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version 1.6, 2002/06/27 17:26:48 version 1.7, 2002/06/28 13:03:40
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 <!DOCTYPE archimedes [ <!DOCTYPE archimedes [
  
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 ]> ]><archimedes>      <info>        <author>Guidobaldo del Monte</author>        <title>Mechanicorum Liber</title>        <date>1577</date>        <place>Pisauri</place> <editor></editor>                <publisher></publisher>        <translator></translator>        <lang>LA</lang>              <chunk unit="page*">page</chunk>      <locator>0000000036</locator>      </info><text>            <front>            
  
  <section>         <pb id="p.0001" xlink:href="pagethumb-la/00000003.JPG"/>             <p id="id.2.1.1.1.0.0.0" type="head">                         
  
 <archimedes> <s id="id.2.1.1.1.2.1.0"> GVIDIV BALDI <lb/>E MARCHIONIBVS <lb/>MONTIS <lb/>MECHANICORVM <lb/>LIBER. </s>     <lb/>              
  
       <info> <s> ZZZ head of figure ZZZ </s>         </p>              <p id="id.2.1.1.1.4.1.0" type="caption">        
  
         <author>Guidobaldo del Monte</author> 
         <title>Mechanicorum Liber</title> 
         <date>1577</date> 
         <place>Pisauri</place> 
         <editor></editor>         
         <publisher></publisher> 
         <translator></translator> 
         <lang>LA</lang> 
          
       <chunk unit="page*">page</chunk> 
       <locator>0000000036</locator> 
       </info> 
  
 <text>         
     <front>        
       <section> 
           <pb id="p.0001" xlink:href="pagethumb-la/00000003.JPG"/>      
         <p id="id.2.1.1.1.0.0.0" type="head">         
  
         
           <s id="id.2.1.1.1.2.1.0"> GVIDIV BALDI <lb/> 
 E MARCHIONIBVS <lb/> 
 MONTIS <lb/> 
 MECHANICORVM <lb/> 
 LIBER. </s>     <lb/> 
         
           <s> ZZZ head of figure ZZZ </s>     
         </p>               
 <p id="id.2.1.1.1.4.1.0" type="caption">         
 <s id="id.2.1.1.1.4.1.0.capt"> YYY </s>     <lb/> <s id="id.2.1.1.1.4.1.0.capt"> YYY </s>     <lb/>
               
 <s id="id.2.1.1.1.6.1.0"> PISAVRI <lb/> <s id="id.2.1.1.1.6.1.0"> PISAVRI <lb/>Apud Hieronymum Concordiam. </s>     <lb/>      
 Apud Hieronymum Concordiam. </s>     <lb/> 
               
 <s id="id.2.1.1.1.8.1.0"> M. D. LXXVII. </s>     <lb/> <s id="id.2.1.1.1.8.1.0"> M. D. LXXVII. </s>     <lb/>
               
 <s id="id.2.1.1.1.10.1.0"> Cum Licentia Superiorum. </s>    </p>        <s id="id.2.1.1.1.10.1.0"> Cum Licentia Superiorum. </s>    </p>       <pb xlink:href="pagethumb-la/00000004.JPG"/>       <p id="id.2.1.1.3.0.0.0" type="head">        
 <pb xlink:href="pagethumb-la/00000004.JPG"/> 
  <s id="id.2.1.1.3.1.1.0"> PRAESENTI OPERE <lb/>CONTENTA. </s>    </p>       <p id="id.2.1.1.4.0.0.0" type="main">        
  
  <s id="id.2.1.1.4.1.1.0"> De Libra. </s>    </p>       <p id="id.2.1.1.5.0.0.0" type="main">        
  
  <s id="id.2.1.1.5.1.1.0"> De Vecte. </s>    </p>       <p id="id.2.1.1.6.0.0.0" type="main">        
  
  <s id="id.2.1.1.6.1.1.0"> De Trochlea. </s>    </p>       <p id="id.2.1.1.7.0.0.0" type="main">        
  
  <s id="id.2.1.1.7.1.1.0"> De Axe in peritrochio. </s>    </p>       <p id="id.2.1.1.8.0.0.0" type="main">        
  
  <s id="id.2.1.1.8.1.1.0"> De Cuneo. </s>    </p>       <p id="id.2.1.1.9.0.0.0" type="main">        
  
  <s id="id.2.1.1.9.1.1.0"> De Cochlea.  </s>    </p>       <p id="id.2.1.1.10.0.0.0" type="head">        <pb xlink:href="pagethumb-la/00000005.JPG"/>      
  
  <s id="id.2.1.1.11.1.1.0"> AD FRANCISCVM <lb/>MARIAM II <lb/>VRBINATVM <lb/>AMPLISSIMVM DVCEM <lb/>GVIDIVBALDI <lb/>E MARCHIONIBVS <lb/>MONTIS </s>     <lb/>      
  
  <s id="id.2.1.1.11.3.1.0"> PRAEFATIO. </s>    </p>       <p id="id.2.1.1.12.0.0.0" type="main">        
  
  <s id="id.2.1.1.12.1.1.0"> DVAE res (AMPLISSIME PRIN&shy;<lb/>CEPS) qu&aelig; ad conciliandas homi<lb/>nibus facultates, vtilitas nemp&egrave;, &amp; <lb/>nobilitas, plurim&ugrave;m valere con&longs;ue<lb/>uerunt.  </s>            
  
  <s id="id.2.1.1.12.1.2.0"> ill&aelig; ad exornandam mecha<lb/>nicam facultatem, &amp; eam pr&aelig; om&shy;<lb/>nibus alijs appetibilem reddendam con&longs;pira&longs;&longs;e <lb/>mihi videntur: nam &longs;i nobilitatem (quod pleriq; <lb/>mod&ograve; faciunt) ortuip&longs;o metimur, occurret hinc <lb/>Geometria, illinc ver&ograve; Phi&longs;ica; quorum gemina<lb/>to complexu nobili&longs;&longs;ima artium prodit mechani&shy;<lb/>ca.  </s>            
  
  <s id="id.2.1.1.12.1.3.0"> &longs;i enim nobilitatem magis, t&ugrave;m &longs;trat&aelig; materi&aelig;, <lb/>t&ugrave;m argumentorum nece&longs;&longs;itati (quod Ari&longs;tote&shy;<lb/>les fatetur aliquand&ograve;) relatam volumus, omnium <lb/>proculdubi&ograve; nobili&longs;&longs;imam per&longs;piciemus.  </s>            
  
  <s id="id.2.1.1.12.1.4.0"> qu&aelig; <pb xlink:href="pagethumb-la/00000006.JPG"/>quidem non &longs;olum geometriam (vt Pappus te&longs;ta<lb/>tur) ab&longs;oluit, &amp; perficit; ver&ugrave;m etiam &amp; phi&longs;ica&shy;<lb/>rum rerum imperium habet: quandoquidem <lb/>quodcunq; Fabris, Architectis, Baiulis, Agricolis, <lb/>Nautis, &amp; qu&agrave;m plurimis alijs (repugnantibus na&shy;<lb/>tur&aelig; legibus) opitulatur; id omne mechanicum <lb/>e&longs;t imperium.  </s>            
  
  <s id="id.2.1.1.12.1.5.0"> quipp&egrave; quod aduer&longs;us naturam <lb/>vel eiu&longs;dem emulata leges exercet; &longs;umma id <lb/>cert&egrave; admiratione dignum; veri&longs;&longs;imum tamen, <lb/>&amp; &agrave; quocunque liberaliter admi&longs;&longs;um, qui pri&shy;<lb/>us ab Ari&longs;totele didicerit, omnia mechanica, <lb/>t&ugrave;m problemata, t&ugrave;m theoremata ad rotundam <lb/>machinam reduci, atq; ideo illo niti principio, <lb/><expan abbr="n&otilde;">non</expan> minus &longs;en&longs;ui, qu&agrave;m rationi noto.  </s>            
  
  <s id="id.2.1.1.12.1.6.0"> Rotunda ma<lb/>china e&longs;t mouenti&longs;&longs;ima, &amp; qu&ograve; maior, e&ograve; mouen&shy;<lb/>tior.  </s>            
  
  <s id="id.2.1.1.12.1.7.0"> Ver&ugrave;m huic nobilitati adnexa e&longs;t &longs;umma re <lb/>rum ad vitam pertinentium vtilitas, qu&aelig; propte&shy;<lb/>rea omnes alias &agrave; diuer&longs;is artibus propagatas an&shy;<lb/>tecellit; qu&ograve;d ali&aelig; facultates po&longs;t mundi gene&longs;im <lb/>longa temporis intercapedine &longs;uos explicarunt <lb/>v&longs;us; i&longs;ta ver&ograve; &amp; in ip&longs;is mundi primordijs ita fuit <lb/>hominibus nece&longs;&longs;aria, vt ea &longs;ublata Sol de mun&shy;<lb/>do &longs;ublatus videretur.  </s>            
  
  <s id="id.2.1.1.12.1.8.0"> nam quacunq; nece&longs;&longs;ita&shy;<lb/>te Ad&aelig; vita degeretur; &amp; quamuis etiam ca&longs;is <lb/>contectis &longs;tramine, &amp; angu&longs;tis tugurijs, ac gurgu&shy;<lb/>&longs;tijs c&oelig;li de fenderet iniurias; &longs;ic &amp; in corporis ve<lb/>&longs;titu, licet ip&longs;e nihil aliud &longs;pectaret, ni&longs;i vt imbres, <pb xlink:href="pagethumb-la/00000007.JPG"/>vt niues, vt ventos; vt Solem, vt frigus arceret; <lb/>quodcunque tamen id fuit, omne mechanicum <lb/>fuit.  </s>            
  
  <s id="id.2.1.1.12.1.9.0"> neq; tamen huic facultati contingit, quod <lb/>ventis &longs;olet, qui c&ugrave;m vnd&egrave; oriuntur, ibi vehe&shy;<lb/>menti&longs;&longs;imi &longs;int, ad longinqua tamen fracti, <expan abbr="de&shy;bilitatiqu&egrave;">de&shy;<lb/>bilitatique</expan> perueniunt: &longs;ed quod magnis flumini&shy;<lb/>bus crebriu&longs; accidit, qu&aelig; c&ugrave;m in ip&longs;o ortu parua <lb/>&longs;int, perpetu&ograve; tamen aucta, e&ograve; ampliori ferun<lb/>tur alueo, qu&ograve; &agrave; fontibus &longs;uis longius rece&longs;&longs;e&shy;<lb/>runt.  </s>            
  
  <s id="id.2.1.1.12.1.10.0"> Nam &amp; temporis progre&longs;&longs;u mechanica fa <lb/>cultas &longs;ub iugo &aelig;quum arationis laborem di&shy;<lb/>&longs;pen&longs;are, atque aratrum agris circumagere c&aelig;&shy;<lb/>pit.  </s>            
  
  <s id="id.2.1.1.12.1.11.0"> deinceps bigis, &amp; quadrigis docuit comea<lb/>tus, merces, onera qu&aelig;libet vehere, &egrave; finibus <lb/>no&longs;tri&longs; ad finitimos populos exportare, &amp; ex il<lb/>lis contra importare ad nos.  </s>            
  
  <s id="id.2.1.1.12.1.12.0"> pr&aelig;terea c&ugrave;m iam <lb/>res non tant&ugrave;m nece&longs;&longs;itate, ver&ugrave;m etiam orna&shy;<lb/>tu, &amp; commoditate metirentur, mechanic&aelig; <lb/>fuit &longs;ubtilitatis, qu&ograve;d nauigia remo impellere&shy;<lb/>mus; qu&ograve;d gubernaculo exiguo in extrema pup<lb/>pi collocato ingentes triremium moles inflecte&shy;<lb/>remus; qu&ograve;d vnius &longs;&aelig;p&egrave; manu pro multis fabro&shy;<lb/>rum manibus mod&ograve; pondera lapidum, &amp; tra&shy;<lb/>bium Fabris, &amp; Architectis &longs;ubleuaremus; <expan abbr="mo&shy;d&ograve;">mo&shy;<lb/>do</expan> tollenonis &longs;pecie aquas &egrave; puteis olitoribus e&shy;<lb/>xhauriremus.  </s>            
  
  <s id="id.2.1.1.12.1.13.0"> hinc etiam &egrave; liquidorum pr&aelig;lis vi<lb/>na, olea, vnguenta expre&longs;&longs;a, &amp; quicquid liquo&shy;<pb xlink:href="pagethumb-la/00000008.JPG"/>ris habent, per&longs;oluere domino compul&longs;a.  </s>            
  
  <s id="id.2.1.1.12.1.14.0"> hinc <lb/>magnas <expan abbr="arbor&utilde;">arborum</expan>, &amp; marmorum moles duobus in <lb/>contrarias partes <expan abbr="di&longs;trah&etilde;tibus">di&longs;trahentibus</expan> vectibus diremp&shy;<lb/>&longs;imus; hinc militi&aelig; in aggeribus extruendis, in <lb/>con&longs;erenda manu, in opugnando, propugnan&shy;<lb/>doq; loca infinit&aelig; fer&egrave; redundarunt vtilitates; <lb/>hinc demum Lignatores, Lapicid&aelig;, Marmorarij <lb/>Vinitores, Olearij, Vnguentarij, Ferrarij, Auri<lb/>fices, Metallici, Chirurgi, Ton&longs;ores, Pi&longs;tores, Sar<lb/>tores, omnes deniq; opifices beneficiarij, tot, tan<lb/>taq; vit&aelig; human&aelig; &longs;uppeditarunt commoda.  </s>            
  
  <s id="id.2.1.1.12.1.15.0"> Eant <lb/>nunc noui logodedali quidam mechanicorum <lb/>contemptores, perfricent frontem, &longs;i quam ha&shy;<lb/>bent, &amp; ignobilitatem, atqu&egrave; inutilitatem fal&longs;&ograve; <lb/>criminari de&longs;inant: qu&ograve;d &longs;i &amp; adhuc id minim&egrave; <lb/>velint, eos qu&aelig;&longs;o in in&longs;citia &longs;ua relinquamus: <lb/>Ari&longs;totelemqu&egrave; potius philo&longs;ophorum cory&shy;<lb/>ph&aelig;um imitemur, cuius mechanici amoris ardo <lb/>rem acuti&longs;&longs;im&aelig; ill&aelig; mechanic&aelig; qu&aelig;&longs;tiones po&longs;te <lb/>ris tradit&aelig; &longs;atis declarant: qua quidem laude <lb/>Platonem magnific&egrave; &longs;uperauit; qui (vt te&longs;tatur <lb/>Plutarcus) Architam, &amp; Eudoxum mechanic&aelig; <lb/>vtilitatem impen&longs;ius colentes ab in&longs;tituto deter<lb/>ruit; qu&ograve;d nobili&longs;&longs;imam philo&longs;ophorum po&longs;&longs;e&longs;&shy;<lb/>&longs;ionem in vulgus indicarent, ac publicarent; &amp; <lb/>velut arcana philo&longs;ophi&aelig; my&longs;teria proderent.  </s>            
  
  <s id="id.2.1.1.12.1.16.0"> <lb/>res &longs;an&egrave; meo quidem iudicio pro&longs;us vituperan&shy;<pb xlink:href="pagethumb-la/00000009.JPG"/>da, ni&longs;i fort&egrave; velimus tam nobilis di&longs;ciplin&aelig; con<lb/>templationem quidem ocio&longs;am laudare; fructum <lb/>ver&ograve;, &amp; v&longs;um, arti&longs;q; finem improbare.  </s>            
  
  <s id="id.2.1.1.12.1.17.0"> &longs;ed pr&aelig; <lb/>omnibus mathematicis vnus Archimedes ore <lb/>laudandus e&longs;t pleniore, quem voluit Deus in me&shy;<lb/>chanicis velut ideam &longs;ingularem e&longs;&longs;e, quam om&shy;<lb/>nes earum &longs;tudio&longs;i ad imitandum &longs;ibi propone&shy;<lb/>rent.  </s>            
  
  <s id="id.2.1.1.12.1.18.0"> is enim C&oelig;le&longs;tem globum exiguo admo&shy;<lb/>dum, fragili qu&egrave; vitreo orbe conclu&longs;um ita efin&shy;<lb/>xit, &longs;imulatis a&longs;tris viuum natur&aelig; opus, ac iura <lb/>poli motibus certis ade&ograve; pr&aelig;&longs;eferentibus; vt <lb/>&aelig;mula natur&aelig; manus tale de &longs;e encomium &longs;it <lb/>promerita: &longs;ic manus naturam, vt natura ma&shy;<lb/>num ip&longs;a immitata putetur.  </s>            
  
  <s id="id.2.1.1.12.1.19.0"> is poli&longs;pa&longs;tu manu <lb/>leua, &amp; &longs;ola, quinquies millenum modiorum <lb/>pondus attraxit.  </s>            
  
  <s id="id.2.1.1.12.1.20.0"> nauem in &longs;iccum litus eductam, <lb/>ac grauius oneratam &longs;olus machinis &longs;uis ad &longs;e <lb/>perind&egrave; pertraxit, ac &longs;i in mari remis, veli&longs;u&egrave; <lb/>impul&longs;a moueretur, <expan abbr="qu&atilde;">quam</expan> &amp; po&longs;tea in litore (quod <lb/>omnes Sicili&aelig; vires non potuerunt) in mare de&shy;<lb/>duxit.  </s>            
  
  <s id="id.2.1.1.12.1.21.0"> ab i&longs;to etiam ea extiterunt bellica tor&shy;<lb/>menta, quibus Syracu&longs;&aelig; aduer&longs;us Marcellum <lb/>ita defen&longs;&aelig; &longs;unt, vt pa&longs;&longs;im eorum machinator <lb/>Briareus, &amp; centimanus &agrave; Romanis appellare&shy;<lb/>tur.  </s>            
  
  <s id="id.2.1.1.12.1.22.0"> demum hac arte confi&longs;us e&ograve; proce&longs;&longs;it au&shy;<lb/>daci&aelig;, vt eam vocem natur&aelig; legibus ade&ograve; re&shy;<lb/>pugnantem protulerit.  </s>            
  
  <s id="id.2.1.1.12.1.23.0"> Da mihi, vbi &longs;i&longs;tam, ter <pb xlink:href="pagethumb-la/00000010.JPG"/>ramq; mouebo.  </s>            
  
  <s id="id.2.1.1.12.1.24.0"> quod tamen non mod&ograve; nos <lb/>vecte tant&ugrave;m fieri potui&longs;&longs;e in pr&aelig;&longs;enti libro doce<lb/>mus; ver&ugrave;m etiam, &amp; omnis antiquitas (quod <lb/>multis forta&longs;&longs;&egrave; mirabile videbitur) id penitus <lb/>credidi&longs;&longs;e mihi videtur; qu&aelig; Neptuno tri&shy;<lb/>dentem tanquam vectem attribuit; cuius ope <lb/>terr&aelig; concu&longs;&longs;or vbiq; nuncupatur &agrave; poetis.  </s>            
  
  <s id="id.2.1.1.12.1.25.0"> ad <lb/>quod etiam a&longs;piciens celeberrimus no&longs;ter poeta <lb/>Neptunum inducit i&longs;ta machina &longs;yrtes, qu&ograve; ma&shy;<lb/>gis apparerent Troianis, &longs;ubleuantem. </s>    </p>       <p id="id.2.1.1.13.0.0.0" type="main">        
  
  <s id="id.2.1.1.13.1.1.0"> &ldquo;Leuat ip&longs;e tridenti <lb/>&amp; va&longs;tas aperit &longs;yrtes.&rdquo; </s>    </p>       <p id="id.2.1.1.14.0.0.0" type="main">        
  
  <s id="id.2.1.1.14.1.1.0"> Mechanici pr&aelig;terea fuerunt Heron, Cte&longs;ibius, <lb/>&amp; Pappus, qui licet ad mechanic&aelig; apicem, perin&shy;<lb/>de atq; Archimedes, euecti forta&longs;&longs;&egrave; minim&egrave; &longs;int; <lb/>mechanicam tamen facultatem egregi&egrave; percal&shy;<lb/>luerunt; tale&longs;q; fuerunt, &amp; pr&aelig;&longs;ertim Pappus, vt <lb/>eum me ducem &longs;equentem nemo (vt opinor) cul<lb/>pauerit.  </s>            
  
  <s id="id.2.1.1.14.1.2.0"> quod &amp; propterea libentius feci, qu&ograve;d <lb/>n&egrave; latum quidem vnguem ab Archimedeis prin&shy;<lb/>cipijs Pappus recedat.  </s>            
  
  <s id="id.2.1.1.14.1.3.0"> ego enim in hac pr&aelig;&longs;ertim <lb/>facultate Archimedis ve&longs;tigijs h&aelig;rere &longs;emper vo <lb/>lui: &amp; licet eius lucubrationes ad <expan abbr="mechanic&atilde;">mechanicam</expan> per&shy;<pb xlink:href="pagethumb-la/00000011.JPG"/>tinentes multis ab hinc annis pa&longs;&longs;im &longs;oleant do&shy;<lb/>ctis de&longs;iderari: eruditi&longs;&longs;imus tamen libellus de &aelig;&shy;<lb/>queponderantibus pr&aelig; manibus <expan abbr="homin&utilde;">hominum</expan> adhuc <lb/>ver&longs;atur, in qu&ograve; tanquam in copio&longs;i&longs;&longs;ima p&oelig;nu <lb/>omnia fer&egrave; mechanica dogmata repo&longs;ita mihi vi&shy;<lb/>dentur; quem &longs;an&egrave; libellum, &longs;i &aelig;tatis no&longs;tr&aelig; mathe<lb/>matici &longs;ibi magis familiarem adhibui&longs;&longs;ent; reperi&longs;<lb/>&longs;ent &longs;an&egrave; <expan abbr="&longs;ent&etilde;tias">&longs;ententias</expan> multas, quas mod&oacute; ip&longs;i firmas, <lb/>&amp; ratas e&longs;&longs;e docent; &longs;ubtili&longs;&longs;im&egrave;, atqu&egrave; <expan abbr="veri&longs;&shy;&longs;im&egrave;">veri&longs;&shy;<lb/>&longs;ime</expan> conuul&longs;as, &amp; labefactatas. </s>            
  
  <s id="id.2.1.1.14.1.4.0"> &longs;ed hoc vi&shy;<lb/>derint ip&longs;i.  </s>            
  
  <s id="id.2.1.1.14.1.5.0"> ego enim ad Pappum redeo, qui <lb/>ad v&longs;um mathematicarum vberiorem, <expan abbr="emulu&shy;mentorumqu&egrave;">emulu&shy;<lb/>mentorumque</expan> acce&longs;&longs;iones amplificandas peni&shy;<lb/>tus conuer&longs;us, de quinque principibus machi&shy;<lb/>nis, Vecte nemp&egrave;, Trochlea, Axe in peri&shy;<lb/>trochio, Cuneo, &amp; Cochlea, multa <expan abbr="egre&shy;gi&egrave;">egre&shy;<lb/>gie</expan> philo&longs;ophatus e&longs;t; demon&longs;trauit qu&egrave; quicquid <lb/>in machinis, aut cogitari perit&egrave;, aut acut&egrave; <lb/>definiri, aut cert&ograve; &longs;tatui pote&longs;t, id omne <expan abbr="quin&shy;qu&egrave;">quin&shy;<lb/>que</expan> illis infinita vi pr&aelig;ditis machinis referen&shy;<lb/>dum e&longs;&longs;e.  </s>            
  
  <s id="id.2.1.1.14.1.6.0"> atqu&egrave; vtinam iniuria temporis ni&shy;<lb/>hil &egrave; tanti viri &longs;criptis abra&longs;i&longs;&longs;et: nec enim tam <lb/>den&longs;a in&longs;citi&aelig; caligo vniuer&longs;um prop&egrave; terra&shy;<lb/>rum orbem obtexi&longs;&longs;et, neque tanta mechani<lb/>c&aelig;facultatis e&longs;&longs;et ignoratio con&longs;ecuta, vt ma&shy;<lb/>thematicarum proceres exi&longs;timarentur illi, qui <lb/>mod&ograve; inepti&longs;&longs;ima quadam di&longs;tinctione, diffi&shy;|cultate<pb xlink:href="pagethumb-la/00000012.JPG"/>s nonnullas, nec illas tamen &longs;atis ar&shy;<lb/>duas, &amp; ob&longs;curas &egrave; medio tollunt.  </s>            
  
  <s id="id.2.1.1.14.1.7.0"> reperiun&shy;<lb/>tur enim aliqui, no&longs;traq; &aelig;tate emunct&aelig; naris <lb/>mathematici, qui mechanicam, t&ugrave;m <expan abbr="mathe&shy;matic&egrave;">mathe&shy;<lb/>matice</expan> &longs;eor&longs;um, t&ugrave;m phi&longs;ic&egrave; con&longs;iderari po&longs;&shy;<lb/>&longs;e affirmant; ac &longs;i aliquando, vel &longs;ine demon<lb/>&longs;trationibus geometricis, vel &longs;ine vero motu <lb/>res mechanic&aelig; con&longs;iderari po&longs;&longs;int: qua &longs;an&egrave; di&shy;<lb/>&longs;tinctione (vt leuius cum illis agam) nihil aliud mi&shy;<lb/>hi commini&longs;ci videntur, qu&agrave;m vt dum &longs;e, t&ugrave;m <lb/>phi&longs;icos, t&ugrave;m mathematicos proferant, vtra&shy;<lb/>que (quod aiunt) &longs;ella excludantur.  </s>            
  
  <s id="id.2.1.1.14.1.8.0"> nequ&egrave; <lb/>enim amplius mechanica, &longs;i &agrave; machinis ab&longs;tra<lb/>hatur, &amp; &longs;eiungatur, mechanica pote&longs;t appel<lb/>lari.  </s>            
  
  <s id="id.2.1.1.14.1.9.0"> Emicuit tamen inter i&longs;tas tenebras (quam&shy;<lb/>uis alij quoqu&egrave; nonnulli fuerint pr&aelig;clari&longs;&longs;imi) <lb/>Solis in&longs;tar Federicus Commandinus, qui multis <lb/>docti&longs;&longs;imis elucubrationibus ami&longs;&longs;um mathema<lb/>ticarum patrimonium non mod&ograve; re&longs;taurauit, <lb/>ver&ugrave;m etiam aucti&ugrave;s, &amp; locupleti&ugrave;s effecit.  </s>            
  
  <s id="id.2.1.1.14.1.10.0"> <lb/>erat enim &longs;ummus i&longs;te vir omnibus ade&ograve; facul&shy;<lb/>tatibus mathematicis ornatus, vt in eo Archi&shy;<lb/>tas, Eudoxus, Heron, Euclides, Theon, Ari&shy;<lb/>&longs;tarcus, Diophantus, Theodo&longs;ius, Ptolem&aelig;us <lb/>Apollonius, Serenus, Pappus, quin &amp; ip&shy;<lb/>&longs;emet Archimedes (&longs;iquidem ip&longs;ius in Archi&shy;<lb/>medem &longs;cripta Archimedis olent lucernam) re <pb xlink:href="pagethumb-la/00000013.JPG"/>uixi&longs;&longs;e viderentur.  </s>            
  
  <s id="id.2.1.1.14.1.11.0"> &amp; ecce repent&egrave; &egrave; tenebris (vt <lb/>confidimus) ac vinculis corporis in lucem, li&shy;<lb/>bertatem qu&egrave; productus mathematicas alieni&longs;&shy;<lb/>&longs;imo tempore optimo, &amp; pr&aelig;&longs;tanti&longs;&longs;imo patre <lb/>orbatas, nos ver&ograve; ita con&longs;ternatos reliquit, vt e&shy;<lb/>ius de&longs;iderium vix longo &longs;ermone mitigare <lb/>po&longs;&longs;e videamur.  </s>            
  
  <s id="id.2.1.1.14.1.12.0"> Ille tamen perpetu&ograve; in alia&shy;<lb/>rum mathematicarum explicationem ver&longs;ans, <lb/>mechanicam facultatem, aut penitus pr&aelig;ter&shy;<lb/>mi&longs;it, aut modic&egrave; attigit.  </s>            
  
  <s id="id.2.1.1.14.1.13.0"> Quapropter in hoc <lb/>&longs;tudium ardenti&ugrave;s ego incumbere c&aelig;pi, nec me <lb/>vnquam per omne mathematum genus vagan<lb/>tem ea &longs;olicitudo de&longs;eruit; ecquid ex vno <lb/>quoqu&egrave; decerpi, ac delibari po&longs;&longs;it; quo ad me<lb/>chanicam expoliendam, &amp; exornandam acco&shy;<lb/>modatior e&longs;&longs;e po&longs;&longs;em.  </s>            
  
  <s id="id.2.1.1.14.1.14.0"> Nunc ver&ograve; c&ugrave;m mihi <lb/>videar, noni ea quidem omnia, qu&aelig; ad mecha<lb/>nicam pertinent, perfeci&longs;&longs;e; &longs;ed e&ograve; v&longs;q; tamen <lb/>progre&longs;&longs;us, vtijs, qui ex Pappo, ex Vitruuio, <lb/>&amp; ex alijs didicerint, quid &longs;it Vectis, quid Tro&shy;<lb/>chlea, quid Axis in peritrochio, quid Cuneus, <lb/>quid Cochlea; quomodoq; vt pondera moueri <lb/>po&longs;&longs;int, aptari debeant; adhuc tamen acciden&shy;<lb/>tia permulta, qu&aelig; inter potentiam, &amp; pondus <lb/>vectis virtute illis in&longs;unt in&longs;trumentis, perdi&longs;ce&shy;<lb/>re cupiunt, opis aliquid adferre po&longs;&longs;im; putaui <lb/>tempus iam po&longs;tulare, vt prodirem; &amp; nauat&aelig; <pb xlink:href="pagethumb-la/00000014.JPG"/>in hoc genere oper&aelig; &longs;pecimen aliquod darem.  </s>            
  
  <s id="id.2.1.1.14.1.15.0"> <lb/>Ver&ugrave;m qu&ograve; facilius totius operis &longs;ub&longs;tructio <lb/>ad fa&longs;tigium &longs;uum per duceretur, nonnulla <expan abbr="quo&shy;qu&egrave;">quo&shy;<lb/>que</expan> de libra fuerunt pertractanda, &amp; pr&aelig;&longs;er&shy;<lb/>tim dum vnico pondere alterum &longs;olum ip&longs;ius <lb/>brachium penitus deprimitur: que in re mi&shy;<lb/>rum e&longs;t quantas fecerint ruinas Iordanus (qui <lb/>inter recentiores maxim&aelig; fuit auctoritatis) &amp; <lb/>alij; qui hanc rem &longs;ibi di&longs;cutiendam propo&longs;ue<lb/>runt.  </s>            
  
  <s id="id.2.1.1.14.1.16.0"> opus &longs;an&egrave; arduum, &amp; for&longs;an viribus no&shy;<lb/>&longs;tris impar aggre&longs;si &longs;umus; in eo tamen digni, vt <lb/>no&longs;tros conatus, &amp; indu&longs;triam ad pr&aelig;clara ten<lb/>dentem bonorum omnium perpetuus applau&shy;<lb/>&longs;us, approbatioq; comitetur; qu&ograve;d ad &longs;tudium <lb/>t&agrave;m illu&longs;tre, tam magnificum, tam laudabile <lb/>contulimus quicquid habuimus virium.  </s>            
  
  <s id="id.2.1.1.14.1.17.0"> quod <lb/>&longs;an&egrave; qualecunq; &longs;it, tibi celeberrime PRINCEPS <lb/>nuncupandum cen&longs;uimus; cuius &longs;an&egrave; con&longs;ilij, <lb/>atq; in&longs;tituti no&longs;tri rationes multas reddere in <lb/>promptu e&longs;t: &amp; prim&ugrave;m h&aelig;reditaria tibi in fa&shy;<lb/>miliam no&longs;tram promerita, quibus nos ita de&shy;<lb/>uictos habes; vt facil&egrave; intelligamus ad fortunas <lb/>non mod&ograve; no&longs;tras, ver&ugrave;m &amp; ad &longs;anguinem, &amp; <lb/>vitam quoq; pro tua dignitate propendendam <lb/>parati&longs;&longs;imos e&longs;&longs;e debere.  </s>            
  
  <s id="id.2.1.1.14.1.18.0"> Pr&aelig;terea illud non <lb/>parui quoq; ponderis accedit, qu&ograve;d &agrave; pueri&shy;<lb/>tia literarum omnium, &longs;ed pr&aelig;cipu&egrave; mathe&shy;<pb xlink:href="pagethumb-la/00000015.JPG"/>maticarum de&longs;iderio ita fueris incen&longs;us, vt ni&shy;<lb/>&longs;i illis adeptis vitam tibi acerbam, atq; in&longs;ua&shy;<lb/>uem &longs;tatueres.  </s>            
  
  <s id="id.2.1.1.14.1.19.0"> proinde in earum &longs;tudio infi&shy;<lb/>xus primam &aelig;tatis partem in illis percipiendis <lb/>exegi&longs;ti, eamqu&egrave; &longs;&aelig;pius ver&egrave; principe dignam <lb/>vocem protuli&longs;ti, te propterea mathematicis <lb/>pr&aelig;&longs;ertim delectari, qu&ograve;d i&longs;t&aelig; maxim&egrave; ex do&shy;<lb/>me&longs;tico illo, &amp; vmbratili vit&aelig; genere in Solem <lb/>(quod dicitur) &amp; puluerem prodire po&longs;sint: cu<lb/>ius &longs;an&egrave; rei tuum flagranti&longs;simum ab ineunte &aelig;ta <lb/>te periti&aelig; militaris de&longs;iderium, exploratum in&shy;<lb/>dicium poterat e&longs;&longs;e, ni&longs;i nimis emendicat&aelig; men&shy;<lb/>tis e&longs;&longs;et ea proponere, qu&aelig; &agrave; te &longs;perari po&longs;&longs;ent; <lb/>quando tu penitus adole&longs;cens, egregia multa fa<lb/>cinora proficere matura&longs;ti.  </s>            
  
  <s id="id.2.1.1.14.1.20.0"> Tu enim c&ugrave;m iam <lb/>&agrave; &longs;ancti&longs;&longs;imo Pontifice Pio V &longs;aluberrim&aelig; Prin&shy;<lb/>cipum Chri&longs;tianorum coniunctionis fundamen&shy;<lb/>ta iacta e&longs;&longs;ent, alacer admodum ad debellan&shy;<lb/>dos Chri&longs;ti ho&longs;tes profectus, &longs;olidi&longs;&longs;imam, ac ve&shy;<lb/>ri&longs;&longs;imam gloriam tibi compara&longs;ti.  </s>            
  
  <s id="id.2.1.1.14.1.21.0"> Tu quoties de <lb/>&longs;umma rerum deliberatum e&longs;t, eas &longs;ententias <lb/>dixi&longs;ti, qu&aelig; &longs;ummam prudentiam c&ugrave;m &longs;umma <lb/>animi excel&longs;itate coniunctam indicarent.  </s>            
  
  <s id="id.2.1.1.14.1.22.0"> ommit&shy;<lb/>taminterim pleraq; alia illis temporibus <expan abbr="egre&shy;gi&egrave;">egre&shy;<lb/>gie</expan>, viriliter qu&egrave; &agrave; te ge&longs;ta, ne tibi ip&longs;i ea, qu&aelig; <lb/>omnibus &longs;unt manife&longs;ta, pal&agrave;m facere videar: <pb xlink:href="pagethumb-la/00000016.JPG"/>qu&aelig; c&ugrave;m omnia magna, &amp; pr&aelig;clara &longs;int; <expan abbr="mul&shy;t&ograve;">mul&shy;<lb/>to</expan> tamen &agrave; te maiora, &amp; pr&aelig;clara expectant <lb/>adhuc homines.  </s>            
  
  <s id="id.2.1.1.14.1.23.0"> Vale interim pr&aelig;&longs;tanti&longs;&longs;imum <lb/>orbis decus, &amp; &longs;i quando aliquid otij nactus <lb/>fueris has meas vigiliolas a&longs;picere ne dedi&shy;<lb/>gneris.  </s>    </p>              <p id="id.2.1.1.15.0.0.0" type="head">                  <pb n="1" xlink:href="pagethumb-la/00000019.JPG"/>                 
  
  <s id="id.2.1.1.16.1.1.0"> GVIDIVBALDI <lb/>E MARCHIONIBVS <lb/>MONTIS. </s>     <lb/>            
               
 <p id="id.2.1.1.3.0.0.0" type="head">         <s id="id.2.1.1.16.3.1.0"> MECHANICORVM <lb/>LIBER. </s>     <lb/>                
 <s id="id.2.1.1.3.1.1.0"> PRAESENTI OPERE <lb/> 
 CONTENTA. </s>    </p>        <s> ZZZ head of figure ZZZ </s>    </p>                 <p id="id.2.1.1.16.5.1.0" type="caption">                  
 <p id="id.2.1.1.4.0.0.0" type="main">         
 <s id="id.2.1.1.4.1.1.0"> De Libra. </s>    </p>        <s id="id.2.1.1.16.5.1.0.capt"> YYY </s>        </p>      </section>      </front>               <body>                  <chap>                    <p id="id.id.2.1.1.16.5.1.0.a">              
 <p id="id.2.1.1.5.0.0.0" type="main">         
 <s id="id.2.1.1.5.1.1.0"> De Vecte. </s>    </p>        <s id="id.2.1.1.16.7.1.0"> DEFINITIONES. </s>   </p>            <p id="id.2.1.1.17.0.0.0" type="main">                      
 <p id="id.2.1.1.6.0.0.0" type="main">         
 <s id="id.2.1.1.6.1.1.0"> De Trochlea. </s>    </p>        <s id="id.2.1.1.17.1.1.0"> Centrvm grauitatis vniu&longs;cu&shy;<lb/>iu&longs;q; corporis e&longs;t punctum quod&shy;<lb/>dam intra po&longs;itum, &agrave; quo &longs;i gra&shy;<lb/>ue appen&longs;um mente concipiatur, <lb/>dum fertur, quie&longs;cit; &amp; &longs;eruat eam, <lb/>quam in principio habebat po&longs;i&shy;<lb/>tionem: neq; in ip&longs;a latione circumuertitur. </s>    </p>              <p id="id.2.1.1.18.0.0.0" type="main">                      
 <p id="id.2.1.1.7.0.0.0" type="main">         
 <s id="id.2.1.1.7.1.1.0"> De Axe in peritrochio. </s>    </p>        <s id="id.2.1.1.18.1.1.0"> Hanc centri grauitatis definitionem Pappus Alexandrinus in <lb/>octauo Mathematicarum collectionum libro tradidit.  </s>                          
 <p id="id.2.1.1.8.0.0.0" type="main">         
 <s id="id.2.1.1.8.1.1.0"> De Cuneo. </s>    </p>        <s id="id.2.1.1.18.1.2.0"> Federicus <lb/>ver&ograve; Commandinus in libro de centro grauitatis &longs;olidorum idem <lb/>centrum de&longs;cribendo ita explicauit. </s>    </p>            <p id="id.2.1.1.19.0.0.0" type="main">                      
 <p id="id.2.1.1.9.0.0.0" type="main">         
 <s id="id.2.1.1.9.1.1.0"> De Cochlea.  </s>    </p>        <s id="id.2.1.1.19.1.1.0"> Centrum grauitatis vniu&longs;cuiu&longs;q; &longs;olid&aelig; figu&shy;<lb/>r&aelig; e&longs;t punctum illud intra po&longs;itum, circa quod <lb/>vndiq; partes &aelig;qualium momentorum con&longs;i&shy;<lb/>&longs;tunt.  </s>                        
 <p id="id.2.1.1.10.0.0.0" type="head">         
 <pb xlink:href="pagethumb-la/00000005.JPG"/> <s id="id.2.1.1.19.1.2.0"> &longs;i enim per tale centrum ducatur planum <lb/>figuram quomodocunq; &longs;ecans &longs;emper in par&shy;<lb/>tes &aelig;queponderantes ip&longs;am diuidet.  </s>    </p>                   <pb xlink:href="pagethumb-la/00000020.JPG"/>       <p id="id.2.1.1.21.0.0.0" type="head">        
         
 <s id="id.2.1.1.11.1.1.0"> AD FRANCISCVM <lb/> 
 MARIAM II <lb/> 
 VRBINATVM <lb/> 
 AMPLISSIMVM DVCEM <lb/> 
 GVIDIVBALDI <lb/> 
 E MARCHIONIBVS <lb/> 
 MONTIS </s>     <lb/> 
         
 <s id="id.2.1.1.11.3.1.0"> PRAEFATIO. </s>    </p>        
 <p id="id.2.1.1.12.0.0.0" type="main">         
 <s id="id.2.1.1.12.1.1.0"> DVAE res (AMPLISSIME PRIN&shy;<lb/> 
 CEPS) qu&aelig; ad conciliandas homi<lb/> 
 nibus facultates, vtilitas nemp&egrave;, &amp; <lb/> 
 nobilitas, plurim&ugrave;m valere con&longs;ue<lb/> 
 uerunt.  </s>              
 <s id="id.2.1.1.12.1.2.0"> ill&aelig; ad exornandam mecha<lb/> 
 nicam facultatem, &amp; eam pr&aelig; om&shy;<lb/> 
 nibus alijs appetibilem reddendam con&longs;pira&longs;&longs;e <lb/> 
 mihi videntur: nam &longs;i nobilitatem (quod pleriq; <lb/> 
 mod&ograve; faciunt) ortuip&longs;o metimur, occurret hinc <lb/> 
 Geometria, illinc ver&ograve; Phi&longs;ica; quorum gemina<lb/> 
 to complexu nobili&longs;&longs;ima artium prodit mechani&shy;<lb/> 
 ca.  </s>              
 <s id="id.2.1.1.12.1.3.0"> &longs;i enim nobilitatem magis, t&ugrave;m &longs;trat&aelig; materi&aelig;, <lb/> 
 t&ugrave;m argumentorum nece&longs;&longs;itati (quod Ari&longs;tote&shy;<lb/> 
 les fatetur aliquand&ograve;) relatam volumus, omnium <lb/> 
 proculdubi&ograve; nobili&longs;&longs;imam per&longs;piciemus.  </s>              
 <s id="id.2.1.1.12.1.4.0"> qu&aelig;  
 <pb xlink:href="pagethumb-la/00000006.JPG"/> 
 quidem non &longs;olum geometriam (vt Pappus te&longs;ta<lb/> 
 tur) ab&longs;oluit, &amp; perficit; ver&ugrave;m etiam &amp; phi&longs;ica&shy;<lb/> 
 rum rerum imperium habet: quandoquidem <lb/> 
 quodcunq; Fabris, Architectis, Baiulis, Agricolis, <lb/> 
 Nautis, &amp; qu&agrave;m plurimis alijs (repugnantibus na&shy;<lb/> 
 tur&aelig; legibus) opitulatur; id omne mechanicum <lb/> 
 e&longs;t imperium.  </s>              
 <s id="id.2.1.1.12.1.5.0"> quipp&egrave; quod aduer&longs;us naturam <lb/> 
 vel eiu&longs;dem emulata leges exercet; &longs;umma id <lb/> 
 cert&egrave; admiratione dignum; veri&longs;&longs;imum tamen, <lb/> 
 &amp; &agrave; quocunque liberaliter admi&longs;&longs;um, qui pri&shy;<lb/> 
 us ab Ari&longs;totele didicerit, omnia mechanica, <lb/> 
 t&ugrave;m problemata, t&ugrave;m theoremata ad rotundam <lb/> 
 machinam reduci, atq; ideo illo niti principio, <lb/> 
 <expan abbr="n&otilde;">non</expan> minus &longs;en&longs;ui, qu&agrave;m rationi noto.  </s>              
 <s id="id.2.1.1.12.1.6.0"> Rotunda ma<lb/> 
 china e&longs;t mouenti&longs;&longs;ima, &amp; qu&ograve; maior, e&ograve; mouen&shy;<lb/> 
 tior.  </s>              
 <s id="id.2.1.1.12.1.7.0"> Ver&ugrave;m huic nobilitati adnexa e&longs;t &longs;umma re <lb/> 
 rum ad vitam pertinentium vtilitas, qu&aelig; propte&shy;<lb/> 
 rea omnes alias &agrave; diuer&longs;is artibus propagatas an&shy;<lb/> 
 tecellit; qu&ograve;d ali&aelig; facultates po&longs;t mundi gene&longs;im <lb/> 
 longa temporis intercapedine &longs;uos explicarunt <lb/> 
 v&longs;us; i&longs;ta ver&ograve; &amp; in ip&longs;is mundi primordijs ita fuit <lb/> 
 hominibus nece&longs;&longs;aria, vt ea &longs;ublata Sol de mun&shy;<lb/> 
 do &longs;ublatus videretur.  </s>              
 <s id="id.2.1.1.12.1.8.0"> nam quacunq; nece&longs;&longs;ita&shy;<lb/> 
 te Ad&aelig; vita degeretur; &amp; quamuis etiam ca&longs;is <lb/> 
 contectis &longs;tramine, &amp; angu&longs;tis tugurijs, ac gurgu&shy;<lb/> 
 &longs;tijs c&oelig;li de fenderet iniurias; &longs;ic &amp; in corporis ve<lb/> 
 &longs;titu, licet ip&longs;e nihil aliud &longs;pectaret, ni&longs;i vt imbres,  
 <pb xlink:href="pagethumb-la/00000007.JPG"/> 
 vt niues, vt ventos; vt Solem, vt frigus arceret; <lb/> 
 quodcunque tamen id fuit, omne mechanicum <lb/> 
 fuit.  </s>              
 <s id="id.2.1.1.12.1.9.0"> neq; tamen huic facultati contingit, quod <lb/> 
 ventis &longs;olet, qui c&ugrave;m vnd&egrave; oriuntur, ibi vehe&shy;<lb/> 
 menti&longs;&longs;imi &longs;int, ad longinqua tamen fracti, <expan abbr="de&shy;bilitatiqu&egrave;">de&shy;<lb/> 
 bilitatique</expan> perueniunt: &longs;ed quod magnis flumini&shy;<lb/> 
 bus crebriu&longs; accidit, qu&aelig; c&ugrave;m in ip&longs;o ortu parua <lb/> 
 &longs;int, perpetu&ograve; tamen aucta, e&ograve; ampliori ferun<lb/> 
 tur alueo, qu&ograve; &agrave; fontibus &longs;uis longius rece&longs;&longs;e&shy;<lb/> 
 runt.  </s>              
 <s id="id.2.1.1.12.1.10.0"> Nam &amp; temporis progre&longs;&longs;u mechanica fa <lb/> 
 cultas &longs;ub iugo &aelig;quum arationis laborem di&shy;<lb/> 
 &longs;pen&longs;are, atque aratrum agris circumagere c&aelig;&shy;<lb/> 
 pit.  </s>              
 <s id="id.2.1.1.12.1.11.0"> deinceps bigis, &amp; quadrigis docuit comea<lb/> 
 tus, merces, onera qu&aelig;libet vehere, &egrave; finibus <lb/> 
 no&longs;tri&longs; ad finitimos populos exportare, &amp; ex il<lb/> 
 lis contra importare ad nos.  </s>              
 <s id="id.2.1.1.12.1.12.0"> pr&aelig;terea c&ugrave;m iam <lb/> 
 res non tant&ugrave;m nece&longs;&longs;itate, ver&ugrave;m etiam orna&shy;<lb/> 
 tu, &amp; commoditate metirentur, mechanic&aelig; <lb/> 
 fuit &longs;ubtilitatis, qu&ograve;d nauigia remo impellere&shy;<lb/> 
 mus; qu&ograve;d gubernaculo exiguo in extrema pup<lb/> 
 pi collocato ingentes triremium moles inflecte&shy;<lb/> 
 remus; qu&ograve;d vnius &longs;&aelig;p&egrave; manu pro multis fabro&shy;<lb/> 
 rum manibus mod&ograve; pondera lapidum, &amp; tra&shy;<lb/> 
 bium Fabris, &amp; Architectis &longs;ubleuaremus; <expan abbr="mo&shy;d&ograve;">mo&shy;<lb/> 
 do</expan> tollenonis &longs;pecie aquas &egrave; puteis olitoribus e&shy;<lb/> 
 xhauriremus.  </s>              
 <s id="id.2.1.1.12.1.13.0"> hinc etiam &egrave; liquidorum pr&aelig;lis vi<lb/> 
 na, olea, vnguenta expre&longs;&longs;a, &amp; quicquid liquo&shy; 
 <pb xlink:href="pagethumb-la/00000008.JPG"/> 
 ris habent, per&longs;oluere domino compul&longs;a.  </s>              
 <s id="id.2.1.1.12.1.14.0"> hinc <lb/> 
 magnas <expan abbr="arbor&utilde;">arborum</expan>, &amp; marmorum moles duobus in <lb/> 
 contrarias partes <expan abbr="di&longs;trah&etilde;tibus">di&longs;trahentibus</expan> vectibus diremp&shy;<lb/> 
 &longs;imus; hinc militi&aelig; in aggeribus extruendis, in <lb/> 
 con&longs;erenda manu, in opugnando, propugnan&shy;<lb/> 
 doq; loca infinit&aelig; fer&egrave; redundarunt vtilitates; <lb/> 
 hinc demum Lignatores, Lapicid&aelig;, Marmorarij <lb/> 
 Vinitores, Olearij, Vnguentarij, Ferrarij, Auri<lb/> 
 fices, Metallici, Chirurgi, Ton&longs;ores, Pi&longs;tores, Sar<lb/> 
 tores, omnes deniq; opifices beneficiarij, tot, tan<lb/> 
 taq; vit&aelig; human&aelig; &longs;uppeditarunt commoda.  </s>              
 <s id="id.2.1.1.12.1.15.0"> Eant <lb/> 
 nunc noui logodedali quidam mechanicorum <lb/> 
 contemptores, perfricent frontem, &longs;i quam ha&shy;<lb/> 
 bent, &amp; ignobilitatem, atqu&egrave; inutilitatem fal&longs;&ograve; <lb/> 
 criminari de&longs;inant: qu&ograve;d &longs;i &amp; adhuc id minim&egrave; <lb/> 
 velint, eos qu&aelig;&longs;o in in&longs;citia &longs;ua relinquamus: <lb/> 
 Ari&longs;totelemqu&egrave; potius philo&longs;ophorum cory&shy;<lb/> 
 ph&aelig;um imitemur, cuius mechanici amoris ardo <lb/> 
 rem acuti&longs;&longs;im&aelig; ill&aelig; mechanic&aelig; qu&aelig;&longs;tiones po&longs;te <lb/> 
 ris tradit&aelig; &longs;atis declarant: qua quidem laude <lb/> 
 Platonem magnific&egrave; &longs;uperauit; qui (vt te&longs;tatur <lb/> 
 Plutarcus) Architam, &amp; Eudoxum mechanic&aelig; <lb/> 
 vtilitatem impen&longs;ius colentes ab in&longs;tituto deter<lb/> 
 ruit; qu&ograve;d nobili&longs;&longs;imam philo&longs;ophorum po&longs;&longs;e&longs;&shy;<lb/> 
 &longs;ionem in vulgus indicarent, ac publicarent; &amp; <lb/> 
 velut arcana philo&longs;ophi&aelig; my&longs;teria proderent.  </s>              
 <s id="id.2.1.1.12.1.16.0"> <lb/> 
 res &longs;an&egrave; meo quidem iudicio pro&longs;us vituperan&shy; 
 <pb xlink:href="pagethumb-la/00000009.JPG"/> 
 da, ni&longs;i fort&egrave; velimus tam nobilis di&longs;ciplin&aelig; con<lb/> 
 templationem quidem ocio&longs;am laudare; fructum <lb/> 
 ver&ograve;, &amp; v&longs;um, arti&longs;q; finem improbare.  </s>              
 <s id="id.2.1.1.12.1.17.0"> &longs;ed pr&aelig; <lb/> 
 omnibus mathematicis vnus Archimedes ore <lb/> 
 laudandus e&longs;t pleniore, quem voluit Deus in me&shy;<lb/> 
 chanicis velut ideam &longs;ingularem e&longs;&longs;e, quam om&shy;<lb/> 
 nes earum &longs;tudio&longs;i ad imitandum &longs;ibi propone&shy;<lb/> 
 rent.  </s>              
 <s id="id.2.1.1.12.1.18.0"> is enim C&oelig;le&longs;tem globum exiguo admo&shy;<lb/> 
 dum, fragili qu&egrave; vitreo orbe conclu&longs;um ita efin&shy;<lb/> 
 xit, &longs;imulatis a&longs;tris viuum natur&aelig; opus, ac iura <lb/> 
 poli motibus certis ade&ograve; pr&aelig;&longs;eferentibus; vt <lb/> 
 &aelig;mula natur&aelig; manus tale de &longs;e encomium &longs;it <lb/> 
 promerita: &longs;ic manus naturam, vt natura ma&shy;<lb/> 
 num ip&longs;a immitata putetur.  </s>              
 <s id="id.2.1.1.12.1.19.0"> is poli&longs;pa&longs;tu manu <lb/> 
 leua, &amp; &longs;ola, quinquies millenum modiorum <lb/> 
 pondus attraxit.  </s>              
 <s id="id.2.1.1.12.1.20.0"> nauem in &longs;iccum litus eductam, <lb/> 
 ac grauius oneratam &longs;olus machinis &longs;uis ad &longs;e <lb/> 
 perind&egrave; pertraxit, ac &longs;i in mari remis, veli&longs;u&egrave; <lb/> 
 impul&longs;a moueretur, <expan abbr="qu&atilde;">quam</expan> &amp; po&longs;tea in litore (quod <lb/> 
 omnes Sicili&aelig; vires non potuerunt) in mare de&shy;<lb/> 
 duxit.  </s>              
 <s id="id.2.1.1.12.1.21.0"> ab i&longs;to etiam ea extiterunt bellica tor&shy;<lb/> 
 menta, quibus Syracu&longs;&aelig; aduer&longs;us Marcellum <lb/> 
 ita defen&longs;&aelig; &longs;unt, vt pa&longs;&longs;im eorum machinator <lb/> 
 Briareus, &amp; centimanus &agrave; Romanis appellare&shy;<lb/> 
 tur.  </s>              
 <s id="id.2.1.1.12.1.22.0"> demum hac arte confi&longs;us e&ograve; proce&longs;&longs;it au&shy;<lb/> 
 daci&aelig;, vt eam vocem natur&aelig; legibus ade&ograve; re&shy;<lb/> 
 pugnantem protulerit.  </s>              
 <s id="id.2.1.1.12.1.23.0"> Da mihi, vbi &longs;i&longs;tam, ter  
 <pb xlink:href="pagethumb-la/00000010.JPG"/> 
 ramq; mouebo.  </s>              
 <s id="id.2.1.1.12.1.24.0"> quod tamen non mod&ograve; nos <lb/> 
 vecte tant&ugrave;m fieri potui&longs;&longs;e in pr&aelig;&longs;enti libro doce<lb/> 
 mus; ver&ugrave;m etiam, &amp; omnis antiquitas (quod <lb/> 
 multis forta&longs;&longs;&egrave; mirabile videbitur) id penitus <lb/> 
 credidi&longs;&longs;e mihi videtur; qu&aelig; Neptuno tri&shy;<lb/> 
 dentem tanquam vectem attribuit; cuius ope <lb/> 
 terr&aelig; concu&longs;&longs;or vbiq; nuncupatur &agrave; poetis.  </s>              
 <s id="id.2.1.1.12.1.25.0"> ad <lb/> 
 quod etiam a&longs;piciens celeberrimus no&longs;ter poeta <lb/> 
 Neptunum inducit i&longs;ta machina &longs;yrtes, qu&ograve; ma&shy;<lb/> 
 gis apparerent Troianis, &longs;ubleuantem. </s>    </p>        
 <p id="id.2.1.1.13.0.0.0" type="main">         
 <s id="id.2.1.1.13.1.1.0"> &ldquo;Leuat ip&longs;e tridenti <lb/> 
 &amp; va&longs;tas aperit &longs;yrtes.&rdquo; </s>    </p>        
 <p id="id.2.1.1.14.0.0.0" type="main">         
 <s id="id.2.1.1.14.1.1.0"> Mechanici pr&aelig;terea fuerunt Heron, Cte&longs;ibius, <lb/> 
 &amp; Pappus, qui licet ad mechanic&aelig; apicem, perin&shy;<lb/> 
 de atq; Archimedes, euecti forta&longs;&longs;&egrave; minim&egrave; &longs;int; <lb/> 
 mechanicam tamen facultatem egregi&egrave; percal&shy;<lb/> 
 luerunt; tale&longs;q; fuerunt, &amp; pr&aelig;&longs;ertim Pappus, vt <lb/> 
 eum me ducem &longs;equentem nemo (vt opinor) cul<lb/> 
 pauerit.  </s>              
 <s id="id.2.1.1.14.1.2.0"> quod &amp; propterea libentius feci, qu&ograve;d <lb/> 
 n&egrave; latum quidem vnguem ab Archimedeis prin&shy;<lb/> 
 cipijs Pappus recedat.  </s>              
 <s id="id.2.1.1.14.1.3.0"> ego enim in hac pr&aelig;&longs;ertim <lb/> 
 facultate Archimedis ve&longs;tigijs h&aelig;rere &longs;emper vo <lb/> 
 lui: &amp; licet eius lucubrationes ad <expan abbr="mechanic&atilde;">mechanicam</expan> per&shy; 
 <pb xlink:href="pagethumb-la/00000011.JPG"/> 
 tinentes multis ab hinc annis pa&longs;&longs;im &longs;oleant do&shy;<lb/> 
 ctis de&longs;iderari: eruditi&longs;&longs;imus tamen libellus de &aelig;&shy;<lb/> 
 queponderantibus pr&aelig; manibus <expan abbr="homin&utilde;">hominum</expan> adhuc <lb/> 
 ver&longs;atur, in qu&ograve; tanquam in copio&longs;i&longs;&longs;ima p&oelig;nu <lb/> 
 omnia fer&egrave; mechanica dogmata repo&longs;ita mihi vi&shy;<lb/> 
 dentur; quem &longs;an&egrave; libellum, &longs;i &aelig;tatis no&longs;tr&aelig; mathe<lb/> 
 matici &longs;ibi magis familiarem adhibui&longs;&longs;ent; reperi&longs;<lb/> 
 &longs;ent &longs;an&egrave; <expan abbr="&longs;ent&etilde;tias">&longs;ententias</expan> multas, quas mod&oacute; ip&longs;i firmas, <lb/> 
 &amp; ratas e&longs;&longs;e docent; &longs;ubtili&longs;&longs;im&egrave;, atqu&egrave; <expan abbr="veri&longs;&shy;&longs;im&egrave;">veri&longs;&shy;<lb/> 
 &longs;ime</expan> conuul&longs;as, &amp; labefactatas. </s>              
 <s id="id.2.1.1.14.1.4.0"> &longs;ed hoc vi&shy;<lb/> 
 derint ip&longs;i.  </s>              
 <s id="id.2.1.1.14.1.5.0"> ego enim ad Pappum redeo, qui <lb/> 
 ad v&longs;um mathematicarum vberiorem, <expan abbr="emulu&shy;mentorumqu&egrave;">emulu&shy;<lb/> 
 mentorumque</expan> acce&longs;&longs;iones amplificandas peni&shy;<lb/> 
 tus conuer&longs;us, de quinque principibus machi&shy;<lb/> 
 nis, Vecte nemp&egrave;, Trochlea, Axe in peri&shy;<lb/> 
 trochio, Cuneo, &amp; Cochlea, multa <expan abbr="egre&shy;gi&egrave;">egre&shy;<lb/> 
 gie</expan> philo&longs;ophatus e&longs;t; demon&longs;trauit qu&egrave; quicquid <lb/> 
 in machinis, aut cogitari perit&egrave;, aut acut&egrave; <lb/> 
 definiri, aut cert&ograve; &longs;tatui pote&longs;t, id omne <expan abbr="quin&shy;qu&egrave;">quin&shy;<lb/> 
 que</expan> illis infinita vi pr&aelig;ditis machinis referen&shy;<lb/> 
 dum e&longs;&longs;e.  </s>              
 <s id="id.2.1.1.14.1.6.0"> atqu&egrave; vtinam iniuria temporis ni&shy;<lb/> 
 hil &egrave; tanti viri &longs;criptis abra&longs;i&longs;&longs;et: nec enim tam <lb/> 
 den&longs;a in&longs;citi&aelig; caligo vniuer&longs;um prop&egrave; terra&shy;<lb/> 
 rum orbem obtexi&longs;&longs;et, neque tanta mechani<lb/> 
 c&aelig;facultatis e&longs;&longs;et ignoratio con&longs;ecuta, vt ma&shy;<lb/> 
 thematicarum proceres exi&longs;timarentur illi, qui <lb/> 
 mod&ograve; inepti&longs;&longs;ima quadam di&longs;tinctione, diffi&shy;|cultate 
 <pb xlink:href="pagethumb-la/00000012.JPG"/> 
 s nonnullas, nec illas tamen &longs;atis ar&shy;<lb/> 
 duas, &amp; ob&longs;curas &egrave; medio tollunt.  </s>              
 <s id="id.2.1.1.14.1.7.0"> reperiun&shy;<lb/> 
 tur enim aliqui, no&longs;traq; &aelig;tate emunct&aelig; naris <lb/> 
 mathematici, qui mechanicam, t&ugrave;m <expan abbr="mathe&shy;matic&egrave;">mathe&shy;<lb/> 
 matice</expan> &longs;eor&longs;um, t&ugrave;m phi&longs;ic&egrave; con&longs;iderari po&longs;&shy;<lb/> 
 &longs;e affirmant; ac &longs;i aliquando, vel &longs;ine demon<lb/> 
 &longs;trationibus geometricis, vel &longs;ine vero motu <lb/> 
 res mechanic&aelig; con&longs;iderari po&longs;&longs;int: qua &longs;an&egrave; di&shy;<lb/> 
 &longs;tinctione (vt leuius cum illis agam) nihil aliud mi&shy;<lb/> 
 hi commini&longs;ci videntur, qu&agrave;m vt dum &longs;e, t&ugrave;m <lb/> 
 phi&longs;icos, t&ugrave;m mathematicos proferant, vtra&shy;<lb/> 
 que (quod aiunt) &longs;ella excludantur.  </s>              
 <s id="id.2.1.1.14.1.8.0"> nequ&egrave; <lb/> 
 enim amplius mechanica, &longs;i &agrave; machinis ab&longs;tra<lb/> 
 hatur, &amp; &longs;eiungatur, mechanica pote&longs;t appel<lb/> 
 lari.  </s>              
 <s id="id.2.1.1.14.1.9.0"> Emicuit tamen inter i&longs;tas tenebras (quam&shy;<lb/> 
 uis alij quoqu&egrave; nonnulli fuerint pr&aelig;clari&longs;&longs;imi) <lb/> 
 Solis in&longs;tar Federicus Commandinus, qui multis <lb/> 
 docti&longs;&longs;imis elucubrationibus ami&longs;&longs;um mathema<lb/> 
 ticarum patrimonium non mod&ograve; re&longs;taurauit, <lb/> 
 ver&ugrave;m etiam aucti&ugrave;s, &amp; locupleti&ugrave;s effecit.  </s>              
 <s id="id.2.1.1.14.1.10.0"> <lb/> 
 erat enim &longs;ummus i&longs;te vir omnibus ade&ograve; facul&shy;<lb/> 
 tatibus mathematicis ornatus, vt in eo Archi&shy;<lb/> 
 tas, Eudoxus, Heron, Euclides, Theon, Ari&shy;<lb/> 
 &longs;tarcus, Diophantus, Theodo&longs;ius, Ptolem&aelig;us <lb/> 
 Apollonius, Serenus, Pappus, quin &amp; ip&shy;<lb/> 
 &longs;emet Archimedes (&longs;iquidem ip&longs;ius in Archi&shy;<lb/> 
 medem &longs;cripta Archimedis olent lucernam) re  
 <pb xlink:href="pagethumb-la/00000013.JPG"/> 
 uixi&longs;&longs;e viderentur.  </s>              
 <s id="id.2.1.1.14.1.11.0"> &amp; ecce repent&egrave; &egrave; tenebris (vt <lb/> 
 confidimus) ac vinculis corporis in lucem, li&shy;<lb/> 
 bertatem qu&egrave; productus mathematicas alieni&longs;&shy;<lb/> 
 &longs;imo tempore optimo, &amp; pr&aelig;&longs;tanti&longs;&longs;imo patre <lb/> 
 orbatas, nos ver&ograve; ita con&longs;ternatos reliquit, vt e&shy;<lb/> 
 ius de&longs;iderium vix longo &longs;ermone mitigare <lb/> 
 po&longs;&longs;e videamur.  </s>              
 <s id="id.2.1.1.14.1.12.0"> Ille tamen perpetu&ograve; in alia&shy;<lb/> 
 rum mathematicarum explicationem ver&longs;ans, <lb/> 
 mechanicam facultatem, aut penitus pr&aelig;ter&shy;<lb/> 
 mi&longs;it, aut modic&egrave; attigit.  </s>              
 <s id="id.2.1.1.14.1.13.0"> Quapropter in hoc <lb/> 
 &longs;tudium ardenti&ugrave;s ego incumbere c&aelig;pi, nec me <lb/> 
 vnquam per omne mathematum genus vagan<lb/> 
 tem ea &longs;olicitudo de&longs;eruit; ecquid ex vno <lb/> 
 quoqu&egrave; decerpi, ac delibari po&longs;&longs;it; quo ad me<lb/> 
 chanicam expoliendam, &amp; exornandam acco&shy;<lb/> 
 modatior e&longs;&longs;e po&longs;&longs;em.  </s>              
 <s id="id.2.1.1.14.1.14.0"> Nunc ver&ograve; c&ugrave;m mihi <lb/> 
 videar, noni ea quidem omnia, qu&aelig; ad mecha<lb/> 
 nicam pertinent, perfeci&longs;&longs;e; &longs;ed e&ograve; v&longs;q; tamen <lb/> 
 progre&longs;&longs;us, vtijs, qui ex Pappo, ex Vitruuio, <lb/> 
 &amp; ex alijs didicerint, quid &longs;it Vectis, quid Tro&shy;<lb/> 
 chlea, quid Axis in peritrochio, quid Cuneus, <lb/> 
 quid Cochlea; quomodoq; vt pondera moueri <lb/> 
 po&longs;&longs;int, aptari debeant; adhuc tamen acciden&shy;<lb/> 
 tia permulta, qu&aelig; inter potentiam, &amp; pondus <lb/> 
 vectis virtute illis in&longs;unt in&longs;trumentis, perdi&longs;ce&shy;<lb/> 
 re cupiunt, opis aliquid adferre po&longs;&longs;im; putaui <lb/> 
 tempus iam po&longs;tulare, vt prodirem; &amp; nauat&aelig;  
 <pb xlink:href="pagethumb-la/00000014.JPG"/> 
 in hoc genere oper&aelig; &longs;pecimen aliquod darem.  </s>              
 <s id="id.2.1.1.14.1.15.0"> <lb/> 
 Ver&ugrave;m qu&ograve; facilius totius operis &longs;ub&longs;tructio <lb/> 
 ad fa&longs;tigium &longs;uum per duceretur, nonnulla <expan abbr="quo&shy;qu&egrave;">quo&shy;<lb/> 
 que</expan> de libra fuerunt pertractanda, &amp; pr&aelig;&longs;er&shy;<lb/> 
 tim dum vnico pondere alterum &longs;olum ip&longs;ius <lb/> 
 brachium penitus deprimitur: que in re mi&shy;<lb/> 
 rum e&longs;t quantas fecerint ruinas Iordanus (qui <lb/> 
 inter recentiores maxim&aelig; fuit auctoritatis) &amp; <lb/> 
 alij; qui hanc rem &longs;ibi di&longs;cutiendam propo&longs;ue<lb/> 
 runt.  </s>              
 <s id="id.2.1.1.14.1.16.0"> opus &longs;an&egrave; arduum, &amp; for&longs;an viribus no&shy;<lb/> 
 &longs;tris impar aggre&longs;si &longs;umus; in eo tamen digni, vt <lb/> 
 no&longs;tros conatus, &amp; indu&longs;triam ad pr&aelig;clara ten<lb/> 
 dentem bonorum omnium perpetuus applau&shy;<lb/> 
 &longs;us, approbatioq; comitetur; qu&ograve;d ad &longs;tudium <lb/> 
 t&agrave;m illu&longs;tre, tam magnificum, tam laudabile <lb/> 
 contulimus quicquid habuimus virium.  </s>              
 <s id="id.2.1.1.14.1.17.0"> quod <lb/> 
 &longs;an&egrave; qualecunq; &longs;it, tibi celeberrime PRINCEPS <lb/> 
 nuncupandum cen&longs;uimus; cuius &longs;an&egrave; con&longs;ilij, <lb/> 
 atq; in&longs;tituti no&longs;tri rationes multas reddere in <lb/> 
 promptu e&longs;t: &amp; prim&ugrave;m h&aelig;reditaria tibi in fa&shy;<lb/> 
 miliam no&longs;tram promerita, quibus nos ita de&shy;<lb/> 
 uictos habes; vt facil&egrave; intelligamus ad fortunas <lb/> 
 non mod&ograve; no&longs;tras, ver&ugrave;m &amp; ad &longs;anguinem, &amp; <lb/> 
 vitam quoq; pro tua dignitate propendendam <lb/> 
 parati&longs;&longs;imos e&longs;&longs;e debere.  </s>              
 <s id="id.2.1.1.14.1.18.0"> Pr&aelig;terea illud non <lb/> 
 parui quoq; ponderis accedit, qu&ograve;d &agrave; pueri&shy;<lb/> 
 tia literarum omnium, &longs;ed pr&aelig;cipu&egrave; mathe&shy; 
 <pb xlink:href="pagethumb-la/00000015.JPG"/> 
 maticarum de&longs;iderio ita fueris incen&longs;us, vt ni&shy;<lb/> 
 &longs;i illis adeptis vitam tibi acerbam, atq; in&longs;ua&shy;<lb/> 
 uem &longs;tatueres.  </s>              
 <s id="id.2.1.1.14.1.19.0"> proinde in earum &longs;tudio infi&shy;<lb/> 
 xus primam &aelig;tatis partem in illis percipiendis <lb/> 
 exegi&longs;ti, eamqu&egrave; &longs;&aelig;pius ver&egrave; principe dignam <lb/> 
 vocem protuli&longs;ti, te propterea mathematicis <lb/> 
 pr&aelig;&longs;ertim delectari, qu&ograve;d i&longs;t&aelig; maxim&egrave; ex do&shy;<lb/> 
 me&longs;tico illo, &amp; vmbratili vit&aelig; genere in Solem <lb/> 
 (quod dicitur) &amp; puluerem prodire po&longs;sint: cu<lb/> 
 ius &longs;an&egrave; rei tuum flagranti&longs;simum ab ineunte &aelig;ta <lb/> 
 te periti&aelig; militaris de&longs;iderium, exploratum in&shy;<lb/> 
 dicium poterat e&longs;&longs;e, ni&longs;i nimis emendicat&aelig; men&shy;<lb/> 
 tis e&longs;&longs;et ea proponere, qu&aelig; &agrave; te &longs;perari po&longs;&longs;ent; <lb/> 
 quando tu penitus adole&longs;cens, egregia multa fa<lb/> 
 cinora proficere matura&longs;ti.  </s>              
 <s id="id.2.1.1.14.1.20.0"> Tu enim c&ugrave;m iam <lb/> 
 &agrave; &longs;ancti&longs;&longs;imo Pontifice Pio V &longs;aluberrim&aelig; Prin&shy;<lb/> 
 cipum Chri&longs;tianorum coniunctionis fundamen&shy;<lb/> 
 ta iacta e&longs;&longs;ent, alacer admodum ad debellan&shy;<lb/> 
 dos Chri&longs;ti ho&longs;tes profectus, &longs;olidi&longs;&longs;imam, ac ve&shy;<lb/> 
 ri&longs;&longs;imam gloriam tibi compara&longs;ti.  </s>              
 <s id="id.2.1.1.14.1.21.0"> Tu quoties de <lb/> 
 &longs;umma rerum deliberatum e&longs;t, eas &longs;ententias <lb/> 
 dixi&longs;ti, qu&aelig; &longs;ummam prudentiam c&ugrave;m &longs;umma <lb/> 
 animi excel&longs;itate coniunctam indicarent.  </s>              
 <s id="id.2.1.1.14.1.22.0"> ommit&shy;<lb/> 
 taminterim pleraq; alia illis temporibus <expan abbr="egre&shy;gi&egrave;">egre&shy;<lb/> 
 gie</expan>, viriliter qu&egrave; &agrave; te ge&longs;ta, ne tibi ip&longs;i ea, qu&aelig; <lb/> 
 omnibus &longs;unt manife&longs;ta, pal&agrave;m facere videar:  
 <pb xlink:href="pagethumb-la/00000016.JPG"/> 
 qu&aelig; c&ugrave;m omnia magna, &amp; pr&aelig;clara &longs;int; <expan abbr="mul&shy;t&ograve;">mul&shy;<lb/> 
 to</expan> tamen &agrave; te maiora, &amp; pr&aelig;clara expectant <lb/> 
 adhuc homines.  </s>              
 <s id="id.2.1.1.14.1.23.0"> Vale interim pr&aelig;&longs;tanti&longs;&longs;imum <lb/> 
 orbis decus, &amp; &longs;i quando aliquid otij nactus <lb/> 
 fueris has meas vigiliolas a&longs;picere ne dedi&shy;<lb/> 
 gneris.  </s>    </p>        
         <p id="id.2.1.1.15.0.0.0" type="head">         
           <pb n="1" xlink:href="pagethumb-la/00000019.JPG"/> 
         
           <s id="id.2.1.1.16.1.1.0"> GVIDIVBALDI <lb/> 
 E MARCHIONIBVS <lb/> 
 MONTIS. </s>     <lb/> 
         
           <s id="id.2.1.1.16.3.1.0"> MECHANICORVM <lb/> 
 LIBER. </s>     <lb/> 
         
           <s> ZZZ head of figure ZZZ </s>    </p>               
         <p id="id.2.1.1.16.5.1.0" type="caption">         
           <s id="id.2.1.1.16.5.1.0.capt"> YYY </s> 
         </p> 
       </section> 
       </front>        
         <body>         
           <chap>         
             <p id="id.id.2.1.1.16.5.1.0.a"> 
               <s id="id.2.1.1.16.7.1.0"> DEFINITIONES. </s> 
         </p> 
             <p id="id.2.1.1.17.0.0.0" type="main">         
               <s id="id.2.1.1.17.1.1.0"> Centrvm grauitatis vniu&longs;cu&shy;<lb/> 
 iu&longs;q; corporis e&longs;t punctum quod&shy;<lb/> 
 dam intra po&longs;itum, &agrave; quo &longs;i gra&shy;<lb/> 
 ue appen&longs;um mente concipiatur, <lb/> 
 dum fertur, quie&longs;cit; &amp; &longs;eruat eam, <lb/> 
 quam in principio habebat po&longs;i&shy;<lb/> 
 tionem: neq; in ip&longs;a latione circumuertitur. </s>    </p>        
             <p id="id.2.1.1.18.0.0.0" type="main">         
               <s id="id.2.1.1.18.1.1.0"> Hanc centri grauitatis definitionem Pappus Alexandrinus in <lb/> 
 octauo Mathematicarum collectionum libro tradidit.  </s>              
               <s id="id.2.1.1.18.1.2.0"> Federicus <lb/> 
 ver&ograve; Commandinus in libro de centro grauitatis &longs;olidorum idem <lb/> 
 centrum de&longs;cribendo ita explicauit. </s>    </p>        
             <p id="id.2.1.1.19.0.0.0" type="main">         
               <s id="id.2.1.1.19.1.1.0"> Centrum grauitatis vniu&longs;cuiu&longs;q; &longs;olid&aelig; figu&shy;<lb/> 
 r&aelig; e&longs;t punctum illud intra po&longs;itum, circa quod <lb/> 
 vndiq; partes &aelig;qualium momentorum con&longs;i&shy;<lb/> 
 &longs;tunt.  </s>              
               <s id="id.2.1.1.19.1.2.0"> &longs;i enim per tale centrum ducatur planum <lb/> 
 figuram quomodocunq; &longs;ecans &longs;emper in par&shy;<lb/> 
 tes &aelig;queponderantes ip&longs;am diuidet.  </s>    </p>        
             <pb xlink:href="pagethumb-la/00000020.JPG"/> 
               
 <p id="id.2.1.1.21.0.0.0" type="head">         
 <s id="id.2.1.1.21.1.1.0"> COMMVNES NOTIONES. </s>     <lb/> <s id="id.2.1.1.21.1.1.0"> COMMVNES NOTIONES. </s>     <lb/>
               
 <s id="id.2.1.1.21.3.1.0"> I </s>    </p>        <s id="id.2.1.1.21.3.1.0"> I </s>    </p>       <p id="id.2.1.1.22.0.0.0" type="main">        
 <p id="id.2.1.1.22.0.0.0" type="main">         
 <s id="id.2.1.1.22.1.1.0"> Si ab &aelig;queponderantibus &aelig;queponderantia au&shy;<lb/> <s id="id.2.1.1.22.1.1.0"> Si ab &aelig;queponderantibus &aelig;queponderantia au&shy;<lb/>ferantur, reliqua &aelig;queponderabunt.  </s>    </p>       <p id="id.2.1.1.23.0.0.0" type="head">        
 ferantur, reliqua &aelig;queponderabunt.  </s>    </p>        
 <p id="id.2.1.1.23.0.0.0" type="head">         <s id="id.2.1.1.23.1.1.0"> II </s>    </p>       <p id="id.2.1.1.24.0.0.0" type="main">        
 <s id="id.2.1.1.23.1.1.0"> II </s>    </p>        
 <p id="id.2.1.1.24.0.0.0" type="main">         <s id="id.2.1.1.24.1.1.0"> Si &aelig;queponderantibus &aelig;queponderantia adii&shy;<lb/>ciantur, tota &longs;imul &aelig;queponderabunt.  </s>    </p>       <p id="id.2.1.1.25.0.0.0" type="head">        
 <s id="id.2.1.1.24.1.1.0"> Si &aelig;queponderantibus &aelig;queponderantia adii&shy;<lb/> 
 ciantur, tota &longs;imul &aelig;queponderabunt.  </s>    </p>        <s id="id.2.1.1.25.1.1.0"> III </s>    </p>       <p id="id.2.1.1.26.0.0.0" type="main">        
 <p id="id.2.1.1.25.0.0.0" type="head">         
 <s id="id.2.1.1.25.1.1.0"> III </s>    </p>        <s id="id.2.1.1.26.1.1.0"> Qu&aelig; eidem &aelig;queponderant, inter &longs;e &aelig;qu&egrave; &longs;unt <lb/>grauia.  </s>    </p>       <p id="id.2.1.1.27.0.0.0" type="head">        
 <p id="id.2.1.1.26.0.0.0" type="main">         
 <s id="id.2.1.1.26.1.1.0"> Qu&aelig; eidem &aelig;queponderant, inter &longs;e &aelig;qu&egrave; &longs;unt <lb/> 
 grauia.  </s>    </p>        
 <p id="id.2.1.1.27.0.0.0" type="head">         
 <s id="id.2.1.1.27.1.1.0"> SVPPOSITIONES. </s>     <lb/> <s id="id.2.1.1.27.1.1.0"> SVPPOSITIONES. </s>     <lb/>
               
 <s id="id.2.1.1.27.3.1.0"> I </s>    </p>        <s id="id.2.1.1.27.3.1.0"> I </s>    </p>       <p id="id.2.1.1.28.0.0.0" type="main">        
 <p id="id.2.1.1.28.0.0.0" type="main">         
 <s id="id.2.1.1.28.1.1.0"> Vnius corporis vnum tant&ugrave;m e&longs;t centrum gra&shy;<lb/> <s id="id.2.1.1.28.1.1.0"> Vnius corporis vnum tant&ugrave;m e&longs;t centrum gra&shy;<lb/>uitatis.  </s>    </p>       <p id="id.2.1.1.29.0.0.0" type="head">        
 uitatis.  </s>    </p>        
 <p id="id.2.1.1.29.0.0.0" type="head">         <s id="id.2.1.1.29.1.1.0"> II </s>    </p>       <p id="id.2.1.1.30.0.0.0" type="main">        
 <s id="id.2.1.1.29.1.1.0"> II </s>    </p>        
 <p id="id.2.1.1.30.0.0.0" type="main">         <s id="id.2.1.1.30.1.1.0"> Vnius corporis centrum grauitatis &longs;emper in <lb/>eodem e&longs;t &longs;itu re&longs;pectu &longs;ui corporis.  </s>    </p>       <p id="id.2.1.1.31.0.0.0" type="head">        
 <s id="id.2.1.1.30.1.1.0"> Vnius corporis centrum grauitatis &longs;emper in <lb/> 
 eodem e&longs;t &longs;itu re&longs;pectu &longs;ui corporis.  </s>    </p>        <s id="id.2.1.1.31.1.1.0"> III </s>    </p>       <p id="id.2.1.1.32.0.0.0" type="main">        
 <p id="id.2.1.1.31.0.0.0" type="head">         
 <s id="id.2.1.1.31.1.1.0"> III </s>    </p>        <s id="id.2.1.1.32.1.1.0"> Secund&ugrave;m grauitatis centrum pondera deor&shy;<lb/>&longs;um feruntur.  </s>    </p>             </chap>      <pb n="2" xlink:href="pagethumb-la/00000021.JPG"/>      <chap><p id="id.2.1.1.33.0.0.0" type="head">        
 <p id="id.2.1.1.32.0.0.0" type="main">         
 <s id="id.2.1.1.32.1.1.0"> Secund&ugrave;m grauitatis centrum pondera deor&shy;<lb/> <s id="id.2.1.1.34.1.1.0"> DE LIBRA. </s>    </p>       <p id="id.2.1.1.35.0.0.0" type="main">        
 &longs;um feruntur.  </s>    </p>        
       </chap> <s id="id.2.1.1.35.1.1.0"> Anteqvam de libra &longs;ermo ha<lb/>beatur, vtres clarior eluce&longs;cat, &longs;it <lb/>libra AB recta linea; CD ver&ograve; <lb/>trutina, qu&aelig; &longs;ecundum commu&shy;<lb/>nem con&longs;uetudinem horizonti <lb/>&longs;emper e&longs;t perpendicularis.  </s>            
       <pb n="2" xlink:href="pagethumb-la/00000021.JPG"/> 
       <chap> <s id="id.2.1.1.35.1.2.0"> pun&shy;<lb/>ctum autem C immobile, circa quod vertitur li&shy;<lb/>bra, centrum libr&aelig; <lb/>vocetur.  </s>            
  
 <p id="id.2.1.1.33.0.0.0" type="head">         <s id="id.2.1.1.35.1.3.0"> itidemque <lb/>(quamuis tamen im&shy;<lb/>proprie) &longs;iue &longs;upra, <lb/>&longs;iue infra libram fue<lb/>rit con&longs;titutum.  </s>            
 <s id="id.2.1.1.34.1.1.0"> DE LIBRA. </s>    </p>        
 <p id="id.2.1.1.35.0.0.0" type="main">         <s id="id.2.1.1.35.1.4.0"> CA <lb/>ver&ograve;, &amp; CB, tum di<lb/>&longs;tanti&aelig;, tum libr&aelig; <lb/>brachia nuncupen&shy;<lb/>tur.  </s>            
 <s id="id.2.1.1.35.1.1.0"> Anteqvam de libra &longs;ermo ha<lb/> 
 beatur, vtres clarior eluce&longs;cat, &longs;it <lb/> <s id="id.2.1.1.35.1.5.0"> &amp; &longs;i &agrave; centro li&shy;<lb/>br&aelig; &longs;upra, vel infra <lb/><figure id="fig1" place="text" xlink:href="figures1577/2000.03.0019.jpg">       </figure><lb/>libram con&longs;tituto ip&longs;i AB perpendicularis duca&shy;<lb/>tur, h&aelig;c perpendiculum vocetur, qu&aelig; libram AB <lb/>&longs;ub&longs;tinebit; &amp; quocunque modo moueatur libra, <lb/>ip&longs;i &longs;emper perpendicularis exi&longs;tet.  </s>    
 libra AB recta linea; CD ver&ograve; <lb/> 
 trutina, qu&aelig; &longs;ecundum commu&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.1.35.2.1.0" type="caption">        
 nem con&longs;uetudinem horizonti <lb/> 
 &longs;emper e&longs;t perpendicularis.  </s>              <s id="id.2.1.1.35.2.1.0.capt"> YYY </s>    </p>       <pb xlink:href="pagethumb-la/00000022.JPG"/>       <p id="id.2.1.1.37.0.0.0" type="head">        
 <s id="id.2.1.1.35.1.2.0"> pun&shy;<lb/> 
 ctum autem C immobile, circa quod vertitur li&shy;<lb/> <s id="id.2.1.1.37.1.1.0"> LEMMA. </s>    </p>       <p id="id.2.1.1.38.0.0.0" type="main">        
 bra, centrum libr&aelig; <lb/> 
 vocetur.  </s>              <s id="id.2.1.1.38.1.1.0"> Sit linea AB horizonti perpendicularis, &amp; dia <lb/>metro AB circulus de&longs;cribatur AEBD, cuius <lb/>centrum C.  </s>    
 <s id="id.2.1.1.35.1.3.0"> itidemque <lb/> 
 (quamuis tamen im&shy;<lb/> <s id="id.2.1.1.38.1.1.0.a"> Dico punctum B infimum e&longs;&longs;e lo&shy;<lb/>cum circumferenti&aelig; circuli AEBD; punctum <lb/>ver&ograve; A &longs;ublimiorem; &amp; qu&aelig;libet puncta, vt DE <lb/>&aelig;qualiter &agrave; puncto A di&longs;tantia &aelig;qualiter e&longs;&longs;e <lb/>deor&longs;um; qu&aelig; ver&ograve; propius &longs;unt ip&longs;i A eis, qu&aelig; <lb/>magis di&longs;tant, &longs;ublimiora e&longs;&longs;e. </s>    </p>       <p id="id.2.1.1.39.0.0.0" type="main">        
 proprie) &longs;iue &longs;upra, <lb/> 
 &longs;iue infra libram fue<lb/> <s id="id.2.1.1.39.1.1.0"> Producatur AB v&longs;q; ad mundi cen&shy;<lb/>trum, quod &longs;it F; deinde in circuli circum&shy;<lb/><arrow.to.target n="note1"></arrow.to.target> ferentia quoduis accipiatur punctum G; <lb/>connectanturq; FG FD FE.   </s>            
 rit con&longs;titutum.  </s>              
 <s id="id.2.1.1.35.1.4.0"> CA <lb/> <s id="id.2.1.1.39.1.2.0"> Quoniam <lb/>n. BF minima e&longs;t omnium, qu&aelig; &agrave; puncto <lb/>F ad circumferentiam AEBD ducun&shy;<lb/>tur; erit BF ip&longs;a FG minor.  </s>            
 ver&ograve;, &amp; CB, tum di<lb/> 
 &longs;tanti&aelig;, tum libr&aelig; <lb/> <s id="id.2.1.1.39.1.3.0"> quare punctum <lb/>B propius erit puncto F, qu&agrave;m G.  </s>    
 brachia nuncupen&shy;<lb/> 
 tur.  </s>              <s id="id.2.1.1.39.1.3.0.a"> hacq; <lb/>ratione o&longs;tendetur punctum B quouis alio <lb/>puncto circumferenti&aelig; circuli AEDB <lb/>mundi centro propius e&longs;&longs;e.  </s>            
 <s id="id.2.1.1.35.1.5.0"> &amp; &longs;i &agrave; centro li&shy;<lb/> 
 br&aelig; &longs;upra, vel infra <lb/> <s id="id.2.1.1.39.1.4.0"> erit igitur pun&shy;<lb/>ctum B circumferenti&aelig; circuli AEBD <lb/>infimus locus.  </s>            
 <figure id="fig1" place="text" xlink:href="figures1577/2000.03.0019.jpg">       </figure><lb/> 
 libram con&longs;tituto ip&longs;i AB perpendicularis duca&shy;<lb/> <s id="id.2.1.1.39.1.5.0"> Deinde quoniam AF per <lb/>centrum ducta maior e&longs;t ip&longs;a GF; erit <lb/>punctum A non <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ip&longs;o G, verum etiam <lb/>quouis alio puncto circumferenti&aelig; circuli <lb/>AEBD &longs;ublimius.  </s>            
 tur, h&aelig;c perpendiculum vocetur, qu&aelig; libram AB <lb/> 
 &longs;ub&longs;tinebit; &amp; quocunque modo moueatur libra, <lb/> <s id="id.2.1.1.39.1.6.0"> Pr&aelig;terea quoniam DF <lb/>FE &longs;unt &aelig;quales; puncta DE &aelig;qualiter <lb/><figure id="fig2" place="text" xlink:href="figures1577/2000.03.0020.jpg">       </figure><lb/>mundi centro di&longs;tabunt.  </s>            
 ip&longs;i &longs;emper perpendicularis exi&longs;tet.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.1.39.1.7.0"> &amp; cum DF maior &longs;it FG; erit pun&shy;<lb/>ctum D ip&longs;i A propius puncto G &longs;ublimius. </s>            
 <p id="id.2.1.1.35.2.1.0" type="caption">         
 <s id="id.2.1.1.35.2.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.1.39.1.8.0"> qu&aelig; omnia demon&shy;<lb/>&longs;trare oportebat.  </s>    
 <pb xlink:href="pagethumb-la/00000022.JPG"/> 
         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.1.39.2.1.0" type="caption">        
 <p id="id.2.1.1.37.0.0.0" type="head">         
 <s id="id.2.1.1.37.1.1.0"> LEMMA. </s>    </p>        <s id="id.2.1.1.39.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.2.1.0.0.0" type="margin">        
 <p id="id.2.1.1.38.0.0.0" type="main">         
 <s id="id.2.1.1.38.1.1.0"> Sit linea AB horizonti perpendicularis, &amp; dia <lb/> <s id="id.2.1.2.1.1.1.0"> <margin.target id="note1"></margin.target>8. <emph type="italics"/>Tertil.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.3.1.0.0.0" type="head">        <pb n="3" xlink:href="pagethumb-la/00000023.JPG"/>      
 metro AB circulus de&longs;cribatur AEBD, cuius <lb/> 
 centrum C.  </s>      <s id="id.2.1.3.1.2.1.0"> PROPOSITIO I. </s>    </p>       <p id="id.2.1.3.2.0.0.0" type="main">        
 <s id="id.2.1.1.38.1.1.0.a"> Dico punctum B infimum e&longs;&longs;e lo&shy;<lb/> 
 cum circumferenti&aelig; circuli AEBD; punctum <lb/> <s id="id.2.1.3.2.1.1.0"> Si Pondus in eius centro grauitatis a recta &longs;u&shy;<lb/>&longs;tineatur linea, nunquam manebit, ni&longs;i eadem li&shy;<lb/>nea horizonti fuerit perpendicularis. </s>    </p>       <p id="id.2.1.3.3.0.0.0" type="main">        
 ver&ograve; A &longs;ublimiorem; &amp; qu&aelig;libet puncta, vt DE <lb/> 
 &aelig;qualiter &agrave; puncto A di&longs;tantia &aelig;qualiter e&longs;&longs;e <lb/> <s id="id.2.1.3.3.1.1.0"> Sit pondus A, cuius centrum gra<lb/>uitatis B, quod &agrave; linea CE &longs;u&longs;ti&shy;<lb/>neatur.  </s>            
 deor&longs;um; qu&aelig; ver&ograve; propius &longs;unt ip&longs;i A eis, qu&aelig; <lb/> 
 magis di&longs;tant, &longs;ublimiora e&longs;&longs;e. </s>    </p>        <s id="id.2.1.3.3.1.2.0"> Dico pondus nunquam <lb/>perman&longs;urum, ni&longs;i CB horizonti <lb/>perpendicularis exi&longs;tat.  </s>            
 <p id="id.2.1.1.39.0.0.0" type="main">         
 <s id="id.2.1.1.39.1.1.0"> Producatur AB v&longs;q; ad mundi cen&shy;<lb/> <s id="id.2.1.3.3.1.3.0"> &longs;it pun&shy;<lb/>ctum C immobile, quod vt pon<lb/>dus &longs;u&longs;tineatur, nece&longs;&longs;e e&longs;t.  </s>            
 trum, quod &longs;it F; deinde in circuli circum&shy;<lb/> 
 <arrow.to.target n="note1"></arrow.to.target> ferentia quoduis accipiatur punctum G; <lb/> <s id="id.2.1.3.3.1.4.0"> &amp; cum <lb/>punctum C &longs;it immobile, &longs;i pon&shy;<lb/>dus A mouebitur, punctum B cir<lb/>culi circumferentiam de&longs;cribet, <lb/>cuius &longs;emidiameter erit CB. qua<lb/>re centro C, &longs;patio ver&ograve; BC, cir&shy;<lb/>culus de&longs;cribatur BFDE.  </s>    
 connectanturq; FG FD FE.   </s>              
 <s id="id.2.1.1.39.1.2.0"> Quoniam <lb/> <s id="id.2.1.3.3.1.4.0.a"> &longs;itq; <lb/><figure id="fig3" place="text" xlink:href="figures1577/2000.03.0021.jpg">       </figure><lb/>primum BC horizonti perpendicular&iacute;s, qu&aelig; v&longs;q; ad D produca&shy;<lb/>tur; atq; punctum C &longs;it infra punctum B.  </s>    
 n. BF minima e&longs;t omnium, qu&aelig; &agrave; puncto <lb/> 
 F ad circumferentiam AEBD ducun&shy;<lb/> <s id="id.2.1.3.3.1.4.0.b"> Quoniam enim pondus <arrow.to.target n="note2"></arrow.to.target><lb/>A &longs;ecundum grauitatis centrum B deor&longs;um mouetur; punctum <lb/>B deor&longs;um in centrum mundi, qu&ograve; naturaliter tendit, per re&shy;<lb/>ctam lineam BD mouebitur: totum ergo pondus A eius cen&shy;<lb/>tro grauitatis B &longs;uper rectam lineam BC graue&longs;cet.  </s>            
 tur; erit BF ip&longs;a FG minor.  </s>              
 <s id="id.2.1.1.39.1.3.0"> quare punctum <lb/> <s id="id.2.1.3.3.1.5.0"> cum au&shy;<lb/>tem pondus &agrave; linea CB &longs;u&longs;tineatur, linea CB totum &longs;u&longs;ti&shy;<lb/>nebit pondus A; &longs;uper quam deor&longs;um moueri non pote&longs;t, cum <lb/>ab ip&longs;a prohibeatur: per definitionem igitur centri grauitatis pun<lb/>ctum B, pondu&longs;q; A in hoc &longs;itu manebunt.  </s>            
 B propius erit puncto F, qu&agrave;m G.  </s>      
 <s id="id.2.1.1.39.1.3.0.a"> hacq; <lb/> <s id="id.2.1.3.3.1.6.0"> &amp; quamquam B quo&shy;<lb/>cunq; alio puncto circuli &longs;it &longs;ublimius, ab hoc tamen &longs;itu deor&longs;um <lb/>per circuli circumferentiam nequaquam mouebitur non enim ver&shy;<lb/>&longs;us F magis, qu&agrave;m ver&longs;us E inclinabitur, cum ex vtraq; parte &aelig;qua&shy;<lb/>lis &longs;it de&longs;cen&longs;us; neq; pondus A in vnam magis, qu&agrave;m in alteram <lb/>partem propen&longs;ionem habeat: quod non accidit in quouis alio <lb/>puncto circumferenti&aelig; circuli (pr&aelig;ter D) &longs;it ponderis eiu&longs;dem <pb xlink:href="pagethumb-la/00000024.JPG"/>centrum grauitatis, vt in F; cum ex <lb/>puncto F ver&longs;us D &longs;it de&longs;cen&longs;us, at <lb/>ver&ograve; ver&longs;us B a&longs;cen&longs;us.  </s>            
 ratione o&longs;tendetur punctum B quouis alio <lb/> 
 puncto circumferenti&aelig; circuli AEDB <lb/> <s id="id.2.1.3.3.1.7.0"> quare pun&shy;<lb/>ctum F deor&longs;um mouebitur. </s>            
 mundi centro propius e&longs;&longs;e.  </s>              
 <s id="id.2.1.1.39.1.4.0"> erit igitur pun&shy;<lb/> <s id="id.2.1.3.3.1.8.0"> &amp; quo<lb/>niam per rectam lineam in centrum <lb/>mundi moueri non pote&longs;t, cum &agrave; <lb/>puncto C immobili propter lineam <lb/>CF prohibeatur; deor&longs;um tamen <lb/>&longs;icuti eius natura po&longs;tulat, &longs;emper <lb/>mouebitur.  </s>            
 ctum B circumferenti&aelig; circuli AEBD <lb/> 
 infimus locus.  </s>              <s id="id.2.1.3.3.1.9.0"> &amp; cum infimus locus &longs;it <lb/>D, per <expan abbr="circumferenti&atilde;">circumferentiam</expan> FD mouebi<lb/>tur, donec in D perueniat, in quo <lb/>&longs;itu manebit, <expan abbr="p&otilde;du&longs;q">pondu&longs;q</expan>; immobile exi <lb/><figure id="fig4" place="text" xlink:href="figures1577/2000.03.0022.1.jpg">       </figure><lb/>&longs;tet.  </s>            
 <s id="id.2.1.1.39.1.5.0"> Deinde quoniam AF per <lb/> 
 centrum ducta maior e&longs;t ip&longs;a GF; erit <lb/> <s id="id.2.1.3.3.1.10.0"> tum quia deor&longs;um amplius moueri non pote&longs;t, cum ex pun&shy;<lb/>cto C &longs;it appen&longs;um; tum etiam, quia in eius centro grauitatis &longs;u&longs;ti<lb/>netur.  </s>            
 punctum A non <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ip&longs;o G, verum etiam <lb/> 
 quouis alio puncto circumferenti&aelig; circuli <lb/> <s id="id.2.1.3.3.1.11.0"> Quando autem F erit in D, erit quoq; linea FC in DC, <lb/>&longs;imulq; horizonti perpendicularis.  </s>            
 AEBD &longs;ublimius.  </s>              
 <s id="id.2.1.1.39.1.6.0"> Pr&aelig;terea quoniam DF <lb/> <s id="id.2.1.3.3.1.12.0"> pondus ergo nunquam mane<lb/>bit, donec linea CF horizonti perpendicularis non exi&longs;tat. quod <lb/>o&longs;tendere oportebat.  </s>            
 FE &longs;unt &aelig;quales; puncta DE &aelig;qualiter <lb/> 
 <figure id="fig2" place="text" xlink:href="figures1577/2000.03.0020.jpg">       </figure><lb/> <s id="id.2.1.3.3.1.13.0"> quod <lb/>o&longs;tendere oportebat. </s>    
 mundi centro di&longs;tabunt.  </s>              
 <s id="id.2.1.1.39.1.7.0"> &amp; cum DF maior &longs;it FG; erit pun&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.3.3.2.1.0" type="caption">        
 ctum D ip&longs;i A propius puncto G &longs;ublimius. </s>              
 <s id="id.2.1.1.39.1.8.0"> qu&aelig; omnia demon&shy;<lb/> 
 &longs;trare oportebat.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.1.39.2.1.0" type="caption">         
 <s id="id.2.1.1.39.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.2.1.0.0.0" type="margin">         
 <s id="id.2.1.2.1.1.1.0"> <margin.target id="note1"></margin.target>8. <emph type="italics"/>Tertil.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.3.1.0.0.0" type="head">         
 <pb n="3" xlink:href="pagethumb-la/00000023.JPG"/> 
         
 <s id="id.2.1.3.1.2.1.0"> PROPOSITIO I. </s>    </p>        
 <p id="id.2.1.3.2.0.0.0" type="main">         
 <s id="id.2.1.3.2.1.1.0"> Si Pondus in eius centro grauitatis a recta &longs;u&shy;<lb/> 
 &longs;tineatur linea, nunquam manebit, ni&longs;i eadem li&shy;<lb/> 
 nea horizonti fuerit perpendicularis. </s>    </p>        
 <p id="id.2.1.3.3.0.0.0" type="main">         
 <s id="id.2.1.3.3.1.1.0"> Sit pondus A, cuius centrum gra<lb/> 
 uitatis B, quod &agrave; linea CE &longs;u&longs;ti&shy;<lb/> 
 neatur.  </s>              
 <s id="id.2.1.3.3.1.2.0"> Dico pondus nunquam <lb/> 
 perman&longs;urum, ni&longs;i CB horizonti <lb/> 
 perpendicularis exi&longs;tat.  </s>              
 <s id="id.2.1.3.3.1.3.0"> &longs;it pun&shy;<lb/> 
 ctum C immobile, quod vt pon<lb/> 
 dus &longs;u&longs;tineatur, nece&longs;&longs;e e&longs;t.  </s>              
 <s id="id.2.1.3.3.1.4.0"> &amp; cum <lb/> 
 punctum C &longs;it immobile, &longs;i pon&shy;<lb/> 
 dus A mouebitur, punctum B cir<lb/> 
 culi circumferentiam de&longs;cribet, <lb/> 
 cuius &longs;emidiameter erit CB. qua<lb/> 
 re centro C, &longs;patio ver&ograve; BC, cir&shy;<lb/> 
 culus de&longs;cribatur BFDE.  </s>      
 <s id="id.2.1.3.3.1.4.0.a"> &longs;itq; <lb/> 
 <figure id="fig3" place="text" xlink:href="figures1577/2000.03.0021.jpg">       </figure><lb/> 
 primum BC horizonti perpendicular&iacute;s, qu&aelig; v&longs;q; ad D produca&shy;<lb/> 
 tur; atq; punctum C &longs;it infra punctum B.  </s>      
 <s id="id.2.1.3.3.1.4.0.b"> Quoniam enim pondus <arrow.to.target n="note2"></arrow.to.target><lb/> 
 A &longs;ecundum grauitatis centrum B deor&longs;um mouetur; punctum <lb/> 
 B deor&longs;um in centrum mundi, qu&ograve; naturaliter tendit, per re&shy;<lb/> 
 ctam lineam BD mouebitur: totum ergo pondus A eius cen&shy;<lb/> 
 tro grauitatis B &longs;uper rectam lineam BC graue&longs;cet.  </s>              
 <s id="id.2.1.3.3.1.5.0"> cum au&shy;<lb/> 
 tem pondus &agrave; linea CB &longs;u&longs;tineatur, linea CB totum &longs;u&longs;ti&shy;<lb/> 
 nebit pondus A; &longs;uper quam deor&longs;um moueri non pote&longs;t, cum <lb/> 
 ab ip&longs;a prohibeatur: per definitionem igitur centri grauitatis pun<lb/> 
 ctum B, pondu&longs;q; A in hoc &longs;itu manebunt.  </s>              
 <s id="id.2.1.3.3.1.6.0"> &amp; quamquam B quo&shy;<lb/> 
 cunq; alio puncto circuli &longs;it &longs;ublimius, ab hoc tamen &longs;itu deor&longs;um <lb/> 
 per circuli circumferentiam nequaquam mouebitur non enim ver&shy;<lb/> 
 &longs;us F magis, qu&agrave;m ver&longs;us E inclinabitur, cum ex vtraq; parte &aelig;qua&shy;<lb/> 
 lis &longs;it de&longs;cen&longs;us; neq; pondus A in vnam magis, qu&agrave;m in alteram <lb/> 
 partem propen&longs;ionem habeat: quod non accidit in quouis alio <lb/> 
 puncto circumferenti&aelig; circuli (pr&aelig;ter D) &longs;it ponderis eiu&longs;dem  
 <pb xlink:href="pagethumb-la/00000024.JPG"/> 
 centrum grauitatis, vt in F; cum ex <lb/> 
 puncto F ver&longs;us D &longs;it de&longs;cen&longs;us, at <lb/> 
 ver&ograve; ver&longs;us B a&longs;cen&longs;us.  </s>              
 <s id="id.2.1.3.3.1.7.0"> quare pun&shy;<lb/> 
 ctum F deor&longs;um mouebitur. </s>              
 <s id="id.2.1.3.3.1.8.0"> &amp; quo<lb/> 
 niam per rectam lineam in centrum <lb/> 
 mundi moueri non pote&longs;t, cum &agrave; <lb/> 
 puncto C immobili propter lineam <lb/> 
 CF prohibeatur; deor&longs;um tamen <lb/> 
 &longs;icuti eius natura po&longs;tulat, &longs;emper <lb/> 
 mouebitur.  </s>              
 <s id="id.2.1.3.3.1.9.0"> &amp; cum infimus locus &longs;it <lb/> 
 D, per <expan abbr="circumferenti&atilde;">circumferentiam</expan> FD mouebi<lb/> 
 tur, donec in D perueniat, in quo <lb/> 
 &longs;itu manebit, <expan abbr="p&otilde;du&longs;q">pondu&longs;q</expan>; immobile exi <lb/> 
 <figure id="fig4" place="text" xlink:href="figures1577/2000.03.0022.1.jpg">       </figure><lb/> 
 &longs;tet.  </s>              
 <s id="id.2.1.3.3.1.10.0"> tum quia deor&longs;um amplius moueri non pote&longs;t, cum ex pun&shy;<lb/> 
 cto C &longs;it appen&longs;um; tum etiam, quia in eius centro grauitatis &longs;u&longs;ti<lb/> 
 netur.  </s>              
 <s id="id.2.1.3.3.1.11.0"> Quando autem F erit in D, erit quoq; linea FC in DC, <lb/> 
 &longs;imulq; horizonti perpendicularis.  </s>              
 <s id="id.2.1.3.3.1.12.0"> pondus ergo nunquam mane<lb/> 
 bit, donec linea CF horizonti perpendicularis non exi&longs;tat. quod <lb/> 
 o&longs;tendere oportebat.  </s>              
 <s id="id.2.1.3.3.1.13.0"> quod <lb/> 
 o&longs;tendere oportebat. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.3.3.2.1.0" type="caption">         
 <s id="id.2.1.3.3.2.1.0.capt"> YYY </s>      <s id="id.2.1.3.3.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.3.3.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.3.3.2.3.0" type="caption">        
 <s id="id.2.1.3.3.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.4.1.0.0.0" type="margin">         <s id="id.2.1.3.3.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.4.1.0.0.0" type="margin">        
 <s id="id.2.1.4.1.1.1.0"> <margin.target id="note2"></margin.target><emph type="italics"/>Supp.<emph.end type="italics"/> 3. <emph type="italics"/>huius.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.5.1.0.0.0" type="main">         <s id="id.2.1.4.1.1.1.0"> <margin.target id="note2"></margin.target><emph type="italics"/>Supp.<emph.end type="italics"/> 3. <emph type="italics"/>huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.5.1.0.0.0" type="main">        
 <s id="id.2.1.5.1.1.1.0"> Ex hoc elici pote&longs;t, pondus quocunq; modo <lb/> 
 in dato puncto &longs;u&longs;tineatur, nunquam manere; ni <lb/> <s id="id.2.1.5.1.1.1.0"> Ex hoc elici pote&longs;t, pondus quocunq; modo <lb/>in dato puncto &longs;u&longs;tineatur, nunquam manere; ni <lb/>&longs;i quando a centro grauitatis ponderis ad id pun<lb/>ctum ducta linea horizonti &longs;it perpendicularis. </s>    </p>       <p id="id.2.1.5.2.0.0.0" type="main">        
 &longs;i quando a centro grauitatis ponderis ad id pun<lb/> 
 ctum ducta linea horizonti &longs;it perpendicularis. </s>    </p>        <s id="id.2.1.5.2.1.1.0"> Vt ii&longs;dem po&longs;itis, &longs;u&longs;tineatur <lb/>pondus &agrave; lineis CG CH.  </s>    
 <p id="id.2.1.5.2.0.0.0" type="main">         
 <s id="id.2.1.5.2.1.1.0"> Vt ii&longs;dem po&longs;itis, &longs;u&longs;tineatur <lb/> <s id="id.2.1.5.2.1.1.0.a"> Dico <lb/>&longs;i ducta BC horizonti &longs;it perpen&shy;<lb/>dicularis, pondus A manere.  </s>            
 pondus &agrave; lineis CG CH.  </s>      
 <s id="id.2.1.5.2.1.1.0.a"> Dico <lb/> <s id="id.2.1.5.2.1.2.0"> &longs;i ver&ograve; <lb/>ducta CF non &longs;it horizonti per&shy;<lb/>pendicularis, punctum F deor&longs;um <lb/>v&longs;q; ad D moueri; in quo &longs;itu pon&shy;<lb/>dus manebit, ductaq; CD horizon<lb/>ti perpendicularis exi&longs;tet.  </s>            
 &longs;i ducta BC horizonti &longs;it perpen&shy;<lb/> 
 dicularis, pondus A manere.  </s>              <s id="id.2.1.5.2.1.3.0"> qu&aelig; om&shy;<lb/>nia eadem ratione o&longs;tendentur. <figure id="fig5" place="text" xlink:href="figures1577/2000.03.0022.2.jpg">       </figure> </s>     <pb n="4" xlink:href="pagethumb-la/00000025.JPG"/>      
 <s id="id.2.1.5.2.1.2.0"> &longs;i ver&ograve; <lb/> 
 ducta CF non &longs;it horizonti per&shy;<lb/> 
 pendicularis, punctum F deor&longs;um <lb/> 
 v&longs;q; ad D moueri; in quo &longs;itu pon&shy;<lb/> 
 dus manebit, ductaq; CD horizon<lb/> 
 ti perpendicularis exi&longs;tet.  </s>              
 <s id="id.2.1.5.2.1.3.0"> qu&aelig; om&shy;<lb/> 
 nia eadem ratione o&longs;tendentur. <figure id="fig5" place="text" xlink:href="figures1577/2000.03.0022.2.jpg">       </figure> </s>      
 <pb n="4" xlink:href="pagethumb-la/00000025.JPG"/> 
               
 <s id="id.2.1.5.2.3.1.0"> PROPOSITIO II. </s>      <s id="id.2.1.5.2.3.1.0"> PROPOSITIO II. </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.5.2.4.1.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.5.2.4.1.0" type="caption">        
 <s id="id.2.1.5.2.4.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.5.3.0.0.0" type="main">         <s id="id.2.1.5.2.4.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.5.3.0.0.0" type="main">        
 <s id="id.2.1.5.3.1.1.0"> Libra horizonti &aelig;quidi&longs;tans, cuius centrum <lb/> 
 &longs;it &longs;upra libram, &aelig;qualia in extremitatibus, &aelig;qua <lb/> <s id="id.2.1.5.3.1.1.0"> Libra horizonti &aelig;quidi&longs;tans, cuius centrum <lb/>&longs;it &longs;upra libram, &aelig;qualia in extremitatibus, &aelig;qua <lb/>literq; &agrave; perpendiculo di&longs;tantia habens pondera, <lb/>&longs;i ab eiu&longs;modi moueatur &longs;itu, in eundem rur&longs;us <lb/>relicta, redibit; ib&iacute;q; manebit. </s>    </p>       <p id="id.2.1.5.4.0.0.0" type="main">        
 literq; &agrave; perpendiculo di&longs;tantia habens pondera, <lb/> 
 &longs;i ab eiu&longs;modi moueatur &longs;itu, in eundem rur&longs;us <lb/> <s id="id.2.1.5.4.1.1.0"> Sit libra AB recta li&shy;<lb/>nea horizonti &aelig;quidi&shy;<lb/>&longs;tans, cuius centrum C <lb/>&longs;it &longs;upral ibram; &longs;itq; CD <lb/><expan abbr="perpendicul&utilde;">perpendiculum</expan>, quod ho&shy;<lb/>rizonti perpendiculare <lb/>erit: atq; di&longs;tantia DA &longs;it <lb/>di&longs;tanti&aelig; DB &aelig;qualis; <lb/>&longs;intq; in AB pondera &aelig;&shy;<lb/>qualia, <expan abbr="quor&utilde;">quorum</expan> grauitatis <lb/>centra &longs;int in AB <expan abbr="p&utilde;ctis">punctis</expan>.  </s>            
 relicta, redibit; ib&iacute;q; manebit. </s>    </p>        
 <p id="id.2.1.5.4.0.0.0" type="main">         <s id="id.2.1.5.4.1.2.0"> <lb/>Moueatur AB libra ab <lb/><figure id="fig6" place="text" xlink:href="figures1577/2000.03.0023.jpg">       </figure><lb/>hoc &longs;itu, put&aacute; in EF, deinde relinquatur.  </s>            
 <s id="id.2.1.5.4.1.1.0"> Sit libra AB recta li&shy;<lb/> 
 nea horizonti &aelig;quidi&shy;<lb/> <s id="id.2.1.5.4.1.3.0"> dico libram EF in AB ho<lb/>rizonti &aelig;quidi&longs;tantem redire, ib&iacute;q; manere.  </s>            
 &longs;tans, cuius centrum C <lb/> 
 &longs;it &longs;upral ibram; &longs;itq; CD <lb/> <s id="id.2.1.5.4.1.4.0"> Quoniam autem pun<lb/>ctum C e&longs;t immobile, dum libra mouetur, punctum D circuli cir&shy;<lb/>cumferentiam de&longs;cribet, cuius &longs;emidiameter erit CD. quare cen&shy;<lb/>tro C, &longs;patio ver&ograve; CD, circulus de&longs;cribatur DGH.  </s>    
 <expan abbr="perpendicul&utilde;">perpendiculum</expan>, quod ho&shy;<lb/> 
 rizonti perpendiculare <lb/> <s id="id.2.1.5.4.1.4.0.a"> Quoniam <lb/>enim CD ip&longs;i libr&aelig; &longs;emper e&longs;t perpendicularis, dum libra erit in <lb/>EF, linea CD erit in CG, ita vt CG &longs;it ip&longs;i EF perpendicula&shy;<lb/>ris.  </s>            
 erit: atq; di&longs;tantia DA &longs;it <lb/> 
 di&longs;tanti&aelig; DB &aelig;qualis; <lb/> <s id="id.2.1.5.4.1.5.0"> C&ugrave;m autem AB bifariam &agrave; puncto D diuidatur, &amp; pondera <lb/>in AB &longs;int &aelig;qualia; erit magnitudinis ex ip&longs;is AB compo&longs;it&aelig; cen <arrow.to.target n="note3"></arrow.to.target><lb/>trum grauitatis in medio, hoc e&longs;t in D. &amp; <expan abbr="qu&atilde;do">quando</expan> libra vn&aacute; cum pon<lb/>deribus erit in EF; erit magnitudinis ex vtri&longs;q; EF compo&longs;it&aelig; cen<lb/>trum grauitatis G.  </s>    
 &longs;intq; in AB pondera &aelig;&shy;<lb/> 
 qualia, <expan abbr="quor&utilde;">quorum</expan> grauitatis <lb/> <s id="id.2.1.5.4.1.5.0.a"> &amp; quoniam CG horizonti non e&longs;t perpendi&shy;<lb/>cularis;  <arrow.to.target n="note4"></arrow.to.target> magnitudo ex ponderibus EF compo&longs;ita in hoc &longs;itu <expan abbr="mi&shy;nim&egrave;">mi&shy;<lb/>nime</expan> per&longs;i&longs;tet, &longs;ed deor&longs;um <expan abbr="&longs;ec&utilde;d&ugrave;m">&longs;ecundum</expan> eius centrum grauitatis G per <lb/>circumferentiam GD mouebitur; donec CG horizonti fiat per&shy;<pb xlink:href="pagethumb-la/00000026.JPG"/>pendicularis, &longs;cilicet do&shy;<lb/>nec CG in CD redeat.  </s>            
 centra &longs;int in AB <expan abbr="p&utilde;ctis">punctis</expan>.  </s>              
 <s id="id.2.1.5.4.1.2.0"> <lb/> <s id="id.2.1.5.4.1.6.0"> <lb/>Quando autem CG erit <lb/>in CD, linea EF, c&ugrave;m <lb/>ip&longs;i CG &longs;emper ad rectos <lb/>&longs;it angulos, erit in AB; in <lb/><arrow.to.target n="note5"></arrow.to.target> quo &longs;itu quoq; manebit.  </s>            
 Moueatur AB libra ab <lb/> 
 <figure id="fig6" place="text" xlink:href="figures1577/2000.03.0023.jpg">       </figure><lb/> <s id="id.2.1.5.4.1.7.0"> li<lb/>bra ergo EF in AB hori&shy;<lb/>zonti <expan abbr="&aelig;quidi&longs;t&atilde;tem">&aelig;quidi&longs;tantem</expan> redi<lb/>bit, ib&iacute;q; manebit. </s>
 hoc &longs;itu, put&aacute; in EF, deinde relinquatur.  </s>              
 <s id="id.2.1.5.4.1.3.0"> dico libram EF in AB ho<lb/> <s id="id.2.1.5.4.1.8.0"> quod <lb/>demon&longs;trare oportebat.  </s>     <lb/>      
 rizonti &aelig;quidi&longs;tantem redire, ib&iacute;q; manere.  </s>              
 <s id="id.2.1.5.4.1.4.0"> Quoniam autem pun<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.5.4.2.1.0" type="caption">        
 ctum C e&longs;t immobile, dum libra mouetur, punctum D circuli cir&shy;<lb/> 
 cumferentiam de&longs;cribet, cuius &longs;emidiameter erit CD. quare cen&shy;<lb/> <s id="id.2.1.5.4.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.6.1.0.0.0" type="margin">        
 tro C, &longs;patio ver&ograve; CD, circulus de&longs;cribatur DGH.  </s>      
 <s id="id.2.1.5.4.1.4.0.a"> Quoniam <lb/> 
 enim CD ip&longs;i libr&aelig; &longs;emper e&longs;t perpendicularis, dum libra erit in <lb/> 
 EF, linea CD erit in CG, ita vt CG &longs;it ip&longs;i EF perpendicula&shy;<lb/> 
 ris.  </s>              
 <s id="id.2.1.5.4.1.5.0"> C&ugrave;m autem AB bifariam &agrave; puncto D diuidatur, &amp; pondera <lb/> 
 in AB &longs;int &aelig;qualia; erit magnitudinis ex ip&longs;is AB compo&longs;it&aelig; cen <arrow.to.target n="note3"></arrow.to.target><lb/> 
 trum grauitatis in medio, hoc e&longs;t in D. &amp; <expan abbr="qu&atilde;do">quando</expan> libra vn&aacute; cum pon<lb/> 
 deribus erit in EF; erit magnitudinis ex vtri&longs;q; EF compo&longs;it&aelig; cen<lb/> 
 trum grauitatis G.  </s>      
 <s id="id.2.1.5.4.1.5.0.a"> &amp; quoniam CG horizonti non e&longs;t perpendi&shy;<lb/> 
 cularis;  <arrow.to.target n="note4"></arrow.to.target> magnitudo ex ponderibus EF compo&longs;ita in hoc &longs;itu <expan abbr="mi&shy;nim&egrave;">mi&shy;<lb/> 
 nime</expan> per&longs;i&longs;tet, &longs;ed deor&longs;um <expan abbr="&longs;ec&utilde;d&ugrave;m">&longs;ecundum</expan> eius centrum grauitatis G per <lb/> 
 circumferentiam GD mouebitur; donec CG horizonti fiat per&shy; 
 <pb xlink:href="pagethumb-la/00000026.JPG"/> 
 pendicularis, &longs;cilicet do&shy;<lb/> 
 nec CG in CD redeat.  </s>              
 <s id="id.2.1.5.4.1.6.0"> <lb/> 
 Quando autem CG erit <lb/> 
 in CD, linea EF, c&ugrave;m <lb/> 
 ip&longs;i CG &longs;emper ad rectos <lb/> 
 &longs;it angulos, erit in AB; in <lb/> 
 <arrow.to.target n="note5"></arrow.to.target> quo &longs;itu quoq; manebit.  </s>              
 <s id="id.2.1.5.4.1.7.0"> li<lb/> 
 bra ergo EF in AB hori&shy;<lb/> 
 zonti <expan abbr="&aelig;quidi&longs;t&atilde;tem">&aelig;quidi&longs;tantem</expan> redi<lb/> 
 bit, ib&iacute;q; manebit. </s> 
 <s id="id.2.1.5.4.1.8.0"> quod <lb/> 
 demon&longs;trare oportebat.  </s>     <lb/> 
         
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.5.4.2.1.0" type="caption">         
 <s id="id.2.1.5.4.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.6.1.0.0.0" type="margin">         
 <s id="id.2.1.6.1.1.1.0"> <margin.target id="note3"></margin.target>4. <emph type="italics"/>primi Archimedis de &aelig;queponderantibus.<emph.end type="italics"/> </s>              <s id="id.2.1.6.1.1.1.0"> <margin.target id="note3"></margin.target>4. <emph type="italics"/>primi Archimedis de &aelig;queponderantibus.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.6.1.1.2.0"> <margin.target id="note4"></margin.target>1. <emph type="italics"/>Huius<emph.end type="italics"/> </s>              <s id="id.2.1.6.1.1.2.0"> <margin.target id="note4"></margin.target>1. <emph type="italics"/>Huius<emph.end type="italics"/> </s>            
 <s id="id.2.1.6.1.1.3.0"> <margin.target id="note5"></margin.target>1. <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.7.1.0.0.0" type="main">         <s id="id.2.1.6.1.1.3.0"> <margin.target id="note5"></margin.target>1. <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.7.1.0.0.0" type="main">        
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.7.1.1.1.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.7.1.1.1.0" type="caption">        
  
 <s id="id.2.1.7.1.1.1.0.capt"> YYY </s>     <lb/> <s id="id.2.1.7.1.1.1.0.capt"> YYY </s>     <lb/>
               
 <s id="id.2.1.7.1.3.1.0"> PROPOSITIO III. </s>    </p>        <s id="id.2.1.7.1.3.1.0"> PROPOSITIO III. </s>    </p>       <p id="id.2.1.7.2.0.0.0" type="main">        
 <p id="id.2.1.7.2.0.0.0" type="main">         
 <s id="id.2.1.7.2.1.1.0"> Libra horizonti &aelig;quidi&longs;tans &aelig;qualia in extre&shy;<lb/> <s id="id.2.1.7.2.1.1.0"> Libra horizonti &aelig;quidi&longs;tans &aelig;qualia in extre&shy;<lb/>mitatibus, &aelig;qualiterq; &agrave; perpendiculo di&longs;tan&shy;<lb/>tia habens pondera, centro infern&egrave; collocato, in <lb/>hoc &longs;itu manebit.  </s>            
 mitatibus, &aelig;qualiterq; &agrave; perpendiculo di&longs;tan&shy;<lb/> 
 tia habens pondera, centro infern&egrave; collocato, in <lb/> <s id="id.2.1.7.2.1.2.0"> &longs;i ver&ograve; inde moueatur, deor&shy;<lb/>&longs;um relicta, &longs;ecund&ugrave;m partem decliuiorem mo&shy;<lb/>uebitur. <figure id="fig7" place="text" xlink:href="figures1577/2000.03.0024.1.jpg">       </figure> </s>    </p>       <p id="id.2.1.7.3.0.0.0" type="main">        
 hoc &longs;itu manebit.  </s>              
 <s id="id.2.1.7.2.1.2.0"> &longs;i ver&ograve; inde moueatur, deor&shy;<lb/> <s id="id.2.1.7.3.1.1.0"> Sit libra AB rect&aacute; li&shy;<lb/>nea horizonti &aelig;quidi&shy;<lb/>&longs;tans, cuius centrum C <lb/>&longs;it infra libram; perpen&shy;<lb/>diculumq; &longs;it CD, quod <lb/>horizonti perpendiculare <lb/>erit; &amp; di&longs;tantia AD &longs;it <lb/>di&longs;tanti&aelig; DB &aelig;qualis; <lb/>&longs;intq; in AB pondera <lb/>&aelig;qualia, quorum grauita&shy;<lb/>tis centra &longs;int in punctis <lb/>AB.  </s>    
 &longs;um relicta, &longs;ecund&ugrave;m partem decliuiorem mo&shy;<lb/> 
 uebitur. <figure id="fig7" place="text" xlink:href="figures1577/2000.03.0024.1.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.7.3.0.0.0" type="main">         
 <s id="id.2.1.7.3.1.1.0"> Sit libra AB rect&aacute; li&shy;<lb/> 
 nea horizonti &aelig;quidi&shy;<lb/> 
 &longs;tans, cuius centrum C <lb/> 
 &longs;it infra libram; perpen&shy;<lb/> 
 diculumq; &longs;it CD, quod <lb/> 
 horizonti perpendiculare <lb/> 
 erit; &amp; di&longs;tantia AD &longs;it <lb/> 
 di&longs;tanti&aelig; DB &aelig;qualis; <lb/> 
 &longs;intq; in AB pondera <lb/> 
 &aelig;qualia, quorum grauita&shy;<lb/> 
 tis centra &longs;int in punctis <lb/> 
 AB.  </s>      
 <s id="id.2.1.7.3.1.1.0.a"> Dico prim&ugrave;m libram AB in hoc &longs;itu manere.  </s>              <s id="id.2.1.7.3.1.1.0.a"> Dico prim&ugrave;m libram AB in hoc &longs;itu manere.  </s>            
 <s id="id.2.1.7.3.1.2.0"> Quoniam <lb/> 
 enim AB bifariam diuiditur &agrave; puncto D, &amp; pondera in AB &longs;unt <lb/> <s id="id.2.1.7.3.1.2.0"> Quoniam <lb/>enim AB bifariam diuiditur &agrave; puncto D, &amp; pondera in AB &longs;unt <lb/>&aelig;qualia; erit punctum D centrum grauitatis magnitudinis ex <pb n="5" xlink:href="pagethumb-la/00000027.JPG"/>vtri&longs;q; AB ponderibus compo&longs;it&aelig;.  </s>            
 &aelig;qualia; erit punctum D centrum grauitatis magnitudinis ex  
 <pb n="5" xlink:href="pagethumb-la/00000027.JPG"/> <s id="id.2.1.7.3.1.3.0"> &amp; CD libram &longs;u&longs;tinens ho&shy;<lb/>rizonti  <arrow.to.target n="note6"></arrow.to.target> e&longs;t perpendicularis, libra ergo AB in hoc &longs;itu manebit. <arrow.to.target n="note7"></arrow.to.target><lb/>moueatur autem libra AB ab hoc &longs;itu, put&agrave; in EF, deinde relinqua<lb/>tur.  </s>            
 vtri&longs;q; AB ponderibus compo&longs;it&aelig;.  </s>              
 <s id="id.2.1.7.3.1.3.0"> &amp; CD libram &longs;u&longs;tinens ho&shy;<lb/> 
 rizonti  <arrow.to.target n="note6"></arrow.to.target> e&longs;t perpendicularis, libra ergo AB in hoc &longs;itu manebit. <arrow.to.target n="note7"></arrow.to.target><lb/> 
 moueatur autem libra AB ab hoc &longs;itu, put&agrave; in EF, deinde relinqua<lb/> 
 tur.  </s>              
 <s id="id.2.1.7.3.1.4.0"> dico libram EF ex parte F moueri.  </s>              <s id="id.2.1.7.3.1.4.0"> dico libram EF ex parte F moueri.  </s>            
 <s id="id.2.1.7.3.1.5.0"> Quoniam igitur CD <lb/> 
 ip&longs;i libr&aelig; &longs;emper e&longs;t perpendicularis, dum libra erit in EF, erit <lb/> <s id="id.2.1.7.3.1.5.0"> Quoniam igitur CD <lb/>ip&longs;i libr&aelig; &longs;emper e&longs;t perpendicularis, dum libra erit in EF, erit <lb/>CD in CG ip&longs;i EF perpendicularis.  </s>            
 CD in CG ip&longs;i EF perpendicularis.  </s>              
 <s id="id.2.1.7.3.1.6.0"> &amp; punctum G magnitudi&shy;<lb/> <s id="id.2.1.7.3.1.6.0"> &amp; punctum G magnitudi&shy;<lb/>nis ex EF compo&longs;it&aelig; centrum grauitatis erit; quod dum moue&shy;<lb/>tur, circuli circumferentiam de&longs;cribet DGH, cuius &longs;emidiameter <lb/>CD, &amp; centrum C.  </s>    
 nis ex EF compo&longs;it&aelig; centrum grauitatis erit; quod dum moue&shy;<lb/> 
 tur, circuli circumferentiam de&longs;cribet DGH, cuius &longs;emidiameter <lb/> <s id="id.2.1.7.3.1.6.0.a"> Quoniam autem CG horizonti non e&longs;t per&shy;<lb/>pendicularis, magnitudo ex EF ponderibus compo&longs;ita in hoc &longs;i&shy;<lb/>tu minim&egrave; manebit; &longs;ed &longs;ecund&ugrave;m eius grauitatis centrum G deor<lb/>&longs;um per circumferentiam GH mouebitur.  </s>            
 CD, &amp; centrum C.  </s>      
 <s id="id.2.1.7.3.1.6.0.a"> Quoniam autem CG horizonti non e&longs;t per&shy;<lb/> <s id="id.2.1.7.3.1.7.0"> libra ergo EF ex par <lb/>te F deor&longs;um mouebitur, quod demon&longs;trare oportebat.  </s>    
 pendicularis, magnitudo ex EF ponderibus compo&longs;ita in hoc &longs;i&shy;<lb/> 
 tu minim&egrave; manebit; &longs;ed &longs;ecund&ugrave;m eius grauitatis centrum G deor<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.7.3.2.1.0" type="caption">        
 &longs;um per circumferentiam GH mouebitur.  </s>              
 <s id="id.2.1.7.3.1.7.0"> libra ergo EF ex par <lb/> <s id="id.2.1.7.3.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.8.1.0.0.0" type="margin">        
 te F deor&longs;um mouebitur, quod demon&longs;trare oportebat.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.7.3.2.1.0" type="caption">         
 <s id="id.2.1.7.3.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.8.1.0.0.0" type="margin">         
 <s id="id.2.1.8.1.1.1.0"> <margin.target id="note6"></margin.target>4. <emph type="italics"/>Primi Archim. de &aelig;quep.<emph.end type="italics"/> </s>              <s id="id.2.1.8.1.1.1.0"> <margin.target id="note6"></margin.target>4. <emph type="italics"/>Primi Archim. de &aelig;quep.<emph.end type="italics"/> </s>            
 <s id="id.2.1.8.1.1.3.0"> <margin.target id="note7"></margin.target>1. <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.9.1.0.0.0" type="head">         <s id="id.2.1.8.1.1.3.0"> <margin.target id="note7"></margin.target>1. <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.9.1.0.0.0" type="head">        
 <s id="id.2.1.9.1.1.1.0"> PROPOSITIO IIII. </s>    </p>        
 <p id="id.2.1.9.2.0.0.0" type="main">         <s id="id.2.1.9.1.1.1.0"> PROPOSITIO IIII. </s>    </p>       <p id="id.2.1.9.2.0.0.0" type="main">        
 <s id="id.2.1.9.2.1.1.0"> Libra horizonti &aelig;quidi&longs;tans &aelig;qualia in ex&shy;<lb/> 
 tremitatibus, &aelig;qualiterq; &agrave; centro in ip&longs;a libra <lb/> <s id="id.2.1.9.2.1.1.0"> Libra horizonti &aelig;quidi&longs;tans &aelig;qualia in ex&shy;<lb/>tremitatibus, &aelig;qualiterq; &agrave; centro in ip&longs;a libra <lb/>collocato, di&longs;tantia habens pondera; &longs;iue inde <lb/>moueatur, &longs;iue minus; vbicunq; relicta, manebit. <figure id="fig8" place="text" xlink:href="figures1577/2000.03.0024.2.jpg">       </figure> </s>    </p>       <p id="id.2.1.9.3.0.0.0" type="main">        
 collocato, di&longs;tantia habens pondera; &longs;iue inde <lb/> 
 moueatur, &longs;iue minus; vbicunq; relicta, manebit. <figure id="fig8" place="text" xlink:href="figures1577/2000.03.0024.2.jpg">       </figure> </s>    </p>        <s id="id.2.1.9.3.1.1.0"> Sit libra recta linea A <lb/>B horizonti &aelig;quidi&longs;tans, <lb/>cuius centrum C in ea&shy;<lb/>dem &longs;it linea AB; di&longs;tan<lb/>tia ver&ograve; CA &longs;it di&longs;tanti&aelig; <lb/>CB &aelig;qualis: &longs;intq; pon&shy;<lb/>dera in AB &aelig;qualia, quo&shy;<lb/>rum centra grauitatis &longs;int <lb/>in puntis AB.  </s>    
 <p id="id.2.1.9.3.0.0.0" type="main">         
 <s id="id.2.1.9.3.1.1.0"> Sit libra recta linea A <lb/> <s id="id.2.1.9.3.1.1.0.a"> Moueatur <lb/>libra, vt in DE, ibiqu&egrave; <lb/>relinquatur.  </s>            
 B horizonti &aelig;quidi&longs;tans, <lb/> 
 cuius centrum C in ea&shy;<lb/> <s id="id.2.1.9.3.1.2.0"> Dico prim&ugrave;m libram DE non moueri, in eoqu&egrave; &longs;itu <lb/>manere.  </s>            
 dem &longs;it linea AB; di&longs;tan<lb/> 
 tia ver&ograve; CA &longs;it di&longs;tanti&aelig; <lb/> <s id="id.2.1.9.3.1.3.0"> Quoniam enim pondera AB &longs;unt &aelig;qualia; erit magni&shy;<lb/>tudinis ex vtroq; pondere, videlicet A, &amp; B compo&longs;it&aelig; centrum <lb/>grauitatis C. quare idem punctum C, &amp; centrum libr&aelig;, &amp; <expan abbr="centr&utilde;">centrum</expan> <lb/>grauitatis totius ponderis erit.  </s>            
 CB &aelig;qualis: &longs;intq; pon&shy;<lb/> 
 dera in AB &aelig;qualia, quo&shy;<lb/> <s id="id.2.1.9.3.1.4.0"> Quoniam autem centrum libr&aelig; <pb xlink:href="pagethumb-la/00000028.JPG"/>C, dum libra AB vn&agrave; <lb/>cum ponderibus in DE <lb/>mouetur, immobile re&shy;<lb/>manet, centrum quoq; <lb/>grauitatis, quod e&longs;t idem <lb/>C, non mouebitur.  </s>            
 rum centra grauitatis &longs;int <lb/> 
 in puntis AB.  </s>      <s id="id.2.1.9.3.1.5.0"> nec <lb/>igitur libra DE mouebi<lb/>tur, per definitionem <lb/>centri grauitatis, cum in <lb/>ip&longs;o &longs;u&longs;pendatur.  </s>            
 <s id="id.2.1.9.3.1.1.0.a"> Moueatur <lb/> 
 libra, vt in DE, ibiqu&egrave; <lb/> <s id="id.2.1.9.3.1.6.0"> Idip&shy;<lb/><figure id="fig9" place="text" xlink:href="figures1577/2000.03.0025.jpg">       </figure><lb/>&longs;um quoq; contingit libra in AB horizonti &aelig;quidi&longs;tante, vel in <lb/>quocunq; alio &longs;itu exi&longs;tente.  </s>            
 relinquatur.  </s>              
 <s id="id.2.1.9.3.1.2.0"> Dico prim&ugrave;m libram DE non moueri, in eoqu&egrave; &longs;itu <lb/> <s id="id.2.1.9.3.1.7.0"> Manebit ergo libra, vbi relinque&shy;<lb/>tur. </s>            
 manere.  </s>              
 <s id="id.2.1.9.3.1.3.0"> Quoniam enim pondera AB &longs;unt &aelig;qualia; erit magni&shy;<lb/> 
 tudinis ex vtroq; pondere, videlicet A, &amp; B compo&longs;it&aelig; centrum <lb/> 
 grauitatis C. quare idem punctum C, &amp; centrum libr&aelig;, &amp; <expan abbr="centr&utilde;">centrum</expan> <lb/> 
 grauitatis totius ponderis erit.  </s>              
 <s id="id.2.1.9.3.1.4.0"> Quoniam autem centrum libr&aelig;  
 <pb xlink:href="pagethumb-la/00000028.JPG"/> 
 C, dum libra AB vn&agrave; <lb/> 
 cum ponderibus in DE <lb/> 
 mouetur, immobile re&shy;<lb/> 
 manet, centrum quoq; <lb/> 
 grauitatis, quod e&longs;t idem <lb/> 
 C, non mouebitur.  </s>              
 <s id="id.2.1.9.3.1.5.0"> nec <lb/> 
 igitur libra DE mouebi<lb/> 
 tur, per definitionem <lb/> 
 centri grauitatis, cum in <lb/> 
 ip&longs;o &longs;u&longs;pendatur.  </s>              
 <s id="id.2.1.9.3.1.6.0"> Idip&shy;<lb/> 
 <figure id="fig9" place="text" xlink:href="figures1577/2000.03.0025.jpg">       </figure><lb/> 
 &longs;um quoq; contingit libra in AB horizonti &aelig;quidi&longs;tante, vel in <lb/> 
 quocunq; alio &longs;itu exi&longs;tente.  </s>              
 <s id="id.2.1.9.3.1.7.0"> Manebit ergo libra, vbi relinque&shy;<lb/> 
 tur. </s>              
 <s id="id.2.1.9.3.1.8.0"> quod demon&longs;trare oportebat. </s>      <s id="id.2.1.9.3.1.8.0"> quod demon&longs;trare oportebat. </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.9.3.2.1.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.9.3.2.1.0" type="caption">        
  
 <s id="id.2.1.9.3.2.1.0.capt"> YYY </s>      <s id="id.2.1.9.3.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.9.3.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.9.3.2.3.0" type="caption">        
 <s id="id.2.1.9.3.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.9.4.0.0.0" type="main">         <s id="id.2.1.9.3.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.9.4.0.0.0" type="main">        
 <s id="id.2.1.9.4.1.1.0"> Cum ver&ograve; in iis, qu&aelig; dicta &longs;unt, grauitatis tant&ugrave;m magnitudi<lb/> 
 num, qu&aelig; in extremitatibus libr&aelig; po&longs;it&aelig; &longs;unt &aelig;quales, ab&longs;q; <expan abbr="l&iacute;&shy;br&aelig;">li&shy;<lb/> <s id="id.2.1.9.4.1.1.0"> Cum ver&ograve; in iis, qu&aelig; dicta &longs;unt, grauitatis tant&ugrave;m magnitudi<lb/>num, qu&aelig; in extremitatibus libr&aelig; po&longs;it&aelig; &longs;unt &aelig;quales, ab&longs;q; <expan abbr="l&iacute;&shy;br&aelig;">li&shy;<lb/>br&aelig;</expan> grauitate con&longs;iderauerimus; quoniam tamen adhuc libr&aelig; bra&shy;<lb/>chia &longs;unt &aelig;qualia, idcirco idem libr&aelig;, eius grauitate con&longs;iderata, <lb/>vn&agrave; cum ponderibus, vel &longs;ine ponderibus eueniet.  </s>            
 br&aelig;</expan> grauitate con&longs;iderauerimus; quoniam tamen adhuc libr&aelig; bra&shy;<lb/> 
 chia &longs;unt &aelig;qualia, idcirco idem libr&aelig;, eius grauitate con&longs;iderata, <lb/> <s id="id.2.1.9.4.1.2.0"> idem enim cen<lb/>trum grauitatis fine ponderibus libr&aelig; tant&ugrave;m grauitatis centrum <lb/>erit.  </s>            
 vn&agrave; cum ponderibus, vel &longs;ine ponderibus eueniet.  </s>              
 <s id="id.2.1.9.4.1.2.0"> idem enim cen<lb/> <s id="id.2.1.9.4.1.3.0"> Similiter &longs;i pondera in libr&aelig; extremitatibus appendantur, vt <lb/>fieri &longs;olet, idem cueniet; dummodo ex &longs;u&longs;pen&longs;ionum punctis ad <lb/>centra grauitatum ponderum duct&aelig; line&aelig; (quocunq; modo mo&shy;<lb/>ueatur libra) &longs;i protrahantur, in centrum mundi concurrant.  </s>            
 trum grauitatis fine ponderibus libr&aelig; tant&ugrave;m grauitatis centrum <lb/> 
 erit.  </s>              <s id="id.2.1.9.4.1.4.0"> vbi <lb/>enim pondera hoc modo &longs;unt appen&longs;a, ibi graue&longs;cunt, ac&longs;i in ii&longs;&shy;<lb/>dem punctis centra grauitatum haberent.  </s>            
 <s id="id.2.1.9.4.1.3.0"> Similiter &longs;i pondera in libr&aelig; extremitatibus appendantur, vt <lb/> 
 fieri &longs;olet, idem cueniet; dummodo ex &longs;u&longs;pen&longs;ionum punctis ad <lb/> <s id="id.2.1.9.4.1.5.0"> pr&aelig;terea, qu&aelig; &longs;equun&shy;<lb/>tur, eodem pror&longs;us modo con&longs;iderare poterimus. </s>    </p>       <p id="id.2.1.9.5.0.0.0" type="main">        
 centra grauitatum ponderum duct&aelig; line&aelig; (quocunq; modo mo&shy;<lb/> 
 ueatur libra) &longs;i protrahantur, in centrum mundi concurrant.  </s>              <s id="id.2.1.9.5.1.1.0"> <arrow.to.target n="note8"></arrow.to.target>Quoniam autem huic determinationi vltim&aelig; multa &agrave; nonnullis <lb/>aliter &longs;entientibus dicta officere videntur; idcirco in hac parte ali&shy;<lb/><arrow.to.target n="note9"></arrow.to.target> quantulum immorari oportebit; &amp; pro viribus, non &longs;olum pro&shy;<lb/>priam &longs;ententiam, &longs;ed Archimedem ip&longs;um, qui in hac eadem e&longs;&longs;e <lb/><arrow.to.target n="note10"></arrow.to.target> &longs;ententia videtur, defendere conabor. <pb n="6" xlink:href="pagethumb-la/00000029.JPG"/><figure id="fig10" place="text" xlink:href="figures1577/2000.03.0026.jpg">       </figure> </s>    </p>       <p id="id.2.1.9.6.0.0.0" type="main">        
 <s id="id.2.1.9.4.1.4.0"> vbi <lb/> 
 enim pondera hoc modo &longs;unt appen&longs;a, ibi graue&longs;cunt, ac&longs;i in ii&longs;&shy;<lb/> <s id="id.2.1.9.6.1.1.0"> Ii&longs;dem po&longs;itis, duca&shy;<lb/>tur FCG ip&longs;i AB, &amp; <lb/>horizonti perpendicula&shy;<lb/>ris; &amp; centro C, <expan abbr="&longs;patio&shy;qu&egrave;">&longs;patio&shy;<lb/>que</expan> CA, circulus de&longs;cri<lb/>batur ADFBEG. erunt <lb/>puncta ADBE in circu<lb/>li circumferentia; cum li&shy;<lb/>br&aelig; brachia &longs;int &aelig;qualia.  </s>            
 dem punctis centra grauitatum haberent.  </s>              
 <s id="id.2.1.9.4.1.5.0"> pr&aelig;terea, qu&aelig; &longs;equun&shy;<lb/> <s id="id.2.1.9.6.1.2.0"> <lb/>&amp; quoniam in vnam con<lb/>ueniunt &longs;ententiam, a&longs;&longs;e&shy;<lb/>rentes &longs;cilicet libram DE <lb/>neq; in FG moueri, ne&shy;<lb/>que in DE manere, &longs;ed in AB horizonti &aelig;quidi&longs;tantem redir&eacute;.  </s>            
 tur, eodem pror&longs;us modo con&longs;iderare poterimus. </s>    </p>        
 <p id="id.2.1.9.5.0.0.0" type="main">         <s id="id.2.1.9.6.1.3.0"> <lb/>hanc eorum &longs;ententiam nullo modo con&longs;i&longs;tere po&longs;&longs;e o&longs;tendam.  </s>            
 <s id="id.2.1.9.5.1.1.0"> <arrow.to.target n="note8"></arrow.to.target>Quoniam autem huic determinationi vltim&aelig; multa &agrave; nonnullis <lb/> 
 aliter &longs;entientibus dicta officere videntur; idcirco in hac parte ali&shy;<lb/> <s id="id.2.1.9.6.1.4.0"> <lb/>Non enim, &longs;ed &longs;i quod aiunt, euenerit, vel ideo erit, quia pondus <lb/>D pondere E grauius fuerit, vel &longs;i pondera &longs;unt &aelig;qualia, di&longs;tanti&aelig;, <lb/>quibus &longs;unt po&longs;ita, non erunt &aelig;quales, hoc e&longs;t CD ip&longs;i CE non erit <lb/>&aelig;qualis, &longs;ed maior.  </s>            
 <arrow.to.target n="note9"></arrow.to.target> quantulum immorari oportebit; &amp; pro viribus, non &longs;olum pro&shy;<lb/> 
 priam &longs;ententiam, &longs;ed Archimedem ip&longs;um, qui in hac eadem e&longs;&longs;e <lb/> <s id="id.2.1.9.6.1.5.0"> Qu&ograve;d autem pondera in DE &longs;int &aelig;qualia, &amp; <lb/>di&longs;tantia CD &longs;it &aelig;qualis di&longs;tanti&aelig; CE: h&aelig;c ex &longs;uppo&longs;itione pa&shy;<lb/>tent.  </s>            
 <arrow.to.target n="note10"></arrow.to.target> &longs;ententia videtur, defendere conabor.  
 <pb n="6" xlink:href="pagethumb-la/00000029.JPG"/> <s id="id.2.1.9.6.1.6.0"> Sed quoniam dicunt pondus in D in eo &longs;itu pondere in E <lb/>grauius e&longs;&longs;e in altero &longs;itu deor&longs;um: dum pondera &longs;unt in DE, pun&shy;<lb/>ctum C non erit amplius centrum grauitatis, nam non manent, &longs;i <lb/>ex C &longs;u&longs;pendantur; &longs;ed erit in linea CD, ex tertia primi Archi&shy;<lb/>medis de &aelig;queponderantibus.  </s>            
 <figure id="fig10" place="text" xlink:href="figures1577/2000.03.0026.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.9.6.0.0.0" type="main">         <s id="id.2.1.9.6.1.7.0"> non autem erit in linea CE, cum pon<lb/>dus D grauius &longs;it pondere E. &longs;it igitur in H, in quo &longs;i &longs;u&longs;pendan&shy;<lb/>tur, manebunt.  </s>            
 <s id="id.2.1.9.6.1.1.0"> Ii&longs;dem po&longs;itis, duca&shy;<lb/> 
 tur FCG ip&longs;i AB, &amp; <lb/> <s id="id.2.1.9.6.1.8.0"> Quoniam autem centrum grauitatis ponderum <lb/>in AB connexorum e&longs;t punctum C; ponderum ver&ograve; in DE e&longs;t <lb/>punctum H: dum igitur pondera AB mouentur in DE, centrum <lb/>grauitatis C ver&longs;us D mouebitur, &amp; ad D propius accedet; quod <lb/>e&longs;t impo&longs;sibile: cum pondera eandem inter &longs;e &longs;e &longs;eruent di&longs;tantiam.  </s>            
 horizonti perpendicula&shy;<lb/> 
 ris; &amp; centro C, <expan abbr="&longs;patio&shy;qu&egrave;">&longs;patio&shy;<lb/> <s id="id.2.1.9.6.1.9.0"> <lb/>Vniu&longs;cuiu&longs;q; enim corporis centrum grauitatis in eodem &longs;emper <arrow.to.target n="note11"></arrow.to.target><lb/>e&longs;t &longs;itu re&longs;pectu &longs;ui corporis.  </s>            
 que</expan> CA, circulus de&longs;cri<lb/> 
 batur ADFBEG. erunt <lb/> <s id="id.2.1.9.6.1.10.0"> &amp; quamquam punctum C &longs;it duo&shy;<lb/>rum corporum AB centrum grauitatis, quia tamen inter &longs;e &longs;e ita &agrave; <lb/>libra connexa &longs;unt, vt &longs;emper eodem modo &longs;e &longs;e habeant; Ideo <lb/>punctum C ita eorum erit centrum grauitatis, ac &longs;i vna tantum <pb xlink:href="pagethumb-la/00000030.JPG"/><arrow.to.target n="note12"></arrow.to.target> e&longs;&longs;et magnitudo.  </s>            
 puncta ADBE in circu<lb/> 
 li circumferentia; cum li&shy;<lb/> <s id="id.2.1.9.6.1.11.0"> libra <lb/>enim vna cum ponderi&shy;<lb/>bus vnum tantum conti<lb/>nuum efficit, cuius cen&shy;<lb/>trum grauitatis erit &longs;em&shy;<lb/>per in medio.  </s>            
 br&aelig; brachia &longs;int &aelig;qualia.  </s>              
 <s id="id.2.1.9.6.1.2.0"> <lb/> <s id="id.2.1.9.6.1.12.0"> non igitur <lb/>pondus in D pondere in <lb/>E e&longs;t grauius.  </s>            
 &amp; quoniam in vnam con<lb/> 
 ueniunt &longs;ententiam, a&longs;&longs;e&shy;<lb/> <s id="id.2.1.9.6.1.13.0"> Si autem <lb/>dicerent centrum graui&shy;<lb/>tatis non in linea CD, <lb/>&longs;ed in CE e&longs;&longs;e debere; <lb/>idem eueniet ab&longs;urdum. <figure id="fig11" place="text" xlink:href="figures1577/2000.03.0027.jpg">       </figure> </s>    </p>       <p id="id.2.1.9.7.0.0.0" type="main">        
 rentes &longs;cilicet libram DE <lb/> 
 neq; in FG moueri, ne&shy;<lb/> <s id="id.2.1.9.7.1.1.0"> Amplius &longs;i pondus D <lb/>deor&longs;um mouebitur, pondus E &longs;ur&longs;um mouebit.  </s>            
 que in DE manere, &longs;ed in AB horizonti &aelig;quidi&longs;tantem redir&eacute;.  </s>              
 <s id="id.2.1.9.6.1.3.0"> <lb/> <s id="id.2.1.9.7.1.2.0"> pondus igitur gra&shy;<lb/>uius, qu&agrave;m &longs;it E, in eodemmet &longs;itu ponderi D &aelig;queponderabit, &amp; <lb/>grauia in&aelig;qualia &aelig;quali di&longs;tantia po&longs;ita &aelig;queponderabunt.  </s>            
 hanc eorum &longs;ententiam nullo modo con&longs;i&longs;tere po&longs;&longs;e o&longs;tendam.  </s>              
 <s id="id.2.1.9.6.1.4.0"> <lb/> <s id="id.2.1.9.7.1.3.0"> Adii&shy;<lb/>ciatur ergo ponderi E aliquod graue, ita vt ip&longs;i D contraponde&shy;<lb/>ret, &longs;i ex C &longs;u&longs;pendantur.  </s>            
 Non enim, &longs;ed &longs;i quod aiunt, euenerit, vel ideo erit, quia pondus <lb/> 
 D pondere E grauius fuerit, vel &longs;i pondera &longs;unt &aelig;qualia, di&longs;tanti&aelig;, <lb/> <s id="id.2.1.9.7.1.4.0"> &longs;ed cum &longs;upra o&longs;ten&longs;um &longs;it punctum C <lb/>centrum e&longs;&longs;e grauitatis &aelig;qualium ponderum in DE; &longs;i igitur pon&shy;<lb/><arrow.to.target n="note13"></arrow.to.target> dus E grauius fuerit pondere D, erit centrum grauitatis in linea <lb/>CE. &longs;itq; hoc centrum K. at per definitionem centri grauitatis, &longs;i <lb/>pondera &longs;u&longs;pendantur ex K, manebunt.  </s>            
 quibus &longs;unt po&longs;ita, non erunt &aelig;quales, hoc e&longs;t CD ip&longs;i CE non erit <lb/> 
 &aelig;qualis, &longs;ed maior.  </s>              <s id="id.2.1.9.7.1.5.0"> ergo &longs;i &longs;u&longs;pendantur ex <lb/>C, non manebunt, quod e&longs;t contra hypote&longs;im: &longs;ed pondus E deor<lb/>&longs;um mouebitur.  </s>            
 <s id="id.2.1.9.6.1.5.0"> Qu&ograve;d autem pondera in DE &longs;int &aelig;qualia, &amp; <lb/> 
 di&longs;tantia CD &longs;it &aelig;qualis di&longs;tanti&aelig; CE: h&aelig;c ex &longs;uppo&longs;itione pa&shy;<lb/> <s id="id.2.1.9.7.1.6.0"> qu&ograve;d &longs;i ex C quoque &longs;u&longs;pen&longs;a &aelig;queponderarent; <lb/><arrow.to.target n="note14"></arrow.to.target> vnius magnitudinis duo e&longs;&longs;ent centra grauitatis; quod e&longs;t impo&longs;si<lb/>bile.  </s>            
 tent.  </s>              
 <s id="id.2.1.9.6.1.6.0"> Sed quoniam dicunt pondus in D in eo &longs;itu pondere in E <lb/> <s id="id.2.1.9.7.1.7.0"> Non igitur pondus in E grauius eo, quod e&longs;t in D, ip&longs;i D &aelig;que&shy;<lb/>ponderabit, cum ex puncto C fiat &longs;u&longs;pen&longs;io.  </s>            
 grauius e&longs;&longs;e in altero &longs;itu deor&longs;um: dum pondera &longs;unt in DE, pun&shy;<lb/> 
 ctum C non erit amplius centrum grauitatis, nam non manent, &longs;i <lb/> <s id="id.2.1.9.7.1.8.0"> Pondera ergo in DE <lb/>&aelig;qualia ex eorum grauitatis centro C &longs;u&longs;pen&longs;a, &aelig;queponderabunt, <lb/>manebuntqu&egrave;.  </s>
 ex C &longs;u&longs;pendantur; &longs;ed erit in linea CD, ex tertia primi Archi&shy;<lb/> 
 medis de &aelig;queponderantibus.  </s>              
 <s id="id.2.1.9.6.1.7.0"> non autem erit in linea CE, cum pon<lb/> 
 dus D grauius &longs;it pondere E. &longs;it igitur in H, in quo &longs;i &longs;u&longs;pendan&shy;<lb/> 
 tur, manebunt.  </s>              
 <s id="id.2.1.9.6.1.8.0"> Quoniam autem centrum grauitatis ponderum <lb/> 
 in AB connexorum e&longs;t punctum C; ponderum ver&ograve; in DE e&longs;t <lb/> 
 punctum H: dum igitur pondera AB mouentur in DE, centrum <lb/> 
 grauitatis C ver&longs;us D mouebitur, &amp; ad D propius accedet; quod <lb/> 
 e&longs;t impo&longs;sibile: cum pondera eandem inter &longs;e &longs;e &longs;eruent di&longs;tantiam.  </s>              
 <s id="id.2.1.9.6.1.9.0"> <lb/> 
 Vniu&longs;cuiu&longs;q; enim corporis centrum grauitatis in eodem &longs;emper <arrow.to.target n="note11"></arrow.to.target><lb/> 
 e&longs;t &longs;itu re&longs;pectu &longs;ui corporis.  </s>              
 <s id="id.2.1.9.6.1.10.0"> &amp; quamquam punctum C &longs;it duo&shy;<lb/> 
 rum corporum AB centrum grauitatis, quia tamen inter &longs;e &longs;e ita &agrave; <lb/> 
 libra connexa &longs;unt, vt &longs;emper eodem modo &longs;e &longs;e habeant; Ideo <lb/> 
 punctum C ita eorum erit centrum grauitatis, ac &longs;i vna tantum  
 <pb xlink:href="pagethumb-la/00000030.JPG"/> 
 <arrow.to.target n="note12"></arrow.to.target> e&longs;&longs;et magnitudo.  </s>              
 <s id="id.2.1.9.6.1.11.0"> libra <lb/> 
 enim vna cum ponderi&shy;<lb/> 
 bus vnum tantum conti<lb/> 
 nuum efficit, cuius cen&shy;<lb/> 
 trum grauitatis erit &longs;em&shy;<lb/> 
 per in medio.  </s>              
 <s id="id.2.1.9.6.1.12.0"> non igitur <lb/> 
 pondus in D pondere in <lb/> 
 E e&longs;t grauius.  </s>              
 <s id="id.2.1.9.6.1.13.0"> Si autem <lb/> 
 dicerent centrum graui&shy;<lb/> 
 tatis non in linea CD, <lb/> 
 &longs;ed in CE e&longs;&longs;e debere; <lb/> 
 idem eueniet ab&longs;urdum. <figure id="fig11" place="text" xlink:href="figures1577/2000.03.0027.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.9.7.0.0.0" type="main">         
 <s id="id.2.1.9.7.1.1.0"> Amplius &longs;i pondus D <lb/> 
 deor&longs;um mouebitur, pondus E &longs;ur&longs;um mouebit.  </s>              
 <s id="id.2.1.9.7.1.2.0"> pondus igitur gra&shy;<lb/> 
 uius, qu&agrave;m &longs;it E, in eodemmet &longs;itu ponderi D &aelig;queponderabit, &amp; <lb/> 
 grauia in&aelig;qualia &aelig;quali di&longs;tantia po&longs;ita &aelig;queponderabunt.  </s>              
 <s id="id.2.1.9.7.1.3.0"> Adii&shy;<lb/> 
 ciatur ergo ponderi E aliquod graue, ita vt ip&longs;i D contraponde&shy;<lb/> 
 ret, &longs;i ex C &longs;u&longs;pendantur.  </s>              
 <s id="id.2.1.9.7.1.4.0"> &longs;ed cum &longs;upra o&longs;ten&longs;um &longs;it punctum C <lb/> 
 centrum e&longs;&longs;e grauitatis &aelig;qualium ponderum in DE; &longs;i igitur pon&shy;<lb/> 
 <arrow.to.target n="note13"></arrow.to.target> dus E grauius fuerit pondere D, erit centrum grauitatis in linea <lb/> 
 CE. &longs;itq; hoc centrum K. at per definitionem centri grauitatis, &longs;i <lb/> 
 pondera &longs;u&longs;pendantur ex K, manebunt.  </s>              
 <s id="id.2.1.9.7.1.5.0"> ergo &longs;i &longs;u&longs;pendantur ex <lb/> 
 C, non manebunt, quod e&longs;t contra hypote&longs;im: &longs;ed pondus E deor<lb/> 
 &longs;um mouebitur.  </s>              
 <s id="id.2.1.9.7.1.6.0"> qu&ograve;d &longs;i ex C quoque &longs;u&longs;pen&longs;a &aelig;queponderarent; <lb/> 
 <arrow.to.target n="note14"></arrow.to.target> vnius magnitudinis duo e&longs;&longs;ent centra grauitatis; quod e&longs;t impo&longs;si<lb/> 
 bile.  </s>              
 <s id="id.2.1.9.7.1.7.0"> Non igitur pondus in E grauius eo, quod e&longs;t in D, ip&longs;i D &aelig;que&shy;<lb/> 
 ponderabit, cum ex puncto C fiat &longs;u&longs;pen&longs;io.  </s>              
 <s id="id.2.1.9.7.1.8.0"> Pondera ergo in DE <lb/> 
 &aelig;qualia ex eorum grauitatis centro C &longs;u&longs;pen&longs;a, &aelig;queponderabunt, <lb/> 
 manebuntqu&egrave;.  </s> 
 <s id="id.2.1.9.7.1.9.0"> quod demon&longs;trare fuerat propo&longs;itum. </s>      <s id="id.2.1.9.7.1.9.0"> quod demon&longs;trare fuerat propo&longs;itum. </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.9.7.2.1.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.9.7.2.1.0" type="caption">        
  
 <s id="id.2.1.9.7.2.1.0.capt"> YYY </s>      <s id="id.2.1.9.7.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.9.7.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.9.7.2.3.0" type="caption">        
 <s id="id.2.1.9.7.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.10.1.0.0.0" type="margin">         <s id="id.2.1.9.7.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.10.1.0.0.0" type="margin">        
  
 <s id="id.2.1.10.1.1.1.0"> <margin.target id="note8"></margin.target><emph type="italics"/>Iordanus de Ponderibus.<emph.end type="italics"/> </s>              <s id="id.2.1.10.1.1.1.0"> <margin.target id="note8"></margin.target><emph type="italics"/>Iordanus de Ponderibus.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.10.1.1.2.0"> <margin.target id="note9"></margin.target><emph type="italics"/>Hyerommus Carda nus de &longs;ubtilitate.<emph.end type="italics"/> </s>              <s id="id.2.1.10.1.1.2.0"> <margin.target id="note9"></margin.target><emph type="italics"/>Hyerommus Carda nus de &longs;ubtilitate.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.10.1.1.3.0"> <margin.target id="note10"></margin.target><emph type="italics"/>Nicolaus Tartalea de qu&aelig;&longs;itis, ac inuentionibus.<emph.end type="italics"/> </s>              <s id="id.2.1.10.1.1.3.0"> <margin.target id="note10"></margin.target><emph type="italics"/>Nicolaus Tartalea de qu&aelig;&longs;itis, ac inuentionibus.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.10.1.1.4.0"> <margin.target id="note11"></margin.target>2. <emph type="italics"/>Sup. huius.<emph.end type="italics"/>  </s>              <s id="id.2.1.10.1.1.4.0"> <margin.target id="note11"></margin.target>2. <emph type="italics"/>Sup. huius.<emph.end type="italics"/>  </s>            
  
 <s id="id.2.1.10.1.1.6.0"> <margin.target id="note12"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 4. <emph type="italics"/>primi Archim de Aequep.<emph.end type="italics"/> </s>              <s id="id.2.1.10.1.1.6.0"> <margin.target id="note12"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 4. <emph type="italics"/>primi Archim de Aequep.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.10.1.1.7.0"> <margin.target id="note13"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 3. <emph type="italics"/>primi Archim de Aequep.<emph.end type="italics"/> </s>              <s id="id.2.1.10.1.1.7.0"> <margin.target id="note13"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 3. <emph type="italics"/>primi Archim de Aequep.<emph.end type="italics"/> </s>            
 <s id="id.2.1.10.1.1.8.0"> <margin.target id="note14"></margin.target>1. <emph type="italics"/>Suppo&longs;. huius.<emph.end type="italics"/> </s>            </p>        
 <p id="id.2.1.11.1.0.0.0" type="main">         <s id="id.2.1.10.1.1.8.0"> <margin.target id="note14"></margin.target>1. <emph type="italics"/>Suppo&longs;. huius.<emph.end type="italics"/> </s>            </p>       <p id="id.2.1.11.1.0.0.0" type="main">        
 <s id="id.2.1.11.1.1.1.0"> <arrow.to.target n="note15"></arrow.to.target> Huic autem po&longs;tremo inconuenienti occurrunt dicentes, im&shy;<lb/> 
 po&longs;sibile e&longs;&longs;e addere ip&longs;i E pondus adeo minimum, quin adhuc &longs;i <lb/> <s id="id.2.1.11.1.1.1.0"> <arrow.to.target n="note15"></arrow.to.target> Huic autem po&longs;tremo inconuenienti occurrunt dicentes, im&shy;<lb/>po&longs;sibile e&longs;&longs;e addere ip&longs;i E pondus adeo minimum, quin adhuc &longs;i <lb/>ex C &longs;u&longs;pendantur, pondus E &longs;emper deor&longs;um ver&longs;us G moueatur.  </s>            
 ex C &longs;u&longs;pendantur, pondus E &longs;emper deor&longs;um ver&longs;us G moueatur.  </s>              
 <s id="id.2.1.11.1.1.2.0"> <lb/> <s id="id.2.1.11.1.1.2.0"> <lb/>quod nos fieri po&longs;&longs;e &longs;uppo&longs;uimus, at que fieri po&longs;&longs;e credebamus.  </s>            
 quod nos fieri po&longs;&longs;e &longs;uppo&longs;uimus, at que fieri po&longs;&longs;e credebamus.  </s>              
 <s id="id.2.1.11.1.1.3.0"> ex&shy;<lb/> <s id="id.2.1.11.1.1.3.0"> ex&shy;<lb/>ce&longs;&longs;um enim ponderis D &longs;upra pondus E, cum quantitatis ratio&shy;<lb/>nem habeat, non &longs;olum minimum e&longs;&longs;e, verum in infinitum diuidi <lb/>po&longs;&longs;e immaginabamur, quod quidem ip&longs;i, non &longs;olum minimum, <pb n="7" xlink:href="pagethumb-la/00000031.JPG"/>&longs;ed ne minimum quidem e&longs;&longs;e, cum reperiri non po&longs;sit, hoc mo&shy;<lb/>do demon&longs;trare nituntur. <figure id="fig12" place="text" xlink:href="figures1577/2000.03.0028.jpg">       </figure> </s>    </p>       <p id="id.2.1.11.2.0.0.0" type="main">        
 ce&longs;&longs;um enim ponderis D &longs;upra pondus E, cum quantitatis ratio&shy;<lb/> 
 nem habeat, non &longs;olum minimum e&longs;&longs;e, verum in infinitum diuidi <lb/> 
 po&longs;&longs;e immaginabamur, quod quidem ip&longs;i, non &longs;olum minimum,  
 <pb n="7" xlink:href="pagethumb-la/00000031.JPG"/> 
 &longs;ed ne minimum quidem e&longs;&longs;e, cum reperiri non po&longs;sit, hoc mo&shy;<lb/> 
 do demon&longs;trare nituntur. <figure id="fig12" place="text" xlink:href="figures1577/2000.03.0028.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.11.2.0.0.0" type="main">         
 <s id="id.2.1.11.2.1.1.0"> Exponantur eadem.  </s>              <s id="id.2.1.11.2.1.1.0"> Exponantur eadem.  </s>            
 <s id="id.2.1.11.2.1.2.0"> <lb/> 
 &agrave; puncti&longs;qu&egrave; DE hori&shy;<lb/> <s id="id.2.1.11.2.1.2.0"> <lb/>&agrave; puncti&longs;qu&egrave; DE hori&shy;<lb/>zonti <expan abbr="perp&etilde;diculares">perpendiculares</expan> du <lb/><expan abbr="c&atilde;tur">cantur</expan> DHEK, atq; alius <lb/>&longs;it circulus LDM, cu&shy;<lb/>ius <expan abbr="centr&utilde;">centrum</expan> N, qui FDG <lb/>in puncto D contingat, <lb/>ip&longs;iq; FDG &longs;it &aelig;qualis: <lb/>erit NC recta linea.  </s>            
 zonti <expan abbr="perp&etilde;diculares">perpendiculares</expan> du <lb/> 
 <expan abbr="c&atilde;tur">cantur</expan> DHEK, atq; alius <lb/> <s id="id.2.1.11.2.1.3.0"> &amp; <arrow.to.target n="note16"></arrow.to.target><lb/>quoniam angulus KEC <lb/>angulo HDN e&longs;t &aelig;qua <arrow.to.target n="note17"></arrow.to.target><lb/>lis, angulusq; CEG an&shy;<lb/>gulo NDM e&longs;t etiam <lb/>&aelig;qualis; cum &agrave; &longs;emidiametris, &aelig;qualibusq; circumferentiis conti&shy;<lb/>neatur; erit reliquus mixtu&longs;qu&egrave; angulus KEG reliquo mixtoqu&egrave; <lb/>HDM &aelig;qualis.  </s>            
 &longs;it circulus LDM, cu&shy;<lb/> 
 ius <expan abbr="centr&utilde;">centrum</expan> N, qui FDG <lb/> <s id="id.2.1.11.2.1.4.0"> &amp; quia &longs;upponunt, qu&ograve; minor e&longs;t angulus linea <lb/>horizonti perpendiculari, &amp; circumferentia contentus, e&ograve; pondus <lb/>in eo &longs;itu grauius e&longs;&longs;e.  </s>            
 in puncto D contingat, <lb/> 
 ip&longs;iq; FDG &longs;it &aelig;qualis: <lb/> <s id="id.2.1.11.2.1.5.0"> vt qu&ograve; minor e&longs;t angulus HD, &amp; circumfe<lb/>rentia DG contentus angulo KEG, hoc e&longs;t angulo HDM; ita &longs;e<lb/>cundum hanc proportionem pondus in D grauius e&longs;&longs;e pondere in <lb/>E.  </s>    
 erit NC recta linea.  </s>              
 <s id="id.2.1.11.2.1.3.0"> &amp; <arrow.to.target n="note16"></arrow.to.target><lb/> <s id="id.2.1.11.2.1.5.0.a"> Proportio autem anguli MDH ad angulum HDG minor e&longs;t <lb/>qualibet proportione, qu&aelig; &longs;it inter maiorem, &amp; minorem quanti<lb/>tatem: ergo proportio ponderum DE omnium proportionum mi<lb/>nima erit.  </s>            
 quoniam angulus KEC <lb/> 
 angulo HDN e&longs;t &aelig;qua <arrow.to.target n="note17"></arrow.to.target><lb/> <s id="id.2.1.11.2.1.6.0"> immo neq; erit fer&egrave; proportio, cum &longs;it omnium pro <lb/>portionum minima.  </s>            
 lis, angulusq; CEG an&shy;<lb/> 
 gulo NDM e&longs;t etiam <lb/> <s id="id.2.1.11.2.1.7.0"> qu&ograve;d autem proportio MDH ad HDG &longs;it <lb/>omnium minima, ex hac nece&longs;sitate o&longs;tendunt; quia MDH exce<lb/>dit HDG angulo curuilineo MDG, qui quidem angulus omnium <lb/>angulorum rectilineorum minimus exi&longs;tit: ergo cum non po&longs;sit da <lb/>ri angulus minor MDG, erit proportio MDH ad HDG <expan abbr="omni&utilde;">omnium</expan> <lb/>proportionum minima.  </s>            
 &aelig;qualis; cum &agrave; &longs;emidiametris, &aelig;qualibusq; circumferentiis conti&shy;<lb/> 
 neatur; erit reliquus mixtu&longs;qu&egrave; angulus KEG reliquo mixtoqu&egrave; <lb/> <s id="id.2.1.11.2.1.8.0"> qu&aelig; ratio inutilis valde videtur e&longs;&longs;e; quia <lb/>quamquam angulus MDG &longs;it omnibus rectilineis angulis minor, <lb/>non idcirco &longs;equitur, ab&longs;olut&egrave;, &longs;impliciterq; omnium e&longs;&longs;e <expan abbr="angulor&utilde;">angulorum</expan> <lb/>minimum: nam ducatur &agrave; puncto D linea DO ip&longs;i NC perpendicu<lb/>laris, h&aelig;c vtra&longs;q; tanget circumferentias LDM FDG in puncto <arrow.to.target n="note18"></arrow.to.target><pb xlink:href="pagethumb-la/00000032.JPG"/>D. quia ver&ograve; circumfe<lb/>renti&aelig; &longs;unt &aelig;quales, erit <lb/>angulus MDO mixtus <lb/>angulo ODG mixto <lb/>&aelig;qualis; alter ergo an<lb/>gulus, vt ODG minor <lb/>erit MDG, hoc e&longs;t mi <lb/>nor minimo.  </s>            
 HDM &aelig;qualis.  </s>              
 <s id="id.2.1.11.2.1.4.0"> &amp; quia &longs;upponunt, qu&ograve; minor e&longs;t angulus linea <lb/> <s id="id.2.1.11.2.1.9.0"> angulus <lb/>deinde OGH minor <lb/>erit angulo MDH; qua <lb/>re ODH ad angulum <lb/><arrow.to.target n="note19"></arrow.to.target> HDG minorem habe<lb/>bit <expan abbr="proportion&etilde;">proportionem</expan>, qu&agrave;m <lb/><figure id="fig13" place="text" xlink:href="figures1577/2000.03.0029.jpg">       </figure><lb/>MDH ad eundem HDG. dabitur ergo quoqu&egrave; proportio mi&shy;<lb/>nor minima, quam in infinitum adhuc minorem ita o&longs;tende&shy;<lb/>mus.  </s>            
 horizonti perpendiculari, &amp; circumferentia contentus, e&ograve; pondus <lb/> 
 in eo &longs;itu grauius e&longs;&longs;e.  </s>              <s id="id.2.1.11.2.1.10.0"> De&longs;cribatur circulus DR, cuius centrum E, &amp; &longs;emidiame&shy;<lb/><arrow.to.target n="note20"></arrow.to.target> ter ED. continget circumferentia DR circumferentiam DG in <lb/><arrow.to.target n="note21"></arrow.to.target> puncto D, lineamqu&egrave; DO in puncto D; quare minor erit angu&shy;<lb/>lus RDG angulo ODG. &longs;imiliter &amp; angulus RDH angulo <lb/>ODH.  </s>    
 <s id="id.2.1.11.2.1.5.0"> vt qu&ograve; minor e&longs;t angulus HD, &amp; circumfe<lb/> 
 rentia DG contentus angulo KEG, hoc e&longs;t angulo HDM; ita &longs;e<lb/> <s id="id.2.1.11.2.1.10.0.a"> minorem igitur proportionem habebit RDH ad HDG, <lb/>qu&agrave;m ODH ad HDG.  </s>    
 cundum hanc proportionem pondus in D grauius e&longs;&longs;e pondere in <lb/> 
 E.  </s>      <s id="id.2.1.11.2.1.10.0.b"> Accipiatur deinde inter EC vtcun&shy;<lb/>que punctum P, ex quo in di&longs;tantia PD alia de&longs;cribatur circum&shy;<lb/>ferentia DQ, qu&aelig; circumferentiam DR, circumferentiamqu&egrave; <lb/>DG in puncto D continget; &amp; angulus QDH minor erit <lb/>angulo RDH: ergo QDH ad HDG minorem habebit propor<lb/>tionem, qu&agrave;m RDH ad HDG. eodemqu&egrave; pror&longs;us modo, &longs;i <lb/>inter PC aliud accipiatur punctum, &amp; inter hoc &amp;C aliud, &amp; &longs;ic <lb/>deinceps, infinit&aelig; de&longs;cribentur circumferenti&aelig; inter DO, &amp; cir<lb/>cumferentiam DG; ex quibus proportionem in infinitum &longs;emper <lb/>minorem inueniemus.  </s>            
 <s id="id.2.1.11.2.1.5.0.a"> Proportio autem anguli MDH ad angulum HDG minor e&longs;t <lb/> 
 qualibet proportione, qu&aelig; &longs;it inter maiorem, &amp; minorem quanti<lb/> <s id="id.2.1.11.2.1.11.0"> atque ideo proportionem ponderis in D <lb/>ad pondus in E non adeo minorem e&longs;&longs;e &longs;equitur, quin ad infini <lb/>tum ip&longs;a &longs;emper minorem reperiri po&longs;sit.  </s>            
 tatem: ergo proportio ponderum DE omnium proportionum mi<lb/> 
 nima erit.  </s>              <s id="id.2.1.11.2.1.12.0"> &amp; quia angulus MDG <lb/>in infinitum diuidi pote&longs;t; exce&longs;&longs;us quoque grauitatis D &longs;upra E <lb/>diuidi ad infinitum poterit.  </s>    
 <s id="id.2.1.11.2.1.6.0"> immo neq; erit fer&egrave; proportio, cum &longs;it omnium pro <lb/> 
 portionum minima.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.11.2.2.1.0" type="caption">        
 <s id="id.2.1.11.2.1.7.0"> qu&ograve;d autem proportio MDH ad HDG &longs;it <lb/> 
 omnium minima, ex hac nece&longs;sitate o&longs;tendunt; quia MDH exce<lb/> 
 dit HDG angulo curuilineo MDG, qui quidem angulus omnium <lb/> 
 angulorum rectilineorum minimus exi&longs;tit: ergo cum non po&longs;sit da <lb/> 
 ri angulus minor MDG, erit proportio MDH ad HDG <expan abbr="omni&utilde;">omnium</expan> <lb/> 
 proportionum minima.  </s>              
 <s id="id.2.1.11.2.1.8.0"> qu&aelig; ratio inutilis valde videtur e&longs;&longs;e; quia <lb/> 
 quamquam angulus MDG &longs;it omnibus rectilineis angulis minor, <lb/> 
 non idcirco &longs;equitur, ab&longs;olut&egrave;, &longs;impliciterq; omnium e&longs;&longs;e <expan abbr="angulor&utilde;">angulorum</expan> <lb/> 
 minimum: nam ducatur &agrave; puncto D linea DO ip&longs;i NC perpendicu<lb/> 
 laris, h&aelig;c vtra&longs;q; tanget circumferentias LDM FDG in puncto <arrow.to.target n="note18"></arrow.to.target> 
 <pb xlink:href="pagethumb-la/00000032.JPG"/> 
 D. quia ver&ograve; circumfe<lb/> 
 renti&aelig; &longs;unt &aelig;quales, erit <lb/> 
 angulus MDO mixtus <lb/> 
 angulo ODG mixto <lb/> 
 &aelig;qualis; alter ergo an<lb/> 
 gulus, vt ODG minor <lb/> 
 erit MDG, hoc e&longs;t mi <lb/> 
 nor minimo.  </s>              
 <s id="id.2.1.11.2.1.9.0"> angulus <lb/> 
 deinde OGH minor <lb/> 
 erit angulo MDH; qua <lb/> 
 re ODH ad angulum <lb/> 
 <arrow.to.target n="note19"></arrow.to.target> HDG minorem habe<lb/> 
 bit <expan abbr="proportion&etilde;">proportionem</expan>, qu&agrave;m <lb/> 
 <figure id="fig13" place="text" xlink:href="figures1577/2000.03.0029.jpg">       </figure><lb/> 
 MDH ad eundem HDG. dabitur ergo quoqu&egrave; proportio mi&shy;<lb/> 
 nor minima, quam in infinitum adhuc minorem ita o&longs;tende&shy;<lb/> 
 mus.  </s>              
 <s id="id.2.1.11.2.1.10.0"> De&longs;cribatur circulus DR, cuius centrum E, &amp; &longs;emidiame&shy;<lb/> 
 <arrow.to.target n="note20"></arrow.to.target> ter ED. continget circumferentia DR circumferentiam DG in <lb/> 
 <arrow.to.target n="note21"></arrow.to.target> puncto D, lineamqu&egrave; DO in puncto D; quare minor erit angu&shy;<lb/> 
 lus RDG angulo ODG. &longs;imiliter &amp; angulus RDH angulo <lb/> 
 ODH.  </s>      
 <s id="id.2.1.11.2.1.10.0.a"> minorem igitur proportionem habebit RDH ad HDG, <lb/> 
 qu&agrave;m ODH ad HDG.  </s>      
 <s id="id.2.1.11.2.1.10.0.b"> Accipiatur deinde inter EC vtcun&shy;<lb/> 
 que punctum P, ex quo in di&longs;tantia PD alia de&longs;cribatur circum&shy;<lb/> 
 ferentia DQ, qu&aelig; circumferentiam DR, circumferentiamqu&egrave; <lb/> 
 DG in puncto D continget; &amp; angulus QDH minor erit <lb/> 
 angulo RDH: ergo QDH ad HDG minorem habebit propor<lb/> 
 tionem, qu&agrave;m RDH ad HDG. eodemqu&egrave; pror&longs;us modo, &longs;i <lb/> 
 inter PC aliud accipiatur punctum, &amp; inter hoc &amp;C aliud, &amp; &longs;ic <lb/> 
 deinceps, infinit&aelig; de&longs;cribentur circumferenti&aelig; inter DO, &amp; cir<lb/> 
 cumferentiam DG; ex quibus proportionem in infinitum &longs;emper <lb/> 
 minorem inueniemus.  </s>              
 <s id="id.2.1.11.2.1.11.0"> atque ideo proportionem ponderis in D <lb/> 
 ad pondus in E non adeo minorem e&longs;&longs;e &longs;equitur, quin ad infini <lb/> 
 tum ip&longs;a &longs;emper minorem reperiri po&longs;sit.  </s>              
 <s id="id.2.1.11.2.1.12.0"> &amp; quia angulus MDG <lb/> 
 in infinitum diuidi pote&longs;t; exce&longs;&longs;us quoque grauitatis D &longs;upra E <lb/> 
 diuidi ad infinitum poterit.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.11.2.2.1.0" type="caption">         
 <s id="id.2.1.11.2.2.1.0.capt"> YYY </s>      <s id="id.2.1.11.2.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.11.2.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.11.2.2.3.0" type="caption">        
 <s id="id.2.1.11.2.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.12.1.0.0.0" type="margin">         <s id="id.2.1.11.2.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.12.1.0.0.0" type="margin">        
  
 <s id="id.2.1.12.1.1.1.0"> <margin.target id="note15"></margin.target><emph type="italics"/>Tartalea &longs;exta propo&longs;itione octaui libri.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.1.0"> <margin.target id="note15"></margin.target><emph type="italics"/>Tartalea &longs;exta propo&longs;itione octaui libri.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.12.1.1.2.0"> <margin.target id="note16"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 12. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.2.0"> <margin.target id="note16"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 12. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.12.1.1.3.0"> <margin.target id="note17"></margin.target>29. <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.3.0"> <margin.target id="note17"></margin.target>29. <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.12.1.1.4.0"> <margin.target id="note18"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18. <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.4.0"> <margin.target id="note18"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18. <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.12.1.1.5.0"> <margin.target id="note19"></margin.target>8. <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.5.0"> <margin.target id="note19"></margin.target>8. <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.12.1.1.6.0"> <margin.target id="note20"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 11. <emph type="italics"/>tertit.<emph.end type="italics"/> </s>              <s id="id.2.1.12.1.1.6.0"> <margin.target id="note20"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 11. <emph type="italics"/>tertit.<emph.end type="italics"/> </s>            
 <s id="id.2.1.12.1.1.7.0"> <margin.target id="note21"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.13.1.0.0.0" type="main">         <s id="id.2.1.12.1.1.7.0"> <margin.target id="note21"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.13.1.0.0.0" type="main">        <pb n="8" xlink:href="pagethumb-la/00000033.JPG"/>      
 <pb n="8" xlink:href="pagethumb-la/00000033.JPG"/> 
         <s id="id.2.1.13.1.2.1.0"> Sed neque pr&aelig;tereundum <lb/>e&longs;t, ip&longs;os in demon&longs;tratio&shy;<lb/>ne angulum KEG maiorem <lb/>e&longs;&longs;e angulo HDG, tanquam <lb/>notum accepi&longs;&longs;e.  </s>            
 <s id="id.2.1.13.1.2.1.0"> Sed neque pr&aelig;tereundum <lb/> 
 e&longs;t, ip&longs;os in demon&longs;tratio&shy;<lb/> <s id="id.2.1.13.1.2.2.0"> quod e&longs;t <lb/>quidem verum, &longs;i DHEK <lb/>inter &longs;e &longs;e &longs;int &aelig;quidi&longs;tan&shy;<lb/>tes.  </s>            
 ne angulum KEG maiorem <lb/> 
 e&longs;&longs;e angulo HDG, tanquam <lb/> <s id="id.2.1.13.1.2.3.0"> Quoniam autem (vt <lb/>ip&longs;i quoque &longs;upponunt) li&shy;<lb/>ne&aelig; DHEK in centrum <lb/>mundi conueniunt; line&aelig; <lb/>DHEK &aelig;quidi&longs;tantes nun<lb/>quam erunt, &amp; angulus KEG <lb/>angulo HDG non &longs;olum <lb/>maior erit, &longs;ed minor.  </s>            
 notum accepi&longs;&longs;e.  </s>              
 <s id="id.2.1.13.1.2.2.0"> quod e&longs;t <lb/> <s id="id.2.1.13.1.2.4.0"> vt <lb/>exempli gratia, producatur <lb/>FG v&longs;que ad centrum mun<lb/>di, quod &longs;it S; <expan abbr="connectan&shy;turqu&eacute;">connectan&shy;<lb/>turque</expan> DSES. o&longs;tenden&shy;<lb/>dum e&longs;t angulum SEG mi<lb/>norem e&longs;&longs;e angulo SDG.  </s>    
 quidem verum, &longs;i DHEK <lb/> 
 inter &longs;e &longs;e &longs;int &aelig;quidi&longs;tan&shy;<lb/> <s id="id.2.1.13.1.2.4.0.a"> du<lb/><figure id="fig14" place="text" xlink:href="figures1577/2000.03.0030.jpg">       </figure><lb/>catur &agrave; puncto E linea ET circulum DGEF contingens, ab eo <lb/>demqu&eacute; puncto ip&longs;i DS &aelig;quidi&longs;tans ducatur EV.  </s>    
 tes.  </s>              
 <s id="id.2.1.13.1.2.3.0"> Quoniam autem (vt <lb/> <s id="id.2.1.13.1.2.4.0.b"> Quoniam igi<lb/>tur EVDS inter &longs;e &longs;e &longs;unt &aelig;quidi&longs;tantes: &longs;imiliter ETDO &aelig;qui <lb/>di&longs;tantes: erit angulus VET angulo SDO &aelig;qualis.  </s>            
 ip&longs;i quoque &longs;upponunt) li&shy;<lb/> 
 ne&aelig; DHEK in centrum <lb/> <s id="id.2.1.13.1.2.5.0"> &amp; angulus <lb/>TEG angulo ODM e&longs;t &aelig;qualis; cum &agrave; lineis contingentibus, <lb/>circumferentii&longs;qu&eacute; &aelig;qualibus contineatur: totus ergo angulus <lb/>VEG angulo SDM &aelig;qualis erit.  </s>            
 mundi conueniunt; line&aelig; <lb/> 
 DHEK &aelig;quidi&longs;tantes nun<lb/> <s id="id.2.1.13.1.2.6.0"> Auferatur ab angulo SDM <lb/>angulus curuilineus MDG; ab angulo autem VEG angulus au&shy;<lb/>feratur VES; &amp; angulus VES rectilineus maior e&longs;t curuilineo <lb/>MDG; erit reliquus angulus SEG minor angulo SDG.  </s>    
 quam erunt, &amp; angulus KEG <lb/> 
 angulo HDG non &longs;olum <lb/> <s id="id.2.1.13.1.2.6.0.a"> <lb/>Quare ex ip&longs;orum &longs;uppo&longs;itionibus non &longs;olum pondus in D gra&shy;<lb/>uius erit pondere in E; ver&ugrave;m &egrave; conuer&longs;o, pondus in E ip&longs;o D <lb/>grauius exi&longs;tet.  </s>    
 maior erit, &longs;ed minor.  </s>              
 <s id="id.2.1.13.1.2.4.0"> vt <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.13.1.3.1.0" type="caption">        
 exempli gratia, producatur <lb/> 
 FG v&longs;que ad centrum mun<lb/> <s id="id.2.1.13.1.3.1.0.capt"> YYY </s>    </p>       <pb xlink:href="pagethumb-la/00000034.JPG"/>       <p id="id.2.1.13.3.0.0.0" type="main">        
 di, quod &longs;it S; <expan abbr="connectan&shy;turqu&eacute;">connectan&shy;<lb/> 
 turque</expan> DSES. o&longs;tenden&shy;<lb/> <s id="id.2.1.13.3.1.1.0"> Rationes tamen af<lb/>ferunt, quibus demon<lb/>&longs;trare nituntur, libram <lb/>DE in AB horizon&shy;<lb/>ti &aelig;quidi&longs;tantem ex <lb/>nece&longs;sitate redire.  </s>            
 dum e&longs;t angulum SEG mi<lb/> 
 norem e&longs;&longs;e angulo SDG.  </s>      <s id="id.2.1.13.3.1.2.0"> <expan abbr="Pri&shy;m&ugrave;m">Pri&shy;<lb/>mum</expan> quidem o&longs;ten&shy;<lb/>dunt, idem pondus <lb/>grauius e&longs;&longs;e in A, <lb/>qu&agrave;min alio &longs;itu, quem <lb/>&aelig;qualitatis &longs;itum no&shy;<lb/>minant, cum linea <lb/>AB &longs;it horizonti &aelig;&shy;<lb/><figure id="fig15" place="text" xlink:href="figures1577/2000.03.0031.jpg">       </figure><lb/>quidi&longs;tans.  </s>            
 <s id="id.2.1.13.1.2.4.0.a"> du<lb/> 
 <figure id="fig14" place="text" xlink:href="figures1577/2000.03.0030.jpg">       </figure><lb/> <s id="id.2.1.13.3.1.3.0"> deinde qu&ograve; propius e&longs;t ip&longs;i A, quouis alio remotiori <lb/>grauius e&longs;&longs;e.  </s>            
 catur &agrave; puncto E linea ET circulum DGEF contingens, ab eo <lb/> 
 demqu&eacute; puncto ip&longs;i DS &aelig;quidi&longs;tans ducatur EV.  </s>      <s id="id.2.1.13.3.1.4.0"> Vt pondus in A grauius e&longs;&longs;e, qu&agrave;m in D; &amp; in D, <lb/>qu&agrave;m in L. &longs;imiliter in A grauius, quam in N; &amp; in N grauius, <lb/>qu&agrave;m in M.  </s>    
 <s id="id.2.1.13.1.2.4.0.b"> Quoniam igi<lb/> 
 tur EVDS inter &longs;e &longs;e &longs;unt &aelig;quidi&longs;tantes: &longs;imiliter ETDO &aelig;qui <lb/> <s id="id.2.1.13.3.1.4.0.a"> Vnum tant&ugrave;m con&longs;iderando pondus in altero libr&aelig; <lb/><arrow.to.target n="note22"></arrow.to.target> brachio &longs;ur&longs;um deor&longs;umq; moto.  </s>            
 di&longs;tantes: erit angulus VET angulo SDO &aelig;qualis.  </s>              
 <s id="id.2.1.13.1.2.5.0"> &amp; angulus <lb/> <s id="id.2.1.13.3.1.5.0"> Quia (inquiunt) po&longs;itat rutina <lb/>in CF, pondus in A longius e&longs;t &agrave; trutina, qu&agrave;m in D: &amp; in D <lb/>longius, qu&agrave;m in L. ductis enim DO LP ip&longs;i CF perpendicula&shy;<lb/><arrow.to.target n="note23"></arrow.to.target> ribus, li&lt;*&gt;ea AC maior e&longs;t, qu&agrave;m DO, &amp; DO ip&longs;a LP. quod <lb/><arrow.to.target n="note24"></arrow.to.target> idem euenit in punctis NM.  </s>    
 TEG angulo ODM e&longs;t &aelig;qualis; cum &agrave; lineis contingentibus, <lb/> 
 circumferentii&longs;qu&eacute; &aelig;qualibus contineatur: totus ergo angulus <lb/> <s id="id.2.1.13.3.1.5.0.a"> deinde ex quo loco (aiunt) pon<lb/>dus velocius mouetur, ibi grauius e&longs;t; velocius autem ex A, qu&agrave;m <lb/>ab alio &longs;itu mouetur; ergo in A grauius e&longs;t.  </s>            
 VEG angulo SDM &aelig;qualis erit.  </s>              
 <s id="id.2.1.13.1.2.6.0"> Auferatur ab angulo SDM <lb/> <s id="id.2.1.13.3.1.6.0"> &longs;imili modo, qu&ograve; <lb/>propius e&longs;t ip&longs;i A, velocius quoque mouetur; ergo in D gra&shy;<lb/><arrow.to.target n="note25"></arrow.to.target> uius erit, qu&agrave;m in L.  </s>    
 angulus curuilineus MDG; ab angulo autem VEG angulus au&shy;<lb/> 
 feratur VES; &amp; angulus VES rectilineus maior e&longs;t curuilineo <lb/> <s id="id.2.1.13.3.1.6.0.a"> Altera deinde cau&longs;a, quam ex rectiori, &amp; obli <lb/><arrow.to.target n="note26"></arrow.to.target> quiori motu deducunt, e&longs;t; qu&ograve; pondus in arcubus &aelig;qualibus re&shy;<lb/>ctius de&longs;cendit, grauius e&longs;&longs;e videtur; cum pondus liberum, atq; <lb/><arrow.to.target n="note27"></arrow.to.target> &longs;olutum &longs;uapt&egrave; natura rect&egrave; moueatur; &longs;ed in A rectius de&longs;cen<lb/>dit; ergo in A grauius erit.  </s>            
 MDG; erit reliquus angulus SEG minor angulo SDG.  </s>      
 <s id="id.2.1.13.1.2.6.0.a"> <lb/> <s id="id.2.1.13.3.1.7.0"> hocq; o&longs;tendunt accipiendo arcum <lb/>AN arcui LD &aelig;qualem; &agrave; puncti&longs;q; NL line&aelig; FG (quam <lb/>etiam directionis vocant) &aelig;quidi&longs;tantes ducantur NRLQ, qu&aelig; <lb/>lineas AB DO &longs;ecent in QR; &amp; &agrave; puncto N ip&longs;i FG perpen<lb/>dicularis ducatur NT. rect&egrave;q; demon&longs;trant LQ ip&longs;i PO &aelig;qua<lb/>lem e&longs;&longs;e, &amp; NR ip&longs;i CT; lineamq; NR ip&longs;a LQ maiorem e&longs;&longs;e.  </s>            
 Quare ex ip&longs;orum &longs;uppo&longs;itionibus non &longs;olum pondus in D gra&shy;<lb/> 
 uius erit pondere in E; ver&ugrave;m &egrave; conuer&longs;o, pondus in E ip&longs;o D <lb/> <s id="id.2.1.13.3.1.8.0"> <lb/>Quoniam autem de&longs;cen&longs;u; ponderis ex A v&longs;q; ad N per circum&shy;<pb n="9" xlink:href="pagethumb-la/00000035.JPG"/>ferentiam AN maiorem portionem line&aelig; FG pertran&longs;it (quod <lb/>ip&longs;i vocant capere de directo) qu&agrave;m de&longs;cen&longs;us ex L in D per cir<lb/>cumferentiam LD; c&ugrave;m de&longs;cen&longs;us AN lineam CT pertran&longs;eat, <lb/>de&longs;cen&longs;us ver&ograve; LD lineam PO; &amp; CT maior e&longs;t PO; rectior erit <lb/>de&longs;cen&longs;us AN, qu&aacute;m de&longs;cen&longs;us LD.  </s>    
 grauius exi&longs;tet.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.13.3.1.8.0.a"> grauius ergo erit pondus <lb/>in A, qu&agrave;m in L, &amp; in quouis alio &longs;itu.  </s>            
 <p id="id.2.1.13.1.3.1.0" type="caption">         
 <s id="id.2.1.13.1.3.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.13.3.1.9.0"> eodemq; pror&longs;us <lb/>modo o&longs;tendunt, qu&ograve; propius e&longs;t ip&longs;i A, grauius e&longs;&longs;e.  </s>            
 <pb xlink:href="pagethumb-la/00000034.JPG"/> 
         <s id="id.2.1.13.3.1.10.0"> <lb/>Vt &longs;int circumferenti&aelig; LD DA inter &longs;e &longs;e &aelig;quales, &amp; &agrave; puncto <lb/>D ip&longs;i AB perpendicularis ducatur DR; erit DR ip&longs;i CO &aelig;qua <arrow.to.target n="note28"></arrow.to.target><lb/>lis.  </s>            
 <p id="id.2.1.13.3.0.0.0" type="main">         
 <s id="id.2.1.13.3.1.1.0"> Rationes tamen af<lb/> <s id="id.2.1.13.3.1.11.0"> lineam deinde DR ip&longs;a LQ maiorem e&longs;&longs;e demon&longs;trant.  </s>            
 ferunt, quibus demon<lb/> 
 &longs;trare nituntur, libram <lb/> <s id="id.2.1.13.3.1.12.0"> di&shy;<lb/>cuntq; de&longs;cen&longs;um DA magis capere de directo de&longs;cen&longs;u LD, ma<lb/>ior enim e&longs;t linea CO, qu&agrave;m OP; quare pondus grauius erit <lb/>in D, qu&agrave;m in L. quod ip&longs;um euenit in punctis NM.  </s>    
 DE in AB horizon&shy;<lb/> 
 ti &aelig;quidi&longs;tantem ex <lb/> <s id="id.2.1.13.3.1.12.0.a"> Suppo&shy;<lb/>&longs;itionem itaq;, qua libram DE in AB redire demon&longs;trant, vt <arrow.to.target n="note29"></arrow.to.target><lb/>notam, manife&longs;tamq; proferunt.  </s>            
 nece&longs;sitate redire.  </s>              
 <s id="id.2.1.13.3.1.2.0"> <expan abbr="Pri&shy;m&ugrave;m">Pri&shy;<lb/> <s id="id.2.1.13.3.1.13.0"> Nemp&egrave; Secund&ugrave;m &longs;itum pon<lb/>dus grauius e&longs;&longs;e, quanto in eodem &longs;itu minus obliquus e&longs;t de&longs;cen<lb/>&longs;us.  </s>            
 mum</expan> quidem o&longs;ten&shy;<lb/> 
 dunt, idem pondus <lb/> <s id="id.2.1.13.3.1.14.0"> huiu&longs;q; reditus cau&longs;am eam e&longs;&longs;e dicunt; Quoniam &longs;cilicet <arrow.to.target n="note30"></arrow.to.target><lb/>de&longs;cen&longs;us ponderis in D rectior e&longs;t de&longs;cen&longs;u ponderis in E, c&ugrave;m <lb/>minus capiat de directo pondus in E de&longs;cendendo, qu&agrave;m pon<arrow.to.target n="note31"></arrow.to.target><lb/>dus in D &longs;im liter de&longs;cendendo.  </s>            
 grauius e&longs;&longs;e in A, <lb/> 
 qu&agrave;min alio &longs;itu, quem <lb/> <s id="id.2.1.13.3.1.15.0"> Vt &longs;i arcus EV &longs;it ip&longs;i DA <lb/>&aelig;qualis, ducanturq; VH ET ip&longs;i FG perpendiculares; maior <lb/>erit DR, qu&agrave;m TH. quare per &longs;uppo&longs;itionem pondus in D ra<lb/>tione &longs;itus grauius erit pondere in E.  </s>    
 &aelig;qualitatis &longs;itum no&shy;<lb/> 
 minant, cum linea <lb/> <s id="id.2.1.13.3.1.15.0.a"> pondus ergo in D, c&ugrave;m &longs;it <lb/>grauius, deor&longs;um mouebitur; pondus ver&ograve; in E &longs;ur&longs;um, donec li <lb/>bra DE in AB redeat. </s>    
 AB &longs;it horizonti &aelig;&shy;<lb/> 
 <figure id="fig15" place="text" xlink:href="figures1577/2000.03.0031.jpg">       </figure><lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.13.3.2.1.0" type="caption">        
 quidi&longs;tans.  </s>              
 <s id="id.2.1.13.3.1.3.0"> deinde qu&ograve; propius e&longs;t ip&longs;i A, quouis alio remotiori <lb/> <s id="id.2.1.13.3.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.14.1.0.0.0" type="margin">        
 grauius e&longs;&longs;e.  </s>              
 <s id="id.2.1.13.3.1.4.0"> Vt pondus in A grauius e&longs;&longs;e, qu&agrave;m in D; &amp; in D, <lb/> <s id="id.2.1.14.1.1.1.0"> <margin.target id="note22"></margin.target><emph type="italics"/>Cardanus primo de &longs;ubtilitate.<emph.end type="italics"/> </s>            
 qu&agrave;m in L. &longs;imiliter in A grauius, quam in N; &amp; in N grauius, <lb/> 
 qu&agrave;m in M.  </s>      <s id="id.2.1.14.1.1.2.0"> <margin.target id="note23"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 15. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>            
 <s id="id.2.1.13.3.1.4.0.a"> Vnum tant&ugrave;m con&longs;iderando pondus in altero libr&aelig; <lb/> 
 <arrow.to.target n="note22"></arrow.to.target> brachio &longs;ur&longs;um deor&longs;umq; moto.  </s>              <s id="id.2.1.14.1.1.3.0"> <margin.target id="note24"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>            
 <s id="id.2.1.13.3.1.5.0"> Quia (inquiunt) po&longs;itat rutina <lb/> 
 in CF, pondus in A longius e&longs;t &agrave; trutina, qu&agrave;m in D: &amp; in D <lb/> <s id="id.2.1.14.1.1.4.0"> <margin.target id="note25"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>            
 longius, qu&agrave;m in L. ductis enim DO LP ip&longs;i CF perpendicula&shy;<lb/> 
 <arrow.to.target n="note23"></arrow.to.target> ribus, li&lt;*&gt;ea AC maior e&longs;t, qu&agrave;m DO, &amp; DO ip&longs;a LP. quod <lb/> <s id="id.2.1.14.1.1.5.0"> <margin.target id="note26"></margin.target><emph type="italics"/>Iordanus propo&longs;itio ne<emph.end type="italics"/> 4. </s>            
 <arrow.to.target n="note24"></arrow.to.target> idem euenit in punctis NM.  </s>      
 <s id="id.2.1.13.3.1.5.0.a"> deinde ex quo loco (aiunt) pon<lb/> 
 dus velocius mouetur, ibi grauius e&longs;t; velocius autem ex A, qu&agrave;m <lb/> 
 ab alio &longs;itu mouetur; ergo in A grauius e&longs;t.  </s>              
 <s id="id.2.1.13.3.1.6.0"> &longs;imili modo, qu&ograve; <lb/> 
 propius e&longs;t ip&longs;i A, velocius quoque mouetur; ergo in D gra&shy;<lb/> 
 <arrow.to.target n="note25"></arrow.to.target> uius erit, qu&agrave;m in L.  </s>      
 <s id="id.2.1.13.3.1.6.0.a"> Altera deinde cau&longs;a, quam ex rectiori, &amp; obli <lb/> 
 <arrow.to.target n="note26"></arrow.to.target> quiori motu deducunt, e&longs;t; qu&ograve; pondus in arcubus &aelig;qualibus re&shy;<lb/> 
 ctius de&longs;cendit, grauius e&longs;&longs;e videtur; cum pondus liberum, atq; <lb/> 
 <arrow.to.target n="note27"></arrow.to.target> &longs;olutum &longs;uapt&egrave; natura rect&egrave; moueatur; &longs;ed in A rectius de&longs;cen<lb/> 
 dit; ergo in A grauius erit.  </s>              
 <s id="id.2.1.13.3.1.7.0"> hocq; o&longs;tendunt accipiendo arcum <lb/> 
 AN arcui LD &aelig;qualem; &agrave; puncti&longs;q; NL line&aelig; FG (quam <lb/> 
 etiam directionis vocant) &aelig;quidi&longs;tantes ducantur NRLQ, qu&aelig; <lb/> 
 lineas AB DO &longs;ecent in QR; &amp; &agrave; puncto N ip&longs;i FG perpen<lb/> 
 dicularis ducatur NT. rect&egrave;q; demon&longs;trant LQ ip&longs;i PO &aelig;qua<lb/> 
 lem e&longs;&longs;e, &amp; NR ip&longs;i CT; lineamq; NR ip&longs;a LQ maiorem e&longs;&longs;e.  </s>              
 <s id="id.2.1.13.3.1.8.0"> <lb/> 
 Quoniam autem de&longs;cen&longs;u; ponderis ex A v&longs;q; ad N per circum&shy; 
 <pb n="9" xlink:href="pagethumb-la/00000035.JPG"/> 
 ferentiam AN maiorem portionem line&aelig; FG pertran&longs;it (quod <lb/> 
 ip&longs;i vocant capere de directo) qu&agrave;m de&longs;cen&longs;us ex L in D per cir<lb/> 
 cumferentiam LD; c&ugrave;m de&longs;cen&longs;us AN lineam CT pertran&longs;eat, <lb/> 
 de&longs;cen&longs;us ver&ograve; LD lineam PO; &amp; CT maior e&longs;t PO; rectior erit <lb/> 
 de&longs;cen&longs;us AN, qu&aacute;m de&longs;cen&longs;us LD.  </s>      
 <s id="id.2.1.13.3.1.8.0.a"> grauius ergo erit pondus <lb/> 
 in A, qu&agrave;m in L, &amp; in quouis alio &longs;itu.  </s>              
 <s id="id.2.1.13.3.1.9.0"> eodemq; pror&longs;us <lb/> 
 modo o&longs;tendunt, qu&ograve; propius e&longs;t ip&longs;i A, grauius e&longs;&longs;e.  </s>              
 <s id="id.2.1.13.3.1.10.0"> <lb/> 
 Vt &longs;int circumferenti&aelig; LD DA inter &longs;e &longs;e &aelig;quales, &amp; &agrave; puncto <lb/> 
 D ip&longs;i AB perpendicularis ducatur DR; erit DR ip&longs;i CO &aelig;qua <arrow.to.target n="note28"></arrow.to.target><lb/> 
 lis.  </s>              
 <s id="id.2.1.13.3.1.11.0"> lineam deinde DR ip&longs;a LQ maiorem e&longs;&longs;e demon&longs;trant.  </s>              
 <s id="id.2.1.13.3.1.12.0"> di&shy;<lb/> 
 cuntq; de&longs;cen&longs;um DA magis capere de directo de&longs;cen&longs;u LD, ma<lb/> 
 ior enim e&longs;t linea CO, qu&agrave;m OP; quare pondus grauius erit <lb/> 
 in D, qu&agrave;m in L. quod ip&longs;um euenit in punctis NM.  </s>      
 <s id="id.2.1.13.3.1.12.0.a"> Suppo&shy;<lb/> 
 &longs;itionem itaq;, qua libram DE in AB redire demon&longs;trant, vt <arrow.to.target n="note29"></arrow.to.target><lb/> 
 notam, manife&longs;tamq; proferunt.  </s>              
 <s id="id.2.1.13.3.1.13.0"> Nemp&egrave; Secund&ugrave;m &longs;itum pon<lb/> 
 dus grauius e&longs;&longs;e, quanto in eodem &longs;itu minus obliquus e&longs;t de&longs;cen<lb/> 
 &longs;us.  </s>              
 <s id="id.2.1.13.3.1.14.0"> huiu&longs;q; reditus cau&longs;am eam e&longs;&longs;e dicunt; Quoniam &longs;cilicet <arrow.to.target n="note30"></arrow.to.target><lb/> 
 de&longs;cen&longs;us ponderis in D rectior e&longs;t de&longs;cen&longs;u ponderis in E, c&ugrave;m <lb/> 
 minus capiat de directo pondus in E de&longs;cendendo, qu&agrave;m pon<arrow.to.target n="note31"></arrow.to.target><lb/> 
 dus in D &longs;im liter de&longs;cendendo.  </s>              
 <s id="id.2.1.13.3.1.15.0"> Vt &longs;i arcus EV &longs;it ip&longs;i DA <lb/> 
 &aelig;qualis, ducanturq; VH ET ip&longs;i FG perpendiculares; maior <lb/> 
 erit DR, qu&agrave;m TH. quare per &longs;uppo&longs;itionem pondus in D ra<lb/> 
 tione &longs;itus grauius erit pondere in E.  </s>      
 <s id="id.2.1.13.3.1.15.0.a"> pondus ergo in D, c&ugrave;m &longs;it <lb/> 
 grauius, deor&longs;um mouebitur; pondus ver&ograve; in E &longs;ur&longs;um, donec li <lb/> 
 bra DE in AB redeat. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.13.3.2.1.0" type="caption">         
 <s id="id.2.1.13.3.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.14.1.0.0.0" type="margin">         
 <s id="id.2.1.14.1.1.1.0"> <margin.target id="note22"></margin.target><emph type="italics"/>Cardanus primo de &longs;ubtilitate.<emph.end type="italics"/> </s>              
 <s id="id.2.1.14.1.1.2.0"> <margin.target id="note23"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 15. <emph type="italics"/>tertii.<emph.end type="italics"/> </s>              
 <s id="id.2.1.14.1.1.3.0"> <margin.target id="note24"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>              
 <s id="id.2.1.14.1.1.4.0"> <margin.target id="note25"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>              
 <s id="id.2.1.14.1.1.5.0"> <margin.target id="note26"></margin.target><emph type="italics"/>Iordanus propo&longs;itio ne<emph.end type="italics"/> 4. </s>              
 <s id="id.2.1.14.1.1.6.0"> <margin.target id="note27"></margin.target><emph type="italics"/>Tartalea propo&longs;itione<emph.end type="italics"/> 5. </s>              <s id="id.2.1.14.1.1.6.0"> <margin.target id="note27"></margin.target><emph type="italics"/>Tartalea propo&longs;itione<emph.end type="italics"/> 5. </s>            
  
 <s id="id.2.1.14.1.1.7.0"> <margin.target id="note28"></margin.target>34 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s id="id.2.1.14.1.1.7.0"> <margin.target id="note28"></margin.target>34 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.14.1.1.8.0"> <margin.target id="note29"></margin.target><emph type="italics"/>Iordanus &longs;uppo&longs;itione<emph.end type="italics"/> 4. </s>              <s id="id.2.1.14.1.1.8.0"> <margin.target id="note29"></margin.target><emph type="italics"/>Iordanus &longs;uppo&longs;itione<emph.end type="italics"/> 4. </s>            
  
 <s id="id.2.1.14.1.1.9.0"> <margin.target id="note30"></margin.target><emph type="italics"/>Iordanus propo&longs;itio ne<emph.end type="italics"/> 3. </s>              <s id="id.2.1.14.1.1.9.0"> <margin.target id="note30"></margin.target><emph type="italics"/>Iordanus propo&longs;itio ne<emph.end type="italics"/> 3. </s>            
 <s id="id.2.1.14.1.1.10.0"> <margin.target id="note31"></margin.target><emph type="italics"/>Tartalea propo&longs;itio ne<emph.end type="italics"/> 5. </s>    </p>        
 <p id="id.2.1.15.1.0.0.0" type="main">         <s id="id.2.1.14.1.1.10.0"> <margin.target id="note31"></margin.target><emph type="italics"/>Tartalea propo&longs;itio ne<emph.end type="italics"/> 5. </s>    </p>       <p id="id.2.1.15.1.0.0.0" type="main">        
 <s id="id.2.1.15.1.1.1.0"> Altera huius quoq; reditus ratio e&longs;t, c&ugrave;m trutina &longs;upra libram <arrow.to.target n="note32"></arrow.to.target><lb/> 
 e&longs;t in CF; linea CG e&longs;t meta.  </s>              <s id="id.2.1.15.1.1.1.0"> Altera huius quoq; reditus ratio e&longs;t, c&ugrave;m trutina &longs;upra libram <arrow.to.target n="note32"></arrow.to.target><lb/>e&longs;t in CF; linea CG e&longs;t meta.  </s>            
 <s id="id.2.1.15.1.1.2.0"> &amp; quoniam angulus GCD ma<lb/> 
 ior e&longs;t angulo GCE, &amp; maior &agrave; meta angulus grauius reddit <lb/> <s id="id.2.1.15.1.1.2.0"> &amp; quoniam angulus GCD ma<lb/>ior e&longs;t angulo GCE, &amp; maior &agrave; meta angulus grauius reddit <lb/>pondus; trutina igitur &longs;uperius exi&longs;tente, grauius erit pondus in <lb/>D, qu&agrave;m in E. idcirco D in A, &amp; E in B redibit. </s>    </p>       <p id="id.2.1.16.1.0.0.0" type="margin">        
 pondus; trutina igitur &longs;uperius exi&longs;tente, grauius erit pondus in <lb/> 
 D, qu&agrave;m in E. idcirco D in A, &amp; E in B redibit. </s>    </p>        <s id="id.2.1.16.1.1.1.0"> <margin.target id="note32"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.17.1.0.0.0" type="main">        
 <p id="id.2.1.16.1.0.0.0" type="margin">         
 <s id="id.2.1.16.1.1.1.0"> <margin.target id="note32"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>    </p>        <s id="id.2.1.17.1.1.1.0"> His itaq; rationibus conantur o&longs;tendere libram DE in AB re<lb/>dire; qu&aelig; meo quidem iuditio facile &longs;olui po&longs;&longs;unt.  </s>    </p>       <pb xlink:href="pagethumb-la/00000036.JPG"/>       <p id="id.2.1.17.3.0.0.0" type="main">        
 <p id="id.2.1.17.1.0.0.0" type="main">         
 <s id="id.2.1.17.1.1.1.0"> His itaq; rationibus conantur o&longs;tendere libram DE in AB re<lb/> <s id="id.2.1.17.3.1.1.0"> Prim&ugrave;m itaq; quan<lb/>tum attinet ad ratio&shy;<lb/>nes pondus in A gra<lb/>uius e&longs;&longs;e, qu&agrave;m in a&shy;<lb/>lio &longs;itu o&longs;tendentes, <lb/>quas ex longiori, &amp; <lb/>propinquiori <expan abbr="di&longs;t&atilde;tia">di&longs;tantia</expan> &agrave; <lb/>linea FG, &amp; ex velo&shy;<lb/>ciori, &amp; rectiori mo <lb/>tu &agrave; puncto A dedu&shy;<lb/>cunt; prim&ugrave;m quidem <lb/>non demon&longs;trant, cur <lb/>pondus ex A velocius <lb/><figure id="fig16" place="text" xlink:href="figures1577/2000.03.0032.jpg">       </figure><lb/>moueatur, qu&agrave;m ex alio &longs;itu.  </s>            
 dire; qu&aelig; meo quidem iuditio facile &longs;olui po&longs;&longs;unt.  </s>    </p>        
 <pb xlink:href="pagethumb-la/00000036.JPG"/> <s id="id.2.1.17.3.1.2.0"> nec quia CA e&longs;t DO maior, <lb/>&amp; DO ip&longs;a LP, propterea &longs;equitur tanquam ex vera cau&longs;a, pon<lb/>dus in A grauius e&longs;&longs;e, qu&agrave;m in D; &amp; in D, qu&agrave;m in L.  </s>    
         
 <p id="id.2.1.17.3.0.0.0" type="main">         <s id="id.2.1.17.3.1.2.0.a"> neq; <lb/>enim intellectus quie&longs;cit, ni&longs;i alia huius o&longs;tendatur cau&longs;a; c&ugrave;m po<lb/>tius &longs;ignum, qu&agrave;m vera cau&longs;a e&longs;&longs;e videatur.  </s>            
 <s id="id.2.1.17.3.1.1.0"> Prim&ugrave;m itaq; quan<lb/> 
 tum attinet ad ratio&shy;<lb/> <s id="id.2.1.17.3.1.3.0"> id ip&longs;um quoq; al&shy;<lb/>teri rationi contintingit, quam ex rectiori &amp; obliquiori motu de&shy;<lb/>ducunt.  </s>            
 nes pondus in A gra<lb/> 
 uius e&longs;&longs;e, qu&agrave;m in a&shy;<lb/> <s id="id.2.1.17.3.1.4.0"> Pr&aelig;terea qu&aelig;cunq; ex velociori, &amp; rectiori motu per&shy;<lb/>&longs;uadent pondus in A grauius e&longs;&longs;e, qu&agrave;m in D; non ideo de&shy;<lb/>mon&longs;trant pondus in A, quatenus e&longs;t in A, grauius e&longs;&longs;e pon<lb/>dere in D, quatenus e&longs;t in D; &longs;ed quatenus &agrave; punctis DA rece<lb/>dit.  </s>            
 lio &longs;itu o&longs;tendentes, <lb/> 
 quas ex longiori, &amp; <lb/> <s id="id.2.1.17.3.1.5.0"> Idcirco antequ&agrave;m vlterius progrediar, o&longs;tendam prim&ugrave;m <lb/>pondus, qu&ograve; propius e&longs;t ip&longs;is FG, minus grauitare; tum qua&shy;<lb/>tenus in eo &longs;itu, in quo reperitur, manet: tum quatenus ab eo <lb/>recedit.  </s>            
 propinquiori <expan abbr="di&longs;t&atilde;tia">di&longs;tantia</expan> &agrave; <lb/> 
 linea FG, &amp; ex velo&shy;<lb/> <s id="id.2.1.17.3.1.6.0"> &longs;imulq; fal&longs;um e&longs;&longs;e, pondus in A grauius e&longs;&longs;e, qu&agrave;m in <lb/>alio &longs;itu.  </s>    
 ciori, &amp; rectiori mo <lb/> 
 tu &agrave; puncto A dedu&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.17.3.2.1.0" type="caption">        
 cunt; prim&ugrave;m quidem <lb/> 
 non demon&longs;trant, cur <lb/> <s id="id.2.1.17.3.2.1.0.capt"> YYY </s>    </p>       <pb n="10" xlink:href="pagethumb-la/00000037.JPG"/>       <p id="id.2.1.17.5.0.0.0" type="main">        
 pondus ex A velocius <lb/> 
 <figure id="fig16" place="text" xlink:href="figures1577/2000.03.0032.jpg">       </figure><lb/> <s id="id.2.1.17.5.1.1.0"> Producatur FG v&longs;q; ad mundi cen<lb/>trum, quod &longs;it S. &amp; &agrave; puncto S circu<lb/>lum AFBG contingens ducatur.  </s>            
 moueatur, qu&agrave;m ex alio &longs;itu.  </s>              
 <s id="id.2.1.17.3.1.2.0"> nec quia CA e&longs;t DO maior, <lb/> <s id="id.2.1.17.5.1.2.0"> neq; <lb/>enim linea &agrave; puncto S circulum con&shy;<lb/>tingere pote&longs;t in A; nam ducta AS <lb/>triangulum ACS duos haberet angu<lb/>los rectos, nemp&egrave; SAC ACS, quod <arrow.to.target n="note33"></arrow.to.target><lb/>e&longs;t impo&longs;sibile.  </s>            
 &amp; DO ip&longs;a LP, propterea &longs;equitur tanquam ex vera cau&longs;a, pon<lb/> 
 dus in A grauius e&longs;&longs;e, qu&agrave;m in D; &amp; in D, qu&agrave;m in L.  </s>      <s id="id.2.1.17.5.1.3.0"> neq; &longs;upra punctum A <lb/>in circumferentia AF continget; cir<lb/>culum enim &longs;ecatet.  </s>            
 <s id="id.2.1.17.3.1.2.0.a"> neq; <lb/> 
 enim intellectus quie&longs;cit, ni&longs;i alia huius o&longs;tendatur cau&longs;a; c&ugrave;m po<lb/> <s id="id.2.1.17.5.1.4.0"> tanget igitur in&shy;<lb/>fra, &longs;itq; SO. connectantur deinde SD <lb/>SL, qu&aelig; circumferentiam AOG in <lb/>punctis KH &longs;ecent. </s>
 tius &longs;ignum, qu&agrave;m vera cau&longs;a e&longs;&longs;e videatur.  </s>              
 <s id="id.2.1.17.3.1.3.0"> id ip&longs;um quoq; al&shy;<lb/> <s id="id.2.1.17.5.1.5.0"> &amp; Ck CH con<lb/>iungantur.  </s>            
 teri rationi contintingit, quam ex rectiori &amp; obliquiori motu de&shy;<lb/> 
 ducunt.  </s>              <s id="id.2.1.17.5.1.6.0"> Et quoniam pondus, quanto <lb/>propius e&longs;t ip&longs;i F, magis quoque inni&shy;<lb/>titur centro; vt pondus in D magis ver&shy;<lb/>&longs;ionis puncto C innititur tanquam <lb/>centro; hoc e&longs;t in D magis &longs;upra li&shy;<lb/>neam CD grauitat, qu&agrave;m &longs;i e&longs;&longs;et in A <lb/>&longs;upra lineam CA; &amp; adhuc magis in <lb/>L &longs;upra lineam CL; Nam c&ugrave;m tres <lb/>anguli cuiu&longs;cunq; trianguli duobus re&shy;<lb/><figure id="fig17" place="text" xlink:href="figures1577/2000.03.0034.jpg">       </figure><lb/>ctis &longs;int &aelig;quales, &amp; trianguli DCk &aelig;quicruris angulus DCk <lb/>minor &longs;it angulo LCH &aelig;quicruris trianguli LCH: erunt reli&shy;<lb/>qui ad ba&longs;im &longs;cilicet CDk CkD &longs;imul &longs;umpti reliquis CLH <lb/>CHL maiores.  </s>            
 <s id="id.2.1.17.3.1.4.0"> Pr&aelig;terea qu&aelig;cunq; ex velociori, &amp; rectiori motu per&shy;<lb/> 
 &longs;uadent pondus in A grauius e&longs;&longs;e, qu&agrave;m in D; non ideo de&shy;<lb/> <s id="id.2.1.17.5.1.7.0"> &amp; horum dimidii; hoc e&longs;t angulus CDS angu<lb/>lo CLS maior erit.  </s>            
 mon&longs;trant pondus in A, quatenus e&longs;t in A, grauius e&longs;&longs;e pon<lb/> 
 dere in D, quatenus e&longs;t in D; &longs;ed quatenus &agrave; punctis DA rece<lb/> <s id="id.2.1.17.5.1.8.0"> c&ugrave;m itaq; CLS &longs;it minor, linea CL ma<lb/>gis adh&aelig;rebit motui naturali ponderis in L pror&longs;us &longs;oluti.  </s>            
 dit.  </s>              
 <s id="id.2.1.17.3.1.5.0"> Idcirco antequ&agrave;m vlterius progrediar, o&longs;tendam prim&ugrave;m <lb/> <s id="id.2.1.17.5.1.9.0"> hoc <lb/>e&longs;t line&aelig; LS, qu&agrave;m CD motui DS.  </s>    
 pondus, qu&ograve; propius e&longs;t ip&longs;is FG, minus grauitare; tum qua&shy;<lb/> 
 tenus in eo &longs;itu, in quo reperitur, manet: tum quatenus ab eo <lb/> <s id="id.2.1.17.5.1.9.0.a"> pondus enim in L libe&shy;<lb/>berum, atq; &longs;olutum in centrum mundi per LS moueretur, pon&shy;<lb/>dusq; in D per DS.  </s>    
 recedit.  </s>              
 <s id="id.2.1.17.3.1.6.0"> &longs;imulq; fal&longs;um e&longs;&longs;e, pondus in A grauius e&longs;&longs;e, qu&agrave;m in <lb/> <s id="id.2.1.17.5.1.9.0.b"> quoniam ver&ograve; pondus in L totum &longs;uper LS <lb/>grauitat, in D ver&ograve; &longs;uper DS: pondus in L magis &longs;upra lineam <lb/>CL grauitabit, qu&agrave;m exi&longs;tens in D &longs;upra lineam DC. ergo <lb/>linea CL pondus magis &longs;u&longs;tentabit, qu&agrave;m linea CD.  </s>    
 alio &longs;itu.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.17.5.1.9.0.c"> <expan abbr="Eodem&shy;qu&eacute;">Eodem&shy;<lb/>que</expan> modo, qu&ograve; pondus propius fuerit ip&longs;i F, magis ob hanc cau&shy;<lb/>&longs;am &agrave; linea CL &longs;u&longs;tineri o&longs;tendetur-&longs;emper enim angulus CLS <pb xlink:href="pagethumb-la/00000038.JPG"/>minor e&longs;&longs;et.  </s>            
 <p id="id.2.1.17.3.2.1.0" type="caption">         
 <s id="id.2.1.17.3.2.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.17.5.1.10.0"> quod etiam patet; quia &longs;i <lb/>line&aelig; CL, &amp; LS in vnam coinciderent <lb/>lineam, quod euenit in FCS; tunc linea <lb/>CF totum &longs;u&longs;tineret pondus in F, im&shy;<lb/>mobilemq; redderet: neq; vllam pror&shy;<lb/>&longs;us grauitatem in circumferentia circu&shy;<lb/>li haberet.  </s>            
 <pb n="10" xlink:href="pagethumb-la/00000037.JPG"/> 
         <s id="id.2.1.17.5.1.11.0"> Idem ergo pondus propter <lb/>&longs;ituum diuer&longs;itatem grauius, leuiu&longs;q; erit.  </s>            
 <p id="id.2.1.17.5.0.0.0" type="main">         
 <s id="id.2.1.17.5.1.1.0"> Producatur FG v&longs;q; ad mundi cen<lb/> <s id="id.2.1.17.5.1.12.0"> <lb/>non autem quia ratione &longs;itus interdum <lb/>maiorem re vera acquirat grauitatem, <lb/>interdum ver&ograve; amittat, c&ugrave;m eiu&longs;dem &longs;it <lb/>&longs;emper grauitatis, vbicunque reperiatur; <lb/>&longs;ed quia magis, minu&longs;u&egrave; in circumferen&shy;<lb/>tia grauitat, vt in D magis &longs;upra circum<lb/>ferentiam DA grauitat, qu&agrave;m in L &longs;upra <lb/>circumferentiam LD.  </s>    
 trum, quod &longs;it S. &amp; &agrave; puncto S circu<lb/> 
 lum AFBG contingens ducatur.  </s>              <s id="id.2.1.17.5.1.12.0.a"> hoc e&longs;t, &longs;i pon<lb/>dus &agrave; circumferentiis, recti&longs;q; lineis &longs;u<lb/>&longs;tineatur; circumferentia AD magis &longs;u<lb/>&longs;tinebit pondus in D, qu&agrave;m circumfe<lb/>rentia DL pondere exi&longs;tente in <emph type="italics"/>L.<emph.end type="italics"/> mi <lb/>nus enim coadiuuat CD, qu&agrave;m CL.  </s>    
 <s id="id.2.1.17.5.1.2.0"> neq; <lb/> 
 enim linea &agrave; puncto S circulum con&shy;<lb/> <s id="id.2.1.17.5.1.12.0.b"> <lb/>Pr&aelig;terea quando pondus e&longs;t in L, &longs;i e&longs;&shy;<lb/><figure id="fig18" place="text" xlink:href="figures1577/2000.03.0035.jpg">       </figure><lb/>&longs;et omnino liberum, penitu&longs;q; &longs;olutum, deor&longs;um per LS moueretur; <lb/>ni&longs;i &agrave; linea CL prohiberetur, qu&aelig; pondus in L vltra lineam LS per <lb/><expan abbr="circumferenti&atilde;">circumferentiam</expan> LD moueri cogit; ip&longs;umq; quodammodo impellit, <lb/>impellendoq; pondus partim &longs;u&longs;tentabit.  </s>            
 tingere pote&longs;t in A; nam ducta AS <lb/> 
 triangulum ACS duos haberet angu<lb/> <s id="id.2.1.17.5.1.13.0"> ni&longs;i enim &longs;u&longs;tineret, ip&longs;iq; <lb/>reniteretur, deor&longs;um per lineam LS moueretur, non autem per <lb/>circumferentiam LD. &longs;imiliter CD ponderi in D renititur, c&ugrave;m <lb/>illud per circumferentiam DA moueri cogat.  </s>            
 los rectos, nemp&egrave; SAC ACS, quod <arrow.to.target n="note33"></arrow.to.target><lb/> 
 e&longs;t impo&longs;sibile.  </s>              <s id="id.2.1.17.5.1.14.0"> eodemq; modo <lb/>exi&longs;tente pondere in A, linea CA pondus vltra lineam AS per <lb/>circumferentiam AO moueri compellet.  </s>            
 <s id="id.2.1.17.5.1.3.0"> neq; &longs;upra punctum A <lb/> 
 in circumferentia AF continget; cir<lb/> <s id="id.2.1.17.5.1.15.0"> e&longs;t enim angulus CAS <lb/>acutus; c&ugrave;m angulus ACS &longs;it rectus.  </s>            
 culum enim &longs;ecatet.  </s>              
 <s id="id.2.1.17.5.1.4.0"> tanget igitur in&shy;<lb/> <s id="id.2.1.17.5.1.16.0"> line&aelig; igitur CA CD ali <lb/>qua ex parte, non tamen ex &aelig;quo ponderi renituntur.  </s>            
 fra, &longs;itq; SO. connectantur deinde SD <lb/> 
 SL, qu&aelig; circumferentiam AOG in <lb/> <s id="id.2.1.17.5.1.17.0"> &amp; quotie&longs; <lb/>cunque angulus in circumferentia circuli &agrave; lineis &agrave; centro <lb/>mundi S, &amp; centro C prodeuntibus, fuerit acutus; idem eue&shy;<lb/>nire &longs;imiliter o&longs;tendemus.  </s>            
 punctis KH &longs;ecent. </s> 
 <s id="id.2.1.17.5.1.5.0"> &amp; Ck CH con<lb/> <s id="id.2.1.17.5.1.18.0"> Quoniam autem mixtus angulus CLD <pb n="11" xlink:href="pagethumb-la/00000039.JPG"/>&aelig;qualis e&longs;t angulo CDA, c&ugrave;m &agrave; &longs;emidiametris, eademq; circumfe<lb/>rentia contineantur; &amp; angulus C<emph type="italics"/>L<emph.end type="italics"/>S angulo CDS e&longs;t minor; <lb/>erit reliquus <emph type="italics"/>s<emph.end type="italics"/>LD reliquo SDA maior.  </s>            
 iungantur.  </s>              
 <s id="id.2.1.17.5.1.6.0"> Et quoniam pondus, quanto <lb/> <s id="id.2.1.17.5.1.19.0"> quare circumferentia <lb/>DA, hoc e&longs;t de&longs;cen&longs;us ponderis in D propior erit motui natu&shy;<lb/>rali ponderis in D &longs;oluti, line&aelig; &longs;cilicet DS, qu&agrave;m circumferen<lb/>tia LD line&aelig; LS.  </s>    
 propius e&longs;t ip&longs;i F, magis quoque inni&shy;<lb/> 
 titur centro; vt pondus in D magis ver&shy;<lb/> <s id="id.2.1.17.5.1.19.0.a"> minus igitur linea CD ponderi in D reniti&shy;<lb/>tur, qu&agrave;m linea CL ponderi in L.  </s>    
 &longs;ionis puncto C innititur tanquam <lb/> 
 centro; hoc e&longs;t in D magis &longs;upra li&shy;<lb/> <s id="id.2.1.17.5.1.19.0.b"> linea ideo CD minus &longs;u&longs;tinet, <lb/>qu&agrave;m CL; pondu&longs;q; magis liberum erit in D, qu&agrave;m in L: <lb/>c&ugrave;m pondus naturaliter magis per DA moueatur, qu&agrave;m per LD. <lb/>quare grauius erit in D, qu&agrave;m in L. &longs;imiliter o&longs;tendemus CA <lb/>minus &longs;u&longs;tinere, qu&agrave;m CD: pondu&longs;q; magis in A, qu&agrave;m in Dli <lb/>berum, grauiu&longs;q, e&longs;&longs;e.  </s>            
 neam CD grauitat, qu&agrave;m &longs;i e&longs;&longs;et in A <lb/> 
 &longs;upra lineam CA; &amp; adhuc magis in <lb/> <s id="id.2.1.17.5.1.20.0"> Ex parte deinde inferiori ob ea&longs;dem cau&longs;as, <lb/>qu&ograve; pondus propius fuerit ip&longs;i G, magis detinebitur, vt in H ma<lb/>gis &agrave; linea CH, qu&agrave;m in K &agrave; linea CK. nam c&ugrave;m angulus CHS <lb/>maior &longs;it angulo CkS, ad rectitudinem magis appropinquabunt <arrow.to.target n="note34"></arrow.to.target><lb/>&longs;e &longs;e line&aelig; CHHS, qu&agrave;m Ck kS; atq; ob id pondus magis deti&shy;<lb/>nebitur &agrave; CH, qu&agrave;m &agrave; Ck &longs;i enim CH HS in vnam conuenirent <lb/>lineam vt euenit pondere exi&longs;tente in G; tunc linea CG totum &longs;u<lb/>&longs;tineret' pondus in G, ita vt immobilis per&longs;i&longs;teret.  </s>            
 L &longs;upra lineam CL; Nam c&ugrave;m tres <lb/> 
 anguli cuiu&longs;cunq; trianguli duobus re&shy;<lb/> <s id="id.2.1.17.5.1.21.0"> qu&ograve; igitur <lb/>minor erit angulus linea CH, &amp; de&longs;cen&longs;u ponderis &longs;oluti, &longs;cilicet <lb/>HS contentus, e&ograve; minus quoq; eiu&longs;modi linea pondus detinebit.  </s>            
 <figure id="fig17" place="text" xlink:href="figures1577/2000.03.0034.jpg">       </figure><lb/> 
 ctis &longs;int &aelig;quales, &amp; trianguli DCk &aelig;quicruris angulus DCk <lb/> <s id="id.2.1.17.5.1.22.0"> <lb/>&amp; vbiminus detinebitur, ibi magis liberum, grauiu&longs;q; exi&longs;tet.  </s>            
 minor &longs;it angulo LCH &aelig;quicruris trianguli LCH: erunt reli&shy;<lb/> 
 qui ad ba&longs;im &longs;cilicet CDk CkD &longs;imul &longs;umpti reliquis CLH <lb/> <s id="id.2.1.17.5.1.23.0"> <lb/>Pr&aelig;terea &longs;i pondus in k liberum e&longs;&longs;et, atq; &longs;olutum, per lineam <lb/>k S moueretur; &agrave; linea ver&ograve; Ck prohibetur, qu&aelig; cogit pondus <lb/>citr&agrave; lineam k S per circumferentiam k H moueri.  </s>            
 CHL maiores.  </s>              
 <s id="id.2.1.17.5.1.7.0"> &amp; horum dimidii; hoc e&longs;t angulus CDS angu<lb/> <s id="id.2.1.17.5.1.24.0"> ip&longs;um enim <lb/>quodammodo retrahit, retrahendoq; &longs;u&longs;tinet. </s>
 lo CLS maior erit.  </s>              
 <s id="id.2.1.17.5.1.8.0"> c&ugrave;m itaq; CLS &longs;it minor, linea CL ma<lb/> 
 gis adh&aelig;rebit motui naturali ponderis in L pror&longs;us &longs;oluti.  </s>              
 <s id="id.2.1.17.5.1.9.0"> hoc <lb/> 
 e&longs;t line&aelig; LS, qu&agrave;m CD motui DS.  </s>      
 <s id="id.2.1.17.5.1.9.0.a"> pondus enim in L libe&shy;<lb/> 
 berum, atq; &longs;olutum in centrum mundi per LS moueretur, pon&shy;<lb/> 
 dusq; in D per DS.  </s>      
 <s id="id.2.1.17.5.1.9.0.b"> quoniam ver&ograve; pondus in L totum &longs;uper LS <lb/> 
 grauitat, in D ver&ograve; &longs;uper DS: pondus in L magis &longs;upra lineam <lb/> 
 CL grauitabit, qu&agrave;m exi&longs;tens in D &longs;upra lineam DC. ergo <lb/> 
 linea CL pondus magis &longs;u&longs;tentabit, qu&agrave;m linea CD.  </s>      
 <s id="id.2.1.17.5.1.9.0.c"> <expan abbr="Eodem&shy;qu&eacute;">Eodem&shy;<lb/> 
 que</expan> modo, qu&ograve; pondus propius fuerit ip&longs;i F, magis ob hanc cau&shy;<lb/> 
 &longs;am &agrave; linea CL &longs;u&longs;tineri o&longs;tendetur-&longs;emper enim angulus CLS  
 <pb xlink:href="pagethumb-la/00000038.JPG"/> 
 minor e&longs;&longs;et.  </s>              
 <s id="id.2.1.17.5.1.10.0"> quod etiam patet; quia &longs;i <lb/> 
 line&aelig; CL, &amp; LS in vnam coinciderent <lb/> 
 lineam, quod euenit in FCS; tunc linea <lb/> 
 CF totum &longs;u&longs;tineret pondus in F, im&shy;<lb/> 
 mobilemq; redderet: neq; vllam pror&shy;<lb/> 
 &longs;us grauitatem in circumferentia circu&shy;<lb/> 
 li haberet.  </s>              
 <s id="id.2.1.17.5.1.11.0"> Idem ergo pondus propter <lb/> 
 &longs;ituum diuer&longs;itatem grauius, leuiu&longs;q; erit.  </s>              
 <s id="id.2.1.17.5.1.12.0"> <lb/> 
 non autem quia ratione &longs;itus interdum <lb/> 
 maiorem re vera acquirat grauitatem, <lb/> 
 interdum ver&ograve; amittat, c&ugrave;m eiu&longs;dem &longs;it <lb/> 
 &longs;emper grauitatis, vbicunque reperiatur; <lb/> 
 &longs;ed quia magis, minu&longs;u&egrave; in circumferen&shy;<lb/> 
 tia grauitat, vt in D magis &longs;upra circum<lb/> 
 ferentiam DA grauitat, qu&agrave;m in L &longs;upra <lb/> 
 circumferentiam LD.  </s>      
 <s id="id.2.1.17.5.1.12.0.a"> hoc e&longs;t, &longs;i pon<lb/> 
 dus &agrave; circumferentiis, recti&longs;q; lineis &longs;u<lb/> 
 &longs;tineatur; circumferentia AD magis &longs;u<lb/> 
 &longs;tinebit pondus in D, qu&agrave;m circumfe<lb/> 
 rentia DL pondere exi&longs;tente in <emph type="italics"/>L.<emph.end type="italics"/> mi <lb/> 
 nus enim coadiuuat CD, qu&agrave;m CL.  </s>      
 <s id="id.2.1.17.5.1.12.0.b"> <lb/> 
 Pr&aelig;terea quando pondus e&longs;t in L, &longs;i e&longs;&shy;<lb/> 
 <figure id="fig18" place="text" xlink:href="figures1577/2000.03.0035.jpg">       </figure><lb/> 
 &longs;et omnino liberum, penitu&longs;q; &longs;olutum, deor&longs;um per LS moueretur; <lb/> 
 ni&longs;i &agrave; linea CL prohiberetur, qu&aelig; pondus in L vltra lineam LS per <lb/> 
 <expan abbr="circumferenti&atilde;">circumferentiam</expan> LD moueri cogit; ip&longs;umq; quodammodo impellit, <lb/> 
 impellendoq; pondus partim &longs;u&longs;tentabit.  </s>              
 <s id="id.2.1.17.5.1.13.0"> ni&longs;i enim &longs;u&longs;tineret, ip&longs;iq; <lb/> 
 reniteretur, deor&longs;um per lineam LS moueretur, non autem per <lb/> 
 circumferentiam LD. &longs;imiliter CD ponderi in D renititur, c&ugrave;m <lb/> 
 illud per circumferentiam DA moueri cogat.  </s>              
 <s id="id.2.1.17.5.1.14.0"> eodemq; modo <lb/> 
 exi&longs;tente pondere in A, linea CA pondus vltra lineam AS per <lb/> 
 circumferentiam AO moueri compellet.  </s>              
 <s id="id.2.1.17.5.1.15.0"> e&longs;t enim angulus CAS <lb/> 
 acutus; c&ugrave;m angulus ACS &longs;it rectus.  </s>              
 <s id="id.2.1.17.5.1.16.0"> line&aelig; igitur CA CD ali <lb/> 
 qua ex parte, non tamen ex &aelig;quo ponderi renituntur.  </s>              
 <s id="id.2.1.17.5.1.17.0"> &amp; quotie&longs; <lb/> 
 cunque angulus in circumferentia circuli &agrave; lineis &agrave; centro <lb/> 
 mundi S, &amp; centro C prodeuntibus, fuerit acutus; idem eue&shy;<lb/> 
 nire &longs;imiliter o&longs;tendemus.  </s>              
 <s id="id.2.1.17.5.1.18.0"> Quoniam autem mixtus angulus CLD  
 <pb n="11" xlink:href="pagethumb-la/00000039.JPG"/> 
 &aelig;qualis e&longs;t angulo CDA, c&ugrave;m &agrave; &longs;emidiametris, eademq; circumfe<lb/> 
 rentia contineantur; &amp; angulus C<emph type="italics"/>L<emph.end type="italics"/>S angulo CDS e&longs;t minor; <lb/> 
 erit reliquus <emph type="italics"/>s<emph.end type="italics"/>LD reliquo SDA maior.  </s>              
 <s id="id.2.1.17.5.1.19.0"> quare circumferentia <lb/> 
 DA, hoc e&longs;t de&longs;cen&longs;us ponderis in D propior erit motui natu&shy;<lb/> 
 rali ponderis in D &longs;oluti, line&aelig; &longs;cilicet DS, qu&agrave;m circumferen<lb/> 
 tia LD line&aelig; LS.  </s>      
 <s id="id.2.1.17.5.1.19.0.a"> minus igitur linea CD ponderi in D reniti&shy;<lb/> 
 tur, qu&agrave;m linea CL ponderi in L.  </s>      
 <s id="id.2.1.17.5.1.19.0.b"> linea ideo CD minus &longs;u&longs;tinet, <lb/> 
 qu&agrave;m CL; pondu&longs;q; magis liberum erit in D, qu&agrave;m in L: <lb/> 
 c&ugrave;m pondus naturaliter magis per DA moueatur, qu&agrave;m per LD. <lb/> 
 quare grauius erit in D, qu&agrave;m in L. &longs;imiliter o&longs;tendemus CA <lb/> 
 minus &longs;u&longs;tinere, qu&agrave;m CD: pondu&longs;q; magis in A, qu&agrave;m in Dli <lb/> 
 berum, grauiu&longs;q, e&longs;&longs;e.  </s>              
 <s id="id.2.1.17.5.1.20.0"> Ex parte deinde inferiori ob ea&longs;dem cau&longs;as, <lb/> 
 qu&ograve; pondus propius fuerit ip&longs;i G, magis detinebitur, vt in H ma<lb/> 
 gis &agrave; linea CH, qu&agrave;m in K &agrave; linea CK. nam c&ugrave;m angulus CHS <lb/> 
 maior &longs;it angulo CkS, ad rectitudinem magis appropinquabunt <arrow.to.target n="note34"></arrow.to.target><lb/> 
 &longs;e &longs;e line&aelig; CHHS, qu&agrave;m Ck kS; atq; ob id pondus magis deti&shy;<lb/> 
 nebitur &agrave; CH, qu&agrave;m &agrave; Ck &longs;i enim CH HS in vnam conuenirent <lb/> 
 lineam vt euenit pondere exi&longs;tente in G; tunc linea CG totum &longs;u<lb/> 
 &longs;tineret' pondus in G, ita vt immobilis per&longs;i&longs;teret.  </s>              
 <s id="id.2.1.17.5.1.21.0"> qu&ograve; igitur <lb/> 
 minor erit angulus linea CH, &amp; de&longs;cen&longs;u ponderis &longs;oluti, &longs;cilicet <lb/> 
 HS contentus, e&ograve; minus quoq; eiu&longs;modi linea pondus detinebit.  </s>              
 <s id="id.2.1.17.5.1.22.0"> <lb/> 
 &amp; vbiminus detinebitur, ibi magis liberum, grauiu&longs;q; exi&longs;tet.  </s>              
 <s id="id.2.1.17.5.1.23.0"> <lb/> 
 Pr&aelig;terea &longs;i pondus in k liberum e&longs;&longs;et, atq; &longs;olutum, per lineam <lb/> 
 k S moueretur; &agrave; linea ver&ograve; Ck prohibetur, qu&aelig; cogit pondus <lb/> 
 citr&agrave; lineam k S per circumferentiam k H moueri.  </s>              
 <s id="id.2.1.17.5.1.24.0"> ip&longs;um enim <lb/> 
 quodammodo retrahit, retrahendoq; &longs;u&longs;tinet. </s> 
 <s id="id.2.1.17.5.1.25.0"> ni&longs;i enim &longs;u&longs;tineret.  </s>       <s id="id.2.1.17.5.1.25.0"> ni&longs;i enim &longs;u&longs;tineret.  </s>      
 <s id="id.2.1.17.5.1.26.0"> <lb/> 
 pondus deor&longs;um per rectam k S moueretur, non autem per cir<lb/> <s id="id.2.1.17.5.1.26.0"> <lb/>pondus deor&longs;um per rectam k S moueretur, non autem per cir<lb/>cumferentiam k H. &longs;imiliter CH pondus retinet, c&ugrave;m per circum<lb/><expan abbr="ferenti&atilde;">ferentiam</expan> HG moueri compellat.  </s>            
 cumferentiam k H. &longs;imiliter CH pondus retinet, c&ugrave;m per circum<lb/> 
 <expan abbr="ferenti&atilde;">ferentiam</expan> HG moueri compellat.  </s>              <s id="id.2.1.17.5.1.27.0"> <expan abbr="Quoni&atilde;">Quoniam</expan> autem angulus CHS ma&shy;<lb/>ior e&longs;t angulo CKS, <expan abbr="d&etilde;ptis">demptis</expan> &aelig;qualibus angulis CHG CkH; erit <lb/>reliquus SHG reliquo SKH maior.  </s>            
 <s id="id.2.1.17.5.1.27.0"> <expan abbr="Quoni&atilde;">Quoniam</expan> autem angulus CHS ma&shy;<lb/> 
 ior e&longs;t angulo CKS, <expan abbr="d&etilde;ptis">demptis</expan> &aelig;qualibus angulis CHG CkH; erit <lb/> <s id="id.2.1.17.5.1.28.0"> circumferentia igitur k H, hoc <lb/>e&longs;t de&longs;cen&longs;us ponderis in k, propior erit motui naturali ponderis in <lb/>k &longs;oluti, hoc e&longs;t line&aelig; k S, qu&agrave;m circumferentia HG line&aelig; HS. mi <lb/>nus idcirco detinet linea Ck, qu&agrave;m CH: c&ugrave;m pondus naturali&shy;<lb/>ter magis moueatur per k H, qu&agrave;m per HG.  </s>    
 reliquus SHG reliquo SKH maior.  </s>              
 <s id="id.2.1.17.5.1.28.0"> circumferentia igitur k H, hoc <lb/> <s id="id.2.1.17.5.1.28.0.a"> &longs;imili ratione o&longs;ten&shy;<lb/>detur, qu&ograve; minor erit angulus SkH, lineam Ck minus &longs;u&longs;tinere.  </s>            
 e&longs;t de&longs;cen&longs;us ponderis in k, propior erit motui naturali ponderis in <lb/> 
 k &longs;oluti, hoc e&longs;t line&aelig; k S, qu&agrave;m circumferentia HG line&aelig; HS. mi <lb/> <s id="id.2.1.17.5.1.29.0"> <pb xlink:href="pagethumb-la/00000040.JPG"/>exi&longs;tente igitur pondere in O, quia angu<lb/>lus SOC non &longs;olum minor e&longs;t angulo <lb/>CKS, ver&ugrave;m etiam omnium angulorum <lb/>&agrave; punctis CS prodeuntium, verticemq; <lb/>in circumferuntia OkG habentium mi&shy;<lb/>nimus; erit anglus SOK, &amp; angulo SkH, <lb/>&amp; eiu&longs;modi omnium minimus.  </s>            
 nus idcirco detinet linea Ck, qu&agrave;m CH: c&ugrave;m pondus naturali&shy;<lb/> 
 ter magis moueatur per k H, qu&agrave;m per HG.  </s>      <s id="id.2.1.17.5.1.30.0"> ergo de&shy;<lb/>&longs;cen&longs;us ponderis in O propior erit motui <lb/>naturali ip&longs;ius in O &longs;oluti, qu&agrave;m in alio <lb/>&longs;itu circumferenti&aelig; OkG. lineaq; CO <lb/>minus pondus &longs;u&longs;tinebit, qu&agrave;m &longs;i pon&shy;<lb/>dusin quouis alio fuerit &longs;itu eiu&longs;dem cir<lb/>cumferenti&aelig; OG.  </s>    
 <s id="id.2.1.17.5.1.28.0.a"> &longs;imili ratione o&longs;ten&shy;<lb/> 
 detur, qu&ograve; minor erit angulus SkH, lineam Ck minus &longs;u&longs;tinere.  </s>              <s id="id.2.1.17.5.1.30.0.a"> &longs;imiliter quoniam con<lb/>tingenti&aelig; angulus SOk, &amp; angulo SDA, <lb/>&amp; SAO, ac quibu&longs;cunq; &longs;imilibus e&longs;t mi <lb/>nor; erit de&longs;cen&longs;us ponderis in O motui <lb/>naturali ip&longs;ius ponderis in O &longs;oluti pro&shy;<lb/>pior, qu&agrave;m in alio &longs;itu circumferenti&aelig; <lb/>ODF.  </s>    
 <s id="id.2.1.17.5.1.29.0">  
 <pb xlink:href="pagethumb-la/00000040.JPG"/> <s id="id.2.1.17.5.1.30.0.b"> Pr&aelig;te reaquoniam linea GO pon<lb/>dus in O dum deor&longs;um mouetur, impelle&shy;<lb/>re nonpote&longs;t, ita vt vltra lineam OS mo<lb/>ueatur; c&ugrave;m linea OS circulum non &longs;ecet, <lb/><figure id="fig19" place="text" xlink:href="figures1577/2000.03.0036.jpg">       </figure><lb/>&longs;ed contingat; angulu&longs;q; SOC &longs;it rectus, &amp; non acutus; pondus <lb/>in O nihil &longs;upra lineam CO grauitabit.  </s>
 exi&longs;tente igitur pondere in O, quia angu<lb/> 
 lus SOC non &longs;olum minor e&longs;t angulo <lb/> 
 CKS, ver&ugrave;m etiam omnium angulorum <lb/> 
 &agrave; punctis CS prodeuntium, verticemq; <lb/> 
 in circumferuntia OkG habentium mi&shy;<lb/> 
 nimus; erit anglus SOK, &amp; angulo SkH, <lb/> 
 &amp; eiu&longs;modi omnium minimus.  </s>              
 <s id="id.2.1.17.5.1.30.0"> ergo de&shy;<lb/> 
 &longs;cen&longs;us ponderis in O propior erit motui <lb/> 
 naturali ip&longs;ius in O &longs;oluti, qu&agrave;m in alio <lb/> 
 &longs;itu circumferenti&aelig; OkG. lineaq; CO <lb/> 
 minus pondus &longs;u&longs;tinebit, qu&agrave;m &longs;i pon&shy;<lb/> 
 dusin quouis alio fuerit &longs;itu eiu&longs;dem cir<lb/> 
 cumferenti&aelig; OG.  </s>      
 <s id="id.2.1.17.5.1.30.0.a"> &longs;imiliter quoniam con<lb/> 
 tingenti&aelig; angulus SOk, &amp; angulo SDA, <lb/> 
 &amp; SAO, ac quibu&longs;cunq; &longs;imilibus e&longs;t mi <lb/> 
 nor; erit de&longs;cen&longs;us ponderis in O motui <lb/> 
 naturali ip&longs;ius ponderis in O &longs;oluti pro&shy;<lb/> 
 pior, qu&agrave;m in alio &longs;itu circumferenti&aelig; <lb/> 
 ODF.  </s>      
 <s id="id.2.1.17.5.1.30.0.b"> Pr&aelig;te reaquoniam linea GO pon<lb/> 
 dus in O dum deor&longs;um mouetur, impelle&shy;<lb/> 
 re nonpote&longs;t, ita vt vltra lineam OS mo<lb/> 
 ueatur; c&ugrave;m linea OS circulum non &longs;ecet, <lb/> 
 <figure id="fig19" place="text" xlink:href="figures1577/2000.03.0036.jpg">       </figure><lb/> 
 &longs;ed contingat; angulu&longs;q; SOC &longs;it rectus, &amp; non acutus; pondus <lb/> 
 in O nihil &longs;upra lineam CO grauitabit.  </s> 
 <s id="id.2.1.17.5.1.31.0"> neq; centro innitetur.  </s>              <s id="id.2.1.17.5.1.31.0"> neq; centro innitetur.  </s>            
 <s id="id.2.1.17.5.1.32.0"> quem <lb/> 
 admodum in quouis alio puncto &longs;upra O accideret. </s>              <s id="id.2.1.17.5.1.32.0"> quem <lb/>admodum in quouis alio puncto &longs;upra O accideret. </s>            
 <s id="id.2.1.17.5.1.33.0"> erit igitur pon<lb/> 
 dus in O magis ob has cau&longs;as liberum, atq; &longs;olutum in hoc &longs;itu, <lb/> <s id="id.2.1.17.5.1.33.0"> erit igitur pon<lb/>dus in O magis ob has cau&longs;as liberum, atq; &longs;olutum in hoc &longs;itu, <lb/>qu&agrave;m in quouis alio circumferenti&aelig; FOG. acidcirco in hoc <lb/>grauius erit, hoc e&longs;t magis grauitabit, qu&agrave;m in alio &longs;itu.  </s>            
 qu&agrave;m in quouis alio circumferenti&aelig; FOG. acidcirco in hoc <lb/> 
 grauius erit, hoc e&longs;t magis grauitabit, qu&agrave;m in alio &longs;itu.  </s>              <s id="id.2.1.17.5.1.34.0"> &amp; qu&ograve; <lb/>propius fuerit ip&longs;i O remotiori grauius erit.  </s>            
 <s id="id.2.1.17.5.1.34.0"> &amp; qu&ograve; <lb/> 
 propius fuerit ip&longs;i O remotiori grauius erit.  </s>              <s id="id.2.1.17.5.1.35.0"> lineaq; CO horizonti <lb/>&aelig;quidi&longs;tans erit.  </s>            
 <s id="id.2.1.17.5.1.35.0"> lineaq; CO horizonti <lb/> 
 &aelig;quidi&longs;tans erit.  </s>              <s id="id.2.1.17.5.1.36.0"> non tamen puncti C horizonti (vt ip&longs;i exi&longs;ti&shy;<lb/>mant) &longs;ed ponderis in O con&longs;tituti, c&ugrave;m ex centro grauitatis <lb/>ponderis &longs;ummendus &longs;it horizon.  </s>
 <s id="id.2.1.17.5.1.36.0"> non tamen puncti C horizonti (vt ip&longs;i exi&longs;ti&shy;<lb/> 
 mant) &longs;ed ponderis in O con&longs;tituti, c&ugrave;m ex centro grauitatis <lb/> <s id="id.2.1.17.5.1.37.0"> qu&aelig; omnia demon&longs;trare opor&shy;<lb/>tebat.  </s>    
 ponderis &longs;ummendus &longs;it horizon.  </s> 
 <s id="id.2.1.17.5.1.37.0"> qu&aelig; omnia demon&longs;trare opor&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.17.5.2.1.0" type="caption">        
 tebat.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.17.5.2.1.0" type="caption">         
 <s id="id.2.1.17.5.2.1.0.capt"> YYY </s>      <s id="id.2.1.17.5.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.17.5.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.17.5.2.3.0" type="caption">        
  
 <s id="id.2.1.17.5.2.3.0.capt"> YYY </s>      <s id="id.2.1.17.5.2.3.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.17.5.2.5.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.17.5.2.5.0" type="caption">        
 <s id="id.2.1.17.5.2.5.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.18.1.0.0.0" type="margin">         <s id="id.2.1.17.5.2.5.0.capt"> YYY </s>    </p>       <p id="id.2.1.18.1.0.0.0" type="margin">        
  
 <s id="id.2.1.18.1.1.1.0"> <margin.target id="note33"></margin.target>18 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>              <s id="id.2.1.18.1.1.1.0"> <margin.target id="note33"></margin.target>18 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>            
 <s id="id.2.1.18.1.1.2.0"> <margin.target id="note34"></margin.target>21 <emph type="italics"/>primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.19.1.0.0.0" type="main">         <s id="id.2.1.18.1.1.2.0"> <margin.target id="note34"></margin.target>21 <emph type="italics"/>primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.19.1.0.0.0" type="main">        <pb n="12" xlink:href="pagethumb-la/00000041.JPG"/>      
 <pb n="12" xlink:href="pagethumb-la/00000041.JPG"/> 
         <s id="id.2.1.19.1.2.1.0"> Si autem libr&aelig; brachium ip&longs;o CO <lb/>fuerit maius, put&aacute; quantitate CD; erit <lb/>quoq; pondus in O grauius.  </s>            
 <s id="id.2.1.19.1.2.1.0"> Si autem libr&aelig; brachium ip&longs;o CO <lb/> 
 fuerit maius, put&aacute; quantitate CD; erit <lb/> <s id="id.2.1.19.1.2.2.0"> circulus de&shy;<lb/>&longs;cribatur OH, cuius centrum &longs;it D, &longs;e <arrow.to.target n="note35"></arrow.to.target><lb/>midiameterq; DO. tanget circulus OH <lb/>circulum FOG in puncto O, lineamq; <arrow.to.target n="note36"></arrow.to.target><lb/>OS, qu&aelig; ponderis in O rectus, natura&shy;<lb/>li&longs;q; e&longs;t de&longs;cen&longs;us, in eodem puncto con <lb/>tinget.  </s>            
 quoq; pondus in O grauius.  </s>              
 <s id="id.2.1.19.1.2.2.0"> circulus de&shy;<lb/> <s id="id.2.1.19.1.2.3.0"> &amp; quoniam angulus SOH mi&shy;<lb/>nor e&longs;t angulo SOG, erit de&longs;cen&longs;us <lb/>ponderis in O per circumferentiam OH <lb/>motui naturali OS propior, qu&agrave;m per <lb/>circumferentiam OG.  </s>    
 &longs;cribatur OH, cuius centrum &longs;it D, &longs;e <arrow.to.target n="note35"></arrow.to.target><lb/> 
 midiameterq; DO. tanget circulus OH <lb/> <s id="id.2.1.19.1.2.3.0.a"> magis ergo li&shy;<lb/>berum, atq; &longs;olutum, ac per con&longs;equens <lb/>grauius erit in O, centro libr&aelig; exi&longs;ten<lb/>te in D, qu&agrave;m in C. &longs;imiliter o&longs;ten&shy;<lb/>detur, qu&ograve; maius fuerit brachium DO, <lb/>pondus in O adhuc grauius e&longs;&longs;e. <figure id="fig20" place="text" xlink:href="figures1577/2000.03.0038.jpg">       </figure> </s>    </p>       <pb xlink:href="pagethumb-la/00000042.JPG"/>       <p id="id.2.1.19.3.0.0.0" type="main">        
 circulum FOG in puncto O, lineamq; <arrow.to.target n="note36"></arrow.to.target><lb/> 
 OS, qu&aelig; ponderis in O rectus, natura&shy;<lb/> <s id="id.2.1.19.3.1.1.0"> Siver&ograve; idem circulus AFBG, <lb/>cuius centrum &longs;it R, propius fuerit <lb/>mundi centro S; circulumqu&eacute; &agrave; pun&shy;<lb/>cto S ducatur contingens ST; punctum <lb/>T (vbi grauius e&longs;t pondus) magis <lb/>&agrave; puncto A di&longs;tabit, qu&agrave;m punctum <lb/>O. ducantur enim &agrave; punctis OT ip&longs;i <lb/>CS perpendiculares OMTN; conne<lb/>ctanturq; RT; &longs;itq; centrum R in li&shy;<lb/>nea CS; lineaq; ARB ip&longs;i ACB &aelig;qui <lb/><arrow.to.target n="note37"></arrow.to.target> di&longs;tans.  </s>            
 li&longs;q; e&longs;t de&longs;cen&longs;us, in eodem puncto con <lb/> 
 tinget.  </s>              <s id="id.2.1.19.3.1.2.0"> Quoniam igitur triangula COS <lb/>RTS &longs;unt rectangula; erit SC ad CO, <lb/>vt CO ad CM. &longs;imiliter SR ad RT, <lb/>vt RT ad RN. c&ugrave;m itaq; &longs;it RT ip&shy;<lb/><arrow.to.target n="note38"></arrow.to.target> &longs;i CO &aelig;qualis, &amp; SC ip&longs;a SR maior: <lb/>maiorem habebit proportionem SC <lb/>ad CO, qu&agrave;m SR ad RT. quare ma <lb/>iorem quoq; proportionem habebit <lb/>CO ad CM, qu&agrave;m RT ad RN.  </s>    
 <s id="id.2.1.19.1.2.3.0"> &amp; quoniam angulus SOH mi&shy;<lb/> 
 nor e&longs;t angulo SOG, erit de&longs;cen&longs;us <lb/> <s id="id.2.1.19.3.1.2.0.a"> mi <lb/><arrow.to.target n="note39"></arrow.to.target> nor ergo erit CM, qu&agrave;m RN. &longs;ecetur <lb/>igitur RN in P, ita vt RP &longs;it ip&longs;i <lb/><figure id="fig21" place="text" xlink:href="figures1577/2000.03.0039.jpg">       </figure><lb/>CM &aelig;qualis; &amp; &agrave; puncto P ip&longs;is MONT &aelig;quidi&longs;tans ducatur <lb/>PQ, qu&aelig; circumferentiam AT &longs;ecet in Q: deniq; connectatur <lb/><expan abbr="Rq.">Rque</expan> quoniam enim du&aelig; CO CM duabus RQRP &longs;unt &aelig;qua <lb/><arrow.to.target n="note40"></arrow.to.target> les, &amp; angulus CMO angulo RPQ e&longs;t &aelig;qualis; erit &amp; angu&shy;<lb/>lus MCO angulo PRQ &aelig;qualis.  </s>            
 ponderis in O per circumferentiam OH <lb/> 
 motui naturali OS propior, qu&agrave;m per <lb/> <s id="id.2.1.19.3.1.3.0"> angulus autem MCA rectus <lb/><arrow.to.target n="note41"></arrow.to.target> recto PRA e&longs;t &aelig;qualis; ergo reliquus OCA reliquo QRA <lb/>&aelig;qualis, &amp; circumferentia OA circumferenti&aelig; QA &aelig;qualis quo&shy;<lb/>que erit.  </s>            
 circumferentiam OG.  </s>      
 <s id="id.2.1.19.1.2.3.0.a"> magis ergo li&shy;<lb/> <s id="id.2.1.19.3.1.4.0"> punctum idcirco T, quia magis &agrave; puncto A di&longs;tat, <lb/>qu&agrave;m Q; magis quoq; &agrave; puncto A di&longs;tabit, qu&agrave;m punctum O. <lb/>&longs;imiliter o&longs;tendetur, qu&ograve; propius fuerit circulus mundi centro, eun&shy;<lb/>dem magis di&longs;tare.  </s>            
 berum, atq; &longs;olutum, ac per con&longs;equens <lb/> 
 grauius erit in O, centro libr&aelig; exi&longs;ten<lb/> <s id="id.2.1.19.3.1.5.0"> atq; ita vt prius demon&longs;trabitur pondus in cir<lb/>cumferentia TAF centro R inniti, in circumferentia ver&ograve; TG <lb/>&agrave; linea detineri; atq; in puncto T grauius e&longs;&longs;e.  </s>    
 te in D, qu&agrave;m in C. &longs;imiliter o&longs;ten&shy;<lb/> 
 detur, qu&ograve; maius fuerit brachium DO, <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.19.3.2.1.0" type="caption">        
 pondus in O adhuc grauius e&longs;&longs;e. <figure id="fig20" place="text" xlink:href="figures1577/2000.03.0038.jpg">       </figure> </s>    </p>        
 <pb xlink:href="pagethumb-la/00000042.JPG"/> 
         
 <p id="id.2.1.19.3.0.0.0" type="main">         
 <s id="id.2.1.19.3.1.1.0"> Siver&ograve; idem circulus AFBG, <lb/> 
 cuius centrum &longs;it R, propius fuerit <lb/> 
 mundi centro S; circulumqu&eacute; &agrave; pun&shy;<lb/> 
 cto S ducatur contingens ST; punctum <lb/> 
 T (vbi grauius e&longs;t pondus) magis <lb/> 
 &agrave; puncto A di&longs;tabit, qu&agrave;m punctum <lb/> 
 O. ducantur enim &agrave; punctis OT ip&longs;i <lb/> 
 CS perpendiculares OMTN; conne<lb/> 
 ctanturq; RT; &longs;itq; centrum R in li&shy;<lb/> 
 nea CS; lineaq; ARB ip&longs;i ACB &aelig;qui <lb/> 
 <arrow.to.target n="note37"></arrow.to.target> di&longs;tans.  </s>              
 <s id="id.2.1.19.3.1.2.0"> Quoniam igitur triangula COS <lb/> 
 RTS &longs;unt rectangula; erit SC ad CO, <lb/> 
 vt CO ad CM. &longs;imiliter SR ad RT, <lb/> 
 vt RT ad RN. c&ugrave;m itaq; &longs;it RT ip&shy;<lb/> 
 <arrow.to.target n="note38"></arrow.to.target> &longs;i CO &aelig;qualis, &amp; SC ip&longs;a SR maior: <lb/> 
 maiorem habebit proportionem SC <lb/> 
 ad CO, qu&agrave;m SR ad RT. quare ma <lb/> 
 iorem quoq; proportionem habebit <lb/> 
 CO ad CM, qu&agrave;m RT ad RN.  </s>      
 <s id="id.2.1.19.3.1.2.0.a"> mi <lb/> 
 <arrow.to.target n="note39"></arrow.to.target> nor ergo erit CM, qu&agrave;m RN. &longs;ecetur <lb/> 
 igitur RN in P, ita vt RP &longs;it ip&longs;i <lb/> 
 <figure id="fig21" place="text" xlink:href="figures1577/2000.03.0039.jpg">       </figure><lb/> 
 CM &aelig;qualis; &amp; &agrave; puncto P ip&longs;is MONT &aelig;quidi&longs;tans ducatur <lb/> 
 PQ, qu&aelig; circumferentiam AT &longs;ecet in Q: deniq; connectatur <lb/> 
 <expan abbr="Rq.">Rque</expan> quoniam enim du&aelig; CO CM duabus RQRP &longs;unt &aelig;qua <lb/> 
 <arrow.to.target n="note40"></arrow.to.target> les, &amp; angulus CMO angulo RPQ e&longs;t &aelig;qualis; erit &amp; angu&shy;<lb/> 
 lus MCO angulo PRQ &aelig;qualis.  </s>              
 <s id="id.2.1.19.3.1.3.0"> angulus autem MCA rectus <lb/> 
 <arrow.to.target n="note41"></arrow.to.target> recto PRA e&longs;t &aelig;qualis; ergo reliquus OCA reliquo QRA <lb/> 
 &aelig;qualis, &amp; circumferentia OA circumferenti&aelig; QA &aelig;qualis quo&shy;<lb/> 
 que erit.  </s>              
 <s id="id.2.1.19.3.1.4.0"> punctum idcirco T, quia magis &agrave; puncto A di&longs;tat, <lb/> 
 qu&agrave;m Q; magis quoq; &agrave; puncto A di&longs;tabit, qu&agrave;m punctum O. <lb/> 
 &longs;imiliter o&longs;tendetur, qu&ograve; propius fuerit circulus mundi centro, eun&shy;<lb/> 
 dem magis di&longs;tare.  </s>              
 <s id="id.2.1.19.3.1.5.0"> atq; ita vt prius demon&longs;trabitur pondus in cir<lb/> 
 cumferentia TAF centro R inniti, in circumferentia ver&ograve; TG <lb/> 
 &agrave; linea detineri; atq; in puncto T grauius e&longs;&longs;e.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.19.3.2.1.0" type="caption">         
 <s id="id.2.1.19.3.2.1.0.capt"> YYY </s>      <s id="id.2.1.19.3.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.19.3.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.19.3.2.3.0" type="caption">        
 <s id="id.2.1.19.3.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.20.1.0.0.0" type="margin">         <s id="id.2.1.19.3.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.20.1.0.0.0" type="margin">        
  
 <s id="id.2.1.20.1.1.1.0"> <margin.target id="note35"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 11 <emph type="italics"/>Ter tit.<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.1.0"> <margin.target id="note35"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 11 <emph type="italics"/>Ter tit.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.20.1.1.2.0"> <margin.target id="note36"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.2.0"> <margin.target id="note36"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 18 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.20.1.1.3.0"> <margin.target id="note37"></margin.target><emph type="italics"/>Cor.<emph.end type="italics"/> 8 <emph type="italics"/>&longs;exti<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.3.0"> <margin.target id="note37"></margin.target><emph type="italics"/>Cor.<emph.end type="italics"/> 8 <emph type="italics"/>&longs;exti<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.20.1.1.4.0"> <margin.target id="note38"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 8 <emph type="italics"/>quinti<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.4.0"> <margin.target id="note38"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 8 <emph type="italics"/>quinti<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.20.1.1.5.0"> <margin.target id="note39"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 10 <emph type="italics"/>quinti.<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.5.0"> <margin.target id="note39"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 10 <emph type="italics"/>quinti.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.20.1.1.6.0"> <margin.target id="note40"></margin.target>7 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>              <s id="id.2.1.20.1.1.6.0"> <margin.target id="note40"></margin.target>7 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>            
 <s id="id.2.1.20.1.1.7.0"> <margin.target id="note41"></margin.target>26 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.21.1.0.0.0" type="main">         <s id="id.2.1.20.1.1.7.0"> <margin.target id="note41"></margin.target>26 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.21.1.0.0.0" type="main">        <pb n="13" xlink:href="pagethumb-la/00000043.JPG"/>      
 <pb n="13" xlink:href="pagethumb-la/00000043.JPG"/> 
         <s id="id.2.1.21.1.2.1.0"> Si autem punctum G e&longs;&longs;et <lb/>in centro mundi; tunc qu&ograve; <lb/>pondus propius fuerit ip&longs;i G, <lb/>grauius erit: &amp; vbicunq; po<lb/>natur pondus pr&aelig;terqu&agrave;m in <lb/>ip&longs;o G, &longs;emper centro C inni<lb/>tetur, vt in K. nam ducta <lb/>G k, efficiet h&aelig;c (&longs;ecun&shy;<lb/>d&ugrave;m quam fit ponderis natu<lb/>ralis motus) vn&aacute; cum libr&aelig; <lb/>brachio k C angulum acu&shy;<lb/>tum.  </s>            
 <s id="id.2.1.21.1.2.1.0"> Si autem punctum G e&longs;&longs;et <lb/> 
 in centro mundi; tunc qu&ograve; <lb/> <s id="id.2.1.21.1.2.2.0"> &aelig;quicruris enim trian&shy;<lb/>guli CkG ad ba&longs;im anguli <lb/>ad k, &amp; G &longs;unt &longs;emper acuti.  </s>            
 pondus propius fuerit ip&longs;i G, <lb/> 
 grauius erit: &amp; vbicunq; po<lb/> <s id="id.2.1.21.1.2.3.0"> <lb/><figure id="fig22" place="text" xlink:href="figures1577/2000.03.0040.jpg">       </figure><lb/>Conferantur autem inuicem h&aelig;c duo, pondus videlicet in k, &amp; <lb/>pondus in D: erit pondus in k grauius, qu&agrave;m in D. nam iuncta <lb/>DG, c&ugrave;m tres anguli cuiu&longs;cunque trianguli duobus &longs;int rectis <lb/>&aelig;quales, &amp; trianguli CDG &aelig;quicruris angulus DCG maior &longs;it <lb/>angulo kCG &aelig;quicruris trianguli CkG: erunt reliqui ad ba&longs;im an<lb/>guli DGC GDC &longs;imul &longs;umpti reliquis KGCGkC &longs;imul &longs;umptis <lb/>minores.  </s>            
 natur pondus pr&aelig;terqu&agrave;m in <lb/> 
 ip&longs;o G, &longs;emper centro C inni<lb/> <s id="id.2.1.21.1.2.4.0"> horumq; dimidii; angulus &longs;cilicet CDG angulo CKG <lb/>minor erit.  </s>            
 tetur, vt in K. nam ducta <lb/> 
 G k, efficiet h&aelig;c (&longs;ecun&shy;<lb/> <s id="id.2.1.21.1.2.5.0"> quare c&ugrave;m pondus in k &longs;olutum naturaliter per <lb/>KG moueatur, pondusq; in D per DG, tanquam per &longs;patia, <lb/>quibus in centrum mundi feruntur; linea CD, hoc e&longs;t libr&aelig; <lb/>brachium magis adh&aelig;rebit motui naturali ponderis in D pror&shy;<lb/>&longs;us &longs;oluti, line&aelig; &longs;cilicet DG; qu&agrave;m Ck motui &longs;ecund&ugrave;m kG <lb/>effecto.  </s>            
 d&ugrave;m quam fit ponderis natu<lb/> 
 ralis motus) vn&aacute; cum libr&aelig; <lb/> 
 brachio k C angulum acu&shy;<lb/> 
 tum.  </s>              
 <s id="id.2.1.21.1.2.2.0"> &aelig;quicruris enim trian&shy;<lb/> 
 guli CkG ad ba&longs;im anguli <lb/> 
 ad k, &amp; G &longs;unt &longs;emper acuti.  </s>              
 <s id="id.2.1.21.1.2.3.0"> <lb/> 
 <figure id="fig22" place="text" xlink:href="figures1577/2000.03.0040.jpg">       </figure><lb/> 
 Conferantur autem inuicem h&aelig;c duo, pondus videlicet in k, &amp; <lb/> 
 pondus in D: erit pondus in k grauius, qu&agrave;m in D. nam iuncta <lb/> 
 DG, c&ugrave;m tres anguli cuiu&longs;cunque trianguli duobus &longs;int rectis <lb/> 
 &aelig;quales, &amp; trianguli CDG &aelig;quicruris angulus DCG maior &longs;it <lb/> 
 angulo kCG &aelig;quicruris trianguli CkG: erunt reliqui ad ba&longs;im an<lb/> 
 guli DGC GDC &longs;imul &longs;umpti reliquis KGCGkC &longs;imul &longs;umptis <lb/> 
 minores.  </s>              
 <s id="id.2.1.21.1.2.4.0"> horumq; dimidii; angulus &longs;cilicet CDG angulo CKG <lb/> 
 minor erit.  </s>              
 <s id="id.2.1.21.1.2.5.0"> quare c&ugrave;m pondus in k &longs;olutum naturaliter per <lb/> 
 KG moueatur, pondusq; in D per DG, tanquam per &longs;patia, <lb/> 
 quibus in centrum mundi feruntur; linea CD, hoc e&longs;t libr&aelig; <lb/> 
 brachium magis adh&aelig;rebit motui naturali ponderis in D pror&shy;<lb/> 
 &longs;us &longs;oluti, line&aelig; &longs;cilicet DG; qu&agrave;m Ck motui &longs;ecund&ugrave;m kG <lb/> 
 effecto.  </s>              
 <s id="id.2.1.21.1.2.6.0"> magis igitur &longs;u&longs;tinebit linea CD, qu&agrave;m Ck.  </s>              <s id="id.2.1.21.1.2.6.0"> magis igitur &longs;u&longs;tinebit linea CD, qu&agrave;m Ck.  </s>            
 <s id="id.2.1.21.1.2.7.0"> ac pro&shy;<lb/> 
 pterea pondus in k ex &longs;uperius dictis grauius erit, qu&agrave;m in D.  </s>      <s id="id.2.1.21.1.2.7.0"> ac pro&shy;<lb/>pterea pondus in k ex &longs;uperius dictis grauius erit, qu&agrave;m in D.  </s>    
 <s id="id.2.1.21.1.2.7.0.a"> <lb/> 
 Pr&aelig;terea quoniam pondus in K &longs;i e&longs;&longs;et omnino liberum, pror&longs;u&longs;q; <lb/> <s id="id.2.1.21.1.2.7.0.a"> <lb/>Pr&aelig;terea quoniam pondus in K &longs;i e&longs;&longs;et omnino liberum, pror&longs;u&longs;q; <lb/>&longs;olutum, deor&longs;um per k G moueretur; ni&longs;i &agrave; linea C k prohibere<lb/>tur, qu&aelig; pondus vltra lineam KG per circumferentiam KH mo&shy;<lb/>ueri cogit; linea C k pondus partim &longs;u&longs;tinebit, ip&longs;iq; renitetur; <lb/>c&ugrave;m illud per circumferentiam k H moueri compellat.  </s>            
 &longs;olutum, deor&longs;um per k G moueretur; ni&longs;i &agrave; linea C k prohibere<lb/> 
 tur, qu&aelig; pondus vltra lineam KG per circumferentiam KH mo&shy;<lb/> <s id="id.2.1.21.1.2.8.0"> &amp; <lb/>quoniam angulus CDG minor e&longs;t angulo CkG, &amp; angulus CDk <lb/>angulo CkH e&longs;t &aelig;qualis; erit reliquus GDk reliquo G k H maior.  </s>            
 ueri cogit; linea C k pondus partim &longs;u&longs;tinebit, ip&longs;iq; renitetur; <lb/> 
 c&ugrave;m illud per circumferentiam k H moueri compellat.  </s>              <s id="id.2.1.21.1.2.9.0"> <lb/>circumferentia igitur k H motui naturali ponderis in k &longs;oluti, li&shy;<pb xlink:href="pagethumb-la/00000044.JPG"/>ne&aelig; &longs;cilicet KG propior erit, <lb/>qu&agrave;m circumferentia Dk li&shy;<lb/>ne&aelig; DG. quare linea CD <lb/>ponderi in D magis renititur, <lb/>qu&agrave;m linea C k ip&longs;i ponde&shy;<lb/>ri in K.  </s>    
 <s id="id.2.1.21.1.2.8.0"> &amp; <lb/> 
 quoniam angulus CDG minor e&longs;t angulo CkG, &amp; angulus CDk <lb/> <s id="id.2.1.21.1.2.9.0.a"> ergo pondus in k <lb/>grauius erit, qu&agrave;m in D.  </s>    
 angulo CkH e&longs;t &aelig;qualis; erit reliquus GDk reliquo G k H maior.  </s>              
 <s id="id.2.1.21.1.2.9.0"> <lb/> <s id="id.2.1.21.1.2.9.0.b"> <lb/>Similiter o&longs;tendetur pondus, <lb/>qu&ograve; fuerit ip&longs;i F propius, vt <lb/>in L, minus grauitare: pro&shy;<lb/>pius ver&ograve; ip&longs;i G, vt in H, <lb/>grauius e&longs;&longs;e. <figure id="fig23" place="text" xlink:href="figures1577/2000.03.0041.jpg">       </figure> </s>    </p>       <p id="id.2.1.21.2.0.0.0" type="main">        
 circumferentia igitur k H motui naturali ponderis in k &longs;oluti, li&shy; 
 <pb xlink:href="pagethumb-la/00000044.JPG"/> <s id="id.2.1.21.2.1.1.0"> Si ver&ograve; centrum mundi <lb/>S e&longs;&longs;et inter puncta CG; <lb/>prim&ugrave;m quidem &longs;imili&shy;<lb/>ter o&longs;tendetur pondus vbi <lb/>cunq; po&longs;itum centro C <lb/>initi, vt in H. ductis enim <lb/>HG HS, angulus ad <lb/>ba&longs;im GHC &aelig;quicruris tri <lb/>anguli CHG e&longs;t &longs;emper <lb/>acutus: quare &amp; SHC ip<lb/>&longs;o minor erit quoq; &longs;em<lb/>per acutus.  </s>            
 ne&aelig; &longs;cilicet KG propior erit, <lb/> 
 qu&agrave;m circumferentia Dk li&shy;<lb/> <s id="id.2.1.21.2.1.2.0"> ducatur au&shy;<lb/>tem &agrave; puncto S ip&longs;i CS <lb/>perpendicularis Sk.  </s>            
 ne&aelig; DG. quare linea CD <lb/> 
 ponderi in D magis renititur, <lb/> <s id="id.2.1.21.2.1.3.0"> di&shy;<lb/><figure id="fig24" place="text" xlink:href="figures1577/2000.03.0042.1.jpg">       </figure><lb/>co pondus grauius e&longs;&longs;e in k, qu&agrave;m in alio &longs;itu circumferenti&aelig; FKG. <lb/>&amp; qu&ograve; propius fuerit ip&longs;i F, vel G, minus grauitare.  </s>            
 qu&agrave;m linea C k ip&longs;i ponde&shy;<lb/> 
 ri in K.  </s>      <s id="id.2.1.21.2.1.4.0"> Accipiantur <lb/>ver&longs;us F puncta DL, connectanturq; LC LS DC DS, produ&shy;<lb/>canturq; LS DS k SHS v&longs;q; ad circuli circumferentiam in EM <lb/>NO; connectanturq; CE, CM, CN, CO.  </s>    
 <s id="id.2.1.21.1.2.9.0.a"> ergo pondus in k <lb/> 
 grauius erit, qu&agrave;m in D.  </s>      <s id="id.2.1.21.2.1.4.0.a"> Quoniam enim <lb/><arrow.to.target n="note42"></arrow.to.target> LE DM &longs;e inuicem &longs;ecant in S; erit rectangulum LSE rectan&shy;<lb/><arrow.to.target n="note43"></arrow.to.target> gulo DSM &aelig;quale.  </s>            
 <s id="id.2.1.21.1.2.9.0.b"> <lb/> 
 Similiter o&longs;tendetur pondus, <lb/> <s id="id.2.1.21.2.1.5.0"> quare vt LS ad DS ita erit SM <lb/><arrow.to.target n="note44"></arrow.to.target> ad SE.  </s>    
 qu&ograve; fuerit ip&longs;i F propius, vt <lb/> 
 in L, minus grauitare: pro&shy;<lb/> 
 pius ver&ograve; ip&longs;i G, vt in H, <lb/> 
 grauius e&longs;&longs;e. <figure id="fig23" place="text" xlink:href="figures1577/2000.03.0041.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.21.2.0.0.0" type="main">         
 <s id="id.2.1.21.2.1.1.0"> Si ver&ograve; centrum mundi <lb/> 
 S e&longs;&longs;et inter puncta CG; <lb/> 
 prim&ugrave;m quidem &longs;imili&shy;<lb/> 
 ter o&longs;tendetur pondus vbi <lb/> 
 cunq; po&longs;itum centro C <lb/> 
 initi, vt in H. ductis enim <lb/> 
 HG HS, angulus ad <lb/> 
 ba&longs;im GHC &aelig;quicruris tri <lb/> 
 anguli CHG e&longs;t &longs;emper <lb/> 
 acutus: quare &amp; SHC ip<lb/> 
 &longs;o minor erit quoq; &longs;em<lb/> 
 per acutus.  </s>              
 <s id="id.2.1.21.2.1.2.0"> ducatur au&shy;<lb/> 
 tem &agrave; puncto S ip&longs;i CS <lb/> 
 perpendicularis Sk.  </s>              
 <s id="id.2.1.21.2.1.3.0"> di&shy;<lb/> 
 <figure id="fig24" place="text" xlink:href="figures1577/2000.03.0042.1.jpg">       </figure><lb/> 
 co pondus grauius e&longs;&longs;e in k, qu&agrave;m in alio &longs;itu circumferenti&aelig; FKG. <lb/> 
 &amp; qu&ograve; propius fuerit ip&longs;i F, vel G, minus grauitare.  </s>              
 <s id="id.2.1.21.2.1.4.0"> Accipiantur <lb/> 
 ver&longs;us F puncta DL, connectanturq; LC LS DC DS, produ&shy;<lb/> 
 canturq; LS DS k SHS v&longs;q; ad circuli circumferentiam in EM <lb/> 
 NO; connectanturq; CE, CM, CN, CO.  </s>      
 <s id="id.2.1.21.2.1.4.0.a"> Quoniam enim <lb/> 
 <arrow.to.target n="note42"></arrow.to.target> LE DM &longs;e inuicem &longs;ecant in S; erit rectangulum LSE rectan&shy;<lb/> 
 <arrow.to.target n="note43"></arrow.to.target> gulo DSM &aelig;quale.  </s>              
 <s id="id.2.1.21.2.1.5.0"> quare vt LS ad DS ita erit SM <lb/> 
 <arrow.to.target n="note44"></arrow.to.target> ad SE.  </s>      
 <s id="id.2.1.21.2.1.5.0.a"> maior autem e&longs;t LS, qu&agrave;m DS; &amp; SM ip&longs;a SE.  </s>      <s id="id.2.1.21.2.1.5.0.a"> maior autem e&longs;t LS, qu&agrave;m DS; &amp; SM ip&longs;a SE.  </s>    
 <s id="id.2.1.21.2.1.5.0.b">  
 <pb n="14" xlink:href="pagethumb-la/00000045.JPG"/> <s id="id.2.1.21.2.1.5.0.b"> <pb n="14" xlink:href="pagethumb-la/00000045.JPG"/>ergo LS SE &longs;imul &longs;umpt&aelig; ip&longs;is DS SM maiores erunt.  </s>            
 ergo LS SE &longs;imul &longs;umpt&aelig; ip&longs;is DS SM maiores erunt.  </s>              
 <s id="id.2.1.21.2.1.6.0"> eademq; <arrow.to.target n="note45"></arrow.to.target><lb/> <s id="id.2.1.21.2.1.6.0"> eademq; <arrow.to.target n="note45"></arrow.to.target><lb/>ratione kN minorem e&longs;&longs;e DM o&longs;tendetur.  </s>            
 ratione kN minorem e&longs;&longs;e DM o&longs;tendetur.  </s>              
 <s id="id.2.1.21.2.1.7.0"> rur&longs;us quoniam re<lb/> <s id="id.2.1.21.2.1.7.0"> rur&longs;us quoniam re<lb/>ctangulum OSH &aelig;quale e&longs;t rectangulo kSN; ob eandem cau&longs;am <lb/>HO maior erit kN. eodemq; pror&longs;us modo kN omnibus a&shy;<lb/>liis per punctum S tran&longs;euntibus minorem e&longs;&longs;e demon&longs;trabitur.  </s>            
 ctangulum OSH &aelig;quale e&longs;t rectangulo kSN; ob eandem cau&longs;am <lb/> 
 HO maior erit kN. eodemq; pror&longs;us modo kN omnibus a&shy;<lb/> <s id="id.2.1.21.2.1.8.0"> <lb/>&amp; quoniam &aelig;quicrurium triangulorum CLE DCM latera LC <lb/>CE lateribus DC CM &longs;unt &aelig;qualia; ba&longs;is ver&ograve; LE maior e&longs;t <lb/>DM: erit angulus LCE angulo DCM maior.  </s>            
 liis per punctum S tran&longs;euntibus minorem e&longs;&longs;e demon&longs;trabitur.  </s>              
 <s id="id.2.1.21.2.1.8.0"> <lb/> <s id="id.2.1.21.2.1.9.0"> quare ad ba&longs;im <arrow.to.target n="note46"></arrow.to.target><lb/>anguli C<emph type="italics"/>L<emph.end type="italics"/>E CEL &longs;imul &longs;umpti angulis CDM CMD mi&shy;<lb/>nores erunt.  </s>            
 &amp; quoniam &aelig;quicrurium triangulorum CLE DCM latera LC <lb/> 
 CE lateribus DC CM &longs;unt &aelig;qualia; ba&longs;is ver&ograve; LE maior e&longs;t <lb/> <s id="id.2.1.21.2.1.10.0"> &amp; horum dimidii, angulus &longs;cilicet CLS angulo CDS <lb/>minor erit.  </s>            
 DM: erit angulus LCE angulo DCM maior.  </s>              
 <s id="id.2.1.21.2.1.9.0"> quare ad ba&longs;im <arrow.to.target n="note46"></arrow.to.target><lb/> <s id="id.2.1.21.2.1.11.0"> ergo pondus in <emph type="italics"/>L<emph.end type="italics"/> magis &longs;upra lineam LC, qu&agrave;m <lb/>in D &longs;upra DC grauitabit, magisqu&eacute; centro innitetur in L, qu&agrave;m <lb/>in D. &longs;imiliter o&longs;tendetur in D magis <expan abbr="c&etilde;tro">centro</expan> C inniti, qu&agrave;m in k.  </s>            
 anguli C<emph type="italics"/>L<emph.end type="italics"/>E CEL &longs;imul &longs;umpti angulis CDM CMD mi&shy;<lb/> 
 nores erunt.  </s>              <s id="id.2.1.21.2.1.12.0"> ergo <lb/>ponds in k grauius erit, qu&agrave;m in D; &amp; in D, qu&agrave;m in L. eademq; pror <lb/>&longs;us ratione quoniam kN minor e&longs;t HO, erit angulus CKS an&shy;<lb/>gulo CHS maior.  </s>            
 <s id="id.2.1.21.2.1.10.0"> &amp; horum dimidii, angulus &longs;cilicet CLS angulo CDS <lb/> 
 minor erit.  </s>              <s id="id.2.1.21.2.1.13.0"> quare pondus in H magis centro C innite&shy;<lb/>tur, qu&agrave;m in k.  </s>            
 <s id="id.2.1.21.2.1.11.0"> ergo pondus in <emph type="italics"/>L<emph.end type="italics"/> magis &longs;upra lineam LC, qu&agrave;m <lb/> 
 in D &longs;upra DC grauitabit, magisqu&eacute; centro innitetur in L, qu&agrave;m <lb/> <s id="id.2.1.21.2.1.14.0"> &amp; hoc modo o&longs;tendetur, vbicunq; in circum&shy;<lb/>ferentia FDG fuerit pondus, minus in K centro C inniti, qu&agrave;m <lb/>in alio &longs;itu: &amp; qu&ograve; propius fuerit ip&longs;i F, vel G, magis inniti.  </s>            
 in D. &longs;imiliter o&longs;tendetur in D magis <expan abbr="c&etilde;tro">centro</expan> C inniti, qu&agrave;m in k.  </s>              
 <s id="id.2.1.21.2.1.12.0"> ergo <lb/> <s id="id.2.1.21.2.1.15.0"> dein&shy;<lb/>de quoniam angulus CkS maior e&longs;t CDS, &amp; CDk &aelig;qualis <lb/>e&longs;t CkH: erit reliquus SkH reliquo SDk minor.  </s>            
 ponds in k grauius erit, qu&agrave;m in D; &amp; in D, qu&agrave;m in L. eademq; pror <lb/> 
 &longs;us ratione quoniam kN minor e&longs;t HO, erit angulus CKS an&shy;<lb/> <s id="id.2.1.21.2.1.16.0"> quare cir&shy;<lb/>cumferentia k H propior erit motui naturali recto ponderis in K <lb/>&longs;oluti, line&aelig; &longs;cilicet k S, qu&agrave;m circumferentia D k motui DS. &amp; <lb/>ideo linea CD magis ip&longs;i ponderi in D renititur, qu&agrave;m CK <lb/>ponderi in k con&longs;tituto.  </s>            
 gulo CHS maior.  </s>              
 <s id="id.2.1.21.2.1.13.0"> quare pondus in H magis centro C innite&shy;<lb/> <s id="id.2.1.21.2.1.17.0"> hacq; ratione o&longs;tendetur angulum <lb/>SHG maiorem e&longs;&longs;e SkH: &amp; per con&longs;equens lineam CH magis <lb/>ponderi in H reniti, qu&agrave;m CK ponderi in K. &longs;imiliter demon&shy;<lb/>&longs;trabitur lineam C<emph type="italics"/>L<emph.end type="italics"/> magis pondus &longs;u&longs;tinere, qu&agrave;m CD: ob <lb/>ea&longs;demq; cau&longs;as o&longs;tendetur pondus in K minus &longs;upra lineam Ck <lb/>grauitare, qu&agrave;m in quouis alio &longs;itu fuerit circumferenti&aelig; FDG. <lb/>&amp; qu&ograve; propius fuerit ip&longs;i F, vel G, minus grauitare.  </s>            
 tur, qu&agrave;m in k.  </s>              
 <s id="id.2.1.21.2.1.14.0"> &amp; hoc modo o&longs;tendetur, vbicunq; in circum&shy;<lb/> <s id="id.2.1.21.2.1.18.0"> grauius ergo <lb/>erit in k, qu&agrave;m in alio &longs;itu: minu&longs;q; graue erit, qu&ograve; propius fue&shy;<lb/>rit ip&longs;i F. vel G. <pb xlink:href="pagethumb-la/00000046.JPG"/> </s>    
 ferentia FDG fuerit pondus, minus in K centro C inniti, qu&agrave;m <lb/> 
 in alio &longs;itu: &amp; qu&ograve; propius fuerit ip&longs;i F, vel G, magis inniti.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.21.2.2.1.0" type="caption">        
 <s id="id.2.1.21.2.1.15.0"> dein&shy;<lb/> 
 de quoniam angulus CkS maior e&longs;t CDS, &amp; CDk &aelig;qualis <lb/> 
 e&longs;t CkH: erit reliquus SkH reliquo SDk minor.  </s>              
 <s id="id.2.1.21.2.1.16.0"> quare cir&shy;<lb/> 
 cumferentia k H propior erit motui naturali recto ponderis in K <lb/> 
 &longs;oluti, line&aelig; &longs;cilicet k S, qu&agrave;m circumferentia D k motui DS. &amp; <lb/> 
 ideo linea CD magis ip&longs;i ponderi in D renititur, qu&agrave;m CK <lb/> 
 ponderi in k con&longs;tituto.  </s>              
 <s id="id.2.1.21.2.1.17.0"> hacq; ratione o&longs;tendetur angulum <lb/> 
 SHG maiorem e&longs;&longs;e SkH: &amp; per con&longs;equens lineam CH magis <lb/> 
 ponderi in H reniti, qu&agrave;m CK ponderi in K. &longs;imiliter demon&shy;<lb/> 
 &longs;trabitur lineam C<emph type="italics"/>L<emph.end type="italics"/> magis pondus &longs;u&longs;tinere, qu&agrave;m CD: ob <lb/> 
 ea&longs;demq; cau&longs;as o&longs;tendetur pondus in K minus &longs;upra lineam Ck <lb/> 
 grauitare, qu&agrave;m in quouis alio &longs;itu fuerit circumferenti&aelig; FDG. <lb/> 
 &amp; qu&ograve; propius fuerit ip&longs;i F, vel G, minus grauitare.  </s>              
 <s id="id.2.1.21.2.1.18.0"> grauius ergo <lb/> 
 erit in k, qu&agrave;m in alio &longs;itu: minu&longs;q; graue erit, qu&ograve; propius fue&shy;<lb/> 
 rit ip&longs;i F. vel G.  
 <pb xlink:href="pagethumb-la/00000046.JPG"/> 
  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.21.2.2.1.0" type="caption">         
 <s id="id.2.1.21.2.2.1.0.capt"> YYY </s>      <s id="id.2.1.21.2.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.21.2.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.21.2.2.3.0" type="caption">        
  
 <s id="id.2.1.21.2.2.3.0.capt"> YYY </s>      <s id="id.2.1.21.2.2.3.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.21.2.2.5.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.21.2.2.5.0" type="caption">        
 <s id="id.2.1.21.2.2.5.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.22.1.0.0.0" type="margin">         <s id="id.2.1.21.2.2.5.0.capt"> YYY </s>    </p>       <p id="id.2.1.22.1.0.0.0" type="margin">        
  
 <s id="id.2.1.22.1.1.1.0"> <margin.target id="note42"></margin.target>35 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>              <s id="id.2.1.22.1.1.1.0"> <margin.target id="note42"></margin.target>35 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.22.1.1.2.0"> <margin.target id="note43"></margin.target>16 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>              <s id="id.2.1.22.1.1.2.0"> <margin.target id="note43"></margin.target>16 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.22.1.1.3.0"> <margin.target id="note44"></margin.target>7 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>              <s id="id.2.1.22.1.1.3.0"> <margin.target id="note44"></margin.target>7 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.22.1.1.4.0"> <margin.target id="note45"></margin.target>25 <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>              <s id="id.2.1.22.1.1.4.0"> <margin.target id="note45"></margin.target>25 <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>            
 <s id="id.2.1.22.1.1.5.0"> <margin.target id="note46"></margin.target>25 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.23.1.0.0.0" type="main">         <s id="id.2.1.22.1.1.5.0"> <margin.target id="note46"></margin.target>25 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.23.1.0.0.0" type="main">        
 <s id="id.2.1.23.1.1.1.0"> Si deniq; centrum C <lb/> 
 e&longs;&longs;et in centro mundi, <lb/> <s id="id.2.1.23.1.1.1.0"> Si deniq; centrum C <lb/>e&longs;&longs;et in centro mundi, <lb/>pondus vbicunque con&shy;<lb/>&longs;titutum manere mani&shy;<lb/>fe&longs;tum e&longs;t.  </s>            
 pondus vbicunque con&shy;<lb/> 
 &longs;titutum manere mani&shy;<lb/> <s id="id.2.1.23.1.1.2.0"> vt po&longs;ito pon<lb/>dere in D, linea CD to&shy;<lb/>tum &longs;u&longs;tinebit pondus; <lb/>c&ugrave;m ip&longs;ius ponderis in D <lb/>horizonti &longs;it perpendicu <lb/><arrow.to.target n="note47"></arrow.to.target> laris.  </s>            
 fe&longs;tum e&longs;t.  </s>              
 <s id="id.2.1.23.1.1.2.0"> vt po&longs;ito pon<lb/> <s id="id.2.1.23.1.1.3.0"> pondus ergo ma <lb/>nebit. <figure id="fig25" place="text" xlink:href="figures1577/2000.03.0042.2.jpg">       </figure> </s>    </p>       <p id="id.2.1.23.2.0.0.0" type="main">        
 dere in D, linea CD to&shy;<lb/> 
 tum &longs;u&longs;tinebit pondus; <lb/> <s id="id.2.1.23.2.1.1.0"> Quoniam autem in his hactenus demon&longs;tratis, nullam de gra<lb/>uitate brachii libr&aelig; mentionem fecimus, idcirco &longs;i brach&longs;i quoq; <lb/>grauitatem con&longs;iderare voluerimus, centrum grauitatis magnitu<lb/>dinis ex pondere, brachioq; compo&longs;it&aelig; inueniri poterit, circulo<lb/>rumq; circumferenti&aelig; &longs;ecundum di&longs;tantiam &agrave; centro libr&aelig; ad <lb/>hoc ip&longs;um grauitatis centrum de&longs;cribentur, ac &longs;i in ip&longs;o (vt re ue<lb/>ra e&longs;t) pondus con&longs;titutum fuerit; omnia, &longs;icuti ab&longs;q; libr&aelig; bra<lb/>chii grauitate con&longs;iderata inuenimus; hoc quoq; modo eius con&longs;i<lb/>derata grauitate reperiemus.  </s>    
 c&ugrave;m ip&longs;ius ponderis in D <lb/> 
 horizonti &longs;it perpendicu <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.23.2.2.1.0" type="caption">        
 <arrow.to.target n="note47"></arrow.to.target> laris.  </s>              
 <s id="id.2.1.23.1.1.3.0"> pondus ergo ma <lb/> <s id="id.2.1.23.2.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.24.1.0.0.0" type="margin">        
 nebit. <figure id="fig25" place="text" xlink:href="figures1577/2000.03.0042.2.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.23.2.0.0.0" type="main">         <s id="id.2.1.24.1.1.1.0"> <margin.target id="note47"></margin.target>1 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.25.1.0.0.0" type="main">        <pb n="15" xlink:href="pagethumb-la/00000047.JPG"/>      
 <s id="id.2.1.23.2.1.1.0"> Quoniam autem in his hactenus demon&longs;tratis, nullam de gra<lb/> 
 uitate brachii libr&aelig; mentionem fecimus, idcirco &longs;i brach&longs;i quoq; <lb/> <s id="id.2.1.25.1.2.1.0"> Ex dictis igitur, con&longs;iderando li&shy;<lb/>bram, vt long&egrave; &agrave; mundi centro a&shy;<lb/>be&longs;t, quemadmodum ip&longs;i fecere, &longs;i&shy;<lb/>cuti etiam actu e&longs;t, apparet fal&longs;itas <lb/>dicentium pondus in A grauius e&longs;&longs;e, <lb/>qu&agrave;m in alio &longs;itu.  </s>            
 grauitatem con&longs;iderare voluerimus, centrum grauitatis magnitu<lb/> 
 dinis ex pondere, brachioq; compo&longs;it&aelig; inueniri poterit, circulo<lb/> <s id="id.2.1.25.1.2.2.0"> &longs;imulq; fal&longs;um e&longs;&longs;e, <lb/>qu&ograve; pondus &agrave; linea FG magis di&longs;tat <lb/>grauiuis e&longs;&longs;e.  </s>            
 rumq; circumferenti&aelig; &longs;ecundum di&longs;tantiam &agrave; centro libr&aelig; ad <lb/> 
 hoc ip&longs;um grauitatis centrum de&longs;cribentur, ac &longs;i in ip&longs;o (vt re ue<lb/> <s id="id.2.1.25.1.2.3.0"> nam punctum O pro&shy;<lb/>pius e&longs;t ip&longs;i FG, qu&agrave;m punctum A. <lb/>e&longs;t enim linea &agrave; puncto O ip&longs;i FG <arrow.to.target n="note48"></arrow.to.target><lb/>perpendicularis ip&longs;a CA minor.  </s>            
 ra e&longs;t) pondus con&longs;titutum fuerit; omnia, &longs;icuti ab&longs;q; libr&aelig; bra<lb/> 
 chii grauitate con&longs;iderata inuenimus; hoc quoq; modo eius con&longs;i<lb/> <s id="id.2.1.25.1.2.4.0"> de&shy;<lb/>inde ex puncto A pondus velocius mo <lb/>ueri, qu&agrave;m ab alio &longs;itu, e&longs;t quoque <lb/>fal&longs;um.  </s>            
 derata grauitate reperiemus.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.25.1.2.5.0"> ex puncto enim O pondus ve&shy;<lb/>locius mouebitur, qu&agrave;m ex puncto <lb/>A; c&ugrave;m in O &longs;it magis liberum, atq; <lb/>&longs;olutum, qu&agrave;m in alio &longs;itu: de&longs;cen&longs;us <lb/>qu&eacute; ex puncto O propior &longs;it motui na&shy;<lb/>turali recto, qu&agrave;m quilibet alius de&shy;<lb/>&longs;cen&longs;us. <figure id="fig26" place="text" xlink:href="figures1577/2000.03.0044.jpg">       </figure> </s>    </p>       <p id="id.2.1.25.2.0.0.0" type="main">        
 <p id="id.2.1.23.2.2.1.0" type="caption">         
 <s id="id.2.1.23.2.2.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.25.2.1.1.0"> Pr&aelig;terea c&ugrave;m ex re&shy;<lb/>ctiori, &amp; obliquiori <expan abbr="defc&etilde;">defcem</expan> <lb/>&longs;u o&longs;tendunt, pondus in <lb/>A grauiur e&longs;&longs;e, qu&agrave;m in <lb/>D; &amp; in D, qu&agrave;m in <lb/>L; prim&ugrave;m quidem fal<lb/>&longs;um exi&longs;timant, &longs;i pon<lb/>dus aliquod collocatum <lb/>fuerit in quocunq; &longs;itu <lb/>circunferenti&aelig;, vt in D, <lb/>rectum eius de&longs;cen&longs;um <lb/>per rectam lineam DR <lb/>ip&longs;i FG parallelam, tam <lb/>qu&agrave;m &longs;ecund&ugrave;m mo&shy;|tum<figure id="fig27" place="text" xlink:href="figures1577/2000.03.0045.1.jpg">       </figure><pb xlink:href="pagethumb-la/00000048.JPG"/> naturalem fieri de&shy;<lb/>bere; &longs;icuti prius dictum <lb/>e&longs;t.  </s>            
 <p id="id.2.1.24.1.0.0.0" type="margin">         
 <s id="id.2.1.24.1.1.1.0"> <margin.target id="note47"></margin.target>1 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>        <s id="id.2.1.25.2.1.2.0"> In quocunq; enim <lb/>&longs;itu pondus aliquod con<lb/>&longs;tituatur, &longs;i naturalem <lb/>eius ad propium locum <lb/>motionem &longs;pectemus, <lb/>c&ugrave;m rect&aacute; ad eum <expan abbr="&longs;ua&shy;pt&egrave;">&longs;ua&shy;<lb/>pte</expan> natura moueatur, &longs;up<lb/>po&longs;ita totius vniuer&longs;i figu<lb/>ra, eiu&longs;modi erit; vt <lb/>&longs;emper <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, per quod <lb/>naturaliter mouetur, ra&shy;<lb/>tionem habere videatur <lb/><figure id="fig28" place="text" xlink:href="figures1577/2000.03.0045.2.jpg">       </figure><lb/>line&aelig; &agrave; circumferentia ad centrum product&aelig;.  </s>            
 <p id="id.2.1.25.1.0.0.0" type="main">         
 <pb n="15" xlink:href="pagethumb-la/00000047.JPG"/> <s id="id.2.1.25.2.1.3.0"> non igitur natura<lb/>les de&longs;cen&longs;us recti cuiuslibet &longs;oluti ponderis per lineas fieri po&longs;<lb/>&longs;unt inter &longs;e &longs;e parallelas; c&ugrave;m omnes in centrum mundi conue&shy;<lb/>niant.  </s>            
         
 <s id="id.2.1.25.1.2.1.0"> Ex dictis igitur, con&longs;iderando li&shy;<lb/> <s id="id.2.1.25.2.1.4.0"> &longs;upponunt deinde ponderis ex D in A per rectam lineam <lb/>ver&longs;us centrum mundi motum eiu&longs;dem e&longs;&longs;e quantitatis, ac &longs;i fui&longs;<lb/>&longs;et ex O in C: ita vt punctum A &aelig;qualiter &agrave; centro mundi &longs;it <lb/>di&longs;tans, vt C. quod e&longs;t etiam fal&longs;um; nam punctum A magis <lb/>&agrave; centro mundi di&longs;tat, qu&agrave;m C: maior enim e&longs;t linea &agrave; cen&shy;<lb/><arrow.to.target n="note49"></arrow.to.target> tro mundi v&longs;q; ad A, qu&agrave;m &agrave; centro mundi v&longs;q; ad C: c&ugrave;m li&shy;<lb/>nea &agrave; centro mundi v&longs;q; ad A rectum &longs;ubtendat angulum &agrave; li&shy;<lb/>neis AC, &amp; &agrave; puncto C ad centrum mundi contentum.  </s>            
 bram, vt long&egrave; &agrave; mundi centro a&shy;<lb/> 
 be&longs;t, quemadmodum ip&longs;i fecere, &longs;i&shy;<lb/> <s id="id.2.1.25.2.1.5.0"> ex qui&shy;<lb/>bus non &longs;olum &longs;uppo&longs;itio illa, qua libram DE in AB redire demon<lb/>&longs;trant, ver&ugrave;m etiam omnes fer&egrave; ip&longs;orum demon&longs;trationes ruunt.  </s>            
 cuti etiam actu e&longs;t, apparet fal&longs;itas <lb/> 
 dicentium pondus in A grauius e&longs;&longs;e, <lb/> <s id="id.2.1.25.2.1.6.0"> <lb/>ni&longs;i forta&longs;&longs;e dixerint, h&aelig;c omnia propter maximam &agrave; centro mun<lb/>di v&longs;q; ad nos di&longs;tantiam adeo in&longs;en&longs;ibilia e&longs;&longs;e, vt propter in&longs;en<lb/>&longs;ibilitatem tanquam vera &longs;upponi po&longs;sint: c&ugrave;m omnes <expan abbr="quid&etilde;">quidem</expan> alii, qui <lb/>h&aelig;c tractauerunt, tanquam nota &longs;uppo&longs;uerint.  </s>            
 qu&agrave;m in alio &longs;itu.  </s>              
 <s id="id.2.1.25.1.2.2.0"> &longs;imulq; fal&longs;um e&longs;&longs;e, <lb/> <s id="id.2.1.25.2.1.7.0"> pr&aelig;&longs;ertim quia <lb/>&longs;en&longs;ibilitas illa non efficit, quin de&longs;cen&longs;us ponderis ex L in D <lb/>(vt eorum verbis vtar) minus capiat de directo, qu&agrave;m de&longs;cen&shy;<lb/>&longs;us DA. &longs;imiliter arcus DA magis de directo capiet, qu&agrave;m cir<lb/>cumferentia EV. quocirca vera erit &longs;uppo&longs;itio; ali&aelig;q; demon&shy;<lb/>&longs;trationes in &longs;uo robore permanebunt.  </s>            
 qu&ograve; pondus &agrave; linea FG magis di&longs;tat <lb/> 
 grauiuis e&longs;&longs;e.  </s>              <s id="id.2.1.25.2.1.8.0"> Concedamus etiam pon <pb n="16" xlink:href="pagethumb-la/00000049.JPG"/>dus in A grauius e&longs;&longs;e, qu&agrave;m in alio &longs;itu; rectumq; ponderis de&shy;<lb/>&longs;cen&longs;um per rectam lineam ip&longs;i FG parallelam fieri debere; &amp; <lb/>qu&aelig;libet puncta in lineis horizonti &aelig;quidi&longs;tantibus accepta &aelig;&shy;<lb/>qualiter &agrave; centro mundi di&longs;tare: non tamen propterea &longs;equetur, <lb/>veram e&longs;&longs;e demon&longs;trationem, qua inferunt pondus in A grauius <lb/>e&longs;&longs;e, qu&agrave;m in alio &longs;itu, vt in L. &longs;i enim verum e&longs;&longs;et, qu&ograve; pon<lb/>dus hoc modo rectius de&longs;cendit, ibi grauius e&longs;&longs;e; &longs;equeretur etiam, <lb/>qu&ograve; idem pondus in &aelig;qualibus arcubus &aelig;qualiter rect&egrave; de&longs;cende <lb/>ret, vt in ii&longs;dem locis &aelig;qualem haberet grauitatem, quod fal<lb/>&longs;um e&longs;&longs;e ita demon&longs;tratur. </s>    
 <s id="id.2.1.25.1.2.3.0"> nam punctum O pro&shy;<lb/> 
 pius e&longs;t ip&longs;i FG, qu&agrave;m punctum A. <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.25.2.2.1.0" type="caption">        
 e&longs;t enim linea &agrave; puncto O ip&longs;i FG <arrow.to.target n="note48"></arrow.to.target><lb/> 
 perpendicularis ip&longs;a CA minor.  </s>              
 <s id="id.2.1.25.1.2.4.0"> de&shy;<lb/> 
 inde ex puncto A pondus velocius mo <lb/> 
 ueri, qu&agrave;m ab alio &longs;itu, e&longs;t quoque <lb/> 
 fal&longs;um.  </s>              
 <s id="id.2.1.25.1.2.5.0"> ex puncto enim O pondus ve&shy;<lb/> 
 locius mouebitur, qu&agrave;m ex puncto <lb/> 
 A; c&ugrave;m in O &longs;it magis liberum, atq; <lb/> 
 &longs;olutum, qu&agrave;m in alio &longs;itu: de&longs;cen&longs;us <lb/> 
 qu&eacute; ex puncto O propior &longs;it motui na&shy;<lb/> 
 turali recto, qu&agrave;m quilibet alius de&shy;<lb/> 
 &longs;cen&longs;us. <figure id="fig26" place="text" xlink:href="figures1577/2000.03.0044.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.25.2.0.0.0" type="main">         
 <s id="id.2.1.25.2.1.1.0"> Pr&aelig;terea c&ugrave;m ex re&shy;<lb/> 
 ctiori, &amp; obliquiori <expan abbr="defc&etilde;">defcem</expan> <lb/> 
 &longs;u o&longs;tendunt, pondus in <lb/> 
 A grauiur e&longs;&longs;e, qu&agrave;m in <lb/> 
 D; &amp; in D, qu&agrave;m in <lb/> 
 L; prim&ugrave;m quidem fal<lb/> 
 &longs;um exi&longs;timant, &longs;i pon<lb/> 
 dus aliquod collocatum <lb/> 
 fuerit in quocunq; &longs;itu <lb/> 
 circunferenti&aelig;, vt in D, <lb/> 
 rectum eius de&longs;cen&longs;um <lb/> 
 per rectam lineam DR <lb/> 
 ip&longs;i FG parallelam, tam <lb/> 
 qu&agrave;m &longs;ecund&ugrave;m mo&shy;|tum<figure id="fig27" place="text" xlink:href="figures1577/2000.03.0045.1.jpg">       </figure> 
 <pb xlink:href="pagethumb-la/00000048.JPG"/> 
  naturalem fieri de&shy;<lb/> 
 bere; &longs;icuti prius dictum <lb/> 
 e&longs;t.  </s>              
 <s id="id.2.1.25.2.1.2.0"> In quocunq; enim <lb/> 
 &longs;itu pondus aliquod con<lb/> 
 &longs;tituatur, &longs;i naturalem <lb/> 
 eius ad propium locum <lb/> 
 motionem &longs;pectemus, <lb/> 
 c&ugrave;m rect&aacute; ad eum <expan abbr="&longs;ua&shy;pt&egrave;">&longs;ua&shy;<lb/> 
 pte</expan> natura moueatur, &longs;up<lb/> 
 po&longs;ita totius vniuer&longs;i figu<lb/> 
 ra, eiu&longs;modi erit; vt <lb/> 
 &longs;emper <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, per quod <lb/> 
 naturaliter mouetur, ra&shy;<lb/> 
 tionem habere videatur <lb/> 
 <figure id="fig28" place="text" xlink:href="figures1577/2000.03.0045.2.jpg">       </figure><lb/> 
 line&aelig; &agrave; circumferentia ad centrum product&aelig;.  </s>              
 <s id="id.2.1.25.2.1.3.0"> non igitur natura<lb/> 
 les de&longs;cen&longs;us recti cuiuslibet &longs;oluti ponderis per lineas fieri po&longs;<lb/> 
 &longs;unt inter &longs;e &longs;e parallelas; c&ugrave;m omnes in centrum mundi conue&shy;<lb/> 
 niant.  </s>              
 <s id="id.2.1.25.2.1.4.0"> &longs;upponunt deinde ponderis ex D in A per rectam lineam <lb/> 
 ver&longs;us centrum mundi motum eiu&longs;dem e&longs;&longs;e quantitatis, ac &longs;i fui&longs;<lb/> 
 &longs;et ex O in C: ita vt punctum A &aelig;qualiter &agrave; centro mundi &longs;it <lb/> 
 di&longs;tans, vt C. quod e&longs;t etiam fal&longs;um; nam punctum A magis <lb/> 
 &agrave; centro mundi di&longs;tat, qu&agrave;m C: maior enim e&longs;t linea &agrave; cen&shy;<lb/> 
 <arrow.to.target n="note49"></arrow.to.target> tro mundi v&longs;q; ad A, qu&agrave;m &agrave; centro mundi v&longs;q; ad C: c&ugrave;m li&shy;<lb/> 
 nea &agrave; centro mundi v&longs;q; ad A rectum &longs;ubtendat angulum &agrave; li&shy;<lb/> 
 neis AC, &amp; &agrave; puncto C ad centrum mundi contentum.  </s>              
 <s id="id.2.1.25.2.1.5.0"> ex qui&shy;<lb/> 
 bus non &longs;olum &longs;uppo&longs;itio illa, qua libram DE in AB redire demon<lb/> 
 &longs;trant, ver&ugrave;m etiam omnes fer&egrave; ip&longs;orum demon&longs;trationes ruunt.  </s>              
 <s id="id.2.1.25.2.1.6.0"> <lb/> 
 ni&longs;i forta&longs;&longs;e dixerint, h&aelig;c omnia propter maximam &agrave; centro mun<lb/> 
 di v&longs;q; ad nos di&longs;tantiam adeo in&longs;en&longs;ibilia e&longs;&longs;e, vt propter in&longs;en<lb/> 
 &longs;ibilitatem tanquam vera &longs;upponi po&longs;sint: c&ugrave;m omnes <expan abbr="quid&etilde;">quidem</expan> alii, qui <lb/> 
 h&aelig;c tractauerunt, tanquam nota &longs;uppo&longs;uerint.  </s>              
 <s id="id.2.1.25.2.1.7.0"> pr&aelig;&longs;ertim quia <lb/> 
 &longs;en&longs;ibilitas illa non efficit, quin de&longs;cen&longs;us ponderis ex L in D <lb/> 
 (vt eorum verbis vtar) minus capiat de directo, qu&agrave;m de&longs;cen&shy;<lb/> 
 &longs;us DA. &longs;imiliter arcus DA magis de directo capiet, qu&agrave;m cir<lb/> 
 cumferentia EV. quocirca vera erit &longs;uppo&longs;itio; ali&aelig;q; demon&shy;<lb/> 
 &longs;trationes in &longs;uo robore permanebunt.  </s>              
 <s id="id.2.1.25.2.1.8.0"> Concedamus etiam pon  
 <pb n="16" xlink:href="pagethumb-la/00000049.JPG"/> 
 dus in A grauius e&longs;&longs;e, qu&agrave;m in alio &longs;itu; rectumq; ponderis de&shy;<lb/> 
 &longs;cen&longs;um per rectam lineam ip&longs;i FG parallelam fieri debere; &amp; <lb/> 
 qu&aelig;libet puncta in lineis horizonti &aelig;quidi&longs;tantibus accepta &aelig;&shy;<lb/> 
 qualiter &agrave; centro mundi di&longs;tare: non tamen propterea &longs;equetur, <lb/> 
 veram e&longs;&longs;e demon&longs;trationem, qua inferunt pondus in A grauius <lb/> 
 e&longs;&longs;e, qu&agrave;m in alio &longs;itu, vt in L. &longs;i enim verum e&longs;&longs;et, qu&ograve; pon<lb/> 
 dus hoc modo rectius de&longs;cendit, ibi grauius e&longs;&longs;e; &longs;equeretur etiam, <lb/> 
 qu&ograve; idem pondus in &aelig;qualibus arcubus &aelig;qualiter rect&egrave; de&longs;cende <lb/> 
 ret, vt in ii&longs;dem locis &aelig;qualem haberet grauitatem, quod fal<lb/> 
 &longs;um e&longs;&longs;e ita demon&longs;tratur. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.25.2.2.1.0" type="caption">         
 <s id="id.2.1.25.2.2.1.0.capt"> YYY </s>      <s id="id.2.1.25.2.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.25.2.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.25.2.2.3.0" type="caption">        
  
 <s id="id.2.1.25.2.2.3.0.capt"> YYY </s>      <s id="id.2.1.25.2.2.3.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.25.2.2.5.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.25.2.2.5.0" type="caption">        
 <s id="id.2.1.25.2.2.5.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.26.1.0.0.0" type="margin">         <s id="id.2.1.25.2.2.5.0.capt"> YYY </s>    </p>       <p id="id.2.1.26.1.0.0.0" type="margin">        
  
 <s id="id.2.1.26.1.1.1.0"> <margin.target id="note48"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 15 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>              <s id="id.2.1.26.1.1.1.0"> <margin.target id="note48"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 15 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>            
 <s id="id.2.1.26.1.1.2.0"> <margin.target id="note49"></margin.target>18 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.27.1.0.0.0" type="main">         <s id="id.2.1.26.1.1.2.0"> <margin.target id="note49"></margin.target>18 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.27.1.0.0.0" type="main">        
 <s id="id.2.1.27.1.1.1.0"> Sint circumferenti&aelig; AL AM inter &longs;e &longs;e &aelig;quales; &amp; conne<lb/> 
 ctatur LM, qu&aelig; AB &longs;ecet in X: erit LM ip&longs;i FG &aelig;quidi&longs;tans, <lb/> <s id="id.2.1.27.1.1.1.0"> Sint circumferenti&aelig; AL AM inter &longs;e &longs;e &aelig;quales; &amp; conne<lb/>ctatur LM, qu&aelig; AB &longs;ecet in X: erit LM ip&longs;i FG &aelig;quidi&longs;tans, <lb/>ip&longs;iq; AB perpendicularis.  </s>            
 ip&longs;iq; AB perpendicularis.  </s>              
 <s id="id.2.1.27.1.1.2.0"> &amp; XM ip&longs;i XL &aelig;qualis erit.  </s>              <s id="id.2.1.27.1.1.2.0"> &amp; XM ip&longs;i XL &aelig;qualis erit.  </s>            
 <s id="id.2.1.27.1.1.3.0"> &longs;i igi<arrow.to.target n="note50"></arrow.to.target><lb/> 
 tur pondus ex L moueatur in A per circumferentiam LA, rectus <lb/> <s id="id.2.1.27.1.1.3.0"> &longs;i igi<arrow.to.target n="note50"></arrow.to.target><lb/>tur pondus ex L moueatur in A per circumferentiam LA, rectus <lb/>eius motus erit &longs;ecund&ugrave;m lineam LX. &longs;i ver&ograve; moueatur ex A <lb/>in M per circum&longs;erentiam AM, &longs;ecund&ugrave;m rectam eius motus <lb/>erit XM. quare de&longs;cen&longs;us ex L in A &aelig;qualis erit de&longs;cen&longs;ui ex A <lb/>in M; tum ob circumferentias &aelig;quales, tum propter rectas li <lb/>neas ip&longs;i AB perpendiculares &aelig;quales.  </s>            
 eius motus erit &longs;ecund&ugrave;m lineam LX. &longs;i ver&ograve; moueatur ex A <lb/> 
 in M per circum&longs;erentiam AM, &longs;ecund&ugrave;m rectam eius motus <lb/> <s id="id.2.1.27.1.1.4.0"> ergo idem pondus in L <lb/>&aelig;qu&egrave; graue erit, vt in A, quod e&longs;t fal&longs;um.  </s>            
 erit XM. quare de&longs;cen&longs;us ex L in A &aelig;qualis erit de&longs;cen&longs;ui ex A <lb/> 
 in M; tum ob circumferentias &aelig;quales, tum propter rectas li <lb/> <s id="id.2.1.27.1.1.5.0"> cum long&eacute; grauius &longs;it <lb/>in A, qu&agrave;m in L. </s>    </p>       <p id="id.2.1.28.1.0.0.0" type="margin">        
 neas ip&longs;i AB perpendiculares &aelig;quales.  </s>              
 <s id="id.2.1.27.1.1.4.0"> ergo idem pondus in L <lb/> <s id="id.2.1.28.1.1.1.0"> <margin.target id="note50"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 3 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.29.1.0.0.0" type="main">        
 &aelig;qu&egrave; graue erit, vt in A, quod e&longs;t fal&longs;um.  </s>              
 <s id="id.2.1.27.1.1.5.0"> cum long&eacute; grauius &longs;it <lb/> <s id="id.2.1.29.1.1.1.0"> Quamuis autem AMLA &aelig;qualiter &longs;ecund&ugrave;m ip&longs;os de directo <lb/>capiant; dicent forta&longs;&longs;e, quia tamen principium de&longs;cen&longs;us ex L <lb/>&longs;cilicet LD minus de directo capit, qu&agrave;m principium de&longs;cen&longs;us <lb/>ex A, &longs;cilicet AN; pondus in A grauius erit, qu&agrave;m in L. nam <lb/>c&ugrave;m circumferentia AN &longs;it ip&longs;i LD (vt &longs;upra po&longs;itum e&longs;t) <lb/>&aelig;qualis, qu&aelig; &longs;ecund&ugrave;m ip&longs;os de directo capit CT; LD ver&ograve; <lb/>de directo capit PO. ideo pondus grauius erit in A, qu&agrave;m in L. <lb/>quod &longs;i verum e&longs;&longs;et, &longs;equeretur idem pondus in eodem &longs;itu diuer<lb/>&longs;o duntaxat modo con&longs;ideratum in habitudine ad eundem &longs;itum, <lb/>tum grauius, tum leuius e&longs;&longs;e.  </s>
 in A, qu&agrave;m in L. </s>    </p>        
 <p id="id.2.1.28.1.0.0.0" type="margin">         
 <s id="id.2.1.28.1.1.1.0"> <margin.target id="note50"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 3 <emph type="italics"/>Tertii.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.29.1.0.0.0" type="main">         
 <s id="id.2.1.29.1.1.1.0"> Quamuis autem AMLA &aelig;qualiter &longs;ecund&ugrave;m ip&longs;os de directo <lb/> 
 capiant; dicent forta&longs;&longs;e, quia tamen principium de&longs;cen&longs;us ex L <lb/> 
 &longs;cilicet LD minus de directo capit, qu&agrave;m principium de&longs;cen&longs;us <lb/> 
 ex A, &longs;cilicet AN; pondus in A grauius erit, qu&agrave;m in L. nam <lb/> 
 c&ugrave;m circumferentia AN &longs;it ip&longs;i LD (vt &longs;upra po&longs;itum e&longs;t) <lb/> 
 &aelig;qualis, qu&aelig; &longs;ecund&ugrave;m ip&longs;os de directo capit CT; LD ver&ograve; <lb/> 
 de directo capit PO. ideo pondus grauius erit in A, qu&agrave;m in L. <lb/> 
 quod &longs;i verum e&longs;&longs;et, &longs;equeretur idem pondus in eodem &longs;itu diuer<lb/> 
 &longs;o duntaxat modo con&longs;ideratum in habitudine ad eundem &longs;itum, <lb/> 
 tum grauius, tum leuius e&longs;&longs;e.  </s> 
 <s id="id.2.1.29.1.1.2.0"> quod e&longs;t impo&longs;sibile.  </s>              <s id="id.2.1.29.1.1.2.0"> quod e&longs;t impo&longs;sibile.  </s>            
 <s id="id.2.1.29.1.1.3.0"> hoc e&longs;t, &longs;i <lb/> 
 de&longs;cen&longs;um con&longs;ideremus ponderis in L, quatenus ex L in A de&shy;<lb/> <s id="id.2.1.29.1.1.3.0"> hoc e&longs;t, &longs;i <lb/>de&longs;cen&longs;um con&longs;ideremus ponderis in L, quatenus ex L in A de&shy;<lb/>&longs;cendit, grauius erit, qu&agrave;m &longs;i eiu&longs;dem ponderis de&longs;cen&longs;um con&shy;<lb/>&longs;ideremus ex L in D tant&ugrave;m.  </s>            
 &longs;cendit, grauius erit, qu&agrave;m &longs;i eiu&longs;dem ponderis de&longs;cen&longs;um con&shy;<lb/> 
 &longs;ideremus ex L in D tant&ugrave;m.  </s>              <s id="id.2.1.29.1.1.4.0"> neq; enim negare po&longs;&longs;unt ex ei&longs;&shy;<lb/>demmet dictis, quin de&longs;cen&longs;us ponderis ex L in A de directo ca <lb/>piat LX, &longs;iue PC. de&longs;cen&longs;us ver&ograve; AM, quin &longs;imiliter de directo <pb xlink:href="pagethumb-la/00000050.JPG"/>capiat XM: c&ugrave;m ip&longs;i <lb/>quoq; hoc modo acci&shy;<lb/>piant, atq; ita accipe&shy;<lb/>re &longs;it nece&longs;&longs;e.  </s>            
 <s id="id.2.1.29.1.1.4.0"> neq; enim negare po&longs;&longs;unt ex ei&longs;&shy;<lb/> 
 demmet dictis, quin de&longs;cen&longs;us ponderis ex L in A de directo ca <lb/> <s id="id.2.1.29.1.1.5.0"> &longs;i enim li&shy;<lb/>bram DE in AB redire <lb/>demon&longs;trare volunt, com<lb/>parando de&longs;cen&longs;us pon&shy;<lb/>deris in D cum de&longs;cen&shy;<lb/>&longs;u ponderis in E, nece&longs;&longs;e <lb/>e&longs;t, vt o&longs;tendant rectum <lb/>de&longs;cen&longs;um OC corre&shy;<lb/>&longs;pondentem circumferen<lb/>ti&aelig; DA maiorem e&longs;&longs;e re<lb/>cto de&longs;cen&longs;u TH circum<lb/><figure id="fig29" place="text" xlink:href="figures1577/2000.03.0046.jpg">       </figure><lb/>ferenti&aelig; EV corre&longs;pondente.  </s>            
 piat LX, &longs;iue PC. de&longs;cen&longs;us ver&ograve; AM, quin &longs;imiliter de directo  
 <pb xlink:href="pagethumb-la/00000050.JPG"/> <s id="id.2.1.29.1.1.6.0"> &longs;i enim partem tant&ugrave;m totius de&shy;<lb/>&longs;cen&longs;us ex D in A acciperent, vt D k; o&longs;tenderentq; magis cape&shy;<lb/>re de directo de&longs;cen&longs;um Dk, qu&agrave;m &aelig;qualis portio de&longs;cen&longs;us ex <lb/>puncto E. &longs;equetur pondus in D &longs;ecund&ugrave;m ip&longs;os grauius e&longs;&longs;e pon<lb/>dere in E; &amp; v&longs;q; ad k tant&ugrave;m deor&longs;um moueri: ita vt libra mo<lb/>ta &longs;it in kI. &longs;imiliter &longs;i libram KI in AB redire demon&longs;trare vo<lb/>lunt accipiendo portionem de&longs;cen&longs;us ex k in A; hoc e&longs;t k S; <lb/>o&longs;tenderentq; k S magis de directo capere, qu&agrave;m ex aduer&longs;o &aelig;&shy;<lb/>qualis de&longs;cen&longs;us ex puncto I: &longs;imili modo &longs;equetur pondus in k <lb/>grauius e&longs;&longs;e, qu&agrave;m in I; &amp; v&longs;q; ad S tant&ugrave;m moueri.  </s>            
 capiat XM: c&ugrave;m ip&longs;i <lb/> 
 quoq; hoc modo acci&shy;<lb/> <s id="id.2.1.29.1.1.7.0"> &amp; &longs;i rur&longs;us <lb/>o&longs;tenderent portionem de&longs;cen&longs;us ex S in A, atq; ita deinceps, re<lb/>ctiorem e&longs;&longs;e &aelig;quali de&longs;cen&longs;u ponderis oppo&longs;iti; &longs;emper &longs;equetur <lb/>libram SI ad AB propius accedere, nunquam tamen in AB per&shy;<lb/>uenire demon&longs;trabunt.  </s>            
 piant, atq; ita accipe&shy;<lb/> 
 re &longs;it nece&longs;&longs;e.  </s>              <s id="id.2.1.29.1.1.8.0"> &longs;i igitur libram DE in AB redire demon<lb/>&longs;trare volunt, nece&longs;&longs;e e&longs;t, vt de&longs;cen&longs;um ponderis ex D in A de di <lb/>recro capere quantitatem line&aelig; ex puncto D ip&longs;i AB ad rectos <lb/>angulos duct&aelig; accipiant.  </s>            
 <s id="id.2.1.29.1.1.5.0"> &longs;i enim li&shy;<lb/> 
 bram DE in AB redire <lb/> <s id="id.2.1.29.1.1.9.0"> atq; ita, &longs;i &aelig;quales de&longs;cen&longs;us DA AN <lb/>inuicem comparemus, qui &aelig;qualiter de directo capient OC CT, <lb/>cueniet idem pondus in D &aelig;qu&egrave; graue e&longs;&longs;e, vt in A. &longs;i ver&ograve; por<lb/>tiones tantum ex D A accipiamus; grauius erit in A, qu&agrave;m <lb/>in D. ergo ex diuer&longs;itate tant&ugrave;m modi con&longs;iderandi, idem pon<lb/>dus, &amp; grauius, &amp; leuius e&longs;&longs;e continget.  </s>
 demon&longs;trare volunt, com<lb/> 
 parando de&longs;cen&longs;us pon&shy;<lb/> <s id="id.2.1.29.1.1.10.0"> non autem exip&longs;a na&shy;<pb n="17" xlink:href="pagethumb-la/00000051.JPG"/>tura rei.  </s>            
 deris in D cum de&longs;cen&shy;<lb/> 
 &longs;u ponderis in E, nece&longs;&longs;e <lb/> <s id="id.2.1.29.1.1.11.0"> In&longs;uper ip&longs;orum &longs;uppo&longs;itio non a&longs;&longs;erit, pondus &longs;ecun<lb/>d&ugrave;m &longs;itum grauius e&longs;&longs;e, quant&ograve; in eodem &longs;itu minus obliquum <lb/>e&longs;t principium ip&longs;ius de&longs;cen&longs;us.  </s>            
 e&longs;t, vt o&longs;tendant rectum <lb/> 
 de&longs;cen&longs;um OC corre&shy;<lb/> <s id="id.2.1.29.1.1.12.0"> Suppo&longs;itio igitur &longs;uperius alla<lb/>ta, hoc e&longs;t, &longs;ecund&ugrave;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo <lb/>dem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us; non &longs;olum ex his, qu&aelig; <lb/>diximus, vllo modo concedi pote&longs;t; &longs;ed quoniam huius oppo&longs;i<lb/>tum o&longs;tendere quoq; non e&longs;t difficile: &longs;cilicet idem pondus in <lb/>&aelig;qualibus circumferentiis, qu&ograve; minus obliquus e&longs;t de&longs;cen&longs;us, ibi <lb/>minus grauitare. </s>    
 &longs;pondentem circumferen<lb/> 
 ti&aelig; DA maiorem e&longs;&longs;e re<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.29.1.2.1.0" type="caption">        
 cto de&longs;cen&longs;u TH circum<lb/> 
 <figure id="fig29" place="text" xlink:href="figures1577/2000.03.0046.jpg">       </figure><lb/> <s id="id.2.1.29.1.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.29.2.0.0.0" type="main">        
 ferenti&aelig; EV corre&longs;pondente.  </s>              
 <s id="id.2.1.29.1.1.6.0"> &longs;i enim partem tant&ugrave;m totius de&shy;<lb/> <s id="id.2.1.29.2.1.1.0"> Sint enim vt prius cir <lb/>cumferentr&aelig; AL AM <lb/>inter &longs;e &longs;e &aelig;quales; &longs;itq; <lb/>punctum L prop&egrave; F. &amp; <lb/>connectatur LM, qu&aelig; <lb/>ip&longs;i AB perpendicularis <lb/>erit.  </s>
 &longs;cen&longs;us ex D in A acciperent, vt D k; o&longs;tenderentq; magis cape&shy;<lb/> 
 re de directo de&longs;cen&longs;um Dk, qu&agrave;m &aelig;qualis portio de&longs;cen&longs;us ex <lb/> <s id="id.2.1.29.2.1.2.0"> &amp; LX ip&longs;i XM <lb/>&aelig;qualis.  </s>            
 puncto E. &longs;equetur pondus in D &longs;ecund&ugrave;m ip&longs;os grauius e&longs;&longs;e pon<lb/> 
 dere in E; &amp; v&longs;q; ad k tant&ugrave;m deor&longs;um moueri: ita vt libra mo<lb/> <s id="id.2.1.29.2.1.3.0"> deinde prop&egrave; <lb/>M inter MG quoduis <lb/>accipiatur punctum P. <lb/>fiatq; circumferentia PO <lb/>circumferenti&aelig; AM &aelig;&shy;<lb/>qualis.  </s>            
 ta &longs;it in kI. &longs;imiliter &longs;i libram KI in AB redire demon&longs;trare vo<lb/> 
 lunt accipiendo portionem de&longs;cen&longs;us ex k in A; hoc e&longs;t k S; <lb/> <s id="id.2.1.29.2.1.4.0"> erit punctum O <lb/><figure id="fig30" place="text" xlink:href="figures1577/2000.03.0048.jpg">       </figure><expan abbr="prop&egrave;"><lb/>prope</expan> A. connectanturq; CL, CO, CM, CP, OP. &amp; &agrave; <lb/>puncto P ip&longs;i OC perpendicularis ducatur PN.  </s>    
 o&longs;tenderentq; k S magis de directo capere, qu&agrave;m ex aduer&longs;o &aelig;&shy;<lb/> 
 qualis de&longs;cen&longs;us ex puncto I: &longs;imili modo &longs;equetur pondus in k <lb/> <s id="id.2.1.29.2.1.4.0.a"> &amp; quoniam cir<lb/>cumferentia AM circumferenti&aelig; OP e&longs;t &aelig;qualis: erit angu&shy;<lb/>lus  <arrow.to.target n="note51"></arrow.to.target> ACM &aelig;qualis angulo OCP; &amp; angulus CXM rectus re&shy;<lb/>cto CNP e&longs;t &aelig;qualis: erit quoq; reliquus XMC trianguli MCX <arrow.to.target n="note52"></arrow.to.target><lb/>reliquo NPC trianguli PCN &aelig;qualis.  </s>            
 grauius e&longs;&longs;e, qu&agrave;m in I; &amp; v&longs;q; ad S tant&ugrave;m moueri.  </s>              
 <s id="id.2.1.29.1.1.7.0"> &amp; &longs;i rur&longs;us <lb/> <s id="id.2.1.29.2.1.5.0"> &longs;ed &amp; latus CM lateri <arrow.to.target n="note53"></arrow.to.target><lb/>CP e&longs;t &aelig;quale: ergo triangulum MCX triangulo PCN &aelig;quale <lb/>erit.  </s>
 o&longs;tenderent portionem de&longs;cen&longs;us ex S in A, atq; ita deinceps, re<lb/> 
 ctiorem e&longs;&longs;e &aelig;quali de&longs;cen&longs;u ponderis oppo&longs;iti; &longs;emper &longs;equetur <lb/> 
 libram SI ad AB propius accedere, nunquam tamen in AB per&shy;<lb/> 
 uenire demon&longs;trabunt.  </s>              
 <s id="id.2.1.29.1.1.8.0"> &longs;i igitur libram DE in AB redire demon<lb/> 
 &longs;trare volunt, nece&longs;&longs;e e&longs;t, vt de&longs;cen&longs;um ponderis ex D in A de di <lb/> 
 recro capere quantitatem line&aelig; ex puncto D ip&longs;i AB ad rectos <lb/> 
 angulos duct&aelig; accipiant.  </s>              
 <s id="id.2.1.29.1.1.9.0"> atq; ita, &longs;i &aelig;quales de&longs;cen&longs;us DA AN <lb/> 
 inuicem comparemus, qui &aelig;qualiter de directo capient OC CT, <lb/> 
 cueniet idem pondus in D &aelig;qu&egrave; graue e&longs;&longs;e, vt in A. &longs;i ver&ograve; por<lb/> 
 tiones tantum ex D A accipiamus; grauius erit in A, qu&agrave;m <lb/> 
 in D. ergo ex diuer&longs;itate tant&ugrave;m modi con&longs;iderandi, idem pon<lb/> 
 dus, &amp; grauius, &amp; leuius e&longs;&longs;e continget.  </s> 
 <s id="id.2.1.29.1.1.10.0"> non autem exip&longs;a na&shy; 
 <pb n="17" xlink:href="pagethumb-la/00000051.JPG"/> 
 tura rei.  </s>              
 <s id="id.2.1.29.1.1.11.0"> In&longs;uper ip&longs;orum &longs;uppo&longs;itio non a&longs;&longs;erit, pondus &longs;ecun<lb/> 
 d&ugrave;m &longs;itum grauius e&longs;&longs;e, quant&ograve; in eodem &longs;itu minus obliquum <lb/> 
 e&longs;t principium ip&longs;ius de&longs;cen&longs;us.  </s>              
 <s id="id.2.1.29.1.1.12.0"> Suppo&longs;itio igitur &longs;uperius alla<lb/> 
 ta, hoc e&longs;t, &longs;ecund&ugrave;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo <lb/> 
 dem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us; non &longs;olum ex his, qu&aelig; <lb/> 
 diximus, vllo modo concedi pote&longs;t; &longs;ed quoniam huius oppo&longs;i<lb/> 
 tum o&longs;tendere quoq; non e&longs;t difficile: &longs;cilicet idem pondus in <lb/> 
 &aelig;qualibus circumferentiis, qu&ograve; minus obliquus e&longs;t de&longs;cen&longs;us, ibi <lb/> 
 minus grauitare. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.29.1.2.1.0" type="caption">         
 <s id="id.2.1.29.1.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.29.2.0.0.0" type="main">         
 <s id="id.2.1.29.2.1.1.0"> Sint enim vt prius cir <lb/> 
 cumferentr&aelig; AL AM <lb/> 
 inter &longs;e &longs;e &aelig;quales; &longs;itq; <lb/> 
 punctum L prop&egrave; F. &amp; <lb/> 
 connectatur LM, qu&aelig; <lb/> 
 ip&longs;i AB perpendicularis <lb/> 
 erit.  </s> 
 <s id="id.2.1.29.2.1.2.0"> &amp; LX ip&longs;i XM <lb/> 
 &aelig;qualis.  </s>              
 <s id="id.2.1.29.2.1.3.0"> deinde prop&egrave; <lb/> 
 M inter MG quoduis <lb/> 
 accipiatur punctum P. <lb/> 
 fiatq; circumferentia PO <lb/> 
 circumferenti&aelig; AM &aelig;&shy;<lb/> 
 qualis.  </s>              
 <s id="id.2.1.29.2.1.4.0"> erit punctum O <lb/> 
 <figure id="fig30" place="text" xlink:href="figures1577/2000.03.0048.jpg">       </figure><expan abbr="prop&egrave;"><lb/> 
 prope</expan> A. connectanturq; CL, CO, CM, CP, OP. &amp; &agrave; <lb/> 
 puncto P ip&longs;i OC perpendicularis ducatur PN.  </s>      
 <s id="id.2.1.29.2.1.4.0.a"> &amp; quoniam cir<lb/> 
 cumferentia AM circumferenti&aelig; OP e&longs;t &aelig;qualis: erit angu&shy;<lb/> 
 lus  <arrow.to.target n="note51"></arrow.to.target> ACM &aelig;qualis angulo OCP; &amp; angulus CXM rectus re&shy;<lb/> 
 cto CNP e&longs;t &aelig;qualis: erit quoq; reliquus XMC trianguli MCX <arrow.to.target n="note52"></arrow.to.target><lb/> 
 reliquo NPC trianguli PCN &aelig;qualis.  </s>              
 <s id="id.2.1.29.2.1.5.0"> &longs;ed &amp; latus CM lateri <arrow.to.target n="note53"></arrow.to.target><lb/> 
 CP e&longs;t &aelig;quale: ergo triangulum MCX triangulo PCN &aelig;quale <lb/> 
 erit.  </s> 
 <s id="id.2.1.29.2.1.6.0"> latu&longs;q; MX lateri NP &aelig;quale.  </s>              <s id="id.2.1.29.2.1.6.0"> latu&longs;q; MX lateri NP &aelig;quale.  </s>            
 <s id="id.2.1.29.2.1.7.0"> quare linea PN ip&longs;i LX &aelig;qua <lb/> 
 lis erit.  </s>              <s id="id.2.1.29.2.1.7.0"> quare linea PN ip&longs;i LX &aelig;qua <lb/>lis erit.  </s>            
 <s id="id.2.1.29.2.1.8.0"> ducatur pr&aelig;terea &agrave; puncto O linea OT ip&longs;i AC &aelig;qui <lb/> 
 di&longs;tans, qu&aelig; NP &longs;ecet in V. atq; ip&longs;i OT &agrave; puncto P perpendi<lb/> <s id="id.2.1.29.2.1.8.0"> ducatur pr&aelig;terea &agrave; puncto O linea OT ip&longs;i AC &aelig;qui <lb/>di&longs;tans, qu&aelig; NP &longs;ecet in V. atq; ip&longs;i OT &agrave; puncto P perpendi<lb/>cularis ducatur, qu&aelig; quidem inter OV cadere non pote&longs;t; nam <lb/>c&ugrave;m angulus ONV &longs;it rectus; erit OVN acutus.  </s>            
 cularis ducatur, qu&aelig; quidem inter OV cadere non pote&longs;t; nam <lb/> 
 c&ugrave;m angulus ONV &longs;it rectus; erit OVN acutus.  </s>              <s id="id.2.1.29.2.1.9.0"> quare OVP <arrow.to.target n="note54"></arrow.to.target><lb/>obtu&longs;us erit.  </s>            
 <s id="id.2.1.29.2.1.9.0"> quare OVP <arrow.to.target n="note54"></arrow.to.target><lb/> 
 obtu&longs;us erit.  </s>              <s id="id.2.1.29.2.1.10.0"> non igitur linea &agrave; puncto P ip&longs;i OT intra OV <pb xlink:href="pagethumb-la/00000052.JPG"/>perpendicularis cadet.  </s>            
 <s id="id.2.1.29.2.1.10.0"> non igitur linea &agrave; puncto P ip&longs;i OT intra OV  
 <pb xlink:href="pagethumb-la/00000052.JPG"/> <s id="id.2.1.29.2.1.11.0"> <lb/>duo enim anguli vnius <lb/>trianguli, vnus quidem <lb/>rectus, alter ver&ograve; ob&shy;<lb/>tu&longs;us e&longs;&longs;et.  </s>
 perpendicularis cadet.  </s>              
 <s id="id.2.1.29.2.1.11.0"> <lb/> <s id="id.2.1.29.2.1.12.0"> quod e&longs;t im<lb/>po&longs;sibile.  </s>            
 duo enim anguli vnius <lb/> 
 trianguli, vnus quidem <lb/> <s id="id.2.1.29.2.1.13.0"> cadet ergo in <lb/>linea OT in parte VT. <lb/>&longs;itq; PT. erit PT &longs;ecun<lb/>d&ugrave;m ip&longs;os rectus circum<lb/>ferenti&aelig; OP de&longs;cen&longs;us.  </s>            
 rectus, alter ver&ograve; ob&shy;<lb/> 
 tu&longs;us e&longs;&longs;et.  </s> <s id="id.2.1.29.2.1.14.0"> <lb/>Quoniam igitur angulus <lb/>ONV e&longs;t rectus; erit <lb/><arrow.to.target n="note55"></arrow.to.target> linea OV ip&longs;a ON ma<lb/>ior.  </s>            
 <s id="id.2.1.29.2.1.12.0"> quod e&longs;t im<lb/> 
 po&longs;sibile.  </s>              <s id="id.2.1.29.2.1.15.0"> quare OT ip&longs;a <lb/><figure id="fig31" place="text" xlink:href="figures1577/2000.03.0049.jpg">       </figure><lb/>quoq; ON maior exi&longs;tet.  </s>            
 <s id="id.2.1.29.2.1.13.0"> cadet ergo in <lb/> 
 linea OT in parte VT. <lb/> <s id="id.2.1.29.2.1.16.0"> C&ugrave;m itaq; lin&egrave;a OP angulos &longs;ubten&shy;<lb/>dat rectos ONP OTP; erit quadratum ex OP quadratis ex <lb/><arrow.to.target n="note56"></arrow.to.target> ON NP &longs;imul &longs;umptis &aelig;quale.  </s>            
 &longs;itq; PT. erit PT &longs;ecun<lb/> 
 d&ugrave;m ip&longs;os rectus circum<lb/> <s id="id.2.1.29.2.1.17.0"> &longs;imiliter quadratis ex OT TP <lb/>&longs;imul &aelig;quale.  </s>            
 ferenti&aelig; OP de&longs;cen&longs;us.  </s>              
 <s id="id.2.1.29.2.1.14.0"> <lb/> <s id="id.2.1.29.2.1.18.0"> quare quadrata &longs;imul ex ON NP quadratis ex <lb/>OT TP &longs;imul &aelig;qualia erunt.  </s>            
 Quoniam igitur angulus <lb/> 
 ONV e&longs;t rectus; erit <lb/> <s id="id.2.1.29.2.1.19.0"> quadratum autem ex OT maius <lb/>e&longs;t quadrato ex ON; cum linea OT &longs;it ip&longs;a ON maior.  </s>            
 <arrow.to.target n="note55"></arrow.to.target> linea OV ip&longs;a ON ma<lb/> 
 ior.  </s>              <s id="id.2.1.29.2.1.20.0"> ergo qua<lb/>dratum ex NP maius erit quadrato ex TP. ac propterea linea <lb/>TP minor erit linea PN, &amp; linea LX. minus obliquus igitur e&longs;t <lb/>de&longs;cen&longs;us arcus LA, qu&agrave;m arcus OP.  </s>    
 <s id="id.2.1.29.2.1.15.0"> quare OT ip&longs;a <lb/> 
 <figure id="fig31" place="text" xlink:href="figures1577/2000.03.0049.jpg">       </figure><lb/> <s id="id.2.1.29.2.1.20.0.a"> ergo pondus in L, ex ip<lb/>&longs;orum dictis, grauius erit, qu&agrave;m in O. quod ex iis, qu&aelig; &longs;upra di<lb/>ximus e&longs;t manife&longs;t&egrave; fal&longs;um, c&ugrave;m pondus in O grauius &longs;it, qu&agrave;m <lb/>in L.  </s>    
 quoq; ON maior exi&longs;tet.  </s>              
 <s id="id.2.1.29.2.1.16.0"> C&ugrave;m itaq; lin&egrave;a OP angulos &longs;ubten&shy;<lb/> <s id="id.2.1.29.2.1.20.0.b"> non igitur ex rectiori, &amp; obliquiori motu ita accepto col&shy;<lb/>ligi pote&longs;t, &longs;ecund&ugrave;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo <lb/>dem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us.  </s>            
 dat rectos ONP OTP; erit quadratum ex OP quadratis ex <lb/> 
 <arrow.to.target n="note56"></arrow.to.target> ON NP &longs;imul &longs;umptis &aelig;quale.  </s>              <s id="id.2.1.29.2.1.21.0"> Atq; hinc oritur omnis <lb/>ferm&eacute; ip&longs;orum error in hacre, atq; deceptio: nam quamuis per <lb/>accidens interdum ex fal&longs;is &longs;equatur verum, per &longs;e tamen ex fal<lb/>&longs;is fal&longs;um &longs;equitur, quemadmodum ex veris &longs;emper verum, nil <lb/>idcirco mirum, &longs;i dum fal&longs;a accipiunt; illi&longs;q; tanquam veri&longs;si&shy;<lb/>mis innituntur; fal&longs;i&longs;sima omnin&ograve; colligunt, atq; concludunt.  </s>            
 <s id="id.2.1.29.2.1.17.0"> &longs;imiliter quadratis ex OT TP <lb/> 
 &longs;imul &aelig;quale.  </s>              <s id="id.2.1.29.2.1.22.0"> <lb/>decipiuntur quinetiam, d&ugrave;m libr&aelig; contemplationem mathemati<lb/>c&egrave; &longs;impliciter a&longs;&longs;ummunt; c&ugrave;m eius con&longs;ideratio &longs;it pror&longs;us me&shy;<lb/>chanica: nec vllo modo ab&longs;q; vero motu, ac ponderibus (en&shy;<pb n="18" xlink:href="pagethumb-la/00000053.JPG"/>tibus omnin&ograve; naturalibus) de ip&longs;a &longs;ermo haberi po&longs;sit: &longs;ine qui&shy;<lb/>bus eorum, qu&aelig; libr&aelig; accidunt, ver&aelig; caul&aelig; reperiri nullo mo <lb/>do po&longs;sint. </s>    
 <s id="id.2.1.29.2.1.18.0"> quare quadrata &longs;imul ex ON NP quadratis ex <lb/> 
 OT TP &longs;imul &aelig;qualia erunt.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.29.2.2.1.0" type="caption">        
 <s id="id.2.1.29.2.1.19.0"> quadratum autem ex OT maius <lb/> 
 e&longs;t quadrato ex ON; cum linea OT &longs;it ip&longs;a ON maior.  </s>              <s id="id.2.1.29.2.2.1.0.capt"> YYY </s>    
 <s id="id.2.1.29.2.1.20.0"> ergo qua<lb/> 
 dratum ex NP maius erit quadrato ex TP. ac propterea linea <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.29.2.2.3.0" type="caption">        
 TP minor erit linea PN, &amp; linea LX. minus obliquus igitur e&longs;t <lb/> 
 de&longs;cen&longs;us arcus LA, qu&agrave;m arcus OP.  </s>      <s id="id.2.1.29.2.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.30.1.0.0.0" type="margin">        
 <s id="id.2.1.29.2.1.20.0.a"> ergo pondus in L, ex ip<lb/> 
 &longs;orum dictis, grauius erit, qu&agrave;m in O. quod ex iis, qu&aelig; &longs;upra di<lb/> <s id="id.2.1.30.1.1.1.0"> <margin.target id="note51"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 27 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>            
 ximus e&longs;t manife&longs;t&egrave; fal&longs;um, c&ugrave;m pondus in O grauius &longs;it, qu&agrave;m <lb/> 
 in L.  </s>      <s id="id.2.1.30.1.1.2.0"> <margin.target id="note52"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 32 <emph type="italics"/>primi.<emph.end type="italics"/> </s>            
 <s id="id.2.1.29.2.1.20.0.b"> non igitur ex rectiori, &amp; obliquiori motu ita accepto col&shy;<lb/> 
 ligi pote&longs;t, &longs;ecund&ugrave;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo <lb/> <s id="id.2.1.30.1.1.3.0"> <margin.target id="note53"></margin.target>26 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 dem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us.  </s>              
 <s id="id.2.1.29.2.1.21.0"> Atq; hinc oritur omnis <lb/> <s id="id.2.1.30.1.1.4.0"> <margin.target id="note54"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 13 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 ferm&eacute; ip&longs;orum error in hacre, atq; deceptio: nam quamuis per <lb/> 
 accidens interdum ex fal&longs;is &longs;equatur verum, per &longs;e tamen ex fal<lb/> <s id="id.2.1.30.1.1.5.0"> <margin.target id="note55"></margin.target>19 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 &longs;is fal&longs;um &longs;equitur, quemadmodum ex veris &longs;emper verum, nil <lb/> 
 idcirco mirum, &longs;i dum fal&longs;a accipiunt; illi&longs;q; tanquam veri&longs;si&shy;<lb/> <s id="id.2.1.30.1.1.6.0"> <margin.target id="note56"></margin.target>47 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.31.1.0.0.0" type="main">        
 mis innituntur; fal&longs;i&longs;sima omnin&ograve; colligunt, atq; concludunt.  </s>              
 <s id="id.2.1.29.2.1.22.0"> <lb/> <s id="id.2.1.31.1.1.1.0"> Pr&aelig;terea &longs;i adhuc &longs;up<lb/>po&longs;itionem conceda&shy;<lb/>mus; &agrave; con&longs;ideratione <lb/>libr&aelig; long&egrave; recedunt; <lb/>dum eo pacto, vt libra <lb/>DE in AB redire de&shy;<lb/>beat, di&longs;currunt.  </s>            
 decipiuntur quinetiam, d&ugrave;m libr&aelig; contemplationem mathemati<lb/> 
 c&egrave; &longs;impliciter a&longs;&longs;ummunt; c&ugrave;m eius con&longs;ideratio &longs;it pror&longs;us me&shy;<lb/> <s id="id.2.1.31.1.1.2.0"> &longs;emper <lb/>enim alterum pondus <lb/>&longs;eor&longs;um accipiunt, put&aacute; <lb/>D, vel E; ac &longs;i mod&ograve; <expan abbr="vn&utilde;">vnum</expan> <lb/>mod&ograve; alterum in libra <lb/>con&longs;titutum e&longs;&longs;et, nec <lb/>vllo modo ambo con&shy;<lb/><figure id="fig32" place="text" xlink:href="figures1577/2000.03.0050.jpg">       </figure><lb/>nexa; cuius tamen oppo&longs;itum omnin&ograve; fieri oportet; neq; alterum <lb/>&longs;ine altero rect&egrave; con&longs;iderari pote&longs;t; c&ugrave;m de ip&longs;is in libra con&longs;ti&shy;<lb/>tutis &longs;ermo habeatur.  </s>            
 chanica: nec vllo modo ab&longs;q; vero motu, ac ponderibus (en&shy; 
 <pb n="18" xlink:href="pagethumb-la/00000053.JPG"/> <s id="id.2.1.31.1.1.3.0"> c&ugrave;m enim dicunt, de&longs;cen&longs;um ponderis in <lb/>D minus obliquum e&longs;&longs;e de&longs;cen&longs;u ponderis in E; erit pondus in <lb/>D per &longs;uppo&longs;itionem grauius pondere in E: quare c&ugrave;m &longs;it graui&shy;<lb/>us, nece&longs;&longs;e e&longs;t deor&longs;um moueri, libramq; DE in AB redire: di<lb/>&longs;cur&longs;us i&longs;te nullius pror&longs;us momenti e&longs;t.  </s>            
 tibus omnin&ograve; naturalibus) de ip&longs;a &longs;ermo haberi po&longs;sit: &longs;ine qui&shy;<lb/> 
 bus eorum, qu&aelig; libr&aelig; accidunt, ver&aelig; caul&aelig; reperiri nullo mo <lb/> <s id="id.2.1.31.1.1.4.0"> Prim&ugrave;m quidem &longs;em&shy;<lb/>per argumentantur, ac &longs;i pondera in DE de&longs;cendere debeant, <lb/>vnius tant&ugrave;m &longs;ine alterius connexione con&longs;iderando de&longs;cen&longs;um.  </s>            
 do po&longs;sint. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.31.1.1.5.0"> <lb/>po&longs;trem&ograve; tamen ob ponderum de&longs;cen&longs;uum comparationem colli&shy;<lb/>gentes inferunt, pondus in D deor&longs;um moueri, &amp; pondus in E <lb/>&longs;ur&longs;um, vtraq; &longs;imul in libra inuicem connexa accipientes.  </s>            
 <p id="id.2.1.29.2.2.1.0" type="caption">         
 <s id="id.2.1.29.2.2.1.0.capt"> YYY </s>      <s id="id.2.1.31.1.1.6.0"> <expan abbr="ve&shy;r&ugrave;m">ve&shy;<lb/>rum</expan> ex ii&longs;demmet, quibus vtuntur, principiis, ac demon&longs;tratio<lb/>nibus, oppo&longs;itum eius, quod defendere conantur, facillim&egrave; col&shy;<lb/>ligi pote&longs;t.  </s>            
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.29.2.2.3.0" type="caption">         <s id="id.2.1.31.1.1.7.0"> Nam &longs;i comparetur de&longs;cen&longs;us ponderis in D cum a&shy;<lb/>&longs;cen&longs;u ponderis in E, vt ductis EK DH ip&longs;i AB perpendicula&shy;<lb/>ribus; c&ugrave;m angulus DCH &longs;it &aelig;qualis angulo ECk; &amp; angulus <arrow.to.target n="note57"></arrow.to.target><lb/>DHC rectus &aelig;qualis e&longs;t recto E k C; &amp; latus DC lateri CE &aelig;qua <lb/>le: erit triangulum CDH triangulo CEk &aelig;quale, &amp; latus DH la-<arrow.to.target n="note58"></arrow.to.target><pb xlink:href="pagethumb-la/00000054.JPG"/>teri Ek &aelig;quale.  </s>            
 <s id="id.2.1.29.2.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.30.1.0.0.0" type="margin">         <s id="id.2.1.31.1.1.8.0"> c&ugrave;m <lb/>autem angulus DCA <lb/>&longs;it angulo ECB &aelig;qua&shy;<lb/>lis: erit quoq; circum&shy;<lb/>ferentia DA cirferen&shy;<lb/>ti&aelig; BE &aelig;qualis.  </s>            
 <s id="id.2.1.30.1.1.1.0"> <margin.target id="note51"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 27 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>              
 <s id="id.2.1.30.1.1.2.0"> <margin.target id="note52"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 32 <emph type="italics"/>primi.<emph.end type="italics"/> </s>              <s id="id.2.1.31.1.1.9.0"> dum <lb/>itaq; pondus in D de&shy;<lb/>&longs;cendit per circumfe&shy;<lb/>rentiam DA, pondus <lb/>in E per circumferen&shy;<lb/>tiam EB ip&longs;i DA &aelig;&shy;<lb/>qualem a&longs;cendit.  </s>            
 <s id="id.2.1.30.1.1.3.0"> <margin.target id="note53"></margin.target>26 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.30.1.1.4.0"> <margin.target id="note54"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 13 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s id="id.2.1.31.1.1.10.0"> &amp; de&shy;<lb/>&longs;cen&longs;us <expan abbr="p&otilde;deris">ponderis</expan> in D de <lb/>directo (more <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan>) <lb/><figure id="fig33" place="text" xlink:href="figures1577/2000.03.0051.jpg">       </figure><lb/>capiet DH; a&longs;cen&longs;us ver&ograve; ponderis in E de directo capiet Ek ip<lb/>&longs;i DH &aelig;qualem: erit itaq; de&longs;cen&longs;us ponderis in D a&longs;cen&longs;ui pon<lb/>deris in E &aelig;qualis, &amp; qualis erit propen&longs;io vnius ad motum deor<lb/>sum, talis etiam erit re&longs;i&longs;tentia alterius ad motum &longs;ur&longs;um.  </s>            
 <s id="id.2.1.30.1.1.5.0"> <margin.target id="note55"></margin.target>19 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.30.1.1.6.0"> <margin.target id="note56"></margin.target>47 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        <s id="id.2.1.31.1.1.11.0"> re&shy;<lb/>&longs;i&longs;tentia &longs;cilicet violenti&aelig; ponderis in E in a&longs;cen&longs;u naturali po&shy;<lb/>tenti&aelig; ponderis in D in de&longs;cen&longs;u contr&agrave; nitendo apponitur; c&ugrave;m <lb/>&longs;it ip&longs;i &aelig;qualis.  </s>            
 <p id="id.2.1.31.1.0.0.0" type="main">         
 <s id="id.2.1.31.1.1.1.0"> Pr&aelig;terea &longs;i adhuc &longs;up<lb/> <s id="id.2.1.31.1.1.12.0"> qu&ograve; enim pondus in D naturali potentia deor<lb/>&longs;um velocius de&longs;cendit, e&ograve; tardius pondus in E violenter a&longs;cendit.  </s>            
 po&longs;itionem conceda&shy;<lb/> 
 mus; &agrave; con&longs;ideratione <lb/> <s id="id.2.1.31.1.1.13.0"> <lb/>quare neutrum ip&longs;orum alteri pr&aelig;ponderabit, c&ugrave;m ab &aelig;quali non <lb/>proueniat actio.  </s>            
 libr&aelig; long&egrave; recedunt; <lb/> 
 dum eo pacto, vt libra <lb/> <s id="id.2.1.31.1.1.14.0"> Non igitur pondus in D pondus in E &longs;ur&longs;um <lb/>mouebit.  </s>            
 DE in AB redire de&shy;<lb/> 
 beat, di&longs;currunt.  </s>              <s id="id.2.1.31.1.1.15.0"> &longs;i enim moueret; nece&longs;&longs;e e&longs;&longs;et, pondus in D maiorem <lb/>habere virtutem de&longs;cendendo, qu&agrave;m pondus in E a&longs;cendendo; <lb/>&longs;ed h&aelig;c &longs;unt &aelig;qualia: ergo pondera manebunt.  </s>            
 <s id="id.2.1.31.1.1.2.0"> &longs;emper <lb/> 
 enim alterum pondus <lb/> <s id="id.2.1.31.1.1.16.0"> &amp; grauitas pon&shy;<lb/>deris in D grauitati ponderis in E &aelig;qualis erit.  </s>            
 &longs;eor&longs;um accipiunt, put&aacute; <lb/> 
 D, vel E; ac &longs;i mod&ograve; <expan abbr="vn&utilde;">vnum</expan> <lb/> <s id="id.2.1.31.1.1.17.0"> Pr&aelig;terea quoniam <lb/>&longs;upponunt, qu&ograve; pondus &agrave; linea directionis FG magis di&longs;tat, e&ograve; <lb/>grauius e&longs;&longs;e: Idcirco ductis quoq; &agrave; punctis DE ip&longs;i FG perpen<lb/>dicularibus DO EI; &longs;imili modo demon&longs;trabitur, triangulum <lb/>CDO triangulo CEI &aelig;qualem e&longs;&longs;e: &amp; lineam DO ip&longs;i EI &aelig;qua<lb/>lem.  </s>            
 mod&ograve; alterum in libra <lb/> 
 con&longs;titutum e&longs;&longs;et, nec <lb/> <s id="id.2.1.31.1.1.18.0"> tam igitur di&longs;tat &agrave; linea FG pondus in D, qu&agrave;m pondus in <lb/>E. ex ip&longs;orum igitur rationibus, atq; &longs;uppo&longs;itionibus, pondera <lb/>in DE &aelig;qu&egrave; grauia erunt.  </s>            
 vllo modo ambo con&shy;<lb/> 
 <figure id="fig32" place="text" xlink:href="figures1577/2000.03.0050.jpg">       </figure><lb/> <s id="id.2.1.31.1.1.19.0"> Amplius quid prohibet, quin libram <lb/>DE ex nece&longs;sitate in FG moueri &longs;imili ratione o&longs;tendatur?  </s>            
 nexa; cuius tamen oppo&longs;itum omnin&ograve; fieri oportet; neq; alterum <lb/> 
 &longs;ine altero rect&egrave; con&longs;iderari pote&longs;t; c&ugrave;m de ip&longs;is in libra con&longs;ti&shy;<lb/> <s id="id.2.1.31.1.1.20.0"> Pri&shy;<pb n="19" xlink:href="pagethumb-la/00000055.JPG"/>m&ugrave;m quidem ex eorummet demon&longs;trationibus colligi pote&longs;t, a&shy;<lb/>&longs;cen&longs;um ponderis in E ver&longs;us B rectiorem e&longs;&longs;e a&longs;cen&longs;u ponderis <lb/>in D ver&longs;us F; hoc e&longs;t minus capere de directo a&longs;cen&longs;um pon&shy;<lb/>deris in D in arcubus &aelig;qualibus a&longs;cen&longs;u ponderis in E.  </s>    
 tutis &longs;ermo habeatur.  </s>              
 <s id="id.2.1.31.1.1.3.0"> c&ugrave;m enim dicunt, de&longs;cen&longs;um ponderis in <lb/> <s id="id.2.1.31.1.1.20.0.a"> &longs;uppona<lb/>tur ergo &longs;ecund&ugrave;m &longs;itum pondus leuius e&longs;&longs;e, quant&ograve; in eodem &longs;i&shy;<lb/>tu minus rectus e&longs;t a&longs;cen&longs;us: qu&aelig; quidem &longs;uppo&longs;itio, ade&ograve; ma&shy;<lb/>nife&longs;ta e&longs;&longs;e videtur, veluti ip&longs;orum altera.  </s>            
 D minus obliquum e&longs;&longs;e de&longs;cen&longs;u ponderis in E; erit pondus in <lb/> 
 D per &longs;uppo&longs;itionem grauius pondere in E: quare c&ugrave;m &longs;it graui&shy;<lb/> <s id="id.2.1.31.1.1.21.0"> Quoniam igitur a&longs;cen&shy;<lb/>&longs;us ponderis in E rectior e&longs;t a&longs;cen&longs;u ponderis in D; per &longs;uppo&longs;i&shy;<lb/>tionem pondus in D leuius erit pondere in E. ergo pondus in <lb/>D &longs;ur&longs;um &agrave; pondere in E mouebitur, ita vt libra in FG perue<lb/>niat.  </s>
 us, nece&longs;&longs;e e&longs;t deor&longs;um moueri, libramq; DE in AB redire: di<lb/> 
 &longs;cur&longs;us i&longs;te nullius pror&longs;us momenti e&longs;t.  </s>              <s id="id.2.1.31.1.1.22.0"> atq; ita demon&longs;trari poterit, libram DE in FG moueri.<lb/>  </s>            
 <s id="id.2.1.31.1.1.4.0"> Prim&ugrave;m quidem &longs;em&shy;<lb/> 
 per argumentantur, ac &longs;i pondera in DE de&longs;cendere debeant, <lb/> <s id="id.2.1.31.1.1.23.0"> qu&aelig; quidem demon&longs;tratio inutilis e&longs;t pror&longs;us, ea&longs;demq; patitur <lb/>difficultates.  </s>            
 vnius tant&ugrave;m &longs;ine alterius connexione con&longs;iderando de&longs;cen&longs;um.  </s>              
 <s id="id.2.1.31.1.1.5.0"> <lb/> <s id="id.2.1.31.1.1.24.0"> licet enim tanqu&agrave;m verum admittatur pondus in E <lb/>a&longs;cendendo grauius e&longs;&longs;e pondere in D &longs;imiliter a&longs;cendendo, <lb/>non tamen ex hoc &longs;equitur, pondus in E de&longs;cendendo grauius <lb/>e&longs;&longs;e pondere in D a&longs;cendendo.  </s>            
 po&longs;trem&ograve; tamen ob ponderum de&longs;cen&longs;uum comparationem colli&shy;<lb/> 
 gentes inferunt, pondus in D deor&longs;um moueri, &amp; pondus in E <lb/> <s id="id.2.1.31.1.1.25.0"> Neutra igitur harum demon&shy;<lb/>&longs;trationum libram DE, vel in AB redire, vel in FG moue&shy;<lb/>ri, o&longs;tendentium, vera e&longs;t. </s>    
 &longs;ur&longs;um, vtraq; &longs;imul in libra inuicem connexa accipientes.  </s>              
 <s id="id.2.1.31.1.1.6.0"> <expan abbr="ve&shy;r&ugrave;m">ve&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.31.1.2.1.0" type="caption">        
 rum</expan> ex ii&longs;demmet, quibus vtuntur, principiis, ac demon&longs;tratio<lb/> 
 nibus, oppo&longs;itum eius, quod defendere conantur, facillim&egrave; col&shy;<lb/> <s id="id.2.1.31.1.2.1.0.capt"> YYY </s>    
 ligi pote&longs;t.  </s>              
 <s id="id.2.1.31.1.1.7.0"> Nam &longs;i comparetur de&longs;cen&longs;us ponderis in D cum a&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.31.1.2.3.0" type="caption">        
 &longs;cen&longs;u ponderis in E, vt ductis EK DH ip&longs;i AB perpendicula&shy;<lb/> 
 ribus; c&ugrave;m angulus DCH &longs;it &aelig;qualis angulo ECk; &amp; angulus <arrow.to.target n="note57"></arrow.to.target><lb/> <s id="id.2.1.31.1.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.32.1.0.0.0" type="margin">        
 DHC rectus &aelig;qualis e&longs;t recto E k C; &amp; latus DC lateri CE &aelig;qua <lb/> 
 le: erit triangulum CDH triangulo CEk &aelig;quale, &amp; latus DH la-<arrow.to.target n="note58"></arrow.to.target> <s id="id.2.1.32.1.1.1.0"> <margin.target id="note57"></margin.target>15 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 <pb xlink:href="pagethumb-la/00000054.JPG"/> 
 teri Ek &aelig;quale.  </s>              <s id="id.2.1.32.1.1.2.0"> <margin.target id="note58"></margin.target>26 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.33.1.0.0.0" type="main">        
 <s id="id.2.1.31.1.1.8.0"> c&ugrave;m <lb/> 
 autem angulus DCA <lb/> <s id="id.2.1.33.1.1.1.0"> Pr&aelig;terea &longs;i ip&longs;orum &longs;uppo&longs;itionem, eorumq; verborum vim <lb/>rect&egrave; perpendamus; alium cert&egrave; habere &longs;en&longs;um con&longs;piciemus.  </s>            
 &longs;it angulo ECB &aelig;qua&shy;<lb/> 
 lis: erit quoq; circum&shy;<lb/> <s id="id.2.1.33.1.1.2.0"> nam <lb/>c&ugrave;m &longs;emper &longs;patium, per quod naturaliter pondus mouetur, &agrave; cen<lb/>tro grauitatis ip&longs;ius ponderis ad centrum mundi, in&longs;tar rect&aelig; li&shy;<lb/>ne&aelig; &agrave; centro grauitatis ad centrum mundi product&aelig;, &longs;it &longs;umendum; <lb/>tant&ograve; huiusmodi ponderis de&longs;cen&longs;us, magis, minusu&egrave; obliquus <lb/>dicetur; quant&ograve; &longs;ecund&ugrave;m &longs;patium in&longs;tar pr&aelig;dict&aelig; line&aelig; de&longs;igna <lb/>tum, magis, aut minus (naturalem tamen locum petens, &longs;emperq; <lb/>magis ip&longs;i appropinquans) mouebitur; ita vt tant&ograve; obliquior de&shy;<lb/>&longs;cen&longs;us dicatur, quant&ograve; recedit ab eiu&longs;modi &longs;patio: rectior ver&ograve;, <lb/>quant&ograve; ad idem accedit.  </s>            
 ferentia DA cirferen&shy;<lb/> 
 ti&aelig; BE &aelig;qualis.  </s>              <s id="id.2.1.33.1.1.3.0"> &amp; in hoc &longs;en&longs;u &longs;uppo&longs;itio illa nemini <lb/>difficultatem parere debet, ade&ograve; enim veritas eius con&longs;picua e&longs;t; <lb/>rationiq; con&longs;entanea: vt nulla pro&longs;us manife&longs;tatione egere vi&shy;<lb/>deatur.  </s>    </p>       <pb xlink:href="pagethumb-la/00000056.JPG"/>       <p id="id.2.1.33.3.0.0.0" type="main">        
 <s id="id.2.1.31.1.1.9.0"> dum <lb/> 
 itaq; pondus in D de&shy;<lb/> <s id="id.2.1.33.3.1.1.0"> Si itaq; pondus &longs;olutum in &longs;itu D <lb/>collocatum ad propium locum mo&shy;<lb/>ueri debeat; proculdubio po&longs;ito cen&shy;<lb/>tro mundi S, per lineam DS moue&shy;<lb/>bitur.  </s>            
 &longs;cendit per circumfe&shy;<lb/> 
 rentiam DA, pondus <lb/> <s id="id.2.1.33.3.1.2.0"> &longs;imiliter pondus in E &longs;olutum <lb/>per lineam ES mouebitur.  </s>            
 in E per circumferen&shy;<lb/> 
 tiam EB ip&longs;i DA &aelig;&shy;<lb/> <s id="id.2.1.33.3.1.3.0"> quare &longs;i <lb/>(vt rei veritas e&longs;t) ponderis de&longs;cen&shy;<lb/>&longs;us magis, minu&longs;u&egrave; obliquus dicetur <lb/>&longs;ecund&ugrave;m rece&longs;&longs;um, &amp; acce&longs;&longs;um ad <lb/>&longs;patia per lineas DSES de&longs;ignata, <lb/>iuxta naturales ip&longs;orum ad propria lo <lb/>ca lationes; con&longs;picuum e&longs;t, minus <lb/>obliquum e&longs;&longs;e de&longs;cen&longs;um ip&longs;ius E <lb/>per EG, qu&agrave;m ip&longs;ius D per DA: <lb/>c&ugrave;m angulum SEG angulo SDA <lb/>minorem e&longs;&longs;e &longs;upra o&longs;ten&longs;um &longs;it.  </s>            
 qualem a&longs;cendit.  </s>              
 <s id="id.2.1.31.1.1.10.0"> &amp; de&shy;<lb/> <s id="id.2.1.33.3.1.4.0"> qua <lb/>re in E pondus magis grauitabit, <lb/>qu&agrave;m in D. quod e&longs;t penitus oppo&shy;<lb/>&longs;itum eius, quod ip&longs;i o&longs;tendere cona<lb/>ti &longs;unt.  </s>            
 &longs;cen&longs;us <expan abbr="p&otilde;deris">ponderis</expan> in D de <lb/> 
 directo (more <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan>) <lb/> <s id="id.2.1.33.3.1.5.0"> In&longs;urgent autem forta&longs;&longs;e <lb/>contranos, &longs;i igitur (dicent) pondus <lb/>in E grauius e&longs;t pondere in D, libra <lb/><figure id="fig34" place="text" xlink:href="figures1577/2000.03.0052.jpg">       </figure><lb/>DE in hoc &longs;itu minim&egrave; per&longs;i&longs;tet, quod <expan abbr="equid&etilde;">equidem</expan> tueri propo&longs;uimus: <lb/>&longs;ed in FG mouebitur.  </s>            
 <figure id="fig33" place="text" xlink:href="figures1577/2000.03.0051.jpg">       </figure><lb/> 
 capiet DH; a&longs;cen&longs;us ver&ograve; ponderis in E de directo capiet Ek ip<lb/> <s id="id.2.1.33.3.1.6.0"> quibus re&longs;pondemus, plurimum referre, &longs;iue <lb/>con&longs;ideremus pondera, quatenus &longs;unt inuicem di&longs;iuncta, &longs;iue quate <lb/>nus &longs;unt &longs;ibi inuicem connexa.  </s>            
 &longs;i DH &aelig;qualem: erit itaq; de&longs;cen&longs;us ponderis in D a&longs;cen&longs;ui pon<lb/> 
 deris in E &aelig;qualis, &amp; qualis erit propen&longs;io vnius ad motum deor<lb/> <s id="id.2.1.33.3.1.7.0"> alia e&longs;t enim ratio ponderis in E &longs;ine <lb/>connexione ponderis in D, alia ver&ograve; eiu&longs;dem alteri ponderi con<lb/>nexi; ita vt alterum &longs;ine altero moueri non po&longs;sit.  </s>            
 sum, talis etiam erit re&longs;i&longs;tentia alterius ad motum &longs;ur&longs;um.  </s>              
 <s id="id.2.1.31.1.1.11.0"> re&shy;<lb/> <s id="id.2.1.33.3.1.8.0"> nam ponde<lb/>ris in E, quatenus e&longs;t &longs;ine alterius ponderis connexione, rectus <lb/>naturalis de&longs;cen&longs;us e&longs;t per lineam ES; quatenus ver&ograve; connexum <lb/>e&longs;t ponderi in D, eius naturalis de&longs;cen&longs;us non erit amplius per <lb/>lineam ES, &longs;ed per lineam ip&longs;i CS parallelam.  </s>            
 &longs;i&longs;tentia &longs;cilicet violenti&aelig; ponderis in E in a&longs;cen&longs;u naturali po&shy;<lb/> 
 tenti&aelig; ponderis in D in de&longs;cen&longs;u contr&agrave; nitendo apponitur; c&ugrave;m <lb/> <s id="id.2.1.33.3.1.9.0"> magnitudo enim <lb/>ex ponderibus ED, &amp; libra DE compo&longs;ita, cuius grauitatis cen&shy;<lb/>trum e&longs;t C, &longs;i nullibi &longs;u&longs;tineatur, deor&longs;um eo modo, quo reperi<lb/>tur, &longs;ecund&ugrave;m grauitatis centrum per rectam &agrave; centro grauita<lb/>tis C ad centrum mundi S ductam naturaliter mouebitur, donec <pb n="20" xlink:href="pagethumb-la/00000057.JPG"/>centrum C in centrum S perueniat.  </s>            
 &longs;it ip&longs;i &aelig;qualis.  </s>              
 <s id="id.2.1.31.1.1.12.0"> qu&ograve; enim pondus in D naturali potentia deor<lb/> <s id="id.2.1.33.3.1.10.0"> libra igitur DE vn&aacute; cum pon<lb/>deribus eo modo, quo reperitur, deor&longs;um mouebitur, ita vt pun&shy;<lb/>ctum C per lineam CS moueatur, donec C in S, libraq; DE in <lb/>Hk perueniat; habeatq; libra in Hk eandem, quam prius habe&shy;<lb/>bat po&longs;itionem; hoc e&longs;t Hk &longs;it ip&longs;i DE &aelig;quidi&longs;tans.  </s>
 &longs;um velocius de&longs;cendit, e&ograve; tardius pondus in E violenter a&longs;cendit.  </s>              
 <s id="id.2.1.31.1.1.13.0"> <lb/> <s id="id.2.1.33.3.1.11.0"> connectantur <lb/>igitur DH Ek.  </s>            
 quare neutrum ip&longs;orum alteri pr&aelig;ponderabit, c&ugrave;m ab &aelig;quali non <lb/> 
 proueniat actio.  </s>              <s id="id.2.1.33.3.1.12.0"> manife&longs;tum e&longs;t, dum libra DE in Hk mouetur pun<lb/>cta DE per lineas DH Ek moueri, quippe exi&longs;tentibus inter &longs;e <arrow.to.target n="note59"></arrow.to.target><lb/>&longs;e, ip&longs;iq; CS &aelig;qualibus, &amp; &aelig;quidi&longs;tantibus.  </s>            
 <s id="id.2.1.31.1.1.14.0"> Non igitur pondus in D pondus in E &longs;ur&longs;um <lb/> 
 mouebit.  </s>              <s id="id.2.1.33.3.1.13.0"> Quare pondera in <lb/>DE, quatenus &longs;unt &longs;ibi inuicem connexa, &longs;i ip&longs;orum naturalem mo <lb/>tum &longs;pectemus, non &longs;ecund&ugrave;m lineas DS ES, &longs;ed &longs;ecund&ugrave;m <lb/>LDH MEk ip&longs;i CS &aelig;quidi&longs;tantes mouebuntur.  </s>            
 <s id="id.2.1.31.1.1.15.0"> &longs;i enim moueret; nece&longs;&longs;e e&longs;&longs;et, pondus in D maiorem <lb/> 
 habere virtutem de&longs;cendendo, qu&agrave;m pondus in E a&longs;cendendo; <lb/> <s id="id.2.1.33.3.1.14.0"> ponderis <expan abbr="ve&shy;r&ograve;">ve&shy;<lb/>ro</expan> in E liberi, ac &longs;oluti, naturalis propen&longs;io erit per ES: ponderis <lb/>autem in D &longs;imiliter &longs;oluti erit per DS. ac propterea non e&longs;t incon&shy;<lb/>ueniens idem pondus mod&ograve; in E, mod&ograve; in D, grauius e&longs;&longs;e in E, <lb/>qu&agrave;m in D.  </s>    
 &longs;ed h&aelig;c &longs;unt &aelig;qualia: ergo pondera manebunt.  </s>              
 <s id="id.2.1.31.1.1.16.0"> &amp; grauitas pon&shy;<lb/> <s id="id.2.1.33.3.1.14.0.a"> &longs;i ver&ograve; pondera in ED &longs;ibi inuicem connexa, quate&shy;<lb/>nusq; &longs;unt connexa con&longs;iderauerimus; erit ponderis in E natura&shy;<lb/>lis propen&longs;io per lineam MEK: grauitas enim alterius ponde&shy;<lb/>ris in D efficit, n&egrave; pondus in E per lineam ES grauitet, &longs;ed per <lb/>Ek.  </s>            
 deris in D grauitati ponderis in E &aelig;qualis erit.  </s>              
 <s id="id.2.1.31.1.1.17.0"> Pr&aelig;terea quoniam <lb/> <s id="id.2.1.33.3.1.15.0"> quod ip&longs;um quoq; grauitas ponderis in E efficit, n&egrave; &longs;cilicet <lb/>pondus in D per rectam DS degrauet; &longs;ed &longs;ecund&ugrave;m DH: vtra&shy;<lb/>que enim &longs;e impediunt, n&egrave; ad propria loca permeent.  </s>            
 &longs;upponunt, qu&ograve; pondus &agrave; linea directionis FG magis di&longs;tat, e&ograve; <lb/> 
 grauius e&longs;&longs;e: Idcirco ductis quoq; &agrave; punctis DE ip&longs;i FG perpen<lb/> <s id="id.2.1.33.3.1.16.0"> C&ugrave;m igi<lb/>tur naturalis de&longs;cen&longs;us rectus ponderum in DE &longs;it &longs;ecund&ugrave;m <lb/>LDH MEK: erit &longs;imliter rectus eorum a&longs;cen&longs;us &longs;ecund&ugrave;m ea&longs; <lb/>dem lineas HDL KEM. atq; a&longs;cen&longs;us ponderis in E magis, mi<lb/>nu&longs;u&egrave; obliquus dicetur; quant&ograve; &longs;ecund&ugrave;m &longs;patium magis, <expan abbr="mi&shy;nu&longs;u&egrave;">mi&shy;<lb/>nu&longs;ue</expan> iuxta lineam Mk mouebitur.  </s>            
 dicularibus DO EI; &longs;imili modo demon&longs;trabitur, triangulum <lb/> 
 CDO triangulo CEI &aelig;qualem e&longs;&longs;e: &amp; lineam DO ip&longs;i EI &aelig;qua<lb/> <s id="id.2.1.33.3.1.17.0"> hocq; pror&longs;us modo iuxta li<lb/>neam LH &longs;ummendus e&longs;t, t&ugrave;m de&longs;cen&longs;us, t&ugrave;m a&longs;cen&longs;us ponde&shy;<lb/>ris in D. &longs;i itaq; pondus in E deor&longs;um per EG moueretur; pon<lb/>dus in D &longs;ur&longs;um per DF moueret.  </s>            
 lem.  </s>              
 <s id="id.2.1.31.1.1.18.0"> tam igitur di&longs;tat &agrave; linea FG pondus in D, qu&agrave;m pondus in <lb/> <s id="id.2.1.33.3.1.18.0"> &amp; quoniam angulus CEK <arrow.to.target n="note60"></arrow.to.target><lb/>&aelig;qualis e&longs;t angulo CDL, &amp; angulus CEG angulo CDF &aelig;qua&shy;<lb/>lis; erit reliquus GEK reliquo LDF &aelig;qualis.  </s>            
 E. ex ip&longs;orum igitur rationibus, atq; &longs;uppo&longs;itionibus, pondera <lb/> 
 in DE &aelig;qu&egrave; grauia erunt.  </s>              <s id="id.2.1.33.3.1.19.0"> c&ugrave;m autem &longs;up&shy;<lb/>po&longs;itio illa, qu&aelig; ait, &longs;ecund&uacute;m &longs;itum pondus grauius e&longs;&longs;e, <expan abbr="quan&shy;t&ograve;">quan&shy;<lb/>to</expan> in eodem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us; tanquam clara, <lb/>atq; con&longs;picua admittatur; proculdubio h&aelig;c quoq; accipienda <lb/>erit; nemp&egrave;, &longs;ecund&uacute;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo&shy;<lb/>dem &longs;itu minus obliquus e&longs;t a&longs;cen&longs;us.  </s>            
 <s id="id.2.1.31.1.1.19.0"> Amplius quid prohibet, quin libram <lb/> 
 DE ex nece&longs;sitate in FG moueri &longs;imili ratione o&longs;tendatur?  </s>              <s id="id.2.1.33.3.1.20.0"> c&ugrave;m non minus manife&longs;ta, <pb xlink:href="pagethumb-la/00000058.JPG"/>rationiq; &longs;it con&longs;entanea.  </s>            
 <s id="id.2.1.31.1.1.20.0"> Pri&shy; 
 <pb n="19" xlink:href="pagethumb-la/00000055.JPG"/> <s id="id.2.1.33.3.1.21.0"> &aelig;qualis <lb/>igitur erit de&longs;cen&longs;us ponderis in E <lb/>a&longs;cen&longs;ui ponderis in D. eandem <lb/>enim obliquitatem habet de&longs;cen&longs;us <lb/>ponderis in E, quam habet a&longs;cen&shy;<lb/>&longs;us ponderis in D; &amp; qualis erit <lb/>propen&longs;io vnius ad motum deor&longs;um, <lb/>talis quoq; erit re&longs;i&longs;tentia alterius ad <lb/>motum &longs;ur&longs;um.  </s>            
 m&ugrave;m quidem ex eorummet demon&longs;trationibus colligi pote&longs;t, a&shy;<lb/> 
 &longs;cen&longs;um ponderis in E ver&longs;us B rectiorem e&longs;&longs;e a&longs;cen&longs;u ponderis <lb/> <s id="id.2.1.33.3.1.22.0"> <expan abbr="n&otilde;">non</expan> ergo pondus in E <lb/>pondus in D &longs;ur&longs;um mouebit.  </s>            
 in D ver&longs;us F; hoc e&longs;t minus capere de directo a&longs;cen&longs;um pon&shy;<lb/> 
 deris in D in arcubus &aelig;qualibus a&longs;cen&longs;u ponderis in E.  </s>      <s id="id.2.1.33.3.1.23.0"> neq; <lb/>pondus in D deor&longs;um mouebitur, ita <lb/>vt &longs;ur&longs;um moueat pondus in E. nam <lb/><expan abbr="c&utilde;">cum</expan> angulus CEB &longs;it ip&longs;i CDA &aelig;qua&shy;<lb/><arrow.to.target n="note61"></arrow.to.target> lis, &amp; Angulus CEM &longs;it angulo <lb/>CDH &aelig;qualis; erit reliquus MEB <lb/>reliquo HDA &aelig;qualis.  </s>            
 <s id="id.2.1.31.1.1.20.0.a"> &longs;uppona<lb/> 
 tur ergo &longs;ecund&ugrave;m &longs;itum pondus leuius e&longs;&longs;e, quant&ograve; in eodem &longs;i&shy;<lb/> <s id="id.2.1.33.3.1.24.0"> de&longs;cen&longs;us <lb/>igitur ponderis in D a&longs;cen&longs;ui ponde<lb/>ris in E &aelig;qualis erit.  </s>            
 tu minus rectus e&longs;t a&longs;cen&longs;us: qu&aelig; quidem &longs;uppo&longs;itio, ade&ograve; ma&shy;<lb/> 
 nife&longs;ta e&longs;&longs;e videtur, veluti ip&longs;orum altera.  </s>              <s id="id.2.1.33.3.1.25.0"> non ergo pon<lb/>dus in D pondus in E &longs;ur&longs;um moue<lb/>bit.  </s>            
 <s id="id.2.1.31.1.1.21.0"> Quoniam igitur a&longs;cen&shy;<lb/> 
 &longs;us ponderis in E rectior e&longs;t a&longs;cen&longs;u ponderis in D; per &longs;uppo&longs;i&shy;<lb/> <s id="id.2.1.33.3.1.26.0"> ex quibus &longs;equitur pondera in <lb/>DE, quatenus &longs;unt &longs;ibi inuicem con<lb/>nexa, &aelig;qu&egrave; grauia e&longs;&longs;e. <figure id="fig35" place="text" xlink:href="figures1577/2000.03.0054.jpg">       </figure> </s>    </p>       <p id="id.2.1.33.4.0.0.0" type="main">        
 tionem pondus in D leuius erit pondere in E. ergo pondus in <lb/> 
 D &longs;ur&longs;um &agrave; pondere in E mouebitur, ita vt libra in FG perue<lb/> <s id="id.2.1.33.4.1.1.0"> Alia deinde ratio, li&shy;<lb/>bram &longs;imiliter DE in AB <lb/>redire o&longs;tendens, c&ugrave;m in&shy;<lb/>quiunt, exi&longs;tente trutina in <lb/>CF meta e&longs;t CG.  </s>    
 niat.  </s> 
 <s id="id.2.1.31.1.1.22.0"> atq; ita demon&longs;trari poterit, libram DE in FG moueri.<lb/>  </s>              <s id="id.2.1.33.4.1.1.0.a"> &amp; quo&shy;<lb/>niam angulus DCG maior <lb/>e&longs;t angulo ECG; pondus <lb/>in D grauius erit pondere <lb/>in E; ergo libra DE in AB <lb/>redibit: nihil meo iudicio <lb/>concludit.  </s>            
 <s id="id.2.1.31.1.1.23.0">  
 qu&aelig; quidem demon&longs;tratio inutilis e&longs;t pror&longs;us, ea&longs;demq; patitur <lb/> <s id="id.2.1.33.4.1.2.0"> figmentumq; <lb/>hoc de trutina, &amp; meta po&shy;<lb/>tius omittendum, ac &longs;ilen&shy;|tio<figure id="fig36" place="text" xlink:href="figures1577/2000.03.0056.1.jpg">       </figure><pb n="21" xlink:href="pagethumb-la/00000059.JPG"/> <expan abbr="pr&aelig;tereund&utilde;">pr&aelig;tereundum</expan> e&longs;&longs;et, qu&agrave;m <expan abbr="verb&utilde;">verbum</expan> <expan abbr="vll&utilde;">vllum</expan> in eius confutatione &longs;umen<lb/>dum; c&ugrave;m &longs;it pror&longs;us voluntarium.  </s>            
 difficultates.  </s>              
 <s id="id.2.1.31.1.1.24.0"> licet enim tanqu&agrave;m verum admittatur pondus in E <lb/> <s id="id.2.1.33.4.1.3.0"> nece&longs;sitas enim cur pondus <lb/>in D ex maiore angulo &longs;it grauius; curq; maior angulus maioris <lb/>&longs;it cau&longs;a grauitatis; nu&longs;quam apparet.  </s>            
 a&longs;cendendo grauius e&longs;&longs;e pondere in D &longs;imiliter a&longs;cendendo, <lb/> 
 non tamen ex hoc &longs;equitur, pondus in E de&longs;cendendo grauius <lb/> <s id="id.2.1.33.4.1.4.0"> &longs;i autem comparentur in&shy;<lb/>uicem anguli, c&ugrave;m angulus GCD &longs;it &aelig;qualis angulo FCE; &longs;i angu<lb/>lus GCD e&longs;t cau&longs;a grauitatis; quare angulus FCE &longs;imiliter gra&shy;<lb/>uitatis non e&longs;t cau&longs;a?  </s>            
 e&longs;&longs;e pondere in D a&longs;cendendo.  </s>              
 <s id="id.2.1.31.1.1.25.0"> Neutra igitur harum demon&shy;<lb/> <s id="id.2.1.33.4.1.5.0"> Huius autem rei eam in medium rationem <lb/>afferre videntur, quoniam CG e&longs;t meta, &amp; CF trutina.  </s>            
 &longs;trationum libram DE, vel in AB redire, vel in FG moue&shy;<lb/> 
 ri, o&longs;tendentium, vera e&longs;t. </s>      <s id="id.2.1.33.4.1.6.0"> &longs;i (inquiunt) <lb/>CG e&longs;&longs;et trutina, &amp; CF meta, tunc angulus FCE grauitatis e&longs;&longs;et <lb/>cau&longs;a; non autem DCG ip&longs;i &aelig;qualis.  </s>            
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.31.1.2.1.0" type="caption">         <s id="id.2.1.33.4.1.7.0"> qu&aelig; quidem ratio imma&shy;<lb/>ginaria pror&longs;us, ac voluntaria e&longs;&longs;e videtur.  </s>            
 <s id="id.2.1.31.1.2.1.0.capt"> YYY </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.33.4.1.8.0"> quid enim refert, &longs;iue tru<lb/>tina &longs;it in CF, &longs;iue in CG, c&ugrave;m libra DE in eodem &longs;emper pun&shy;<lb/>cto C &longs;u&longs;tineatur?  </s>            
 <p id="id.2.1.31.1.2.3.0" type="caption">         
 <s id="id.2.1.31.1.2.3.0.capt"> YYY </s>    </p>        <s id="id.2.1.33.4.1.9.0"> Vt autem eorum deceptio clarius appa&shy;<lb/>reat. </s>    
 <p id="id.2.1.32.1.0.0.0" type="margin">         
 <s id="id.2.1.32.1.1.1.0"> <margin.target id="note57"></margin.target>15 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.33.4.2.1.0" type="caption">        
 <s id="id.2.1.32.1.1.2.0"> <margin.target id="note58"></margin.target>26 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.33.1.0.0.0" type="main">         <s id="id.2.1.33.4.2.1.0.capt"> YYY </s>    
 <s id="id.2.1.33.1.1.1.0"> Pr&aelig;terea &longs;i ip&longs;orum &longs;uppo&longs;itionem, eorumq; verborum vim <lb/> 
 rect&egrave; perpendamus; alium cert&egrave; habere &longs;en&longs;um con&longs;piciemus.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.33.4.2.3.0" type="caption">        
 <s id="id.2.1.33.1.1.2.0"> nam <lb/> 
 c&ugrave;m &longs;emper &longs;patium, per quod naturaliter pondus mouetur, &agrave; cen<lb/> <s id="id.2.1.33.4.2.3.0.capt"> YYY </s>    
 tro grauitatis ip&longs;ius ponderis ad centrum mundi, in&longs;tar rect&aelig; li&shy;<lb/> 
 ne&aelig; &agrave; centro grauitatis ad centrum mundi product&aelig;, &longs;it &longs;umendum; <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.33.4.2.5.0" type="caption">        
 tant&ograve; huiusmodi ponderis de&longs;cen&longs;us, magis, minusu&egrave; obliquus <lb/> 
 dicetur; quant&ograve; &longs;ecund&ugrave;m &longs;patium in&longs;tar pr&aelig;dict&aelig; line&aelig; de&longs;igna <lb/> <s id="id.2.1.33.4.2.5.0.capt"> YYY </s>    </p>       <p id="id.2.1.34.1.0.0.0" type="margin">        
 tum, magis, aut minus (naturalem tamen locum petens, &longs;emperq; <lb/> 
 magis ip&longs;i appropinquans) mouebitur; ita vt tant&ograve; obliquior de&shy;<lb/> <s id="id.2.1.34.1.1.1.0"> <margin.target id="note59"></margin.target>33 <emph type="italics"/>Prmi.<emph.end type="italics"/> </s>            
 &longs;cen&longs;us dicatur, quant&ograve; recedit ab eiu&longs;modi &longs;patio: rectior ver&ograve;, <lb/> 
 quant&ograve; ad idem accedit.  </s>              <s id="id.2.1.34.1.1.2.0"> <margin.target id="note60"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 <s id="id.2.1.33.1.1.3.0"> &amp; in hoc &longs;en&longs;u &longs;uppo&longs;itio illa nemini <lb/> 
 difficultatem parere debet, ade&ograve; enim veritas eius con&longs;picua e&longs;t; <lb/> <s id="id.2.1.34.1.1.3.0"> <margin.target id="note61"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.35.1.0.0.0" type="main">        
 rationiq; con&longs;entanea: vt nulla pro&longs;us manife&longs;tatione egere vi&shy;<lb/> 
 deatur.  </s>    </p>        <s id="id.2.1.35.1.1.1.0"> Sit eadem libra AB, cu&shy;<lb/>ius medium C. &longs;it deinde <lb/>tota FG trutina.  </s>            
 <pb xlink:href="pagethumb-la/00000056.JPG"/> 
         <s id="id.2.1.35.1.1.2.0"> eaq; im<lb/>mobilis exi&longs;tat; qu&aelig; libram <lb/>AB in puncto C &longs;u&longs;tineat.  </s>            
 <p id="id.2.1.33.3.0.0.0" type="main">         
 <s id="id.2.1.33.3.1.1.0"> Si itaq; pondus &longs;olutum in &longs;itu D <lb/> <s id="id.2.1.35.1.1.3.0"> <lb/>moueaturq; libra in DE. &amp; <lb/>quoniam trutina e&longs;t, &amp; &longs;u&shy;<lb/>pra, &amp; infra libram, quis <lb/>nam angulus erit cau&longs;a gra&shy;<lb/>uitatis, c&ugrave;m libra DE in <lb/><figure id="fig37" place="text" xlink:href="figures1577/2000.03.0056.2.jpg">       </figure><expan abbr="eod&etilde;"><lb/>eodem</expan> &longs;emper puncto &longs;u&longs;tineatur?  </s>            
 collocatum ad propium locum mo&shy;<lb/> 
 ueri debeat; proculdubio po&longs;ito cen&shy;<lb/> <s id="id.2.1.35.1.1.4.0"> dicent for&longs;an, &longs;i trutina &agrave; potentia <lb/>in F &longs;u&longs;titencatur, tunc CG erit tanquam meta, &amp; angulus <lb/>DCG grauitatis erit cau&longs;a.  </s>            
 tro mundi S, per lineam DS moue&shy;<lb/> 
 bitur.  </s>              <s id="id.2.1.35.1.1.5.0"> &longs;i ver&ograve; &longs;u&longs;tineatur in G, tunc FCE <lb/>erit cau&longs;a grauitatis, CF ver&ograve; tanquam meta erit.  </s>            
 <s id="id.2.1.33.3.1.2.0"> &longs;imiliter pondus in E &longs;olutum <lb/> 
 per lineam ES mouebitur.  </s>              <s id="id.2.1.35.1.1.6.0"> cuius quidem <lb/>rei nulla videtur e&longs;&longs;e cau&longs;a, ni&longs;i immaginaria.  </s>            
 <s id="id.2.1.33.3.1.3.0"> quare &longs;i <lb/> 
 (vt rei veritas e&longs;t) ponderis de&longs;cen&shy;<lb/> <s id="id.2.1.35.1.1.7.0"> meta enim (quod <lb/>aiunt) nullam pror&longs;us vim attractiuam, quandoq; ex maioris an&shy;<lb/>guli parte, quandoq; ex parte minoris habere videtur.  </s>            
 &longs;us magis, minu&longs;u&egrave; obliquus dicetur <lb/> 
 &longs;ecund&ugrave;m rece&longs;&longs;um, &amp; acce&longs;&longs;um ad <lb/> <s id="id.2.1.35.1.1.8.0"> Ver&ugrave;m &agrave; dua<lb/>bus potentiis &longs;u&longs;tineatur trutina, in F &longs;cilicet, &amp; in G, quod pr&aelig; ne<lb/>ce&longs;sitate fieri pote&longs;t, veluti &longs;i potentia in F &longs;it ade&ograve; debilis, vt ex &longs;e <lb/>ip&longs;a medietatem tant&ugrave;m ponderis &longs;u&longs;tinere qu&aelig;at: &longs;itq; potentia in <lb/>Gip&longs;i potenti&aelig; in F &aelig;qualis, vtr&aelig;q; <expan abbr="aut&etilde;">autem</expan> &longs;imul libram vn&aacute; cum pon<lb/>deribus &longs;u&longs;tineant.  </s>            
 &longs;patia per lineas DSES de&longs;ignata, <lb/> 
 iuxta naturales ip&longs;orum ad propria lo <lb/> <s id="id.2.1.35.1.1.9.0"> tunc quis nam angulus erit cau&longs;a grauitatis?  </s>            
 ca lationes; con&longs;picuum e&longs;t, minus <lb/> 
 obliquum e&longs;&longs;e de&longs;cen&longs;um ip&longs;ius E <lb/> <s id="id.2.1.35.1.1.10.0"> non <pb xlink:href="pagethumb-la/00000060.JPG"/>FCE, quia trutina e&longs;t in <lb/>CF, &amp; in F &longs;u&longs;tinetur.  </s>            
 per EG, qu&agrave;m ip&longs;ius D per DA: <lb/> 
 c&ugrave;m angulum SEG angulo SDA <lb/> <s id="id.2.1.35.1.1.11.0"> neq; <lb/>DCG, c&ugrave;m trutina &longs;it in <lb/>CG, &amp; in G quoq; &longs;u&longs;ti<lb/>neatur; non igitur anguli <lb/>grauitatis cau&longs;a erunt.  </s>            
 minorem e&longs;&longs;e &longs;upra o&longs;ten&longs;um &longs;it.  </s>              
 <s id="id.2.1.33.3.1.4.0"> qua <lb/> <s id="id.2.1.35.1.1.12.0"> ergo <lb/>neq; libra DE ab hoc &longs;itu <lb/>ob hanc cau&longs;am mo uebi&shy;<lb/><arrow.to.target n="note62"></arrow.to.target> tur.  </s>            
 re in E pondus magis grauitabit, <lb/> 
 qu&agrave;m in D. quod e&longs;t penitus oppo&shy;<lb/> <s id="id.2.1.35.1.1.13.0"> Hanc autem eorum <lb/>&longs;ententiam dupliciter con&shy;<lb/><figure id="fig38" place="text" xlink:href="figures1577/2000.03.0057.jpg">       </figure><lb/>firmare videntur.  </s>            
 &longs;itum eius, quod ip&longs;i o&longs;tendere cona<lb/> 
 ti &longs;unt.  </s>              <s id="id.2.1.35.1.1.14.0"> prim&ugrave;m quidem a&longs;&longs;erunt Ari&longs;totelem in qu&aelig;&longs;tio<lb/>nibus mechanicis has duas tant&ugrave;m qu&aelig;&longs;tiones propo&longs;ui&longs;&longs;e; eiu&longs;q; <lb/>demon&longs;trationes, tum maiori, &amp; minori angulo, t&ugrave;m trutin&aelig; po&longs;i<lb/>tioni inniti.  </s>            
 <s id="id.2.1.33.3.1.5.0"> In&longs;urgent autem forta&longs;&longs;e <lb/> 
 contranos, &longs;i igitur (dicent) pondus <lb/> <s id="id.2.1.35.1.1.15.0"> Affirmant deinde experientiam hoc idem docere; <lb/>hoc e&longs;t libram DE trutina exi&longs;tente in CF, in AB horizonti <lb/>&aelig;quidi&longs;tantem redire.  </s>            
 in E grauius e&longs;t pondere in D, libra <lb/> 
 <figure id="fig34" place="text" xlink:href="figures1577/2000.03.0052.jpg">       </figure><lb/> <s id="id.2.1.35.1.1.16.0"> quando autem trutina e&longs;t in CG, in FG <lb/>moueri.  </s>            
 DE in hoc &longs;itu minim&egrave; per&longs;i&longs;tet, quod <expan abbr="equid&etilde;">equidem</expan> tueri propo&longs;uimus: <lb/> 
 &longs;ed in FG mouebitur.  </s>              <s id="id.2.1.35.1.1.17.0"> Ver&ugrave;m neq; Ari&longs;toteles, neq; experientia huic eorum <lb/>opinioni fauent, quin potius aduer&longs;antur.  </s>            
 <s id="id.2.1.33.3.1.6.0"> quibus re&longs;pondemus, plurimum referre, &longs;iue <lb/> 
 con&longs;ideremus pondera, quatenus &longs;unt inuicem di&longs;iuncta, &longs;iue quate <lb/> <s id="id.2.1.35.1.1.18.0"> quant&ugrave;m enim atti&shy;<lb/>net ad experientiam decipiuntur, ip&longs;a quidem experientia ma&shy;<lb/>nife&longs;tum e&longs;t hoc accidere, quando libr&aelig; quoq; centrum, vel &longs;u&shy;<lb/>pra, vel infra libram fuerit collocatum: non autem trutina dun<lb/>taxat &longs;upra, vel infra exi&longs;tente, id contingere.  </s>    
 nus &longs;unt &longs;ibi inuicem connexa.  </s>              
 <s id="id.2.1.33.3.1.7.0"> alia e&longs;t enim ratio ponderis in E &longs;ine <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.35.1.2.1.0" type="caption">        
 connexione ponderis in D, alia ver&ograve; eiu&longs;dem alteri ponderi con<lb/> 
 nexi; ita vt alterum &longs;ine altero moueri non po&longs;sit.  </s>              <s id="id.2.1.35.1.2.1.0.capt"> YYY </s>    
 <s id="id.2.1.33.3.1.8.0"> nam ponde<lb/> 
 ris in E, quatenus e&longs;t &longs;ine alterius ponderis connexione, rectus <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.35.1.2.3.0" type="caption">        
 naturalis de&longs;cen&longs;us e&longs;t per lineam ES; quatenus ver&ograve; connexum <lb/> 
 e&longs;t ponderi in D, eius naturalis de&longs;cen&longs;us non erit amplius per <lb/> <s id="id.2.1.35.1.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.36.1.0.0.0" type="margin">        
 lineam ES, &longs;ed per lineam ip&longs;i CS parallelam.  </s>              
 <s id="id.2.1.33.3.1.9.0"> magnitudo enim <lb/> <s id="id.2.1.36.1.1.1.0"> <margin.target id="note62"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.37.1.0.0.0" type="main">        <pb n="22" xlink:href="pagethumb-la/00000061.JPG"/>      
 ex ponderibus ED, &amp; libra DE compo&longs;ita, cuius grauitatis cen&shy;<lb/> 
 trum e&longs;t C, &longs;i nullibi &longs;u&longs;tineatur, deor&longs;um eo modo, quo reperi<lb/> <s id="id.2.1.37.1.2.1.0"> Nam &longs;i libra AB habeat <lb/>centrum C &longs;upra libram; <lb/>&longs;itq; trutina CD infra li&shy;<lb/>bram; moueaturq; libra in <lb/>EF; tunc EF rur&longs;us in AB <lb/>horizonti &aelig;quidi&longs;tantem <arrow.to.target n="note63"></arrow.to.target><lb/>redibit.  </s>            
 tur, &longs;ecund&ugrave;m grauitatis centrum per rectam &agrave; centro grauita<lb/> 
 tis C ad centrum mundi S ductam naturaliter mouebitur, donec  <s id="id.2.1.37.1.2.2.0"> &longs;imiliter &longs;i libra <lb/>centrum C habeat infra li<lb/>bram, &longs;itq; trutina CD &longs;u<lb/>pra libram, &amp; moueatur <lb/>libra in EF; patet libram <arrow.to.target n="note64"></arrow.to.target><lb/>ex parte F deor&longs;um moue <lb/>ri, trutina &longs;upra libram e&shy;<lb/>xi&longs;tente.  </s>            
 <pb n="20" xlink:href="pagethumb-la/00000057.JPG"/> 
 centrum C in centrum S perueniat.  </s>              <s id="id.2.1.37.1.2.3.0"> &amp; in quocunq; a&shy;<lb/>lio &longs;itu fuerit trutina, idem <lb/>&longs;emper eueniet.  </s>            
 <s id="id.2.1.33.3.1.10.0"> libra igitur DE vn&aacute; cum pon<lb/> 
 deribus eo modo, quo reperitur, deor&longs;um mouebitur, ita vt pun&shy;<lb/> <s id="id.2.1.37.1.2.4.0"> non igitur <lb/>trutina, &longs;ed centrum libr&aelig; <lb/>harum diuer&longs;itatum cau&shy;<lb/>&longs;a erit. <figure id="fig39" place="text" xlink:href="figures1577/2000.03.0058.jpg">       </figure> </s>    </p>       <p id="id.2.1.37.2.0.0.0" type="main">        
 ctum C per lineam CS moueatur, donec C in S, libraq; DE in <lb/> 
 Hk perueniat; habeatq; libra in Hk eandem, quam prius habe&shy;<lb/> <s id="id.2.1.37.2.1.1.0"> Animaduertendum e&longs;t <lb/>itaq; in hac parte difficulter materialem libram con&longs;titui po&longs;&longs;e, <lb/>qu&aelig; in vno tant&ugrave;m puncto &longs;u&longs;tineatur; quemadmodum mente <lb/>concipimus.  </s>            
 bat po&longs;itionem; hoc e&longs;t Hk &longs;it ip&longs;i DE &aelig;quidi&longs;tans.  </s> 
 <s id="id.2.1.33.3.1.11.0"> connectantur <lb/> <s id="id.2.1.37.2.1.2.0"> brachiaq; ab eiu&longs;modi centro ade&ograve; &aelig;qualia habeat, <lb/>non &longs;olum in longitudine, ver&ugrave;m etiam in latitudine, &amp; profun<lb/>ditate, vt omnes partes hinc ind&eacute; ad vnguem &aelig;queponderent.  </s>            
 igitur DH Ek.  </s>              
 <s id="id.2.1.33.3.1.12.0"> manife&longs;tum e&longs;t, dum libra DE in Hk mouetur pun<lb/> <s id="id.2.1.37.2.1.3.0"> <lb/>hoc enim materia difficilim&egrave; patitur.  </s>            
 cta DE per lineas DH Ek moueri, quippe exi&longs;tentibus inter &longs;e <arrow.to.target n="note59"></arrow.to.target><lb/> 
 &longs;e, ip&longs;iq; CS &aelig;qualibus, &amp; &aelig;quidi&longs;tantibus.  </s>              <s id="id.2.1.37.2.1.4.0"> quocirca &longs;i centrum in ip&longs;a <lb/>libra e&longs;&longs;e con&longs;iderauerimus, ad &longs;en&longs;um confugiendum non e&longs;t: <lb/>c&ugrave;m artificilia ad &longs;ummum illud perfectionis gradum ab artifice <lb/>deduci minim&egrave; po&longs;sint.  </s>            
 <s id="id.2.1.33.3.1.13.0"> Quare pondera in <lb/> 
 DE, quatenus &longs;unt &longs;ibi inuicem connexa, &longs;i ip&longs;orum naturalem mo <lb/> <s id="id.2.1.37.2.1.5.0"> In aliis ver&ograve; experientia quidem appa&shy;<lb/>rentia docere poterit; proptereaquod, quamquam centrum libr&aelig; <lb/>&longs;it &longs;emper punctum, quando tamen &longs;upra libram fuerit, par&ugrave;m re&shy;<lb/>fert, &longs;i libra in eo puncto adamu&longs;&longs;im minim&egrave; &longs;u&longs;tineatur; quia c&ugrave;m <lb/>&longs;it &longs;emper &longs;upra libram, idem &longs;emper eueniet.  </s>            
 tum &longs;pectemus, non &longs;ecund&ugrave;m lineas DS ES, &longs;ed &longs;ecund&ugrave;m <lb/> 
 LDH MEk ip&longs;i CS &aelig;quidi&longs;tantes mouebuntur.  </s>              <s id="id.2.1.37.2.1.6.0"> &longs;imili quoq; modo <lb/>quando e&longs;t infra libram: quod tamen non accidit centro in ip&longs;a li&shy;<lb/>bra exi&longs;tente.  </s>            
 <s id="id.2.1.33.3.1.14.0"> ponderis <expan abbr="ve&shy;r&ograve;">ve&shy;<lb/> 
 ro</expan> in E liberi, ac &longs;oluti, naturalis propen&longs;io erit per ES: ponderis <lb/> <s id="id.2.1.37.2.1.7.0"> &longs;i enim ad vnguem &longs;emper in illo medio non &longs;u&shy;<lb/>&longs;tineatur, diuer&longs;itatem efficiet; c&ugrave;m facillimum &longs;it, centrum il&shy;<pb xlink:href="pagethumb-la/00000062.JPG"/>lud, d&ugrave;m libra mouetur, proprium mutare &longs;itum. </s>    
 autem in D &longs;imiliter &longs;oluti erit per DS. ac propterea non e&longs;t incon&shy;<lb/> 
 ueniens idem pondus mod&ograve; in E, mod&ograve; in D, grauius e&longs;&longs;e in E, <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.37.2.2.1.0" type="caption">        
 qu&agrave;m in D.  </s>      
 <s id="id.2.1.33.3.1.14.0.a"> &longs;i ver&ograve; pondera in ED &longs;ibi inuicem connexa, quate&shy;<lb/> <s id="id.2.1.37.2.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.38.1.0.0.0" type="margin">        
 nusq; &longs;unt connexa con&longs;iderauerimus; erit ponderis in E natura&shy;<lb/> 
 lis propen&longs;io per lineam MEK: grauitas enim alterius ponde&shy;<lb/> <s id="id.2.1.38.1.1.1.0"> <margin.target id="note63"></margin.target>2 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>            
 ris in D efficit, n&egrave; pondus in E per lineam ES grauitet, &longs;ed per <lb/> 
 Ek.  </s>              <s id="id.2.1.38.1.1.2.0"> <margin.target id="note64"></margin.target>3 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.39.1.0.0.0" type="main">        
 <s id="id.2.1.33.3.1.15.0"> quod ip&longs;um quoq; grauitas ponderis in E efficit, n&egrave; &longs;cilicet <lb/> 
 pondus in D per rectam DS degrauet; &longs;ed &longs;ecund&ugrave;m DH: vtra&shy;<lb/> <s id="id.2.1.39.1.1.1.0"> Qu&ograve;d autem Ari&longs;toteles duas tant&ugrave;m qu&aelig;&longs;tiones propo&shy;<lb/>&longs;uerit, cur &longs;cilicet trutina &longs;uperius exi&longs;tente, &longs;i libra non &longs;it <lb/>horizonti &aelig;quidi&longs;tans in &aelig;quilibrium, hoc e&longs;t horizonti &aelig;qui <lb/>di&longs;tans redit: &longs;i autem trutina deor&longs;um fuerit con&longs;tituta, non <lb/>redit; &longs;ed adhuc &longs;ecund&ugrave;m partem depre&longs;&longs;am mouetur: verum <lb/>quidem e&longs;t.  </s>            
 que enim &longs;e impediunt, n&egrave; ad propria loca permeent.  </s>              
 <s id="id.2.1.33.3.1.16.0"> C&ugrave;m igi<lb/> <s id="id.2.1.39.1.1.2.0"> non tamen eius demon&longs;trationes maiori, &amp; mino <lb/>ri angulo, po&longs;itioniqu&eacute; trutin&aelig; (vt ip&longs;i dicunt) innituntur.  </s>            
 tur naturalis de&longs;cen&longs;us rectus ponderum in DE &longs;it &longs;ecund&ugrave;m <lb/> 
 LDH MEK: erit &longs;imliter rectus eorum a&longs;cen&longs;us &longs;ecund&ugrave;m ea&longs; <lb/> <s id="id.2.1.39.1.1.3.0"> In <lb/>hoc enim mentem philo&longs;ophi a&longs;ignantis rationem diuer&longs;itatis <lb/>motuum libr&aelig; minim&egrave; attingunt.  </s>            
 dem lineas HDL KEM. atq; a&longs;cen&longs;us ponderis in E magis, mi<lb/> 
 nu&longs;u&egrave; obliquus dicetur; quant&ograve; &longs;ecund&ugrave;m &longs;patium magis, <expan abbr="mi&shy;nu&longs;u&egrave;">mi&shy;<lb/> <s id="id.2.1.39.1.1.4.0"> tant&ugrave;m enim abe&longs;t philo&longs;o&shy;<lb/>phum has diuer&longs;itates in angulos referre, vt potius in cau&longs;a e&longs;&longs;e <lb/>dicat magnitudinis alterius brachii libr&aelig; exce&longs;&longs;um &agrave; perpendiculo, <lb/>mod&ograve; ex vna, mod&ograve; ex altera parte contingentem. </s>    </p>       <p id="id.2.1.39.2.0.0.0" type="main">        
 nu&longs;ue</expan> iuxta lineam Mk mouebitur.  </s>              
 <s id="id.2.1.33.3.1.17.0"> hocq; pror&longs;us modo iuxta li<lb/> <s id="id.2.1.39.2.1.1.0"> Vt trutina &longs;uperius in <lb/>CF exi&longs;tente, perpendicu<lb/>lum erit FCG, quod <expan abbr="&longs;e&shy;cund&ugrave;m">&longs;e&shy;<lb/>cundum</expan> ip&longs;um in centrum <lb/>mundi &longs;emper vergit; <lb/>quod quidem libram mo&shy;<lb/>tam in DE in partes di&shy;<lb/>uidit in&aelig;quales; &amp; maior <lb/>pars e&longs;t ver&longs;us D: id au&shy;<lb/>tem, quod plus e&longs;t, deor<lb/>&longs;um fertur; ergo ex par&shy;<lb/>te D deor&longs;um libra moue<lb/>bitur, donec in AB re&shy;<lb/>deat.  </s>            
 neam LH &longs;ummendus e&longs;t, t&ugrave;m de&longs;cen&longs;us, t&ugrave;m a&longs;cen&longs;us ponde&shy;<lb/> 
 ris in D. &longs;i itaq; pondus in E deor&longs;um per EG moueretur; pon<lb/> <s id="id.2.1.39.2.1.2.0"> &longs;i ver&ograve; trutina &longs;it <lb/><figure id="fig40" place="text" xlink:href="figures1577/2000.03.0059.jpg">       </figure><lb/>in CG deor&longs;um, erit GCF perpendiculum, quod libram DE <lb/>in partes in&aelig;quales &longs;imiliter diuidit: maior autem pars erit ver&longs;us <lb/>E; quare ex parte E deor&longs;um libra mouebitur.  </s>            
 dus in D &longs;ur&longs;um per DF moueret.  </s>              
 <s id="id.2.1.33.3.1.18.0"> &amp; quoniam angulus CEK <arrow.to.target n="note60"></arrow.to.target><lb/> <s id="id.2.1.39.2.1.3.0"> quod vt rect&egrave; in&shy;<lb/>telligatur, c&ugrave;m trutina e&longs;t &longs;upra libram, libr&aelig; quoq; centrum &longs;u&shy;<lb/>pra libram e&longs;&longs;e intelligendum e&longs;t; &amp; &longs;i deor&longs;um, centrum quoque <lb/>deor&longs;um: vt infra patebit.  </s>            
 &aelig;qualis e&longs;t angulo CDL, &amp; angulus CEG angulo CDF &aelig;qua&shy;<lb/> 
 lis; erit reliquus GEK reliquo LDF &aelig;qualis.  </s>              <s id="id.2.1.39.2.1.4.0"> Aliter ip&longs;a Ari&longs;totelis demon&longs;tratio <lb/>nihil concluderet.  </s>            
 <s id="id.2.1.33.3.1.19.0"> c&ugrave;m autem &longs;up&shy;<lb/> 
 po&longs;itio illa, qu&aelig; ait, &longs;ecund&uacute;m &longs;itum pondus grauius e&longs;&longs;e, <expan abbr="quan&shy;t&ograve;">quan&shy;<lb/> <s id="id.2.1.39.2.1.5.0"> exi&longs;tente enim centro in ip&longs;a libra, vt in C; quo&shy;<lb/>cunq; modo moueatur libra, nunquam perpendiculum FG libram, <pb n="23" xlink:href="pagethumb-la/00000063.JPG"/>ni&longs;i in puncto C, &amp; in partes diuidet &aelig;quales.  </s>            
 to</expan> in eodem &longs;itu minus obliquus e&longs;t de&longs;cen&longs;us; tanquam clara, <lb/> 
 atq; con&longs;picua admittatur; proculdubio h&aelig;c quoq; accipienda <lb/> <s id="id.2.1.39.2.1.6.0"> quare Ari&longs;totelis <lb/>&longs;ententia ip&longs;is non &longs;olum non fauet, ver&ugrave;m etiam maxim&egrave; aduer&shy;<lb/>&longs;atur.  </s>            
 erit; nemp&egrave;, &longs;ecund&uacute;m &longs;itum pondus grauius e&longs;&longs;e, quant&ograve; in eo&shy;<lb/> 
 dem &longs;itu minus obliquus e&longs;t a&longs;cen&longs;us.  </s>              <s id="id.2.1.39.2.1.7.0"> qu&ograve;d non &longs;olum ex &longs;ecunda, &amp; tertia huius liquet; ver&ugrave;m <lb/>quia exi&longs;tente centro &longs;upra libram pondus eleuatum maiorem <lb/>propter &longs;itum acquirit grauitatem.  </s>            
 <s id="id.2.1.33.3.1.20.0"> c&ugrave;m non minus manife&longs;ta,  
 <pb xlink:href="pagethumb-la/00000058.JPG"/> <s id="id.2.1.39.2.1.8.0"> ex qu&ograve; contingit redditus li&shy;<lb/>br&aelig; ad &aelig;qualem horizonti di&longs;tantiam.  </s>            
 rationiq; &longs;it con&longs;entanea.  </s>              
 <s id="id.2.1.33.3.1.21.0"> &aelig;qualis <lb/> <s id="id.2.1.39.2.1.9.0"> &egrave; contra ver&ograve;, quando <lb/>centrum e&longs;t infra libram.  </s>            
 igitur erit de&longs;cen&longs;us ponderis in E <lb/> 
 a&longs;cen&longs;ui ponderis in D. eandem <lb/> <s id="id.2.1.39.2.1.10.0"> Qu&aelig; omnia hoc modo o&longs;tendentur; <lb/>&longs;upponendo ea, qu&aelig; &longs;upra declarata &longs;unt.  </s>            
 enim obliquitatem habet de&longs;cen&longs;us <lb/> 
 ponderis in E, quam habet a&longs;cen&shy;<lb/> <s id="id.2.1.39.2.1.11.0"> &longs;cilicet pondus ex qu&ograve; <lb/>loco rectius de&longs;cendit, grauius fieri.  </s>            
 &longs;us ponderis in D; &amp; qualis erit <lb/> 
 propen&longs;io vnius ad motum deor&longs;um, <lb/> <s id="id.2.1.39.2.1.12.0"> &amp; ex quo rectius a&longs;cendit, gra<lb/>uius quoq; reddi. </s>    
 talis quoq; erit re&longs;i&longs;tentia alterius ad <lb/> 
 motum &longs;ur&longs;um.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.39.2.2.1.0" type="caption">        
 <s id="id.2.1.33.3.1.22.0"> <expan abbr="n&otilde;">non</expan> ergo pondus in E <lb/> 
 pondus in D &longs;ur&longs;um mouebit.  </s>              <s id="id.2.1.39.2.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.39.3.0.0.0" type="main">        
 <s id="id.2.1.33.3.1.23.0"> neq; <lb/> 
 pondus in D deor&longs;um mouebitur, ita <lb/> <s id="id.2.1.39.3.1.1.0"> Sit libra AB horizonti <lb/>&aelig;quidi&longs;tans, cuius centrum <lb/>C &longs;it &longs;upra libram, perpen&shy;<lb/>diculumq; &longs;it CD. &longs;intq; in <lb/>AB ponderum &aelig;qualium <lb/>centra grauitatis po&longs;ita: mo<lb/>taq; &longs;it libra in EF.  </s>    
 vt &longs;ur&longs;um moueat pondus in E. nam <lb/> 
 <expan abbr="c&utilde;">cum</expan> angulus CEB &longs;it ip&longs;i CDA &aelig;qua&shy;<lb/> <s id="id.2.1.39.3.1.1.0.a"> Dico <lb/>pondus in E maiorem ha&shy;<lb/>bere grauitatem, qu&agrave;m pon<lb/>dus in F. &amp; ob id libram <lb/>EF in AB redire.  </s>            
 <arrow.to.target n="note61"></arrow.to.target> lis, &amp; Angulus CEM &longs;it angulo <lb/> 
 CDH &aelig;qualis; erit reliquus MEB <lb/> <s id="id.2.1.39.3.1.2.0"> Produ<lb/>catur prim&ugrave;m CD v&longs;q; ad <lb/>mundi <expan abbr="centr&utilde;">centrum</expan>, quod &longs;it S. de <lb/>inde AC CB EC CF HS <lb/><expan abbr="c&otilde;nectantur">connectantur</expan>, &agrave; puncti&longs;q; EF <lb/>ip&longs;i HS &aelig;quidi&longs;tantes du<lb/>cantur Ek GFL.  </s>    
 reliquo HDA &aelig;qualis.  </s>              
 <s id="id.2.1.33.3.1.24.0"> de&longs;cen&longs;us <lb/> <s id="id.2.1.39.3.1.2.0.a"> Quoniam <lb/>igitur naturalis de&longs;cen&longs;us re<lb/>ctus totius magnitudinis, <lb/>libr&aelig; &longs;cilicet EF &longs;ic con&longs;ti&shy;<lb/>tut&aelig; vn&aacute; cum ponderibus, <lb/>e&longs;t &longs;cund&ugrave;m grauitatis cen<lb/>trum H per rectam HS; erit <lb/><figure id="fig41" place="text" xlink:href="figures1577/2000.03.0060.jpg">       </figure><lb/>quoq; ponderum in EF ita po&longs;sitorum de&longs;cen&longs;us &longs;ecund&ugrave;m re&shy;<lb/>ctas Ek FL ip&longs;i HS parallelas; &longs;icuti &longs;upra demon&longs;trauimus.  </s>            
 igitur ponderis in D a&longs;cen&longs;ui ponde<lb/> 
 ris in E &aelig;qualis erit.  </s>              <s id="id.2.1.39.3.1.3.0"> <pb xlink:href="pagethumb-la/00000064.JPG"/>De&longs;cen&longs;us igitur, &amp; a&longs;cen&shy;<lb/>&longs;us ponderum in EF ma&shy;<lb/>gis, minu&longs;u&egrave; obliquus di&shy;<lb/>cetur &longs;ecund&ugrave;m acce&longs;&longs;um, <lb/>&amp; rece&longs;&longs;um iuxta lineas Ek <lb/>FL de&longs;ignatum.  </s>            
 <s id="id.2.1.33.3.1.25.0"> non ergo pon<lb/> 
 dus in D pondus in E &longs;ur&longs;um moue<lb/> <s id="id.2.1.39.3.1.4.0"> <expan abbr="Quoni&atilde;">Quoniam</expan> au<lb/><expan abbr="t&etilde;">tem</expan> duo latera AD DC duo<lb/>bus lateribus BD DE &longs;unt <lb/>&aelig;qualia; anguliq; ad D &longs;unt <lb/><arrow.to.target n="note65"></arrow.to.target> recti; erit latus AC lateri <lb/>CB &aelig;quale.  </s>            
 bit.  </s>              
 <s id="id.2.1.33.3.1.26.0"> ex quibus &longs;equitur pondera in <lb/> <s id="id.2.1.39.3.1.5.0"> &amp; c&ugrave;m pun&shy;<lb/>ctum C &longs;it immobile; dum <lb/>puncta AB mouentur, cir<lb/>culi circumferentiam de&longs;cri<lb/>bent, cuius &longs;emidiameter <lb/>erit AC. quare centro C, <lb/>circulus de&longs;cribatur AEBF. <lb/>puncta AB EF in circuli <lb/>circumferentia erunt.  </s>            
 DE, quatenus &longs;unt &longs;ibi inuicem con<lb/> 
 nexa, &aelig;qu&egrave; grauia e&longs;&longs;e. <figure id="fig35" place="text" xlink:href="figures1577/2000.03.0054.jpg">       </figure> </s>    </p>        <s id="id.2.1.39.3.1.6.0"> &longs;ed <lb/>c&ugrave;m EF &longs;it ip&longs;i AB &aelig;qua <lb/><arrow.to.target n="note66"></arrow.to.target> lis; erit circumferentia <lb/>EAF circumferenti&aelig; AFB <lb/>&aelig;qualis.  </s>            
 <p id="id.2.1.33.4.0.0.0" type="main">         
 <s id="id.2.1.33.4.1.1.0"> Alia deinde ratio, li&shy;<lb/> <s id="id.2.1.39.3.1.7.0"> quare dempta <lb/><figure id="fig42" place="text" xlink:href="figures1577/2000.03.0061.jpg">       </figure><lb/>communi AF, erit circumferentia EA circumferenti&aelig; FB &aelig;qua <lb/>lis.  </s>            
 bram &longs;imiliter DE in AB <lb/> 
 redire o&longs;tendens, c&ugrave;m in&shy;<lb/> <s id="id.2.1.39.3.1.8.0"> Quoniam autem mixtus angulus CEA e&longs;t &aelig;qualis mixto <lb/>CFB; &amp; HFB ip&longs;o CFB e&longs;t maior; angulus ver&ograve; HEA ip&longs;o <lb/>CEA minor; erit angulus HFB angulo HEA maior.  </s>            
 quiunt, exi&longs;tente trutina in <lb/> 
 CF meta e&longs;t CG.  </s>      <s id="id.2.1.39.3.1.9.0"> &agrave; quibus <lb/><arrow.to.target n="note67"></arrow.to.target> &longs;i auferantur anguli HFG HEk &aelig;quales; erit angulus GFB an <lb/>gulo kEA maior.  </s>            
 <s id="id.2.1.33.4.1.1.0.a"> &amp; quo&shy;<lb/> 
 niam angulus DCG maior <lb/> <s id="id.2.1.39.3.1.10.0"> ergo de&longs;cen&longs;us ponderis in E minus obliquus <lb/>erit a&longs;cen&longs;u ponderis in F. &amp; quamquam pondus in E de&longs;cen<lb/>dendo, &amp; pondus in F a&longs;cendendo per circumferentias mouean<lb/>tur &aelig;quales; quia tamen pondus in E ex hoc loco rectius de&longs;cen<lb/>dit, qu&agrave;m pondus in F a&longs;cendit: idcirco naturalis potentia pon<lb/>deris in E re&longs;i&longs;tentiam violenti&aelig; ponderis F &longs;uperabit.  </s>            
 e&longs;t angulo ECG; pondus <lb/> 
 in D grauius erit pondere <lb/> <s id="id.2.1.39.3.1.11.0"> quare <lb/>maiorem grauitatem habebit pondus in E, qu&agrave;m pondus in F.  </s>    
 in E; ergo libra DE in AB <lb/> 
 redibit: nihil meo iudicio <lb/> <s id="id.2.1.39.3.1.11.0.a"> <lb/>ergo pondus in E deor&longs;um, pondus ver&ograve; in F &longs;ur&longs;um mouebitur: <pb n="24" xlink:href="pagethumb-la/00000065.JPG"/>donec libra EF in AB redeat. </s>            
 concludit.  </s>              
 <s id="id.2.1.33.4.1.2.0"> figmentumq; <lb/> <s id="id.2.1.39.3.1.12.0"> quod demon&longs;trare oportebat. </s>    
 hoc de trutina, &amp; meta po&shy;<lb/> 
 tius omittendum, ac &longs;ilen&shy;|tio<figure id="fig36" place="text" xlink:href="figures1577/2000.03.0056.1.jpg">       </figure> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.39.3.2.1.0" type="caption">        
 <pb n="21" xlink:href="pagethumb-la/00000059.JPG"/> 
  <expan abbr="pr&aelig;tereund&utilde;">pr&aelig;tereundum</expan> e&longs;&longs;et, qu&agrave;m <expan abbr="verb&utilde;">verbum</expan> <expan abbr="vll&utilde;">vllum</expan> in eius confutatione &longs;umen<lb/> 
 dum; c&ugrave;m &longs;it pror&longs;us voluntarium.  </s>              
 <s id="id.2.1.33.4.1.3.0"> nece&longs;sitas enim cur pondus <lb/> 
 in D ex maiore angulo &longs;it grauius; curq; maior angulus maioris <lb/> 
 &longs;it cau&longs;a grauitatis; nu&longs;quam apparet.  </s>              
 <s id="id.2.1.33.4.1.4.0"> &longs;i autem comparentur in&shy;<lb/> 
 uicem anguli, c&ugrave;m angulus GCD &longs;it &aelig;qualis angulo FCE; &longs;i angu<lb/> 
 lus GCD e&longs;t cau&longs;a grauitatis; quare angulus FCE &longs;imiliter gra&shy;<lb/> 
 uitatis non e&longs;t cau&longs;a?  </s>              
 <s id="id.2.1.33.4.1.5.0"> Huius autem rei eam in medium rationem <lb/> 
 afferre videntur, quoniam CG e&longs;t meta, &amp; CF trutina.  </s>              
 <s id="id.2.1.33.4.1.6.0"> &longs;i (inquiunt) <lb/> 
 CG e&longs;&longs;et trutina, &amp; CF meta, tunc angulus FCE grauitatis e&longs;&longs;et <lb/> 
 cau&longs;a; non autem DCG ip&longs;i &aelig;qualis.  </s>              
 <s id="id.2.1.33.4.1.7.0"> qu&aelig; quidem ratio imma&shy;<lb/> 
 ginaria pror&longs;us, ac voluntaria e&longs;&longs;e videtur.  </s>              
 <s id="id.2.1.33.4.1.8.0"> quid enim refert, &longs;iue tru<lb/> 
 tina &longs;it in CF, &longs;iue in CG, c&ugrave;m libra DE in eodem &longs;emper pun&shy;<lb/> 
 cto C &longs;u&longs;tineatur?  </s>              
 <s id="id.2.1.33.4.1.9.0"> Vt autem eorum deceptio clarius appa&shy;<lb/> 
 reat. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.33.4.2.1.0" type="caption">         
 <s id="id.2.1.33.4.2.1.0.capt"> YYY </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.33.4.2.3.0" type="caption">         
 <s id="id.2.1.33.4.2.3.0.capt"> YYY </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.33.4.2.5.0" type="caption">         
 <s id="id.2.1.33.4.2.5.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.34.1.0.0.0" type="margin">         
 <s id="id.2.1.34.1.1.1.0"> <margin.target id="note59"></margin.target>33 <emph type="italics"/>Prmi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.34.1.1.2.0"> <margin.target id="note60"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.34.1.1.3.0"> <margin.target id="note61"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.35.1.0.0.0" type="main">         
 <s id="id.2.1.35.1.1.1.0"> Sit eadem libra AB, cu&shy;<lb/> 
 ius medium C. &longs;it deinde <lb/> 
 tota FG trutina.  </s>              
 <s id="id.2.1.35.1.1.2.0"> eaq; im<lb/> 
 mobilis exi&longs;tat; qu&aelig; libram <lb/> 
 AB in puncto C &longs;u&longs;tineat.  </s>              
 <s id="id.2.1.35.1.1.3.0"> <lb/> 
 moueaturq; libra in DE. &amp; <lb/> 
 quoniam trutina e&longs;t, &amp; &longs;u&shy;<lb/> 
 pra, &amp; infra libram, quis <lb/> 
 nam angulus erit cau&longs;a gra&shy;<lb/> 
 uitatis, c&ugrave;m libra DE in <lb/> 
 <figure id="fig37" place="text" xlink:href="figures1577/2000.03.0056.2.jpg">       </figure><expan abbr="eod&etilde;"><lb/> 
 eodem</expan> &longs;emper puncto &longs;u&longs;tineatur?  </s>              
 <s id="id.2.1.35.1.1.4.0"> dicent for&longs;an, &longs;i trutina &agrave; potentia <lb/> 
 in F &longs;u&longs;titencatur, tunc CG erit tanquam meta, &amp; angulus <lb/> 
 DCG grauitatis erit cau&longs;a.  </s>              
 <s id="id.2.1.35.1.1.5.0"> &longs;i ver&ograve; &longs;u&longs;tineatur in G, tunc FCE <lb/> 
 erit cau&longs;a grauitatis, CF ver&ograve; tanquam meta erit.  </s>              
 <s id="id.2.1.35.1.1.6.0"> cuius quidem <lb/> 
 rei nulla videtur e&longs;&longs;e cau&longs;a, ni&longs;i immaginaria.  </s>              
 <s id="id.2.1.35.1.1.7.0"> meta enim (quod <lb/> 
 aiunt) nullam pror&longs;us vim attractiuam, quandoq; ex maioris an&shy;<lb/> 
 guli parte, quandoq; ex parte minoris habere videtur.  </s>              
 <s id="id.2.1.35.1.1.8.0"> Ver&ugrave;m &agrave; dua<lb/> 
 bus potentiis &longs;u&longs;tineatur trutina, in F &longs;cilicet, &amp; in G, quod pr&aelig; ne<lb/> 
 ce&longs;sitate fieri pote&longs;t, veluti &longs;i potentia in F &longs;it ade&ograve; debilis, vt ex &longs;e <lb/> 
 ip&longs;a medietatem tant&ugrave;m ponderis &longs;u&longs;tinere qu&aelig;at: &longs;itq; potentia in <lb/> 
 Gip&longs;i potenti&aelig; in F &aelig;qualis, vtr&aelig;q; <expan abbr="aut&etilde;">autem</expan> &longs;imul libram vn&aacute; cum pon<lb/> 
 deribus &longs;u&longs;tineant.  </s>              
 <s id="id.2.1.35.1.1.9.0"> tunc quis nam angulus erit cau&longs;a grauitatis?  </s>              
 <s id="id.2.1.35.1.1.10.0"> non  
 <pb xlink:href="pagethumb-la/00000060.JPG"/> 
 FCE, quia trutina e&longs;t in <lb/> 
 CF, &amp; in F &longs;u&longs;tinetur.  </s>              
 <s id="id.2.1.35.1.1.11.0"> neq; <lb/> 
 DCG, c&ugrave;m trutina &longs;it in <lb/> 
 CG, &amp; in G quoq; &longs;u&longs;ti<lb/> 
 neatur; non igitur anguli <lb/> 
 grauitatis cau&longs;a erunt.  </s>              
 <s id="id.2.1.35.1.1.12.0"> ergo <lb/> 
 neq; libra DE ab hoc &longs;itu <lb/> 
 ob hanc cau&longs;am mo uebi&shy;<lb/> 
 <arrow.to.target n="note62"></arrow.to.target> tur.  </s>              
 <s id="id.2.1.35.1.1.13.0"> Hanc autem eorum <lb/> 
 &longs;ententiam dupliciter con&shy;<lb/> 
 <figure id="fig38" place="text" xlink:href="figures1577/2000.03.0057.jpg">       </figure><lb/> 
 firmare videntur.  </s>              
 <s id="id.2.1.35.1.1.14.0"> prim&ugrave;m quidem a&longs;&longs;erunt Ari&longs;totelem in qu&aelig;&longs;tio<lb/> 
 nibus mechanicis has duas tant&ugrave;m qu&aelig;&longs;tiones propo&longs;ui&longs;&longs;e; eiu&longs;q; <lb/> 
 demon&longs;trationes, tum maiori, &amp; minori angulo, t&ugrave;m trutin&aelig; po&longs;i<lb/> 
 tioni inniti.  </s>              
 <s id="id.2.1.35.1.1.15.0"> Affirmant deinde experientiam hoc idem docere; <lb/> 
 hoc e&longs;t libram DE trutina exi&longs;tente in CF, in AB horizonti <lb/> 
 &aelig;quidi&longs;tantem redire.  </s>              
 <s id="id.2.1.35.1.1.16.0"> quando autem trutina e&longs;t in CG, in FG <lb/> 
 moueri.  </s>              
 <s id="id.2.1.35.1.1.17.0"> Ver&ugrave;m neq; Ari&longs;toteles, neq; experientia huic eorum <lb/> 
 opinioni fauent, quin potius aduer&longs;antur.  </s>              
 <s id="id.2.1.35.1.1.18.0"> quant&ugrave;m enim atti&shy;<lb/> 
 net ad experientiam decipiuntur, ip&longs;a quidem experientia ma&shy;<lb/> 
 nife&longs;tum e&longs;t hoc accidere, quando libr&aelig; quoq; centrum, vel &longs;u&shy;<lb/> 
 pra, vel infra libram fuerit collocatum: non autem trutina dun<lb/> 
 taxat &longs;upra, vel infra exi&longs;tente, id contingere.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.35.1.2.1.0" type="caption">         
 <s id="id.2.1.35.1.2.1.0.capt"> YYY </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.35.1.2.3.0" type="caption">         
 <s id="id.2.1.35.1.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.36.1.0.0.0" type="margin">         
 <s id="id.2.1.36.1.1.1.0"> <margin.target id="note62"></margin.target><emph type="italics"/>Cardanus.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.37.1.0.0.0" type="main">         
 <pb n="22" xlink:href="pagethumb-la/00000061.JPG"/> 
         
 <s id="id.2.1.37.1.2.1.0"> Nam &longs;i libra AB habeat <lb/> 
 centrum C &longs;upra libram; <lb/> 
 &longs;itq; trutina CD infra li&shy;<lb/> 
 bram; moueaturq; libra in <lb/> 
 EF; tunc EF rur&longs;us in AB <lb/> 
 horizonti &aelig;quidi&longs;tantem <arrow.to.target n="note63"></arrow.to.target><lb/> 
 redibit.  </s>              
 <s id="id.2.1.37.1.2.2.0"> &longs;imiliter &longs;i libra <lb/> 
 centrum C habeat infra li<lb/> 
 bram, &longs;itq; trutina CD &longs;u<lb/> 
 pra libram, &amp; moueatur <lb/> 
 libra in EF; patet libram <arrow.to.target n="note64"></arrow.to.target><lb/> 
 ex parte F deor&longs;um moue <lb/> 
 ri, trutina &longs;upra libram e&shy;<lb/> 
 xi&longs;tente.  </s>              
 <s id="id.2.1.37.1.2.3.0"> &amp; in quocunq; a&shy;<lb/> 
 lio &longs;itu fuerit trutina, idem <lb/> 
 &longs;emper eueniet.  </s>              
 <s id="id.2.1.37.1.2.4.0"> non igitur <lb/> 
 trutina, &longs;ed centrum libr&aelig; <lb/> 
 harum diuer&longs;itatum cau&shy;<lb/> 
 &longs;a erit. <figure id="fig39" place="text" xlink:href="figures1577/2000.03.0058.jpg">       </figure> </s>    </p>        
 <p id="id.2.1.37.2.0.0.0" type="main">         
 <s id="id.2.1.37.2.1.1.0"> Animaduertendum e&longs;t <lb/> 
 itaq; in hac parte difficulter materialem libram con&longs;titui po&longs;&longs;e, <lb/> 
 qu&aelig; in vno tant&ugrave;m puncto &longs;u&longs;tineatur; quemadmodum mente <lb/> 
 concipimus.  </s>              
 <s id="id.2.1.37.2.1.2.0"> brachiaq; ab eiu&longs;modi centro ade&ograve; &aelig;qualia habeat, <lb/> 
 non &longs;olum in longitudine, ver&ugrave;m etiam in latitudine, &amp; profun<lb/> 
 ditate, vt omnes partes hinc ind&eacute; ad vnguem &aelig;queponderent.  </s>              
 <s id="id.2.1.37.2.1.3.0"> <lb/> 
 hoc enim materia difficilim&egrave; patitur.  </s>              
 <s id="id.2.1.37.2.1.4.0"> quocirca &longs;i centrum in ip&longs;a <lb/> 
 libra e&longs;&longs;e con&longs;iderauerimus, ad &longs;en&longs;um confugiendum non e&longs;t: <lb/> 
 c&ugrave;m artificilia ad &longs;ummum illud perfectionis gradum ab artifice <lb/> 
 deduci minim&egrave; po&longs;sint.  </s>              
 <s id="id.2.1.37.2.1.5.0"> In aliis ver&ograve; experientia quidem appa&shy;<lb/> 
 rentia docere poterit; proptereaquod, quamquam centrum libr&aelig; <lb/> 
 &longs;it &longs;emper punctum, quando tamen &longs;upra libram fuerit, par&ugrave;m re&shy;<lb/> 
 fert, &longs;i libra in eo puncto adamu&longs;&longs;im minim&egrave; &longs;u&longs;tineatur; quia c&ugrave;m <lb/> 
 &longs;it &longs;emper &longs;upra libram, idem &longs;emper eueniet.  </s>              
 <s id="id.2.1.37.2.1.6.0"> &longs;imili quoq; modo <lb/> 
 quando e&longs;t infra libram: quod tamen non accidit centro in ip&longs;a li&shy;<lb/> 
 bra exi&longs;tente.  </s>              
 <s id="id.2.1.37.2.1.7.0"> &longs;i enim ad vnguem &longs;emper in illo medio non &longs;u&shy;<lb/> 
 &longs;tineatur, diuer&longs;itatem efficiet; c&ugrave;m facillimum &longs;it, centrum il&shy; 
 <pb xlink:href="pagethumb-la/00000062.JPG"/> 
 lud, d&ugrave;m libra mouetur, proprium mutare &longs;itum. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.37.2.2.1.0" type="caption">         
 <s id="id.2.1.37.2.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.38.1.0.0.0" type="margin">         
 <s id="id.2.1.38.1.1.1.0"> <margin.target id="note63"></margin.target>2 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>              
 <s id="id.2.1.38.1.1.2.0"> <margin.target id="note64"></margin.target>3 <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.39.1.0.0.0" type="main">         
 <s id="id.2.1.39.1.1.1.0"> Qu&ograve;d autem Ari&longs;toteles duas tant&ugrave;m qu&aelig;&longs;tiones propo&shy;<lb/> 
 &longs;uerit, cur &longs;cilicet trutina &longs;uperius exi&longs;tente, &longs;i libra non &longs;it <lb/> 
 horizonti &aelig;quidi&longs;tans in &aelig;quilibrium, hoc e&longs;t horizonti &aelig;qui <lb/> 
 di&longs;tans redit: &longs;i autem trutina deor&longs;um fuerit con&longs;tituta, non <lb/> 
 redit; &longs;ed adhuc &longs;ecund&ugrave;m partem depre&longs;&longs;am mouetur: verum <lb/> 
 quidem e&longs;t.  </s>              
 <s id="id.2.1.39.1.1.2.0"> non tamen eius demon&longs;trationes maiori, &amp; mino <lb/> 
 ri angulo, po&longs;itioniqu&eacute; trutin&aelig; (vt ip&longs;i dicunt) innituntur.  </s>              
 <s id="id.2.1.39.1.1.3.0"> In <lb/> 
 hoc enim mentem philo&longs;ophi a&longs;ignantis rationem diuer&longs;itatis <lb/> 
 motuum libr&aelig; minim&egrave; attingunt.  </s>              
 <s id="id.2.1.39.1.1.4.0"> tant&ugrave;m enim abe&longs;t philo&longs;o&shy;<lb/> 
 phum has diuer&longs;itates in angulos referre, vt potius in cau&longs;a e&longs;&longs;e <lb/> 
 dicat magnitudinis alterius brachii libr&aelig; exce&longs;&longs;um &agrave; perpendiculo, <lb/> 
 mod&ograve; ex vna, mod&ograve; ex altera parte contingentem. </s>    </p>        
 <p id="id.2.1.39.2.0.0.0" type="main">         
 <s id="id.2.1.39.2.1.1.0"> Vt trutina &longs;uperius in <lb/> 
 CF exi&longs;tente, perpendicu<lb/> 
 lum erit FCG, quod <expan abbr="&longs;e&shy;cund&ugrave;m">&longs;e&shy;<lb/> 
 cundum</expan> ip&longs;um in centrum <lb/> 
 mundi &longs;emper vergit; <lb/> 
 quod quidem libram mo&shy;<lb/> 
 tam in DE in partes di&shy;<lb/> 
 uidit in&aelig;quales; &amp; maior <lb/> 
 pars e&longs;t ver&longs;us D: id au&shy;<lb/> 
 tem, quod plus e&longs;t, deor<lb/> 
 &longs;um fertur; ergo ex par&shy;<lb/> 
 te D deor&longs;um libra moue<lb/> 
 bitur, donec in AB re&shy;<lb/> 
 deat.  </s>              
 <s id="id.2.1.39.2.1.2.0"> &longs;i ver&ograve; trutina &longs;it <lb/> 
 <figure id="fig40" place="text" xlink:href="figures1577/2000.03.0059.jpg">       </figure><lb/> 
 in CG deor&longs;um, erit GCF perpendiculum, quod libram DE <lb/> 
 in partes in&aelig;quales &longs;imiliter diuidit: maior autem pars erit ver&longs;us <lb/> 
 E; quare ex parte E deor&longs;um libra mouebitur.  </s>              
 <s id="id.2.1.39.2.1.3.0"> quod vt rect&egrave; in&shy;<lb/> 
 telligatur, c&ugrave;m trutina e&longs;t &longs;upra libram, libr&aelig; quoq; centrum &longs;u&shy;<lb/> 
 pra libram e&longs;&longs;e intelligendum e&longs;t; &amp; &longs;i deor&longs;um, centrum quoque <lb/> 
 deor&longs;um: vt infra patebit.  </s>              
 <s id="id.2.1.39.2.1.4.0"> Aliter ip&longs;a Ari&longs;totelis demon&longs;tratio <lb/> 
 nihil concluderet.  </s>              
 <s id="id.2.1.39.2.1.5.0"> exi&longs;tente enim centro in ip&longs;a libra, vt in C; quo&shy;<lb/> 
 cunq; modo moueatur libra, nunquam perpendiculum FG libram,  
 <pb n="23" xlink:href="pagethumb-la/00000063.JPG"/> 
 ni&longs;i in puncto C, &amp; in partes diuidet &aelig;quales.  </s>              
 <s id="id.2.1.39.2.1.6.0"> quare Ari&longs;totelis <lb/> 
 &longs;ententia ip&longs;is non &longs;olum non fauet, ver&ugrave;m etiam maxim&egrave; aduer&shy;<lb/> 
 &longs;atur.  </s>              
 <s id="id.2.1.39.2.1.7.0"> qu&ograve;d non &longs;olum ex &longs;ecunda, &amp; tertia huius liquet; ver&ugrave;m <lb/> 
 quia exi&longs;tente centro &longs;upra libram pondus eleuatum maiorem <lb/> 
 propter &longs;itum acquirit grauitatem.  </s>              
 <s id="id.2.1.39.2.1.8.0"> ex qu&ograve; contingit redditus li&shy;<lb/> 
 br&aelig; ad &aelig;qualem horizonti di&longs;tantiam.  </s>              
 <s id="id.2.1.39.2.1.9.0"> &egrave; contra ver&ograve;, quando <lb/> 
 centrum e&longs;t infra libram.  </s>              
 <s id="id.2.1.39.2.1.10.0"> Qu&aelig; omnia hoc modo o&longs;tendentur; <lb/> 
 &longs;upponendo ea, qu&aelig; &longs;upra declarata &longs;unt.  </s>              
 <s id="id.2.1.39.2.1.11.0"> &longs;cilicet pondus ex qu&ograve; <lb/> 
 loco rectius de&longs;cendit, grauius fieri.  </s>              
 <s id="id.2.1.39.2.1.12.0"> &amp; ex quo rectius a&longs;cendit, gra<lb/> 
 uius quoq; reddi. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.39.2.2.1.0" type="caption">         
 <s id="id.2.1.39.2.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.39.3.0.0.0" type="main">         
 <s id="id.2.1.39.3.1.1.0"> Sit libra AB horizonti <lb/> 
 &aelig;quidi&longs;tans, cuius centrum <lb/> 
 C &longs;it &longs;upra libram, perpen&shy;<lb/> 
 diculumq; &longs;it CD. &longs;intq; in <lb/> 
 AB ponderum &aelig;qualium <lb/> 
 centra grauitatis po&longs;ita: mo<lb/> 
 taq; &longs;it libra in EF.  </s>      
 <s id="id.2.1.39.3.1.1.0.a"> Dico <lb/> 
 pondus in E maiorem ha&shy;<lb/> 
 bere grauitatem, qu&agrave;m pon<lb/> 
 dus in F. &amp; ob id libram <lb/> 
 EF in AB redire.  </s>              
 <s id="id.2.1.39.3.1.2.0"> Produ<lb/> 
 catur prim&ugrave;m CD v&longs;q; ad <lb/> 
 mundi <expan abbr="centr&utilde;">centrum</expan>, quod &longs;it S. de <lb/> 
 inde AC CB EC CF HS <lb/> 
 <expan abbr="c&otilde;nectantur">connectantur</expan>, &agrave; puncti&longs;q; EF <lb/> 
 ip&longs;i HS &aelig;quidi&longs;tantes du<lb/> 
 cantur Ek GFL.  </s>      
 <s id="id.2.1.39.3.1.2.0.a"> Quoniam <lb/> 
 igitur naturalis de&longs;cen&longs;us re<lb/> 
 ctus totius magnitudinis, <lb/> 
 libr&aelig; &longs;cilicet EF &longs;ic con&longs;ti&shy;<lb/> 
 tut&aelig; vn&aacute; cum ponderibus, <lb/> 
 e&longs;t &longs;cund&ugrave;m grauitatis cen<lb/> 
 trum H per rectam HS; erit <lb/> 
 <figure id="fig41" place="text" xlink:href="figures1577/2000.03.0060.jpg">       </figure><lb/> 
 quoq; ponderum in EF ita po&longs;sitorum de&longs;cen&longs;us &longs;ecund&ugrave;m re&shy;<lb/> 
 ctas Ek FL ip&longs;i HS parallelas; &longs;icuti &longs;upra demon&longs;trauimus.  </s>              
 <s id="id.2.1.39.3.1.3.0">  
 <pb xlink:href="pagethumb-la/00000064.JPG"/> 
 De&longs;cen&longs;us igitur, &amp; a&longs;cen&shy;<lb/> 
 &longs;us ponderum in EF ma&shy;<lb/> 
 gis, minu&longs;u&egrave; obliquus di&shy;<lb/> 
 cetur &longs;ecund&ugrave;m acce&longs;&longs;um, <lb/> 
 &amp; rece&longs;&longs;um iuxta lineas Ek <lb/> 
 FL de&longs;ignatum.  </s>              
 <s id="id.2.1.39.3.1.4.0"> <expan abbr="Quoni&atilde;">Quoniam</expan> au<lb/> 
 <expan abbr="t&etilde;">tem</expan> duo latera AD DC duo<lb/> 
 bus lateribus BD DE &longs;unt <lb/> 
 &aelig;qualia; anguliq; ad D &longs;unt <lb/> 
 <arrow.to.target n="note65"></arrow.to.target> recti; erit latus AC lateri <lb/> 
 CB &aelig;quale.  </s>              
 <s id="id.2.1.39.3.1.5.0"> &amp; c&ugrave;m pun&shy;<lb/> 
 ctum C &longs;it immobile; dum <lb/> 
 puncta AB mouentur, cir<lb/> 
 culi circumferentiam de&longs;cri<lb/> 
 bent, cuius &longs;emidiameter <lb/> 
 erit AC. quare centro C, <lb/> 
 circulus de&longs;cribatur AEBF. <lb/> 
 puncta AB EF in circuli <lb/> 
 circumferentia erunt.  </s>              
 <s id="id.2.1.39.3.1.6.0"> &longs;ed <lb/> 
 c&ugrave;m EF &longs;it ip&longs;i AB &aelig;qua <lb/> 
 <arrow.to.target n="note66"></arrow.to.target> lis; erit circumferentia <lb/> 
 EAF circumferenti&aelig; AFB <lb/> 
 &aelig;qualis.  </s>              
 <s id="id.2.1.39.3.1.7.0"> quare dempta <lb/> 
 <figure id="fig42" place="text" xlink:href="figures1577/2000.03.0061.jpg">       </figure><lb/> 
 communi AF, erit circumferentia EA circumferenti&aelig; FB &aelig;qua <lb/> 
 lis.  </s>              
 <s id="id.2.1.39.3.1.8.0"> Quoniam autem mixtus angulus CEA e&longs;t &aelig;qualis mixto <lb/> 
 CFB; &amp; HFB ip&longs;o CFB e&longs;t maior; angulus ver&ograve; HEA ip&longs;o <lb/> 
 CEA minor; erit angulus HFB angulo HEA maior.  </s>              
 <s id="id.2.1.39.3.1.9.0"> &agrave; quibus <lb/> 
 <arrow.to.target n="note67"></arrow.to.target> &longs;i auferantur anguli HFG HEk &aelig;quales; erit angulus GFB an <lb/> 
 gulo kEA maior.  </s>              
 <s id="id.2.1.39.3.1.10.0"> ergo de&longs;cen&longs;us ponderis in E minus obliquus <lb/> 
 erit a&longs;cen&longs;u ponderis in F. &amp; quamquam pondus in E de&longs;cen<lb/> 
 dendo, &amp; pondus in F a&longs;cendendo per circumferentias mouean<lb/> 
 tur &aelig;quales; quia tamen pondus in E ex hoc loco rectius de&longs;cen<lb/> 
 dit, qu&agrave;m pondus in F a&longs;cendit: idcirco naturalis potentia pon<lb/> 
 deris in E re&longs;i&longs;tentiam violenti&aelig; ponderis F &longs;uperabit.  </s>              
 <s id="id.2.1.39.3.1.11.0"> quare <lb/> 
 maiorem grauitatem habebit pondus in E, qu&agrave;m pondus in F.  </s>      
 <s id="id.2.1.39.3.1.11.0.a"> <lb/> 
 ergo pondus in E deor&longs;um, pondus ver&ograve; in F &longs;ur&longs;um mouebitur:  
 <pb n="24" xlink:href="pagethumb-la/00000065.JPG"/> 
 donec libra EF in AB redeat. </s>              
 <s id="id.2.1.39.3.1.12.0"> quod demon&longs;trare oportebat. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.39.3.2.1.0" type="caption">         
 <s id="id.2.1.39.3.2.1.0.capt"> YYY </s>      <s id="id.2.1.39.3.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.39.3.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.39.3.2.3.0" type="caption">        
 <s id="id.2.1.39.3.2.3.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.40.1.0.0.0" type="margin">         <s id="id.2.1.39.3.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.40.1.0.0.0" type="margin">        
  
 <s id="id.2.1.40.1.1.1.0"> <margin.target id="note65"></margin.target>4 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s id="id.2.1.40.1.1.1.0"> <margin.target id="note65"></margin.target>4 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
  
 <s id="id.2.1.40.1.1.2.0"> <margin.target id="note66"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 28 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>              <s id="id.2.1.40.1.1.2.0"> <margin.target id="note66"></margin.target><emph type="italics"/>Ex<emph.end type="italics"/> 28 <emph type="italics"/>Ter tii.<emph.end type="italics"/> </s>            
 <s id="id.2.1.40.1.1.3.0"> <margin.target id="note67"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.41.1.0.0.0" type="main">         <s id="id.2.1.40.1.1.3.0"> <margin.target id="note67"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.41.1.0.0.0" type="main">        
 <s id="id.2.1.41.1.1.1.0"> Huius autem effectus ratio ab Ari&longs;totele po&longs;ita, hic manife&longs;ta in <arrow.to.target n="note68"></arrow.to.target><lb/> 
 tueri pote&longs;t.  </s>              <s id="id.2.1.41.1.1.1.0"> Huius autem effectus ratio ab Ari&longs;totele po&longs;ita, hic manife&longs;ta in <arrow.to.target n="note68"></arrow.to.target><lb/>tueri pote&longs;t.  </s>            
  
 <s id="id.2.1.41.1.1.2.0"> &longs;it enim punctum N vbi CS EF &longs;e inuicem &longs;ecant.  </s>              <s id="id.2.1.41.1.1.2.0"> &longs;it enim punctum N vbi CS EF &longs;e inuicem &longs;ecant.  </s>            
 <s id="id.2.1.41.1.1.3.0"> <lb/> 
 &amp; quoniam HE e&longs;t ip&longs;i HF &aelig;qualis; erit NE maior NF. li&shy;<lb/> <s id="id.2.1.41.1.1.3.0"> <lb/>&amp; quoniam HE e&longs;t ip&longs;i HF &aelig;qualis; erit NE maior NF. li&shy;<lb/>nea ergo CS, quam perpendiculum vocat, libram EF in partes di <lb/>uidet in&aelig;quales.  </s>            
 nea ergo CS, quam perpendiculum vocat, libram EF in partes di <lb/> 
 uidet in&aelig;quales.  </s>              <s id="id.2.1.41.1.1.4.0"> c&ugrave;m itaq; pars libr&aelig; NE &longs;it maior NF; atq; id, <lb/>quod plus e&longs;t, nece&longs;&longs;e e&longs;t, deor&longs;um ferri: libra ergo EF ex parte E <lb/>deor&longs;um mouebitur, donec in AB redeat. </s>    </p>       <p id="id.2.1.42.1.0.0.0" type="margin">        
 <s id="id.2.1.41.1.1.4.0"> c&ugrave;m itaq; pars libr&aelig; NE &longs;it maior NF; atq; id, <lb/> 
 quod plus e&longs;t, nece&longs;&longs;e e&longs;t, deor&longs;um ferri: libra ergo EF ex parte E <lb/> <s id="id.2.1.42.1.1.1.0"> <margin.target id="note68"></margin.target><emph type="italics"/>Ari&longs;totelis ratio.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.43.1.0.0.0" type="main">        
 deor&longs;um mouebitur, donec in AB redeat. </s>    </p>        
 <p id="id.2.1.42.1.0.0.0" type="margin">         <s id="id.2.1.43.1.1.1.0"> Ex iis pr&aelig;terea, qu&aelig; ha<lb/>ctenus dicta &longs;unt inferre li<lb/>cet, libram EF velocius ab <lb/>eo &longs;itu in AB moueri; vnd&egrave; <lb/>linea EF in directum pro&shy;<lb/>tracta in centrum mundi <lb/>perueniat.  </s>            
 <s id="id.2.1.42.1.1.1.0"> <margin.target id="note68"></margin.target><emph type="italics"/>Ari&longs;totelis ratio.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.43.1.0.0.0" type="main">         <s id="id.2.1.43.1.1.2.0"> vt &longs;it EFS recta <lb/>linea.  </s>            
 <s id="id.2.1.43.1.1.1.0"> Ex iis pr&aelig;terea, qu&aelig; ha<lb/> 
 ctenus dicta &longs;unt inferre li<lb/> <s id="id.2.1.43.1.1.3.0"> &amp; quoniam CD <lb/>CH, &longs;unt inter &longs;e &longs;e &aelig;qua<lb/>les.  </s>            
 cet, libram EF velocius ab <lb/> 
 eo &longs;itu in AB moueri; vnd&egrave; <lb/> <s id="id.2.1.43.1.1.4.0"> &longs;i igitur centro C, &longs;pa<lb/>tioq; CD, circulus de&longs;cri&shy;<lb/>batur DHM; erunt pun&shy;<lb/>cta DH in circuli circum&shy;<lb/>ferentia.  </s>            
 linea EF in directum pro&shy;<lb/> 
 tracta in centrum mundi <lb/> <s id="id.2.1.43.1.1.5.0"> Quoniam au&shy;<lb/>tem CH ip&longs;i EF e&longs;t per&shy;<lb/>pendicularis; continget li&shy;<lb/>nea EHS circulum DHM <lb/>in puncto H.  </s>    
 perueniat.  </s>              
 <s id="id.2.1.43.1.1.2.0"> vt &longs;it EFS recta <lb/> <s id="id.2.1.43.1.1.5.0.a"> pondus igi&shy;<lb/>tur in H (&longs;icuti &longs;upra de&shy;<lb/>mon&longs;trauimus) grauius <lb/><figure id="fig43" place="text" xlink:href="figures1577/2000.03.0062.jpg">       </figure><lb/>erit, qu&agrave;m in alio &longs;itu circuli DHM.  </s>    
 linea.  </s>              
 <s id="id.2.1.43.1.1.3.0"> &amp; quoniam CD <lb/> <s id="id.2.1.43.1.1.5.0.b"> ergo magnitudo ex EF <lb/>ponderibus, &amp; libra EF compo&longs;ita, cuius centrum grauitatis e&longs;t <lb/>in H, in hoc &longs;itu magis grauitabit, qu&agrave;m in quocunq; alio &longs;itu <pb xlink:href="pagethumb-la/00000066.JPG"/>circuli fuerit punctum H. <lb/>ab hoc igitur &longs;itu velo&shy;<lb/>cius, qu&agrave;m &agrave; quocunq; <lb/>alio mouebitur.  </s>            
 CH, &longs;unt inter &longs;e &longs;e &aelig;qua<lb/> 
 les.  </s>              <s id="id.2.1.43.1.1.6.0"> &amp; &longs;i H <lb/>propius fuerit ip&longs;i D mi <lb/>nus grauitabit, minu&longs;q; <lb/>ab eo &longs;itu mouebitur.  </s>            
 <s id="id.2.1.43.1.1.4.0"> &longs;i igitur centro C, &longs;pa<lb/> 
 tioq; CD, circulus de&longs;cri&shy;<lb/> <s id="id.2.1.43.1.1.7.0"> <lb/>&longs;emper enim de&longs;cen&longs;us <lb/>obliquior e&longs;t, &amp; minus re<lb/>ctus.  </s>            
 batur DHM; erunt pun&shy;<lb/> 
 cta DH in circuli circum&shy;<lb/> <s id="id.2.1.43.1.1.8.0"> libra ergo EF velo<lb/>cius ab hoc &longs;itu mouebi&shy;<lb/>tur, qu&agrave;m ab alio &longs;itu.  </s>            
 ferentia.  </s>              
 <s id="id.2.1.43.1.1.5.0"> Quoniam au&shy;<lb/> <s id="id.2.1.43.1.1.9.0"> &amp; <lb/>&longs;i propius ad AB acce&shy;<lb/>det, inde minus mouebi<lb/>tur.  </s>            
 tem CH ip&longs;i EF e&longs;t per&shy;<lb/> 
 pendicularis; continget li&shy;<lb/> <s id="id.2.1.43.1.1.10.0"> Deinde qu&ograve; longius <lb/>punctum H &agrave; puncto C <lb/>di&longs;tabit, velocius moue&shy;<lb/>bitur; quod <expan abbr="n&otilde;">non</expan> <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ex Ari<lb/>&longs;totele in principio qu&aelig;&longs;t&shy;<lb/>io num mechanicarum, &amp; <lb/><figure id="fig44" place="text" xlink:href="figures1577/2000.03.0063.jpg">       </figure><lb/>ex &longs;uperius dictis patet; ver&ugrave;m etiam ex iis, qu&aelig; infra in &longs;exta <lb/>propo&longs;itione dicemus, manife&longs;tum erit.  </s>            
 nea EHS circulum DHM <lb/> 
 in puncto H.  </s>      <s id="id.2.1.43.1.1.11.0"> libra igitur EF, qu&ograve; ma<lb/>gis ab eius centro di&longs;tabit, adhuc velocius mouebitur.  </s>    
 <s id="id.2.1.43.1.1.5.0.a"> pondus igi&shy;<lb/> 
 tur in H (&longs;icuti &longs;upra de&shy;<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.43.1.2.1.0" type="caption">        
 mon&longs;trauimus) grauius <lb/> 
 <figure id="fig43" place="text" xlink:href="figures1577/2000.03.0062.jpg">       </figure><lb/> 
 erit, qu&agrave;m in alio &longs;itu circuli DHM.  </s>      
 <s id="id.2.1.43.1.1.5.0.b"> ergo magnitudo ex EF <lb/> 
 ponderibus, &amp; libra EF compo&longs;ita, cuius centrum grauitatis e&longs;t <lb/> 
 in H, in hoc &longs;itu magis grauitabit, qu&agrave;m in quocunq; alio &longs;itu  
 <pb xlink:href="pagethumb-la/00000066.JPG"/> 
 circuli fuerit punctum H. <lb/> 
 ab hoc igitur &longs;itu velo&shy;<lb/> 
 cius, qu&agrave;m &agrave; quocunq; <lb/> 
 alio mouebitur.  </s>              
 <s id="id.2.1.43.1.1.6.0"> &amp; &longs;i H <lb/> 
 propius fuerit ip&longs;i D mi <lb/> 
 nus grauitabit, minu&longs;q; <lb/> 
 ab eo &longs;itu mouebitur.  </s>              
 <s id="id.2.1.43.1.1.7.0"> <lb/> 
 &longs;emper enim de&longs;cen&longs;us <lb/> 
 obliquior e&longs;t, &amp; minus re<lb/> 
 ctus.  </s>              
 <s id="id.2.1.43.1.1.8.0"> libra ergo EF velo<lb/> 
 cius ab hoc &longs;itu mouebi&shy;<lb/> 
 tur, qu&agrave;m ab alio &longs;itu.  </s>              
 <s id="id.2.1.43.1.1.9.0"> &amp; <lb/> 
 &longs;i propius ad AB acce&shy;<lb/> 
 det, inde minus mouebi<lb/> 
 tur.  </s>              
 <s id="id.2.1.43.1.1.10.0"> Deinde qu&ograve; longius <lb/> 
 punctum H &agrave; puncto C <lb/> 
 di&longs;tabit, velocius moue&shy;<lb/> 
 bitur; quod <expan abbr="n&otilde;">non</expan> <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ex Ari<lb/> 
 &longs;totele in principio qu&aelig;&longs;t&shy;<lb/> 
 io num mechanicarum, &amp; <lb/> 
 <figure id="fig44" place="text" xlink:href="figures1577/2000.03.0063.jpg">       </figure><lb/> 
 ex &longs;uperius dictis patet; ver&ugrave;m etiam ex iis, qu&aelig; infra in &longs;exta <lb/> 
 propo&longs;itione dicemus, manife&longs;tum erit.  </s>              
 <s id="id.2.1.43.1.1.11.0"> libra igitur EF, qu&ograve; ma<lb/> 
 gis ab eius centro di&longs;tabit, adhuc velocius mouebitur.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.43.1.2.1.0" type="caption">         
 <s id="id.2.1.43.1.2.1.0.capt"> YYY </s>      <s id="id.2.1.43.1.2.1.0.capt"> YYY </s>    
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.43.1.2.3.0" type="caption">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.43.1.2.3.0" type="caption">        
 <s id="id.2.1.43.1.2.3.0.capt"> YYY </s>    </p>        
 <pb n="25" xlink:href="pagethumb-la/00000067.JPG"/> <s id="id.2.1.43.1.2.3.0.capt"> YYY </s>    </p>       <pb n="25" xlink:href="pagethumb-la/00000067.JPG"/>       <p id="id.2.1.43.3.0.0.0" type="main">        
         
 <p id="id.2.1.43.3.0.0.0" type="main">         <s id="id.2.1.43.3.1.1.0"> Sit deinde libra AB, <lb/>cuius centrum C &longs;it infra li<lb/>bram; &longs;intq; in AB pon<lb/>dera &aelig;qualia; libraq; &longs;it <lb/>mota in EF.  </s>    
 <s id="id.2.1.43.3.1.1.0"> Sit deinde libra AB, <lb/> 
 cuius centrum C &longs;it infra li<lb/> <s id="id.2.1.43.3.1.1.0.a"> Dico maio&shy;<lb/>rem habere grauitatem <lb/>pondus in F, qu&agrave;m pondus <lb/>in E. atq; ideo libram EF <lb/>deor&longs;um ex parte F moue&shy;<lb/>ri.  </s>            
 bram; &longs;intq; in AB pon<lb/> 
 dera &aelig;qualia; libraq; &longs;it <lb/> <s id="id.2.1.43.3.1.2.0"> Producatur DC ex <lb/>vtraq; parte v&longs;q; ad mun&shy;<lb/>di centrum S, &amp; v&longs;q; ad <lb/>O, lineaq; HS ducatur, <lb/>cui &agrave; punctis EF &aelig;quidi&shy;<lb/>&longs;tantes ducantur GEk FL; <lb/>connectanturq; CE CF: <lb/>atq; centro C, &longs;patioq; CE <lb/>circulus de&longs;cribatur AEO <lb/>BF.  </s>    
 mota in EF.  </s>      
 <s id="id.2.1.43.3.1.1.0.a"> Dico maio&shy;<lb/> <s id="id.2.1.43.3.1.2.0.a"> &longs;imiliter demon&longs;tra&shy;<lb/>bitur puncta ABEF in <lb/>circuli circumferentia e&longs;&longs;e; <lb/>de&longs;cen&longs;umq; libr&aelig; EF vn&aacute; <lb/>cum ponderibus rectum &longs;e<lb/>cund&ugrave;m lineam HS fieri; <lb/>ponderumq; in EF &longs;ecun <lb/><figure id="fig45" place="text" xlink:href="figures1577/2000.03.0064.jpg">       </figure><expan abbr="d&ugrave;m"><lb/>dum</expan> lineas GK FL ip&longs;i HS &aelig;quidi&longs;tantes.  </s>            
 rem habere grauitatem <lb/> 
 pondus in F, qu&agrave;m pondus <lb/> <s id="id.2.1.43.3.1.3.0"> Quoniam autem an<lb/>gulus CFP &aelig;qualis e&longs;t angulo CEO: erit angulus HFP angulo <lb/>HEO maior.  </s>            
 in E. atq; ideo libram EF <lb/> 
 deor&longs;um ex parte F moue&shy;<lb/> <s id="id.2.1.43.3.1.4.0"> angulus ver&ograve; HFL &aelig;qualis e&longs;t angulo HEG. &agrave; <arrow.to.target n="note69"></arrow.to.target><lb/>quibus igitur &longs;i demantur anguli HFP HEO, erit angulus <lb/>LFP angulo GEO minor.  </s>            
 ri.  </s>              
 <s id="id.2.1.43.3.1.2.0"> Producatur DC ex <lb/> <s id="id.2.1.43.3.1.5.0"> quare de&longs;cen&longs;us ponderis in F rectior <lb/>erit a&longs;cen&longs;u ponderis in E. ergo naturalis potentia ponderis in <lb/>F re&longs;i&longs;tentiam violenti&aelig; ponderis in E &longs;uperabit.  </s>            
 vtraq; parte v&longs;q; ad mun&shy;<lb/> 
 di centrum S, &amp; v&longs;q; ad <lb/> <s id="id.2.1.43.3.1.6.0"> &amp; ideo ma&shy;<lb/>iorem habebit grauitatem pondus in F, qu&agrave;m pondus in E.  </s>    
 O, lineaq; HS ducatur, <lb/> 
 cui &agrave; punctis EF &aelig;quidi&shy;<lb/> <s id="id.2.1.43.3.1.6.0.a"> <lb/>Pondus igitur in F deor&longs;um, pondus ver&ograve; in E &longs;ur&longs;um mo&shy;<lb/>uebitur. </s>    
 &longs;tantes ducantur GEk FL; <lb/> 
 connectanturq; CE CF: <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.43.3.2.1.0" type="caption">        
 atq; centro C, &longs;patioq; CE <lb/> 
 circulus de&longs;cribatur AEO <lb/> <s id="id.2.1.43.3.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.44.1.0.0.0" type="margin">        
 BF.  </s>      
 <s id="id.2.1.43.3.1.2.0.a"> &longs;imiliter demon&longs;tra&shy;<lb/> <s id="id.2.1.44.1.1.1.0"> <margin.target id="note69"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.45.1.0.0.0" type="main">        
 bitur puncta ABEF in <lb/> 
 circuli circumferentia e&longs;&longs;e; <lb/> 
 de&longs;cen&longs;umq; libr&aelig; EF vn&aacute; <lb/> 
 cum ponderibus rectum &longs;e<lb/> 
 cund&ugrave;m lineam HS fieri; <lb/> 
 ponderumq; in EF &longs;ecun <lb/> 
 <figure id="fig45" place="text" xlink:href="figures1577/2000.03.0064.jpg">       </figure><expan abbr="d&ugrave;m"><lb/> 
 dum</expan> lineas GK FL ip&longs;i HS &aelig;quidi&longs;tantes.  </s>              
 <s id="id.2.1.43.3.1.3.0"> Quoniam autem an<lb/> 
 gulus CFP &aelig;qualis e&longs;t angulo CEO: erit angulus HFP angulo <lb/> 
 HEO maior.  </s>              
 <s id="id.2.1.43.3.1.4.0"> angulus ver&ograve; HFL &aelig;qualis e&longs;t angulo HEG. &agrave; <arrow.to.target n="note69"></arrow.to.target><lb/> 
 quibus igitur &longs;i demantur anguli HFP HEO, erit angulus <lb/> 
 LFP angulo GEO minor.  </s>              
 <s id="id.2.1.43.3.1.5.0"> quare de&longs;cen&longs;us ponderis in F rectior <lb/> 
 erit a&longs;cen&longs;u ponderis in E. ergo naturalis potentia ponderis in <lb/> 
 F re&longs;i&longs;tentiam violenti&aelig; ponderis in E &longs;uperabit.  </s>              
 <s id="id.2.1.43.3.1.6.0"> &amp; ideo ma&shy;<lb/> 
 iorem habebit grauitatem pondus in F, qu&agrave;m pondus in E.  </s>      
 <s id="id.2.1.43.3.1.6.0.a"> <lb/> 
 Pondus igitur in F deor&longs;um, pondus ver&ograve; in E &longs;ur&longs;um mo&shy;<lb/> 
 uebitur. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.43.3.2.1.0" type="caption">         
 <s id="id.2.1.43.3.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.44.1.0.0.0" type="margin">         
 <s id="id.2.1.44.1.1.1.0"> <margin.target id="note69"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.45.1.0.0.0" type="main">         
 <s id="id.2.1.45.1.1.1.0"> Ari&longs;totelis quoq; ratio hic per&longs;picua erit.  </s>              <s id="id.2.1.45.1.1.1.0"> Ari&longs;totelis quoq; ratio hic per&longs;picua erit.  </s>            
 <s id="id.2.1.45.1.1.2.0"> &longs;it enim punctum <arrow.to.target n="note70"></arrow.to.target> 
 <pb xlink:href="pagethumb-la/00000068.JPG"/> <s id="id.2.1.45.1.1.2.0"> &longs;it enim punctum <arrow.to.target n="note70"></arrow.to.target><pb xlink:href="pagethumb-la/00000068.JPG"/>N vbi CO EF &longs;e inuicem <lb/>&longs;ecant; erit NF maior <lb/>NE.  </s>    
 N vbi CO EF &longs;e inuicem <lb/> 
 &longs;ecant; erit NF maior <lb/> <s id="id.2.1.45.1.1.2.0.a"> &amp; quoniam CO per <lb/>pendiculum (&longs;ecund&ugrave;m <lb/>ip&longs;um) libram EF in par <lb/>tes in&aelig;quales diuidit, &amp; <lb/>maior pars e&longs;t ver&longs;us F, hoc <lb/>e&longs;t NF; libra EF ex par <lb/>te F deor&longs;um mouebitur: <lb/>c&ugrave;mid, quod plus e&longs;t, deor<lb/>&longs;um feratur. </s>    </p>       <p id="id.2.1.46.1.0.0.0" type="margin">        
 NE.  </s>      
 <s id="id.2.1.45.1.1.2.0.a"> &amp; quoniam CO per <lb/> <s id="id.2.1.46.1.1.1.0"> <margin.target id="note70"></margin.target><emph type="italics"/>Ari&longs;totelis ratio.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.47.1.0.0.0" type="main">        
 pendiculum (&longs;ecund&ugrave;m <lb/> 
 ip&longs;um) libram EF in par <lb/> <s id="id.2.1.47.1.1.1.0"> Similiter, &eacute;x dictis <lb/>quoq; eliciemus libram EF <lb/>centrum habens infra li&shy;<lb/>bram, qu&ograve; magis &agrave; &longs;itu <lb/>AB di&longs;tabit, velocius mo <lb/>ueri.  </s>            
 tes in&aelig;quales diuidit, &amp; <lb/> 
 maior pars e&longs;t ver&longs;us F, hoc <lb/> <s id="id.2.1.47.1.1.2.0"> centrum enim graui <lb/>tatis H, qu&ograve; magis &aacute; pun&shy;<lb/>cto D di&longs;tat, e&ograve; volecius <lb/>pondus ex EF ponderibus, <lb/>libraq; EF compo&longs;itum <lb/>mouebitur, donec angulus <lb/>CHS rectus euadat.  </s>            
 e&longs;t NF; libra EF ex par <lb/> 
 te F deor&longs;um mouebitur: <lb/> <s id="id.2.1.47.1.1.3.0"> ad&shy;<lb/>huc in&longs;uper velocius moue<lb/>bitur, qu&ograve; libram &agrave; centro <lb/>C magis di&longs;tabit. <figure id="fig46" place="text" xlink:href="figures1577/2000.03.0065.jpg">       </figure> </s>    </p>       <p id="id.2.1.47.2.0.0.0" type="main">        
 c&ugrave;mid, quod plus e&longs;t, deor<lb/> 
 &longs;um feratur. </s>    </p>        <s id="id.2.1.47.2.1.1.0"> Ex ip&longs;orum quinetiam rationibus, ac fal&longs;is &longs;upo&longs;itionibus iam <lb/>declaratos libr&aelig; effectus, ac motus deducere, ac manife&longs;tare libet; <lb/>vt quanta &longs;it veritatis efficacia appareat, quipp&egrave; ex fal&longs;is etiam <lb/>eluce&longs;cere contendit.  </s>    
 <p id="id.2.1.46.1.0.0.0" type="margin">         
 <s id="id.2.1.46.1.1.1.0"> <margin.target id="note70"></margin.target><emph type="italics"/>Ari&longs;totelis ratio.<emph.end type="italics"/> </s>    </p>        <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.47.2.2.1.0" type="caption">        
 <p id="id.2.1.47.1.0.0.0" type="main">         
 <s id="id.2.1.47.1.1.1.0"> Similiter, &eacute;x dictis <lb/> <s id="id.2.1.47.2.2.1.0.capt"> YYY </s>    </p>       <pb n="26" xlink:href="pagethumb-la/00000069.JPG"/>       <p id="id.2.1.47.4.0.0.0" type="main">        
 quoq; eliciemus libram EF <lb/> 
 centrum habens infra li&shy;<lb/> <s id="id.2.1.47.4.1.1.0"> Exponantur eadem, &longs;ci <lb/>licet &longs;it circulus AEBF; <lb/>libraqu&eacute; AB, cuius cen&shy;<lb/>trum C &longs;it &longs;upra libram, <lb/>moueatur in EF.  </s>    
 bram, qu&ograve; magis &agrave; &longs;itu <lb/> 
 AB di&longs;tabit, velocius mo <lb/> <s id="id.2.1.47.4.1.1.0.a"> dico <lb/>pondus in E maiorem ibi <lb/>habere grauitatem, qu&agrave;m <lb/>pondus in F; libramq; EF <lb/>in AB redire.  </s>            
 ueri.  </s>              
 <s id="id.2.1.47.1.1.2.0"> centrum enim graui <lb/> <s id="id.2.1.47.4.1.2.0"> Ducantur <lb/>&agrave; punctis EF ip&longs;i AB <lb/>perpendiculares EL FM, <lb/>qu&aelig; inter &longs;e &aelig;quidi&longs;tan&shy;<lb/>tes  <arrow.to.target n="note71"></arrow.to.target><figure id="fig47" place="text" xlink:href="figures1577/2000.03.0066.jpg">       </figure> erunt; &longs;itq; punctum N, vbi AB EF &longs;e inuicem &longs;ecant.  </s>            
 tatis H, qu&ograve; magis &aacute; pun&shy;<lb/> 
 cto D di&longs;tat, e&ograve; volecius <lb/> <s id="id.2.1.47.4.1.3.0"> <lb/>Quoniam igitur angulus FNM e&longs;t &aelig;qualis angulo ENL, &amp; an&shy;<lb/>gulus  <arrow.to.target n="note72"></arrow.to.target> F MN rectus recto ELN &aelig;qualis, ac reliquus NFM reli&shy;<lb/>quo  <arrow.to.target n="note73"></arrow.to.target> NEL e&longs;t etiam &aelig;qualis; erit triangulum NLE triangu<lb/>lo NMF &longs;imile.  </s>            
 pondus ex EF ponderibus, <lb/> 
 libraq; EF compo&longs;itum <lb/> <s id="id.2.1.47.4.1.4.0"> vt igitur NE ad EL, ita NF ad FM; &amp; per <arrow.to.target n="note74"></arrow.to.target><lb/>mutando vt EN ad NF, ita EL ad FM. &longs;ed c&ugrave;m &longs;it HE ip&longs;i <arrow.to.target n="note75"></arrow.to.target><lb/>HF &aelig;qualis, erit EN maior NF; quare &amp; EL maior erit FM.  </s>    
 mouebitur, donec angulus <lb/> 
 CHS rectus euadat.  </s>              <s id="id.2.1.47.4.1.4.0.a"> <lb/>&amp; quoniam dum pondus in E per circumferentiiam EA de&longs;cendit, <lb/>pondus in F per circumferentiam FB ip&longs;i circumferenti&aelig; EA <lb/>&aelig;qualem a&longs;cendit; de&longs;cen&longs;u&longs;q; ponderis in E de directo (vt ip&shy;<lb/>&longs;i dicunt) capit EL: a&longs;cen&longs;us ver&ograve; ponderis in F de directo ca&shy;<lb/>pit FM; minus de directo capiet a&longs;cen&longs;us ponderis in F, qu&agrave;m <lb/>de&longs;cen&longs;us ponderis in E. maiorem igitur grauitatem habebit pon<lb/>dus in E, qu&agrave;m pondus in F. </s>    
 <s id="id.2.1.47.1.1.3.0"> ad&shy;<lb/> 
 huc in&longs;uper velocius moue<lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.47.4.2.1.0" type="caption">        
 bitur, qu&ograve; libram &agrave; centro <lb/> 
 C magis di&longs;tabit. <figure id="fig46" place="text" xlink:href="figures1577/2000.03.0065.jpg">       </figure> </s>    </p>        <s id="id.2.1.47.4.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.48.1.0.0.0" type="margin">        
 <p id="id.2.1.47.2.0.0.0" type="main">         
 <s id="id.2.1.47.2.1.1.0"> Ex ip&longs;orum quinetiam rationibus, ac fal&longs;is &longs;upo&longs;itionibus iam <lb/> <s id="id.2.1.48.1.1.1.0"> <margin.target id="note71"></margin.target>28 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 declaratos libr&aelig; effectus, ac motus deducere, ac manife&longs;tare libet; <lb/> 
 vt quanta &longs;it veritatis efficacia appareat, quipp&egrave; ex fal&longs;is etiam <lb/> <s id="id.2.1.48.1.1.2.0"> <margin.target id="note72"></margin.target>15 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 eluce&longs;cere contendit.  </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.48.1.1.3.0"> <margin.target id="note73"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>            
 <p id="id.2.1.47.2.2.1.0" type="caption">         
 <s id="id.2.1.47.2.2.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.48.1.1.4.0"> <margin.target id="note74"></margin.target>4 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>            
 <pb n="26" xlink:href="pagethumb-la/00000069.JPG"/> 
         <s id="id.2.1.48.1.1.5.0"> <margin.target id="note75"></margin.target>16 <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.49.1.0.0.0" type="main">        
 <p id="id.2.1.47.4.0.0.0" type="main">         
 <s id="id.2.1.47.4.1.1.0"> Exponantur eadem, &longs;ci <lb/> <s id="id.2.1.49.1.1.1.0"> Producatur CD ex vtraq; parte in OP, qu&aelig; lineam EF in <lb/>puncto S &longs;ecet.  </s>            
 licet &longs;it circulus AEBF; <lb/> 
 libraqu&eacute; AB, cuius cen&shy;<lb/> <s id="id.2.1.49.1.1.2.0"> &amp; quoniam (vt aiunt) qu&ograve; magis pondus &agrave; li&shy;<lb/>nea directionis OP di&longs;tat, e&ograve; fit grauius; idcirco hoc quoq; me <lb/>dio pondus in E maiorem habere grauitauitatem pondere in F o&shy;<lb/>&longs;tendetur.  </s>            
 trum C &longs;it &longs;upra libram, <lb/> 
 moueatur in EF.  </s>      <s id="id.2.1.49.1.1.3.0"> Ducantur &agrave; punctis EF ip&longs;i OP perpendiculares EQ <lb/>FR. &longs;imili ratione o&longs;tendetur, triangulum QES triangulo RFS <lb/>&longs;imile e&longs;&longs;e; lineamq; EQ ip&longs;a RF maiorem e&longs;&longs;e.  </s>            
 <s id="id.2.1.47.4.1.1.0.a"> dico <lb/> 
 pondus in E maiorem ibi <lb/> <s id="id.2.1.49.1.1.4.0"> pondus itaq; <lb/>in E magis &agrave; linea OP di&longs;tabit, qu&agrave;m pondus in F; ac propterea <lb/>pondus in E maiorem habebit grauitatem pondere in F. ex quibus <lb/>reditus libr&aelig; EF in AB manife&longs;tus apparet.  </s>    </p>       <pb xlink:href="pagethumb-la/00000070.JPG"/>       <p id="id.2.1.49.3.0.0.0" type="main">        
 habere grauitatem, qu&agrave;m <lb/> 
 pondus in F; libramq; EF <lb/> <s id="id.2.1.49.3.1.1.0"> Si autem centrum libr&aelig; <lb/>&longs;it infra libram, tunc pon&shy;<lb/>dus depre&longs;&longs;um maiorem <lb/>habere grauitatem eleuato <lb/>ii&longs;dem mediis o&longs;tendetur.  </s>            
 in AB redire.  </s>              
 <s id="id.2.1.47.4.1.2.0"> Ducantur <lb/> <s id="id.2.1.49.3.1.2.0"> <lb/>ducantur &agrave; punctis EF ip&shy;<lb/>&longs;i AB perpendiculares EL <lb/>FM. &longs;imiliter demon&longs;tra<lb/>bitur EL maiorem e&longs;&longs;e <lb/>FM; &amp; ob id de&longs;cen&longs;us <lb/>ponderis in F minus de di <lb/>recto capiet, qu&agrave;m a&longs;cen&shy;<lb/><figure id="fig48" place="text" xlink:href="figures1577/2000.03.0067.jpg">       </figure><lb/>&longs;us ponderis in E: quocirca re&longs;i&longs;tentia violenti&aelig; ponderis in E &longs;u<lb/>perabit naturalem propen&longs;ionem ponderis in F. ergo pondus in E <lb/>pondere in F grauius erit. </s>    
 &agrave; punctis EF ip&longs;i AB <lb/> 
 perpendiculares EL FM, <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.49.3.2.1.0" type="caption">        
 qu&aelig; inter &longs;e &aelig;quidi&longs;tan&shy;<lb/> 
 tes  <arrow.to.target n="note71"></arrow.to.target><figure id="fig47" place="text" xlink:href="figures1577/2000.03.0066.jpg">       </figure> erunt; &longs;itq; punctum N, vbi AB EF &longs;e inuicem &longs;ecant.  </s>              <s id="id.2.1.49.3.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.49.4.0.0.0" type="main">        
 <s id="id.2.1.47.4.1.3.0"> <lb/> 
 Quoniam igitur angulus FNM e&longs;t &aelig;qualis angulo ENL, &amp; an&shy;<lb/> <s id="id.2.1.49.4.1.1.0"> Producatur etiam CD ex vtraq; parte in OP; ip&longs;iq; &agrave; punctis <lb/>EF perpendiculares ducantur EQ FR. eodem pror&longs;us modo <lb/>o&longs;tendetur, lineam EQ maiorem e&longs;&longs;e FR. pondus ide&ograve; in E ma<lb/>gis &agrave; linea directionis OP di&longs;tabit, qu&agrave;m pondus in F. maio&shy;<lb/>rem igitur grauitatem habebit pondus in E, qu&agrave;m pondus in F. <lb/>ex quibus &longs;equitur, libram EF ex parte E deor&longs;um moueri. </s>    </p>       <p id="id.2.1.49.5.0.0.0" type="main">        
 gulus  <arrow.to.target n="note72"></arrow.to.target> F MN rectus recto ELN &aelig;qualis, ac reliquus NFM reli&shy;<lb/> 
 quo  <arrow.to.target n="note73"></arrow.to.target> NEL e&longs;t etiam &aelig;qualis; erit triangulum NLE triangu<lb/> <s id="id.2.1.49.5.1.1.0"> Ari&longs;toteles itaq; has duas tant&ugrave;m qu&aelig;&longs;tiones propo&longs;uit, ter&shy;<lb/>tiamq; reliquit; &longs;cilicet c&ugrave;m centrum libr&aelig; in ip&longs;a e&longs;t libra: hanc <lb/>autem ommi&longs;sit, vt notam, quemadmodum res valde notas pr&aelig;&shy;<lb/>termittere &longs;olet.  </s>            
 lo NMF &longs;imile.  </s>              
 <s id="id.2.1.47.4.1.4.0"> vt igitur NE ad EL, ita NF ad FM; &amp; per <arrow.to.target n="note74"></arrow.to.target><lb/> <s id="id.2.1.49.5.1.2.0"> nam cui dubium, &longs;i pondus in eius centro gra<lb/>uitatis &longs;u&longs;tineatur, quin maneat?  </s>            
 mutando vt EN ad NF, ita EL ad FM. &longs;ed c&ugrave;m &longs;it HE ip&longs;i <arrow.to.target n="note75"></arrow.to.target><lb/> 
 HF &aelig;qualis, erit EN maior NF; quare &amp; EL maior erit FM.  </s>      <s id="id.2.1.49.5.1.3.0"> Ea ver&ograve;, qu&aelig; ex ip&longs;ius &longs;enten<lb/>tia attulimus, aliquis reprehendere po&longs;&longs;et, nos integram eius &longs;enten<lb/>tiam minim&egrave; protuli&longs;&longs;e affimans.  </s>            
 <s id="id.2.1.47.4.1.4.0.a"> <lb/> 
 &amp; quoniam dum pondus in E per circumferentiiam EA de&longs;cendit, <lb/> <s id="id.2.1.49.5.1.4.0"> nam c&ugrave;m in &longs;ecunda parte &longs;e<lb/>cund&aelig; qu&aelig;&longs;tionis proponit, cur libra, trutina deor&longs;um con&longs;tituta, <lb/>quando deor&longs;um lato pondere qui&longs;piam id amouet, non a&longs;cen<lb/>dit, &longs;ed manet?  </s>            
 pondus in F per circumferentiam FB ip&longs;i circumferenti&aelig; EA <lb/> 
 &aelig;qualem a&longs;cendit; de&longs;cen&longs;u&longs;q; ponderis in E de directo (vt ip&shy;<lb/> <s id="id.2.1.49.5.1.5.0"> non a&longs;&longs;erit adhuc libram deor&longs;um moueri; &longs;ed <lb/>manere.  </s>            
 &longs;i dicunt) capit EL: a&longs;cen&longs;us ver&ograve; ponderis in F de directo ca&shy;<lb/> 
 pit FM; minus de directo capiet a&longs;cen&longs;us ponderis in F, qu&agrave;m <lb/> <s id="id.2.1.49.5.1.6.0"> quod in vltima quoq; conclu&longs;ione colligi&longs;&longs;e videtur.  </s>            
 de&longs;cen&longs;us ponderis in E. maiorem igitur grauitatem habebit pon<lb/> 
 dus in E, qu&agrave;m pondus in F. </s>      <s id="id.2.1.49.5.1.7.0"> Ve <lb/>r&ugrave;m hoc non &longs;olum nobis non repugnat, &longs;ed &longs;i rect&egrave; intelligitur, <lb/>maxim&egrave; &longs;uffragatur.  </s>    </p>       <pb n="27" xlink:href="pagethumb-la/00000071.JPG"/>       <p id="id.2.1.49.7.0.0.0" type="main">        
 <s> ZZZ head of figure ZZZ </s>    </p>               
 <p id="id.2.1.47.4.2.1.0" type="caption">         <s id="id.2.1.49.7.1.1.0"> Sit enim libra AB <lb/>horizonti &aelig;quidi&longs;tans, <lb/>cuius centrum E &longs;it <lb/>infra libram.  </s>            
 <s id="id.2.1.47.4.2.1.0.capt"> YYY </s>    </p>        
 <p id="id.2.1.48.1.0.0.0" type="margin">         <s id="id.2.1.49.7.1.2.0"> quia ve <lb/>r&ograve; Ari&longs;toteles libram, <lb/>&longs;icuti actu e&longs;t, con&longs;ide<lb/>rat; ide&ograve; nece&longs;&longs;e e&longs;t <lb/>trutinam, vel aliquid <lb/>aliud infra centrum E <lb/>collocare, vt EF <lb/>(quod quidem truti&shy;<lb/>na erit) ita vt centrum <lb/>E &longs;u&longs;tineat.  </s>            
 <s id="id.2.1.48.1.1.1.0"> <margin.target id="note71"></margin.target>28 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.48.1.1.2.0"> <margin.target id="note72"></margin.target>15 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              <s id="id.2.1.49.7.1.3.0"> &longs;itq; per&shy;<lb/><figure id="fig49" place="text" xlink:href="figures1577/2000.03.0068.jpg">       </figure><lb/>pendiculum ECD. &amp; vt libra AB ab hoc moueatur &longs;itu; dicit <lb/>Ari&longs;toteles, ponatur pondus in B, quod c&ugrave;m &longs;it graue, libram ex <lb/>parte B deor&longs;um mouebit; put&aacute; in G. ita vt propter impedimen<lb/>tum deor&longs;um amplius moueri non poterit.  </s>            
 <s id="id.2.1.48.1.1.3.0"> <margin.target id="note73"></margin.target>29 <emph type="italics"/>Primi.<emph.end type="italics"/> </s>              
 <s id="id.2.1.48.1.1.4.0"> <margin.target id="note74"></margin.target>4 <emph type="italics"/>Sexti.<emph.end type="italics"/> </s>              <s id="id.2.1.49.7.1.4.0"> non enim dicit Ari<lb/>&longs;toteles, moueatur libra ex parte B deor&longs;um, quou&longs;q; libuerit; dein <lb/>de relinquatur, vt nos diximus: &longs;ed pr&aelig;cipit, vt in ip&longs;o B po&shy;<lb/>natur pondus, quod ex ip&longs;ius natura deor&longs;um &longs;emper mouebi&shy;<lb/>tur; donec libra trutin&aelig;, &longs;iue alicui alii adh&aelig;reat.  </s>            
 <s id="id.2.1.48.1.1.5.0"> <margin.target id="note75"></margin.target>16 <emph type="italics"/>Quinti.<emph.end type="italics"/> </s>    </p>        
 <p id="id.2.1.49.1.0.0.0" type="main">         <s id="id.2.1.49.7.1.5.0"> &amp; quando B erit <lb/>in G, erit libra in GH; in quo &longs;itu, ablato pondere, manebit: <lb/>c&ugrave;m maior pars libr&aelig; &agrave; perpendiculo &longs;it ver&longs;us G, qu&aelig; e&longs;t DG, <lb/>qu&agrave;m DH.  </s>    
 <s id="id.2.1.49.1.1.1.0"> Producatur CD ex vtraq; parte in OP, qu&aelig; lineam EF in <lb/> 
 puncto S &longs;ecet.  </s>              <s id="id.2.1.49.7.1.5.0.a"> nec deor&longs;um amplius mouebitur; nam libra, vel <lb/>trutin&aelig;, vel alteri cuipiam, quod centrum libr&aelig; &longs;u&longs;tineat, incum<lb/>bet.  </s>            
 <s id="id.2.1.49.1.1.2.0"> &amp; quoniam (vt aiunt) qu&ograve; magis pondus &agrave; li&shy;<lb/> 
 nea directionis OP di&longs;tat, e&ograve; fit grauius; idcirco hoc quoq; me <lb/> <s id="id.2.1.49.7.1.6.0"> &longs;i enim huic non adh&aelig;reret, libra ex parte G deor&longs;um ex <lb/>ip&longs;ius &longs;ententia moueretur; c&ugrave;m id, quod plus e&longs;t, &longs;cilicet DG, <lb/>deor&longs;um ferri &longs;it nece&longs;&longs;e. </s>    
 dio pondus in E maiorem habere grauitauitatem pondere in F o&shy;<lb/> 
 &longs;tendetur.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.49.7.2.1.0" type="caption">        
 <s id="id.2.1.49.1.1.3.0"> Ducantur &agrave; punctis EF ip&longs;i OP perpendiculares EQ <lb/> 
 FR. &longs;imili ratione o&longs;tendetur, triangulum QES triangulo RFS <lb/> <s id="id.2.1.49.7.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.49.8.0.0.0" type="main">        
 &longs;imile e&longs;&longs;e; lineamq; EQ ip&longs;a RF maiorem e&longs;&longs;e.  </s>              
 <s id="id.2.1.49.1.1.4.0"> pondus itaq; <lb/> <s id="id.2.1.49.8.1.1.0"> C&aelig;terum quis adhuc dicere poterit, &longs;i paruum imponatur pon<lb/>dus in B, mouebitur quidem libra deor&longs;um, non autem v&longs;q; ad <lb/>G. in qu&ograve; &longs;itu &longs;ecund&ugrave;m Ari&longs;totelem, ablato pondere, mane&shy;<lb/>re deberet.  </s>            
 in E magis &agrave; linea OP di&longs;tabit, qu&agrave;m pondus in F; ac propterea <lb/> 
 pondus in E maiorem habebit grauitatem pondere in F. ex quibus <lb/> <s id="id.2.1.49.8.1.2.0"> quod experimento patet; c&ugrave;m in vna tant&ugrave;m libr&aelig; <lb/>extremitate, impo&longs;ito onere, hocq; vel maiore, vel minore, libra <lb/>plus, minu&longs;u&egrave; inclinetur.  </s>            
 reditus libr&aelig; EF in AB manife&longs;tus apparet.  </s>    </p>        
 <pb xlink:href="pagethumb-la/00000070.JPG"/> <s id="id.2.1.49.8.1.3.0"> Quod e&longs;t quidem veri&longs;&longs;imum, centro &longs;upra <lb/>libram, non autem infra, neq; in ip&longs;a libra collocato.  </s>            
         
 <p id="id.2.1.49.3.0.0.0" type="main">         <s id="id.2.1.49.8.1.4.0"> Vt exempli <lb/>gratia.  </s>    </p>       <pb xlink:href="pagethumb-la/00000072.JPG"/>       <p id="id.2.1.49.10.0.0.0" type="main">        
 <s id="id.2.1.49.3.1.1.0"> Si autem centrum libr&aelig; <lb/> 
 &longs;it infra libram, tunc pon&shy;<lb/> <s id="id.2.1.49.10.1.1.0"> Sit libra horizonti &aelig;&shy;<lb/>quidi&longs;tans AB, cuius cen<lb/>trum C &longs;it &longs;upra libram, <lb/>perpendiculumq; CD ho<lb/>rizonti perpendiculare, <lb/>quod ex parte D produca<lb/>tur in H.  </s>    
 dus depre&longs;&longs;um maiorem <lb/> 
 habere grauitatem eleuato <lb/> <s id="id.2.1.49.10.1.1.0.a"> Quoniam enim <lb/>con&longs;iderata libr&aelig; grauita&shy;<lb/>te, erit punctum D libr&aelig; <lb/>centrum grauitatis.  </s>            
 ii&longs;dem mediis o&longs;tendetur.  </s>              
 <s id="id.2.1.49.3.1.2.0"> <lb/> <s id="id.2.1.49.10.1.2.0"> &longs;i ergo <lb/>in B paruum imponatur <lb/>pondus, cuius centrum <lb/><figure id="fig50" place="text" xlink:href="figures1577/2000.03.0069.jpg">       </figure><lb/>grauitatis &longs;it in puncto B; magnitudinis ex libra AB, &amp; pondere <lb/>in B compo&longs;it&aelig; non erit amplius centrum grauitatis D; &longs;ed erit in <lb/><arrow.to.target n="note76"></arrow.to.target> linea DB, vt in E: ita vt DE ad EB &longs;it, vt pondus in B ad gra&shy;<lb/>uitatem libr&aelig; AB. Connectatur CE.  </s>    
 ducantur &agrave; punctis EF ip&shy;<lb/> 
 &longs;i AB perpendiculares EL <lb/> <s id="id.2.1.49.10.1.2.0.a"> Quoniam autem pun&shy;<lb/>ctum Ce&longs;t immobile, dum libra mouetur, punctum E circuli cir<lb/>cumferentiam EFG de&longs;cribet, cuius &longs;emidiameter CE, &amp; cen&shy;<lb/>trum C. quia ver&ograve; CD horizonti e&longs;t perpendicularis, linea CE <lb/>horizonti perpendicularis nequaquam erit.  </s>            
 FM. &longs;imiliter demon&longs;tra<lb/> 
 bitur EL maiorem e&longs;&longs;e <lb/> <s id="id.2.1.49.10.1.3.0"> quare magnitudo ex <lb/>AB, &amp; pondere in B compo&longs;ita minim&egrave; in hoc &longs;itu manebit; &longs;ed <lb/><arrow.to.target n="note77"></arrow.to.target> deor&longs;um &longs;ecund&ugrave;m eius grauitatis centrum E per circumferen&shy;<lb/>tiam EFG mouebitur; donec CE horizonti perpendicularis eua<lb/>dat; hoc e&longs;t, donec CE in CDF perueniat.  </s>            
 FM; &amp; ob id de&longs;cen&longs;us <lb/> 
 ponderis in F minus de di <lb/> <s id="id.2.1.49.10.1.4.0"> atq; tunc libra AB <lb/>mota erit in kL, in quo &longs;itu libra vn&aacute; cum pondere manebit.  </s>            
 recto capiet, qu&agrave;m a&longs;cen&shy;<lb/> 
 <figure id="fig48" place="text" xlink:href="figures1577/2000.03.0067.jpg">       </figure><lb/> <s id="id.2.1.49.10.1.5.0"> nec <lb/>deor&longs;um amplius mouebitur.  </s>            
 &longs;us ponderis in E: quocirca re&longs;i&longs;tentia violenti&aelig; ponderis in E &longs;u<lb/> 
 perabit naturalem propen&longs;ionem ponderis in F. ergo pondus in E <lb/> <s id="id.2.1.49.10.1.6.0"> Si ver&ograve; in B ponatur pondus graui&shy;<lb/>us; centrum grauitatis totius magnitudinis erit ip&longs;i B propius, vt in <lb/>M. &amp; tunc libra deor&longs;um, donec iuncta CM in linea CDH per <lb/>ueniat, mouebitur.  </s>            
 pondere in F grauius erit. </s>      
 <s> ZZZ head of figure ZZZ </s>    </p>               <s id="id.2.1.49.10.1.7.0"> Ex maiore igitur, &amp; minore pondere in B po<lb/>&longs;ito, libra plus, minu&longs;u&egrave; inclinabitur.  </s>            
 <p id="id.2.1.49.3.2.1.0" type="caption">         
 <s id="id.2.1.49.3.2.1.0.capt"> YYY </s>    </p>        <s id="id.2.1.49.10.1.8.0"> ex quo &longs;equitur pondus B <lb/>quarta circuli parte minorem &longs;emper circumferentiam de&longs;cribe&shy;<lb/>re, c&ugrave;m angulus FCE &longs;it &longs;emper acutus.  </s>            
 <p id="id.2.1.49.4.0.0.0" type="main">         
 <s id="id.2.1.49.4.1.1.0"> Producatur etiam CD ex vtraq; parte in OP; ip&longs;iq; &agrave; punctis <lb/> <s id="id.2.1.49.10.1.9.0"> nunquam enim punctum <lb/>B v&longs;q; ad lineam CH perueniet, c&ugrave;m centrum grauitatis ponde&shy;<lb/>ris, &amp; libr&aelig; &longs;imul &longs;emper inter DB exi&longs;tat.  </s>            
 EF perpendiculares ducantur EQ FR. eodem pror&longs;us modo <lb/> 
 o&longs;tendetur, lineam EQ maiorem e&longs;&longs;e FR. pondus ide&ograve; in E ma<lb/> <s id="id.2.1.49.10.1.10.0"> qu&ograve; tamen pondus <lb/>in B grauius fuerit, maiorem quoq; circumferentiam de&longs;cribet.  </s>            
 gis &agrave; linea directionis OP di&longs;tabit, qu&agrave;m pondus in F. maio&shy;<lb/> 
 rem igitur grauitatem habebit pondus in E, qu&agrave;m pondus in F. <lb/> <s id="id.2.1.49.10.1.11.0"> <lb/>e&ograve; enim magis punctum B ad lineam CH accedet.  </s>    
 ex quibus &longs;equitur, libram EF ex parte E deor&longs;um moueri. </s>    </p>        
 <p id="id.2.1.49.5.0.0.0" type="main">         <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.49.10.2.1.0" type="caption">        
 <s id="id.2.1.49.5.1.1.0"> Ari&longs;toteles itaq; has duas tant&ugrave;m qu&aelig;&longs;tiones propo&longs;uit, ter&shy;<lb/> 
 tiamq; reliquit; &longs;cilicet c&ugrave;m centrum libr&aelig; in ip&longs;a e&longs;t libra: hanc <lb/> <s id="id.2.1.49.10.2.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.50.1.0.0.0" type="margin">        
 autem ommi&longs;sit, vt notam, quemadmodum res valde notas pr&aelig;&shy;<lb/> 
 termittere &longs;olet.  </s>              <s id="id.2.1.50.1.1.1.0"> <margin.target id="note76"></margin.target>6 <emph type="italics"/>Primi Archim. de &aelig;quep.<emph.end type="italics"/>  </s>  
 <s id="id.2.1.49.5.1.2.0"> nam cui dubium, &longs;i pondus in eius centro gra<lb/> 
 uitatis &longs;u&longs;tineatur, quin maneat?  </s>              <s id="id.2.1.50.1.1.3.0"> <margin.target id="note77"></margin.target>1. <emph type="italics"/>Huius.<emph.end type="italics"/> </s>    </p>       <p id="id.2.1.51.1.0.0.0" type="main">        <pb n="28" xlink:href="pagethumb-la/00000073.JPG"/>      
 <s id="id.2.1.49.5.1.3.0"> Ea ver&ograve;, qu&aelig; ex ip&longs;ius &longs;enten<lb/> 
 tia attulimus, aliquis reprehendere po&longs;&longs;et, nos integram eius &longs;enten<lb/> <s id="id.2.1.51.1.2.1.0"> Habeat autem libra AB <lb/>centrum C in ip&longs;a libra, atq; <lb/>in eius medio: erit C libr&aelig; <lb/>centrum quoq; grauitatis; <lb/>&agrave; quo ip&longs;i AB, horizontiq; <lb/>perpendicularis ducatur FC <lb/>G. ponatur deinde in B <lb/>quoduis pondus; erit totius <lb/>magnitudinis centrum gra&shy;<lb/>uitatis put&aacute; in E; ita vt CE <lb/><figure id="fig51" place="text" xlink:href="figures1577/2000.03.0070.jpg">       </figure><lb/>ad EB &longs;it, vt pondus in B ad libr&aelig; grauitatem.  </s>            
 tiam minim&egrave; protuli&longs;&longs;e affimans.  </s>              
 <s id="id.2.1.49.5.1.4.0"> nam c&ugrave;m in &longs;ecunda parte &longs;e<lb/> <s id="id.2.1.51.1.2.2.0"> &amp; quoniam CE <lb/>non e&longs;t horizonti perpendicularis, libra AB, atq; pondus in B <lb/>in hoc &longs;itu nunquam manebunt; &longs;ed deor&longs;um ex parte B mouebun<lb/>tur, donec CE horizonti fiat perpendicularis.  </s>            
 cund&aelig; qu&aelig;&longs;tionis proponit, cur libra, trutina deor&longs;um con&longs;tituta, <lb/> 
 quando deor&longs;um lato pondere qui&longs;piam id amouet, non a&longs;cen<lb/> <s id="id.2.1.51.1.2.3.0"> hoc e&longs;t donec li&shy;<lb/>bra AB in FG perueniat.  </s>            
 dit, &longs;ed manet?  </s>              
 <s id="id.2.1.49.5.1.5.0"> non a&longs;&longs;erit adhuc libram deor&longs;um moueri; &longs;ed <lb/> <s id="id.2.1.51.1.2.4.0"> ex quo patet, quolibet pondus in B <lb/>circuli quartam &longs;emper de&longs;cribere. </s>    
 manere.  </s>              
 <s id="id.2.1.49.5.1.6.0"> quod in vltima quoq; conclu&longs;ione colligi&longs;&longs;e videtur.  </s>              <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.51.1.3.1.0" type="caption">        
 <s id="id.2.1.49.5.1.7.0"> Ve <lb/> 
 r&ugrave;m hoc non &longs;olum nobis non repugnat, &longs;ed &longs;i rect&egrave; intelligitur, <lb/> <s id="id.2.1.51.1.3.1.0.capt"> YYY </s>    </p>       <p id="id.2.1.51.2.0.0.0" type="main">        
 maxim&egrave; &longs;uffragatur.  </s>    </p>        
 <pb n="27" xlink:href="pagethumb-la/00000071.JPG"/> <s id="id.2.1.51.2.1.1.0"> Sit autem centrum Cin&shy;<lb/>fra libram AB. &longs;itq; DCE <lb/>perpendiculum.  </s>            
         
 <p id="id.2.1.49.7.0.0.0" type="main">         <s id="id.2.1.51.2.1.2.0"> &longs;imiliter <lb/>po&longs;ito in B pondere, cen&shy;<lb/>trum grauitatis magnitudi<lb/>nis ex AB libra, &amp; ponde<lb/>re in B compo&longs;it&aelig; in linea <lb/>DB erit; vt in F; ita vt DF <lb/>ad FB &longs;it, vt pondus in B <lb/><figure id="fig52" place="text" xlink:href="figures1577/2000.03.0071.1.jpg">       </figure><lb/>ad libr&aelig; pondus.  </s>            
 <s id="id.2.1.49.7.1.1.0"> Sit enim libra AB <lb/> 
 horizonti &aelig;quidi&longs;tans, <lb/> <s id="id.2.1.51.2.1.3.0"> Iungatur CF. &amp; quoniam CD horizonti e&longs;t <lb/>perpendicularis; linea CF horizonti nequaquam perpendicula&shy;<lb/>ris exi&longs;tet.  </s>            
 cuius centrum E &longs;it <lb/> 
 infra libram.  </s>              <s id="id.2.1.51.2.1.4.0"> quare magnitudo ex AB libra, ac pondere in B com<lb/>po&longs;ita in hoc &longs;itu nunquam per&longs;i&longs;tet; &longs;ed deor&longs;um, ni&longs;i aliquid <lb/>impediat, mouebitur; donec CF in DCE perueniat: in quo &longs;itu <lb/>libra vn&aacute; cum pondere manebit.  </s>            
 <s id="id.2.1.49.7.1.2.0"> quia ve <lb/> 
 r&ograve; Ari&longs;toteles libram, <lb/> <s id="id.2.1.51.2.1.5.0"> &amp; punctum B erit vt in G, atq; <lb/>punctum A in H, libraq; GH non amplius centrum infra, &longs;ed &longs;u<lb/>pra ip&longs;am habebit.  </s>            
 &longs;icuti actu e&longs;t, con&longs;ide<lb/> 
 rat; ide&ograve; nece&longs;&longs;e e&longs;t <lb/> <s id="id.2.1.51.2.1.6.0"> quod idem &longs;emper eueniet; quamuis mini&shy;<lb/>mum imponatur pondus in B. ergo priu&longs;quam B perueniat ad <lb/>G; nece&longs;&longs;e e&longs;t libram, &longs;iue trutin&aelig; deor&longs;um po&longs;it&aelig;, vel alicui <pb xlink:href="pagethumb-la/00000074.JPG"/>alteri, quod centrum C &longs;u&shy;<lb/>&longs;tineat, occurrere; ibiq; ad&shy;<lb/>h&aelig;rere.  </s>            
 trutinam, vel aliquid <lb/> 
 aliud infra centrum E <lb/> <s id="id.2.1.51.2.1.7.0"> ex hoc &longs;equitur, pon<lb/>dus in B vltra lineam Dk <lb/>&longs;emper moueri; ac circuli <lb/>quarta maiorem &longs;emper cir<lb/><expan abbr="cumfer&etilde;tiam">cumferentiam</expan> de&longs;cribere: e&longs;t <lb/>enim angulus FCE &longs;emper <lb/>obtu&longs;us, c&ugrave;m angulus DCF <lb/>&longs;emper &longs;it acutus.  </s>            
 collocare, vt EF <lb/> 
 (quod quidem truti&shy;<lb/> <s id="id.2.1.51.2.1.8.0"> qu&ograve; au&shy;<lb/><figure id="fig53" place="text" xlink:href="figures1577/2000.03.0071.2.jpg">       </figure><lb/>tem pondus in B fuerit leuius, maiorem tamen adhuc circumfe&shy;<lb/>rentiam de&longs;cribet.  </s>            
 na erit) ita vt centrum <lb/> 
 E &longs;u&longs;tineat.  </s>              <s id="id.2.1.51.2.1.9.0"> nam qu&ograve; pondus in G leuius fuerit, e&ograve; ma&shy;<lb/>gis pondus in G eleuabitur; libraq; GH ad &longs;itum horizonti &aelig;qui<lb/>di&longs;tantem propius accedet.  </s>            
 <s id="id.2.1.49.7.1.3.0"> &longs;itq; per&shy;<lb/> 
 <figure id="fig49" place="text" xlink:href="figures1577/2000.03.0068.jpg">       </figure><lb/> <s id="id.2.1.51.2.1.10.0"> qu&aelig; omnia ex iis, qu&aelig; &longs;upra dixi&shy;<lb/>mus, manife&longs;ta &longs;unt. </s>    
 pendiculum ECD. &amp; vt libra AB ab hoc moueatur &longs;itu; dicit <lb/> 
 Ari&longs;toteles, ponatur pondus in B, quod c&ugrave;m &longs;it graue, libram ex <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.51.2.2.1.0" type="caption">        
 parte B deor&longs;um mouebit; put&aacute; in G. ita vt propter impedimen<lb/> 
 tum deor&longs;um amplius moueri non poterit.  </s>              <s id="id.2.1.51.2.2.1.0.capt"> YYY </s>    
 <s id="id.2.1.49.7.1.4.0"> non enim dicit Ari<lb/> 
 &longs;toteles, moueatur libra ex parte B deor&longs;um, quou&longs;q; libuerit; dein <lb/> <s> ZZZ head of figure ZZZ </s>    </p>              <p id="id.2.1.51.2.2.3.0" type="caption">        
 de relinquatur, vt nos diximus: &longs;ed pr&aelig;cipit, vt in ip&longs;o B po&shy;<lb/> 
 natur pondus, quod ex ip&longs;ius natura deor&longs;um &longs;emper mouebi&shy;<lb/> <s id="id.2.1.51.2.2.3.0.capt"> YYY </s>    </p>       <p id="id.2.1.51.3.0.0.0" type="main">        
 tur; donec libra trutin&aelig;, &longs;iue alicui alii adh&aelig;reat.  </s>              
 <s id="id.2.1.49.7.1.5.0"> &amp; quando B erit <lb/> <s id="id.2.1.51.3.1.1.0"> His demon&longs;tratis.  </s>            
 in G, erit libra in GH; in quo &longs;itu, ablato pondere, manebit: <lb/> 
 c&ugrave;m maior pars libr&aelig; &agrave; perpendiculo &longs;it ver&longs;us G, qu&aelig; e&longs;t DG, <lb/> <s id="id.2.1.51.3.1.2.0"> Manife&longs;tum e&longs;t, centrum libr&aelig; cau&longs;am e&longs;&longs;e <lb/>diuer&longs;itatis effectuum in libra.  </s>            
 qu&agrave;m DH.  </s>