> h&aelig;c pyramis verticem in centro oculi, &amp; po&longs;tea dilatatur ad dilata&shy;<lb/>
tionem foraminis vue&aelig;, quod e&longs;t pupilla. </s>
          <s id="s.005023">ver&ugrave;m nos nunquam experimur <lb/>
plura obiecta compr&aelig;hendere in vmbra, quam in Sole.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005024">Quint&ograve;, &longs;i illa dilatatio vera e&longs;&longs;et, pupilla non &longs;emper in homine videre&shy;<lb/>
tur nigra; magnitudo enim foraminis multum luminis intra oculum admit&shy;<lb/>
teret, quod opacitatem, &amp; nigredinem illam omnem fugaret; hac enim de <lb/>
cau&longs;a in bobus, &amp; capris alba cernitur. </s>
          <s id="s.005025">quapropter cert&ograve; certius, &amp; luce <lb/>
clarius, motum hunc non verum, &longs;ed apparentem e&longs;&longs;e mihi, <expan abbr="atq;">atque</expan> alijs per&shy;<lb/>
&longs;uadebam.</s>
        </p>
        <p type="main">
          <s id="s.005026">Verumenimuer&ograve; Gr&aelig;corum illud adagium, &longs;ecund&aelig; cogitationes &longs;unt <lb/>
&longs;apientiores, veri&longs;&longs;imum e&longs;t, nam quinquennio po&longs;tquam h&aelig;c de pupill&aelig; di&shy;<lb/>
latatione con&longs;crip&longs;eram, c&ugrave;m iterum opticam public&egrave; aggrederer, oculi <lb/>
fabricam, <expan abbr="atq;">atque</expan> pupill&aelig; motum i&longs;tum attentius con&longs;iderans, conatus &longs;um ob <lb/>
&longs;equentes rationes pr&aelig;dictis euidentiores mutare &longs;ententiam, <expan abbr="atq;">atque</expan> a&longs;&longs;erere <lb/>
ver&egrave; pupillam augeri, ac minui, e&ograve; quod vuea ip&longs;a in luce ver&egrave; con&longs;tringa&shy;<lb/>
tur, in opacitate ver&ograve;, ac tenebris magno natur&aelig; miraculo dilatetur.</s>
        </p>
        <p type="main">
          <s id="s.005027">Prima ratio, c&ugrave;m pupilla minuitur, eam perpetu&ograve; vue&etail; colores <expan abbr="c&otilde;&longs;equun-tur">con&longs;equun&shy;<lb/>
tur</expan>, <expan abbr="eam&qacute;">eamque</expan>; circundant, &longs;iue cum ip&longs;a con&longs;tringuntur; quod minim&egrave; fieret, <lb/>
ni&longs;i vuea ip&longs;a con&longs;tringeretur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>, foramen illud imminueret.</s>
        </p>
        <pb pagenum="283" xlink:href="009/01/283.jpg"/>
        <p type="main">
          <s id="s.005028">Secunda, ex hac experientia; fac vt aliquis alterum &longs;ibi oculum manum <lb/>
illi applicans tegat: &amp; illic&ograve; &longs;ine vlla lucis mutatione videbis alterius ocu&shy;<lb/>
li pupillam modic&ugrave;m, &longs;ed tamen &longs;en&longs;ibiliter &longs;atis dilatari.</s>
        </p>
        <p type="main">
          <s id="s.005029">Tertia, animalia qu&aelig;dam, vt Catus, quando pupillam &longs;uam hanc dila&shy;<lb/>
tant, eam in orbem dilatant: quando ver&ograve; con&longs;tringunt, eam in oualem, ac <lb/>
tandem rimulam quandam con&longs;tringunt: <expan abbr="id&qacute;">idque</expan>; in eadem opacitate, qu&aelig; ar&shy;<lb/>
gumento &longs;unt vueam ip&longs;am moueri.</s>
        </p>
        <p type="main">
          <s id="s.005030">Quarta, e&longs;t quidam oculorum morbus, quo &aelig;ger <expan abbr="ab&longs;q;">ab&longs;que</expan> magno dolore lu&shy;<lb/>
cem nequit a&longs;picere: erg&ograve; &longs;ignum lucem aliquid intra oculum mouere po&longs;&shy;<lb/>
&longs;e, ex quo motu &aelig;ger doleat; huiu&longs;modi &aelig;grotum quendam ego aliquando <lb/>
magna admiratione inui&longs;i. </s>
          <s id="s.005031">h&aelig;c ade&ograve; miranda in nobis &longs;ummus natur&aelig; opi&shy;<lb/>
fex perpetu&ograve; operatur.</s>
        </p>
        <p type="main">
          <s id="s.005032">Reliquum e&longs;t, vt &longs;uperioribus rationibus, quibus me di&ugrave; deceptum fui&longs;&longs;e <lb/>
exi&longs;timo, &longs;atisfaciam.</s>
        </p>
        <p type="main">
          <s id="s.005033">Ad primam igitur re&longs;pondeo, etiam&longs;i vuea ver&egrave; dilatetur, non ind&egrave; ne&shy;<lb/>
ce&longs;&longs;ari&ograve; &longs;equi connexionem illam &longs;cindi debere: po&longs;&longs;unt enim tenui&longs;&longs;im&aelig; il&shy;<lb/>
l&aelig; fibr&aelig; intendi, ac remitti: <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; motui vue&aelig; obtemperare.</s>
        </p>
        <p type="main">
          <s id="s.005034">Ad &longs;ecundam, cau&longs;am efficientem huius dilatationis e&longs;&longs;e &longs;piritus; non <lb/>
partem quampiam, aut organum materiale.</s>
        </p>
        <p type="main">
          <s id="s.005035">Ad tertiam negandum e&longs;t illud Medicorum placitum.</s>
        </p>
        <p type="main">
          <s id="s.005036">Ad quartam concedenda e&longs;t tota, &longs;ed tamen addendum e&longs;t, nos non ad&shy;<lb/>
uertere mod&ograve; plura obiecta, mod&ograve; pauciora videre, quia valde difficile e&longs;t <lb/>
id ob&longs;eruare, porr&ograve; fateor difficile e&longs;&longs;e huic rationi &longs;atisfacere, quia non, <lb/>
omnin&ograve; con&longs;tat, qua ratione, &amp; quo loco oculi fiat vi&longs;io.</s>
        </p>
        <p type="main">
          <s id="s.005037">Ad quintam dicendum e&longs;t, nunquam foramen illud pupill&aelig; ad <expan abbr="t&atilde;tam">tantam</expan> ma&shy;<lb/>
gnitudinem euadere, vt &longs;atis lucis admittat ad oculi internam opacitatem <lb/>
fugandam. </s>
          <s id="s.005038">Pr&aelig;terea, quando dilatatur e&longs;t in loco &longs;atis opaco, vnde fit, vt <lb/>
opacitas ambientis aeris minim&egrave; expellat oculi opacitatem; quin potius <lb/>
eam iuuet nece&longs;&longs;e e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005039">9. Cur altero oculorum tecto, alterius pupilla aliquantulum dilatatur? <lb/>
</s>
          <s id="s.005040">R. &longs;ciendum miram e&longs;&longs;e oculorum &longs;ocietatem, qu&ograve; vnus intuetur, alter e&ograve; <lb/>
etiam con&longs;pirat: quor&longs;um alter conuertitur, eor&longs;um &amp; alter: anima enim <lb/>
vtitur duobus oculis tanquam vno. </s>
          <s id="s.005041">quia igitur dum alter tegitur, ei &longs;imul <lb/>
tenebr&aelig; offunduntur, quibus pr&aelig;&longs;entibus pupilla illius ampliatur, vt &longs;upra <lb/>
vidimus, nece&longs;&longs;e e&longs;t, ob oculorum fidam &longs;ocietatem, vt alterius etiam pu&shy;<lb/>
pilla augeatur. </s>
          <s id="s.005042">huic <expan abbr="re&longs;p&otilde;&longs;ioni">re&longs;pon&longs;ioni</expan> quis in hunc modum obijciet: c&ugrave;m alter ocu&shy;<lb/>
lus &longs;it in lumine, ac eapropter pupillam con&longs;tringere debeat; cur non ei po&shy;<lb/>
tius alter morem gerit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; pupillam, pr&aelig;&longs;entibus etiam tenebris in &longs;uo <lb/>
&longs;tatu continet. </s>
          <s id="s.005043">huic iterum re&longs;pondeo, quoniam alter, qui obtenebratur pu&shy;<lb/>
pillam ampliare, alter ver&ograve;, qui illuminatur coarctare &longs;tudet, fit vt <expan abbr="vterq;">vterque</expan> <lb/>
pupillam, modicum tamen, vt experientia docet, in orbem diducat.</s>
        </p>
        <p type="main">
          <s id="s.005044"><expan abbr="Atq;">Atque</expan> h&aelig;c &longs;unt, qu&aelig; nuper circa oculi pupillam ob&longs;eruata, huic loco ad&shy;<lb/>
denda exi&longs;timaui.</s>
        </p>
        <p type="head">
          <s id="s.005045">LAVS DEO.</s>
        </p>
      </chap>
      <pb xlink:href="009/01/284.jpg"/>
      <pb xlink:href="009/01/285.jpg"/>
      <chap>
        <p type="head">
          <s id="s.005046">DE <lb/>
MATHEMATICARVM <lb/>
NATVRA DISSERTATIO.</s>
        </p>
        <p type="head">
          <s id="s.005047">VNA CVM CLARORVM <lb/>
<emph type="italics"/>MATHEMATICORVM <lb/>
CHRONOLOGIA.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.005048">AD ILLVSTRISSIMVM AC NOBILISSIMVM <lb/>
PETRVMFRANCISCVM MALASPINAM <lb/>
&AElig;DIFICIORVM MARCHIONEM.</s>
        </p>
        <p type="head">
          <s id="s.005049"><emph type="italics"/>Authore eodem Io&longs;epho Blancano &egrave; Societate IESV, <lb/>
Mathematicarum in Parmen&longs;i Academia profe&longs;&longs;ore.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.005050">BONONI&AElig; M. DC. XV.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.005051">Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>
          <s id="s.005052">Superiorum permi&longs;&longs;u.</s>
        </p>
        <p type="head">
          <s id="s.005053">Sumptibus Hieronymi Tamburini.</s>
        </p>
        <pb xlink:href="009/01/286.jpg"/>
        <pb pagenum="3" xlink:href="009/01/287.jpg"/>
        <p type="head">
          <s id="s.005054">ILLVSTRISSIMO <lb/>
AC NOBILISSIMO <lb/>
PETROFRANCISCO <lb/>
MALASPINAE<emph type="italics"/><lb/>&AElig;DIFICIORVM MARCHIONI.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.005055">Io&longs;eph Blancanus &egrave; Societate Ie&longs;u. <!-- REMOVE S-->S.P.D.</s>
        </p>
        <p type="main">
          <s id="s.005056"><emph type="italics"/>Meam hanc de Mathematicarum natu&shy;<lb/>
ra Di&longs;&longs;ertationem, vn&agrave; cum illustrium, <lb/>
Mathematicorum Chronologia, tibi Illu&shy;<lb/>
stri&szlig;. <!-- REMOVE S-->Marchio iure merit&ograve; dicare, ac &longs;ub <lb/>
clari&szlig;imi tui nominis patrocinio in lucem <lb/>dare constitui. </s>
          <s id="s.005057">primum quidem, vt mei perpetui erga te <lb/>
amoris, &amp; ob&longs;eruanti&aelig; hoc vnum &longs;altem specimen exta&shy;<lb/>
ret; tum vt idoneum, &aelig;quumqu&eacute; propo&longs;it&aelig; Qu&aelig;stionis iu&shy;<lb/>
dicem nanci&longs;cerer. </s>
          <s id="s.005058">C&ugrave;m enim ad iu&longs;tum arbitrum duo <lb/>
poti&szlig;imum requirantur, rerum &longs;cilicet cognitio, atque pru&shy;<lb/>
dentia, quem te rei, de qua agitur peritiorem, quemque pru&shy;<lb/>
dentiorem; inuenire potuerim? </s>
          <s id="s.005059">tu enim c&ugrave;m Phy&longs;iologi&aelig;, <lb/>
ac Mathematicarum omnium Encyclop&aelig;diam mirum, <lb/>
in modum excolueris, ad intima Mathematicarum pene-<emph.end type="italics"/>


<pb pagenum="4" xlink:href="009/01/288.jpg"/><emph type="italics"/>tralia ita perua&longs;isti, vt Archimedis, &amp; Apollon&yuml; ad&shy;<lb/>mirandis, ac &longs;ubtili&szlig;imis demon&longs;trationibus detinearis. <lb/>
</s>
          <s id="s.005060">Quanta porr&ograve; in rebus agendis prudentia valeas toti pen&egrave; <lb/>Europ&aelig; innotuit, c&ugrave;m pro no&longs;tris Sereni&szlig;. <!-- REMOVE S-->Ducibus non <lb/>
&longs;ol&ugrave;m ad omnes fer&egrave; Itali&aelig;, atque Germani&aelig; Principes, <lb/>
ver&ugrave;m etiam ad C&aelig;&longs;aream Maie&longs;tatem, rebus f&oelig;liciter <lb/>ge&longs;tis, Legatus decim&ugrave;m extiteris: ac demum &agrave; Sereni&szlig;. <lb/>
<!-- REMOVE S-->Duce Ranutio inter primarios de Rep. <!-- KEEP S--></s>
          <s id="s.005061">Con&longs;iliorum Au&shy;<lb/>
thores, ad&longs;citus fueris. </s>
          <s id="s.005062">C&aelig;ter&ugrave;m in Clarorum Mathe&shy;<lb/>
maticorum Chronologia perlegenda, &longs;&aelig;pi&szlig;im&egrave; tibi nobili&longs;&shy;<lb/>&longs;imi &aelig;qu&egrave;, ac docti&szlig;imi Viri, tui omnin&ograve; per&longs;imiles, oc&shy;<lb/>
current, quod tibi nonni&longs;i grati&szlig;imum accidere po&longs;&longs;e arbi&shy;<lb/>
tror. </s>
          <s id="s.005063">Complectere igitur,qu&agrave; &longs;oles benignitate, atque clemen&shy;<lb/>tia no&longs;tra h&aelig;c quantulacunque munu&longs;cula, qu&aelig; &longs;i tibi acce&shy;<lb/>
pta e&longs;&longs;e intellexero, t&ugrave;m demum maximorum mu&shy;<lb/>
nerum loco habenda e&longs;&longs;e cen&longs;ebo. </s>
          <s id="s.005064">incolu&shy;<lb/>
mem tibi, ac f&oelig;licem D. O. M. <lb/>
long &aelig;uitatem tueatur. <lb/>
</s>
          <s id="s.005065">Vale.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.005066"><emph type="italics"/>Parm&aelig; Idibus Nouembris M. DC. XIIII.<emph.end type="italics"/><lb/>
<!-- KEEP S--></s>
        </p>
        <pb pagenum="5" xlink:href="009/01/289.jpg"/>
        <p type="head">
          <s id="s.005067"><emph type="bold"/>ADDITAMENTVM.<emph.end type="bold"/></s>
        </p>
        <p type="head">
          <s id="s.005068"><emph type="italics"/>DE NATVRA SCIENTIARVM <lb/>
MATHEMATICARVM.<emph.end type="italics"/></s>
        </p>
      </chap>
      <chap>
        <p type="main">
          <s id="s.005069">Qvoniam in hoc Opere multa ad Mathematicarum natu&shy;<lb/>ram &longs;pectantia &longs;par&longs;im dicta &longs;unt, non ab re, <expan abbr="neq;">neque</expan> ingratum <lb/>
Lectori fore duxi, ea quodammodo huc in vnum congerere, <lb/>
qu&aelig; ad earum naturam rit&egrave; percipiendam nece&longs;&longs;aria e&longs;&longs;e vi&shy;<lb/>
derentur. </s>
          <s id="s.005070">pr&aelig;&longs;ertim c&ugrave;m recentiorum quamplurimi, qui eas <lb/>
l&aelig;uiter nimis attigerunt, hac de re, veluti c&aelig;ci de colore, plu&shy;<lb/>
ribus ad internam tamen earum naturam minim&egrave; &longs;pectantibus, garrire ge&shy;<lb/>
&longs;tiant. </s>
          <s id="s.005071">Vt autem tractatio euadat planior, eam &longs;ic commod&egrave; partiemur, vt</s>
        </p>
        <p type="main">
          <s id="s.005072">Primo, De materia, &longs;eu &longs;ubiecto harum di&longs;ciplinarum agamus.</s>
        </p>
        <p type="main">
          <s id="s.005073">2. De medio Demon&longs;trationum Geometricarum, &longs;eu, vtrum &longs;int De&shy;<lb/>
mon&longs;trationes poti&longs;&longs;im&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.005074">3. De pr&aelig;&longs;tantia &longs;cienti&aelig;, quam nobis pariunt.</s>
        </p>
        <p type="main">
          <s id="s.005075">4. Aliquot calumniarum dilutio.</s>
        </p>
        <p type="main">
          <s id="s.005076">5. De Mathematicis medijs.</s>
        </p>
        <p type="head">
          <s id="s.005077"><emph type="italics"/>De&longs;ubiecto Geometr&aelig;, &amp; Arithmetic&aelig;, quod &longs;olet dici <lb/>
Materia intelligibilis. </s>
          <s id="s.005078">Cap. 1.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005079">Prim&ograve;, agemus de puris Mathematicis Geometria, &amp; Arithmetica, <lb/>
quarum e&longs;t diuer&longs;a ratio &agrave; medijs, A&longs;tronomia, &longs;cilicet Per&longs;pecti&shy;<lb/>
ua, Mechanica, &amp; Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005080">Quantitas igitur ab&longs;tracta &agrave; materia <lb/>
&longs;en&longs;ibili dupliciter con&longs;iderari &longs;olet. </s>
          <s id="s.005081">con&longs;ideratur enim &agrave; Phy&longs;ico, <lb/>
&amp; Mathematico &longs;ecundum &longs;e, ide&longs;t, ab&longs;olut&egrave;, quatenus Quantitas e&longs;t; &longs;iue <lb/>terminata &longs;it, &longs;iue non; qua ratione affectiones ip&longs;ius &longs;unt, diui&longs;ibilitas, lo&shy;<lb/>
cabilitas, figurabilitas, &amp;c. </s>
          <s id="s.005082">&agrave; Geometra ver&ograve;, &amp; Arithmetico con&longs;idera&shy;<lb/>tur non ab&longs;olut&egrave;, &longs;ed quatenus e&longs;t terminata, vt &longs;unt in quantitate continua <lb/>
line&aelig; finit&aelig; rect&aelig;, aut curu&aelig;, vt &longs;unt &longs;uperficies terminat&aelig;, ex quibus vari&aelig; <lb/>
fiunt figur&aelig;, vt circulus, triangulum, &amp;c. </s>
          <s id="s.005083">vt tandem &longs;unt &longs;olida item termi&shy;<lb/>
nata, ex quibus vari&aelig; exi&longs;tunt &longs;pecies &longs;olidarum figurarum, veluti, pyramis, <lb/>
cubus, conus, cylindrus, &amp;c. </s>
          <s id="s.005084">qu&aelig; ad Geometram pertinent. </s>
          <s id="s.005085">Qu&aelig; omnia in <lb/>
quantitate etiam di&longs;creta, &longs;eu in numeris proportionaliter reperiuntur,


<pb pagenum="6" xlink:href="009/01/290.jpg"/>quos &longs;ol&ugrave;m terminatos Arithmeticus accipit. </s>
          <s id="s.005086">e&longs;&longs;e autem genera h&aelig;c termi&shy;<lb/>
nat&aelig; Quantitatis Geometri&aelig;, aut Arithmetic&aelig; &longs;ubiectum, ex eo patet, quod <lb/>
eas &longs;olas quantitates ip&longs;i definiunt, <expan abbr="de&qacute;">deque</expan>; ip&longs;is varias pa&longs;&longs;iones <expan abbr="demon&longs;tr&atilde;t">demon&longs;trant</expan>, <lb/>
<expan abbr="eas&qacute;">easque</expan>; omnin&ograve; ab eis diuer&longs;as, quas Phy&longs;icus, &amp; Metaphy&longs;icus in ea ab&longs;olu&shy;<lb/>
t&egrave; &longs;pectata con&longs;iderant. </s>
          <s id="s.005087">Vnde manife&longs;tum e&longs;t, has affectiones, quas Ma&shy;<lb/>
thematicus contemplatur ab ip&longs;a Quantitate, quatenus terminata e&longs;t ema&shy;<lb/>
nare; &longs;unt autem &aelig;qualitas, in&aelig;qualitas, talis diui&longs;io, transfiguratio, pro&shy;<lb/>
portiones vari&aelig;, commen&longs;uratio, incommen&longs;uratio, figurarum <expan abbr="c&otilde;&longs;tructio-nes">con&longs;tructio&shy;<lb/>
nes</expan>, &amp;c. </s>
          <s id="s.005088">Qu&aelig; &longs;an&egrave; affectiones ab intrin&longs;eca Quantitatis natura minim&egrave; <lb/>
fluunt, po&longs;ita enim ea interminata, pr&aelig;dict&aelig; pa&longs;&longs;iones non con&longs;equuntur, <lb/>
nihil enim, ea &longs;ic po&longs;ita, e&longs;t &aelig;quale, aut in&aelig;quale, &amp;c. </s>
          <s id="s.005089">&longs;ed addita Quantita&shy;<lb/>
ti terminatione, e&aelig; ab ea per emanationem profluunt. </s>
          <s id="s.005090">Quapropter inr&egrave; di&shy;<lb/>
xeris formalem rationem Mathematic&aelig; con&longs;iderationis e&longs;&longs;e Terminatio&shy;<lb/>
nem; &amp; obiectum totale ad&aelig;quatum e&longs;&longs;e Quantitatem terminatam, qua&shy;<lb/>
tenus terminata e&longs;t. </s>
          <s id="s.005091">Ex hac enim terminatione vari&aelig; oriuntur figur&aelig;, &amp; <lb/>
numeri, quas Mathematicus definit, <expan abbr="de&qacute;">deque</expan>; ip&longs;is varia demon&longs;trat. </s>
          <s id="s.005092"><expan abbr="Atq;">Atque</expan> h&aelig;c <lb/>e&longs;t illa Quantitas, qu&aelig; dici &longs;olet materia intelligibilis, ad differentiam ma&shy;<lb/>
teri&aelig; &longs;en&longs;ibilis, qu&aelig; ad Phy&longs;icum &longs;pectat; illa enim ab hac per intellectum <lb/>
&longs;eparatur, ac &longs;olo intellectu percipitur. </s>
          <s id="s.005093">Continuum igitur, &amp; di&longs;cretum, <lb/>
<expan abbr="vtrumq;">vtrumque</expan> <expan abbr="terminat&utilde;">terminatum</expan>, e&longs;t materia intelligibilis, illud Geometri&aelig;, i&longs;tud Arith&shy;<lb/>
metic&aelig;. </s>
          <s id="s.005094">Hinc etiam patet, cur dicatur Mathematicus con&longs;iderare Quan&shy;<lb/>
titatem finitam, quia accipit terminatam, qu&aelig; finita e&longs;t: quod enim habet <lb/>
terminus, &longs;eu fines, finitum e&longs;t. </s>
          <s id="s.005095">quod &longs;i dari po&longs;&longs;et quantitas aliqua termi&shy;<lb/>
nata, &amp; &longs;imul infinita, de ea etiam Demon&longs;trationes Euclidis fieri po&longs;&longs;ent; <lb/>
&longs;i enim daretur triangulum infinitum, eodem modo de eo o&longs;tendi po&longs;&longs;et ha&shy;<lb/>
bere tres angulos &aelig;quales duobus rectis. </s>
          <s id="s.005096">Porr&ograve; hanc terminatam Quanti&shy;<lb/>tatem e&longs;&longs;e Geometri&aelig;, &amp; Arithmetic&aelig; &longs;ubiectum minim&egrave; cognouerunt ij, <lb/>
qui Geometricas demon&longs;trationes impugnarunt, vt in eorum &longs;criptis vide&shy;<lb/>
re e&longs;t, qu&aelig; prima eis fuit errandi occa&longs;io.</s>
        </p>
        <p type="main">
          <s id="s.005097">Porr&ograve; ex hac mathematica ab&longs;tractione &agrave; materia &longs;en&longs;ibili, fit vt materia <lb/>
h&aelig;c ab&longs;tracta perfectionem quandam acquirat, quam perfectionem mathe&shy;<lb/>
maticam appellant. </s>
          <s id="s.005098">v. <!-- REMOVE S-->g. <!-- REMOVE S-->triangulum ab&longs;tractum e&longs;t omnin&ograve; planum ex tri&shy;<lb/>
bus lineis omnin&ograve; rectis, <expan abbr="tribus&qacute;">tribusque</expan>; angulis punctis omnin&ograve; indiuiduis con&shy;<lb/>
&longs;titutum, quale in rerum natura &lpar;exceptis fort&egrave; c&oelig;le&longs;tibus&rpar; vix puto repe&shy;<lb/>
riri po&longs;&longs;e. </s>
          <s id="s.005099">vnde nonnulli &longs;olent Mathematicis illud obijcere; entia &longs;cilicet <lb/>
mathematica non extare, ni&longs;i per &longs;olum intellectum. </s>
          <s id="s.005100">Verumenimuer&ograve; &longs;cien&shy;<lb/>
dum e&longs;t entia h&aelig;c mathematica, quamuis in ea perfectione non extent, id <lb/>
tamen e&longs;&longs;e per accidens, con&longs;tat enim naturam, &amp; artem figuras mathema&shy;<lb/>
ticas pr&aelig;cipu&egrave; intendere, quamuis propter materi&aelig; &longs;en&longs;ibilis ruditatem, &amp; <lb/>
imperfectionem, qu&aelig; perfectas omnin&ograve; figuras &longs;u&longs;cipere nequit, &longs;uo &longs;ine <lb/>
fru&longs;trentur; natura enim in truncis arborum cylindri figuram affectat, in <lb/>pomis, &amp; vuarum acinis aut &longs;ph&aelig;ricam, aut &longs;ph&aelig;roidem, in cornea oculi <lb/>
circulum; im&ograve; oculus ip&longs;&aelig; maxim&egrave; &longs;ph&aelig;ricus e&longs;t. </s>
          <s id="s.005101">Sol, <expan abbr="reliqua&qacute;">reliquaque</expan>; a&longs;tra com&shy;<lb/>
muni omnium con&longs;en&longs;u omnin&ograve; &longs;ph&aelig;rica &longs;unt. </s>
          <s id="s.005102">ip&longs;a aqu&aelig; &longs;uperficies globo&shy;<lb/>
&longs;a e&longs;t. </s>
          <s id="s.005103"><expan abbr="terra&qacute;">terraque</expan>; ip&longs;a ni&longs;i ob&longs;taret materi&aelig; cra&longs;&longs;ities, &amp; diuer&longs;itas, rotunda pla&shy;<lb/>
n&egrave; euaderet. </s>
          <s id="s.005104">line&aelig; &longs;pirales conic&aelig; nonne manife&longs;t&egrave; in marinis cochl&aelig;is de&shy;<pb pagenum="7" xlink:href="009/01/291.jpg"/>&longs;ignantur? </s>
          <s id="s.005105">Cylindric&aelig;, &amp; plan&aelig; in nonnullis herbis? </s>
          <s id="s.005106">Ars pr&aelig;terea pal&agrave;m <lb/>
magis ea&longs;dem figuras pro&longs;equitur; artifices enim omnia fer&egrave; opificia qua&shy;<lb/>dratis figuris, aut rotundis, aut circulis, aut ellip&longs;ibus induunt. </s>
          <s id="s.005107">Verum ip&longs;a <lb/>
<expan abbr="quoq;">quoque</expan> ars, non &longs;ecus ac natura, quam imitatur &longs;uo fine ob materi&aelig; rudita&shy;<lb/>
tem defraudatur. </s>
          <s id="s.005108">Quamuis igitur re ip&longs;a non exi&longs;tant, quia tamen tamin <lb/>
mente Auctoris natur&aelig;, qu&agrave;m in humana, eorum Ide&aelig; tamquam exacti&longs;&longs;i&shy;<lb/>
mi rerum typi, necnon tamquam exacta entia Mathematica exi&longs;tunt; Ideo <lb/>
de ip&longs;is eorum id&aelig;is, qu&aelig; per &longs;e prim&ograve; intenduntur, &amp; qu&aelig; vera &longs;unt entia, <lb/>
agit Mathematicus. </s>
          <s id="s.005109">Quapropter dicendum e&longs;t, entia h&aelig;c Geometrica om&shy;<lb/>
nibus numeris ab&longs;oluta e&longs;&longs;e entia per &longs;e, &amp; vera; figur&aelig; ver&ograve; tum natura&shy;<lb/>
les, tum artificiales, qu&aelig; in rebus exi&longs;tunt, c&ugrave;m &agrave; nullo efficiente intendan&shy;<lb/>
tur, e&longs;&longs;e entia per accidens, imperfecta, &amp; fal&longs;a. </s>
          <s id="s.005110">v. <!-- REMOVE S-->g. <!-- REMOVE S-->triangulum in aliqua <lb/>
charta depictum, non e&longs;t verum triangulum, &longs;ed verum <expan abbr="triangul&utilde;">triangulum</expan> illud e&longs;t, <lb/>
quod in id&aelig;a diuina e&longs;t. </s>
          <s id="s.005111">ex quibus obiter illud intelligas, cur &longs;cilicet ali&shy;<lb/>
quando Plato dixerit Deum geometrizare, ide&longs;t tanquam verum Geome&shy;<lb/>
tram non ni&longs;i perfecti&longs;&longs;imas id&aelig;as contemplari. </s>
          <s id="s.005112">Eodem etiam modo, Poe&shy;<lb/>
t&aelig;, qu&igrave; res perfectas imitari debent, eas &longs;altem vt plurimum, non vt exti&shy;<lb/>
terunt ver&longs;ibus decantant; &longs;ed quales e&longs;&longs;e debuerunt, confingunt, <expan abbr="atq;">atque</expan> lecto&shy;<lb/>
ribus, aut &longs;pectatoribus repr&aelig;&longs;entant. </s>
          <s id="s.005113">Vltim&ograve; dici pote&longs;t; h&aelig;c entia e&longs;&longs;e <lb/>
po&longs;&longs;ibilia, quis enim neget Angelum, aut Deum ea po&longs;&longs;e efficere? </s>
          <s id="s.005114">ad obie&shy;<lb/>
ctum autem &longs;cienti&aelig; &longs;atis e&longs;t e&longs;&longs;e po&longs;&longs;ibile; &longs;cientia enim ab&longs;trahit ab exi&shy;<lb/>
&longs;tentia &longs;ubiecti.</s>
        </p>
        <p type="main">
          <s id="s.005115">In hac pr&aelig;terea intelligibili materia, alio modo materia alia accipitur, <lb/>
c&ugrave;m partes &longs;cilicet dicuntur materia totius, vt quando duo triangula com&shy;<lb/>
ponunt quodpiam quadrilaterum, &longs;unt illa duo trigona materia totius il&shy;<lb/>
lius quadrilateri.</s>
        </p>
        <p type="main">
          <s id="s.005116">Similiter aliquando plures anguli partiales componunt tanquam mate&shy;<lb/>
riam totalem angulum. </s>
          <s id="s.005117">Idem dicendum de alijs &longs;imilibus, pariter e&longs;&longs;e ali&shy;<lb/>
cuius dimidium, aut tertiam partem, aut duplum, aut reliquum cuiu&longs;piam <lb/>
totius, referuntur ad veram cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; te&longs;te Ari&longs;t. tex. <!-- REMOVE S-->31.2. <lb/>
&amp; tex. <!-- REMOVE S-->3. 5. Metaph. &amp; omnibus Philo&longs;ophis. </s>
          <s id="s.005118">qu&aelig; quidem materi&aelig; accep&shy;<lb/>
tio, &longs;imilis e&longs;t acceptioni materi&aelig; phy&longs;ic&aelig;, ex qua tanquam ex parte <expan abbr="c&otilde;po-&longs;itum">compo&shy;<lb/>
&longs;itum</expan> con&longs;tatur: conflatur enim ex materia, &amp; forma, tanquam partibus. <lb/>
</s>
          <s id="s.005119">diuer&longs;a ver&ograve; e&longs;t ab ea, qu&agrave;m phy&longs;ici pa&longs;&longs;im v&longs;urpant, dum con&longs;iderant ma&shy;<lb/>teriam, in qua, aut circa quam, vt aiunt. </s>
          <s id="s.005120">hoc tamen non ob&longs;tat, quominus <lb/>
illa veram cau&longs;&aelig; materialis rationem non obtineat. </s>
          <s id="s.005121">Quod etiam Geome&shy;<lb/>
tricarum demon&longs;trationum impugnatores videntur minim&egrave; aduerti&longs;&longs;e. </s>
          <s id="s.005122">qu&aelig; <lb/>
illis &longs;ecunda errandi cau&longs;a extitit.</s>
        </p>
        <p type="main">
          <s id="s.005123">Po&longs;trem&ograve; aduertendum, qu&ograve;d magni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;t, definitiones tam Geo&shy;<lb/>
metric&aelig;, qu&agrave;m Arithmetic&aelig; e&longs;&longs;e omnino e&longs;&longs;entiales, qu&aelig; &longs;cilicet totam rei <lb/>quid ditatem explicent; minim&egrave; ver&ograve; e&longs;&longs;e tantummodo nominis explicatio&shy;<lb/>
nes, aut definitiones, vt ijdem perperam exi&longs;timarunt, qui eorum tertius <lb/>
e&longs;t error. </s>
          <s id="s.005124">quod quidem Ari&longs;t. &longs;en&longs;i&longs;&longs;e manife&longs;tum e&longs;t, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim in <lb/>Analyticis de &longs;cientiarum principijs loquitur, inter ea definitiones Geome<lb/>
tri&aelig;, &amp; Arithmetic&aelig; &longs;emper <expan abbr="c&otilde;numerat">connumerat</expan>, quod minim&egrave; feci&longs;&longs;et, &longs;i &longs;ol&ugrave;m no&shy;<lb/>
minis e&longs;&longs;ent explicationes. </s>
          <s id="s.005125">Verum quidem e&longs;t eas, vt plurimum e&longs;&longs;e &longs;imul,


<pb pagenum="8" xlink:href="009/01/292.jpg"/>&amp; rei, &amp; nominis expo&longs;itiones. </s>
          <s id="s.005126">quod &longs;&aelig;p&egrave; accidit, c&ugrave;m &longs;cilicet nomina val&shy;<lb/>
d&egrave; perfecta, ac rei omnino conuenientia &longs;unt; nam</s>
        </p>
        <p type="main">
          <s id="s.005127"><emph type="italics"/>Conueniunt rebus nomina &longs;&aelig;p&egrave; &longs;uis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005128">Huiu&longs;modi &longs;&aelig;p&egrave; &longs;unt, qu&aelig; perfectam continent etymologiam, vbi ip&longs;a <lb/>
nominis expo&longs;itio, &longs;imul etiam e&longs;t rei e&longs;&longs;entialis definitio. </s>
          <s id="s.005129">tales &longs;unt &longs;&aelig;p&egrave; <lb/>
nomina, &amp; definitiones Geometric&aelig;. <!-- KEEP S--></s>
          <s id="s.005130">Exempli cau&longs;a, talis e&longs;t definitio qua&shy;<lb/>
drati, nam quando dico, quadratum e&longs;t figura plana quatuor rectis lineis, <lb/>
&amp; quatuor angulis rectis con&longs;tans, explico &longs;imul rationem nominis, &amp; ra&shy;<lb/>
tionem rei: dicitur enim quadratum &aacute; quatuor illis lineis. </s>
          <s id="s.005131">Explico deinde <lb/>
totam eius e&longs;&longs;entiam, quando dico ip&longs;um con&longs;tare ex quatuor lineis rectis, <lb/>
&amp; quatuor angulis rectis, qu&aelig; duo &longs;imul iuncta con&longs;tituunt totam quadrati <lb/>
e&longs;&longs;entiam, &longs;unt enim ip&longs;ius differentia con&longs;titutiua; loco autem generis e&longs;t <lb/>
figura plana quadrilatera: quapropter erit h&aelig;c perfecti&longs;&longs;ima definitio, c&ugrave;m <lb/>non &longs;olum nominis, &longs;ed etiam rei e&longs;&longs;entiam rotam patefaciat; &longs;tatim enim, <lb/>
ac cogno&longs;cimus quadratum ex pr&aelig;dictis <expan abbr="c&otilde;&longs;tare">con&longs;tare</expan> nihil amplius de ip&longs;ius e&longs;&shy;<lb/>
&longs;entia animus &longs;cire de&longs;iderat, &longs;ed acquie&longs;cit, vnde eam e&longs;&longs;e optimam defi&shy;<lb/>
nitionem manife&longs;tum e&longs;t. </s>
          <s id="s.005132">Huiu&longs;modi <expan abbr="quoq;">quoque</expan> e&longs;t definitio figur&aelig; altera par&shy;<lb/>
te longioris, nam c&ugrave;m dicitur, ea e&longs;t figura plana quadrilatera, qu&aelig; <expan abbr="rect&atilde;-gula">rectan&shy;<lb/>
gula</expan> quidem, &amp; &aelig;quilatera non e&longs;t, patet inde, cur dicatur altera parte <expan abbr="l&otilde;-gior">lon&shy;<lb/>
gior</expan>, qu&ograve;d e&longs;t ip&longs;ius etymon: deinde ip&longs;ius e&longs;&longs;entia, ita innote&longs;cit, vt nihil <lb/>
amplius de ea qu&aelig;rendum &longs;uper&longs;it. </s>
          <s id="s.005133">Similiter cum dicitur, <expan abbr="&aelig;quilater&utilde;">&aelig;quilaterum</expan> trian&shy;<lb/>
gulum e&longs;t, quod tria latera habet &aelig;qualia, ecce tibi, &amp; nominis, &amp; rei cau&shy;<lb/>
&longs;a. </s>
          <s id="s.005134">talis e&longs;t etiam prima 6. definitio, &longs;imiles figur&aelig; rectiline&aelig; &longs;unt, qu&aelig; &amp; an&shy;<lb/>
gulos &longs;ingulos &longs;ingulis &aelig;quales habent, atque etiam latera, qu&aelig; <expan abbr="circ&utilde;">circum</expan> &aelig;qua&shy;<lb/>
les proportionalia; hic enim etymologia, &amp; rei natura manife&longs;tatur. </s>
          <s id="s.005135">talis <lb/>
adhuc e&longs;t prima definitio 10. commen&longs;urabiles magnitudines <expan abbr="dic&utilde;tur">dicuntur</expan>, quas <lb/>
eadem men&longs;ura metitur. </s>
          <s id="s.005136">innumeras huiu&longs;modi alias, qu&aelig; apud alios Geo&shy;<lb/>
metras reperiuntur, mi&longs;&longs;as facio, ne in re tam clara longior &longs;im. </s>
          <s id="s.005137">&longs;ed alias <lb/>
contemplemus, qu&aelig; nullo modo &longs;unt nominis definitionis, &longs;ed rei tantum, <lb/>prima Euclidis definitio, qu&aelig; e&longs;t Puncti, iuxta puncti naturam bipartita e&longs;t, <lb/>
habet enim e&longs;&longs;e partim ab&longs;olutum, partim relatiuum; c&ugrave;m in prima defi&shy;<lb/>
nitione dicitur. </s>
          <s id="s.005138">Punctum e&longs;t, cuius nulla pars e&longs;t, definitur quatenus ab&longs;o&shy;<lb/>
lutum, c&ugrave;m po&longs;tea in tertia definitione dicitur, termini line&aelig; &longs;unt puncta, <lb/>
definitur quatenus e&longs;t quid alterius: ex quibus tota puncti natura fit mani&shy;<lb/>
fe&longs;ta; etymologia ver&ograve; ne <expan abbr="quaqu&atilde;">quaquam</expan>; nam dicitur punctum &agrave; pungendo, qua&longs;i <lb/>
&longs;it punctura qu&aelig;dam, qu&aelig; notio in Euclidis definitione minim&egrave; attingitur. <lb/>
</s>
          <s id="s.005139">Similiter cum dicitur, line a e&longs;t longitudo latitudinis expers, vbinam nomi&shy;<lb/>
nis ratio? </s>
          <s id="s.005140">nam linea dicitur &agrave; lino, qua&longs;i lineum filum; antiquitus enim ex <lb/>lino fila fiebant, quibus fabri ad de&longs;ignationes vtebantur, quemadmodum <lb/>
nunc ex cannabe: at in Euclidis definitione ridiculum e&longs;t hanc <expan abbr="ration&etilde;">rationem</expan> que&shy;<lb/>
rere; in qua tamen line&aelig; e&longs;&longs;entia perfect&egrave; apparet.</s>
        </p>
        <p type="main">
          <s id="s.005141">Pariter quando definit &longs;uperficiem e&longs;&longs;e eam, qu&aelig; longitudinem, <expan abbr="latitudi-nem&qacute;">latitudi&shy;<lb/>
nemque</expan>; <expan abbr="t&atilde;tum">tantum</expan> habet, apparet quidem rei natura, at ver&ograve; vbi nominis defi&shy;<lb/>
nitio, qu&aelig; e&longs;t, dici &longs;uperficiem, qua&longs;i &longs;upremam faciem? </s>
          <s id="s.005142">C&ugrave;m dicitur An&shy;<lb/>
gulus e&longs;t duarum linearum, &longs;e mutu&ograve; tangentium inclinatio, vbinam vocis <lb/>
notio? </s>
          <s id="s.005143">aperitur tamen rei natura, &amp; quidditas. </s>
          <s id="s.005144">Sed magis manife&longs;tum e&longs;t<pb pagenum="9" xlink:href="009/01/293.jpg"/>in linea perpendiculari, qu&aelig; proculdubio denominata e&longs;t &agrave; perpendiculo, <lb/>
in definitione tamen nullum huius ve&longs;tigium: at ver&ograve; quid ip&longs;a &longs;it, optim&egrave; <lb/>
explicatur. </s>
          <s id="s.005145">Definitio porr&ograve; circuli videtur a&longs;&longs;ignari non per intrin&longs;eca, <lb/>
&longs;ed tamen &aelig;quiualet intrin&longs;ec&aelig; definitioni; quando enim dicitur circulus <lb/>
e&longs;t figura plana, vncia linea contenta, ad quam ab vno puncto eorum, qu&aelig; <lb/>
intra figuram &longs;unt, duct&aelig; omnes line&aelig; &longs;unt &aelig;quales, perinde e&longs;t, ac &longs;i dice&shy;<lb/>
ret, circulus e&longs;t figura plana, cuius medium &aelig;quidi&longs;tat ab extremis, qu&etail; e&longs;t <lb/>
e&longs;&longs;entialis; po&longs;ita enim hac &aelig;quidi&longs;tantia, ponitur nece&longs;&longs;ari&ograve; circulus. </s>
          <s id="s.005146">Ve&shy;<lb/>
r&ugrave;m centri definitionem e&longs;&longs;e tantum nominis explicationem; ab&longs;urdum e&longs;t: <lb/>centrum enim vox gr&etail;ca e&longs;t, qu&aelig; primo &longs;ignificat &longs;timulum, vel aculeum il&shy;<lb/>
lum. </s>
          <s id="s.005147">quo Boues agit bubulcus.</s>
        </p>
        <p type="main">
          <s id="s.005148">At Rhombi definitionem, qu&agrave;m ridiculum e&longs;t, eam nominis &longs;olum expli&shy;<lb/>
cationem continere, c&ugrave;m nihil minus. </s>
          <s id="s.005149">Dicitur enim Rhombus &agrave; cuiu&longs;dam <lb/>
pi&longs;cis, vel cuiu&longs;dam textorij in&longs;trumenti <expan abbr="&longs;imilitudin&etilde;">&longs;imilitudinem</expan>, cuius figuram refert. <lb/>
</s>
          <s id="s.005150">naturam tamen ip&longs;ius definitio aperit, ide&longs;t Rhombus e&longs;t figura plana qua&shy;<lb/>
drilatera, &aelig;quilatera, &longs;ed non rectangula. </s>
          <s id="s.005151">Idem per&longs;picere licet in defini&shy;<lb/>tionibus corporum, quarum prima e&longs;t, &longs;olidum e&longs;t, qu&ograve;d longitudinem, la&shy;<lb/>
titudinem, &amp; cra&longs;&longs;itudinem habet; ex qua clar&egrave; tota rei natura per&longs;picitur. <lb/>
</s>
          <s id="s.005152">Sed ne longior &longs;im, innumeras pene alias apud omnes Geometras reperies <lb/>
omnino e&longs;&longs;entiales, quas pr&aelig;tero: eadem pror&longs;us de Arithmetic&etail; defini&shy;<lb/>tionibus &longs;unt intelligenda, vt eas con&longs;ideranti &longs;tatim patebit. </s>
          <s id="s.005153">Quod &longs;i quis <lb/>iam fateatur ha&longs;ce definitiones e&longs;&longs;entiales e&longs;&longs;e, &longs;ed tamen adhuc Mathema&shy;<lb/>
ticis illas definitiones cau&longs;ales, quas demon&longs;tratio requirit, deneget; is &longs;i&shy;<lb/>
bi refragrantem audiat Ari&longs;t. qui tex. <!-- REMOVE S-->12. 2. de Anima; ait Tetragoni&longs;mi <lb/>extare duas definitiones, vnam formalem, &longs;eu e&longs;&longs;entialem, qu&etail; e&longs;t, Tetrago&shy;<lb/>
ni&longs;mus e&longs;t effectio quadrati &aelig;qualis dato &aelig;quilatero; altera ver&ograve; cau&longs;alis, <lb/>&longs;cilicet Tetragoni&longs;mus e&longs;t inuentio medi&etail; proportionalis, quia linea illa me <lb/>dia proportionali, e&longs;t cau&longs;a quadrati &aelig;qualis dat&aelig; figur&aelig;: vide no&longs;tram hu&shy;<lb/>
ius loci explicationem. </s>
          <s id="s.005154">Concedat is igitur oportet, Geometricas de fini&shy;<lb/>
tiones non &longs;olum nominales, &longs;ed etiam formales, &amp; cau&longs;ales e&longs;&longs;e. </s>
          <s id="s.005155">quo no&shy;<lb/>
mine Mathematicas definitiones reliquarum &longs;cientiarum definitiones an&shy;<lb/>
tecellere iam certum e&longs;&longs;e pote&longs;t; c&ugrave;m apud omnes Philo&longs;ophos in confe&longs;&longs;o <lb/>
&longs;it, vltimas rerum <expan abbr="differ&etilde;tias">differentias</expan> nos latere, &longs;ine quibus vera definitio nulla e&longs;t; <lb/>ade&ograve;, vt etiam apud eo&longs;dem ambigatur, vtrum illa definitio hominis, ani&shy;<lb/>
mal rationale, vera &longs;it definitio nec ne.</s>
        </p>
        <p type="main">
          <s id="s.005156">Obijces fort&egrave; iterum, definitiones ha&longs;ce Mathematicarum e&longs;&longs;e vt pluri&shy;<lb/>mum definitiones &longs;ubiecti: at in poti&longs;&longs;ima demon&longs;tratione, ad quam tendi&shy;<lb/>
mus, requiri cau&longs;ales definitiones pa&longs;&longs;ionis prim&ograve;, &amp; per &longs;e; definitionem <lb/>ver&ograve; &longs;ubiecti per accidens, vt quando aliquid immediat&egrave; ab ea procedens <lb/>
de &longs;ubiecto ip&longs;o <expan abbr="demon&longs;rand&utilde;">demon&longs;trandum</expan> e&longs;t. </s>
          <s id="s.005157">re&longs;pondendum cen&longs;eo, prim&ograve;, quod c&ugrave;m <lb/>definitio cau&longs;alis pa&longs;&longs;ionis non &longs;it aliud, quam cau&longs;a ip&longs;ius, &longs;i in definitione <lb/>
&longs;ubiecti continetur causa pa&longs;&longs;ionis, a&longs;&longs;umendo definitionem &longs;ubiecti, a&longs;&longs;u&shy;<lb/>metur etiam definitio cau&longs;alis pa&longs;&longs;ionis. </s>
          <s id="s.005158">&longs;ecund&ograve;, quod in Mathematicis <lb/>definitiones ip&longs;ius &longs;ubiecti &longs;&aelig;pe euadunt definitiones pa&longs;&longs;ionis, vt infra cla&shy;<lb/>r&egrave; patebit, quando nimirum ip&longs;um &longs;ubiectum. </s>
          <s id="s.005159">v. <!-- REMOVE S-->g. <!-- REMOVE S-->quadratum veluti pa&longs;&longs;io <lb/>de figuratione quapiam demon&longs;tratur; &longs;iue quando o&longs;tenditur ex quapiam <pb pagenum="10" xlink:href="009/01/294.jpg"/>con&longs;tructione rect&egrave; fieri quadratum, triangulum, lineam perpendicularem, <lb/>
&amp; &longs;imilia. </s>
          <s id="s.005160">terti&ograve;, in pr&aelig;cedenti dubitatione dictum e&longs;&longs;e ex mente Ari&longs;tot. <lb/>
etiam in Mathematicis e&longs;&longs;e definitiones cau&longs;ales, <expan abbr="id&qacute;">idque</expan>; <expan abbr="ex&etilde;plo">exemplo</expan> tetragoni&longs;mi <lb/>
confirmatum. </s>
          <s id="s.005161">Ex his, qu&aelig; de &longs;cientiarum definitionibus dicta &longs;unt, notan&shy;<lb/>
da e&longs;t qu&aelig;dam di&longs;paritas inter alias &longs;cientias, &amp; Mathematicas in modo <lb/>
procedendi ad &longs;ubiecti proprij cognitionem. </s>
          <s id="s.005162">nam in demon&longs;trationibus &agrave; <lb/>
&longs;igno, &agrave; quibus incipiunt vt plurimum ali&aelig; &longs;cienti&aelig;, &longs;ola cognitio nominis <lb/>
&longs;ubiecti requiritur, non autem e&longs;&longs;entialis definitio; eius enim e&longs;&longs;entia, qu&aelig; <lb/>
occulta e&longs;t, per accidentia, &amp; proprietates &agrave; po&longs;teriori indagatur; qua de&shy;<lb/>tecta ab ea iterum ad demon&longs;trandas pa&longs;&longs;iones di&longs;tinct&egrave;, &amp; &longs;cientific&egrave; re&shy;<lb/>
gredimur. </s>
          <s id="s.005163">quod &longs;i prim&ograve; perfecta obiecti cognitio obijceretur, vt &longs;it in Ma&shy;<lb/>
thematicis ob perfectus earum definitiones pulcherrimo natur&aelig; ordine ab <lb/>
e&longs;&longs;entia ip&longs;ius ad pa&longs;&longs;iones demon&longs;trandas procederemus, vt fit in demon&shy;<lb/>
&longs;trationibus &agrave; cau&longs;a, quales fer&egrave; &longs;emper &longs;unt in Geometria, &amp; Arithmetica <lb/>
exceptis demon&longs;trationibus ab impo&longs;sibili, vbi nobis prim&ograve; tota &longs;ubiecti <lb/>
natura ex pr&aelig;mi&longs;sis definitionibus obijcitur, ex qua deinde &longs;emper &agrave; priori <lb/>
ad inue&longs;tigandas illius pa&longs;siones procedimus; in quo proce&longs;&longs;u definitio &longs;u&shy;<lb/>
biecti pr&etail;mitti, <expan abbr="eius&qacute;">eiusque</expan>; quidditas &longs;upponi debet. </s>
          <s id="s.005164">vnde etiam &longs;equitur Mathe&shy;<lb/>
maticas ha&longs;ce &agrave; notioribus nobis, &amp; natura, vt vult Auerroes, &amp; c&aelig;teri fer&egrave; <lb/>
omnes, &amp; ex no&longs;tris maxim&egrave; Toletus qu&etail;&longs;t. </s>
          <s id="s.005165">4. &longs;ecundi Phy&longs;. procedere. </s>
          <s id="s.005166">no&shy;<lb/>tioribus nobis, quia primum omnium manife&longs;ta e&longs;t tota figur&aelig; e&longs;&longs;entia ex <lb/>
definitione ip&longs;ius allata, ignotis adhuc ip&longs;ius affectionibus, notioribus na&shy;<lb/>
tura, quia prius natura e&longs;t &longs;ubiecti e&longs;&longs;entia, qu&agrave;m pa&longs;siones, qu&aelig; ab ea ma&shy;<lb/>
nant, <expan abbr="de&qacute;">deque</expan>; ea demon&longs;trantur: <expan abbr="atq;">atque</expan> h&aelig;c cau&longs;&aelig; e&longs;t, cur &longs;emper tanti fact&aelig; &longs;ine <lb/>
Geometric&aelig; demon&longs;trationes, <expan abbr="primum&qacute;">primumque</expan>; certitudinis gradum obtineant.</s>
        </p>
        <p type="head">
          <s id="s.005167"><emph type="italics"/>De medio Demonstrationum Geometri&aelig;, &amp; Arith&shy;<lb/>
metic&aelig;, &longs;eu, An &longs;int poti&szlig;im&aelig; Demon&longs;trationes. <lb/>
</s>
          <s id="s.005168">Cap. 2.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005169">Coguntur huius tempe&longs;tatis Mathematici ea, qu&aelig; antiqui&longs;simo po&longs;&shy;<lb/>
&longs;e&longs;sionis iure tut&ograve; hactenus po&longs;siderunt, &agrave; nonnullis recentioribus <lb/>
ea diripere volentibus, omni conatu tutari. </s>
          <s id="s.005170">quis enim vnquam <lb/>alicuius nominis philo&longs;ophus ante Alexandrum Piccolomineum <lb/>
extitit, qui Geometris poti&longs;simas Demon&longs;trationes eripere tentauerit? <lb/>
</s>
          <s id="s.005171">profect&ograve; nullus fatetur ip&longs;e &longs;e primum inter recentiores hanc veritatem <lb/>
olfeci&longs;&longs;e, &longs;ed ver&egrave; omnium etiam antiquorum primus ip&longs;e fuit, nam duos, <lb/>
vel tres, quos ex antiquis in &longs;uam &longs;ententiam pertrahere conatur, re vera, <lb/>
vt infra patebit, minim&egrave; pertrahit.</s>
        </p>
        <p type="main">
          <s id="s.005172">Primo igitur antiquorum auctoritates, pr&aelig;cipu&egrave; ver&ograve; Ari&longs;t. pro parte af&shy;<lb/>
firmatiua afferemus. </s>
          <s id="s.005173">&amp; ver&ograve; indignum, <expan abbr="atq;">atque</expan> &longs;uperuacaneum exi&longs;timo, c&ugrave;m <lb/>eo, qui Ari&longs;t. <!-- REMOVE S-->Analyticos po&longs;teriores legerit, de ip&longs;ius &longs;ententia di&longs;putare, <lb/>
<expan abbr="cius&qacute;">eiusque</expan>; mentem, qua&longs;i in fru&longs;ta locis aliquot citandis &longs;ecare, c&ugrave;m totis duo&shy;<lb/>
bus libris nihil aliud agere videatur, qu&agrave;m <expan abbr="perfect&atilde;">perfectam</expan> Demon&longs;trationis id&etail;am <pb pagenum="11" xlink:href="009/01/295.jpg"/>ex Geometricis delineare; quippe qui omnes conditiones, <expan abbr="omnia&qacute;">omniaque</expan>; ad per&shy;<lb/>
fectam demon&longs;trationem nece&longs;&longs;aria, <expan abbr="vbiq;">vbique</expan> Geometricis demon&longs;trationibus <lb/>
attribuat, <expan abbr="id&qacute;">idque</expan>; non &longs;ol&ugrave;m pr&aelig;ceptis, &longs;ed etiam exemplis perpetu&ograve; confir&shy;<lb/>
met: ego quidem nihil vnquam Ari&longs;t. clarius expre&longs;si&longs;&longs;e, nihil fu&longs;ius com&shy;<lb/>
proba&longs;&longs;e exi&longs;timo, qu&agrave;m Geometri&aelig; demon&longs;trationes omnibus numeris ab&shy;<lb/>
&longs;olutas e&longs;&longs;e, ita vt Philo&longs;opho indignum omnin&ograve; videatur &longs;ententiam ip&longs;ius <lb/>
ade&ograve; manife&longs;tam ali&ograve; detorquere; &longs;atius e&longs;&longs;et, meo iudicio, pal&agrave;m peri&shy;<lb/>
patetici nomen ex hac parte deponere, qu&agrave;m hoc modo Peripateticorum <lb/>
doctrinam, vt nonnulli faciunt, vel di&longs;simulare, vel tam perperam interpre&shy;<lb/>
tari. </s>
          <s id="s.005174">quamuis igitur &longs;atis e&longs;&longs;et lectorem ad libros analyticos, <expan abbr="corum&qacute;">eorumque</expan>; in&shy;<lb/>
terpretes amandare, non grauabor tamen loca aliquot &longs;electa, atque ade&ograve; <lb/>
manife&longs;ta in medium afferre, vt magnopere mirandum &longs;it <expan abbr="c&otilde;trari&aelig;">contrari&aelig;</expan> opinio&shy;<lb/>nis authores ea pro libito interpretari. </s>
          <s id="s.005175">quorum primus &longs;it tex. <!-- REMOVE S-->23. primi Po&shy;<lb/>
&longs;ter. <emph type="italics"/>&lpar;<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus non &longs;ecundum accidens, quando &longs;ecundum illud <lb/>cogno&longs;cimus, &longs;ecundum quod ine&longs;t, ex principijs illius, &longs;ecundum quod illud, vt <lb/>
duobus rectis &aelig;quales habere, cui inest per &longs;e ex principijs huius&rpar;<emph.end type="italics"/> vbi manife&longs;t&egrave; <lb/>
vides Ari&longs;t. a&longs;&longs;erere demon&longs;trationem illam, qua Geometra o&longs;tendit, omne <lb/>
<expan abbr="tri&atilde;gulum">triangulum</expan> habere tres angulos &aelig;quales duobus rectis procedere ex primis, <lb/>
immediatis, ex ijs, qu&aelig; &longs;unt per &longs;e, &amp; &longs;ecundum quod ip&longs;um; nullo autem <lb/>
modo ex ijs, qu&aelig; &longs;unt per accidens. </s>
          <s id="s.005176">perinde ac &longs;i diceret eam e&longs;&longs;e poti&longs;si&shy;<lb/>
mam, <expan abbr="atq;">atque</expan> omnibus numeris ab&longs;olutam. </s>
          <s id="s.005177">ver&ugrave;m de hac demon&longs;tratione in&shy;<lb/>
ferius pluribus dicetur, interim vide citati loci no&longs;tram explicationem &longs;u&shy;<lb/>
pra in locis Mathem.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005178">Textu deinde 29. primi Po&longs;ter. <emph type="italics"/>&lpar;Conuertuntur autem magis qu&aelig; &longs;unt in Ma&shy;<lb/>thematicis, quoniam nullum accidens &lpar;&longs;ed &amp; hoc differunt ab ijs, qu&aelig; &longs;unt in di&shy;<lb/>
&longs;putationibus&rpar; &longs;ed definitiones&rpar;<emph.end type="italics"/> vbi vides Mathematicos nullum <expan abbr="accid&etilde;s">accidens</expan>, &longs;en <lb/>
contingens accipere, &longs;ed definitiones, ide&longs;t, non per aliquod contingens, <lb/>
&longs;ed per cau&longs;am formalem. </s>
          <s id="s.005179">tex. <!-- REMOVE S-->ver&ograve; 31. <emph type="italics"/>&lpar;Figurarum autem maxim&egrave; &longs;cientialis <lb/>
est prima, mathematic&aelig; <expan abbr="namq;">namque</expan> <expan abbr="&longs;ci&etilde;ti&aelig;">&longs;cienti&aelig;</expan> per hanc demon&longs;trationes ferunt, vt Arith&shy;<lb/>
metica, &amp; Geometria, &amp; Per&longs;pectiua, &amp; fer&egrave; dixerim qu&aelig;cunque ip&longs;ius Propter <lb/>
quid con&longs;iderationem faciunt&rpar;<emph.end type="italics"/> po&longs;tea tex. <!-- REMOVE S-->11. 2. Po&longs;ter. a&longs;&longs;erit demon&longs;tratio&shy;<lb/>nem illam, qua Geometra probat, angulum in &longs;emicirculo e&longs;&longs;e rectum, e&longs;&longs;e <lb/>
&agrave; cau&longs;a materiali, im&ograve; eam tanquam optimum huiu&longs;modi demon&longs;trationis <lb/>
exemplum affert. </s>
          <s id="s.005180">&longs;ed de hac eadem demon&longs;tratione infra iterum dicendum <lb/>
erit; vide interim pr&aelig;dicti loci explicationem &longs;upra in locis Mathemat. </s>
          <s id="s.005181">al&shy;<lb/>
latam. </s>
          <s id="s.005182">h&aelig;c ex Logica &longs;ufficiant, ne huc toti po&longs;teriores in&longs;erantur. </s>
          <s id="s.005183">tex. <!-- REMOVE S-->68. <lb/>
2. Phy&longs;. <emph type="italics"/>&lpar;Aut enim ad ip&longs;um Quid est, reducitur ip&longs;um Propter quid vltimum in <lb/>immobilibus, vt in mathematicis, ad definitionem enim recti, aut commen&longs;urabi&shy;<lb/>lis, aut alterius cuiu&longs;piam reducitur vltimum&rpar;<emph.end type="italics"/> ecce iterum cau&longs;a formalis in <lb/>
Mathematicis demon&longs;trationibus. </s>
          <s id="s.005184">vide huius loci explicationem &longs;upra &agrave; <lb/>
nobis allatam. </s>
          <s id="s.005185">6. Metaph. tex. <!-- REMOVE S-->1. <emph type="italics"/>&lpar;Mathematicorum <expan abbr="quoq;">quoque</expan> principia, elementa, <lb/>
&amp; cau&longs;&aelig; &longs;unt&rpar;<emph.end type="italics"/> 11. Metaph. cap. 1. &longs;umm&aelig; 3. <emph type="italics"/>&lpar;Patet igitur tria e&longs;&longs;e genera &longs;pe&shy;<lb/>
culatiuarum &longs;cientiarum, Naturalem, Mathematicam, Theologiam&rpar;<emph.end type="italics"/> ecce tibi, <lb/>
quam clara &longs;it Ari&longs;t. &longs;ententia.</s>
        </p>
        <p type="main">
          <s id="s.005186">Quod ad Platonis auctoritatem attinet, certum e&longs;t, eum in Mathematicis <lb/>
cau&longs;am materialem, &amp; formalem agnoui&longs;&longs;e, nam te&longs;te Ari&longs;t. primo Metaph.


<pb pagenum="12" xlink:href="009/01/296.jpg"/>cap. 7. ip&longs;e non credebat aliarum cau&longs;arum, qu&agrave;m formalis, &amp; materialis, <lb/>
quas Mathematici tractant, &longs;peculationem <expan abbr="philo&longs;ophic&atilde;">philo&longs;ophicam</expan> e&longs;&longs;e magnifacien&shy;<lb/>
dam; efficientem enim, &amp; finalem <expan abbr="n&utilde;quam">nunquam</expan> explicuit, proptereaquod &agrave; Ma&shy;<lb/>
thematicis, nunquam tractarentur. </s>
          <s id="s.005187">Proclus pr&aelig;terea cap. 10. lib. 7. in Eu&shy;<lb/>
clidem, ait; Mathematicam ver&ograve; omnin&ograve; rerum &longs;empiternarum vim ha&shy;<lb/>
bentem, &longs;cientiam appellat Plato. </s>
          <s id="s.005188">&amp; paulo po&longs;t, ne dicamus igitur, quod <lb/>
Mathematicam &agrave; &longs;cientiarum numero Plato expellit. </s>
          <s id="s.005189">&amp; in fine cap. ait. <lb/>
<emph type="italics"/>&lpar;Mathematica tamen e&longs;t &longs;cientia, non vt &agrave; &longs;uppo&longs;itione immunis, &longs;ed vt propria&shy;<lb/>rum in anima rationum cognitrix, &amp; vt cau&longs;as conclu&longs;ionum afferens&rpar;<emph.end type="italics"/> nota illud, <lb/>
cau&longs;as conclu&longs;ionum afferens. </s>
          <s id="s.005190">concludit po&longs;tea &longs;ic, h&aelig;c omnia de Platonis <lb/>
&longs;ententia pro Mathematicis dicta &longs;int.</s>
        </p>
        <p type="main">
          <s id="s.005191">Ip&longs;um pr&aelig;terea exi&longs;tima&longs;&longs;e eas e&longs;&longs;e ab&longs;oluti&longs;simas &longs;cientias ex multis ip&shy;<lb/>
&longs;ius dictis par e&longs;t credere; cur enim dixi&longs;&longs;et, Deum Geometrizare, ni&longs;i ob <lb/>
&longs;ummam Geometri&aelig; excellentiam? </s>
          <s id="s.005192">cur omnes ageometretos &egrave; gymna&longs;io <lb/>
&longs;uo arcebat? </s>
          <s id="s.005193">cur eas in a&longs;cen&longs;u ad &longs;ummi Boni cognitionem naturali Phi&shy;<lb/>
lo&longs;ophi&aelig; pr&aelig;tulit? </s>
          <s id="s.005194">qu&agrave;m autem immerit&ograve; in <expan abbr="contrari&atilde;">contrariam</expan> &longs;ententiam alij eum <lb/>
ad &longs;e pertrahant, infra apparebit, c&ugrave;m calumnias diluemus.</s>
        </p>
        <p type="main">
          <s id="s.005195">Sequatur tertio loco Procli ip&longs;ius authoritas, qui in primo, &amp; &longs;ecundo <lb/>
libro <expan abbr="c&otilde;m">comm</expan>. <!-- REMOVE S-->in Euclidem, totus e&longs;t in Mathematicis, pr&aelig;cipu&egrave; ver&ograve; in Geo&shy;<lb/>
metria &longs;ummis laudibus cumulandis, <expan abbr="eas&qacute;">easque</expan>; e&longs;&longs;e perfecti&longs;&longs;imas &longs;cientias &longs;&aelig;&shy;<lb/>
pius non &longs;olum a&longs;&longs;erit, &longs;ed etiam demon&longs;trat. </s>
          <s id="s.005196">Id igitur primum cap. 10. lib. <lb/>
primi aggreditur, vbi fus&egrave; o&longs;tendit ex Platone e&longs;&longs;e &longs;cientias, qu&aelig; <expan abbr="c&otilde;clu&longs;io-num">conclu&longs;io&shy;<lb/>
num</expan> cau&longs;as afferant. </s>
          <s id="s.005197">i. </s>
          <s id="s.005198">perfecti&longs;&longs;imas habere <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan>. </s>
          <s id="s.005199">&amp; cap. 5. lib. 2. <lb/>
de Euclide loquens, ait <emph type="italics"/>&lpar;Pr&aelig;cipu&egrave; ver&ograve; circa Geometricam elementorum in&longs;ti&shy;<lb/>
tutionem eum qui&longs;piam admirabitur propter ordinem, &amp; electionem eorum, qu&aelig; <lb/>
per elementa di&longs;tribuit, etenim non ca a&longs;&longs;ump&longs;it omnia, qu&aelig; poterat dicere, &longs;ed ea <lb/>
duntaxat, qu&aelig; elementari tradere potuit ordine. </s>
          <s id="s.005200">Adhuc autem omnis generis &longs;yl&shy;<lb/>
logi&longs;morum modus, alios quidem &agrave; cau&longs;is fidem &longs;u&longs;cipientes, alios ver&ograve; &agrave; certis no&shy;<lb/>
tis perfectos, omnes autem inuincibiles, &amp; certos, ad &longs;cientiamqu&eacute;, accommodatos&rpar;<emph.end type="italics"/><lb/>notanda &longs;unt illa; &agrave; cau&longs;is fidem &longs;u&longs;cipientes, quibus pr&aelig;cipu&egrave; indicat, &longs;e in <lb/>
Demon&longs;trationibus Euclidianis cau&longs;as agno&longs;cere.</s>
        </p>
        <p type="main">
          <s id="s.005201">Lib. deinde 3. in comm. <!-- REMOVE S-->ad primam Euclidis propo&longs;it. </s>
          <s id="s.005202">h&aelig;c habet; <expan abbr="Qu&atilde;-do">Quan&shy;<lb/>
do</expan> igitur &longs;yllogi&longs;mus Geometris per impo&longs;&longs;ibile fuerit, &longs;ymptoma tant&ugrave;m <lb/>
inuenire cupiunt, quando autem per pr&aelig;cipuam Demon&longs;trationem, tunc <lb/>
rur&longs;us &longs;iquidem in particulari demon&longs;trationes fiant, cau&longs;a nondum mani&shy;<lb/>
fe&longs;ta e&longs;t, &longs;i ver&ograve; in vniuer&longs;ali, in omnibus &longs;imilibus continu&ograve; &amp; ip&longs;um pro&shy;<lb/>
pter quid manife&longs;tam fit. </s>
          <s id="s.005203">Ecce tibi iterum ip&longs;um Propter quid in Geome&shy;<lb/>
tricis. </s>
          <s id="s.005204">&amp; in eod. </s>
          <s id="s.005205">com. </s>
          <s id="s.005206">po&longs;t multa; illam autem, qu&aelig; demon&longs;tratio dicitur, <lb/>
quandoquidem propria <expan abbr="Dem&otilde;&longs;trationi">Demon&longs;trationi</expan> habentem inueniemus, &amp; definitio&shy;<lb/>nibus Medijs qu&aelig;&longs;itum o&longs;tendentem; h&aelig;c enim Demon&longs;trationis perfectio <lb/>
e&longs;t. </s>
          <s id="s.005207">Vbi ob&longs;eruandum e&longs;t apud Proclum Geometram vti definitionibus pro <lb/>
Medio; qu&ograve;d requiritur ad exacti&longs;&longs;imam <expan abbr="Demon&longs;tration&etilde;">Demon&longs;trationem</expan>, vt ip&longs;e ait: quod <lb/>
declarat exemplo prim&aelig; <expan abbr="Dem&otilde;&longs;trationis">Demon&longs;trationis</expan> Euclidis, c&ugrave;m ait, quando autem <lb/>
per de&longs;criptionem circulorum, quod con&longs;titutum e&longs;t Triangulum &aelig;quilate&shy;<lb/>
rum e&longs;&longs;e o&longs;tenditur, &agrave; cau&longs;a apprehen&longs;io fit, &aelig;qualitatem enim circulorum <lb/>cau&longs;am &aelig;qualitatis laterum illius e&longs;&longs;e dicemus. </s>
          <s id="s.005208">Quid igitur apud Proclum <pb pagenum="13" xlink:href="009/01/297.jpg"/>clarius dici poterat? </s>
          <s id="s.005209">qu&aelig; tamen omnia aduer&longs;arij videntur clau&longs;is de indu&shy;<lb/>
&longs;tria oculis pr&aelig;terij&longs;&longs;e; con&longs;tat enim ex opu&longs;culo Piccolominei ip&longs;um dili&shy;<lb/>
genter hoc con&longs;ilio Proclum perlegi&longs;&longs;e; qu&igrave; igitur fieri potuit, quin ea vi&shy;<lb/>
derit. </s>
          <s id="s.005210">Sed hodie plurimi non ad verum, &longs;ed ad libitum philo&longs;ophamur.</s>
        </p>
        <p type="main">
          <s id="s.005211">Placuit hos tres &longs;olos Platonem, Ari&longs;totilem, &amp; Proclum ex veteribus pro <lb/>
no&longs;tra &longs;ententia in <expan abbr="medi&utilde;">medium</expan> adducere, propterea quod eos &longs;ibi adiungere <expan abbr="c&otilde;-tra">con&shy;<lb/>
tra</expan> omnem rationem nitantur aduer&longs;arij, vt ex pr&aelig;dictis iam &longs;atis liquid&egrave; <lb/>
con&longs;tat. </s>
          <s id="s.005212">Reliquorum ver&ograve; Philo&longs;ophorum, t&agrave;m Gr&aelig;corum, qu&agrave;m <expan abbr="Arab&utilde;">Arabum</expan>, <lb/>
aut Latinorum placita citare &longs;uper&longs;edeo, etiam &longs;i omnes vno ore Geome&shy;<lb/>tricas demon&longs;trationes tanquam omnium exacti&longs;&longs;imas celebrauerint, vel <lb/>te&longs;te ip&longs;o Piccolomineo, qui initio libelli de certitudine, Mathematica, &longs;ic <lb/>
ait; omnes fer&egrave; Latini, vt D. Albertus, D. <!-- REMOVE S-->Tho nas, Mar&longs;ilius, Egydius, Zi&shy;<lb/>
mara, &amp; <expan abbr="pleri&qacute;">plerique</expan>, alij vno ore Auerroem interpretati &longs;unt, dicere Mathema&shy;<lb/>
ticas demon&longs;trationes e&longs;&longs;e in primo gradu certitudinis, quod Mathemati&shy;<lb/>
cus ex notioribus nobis, &amp; natura demon&longs;tret, quippequi vel &longs;olus, vel ma&shy;<lb/>
xim&egrave; demon&longs;tratione illa, quam poti&longs;&longs;imam appellant, vtatur, qua. </s>
          <s id="s.005213">&longs;. </s>
          <s id="s.005214">&longs;imul <lb/>
&amp; quod effectus &longs;it, &amp; cur &longs;it liquid&ograve; innote&longs;cit. </s>
          <s id="s.005215">Verum ip&longs;e omnium pri&shy;<lb/>mus ab&longs;olut&egrave; dici pote&longs;t, cum nullus ante ip&longs;um, cuius opera extent, id di&shy;<lb/>
cat; quamuis ip&longs;e fallo Proclum, Ari&longs;t. &amp; Platonem &longs;ibi conetur adiungere. <lb/>
</s>
          <s id="s.005216">Po&longs;t ip&longs;um ver&ograve; &longs;oli duo fer&egrave; Pererius, &amp; Conimbric. </s>
          <s id="s.005217">eum &longs;equuti &longs;unt. </s>
          <s id="s.005218">At <lb/>
ver&ograve; contrariam <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> reliqui omnes po&longs;t ip&longs;um amplexi &longs;unt; ex qui&shy;<lb/>
bus &longs;olos duos, <expan abbr="eos&qacute;">eosque</expan>; pr&aelig;&longs;tanti&longs;&longs;ios huiu&longs;ce tempe&longs;tatis philo&longs;ophos alle&shy;<lb/>
ga&longs;&longs;e &longs;it &longs;atis. </s>
          <s id="s.005219">Toletum. </s>
          <s id="s.005220">&longs;. </s>
          <s id="s.005221">&amp; Zabarellam. <!-- KEEP S--></s>
          <s id="s.005222">Toletus enim qu&aelig;&longs;t. </s>
          <s id="s.005223">4. 2. Phy&longs;. <lb/>
<!-- REMOVE S-->in 3. conclu&longs;ione habet i&longs;ta; Phy&longs;icus, &amp; Mathematicus differunt in modo <lb/>demon&longs;trandi, Phy&longs;icus enim frequenter vtitur demon&longs;tratione &longs;igni, &amp; ef&shy;<lb/>fectus, quia ip&longs;ius cau&longs;&aelig; frequentius &longs;unt occult&aelig;, nec per &longs;e &longs;en&longs;ibiles, effe&shy;<lb/>
ctus ver&ograve; &longs;unt &longs;en&longs;ibiles, vt mors, motus, &amp;c. </s>
          <s id="s.005224">qu&aelig; ad &longs;en&longs;um patent, <expan abbr="quor&utilde;">quorum</expan> <lb/>
cau&longs;&aelig; &agrave; &longs;en&longs;ibus &longs;unt remot&aelig;. </s>
          <s id="s.005225">At Mathematicus frequentius &agrave; prioribus <lb/>
procedit cum eius cau&longs;&aelig; notiores &longs;int effectibus, &agrave; &longs;en&longs;u enim ab&longs;trahit, &amp; <lb/>
in intellectu notius e&longs;t, quod prius e&longs;t. </s>
          <s id="s.005226">videas Lector, qu&agrave;m &longs;yncer&egrave; natu&shy;<lb/>
ralis philo&longs;ophi&aelig; profe&longs;&longs;or vera de Mathematicis loquatur, ita vt etiam eas <lb/>
illi pr&aelig;ferat. </s>
          <s id="s.005227">Iacobus autem Zabarella in toto &longs;uo opere logico, perpetu&ograve; <lb/>Mathematicas demon&longs;trationes, vt poti&longs;&longs;imas agno&longs;cit, <expan abbr="exempla&qacute;">exemplaque</expan>; Ari&longs;t. <lb/>
geometrica exponit tanquam vera, &amp; omnino rebus ip&longs;is accommodata; <lb/>
quare non e&longs;t, cur vnum, aut alterum ip&longs;ius locum hic de&longs;cribamus. </s>
          <s id="s.005228">illud <lb/>
non pr&aelig;termittam, ip&longs;um fateri &longs;e bis, teru&egrave; totum Euclidem &longs;edul&ograve; perle&shy;<lb/>
gi&longs;&longs;e, vt prob&egrave; po&longs;&longs;et Ari&longs;t. mentem circa <expan abbr="dem&otilde;&longs;trationis">demon&longs;trationis</expan> naturam a&longs;&longs;equi, <lb/>
c&ugrave;m videret Ari&longs;t. <!-- REMOVE S--><expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> de demon&longs;tratione pr&aelig;ciperet, omnia ad Geo&shy;<lb/>
metricam normam, tanquam ad lydium lapidem examinare. </s>
          <s id="s.005229">Locus, vbi <lb/>
h&aelig;c ait, mihi &egrave; memoria excidit, certus tamen &longs;um apud ip&longs;um ea me le&shy;<lb/>
gi&longs;&longs;e. </s>
          <s id="s.005230">quarto tandem loco, communi authoritate omnium antiquorum idem <lb/>
comprobatur, apud quos &longs;emper demon&longs;trationes Geometric&etail; appellat&aelig; <lb/>
&longs;unt per antonoma&longs;iam demon&longs;trationes, non rationes, non opiniones, non <lb/>
&longs;ententi&aelig;, quemadmodum in reliquis philo&longs;ophi&aelig; partibus fieri &longs;olet. </s>
          <s id="s.005231">Sed <lb/>
iam ab authoritatibus ad rationes.</s>
        </p>
        <p type="main">
          <s id="s.005232">Prima, Vera, &amp; perfecta demon&longs;tratio ex Auerrois &longs;ententia debet &agrave; no&shy;<pb pagenum="14" xlink:href="009/01/298.jpg"/>tioribus nobis, &amp; natura procedere, tales &longs;unt Geometric&aelig; vt paulo &longs;upra <lb/>
patuit, erg&ograve; ip&longs;&aelig; poti&longs;&longs;im&aelig; erunt demon&longs;trationes.</s>
        </p>
        <p type="main">
          <s id="s.005233">2. Ex Themi&longs;tio cap, 2. &longs;u&aelig; paraphr. </s>
          <s id="s.005234">2. Po&longs;ter. Demon&longs;tratio poti&longs;&longs;ima <lb/>
debet o&longs;tendere, &amp; quod, &amp; Propter quid. </s>
          <s id="s.005235">quod profect&ograve; c&aelig;teris demon&shy;<lb/>
&longs;trationibus melius pr&aelig;&longs;tant Geometric&aelig;, &amp; Arithmetic&aelig;. <!-- KEEP S--></s>
          <s id="s.005236">v. <!-- REMOVE S-->g. <!-- REMOVE S-->demon&longs;tra&shy;<lb/>
tio 32. 3. o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum, quod omnin&ograve; igno&shy;<lb/>
tum erat; &amp; affert cau&longs;am, qu&aelig; pariter ignorabatur. </s>
          <s id="s.005237">Idem fer&egrave; faciunt ali&aelig; <lb/>
omnes. </s>
          <s id="s.005238">in Mathematicis ver&ograve; medijs, in Phy&longs;ica, &amp; Metaphy&longs;ica effectus <lb/>
<expan abbr="plerumq;">plerumque</expan> noti &longs;unt, &longs;ed cau&longs;&aelig; latent; dicendum igitur Geometricas demon&shy;<lb/>&longs;trationes ex Auerroe, &amp; Themi&longs;tio pr&aelig;&longs;tanti&longs;&longs;imas e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.005239">Tertia, qu&aelig; e&longs;t euidenti&longs;&longs;ima, &longs;umatur ex re&longs;olutione aliquot demon&longs;tra&shy;<lb/>
tionum. </s>
          <s id="s.005240">Quid enim opus e&longs;t di&longs;putationem hanc per extraneas ambages <lb/>
agitare? </s>
          <s id="s.005241">cum licear qua&longs;i in rem pr&aelig;&longs;entem ire, &amp; veluti demon&longs;trationum <lb/>
anatome facta oculis ip&longs;is earum media contueri. </s>
          <s id="s.005242">&longs;ed prius in memoriam <lb/>
redigendum e&longs;t, illam e&longs;&longs;e perfecti&longs;&longs;imam demon&longs;trationem, qu&aelig; non &longs;ol&ugrave;m <lb/>
rei demon&longs;trand&aelig; cau&longs;am propriam, &amp; ad&aelig;quatam affert, ver&ugrave;m etiam <lb/>
euidenti&longs;&longs;im&egrave; o&longs;tendit talem pa&longs;&longs;ionem ab illa cau&longs;a procedere, ita vt non <lb/>
po&longs;sit, vt ait Ari&longs;t. aliter res &longs;e habere, in quo profect&ograve; Mathematic&aelig; ex&shy;<lb/>
cellunt. </s>
          <s id="s.005243">Cau&longs;a ver&ograve; h&aelig;c in Geometria, &amp; Arithmetica aliquando e&longs;t mate&shy;<lb/>
rialis, quando &longs;cilicet vtuntur pro Medio partibus, re&longs;pectu totius; vel e&longs;t <lb/>
formalis, quando nimirum Medium e&longs;t definitio &longs;ubiecti, aut pa&longs;sionis. </s>
          <s id="s.005244">non <lb/>
me tamen latet omnem perfectam demon&longs;trationem alio &longs;en&longs;u dici &agrave; qui&shy;<lb/>
bu&longs;dam procedere per cau&longs;am formalem, quia in ea continetur cau&longs;alis de&shy;<lb/>
finitio pa&longs;sionis, qu&aelig; definitio cau&longs;am ip&longs;ius exhibet, &amp; proinde tanquam <lb/>
forma ip&longs;ius e&longs;t, qu&aelig; rem in e&longs;&longs;e con&longs;tituat.</s>
        </p>
        <p type="main">
          <s id="s.005245">Secund&ograve; notandum e&longs;t: Omnem demon&longs;trationis di&longs;cur&longs;um re&longs;olui tan&shy;<lb/>
dem in aliquid, aut per &longs;e notum, aut &agrave; po&longs;teriori comprobatum. </s>
          <s id="s.005246">Satis. </s>
          <s id="s.005247">n. <lb/>
</s>
          <s id="s.005248">e&longs;t, vt cau&longs;a euidentur appareat, <expan abbr="quocunq;">quocunque</expan> id modo fiat. </s>
          <s id="s.005249">hoc dixi propter <lb/>nonnullos, qui c&ugrave;m in Geometric&etail; demon&longs;trationibus lineam, aut diui&longs;ionem <lb/>
aliquam, rei, qu&aelig; o&longs;tenditur, non intrin&longs;ecam animaduertunt, &longs;tatim exi&shy;<lb/>
&longs;timant eas per extrin&longs;eca <expan abbr="dem&otilde;&longs;trare">demon&longs;trare</expan>: &longs;ed decipiuntur; quia non animad&shy;<lb/>uertunt lineas illas, aut partitiones, non e&longs;&longs;e medium demon&longs;trationis, &longs;ed <lb/>
adhiberi ad medij inuentionem, &amp; connexionem cum pa&longs;&longs;ione. </s>
          <s id="s.005250">Quod au&shy;<lb/>
tem eorum dubitatio omnin&ograve; vana &longs;it ex eo patet, quod plurim&aelig; &longs;unt de&shy;<lb/>
mon&longs;trationes, qu&aelig; &longs;ine vlla linearum con&longs;tructione, aut diui&longs;ione compro&shy;<lb/>
bentur, vti &longs;unt 15.33 34.42. 36. in &longs;olo primo elementorum. </s>
          <s id="s.005251">atque h&aelig;c <lb/>
erroris eorum pr&aelig;cipua cau&longs;a e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005252">His pr&aelig;mi&longs;&longs;is, prim&ograve; o&longs;tendemus cau&longs;am formalem in Geometric&aelig; de&shy;<lb/>
mon&longs;trationibus reperiri deinde materialem. </s>
          <s id="s.005253"><expan abbr="id&qacute;">idque</expan>; prim&ograve; per re&longs;olutionem <lb/>
prim&etail; Euclidis, qu&aelig; &agrave; cau&longs;a formali procedit. </s>
          <s id="s.005254">&amp; quia h&aelig;c demon&longs;tratio <lb/>
non theorema, &longs;ed problema e&longs;t, ide&ograve; &longs;ciendum, qu&ograve;d minim&egrave; aduer&longs;arij <lb/>
animaduerterunt, in omni problemate per <expan abbr="quand&atilde;">quandam</expan> <expan abbr="linear&utilde;">linearum</expan> con&longs;tructionem <lb/>
doceri aliquid effici. </s>
          <s id="s.005255">v. <!-- REMOVE S-->g. <!-- REMOVE S-->in pr&aelig;&longs;enti docet Euclides, qua ratione de&longs;crip&shy;<lb/>
tis <expan abbr="quibu&longs;d&atilde;">quibu&longs;dam</expan> circulis circa datam lineam, <expan abbr="ductis&qacute;">ductisque</expan>; aliquot lineis modo pr&etail;&shy;<lb/>
&longs;cripto, gignatur <expan abbr="triangul&utilde;">triangulum</expan> &aelig;quilaterum, vt rem con&longs;ideranti manife&longs;tum <lb/>
e&longs;t. </s>
          <s id="s.005256">quare nullo modo lineamenta illa, vt ill&etail; circulorum &longs;emidiametri &longs;unt <pb pagenum="15" xlink:href="009/01/299.jpg"/>extrin&longs;eca rei, de qua demon&longs;tratur; quinim&ograve; &longs;ubiectum ip&longs;ius &longs;unt. </s>
          <s id="s.005257">Quia <lb/>
ver&ograve; facta con&longs;tructione, &longs;tatim per&longs;picu&egrave; apparet ortum e&longs;&longs;e triangulum, <lb/>
&aelig;quilaterum, non e&longs;t illi cur&etail; probare illud e&longs;&longs;e triangulum, &longs;ed quia an &longs;it <lb/>
&aelig;quilaterum ignoratur, idcirc&ograve; totus demon&longs;trationis di&longs;cur&longs;us ver&longs;atur in <lb/>
demon&longs;tranda trium illarum linearum &aelig;qualitate.</s>
        </p>
        <p type="main">
          <s id="s.005258">Quem <expan abbr="quid&etilde;">quidem</expan> di&longs;cur&longs;um continere cau&longs;am, quamuis per &longs;e pateat, vt mox <lb/>
apparebit, non dee&longs;t <expan abbr="tam&etilde;">tamen</expan> Procli authoritas ade&ograve; clara, vt magnopere mi&shy;<lb/>
rer Piccolomineum Procli &longs;tudio&longs;um, eam non vidi&longs;&longs;e: Proclus enim in <expan abbr="c&otilde;-men">conm<lb/>
men</expan>. <!-- REMOVE S-->huius demon&longs;trationis h&aelig;c habet; quando autem per de&longs;criptionem <lb/>circulorum, quod con&longs;tructum e&longs;t triangulum &aelig;quilaterum e&longs;&longs;e o&longs;tenditur, <lb/>
&agrave; cau&longs;a apprehen&longs;io fit; &longs;imilitudinem. </s>
          <s id="s.005259">n. </s>
          <s id="s.005260">&amp; &aelig;qualitatem circulorum cau&longs;am <lb/>
dicimus e&longs;&longs;e &aelig;qualitatis laterum illius trianguli. </s>
          <s id="s.005261">Quibus verbis non &longs;olum <lb/>
authoritas, &longs;ed ratio etiam optima, cur h&aelig;c &longs;it demon&longs;tratio &agrave; cau&longs;a, con&shy;<lb/>tinetur, quia nimirum o&longs;tendit cau&longs;am &aelig;qualitatis laterum e&longs;&longs;e, quia &longs;int <lb/>
&longs;emidiametri &aelig;qualium circulorum. </s>
          <s id="s.005262">Qu&aelig; argumentatio procedit &agrave; defini&shy;<lb/>
tione &longs;ubiecti, quod e&longs;t circulus: quamuis non tota, &longs;ed tantum quatenus <lb/>nece&longs;&longs;aria e&longs;t, afferatur, ide&longs;t definitio &longs;emidiametrorum, quod ad demon&shy;<lb/>
&longs;trandum &longs;ufficit, vt ben&egrave; notat Zabarella, loquens de hac ip&longs;a demon&longs;tra&shy;<lb/>
tione; c&ugrave;m igitur medium &longs;it definitio &longs;ubiecti, patet eam e&longs;&longs;e perfectam <lb/>
demon&longs;trationem, in qua pa&longs;&longs;ionis o&longs;ten&longs;&aelig; allata e&longs;t propria, &amp; ad&aelig;quata <lb/>
cau&longs;a, qu&aelig; e&longs;t natura circuli. </s>
          <s id="s.005263"><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; Euclides optim&egrave; demon&longs;traujt ex con&shy;<lb/>
&longs;tructione, qu&agrave;m pr&aelig;ceperat, gigni triangulum &aelig;quilaterum. </s>
          <s id="s.005264">Subiectum <lb/>
igitur e&longs;t il a circulorum, ac linearum configuratio, medium definitio cir&shy;<lb/>
culi, pa&longs;&longs;io triangulum <expan abbr="&aelig;quilater&utilde;">&aelig;quilaterum</expan>. </s>
          <s id="s.005265">ex qua <expan abbr="dem&otilde;&longs;tratione">demon&longs;tratione</expan> erui pote&longs;t etiam <lb/>
definitio pa&longs;&longs;ionis cau&longs;alis, ide&longs;t, e&longs;&longs;e triangulum &aelig;quilaterum ex tali <expan abbr="c&otilde;&longs;tru-ctione">con&longs;tru&shy;<lb/>
ctione</expan> ortum. </s>
          <s id="s.005266">Quare huic nihil dee&longs;t ad perfectam <expan abbr="demon&longs;tration&etilde;">demon&longs;trationem</expan>. </s>
          <s id="s.005267">ex qui&shy;<lb/>
bus videas, qu&agrave;m immerit&ograve; nonnulli eam impugnent, putantes eam e&longs;&longs;e per <lb/>
extranea; cau&longs;a erroris fuit, quia exi&longs;timarunt ab&longs;olut&egrave; demon&longs;trari <expan abbr="tri&atilde;-gulum">trian&shy;<lb/>
gulum</expan> illud e&longs;&longs;e &aelig;quilaterum. </s>
          <s id="s.005268">ver&ugrave;m decepti &longs;unt, quia in hoc, &amp; in omni&shy;<lb/>
bus alijs problematis, demon&longs;tratur talem con&longs;tructionem parere triangu&shy;<lb/>
lum, vel <expan abbr="quadrat&utilde;">quadratum</expan>, vel quid aliud, vt patet Euclidem, vel obiter <expan abbr="in&longs;pici&etilde;ti">in&longs;picienti</expan>.</s>
        </p>
        <p type="main">
          <s id="s.005269">Placet adhuc alteram &agrave; formali cau&longs;a procedentem expendere. </s>
          <s id="s.005270">ea e&longs;t 46. <lb/>
primi elem. </s>
          <s id="s.005271">qu&aelig; &longs;imiliter problema e&longs;t, quo docet Euclides, qua ratione &longs;u&shy;<lb/>
pra data recta linea quadratum de&longs;cribatur. </s>
          <s id="s.005272">tradit igitur quandam linea&shy;<lb/>
rum con&longs;tructionem, ex qua po&longs;tea demon&longs;trat ortum e&longs;&longs;e quadratum, ita <lb/>
vt con&longs;tructio illa &longs;it loco &longs;ubiecti, de qua demon&longs;tratvr e&longs;&longs;e quadratum. </s>
          <s id="s.005273">non <lb/>
igitur intendit, vt nonnulli fals&ograve; putant, <expan abbr="dem&otilde;&longs;trare">demon&longs;trare</expan> ab&longs;olut&egrave; illud e&longs;&longs;e qua&shy;<lb/>
dratum, &longs;ed ex tali con&longs;tructione ortum e&longs;&longs;e quadratum duo autem &longs;unt de <lb/>e&longs;&longs;entia quadrati, primum habere quatuor latera &aelig;qualia, &longs;ecundum habe&shy;<lb/>
re quatuor angulos rectos, vt ex definitione con&longs;tat. </s>
          <s id="s.005274">Neutrum autem &longs;ine <lb/>
altero &longs;ufficit, <expan abbr="n&atilde;">nam</expan> &amp; Rhombus quatuor latera &aelig;qualia habet, &amp; Altera par&shy;<lb/>
te longius habet quatuor angulos rectos, neutrum tamen quadratum e&longs;t. </s>
          <s id="s.005275">&longs;i <lb/>
ver&ograve; <expan abbr="vtrunq;">vtrunque</expan> &longs;imul cuipiam figur&aelig; competat, illam nece&longs;&longs;ari&ograve; quadratum <lb/>
e&longs;&longs;e efficient. </s>
          <s id="s.005276">Probat igitur Euclid. <!-- REMOVE S-->vtraq, euidenter ine&longs;&longs;e illi figur&aelig; ex vi <lb/>
illius con&longs;tructionis, &amp; ide&ograve; illi quadrati definitionem competere. </s>
          <s id="s.005277">Quare <lb/>
h&etail;c erit poti&longs;&longs;ima demon&longs;tratio, c&ugrave;m cau&longs;am afferat <expan abbr="intrin&longs;ec&atilde;">intrin&longs;ecam</expan>, propriam,


<pb pagenum="16" xlink:href="009/01/300.jpg"/>&amp; ad&aelig;quatam, propter quam res e&longs;t. </s>
          <s id="s.005278">Vbi notandum effectum re vera di&longs;tin&shy;<lb/>
gui &agrave; &longs;ua cau&longs;a, e&longs;&longs;e enim quadratum &lpar;qui effectus e&longs;t&rpar; non e&longs;t habere, qua&shy;<lb/>
tuor angulos rectos &longs;olum: <expan abbr="neq;">neque</expan> habere quatuor latera &aelig;qualia &longs;olum, &longs;ed <lb/>
<expan abbr="vtrunq;">vtrunque</expan> &longs;imul in eodem; vnde re&longs;ultat totum, &longs;eu <expan abbr="compo&longs;it&utilde;">compo&longs;itum</expan>, quod e&longs;t quid <lb/>
diuer&longs;um &agrave; partibus &longs;eor&longs;um &longs;umptis. </s>
          <s id="s.005279">in demon&longs;tratione autem hac, cau&longs;a <lb/>
&longs;unt partes &longs;eor&longs;im &longs;umpt&aelig;; effectus ver&ograve; e&longs;t compo&longs;itum, ex earum vnione <lb/>
re&longs;ultans. </s>
          <s id="s.005280">Notandum pr&aelig;terea eandem demon&longs;trationem procedere &agrave; de&shy;<lb/>
finitione &longs;ubiecti, nam illa duo quadrati e&longs;&longs;entialia, ex definitione eorum, <lb/>qu&aelig; &longs;unt in con&longs;titutione petuntur, qu&aelig; con&longs;titutio e&longs;t in&longs;tar &longs;ubiecti, vt &longs;u&shy;<lb/>
pra monui: ex hac autem definitione partium &longs;ubiecti in demon&longs;tratione <lb/>
contenta, eruitur definitio cau&longs;alis ip&longs;ius pa&longs;sionis, qu&aelig; e&longs;t, quadratum e&longs;t <lb/>
figura habens quatuor angulos rectos, &amp; quatuor latera &aelig;qualia, ex tali <expan abbr="c&otilde;-&longs;tructione">con&shy;<lb/>
&longs;tructione</expan> producta. </s>
          <s id="s.005281">Notandum tandem quouis modo &longs;iue &agrave; cau&longs;a, &longs;iue ab <lb/>effectu o&longs;tendantur illa duo e&longs;&longs;entialia quadrati, ine&longs;&longs;e ip&longs;i, nihil referre ad <lb/>
demon&longs;trationis perfectionem. </s>
          <s id="s.005282">Satis. </s>
          <s id="s.005283">n. </s>
          <s id="s.005284">e&longs;t, &longs;i habeamus rei cau&longs;am <expan abbr="propri&atilde;">propriam</expan>, <lb/>
ita vt aliter &longs;e habere nequeat. </s>
          <s id="s.005285">&longs;excent&aelig; huiu&longs;modi per formalem cau&longs;am, <lb/>
apud Euclid. <!-- REMOVE S-->Archim Appoll. <!-- KEEP S--></s>
          <s id="s.005286">&amp; alios Geometras reperies. </s>
          <s id="s.005287">vide Appendi&shy;<lb/>
cem, ad finem operis, in qua omnes primi elem. </s>
          <s id="s.005288">demon&longs;trationes re&longs;olutas <lb/>
inuenies, <expan abbr="plurimas&qacute;">plurimasque</expan>; &agrave; cu&longs;a formali.</s>
        </p>
        <p type="main">
          <s id="s.005289">Sed iam materialem cau&longs;am indagemus, <expan abbr="id&qacute;">idque</expan>; duce Ari&longs;t. accipiamus igi<lb/>tur celeberrimam illam 32. primi elem. </s>
          <s id="s.005290">quam Mathematicis <expan abbr="&longs;oi&etilde;t">&longs;olent</expan> aduer&longs;a&shy;<lb/>
rij opponere. </s>
          <s id="s.005291">&amp; quoniam &longs;upra tex. <!-- REMOVE S-->23. 1. Po&longs;ter. nos eam per cau&longs;am ma&shy;<lb/>terialem procedere o&longs;tendimus, ide&ograve; ne actum agamus, <expan abbr="explication&etilde;">explicationem</expan> illam <lb/>
nunc opus e&longs;t relegere. </s>
          <s id="s.005292">Hoc tamen loco partem ip&longs;ius primam, angulum, <lb/>
videlicet externum cuiu&longs;uis trianguli, &aelig;qualem e&longs;&longs;e duobus internis, &amp; op&shy;<lb/>
po&longs;itis, examinabo; cuius medium, &longs;i ad rigorem demon&longs;trationis rediga&shy;<lb/>
tur, e&longs;t hoc; externus angulus e&longs;t diui&longs;ibilis in duos angulos, quorum &longs;ingu&shy;<lb/>
li &longs;ingulis internis &longs;unt &aelig; quales, ergo <expan abbr="eti&atilde;">etiam</expan> totalis anguius erit &aelig;qualis am&shy;<lb/>
bobus internis &longs;imul &longs;umptis. </s>
          <s id="s.005293">Quod autem externus angulus &longs;it diui&longs;ibilis <lb/>
in duas partes &aelig;quales internis angulis probat diuidendo illum per lineam <lb/>
illam oppo&longs;ito trianguli lateri parallelam, vnde &longs;tatim ex parallelarum na <lb/>tura apparet partiales angulos anguli externi &aelig;quales e&longs;&longs;e internis triangu<lb/>
li; ex quo &longs;equitur totum externum angulum e&longs;&longs;e &aelig;qualem duobus internis <lb/>
&longs;imul &longs;umptis. </s>
          <s id="s.005294">Hic autem modus argumentandus, &agrave; partibus po&longs;sibilibus ad <lb/>
totum, e&longs;&longs;e &agrave; cau&longs;a materiali, apud omnes Philo&longs;ophos in <expan abbr="c&otilde;fe&longs;&longs;o">confe&longs;&longs;o</expan> e&longs;t, &amp; Ari&shy;<lb/>
&longs;tot. ip&longs;e tex. <!-- REMOVE S-->3. 5. Metaph. id a&longs;&longs;erit. </s>
          <s id="s.005295">&amp; tex. <!-- REMOVE S-->11. 2. Po&longs;ter. vtitur &longs;imili <expan abbr="ex&etilde;-plo">exem&shy;<lb/>
plo</expan> ad <expan abbr="material&etilde;">materialem</expan> cau&longs;am explicandam. </s>
          <s id="s.005296">quamuis autem Geometr&aelig; non di&shy;<lb/>
cant talem angulum, vel talem figuram e&longs;&longs;e <expan abbr="diui&longs;ibil&etilde;">diui&longs;ibilem</expan> in partes &aelig;quales alijs <lb/>
quibu&longs;dam, &longs;ed &longs;tatim diuidant, id faciunt breuitatis cau&longs;a; vtuntur enim <lb/>
actu pro potentia, quia actus potentiam &longs;upponit, qu&ograve;d optim&egrave; Ari&longs;tot. 9. <lb/>
Metaphy&longs;. tex. <!-- REMOVE S-->20. annotauit, &longs;ic; De&longs;criptiones quoque actu inueniuntur, <lb/>diuidentes namque inueniunt, qu&ograve;d &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife&longs;t&aelig; e&longs;&longs;ent, nunc <lb/>
autem in&longs;unt potentia, &amp;c. </s>
          <s id="s.005297">Cuius loci no&longs;tram &longs;uperius allatam explicatio&shy;<lb/>
nem habes. </s>
          <s id="s.005298">per de&longs;criptiones autem intelligit Geometricas demon&longs;tratio&shy;<lb/>
nes, vt &longs;&aelig;pius &longs;upra in opere o&longs;ten&longs;um e&longs;t. </s>
          <s id="s.005299">Innumer&aelig; &longs;unt apud Geometras, <lb/>
qu&etail; per hanc po&longs;sibilem diui&longs;ionem procedunt, <expan abbr="qu&etail;q;">qu&etail;que</expan> ide&ograve; &longs;unt &agrave; cau&longs;a ma&shy;


<pb pagenum="17" xlink:href="009/01/301.jpg"/>teriali; plures autem e&longs;&longs;e in primo elem. </s>
          <s id="s.005300">con&longs;tat ex appendice in fine ope&shy;<lb/>
ris addita. </s>
          <s id="s.005301">Notandum hic <expan abbr="quoq;">quoque</expan> cau&longs;am e&longs;&longs;e natura &longs;ua di&longs;tinctam ab effe&shy;<lb/>
ctu, non &longs;ecus ac potentia ab actu; nam ex eo, qu&ograve;d po&longs;&longs;it aliquid diuidi in <lb/>
partes &aelig;quales aliquibus, &longs;equitur illud totum e&longs;&longs;e actu &aelig;quale alteri, &amp; e&longs;t <lb/>&agrave; priori, quia partes natura prius &longs;unt toto, c&ugrave;m &longs;int ip&longs;ius cau&longs;a. </s>
          <s id="s.005302">Notan&shy;<lb/>
dum hic etiam parallelam illam, qua angulus diuiditur, duci ad <expan abbr="medi&utilde;">medium</expan> de&shy;<lb/>
mon&longs;trationis indagandum, nequaquam ver&ograve; ip&longs;am e&longs;&longs;e medium, &amp; idcir&shy;<lb/>
c&ograve; demon&longs;trationem hanc non e&longs;&longs;e per extrin&longs;eca, ni&longs;i velis minorem <expan abbr="pro-po&longs;ition&etilde;">pro&shy;<lb/>
po&longs;itionem</expan> per extrin&longs;eca o&longs;tendi, qu&ograve;d libenter concedimus, c&ugrave;m i&longs;tud de&shy;<lb/>
mon&longs;trationi nihil deroget. </s>
          <s id="s.005303">E&longs;t autem per intrin&longs;ecam, propriam, &amp; ad&aelig;&shy;<lb/>
quatam cau&longs;am illius &aelig;qualitatis, partes enim re&longs;pectu totius &longs;unt tales. <lb/>
</s>
          <s id="s.005304">e&longs;t igitur poti&longs;&longs;ima demon&longs;tratio, qu&ograve;d erat demon&longs;trandum.</s>
        </p>
        <p type="main">
          <s id="s.005305">Po&longs;tquam Euclides hanc primam propo&longs;itionis partem demon&longs;trauit, <lb/>
o&longs;tendit alteram. </s>
          <s id="s.005306">&longs;. </s>
          <s id="s.005307">omne triangulum habere tres, &amp;c. </s>
          <s id="s.005308">quoniam partes duo&shy;<lb/>
rum rectorum &longs;unt &aelig;quales tribus angulis illis. </s>
          <s id="s.005309">quod medium pariter e&longs;t &agrave; <lb/>
cau&longs;a materiali, &agrave; partibus ad totum. </s>
          <s id="s.005310">Vide huius explicationem tex. <!-- REMOVE S-->23. <lb/>
1. Po&longs;ter. vbi etiam videbis eam po&longs;&longs;e demon&longs;trari modo Pythagoreorum, <lb/>
ab&longs;que vlla diui&longs;ione, &longs;ed per partes actu exi&longs;tentes. </s>
          <s id="s.005311">hoc dico propter eos, <lb/>
qui per ha&longs;ce diui&longs;iones timent, ne non inueniatur medium &aacute; priori. </s>
          <s id="s.005312">&longs;ed vt <lb/>deponant penitus hunc &longs;crupulum, &longs;ciant in huiu&longs;modi demon&longs;trationibus, <lb/>
quibus aliquid &etail;quale alteri adhibita diui&longs;ione demon&longs;tratur, &longs;&etail;p&egrave; accide&shy;<lb/>
re, vt non diuidatur, ni&longs;i vnus terminorum &etail;qualitatis, quare ex parte in&shy;<lb/>
diui&longs;i &etail;qualitas cau&longs;abitur &agrave; partibus actu pr&etail;cedentibus, &amp; <expan abbr="con&longs;titu&etilde;tibus">con&longs;tituentibus</expan> <lb/>
totum; quod videre e&longs;t in <expan abbr="vtraq;">vtraque</expan> parte huius. </s>
          <s id="s.005313">32. &longs;ecundum Euclidem, &amp; in <lb/>
47. primi elem. </s>
          <s id="s.005314">&amp; alijs plurimis.</s>
        </p>
        <p type="main">
          <s id="s.005315">Sed prim&ograve; Piccolom. <!-- REMOVE S-->ex Proclo obijcit h&etail;c <emph type="italics"/>&lpar;Quando enim eo, qu&ograve;d extrin&shy;<lb/>&longs;ecus angulus duobus internis, &amp; oppo&longs;itis &aelig;qualis est, o&longs;tenditur triangulum ha&shy;<lb/>
bere tres angulos &aelig;quales duobus rectis, quomodo &agrave; cau&longs;a e&longs;t <expan abbr="dem&otilde;stratio">demonstratio</expan> h&aelig;c? </s>
          <s id="s.005316">non <lb/>
ne medium certum &longs;ignum est? </s>
          <s id="s.005317">etenim <expan abbr="neq;">neque</expan> externo exi&longs;tente angulo c&ugrave;m interni <lb/>
exi&longs;tant, duobus rectis &aelig;quales &longs;unt; e&longs;t. </s>
          <s id="s.005318">n. </s>
          <s id="s.005319">triangulum latere etiam non producto&rpar;<emph.end type="italics"/><lb/>
Pergit deinde Proclus demon&longs;trare primam Euclid&igrave;s demon&longs;trationem e&longs;&longs;e <lb/>
per cau&longs;am, &amp; proinde veram demon&longs;trationem, qu&ograve;d Piccolomin. <!-- REMOVE S-->in &longs;ua <lb/>citatione callid&egrave; videtur reticui&longs;&longs;e. </s>
          <s id="s.005320">Ad <expan abbr="obiection&etilde;">obiectionem</expan> re&longs;pondeo prim&ograve;. </s>
          <s id="s.005321">angu&shy;<lb/>
lum externum in Euclidiana demon&longs;tratione minim&egrave; extraneum e&longs;&longs;e, quia <lb/>
in hac &longs;ecunda parte a&longs;&longs;umitur pro &longs;ubiecto demon&longs;trationis, ide&longs;t pro par&shy;<lb/>te duorum rectorum, ip&longs;e enim cum angulo &longs;ibi deinceps facit duos angulos <lb/>
rectos, quibus tres anguli trianguli probantur &etail;quales: quod Proclus <expan abbr="n&otilde;">non</expan> vi&shy;<lb/>
detur vidi&longs;&longs;e. </s>
          <s id="s.005322">Secund&ograve;, &longs;i h&etail;c Euclidiana illi <expan abbr="n&otilde;">non</expan> probatur, accipiat de eadem <lb/>
re Pythagoricam, qu&etail; ab&longs;que angulo externo, &amp; ab <expan abbr="q;">que</expan> vlla diui&longs;ione probat <lb/>intentum; &amp; erit omnis &longs;ublata dubitatio. </s>
          <s id="s.005323">Terti&ograve;, &longs;i conuincerent aduer&shy;<lb/>
farij, qu&ograve;d nequaquam faciunt, hanc non e&longs;&longs;e &agrave; priori, &longs;equitur ne propte&shy;<lb/>
rea reliquas omnes e&longs;&longs;e ei &longs;imiles, vt ip&longs;i inferre conantur? </s>
          <s id="s.005324">minim&egrave; <expan abbr="genti&utilde;">gentium</expan>. <lb/>
</s>
          <s id="s.005325">quo logico iure ab vno particulari inferre volunt vniuer&longs;ale?</s>
        </p>
        <p type="main">
          <s id="s.005326">Secund&ograve;, obijcies, pa&longs;&longs;ionem hanc, habere tres angulos, &amp;c. </s>
          <s id="s.005327">non recipro&shy;<lb/>
cari cum triangulo, &longs;eu non e&longs;&longs;e &longs;ecundum quod ip&longs;um, vt aiunt Logici: re&shy;<lb/>peritur enim figura qu&etail;dam pr&etail;ter triangulum, vt patet apud Proclum, qu&etail; <pb pagenum="18" xlink:href="009/01/302.jpg"/>eandem habet proprietatem. </s>
          <s id="s.005328">Re&longs;pondeo habere tres angulos rectilineos <lb/>
&lpar;de his. </s>
          <s id="s.005329">n. </s>
          <s id="s.005330">Euclides agit&rpar; &aelig;quales, &amp;c. </s>
          <s id="s.005331">c&ugrave;m triangulo conuerti, nam Proclus <lb/>
eam conuertit. </s>
          <s id="s.005332">figura autem illa alia, qu&etail; habet tres angulos &etail;quales duo&shy;<lb/>
bus rectis, non habet angulos rectilineos, <expan abbr="neq;">neque</expan>. </s>
          <s id="s.005333">n. </s>
          <s id="s.005334">rectilinea e&longs;t, vt apud Pro&shy;<lb/>
clum videre e&longs;t: &amp; ide&ograve; non e&longs;t ad mentem Euclidis, aut Pythagor&etail;. </s>
          <s id="s.005335">&longs;ed iam <lb/>
cum Proclo concludamus, &longs;ic; quia etiam illud <expan abbr="quoq;">quoque</expan> dicendum e&longs;t, qu&ograve;d <lb/>
internos angulos duobus rectis &aelig;quales habere, per &longs;e, &amp; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quod ip&shy;<lb/>
&longs;um triangulo ine&longs;t: idcirc&ograve; &amp; Ari&longs;tot. in tractatu de demon&longs;tratione hoc <lb/>
exemplum habet in promptu, &longs;ecundum quod ip&longs;um con&longs;iderans, h&etail;c ille.</s>
        </p>
        <p type="main">
          <s id="s.005336">Aliam per cau&longs;am <expan abbr="material&etilde;">materialem</expan> ex mente Ari&longs;t. expendimus tex. <!-- REMOVE S-->11. 2. Po&shy;<lb/>
&longs;terior. <!-- REMOVE S-->vbi ait, angulum in &longs;emicirculo e&longs;&longs;e rectum, quoniam e&longs;t dimidium <lb/>
duorum rectorum, quod medium e&longs;t in cau&longs;a materiali, e&longs;&longs;e enim dimidium <lb/>
e&longs;t e&longs;&longs;e partem. </s>
          <s id="s.005337">Cau&longs;a igitur, qu&aelig; facit angulum illum e&longs;&longs;e rectum, e&longs;t di&shy;<lb/>
midia quantitas duorum rectorum, qu&etail; ip&longs;um con&longs;tituit; &longs;ed fort&egrave; melius <lb/>
dicemus, &longs;i dixerimus, ide&ograve; e&longs;&longs;e rectum, quia e&longs;t diui&longs;ibilis in duas partes, <lb/>
qu&etail; &longs;imul &longs;umpt&etail;, &longs;unt &aelig;quales dimidio duorum rectorum, &longs;iue vni recto. <lb/>
</s>
          <s id="s.005338">Linea ver&ograve; per quam diuiditur, non e&longs;t medium, &longs;ed medij manife&longs;tiua. <lb/>
</s>
          <s id="s.005339">In &longs;equenti appendice ad finem Operis plures alias videbis in &longs;olo primo <lb/>
elem. </s>
          <s id="s.005340">&agrave; cau&longs;a materiali.</s>
        </p>
        <p type="main">
          <s id="s.005341"><expan abbr="Neq;">Neque</expan> ver&ograve; nece&longs;&longs;e e&longs;&longs;e exi&longs;timo <expan abbr="demon&longs;tration&etilde;">demon&longs;trationem</expan> quampiam ex Arithme&shy;<lb/>
tica examinare, c&ugrave;m <expan abbr="c&otilde;&longs;tet">con&longs;tet</expan> eam eodem pror&longs;us modo cum Geometria de&shy;<lb/>
mon&longs;trare, vt plan&egrave; in 78. &amp; 9. elem. </s>
          <s id="s.005342">videre licet: im&ograve; <expan abbr="qu&etail;cunq;">qu&etail;cunque</expan> hactenus <lb/>
de altera &longs;unt dicta, de vtraque intelligenda e&longs;&longs;e volumus, nam vt e&longs;t apud <lb/>
Eutocium in comm. <!-- REMOVE S-->Apollonij: <foreign lang="greek">tauta gar maqhmata, dokounti eimen adelfa</foreign>.</s>
        </p>
        <p type="head">
          <s id="s.005343"><emph type="italics"/>Contra pr&aelig;dicta generatim obijciuntur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005344">Prim&ograve;, cau&longs;&aelig; i&longs;t&aelig; Geometric&etail; non videntur ver&aelig; cau&longs;&etail;, <expan abbr="non.n.">nonnisi</expan></s>
          <s id="s.005345">&longs;atis <lb/>
videntur ab effectibus &longs;uis di&longs;tingui: nam in cau&longs;a formali partes <lb/>
definitionis &longs;unt <expan abbr="id&etilde;">idem</expan> cum definito; &amp; in cau&longs;a materiali partes &longs;unt <lb/>
idem cum toto, ergo non &longs;unt ver&etail; cau&longs;&aelig;, &amp; proinde <expan abbr="neq;">neque</expan> ver&aelig; de&shy;<lb/>
mon&longs;trationes. </s>
          <s id="s.005346">Re&longs;pondeo prim&ograve;, &longs;upra dictum e&longs;t, quando partes &longs;eor&shy;<lb/>&longs;im, &amp; non vt totum componentes &longs;umuntur, di&longs;tingui &agrave; toto, quod partes <lb/>
vnitas &longs;ignificat, &amp; pr&aelig;terea formam compo&longs;iti; qu&aelig; di&longs;tinctio non e&longs;t &longs;o&shy;<lb/>
lius rationis.</s>
        </p>
        <p type="main">
          <s id="s.005347">Secund&ograve;, licet non appareat tanta di&longs;tinctio hic, quanta in Mathemati&shy;<lb/>
cis medijs, &amp; Phy&longs;ica, e&longs;t tamen tanta, qu&etail; &longs;ufficiat ad perfecti&longs;&longs;imam de&shy;<lb/>
mon&longs;trationem, quod patet authoritate Ari&longs;t. <!-- REMOVE S-->Platonis, Procli, &amp; omnium <lb/>Gr&etail;corum, Arabum, &amp; Latinorum &lpar;pr&aelig;ter duos, vel tres recentiores&rpar; qui <lb/>
<expan abbr="o&etilde;s">omnes</expan> ha&longs;ce demon&longs;trationes per&longs;ecti&longs;&longs;imas, e&longs;&longs;e con&longs;entiunt, vt &longs;up. </s>
          <s id="s.005348">diximus.</s>
        </p>
        <p type="main">
          <s id="s.005349">Terti&ograve;, <expan abbr="quantacunq;">quantacunque</expan> &longs;it h&aelig;c di&longs;tinctio, certum e&longs;t eam non e&longs;&longs;e &longs;olius ra&shy;<lb/>
tionis, quod clarum e&longs;t, primo apud eos, qui putant relationem di&longs;tingui &agrave; <lb/>
fundamento, vt aiunt, realiter, modaliter, vel formaliter. </s>
          <s id="s.005350">Secund&ograve;, <expan abbr="c&otilde;&longs;tat">con&longs;tat</expan> <lb/>
etiam apud reliquos omnes, pr&aelig;&longs;ertim apud recentiores, qui vari&aelig; eam de&shy;<lb/>
nominant, alij. </s>
          <s id="s.005351">n. </s>
          <s id="s.005352">eam formalem, alij realem, alij modalem, alij ex natura <pb pagenum="19" xlink:href="009/01/303.jpg"/>rei, alij realem modalem, &amp; alij alijs formalitatibus eam appellant; qui&shy;<lb/>
bus &longs;ingulis aliquam realitatem illi ine&longs;&longs;e &longs;ignificant, qu&aelig; &longs;ufficit ad per&longs;e&shy;<lb/>
ctam demon&longs;trationem. </s>
          <s id="s.005353">&longs;atis enim e&longs;t ad perfectam demon&longs;trationem, vt <lb/>
per eam cau&longs;a propria, &amp; ad&aelig;quata effectus, iuxta rei naturam, detegatur, <lb/>
&longs;ic enim intellectui no&longs;tro fit &longs;atis, vt acquie&longs;cat, &amp; verum intueatur, quod <lb/>
e&longs;t finis perfect&aelig; demon&longs;trationis. </s>
          <s id="s.005354"><expan abbr="neq;">neque</expan> ver&ograve; maior, aut minor di&longs;tinctio fa&shy;<lb/>
cit, vt cau&longs;a &longs;it magis, aut minus vera, &longs;ed vera illa e&longs;t cau&longs;a, qu&aelig; ver&egrave; cau&shy;<lb/>
&longs;at effectum &agrave; &longs;e non ratione tantum di&longs;tinctum: &amp; proinde vera illa demon&shy;<lb/>
&longs;tratio e&longs;t, qu&aelig; p&eacute;r eam demon&longs;trat. </s>
          <s id="s.005355">quart&ograve; h&aelig;c, quamuis parua di&longs;tinctio, <lb/>multum tamen ex alia parte conducit ad demon&longs;trationis perfectionem, ex <lb/>
ea enim fit, vt in demon&longs;tratione liquid&ograve; appareat, cau&longs;am illam e&longs;&longs;e ve&shy;<lb/>
ram, &amp; propriam affectionis demon&longs;trat&aelig;, ita vt non po&longs;&longs;it &agrave; propinquiori <lb/>
procedere; quod in nulla alia &longs;cientia tam euidenter apparet.</s>
        </p>
        <p type="main">
          <s id="s.005356">Obiectio 2. Geometra o&longs;tendit eandem conclu&longs;ionem per plures demon&shy;<lb/>
&longs;trationes, erg&ograve; per diuer&longs;a media, atqui vnius effectus e&longs;t vna tantum cau&shy;<lb/>
&longs;a propria, &amp; ad&aelig;quata.</s>
        </p>
        <p type="main">
          <s id="s.005357">Re&longs;pondeo prim&ograve;, eandem rem o&longs;tendi quidem per plures demon&longs;tratio&shy;<lb/>
nes, quarum vna e&longs;t &agrave; priori, altera ver&ograve; &agrave; po&longs;teriori. </s>
          <s id="s.005358">&longs;ecund&ograve;, &longs;i omnes &longs;int <lb/>
&agrave; priori, tunc e&longs;&longs;entialiter e&longs;&longs;e vnam tantum, plures ver&ograve; accidentaliter, <lb/>
quia in omnibus erit idem medium pr&aelig;cipuum, &longs;ed con&longs;tructio, qua illud <lb/>
detegitur diuer&longs;a, vt patet in 32. primi, quam aliter Pythagorici, aliter Eu&shy;<lb/>
clides, aliter Proclus demon&longs;trarunt, &longs;ed tamen in omnibus e&longs;t idem Me&shy;<lb/>
dium, cau&longs;a &longs;cilicet materialis, quamuis diuer&longs;a &longs;it con&longs;tructio.</s>
        </p>
        <p type="main">
          <s id="s.005359">Obiectio 3. Demon&longs;trationes Geometric&aelig; non con&longs;tant ex proprijs, &amp; <lb/>
per &longs;e, non enim Geometra con&longs;iderat e&longs;&longs;entiam Quantitatis, neque eius <lb/>
pa&longs;siones, quatenus ab illius e&longs;&longs;entia manant, quare ex communibus qui&shy;<lb/>
bu&longs;dam, &amp; mer&egrave; extrin&longs;ecis nece&longs;&longs;e e&longs;t procedere. </s>
          <s id="s.005360">Re&longs;pondeo ex dictis cap. <lb/>
1. de materia intelligibili, &amp; definitionibus Geometricis huic obiectioni <lb/>
abund&egrave; fieri &longs;atis. </s>
          <s id="s.005361">materia enim Geometri&aelig; non e&longs;t quantitas &longs;ecundum &longs;e, <lb/>&longs;ed quatenus terminata, cuius totam e&longs;&longs;entiam ex definitionibus e&longs;&longs;entiali&shy;<lb/>
bus Geometra cogno&longs;cit: quorum <expan abbr="vtrumq;">vtrumque</expan> aduer&longs;arios latuit.</s>
        </p>
        <p type="main">
          <s id="s.005362">Pr&aelig;terea fal&longs;um e&longs;t, Geometram ex communibus pluribus &longs;cientijs pro&shy;<lb/>
cedere, quod vetat Ari&longs;t. 1. Po&longs;ter. procedit enim ex principijs communi&shy;<lb/>
bus quantitatibus terminatis, ide&longs;t figuris, &amp; numeris; quod non &longs;olum li&shy;<lb/>
cet, &longs;ed etiam debet fieri ex 1. Po&longs;ter. tex. <!-- REMOVE S-->20. &amp; 25. <expan abbr="neq;">neque</expan> vnquam idem prin&shy;<lb/>
cipium repetit, ni&longs;i vbi e&longs;t effectus formalis ip&longs;ius, &amp; non ni&longs;i contrahendo <lb/>
ad illud particulare.</s>
        </p>
        <p type="head">
          <s id="s.005363"><emph type="italics"/>Recentiorum calumni&aelig; aduer&longs;us Mathematicas <lb/>
diluuntur. </s>
          <s id="s.005364">Cap. 3.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005365">Prima e&longs;t, qua Alexander Piccolomineus, &amp; eius &longs;ectatores mal&egrave; con&shy;<lb/>
tra Mathematicos Proclum adducunt, quod, vt manife&longs;t&egrave; videas, <lb/>
hic tibi de&longs;cribam integram Procli &longs;ententiam, quam ille mutila&shy;<lb/>
tam citat, &amp; quidem gr&aelig;c&egrave;, vt melius lateat. </s>
          <s id="s.005366">libro igitur 3. in Eu&shy;


<pb pagenum="20" xlink:href="009/01/304.jpg"/>clid. <!-- REMOVE S-->&longs;ic habet: At cau&longs;am, &amp; ip&longs;um Propter quid Geometriam minim&egrave; <lb/>
contemplari pluribus vi&longs;um e&longs;t, huiu&longs;ce enim &longs;ententi&aelig; e&longs;t Amphinomus <lb/>
Ari&longs;t. duce. </s>
          <s id="s.005367">h&aelig;c &longs;unt, qu&aelig; Piccolomineus gr&aelig;c&egrave; citat, quibus deinde &longs;ubdit, <lb/>
quid amplius qu&aelig;rimus pro hac &longs;ententia? </s>
          <s id="s.005368">&longs;ed non ne aduertis Lector, pr&aelig;&shy;<lb/>
dictum &longs;ententiam non e&longs;&longs;e Procli, &longs;ed Amphinomi cuiu&longs;dam nullius nomi&shy;<lb/>nis philo&longs;ophi, qui &longs;ub fals&ograve; Ari&longs;t. patrocinio Geometric&aelig; cau&longs;as auferre <lb/>
conabatur, qu&aelig; tamen ac &longs;i Procli ip&longs;ius e&longs;&longs;et &agrave; Piccolomineo in medium, <lb/>
affertur. </s>
          <s id="s.005369">&longs;ed videamus, qu&aelig; Piccolomineus pr&aelig;termi&longs;it, pergit po&longs;tea <lb/>
Procius, inueniet autem aliquis &lpar;inquit Geminus&rpar; huius etiam inqui&longs;itio&shy;<lb/>
nem in Geometria, quo modo Geometr&aelig; non e&longs;t qu&aelig;rere qua de cau&longs;a, in <lb/>
circulis quidem infinita multiangula in&longs;cribantur: in &longs;ph&aelig;ris ver&ograve; multian&shy;<lb/>gula &longs;olida &aelig;quilatera, &amp; &aelig;quiangula ex &longs;imilibus planis con&longs;tructa infinita <lb/>
in&longs;cribere e&longs;t impo&longs;sibile. </s>
          <s id="s.005370">ad quem enim &longs;pectaret hoc inue&longs;tigare pr&aelig;ter <lb/>
Geometram? </s>
          <s id="s.005371">H&aelig;c e&longs;t &longs;ententia Gemini &agrave; Proclo allata ad Amphinomi opi&shy;<lb/>
nionem confutandam. </s>
          <s id="s.005372">Pergit po&longs;tea Proclus ex propria &longs;ententia &longs;ic; Quan&shy;<lb/>
do igitur Geometris &longs;yllogi&longs;mus per impo&longs;sibile fuerit, &longs;ymptoma t&agrave;ntum <lb/>
inuenire cupiunt, <expan abbr="qu&atilde;do">quando</expan> autem per pr&aelig;cipuam demon&longs;trationem, tunc rur&shy;<lb/>
&longs;us, &longs;i quidem in particulari demon&longs;trationes fiunt, cau&longs;a nondum manife&shy;<lb/>
&longs;ta e&longs;t, &longs;i ver&ograve; in vniuer&longs;ali, in <expan abbr="omnibus&qacute;">omnibusque</expan>; &longs;imilibus <expan abbr="c&otilde;tinu&ograve;">continu&ograve;</expan> &amp; ip&longs;um Propter <lb/>
quid manife&longs;tum e&longs;t. </s>
          <s id="s.005373">h&aelig;c e&longs;t tota illius loci integra &longs;eries, qu&agrave;m aduer&longs;arius <lb/>
mutilatam obtrudebat. </s>
          <s id="s.005374">vbi apert&egrave; vides, Procli de Geometria &longs;ententiam.</s>
        </p>
        <p type="main">
          <s id="s.005375">Secunda calumnia e&longs;t, qua contra Mathematicos Ari&longs;t. quamuis inuitum <lb/>
interpretantur. </s>
          <s id="s.005376"><expan abbr="neq;">neque</expan> &longs;olum loca ip&longs;ius clari&longs;sima ex analyticis, phy&longs;icis, &amp; <lb/>
metaphy&longs;icis, qu&aelig; &longs;uperius recitauimus in alienum &longs;en&longs;um detorquent; &longs;ed <lb/>
pr&aelig;ter ea vnicum tantum locum, qui expre&longs;s&egrave; Mathematicis refragari vi&shy;<lb/>
deatur, afferunt, <expan abbr="cum&qacute;">cumque</expan>; &longs;ibi fals&ograve; fauere <expan abbr="c&otilde;fingunt">confingunt</expan>. </s>
          <s id="s.005377">is e&longs;t in angulo quodam <lb/>
operum ip&longs;ius, in &longs;ecund&ograve; videlicet Moral. Eudem. cap. 7. &longs;ic, in immobi&shy;<lb/>
libus autem, vt in Mathematicis non per &longs;e, &longs;ed &longs;imilitudine quadam prin&shy;<lb/>
cipia appellantur. </s>
          <s id="s.005378">cuius germana interpretatio non contra, &longs;ed pro Mathe&shy;<lb/>
maticis e&longs;t: loquitur enim ibi Ari&longs;t. de principio <expan abbr="effici&etilde;te">efficiente</expan>, &agrave; quo fiunt actio&shy;<lb/>
nes human&aelig;, &amp; per motum, vt doceret in homine e&longs;&longs;e principia quarundam <lb/>
actionum, qu&aelig; propri&aelig; &longs;unt hominis, &amp; liber&aelig;. </s>
          <s id="s.005379">talia autem principia ne&shy;<lb/>
gant e&longs;&longs;e in immobilibus, quoniam &longs;unt entia nece&longs;&longs;aria, &amp; libertatis exper&shy;<lb/>
tia; e&longs;&longs;e tamen &longs;ecundum &longs;imilitudinem, ide&longs;t, vt &longs;e habent principia libera <lb/>
ad actiones liberas, ita principia nece&longs;&longs;aria ad actiones nece&longs;&longs;arias: vnde <lb/>
&longs;equitur, quod <expan abbr="quemadmod&utilde;">quemadmodum</expan> principia libera &longs;unt ad&aelig;quata cau&longs;a illarum <lb/>
actionum; &longs;ic etiam principia Mathematica erunt cau&longs;&aelig; ad&aelig;quat&aelig; <expan abbr="pa&longs;sio-n&utilde;">pa&longs;sio&shy;<lb/>
num</expan> Mathematicarum; quod ip&longs;e Ari&longs;t. te&longs;tatur paulo po&longs;t, his verbis: nam <lb/>
&longs;i habente trigono duos rectos, nece&longs;&longs;e e&longs;t, tetragonum quatuor rectis con&shy;<lb/>
&longs;tare, clarum e&longs;t, quod trigonus duos rectos habens cau&longs;a eius exi&longs;tit. </s>
          <s id="s.005380">&amp; vt <lb/>
intelligamus eum loqui de propria cau&longs;a, qu&aelig; &longs;it medium demon&longs;trationis, <lb/>
&longs;ubdit; id autem nece&longs;&longs;ari&ograve; euenire patet ex analyticis. </s>
          <s id="s.005381">quare Mathemati&shy;<lb/>
cis maxim&egrave; fauet hic locus, contra qu&agrave;m aduer&longs;arij autumabant. </s>
          <s id="s.005382">nullus igi&shy;<lb/>
tur locus apud Ari&longs;t. reliquus e&longs;t, qui no&longs;tr&aelig; &longs;ententi&aelig; apert&egrave; non faueat.</s>
        </p>
        <p type="main">
          <s id="s.005383">Tertia, qua contra Mathematicos Platonem ip&longs;um eximium Mathema&shy;<lb/>ticarum fautorem, ac &longs;tudio&longs;um excitare conantur; aiunt enim ip&longs;um 7. de <pb pagenum="21" xlink:href="009/01/305.jpg"/>Rep. <!-- REMOVE S-->dicere Mathematicos circa quantitatem &longs;omniare. </s>
          <s id="s.005384">Ver&ugrave;m, ne falla&shy;<lb/>
cia &longs;ub&longs;it, ecce tibi Platonis verba &egrave; gr&aelig;co &longs;yncer&egrave; tran&longs;lata. </s>
          <s id="s.005385">Reliqu&aelig; ve&shy;<lb/>
r&ograve;, quas diximus verarum <expan abbr="rer&utilde;">rerum</expan> quoquo modo e&longs;&longs;e participes, Geometriam <lb/>
&longs;cilicet, <expan abbr="eius&qacute;">eiusque</expan>; comites circa ip&longs;am e&longs;&longs;entiam quodammodo &longs;omniant: &longs;yn&shy;<lb/>
cer&egrave; autem quicquam ab illis cernere impo&longs;&longs;ibile e&longs;t, tanti&longs;per dum &longs;uppo&shy;<lb/>
&longs;itionibus h&aelig;rent, <expan abbr="eas&qacute;">easque</expan>; ratas, &amp; immobiles adeo &longs;eruant, vt illarum ratio&shy;<lb/>
nem reddere nequeant. </s>
          <s id="s.005386">Aduerte prim&ograve; Platonem non dicere Geometram <lb/>
ab&longs;olut&egrave; &longs;omniare, &longs;ed quodammodo &longs;omniare: deinde non dicere circa <lb/>
quantitatem, &longs;ed circa e&longs;&longs;entiam: vnde &longs;i liberet funem cum eis trahere <lb/>
contentio&longs;um, <expan abbr="verbis&qacute;">verbisque</expan>; h&aelig;rere, vt ip&longs;i faciunt, nihil contra Mathematicos <lb/>
facerent. </s>
          <s id="s.005387">&longs;ed e&longs;to intelligat ip&longs;am quantitatem, videamus quid &longs;ibi velit. </s>
          <s id="s.005388">vt <lb/>
autem i&longs;tud videamus, &longs;ciendum e&longs;t, totius 7. de Rep. <!-- REMOVE S-->di&longs;cur&longs;um e&longs;&longs;e in con&shy;<lb/>
&longs;tituendo Reip. <!-- REMOVE S-->Cu&longs;tode, &amp; Gubernatore, quem in primis vult e&longs;&longs;e optim&egrave; <lb/>
natura, tam ad agendum, qu&agrave;m ad &longs;peculandum idoneum: vult pr&aelig;terea <lb/>
ip&longs;um &longs;apienti&longs;&longs;imum e&longs;&longs;e, ide&longs;t Theologiam, qu&agrave;m etiam Dialecticam no&shy;<lb/>
minat, optim&egrave; callere, per quam <expan abbr="ab&longs;q;">ab&longs;que</expan> vllo di&longs;cur&longs;u <expan abbr="rer&utilde;">rerum</expan>, ac pr&aelig;cipu&egrave; &longs;um&shy;<lb/>
mi Boni e&longs;&longs;entias contempletur. </s>
          <s id="s.005389">ad hanc diuinam contemplationem, vt <lb/>
peruenire po&longs;&longs;it, opus ait e&longs;&longs;e eum humanis aliquot di&longs;ciplinis imbutum e&longs;&shy;<lb/>
&longs;e. </s>
          <s id="s.005390">totam autem Philo&longs;ophiam inibi partitur in tres partes, in Dialecticam, <lb/>
&longs;eu Theologiam, quam intellectui attribuit ab&longs;que vlla &longs;uppo&longs;itione, &amp; di&shy;<lb/>
&longs;cur&longs;u: <expan abbr="hanc&qacute;">hancque</expan>; &longs;olam &longs;cienti&aelig; nomine dignam e&longs;&longs;e exi&longs;timat. </s>
          <s id="s.005391">&longs;ecund&ograve;, in <lb/>
Mathematicam, quam in cognitione, &longs;eu ratiocinatione collocat, &amp; pro&shy;<lb/>
pterea principia &longs;upponit. </s>
          <s id="s.005392">terti&ograve; tandem in opinionem, qu&aelig; ver&longs;atur circa <lb/>
res naturales, qu&aelig; in imaginatione ab eo collocatur. </s>
          <s id="s.005393">Iuxta hanc trimem&shy;<lb/>
brem diui&longs;ionem ex Platonis &longs;ententia &longs;ic habet Mar&longs;ilius Ficinus in argu&shy;<lb/>
mento huius 7. de Rep. <!-- KEEP S--></s>
          <s id="s.005394">Diuina &longs;iquidem in tribus aquis repr&etail;&longs;entari viden&shy;<lb/>
tur, prim&ograve; quidem licet <expan abbr="c&otilde;fu&longs;ius">confu&longs;ius</expan> in rationibus phy&longs;icis. </s>
          <s id="s.005395">&longs;ecund&ograve;, di&longs;tinctius <lb/>
in Mathematicis. <!-- KEEP S--></s>
          <s id="s.005396">terti&ograve;, clari&longs;&longs;im&egrave; in Metaphy&longs;icis. </s>
          <s id="s.005397">&amp; paulo po&longs;t: Diuinas <lb/>
<expan abbr="deniq;">denique</expan> formas omnin&ograve; immortales, <expan abbr="res&qacute;">resque</expan>; veras Plato exi&longs;timat, quarum, <lb/>
imagines quidem &longs;unt mathematic&aelig; form&aelig;, vmbr&aelig; ver&ograve; res naturales. </s>
          <s id="s.005398">&amp; <lb/>
po&longs;tea: C&ugrave;m autem animaduertat Thaletem, Democritum, Anaxagoram, <lb/>
tam negligentes in rebus diuinis fui&longs;&longs;e, qu&agrave;m <expan abbr="dilig&etilde;tes">diligentes</expan> in naturalibus; Ph&aelig;&shy;<lb/>
recidem contra, &amp; Pythagoram, <expan abbr="Pythagoreos&qacute;">Pythagoreosque</expan>; omnes Mathematicorum <lb/>
Principes pariter &longs;ummos extiti&longs;&longs;e Theologos, <expan abbr="moribus&qacute;">moribusque</expan>; diuinos, merit&ograve; <lb/>
partim ratione, partim experientia conclu&longs;it curio&longs;um naturalium &longs;tudium <lb/>
animum &agrave; diuinis &longs;&aelig;p&egrave; auertere. </s>
          <s id="s.005399">&amp; po&longs;t nonnulla: Quare &longs;eptimus hic liber <lb/>de Rep. vbi animum ad &longs;ummum Bonum, Solemque, ide&longs;t Deum, <expan abbr="id&aelig;as&qacute;">id&aelig;asque</expan>; <lb/>
diuinas, qua&longs;i &longs;tellas, conuenientibus producit gradibus, nullam in ip&longs;o <lb/>
a&longs;cen&longs;u naturalis periti&aelig; facit mentionem, &longs;ed mathematicos quo&longs;dam gra&shy;<lb/>
dus ad Diuina commodius perducentes adducit in medium, inter quos duo <lb/>
&longs;unt puri, Arithmetica, &amp; Geometria, &amp;c. </s>
          <s id="s.005400">reliquas deinde Mathematicas <lb/>
Plato enumerat, ac &longs;ingillatim commendat, <expan abbr="atq;">atque</expan> in Rempub. <!-- REMOVE S-->admittit. </s>
          <s id="s.005401">po&longs;t <lb/>
multa iterum Ficinus &longs;ic, c&ugrave;m erg&ograve; dicit, animam &agrave; lucerna ad Lunam, &agrave; <lb/>
Luna ad Solem attolli, &longs;ignificat Plato &agrave; formis naturalibus ad Mathemati&shy;<lb/>
cas, ab his ad diuinas <expan abbr="deniq;">denique</expan> eleuari. </s>
          <s id="s.005402">&amp; nonnullis intermi&longs;&longs;is, <expan abbr="deniq;">denique</expan> Theo&shy;<lb/>
logiam, quam etiam Metaphy&longs;icam, &amp; Dialecticam dicit, omnibus facul&shy;


<pb pagenum="22" xlink:href="009/01/306.jpg"/>tatibus anteponit, vt ducentem omnes, &amp; ad &longs;uum officium vtentem mini&shy;<lb/>
&longs;terio &longs;ingularum. </s>
          <s id="s.005403">officium autem eius e&longs;&longs;e per totam entis progredi latitu&shy;<lb/>
dinem, <expan abbr="atq;">atque</expan> ad ip&longs;um Bonum totius entis cau&longs;am, &longs;e <expan abbr="c&otilde;ferre">conferre</expan>, &amp; quid <expan abbr="vnum-quodq;">vnum&shy;<lb/>
quodque</expan> &longs;it definire, rationem <expan abbr="cuius&qacute;">cuiusque</expan>; e&longs;&longs;enti&aelig; a&longs;&longs;ignando, quidu&egrave; quamlibet <lb/>
&longs;equatur e&longs;&longs;entiam demon&longs;trare. </s>
          <s id="s.005404">C&aelig;teras autem facultates pr&aelig; huius no&shy;<lb/>
bilitate iudicat e&longs;&longs;e &longs;eruiles: aut enim ad opiniones hominum declinant, aut <lb/>
&longs;altem et&longs;i ad incorporea &longs;e &longs;e pro viribus erigunt, nihilominus circa illa <lb/>
quodammodo &longs;omniant, quales e&longs;&longs;e inquit Mathematicas. <!-- KEEP S--></s>
          <s id="s.005405">ex quibus iam <lb/>
clar&egrave; vides Platonem dixi&longs;&longs;e Mathematicas quodam modo &longs;omniare circa <lb/>
e&longs;&longs;entiam rerum, non ab&longs;olut&egrave;, &longs;ed comparatione ad Theologiam: intelli&shy;<lb/>
gis etiam cur Mathematicas nolit &longs;cientias appellari, quia nimirum &longs;olam <lb/>
Theologiam hoc nomine dignam cen&longs;ebat: qua de cau&longs;a minus Phy&longs;icam, <lb/>
eodem nomine dignam putauit, c&ugrave;m eam opinionem, Mathematicam ver&ograve; <lb/>
cogitationem, vel ratiocinationem dicat. </s>
          <s id="s.005406">ob eandem comparationem a&longs;&longs;e&shy;<lb/>
rit etiam Mathematicas minus e&longs;&longs;e certas, quam Theologiam, quoniam, <lb/>
&longs;cilicet h&aelig;c nihil &longs;upponit, <expan abbr="nihil&qacute;">nihilque</expan>; di&longs;currit, &longs;ed intuetur: ill&aelig; ver&ograve; iactis <lb/>
quibu&longs;dam principijs, qu&aelig; probari nequeunt, di&longs;currunt, <expan abbr="propterea&qacute;">proptereaque</expan>; in <lb/>
ip&longs;o di&longs;cur&longs;u pote&longs;t error aliquis contingere. </s>
          <s id="s.005407">eandem huius loci explica&shy;<lb/>
tionem habes apud Proclum cap. 10. lib. 1. in Euclid. <!-- REMOVE S-->&longs;ic; Verum quid &longs;ibi <lb/>
velit Plato, quando in libris de Rep. <!-- REMOVE S-->&agrave; Mathematica &longs;cienti&aelig; nomen ab&longs;tu&shy;<lb/>
lit breuiter dicam. </s>
          <s id="s.005408">&amp; paulo po&longs;t; hanc <expan abbr="deniq;">denique</expan> &longs;cientiam, quam ab artibus <lb/>
di&longs;tinguimus diuidens, vnam quidem &longs;uppo&longs;itionis expertem e&longs;&longs;e vult, alte&shy;<lb/>
ram ver&ograve; ex &longs;uppo&longs;itione &longs;caturire. </s>
          <s id="s.005409">&amp; po&longs;t pauca: &amp; &longs;ic ait Mathematicam <lb/>tanquam &longs;uppo&longs;itionibus vtentem ab ea, qu&aelig; &longs;uppo&longs;itionibus caret, <expan abbr="perfe-cta&qacute;">perfe&shy;<lb/>
ctaque</expan>; e&longs;t &longs;cientia deficere: vna enim ver&egrave; e&longs;t &longs;cientia, per quam omnia, qu&aelig; <lb/>
&longs;unt cogno&longs;cere apti &longs;umus. </s>
          <s id="s.005410">per&longs;picu&egrave; igitur vides auctoritate horum phi&shy;<lb/>
lo&longs;ophorum h&aelig;c omnia Platonem non ab&longs;olut&egrave;, &longs;ed comparat&egrave; dixi&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.005411">Po&longs;t h&aelig;c Ficinus iterum ex &longs;ententia Platonis &longs;ic pergit: quoniam ver&ograve; <lb/>
di&longs;&longs;erendi facultas, &longs;i adole&longs;centibus tradatur opinionem hone&longs;ti debilitat, <lb/>
vnde euadunt <expan abbr="intemper&atilde;tes">intemperantes</expan>, im&ograve; &amp; &longs;uperbi, &amp; impij, vt in Philebo quoque, <lb/>
&amp; legibus dicitur, idcirc&ograve; ante trige&longs;imum &aelig;tatis annum in Mathematicis <lb/>erudiendi &longs;unt, <expan abbr="atq;">atque</expan> in publicis negotijs per interualla pariter exercendi. <lb/>
</s>
          <s id="s.005412">concludamus tandem h&aelig;c pulcherrimo eiu&longs;dem 7. de Rep. <!-- REMOVE S-->loco, quem etiam <lb/>
Proclus lib. 1. cap. 8. ad verbum fer&egrave; &longs;ic recitat: Ideo &amp; in Repub. <!-- REMOVE S-->Socrates <lb/>
rect&egrave; dixit, oculus, nimirum anim&aelig;, qui ab alijs &longs;tudijs exc&oelig;catur, <expan abbr="defodi-tur&qacute;">defodi&shy;<lb/>
turque</expan>; &agrave; Mathematicis tantum di&longs;ciplinis recreari, <expan abbr="excitari&qacute;">excitarique</expan>; rur&longs;us ad eius, <lb/>
qui e&longs;t, contemplationem, &amp; &agrave; &longs;imulacris ad ea, qu&aelig; vera &longs;unt: nam pulchri&shy;<lb/>
tudo, &amp; ordo Mathematicarum rationum, firmitudoque, ac &longs;tabilitas con&shy;<lb/>
templationis, nos ip&longs;is coniungit intellectibus, <expan abbr="perfect&egrave;&qacute;">perfect&egrave;que</expan>; in ip&longs;is obfirmat, <lb/>
perpetu&ograve; quidem manentibus, &amp; diuina pulchritudine collucentibus, ac mu&shy;<lb/>
tuum ordinem &longs;eruantibus. </s>
          <s id="s.005413">Animaduerti&longs;ti Lector ex his paucis, quot lau&shy;<lb/>
dibus in hoc 7. de Repub. <!-- REMOVE S-->Mathematic&aelig; &agrave; Platone cumulentur, vt totus fer&egrave; <lb/>
liber quoddam ip&longs;arum encomium videatur: vnde mirum &longs;it, i&longs;tos ex eo&shy;<lb/>
dem &longs;eptimum locum illum contra Mathematicas, inter tot ip&longs;arum pr&aelig;&shy;<lb/>
conia &longs;edul&ograve; emendica&longs;&longs;e, ac perperam interpretatos e&longs;&longs;e: &longs;icque Araneos <lb/>imitatos e&longs;&longs;e, qui ex mellifluis floribus, ex quibus Apes mella, venenum col&shy;<pb pagenum="23" xlink:href="009/01/307.jpg"/>ligunt. </s>
          <s id="s.005414">Verumenimuer&ograve; quis vnquam de Platonis mente erga Mathemati&shy;<lb/>
cas dubitare poterit, c&ugrave;m ip&longs;e omnes ageometretos &egrave; &longs;uo gymna&longs;io reijce&shy;<lb/>
ret; c&ugrave;m quotidie, vt ex Philopono refert ip&longs;e Piccolomineus auditoribus <lb/>
&longs;uis aliquod Problema Mathematicum proponeret. </s>
          <s id="s.005415">qui de legibus 6. &amp; 7. <lb/>
de &longs;ingulis Mathematicis addi&longs;cendis leges &longs;ancit, vbi <expan abbr="Geometri&atilde;">Geometriam</expan> ade&ograve; ex&shy;<lb/>
tollit, vt a&longs;&longs;erat, a&longs;ymetriam quantitatum ignorare, non <expan abbr="homin&utilde;">hominum</expan>, &longs;ed por&shy;<lb/>
corum, ac pecorum ignorantiam e&longs;&longs;e. </s>
          <s id="s.005416">In Epinomide tandem qu&agrave;m digna, <lb/>
<expan abbr="quam&qacute;">quamque</expan>; pr&aelig;clar&egrave; de A&longs;tronomia, <expan abbr="de&qacute;">deque</expan>; Geometria, &amp; Arithmetica, qu&aelig; ad <lb/>
eam conferunt, pr&aelig;dicat. </s>
          <s id="s.005417">pr&aelig;cipua autem A&longs;tronomi&aelig; laus ibi tradita e&longs;t, <lb/>
quod ea, inter omnes &longs;cientias, animum ad c&oelig;le&longs;tia, <expan abbr="atq;">atque</expan> diuina attollit, <expan abbr="in-de&qacute;">in&shy;<lb/>
deque</expan>; ad &longs;ummi Boni cognitionem, <expan abbr="atq;">atque</expan> amorem allicit, quam veram e&longs;&longs;e <expan abbr="&longs;a-pi&etilde;tiam">&longs;a&shy;<lb/>
pientiam</expan> diuinitus inibi Plato pluribus fatetur. </s>
          <s id="s.005418">plura alia Platonis loca bre&shy;<lb/>
uitatis cau&longs;a, pr&aelig;tereo; quis enim, vel leuiter eum attingit, qu&igrave; non per&shy;<lb/>
&longs;picu&egrave; videat, eum &longs;uper omnes Philo&longs;ophos e&longs;&longs;e Mathematicarum com&shy;<lb/>
mendatorem eximium.</s>
        </p>
        <p type="main">
          <s id="s.005419">Quarta e&longs;t Mathematicas, Geometriam pre&longs;ertim con&longs;i&longs;tere in imagi&shy;<lb/>
natione potius, qu&agrave;m in di&longs;cur&longs;u, &amp; proinde &longs;cientias e&longs;&longs;e puerilis ingenij, <lb/>
c&ugrave;m pueri valeant imaginatione. </s>
          <s id="s.005420">accedit authoritas Ari&longs;t. qui 6. Eth. cap. 8, <lb/>
ait, quid e&longs;t, qu&ograve;d puer fieri Mathem. pote&longs;t, &longs;apiens, aut naturalis non po&shy;<lb/>
te&longs;t? </s>
          <s id="s.005421">pr&aelig;terea, quia antiquitus pueris ante alias tradebantur. </s>
          <s id="s.005422">Re&longs;pondeo, <lb/>
qu&ograve;d, vt in pr&aelig;cedenti re&longs;pon&longs;ione dictum e&longs;t ex Plat. <!-- REMOVE S-->&longs;ententia, non ima&shy;<lb/>ginatio, &longs;ed ratiocinatio, &longs;eu cogitatio ver&longs;atur circa Mathematicas, ima&shy;<lb/>
ginatio autem circa naturalem Philo&longs;ophiam; &longs;ed audi Platonem in eodem <lb/>
&longs;eptimo. </s>
          <s id="s.005423">Placet igitur, ait, primam partem vocare &longs;cientiam, &longs;ecundam <lb/>
cogitationem, tertiam fidem, po&longs;tremam imaginationem. </s>
          <s id="s.005424">Con&longs;tat autem <lb/>
vltimas duas ab ip&longs;o collocari in naturali peritia. </s>
          <s id="s.005425">ade&longs;t etiam Procli autho<lb/>
ritas, qui cap. 5. lib. 1. &longs;ic habet; In&longs;trumentum <expan abbr="itaq;">itaque</expan> aptum ad iudicandum <lb/>
cunctas res Mathematicas cogitationem ex Platonis &longs;ententia &longs;tatuimus, <lb/>
quippequ&aelig; opinione quidem &longs;uperior e&longs;t, ab intelligentia ver&ograve; &longs;uperatur. <lb/>
</s>
          <s id="s.005426">Per cogitationem ver&ograve; intelligendum e&longs;&longs;e quendam mentis motum, ide&longs;t <lb/>
di&longs;cur&longs;um, tum ex vi gr&aelig;c&egrave; vocis <foreign lang="greek">Nohmatos,</foreign> tum ex vi Latin&aelig; vocis manife&shy;<lb/>
&longs;tum e&longs;t; cogitatio enim dicitur qua&longs;i coagitatio. </s>
          <s id="s.005427">&longs; <expan abbr="m&etilde;tis">mentis</expan>, qu&aelig; idem e&longs;t c&ugrave;m <lb/>
di&longs;cur&longs;u, aut ratiocinatione: quare manife&longs;tum e&longs;t horum Philo&longs;ophorum <lb/>
authoritate ratiocinationem ver&longs;ari circa Mathematicas, imaginationem <lb/>
ver&ograve; circa res phy&longs;icas, contra quam ip&longs;i contendebat. </s>
          <s id="s.005428">Verum quid opus <lb/>
e&longs;t authoritate, vbi res ip&longs;a videri pote&longs;t, con&longs;ideret quilibet Geometricas <lb/>
demon&longs;trationes, clar&egrave; videbit opus quidem e&longs;&longs;e non mediocri imagina&shy;<lb/>
tione, &longs;ed multo maiori di&longs;cur&longs;u, &longs;unt enim in nonnullis, 50. &amp; 60. con&longs;e&shy;<lb/>
quenti&aelig;, vna po&longs;t alteram inuicem connex&aelig;. </s>
          <s id="s.005429">Sed quid dico in nonnullis c&ugrave;m <lb/>
totum Euclidis opus &longs;it perpetua qu&aelig;dam illationum catena mirabilis, ita <lb/>vt vltim&aelig; ip&longs;ius demon&longs;trationes contineant, &longs;i re&longs;oluantur con&longs;ecutionum <lb/>
miriadas; at ver&ograve; omnis illationis expers pror&longs;us e&longs;t imaginatio. </s>
          <s id="s.005430">Si ver&ograve; <lb/>
ip&longs;arum inuentionem con&longs;ideremus, admirabiles omnin&ograve; videbuntur, tum <lb/>
quia res omnino ab&longs;tru&longs;as, &amp; abditas <expan abbr="dem&otilde;&longs;trant">demon&longs;trant</expan>, tum quia media, quibus <lb/>
eas <expan abbr="c&otilde;probant">comprobant</expan>, diuino ingenij acumine indigent, vt inue&longs;tigentur; vt prop&shy;<lb/>
terea earum authores nomina &longs;ua immortalitati con&longs;ecrarint; &longs;ic Thale&shy;


<pb pagenum="24" xlink:href="009/01/308.jpg"/>tis Mile&longs;ij 5. primi; Oenipodis 11. Pythagoreorum 32. Pythagor&aelig; ip&longs;ius <lb/>
47. <expan abbr="inuentor&utilde;">inuentorum</expan> adhuc nomina celebrantur: Hippocrati quadra&longs;&longs;e lunulam, <lb/>
Archimedi Parabolam, quantam gloriam peperit? </s>
          <s id="s.005431">Apollonij Perg&etail;i Coni&shy;<lb/>
ca magni Geometr&aelig; nomen ei compararunt. </s>
          <s id="s.005432">h&aelig;c &amp; plura alia non &longs;olum <lb/>
puerilis ingenij acumen, verum etiam virilis captum magnis &longs;patijs &longs;upe&shy;<lb/>
rare videntur. </s>
          <s id="s.005433">Cur autem Ari&longs;t. dixerit puerum fieri po&longs;&longs;e Mathematicum <lb/>non autem &longs;apientem, aut naturalem, ip&longs;e declarat, quia <expan abbr="nimir&utilde;">nimirum</expan> in <expan abbr="vtraq;">vtraque</expan> <lb/>
eorum opus e&longs;t experientia, qu&aelig; in puero non e&longs;t, experientiam enim affert <lb/>
temporis longitudo: facilius tamen puer moralia intelligit, quam Geome&shy;<lb/>
trica, facilius enim e&longs;t intelligere quid virtus, quid vitium, &amp;c. </s>
          <s id="s.005434">quam quin&shy;<lb/>
tam, aut &longs;eptimam primi; non ideo tamen puer erit prudens, quia pruden&shy;<lb/>
tia non &longs;peculatiua, &longs;ed practica e&longs;t, <expan abbr="Itaq;">Itaque</expan> quod puer &longs;apiens, aut natura&shy;<lb/>
lis e&longs;&longs;e nequeat, defectus non e&longs;t ex parte intellectus, &longs;ed ex parte experien&shy;<lb/>
ti&etail;. </s>
          <s id="s.005435">Neque pr&aelig;terea dicend&aelig; pueriles &longs;unt, qu&ograve;d antiquitus, vt vult etiam <lb/>
Plato, pueris prim&ograve; <expan abbr="trader&etilde;tur">traderentur</expan>, quandoquidem in illis totius &aelig;tatis robur, <lb/>&amp; florem in&longs;umebant, c&ugrave;m ad 30. v&longs;q; &aelig;tatis annum in eis, occuparentur. <lb/>
</s>
          <s id="s.005436">pueriles merit&ograve; dicerentur, &longs;i in pueritia tant&ugrave;m eis operam dedi&longs;&longs;ent. </s>
          <s id="s.005437">Di&shy;<lb/>
cam &longs;yncer&egrave;, quod ip&longs;e, dum eas per plures annos docerem expertus &longs;um; <lb/>
<expan abbr="quo&longs;cunq;">quo&longs;cunque</expan> reperi ingenio in Mathematicis pollere, hi pariter in alijs omni&shy;<lb/>
bus excellebant. </s>
          <s id="s.005438">Requirit enim &longs;tudium i&longs;tud omnes ingenij partes, imagi&shy;<lb/>
nationem, di&longs;cur&longs;um, &amp; memoriam. </s>
          <s id="s.005439">Idcirc&ograve; veteres puerorum ingenium <lb/>
ad Mathematicas qua&longs;i ad Lydium lapidem experiebantur; <expan abbr="ijs&qacute;">ijsque</expan> inepti &agrave; <lb/>
reliquis &longs;tudijs arcebantur. </s>
          <s id="s.005440">audi Platonem 7. de Repub. <!-- KEEP S--></s>
          <s id="s.005441">An &amp; hoc aduer&shy;<lb/>
ti&longs;ti, quod homines natura Arithmetici ad omnes doctrinas, vt ita dixerim <lb/>acuti videantur.&rpar; &amp; po&longs;tea concludens ait, propter omnes, quas adduxi&shy;<lb/>
mus rationes, haud quaquam negligenda h&aelig;c &longs;unt, &longs;ed in his pr&aelig;cipu&egrave; eru&shy;<lb/>
diendi, qui optimis &longs;unt ingenijs.</s>
        </p>
        <p type="main">
          <s id="s.005442">Quinta, Geometria carpitur, qu&ograve;d plures habeat demon&longs;trationes per <lb/>
&longs;uperpo&longs;itionem factas, qui modus demon&longs;trandi videtur aduer&longs;arijs vald&egrave; <lb/>
imperfectus, ac pen&egrave; ridiculus. </s>
          <s id="s.005443">Sed <expan abbr="&longs;ci&etilde;dum">&longs;ciendum</expan> prim&ograve; in toto Euclide e&longs;&longs;e <expan abbr="tan-t&utilde;modo">tan&shy;<lb/>
tummodo</expan> tres per &longs;uperpo&longs;itionem. </s>
          <s id="s.005444">Secund&ograve;, eas e&longs;&longs;e tam perfectas, ac eui&shy;<lb/>dentes, qu&agrave;m reliqu&aelig;; falluntur, qui putant illam &longs;uperpo&longs;itionem e&longs;&longs;e de&shy;<lb/>
mon&longs;trationis medium, e&longs;t enim loco con&longs;tructionis: neque, qu&aelig; proban&shy;<lb/>
da &longs;unt &aelig;qualia, ea &longs;uperponuntur, vt ip&longs;i putant, h&aelig;c enim ratio nullius e&longs;&shy;<lb/>
&longs;et momenti, nec Geometrica, &longs;ed Phy&longs;ica potius, niteretur enim &longs;en&longs;ibus: <lb/>
&longs;ed &longs;uperponuntur qu&aelig;dam, qu&aelig; &aelig;qualia &longs;unt, vt ex eorum &longs;uperpo&longs;itione <lb/>
appareat &aelig;qualitas eorum, qu&aelig; non &longs;uperponuntur. </s>
          <s id="s.005445">Con&longs;idera quartam <lb/>
primi videbis ibi &longs;uperponi qu&aelig;dam latera &aelig;qualia duorum triangulorum, <lb/>
vt deinde ba&longs;es, qu&aelig; non &longs;uperponuntur, inferantur e&longs;&longs;e &aelig;quales: &amp; ratio, <lb/>
qua probantur &aelig;quales e&longs;t, quia congruunt, non quia &longs;uperponuntur, vt ip&longs;i <lb/>
putant, nec intelligunt, quodnam &longs;it illius demon&longs;trationis medium.</s>
        </p>
        <p type="main">
          <s id="s.005446">Sexta calumnia ridicula, e&longs;t cuiu&longs;dam, qui Geometras reprehendit, qu&ograve;d <lb/>
&longs;&aelig;p&egrave; vtantur circulo, vt patet, inquit, in prima, 6. 4. &amp; 8. primi elem. </s>
          <s id="s.005447">&longs;i. </s>
          <s id="s.005448">n. </s>
          <s id="s.005449">lo&shy;<lb/>
quatur de circulo, qui figura e&longs;t, in &longs;ola <expan abbr="car&utilde;">carum</expan> prima is adhibetur, vt patet, vel <lb/>
figuras ip&longs;as more puerorum &longs;pectanti: &longs;i loquatur de circulo, qu&ograve;d vitium <lb/>
e&longs;t in <expan abbr="dem&otilde;&longs;trando">demon&longs;trando</expan>, id multo magis fal&longs;um e&longs;t, c&ugrave;m in nulla <expan abbr="ear&utilde;">earum</expan> reperiatur.</s>
        </p>
        <pb pagenum="25" xlink:href="009/01/309.jpg"/>
        <p type="main">
          <s id="s.005450">Septima e&longs;t, qua dicunt Geometras non habere materiam veram, &amp; pro&shy;<lb/>
priam, ea enim Phy&longs;ica e&longs;t, &amp; proinde <expan abbr="neq;">neque</expan> cau&longs;am materialem. </s>
          <s id="s.005451">Sed dic&eacute;&shy;n<lb/>
dum e&longs;t Geometras <expan abbr="quid&etilde;">quidem</expan> carere propria materia phy&longs;ica, non carere ta&shy;<lb/>
men propria materia Mathematica, qu&aelig; e&longs;t illa intelligibilis, de qua cap. 1. <lb/>
dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005452">Octaua, e&longs;t cuiu&longs;dam dicentis, opinionem <expan abbr="commun&etilde;">communem</expan> e&longs;&longs;e, Mathematicam <lb/>non e&longs;&longs;e propri&egrave; &longs;cientiam; &longs;ed hoc manife&longs;t&egrave; fal&longs;um e&longs;t, cum inter tot Phi&shy;<lb/>lo&longs;ophos Gr&aelig;cos, Arabes, Latinos, &longs;ol&ugrave;m ip&longs;e duos, vel tres huius &longs;enten&shy;<lb/>
ti&aelig; in medium po&longs;&longs;it afferre, Piccolom. .&longs;. </s>
          <s id="s.005453">quem &longs;equitur Pererius.</s>
        </p>
        <p type="main">
          <s id="s.005454">Nona, e&longs;t alterius, qui Geometras damnat, qu&ograve;d plura reuocant ad illud <lb/>
vniuer&longs;ale axioma, qu&aelig; &longs;unt eadem vni tertio, &longs;unt eadem inter &longs;e. </s>
          <s id="s.005455">Ver&ugrave;m <lb/>
i&longs;te mal&egrave; Geometrarum principia nouit, axioma enim illud, nu&longs;quam apud <lb/>
Mathematicos reperitur, <expan abbr="neq;">neque</expan> reperiri <expan abbr="p&otilde;t">pot.</expan>, cum <expan abbr="quantitat&etilde;">quantitatem</expan> non inuoluat.</s>
        </p>
        <p type="main">
          <s id="s.005456">Decima, qua dicunt entia Mathematica non extare: &longs;ed ex initio dictis <lb/>
de materia intelligibili h&etail;c nota &longs;atis detergitur.</s>
        </p>
        <p type="main">
          <s id="s.005457">Vndecima, ab&longs;tractionem &agrave; materia <expan abbr="mult&utilde;">multum</expan> derogare perfectioni Mathe&shy;<lb/>
maticarum demon&longs;trationum; cui re&longs;pondeat eruditi&longs;&longs;imus Toletus, qui <lb/>
in 2. Phy&longs;. qu&aelig;&longs;t. </s>
          <s id="s.005458">4. &longs;ic ait: Phy&longs;icus frequentet vtitur demon&longs;tratione effe&shy;<lb/>
ctus, &amp; &longs;igni, quia ip&longs;ius cau&longs;&aelig; frequentius &longs;unt occult&aelig; nec per &longs;e &longs;en&longs;ibiles, <lb/>
at Mathematicus frequentius &agrave; prioribus procedit, c&ugrave;m eius cau&longs;&aelig; notio&shy;<lb/>
res &longs;int effectibus, &agrave; &longs;en&longs;u .n. </s>
          <s id="s.005459">ab&longs;trahit, &amp; in intellectu notius e&longs;t, qu&ograve;d prius <lb/>
e&longs;t. </s>
          <s id="s.005460">Po&longs;tea in 4. conclu&longs;. </s>
          <s id="s.005461">&longs;ic ait: omnem phy&longs;ic&aelig; imperfectionem &agrave; materia <lb/>
pendere, vnde Ari&longs;t. 2. Metaphy. <!-- REMOVE S-->tex. <!-- REMOVE S-->16. tradens huius non exact&aelig; certitu&shy;<lb/>
dinis rationem ait: natura materiam habet: &amp; po&longs;t pauca: At res Mathe&shy;<lb/>
matic&aelig;, c&ugrave;m ab hac materia &longs;eparent &longs;impliciter nece&longs;&longs;ari&aelig; &longs;unt, &longs;emper <lb/>
enim omnis triangulus habet tres angulos &aelig;quales duobus rectis. </s>
          <s id="s.005462">ex quibus <lb/>
apparet omnem Mathematicarum perfectionem oriri ex ab&longs;tractione, con&shy;<lb/>
tr&agrave; qu&agrave;m putabat aduer&longs;arius.</s>
        </p>
        <p type="main">
          <s id="s.005463">Duodecima e&longs;t, Mathematicas ab&longs;trahere &agrave; Bono: ver&ugrave;m eas ab ea libe&shy;<lb/>
rat Ari&longs;t. dum lib. 13. Metaphy&longs;. ait: qui dicunt Mathematicas &longs;cientias ni&shy;<lb/>
hil de bono, vel pulchro dicere, fal&longs;um dicunt: dicunt enim, &amp; maxim&egrave; <expan abbr="o&longs;t&etilde;-dunt">o&longs;ten&shy;<lb/>
dunt</expan>, nam etiam&longs;i non nominant, quia tamen opera, &amp; rationes o&longs;tendunt, <lb/>
non ne dicunt de eis? </s>
          <s id="s.005464">pulchri <expan abbr="nam&qacute;">namque</expan>; maxim&egrave; &longs;pecies &longs;unt, ordo, commen&shy;<lb/>
&longs;uratio, &amp; definitum, qu&aelig; maxim&egrave; &agrave; Mathematicis &longs;cientijs o&longs;tenduntur.</s>
        </p>
        <p type="main">
          <s id="s.005465">Decimatertia e&longs;t, <expan abbr="Geometri&atilde;">Geometriam</expan>, &amp; <expan abbr="Arithmetic&atilde;">Arithmeticam</expan>, vt &longs;unt &longs;peculatiu&aelig; &longs;cien&shy;<lb/>
ti&etail; e&longs;&longs;e inutiles, <expan abbr="atq;">atque</expan> iniucundas. </s>
          <s id="s.005466">Sed h&aelig;c oppo&longs;itio in omnes quadrat &longs;pe&shy;<lb/>
culatiuas, qu&aelig; non vtiles, &longs;ed gratia &longs;ui &longs;unt. </s>
          <s id="s.005467">quod maxim&egrave; ij &longs;olent oppo&shy;<lb/>
nere, qui &longs;cientias, vt ille cecinit cauponantur, &longs;eu qui eas qu&aelig;&longs;tuo&longs;as fa&shy;<lb/>
ciunt. </s>
          <s id="s.005468">Ver&ugrave;m hos animo mercatores potius, qu&agrave;m Philo&longs;ophos amande&shy;<lb/>
mus ad cap. 8. 9. &amp; 10. libri primi Procli, vbi fus&egrave; de vtilitate <expan abbr="ear&utilde;">earum</expan> omnium <lb/>
di&longs;&longs;erit. </s>
          <s id="s.005469">Quod &longs;i Philo&longs;ophus &longs;it, qui h&aelig;c opponat; huic illa &longs;ufficiat vtili&shy;<lb/>
tas, qua loca omnia Ari&longs;t. Mathematica, qu&etail; fer&egrave; <expan abbr="quadring&etilde;ta">quadringenta</expan> &longs;unt, facil&egrave; <lb/>
Mathematicarum auxilio intelliguntur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; ad plenam totius Ari&longs;t. intel&shy;<lb/>
ligentiam, tandem perueniri pote&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005470">Quod attinet ad delectationem inuenient, inibi apud Proclum h&aelig;c, cui <lb/>Mathematicarum di&longs;ciplinarum cognitionem &longs;pernunt, voluptates, qu&aelig; in <pb pagenum="26" xlink:href="009/01/310.jpg"/>ip&longs;is &longs;unt, minim&egrave; degu&longs;tarunt. </s>
          <s id="s.005471">&amp; qu&igrave; Mathematicas ignorant iecunas ca&shy;<lb/>
piunt voluptates. </s>
          <s id="s.005472">Ex quibus fit, vt viri nobiles, ac Principes, qu&igrave; non lu&shy;<lb/>
crandi, &longs;ed philo&longs;ophandi cau&longs;a literis dant operam, Mathematicis maxi&shy;<lb/>
m&egrave; &longs;tudijs delectentur. </s>
          <s id="s.005473">inter quos celeberrimi extiterunt, ex antiquis qui&shy;<lb/>
dem Archimedes Regum Sicili&aelig; con&longs;anguineus; Boetius vir con&longs;ularis; <lb/>
Alphon&longs;us Rex <expan abbr="Hi&longs;paniar&utilde;">Hi&longs;paniarum</expan>: no&longs;tra ver&ograve; &aelig;tate Marchio Guidobaldus, Prin&shy;<lb/>
ceps Ticho Brahe; Franci&longs;cus Candalla, &amp; alij complures, quorum monu&shy;<lb/>
menta in omne &aelig;uum perman&longs;ura mundus admirabitur.</s>
        </p>
        <p type="main">
          <s id="s.005474">Decimaquarta, &longs;ubiecti ignobilitatem Mathematicis exprobrant, quod <lb/>
videlicet &longs;it accidens. </s>
          <s id="s.005475">&longs;ed re&longs;pondetur prim&ograve;, quod quamuis &longs;it accidens, <lb/>
e&longs;t tamen immateriale, &amp; ab&longs;tractum, qua ratione inter &longs;ubiectum Phy&longs;ic&aelig;, <lb/>
&amp; Mathematic&aelig; collocatur. </s>
          <s id="s.005476">&longs;ecund&ograve;, melius e&longs;&longs;e de aliquo accidente veri&shy;<lb/>tates innumeras cogno&longs;cere, <expan abbr="eas&qacute;">easque</expan>; admirabiles, qu&agrave;m circa <expan abbr="&longs;ub&longs;tanti&atilde;">&longs;ub&longs;tantiam</expan> ma&shy;<lb/>
terialem pr&aelig;&longs;ertim, mille opinionum turbis, ac di&longs;&longs;en&longs;ionibus perpetu&ograve; huc <lb/>
illuc agitari, <expan abbr="neq;">neque</expan> vnquam ad vllius &longs;ub&longs;tanti&aelig; cognitionem peruenire. </s>
          <s id="s.005477">ter&shy;<lb/>
ti&ograve;, in Mathematicis medijs aliter &longs;e habere, vbi non nudam quantitatem, <lb/>
&longs;ed vel c&oelig;le&longs;tia corpora omnium nobili&longs;&longs;ima, vel &longs;onos mu&longs;icos, vel vi&longs;ionis <lb/>
modos, ac deceptiones, vel cau&longs;as virium machinarum eodem fine, ac &longs;co&shy;<lb/>
po, quo c&aelig;teri Philo&longs;ophi c&aelig;tera contemplantur.</s>
        </p>
        <p type="main">
          <s id="s.005478">Decimaquinta e&longs;t, quod &longs;iue ioco, &longs;iue ex eruditionis ignoratione addunt <lb/>
Mathematicos legibus tum prophanis, tum &longs;acris &longs;&aelig;pius pro&longs;criptos, ac <lb/>
damnatos fui&longs;&longs;e; <expan abbr="atq;">atque</expan> olim non rar&ograve; Imperatorum editis Romano imperio <lb/>
pul&longs;os. </s>
          <s id="s.005479">Ver&ugrave;m i&longs;tis nequaquam opus e&longs;&longs;et re&longs;pondere, c&ugrave;m vix nullus ade&ograve; <lb/>
eruditionis expers reperiatur, qu&igrave; ignoret illos p&longs;eudomathematicos fui&longs;&longs;e <lb/>
eos, qu&igrave;, &amp; quidem aptius, &amp; Genethliaci, &amp; Chald&aelig;i, &amp; Iudiciarij dice&shy;<lb/>
bantur. </s>
          <s id="s.005480">quorum doctrina nullo mihi pacto probari pote&longs;t, c&ugrave;m nullis nec <lb/>
experientijs, nec rationibus fulciatur, &longs;ed mera vanitas, <expan abbr="atq;">atque</expan> impo&longs;tura, &longs;&aelig;&shy;<lb/>
p&egrave; etiam &longs;uper&longs;titio &longs;it. </s>
          <s id="s.005481">vt propterea mirandum &longs;it, cur non p&etail;nitus huiu&longs;&shy;<lb/>
modi artes de medio tollantur, &longs;ed quod ait Cor. <!-- REMOVE S-->Tacitus lib. 1. hi&longs;tor. </s>
          <s id="s.005482">hoc <lb/>
genus hominum potentibus infidum, &longs;perantibus fallax, in Ciuitate no&shy;<lb/>
&longs;tra, &amp; vetabitur &longs;emper, &amp; retinebitur. </s>
          <s id="s.005483">lege libros 12. Pici Mirandulani <lb/>
contra A&longs;trologos. <!-- KEEP S--></s>
          <s id="s.005484">accedunt pr&aelig;terea Tycho, &amp; Keplerus, qu&igrave; quamuis <lb/>
A&longs;tronomi, A&longs;tronomiam tamen i&longs;tam pluribus improbarunt. </s>
          <s id="s.005485">Calumnios&egrave; <lb/>
tamen ij faciunt, qu&igrave; illorum nebulonum culpam in omnes Mathematicos <lb/>
transferre ge&longs;tiunt. </s>
          <s id="s.005486"><expan abbr="Atq;">Atque</expan> h&aelig;c tantummodo dicta velim, ne &longs;impliciores ab <lb/>
i&longs;tis calumniatoribus decipiantur.</s>
        </p>
        <p type="main">
          <s id="s.005487">Decima&longs;exta, qua in vniuer&longs;um proponunt hoc modo, vtrum Mathema&shy;<lb/>
tic&aelig; h. </s>
          <s id="s.005488">beant perfectas demon&longs;trationes, po&longs;tea in di&longs;cur&longs;u multa contra <lb/>eas adducunt, qu&aelig; tandem in fine tractationis contra &longs;olas Geometriam, &amp; <lb/>
Arithmeticam valere fatentur. </s>
          <s id="s.005489">Quare ni&longs;i lector ad finem <expan abbr="v&longs;q;">v&longs;que</expan> omnia per&shy;<lb/>
legerit, quod rar&ograve; accidit, decipitur, putat enim in omnes Mathematicas <lb/>
illa quadrare, c&ugrave;m tamen ip&longs;i fateantur, &longs;e nunquam loquutos e&longs;&longs;e de me&shy;<lb/>
dijs A&longs;tronomia, Mu&longs;ica, Optica, Mechanica, quibus ine&longs;&longs;e veram &longs;cienti&aelig; <lb/>
demon&longs;tratiu&aelig; rationem libenter concedunt.</s>
        </p>
        <p type="main">
          <s id="s.005490">Decima&longs;eptima, e&longs;t cuiu&longs;dam recenti&longs;&longs;imi Philo&longs;ophi, qu&igrave; vbi pluribus <lb/>
contra Mathematicas di&longs;&longs;eruit, nihil, vt fieri &longs;olet, &longs;ibi obijcit, <expan abbr="ver&utilde;">verum</expan> com&shy;


<pb pagenum="27" xlink:href="009/01/311.jpg"/>plura Ari&longs;t. &amp; veterum philo&longs;ophorum loca &longs;ibi aduer&longs;antia di&longs;&longs;imulat: tan&shy;<lb/>
dem, quod nullus adhuc au&longs;us e&longs;t, concludit Mathematicam nullam e&longs;&longs;e <lb/>
Philo&longs;ophi&aelig; partem, c&ugrave;m tamen apud Ari&longs;t. &amp; omnes peripateticos nihil <lb/>
frequentius occurrat, quam tres e&longs;&longs;e philo&longs;ophi&aelig; partes, Phy&longs;icam, Mathe&shy;<lb/>
maticam, &amp; Metaphy&longs;icam. </s>
          <s id="s.005491">ait pr&aelig;terea &longs;&aelig;pius certitudinem Mathemati&shy;<lb/>
cam ex eo prouenire, quod ad &longs;en&longs;um o&longs;tendant, &longs;eu quod &longs;en&longs;u ip&longs;arum ve&shy;<lb/>
ritates percipiantur; quod omnin&ograve; fal&longs;um e&longs;&longs;e &longs;&aelig;pius &longs;upra probatum e&longs;t, <lb/>
c&ugrave;m eorum materia &longs;it omnin&ograve; intelligibilis, non autem &longs;en&longs;ibilis, &amp; nullus <lb/>
e&longs;t, qui eas, vel leuiter attigerit, qu&igrave; i&longs;tud pal&agrave;m non fateatur.</s>
        </p>
        <p type="main">
          <s id="s.005492">Scias <expan abbr="deniq;">denique</expan> candide Lector, me &longs;yncer&egrave; omnia, &amp; &longs;olius veritatis amo&shy;<lb/>
re hucu&longs;que dixi&longs;&longs;e, vt experiri poteris, &longs;i authores, quos citaui, adieris, <lb/>quod vt facias, ob&longs;ecro, plura enim, quam dixi, reperies. </s>
          <s id="s.005493">&egrave; contrari&ograve; vi&shy;<lb/>
di&longs;ti, qu&agrave;m &longs;olicit&egrave;, alij, quorum munus e&longs;&longs;et eas fouere, ac tueri, <expan abbr="c&otilde;tra">contra</expan> pul&shy;<lb/>cherrimas ha&longs;ce facultates, ne&longs;cio quo con&longs;ilio tam &longs;olicit&egrave; egerint.</s>
        </p>
        <p type="head">
          <s id="s.005494"><emph type="italics"/>De pr&aelig;stantia &longs;cienti&aelig;, quam nobis pariunt Geometria, <lb/>
&amp; Arithmetica. <!-- KEEP S--></s>
          <s id="s.005495">Cap. 4.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005496">Scientiarum nobilitas, <expan abbr="atq;">atque</expan> pr&aelig;&longs;tantia non ex &longs;ubiecto, &amp; medio &longs;o&shy;<lb/>
lum, ver&ugrave;m etiam, &amp; quidem mult&ograve; magis ex notitia, qu&aelig; per illas <lb/>
acquiritur, <expan abbr="quippe&qacute;">quippeque</expan>; illarum finis e&longs;t, pen&longs;anda e&longs;t: quanto enim h&aelig;c <lb/>
pr&aelig;&longs;tantior, ac nobilior e&longs;t, tanto etiam ill&aelig; excellentiores &longs;unt ha&shy;<lb/>
bend&aelig;. </s>
          <s id="s.005497">Verumenimuer&ograve;, vt ait Ari&longs;t. initio 2. Metaphyl. <!-- KEEP S--></s>
          <s id="s.005498">Finis &longs;cienti&aelig; e&longs;t <lb/>
veritas. </s>
          <s id="s.005499">quod &amp; Plato confirmat, dum in Sympo&longs;io a&longs;&longs;erit, animi cibum e&longs;&shy;<lb/>
&longs;e veritatem, atqui Geometria, &amp; Arithmetica, c&ugrave;m &longs;emper euidentiam <lb/>
pariant, &longs;emper etiam veritatem con&longs;equentur, vnde Ari&longs;t. 1. Ethic. <!-- REMOVE S-->cap. 7. <lb/>
Geometram appellat veritatis &longs;peculatorem. </s>
          <s id="s.005500">c&ugrave;m pr&aelig;terea reliqu&aelig; &longs;cien&shy;<lb/>
ti&aelig; &lpar;Mathematicis medijs exceptis&rpar; rar&ograve; euidentiam pariant, rar&ograve; etiam <lb/>
veritatem a&longs;&longs;equentur, &longs;ed fer&egrave; &longs;emper opiniones gignent, vnde eas merit&ograve; <lb/>
non &longs;cientias, &longs;ed opiniones Plato voluit appellari: &longs;equitur ab&longs;olut&egrave; di&shy;<lb/>
cendum e&longs;&longs;e, Mathematicas reliquarum &longs;cientiarum pr&aelig;&longs;tanti&longs;&longs;imas e&longs;&longs;e; <lb/>
quemadmodum inter opiniones pr&aelig;&longs;tanti&longs;&longs;imum quid e&longs;t veritas.</s>
        </p>
        <p type="main">
          <s id="s.005501"><expan abbr="Neq;">Neque</expan> ver&ograve; &longs;olum huius notiti&aelig; excellentia &agrave; veritate de&longs;umitur, verum <lb/>
etiam ab admirabilitate, &longs;unt enim conclu&longs;iones Mathematic&aelig; &lpar;paruis ex&shy;<lb/>
ceptis&rpar; admirabiles veritates, licet enim c&ugrave;m Cicer. <!-- REMOVE S-->primo de orat &longs;ic ad&shy;<lb/>
mirati; quis ignorat, ij, qui Mathematici vocantur quanta in ob&longs;curitate <lb/>
rerum, &amp; qu&agrave;m in recondita arte, &amp; multiplici, <expan abbr="&longs;ubtili&qacute;">&longs;ubtilique</expan>; ver&longs;antur? </s>
          <s id="s.005502">Et ve&shy;<lb/>
r&ograve; quis non admiratur, c&ugrave;m intelligit, omne triangulum habere tres angu&shy;<lb/>
los &aelig;quales duobus rectis? </s>
          <s id="s.005503">&amp; omnem figuram rectilineam habere angulos <lb/>
externos, etiam&longs;i mille &longs;int, &aelig;quales tantummodo quatuor rectis? </s>
          <s id="s.005504">Item <lb/>
duo parallelogramma &longs;uper eadem ba&longs;i, &amp; in ij&longs;dem parallelis con&longs;tituta <lb/>
&aelig;qualia e&longs;&longs;e, etiam&longs;i alterum quantumuis longum efficiatur? </s>
          <s id="s.005505">qu&agrave;m admira&shy;<lb/>
bilis e&longs;t 47. primi, pro cuius inuentione Pythagoras Mu&longs;is Hecatombas <lb/>
immolauit? </s>
          <s id="s.005506">In &longs;ecund&ograve; deinde Elem. lib. qu&agrave;m &longs;ubtilis e&longs;t 14. qu&aelig; rectili&shy;<lb/>
neo cuiuis quadratum exhibet &aelig;quale. </s>
          <s id="s.005507">In terti&ograve; po&longs;tea, quot <expan abbr="quanta&qacute;">quantaque</expan>; an&shy;


<pb pagenum="28" xlink:href="009/01/312.jpg"/>gulus ille contingenti&aelig; continet miracula, qui quamuis quantus &longs;it, neque <lb/>
tamen &agrave; linea recta partiri. </s>
          <s id="s.005508">&longs;ed ne longior &longs;im, quis in 10. libro con&longs;iderans <lb/>
illam tot magnitudinum a&longs;ymetriam, &amp; diametrum e&longs;&longs;e co&longs;t&aelig; incommen&shy;<lb/>
&longs;urabilem, non magnopere ob&longs;tupe&longs;cit, <expan abbr="atq;">atque</expan> cum Platone non a&longs;&longs;erit illius <lb/>
ignorantiam, non hominum, &longs;ed &longs;uum, ac pecorum e&longs;&longs;e? </s>
          <s id="s.005509">In 13. quanto <lb/>
&longs;tupore afficimur in illa <expan abbr="quinq;">quinque</expan> regularium corporum in eadem &longs;ph&aelig;ra in&shy;<lb/>
&longs;criptione? </s>
          <s id="s.005510">&amp; cum intelligimus <expan abbr="quinq;">quinque</expan> tantum in tota rerum natura repe&shy;<lb/>
riri po&longs;&longs;e &longs;olida regularia? </s>
          <s id="s.005511">merit&ograve; igitur Cardanus lib. 16. de &longs;ubtilit. </s>
          <s id="s.005512">ait; <lb/>
Euclidis &longs;unt du&aelig; pr&aelig;cipu&aelig; laudes, inconcu&longs;&longs;a dogmatum firmitas libri <lb/>
elementorum, <expan abbr="perfectio&qacute;">perfectioque</expan>; ade&ograve; ab&longs;oluta, vt nullum opus iur&egrave; huic compa&shy;<lb/>
rare audeas, quibus fit, vt ade&ograve; veritatis lux in eo refulgeat, vt ij &longs;oli in ar&shy;<lb/>
duis qu&aelig;&longs;tionibus videantur po&longs;&longs;e verum &agrave; fals&ograve; di&longs;cernere, qu&igrave; Euclidem <lb/>
habeant familiarem.</s>
        </p>
        <p type="main">
          <s id="s.005513">Quod &longs;i ad Archimedis opera oculum conuertamus, quam &longs;&aelig;p&egrave; nos ea <lb/>
reddunt &longs;tupefactos? </s>
          <s id="s.005514">vt dum o&longs;tendit triangulum quoddam e&longs;&longs;e dato cir&shy;<lb/>
culo &aelig;quale. </s>
          <s id="s.005515">dum Parabolam ad quadratum redigit: dum planorum centra <lb/>
grauitatis rimatur: dum totius aren&aelig; mundum vniuer&longs;um complentis nu&shy;<lb/>
merum &longs;ubducit: dum quodlibet pondus, <expan abbr="atq;">atque</expan> ade&ograve; mundi machinam loco <lb/>
dimoueri po&longs;&longs;e, vel ab vnica formica demon&longs;trat. </s>
          <s id="s.005516">quamquam h&aelig;c duo ad <lb/>
medias pertinent. </s>
          <s id="s.005517">At libellus de lineis &longs;piralibus, &amp; alter de ijs, qu&aelig; in aqua <lb/>
vehuntur, quam admirandi &longs;unt? </s>
          <s id="s.005518">De &longs;ph&aelig;ra po&longs;tea, &amp; cylindro varia de&shy;<lb/>mon&longs;trans, quanto &amp; alios, ac &longs;e ip&longs;um &longs;patio &longs;uperat, vt dum inter c&aelig;tera <lb/>
diuino plan&egrave; acumine o&longs;tendit cuiu&longs;libet &longs;ph&aelig;r&aelig; &longs;uperficiem quadruplam <lb/>e&longs;&longs;e circuli eiu&longs;dem maximi. </s>
          <s id="s.005519">Item &longs;i tria h&aelig;c, cylindrus, &longs;ph&aelig;ra, &amp; conus, <lb/>
&longs;int in eadem altitudine, <expan abbr="eorum&qacute;">eorumque</expan>; ba&longs;es &longs;int circuli maximi illius &longs;ph&aelig;r&aelig;, <lb/>
habere inuicem proportionem, quam <expan abbr="hab&etilde;t">habent</expan> hi numeri 3. 2. 1. quare ob tam <lb/>
pr&aelig;clarum ingenij monumentum, &longs;epulcro ip&longs;ius marmoreo &longs;ph&aelig;ra, &amp; cy&shy;<lb/>lindrus marmorei &longs;unt impo&longs;iti, quemadmodum Cicero lib. 5. Tu&longs;cinarrat, <lb/>
vbi etiam magnopere gloriatur, &longs;e cum in Sicilia Qu&aelig;&longs;tor e&longs;&longs;et, illud igno&shy;<lb/>ratum ab Syracu&longs;anis &longs;eptum vndique, ac ve&longs;titum vepribus, &amp; dumetis in&shy;<lb/>
daga&longs;&longs;e &longs;epulcrum. </s>
          <s id="s.005520">merit&ograve; igitur Cardanus lib. 16. de &longs;ubtil. </s>
          <s id="s.005521">eum tanquam <lb/>
ingeniorum Ph&aelig;nicem &longs;upra omnes &longs;ubtilitate pr&aelig;&longs;tantes viros, <expan abbr="atq;">atque</expan> adeo <lb/>
&longs;upra Ari&longs;tot. ip&longs;um duplici ordine euexit; Archimedes, inquit, primus &longs;it <lb/>
non &longs;olum ob monumenta illius nunc vulgata, &longs;ed ob mechanica, quibus <lb/>
vires Romanorum &longs;&aelig;pius fregit. </s>
          <s id="s.005522">Apollonius deinde perg&aelig;us cognomento <lb/>
Magnus Geometra, nulla ratione Archimede inferior, quam mira, quam <lb/>
ab&longs;tru&longs;a in &longs;uis conicis in lucem profert? </s>
          <s id="s.005523">&longs;ed inter c&aelig;tera illud <expan abbr="admir&atilde;dum">admirandum</expan>; <lb/>
inueniri duas lineas, quas vocat a&longs;ymptotos, qu&aelig; &longs;i in infinitum producan&shy;<lb/>
tur, &longs;emper magis inuicem accedunt, nunquam tamen concurrunt. </s>
          <s id="s.005524">mi&longs;&longs;os <lb/>
facio Hip&longs;iclem, Theodo&longs;ium tripolitam, Menelaum, Serenum, Pappum, &amp; <lb/>
alios, quorum opera omnem &longs;uperant admirationem, <expan abbr="ea&qacute;">eaque</expan>; mirabili adeo <lb/>
connexione, ac certitudine tradita, vt nullus &longs;it, qui pri&longs;cis illis Geometris <lb/>
ingenio cedere libenter nolit. </s>
          <s id="s.005525">Quapropter cum Cardano lib. 16. de &longs;ubtil. <lb/>
</s>
          <s id="s.005526">hanc partem concludamus; nihil mirum igitur, inquit, Geometriam e&longs;&longs;e <lb/>omnium &longs;cientiarum &longs;ubtili&longs;&longs;imam, qu&aelig; c&ugrave;m tamen &agrave; manife&longs;ti&longs;&longs;imis ini&shy;<lb/>
tium ducat, merit&ograve; an&longs;am pr&aelig;buit, vt prima omnium etiam pueros doce&shy;


<pb pagenum="29" xlink:href="009/01/313.jpg"/>retur. </s>
          <s id="s.005527">mirum e&longs;t, quam breui ex aperti&longs;&longs;imis ad ob&longs;curi&longs;&longs;ima trahat, &amp; ex <lb/>
humillimis in alti&longs;&longs;ima &longs;tatim a&longs;&longs;urgat.</s>
        </p>
        <p type="main">
          <s id="s.005528">Sed iam Arithmetic&aelig; etiam fructus in&longs;piciamus: in qua pr&etail;ter ea, qu&aelig; <lb/>
Euclides, Iordanus, &amp; Maurolicus egregia &longs;an&egrave; adinuenerunt, qu&agrave;m mira&shy;<lb/>
bile e&longs;t illud veluti &longs;cientiarum mon&longs;trum, ac portentum, quod Algebram <lb/>
vocant? </s>
          <s id="s.005529">nihil forta&longs;&longs;e in tota periti&aelig; Encyclopedia &longs;ubtilius, profundius ni&shy;<lb/>
hil, non humano ingenio par e&longs;t, &longs;ed quid c&oelig;litus reuelatum dixeris: nume&shy;<lb/>
ros illos, quos &longs;urdos vocant, &amp; qui nullo modo exprimi po&longs;&longs;unt, addit, &longs;ub&shy;<lb/>
trahit, multiplicat, diuidit, perinde ac &longs;i numeri communes e&longs;&longs;ent: illis ve&shy;<lb/>
r&ograve;, quos minores, qu&agrave;m nihil <expan abbr="c&otilde;fingit">confingit</expan>, quid ab&longs;tru&longs;ius? </s>
          <s id="s.005530">quibus tamen <expan abbr="vtri&longs;&qacute;">vtri&longs;que</expan>; <lb/>admirandas ade&ograve; di&longs;&longs;oluit qu&aelig;&longs;tiones, &amp; enigmata, vt ij, qui hanc callent <lb/>
eruditionem, nihil in numerorum infinita ditione <expan abbr="ob&longs;cur&utilde;">ob&longs;curum</expan>, nihil arduum ti&shy;<lb/>
meant; vt propterea eos non homines, &longs;ed vel intelligentias qua&longs;dam &longs;epa&shy;<lb/>
ratas, aut pr&aelig;&longs;tigiatores quo&longs;dam e&longs;&longs;e exi&longs;times.</s>
        </p>
        <p type="main">
          <s id="s.005531">Hanc tandem Geometri&aelig;, &amp; Arithmetic&aelig; tractationem ab&longs;oluentes, ex <lb/>
pr&etail;dictis breuiter earum pr&aelig;rogatiuas &longs;ic per&longs;tringamus: quarum.</s>
        </p>
        <p type="main">
          <s id="s.005532">Prima &longs;it, qu&ograve;d omnes &longs;cienti&aelig; partes ab inuicem di&longs;tinctas obtinent, vi&shy;<lb/>
delicet primo loco definitiones, <expan abbr="eas&qacute;">easque</expan>; e&longs;&longs;entiales. </s>
          <s id="s.005533">Secund&ograve;, po&longs;tulata. </s>
          <s id="s.005534">Ter&shy;<lb/>ti&ograve;, axiomata, qu&etail; &longs;unt tria principiorum genera; ex quibus &longs;cientia dedu<lb/>
citur. </s>
          <s id="s.005535">quapropter quarto loco &longs;uccedunt propo&longs;itiones cum &longs;uis demon&shy;<lb/>&longs;trationibus: qu&aelig; partim problemata, partim Theoremata &longs;unt. </s>
          <s id="s.005536">hunc por&shy;<lb/>
r&ograve; doctrin&aelig; ordinem pulcherrimum ab Ari&longs;t. etiam traditum, pr&aelig;terquam <lb/>
in Mathematicis, &amp; maxim&egrave; hi&longs;ce puris nu&longs;quam e&longs;t reperire.</s>
        </p>
        <p type="main">
          <s id="s.005537">Secunda, ex principiorum autem pr&aelig;mi&longs;&longs;orum certitudine fit, vt proce&shy;<lb/>
dant &agrave; notioribus nobis, &amp; natura.</s>
        </p>
        <p type="main">
          <s id="s.005538">Tertia, quod omnes earum comprobationes &longs;unt <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan>, partim <lb/>
&agrave; priori, partim &agrave; po&longs;teriori, vbi nihil probabile, nulla opinionum di&longs;cordia, <lb/>
&longs;ed totum euidens, concors, &amp; verum cernitur.</s>
        </p>
        <p type="main">
          <s id="s.005539">Quarta, demon&longs;trationes &agrave; priori &longs;unt tantum &agrave; cau&longs;is intrin&longs;ecis mate&shy;<lb/>
ria, &amp; forma.</s>
        </p>
        <p type="main">
          <s id="s.005540">Quinta, demon&longs;trationes earum, vt plurimum, &amp; quod, &amp; propter quid <lb/>
&longs;imul manife&longs;tant.</s>
        </p>
        <p type="main">
          <s id="s.005541">Sexta, e&longs;t mirabilis, &amp; perpetua demon&longs;trationum connexio, &amp; depen&shy;den<lb/>
tia ab inuicem.</s>
        </p>
        <p type="head">
          <s id="s.005542"><emph type="italics"/>De Mathematicis medijs, A&longs;tronomia, Per&longs;pectiua, <lb/>
Mathematica, Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005543">Cap. 5.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005544">De materia harum, c&ugrave;m apud Philo&longs;ophos conueniat, nihil e&longs;t, <lb/>
cur de ea dicamus. </s>
          <s id="s.005545">Eas ver&ograve; habere perfecti&longs;&longs;imas demon&longs;tra&shy;<lb/>
tiones, quibus etiam mirabiles veritates, <expan abbr="eas&qacute;">easque</expan>; &longs;citu iucundi&longs;&longs;i&shy;<lb/>
mas nobis patefaciunt, vna, <expan abbr="eadem&qacute;">eademque</expan>, opera breuiter demon&longs;tra&shy;<lb/>
bimus. </s>
          <s id="s.005546">non dee&longs;t tamen Ari&longs;t. authoritas 1. Po&longs;ter. tex. <!-- REMOVE S-->30. a&longs;&longs;erentis eas <lb/>
habere cau&longs;as demon&longs;trationum, &longs;ic. </s>
          <s id="s.005547">Hic enim ip&longs;um quidem qu&ograve;d &longs;en&longs;i&shy;<lb/>
tiuorum e&longs;t &longs;cire, ip&longs;um ver&ograve; propter quid Mathematicorum, hi <expan abbr="nam&qacute;">namque</expan>; ha&shy;


<pb pagenum="30" xlink:href="009/01/314.jpg"/>bent cau&longs;arum demon&longs;trationes. </s>
          <s id="s.005548">loquitur ibi de medijs hi&longs;ce facultatibus. <lb/>
</s>
          <s id="s.005549">vide no&longs;tram illius loci explicationem &longs;uperius allatam; aut &longs;i mais <expan abbr="alior&utilde;">aliorum</expan>. <lb/>
</s>
          <s id="s.005550">&longs;ed iam rem ip&longs;am oculis in&longs;piciamus.</s>
        </p>
        <p type="main">
          <s id="s.005551">Et, vt ab A&longs;tronomia <expan abbr="initi&utilde;">initium</expan> faciamus, <expan abbr="dem&otilde;&longs;tratio">demon&longs;tratio</expan> eclyp&longs;is Lun&aelig; &lpar;etiam <lb/>
Ari&longs;t. <!-- REMOVE S--><expan abbr="eius&qacute;">eiusque</expan>; interpretibus pr&aelig;cipu&egrave; Zabarella te&longs;tibus&rpar; non ne poti&longs;&longs;ima? <lb/>
</s>
          <s id="s.005552">nam affectionis illius, &longs;eu defectus propriam, &amp; ad&aelig;quatam cau&longs;am euiden<lb/>
tem facit, interpo&longs;itionem, videlicet terr&etail;. </s>
          <s id="s.005553">Idem de &longs;olari defectu dicen&shy;<lb/>
dum, cuius cau&longs;am o&longs;tendunt e&longs;&longs;e Lun&aelig; obiectionem. </s>
          <s id="s.005554">quas demon&longs;tratio&shy;<lb/>
nes ab A&longs;tronomis inuentas e&longs;&longs;e ex <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan> libris con&longs;tat. </s>
          <s id="s.005555">&amp; qu&ograve;d medio <expan abbr="vt&atilde;-tur">vtan&shy;<lb/>
tur</expan> Geometrico, nimirum circulo, &amp; diametris, &amp; diametrali oppo&longs;itione. <lb/>
</s>
          <s id="s.005556">qu&agrave;m deinde cert&aelig; &longs;int, patet ex eclyp&longs;ium infallibili pr&aelig;dictione.</s>
        </p>
        <p type="main">
          <s id="s.005557">Secund&ograve;, cur Sol plures dies in parte Zodiaci &aelig;&longs;tiua; qu&agrave;m in hyberna <lb/>
moratur? </s>
          <s id="s.005558">cau&longs;am afferunt Apog&aelig;um.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005559">Terti&ograve;, cur Luna &longs;ucce&longs;&longs;iu&egrave; illuminatur? </s>
          <s id="s.005560">quia &longs;ph&aelig;rica e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005561">Quart&ograve;, cur in horologijs &longs;olaribus tropici &longs;unt line&aelig; curu&etail;? </s>
          <s id="s.005562">&aelig;quator <lb/>
ver&ograve; linea recta? </s>
          <s id="s.005563">quia illi &longs;unt &longs;ectiones conic&etail;, &aelig;quator ver&ograve; e&longs;t &longs;ectio duo&shy;<lb/>
rum planorum.</s>
        </p>
        <p type="main">
          <s id="s.005564">Quint&ograve;, cur Sol non totam &longs;imul terram illuminat, &longs;ed &longs;ucce&longs;&longs;iu&egrave;? </s>
          <s id="s.005565">quia <lb/>
terra &longs;ph&aelig;rica e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005566">Quam deinde mirabiles, ac iucund&aelig; &longs;unt cognitiones ill&aelig;, de quibus ip&longs;&aelig; <lb/>
&longs;acr&aelig; liter&aelig; mirabund&aelig; loquuntur? </s>
          <s id="s.005567">altitudinem videlicet C&oelig;li, <expan abbr="atq;">atque</expan> pro&shy;<lb/>
funditatem aby&longs;&longs;i improbo &longs;an&egrave; au&longs;u per&longs;crutari? </s>
          <s id="s.005568">terr&aelig;, Lun&aelig;, Solis magni&shy;<lb/>
tudines, ac di&longs;tantias acumine plan&egrave; diuino nobis euidenter tradidi&longs;&longs;e? </s>
          <s id="s.005569">to&shy;<lb/>
tius <expan abbr="deniq;">denique</expan> mundi fabricam, ac &longs;ymmetriam, qua cognitione nihil pr&aelig;&longs;tan&shy;<lb/>
tius, poti&longs;sima h&aelig;c nobis philo&longs;ophia manife&longs;tum facit; vt jure liceat illud <lb/>
accinere:</s>
        </p>
        <p type="main">
          <s id="s.005570"><emph type="italics"/>Felices anim&aelig;, quibus h&aelig;c cogno&longs;cere primum<emph.end type="italics"/>, <lb/>
<emph type="italics"/>Inque domos &longs;uper as &longs;candere cura fuit. <lb/>
</s>
          <s id="s.005571">Admouere oculis di&longs;tantia &longs;ydera no&longs;tris<emph.end type="italics"/>, <lb/>
<emph type="italics"/>Aetheraqu&eacute;, ingenio &longs;uppo&longs;uere &longs;uo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005572">A&longs;tronomi&aelig; pars iucunda &aelig;qu&egrave;, ac mirabilis e&longs;t Geographia: qua, vel in <lb/>
globo, vel in tabula, terras omnes, maria omnia, qua&longs;i pr&aelig;&longs;entes lic&egrave;t <expan abbr="c&otilde;-templari">con&shy;<lb/>
templari</expan>. </s>
          <s id="s.005573">quoque loco vnumquodque &longs;it, qua zona, quo climate, magna iu&shy;<lb/>
cunditate percipitur.</s>
        </p>
        <p type="main">
          <s id="s.005574">In per&longs;pectiua etiam <expan abbr="neq;">neque</expan> de&longs;unt perfect&aelig; demon&longs;trationes, v. <!-- REMOVE S-->g. <!-- REMOVE S-->cur ocu&shy;<lb/>
lus &longs;ph&aelig;ricus? </s>
          <s id="s.005575">vt illi <expan abbr="vndiq;">vndique</expan> line&aelig; perpendiculares po&longs;&longs;int accidere. </s>
          <s id="s.005576">Sed cur <lb/>
line&aelig; perpendiculares? </s>
          <s id="s.005577">vt di&longs;tincta fieret vi&longs;io; ecce cau&longs;&aelig; finales. </s>
          <s id="s.005578">Cur <expan abbr="c&otilde;-cau&utilde;">con&shy;<lb/>
cauum</expan> <expan abbr="&longs;pecul&utilde;">&longs;peculum</expan> ibi vrit? </s>
          <s id="s.005579">quia &longs;olares radij reflexi illuc congregantur. </s>
          <s id="s.005580">Cur bacu<lb/>
lus in aqua fractus apparet? </s>
          <s id="s.005581">quia per lineas refractas videtur. </s>
          <s id="s.005582">Cur Iris <expan abbr="rot&utilde;-da">rotun&shy;<lb/>
da</expan>? </s>
          <s id="s.005583">quia non videtur, ni&longs;i &longs;ub &longs;tatuto angulo, qui non ni&longs;i in orbem collo&shy;<lb/>
cari pote&longs;t. </s>
          <s id="s.005584">vbi &longs;imul vides, qu&agrave;m dign&aelig; <expan abbr="quoq;">quoque</expan> &longs;int h&aelig; cognitiones.</s>
        </p>
        <p type="main">
          <s id="s.005585">In mechanicis po&longs;tea: cur cuneus tantas obtinet vires? </s>
          <s id="s.005586">quia e&longs;t vectis <lb/>
geminatus. </s>
          <s id="s.005587">Vnde cochle&aelig; tanta vis? </s>
          <s id="s.005588">quia con&longs;tat cuneo, &amp; vecte. </s>
          <s id="s.005589">Verum <lb/>
quid admirabilius, qu&agrave;m quodlibet pondus, vel ip&longs;um vniuer&longs;um, vnius for&shy;<lb/>
mic&aelig; vi po&longs;&longs;e commoueri? </s>
          <s id="s.005590"><expan abbr="ip&longs;am&qacute;">ip&longs;amque</expan>; naturam, vt ait Ari&longs;t. vel inuitam &longs;upe&shy;<lb/>
rare. </s>
          <s id="s.005591">qu&agrave;m &longs;ubt&igrave;lia &longs;unt ea, qu&aelig; de centro grauitatis Archimedes olim, nu&shy;<pb pagenum="31" xlink:href="009/01/315.jpg"/>per ver&ograve; Commandinus, &amp; Lucas Valerius demon&longs;trarunt.</s>
        </p>
        <p type="main">
          <s id="s.005592">Mu&longs;ica tandem &longs;uas habet <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan>, v. <!-- REMOVE S-->g. <!-- REMOVE S-->Tonum con&longs;tare ex duo&shy;<lb/>
bus &longs;emitonijs minoribus, &amp; commate, quia ratio &longs;e&longs;quioctaua duobus &longs;e&shy;<lb/>
mitonijs minoribus, &amp; vno commate con&longs;tat. </s>
          <s id="s.005593">Tonus autem in &longs;e&longs;quiocta&shy;<lb/>
ua ratione con&longs;i&longs;tit. </s>
          <s id="s.005594">Item Diapentem con&longs;tare ex tribus tonis, &amp; &longs;emitonio <lb/>
minori; quia &longs;i ex &longs;e&longs;quialtero interuallo, qu&ograve;d e&longs;t diapentes demas &longs;e&longs;qui&shy;<lb/>
tertium, re&longs;tat &longs;e&longs;quioctauum. </s>
          <s id="s.005595"><expan abbr="Se&longs;quiterti&utilde;">Se&longs;quitertium</expan> ver&ograve; continet duos tonos cum <lb/>
&longs;emitonio minori; ecce cau&longs;&aelig; materiales. </s>
          <s id="s.005596">Cur bis diapente, aut bis dia&shy;<lb/>
te&longs;&longs;aron con&longs;onantia <expan abbr="c&otilde;poni">componi</expan> non pote&longs;t? </s>
          <s id="s.005597">cau&longs;am huius habes &longs;upra &longs;ectio&shy;<lb/>
ne 19. problem. </s>
          <s id="s.005598">nu. </s>
          <s id="s.005599">34. &longs;ed qu&agrave;m mirum e&longs;t Pythagoram &longs;onos in propor&shy;<lb/>
tiones diui&longs;i&longs;&longs;e, non &longs;ecus, ac &longs;i quantitates qu&aelig;dam permanentes e&longs;&longs;ent?</s>
        </p>
        <p type="main">
          <s id="s.005600">Reliquum e&longs;&longs;et de Mathematicis etiam practicis <expan abbr="n&otilde;nulla">nonnulla</expan> dicere, in qui&shy;<lb/>
bus omnes <expan abbr="quoq;">quoque</expan> cau&longs;&aelig; manife&longs;t&aelig; reperiuntur; ex e&ograve; enim, qu&ograve;d practic&aelig; <lb/>
&longs;unt, nece&longs;&longs;ari&ograve; finem inuoluunt. </s>
          <s id="s.005601">efficientem ver&ograve; <expan abbr="materi&atilde;">materiam</expan>, &amp; formam &longs;&aelig;&shy;<lb/>
p&egrave; adhibent ad pr&aelig;mi&longs;&longs;as probandas, quas a&longs;&longs;umunt ad concludendum id, <lb/>
quod principaliter intendunt. </s>
          <s id="s.005602">Porr&ograve; inter practicas omnium pr&aelig;&longs;tanti&longs;&longs;i&shy;<lb/>
ma e&longs;t Geometria practica; quis enim non admiratur, c&ugrave;m audit Geome&shy;<lb/>
tram &longs;olo vi&longs;u inacce&longs;&longs;as etiam magnitudines qua&longs;cunque, vt turres, vel <lb/>
montes men&longs;urare?</s>
        </p>
        <p type="main">
          <s id="s.005603">Ex quibus liquid&ograve; con&longs;tant Mathematicas habere perfecti&longs;&longs;imas <expan abbr="dom&otilde;-&longs;trationes">demon&shy;<lb/>
&longs;trationes</expan>, quarum cau&longs;&etail; ita ab effectu di&longs;tinguntur, vt nullis calumnijs &longs;int <lb/>
obnoxi&aelig;: quare etiam &longs;i aduer&longs;arij conuincant, qu&ograve;d neutiquam faciunt, <lb/>
Geometriam, &amp; Arithmeticam illis carere; reliquis tamen pr&aelig;dictis con&shy;<lb/>
cedere coguntur: <expan abbr="eas&qacute;">easque</expan>; per omne <expan abbr="cau&longs;ar&utilde;">cau&longs;arum</expan> genus excurrere, qu&ograve;d tan&shy;<lb/>ta pr&aelig;terea euidentia pr&aelig;&longs;tant, vt nihil ambiguum, nihil contro&shy;<lb/>
uer&longs;um relinquatur: Mathematic&etail; <expan abbr="namq;">namque</expan> te&longs;te etiam Ari&longs;t. <lb/>
1. Elenchorum non &longs;unt contentio&longs;&aelig;. </s>
          <s id="s.005604">Vnde &longs;it, vt to&shy;<lb/>
ta h&aelig;c ade&ograve; digna, <expan abbr="atq;">atque</expan> admiranda cognitio &longs;it <lb/>
mera veritas, qu&aelig; omnium &longs;cientiarum finis <lb/>
atque anim&aelig; no&longs;tr&aelig; cibus e&longs;t.</s>
        </p>
        <p type="head">
          <s id="s.005605">LAVS DEO.</s>
        </p>
      </chap>
      <pb pagenum="32" xlink:href="009/01/316.jpg"/>
      <chap>
        <p type="head">
          <s id="s.005606">APPENDIX.</s>
        </p>
        <p type="main">
          <s id="s.005607"><emph type="italics"/>Placet nunc demum, vt melius &agrave;dhuc Mathematica&shy;<lb/>
rum natur a pateat, locaqu&eacute; Arist. <!-- REMOVE S-->Mathematica ma&shy;<lb/>
gis illustrentur, Demon&longs;trationes primi Elemento&shy;<lb/>rum Euclidis breuiter expendere, atque vnamquamque <lb/>
ad &longs;uum demon&longs;trationis genus referre.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005608">Prima igitur Demon&longs;tratione Euclides o&longs;tendit Triangulum il&shy;<lb/>
lud eo modo <expan abbr="c&otilde;&longs;trnctum">con&longs;tructum</expan> e&longs;&longs;e &aelig;quilaterum, hoc proximo medio, <lb/>
quia &longs;cilicet habet tria latera &aelig;qualia, quod medium e&longs;t ip&longs;ius <lb/>
&longs;ubiecti demon&longs;trationis, &longs;iue trianguli &aelig;quilateri definitio: <lb/>
quare h&aelig;c demon&longs;tratio erit per cau&longs;am formalem.</s>
        </p>
        <p type="main">
          <s id="s.005609">Secunda Demon&longs;tratione o&longs;tendit duas lineas e&longs;&longs;e &aelig;quales, quoniam am&shy;<lb/>
b&aelig; &longs;unt vni terti&aelig; &aelig;quales, qu&aelig; ratio nititur illi axiomati, qu&aelig; &longs;unt &aelig;qualia <lb/>
vni tertio, &longs;unt etiam inter &longs;e. </s>
          <s id="s.005610">e&longs;t quidem demon&longs;tratio o&longs;ten&longs;iua, &longs;ed non <lb/>
per cau&longs;am, verum &agrave; &longs;igno: e&longs;&longs;e enim &aelig;quales vni terti&aelig;, e&longs;t &longs;ignum &aelig;quali&shy;<lb/>
tatis earum.</s>
        </p>
        <p type="main">
          <s id="s.005611">Tertia Demon&longs;tratio eodem medio vtitur, quo &longs;ecunda.</s>
        </p>
        <p type="main">
          <s id="s.005612">Quarta Demon&longs;tratio o&longs;tendit, prim&ograve; de illis duobus triangulis, quod <lb/>
habent ba&longs;es &aelig;quales, quia ba&longs;es congruunt &longs;ibi mutuo. </s>
          <s id="s.005613">&longs;ecund&ograve;, o&longs;tendit <lb/>
alios duos angulos e&longs;&longs;e &aelig;quales alijs duobus <expan abbr="vtrum&qacute;">vtrumque</expan>; <expan abbr="vtri&qacute;">vtrique</expan>; eadem ratione, <lb/>
quia nimirum &longs;ibi mutu&ograve; congruunt. </s>
          <s id="s.005614">&longs;i dixeris igitur, quod &longs;ibi mutu&ograve; con&shy;<lb/>
gruere &longs;it definitio &aelig;qualis, erit demon&longs;tratio per cau&longs;am formalem; &longs;i au&shy;<lb/>
tem dixeris e&longs;&longs;e &longs;ignum &aelig;qualitatis, erit &agrave; &longs;igno, &amp; &agrave; po&longs;teriori.</s>
        </p>
        <p type="main">
          <s id="s.005615">5. O&longs;tendit de Triangulo I&longs;o&longs;cele, prim&ograve;, quod Anguli, qui &longs;unt ad ba&shy;<lb/>
&longs;im, &longs;unt &aelig;quales, ratio e&longs;t, quia ablatis &aelig;qualibus ab &aelig;qualibus ip&longs;i &longs;unt <lb/>
reliqui. </s>
          <s id="s.005616">Qu&aelig; quidem ratio etiam Ari&longs;t. te&longs;te, e&longs;t per cau&longs;am materialem; <lb/>
nam e&longs;&longs;e dimidium, tertiam partem, duplum, reliquum, alicuius totius, &amp; <lb/>
&longs;imilia, nihil aliud e&longs;t, qu&agrave;m e&longs;&longs;e partes re&longs;pectu totius; partes autem &longs;unt <lb/>
materia, vt apert&egrave; docet Ari&longs;t. tex. <!-- REMOVE S-->3. lib. 5. Metaph. quem &longs;upra <expan abbr="c&utilde;">cum</expan> alijs <expan abbr="ex-plicat&utilde;">ex&shy;<lb/>
plicatum</expan> habes. </s>
          <s id="s.005617">&longs;ecund&ograve;, demon&longs;trat de eodem I&longs;o&longs;cele, angulos infra ba&longs;im <lb/>
e&longs;&longs;e &aelig;quales, ratio, quia opponuntur &etail;qualibus lateribus <expan abbr="triangulor&utilde;">triangulorum</expan> quar&shy;<lb/>
t&aelig; pr&aelig;cedentis, qu&aelig; ratio videtur &longs;ignum quoddam &aelig;qualitatis eorum e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.005618">6. Probat duo illa latera illius trianguli e&longs;&longs;e &aelig;qualia, ab impo&longs;&longs;ibili, quia <lb/>
&longs;equeretur partem e&longs;&longs;e &aelig;qualem toti.</s>
        </p>
        <p type="main">
          <s id="s.005619">7. Duas po&longs;teriores lineas cum duabus prioribus nece&longs;&longs;ari&ograve; coincidere <lb/>
demon&longs;trat, quia aliter &longs;equeretur, vel partem e&longs;&longs;e &aelig;qualem toti: vel angu&shy;<lb/>
los l&longs;olcelis &longs;ub ba&longs;i e&longs;&longs;e in&aelig;quales, vel etiam eos, qui &longs;upra ba&longs;im, contra <lb/>
qu&agrave;m o&longs;ten&longs;um e&longs;t in quinta.</s>
        </p>
        <p type="main">
          <s id="s.005620">8. Probat angulos illos fore &aelig;quales, quia congruunt: per 8. &longs;cilicet <lb/>
axioma: videtur &agrave; &longs;igno.</s>
        </p>
        <pb pagenum="33" xlink:href="009/01/317.jpg"/>
        <p type="main">
          <s id="s.005621">9 Probat angulum illum diui&longs;um e&longs;&longs;e bifariam, per <expan abbr="octau&atilde;">octauam</expan> pr&etail;cedentem: <lb/>
e&longs;t ergo eiu&longs;dem natur&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.005622">10 Probat lineam <expan abbr="ill&atilde;">illam</expan> e&longs;&longs;e diui&longs;am in duas lineas &aelig;quales, quia ill&aelig; du&aelig; <lb/>
&longs;unt ba&longs;es triangulorum quart&etail;; hoc autem, e&longs;&longs;e ba&longs;es talium <expan abbr="triangulor&utilde;">triangulorum</expan>, <lb/>
videtur e&longs;&longs;e definitio; quare h&aelig;c demon&longs;tratio e&longs;&longs;et &agrave; definitione &longs;ubiecti, <lb/>
&amp; per cau&longs;am formalem.</s>
        </p>
        <p type="main">
          <s id="s.005623">11 Probat illam lineam facere angulos rectos, quia facit angulos cum <lb/>
&longs;ubiecta linea aquales; nam ex decima definitione &longs;i illi anguli &longs;int &aelig;quales, <lb/>
qui fiunt &agrave; tali linea, erunt ip&longs;i quoque recti. </s>
          <s id="s.005624">demon&longs;tratio igitur e&longs;t &agrave; de&shy;<lb/>
finitione.</s>
        </p>
        <p type="main">
          <s id="s.005625">12 Probat lineam illam e&longs;&longs;e perpendicularem ex definitione line&aelig; per&shy;<lb/>pendicularis, quia nimirum facit angulos, cum &longs;ubiecta linea &aelig;quales, re&shy;<lb/>
cto&longs;u&egrave;; e&longs;t igitur demon&longs;tratio &agrave; definitione, &agrave; priori, per cau&longs;am formalem.</s>
        </p>
        <p type="main">
          <s id="s.005626">13 Probat duos angulos e&longs;&longs;e &aelig;quales duobus angulis rectis, <expan abbr="quoni&atilde;">quoniam</expan> <expan abbr="vtri-&qacute;ue">vtri&shy;<lb/>
que</expan> &longs;unt &aelig;quales vni terti&aelig; rei. </s>
          <s id="s.005627">quare e&longs;t &agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005628">14 Probat intentum, quia aliter &longs;equeretur, partem toti &aelig;qualem e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.005629">15 Probat angulos ad verticem &aelig;quales e&longs;&longs;e, quia &longs;i ab &aelig;qualibus, &aelig;qua&shy;<lb/>lia demas ip&longs;i remaneat: vel &longs;unt reliqui. </s>
          <s id="s.005630">E&longs;t igitur demon&longs;tratio per cau&shy;<lb/>
&longs;am materialem, vt dictum e&longs;t in quinta.</s>
        </p>
        <p type="main">
          <s id="s.005631">16 Probat angulum externum maiorem e&longs;&longs;e interno, quia e&longs;t maior alio <lb/>
angulo &aelig;quali ip&longs;i interno. </s>
          <s id="s.005632">e&longs;t &agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005633">17 Probat duos angulos e&longs;&longs;e minores alijs duobus angulis, ex 4. axiom. <lb/>
</s>
          <s id="s.005634">quia. </s>
          <s id="s.005635">&longs;. </s>
          <s id="s.005636">&longs;i in&aelig;qualibus adiecta &longs;int &aelig;qualia, tota erunt in&aelig;qualia: vbi cau&longs;a <lb/>
in&aelig;qualitatis totorum, e&longs;t adiectum illud, quo adiecto conflatur duo tota: <lb/>
quare adiectum illud e&longs;t; pars autem e&longs;t materia totius. </s>
          <s id="s.005637">demon&longs;trat igitur <lb/>
per cau&longs;am materialem.</s>
        </p>
        <p type="main">
          <s id="s.005638">18 Probat angulum vnum e&longs;&longs;e altero <expan abbr="maior&etilde;">maiorem</expan>, quia ille &longs;it veluti totum, <lb/>
i&longs;te ver&ograve; illius pars. </s>
          <s id="s.005639">reducitur ad cau&longs;am materialem.</s>
        </p>
        <p type="main">
          <s id="s.005640">19 Probat propo&longs;itum ab impo&longs;&longs;ibili.</s>
        </p>
        <p type="main">
          <s id="s.005641">20 Probat duo illa latera e&longs;&longs;e reliquo maiora, quia &longs;unt &aelig;qualia vni li&shy;<lb/>
ne&aelig;, qu&aelig; ip&longs;a reliquo latere maior e&longs;t. </s>
          <s id="s.005642">e&longs;t &agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005643">21 Probat illas duas rectas e&longs;&longs;e minores alijs duabus, ex eo, qu&ograve;d &longs;int <lb/>
minores quadam quantitate, qu&aelig; quantitas minor e&longs;t illis duabus. </s>
          <s id="s.005644">&agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005645">Secund&ograve;, probat <expan abbr="angul&utilde;">angulum</expan> illum e&longs;&longs;e maiorem altero, quia. </s>
          <s id="s.005646">f. </s>
          <s id="s.005647">e&longs;t maior quo&shy;<lb/>
dam angulo, qui maior e&longs;t illo altero. </s>
          <s id="s.005648">pariter &agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005649">22 Probat per illud axioma, qu&aelig; &longs;unt &aelig;qualia vni tertio, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.005650">23 Probat duos angulos e&longs;&longs;e &aelig;quales, qu&ograve;d &longs;int anguli oppo&longs;iti ba&longs;ibus <lb/>
triangulorum octau&aelig;. </s>
          <s id="s.005651">videtur &agrave; definitione horum angulorum.</s>
        </p>
        <p type="main">
          <s id="s.005652">24 Probat latus illud e&longs;&longs;e maius altero latere, ex eo, qu&ograve;d &longs;it &aelig;quale cui&shy;<lb/>
dam lateri, quod etiam e&longs;t maius illo latere.</s>
        </p>
        <p type="main">
          <s id="s.005653">25 Probat propo&longs;itionem, deducens ad ab&longs;urdum.</s>
        </p>
        <p type="main">
          <s id="s.005654">26 Demon&longs;trat deducendo ad inconueniens.</s>
        </p>
        <p type="main">
          <s id="s.005655">27 Probat illas e&longs;&longs;e parallelas, quia nunquam concurrere po&longs;&longs;unt; e&longs;t &agrave; <lb/>
definitione parallelarum.</s>
        </p>
        <p type="main">
          <s id="s.005656">28 Puto &agrave; cau&longs;a demon&longs;trare, o&longs;tendit enim duas rectas e&longs;&longs;e &aelig;quidi&longs;tan&shy;<lb/>
tes, quia earum anguli alterni &longs;int &aelig;quales, illi enim anguli &longs;unt cau&longs;a &aelig;qui&shy;


<pb pagenum="34" xlink:href="009/01/318.jpg"/>di&longs;tanti&aelig; linearum. </s>
          <s id="s.005657">&longs;imile dicendum e&longs;t de &longs;ecunda parte demon&longs;trationis.</s>
        </p>
        <p type="main">
          <s id="s.005658">29 Prima pars probatur ab impo&longs;&longs;ibili. </s>
          <s id="s.005659">&longs;ecunda &agrave; &longs;igno, qu&aelig; &longs;uat &aelig;qua&shy;<lb/>
lia vni tertio &amp;c. </s>
          <s id="s.005660">Idem dicendum de tertia parte.</s>
        </p>
        <p type="main">
          <s id="s.005661">30 Probat e&longs;&longs;e parallelas ex 27. primi, quare est <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> natur&aelig; cum illa.</s>
        </p>
        <p type="main">
          <s id="s.005662">31 <expan abbr="Eand&etilde;">Eandem</expan> habet <expan abbr="ration&etilde;">rationem</expan>, quam 27. primi. </s>
          <s id="s.005663">per cau&longs;am igitur formalem.</s>
        </p>
        <p type="main">
          <s id="s.005664">32 Prim&ograve;, probat <expan abbr="angui&utilde;">anguium</expan> externum e&longs;&longs;e &aelig;qualem duabus internis, &amp; ap&shy;<lb/>
po&longs;itis ex eo, qu&ograve;d partes anguli externi, &longs;int &aelig;quales partibus illorum: ex <lb/>
&aelig;qualitate.&longs; partium infert <expan abbr="&aelig;qualitat&etilde;">&aelig;qualitatem</expan> totorum: qu&aelig; demon&longs;tratio e&longs;t per <lb/>
cau&longs;am materialem. </s>
          <s id="s.005665">Secund&ograve;, probat illam ade&ograve; celeberrimam, omnis <lb/>
triangulus habet tres, &amp;c. </s>
          <s id="s.005666">qu&agrave;m fu&longs;i&longs;&longs;im&egrave; explicaui &longs;upra ad tex. <!-- REMOVE S-->23. primi <lb/>
Po&longs;ter. vbi Ari&longs;t. eam in exemplum perfecti&longs;&longs;im&aelig; demon&longs;trationis adducit.</s>
        </p>
        <p type="main">
          <s id="s.005667">33 Partim per 4. primi, partim per 27. primi <expan abbr="dem&otilde;&longs;trat">demon&longs;trat</expan>: quapropter ad <lb/>
earum naturam &longs;unt referend&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.005668">34 Tria probat. </s>
          <s id="s.005669"><expan abbr="prim&utilde;">primum</expan>, per 26. primi, <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> per illud axioma, &longs;i &aelig;qua&shy;<lb/>libus &aelig;qualia adijcias, tota &longs;unt &aelig;qualia, quod duobus angulis applicat. <lb/>
</s>
          <s id="s.005670">qu&aelig; demon&longs;tratio e&longs;t &agrave; partibus ad tota: &agrave; cau&longs;a nimirum materiali. </s>
          <s id="s.005671">ter&shy;<lb/>
tium per 4. primi concludit.</s>
        </p>
        <p type="main">
          <s id="s.005672">35 Procedit per cau&longs;am materialem: in omni enim ca&longs;u probat illa duo <lb/>
parallelogramma e&longs;&longs;e &aelig;qualia, quia &longs;i &aelig;qualibus &aelig;qualia adijciantur, tota <lb/>
erunt &aelig;qualia: vt in pr&aelig;cedenti dictum e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.005673">36 Probat duo e&longs;&longs;e &aelig;qualia, quia &longs;unt vni tertio &aelig;qualia: videlicet &agrave; &longs;i&shy;<lb/>
gno, &agrave; po&longs;teriori.</s>
        </p>
        <p type="main">
          <s id="s.005674">37 Probat duo triangula e&longs;&longs;e &aelig;qualia, qu&ograve;d &longs;int dimidia duorum paral&shy;<lb/>
lelogrammorum &aelig;qualium: e&longs;t <expan abbr="itaq;">itaque</expan> &agrave; cau&longs;a materiali.</s>
        </p>
        <p type="main">
          <s id="s.005675">38 Eadem ratione demon&longs;trat in hac, <expan abbr="atq;">atque</expan> in pr&aelig;cedenti.</s>
        </p>
        <p type="main">
          <s id="s.005676">39 Propo&longs;itum probat, ad ab&longs;urdum deducendo aduer&longs;arium.</s>
        </p>
        <p type="main">
          <s id="s.005677">40 Similiter demon&longs;trat ac in pr&aelig;cedenti 39.</s>
        </p>
        <p type="main">
          <s id="s.005678">41 Probat vnum e&longs;&longs;e duplum alterius, qu&ograve;d &longs;it duplum alterius, quod il&shy;<lb/>
li &aelig;quale e&longs;t. </s>
          <s id="s.005679">videtur &agrave; &longs;igno.</s>
        </p>
        <p type="main">
          <s id="s.005680">42 Probat parallelogrammum, &amp; <expan abbr="triangul&utilde;">triangulum</expan> e&longs;&longs;e &aelig;qualia, quoniam <expan abbr="vtr&utilde;-que">vtrun&shy;<lb/>
que</expan> duplum &longs;it eiu&longs;dem trianguli: videlicet per cau&longs;am materialem.</s>
        </p>
        <p type="main">
          <s id="s.005681">43 Probat duo parallelogramma e&longs;&longs;e &etail;qualia, quoniam ablatis &aelig;quali&shy;<lb/>
bus ab &aelig;qualibus &longs;int re&longs;idua. </s>
          <s id="s.005682">cau&longs;a e&longs;t materialis.</s>
        </p>
        <p type="main">
          <s id="s.005683">44 Probat parallelogrammum &aelig;quari triangulo, quia <expan abbr="vtrunq;">vtrunque</expan> cuidam <lb/>
tertio &aelig;quatur. </s>
          <s id="s.005684">&agrave; &longs;igno videlicet.</s>
        </p>
        <p type="main">
          <s id="s.005685">45 Probat totum parallelogrammum &aelig;quari toti rectilineo; eo, qu&ograve;d <lb/>
partes amborum totorum &longs;int &aelig;quales: e&longs;t per&longs;picua cau&longs;a materialis.</s>
        </p>
        <p type="main">
          <s id="s.005686">46 Probat quadrilaterum quoddam e&longs;&longs;e quadratum ex definitione qua&shy;<lb/>
drati, quia &longs; habet quatuor angulos rectos, &amp; quatuor latera &aelig;qualia. </s>
          <s id="s.005687">e&longs;t <lb/>
igitur &agrave; cau&longs;a formali.</s>
        </p>
        <p type="main">
          <s id="s.005688">47 Probat quadratum lateris angulo recto &longs;ub&longs;en&longs;i, e&longs;&longs;e &aelig;quale duobus <lb/>
quadratis reliquorum <expan abbr="later&utilde;">laterum</expan> trianguli illius: &amp; ratio de&longs;umpta e&longs;t &agrave; parti&shy;<lb/>
bus, quia. </s>
          <s id="s.005689">&longs;. </s>
          <s id="s.005690">partes pr&aelig;dicti quadrati &aelig;quales &longs;unt &longs;ingillatim pr&etail;dictis qua&shy;<lb/>
dratis; ergo totum quadratum totis illis quadratis &aelig;quale e&longs;t. </s>
          <s id="s.005691">manife&longs;ta e&longs;t <lb/>
cau&longs;a materialis.</s>
        </p>
        <p type="main">
          <s id="s.005692">48 Probat angulum quendam e&longs;&longs;e rectum, eo, qu&ograve;d &aelig;qualis &longs;it cuidam <lb/>
angulo recto. </s>
          <s id="s.005693">e&longs;t &agrave; &longs;igno.</s>
        </p>
        <pb pagenum="35" xlink:href="009/01/319.jpg"/>
        <p type="main">
          <s id="s.005694">H&aelig;c pauca &longs;ufficiant, vt Philo&longs;ophi habeant, vnde po&longs;&longs;int de Geometri&shy;<lb/>
cis demon&longs;trationibus dijudicare. </s>
          <s id="s.005695">non tamen qui&longs;piam exi&longs;timet idem iu&shy;<lb/>
dicium de reliquis Mathematicis e&longs;&longs;e faciendum, A&longs;tronomia enim, Opti&shy;<lb/>
ca, &amp; ali&etail; vtuntur etiam alijs cau&longs;arum generibus in demon&longs;trando, vt &longs;up. <lb/>
</s>
          <s id="s.005696">cap. 5. de natura Mathem. patuit. </s>
          <s id="s.005697">Et quamuis &longs;&etail;p&egrave; demon&longs;trent ab effe&shy;<lb/>ctu, perpetu&ograve; tamen euidentiam efficiunt eam, vt nullam, vt ait Themi&longs;tius, <lb/>
patiantur in&longs;tantiam.</s>
        </p>
        <p type="main">
          <s id="s.005698">Hortabantur me nonnulli, vt eandem operam locis Mathematicis, qu&aelig; <lb/>
apud Platonem &longs;unt, impenderem: quibus dum obtemperare vellem repe&shy;<lb/>
ri Theonem quendam Smirn&aelig;um Scriptorem Gr&aelig;cum, iam pridem idem <lb/>
pr&aelig;&longs;titi&longs;&longs;e, cuius opus adhuc Gr&aelig;cum a&longs;&longs;eruatur in Vaticana Bibliotheca, <lb/>
vt ait Io&longs;ephus Auria in pr&aelig;f. </s>
          <s id="s.005699">ad &longs;uum Theodo&longs;ium Tripolitam; vbi <lb/>&longs;pondet &longs;e breui eum &egrave; Gr&etail;co &agrave; &longs;e conuer&longs;um, in lucem editu&shy;<lb/>
rum, quod an pr&etail;&longs;titerit ignoro. </s>
          <s id="s.005700">Curandum igitur e&longs;t, <lb/>
&agrave; recentioribus Platonicis, vt tandem aliquan&shy;<lb/>
do, ne &agrave; quopiam actum agatur latina <lb/>
voce, ac luce pariter donetur.</s>
        </p>
        <p type="head">
          <s id="s.005701"><emph type="italics"/>LAVS DEO.<emph.end type="italics"/></s>
        </p>
        <pb xlink:href="009/01/320.jpg"/>
        <pb xlink:href="009/01/321.jpg"/>
        <p type="head">
          <s id="s.005702">CLARORVM <lb/>
MATHEMATICORVM <lb/>
CHRONOLOGIA</s>
        </p>
        <p type="head">
          <s id="s.005703">Eorum videlicet, qui rebus, aut &longs;criptis cla&shy;<lb/>
ruerunt, ex certis hi&longs;torijs deprompta.</s>
        </p>
        <p type="head">
          <s id="s.005704"><emph type="italics"/>Omi&szlig;is tum fabulo&longs;is, tum ob nimiam antiquitatem incertis, <lb/>veluti &longs;unt ea, qu&aelig; de Athlante, Zoroa&longs;tro, Endimione, <lb/>
Orpheo, Lino, alijsqu&eacute; traduntur.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.005705">Iubal ver&ograve; pater canentium cithara, &amp; organo, hoc e&longs;t Mu&longs;ic&aelig; <lb/>
auctor, omi&longs;&longs;us e&longs;t e&ograve;, qu&ograve;d nimio interuallo <lb/>
c&aelig;teros antecedat.</s>
        </p>
        <pb xlink:href="009/01/322.jpg"/>
        <pb pagenum="39" xlink:href="009/01/323.jpg"/>
        <p type="head">
          <s id="s.005706"><emph type="italics"/>PRIMVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table7"/></s>
        </p>
        <table>
          <table.target id="table7"/>
          <row>
            <cell>Ab Orbe cond. anno</cell>
            <cell>3237</cell>
          </row>
          <row>
            <cell>Ante primam Olymp. ann.</cell>
            <cell>76</cell>
          </row>
          <row>
            <cell>Ante Vrbem cond. ann.</cell>
            <cell>100</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti natiuitatem ann.</cell>
            <cell>852</cell>
          </row>
          <row>
            <cell>Io&longs;aphat Iud&aelig;orum Rege.</cell>
            <cell/>
          </row>
          <row>
            <cell>Aremulo Latinorum Rege.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.005707"><emph type="italics"/>Singula porr&ograve; &longs;ecula ex 100. annis constant. </s>
          <s id="s.005708">Anno huius &longs;eculi 76. <lb/>
vel ante Vrb. <!-- REMOVE S-->cond. </s>
          <s id="s.005709">24. Olympiades initium &longs;ump&longs;erunt.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005710">TERPANDER THEBANVS mu&longs;icus celeberrimus, Ho&shy;<lb/>
meri pronepos, de quo Ari&longs;t. in probl. </s>
          <s id="s.005711">&amp; alij omnes veteres me&shy;<lb/>
minerunt: claruit paulo ante primam Olympiad. <!-- REMOVE S-->hoc e&longs;t ante <lb/>
Chri&longs;ti natiuitatem 800. circiter annis. </s>
          <s id="s.005712">Lyram, quam olim <lb/>
Orpheus tetrachordum fecerat, ip&longs;e heptachordum reddidit. <lb/>
</s>
          <s id="s.005713">modulos lyricos, &amp; leges fidium inuenit. </s>
          <s id="s.005714">adiecit &longs;uis, &amp; Homeri carminibus <lb/>
modos, quibus canerentur. </s>
          <s id="s.005715">Primus de Mu&longs;ica &longs;crip&longs;it. </s>
          <s id="s.005716">Lac&aelig;demonios in&shy;<lb/>
ter &longs;e di&longs;&longs;identes cantus &longs;uauitate &longs;edauit. </s>
          <s id="s.005717">quaternas in ludis Pythijs victo&shy;<lb/>
rias retuli&longs;&longs;e publicis monumentis traditum e&longs;t. </s>
          <s id="s.005718">ex Plutar. <!-- REMOVE S-->de Mu&longs;ica.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005719">Vt autem intelligas quidnam e&longs;&longs;ent leges, de quibus hic, &amp; infra pa&longs;&longs;im <lb/>
fit mentio, audi Plutarchum de Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005720">Omnin&ograve; inquit cythar&aelig; <expan abbr="c&atilde;tus">cantus</expan> Ter&shy;<lb/>
pandri ratio omni ex parte &longs;implex perexit e&longs;&longs;e <expan abbr="v&longs;q;">v&longs;que</expan> ad &aelig;tatem Phrynidis, <lb/>
non enim antiquitus pro libidine cuiu&longs;que &lpar;vti nunc&rpar; licebat fidibus cane&shy;<lb/>
re, nec rithmus, concentu&longs;u&egrave; transferre: in ip&longs;is <expan abbr="namq;">namque</expan> legibus accommo&shy;<lb/>
datam <expan abbr="cuiq;">cuique</expan> tentionem tuebatur, cuius rei cau&longs;a id nominis inditum erat: <lb/>
leges enim &longs;unt vocat&aelig;, quoniam pr&aelig;&longs;criptum qua&longs;i lege, <expan abbr="cautum&qacute;">cautumque</expan>; erat, <lb/>
ne quis per quamlibet vnam &longs;peciem, <expan abbr="formam&qacute;">formamque</expan>; tentionis tran&longs;grederetur.</s>
        </p>
        <p type="main">
          <s id="s.005721">XENOCRATES Italus Locren&longs;is, po&longs;t Terpandrum, &amp; ante Saca&shy;<lb/>
dam vixit, fuit P&aelig;anum conditor. </s>
          <s id="s.005722">Patritius in Poetica.</s>
        </p>
        <p type="main">
          <s id="s.005723">ARDVLVS TR&AElig;ZENIVS prior Clona, Tibianam mu&longs;icam <lb/>
con&longs;tituit. </s>
          <s id="s.005724">Plutarchus de Mu&longs;ica.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005725">CLONAS ad imitationem Terpandri, primus leges Tibiarum fecit. <lb/>
</s>
          <s id="s.005726">circa primam Olymp. <!-- REMOVE S-->Plut. <!-- REMOVE S-->de Mu&longs;ica.<!-- KEEP S--></s>
        </p>
        <pb pagenum="40" xlink:href="009/01/324.jpg"/>
        <p type="head">
          <s id="s.005727"><emph type="italics"/>SECVNDVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table8"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table8"/>
          <row>
            <cell>Ab Vrbecondita.</cell>
            <cell/>
          </row>
          <row>
            <cell>Ab Orbe cond. ann.</cell>
            <cell>3337</cell>
          </row>
          <row>
            <cell>Olympiadis 6. ann.</cell>
            <cell>4</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti natiuitatem ann.</cell>
            <cell>752</cell>
          </row>
          <row>
            <cell>Ozia lud&aelig;orum Rege.</cell>
            <cell/>
          </row>
          <row>
            <cell>Romulo Latinorum Rege.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.005728">SACADAS ARGIVVS conditor Modorum: &amp; inuentor legis <lb/>
Tripartilis. </s>
          <s id="s.005729">circa Ro. <!-- REMOVE S-->cond. </s>
          <s id="s.005730">Pindaro antiquior. </s>
          <s id="s.005731">ter vicit in ludis Py&shy;<lb/>
thijs. </s>
          <s id="s.005732">Plaut. <!-- REMOVE S-->&amp; Patric.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005733">EVPHORBVS PHRYX ante Thaletem contemplationem <lb/>
de lineis fecit, &amp; triangulum Scalenum inuenit, ide&longs;t &lpar;ve opinor&rpar; modum <lb/>
ip&longs;um con&longs;truendi excogitauit, hic igitur primus geometrizare c&oelig;pit. <lb/>
</s>
          <s id="s.005734">Laertius in Thalete.</s>
        </p>
        <p type="head">
          <s id="s.005735"><emph type="italics"/>TERTIVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table9"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table9"/>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>101</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti natiuitatem ann.</cell>
            <cell>652</cell>
          </row>
          <row>
            <cell>Mana&longs;&longs;e Iud&aelig;orum.</cell>
            <cell/>
          </row>
          <row>
            <cell>Tullo Ho&longs;tilio Romanorum Rege.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.005736">THALES MILESIVS ab Vrbe cond. </s>
          <s id="s.005737">ann. </s>
          <s id="s.005738">120. natus. </s>
          <s id="s.005739">hic pri&shy;<lb/>
mus omnium &longs;eptem Sapientum appellatus e&longs;t Sapiens. </s>
          <s id="s.005740">ex Aegy&shy;<lb/>
pto primus in Gr&aelig;ciam Geometriam tran&longs;tulit. </s>
          <s id="s.005741">inuenit triangu&shy;<lb/>
lum in circulo orthogonicum, hoc e&longs;t, ni fallor, 31. tertij Elem. <lb/>
<!-- KEEP S--></s>
          <s id="s.005742">Quintam, &amp; 15. &amp; 26. primi Elemen. <!-- REMOVE S-->adinuenit. </s>
          <s id="s.005743">illud etiam demon&longs;trauit, <lb/>
Diametrum circulum bifariam &longs;ecare. </s>
          <s id="s.005744">tropicos, &amp; &aelig;quinoctialem de&longs;igna&shy;<lb/>uit. </s>
          <s id="s.005745">primus eclyp&longs;es Solis pr&aelig;dixit: quarum prima te&longs;te Piin. <!-- REMOVE S-->lib 2. cap. 12. <lb/>
contigit ann. </s>
          <s id="s.005746">V. C. 170. men&longs;us e&longs;t Aegypti Pyramides ex vmbra. </s>
          <s id="s.005747">inuentor <lb/>
fuit Vr&longs;&aelig; minoris, ide&longs;t, eam primus ob&longs;eruauit, &amp; alios docuit. </s>
          <s id="s.005748">ex pr&aelig;no&shy;<lb/>
tione, atque oliuarum emptione diuitias &longs;ibi comparauit. </s>
          <s id="s.005749">ante Methonem <lb/>
ann. </s>
          <s id="s.005750">132.</s>
        </p>
        <p type="main">
          <s id="s.005751">SIMONIDES LYRICVS octauam lyr&aelig; chordam addidit: hic <lb/>
fuit inuentor Artis memori&aelig;. </s>
          <s id="s.005752">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005753">LYCAON Mu&longs;icus, nouum chordarum ordinem inuexit, quem habes <lb/>
loco. </s>
          <s id="s.005754">344. locorum Mathematicorum, &amp; octauam lyr&aelig; chordam addidit. <lb/>
</s>
          <s id="s.005755">Boetius. </s>
          <s id="s.005756">Zarlinus.</s>
        </p>
        <p type="main">
          <s id="s.005757">MAMERTINVS in&longs;ignis Geometra, <expan abbr="qui&qacute;">quique</expan>; multa geometrica ad&shy;<lb/>
inuenit. </s>
          <s id="s.005758">Thaleti &longs;ucce&longs;&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.005759">ANAXIMANDER MILESIVS Thaleti &longs;ucce&longs;&longs;or. </s>
          <s id="s.005760">Horologium <pb pagenum="41" xlink:href="009/01/325.jpg"/>Solare, Sph&aelig;ram, <expan abbr="Gnomonem&qacute;">Gnomonemque</expan>, reperit, obliquitatem Zodiaci ob&longs;eruauit. <lb/>
</s>
          <s id="s.005761">Terr&aelig; circuitum reperit. </s>
          <s id="s.005762">primus tabulam Geographicam expo&longs;uit. </s>
          <s id="s.005763">primus <lb/>
Lunam aliena luce lucere demon&longs;trauit. </s>
          <s id="s.005764">&longs;ph&aelig;ram con&longs;truxit. </s>
          <s id="s.005765">Plin. Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005766">CLEOSTRATVS Zodiacum in 12. &longs;igna diui&longs;it. </s>
          <s id="s.005767">paulo po&longs;t Ana&shy;<lb/>
ximandrum. </s>
          <s id="s.005768">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005769">HECATEVS MILESIVS primus codicem de &longs;itu orbis reliquit. <lb/>
</s>
          <s id="s.005770">paulo po&longs;t Thaletem. </s>
          <s id="s.005771">Proclus in comm. <!-- REMOVE S-->Euclidis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005772">AMETISTVS &longs;ummus Geometra, atque rerum geometricarum in&shy;<lb/>
uentor, frater Ste&longs;ichori poet&aelig;. </s>
          <s id="s.005773">inter Thaletem, &amp; Pyth. <!-- KEEP S--></s>
          <s id="s.005774">Proclus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005775">POLEMON auditor Panetij Rhodij, tempore Ari&longs;tophanis gram&shy;<lb/>
matiei, orbis de&longs;criptionem fecit. </s>
          <s id="s.005776">Suidas.</s>
        </p>
        <p type="main">
          <s id="s.005777">SAPPHO Poetria, &amp; Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005778">prima Plectri v&longs;um inuexit, c&ugrave;m prius <lb/>
digitis &longs;olum pul&longs;arent. </s>
          <s id="s.005779">inuentrix etiam Mixtolydij concentus. </s>
          <s id="s.005780">Plut.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005781">PYTHAGORAS SAMIVS, Aegypto, ac Per&longs;ide perlu&longs;trata, in <lb/>
Mathematicis excelluit. </s>
          <s id="s.005782">primus Numerorum &longs;cientiam apud gr&aelig;cos illu&shy;<lb/>
&longs;trauit. </s>
          <s id="s.005783">Mu&longs;ic&aelig; theoricam ex Fabri malleis adinuenit. </s>
          <s id="s.005784">Luciferum, <expan abbr="atq;">atque</expan> He&shy;<lb/>
&longs;perum, qu&aelig; duo &longs;ydera putabantur, e&longs;&longs;e vnum, <expan abbr="atq;">atque</expan> idem Veneris a&longs;trum <lb/>
docuit. </s>
          <s id="s.005785">omne triangulum habere tres, &amp;c. </s>
          <s id="s.005786">qu&aelig; e&longs;t 32. primi Elem. primi <lb/>
Pythag. <!-- REMOVE S-->demon&longs;trarunt. </s>
          <s id="s.005787">47. primi Elem. reperit, pro qua Mu&longs;is Hecatombas <lb/>
immolauit. </s>
          <s id="s.005788">primus Mathematic&aelig; ludum aperuit. </s>
          <s id="s.005789">Proclus. <!-- KEEP S--></s>
          <s id="s.005790">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005791">TELAVGES filius Pythagor&aelig;, &amp; magi&longs;ter Empedoclis, &longs;crip&longs;it de <lb/>
Quaternario libros 4.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005792">ANAXIMENAS MILESIVS tempore Pythagor&aelig;, dixit &longs;ydera <lb/>
non &longs;olum &longs;upra terram, &longs;ed circa terram moueri. </s>
          <s id="s.005793">Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005794">DAMON Mu&longs;icus, Pythag. <!-- REMOVE S--><expan abbr="adole&longs;c&etilde;tes">adole&longs;centes</expan>, aliquot luxuri&aelig; deditos, har&shy;<lb/>
monicis canticis ad bonam frugem reuocauit. </s>
          <s id="s.005795">Zarlinus.</s>
        </p>
        <p type="head">
          <s id="s.005796"><emph type="italics"/>QVARTVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table10"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table10"/>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>201</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;tum ann.</cell>
            <cell>552</cell>
          </row>
          <row>
            <cell>Sub Babylonica captiuitate Iud&aelig;orum.</cell>
            <cell/>
          </row>
          <row>
            <cell>Seruio Tullio Romanorum Rege.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.005797"><emph type="italics"/>Anno 44. huius &longs;eculi, Rom&aelig; exactis Regibus Con&longs;&longs;. <!-- REMOVE S-->&longs;ufficiuntur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005798">ANAXAGORAS CLAZOMENIVS primus lunarem <lb/>
eclyp&longs;im pr&aelig;dixit, <expan abbr="eius&qacute;">eiusque</expan>; cau&longs;am patefecit. </s>
          <s id="s.005799">primus librum in lu&shy;<lb/>cem edidit. </s>
          <s id="s.005800">dixit Solem e&longs;&longs;e maiorem Pelopomne&longs;o. </s>
          <s id="s.005801">&longs;crip&longs;it de <lb/>
radijs vi&longs;iuis, vel de ratione &longs;cenographices. </s>
          <s id="s.005802">Vitr. lib. 7. Val. <lb/>
<!-- REMOVE S-->Max. <!-- REMOVE S-->Diog. Laert.</s>
        </p>
        <p type="main">
          <s id="s.005803">OENIPEDES CHIVS Democriti &longs;yncronus, inuenit 12. &amp; 23. <lb/>
primi Elem. huius di&longs;cipulus fuit Zenodorus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005804">ZENODORVS auctor tractatus de figuris I&longs;operimetris, qui e&longs;t <lb/>
apud Clauium in &longs;ph&aelig;ra, &amp; in Geometric. <!-- REMOVE S-->pract. <!-- KEEP S--></s>
          <s id="s.005805">Theon enim, ex quo de&shy;<pb pagenum="42" xlink:href="009/01/326.jpg"/>&longs;ump&longs;it Clauius, eum Zenodoro attribuit.</s>
        </p>
        <p type="main">
          <s id="s.005806">PERICLES di&longs;cipulus Anaxagor&aelig;, &amp; Athenien&longs;ium Princeps; Athe&shy;<lb/>
nien&longs;es ob tetram Solis eclyp&longs;im trepidantes, &amp; palantes, eclyp&longs;is natura <lb/>
expo&longs;ita, &longs;edauit. </s>
          <s id="s.005807">Val. <!-- REMOVE S-->Max.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005808">HIPPOCRATES CHIVS, qui dum circulum quadrare conare&shy;<lb/>
tur, lunulam quadrauit. </s>
          <s id="s.005809">eius circuli quadraturam Ari&longs;t. &longs;&aelig;p&egrave; in paralogi&longs;mi <lb/>
exemplum adducit, <expan abbr="eam&qacute;">eamque</expan>; breuiter expo&longs;uit. </s>
          <s id="s.005810">primus Elementa Geometri&shy;<lb/>
ca con&longs;crip&longs;it. </s>
          <s id="s.005811">primus in&longs;pexit duabus medijs proportionalibus <expan abbr="inu&etilde;tis">inuentis</expan> cu&shy;<lb/>bum duplari po&longs;&longs;e. </s>
          <s id="s.005812">Erato&longs;thenes apud Eutocium in commen. <!-- REMOVE S-->Archimedis. <lb/>
<!-- KEEP S--></s>
          <s id="s.005813">Proclus etiam.</s>
        </p>
        <p type="main">
          <s id="s.005814">THEODORVS CYRENEVS &longs;odalis Hippocratis Chij, multis <lb/>
Geometriam auxit. </s>
          <s id="s.005815">Proclus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005816">PHRINIS in&longs;ignis Cytharedus. </s>
          <s id="s.005817">primus apud Athenien&longs;es cithara ce&shy;<lb/>
cinit. </s>
          <s id="s.005818"><expan abbr="primas&qacute;">primasque</expan>; in Panathenaicis tulit. </s>
          <s id="s.005819">fuit di&longs;cipulus Ari&longs;toclis, qui ex Ter&shy;<lb/>
pandri familia ortum trahebat.</s>
        </p>
        <p type="main">
          <s id="s.005820">PHRINICVS, cuius Ari&longs;t. in Problem. mu&longs;icis cecinit: in&longs;ignis mu&shy;<lb/>
&longs;icus, ac tetrametri carminis inuentor.</s>
        </p>
        <p type="main">
          <s id="s.005821">LASVS HERMIN&AElig;VS primus omnium de Mu&longs;ica &longs;crip&longs;it. </s>
          <s id="s.005822">Darij <lb/>
Hida&longs;pis tempore. </s>
          <s id="s.005823">Suida.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005824">DIOCLES de Mu&longs;ica &longs;crip&longs;it. </s>
          <s id="s.005825">Suida.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005826">ISMENIVS CHORAVLES, te&longs;te Boetio, multis &aelig;gritudine la&shy;<lb/>
borantibus, &longs;ono, &amp; cantu omnes animi mole&longs;tias deter&longs;it. </s>
          <s id="s.005827">eius &aelig;qualis fuit <lb/>
Diony&longs;iodorus, &amp; Nicomachus. </s>
          <s id="s.005828">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005829">NICOMACHVS Arithmeticus, quem Boetius &longs;equitur, &amp; cuius ex&shy;<lb/>
tat gr&aelig;ca arithmetica, vbi &amp; de mu&longs;ica tractat ex Zarlino 8. &longs;upplem. </s>
          <s id="s.005830">mu&shy;<lb/>
&longs;icalium. </s>
          <s id="s.005831">Pappus lib. 3. eum Pythagoricum appellat; I&longs;idorus lib. 3. ethym. <lb/>
</s>
          <s id="s.005832">videtur eum paulo po&longs;t Pythagoram collocare. </s>
          <s id="s.005833">eiu&longs;dem meminit Eutocius.</s>
        </p>
        <p type="main">
          <s id="s.005834">EMPEDOCLES AGRIGENTINVS Pythagoricus, cantu furibundum <lb/>
adole&longs;centem, ac nudo ferro ho&longs;tem impetentem compre&longs;&longs;it, ac &longs;edauit.</s>
        </p>
        <p type="main">
          <s id="s.005835">TIM&AElig;VS LOCRVS Pythagoricus, Mathemata &longs;crip&longs;it, te&longs;te Sui&shy;<lb/>
da. </s>
          <s id="s.005836">paulo maior Platone, &agrave; quo Plato &longs;uum Tim&aelig;um in&longs;crip&longs;it, ac partim <lb/>
de&longs;crip&longs;it. </s>
          <s id="s.005837">extat adhuc ip&longs;ius monumentum de natura mundi.</s>
        </p>
        <p type="main">
          <s id="s.005838">SIMON Philo&longs;ophus Socratis amicus; &longs;crip&longs;it Dialogum de mu&longs;ica. <lb/>
</s>
          <s id="s.005839">Diog. <!-- REMOVE S-->Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005840">CRATISTVS, qui &longs;olo natur&aelig; acumine, quoduis geometricum Pro&shy;<lb/>
blema, quamuis difficile re&longs;oluebat. </s>
          <s id="s.005841">Proclus.<!-- KEEP S--></s>
        </p>
        <pb pagenum="43" xlink:href="009/01/327.jpg"/>
        <p type="head">
          <s id="s.005842"><emph type="italics"/>QVINTVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table11"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table11"/>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>301</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;tum ann.</cell>
            <cell>452</cell>
          </row>
          <row>
            <cell>P. Sextio, T. Memnio Con&longs;&longs;.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.005843"><emph type="italics"/>In quo Socrates &longs;eptuagenarius anno ab Vrbe cond. </s>
          <s id="s.005844">353. <lb/>
Olymp. <!-- REMOVE S-->95. ann. </s>
          <s id="s.005845">1. moruur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005846">DEMOCRITVS MILESIVS anno vno maior natu qu&agrave;m <lb/>
Socrates. </s>
          <s id="s.005847">&longs;crip&longs;it de contactu circuli, &amp; &longs;ph&aelig;r&aelig;. </s>
          <s id="s.005848">de Geometria. <lb/>
<!-- KEEP S--></s>
          <s id="s.005849">de lineis irrationalibus. </s>
          <s id="s.005850">de &longs;olidis. </s>
          <s id="s.005851">de numeris geometricis. </s>
          <s id="s.005852">Har&shy;<lb/>
monica, &longs;iue de Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005853">de concentu, &amp; harmonia. </s>
          <s id="s.005854">Actinogra&shy;<lb/>
phiam, &longs;iue de radijs, &longs;iue de Per&longs;pectiua, &longs;iue de Scenographice. </s>
          <s id="s.005855">certamen <lb/>
Clep&longs;ydr&aelig;. </s>
          <s id="s.005856">de Planetis, de anno magno. </s>
          <s id="s.005857">C&oelig;li, <expan abbr="t&etail;rr&aelig;&qacute;">t&etail;rr&aelig;que</expan>; <expan abbr="de&longs;cription&etilde;">de&longs;criptionem</expan>. </s>
          <s id="s.005858">Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005859">ANTISTHENES Socratis auditor de Mu&longs;ica <expan abbr="c&otilde;mentatus">commentatus</expan> e&longs;t. </s>
          <s id="s.005860">Laer.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005861">SIMMIAS Thebanus di&longs;cipulus Socratis, de Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.005862">Laert. <!-- KEEP S--></s>
          <s id="s.005863">Suid.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005864">PARMENIDES ELEATES primus dixit terram e&longs;&longs;e <expan abbr="rot&utilde;dam">rotundam</expan>, <lb/>
&amp; in medio mundi &longs;itam. </s>
          <s id="s.005865">Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005866">PROTAGORAS de Mathematicis &longs;crip&longs;it. </s>
          <s id="s.005867">Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005868">EPICVRVS ille Epicureorum Sectarius, de Mu&longs;ica &longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.005869">METON, &amp; EVCTEMON ante Alex. Mag. obitum ann. </s>
          <s id="s.005870">108. Athenis &longs;ol&longs;ti&shy;<lb/>
tium ob&longs;eruarunt. </s>
          <s id="s.005871">Methon primus tempe&longs;tatum <lb/>
progno&longs;tica &longs;ingulis annis edidit. </s>
          <s id="s.005872">primus cyclum Enneadecaterida, vel Au&shy;<lb/>
reum numerum in Gr&aelig;cia in&longs;tituit; qui annus Methonis dicitur.</s>
        </p>
        <p type="main">
          <s id="s.005873">PLATO, Socratis auditor, fuit maxim&egrave; Mathematum &longs;tudio&longs;us; nam <lb/>
&longs;ingulis diebus auditorib. </s>
          <s id="s.005874">&longs;uis geometricum problema proponebat. </s>
          <s id="s.005875">Ageo&shy;<lb/>
metretos &egrave; &longs;chola arcebat. </s>
          <s id="s.005876">primus &longs;ectiones conicas, &amp; cylindericas inchoa&shy;<lb/>
uit. </s>
          <s id="s.005877">Modum demon&longs;trandi per Analy&longs;im inuenit, item modum agri dime&shy;<lb/>
tiendi pulcherrimum, vt apud Vitr. con&longs;tat. </s>
          <s id="s.005878">Delij eum tanquam oraculum <lb/>
con&longs;uluerunt de modo ar&aelig;, &longs;iue cubi duplicandi, quos tamen ip&longs;e ad Eucli&shy;<lb/>
dem Geometram mode&longs;t&egrave; abire iu&longs;&longs;it: non <expan abbr="tam&etilde;">tamen</expan> omnino &agrave; problemate ab&shy;<lb/>
&longs;tinuit, extat enim apud <expan abbr="Eutoci&utilde;">Eutocium</expan> Platonis modus inuendi duas medias pro&shy;<lb/>
portionales, quibus inuentis, cubi duplicatio peracta e&longs;&longs;et. </s>
          <s id="s.005879">in &longs;uis pr&etail;terea <lb/>
Dialogis <expan abbr="c&otilde;plura">complura</expan> habet Mathematica, qu&aelig; olim Theon Smyrneus, ac Phi&shy;<lb/>
lippus Mend&aelig;us commentarijs illu&longs;trarunt. </s>
          <s id="s.005880">Proclus Lucr.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005881">AMICLAS HERACLEOTES Platonis familiaris geometricas <lb/>
inuentiones amplificauit.</s>
        </p>
        <p type="main">
          <s id="s.005882">LEODAMAS THASIVS &agrave; Platone Analy&longs;im didicit, cuius ope <lb/>
multa geometrica excogitauit.</s>
        </p>
        <p type="main">
          <s id="s.005883">NEOCLIDES LEODAMANTE iunior, inter rerum geome&shy;<lb/>
tricarum repertores connumeratur. </s>
          <s id="s.005884">Proc.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005885">LEON di&longs;cipulus Neoclidis: Determinationem geometricam inuenit, <lb/>
qu&aelig; di&longs;tinguit problema po&longs;&longs;ibile ab impo&longs;&longs;ibili. </s>
          <s id="s.005886">Geometrica elementa, <lb/>&longs;ecundus ab Hippocrate, &longs;ed accuratius con&longs;truxit. </s>
          <s id="s.005887">Procl.<!-- KEEP S--></s>
        </p>
        <pb pagenum="44" xlink:href="009/01/328.jpg"/>
        <p type="main">
          <s id="s.005888">EVDOXIVS GNIDVIS A&longs;tronomus, Leonte iunior, &amp; Platonis <lb/>
Comes in Aegyptum. </s>
          <s id="s.005889">Quintum elem. </s>
          <s id="s.005890">Euclidis de proportionibus inuenit. <lb/>
</s>
          <s id="s.005891">Theoremata multa vniuer&longs;alia reddidit, inuenit etiam Arachnen, horolo&shy;<lb/>
gium, videlicet &longs;olare, in quo line&aelig; horari&aelig;, &amp; arcus &longs;ignorum in modum <lb/>arane&aelig; &longs;e &longs;ecant. </s>
          <s id="s.005892">Vitr. <!-- KEEP S--></s>
          <s id="s.005893">Octaetidem, ide&longs;t, Solis, ac Lun&aelig; per octonos an&shy;<lb/>
nos recur&longs;us docuit. </s>
          <s id="s.005894">&longs;crip&longs;it de Geometria, &amp; A&longs;tronomia. <!-- KEEP S--></s>
          <s id="s.005895">Mathematicas <lb/>
ad v&longs;um mechanicum vn&agrave; cum Archita traducere conatus e&longs;t: quos am&shy;<lb/>
bos Plato redarguit, qu&ograve;d Philo&longs;ophiam pro&longs;titui&longs;&longs;ent.</s>
        </p>
        <p type="main">
          <s id="s.005896">ARCHITA TERENTIVS Mechanice inuentor: reprehen&longs;us &agrave; <lb/>Platone, vt modo dictum e&longs;t. </s>
          <s id="s.005897">Cubum reperit. </s>
          <s id="s.005898">ligneam <expan abbr="columb&atilde;">columbam</expan> volantem <lb/>
exhibuit. </s>
          <s id="s.005899">qua pr&aelig;terea ratione duas medias reperiret, extat apud <expan abbr="Eutoci&utilde;">Eutocium</expan>.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005900">THE&AElig;TETVS ATHENIENSIS Archit&aelig; Tarentini &longs;odalis, <lb/>
cum quo Geometrica auxit. </s>
          <s id="s.005901">Procl. <!-- REMOVE S-->primus de <expan abbr="quinq;">quinque</expan> &longs;olidis tractauit. </s>
          <s id="s.005902">Laer. <lb/>
<!-- REMOVE S-->inuenit 10. decimi.</s>
        </p>
        <p type="main">
          <s id="s.005903">BRYSO, &amp; ANTIPHON Circuli quadrationem inuenire conantur. </s>
          <s id="s.005904">extant <lb/>
ip&longs;orum conatus apud Ari&longs;t. quos explicauimus in <lb/>
locis Math.</s>
        </p>
        <p type="main">
          <s id="s.005905">PHILIPPVS MEND&AElig;VS di&longs;cipulus Platonis. </s>
          <s id="s.005906">loca Mathema&shy;<lb/>
tica operum Platonis explicauit. </s>
          <s id="s.005907">Comperit Iridem in&longs;equentes &longs;e fugere, <lb/>
fugientes ver&ograve; in&longs;equi.</s>
        </p>
        <p type="main">
          <s id="s.005908">HELICO CYGICENVS Platonis familiaris, c&ugrave;m Dyoni&longs;io Re&shy;<lb/>
gi &longs;olis defectum, qui tunc accidit, antea mult&ograve; pr&aelig;nuncia&longs;&longs;et, Rex &longs;umma <lb/>
admiratione affectus, argenti talentum ei donauit.</s>
        </p>
        <p type="main">
          <s id="s.005909">PHILOSOPHVS, Platonis auditor. </s>
          <s id="s.005910">De interuallo Solis, &amp; Lun&aelig;. <!-- KEEP S--></s>
          <s id="s.005911">de <lb/>
eclyp&longs;i. </s>
          <s id="s.005912">de magnitudine Solis, Lun&aelig;, &amp; terr&aelig;. </s>
          <s id="s.005913">de Planetis. </s>
          <s id="s.005914">de Arithmetica. <lb/>
<!-- KEEP S--></s>
          <s id="s.005915">de numeris fecundis, de opticis, de circularibus, &amp; medietatibus egit. </s>
          <s id="s.005916">Suida.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.005917"><emph type="italics"/>SEXTVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table12"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table12"/>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>401</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti Natiuitatem ann.</cell>
            <cell>352</cell>
          </row>
          <row>
            <cell>Tito Manlio Dictatore.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.005918"><emph type="italics"/>In quo Alex. Mag. imperauit: <expan abbr="obijt&qacute;">obijtque</expan>; ann. </s>
          <s id="s.005919">ab Orbe cond. </s>
          <s id="s.005920">3791. <lb/>
ab Vrbe cond. </s>
          <s id="s.005921">425.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005922">THEVDIVS MAGNES, elementa geometrica tertius con&shy;<lb/>
&longs;truxit. </s>
          <s id="s.005923">Procl.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005924">CYGICINVS ATHENIENSIS geometrica amplia&shy;<lb/>
uit. </s>
          <s id="s.005925">Procl.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005926">HERMOTIMVS COLOPHONIVS, quartus elementa geo&shy;<lb/>
metrica vberiora reddidit.</s>
        </p>
        <p type="main">
          <s id="s.005927">ARIST&AElig;VS &longs;enior, ante Euclidem demon&longs;trauit de conicis: quem <lb/>Euclides in ij&longs;dem &longs;equutus e&longs;t. </s>
          <s id="s.005928">Item de re&longs;olutione. </s>
          <s id="s.005929">Item de locis &longs;olidis, <lb/>
lib. 5. Pappus.</s>
        </p>
        <pb pagenum="45" xlink:href="009/01/329.jpg"/>
        <p type="main">
          <s id="s.005930">GEMINVS demon&longs;trauit linearum tres tant&ugrave;m e&longs;&longs;e &longs;imilares, <expan abbr="rect&atilde;">rectam</expan>, <lb/>
circularem, &amp; &longs;piralem cylindricam. </s>
          <s id="s.005931">Ortus <expan abbr="quoq;">quoque</expan> linearum &longs;piricarum, &amp; <lb/>
conchoidum, &amp; ci&longs;&longs;oidum, tradidit. </s>
          <s id="s.005932">Propo&longs;itionem quintam primi ele&shy;<lb/>
mentorum vniuer&longs;alius, quam Thales, demon&longs;trauit; o&longs;tendit enim &aelig;qua&shy;<lb/>les lineas rectas ab vno puncto ad vnam &longs;imilium partium lineam, ide&longs;t, vel <lb/>
ad rectam, vel ad circularem, vel ad cylindricam, <expan abbr="incid&etilde;tes">incidentes</expan>, facere angulos <lb/>
ad ba&longs;im &aelig;quales. </s>
          <s id="s.005933">Scrip&longs;it pr&aelig;terea lib. 6. <expan abbr="geometricar&utilde;">geometricarum</expan> <expan abbr="enarration&utilde;">enarrationum</expan>. </s>
          <s id="s.005934">Procl.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005935">PERSEVS CITTICVS Po&longs;t Geminum: inuenit lineas &longs;piricas. <lb/>
</s>
          <s id="s.005936">Proclus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005937">MENECHMVS EVDOXI di&longs;cipulus, &longs;ectiones conicas reperit. <lb/>
</s>
          <s id="s.005938">Tribus proportionibus tres alias adiecit. </s>
          <s id="s.005939">modus ip&longs;ius <expan abbr="inueni&etilde;di">inueniendi</expan> duas me&shy;<lb/>
dias, extat apud Eutocium.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005940">DINOSTRATVS Menechmi frater, geometrica <expan abbr="c&otilde;plura">complura</expan> reperit.</s>
        </p>
        <p type="main">
          <s id="s.005941">XENOCRATES CHALCEDONIVS Platonis audit. </s>
          <s id="s.005942">de geo&shy;<lb/>
metria primum duos, deinde <expan abbr="quinq;">quinque</expan> lib. compo&longs;uit. </s>
          <s id="s.005943">Item de numeris lib. 1. <lb/>
De a&longs;trologia lib. 6. Diog. <!-- REMOVE S-->Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005944">EVCLIDES Megaren&longs;is geometra, Platonis tempore, &longs;iquidem te&shy;<lb/>
&longs;te Valer. <!-- REMOVE S-->Maxim. <!-- REMOVE S-->ad eum Plato, Delios ar&aelig; &longs;acr&etail; conductores amandauit. <lb/>
</s>
          <s id="s.005945">Alexandri&aelig; longo tempore dedit operatu di&longs;cipulis, vnde excellentem in <lb/>
Mathematicis habitum con&longs;equutus e&longs;t, <expan abbr="neq;">neque</expan> <expan abbr="v&longs;qu&atilde;">v&longs;quam</expan> deceptus e&longs;t. </s>
          <s id="s.005946">Papp. <!-- REMOVE S-->lib. 7. <lb/>
vixit autem, &amp; claru&iacute;t, v&longs;que ad Ptol&aelig;meum primum Aegypti Regem, vt <lb/>vult Procl &longs;it ne idem cum Euclide Megaren&longs;i auctore &longs;ect&aelig; Megaric&aelig;, du&shy;<lb/>
bitatur. </s>
          <s id="s.005947">Quintus geometrica elementa mira methodo contexuit. </s>
          <s id="s.005948">ip&longs;ius ex&shy;<lb/>
tant etiam Ph&oelig;nomena, optica; catoptrica. </s>
          <s id="s.005949">mu&longs;ica. </s>
          <s id="s.005950">data. </s>
          <s id="s.005951">Item de re&longs;olu&shy;<lb/>
tione, de fallacijs, de locis ad &longs;uperficiem lib. 2. Conicorum lib. 4. Item <lb/>
Pori&longs;matum lib. 3. qu&aelig; perierunt. </s>
          <s id="s.005952">Pappus, &amp; Procl.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005953">L. PAPYRIVS cur&longs;or Rom&etail; primum &longs;olare horologium publico lo&shy;<lb/>
co con&longs;truxit. </s>
          <s id="s.005954">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005955">HERMOPHILVS c&oelig;cus Theopompum Geometriam &longs;ine abaco, <lb/>
ac radio docuit.</s>
        </p>
        <p type="main">
          <s id="s.005956">ARATVS Poeta Gr&aelig;cus, ante Hipparchum centum fer&egrave; annis, de <lb/>
C&oelig;lo, <expan abbr="&longs;tellis&qacute;">&longs;tellisque</expan>; eleganter cecinit.</s>
        </p>
        <p type="main">
          <s id="s.005957">CALIPPVS Cygicenus a&longs;tronomus in&longs;ignis, cuius Ari&longs;tot. in Meta&shy;<lb/>
phy&longs;ic. <!-- REMOVE S-->meminit. </s>
          <s id="s.005958">periodum 76. annorum ex quatuor Methonis cyclis con&shy;<lb/>
flauit, qua Sol, &amp; Luna iterum ad pri&longs;tina re&longs;tituantur: initium prime pe&shy;<lb/>
riodi &longs;tatuit <expan abbr="obit&utilde;">obitum</expan> Darij Regis, &longs;eu initium Monarchi&aelig; Gr&etail;corum. </s>
          <s id="s.005959">ex Al&shy;<lb/>
mag. <!-- REMOVE S-->Ptol.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005960">ARISTOT. <!-- KEEP S--></s>
          <s id="s.005961">Platonis auditor, &amp; Alex. Magn. <!-- REMOVE S-->pr&aelig;ceptor, &longs;crip&longs;it Me&shy;<lb/>
chanicas qu&aelig;&longs;tiones. </s>
          <s id="s.005962">librum vnum, quem appellauit <expan abbr="Mathematic&utilde;">Mathematicum</expan>. </s>
          <s id="s.005963">&longs;ect. </s>
          <s id="s.005964">19. <lb/>
problematum de mu&longs;ica Item alium librum de mu&longs;ica. </s>
          <s id="s.005965">Halonis, &amp; Iridis <lb/>
demon&longs;trationes apud ip&longs;um primum reperiuntur. </s>
          <s id="s.005966">pa&longs;&longs;im in &longs;uis operibus <lb/>omnis generis Mathemata ingerit.</s>
        </p>
        <p type="main">
          <s id="s.005967">AVTOLYCVS pr&aelig;ceptor Arce&longs;ilai, floruit circa Olymp. <!-- REMOVE S-->120. extat <lb/>eius &longs;ubtilis admodum liber de &longs;ph&aelig;ra, qu&aelig; mouetur, &amp; alter de vario ortu <lb/>
&amp; occa&longs;u &longs;yderum. </s>
          <s id="s.005968">Diog Laer. <!-- REMOVE S-->in Arcelilao.</s>
        </p>
        <p type="main">
          <s id="s.005969">THEOPHRASTVS Eri&longs;&longs;ius Ari&longs;t. di&longs;cipulus, &amp; succe&longs;&longs;or, reliquit <pb pagenum="46" xlink:href="009/01/330.jpg"/>tres libros de mu&longs;ica, vnum de mu&longs;icis. </s>
          <s id="s.005970">Harmonicorum vnum. </s>
          <s id="s.005971">de men&longs;u&shy;<lb/>
ris vnum. </s>
          <s id="s.005972">de numeris vnum. </s>
          <s id="s.005973">Hi&longs;toriarum geometricarum quatuor. </s>
          <s id="s.005974">A&longs;tro&shy;<lb/>
logic&aelig; hi&longs;tori&aelig; 6. Arithmeticarum hi&longs;toriarum vnum. </s>
          <s id="s.005975">de lineis indiuiduis. <lb/>
</s>
          <s id="s.005976">Diog. <!-- REMOVE S-->Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005977">HERACLIDES Ponticus, Speu&longs;ippi, &amp; Ari&longs;t. auditor. </s>
          <s id="s.005978">de Mu&longs;ica <lb/>
lib. duos. </s>
          <s id="s.005979">de Geometria etiam &longs;crip&longs;it. </s>
          <s id="s.005980">Diog. <!-- REMOVE S-->Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005981">DICEARCHVS Siculus, Ari&longs;t, auditor, primus montium altitudi&shy;<lb/>
nem perpendicularem dimen&longs;us e&longs;t; alti&longs;&longs;imum prodidit Pelion, nimirum <lb/>
1250. pa&longs;&longs;uum. </s>
          <s id="s.005982">Plinius lib. 2. c. <!-- REMOVE S-->67.</s>
        </p>
        <p type="main">
          <s id="s.005983">ARISTOXENVS Tarentinus Mu&longs;icus, auditor Ari&longs;t. eius extant <lb/>
harmonicorum lib. 3. Suid.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005984">CONON Geometra, &amp; A&longs;tronomus in&longs;ignis. </s>
          <s id="s.005985">Ptol&aelig;meo Philadelpho <lb/>
gratificaturus, Berenices Comam in C&oelig;lum tran&longs;ulit. </s>
          <s id="s.005986">libros 6. de A&longs;trolo&shy;<lb/>
gia compo&longs;uit. </s>
          <s id="s.005987">de eo Virgil.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005988"><emph type="italics"/>In medio duo &longs;igna, Conon. &amp; quis fuit alter.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.005989">ille ver&ograve; alter Pontano no&longs;tro in Virgilium e&longs;t Archimedes Cononi &longs;ynero&shy;<lb/>
nus, &amp; familiaris. </s>
          <s id="s.005990">Hunc plurimi faciebat Archimedes, <expan abbr="eius&qacute;">eiusque</expan>; propterea <lb/>
mortem in lib. de Quadrat. </s>
          <s id="s.005991">Parab. <!-- REMOVE S-->deflet.</s>
        </p>
        <p type="main">
          <s id="s.005992">TIMOTHEVS Mu&longs;icus, c&ugrave;m ad Alexandri magni men&longs;am orthium <lb/>
modum caneret, regem velut in&longs;anum coegit ad arma: rur&longs;us remittente <lb/>
cantu, regis etiam furorem remi&longs;it. </s>
          <s id="s.005993">Chromaticum genus inuexit. </s>
          <s id="s.005994">&longs;eptem <lb/>
Terpandri chordis quatuor addidit. </s>
          <s id="s.005995">Plut. <!-- REMOVE S-->de mu&longs;ic.</s>
        </p>
        <p type="main">
          <s id="s.005996">ARCHELAVS Chorographus, omnem terram ab Alex. Mag. pera&shy;<lb/>
gratam de&longs;crip&longs;it. </s>
          <s id="s.005997">Diog. Laert.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.005998">XENOPHANTVS Mu&longs;icus, certis modis Alex. Magn. <!-- REMOVE S-->ad arma pro <lb/>
libito concitabat.</s>
        </p>
        <p type="main">
          <s id="s.005999">ARISTARCHVS Samius, hoc tempore ante <expan abbr="Hipparch&utilde;">Hipparchum</expan> 200. ann. <lb/>
</s>
          <s id="s.006000">Scaphen, &longs;eu Hemi&longs;ph&aelig;rium, hoc e&longs;t horologium &longs;ciothericum in concauo <lb/>
hemi&longs;ph&aelig;rico de&longs;crip&longs;it Vitr. extat ip&longs;ius egregium monumentum ingenij, <lb/>
libellus de magnitudine, &amp; di&longs;tantijs Solis, &amp; Lun&aelig;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006001">BEROSVS Chald&aelig;us, tempore Antiochi Sotheris hemicyclium ex&shy;<lb/>
cauatum, genus horologij &longs;olaris reperit. </s>
          <s id="s.006002">dicebat Lunam e&longs;&longs;e pilam ex di&shy;<lb/>
midia parte candentem: reliqua habere ceruleo colore. </s>
          <s id="s.006003">c&aelig;tera apud Vitr. <lb/>
<!-- REMOVE S-->lib. 9. ei Athenien&longs;es ob diuinas pr&aelig;dictiones public&egrave; in gymna&longs;io &longs;tatuam <lb/>
inaurata lingua &longs;tatuere. </s>
          <s id="s.006004">Plin.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006005">ARISTILLVS A&longs;tronomus, cuius ob&longs;eruationes circa inerrantes <lb/>
&longs;tellas, &longs;&aelig;p&egrave; Ptol. <!-- REMOVE S-->7. Magn&aelig; con&longs;tr. </s>
          <s id="s.006006">recen&longs;et. </s>
          <s id="s.006007"><expan abbr="videtur&qacute;">videturque</expan>; eum Timocharide <lb/>
paul&ograve; antiquiorem facere.</s>
        </p>
        <p type="main">
          <s id="s.006008">TIMOCHARIS ante Hipparchum ann. </s>
          <s id="s.006009">156. ab obitu ver&ograve; Alexan. <lb/>
<!-- REMOVE S-->Mag. ann. </s>
          <s id="s.006010">41. &longs;uas ob&longs;eruationes habuit, quas Ptol&aelig;meus in Almage&longs;to re&shy;<lb/>
cen&longs;et. </s>
          <s id="s.006011">ob&longs;eruauit primam &longs;tellam Arietis po&longs;t &longs;ectionem vernalem gr. <!-- REMOVE S-->2.<!-- KEEP S--></s>
        </p>
        <pb pagenum="47" xlink:href="009/01/331.jpg"/>
        <p type="head">
          <s id="s.006012"><emph type="italics"/>SEPTIMVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/>
<arrow.to.target n="table13"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table13"/>
          <row>
            <cell>Ab Vrbe cond. anno</cell>
            <cell>501</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti natiuitatem ann.</cell>
            <cell>252</cell>
          </row>
        </table>
        <p type="main">
          <s id="s.006013">Con&longs;&longs;. <!-- REMOVE S-->D. Lunio.</s>
        </p>
        <p type="main">
          <s id="s.006014">L. Po&longs;thumio.</s>
        </p>
        <p type="main">
          <s id="s.006015">ERATOSTHENES Cyreneus &longs;ub Ptolym&aelig;o Euergete primo, &amp; <lb/>
duobus &longs;equentibus regibus, ab obitu Alex. ann. </s>
          <s id="s.006016">90. &amp; totidem an&shy;<lb/>
te Hipparchum, a&longs;tronomicis in Aegypto vacabat, <expan abbr="reperit&qacute;">reperitque</expan>; Solis <lb/>
declinationem gr. <!-- REMOVE S-->23. 51. primus terr&aelig; ambitum ratione vmbrarum <lb/>
Solis inue&longs;tigauit, vt ex Cleomede refert Clauius in &longs;ph&aelig;ra, vbi eam fus&egrave; <lb/>
explicat. </s>
          <s id="s.006017">Duplicandi cubi &longs;ummus fuit artifex, vt patet ex eius Me&longs;olabio <lb/>
apud Pappum, &amp; Eutocium, <expan abbr="atq;">atque</expan> ob id votiuam tabellam in templo con&longs;e&shy;<lb/>
crauit. </s>
          <s id="s.006018">extat epi&longs;tola ip&longs;ius ad Regem Ptol&aelig;meum apud Eutocium, de ra&shy;<lb/>
tione cubi duplicandi.</s>
        </p>
        <p type="main">
          <s id="s.006019">ARCHIMEDES Syracu&longs;anus ingeniorum Ph&oelig;nix: quadraginta <lb/>
ip&longs;ius mira adinuenta Mechanica fui&longs;&longs;e, tradit Pappus lib. 8. quorum vnum <lb/>
fuit; datum pondus data potentia mouere, in quo fertur dixi&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.006020"><emph type="italics"/>Dic vbi contestam, &amp; c&oelig;lum terramqu&eacute; mouebo.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006021">Alterum, quo portionem argenti auro mixtam in Corona illa deprehendit; <lb/>
vnde pr&aelig; l&aelig;titia &egrave; balneo nudus exiliuit; <expan abbr="atq;">atque</expan> per Vrbem domum <expan abbr="proper&atilde;s">properans</expan> <lb/>
clamabat <foreign lang="greek">e&lpar;urhka, e&lpar;urhka.</foreign></s>
        </p>
        <p type="main">
          <s id="s.006022">Tertium &longs;it &longs;ph&aelig;ra illa vitrea, Automa celebre, qu&aelig; &longs;yderum <expan abbr="omni&utilde;">omnium</expan> mo&shy;<lb/>
tus mir&egrave; imitabatur. </s>
          <s id="s.006023">de qua Claudianus pulcherrimum illud texit epigram&shy;<lb/>
ma: Iupiter in paruo, &amp;c.</s>
        </p>
        <p type="main">
          <s id="s.006024">Quartum, &longs;pecula parabolica con&longs;truxit, quibus ho&longs;tium naues procul <lb/>
comburerentur.</s>
        </p>
        <p type="main">
          <s id="s.006025">Quintum, chocleam aquaticam &lpar;ex Vitruuio, &amp; Diodoro&rpar; qua in altum <lb/>
aqua effertur excogitauit. </s>
          <s id="s.006026">quam Io&longs;ephus Cedretus no&longs;tra tempe&longs;tate re&shy;<lb/>
&longs;taurauit.</s>
        </p>
        <p type="main">
          <s id="s.006027">Sextum, nauim graui pondere oneratam, machina quadam facillim&egrave; in <lb/>
litus attraxit.</s>
        </p>
        <p type="main">
          <s id="s.006028">Septimum, complures bellicas machinas fabricatus e&longs;t, quibus per trien&shy;<lb/>
nium contra ho&longs;tes Romanos patriam &longs;olus tutatus e&longs;t. </s>
          <s id="s.006029">reliqua ip&longs;ius adin&shy;<lb/>
uenta perierunt. </s>
          <s id="s.006030">Verumenimuer&ograve; admiranda mihi magis ip&longs;ius &longs;cripta mo&shy;<lb/>
numenta videntur, in quibus quidquid e&longs;t, totum Archimedis e&longs;t. </s>
          <s id="s.006031">quorum <lb/>
memoria extat, h&aelig;c &longs;unt. </s>
          <s id="s.006032">De &aelig;quaponderantibus lib. 2. Circuli dimen&longs;io. <lb/>
</s>
          <s id="s.006033">de lineis &longs;piralibus. </s>
          <s id="s.006034">quadratura paraboles. </s>
          <s id="s.006035">de conoidibus, &amp; &longs;ph&aelig;roidibus. <lb/>
</s>
          <s id="s.006036">de aren&aelig; numero. </s>
          <s id="s.006037">de ijs, qu&aelig; vehuntur in aqua. </s>
          <s id="s.006038">de &longs;ph&aelig;ra, &amp; cylindro. </s>
          <s id="s.006039">de li&shy;<lb/>
bra. </s>
          <s id="s.006040">viaticum. </s>
          <s id="s.006041">de &longs;ph&aelig;r&aelig; <expan abbr="c&otilde;&longs;tructione">con&longs;tructione</expan>. </s>
          <s id="s.006042">de 13. &longs;olidis &agrave; &longs;e inuentis. </s>
          <s id="s.006043">lemmata. <lb/>
</s>
          <s id="s.006044">de &longs;ectione circuli. </s>
          <s id="s.006045">de &longs;peculis comburentibus. </s>
          <s id="s.006046">M. <!-- REMOVE S-->Marcellus interdixerat <lb/>
ne ille vnus captis Syracu&longs;is occideretur: tantus virtuti honos, vel ab ho&longs;ti&shy;<lb/>
bus haberi par e&longs;t. </s>
          <s id="s.006047">occi&longs;us e&longs;t autem ab ignaro milite, dum in patri&aelig; dire&shy;<lb/>
ptione totus cuidam demon&longs;trationi vacaret.</s>
        </p>
        <pb pagenum="48" xlink:href="009/01/332.jpg"/>
        <p type="main">
          <s id="s.006048">CTESIBVS Machinator &longs;ubtili&longs;&longs;imus: Pneumatica inuenit, ide&longs;t, <lb/>
qu&aelig; &longs;piritu, ac vento motus efficerent, qua&longs;i &longs;piritalia. </s>
          <s id="s.006049">hydraulicas machi&shy;<lb/>
nas primus con&longs;truxit. </s>
          <s id="s.006050">adhuc viget machina illa Cte&longs;ibij, de qua Vitr. <!-- REMOVE S-->Hy&shy;<lb/>
draulica etiam horologia primus exhibuit.</s>
        </p>
        <p type="main">
          <s id="s.006051">SVLPITIVS GALLVS <expan abbr="C&otilde;&longs;ul">Con&longs;ul</expan>, primus Romani generis rationem <lb/>
eclyp&longs;ium in vulgus edidit, &amp; pridie quam P. <!-- REMOVE S-->Aemilius Per&longs;en Regem &longs;upe&shy;<lb/>
raret, animos militum ob futuram &longs;equenti die eclyp&longs;im trepidaturos, bre&shy;<lb/>
ui futuri euentus, admonitione habita, confirmauit. </s>
          <s id="s.006052">Plin. Val. <!-- KEEP S--></s>
          <s id="s.006053">Max.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006054"><emph type="italics"/>OCTAVVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table14"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table14"/>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>601</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti natiuitatem</cell>
            <cell>152</cell>
          </row>
          <row>
            <cell>Con&longs;. L. Mummio.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006055">APOLLONIVS PERG&AElig;VS &longs;ub Ptol&aelig;meo euergete &longs;ecun&shy;<lb/>
do cognomento magnus Geometra, quod vniuer&longs;aliter de omni <lb/>
Cono <expan abbr="elem&etilde;ta">elementa</expan> conica octo libris &longs;ubtili&longs;&longs;imis demon&longs;tra&longs;&longs;et. </s>
          <s id="s.006056">&longs;cri&shy;<lb/>
p&longs;it pr&aelig;terea de &longs;ectione proportionis, &amp; &longs;patij. </s>
          <s id="s.006057">de locis planis <lb/>
lib. 2. de perturbatis rationibus. </s>
          <s id="s.006058">de tactionibus. </s>
          <s id="s.006059">de inclinationibus. </s>
          <s id="s.006060">de cho&shy;<lb/>
clea. </s>
          <s id="s.006061">Pappus. </s>
          <s id="s.006062">modus ip&longs;ius inueniendi duas medias, extat apud Eutocium in <lb/>
comm. <!-- REMOVE S-->Archimedis. <!-- KEEP S--></s>
          <s id="s.006063">pharetram. </s>
          <s id="s.006064">&longs;olaris horologij genus reperit. </s>
          <s id="s.006065">Vitr.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006066">ISIDORVS Philo&longs;ophus, Hyp&longs;iclis Alexandrini pr&aelig;ceptor; nam <lb/>
Hyp&longs;icles in 15. Elem. vbi ponit inclinationes <expan abbr="quinq;">quinque</expan> <expan abbr="corpor&utilde;">corporum</expan> regularium, <lb/>
ait &longs;e eas ab I&longs;idoro Magno pr&aelig;ceptore &longs;uo accepi&longs;&longs;e. </s>
          <s id="s.006067">Plinius eum citat in <lb/>
Geographicis. <!-- KEEP S--></s>
          <s id="s.006068">Suidas ver&ograve; &longs;ic, I&longs;idorus Philo&longs;ophus, vt &longs;i quis alius philo&shy;<lb/>
&longs;ophatus e&longs;t in Mathematis.</s>
        </p>
        <p type="main">
          <s id="s.006069">YPSICLES Alexandrinus, I&longs;idori di&longs;cipulus, qui libros duos Elemen&shy;<lb/>
torum 14. &amp; 15. Euclidi addidit. </s>
          <s id="s.006070">nominat Apollonium. </s>
          <s id="s.006071">videtur his tempo&shy;<lb/>
ribus extiti&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.006072">PHILO BIZANTIVS mechanicus, mechanica fecit ante Hero&shy;<lb/>nem, &agrave; quo memoratur; hunc exi&longs;timo eum e&longs;&longs;e, cuius Proclus ad octauam <lb/>
primi meminit, referens ip&longs;ius demon&longs;trationem. </s>
          <s id="s.006073">modus ip&longs;ius inueniendi <lb/>
duas medias legitur apud Eutocium in Archim.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006074">POSSIDONIVS Philo&longs;ophus Panetij di&longs;cipulus, qui Rhodi tempo&shy;<lb/>
re Ciceronis docebat, &agrave; Plinio Mathematicus appellatur: &agrave; Strabone ve&shy;<lb/>
r&ograve; citatur in Geographicis. <!-- KEEP S--></s>
          <s id="s.006075">Geographica igitur &longs;crip&longs;it. </s>
          <s id="s.006076">huius ianu&aelig; c&ugrave;m <lb/>
ad eum audiendum Pomponius Magnus adiret, Imperij fa&longs;ces &longs;ubmi&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006077">SERENVS Antin&longs;en&longs;is: cuius &longs;unt Cylindricorum lib. 2. &longs;ubtili&longs;&longs;imi. <lb/>
</s>
          <s id="s.006078">videtur in h&aelig;c tempora po&longs;t Apollonium incidi&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.006079">HERO <expan abbr="Alex&atilde;drinus">Alexandrinus</expan> Cte&longs;ibij di&longs;cipulus, eius &longs;unt Automata; Spirita&shy;<lb/>
lia: de Balli&longs;tis. </s>
          <s id="s.006080">Mechanica. </s>
          <s id="s.006081">Barulcos. </s>
          <s id="s.006082">de Rotulis. </s>
          <s id="s.006083">de Horologijs aquaticis. <lb/>
</s>
          <s id="s.006084">Camaricha. </s>
          <s id="s.006085">Cambe&longs;tria. </s>
          <s id="s.006086">modus ip&longs;ius <expan abbr="inueni&etilde;di">inueniendi</expan> duas medias legitur apud <lb/>
Eutocium. <!-- KEEP S--></s>
          <s id="s.006087">Geometrumenon, ide&longs;t Geometria practica. </s>
          <s id="s.006088">de eo fit mentio ad <lb/>
&longs;ecundam, &amp; 25. primi elem. </s>
          <s id="s.006089">Proclus. <!-- KEEP S--></s>
          <s id="s.006090">Pappus. </s>
          <s id="s.006091">Vitr.<!-- KEEP S--></s>
        </p>
        <pb pagenum="49" xlink:href="009/01/333.jpg"/>
        <p type="main">
          <s id="s.006092">HIPPARCVS, qui &amp; Abrachis dicitur ab obitu Alexandri ann. </s>
          <s id="s.006093">100. <lb/>
ante Ptolem&aelig;um 280. ob&longs;eruauit maximam Solis declinationem gr. <!-- REMOVE S-->23. 51. <lb/>
Inuenit primam Arietis po&longs;t &aelig;quinotij Venrni punctum, gr. <!-- REMOVE S-->4. <expan abbr="nou&atilde;">nouam</expan> &longs;tellam <lb/>
&longs;uo &aelig;uo genitam deprehendit, cuius occa&longs;ione in &longs;yderalem &longs;cientiam &longs;eri&ograve; <lb/>
incubuit. </s>
          <s id="s.006094">primus igitur &longs;tellas numerauit, <expan abbr="&longs;uis&qacute;">&longs;uisque</expan>; locis a&longs;&longs;ignauit, organis <lb/>
ad id excogitatis. </s>
          <s id="s.006095">Plin. Scrip&longs;it de motu Lun&aelig; in latitudinem, &amp; de Arati <lb/>
ph&aelig;nomenis. </s>
          <s id="s.006096">ex Suida. <!-- KEEP S--></s>
          <s id="s.006097">Tabulas etiam a&longs;tronomicas, te&longs;te Ptol. <!-- REMOVE S-->condidit. <lb/>
</s>
          <s id="s.006098">Adhuc extant eius lib. 3. in Arati Ph&aelig;nomena: &amp; vnus A&longs;teri&longs;morum, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; <lb/>
Gr&aelig;c&egrave; nuper editi.</s>
        </p>
        <p type="main">
          <s id="s.006099">CLEOMEDES his &longs;eculis gr&etail;c&egrave; &longs;cribit Meteora, quibus tractat ea, <lb/>
qu&aelig; in &longs;ph&etail;ra &longs;olent doceri. </s>
          <s id="s.006100">extat gr&aelig;colatinus interprete, &amp; &longs;cholia&longs;te Ro&shy;<lb/>
berto Balforeo, qui eum inter Po&longs;&longs;idonium, &amp; Ptolem&aelig;um collocat. </s>
          <s id="s.006101">Item <lb/>
Arithmeticam, &amp; Harmonicam, qu&aelig; a&longs;&longs;eruantur in Bibliotecha Vaticana, <lb/>
&amp; S. Flor&aelig;. </s>
          <s id="s.006102">ex eodem Roberto.</s>
        </p>
        <p type="head">
          <s id="s.006103"><emph type="italics"/>NONVM SEMISECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table15"/></s>
        </p>
        <table>
          <table.target id="table15"/>
          <row>
            <cell>Continens ann.</cell>
            <cell>52</cell>
          </row>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>701</cell>
          </row>
          <row>
            <cell>Ante Chri&longs;ti ortum ann.</cell>
            <cell>52</cell>
          </row>
          <row>
            <cell>Con&longs;. C. Pomp. Magno. <expan abbr="q.">que</expan> C&aelig;cilio.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006104">THEODOSIVS Tripolita de habitationibus. </s>
          <s id="s.006105">de diebus, &amp; no&shy;<lb/>
ctibus. </s>
          <s id="s.006106">&longs;ph&aelig;ricorum lib. 3. de lineatione &aelig;dium. </s>
          <s id="s.006107">Commentaria <lb/>
in Theud&etail; capita. </s>
          <s id="s.006108">in viaticum Archimedis. <!-- KEEP S--></s>
          <s id="s.006109">Sceptica capita a&longs;tro <lb/>
logica. </s>
          <s id="s.006110">de vere. </s>
          <s id="s.006111">Horologium ad omne clima, ide&longs;t vniuer&longs;ale ex&shy;<lb/>
cogitauit. </s>
          <s id="s.006112">Vitr.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006113">SOSIGENES A&longs;tronomus, cuius opera Iulius C&aelig;&longs;. <!-- REMOVE S-->Calend. <!-- REMOVE S-->correxit.</s>
        </p>
        <p type="main">
          <s id="s.006114">Sequentes quinque extiterunt ante Vitr. ex quo eos de&longs;ump&longs;imus: &longs;ed <lb/>
quanto ignoratur.</s>
        </p>
        <p type="main">
          <s id="s.006115">ATHEN&AElig;VS de machinis, cuius extant duo fragmenta gr&aelig;ca apud <lb/>
Vitr in fine. </s>
          <s id="s.006116">non e&longs;t ille Dipno&longs;ophi&longs;tarum, ille enim vixit in &longs;ecundo Chri&shy;<lb/>
&longs;ti &longs;eculo. </s>
          <s id="s.006117">Eiu&longs;dem mechanica.</s>
        </p>
        <p type="main">
          <s id="s.006118">DIONYSIODORVS, cuius fragmentum extat apud Eut. <!-- REMOVE S-->in <expan abbr="c&otilde;-men">com&shy;<lb/>
men</expan>. <!-- REMOVE S-->Archimedis, quo &longs;ubtili&longs;&longs;ima demon&longs;tratio continetur &longs;ecandi &longs;ph&aelig;&shy;<lb/>
ram in datam rationem. </s>
          <s id="s.006119">Inuenit conum, ide&longs;t horologij &longs;olaris genus, fi&shy;<lb/>
guram conicam referens, vel in cono de&longs;criptam.</s>
        </p>
        <p type="main">
          <s id="s.006120">SCOPAS Siracu&longs;anus Plinthum reperit genus horologij in Plintho de&shy;<lb/>
&longs;cripti: in&longs;tar quadrat&aelig; trabis erect&aelig;, in cuius &longs;ummo erat horizontale, in <lb/>
quatuor ver&ograve; lateribus erant duo verticalia, au&longs;trale, &amp; boreale. </s>
          <s id="s.006121">necnon <lb/>
duo meridiana, orientale, &amp; occidentale.</s>
        </p>
        <p type="main">
          <s id="s.006122">PATROCLES fuit inuentor <foreign lang="greek">peleki/nou</foreign>, ide&longs;t <expan abbr="bip&etilde;nis">bipennis</expan>, qu&ograve;d genus ho&shy;<lb/>
rologij &longs;olaris erat, figuram bipennis referens.</s>
        </p>
        <p type="main">
          <s id="s.006123">PARMENION <foreign lang="greek">pros ta isoroumena</foreign> excogitauit, horologia videlicet, <lb/>
qu&aelig; c&oelig;li hi&longs;toriam narrarent, horas, dies, men&longs;es, &longs;igna Zodiaci, &amp; c.<!-- KEEP S--></s>
        </p>
        <pb pagenum="50" xlink:href="009/01/334.jpg"/>
        <p type="main">
          <s id="s.006124">ANDRONICVS CYRESTES Athenis in turri octogona <expan abbr="Ane-mo&longs;copi&utilde;">Ane&shy;<lb/>
mo&longs;copium</expan> primus collocauit. </s>
          <s id="s.006125">ex Vitruuio. <!-- KEEP S--></s>
          <s id="s.006126">ponendus igitur ante <expan abbr="Vitruui&utilde;">Vitruuium</expan>, <lb/>
quanto tamen ignoratur. </s>
          <s id="s.006127"><expan abbr="Anemo&longs;copi&utilde;">Anemo&longs;copium</expan> e&longs;t machina, continens ventorum <lb/>
figuras, ac &longs;itus. </s>
          <s id="s.006128">cum indice mobili, qui ventum perflantem common&longs;trat: <lb/>
quale Bononi&aelig; e&longs;t in Epi&longs;copio.</s>
        </p>
        <p type="main">
          <s id="s.006129">M. AGRIPPA, Augu&longs;ti gener, &amp; Con&longs;. <!-- REMOVE S-->terrarum orbem proprijs <expan abbr="c&otilde;-mentarijs">com<lb/>
mentarijs</expan> de&longs;criptum, po&longs;tea in porticu depictum Pop. <!-- REMOVE S-->Rom. <!-- REMOVE S-->&longs;pectandum <lb/>
propo&longs;uit. </s>
          <s id="s.006130">Plin. lib. 3. cap. 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006131">C. IVLIVS C&AElig;SAR Monarcha, primus &longs;crip&longs;it Metaphra&longs;im in <lb/>
Arati Ph&oelig;mena. </s>
          <s id="s.006132">Suid.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006133">VITRVVIVS, qui in &longs;uo de architectura opere <expan abbr="c&otilde;plura">complura</expan> mi&longs;cet ma&shy;<lb/>
thematica. </s>
          <s id="s.006134">pr&aelig;cipu&egrave; illud, qu&ograve;d de horologijs &longs;olaribus ex Analemmate <lb/>
primus ex latinis, literis con&longs;ignauit. </s>
          <s id="s.006135">ait Venerem, &amp; Mercurium circa So&shy;<lb/>
lem, tanquam centrum circumferri. </s>
          <s id="s.006136">&longs;uum opus Augu&longs;to dicauit.</s>
        </p>
        <p type="main">
          <s id="s.006137">C. MANILIVS Antiochenus A&longs;trologus, &amp; Poeta, primus latinis car&shy;<lb/>
minibus, quamuis Gr&aelig;cus, a&longs;tronomica cecinit. </s>
          <s id="s.006138">extat ip&longs;ius a&longs;tronomicon. <lb/>
</s>
          <s id="s.006139">floruit &longs;ub Augu&longs;to.</s>
        </p>
        <p type="head">
          <s id="s.006140"><emph type="italics"/>DECIMVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table16"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table16"/>
          <row>
            <cell>Sed primum &agrave; natiuitate Chri&longs;ti.</cell>
            <cell/>
          </row>
          <row>
            <cell>Ab Orbe cond. ann.</cell>
            <cell>4089</cell>
          </row>
          <row>
            <cell>Ab Vrbe cond. ann.</cell>
            <cell>752</cell>
          </row>
          <row>
            <cell>Olympiade exacta</cell>
            <cell>194</cell>
          </row>
          <row>
            <cell>Octauiani Augu&longs;ti Imper. ann.</cell>
            <cell>42</cell>
          </row>
        </table>
        <p type="main">
          <s id="s.006141">DIONYSIVS AFER, qui Gr&aelig;co poemate orbis &longs;itum de&shy;<lb/>
cantauit.</s>
        </p>
        <p type="main">
          <s id="s.006142">MARINVS TYRIVS &longs;crip&longs;it de Geographia. <!-- KEEP S--></s>
          <s id="s.006143">eum Pto&shy;<lb/>
lem&aelig;us reprehendit.</s>
        </p>
        <p type="main">
          <s id="s.006144">STRABO eruditi&longs;&longs;im&egrave;, ac fus&egrave; orbis &longs;itum, cuius <expan abbr="magn&atilde;">magnam</expan> partem pe&shy;<lb/>
ragrauerat, de&longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006145">SOLINVS, &amp; P. MELA De &longs;itu orbis pariter con&longs;crip&longs;erat.</s>
        </p>
        <p type="main">
          <s id="s.006146">STRATON AMASENVS Philo&longs;ophus, lib. 7. Geographicos <lb/>
edidit Suid.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006147">PLINIVS, omnis generis Mathemata &longs;uo operi <expan abbr="c&otilde;mi&longs;cuit">commi&longs;cuit</expan>. </s>
          <s id="s.006148">&longs;ed pr&aelig;&shy;<lb/>
cipu&egrave; Geographica &agrave; 2. lib. <!-- REMOVE S--><expan abbr="v&longs;q;">v&longs;que</expan> ad 6.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006149">ARTEMIDORVS tempore Strabonis, &longs;crip&longs;it Geographica, vt <lb/>
patet ex Plinio, &amp; Strabone, eum &longs;&aelig;p&egrave; citante.</s>
        </p>
        <p type="main">
          <s id="s.006150">IV. HIGINIVS de &longs;ignis c&oelig;le&longs;tibus. </s>
          <s id="s.006151">de mundo, &amp; &longs;ph&aelig;ra ad Quin&shy;<lb/>
tilianum.</s>
        </p>
        <p type="main">
          <s id="s.006152">ANDROMACHVS Creteu&longs;is quem Theoricarum inuentorem fa&shy;<lb/>
cit Clauius.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006153">MENELAVS, qui &amp; Mile&longs;ius, po&longs;t Hipparchum a. </s>
          <s id="s.006154">224. ante Ptole&shy;


<pb pagenum="51" xlink:href="009/01/335.jpg"/>m&etail;um 41. a&longs;tronomicis ob&longs;eruationibus dedit operam. </s>
          <s id="s.006155"><expan abbr="prim&atilde;">primam</expan> Arietis po&longs;t <lb/>
&aelig;quinoctium gr. <!-- REMOVE S-->6. 12. deprehendit. </s>
          <s id="s.006156">lib. 6. de &longs;ubten&longs;is, &longs;eu chordis. </s>
          <s id="s.006157">Item <lb/>
lib. 3. de &longs;ph&etail;ricis triangulis, qui extant.</s>
        </p>
        <p type="main">
          <s id="s.006158">PLVTARCHVS libellum de mu&longs;ica optima eruditione, ac doctrina <lb/>
refertum reliquit; quem &longs;uperius &longs;&aelig;p&egrave; citauimus.</s>
        </p>
        <p type="head">
          <s id="s.006159"><emph type="italics"/>VNDECIMVM SECVLVM<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006160">Secundum ver&ograve; &agrave; Chri&longs;to incipiens ab ann. <lb/>
</s>
          <s id="s.006161">Chri&longs;ti 101.</s>
        </p>
        <p type="main">
          <s id="s.006162">Clemente &longs;ummo Chri&longs;tianorum Pont.<!-- REMOVE S-->Imperante Traiano.</s>
        </p>
        <p type="main">
          <s id="s.006163">DIOPHANTES Alexandrinus Algebr&aelig;, quam hodie vocant <lb/>
mirabilis artifex: extant eius 13. libri Gr&aelig;ci Arithmeticorum. <lb/>
</s>
          <s id="s.006164">ponitur &longs;ub Antonino &agrave; Raphaele Bombello in Algebr&aelig; pr&aelig;fa&shy;<lb/>
tione.</s>
        </p>
        <p type="main">
          <s id="s.006165">PTOLEM&AElig;VS Alexandr. <!-- REMOVE S-->A&longs;tronomorum princeps. </s>
          <s id="s.006166">ob&longs;eruabat &agrave; <lb/>
Natiuit. </s>
          <s id="s.006167">Chri&longs;ti ann. </s>
          <s id="s.006168">130. maximam Solis declinationem gr. <!-- REMOVE S-->23. 50. primam <lb/>
Arietis po&longs;t &aelig;quinot. </s>
          <s id="s.006169">gr. <!-- REMOVE S-->6. 40. &longs;crip&longs;it magnam con&longs;tructionem, quam Al&shy;<lb/>
mage&longs;tum vocant. </s>
          <s id="s.006170">de Annalemmate. </s>
          <s id="s.006171">de momentis. </s>
          <s id="s.006172">Geographiam. <!-- KEEP S--></s>
          <s id="s.006173">Plani&longs;&shy;<lb/>
ph&aelig;rium. </s>
          <s id="s.006174">de &longs;peculis. </s>
          <s id="s.006175">libros mechanicos 3. canonem expeditum. </s>
          <s id="s.006176">de iudi&shy;<lb/>
cijs 4. centiloquium. </s>
          <s id="s.006177">&longs;tellarum inenarrantium &longs;ignificationes.</s>
        </p>
        <p type="main">
          <s id="s.006178">SEXTVS EMPIRICVS, qui dum de Mathematicis in vtranque <lb/>
partem &longs;ubtiliter di&longs;putat, de eis plura doct&egrave; in medium profert. </s>
          <s id="s.006179">ex Gen&shy;<lb/>
tiano Herueto eius interprete.</s>
        </p>
        <p type="head">
          <s id="s.006180"><emph type="italics"/>DVODECIMVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table17"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table17"/>
          <row>
            <cell>Tertium autem &agrave; Chri&longs;to incipiens</cell>
            <cell/>
          </row>
          <row>
            <cell>Ab ann. Chri&longs;ti</cell>
            <cell>201</cell>
          </row>
          <row>
            <cell>Victore &longs;ummo Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imperante Septimio Seuero.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006181">PORPHIRIVS Philo&longs;ophus Platonicus &longs;crip&longs;it I&longs;agogem a&longs;tro&shy;<lb/>
nomicarum rerum lib. 3. Suid. <!-- KEEP S--></s>
          <s id="s.006182">is e&longs;t, cuius e&longs;t I&longs;agoge, de quinque <lb/>
vniuer&longs;alibus. </s>
          <s id="s.006183">eius Proclus meminit ad 14. 18. &amp; 20. propo&longs;itionem <lb/>
primi elem. </s>
          <s id="s.006184">vbi illius demon&longs;trationes affert. </s>
          <s id="s.006185">Item Hypothipo&longs;es <lb/>
a&longs;tronomicarum po&longs;itionum, ide&longs;t expo&longs;itio in Almage&longs;tum.</s>
        </p>
        <p type="main">
          <s id="s.006186">CENSORINVS in eruditi&longs;&longs;imo libello de die Natali, plura habet <lb/>
ad Mathematicas, pr&aelig;&longs;ertim ver&ograve; ad A&longs;tronomum &longs;pectantia.</s>
        </p>
        <p type="main">
          <s id="s.006187">HIPPOLYTVS Epi&longs;copus, ob di&longs;cordias inter Latinos, &amp; Gr&aelig;cos <lb/>de celebrando Pa&longs;chate paulo ante excitatas, primus &longs;cribit de cyclo Pa&longs;&shy;<lb/>
cali, <expan abbr="eius&qacute;">eiusque</expan>; inuentor celebratur. </s>
          <s id="s.006188">I&longs;idorus.<!-- KEEP S--></s>
        </p>
        <pb pagenum="52" xlink:href="009/01/336.jpg"/>
        <p type="head">
          <s id="s.006189"><emph type="italics"/>DECIMVMTERTIVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table18"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table18"/>
          <row>
            <cell>Quartum ver&ograve; Chr. ab ann. Chri&longs;ti</cell>
            <cell>301</cell>
          </row>
          <row>
            <cell>Marcellino &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Diocletiano, &amp; Maximiano Impp.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006190"><emph type="italics"/>Quo Schol&aelig; florenti&longs;&longs;im&aelig; Rom&aelig;, Athenis, C&aelig;&longs;are&aelig;, <lb/>
Constantinopoli, frequentabantur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006191">SEXTVS AVIENVS RVFFVS Arati ph&etail;nomena, &amp; Dyoni&shy;<lb/>
&longs;ij Afri de &longs;itu orbis poema latine interpretatus e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.006192">IVL. MATERNVS Siculus latin&egrave; &longs;crip&longs;it: &longs;ed de iudicijs.</s>
        </p>
        <p type="main">
          <s id="s.006193">THEOPHILVS Epi&longs;copus <expan abbr="Alex&atilde;drinus">Alexandrinus</expan> inter Aegyptios Ma&shy;<lb/>
thematicos celebris iu&longs;&longs;u Theodo&longs;ij &longs;enioris Imper. <!-- REMOVE S-->cyclum Pa&longs;chalem or&shy;<lb/>
dinauit: cui alium paulo po&longs;t contrarium Romanis Dyoni&longs;ius Abbas pro&shy;<lb/>
po&longs;uit.</s>
        </p>
        <p type="main">
          <s id="s.006194">ABIFELDEA Princeps Syri&aelig;, A&longs;syri&aelig;, &amp; Per&longs;idis, Geographus in&shy;<lb/>
&longs;ignis. </s>
          <s id="s.006195">eius Geographia a&longs;&longs;eruatur in Bibliotheca Palatina Arabic&egrave; &longs;cripta. <lb/>
</s>
          <s id="s.006196">Corradus Ge&longs;nerus in Alfraganum.</s>
        </p>
        <p type="main">
          <s id="s.006197">VALENS huius &aelig;tatis in&longs;ignis Mathematicus, qui iu&longs;&longs;u Con&longs;tantini <lb/>
Magni, Vrbis Con&longs;tantinopolitan&aelig;, quam tunc ip&longs;e &aelig;dificabat, genituram <lb/>
ex c&oelig;le&longs;ti Themate inani labore dijudicauit. </s>
          <s id="s.006198">Zonaras.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006199">EVSEBIVS C&aelig;&longs;arien&longs;is Epi&longs;copus &longs;cribit de cyclo Pa&longs;chali. </s>
          <s id="s.006200">I&longs;id.</s>
        </p>
        <p type="main">
          <s id="s.006201">MAXIMVS Epirota &longs;ub Iuliano Apo&longs;tata &longs;crip&longs;it de numeris. </s>
          <s id="s.006202">Suid.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006203">Quinque <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> ponendi &longs;unt inter Archimedem, &amp; Proclum; quo au&shy;<lb/>
tem loco ignoratur; Proclus enim recen&longs;ens Mathematicos v&longs;que ad Ar&shy;<lb/>
chimedem, de eis &longs;ilet.</s>
        </p>
        <p type="main">
          <s id="s.006204">NICOMEDES, qui de line is conchoidibus &longs;crip&longs;it, per quas duas <lb/>
medias proportionales exhibeat, <expan abbr="atq;">atque</expan> hinc cubum duplicabat. </s>
          <s id="s.006205">ij&longs;dem con&shy;<lb/>choidibus angulum datum rectilineum trifariam &longs;ecabat. </s>
          <s id="s.006206">extant ip&longs;ius &longs;ub&shy;<lb/>
tili&longs;&longs;imi conatus apud Eutocium, &amp; Pappum, &amp; P. <!-- REMOVE S-->Clauium in Geometria <lb/>
practica.</s>
        </p>
        <p type="main">
          <s id="s.006207">EVDEMVS, qui Geometricas enarrationes con&longs;crip&longs;it. </s>
          <s id="s.006208">Item libel&shy;<lb/>
lum de angulo. </s>
          <s id="s.006209">Proclus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006210">MENELAVS Alexandrinus, cuius demon&longs;trationes affert Proclus <lb/>
ad vige&longs;imamquintam primi elementi.</s>
        </p>
        <p type="main">
          <s id="s.006211">GEMINVS RHODIVS, Procli Diadochi pr&aelig;ceptor, gr&aelig;c&egrave; &longs;cri&shy;<lb/>
p&longs;it ph&aelig;nomena: qu&aelig; Mediolani in Bibliotheca Ambro&longs;iana a&longs;&longs;eruantur:<lb/>
&amp; quidem gr&aelig;colatina, Edone Stildario interprete. </s>
          <s id="s.006212">Pr&aelig;terea de ortu li&shy;<lb/>
nearum &longs;piralium, conchoidarum, ci&longs;&longs;oidarum, <expan abbr="earum&qacute;">earumque</expan>; pa&longs;&longs;ionibus. </s>
          <s id="s.006213">Item <lb/>
de Mathematicarum ordine.</s>
        </p>
        <p type="main">
          <s id="s.006214">Circa finem huius quarti &longs;eculi fiunt <expan abbr="vndiq;">vndique</expan> Barbarorum irruptiones in <lb/>
Rom. <!-- KEEP S--></s>
          <s id="s.006215">Imperium: Gothi &longs;ub Alarico Gr&aelig;cias inuadunt, <expan abbr="Athenas&qacute;">Athenasque</expan>; <expan abbr="capi&utilde;t">capiunt</expan>, <lb/>
ac diripiunt.</s>
        </p>
        <pb pagenum="53" xlink:href="009/01/337.jpg"/>
        <p type="head">
          <s id="s.006216"><emph type="italics"/>DECIMVMQVARTVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table19"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table19"/>
          <row>
            <cell>Quintum ver&ograve; Chri&longs;ti.</cell>
            <cell/>
          </row>
          <row>
            <cell>Ab ann. Chri&longs;ti</cell>
            <cell>401</cell>
          </row>
          <row>
            <cell>Ana&longs;ta&longs;io &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Arcadio orienti, &amp; Honorio occidenti.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006217"><emph type="italics"/>Quo Roma ter capta, &amp; imperio occidentis ab Odoacre exci&longs;o liter&aelig;, <lb/>
&amp; artes pa&longs;&longs;im pe&longs;&longs;undari incipiunt.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006218">Sequentes duo ponendi &longs;unt ante Eutocium, &longs;ed quanto non comperio.</s>
        </p>
        <p type="main">
          <s id="s.006219">DIOCLES, cuius modum inueniendi duas medias proportio&shy;<lb/>
nales, &amp; modum &longs;ecandi &longs;ph&aelig;ram in datam rationem, refert Euto&shy;<lb/>
cius, de&longs;umptum ex libro de Pyrijs, &longs;eu igniarijs.</s>
        </p>
        <p type="main">
          <s id="s.006220">SPORVS Nicenus, cuius etiam duarum mediarum inuentio e&longs;t apud <lb/>
Eutocium in comm. <!-- REMOVE S-->Archim.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006221">PROCLVS DIADOCHVS, qui Athenis Platonic&aelig; &longs;chol&aelig; pr&aelig;&shy;<lb/>
fuit. </s>
          <s id="s.006222">&longs;crip&longs;it comm. <!-- REMOVE S-->in Euclidem eruditi&longs;s. </s>
          <s id="s.006223">Suid. <!-- KEEP S--></s>
          <s id="s.006224">Georgius Heni&longs;chius. </s>
          <s id="s.006225">Hy&shy;<lb/>
potypo&longs;es a&longs;tronomicas. </s>
          <s id="s.006226">&longs;ph&aelig;ram. </s>
          <s id="s.006227">Archimedem imitatus v&longs;torijs &longs;peculis, <lb/>
Valentis naues Con&longs;tantinopolim ob&longs;identes combu&longs;&longs;it. </s>
          <s id="s.006228">Zenoras, qui eum <lb/>
mir&egrave; commendat.</s>
        </p>
        <p type="main">
          <s id="s.006229">CYRILLVS Epi&longs;copus Alexandrinus &longs;cribit de Cyclo pa&longs;chali. </s>
          <s id="s.006230">I&longs;id.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006231">S. AVGVSTINVS Epi&longs;copus lib. 6. de Mu&longs;ica, Item de principijs <lb/>
Geometri&aelig;, &amp; Arithmetic&aelig; &longs;cribit.</s>
        </p>
        <p type="main">
          <s id="s.006232">MARINVS Philo&longs;ophus Neapolitanus Procli di&longs;cipulus. </s>
          <s id="s.006233">eius e&longs;t Pro&shy;<lb/>
theoria in data Euclidis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006234">DEMETRIVS <expan abbr="Alex&atilde;drinus">Alexandrinus</expan>, lineares aggre&longs;&longs;iones fecit. </s>
          <s id="s.006235">Papp. <!-- REMOVE S-->p.61.</s>
        </p>
        <p type="main">
          <s id="s.006236">PHILO TYAN&AElig;VS de lineis genitis ex implicatione <foreign lang="greek">plhktoeidwn</foreign>,<lb/>
&amp; aliarum varij generis &longs;uperficierum. </s>
          <s id="s.006237">Pappus p. </s>
          <s id="s.006238">61.</s>
        </p>
        <p type="main">
          <s id="s.006239">S. PROSPER Aquitanus de Cyclo pa&longs;chali. </s>
          <s id="s.006240">compo&longs;uit Cyclum ma&shy;<lb/>
gnum annorum 532. 10. Lucidus. <!-- KEEP S--></s>
          <s id="s.006241">I&longs;idorus.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006242">PAPPVS Alexandrinus: cuius Mathematic&aelig; collectiones extant. </s>
          <s id="s.006243">&amp; <lb/>
comm. <!-- REMOVE S-->in 5. Ptol&aelig;mei magn&aelig; &longs;yntaxis. </s>
          <s id="s.006244">fecit etiam vniuer&longs;alem orbis de&longs;cri&shy;<lb/>
ptionem. </s>
          <s id="s.006245">de fluuijs Lybi&aelig;. </s>
          <s id="s.006246">extant eius lemmata in Apollonium Perg&aelig;um.</s>
        </p>
        <p type="main">
          <s id="s.006247">THEON Alexandrinus, cuius &longs;unt gr&aelig;ca comm. <!-- REMOVE S-->in magnam &longs;yntaxim <lb/>
Ptol&aelig;mei, pr&aelig;terea de Arithmetica. <!-- KEEP S--></s>
          <s id="s.006248">de ortu Canicul&aelig;. <!-- KEEP S--></s>
          <s id="s.006249">de Nili a&longs;cen&longs;u. <lb/>
</s>
          <s id="s.006250">comm. <!-- REMOVE S-->in paruum A&longs;trolabium. <!-- KEEP S--></s>
          <s id="s.006251">ex Suid. <!-- REMOVE S-->fuit Pappi &longs;yncronus.</s>
        </p>
        <p type="main">
          <s id="s.006252">HYPATIA Theonis Geometr&aelig; filia Alex. Diophantis Arithmeticam <lb/>
comment. </s>
          <s id="s.006253">illu&longs;trauit. </s>
          <s id="s.006254">pr&etail;terea in Conica Apollonij &longs;crip&longs;it. </s>
          <s id="s.006255">a&longs;tronomicum <lb/>
canonem con&longs;truxit. </s>
          <s id="s.006256">claruit &longs;ub Arcadio, &amp; Honorio.</s>
        </p>
        <p type="main">
          <s id="s.006257">VICTORINVS Aquitanus A&longs;tronomus, ab Hilario Papa Romam <lb/>
inuitatur ad Calendarij correctionem.</s>
        </p>
        <p type="main">
          <s id="s.006258">EVTOCIVS A&longs;calonita po&longs;t Theonem, &amp; Pappum &longs;crip&longs;it, eos enim <lb/>
nominat. </s>
          <s id="s.006259">&longs;crip&longs;it commentaria in conica Apollonij, &amp; in Archimedem de <lb/>
&longs;ph&aelig;ra, &amp; cylindro, de circuli dimen&longs;ione; &amp; de &aelig;queponderantibus.</s>
        </p>
        <pb pagenum="54" xlink:href="009/01/338.jpg"/>
        <p type="head">
          <s id="s.006260"><emph type="italics"/>DECIMUMQVINTVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table20"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table20"/>
          <row>
            <cell>Sextum ver&ograve; Chri&longs;ti.</cell>
            <cell/>
          </row>
          <row>
            <cell>Ab ann. Chri&longs;ti</cell>
            <cell>501</cell>
          </row>
          <row>
            <cell>Symmacho &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imperante Ana&longs;ta&longs;io orienti.</cell>
            <cell/>
          </row>
          <row>
            <cell>Theodorico Rege Goth. Itali&aelig;.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006261"><emph type="italics"/>Hoc &longs;&aelig;culo Roma quart&ograve; capitur &agrave; Totila: &amp; Longobardi <lb/>
Italiam inuadunt.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006262">BOETIVS vir clari&longs;&longs;imus, &amp; Con&longs;ularis, latin&egrave; de Arithmetica, <lb/>
de Mu&longs;ica, de Geometria practica: inuenit Chiterinum mu&longs;icum <lb/>
in&longs;trumentum. </s>
          <s id="s.006263">Supplem. <!-- REMOVE S-->chron.</s>
        </p>
        <p type="main">
          <s id="s.006264">CASSIODORVS vir clari&longs;&longs;imus, &amp; Con&longs;ularis, &longs;cribit de <lb/>
Arithmetica, de Geometria, de Mu&longs;ica, de A&longs;tronomia, de Pa&longs;chali com&shy;<lb/>
puto. </s>
          <s id="s.006265">Baronius.</s>
        </p>
        <p type="main">
          <s id="s.006266">IOANNES <expan abbr="Gr&atilde;maticus">Grammaticus</expan> cognominato Philoponus, &longs;crip&longs;it de Arith&shy;<lb/>
metics. </s>
          <s id="s.006267">modus etiam quidam inueniendi duas medias ei tribuitur, vt apud <lb/>
Clau. <!-- REMOVE S-->in Geometria practica. </s>
          <s id="s.006268">comm. <!-- REMOVE S-->in Nicomachi arithmeticam &longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006269">HERO Mechanicus, qui e&longs;t alius ab Herone Philo&longs;opho mechanico, de <lb/>
quo &longs;uperius. </s>
          <s id="s.006270">eius extat liber de Geod&aelig;&longs;ia, &amp; alter de machinis bellicis. </s>
          <s id="s.006271">ait <lb/>ip&longs;e in Geod&aelig;&longs;ia &longs;tellas fixas po&longs;t Ptolem&aelig;um, v&longs;que ad &longs;uam &aelig;tatem pro&shy;<lb/>
gre&longs;&longs;os e&longs;&longs;e grad. <!-- REMOVE S-->7. qui progre&longs;&longs;us, &longs;i Albatignio credimus annos &longs;altem 460. <lb/>
importat, qui Ptolem&aelig;i &aelig;tati aditi Heronem in hoc &longs;eculum transferunt.</s>
        </p>
        <p type="main">
          <s id="s.006272">HELIODORVS Lari&longs;&longs;eus, cuius extant optica gr&aelig;ca. </s>
          <s id="s.006273">citat Hero&shy;<lb/>
nem mechanicum.</s>
        </p>
        <p type="main">
          <s id="s.006274">DIONYSIVS exiguus Abbas Romanus, computum, &amp; cyclum pa&shy;<lb/>
&longs;chalem aliter ac Gr&aelig;ci ordinauit a. </s>
          <s id="s.006275">D. 532. quem latina Eccle&longs;ia po&longs;tea <lb/>
<expan abbr="v&longs;q;">v&longs;que</expan> ad Calendarij correctionem &longs;ub Greg. <!-- REMOVE S-->13. factam, &longs;equuta e&longs;t: primus <lb/>
annos &agrave; Chri&longs;to Domino numerare c&oelig;pit, qui prius &agrave; Diocletiano, &longs;iue &agrave; <lb/>
per&longs;ecutione Diocletiani numerabantur. </s>
          <s id="s.006276">Chri&longs;tmanus in Alfrag.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006277">S. GREGORIVS Magnus Papa in mu&longs;icis excelluit, <expan abbr="ei&qacute;">eique</expan>, adeo fuit <lb/>
addictus, vt Clericos ip&longs;e mu&longs;icam doceret. </s>
          <s id="s.006278">canticum Eccle&longs;ia&longs;ticum ordi&shy;<lb/>
nauit, qui ab eo denominatur. </s>
          <s id="s.006279">choro etiam modum con&longs;tituit.</s>
        </p>
        <pb pagenum="55" xlink:href="009/01/339.jpg"/>
        <p type="head">
          <s id="s.006280"><emph type="italics"/>DECIMUMSEXTVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table21"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table21"/>
          <row>
            <cell>Septimum ver&ograve; Chri. ab ann. Chri&longs;ti</cell>
            <cell>601</cell>
          </row>
          <row>
            <cell>Gregorio magno &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Mauritio Imperatore orientis.</cell>
            <cell/>
          </row>
          <row>
            <cell>Longobardis in Italia regnantibus.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006281"><emph type="italics"/>Arabes in A&longs;ia, &amp; Africa, &amp; Europa complura regna occupant.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006282">ISIDORVS Hi&longs;palentis Epi&longs;copus, in &longs;uis de originibus libris om&shy;<lb/>
nium Mathematicarum compendia in&longs;erit: &amp; de cyclo pa&longs;chali plu&shy;<lb/>
ribus agit: &amp; in libro de Mundo breuiter tractatum de &longs;ph&aelig;ra per&shy;<lb/>
&longs;tringit.</s>
        </p>
        <p type="main">
          <s id="s.006283">MARTIANVS CAPELLA, qui etiam F&oelig;lix Mineus dicitur, ad <lb/>
h&aelig;c tempora &agrave; Patricio in Poetica refertur, &longs;cilicet paulo ante Eraclium <lb/>
Imper. <!-- REMOVE S-->&longs;crip&longs;it in &longs;uis nuptijs Mercurij cum Philologia, de 4. Mathematicis <lb/>
Geometria, Arithmetica, Mu&longs;ica, A&longs;tronomia.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006284"><emph type="italics"/>DECIMVMSEPTIMVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table22"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table22"/>
          <row>
            <cell>Octauum autem Chr. ab ann. Chri&longs;ti</cell>
            <cell>701</cell>
          </row>
          <row>
            <cell>Sergio &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imper. Tiberio Ab&longs;imero orientis.</cell>
            <cell/>
          </row>
          <row>
            <cell>Longobardis in Italia.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006285">VENERABILIS BEDA de Arithmetica. <!-- KEEP S--></s>
          <s id="s.006286">de Mu&longs;ica. <!-- KEEP S--></s>
          <s id="s.006287">de <lb/>
A&longs;trolabio. <!-- KEEP S--></s>
          <s id="s.006288">de Horologio &longs;olari. </s>
          <s id="s.006289">de computo Eccle&longs;ia&longs;tico. <lb/>
</s>
          <s id="s.006290">Ecce tibi quanta literatorum paucitas Barbaris Imperium de&shy;<lb/>
ua&longs;tantibus.</s>
        </p>
        <p type="head">
          <s id="s.006291"><emph type="italics"/>DECIMUMOCTAVVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table23"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table23"/>
          <row>
            <cell>Nonum ver&ograve; Chr. ab ann. Chri&longs;ti</cell>
            <cell>801</cell>
          </row>
          <row>
            <cell>Leone &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imper. occidenti Carolo Magno.</cell>
            <cell/>
          </row>
          <row>
            <cell>Irene ver&ograve; orienti.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006292"><emph type="italics"/>Liter&aelig; apud Arabes florere incipiunt.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006293">ALMEON, &longs;iue Almamom Rex Arabum, ante Albategnium <lb/>
ann. </s>
          <s id="s.006294">50. ob&longs;eruauit Solis maximam declinationem 23. 51. repe&shy;<lb/>
rit vni gradui terr&aelig; deberi mill. <!-- REMOVE S-->56. in campis Singar prop&egrave; Ba&shy;<lb/>
byloniam.</s>
        </p>
        <pb pagenum="56" xlink:href="009/01/340.jpg"/>
        <p type="main">
          <s id="s.006295">ALBATEGNIVS ARACENSIS Arabs, po&longs;t Ptolem&aelig;um ann. <lb/>
</s>
          <s id="s.006296">750. &agrave; nat. </s>
          <s id="s.006297">Chri&longs;ti 880. ante Alfarabium 381. ob&longs;eruat Solis maximam de&shy;<lb/>
clinationem 23. 35. &amp; primam Arietis po&longs;t &aelig;quinoctium grad. <!-- REMOVE S-->18. 2. Ara&shy;<lb/>
cta e&longs;t vrbs Syri&aelig;, &amp; patria ip&longs;ius, &agrave; qua dicitur Aracen&longs;is. </s>
          <s id="s.006298">extat liber eius <lb/>
de &longs;cientia &longs;tellarum.</s>
        </p>
        <p type="main">
          <s id="s.006299">MICHAEL PSELLVS Gr&aelig;cus Quadriuium, hoc e&longs;t de 4. Mathe&shy;<lb/>
maticis compendios&egrave; &longs;crip&longs;it, &amp; extat. </s>
          <s id="s.006300">Docuit filios Imperatoris. </s>
          <s id="s.006301">hic po&shy;<lb/>
nitur &agrave; Baronio.</s>
        </p>
        <p type="main">
          <s id="s.006302">Sequentes 5. ponendi &longs;unt ante &longs;eculum 10. quo Suida &longs;cribens, eos me&shy;<lb/>
morat: quanto autem, ne&longs;cire fateor.</s>
        </p>
        <p type="main">
          <s id="s.006303">PAVLVS Philo&longs;ophus, introductionem A&longs;trologi&aelig; compo&longs;uit.</s>
        </p>
        <p type="main">
          <s id="s.006304">PETOSCIRIS Aegyptius, A&longs;trologica &egrave; &longs;acris libris pertractauit.</s>
        </p>
        <p type="main">
          <s id="s.006305">ACHILLES STATIVS Alexandrinus Epi&longs;copus. </s>
          <s id="s.006306">de &longs;ph&aelig;ra.</s>
        </p>
        <p type="main">
          <s id="s.006307">ZOROMASDVS Chald&aelig;us. </s>
          <s id="s.006308">Mathematica &longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006309">PELLES Aegien&longs;is. </s>
          <s id="s.006310">Arithmeticorum lib. 2.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006311">GEBER Arabs, cuius extat Opus a&longs;tronomicum 9. libris di&longs;tinctum, <lb/>quo Ptolem&aelig;i Almage&longs;tum exponit, ac corrigit. </s>
          <s id="s.006312">initio agit de Triangulis <lb/>
&longs;ph&aelig;ricis, quantum a&longs;tronomicis calculis opus e&longs;t.</s>
        </p>
        <p type="head">
          <s id="s.006313"><emph type="italics"/>DECIMUMNONUM SECULUM<emph.end type="italics"/><lb/>
<arrow.to.target n="table24"/></s>
        </p>
        <table>
          <table.target id="table24"/>
          <row>
            <cell>Decimum ver&ograve; Chr. ab ann. Chri&longs;ti</cell>
            <cell>901</cell>
          </row>
          <row>
            <cell>Ioanne &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Ludouico 4. occid.</cell>
            <cell/>
          </row>
          <row>
            <cell>Leone 6. orien.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006314"><emph type="italics"/>Lingua vulgaris Italica incipit emergere. </s>
          <s id="s.006315">Baron.<emph.end type="italics"/><!-- REMOVE S-->GVIDO ARETINVS Monachus S. Benedicti, Rom&aelig; &longs;crip&longs;it <lb/>
de Mu&longs;ica. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006316">nouam rationem cantus excogitauit. </s>
          <s id="s.006317">eius opera &longs;unt <lb/>
Introductorium mu&longs;ic&aelig;, in quo ip&longs;e primus vocibus nomina in&shy;<lb/>
didit, Vt, Re, Mi, Fa, Sol, La: Item Micrologus de Mu&longs;ica.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006318">ALFARABIVS Arabs, A&longs;tronomus celebris.</s>
        </p>
        <p type="main">
          <s id="s.006319">ALBVMASAR Arabs, A&longs;tronomus celebris. </s>
          <s id="s.006320">de magnis coniunctio&shy;<lb/>
nibus, &amp; alia iudiciaria.</s>
        </p>
        <p type="main">
          <s id="s.006321">ALFRAGANVS Arabs, A&longs;tronomica elementa edidit.</s>
        </p>
        <p type="main">
          <s id="s.006322">BAGDADINVS Arabs. <!-- KEEP S--></s>
          <s id="s.006323">de diui&longs;ione figurarum, extat.</s>
        </p>
        <p type="main">
          <s id="s.006324">BEN MVSA Arabs. <!-- KEEP S--></s>
          <s id="s.006325">de figuris planis, &amp; &longs;ph&aelig;ricis.</s>
        </p>
        <pb pagenum="57" xlink:href="009/01/341.jpg"/>
        <p type="head">
          <s id="s.006326"><emph type="italics"/>VIGESIMVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table25"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table25"/>
          <row>
            <cell>Vndecimum <expan abbr="ver&otilde;">verom</expan> Chr. ab ann. Chri&longs;ti</cell>
            <cell>1001</cell>
          </row>
          <row>
            <cell>Silue&longs;tro &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Ottone 3. occid.</cell>
            <cell/>
          </row>
          <row>
            <cell>Ba&longs;ilio, &amp; Con&longs;t. orient.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006327">ALHAZENVS Arabs: eius extant optica doct&egrave;, ac &longs;ubtiliter <lb/>
pertractata. </s>
          <s id="s.006328">Item opu&longs;culum de crepu&longs;culis, vbi aeris &longs;uprema <lb/>
altitudinem acuti&longs;&longs;im&egrave; rimatur.</s>
        </p>
        <p type="main">
          <s id="s.006329">CAMPANVS Italus, ac Nouaren&longs;is, primus Euclidem ex <lb/>
Arabico in latinum tran&longs;tulit, ac &longs;cholijs illu&longs;trauit. </s>
          <s id="s.006330">Fuit optimus A&longs;tro&shy;<lb/>
nomus: &longs;crip&longs;it computum minorem, &amp; maiorem, anno 1200. vt ip&longs;e ait. <lb/>
</s>
          <s id="s.006331">Item &longs;ph&aelig;ram, &amp; theoricas planetarum.</s>
        </p>
        <p type="main">
          <s id="s.006332">ARZAEL Arabs Po&longs;t Albategnium ann. </s>
          <s id="s.006333">190. reperit Solis maximam <lb/>
declinationem gr. <!-- REMOVE S-->23. 34.</s>
        </p>
        <p type="main">
          <s id="s.006334">IS A CIVS ARGYRVS Gr&aelig;cus, de Pa&longs;chatis correctione. </s>
          <s id="s.006335">Cla&shy;<lb/>
uius in Calendario.</s>
        </p>
        <p type="head">
          <s id="s.006336"><emph type="italics"/>VIGESIMVMPRIMVM SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table26"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table26"/>
          <row>
            <cell>Duodec. ver&ograve; &agrave; Chr. ab ann. Chri&longs;ti</cell>
            <cell>1001.</cell>
          </row>
          <row>
            <cell>Pa&longs;chali &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Henrico 3. occid.</cell>
            <cell/>
          </row>
          <row>
            <cell>Alexio Commeno orient.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006337">RABBI Abraham de Sph&aelig;ra. </s>
          <s id="s.006338">Chri&longs;tm. <!-- REMOVE S-->in Alfrag.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006339">IORDANVS Nemorarius, qui &longs;cribit de ponderibus, citat <lb/>
Campanum, &amp; Campanus in def. </s>
          <s id="s.006340">5. <expan abbr="elem&etilde;">elemen</expan>. </s>
          <s id="s.006341">citat Iordanum, qui <lb/>
&longs;crip&longs;it de Arithmetica lib. 12. &amp; data Arithmetica. <!-- KEEP S--></s>
          <s id="s.006342">&amp; de A&longs;tro&shy;<lb/>
labio. </s>
          <s id="s.006343">qui &longs;cribit de Arithmetica appellatur etiam Nemorarius, vnde vnus, <lb/>
&amp; idem Iordanus videtur e&longs;&longs;e.</s>
        </p>
        <p type="main">
          <s id="s.006344">AVERROES Arabs magnus commentator, fecit Epitomen Alma&shy;<lb/>
gi&longs;ti. </s>
          <s id="s.006345">Picus Mir. <!-- REMOVE S-->contra A&longs;trologos.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006346">ALMEON Alman&longs;orius Arabs, po&longs;t Arzaelem ann. </s>
          <s id="s.006347">70. anno Domi&shy;<lb/>
ni 1140. declinationem Solis maximam reperit 23. 33.</s>
        </p>
        <p type="main">
          <s id="s.006348">ALPETRAGIVS Arabs Almconis co&aelig;taneus ann. </s>
          <s id="s.006349">Domini 1145. <lb/>
eandem cum eo in&longs;pexit declinationem.</s>
        </p>
        <p type="main">
          <s id="s.006350">HVMENVS Aegyptius, cuius tabul&aelig; a&longs;tronomi&aelig; arabic&egrave; &longs;cript&aelig; a&longs;&shy;<lb/>
&longs;eru&agrave;ntur in Biblioth. <!-- REMOVE S-->Palatina. </s>
          <s id="s.006351">Chri&longs;tmanus in Alfr.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006352">IOANNES Hi&longs;palen&longs;is circa 1142. conuertit Alfragnum in latinum. <lb/>
</s>
          <s id="s.006353">ex Chri&longs;tmanno.</s>
        </p>
        <p type="main">
          <s id="s.006354">THEON Smyrneus, circa h&aelig;c &longs;ecula, Gr&aelig;c&egrave; loco Mathematica apud <lb/>
Platonem interpretatur. </s>
          <s id="s.006355">opus eius Gr&aelig;cum extat in Vatic. <!-- REMOVE S-->ex Io&longs;. <!-- REMOVE S-->Auria.</s>
        </p>
        <pb pagenum="58" xlink:href="009/01/342.jpg"/>
        <p type="head">
          <s id="s.006356"><emph type="italics"/>XXII. SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table27"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table27"/>
          <row>
            <cell>Decimum autem tertium Chr. ab ann. Domini</cell>
            <cell>1201</cell>
          </row>
          <row>
            <cell>Innocentio &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Ottone 4. occid.</cell>
            <cell/>
          </row>
          <row>
            <cell>I&longs;acio orient.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006357">VITELLIO, qui maiorum Optica in vnum conge&longs;&longs;it, ac dige&longs;&shy;<lb/>
&longs;it. </s>
          <s id="s.006358">Ri&longs;nerus.</s>
        </p>
        <p type="main">
          <s id="s.006359">NICOLAVS CABASILLA Gr&aelig;cus, Ptolem&aelig;i &longs;ynta&shy;<lb/>
xis commentator.</s>
        </p>
        <p type="main">
          <s id="s.006360">FEDERICVS Secundus Imperat. <!-- REMOVE S-->primus Almage&longs;tum ex Arabo in <lb/>
latinum conuerti curauit, <expan abbr="adeo&qacute;">adeoque</expan>; a&longs;tronomiam omnem excoluit. </s>
          <s id="s.006361">Chri&longs;tm.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006362">ALPHONSVS Rex Hi&longs;paniarum, cuius &longs;unt tabul&aelig; Alphon&longs;in&aelig;. </s>
          <s id="s.006363">ob. <lb/>
</s>
          <s id="s.006364">&longs;eruauit ann. </s>
          <s id="s.006365">Domini 1250. primam Arietis po&longs;t &aelig;quinoctium gra. </s>
          <s id="s.006366">23. 40. <lb/>
hic quadraginta <expan abbr="aureor&utilde;">aureorum</expan> millia ad <expan abbr="a&longs;tronomi&atilde;">a&longs;tronomiam</expan> in lucem reuocandam cum <lb/>
&longs;empiterna &longs;ui nominis gloria contulit.</s>
        </p>
        <p type="main">
          <s id="s.006367">IOAN. de Sacrobo&longs;co angulus &longs;crip&longs;it de &longs;ph&aelig;ra; &amp; de <expan abbr="c&otilde;puto">computo</expan> Eccle&longs;.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006368">IOANNES autor &longs;umm&aelig; Angel.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006369">THEBIT Arabs, po&longs;t Almeonem an. <!-- REMOVE S-->50. an. <!-- REMOVE S-->1270. primus motum tre&shy;<lb/>
pidationis octau&aelig; &longs;ph&aelig;r&etail; rimatus e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.006370">PROFATIVS Iud&aelig;us ann. </s>
          <s id="s.006371">Dom. <!-- REMOVE S-->1300. po&longs;t Almeon ann. </s>
          <s id="s.006372">160. Solis <lb/>
declinationem maximam annotauit. </s>
          <s id="s.006373">gr. <!-- REMOVE S-->23. 32.</s>
        </p>
        <p type="main">
          <s id="s.006374">IOANNES GIRA Amalphen&longs;is inuen it <expan abbr="mir&atilde;">miram</expan> illam magnetis pro&shy;<lb/>
prietatem, qua ad polum &longs;emper conuertitur: vnde maxima rei Nautic&aelig; <lb/>
vtilitas, &amp; acce&longs;&longs;io facta e&longs;t:</s>
        </p>
        <p type="main">
          <s id="s.006375"><emph type="italics"/>Prima dedit nautis v&longs;um magnetis Amalphis.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006376">Panormitanus. </s>
          <s id="s.006377">Ortelius tab. </s>
          <s id="s.006378">6.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006379"><emph type="italics"/>XXIII. SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table28"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table28"/>
          <row>
            <cell>Decimum ver&ograve; quartum Chr. ab ann. Domini</cell>
            <cell>1301</cell>
          </row>
          <row>
            <cell>Bonifacio &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Impp. Alberto primo Au&longs;triaco occid.</cell>
            <cell/>
          </row>
          <row>
            <cell>Andronico Paleologo orient.</cell>
            <cell/>
          </row>
        </table>
        <p type="main">
          <s id="s.006380">BARLAAM Monacus. <!-- KEEP S--></s>
          <s id="s.006381">Gr&aelig;c&egrave; de Arithmetica, nondum editus.</s>
        </p>
        <p type="main">
          <s id="s.006382">ROGERIVS BACCON &longs;ub Clem. <!-- REMOVE S-->5. per&longs;pectiuam laudati&longs;&longs;i&shy;<lb/>
mam &longs;cribit. </s>
          <s id="s.006383">Item de loco &longs;tellarum. </s>
          <s id="s.006384">Item &longs;pecula Mathemati&shy;<lb/>
ca. <!-- KEEP S--></s>
          <s id="s.006385">10. Lucidus. <!-- KEEP S--></s>
          <s id="s.006386">Collim.<!-- REMOVE S-->MARCVS POLVS Venetus, per totum Orientem peruagatus, plurima <lb/>
&longs;citu digni&longs;&longs;ima, de regnis A&longs;i&aelig; Orientalibus breui comm. <!-- REMOVE S-->materna lingua <lb/>
complexus e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.006387">IOANNES Archiep. <!-- REMOVE S-->Cantuar. <!-- KEEP S--></s>
          <s id="s.006388">auctor per&longs;pectiu&aelig; communis. </s>
          <s id="s.006389">po&longs;t Vitell. <lb/>
<!-- REMOVE S-->&amp; mult&ograve; ante 1500. ann. </s>
          <s id="s.006390">ex Gaurico.</s>
        </p>
        <pb pagenum="59" xlink:href="009/01/343.jpg"/>
        <p type="head">
          <s id="s.006391"><emph type="italics"/>XXIIII. SECVLVM<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006392">Decimum ver&ograve; quintum Chr. <!-- REMOVE S-->ab an. <!-- REMOVE S-->Dom. <!-- REMOVE S-->1401. incipiens.</s>
        </p>
        <p type="main">
          <s id="s.006393">Bonifacio &longs;um. <!-- REMOVE S-->Pont.<!-- REMOVE S--> <lb/>Impp. <!-- REMOVE S-->Ruberto Au&longs;triaco occid.<!-- REMOVE S--> &lt;/lb&gt;Emanuele Paleologo orien. <lb/><!-- REMOVE S--><emph type="italics"/>Anno 1453. Imperium orientis capitur &agrave; Mahumeto 2. <lb/>
Turcarum Imperatore.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006394"><emph type="italics"/>Nouus orbis circa finem huius &longs;eculi detegitur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006395">LEONARDVS Pi&longs;anus, primus ex recentioribus de Algebra la&shy;<lb/>
tin&egrave; &longs;crip&longs;it. </s>
          <s id="s.006396">nondum editus.</s>
        </p>
        <p type="main">
          <s id="s.006397">GEORGIVS PVRBACHIVS, Theoricas planetarum, edidit. <lb/>
</s>
          <s id="s.006398">epitomen almage&longs;ti inchoauit, quam po&longs;tea Ioannes de Montere&shy;<lb/>
gio ab&longs;oluit. </s>
          <s id="s.006399">Item tabul. </s>
          <s id="s.006400">eclyp&longs;ium. </s>
          <s id="s.006401">declinationem Solis maximam, 23.28. <lb/>
prodidit. </s>
          <s id="s.006402">&longs;crip&longs;it de horologio &longs;olari, &amp; a&longs;&longs;eruatur in Bibliotheca <expan abbr="Vienn&etilde;&longs;i">Viennen&longs;i</expan>. <lb/>
</s>
          <s id="s.006403">public&egrave; Mathematicas, Vienn&aelig;, &amp; Ferrari&etail; docuit.</s>
        </p>
        <p type="main">
          <s id="s.006404">IACOBVS FABER Stapulen&longs;is edit <expan abbr="c&otilde;mentaria">commentaria</expan> in arthmeticam <lb/>
Iordani. </s>
          <s id="s.006405">Item elementa mu&longs;ic&aelig; libris quatuor.</s>
        </p>
        <p type="main">
          <s id="s.006406">FRANCHINVS GAFFVRIVS Lauden&longs;is, latin&egrave; <expan abbr="Mu&longs;ic&atilde;">Mu&longs;icam</expan>, Theoricam, <lb/>
&amp; Practicam &longs;cribit 1496.</s>
        </p>
        <p type="main">
          <s id="s.006407">IOANNES de Monteregio, Purbacchij di&longs;cipulus. </s>
          <s id="s.006408">Epitomen alme&shy;<lb/>
gi&longs;ti ab&longs;oluit. </s>
          <s id="s.006409">opus de triangulis planis, &amp; &longs;ph&aelig;ricis. </s>
          <s id="s.006410">Tabulas directionum <lb/>
fecit. </s>
          <s id="s.006411">primus ephemerides a&longs;tronomicas ad plures annos edidit. </s>
          <s id="s.006412">tangentes <lb/>
lineas inuenit. </s>
          <s id="s.006413">item libellum de Cometa. </s>
          <s id="s.006414">Mathias Rex Vngari&aelig; multis eum <lb/>
auxit honoribus, &amp; diuitijs. </s>
          <s id="s.006415">tandem Romam &agrave; Summo Pontifice ad Calen&shy;<lb/>
darij correctionem euocatus, ibi obijt, <expan abbr="&longs;epultus&qacute;">&longs;epultusque</expan>; e&longs;t in Pantheone. </s>
          <s id="s.006416">declina&shy;<lb/>
tionem Solis maximam. </s>
          <s id="s.006417">23.30. edixit. </s>
          <s id="s.006418">Monteregio plurimum debet omnis <lb/>literatorum po&longs;teritas, qu&ograve;d veterum Gr&aelig;corum fer&egrave; omnium, Archime&shy;<lb/>
dis, Apollonij, Sereni, Ptolem&aelig;i, &amp; aliorum opera numero fer&egrave; triginta, in <lb/>
latinum conuer&longs;a, Typis mandari curauerit. </s>
          <s id="s.006419">Ex Collimitij indice ante ta&shy;<lb/>
bulam primi mobilis Monteregij.</s>
        </p>
        <p type="main">
          <s id="s.006420">PETRVS de ALIACO Card. <!-- REMOVE S-->Cameracen&longs;is 1414. &longs;ua&longs;it Concilio <expan abbr="C&otilde;-&longs;tantien&longs;i">Con&shy;<lb/>
&longs;tantien&longs;i</expan> correctionem Calendarij Romani. <!-- KEEP S--></s>
          <s id="s.006421">&longs;crip&longs;it de Calendarij corre&shy;<lb/>
ctione. </s>
          <s id="s.006422">de parallelis, &amp;c. </s>
          <s id="s.006423">Chri&longs;tmanus in Alfraganum.</s>
        </p>
        <p type="main">
          <s id="s.006424">F. LVCAS de Burgo edidit magnum volumen Italica lingua de arith&shy;<lb/>
metica, in quo algebram ex Leonardo Pi&longs;ano partim acceptam vulgauit: <lb/>
ibi etiam de geometria practica. </s>
          <s id="s.006425">Item librum de diuina proportione.</s>
        </p>
        <p type="main">
          <s id="s.006426">CHRISTOPHORVS, COLVMBVS Ligur, <expan abbr="Argonaut&utilde;">Argonautum</expan> princeps A&longs;tro&shy;<lb/>nomi&aelig;, &amp; Geographi&aelig; &longs;cientia fretus nouum Orbem, magno, ac f&etail;lici au&shy;<lb/>
&longs;u detexit.</s>
        </p>
        <p type="main">
          <s id="s.006427">NICOLAVS CVSANVS Cardinalis, de Transformatione figurarum.</s>
        </p>
        <pb pagenum="60" xlink:href="009/01/344.jpg"/>
        <p type="head">
          <s id="s.006428"><emph type="italics"/>XXV. SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table29"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table29"/>
          <row>
            <cell>Decimum ver&ograve; &longs;extum Chr. ab ann. Chri&longs;ti</cell>
            <cell>1501</cell>
          </row>
          <row>
            <cell>Alexandro 6. &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imper. Maximiliano occid.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006429"><emph type="italics"/>Totius orbis circumnauigatio: &amp; nouarum &longs;tellarum <lb/>
fixarum apparitio.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006430">IOANNES VERNERVS Germanus, a&longs;tronomicas Tabulas, quibus <lb/>loca &longs;tellarum exponit, declinationi Solis max. tribuit grad. <!-- REMOVE S-->23.28. <lb/>
<expan abbr="prim&atilde;">primam</expan> Arietis po&longs;t &aelig;quinoct. </s>
          <s id="s.006431">gr. <!-- REMOVE S-->26. an. <!-- REMOVE S-->15 4. de motu octau&aelig; &longs;ph&aelig;r&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.006432">FERDINANDVS MEGALANES rei nautic&aelig;, ac proinde a&longs;tro&shy;<lb/>
nomi&aelig; periti&longs;&longs;imus, fretum &longs;ibi cognomen inue&longs;tigauit, vnde po&longs;tea nauis <lb/>
ip&longs;ius ver&egrave; Victoria totius terr&aelig; <expan abbr="glob&utilde;">globum</expan> prima <expan abbr="omni&utilde;">omnium</expan> <expan abbr="circ&utilde;nauigauit">circunnauigauit</expan>. </s>
          <s id="s.006433">1519.</s>
        </p>
        <p type="main">
          <s id="s.006434">IOAN. BLANCHINVS Ferrarien&longs;is, Tabulas a&longs;tronomicas compo&longs;uit.</s>
        </p>
        <p type="main">
          <s id="s.006435">LVDOVICVS FOLIANVS Mutinen. <!-- REMOVE S-->latin&egrave; de mu&longs;ica Theorica. <!-- KEEP S--></s>
          <s id="s.006436">1529.</s>
        </p>
        <p type="main">
          <s id="s.006437">NICOLAVS COPERNICVS, nouis ob&longs;eruationibus c&oelig;le&longs;tes motus <lb/>
corrigit. </s>
          <s id="s.006438">1515. antiquam Cleantis opinione de motu terr&aelig; &longs;u&longs;citauit. </s>
          <s id="s.006439">ait <lb/>
pr&aelig;terea, Solem in centro mundi quie&longs;cere. </s>
          <s id="s.006440">1530.</s>
        </p>
        <p type="main">
          <s id="s.006441">ORONTIVS FIN&AElig;VS, Pari&longs;ijs Mathematicas docuit. </s>
          <s id="s.006442">varia compo&shy;<lb/>
&longs;uit, qu&aelig; pa&longs;&longs;im reperiuntur; legenda tamen cum antidoto Petri Nonij de <lb/>
erratis Oren&longs;ij. </s>
          <s id="s.006443">1530.</s>
        </p>
        <p type="main">
          <s id="s.006444">ERASMVS REINOLDVS eruditi&longs;&longs;imas Tabulas prutenicas. </s>
          <s id="s.006445">Item <expan abbr="c&otilde;-mentaria">com&shy;<lb/>
mentaria</expan> in Theoricas Purbachij edidit.</s>
        </p>
        <p type="main">
          <s id="s.006446">BARTHOLOM&AElig;VS ZAMBERTVS, qui Euclidis Elementa, Optica, <lb/>
Catoptrica, Ph&aelig;nomena, &amp; Data ex Gr&aelig;cis Latina fecit.</s>
        </p>
        <p type="main">
          <s id="s.006447">PAVLVS Epi&longs;copus Foro&longs;empronij. </s>
          <s id="s.006448">opus de Calendarij correctione, <lb/>
quod Paulina dicitur. </s>
          <s id="s.006449">&longs;ub Leone X. con&longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006450">ANDREAS SCHONERVS. de Gnomonica acuti&longs;&longs;im&egrave; &longs;cribit.</s>
        </p>
        <p type="main">
          <s id="s.006451">PETRVS APPIANVS de Geographia.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006452">GEMMA Fri&longs;ius arithmeticam practicam, a&longs;trolabium, &amp;c. </s>
          <s id="s.006453">&longs;cribit.</s>
        </p>
        <p type="main">
          <s id="s.006454">MICHAEL STIFELIVS arithmeticam integram, in qua Algebram op&shy;<lb/>
tima methodo tradit.</s>
        </p>
        <p type="main">
          <s id="s.006455">ALOYSIVS LILIVS, alter no&longs;tri &aelig;ui So&longs;igenes, Calendarij <expan abbr="correction&etilde;">correctionem</expan> <lb/>
excogitauit, qua cyclum Lun&aelig; perpetuum, necnon &longs;tabilem &aelig;quinoctij &longs;e&shy;<lb/>
dem fa&longs;tis Eccle&longs;ia&longs;ticis indidit, quem &longs;equutus e&longs;t Greg. <!-- REMOVE S-->XIII. Papa, dum <lb/>
anno Chri&longs;ti 1572. exemptis decem diebus, vniuer&longs;o Chri&longs;tiano orbi <expan abbr="Cal&etilde;-darium">Calen&shy;<lb/>
darium</expan> in perpetuum emendatum exhibuit. </s>
          <s id="s.006456">Eius frater Antonius Lilius <lb/>
vixit &longs;ub Gregorio XIII.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006457">RAPHAEL BOMBELLVS Bononien&longs;is. </s>
          <s id="s.006458">Italic&egrave; de Algebra.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006459">PETRVS NONIVS Salacien&longs;is, vnico volumine varia pertractat. </s>
          <s id="s.006460">De <lb/>
nautica. </s>
          <s id="s.006461">in Theoricas Parbachij. </s>
          <s id="s.006462">de erratis Orontij. </s>
          <s id="s.006463">de crepu&longs;culis.</s>
        </p>
        <p type="main">
          <s id="s.006464">LVCAS GAVRICVS Epi&longs;copus Ciuitaten&longs;is, de Calendarij correctio&shy;<lb/>
ne. </s>
          <s id="s.006465">Schol. <!-- REMOVE S-->in almag.</s>
        </p>
        <pb pagenum="61" xlink:href="009/01/345.jpg"/>
        <p type="main">
          <s id="s.006466">IOANNES BVTEO Logi&longs;tices, lib. 5. de arca Noe. </s>
          <s id="s.006467">de quadraturis cir&shy;<lb/>
culorum. </s>
          <s id="s.006468">tam antiquis, quam nouis.</s>
        </p>
        <p type="main">
          <s id="s.006469">FRANCISCVS MAVROLY VS Abbas Siculus, <expan abbr="Co&longs;mographi&atilde;">Co&longs;mographiam</expan>. <!-- KEEP S--></s>
          <s id="s.006470">Ari&shy;<lb/>
thmeticorum lib. 3. de lineis horarijs Photi&longs;mos. </s>
          <s id="s.006471">&amp; alia nonnulla, partim <lb/>
nondum edita, quorum index habetur in &longs;ua Co&longs;mographia. </s>
          <s id="s.006472">primus de li&shy;<lb/>
neis &longs;ecantibus &longs;crip&longs;it.</s>
        </p>
        <p type="main">
          <s id="s.006473">HIERONYMVS CARDANVS, artem magnam &longs;cribit, in qua de al&shy;<lb/>
gebra. </s>
          <s id="s.006474">ob&longs;eruauit Cometas e&longs;&longs;e in c&oelig;lo. </s>
          <s id="s.006475">in libris de &longs;ubtilitate, &amp; varieta&shy;<lb/>
te plurima mi&longs;cet ex omnibus Mathematicis.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006476">IOANNES Padouanus de horolgijs.</s>
        </p>
        <p type="main">
          <s id="s.006477">FRANCISCVS FLVSSATES CANDALLA Gallus, nobili&longs;&longs;imo gene&shy;<lb/>
re ortus, commentaria in Euclidem: cui propria Minerua adiecit. </s>
          <s id="s.006478">16. li&shy;<lb/>
brum. </s>
          <s id="s.006479">hic in Academia Burdigalen&longs;i Mathematicarum profe&longs;&longs;ori, annuum <lb/>
&longs;tipendium in perpetuum reliquit. </s>
          <s id="s.006480">&longs;i<expan abbr="&qacute;">que</expan>; eam Cathedram fundauit.</s>
        </p>
        <p type="main">
          <s id="s.006481">FEDERICVS COMMANDINVS optim&egrave; meritus, &longs;i qui&longs;quam alius <lb/>
de Mathematicis. <!-- KEEP S--></s>
          <s id="s.006482">Gr&aelig;corum enim egregia monumenta nobis mira f&etail;lici&shy;<lb/>
tate traduxit, &amp; expo&longs;uit. </s>
          <s id="s.006483">elementa Euclidis. <!-- KEEP S--></s>
          <s id="s.006484">conica Apollonij. <!-- KEEP S--></s>
          <s id="s.006485">opera Ar&shy;<lb/>
chimedis. </s>
          <s id="s.006486">Ari&longs;tarchum Samium. </s>
          <s id="s.006487">Bagdadinum de diui&longs;ione figurarum. </s>
          <s id="s.006488">Ne&shy;<lb/>
ronis &longs;piritalia. </s>
          <s id="s.006489">Pappum Alexandrinum. </s>
          <s id="s.006490">Analemma Ptolem&aelig;i. </s>
          <s id="s.006491">ex proprijs <lb/>
ver&ograve;. </s>
          <s id="s.006492">de centro grauit: &longs;olidorum. </s>
          <s id="s.006493">de lineis horarijs.</s>
        </p>
        <p type="main">
          <s id="s.006494">IOANNES de ROIAS a&longs;trolabium.</s>
        </p>
        <p type="main">
          <s id="s.006495">IOANNES STOFLERVS de fabrica, &amp; v&longs;u a&longs;trolabij. </s>
          <s id="s.006496">commentaria <lb/>
in &longs;ph&aelig;ram Procli. </s>
          <s id="s.006497">de calendario.</s>
        </p>
        <p type="main">
          <s id="s.006498">ABRAHAMVS ORTELIVS Geographus. </s>
          <s id="s.006499">Theatrum mundi, &amp; the&longs;au&shy;<lb/>
rum geographicum.</s>
        </p>
        <p type="main">
          <s id="s.006500">GERARDVS MERCATOR Geographus, Ptolem&aelig;i geographiam re&shy;<lb/>
&longs;tituit. </s>
          <s id="s.006501">Atlas, opus geographicum eius e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.006502">ALEXANDER PICCOLOMIN. &longs;cripfit Italic&egrave; &longs;ph&aelig;ram. </s>
          <s id="s.006503">Theoricas <lb/>
planetarum. </s>
          <s id="s.006504">de &longs;tellis fixis. </s>
          <s id="s.006505">de magnitudine terr&aelig;, &amp; aqu&aelig;.</s>
        </p>
        <p type="main">
          <s id="s.006506">IOSEPHVS ZARLINVS de mu&longs;ica duos tomos Italic&egrave;.</s>
        </p>
        <p type="main">
          <s id="s.006507">VINCENTIVS GALILEVS Florentinus. </s>
          <s id="s.006508">Italic&egrave; &longs;cribit quinque Dia&shy;<lb/>
logos de mu&longs;ica veteri, &amp; noua: vbi optim&egrave; <expan abbr="recentior&utilde;">recentiorum</expan> Contrapunti&longs;tarum <lb/>
&lpar;vt vocant&rpar; errata ab&longs;urdi&longs;&longs;ima manife&longs;tat.</s>
        </p>
        <p type="main">
          <s id="s.006509">IO. BAPTISTA BENEDICTVS Gnomonica, &amp; &longs;peculationes varias.</s>
        </p>
        <p type="main">
          <s id="s.006510">M. IACOBVS CHRISTMANVS comm. in Alfraganum: cui addidit <expan abbr="c&omacr;-mentum">com<lb/>
mentum</expan> eruditi&longs;&longs;imum de Calendarijs, &amp; temporum connexione.</s>
        </p>
        <p type="main">
          <s id="s.006511">IOSEPHVS AVRIA Neapolitanus optim&egrave; de Mathematicis meritus, <lb/>
&longs;iquidem qua&longs;i alter <expan abbr="C&otilde;mandmus">Commandinus</expan> pri&longs;corum monumenta Gr&aelig;ca nobis ex&shy;<lb/>
ponere laborauit. </s>
          <s id="s.006512">eius &longs;unt: Autolycus de &longs;phera, qu&aelig; mouetur. </s>
          <s id="s.006513">Euclidis <lb/>
ph&aelig;nomena. </s>
          <s id="s.006514">Theodo&longs;ius Tripolita de habitationibus: &amp; de dicbus, &amp; no&shy;<lb/>
ctibus. </s>
          <s id="s.006515">Item data Euclidis, nondum edita, qu&aelig; vt edantur, &longs;atago. </s>
          <s id="s.006516">plura <lb/>
alia dedi&longs;&longs;et, ni mors interce&longs;&longs;i&longs;&longs;et.</s>
        </p>
        <p type="main">
          <s id="s.006517">NICOLAVS RAIMARVS, libellum edit, quo acut&egrave; per &longs;olam pro&longs;tha&shy;<lb/>
phere&longs;im, totum &longs;ph&aelig;ricorum triangulorum calculum ab&longs;oluit. </s>
          <s id="s.006518">P. Clauius <lb/>
in a&longs;trolabio.</s>
        </p>
        <p type="main">
          <s id="s.006519">IOANNES BAPT. Vicomercatus, de horologio &longs;olari inuenit modum <pb pagenum="62" xlink:href="009/01/346.jpg"/>de&longs;cribendi plura horologia, &amp; varia vna, &amp; eadem opera ad Solem.</s>
        </p>
        <p type="main">
          <s id="s.006520">FRANCISCVS BAROCIVS patricius Venetus, cui plutimum debe&shy;<lb/>
mus, tum ob Procli in Euclidem commentaria in latinum diligenter tran&shy;<lb/>
&longs;lata, tum propter Heronis Mechanici de machinis bellicis, necnon de Geo&shy;<lb/>
d&aelig;&longs;ia tran&longs;lationem, <expan abbr="atq;">atque</expan> illu&longs;trationem. </s>
          <s id="s.006521">edidit pr&aelig;terea Co&longs;mographiam.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006522">P. ALEXANDER FLORAVANTVS Capucinus, ingenio&longs;i&longs;&longs;imum, ac <lb/>
commodi&longs;&longs;imum in&longs;trumentum ad horologia in muri de&longs;cribenda excogi&shy;<lb/>
tauit; quod Retehorarium appellauit. </s>
          <s id="s.006523">F. <!-- KEEP S--></s>
          <s id="s.006524">Cherubinus in &longs;uo de horologijs <lb/>
Thaumalemmate.</s>
        </p>
        <p type="main">
          <s id="s.006525">GVIDVS VBALDVS Marchio, ex nobili&longs;&longs;ima familia de Monte. </s>
          <s id="s.006526">edidit <lb/>
Mechanica, Paraphra&longs;im in &aelig;quepond. </s>
          <s id="s.006527">Archimedis. <!-- KEEP S--></s>
          <s id="s.006528">A&longs;trolabium, Per&longs;pe&shy;<lb/>
ctiuam, omnia probati&longs;&longs;ima, &amp; proprio marte adinuenta. </s>
          <s id="s.006529">Po&longs;thuma &longs;unt <lb/>
Problem. a&longs;tron. </s>
          <s id="s.006530">&amp; opus de Cochlea.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006531">TICHO BRAHE Baro Danus, verus A&longs;tronomi&aelig; in&longs;taurator. </s>
          <s id="s.006532">in id ad <lb/>200. aureorum millia in&longs;ump&longs;it; nam, &amp; Palatium, &amp; in&longs;trumenta &longs;umptuo&shy;<lb/>
&longs;a con&longs;truxit, &amp; operas plurimas aluit. </s>
          <s id="s.006533">opera eius edita &longs;unt, tomus primus <lb/>
de &longs;tella noua. </s>
          <s id="s.006534">alter de cometis, quas in c&oelig;lo reperit. </s>
          <s id="s.006535">epi&longs;tol&aelig;. </s>
          <s id="s.006536">mechanica. <lb/>
</s>
          <s id="s.006537">alia expectantur. </s>
          <s id="s.006538">a&longs;&longs;erit c&oelig;lum e&longs;&longs;e liquidum, &amp; quartum ignis elementum <lb/>
irridet. </s>
          <s id="s.006539">Venerem, &amp; Martem mod&ograve; &longs;upra Solem, mod&ograve; infra ferri ob&longs;erua&shy;<lb/>
uit. </s>
          <s id="s.006540">obijt 1601.</s>
        </p>
        <p type="main">
          <s id="s.006541">IO. BAPT. VILLALPVNDVS Soc. <!-- KEEP S--><!-- REMOVE S-->Ie&longs;u. <!-- REMOVE S-->in tertio tomo commentario&shy;<lb/>
rum in Ezechielem, librum vnum iu&longs;t&aelig; magnitudinis habet, nouis demon&shy;<lb/>
&longs;trationibus Geometricis, &amp; alijs pluribus, tum ad mechanicam, tum ad <lb/>
men&longs;uras geometricas pertinentibus refertum.</s>
        </p>
        <p type="main">
          <s id="s.006542">FRANCISCVS VIETA Gallus edidit, Canonem mathematicum, opus <lb/>
re&longs;titut&aelig; Mathematic&aelig; analy&longs;eos, munimen aduer&longs;us nouam Cyclometri&shy;<lb/>
cam, P&longs;eudome&longs;olabum. </s>
          <s id="s.006543">Apollonius Gallus. <!-- KEEP S--></s>
          <s id="s.006544">Zetetica: &amp; alia nonnulla.</s>
        </p>
        <p type="main">
          <s id="s.006545">SIMON STEVINIVS Brugen&longs;is, edidit Problem. Geometric. <!-- REMOVE S-->lib. 5.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006546"><emph type="italics"/>XXVI. SECVLVM<emph.end type="italics"/><lb/>
<arrow.to.target n="table30"/><!-- KEEP S--></s>
        </p>
        <table>
          <table.target id="table30"/>
          <row>
            <cell>Decimum ver&ograve; &longs;eptimum Chr. ab ann. Domini</cell>
            <cell>1601</cell>
          </row>
          <row>
            <cell>Clemente 8. &longs;um. Pont.</cell>
            <cell/>
          </row>
          <row>
            <cell>Imp. Rodulpho 2. occid.</cell>
            <cell/>
          </row>
        </table>
        <p type="head">
          <s id="s.006547"><emph type="italics"/>Reperitur Telo&longs;copium, quo in c&oelig;lo admiranda, ac noua <lb/>
primum &longs;pectantur.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.006548">CHRISTOPHORVS CLAVIVS Bambergien&longs;is &egrave; Soc. <!-- KEEP S--><!-- REMOVE S-->Ie&longs;u, <lb/>
pr&aelig;ceptor meus. </s>
          <s id="s.006549">ip&longs;ius opera &longs;unt: &longs;ph&aelig;ra. </s>
          <s id="s.006550">gnomonica. </s>
          <s id="s.006551">commen&shy;<lb/>
taria in Euclidem. <!-- KEEP S--></s>
          <s id="s.006552">in Theodo&longs;ij &longs;ph&aelig;rica. </s>
          <s id="s.006553">de Triangulis planis, &amp; <lb/>
&longs;ph&aelig;ricis. </s>
          <s id="s.006554">A&longs;trolabium. <!-- KEEP S--></s>
          <s id="s.006555">in&longs;trumentum ad horologia de&longs;criben&shy;<lb/>
da. </s>
          <s id="s.006556">nona horologij de&longs;criptio per <expan abbr="Tang&etilde;tes">Tangentes</expan>. </s>
          <s id="s.006557">Arithmetica practica. </s>
          <s id="s.006558">Geome&shy;<lb/>
tria practica. </s>
          <s id="s.006559">Calendarij Romani &agrave; Greg. <!-- REMOVE S-->13. re&longs;tituti explicatio. </s>
          <s id="s.006560">Apologia <lb/>eiu&longs;dem Calendarij contra M&aelig;&longs;tlinum, &amp; contra Io&longs;ephum Scaligerum. <pb pagenum="63" xlink:href="009/01/347.jpg"/>Algebra. <!-- KEEP S--></s>
          <s id="s.006561">in quibus multa partim &agrave; &longs;e inuenta optim&egrave; demon&longs;trat. </s>
          <s id="s.006562">obijt ann. <lb/>
</s>
          <s id="s.006563">Domini 1612. 5. Februarij paulo po&longs;t mediam noctem annorum 75. fere.</s>
        </p>
        <p type="main">
          <s id="s.006564">IO. ANTONIVS MAGINVS Bononi&aelig; publicus <expan abbr="Mathematicar&utilde;">Mathematicarum</expan> pro&shy;<lb/>
fe&longs;&longs;or. </s>
          <s id="s.006565">Geometriam practicam. </s>
          <s id="s.006566">Theoricas planetarum nouas, iuxta ob&longs;er&shy;<lb/>
uationes Copernici. <!-- KEEP S--></s>
          <s id="s.006567">Tabulas &longs;ecundorum mobilium. </s>
          <s id="s.006568">Primum mobile. </s>
          <s id="s.006569">Ta&shy;<lb/>
bulas directionum. </s>
          <s id="s.006570">commentaria in Ptolem&aelig;i Geographiam. <!-- KEEP S--></s>
          <s id="s.006571">Ephemerides <lb/>
ad annos 50. &amp; Italic&egrave; de admirandis effectibus &longs;peculi &longs;ph&aelig;rici &longs;crip&longs;it. <lb/>
</s>
          <s id="s.006572">nunc Italiam magnum opus adornat.</s>
        </p>
        <p type="main">
          <s id="s.006573">MARINVS GHETALDVS patricius Ragu&longs;inus. </s>
          <s id="s.006574">Promotus Archime&shy;<lb/>
des. </s>
          <s id="s.006575">de parabola, &amp; &longs;peculo v&longs;torio. </s>
          <s id="s.006576">item Apollonius rediuiuus. </s>
          <s id="s.006577">&amp; &longs;upplem. <lb/>
</s>
          <s id="s.006578">Apoll. <!-- REMOVE S-->Galli. </s>
          <s id="s.006579">adhuc viuit.</s>
        </p>
        <p type="main">
          <s id="s.006580">LVCAS VALERIVS Rom&aelig; publicus Mathematicarum profe&longs;&longs;or. </s>
          <s id="s.006581">de <lb/>
centro grauit. </s>
          <s id="s.006582">&longs;olidorum. </s>
          <s id="s.006583">opus magno acumine con&longs;criptum. </s>
          <s id="s.006584">Item Qua&shy;<lb/>
dratura Paraboles aliter, qu&agrave;m Archimedes adhuc viuit.</s>
        </p>
        <p type="main">
          <s id="s.006585">ADRIANVS ROMANVS Belga, eius &longs;unt, Id&aelig;a Mathematica. <!-- KEEP S--></s>
          <s id="s.006586">Vra&shy;<lb/>
nographia. </s>
          <s id="s.006587">expo&longs;itio Archimedis de circuli dimen&longs;ione. </s>
          <s id="s.006588">exercitationes cy&shy;<lb/>
clic&aelig;. </s>
          <s id="s.006589">de Triangulis &longs;ph&aelig;ricis.</s>
        </p>
        <p type="main">
          <s id="s.006590">Nobili&longs;&longs;imus CAROLVS GESVALDVS Princeps Venu&longs;inus, no&longs;tr&aelig; <lb/>
tempe&longs;tatis Mu&longs;icorum, ac Melop&aelig;orum princeps, ac veteris Mu&longs;ic&aelig; re&shy;<lb/>
&longs;taurator. </s>
          <s id="s.006591">hic enim rithmis in Mu&longs;icam reuocatis, eos tum ad cantum, tum <lb/>
ad &longs;onum Modulos adhibuit, vt c&aelig;teri omnes Mu&longs;ici, ei primas libenter de&shy;<lb/>
tulerint, <expan abbr="eius&qacute;">eiusque</expan>; Modos Cantores, ac Fidicines omnes, reliquis po&longs;thabitis, <lb/>
<expan abbr="vbiq;">vbique</expan> auid&egrave; complectantur. </s>
          <s id="s.006592">obijt 1614.</s>
        </p>
        <p type="main">
          <s id="s.006593">IO. BAPT. PORTA, eruditi&longs;&longs;imus &aelig;qu&egrave;, ac nobili&longs;&longs;imus. </s>
          <s id="s.006594">editi &longs;unt eius <lb/>
lib. 9. de Refractione optices. </s>
          <s id="s.006595">elementorum curuilineorum lib. 3. Interpre&shy;<lb/>
tatio primi Almage&longs;ti, cum comm. <!-- REMOVE S-->Theonis. </s>
          <s id="s.006596">de Munitione lib. 3. Pneuma&shy;<lb/>
ticorum lib. 3. Catoptrica nondum edita.</s>
        </p>
        <p type="main">
          <s id="s.006597">P. BERNARDINVS SALINVS de Soc. <!-- KEEP S--><!-- REMOVE S-->Ie&longs;u. <!-- REMOVE S-->libri 11. in quibus &longs;uppo&shy;<lb/>
&longs;ita recta &aelig;quali circumferenti&aelig; plurima veluti corollaria demon&longs;trantur. <lb/>
</s>
          <s id="s.006598">de horologijs lib. 2. varia problemata a&longs;tronomica lib. 1. de men&longs;uris geo&shy;<lb/>
metricis lib. 1. qu&aelig; nondum edita a&longs;&longs;eruantur Genu&aelig; in Colleg. <!-- REMOVE S-->Soc. <!-- KEEP S--><!-- REMOVE S-->no&longs;tr&aelig;. <lb/>
</s>
          <s id="s.006599">obijt ann. </s>
          <s id="s.006600">Domini circiter 1608.</s>
        </p>
        <p type="main">
          <s id="s.006601">PETRVS ANTONIVS CATTALDVS Bononien&longs;is, <expan abbr="publicus&qacute;">publicusque</expan>; Bo&shy;<lb/>
noni&aelig; Mathematicarum profe&longs;&longs;or. </s>
          <s id="s.006602">cuius opera iam edita &longs;unt, Elementa <lb/>
numerorum arithmeticorum. </s>
          <s id="s.006603">Elementa Geometricorum. </s>
          <s id="s.006604">Algebra pro&shy;<lb/>
portionalis. </s>
          <s id="s.006605">de lineis rectis &aelig;quidi&longs;tantibus, &amp; non &aelig;quidi&longs;tantibus; vbi <lb/>
Po&longs;tulatum quintum, &amp; &longs;eptimum primi Euclid. <!-- REMOVE S-->o&longs;ten&longs;iu&egrave;, ac breuiter de&shy;<lb/>
mon&longs;trat. </s>
          <s id="s.006606">De numeris perfectis. </s>
          <s id="s.006607">Transformatio Geometrica, qua o&longs;ten&shy;<lb/>
dit datum rectilineum, illud ip&longs;um reducere ad formam propo&longs;iti rectilinei. <lb/>
</s>
          <s id="s.006608">De radice quadrata breui&longs;&longs;im&egrave; inuenienda. </s>
          <s id="s.006609">De quadratura circuli. </s>
          <s id="s.006610">Plures <lb/>
lectiones mathematic&aelig;. </s>
          <s id="s.006611">Apud ip&longs;um ver&ograve; ab&longs;oluta, <expan abbr="atq;">atque</expan> ad Typum para&shy;<lb/>
ta hec &longs;unt: Archimedis defen&longs;io. </s>
          <s id="s.006612">Euclidis defen&longs;io. </s>
          <s id="s.006613">Algebra numeralis, <lb/>
linealis, &amp; applicata. </s>
          <s id="s.006614">Elementa numerorum denominatorum. </s>
          <s id="s.006615">De regula <lb/>
aurea &longs;umma breuitate. </s>
          <s id="s.006616">Transformatio geometrica figur&etail;, in aliam cuius <lb/>
ambitus, ac laterum numerus &longs;it propo&longs;itus. </s>
          <s id="s.006617">Algebra triangularis. </s>
          <s id="s.006618">Hor&shy;<lb/>
tus mathematicus. </s>
          <s id="s.006619">Continuatio algebr&aelig; proportionalis, vbi acuti&longs;&longs;imum <pb pagenum="64" xlink:href="009/01/348.jpg"/>opus zeteticorum docti&longs;&longs;imi Franci&longs;ci Viet&aelig; exponit. </s>
          <s id="s.006620">Examen geometri&aelig; <lb/>
Caroli Bouilij.</s>
        </p>
        <p type="main">
          <s id="s.006621">IOANNES KEPLERVS Mathematicus C&aelig;&longs;areus, &agrave; quo edita &longs;unt; <lb/>
My&longs;terium co&longs;mographicum. </s>
          <s id="s.006622">De &longs;tellis nouis. </s>
          <s id="s.006623">Paralipomena ad Vitell. <lb/>
<!-- REMOVE S-->vn&agrave; cum Optica a&longs;tronomica. </s>
          <s id="s.006624">Opus de &longs;tella Martis. <!-- KEEP S--></s>
          <s id="s.006625">Dioprice.</s>
        </p>
        <p type="main">
          <s id="s.006626">GALIL&AElig;VS GALIL&AElig;VS Florentinus, cui plurim&ugrave;m debet tota po&longs;te&shy;<lb/>
ritas, nam ope Tele&longs;copij nuper &agrave; Belgis inuenti, reperit quatuor planetas <lb/>
circa Iouem errantes; &amp; innumeras alias fixas; in Luna montes, ac valles; <lb/>nebulo&longs;as e&longs;&longs;e &longs;tellularum greges, Gallaxiam e&longs;&longs;e exiguorum a&longs;teri&longs;corum <lb/>
agmen; Venerem in&longs;tar Lun&aelig; augeri, &amp; minui; Saturnum duobus &longs;tipari <lb/>
&longs;atellitibus; h&aelig;c partim in &longs;uo Sydereo Nuncio exponit; partim in libro <lb/>
Italic&egrave; &longs;cripto de Maculis &longs;olaribus, vbi &longs;e primum earum repertorem e&longs;&longs;e <lb/>
contendit. </s>
          <s id="s.006627">Item Italic&egrave; de ijs, qu&aelig; natant, aut mouentur in aqua; opus <lb/>
acuti&longs;&longs;imum; vbi aliquot Ari&longs;t. loca Mathematica expendit. </s>
          <s id="s.006628">adhuc viuit, <lb/>
&amp; nouum mundi Sy&longs;tema adornat.</s>
        </p>
        <p type="main">
          <s id="s.006629">APELLES po&longs;t tabulam latens &lpar;&longs;ic ficto nomine appellari voluit P. <!-- REMOVE S-->Chri&shy;<lb/>&longs;tophorus Scheiner Germanus &egrave; Societate no&longs;tra&rpar; maculas &longs;olares proprio <lb/>
Marte animaduertit, quid circa eas eodem fer&egrave; tempore alij agerent, om&shy;<lb/>
nin&ograve; ne&longs;cius. </s>
          <s id="s.006630">eas tamen primus, libello ficti nominis, publici iuris fecit. <lb/>
</s>
          <s id="s.006631">item libellum de Sole elliptico. </s>
          <s id="s.006632">1612.</s>
        </p>
        <p type="main">
          <s id="s.006633">MARCVSANTONIVS de DOMINIS Archiepi&longs;copus Spalatri. </s>
          <s id="s.006634">de ra&shy;<lb/>
dijs vi&longs;us, &amp; lucis: vbi inquirit Tele&longs;copij demon&longs;trationem.</s>
        </p>
        <p type="main">
          <s id="s.006635">P. CHRISTOPHORVS GREIMBERGERVS &egrave; Societ. <!-- KEEP S--><!-- REMOVE S-->no&longs;tra, qui ad <lb/>
A&longs;trolabium, &amp; Horologia attulit non pauca ip&longs;o Clauio te&longs;te. </s>
          <s id="s.006636">nuper edi&shy;<lb/>
dit Catalogum veteres affixarum longitudines, &amp; latitudines <expan abbr="confer&etilde;s">conferens</expan> cum <lb/>
nouis. </s>
          <s id="s.006637">Item libellum de &longs;peculo v&longs;torio; &amp; Appendicem ad practicam Co&shy;<lb/>
ni &longs;ectionem, cui annexa &longs;unt con&longs;ectaria, qu&aelig; circulorum contactui, <expan abbr="&longs;ectio-nem&qacute;">&longs;ectio&shy;<lb/>
nemque</expan>; angulorum curuilineorum concernunt.</s>
        </p>
        <p type="main">
          <s id="s.006638">P. Fr. <!-- REMOVE S-->AGVILLONIVS BELGA &egrave; no&longs;tra Societ. <!-- KEEP S--><!-- REMOVE S-->edidit eleganti&longs;&longs;imum <lb/>
Optic&aelig; volumen; &amp; alterum adornat.</s>
        </p>
        <p type="main">
          <s id="s.006639">Huius &longs;eculi pr&aelig;cedens pars de&longs;init in anno Dom. <!-- REMOVE S-->1614. quo ip&longs;a Chro&shy;<lb/>
nologia pariter ab&longs;oluta e&longs;t.</s>
        </p>
        <p type="main">
          <s id="s.006640"><expan abbr="Atq;">Atque</expan> hic finis e&longs;to breuis huius Chronologi&aelig;, qu&aelig; continet auctores fer&egrave; <lb/>
257. annos ver&ograve; 2464. in 26. &longs;ecula di&longs;tributa; in quam ex antiquis omnes <lb/>
quot quot reperire potuimus, ex recentioribus &longs;electiores, qui aut &longs;crip&shy;<lb/>tis, aut rebus claruerint, cooptauimus; alioquin recen&longs;endi fui&longs;&longs;ent omnes <lb/>
Pythagorici, <expan abbr="atq;">atque</expan> omnes Platonici, qui omnes Mathematicis eximi&eacute; naua&shy;<lb/>
bant operam. </s>
          <s id="s.006641">omnes pr&aelig;terea Poet&aelig; ab Homero <expan abbr="v&longs;q;">v&longs;que</expan> ad Chri&longs;t<emph type="italics"/>i<emph.end type="italics"/> fer&egrave; &longs;ecu&shy;<lb/>lum annumerandi fui&longs;&longs;ent, erant enim antiquitus poet&aelig; omnes &longs;imul etiam <lb/>
mu&longs;ici, vt per&longs;picuum e&longs;t ex ijs, qu&aelig; in libro de mu&longs;ica Plutarchus in hunc <lb/>
modum ait; non equidem fui&longs;&longs;e immunem metri, numeriu&egrave; rati dictionem <lb/>
poematum mu&longs;icorum, &longs;ed qualis Stetichori fuit, &amp; veterum aliorum poe&shy;<lb/>
tarum, qui carmina adhibitis modulis condidere, Terpandrum <expan abbr="nanq;">nanque</expan> tra&shy;<lb/>
dunt adiectis ad &longs;ua, <expan abbr="atq;">atque</expan> Homeri carmina, per &longs;ingulas leges modis, &longs;oli&shy;<lb/>
tum in ludis cum concertatione editis canere.</s>
        </p>
        <p type="main">
          <s id="s.006642"><expan abbr="Neq;">Neque</expan> mireris, qu&ograve;d <expan abbr="rec&etilde;tcs">recentes</expan> mu&longs;icos omnes, quos Contrapunti&longs;tas appel&shy;


<pb pagenum="65" xlink:href="009/01/349.jpg"/>lant, omi&longs;erim, id enim con&longs;ult&ograve;, ac merit&ograve; feci, c&ugrave;m mihi ob&longs;equentes ra&shy;<lb/>
tiones, quas breuiter ex Dialogis de mu&longs;ica Vincentij Galil&aelig;i decerp&longs;i, <lb/>
nomine mu&longs;ici, indigni videantur.</s>
        </p>
        <p type="main">
          <s id="s.006643">Prim&ograve;, quia officio mu&longs;ici minim&egrave; funguntur: e&longs;t autem ex Platonis, <expan abbr="atq;">atque</expan> <lb/>
Ari&longs;tot. &longs;ententia, officium mu&longs;ici, rithmis, &longs;iue numeris vti ad auditorum <lb/>
affectus excitandos: Contrapunti&longs;t&aelig; ver&ograve; i&longs;ti rithmum omnem, aut nume&shy;<lb/>
rum a &longs;pernantur.</s>
        </p>
        <p type="main">
          <s id="s.006644">Secund&ograve;, quia &longs;uas illas quatuor, aut quinque partes &longs;ic &longs;imul <expan abbr="confund&utilde;t">confundunt</expan>, <lb/>
vt nullum verbum, <expan abbr="nullus&qacute;">nullusque</expan>; rithmus percipiatur: &longs;ed mera tantummodo <lb/>
mu&longs;ica qu&aelig;dam confu&longs;io: quam, qui audit ne&longs;cit quid audiat.</s>
        </p>
        <p type="main">
          <s id="s.006645">Terti&ograve;, quia eodem modo carmina, ac &longs;olutam orationem canunt, vt in&shy;<lb/>
telligere nequeas carmina ne, an pro&longs;am decantent. </s>
          <s id="s.006646">quod quidem maxim&egrave; <lb/>
e&longs;t inconueniens, &amp; veteri mu&longs;ic&aelig; contrarium. </s>
          <s id="s.006647"><expan abbr="neq;">neque</expan> enim mu&longs;ica carminis <lb/>
numerum offu&longs;care; &longs;ed eum magis exornare, <expan abbr="atq;">atque</expan> viuidum reddere debet.</s>
        </p>
        <p type="main">
          <s id="s.006648">Quart&ograve;, quia cantilen&aelig; &longs;en&longs;um omnem, dum diuer&longs;a verba &longs;imul plures, <lb/>
in cantu pronunciant, ita tollunt, vt nihil omnino intelligatur: c&ugrave;m tamen <lb/>
mu&longs;ici officium &longs;it, cantilen&aelig; &longs;ententiam cantu, &amp; rithmo auditorum ani&shy;<lb/>
mis ita in genere, vt eos iuxta &longs;ententi&aelig; illius <expan abbr="affect&utilde;">affectum</expan>, afficiat, ac <expan abbr="c&otilde;moueat">commoueat</expan>.</s>
        </p>
        <p type="main">
          <s id="s.006649">Quint&ograve;, quia de indu&longs;tria <expan abbr="c&otilde;tra">contra</expan> leges antiquas repetitiones eiu&longs;dem, vel <lb/>
<expan abbr="con&longs;on&atilde;ti&aelig;">con&longs;onanti&aelig;</expan>, vel cadenti&aelig;, aut aiunt, <expan abbr="atq;">atque</expan> <expan abbr="eti&atilde;">etiam</expan> rithmi maxim&egrave; vitant: quod <lb/>
tamen ad animorum motus ciendos plurim&ugrave;m valet.</s>
        </p>
        <p type="main">
          <s id="s.006650">Sext&ograve;, quia non mu&longs;ic&egrave;, &longs;ed mimic&egrave;, ide&longs;t non rithmis, &longs;ed modis &agrave; natu&shy;<lb/>
ra mu&longs;ic&aelig; alienis, ac ridiculis frequenter imitari ge&longs;tiunt.</s>
        </p>
        <p type="main">
          <s id="s.006651">Hac igitur no&longs;tra <expan abbr="qualicunq;">qualicunque</expan> fruere lucubratiuncula: <expan abbr="atq;">atque</expan> in ea contem&shy;<lb/>
plare, quo <expan abbr="t&etilde;pore">tempore</expan>, &amp; &agrave; quibus non &longs;ol&ugrave;m Mathematica, &longs;ed ali&aelig; etiam <expan abbr="&longs;ci&etilde;-ti&aelig;">&longs;cien&shy;<lb/>
ti&aelig;</expan> ortum habuerunt: quando &amp; apud quos floruerint, aut de&longs;ierint; ac <expan abbr="t&atilde;-dem">tan&shy;<lb/>
dem</expan> iterum reuiui&longs;cere c&etail;perint.</s>
        </p>
        <p type="main">
          <s id="s.006652">Qu&ograve;d &longs;i qu&aelig;ras, <expan abbr="quibu&longs;n&atilde;">quibu&longs;nam</expan> &longs;tudijs, tribus illis annorum millibus, qu&aelig; chro&shy;<lb/>
nologiam hanc no&longs;tram pr&aelig;ce&longs;&longs;erunt, homines vacauerint, ac proinde, cur <lb/>
tam &longs;er&ograve; literis operam nauare c&aelig;perint: re&longs;pondendum e&longs;&longs;e arbitror, <lb/>
toto illo tempore homines fui&longs;&longs;e totos, tum in artibus inue&shy;<lb/>
niendis, atque excolendis, tum in vrbibus, atque <lb/>
rebus publicis con&longs;tituendis: quippe&shy;<lb/>
qu&aelig; magis human&aelig; vit&aelig; ne&shy;<lb/>
ce&longs;&longs;aria erant. <lb/>
</s>
          <s id="s.006653">Vale.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.006654">DEO OPT. MAX. LAVS.</s>
        </p>
        <pb xlink:href="009/01/350.jpg"/>
        <p type="head">
          <s id="s.006655">INDEX<lb/>
In pr&aelig;cedentem Chronologiam.<lb/>
<arrow.to.target n="table31"/></s>
        </p>
        <table>
          <table.target id="table31"/>
          <row>
            <cell><emph type="italics"/>A<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Ardalus mu&longs;icus.<emph.end type="italics"/></cell>
            <cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/> 1</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Anaximander a&longs;tron.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ameti&longs;tus geomctra.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Anaximenes a&longs;tron.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Anaxagoras astron.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Anti&longs;thenes mu&longs;icus.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Amiclas geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Antiphon geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ari&longs;t&aelig;us geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aratus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aristoteles mathem.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Autolycus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ari&longs;toxenes mu&longs;.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Archelaws geographus.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ari&longs;tarchus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ar&ccedil;himedes mathem.<emph.end type="italics"/></cell>
            <cell>7</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Apoll&oacute;nius magnus geometra.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Athen&aelig;us mechan.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Andronicus mechan.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Artemidorus geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Andromachus astron.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Abifeldea geogr.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S. Augu&longs;tmus mathem.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Almaon Rex a&longs;tron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Albaregnius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Achilles a&longs;tron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alfarabius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alhuma&longs;ar a&longs;tron.<emph.end type="italics"/></cell>
            <cell>19</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alfraganus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>19</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alhazenus opticus.<emph.end type="italics"/></cell>
            <cell>20</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Arzael a&longs;tron.<emph.end type="italics"/></cell>
            <cell>20</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Auerroes a&longs;tron.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Almeon Alman&longs;orius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alpetragius a&longs;tr.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <row>
            <cell><emph type="italics"/>R. Abraham a&longs;tr.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alfon&longs;us Rex a&longs;tr.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Andreas Schonerus gnonom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Aloy&longs;ius Lihus a&longs;ir.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Abrahamus Ortelius geogr.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Alexand. Florauantes gnom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Adrianus R. B. mathem.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Apelles Latens a&longs;tr.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>B<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Bry&longs;o geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bero&longs;us a&longs;tr.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Boetius mathem.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>V. Beda mathem.<emph.end type="italics"/></cell>
            <cell>17</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bagdadinus geom.<emph.end type="italics"/></cell>
            <cell>19</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ben Mu&longs;a geom.<emph.end type="italics"/></cell>
            <cell>19</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Barlaam arithm.<emph.end type="italics"/></cell>
            <cell>23</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bart. Zambertus geom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Bernardinus Salinus geom.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>C<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Carolus Ge&longs;ualdus mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Clonas mu&longs;ic. &longs;ec.<emph.end type="italics"/></cell>
            <cell>1</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cleo&longs;tratus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cratistus geom.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cygicinus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Calippus astron.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Conon mathem.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cte&longs;ibius mechan.<emph.end type="italics"/></cell>
            <cell>7</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cleomedes a&longs;tr.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>C. Manlius a&longs;tr.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cen&longs;orinu a&longs;tr.<emph.end type="italics"/></cell>
            <cell>12</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cyrillus Epi&longs;c. astr.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ca&longs;&longs;iodorus math.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Campanus geom.<emph.end type="italics"/></cell>
            <cell>20</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Chri&longs;toph. Columb. nautic.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cbr. Clauius mathem.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Chr. Gruenbergeius mathem.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cardanus a&longs;tr.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Cattaldus arithm.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>D<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Damon mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diocles mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Democritus mathem.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Dino&longs;tratus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Dicearcbus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diony&longs;iodorus geom.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <pb xlink:href="009/01/351.jpg"/>
          <row>
            <cell><emph type="italics"/>Diony&longs;ius Afer geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diophantes arithm.<emph.end type="italics"/></cell>
            <cell>11</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diocles geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Demetrius geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Diony&longs;ius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>E<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Evshorbus geometra.<emph.end type="italics"/></cell>
            <cell>2</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Empedocles mu&longs;.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Epicurus mu&longs;.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Euctemon a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Eudoxius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Euclides geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Erato&longs;thenes a&longs;tron.<emph.end type="italics"/></cell>
            <cell>7</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Eu&longs;ebius Epi&longs;c. a&longs;tron.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Eudemus geom.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Eutocius geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Era&longs;mus Reinoldus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>F<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Franchinus mu&longs;.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Lucas arithm.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ferd. Megalanes naut.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Maurolycus mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Flu&longs;&longs;as geom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Feder. Command. mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Barocius mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Vieta mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Fr. Aguillonius optic.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>G<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Geminus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Geminus Rhodius a&longs;tr. &amp; geom.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S. Greg. mag. mu&longs;.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Geber a&longs;tron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Guido Aret. mu&longs;.<emph.end type="italics"/></cell>
            <cell>19</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Geor. Purbachius astron.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Gemma Fri&longs;ius mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Gerardus Mercator geogr.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Guidu&longs;ubaldus mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Galil&aelig;us Galil&aelig;us a&longs;tron.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>H<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Hecateus geogr.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hippocr. Chius geom.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Helicon a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hermotimus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hermophilus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Heraclides mu&longs;.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hero mechan.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hipparchus astron.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hippolytus Epi&longs;c. a&longs;tron.<emph.end type="italics"/></cell>
            <cell>12</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hypatia a&longs;tron. &amp; arithm.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Hero mechan. alter.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Heliodorus optic.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>I<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Ismenius mu&longs;.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>I&longs;idorus geom.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iul. C&aelig;&longs;ar astron.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iul. Higinius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iul. Maternus a&longs;trol.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Grammat. arithm.<emph.end type="italics"/></cell>
            <cell>15</cell>
          </row>
          <row>
            <cell><emph type="italics"/>I&longs;idorus mathem.<emph.end type="italics"/></cell>
            <cell>16</cell>
          </row>
          <row>
            <cell><emph type="italics"/>I&longs;acius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>20</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iordanes arithm.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. de Sacrobo&longs;co a&longs;tron.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Gira nautic.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Epi&longs;c. optic.<emph.end type="italics"/></cell>
            <cell>23</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iacob. Faber mu&longs;.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Monteregius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Vernerus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Blanchinus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Buteo mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Paduanus gnomon:<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Roias a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Sto&longs;terus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io&longs;ephus Zarlinus mu&longs;.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Bapt. Benedictus gnomon.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io&longs;ephus Auria mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Iacob. Chri&longs;tm. a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Bapt. Vicomerc. gnomon.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Villalpandus geom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Ant. Maginus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Io. Keplerus mathem.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>L<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Licaon mu&longs;.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>La&longs;us mu&longs;.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Leodamas geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Leon geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>L. Papirius gnomon.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Leonardus algebrat.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ludouicus Folianus mu&longs;.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lucas Gaur. a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Lucas Valerius mechan.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <pb xlink:href="009/01/352.jpg"/>
          <row>
            <cell><emph type="italics"/>M<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Mamertimis geom.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Methon a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Menechmus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>M. Agrippa geogr.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Marinus geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Menelaus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Maximus arithm.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Menelaus geom.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Marinus Neapolit. geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Martianus mathem.<emph.end type="italics"/></cell>
            <cell>16</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Michael P&longs;eltus mathem.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Mar. Polus geogr.<emph.end type="italics"/></cell>
            <cell>23</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Michael Stif. arithra.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Marinus Ghetaldus mechan.<emph.end type="italics"/></cell>
            <cell>26</cell>
          </row>
          <row>
            <cell><emph type="italics"/>N<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Nicomachus arithm.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Neoclides geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nicomedes geom.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nicolaus Caba&longs;illa a&longs;tron.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nicolaus Cu&longs;anus geom.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nic. Copern. astron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Nic. Raimarus geom.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>O<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Oenipedes geom.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Orontius matbem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>P<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Polemon geogr.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pythagoras mathem. &longs;ummus.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pericles a&longs;tron.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Phrinis mu&longs;.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Phrinicus mu&longs;.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Parmenides a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Protagoras mathem.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Plato mathem.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Philippus mathem.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Philo&longs;ophus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Per&longs;eus geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Philo mechan.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Po&longs;&longs;idonius mathem.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Patroclus gnomon.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Parmenion gnomon.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>P. Mela geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Plinius geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Plutarchus mu&longs;.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ptolem&aelig;us astron.<emph.end type="italics"/></cell>
            <cell>11</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Porphirius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>12</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Philo geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Proclus geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S. Pro&longs;per a&longs;tron.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pappus geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Paulus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Peto&longs;iris astron.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Pelles arithm.<emph.end type="italics"/></cell>
            <cell>18</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Petrus de Aliaco a&longs;tron.<emph.end type="italics"/></cell>
            <cell>24</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Paulus Epi&longs;c. a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Petrus Appianus geogr.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Petrus Nonius mathem.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>R<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Rogerius Baccon optic.<emph.end type="italics"/></cell>
            <cell>23</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Raphael arithm.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Sacadas mu&longs;.<emph.end type="italics"/></cell>
            <cell>2</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Simonides lyric.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Sappho mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Simon mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Simmias mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Sulpitius a&longs;tron.<emph.end type="italics"/></cell>
            <cell>7</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Serenus geom.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>So&longs;igenes a&longs;tron.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Scopas gnomon.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Strabo geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Solinus geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Straton geogr.<emph.end type="italics"/></cell>
            <cell>10</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Sextus Empir. mathem.<emph.end type="italics"/></cell>
            <cell>11</cell>
          </row>
          <row>
            <cell><emph type="italics"/>S. Auienus geogr.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Sporus geom.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>T<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Terpander mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>1</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Thales Mile&longs;ius.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Telauges arithm.<emph.end type="italics"/></cell>
            <cell>3</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theodorus geom.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Timeus mathem.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
          <row>
            <cell><emph type="italics"/>The&aelig;tetus geom.<emph.end type="italics"/></cell>
            <cell>5</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theudius geom.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theophra&longs;tus mathem.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Timotheus mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Timocharis a&longs;tron.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theodoricus a&longs;tron.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theophilus Epi&longs;c. astron.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theon a&longs;tron.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Theon Smyrn&aelig;us mathem.<emph.end type="italics"/></cell>
            <cell>21</cell>
          </row>
          <pb xlink:href="009/01/353.jpg"/>
          <row>
            <cell><emph type="italics"/>Thebit a&longs;tron.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Ticho a&longs;tron.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>V<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Vincentius Galil&aelig;us mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>25</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vitellio optic.<emph.end type="italics"/></cell>
            <cell>22</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Victorinus astron.<emph.end type="italics"/></cell>
            <cell>14</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Vitruuius gnomon.<emph.end type="italics"/></cell>
            <cell>9</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Valens a&longs;trol.<emph.end type="italics"/></cell>
            <cell>13</cell>
          </row>
          <row>
            <cell><emph type="italics"/>X<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Xenocrates mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>1</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Xenocrates mathem.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Xenophantus mu&longs;ic.<emph.end type="italics"/></cell>
            <cell>6</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Y<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Yp&longs;icles geometra.<emph.end type="italics"/></cell>
            <cell>8</cell>
          </row>
          <row>
            <cell><emph type="italics"/>Z<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell><emph type="italics"/>Zenodorus geometra.<emph.end type="italics"/></cell>
            <cell>4</cell>
          </row>
        </table>
        <p type="head">
          <s id="s.006656"><emph type="italics"/>FINIS.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.006657">Ego Fr. <!-- REMOVE S-->Hieronymus Onuphrius Romanus, ex Conuentu S. <!-- REMOVE S-->Mari&aelig; Gra&shy;<lb/>
tiarum, Doctor Colleg. <!-- REMOVE S-->&amp; Lector publicus, ac Sancti&longs;s. <!-- REMOVE S-->Inqui&longs;itionis <lb/>
Con&longs;ultor, vel libenti&longs;&longs;im&egrave; vidi, ac perlegi Opus hoc aureum in&longs;criptum, <lb/>
LOCA ARISTOTELIS MATHEMATICA, &amp; con&longs;criptum <lb/>
ab Excellenti&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Io&longs;epho Blancano de Societ. <!-- KEEP S--><!-- REMOVE S-->IESV. &amp; c&ugrave;m in eo nihil re&shy;<lb/>
periatur, quod aut &longs;it contra Eccle&longs;ia&longs;ticas di&longs;ciplinas, aut quod pias aures <lb/>
offendat, quinimo maxima emergat vtilitas ijs, qui Ari&longs;totelicum textum <lb/>
con&longs;ult&ograve; amplectuntur, ide&ograve; po&longs;&longs;e typis dari cen&longs;ui, &amp;c.</s>
        </p>
        <p type="head">
          <s id="s.006658">Imprimatur</s>
        </p>
        <p type="head">
          <s id="s.006659"><emph type="italics"/>Idem qui &amp; &longs;upra nomine Reuerendi&longs;&longs;. <!-- REMOVE S-->P. Inqui&longs;it. <!-- REMOVE S-->Bonon.<emph.end type="italics"/></s>
        </p>
        <pb xlink:href="009/01/354.jpg"/>
        <p type="head">
          <s id="s.006660"><emph type="italics"/>Errata, qu&aelig; Lectorem &longs;isterent, &longs;ic corrigantur.<emph.end type="italics"/><lb/>
<arrow.to.target n="table32"/></s>
        </p>
        <table>
          <table.target id="table32"/>
          <row>
            <cell><emph type="italics"/>pag. linea. erratum. correctum.<emph.end type="italics"/></cell>
            <cell/>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>4</cell>
            <cell>2</cell>
            <cell>per&longs;ua&longs;i&longs;ti</cell>
            <cell>perua&longs;i&longs;ti</cell>
          </row>
          <row>
            <cell>18</cell>
            <cell>22</cell>
            <cell>quadratum</cell>
            <cell>quadrangulum</cell>
          </row>
          <row>
            <cell>36</cell>
            <cell>34</cell>
            <cell>inue&longs;tare</cell>
            <cell>inueftigare</cell>
          </row>
          <row>
            <cell>38</cell>
            <cell>15</cell>
            <cell>A G,</cell>
            <cell>A C G,</cell>
          </row>
          <row>
            <cell>39</cell>
            <cell>22</cell>
            <cell>&aelig;quatiorem</cell>
            <cell>&aelig;quatorem</cell>
          </row>
          <row>
            <cell>51</cell>
            <cell>46</cell>
            <cell><expan abbr="vnoq;">vnoque</expan></cell>
            <cell><expan abbr="vnoquoq;">vnoquoque</expan></cell>
          </row>
          <row>
            <cell>70</cell>
            <cell>in figura defiderantur du&aelig; lineol&aelig; rect&aelig; A I, &amp; I E,</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>80</cell>
            <cell>13</cell>
            <cell>Tex.</cell>
            <cell>Textus 59.</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>in figura pro O, ponatur C,</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>82</cell>
            <cell>13</cell>
            <cell>Tex.</cell>
            <cell>Tex. 110.</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>45</cell>
            <cell>Vr&longs;am</cell>
            <cell>ad Vr&longs;am</cell>
          </row>
          <row>
            <cell>83</cell>
            <cell>42</cell>
            <cell>Tex.</cell>
            <cell>Tex. 65.</cell>
          </row>
          <row>
            <cell>107</cell>
            <cell>10</cell>
            <cell>fides</cell>
            <cell>fidem</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>11</cell>
            <cell>&longs;axiatritu</cell>
            <cell>&longs;ci&longs;&longs;a, &amp; attrita</cell>
          </row>
          <row>
            <cell>166</cell>
            <cell>in 2 figura de&longs;ideratur linea P R.</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>127</cell>
            <cell>28</cell>
            <cell>L,</cell>
            <cell>C,</cell>
          </row>
          <row>
            <cell>155</cell>
            <cell>in 2. figura dee&longs;t linea K P:</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell/>
            <cell>altera ver&ograve;, qu&aelig; dextror&longs;um vergit, &longs;uperflua e&longs;t.</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>220</cell>
            <cell>45</cell>
            <cell>quadratum</cell>
            <cell>quadrangulum</cell>
          </row>
          <row>
            <cell>221</cell>
            <cell>1</cell>
            <cell>quadratum</cell>
            <cell>quadrangulum</cell>
          </row>
          <row>
            <cell>231</cell>
            <cell>30</cell>
            <cell>incrementa</cell>
            <cell>decrementa</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>31</cell>
            <cell>decrementis</cell>
            <cell>incrementis</cell>
          </row>
          <row>
            <cell>235</cell>
            <cell>19</cell>
            <cell>L O,</cell>
            <cell>M N,</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>21</cell>
            <cell>N M,</cell>
            <cell>O L,</cell>
          </row>
          <row>
            <cell>ibid.</cell>
            <cell>34</cell>
            <cell>H L,</cell>
            <cell>N L,</cell>
          </row>
          <row>
            <cell>237</cell>
            <cell>in figura linea K D L, deberet direct&egrave; ad punctum A, tendere</cell>
            <cell/>
            <cell/>
          </row>
          <row>
            <cell>256</cell>
            <cell>4</cell>
            <cell>toto</cell>
            <cell>tono</cell>
          </row>
          <row>
            <cell>264</cell>
            <cell>14</cell>
            <cell>numeris</cell>
            <cell>neruis</cell>
          </row>
          <row>
            <cell>266</cell>
            <cell>44</cell>
            <cell>c&aelig;teris</cell>
            <cell>c&aelig;teri</cell>
          </row>
          <row>
            <cell>267</cell>
            <cell>45</cell>
            <cell>indicium</cell>
            <cell>indicium</cell>
          </row>
          <row>
            <cell>274</cell>
            <cell>27</cell>
            <cell>contr&agrave; verum</cell>
            <cell>contr&agrave;, verum</cell>
          </row>
          <row>
            <cell>279</cell>
            <cell>30</cell>
            <cell>MKINQ,</cell>
            <cell>MHINQ,</cell>
          </row>
          <row>
            <cell/>
            <cell/>
            <cell><emph type="italics"/>In Additamento.<emph.end type="italics"/></cell>
            <cell/>
          </row>
          <row>
            <cell>9</cell>
            <cell>5</cell>
            <cell>vnc&igrave;a</cell>
            <cell>vnica</cell>
          </row>
          <row>
            <cell>9</cell>
            <cell>28</cell>
            <cell>proportionali</cell>
            <cell>proportionalis</cell>
          </row>
          <row>
            <cell>14</cell>
            <cell>28</cell>
            <cell>diuionem</cell>
            <cell>diui&longs;ionem</cell>
          </row>
          <row>
            <cell>18</cell>
            <cell>22</cell>
            <cell>78.</cell>
            <cell>7. 8.</cell>
          </row>
        </table>
        <pb xlink:href="009/01/355.jpg"/>
        <p type="head">
          <s id="s.006661">BONONI&AElig;</s>
        </p>
        <p type="head">
          <s id="s.006662">Apud Bartholom&aelig;um Coch&igrave;um. </s>
          <s id="s.006663">1615.</s>
        </p>
        <p type="head">
          <s id="s.006664">Superiorum permi&longs;&longs;u.<lb/>
</s>
        </p>
      </chap>
    </body>
  </text>
</archimedes>