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Colored diff for /texts/archimedes/xml/Attic/varro_demot_01_la_1584.xml between version 1.1 and 1.2

version 1.1, 2002/06/18 09:37:14 version 1.2, 2002/06/24 18:03:56
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 <!ELEMENT s  <!ELEMENT s
  
 (#PCDATA| foreign | expan | foot.target|margin.target|arrow.to.target|pb|lb|emph|emph.end|gap)* > (#PCDATA| foreign | figure | expan | foot.target|margin.target|arrow.to.target|pb|lb|emph|emph.end|gap)* >
  
  
 <!ATTLIST s <!ATTLIST s
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       <info>       <info>
  
  
         <author>Michael Varro</author>         <author>Varro, Michael</author>
         <title>De Motu Tractatus</title>         <title>De Motu Tractatus</title>
         <date></date>         <date>1584</date>
          
 <place></place> <place></place>
         <editor></editor>                 <editor></editor>        
          
 <publisher></publisher> <publisher></publisher>
         <translator></translator>         <translator></translator>
         <lang></lang>         <lang>la</lang>
                  
       <chunk unit="page*">page</chunk>       <chunk unit="page*">page</chunk>
      <locator>000000079.xml</locator>      <locator>000000079.xml</locator>
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 <s>Vis ver&ograve; naturalis, qua res qu&ecedil;libet ad <expan abbr="loc&utilde;">locum</expan> &longs;uum <lb/>naturalem tendit, &longs;ubiectum &longs;uum, motu continu&egrave; <lb/>&amp; ordinatim cre&longs;cente, mouet. Illius autem motus <lb/>cau&longs;a e&longs;t qu&ograve;d facili&ugrave;s id moueatur, quod in motu <lb/>e&longs;t, qu&agrave;m quod quie&longs;cit. Vis igitur eadem, <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan> <lb/>quod iam in motu e&longs;t premens, illud magis moue&shy;<lb/>bit, qu&agrave;m &longs;i quie&longs;cat, &amp; magis motum, magis etiam <lb/>mouebit: ita vt eadem vis motione maior fiat, qu&agrave;m <lb/>per &longs;e &longs;it. Et h&aelig;c e&longs;t cau&longs;a cur ictus, quo magis ab al&shy;<lb/>tero venit, eo vehementior &longs;it. Motus autem huius  <s>Vis ver&ograve; naturalis, qua res qu&ecedil;libet ad <expan abbr="loc&utilde;">locum</expan> &longs;uum <lb/>naturalem tendit, &longs;ubiectum &longs;uum, motu continu&egrave; <lb/>&amp; ordinatim cre&longs;cente, mouet. Illius autem motus <lb/>cau&longs;a e&longs;t qu&ograve;d facili&ugrave;s id moueatur, quod in motu <lb/>e&longs;t, qu&agrave;m quod quie&longs;cit. Vis igitur eadem, <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan> <lb/>quod iam in motu e&longs;t premens, illud magis moue&shy;<lb/>bit, qu&agrave;m &longs;i quie&longs;cat, &amp; magis motum, magis etiam <lb/>mouebit: ita vt eadem vis motione maior fiat, qu&agrave;m <lb/>per &longs;e &longs;it. Et h&aelig;c e&longs;t cau&longs;a cur ictus, quo magis ab al&shy;<lb/>tero venit, eo vehementior &longs;it. Motus autem huius
 <pb pagenum="13"/>&longs;patia hanc celeritatis proportionem &longs;eruant, vt qu&ecedil;<lb/>e&longs;t ratio totius &longs;patij, per quod fit ille motus ad par&shy;<lb/>tem ip&longs;ius (vtriu&longs;que initio inde &longs;umpto, vbi e&longs;t mo|| <lb/>tus initium) eadem &longs;it celeritatis ad celeritatem. <lb/> <pb pagenum="13"/>&longs;patia hanc celeritatis proportionem &longs;eruant, vt qu&ecedil;<lb/>e&longs;t ratio totius &longs;patij, per quod fit ille motus ad par&shy;<lb/>tem ip&longs;ius (vtriu&longs;que initio inde &longs;umpto, vbi e&longs;t mo|| <lb/>tus initium) eadem &longs;it celeritatis ad celeritatem. <lb/>
 <arrow.to.target n="fig1"></arrow.to.target><lb/>Exempli gratia, &longs;i vis aliqua per lineam ABC <lb/>mouerit, &longs;itque AB illius line&aelig; pars, qu&aelig; erit <lb/>ratio AC ad AB, eadem erit celeritatis motus <lb/>in puncto C ad <expan abbr="celeritat&etilde;">celeritatem</expan> motus in puncto B. <lb/>Cuiu&longs;modi proportio ob&longs;eruatur in paralle&shy;<lb/>lis triangulum &longs;ecantibus. Vt enim &longs;e habet <lb/> <figure id="fig1"></figure><lb/>Exempli gratia, &longs;i vis aliqua per lineam ABC <lb/>mouerit, &longs;itque AB illius line&aelig; pars, qu&aelig; erit <lb/>ratio AC ad AB, eadem erit celeritatis motus <lb/>in puncto C ad <expan abbr="celeritat&etilde;">celeritatem</expan> motus in puncto B. <lb/>Cuiu&longs;modi proportio ob&longs;eruatur in paralle&shy;<lb/>lis triangulum &longs;ecantibus. Vt enim &longs;e habet <lb/>
 <arrow.to.target n="fig2"></arrow.to.target><lb/>AC ad AB, &longs;ic CG ad BF, &amp; vt AD ad <lb/>AC, &longs;ic DH ad CG. Itaque &longs;i in &longs;patia ali&shy;<lb/>quot &aelig;qualia diuidatur totius motus &longs;pa|| <lb/>tium, finis &longs;ecundi duplo citi&ugrave;s feretur, <lb/>qu&agrave;m finis primi: finis ver&ograve; tertijtriplo <lb/>citi&ugrave;s qu&agrave;m finis primi, &amp; &longs;ic deinceps. <lb/>Hac autem ratione fit, vt &longs;patiorum illo&shy;<lb/>rum initio maxima &longs;it celeritatis <expan abbr="differ&etilde;-tia">differen&shy;<lb/>tia</expan>: progre&longs;&longs;u ver&ograve; &longs;emper minuatur, ac tandem fer&shy;<lb/>m&egrave; eadem &longs;it, vt fit in trianguli lateribus, qu&aelig; lon&shy;<lb/>gi&longs;&longs;im&egrave; producta &aelig;qu&egrave; di&longs;tare videntur. E&aacute;que e&longs;t <lb/>ratio cur Solis &amp; Lun&aelig; radij, etiam&longs;i concurrant (in <lb/>ip&longs;orum &longs;cilicet corporibus, aut vltra res quas <expan abbr="illu-&longs;tr&atilde;t">illu&shy;<lb/>&longs;trant</expan>) paralleli <expan abbr="tam&etilde;">tamen</expan> <expan abbr="appare&atilde;t">appareant</expan>. <expan abbr="Ead&etilde;">Eadem</expan> <expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t cur <lb/>line&ecedil; omnes ad <expan abbr="perp&etilde;dicul&utilde;">perpendiculum</expan> in <expan abbr="terr&atilde;">terram</expan> cadentes, paral&shy;<lb/>lel&aelig; videantur, c&ugrave;m <expan abbr="tam&etilde;">tamen</expan> in centro terr&aelig; <expan abbr="c&otilde;currant">concurrant</expan>. </s> <figure id="fig2"></figure><lb/>AC ad AB, &longs;ic CG ad BF, &amp; vt AD ad <lb/>AC, &longs;ic DH ad CG. Itaque &longs;i in &longs;patia ali&shy;<lb/>quot &aelig;qualia diuidatur totius motus &longs;pa|| <lb/>tium, finis &longs;ecundi duplo citi&ugrave;s feretur, <lb/>qu&agrave;m finis primi: finis ver&ograve; tertijtriplo <lb/>citi&ugrave;s qu&agrave;m finis primi, &amp; &longs;ic deinceps. <lb/>Hac autem ratione fit, vt &longs;patiorum illo&shy;<lb/>rum initio maxima &longs;it celeritatis <expan abbr="differ&etilde;-tia">differen&shy;<lb/>tia</expan>: progre&longs;&longs;u ver&ograve; &longs;emper minuatur, ac tandem fer&shy;<lb/>m&egrave; eadem &longs;it, vt fit in trianguli lateribus, qu&aelig; lon&shy;<lb/>gi&longs;&longs;im&egrave; producta &aelig;qu&egrave; di&longs;tare videntur. E&aacute;que e&longs;t <lb/>ratio cur Solis &amp; Lun&aelig; radij, etiam&longs;i concurrant (in <lb/>ip&longs;orum &longs;cilicet corporibus, aut vltra res quas <expan abbr="illu-&longs;tr&atilde;t">illu&shy;<lb/>&longs;trant</expan>) paralleli <expan abbr="tam&etilde;">tamen</expan> <expan abbr="appare&atilde;t">appareant</expan>. <expan abbr="Ead&etilde;">Eadem</expan> <expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t cur <lb/>line&ecedil; omnes ad <expan abbr="perp&etilde;dicul&utilde;">perpendiculum</expan> in <expan abbr="terr&atilde;">terram</expan> cadentes, paral&shy;<lb/>lel&aelig; videantur, c&ugrave;m <expan abbr="tam&etilde;">tamen</expan> in centro terr&aelig; <expan abbr="c&otilde;currant">concurrant</expan>. </s>
 </p> </p>
 <pb pagenum="14"/> <pb pagenum="14"/>
 <figure id="fig1"></figure> 
 <figure id="fig2"></figure> 
 <p type="main"> <p type="main">
  
 <s>Hunc igitur motum vis naturalis efficit, mod&ograve; <lb/>nulla quies intercedat. </s> <s>Hunc igitur motum vis naturalis efficit, mod&ograve; <lb/>nulla quies intercedat. </s>
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 <s>Horum autem mediorum opera fit vt vires illis <lb/>applicat&aelig;, quarum iidem &longs;unt nutus, contrariis mo&shy;<lb/>tibus moueantur. Id <expan abbr="aut&etilde;">autem</expan> fit c&ugrave;m in mediis illis inter <lb/><expan abbr="eor&utilde;">eorum</expan> extrema interiacet quies vna vel plures. <expan abbr="Ex&etilde;pli">Exempli</expan> <lb/>gratia, &longs;i duo pondera funis extremitatibus alligata <lb/>&longs;int, &amp; funis clauo fixo &amp; immobili incumbat pro&shy;<lb/>pter illam quietem inter <expan abbr="vtrumq;">vtrumque</expan> pondus <expan abbr="po&longs;it&atilde;">po&longs;itam</expan> <expan abbr="n&otilde;">non</expan> <lb/>poterit <expan abbr="alter&utilde;">alterum</expan> deor&longs;um moueri, quin <expan abbr="alter&utilde;">alterum</expan> &longs;ur&longs;um <lb/>moueatur. <expan abbr="Id&etilde;">Idem</expan> fiet in linea recta, &longs;i enim illius extre&shy;<lb/>mitatibus pondera duo annexa &longs;int, &amp; inter ea &longs;it in <lb/>illa <expan abbr="punct&utilde;">punctum</expan> aliquod quie&longs;cens, dum alterum ex illis <lb/>ponderibus deor&longs;um feretur, alterum a&longs;cendet. <expan abbr="P&utilde;-ctum">Pun&shy;<lb/>ctum</expan> autem illud quie&longs;cens in linea illa recta, Gr&ecedil;cis <lb/>hypomochlium dicitur, e&ograve; qu&ograve;d vecti, quem <foreign lang="greek">mo/xlon</foreign><lb/>vocant, &longs;ubiiciatur. Huius autem hypomochlij, in <lb/>recta linea &longs;e vecte collocatio faciet, vt line&aelig; extre&shy;<lb/>ma &longs;ecundum datam rationem moueantur. Si enim <lb/>recta linea in datam rationem diui&longs;a fuerit, hoc e&longs;t, <lb/>vt pars altera ad <expan abbr="alter&atilde;">alteram</expan> eam habeat <expan abbr="ration&etilde;">rationem</expan>, <expan abbr="qu&atilde;">quam</expan> quis <lb/>voluerit. (Quod <expan abbr="quid&etilde;">quidem</expan> quo modo fiat docet Euc.) &amp; <lb/>in puncto diui&longs;ionis collocetur <expan abbr="hypomochli&utilde;">hypomochlium</expan>, illius <lb/>line&aelig; extrema &longs;ecundum <expan abbr="ill&atilde;">illam</expan> <expan abbr="ration&etilde;">rationem</expan> mouebuntur: <lb/>&longs;iue enim con&longs;ideretur <expan abbr="circulor&utilde;">circulorum</expan>, quos illa extrema <lb/>de&longs;cribent, proportio &longs;iue &longs;patium quod illa in linea <lb/>perpendiculari notabunt vtroque modo illi motus,  <s>Horum autem mediorum opera fit vt vires illis <lb/>applicat&aelig;, quarum iidem &longs;unt nutus, contrariis mo&shy;<lb/>tibus moueantur. Id <expan abbr="aut&etilde;">autem</expan> fit c&ugrave;m in mediis illis inter <lb/><expan abbr="eor&utilde;">eorum</expan> extrema interiacet quies vna vel plures. <expan abbr="Ex&etilde;pli">Exempli</expan> <lb/>gratia, &longs;i duo pondera funis extremitatibus alligata <lb/>&longs;int, &amp; funis clauo fixo &amp; immobili incumbat pro&shy;<lb/>pter illam quietem inter <expan abbr="vtrumq;">vtrumque</expan> pondus <expan abbr="po&longs;it&atilde;">po&longs;itam</expan> <expan abbr="n&otilde;">non</expan> <lb/>poterit <expan abbr="alter&utilde;">alterum</expan> deor&longs;um moueri, quin <expan abbr="alter&utilde;">alterum</expan> &longs;ur&longs;um <lb/>moueatur. <expan abbr="Id&etilde;">Idem</expan> fiet in linea recta, &longs;i enim illius extre&shy;<lb/>mitatibus pondera duo annexa &longs;int, &amp; inter ea &longs;it in <lb/>illa <expan abbr="punct&utilde;">punctum</expan> aliquod quie&longs;cens, dum alterum ex illis <lb/>ponderibus deor&longs;um feretur, alterum a&longs;cendet. <expan abbr="P&utilde;-ctum">Pun&shy;<lb/>ctum</expan> autem illud quie&longs;cens in linea illa recta, Gr&ecedil;cis <lb/>hypomochlium dicitur, e&ograve; qu&ograve;d vecti, quem <foreign lang="greek">mo/xlon</foreign><lb/>vocant, &longs;ubiiciatur. Huius autem hypomochlij, in <lb/>recta linea &longs;e vecte collocatio faciet, vt line&aelig; extre&shy;<lb/>ma &longs;ecundum datam rationem moueantur. Si enim <lb/>recta linea in datam rationem diui&longs;a fuerit, hoc e&longs;t, <lb/>vt pars altera ad <expan abbr="alter&atilde;">alteram</expan> eam habeat <expan abbr="ration&etilde;">rationem</expan>, <expan abbr="qu&atilde;">quam</expan> quis <lb/>voluerit. (Quod <expan abbr="quid&etilde;">quidem</expan> quo modo fiat docet Euc.) &amp; <lb/>in puncto diui&longs;ionis collocetur <expan abbr="hypomochli&utilde;">hypomochlium</expan>, illius <lb/>line&aelig; extrema &longs;ecundum <expan abbr="ill&atilde;">illam</expan> <expan abbr="ration&etilde;">rationem</expan> mouebuntur: <lb/>&longs;iue enim con&longs;ideretur <expan abbr="circulor&utilde;">circulorum</expan>, quos illa extrema <lb/>de&longs;cribent, proportio &longs;iue &longs;patium quod illa in linea <lb/>perpendiculari notabunt vtroque modo illi motus,
 <pb pagenum="27"/><expan abbr="parti&utilde;">partium</expan> <expan abbr="illar&utilde;">illarum</expan> <expan abbr="proportion&etilde;">proportionem</expan> <expan abbr="&longs;eruab&utilde;t">&longs;eruabunt</expan>. Sit <expan abbr="ex&etilde;pli">exempli</expan> gratia <lb/>linea AB, qu&aelig; in puncto C in datam rationem &longs;ecta <lb/>&longs;it, puta vt pars AC quadrupla &longs;it ad partem CB, mo&shy;<lb/>ueat&uacute;rque circa centrum C, punctum A de&longs;cribet cir|| <lb/>culum <expan abbr="quadrupl&utilde;">quadruplum</expan> ad illum quem B <lb/>de&longs;cribet. E&longs;t enim <expan abbr="ead&etilde;">eadem</expan> ratio in cir&shy;<lb/>culo diametri ad <expan abbr="diametr&utilde;">diametrum</expan>, qu&aelig; e&longs;t <lb/>circunferenti&aelig; ad <expan abbr="circunferenti&atilde;">circunferentiam</expan> (vt <lb/>alibi demon&longs;trauimus.) Hac igitur <lb/>ratione A puncti motus quadruplus <lb/> <pb pagenum="27"/><expan abbr="parti&utilde;">partium</expan> <expan abbr="illar&utilde;">illarum</expan> <expan abbr="proportion&etilde;">proportionem</expan> <expan abbr="&longs;eruab&utilde;t">&longs;eruabunt</expan>. Sit <expan abbr="ex&etilde;pli">exempli</expan> gratia <lb/>linea AB, qu&aelig; in puncto C in datam rationem &longs;ecta <lb/>&longs;it, puta vt pars AC quadrupla &longs;it ad partem CB, mo&shy;<lb/>ueat&uacute;rque circa centrum C, punctum A de&longs;cribet cir|| <lb/>culum <expan abbr="quadrupl&utilde;">quadruplum</expan> ad illum quem B <lb/>de&longs;cribet. E&longs;t enim <expan abbr="ead&etilde;">eadem</expan> ratio in cir&shy;<lb/>culo diametri ad <expan abbr="diametr&utilde;">diametrum</expan>, qu&aelig; e&longs;t <lb/>circunferenti&aelig; ad <expan abbr="circunferenti&atilde;">circunferentiam</expan> (vt <lb/>alibi demon&longs;trauimus.) Hac igitur <lb/>ratione A puncti motus quadruplus <lb/>
 <arrow.to.target n="fig3"></arrow.to.target><lb/>erit ad puncti B <expan abbr="mot&utilde;">motum</expan>. Si ver&ograve; ponamus AD <expan abbr="perpen-dicular&etilde;">perpen&shy;<lb/>dicularem</expan> e&longs;&longs;e, &amp; linea AB illi prim&ugrave;m <expan abbr="coincid&etilde;s">coincidens</expan> circa <lb/>punctum C, moueatur donec A ad D perueniat: tum <lb/><expan abbr="eod&etilde;">eodem</expan> momento B perueniet ad E: motum igitur erit <lb/>A in linea <expan abbr="perp&etilde;diculari">perpendiculari</expan> tota circuli maioris diame&shy;<lb/>tro, qu&aelig; e&longs;t AD:B ver&ograve; in <expan abbr="ead&etilde;">eadem</expan> linea, minoris <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> <lb/>circuli diametro <expan abbr="mot&utilde;">motum</expan> erit, qu&ecedil; e&longs;t BE. Atqui diame|| <lb/>ter AD quadrupla e&longs;t ad BE, quia ex hypothe&longs;i <expan abbr="&longs;emi-diametror&utilde;">&longs;emi&shy;<lb/>diametrorum</expan> <expan abbr="illor&utilde;">illorum</expan> <expan abbr="circulor&utilde;">circulorum</expan> proportio e&longs;t, vt 4 ad 1. <lb/>Motus igitur <expan abbr="p&utilde;cti">puncti</expan> in linea A <expan abbr="perp&etilde;diculari">perpendiculari</expan> ad <expan abbr="mot&utilde;">motum</expan> <lb/><expan abbr="p&utilde;cti">puncti</expan> B quadruplus erit: <expan abbr="Id&etilde;">Idem</expan> dicetur &longs;i in data aliqua <lb/>alia ratione &longs;ecta &longs;it linea AB. <expan abbr="Dem&otilde;&longs;trat&utilde;">Demon&longs;tratum</expan> igitur e&longs;t <lb/>quomodo fieri po&longs;&longs;it vt rect&aelig; line&ecedil; extrema <expan abbr="&longs;ec&utilde;d&utilde;">&longs;ecundum</expan> <lb/><expan abbr="dat&atilde;">datam</expan> <expan abbr="ration&etilde;">rationem</expan> moueantur. Si igitur illis extremis du&aelig; <lb/>vires applicentur, <expan abbr="moueb&utilde;tur">mouebuntur</expan> <expan abbr="eod&etilde;">eodem</expan> ip&longs;o motu: ergo <lb/>&longs;ecundum datam vel propo&longs;itam rationem. Quod <lb/>a&longs;&longs;umptum erat. </s> <figure id="fig3"></figure><lb/>erit ad puncti B <expan abbr="mot&utilde;">motum</expan>. Si ver&ograve; ponamus AD <expan abbr="perpen-dicular&etilde;">perpen&shy;<lb/>dicularem</expan> e&longs;&longs;e, &amp; linea AB illi prim&ugrave;m <expan abbr="coincid&etilde;s">coincidens</expan> circa <lb/>punctum C, moueatur donec A ad D perueniat: tum <lb/><expan abbr="eod&etilde;">eodem</expan> momento B perueniet ad E: motum igitur erit <lb/>A in linea <expan abbr="perp&etilde;diculari">perpendiculari</expan> tota circuli maioris diame&shy;<lb/>tro, qu&aelig; e&longs;t AD:B ver&ograve; in <expan abbr="ead&etilde;">eadem</expan> linea, minoris <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> <lb/>circuli diametro <expan abbr="mot&utilde;">motum</expan> erit, qu&ecedil; e&longs;t BE. Atqui diame|| <lb/>ter AD quadrupla e&longs;t ad BE, quia ex hypothe&longs;i <expan abbr="&longs;emi-diametror&utilde;">&longs;emi&shy;<lb/>diametrorum</expan> <expan abbr="illor&utilde;">illorum</expan> <expan abbr="circulor&utilde;">circulorum</expan> proportio e&longs;t, vt 4 ad 1. <lb/>Motus igitur <expan abbr="p&utilde;cti">puncti</expan> in linea A <expan abbr="perp&etilde;diculari">perpendiculari</expan> ad <expan abbr="mot&utilde;">motum</expan> <lb/><expan abbr="p&utilde;cti">puncti</expan> B quadruplus erit: <expan abbr="Id&etilde;">Idem</expan> dicetur &longs;i in data aliqua <lb/>alia ratione &longs;ecta &longs;it linea AB. <expan abbr="Dem&otilde;&longs;trat&utilde;">Demon&longs;tratum</expan> igitur e&longs;t <lb/>quomodo fieri po&longs;&longs;it vt rect&aelig; line&ecedil; extrema <expan abbr="&longs;ec&utilde;d&utilde;">&longs;ecundum</expan> <lb/><expan abbr="dat&atilde;">datam</expan> <expan abbr="ration&etilde;">rationem</expan> moueantur. Si igitur illis extremis du&aelig; <lb/>vires applicentur, <expan abbr="moueb&utilde;tur">mouebuntur</expan> <expan abbr="eod&etilde;">eodem</expan> ip&longs;o motu: ergo <lb/>&longs;ecundum datam vel propo&longs;itam rationem. Quod <lb/>a&longs;&longs;umptum erat. </s>
 </p> </p>
 <pb pagenum="28"/> <pb pagenum="28"/>
 <figure id="fig3"></figure> 
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 <s>Quod autem in vecte demon&longs;tratum e&longs;t, illud e&shy;<lb/>tiam in reliquis mediis demon&longs;trandum erit, et&longs;i <lb/>lemmati &longs;atisfactum e&longs;t, dum in vno exemplo id <lb/>probatum e&longs;t. Ante igitur &longs;ecundum lemma de&shy;<lb/>mon&longs;trabimus. </s> <s>Quod autem in vecte demon&longs;tratum e&longs;t, illud e&shy;<lb/>tiam in reliquis mediis demon&longs;trandum erit, et&longs;i <lb/>lemmati &longs;atisfactum e&longs;t, dum in vno exemplo id <lb/>probatum e&longs;t. Ante igitur &longs;ecundum lemma de&shy;<lb/>mon&longs;trabimus. </s>
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 <s>Sed &amp; alia ratione eo vti po&longs;&longs;umus, ip&longs;um &longs;cilicet <lb/>triangulum mouendo, qui tunc cuneus dicitur. Vt <lb/>autem eo hac ratione vtamur, vires ita di&longs;ponere o&shy;<lb/>portet, vt altera illarum vni ex lateribus angulum <lb/>rectum con&longs;tituentibus incumbat, altera ver&ograve; lateri <lb/>ip&longs;um &longs;ubtendenti. Illa enim tant&ugrave;m mouebitur, <lb/>quantum latus cui altera incumbit. Sit exempli gra&shy; <s>Sed &amp; alia ratione eo vti po&longs;&longs;umus, ip&longs;um &longs;cilicet <lb/>triangulum mouendo, qui tunc cuneus dicitur. Vt <lb/>autem eo hac ratione vtamur, vires ita di&longs;ponere o&shy;<lb/>portet, vt altera illarum vni ex lateribus angulum <lb/>rectum con&longs;tituentibus incumbat, altera ver&ograve; lateri <lb/>ip&longs;um &longs;ubtendenti. Illa enim tant&ugrave;m mouebitur, <lb/>quantum latus cui altera incumbit. Sit exempli gra&shy;
 <pb pagenum="38"/> <pb pagenum="38"/>
 <arrow.to.target n="fig4"></arrow.to.target><lb/>tia triangulus ABC, cuius angulus B <lb/>rectus &longs;it, latus ver&ograve; illum &longs;ubtendens <lb/>&longs;it AC, incumb&aacute;tque vis D lateri AB, <lb/>vis ver&ograve; E lateri AC, &longs;itque vis D nutus <lb/>linea BC, vis ver&ograve; E nutus &longs;it linea AB, erigat&uacute;rque &agrave; <lb/>puncto C linea CF <expan abbr="perp&etilde;dicularis">perpendicularis</expan> ad BC &aelig;qualis AB, <lb/>&agrave; qua vis E <expan abbr="n&otilde;">non</expan> di&longs;cedat. Si triangulum illud in plano <lb/>fixo moueatur, donec AB perueniat ad CF, mota e&shy;<lb/>rit vis D nutu &longs;uo tant&ugrave;m, quanta e&longs;t linea BC, vis ve&shy;<lb/>r&ograve; E tantum, quanta e&longs;t linea AB. C&ugrave;m autem po&longs;&longs;it <lb/>in infinitum augeri &amp; minui, laterum illorum pro&shy;<lb/>portio, po&longs;&longs;unt etiam duorum illorum <expan abbr="extremor&utilde;">extremorum</expan> <lb/>motus in data ratione con&longs;titui. Quanta enim erit <lb/>BC ad AB, tantus erit motus vis D ad motum vis E: <lb/>ergo &amp; in hoc medio primum lemma no&longs;trum de&shy;<lb/>mon&longs;tratum e&longs;t. </s> <figure id="fig4"></figure><lb/>tia triangulus ABC, cuius angulus B <lb/>rectus &longs;it, latus ver&ograve; illum &longs;ubtendens <lb/>&longs;it AC, incumb&aacute;tque vis D lateri AB, <lb/>vis ver&ograve; E lateri AC, &longs;itque vis D nutus <lb/>linea BC, vis ver&ograve; E nutus &longs;it linea AB, erigat&uacute;rque &agrave; <lb/>puncto C linea CF <expan abbr="perp&etilde;dicularis">perpendicularis</expan> ad BC &aelig;qualis AB, <lb/>&agrave; qua vis E <expan abbr="n&otilde;">non</expan> di&longs;cedat. Si triangulum illud in plano <lb/>fixo moueatur, donec AB perueniat ad CF, mota e&shy;<lb/>rit vis D nutu &longs;uo tant&ugrave;m, quanta e&longs;t linea BC, vis ve&shy;<lb/>r&ograve; E tantum, quanta e&longs;t linea AB. C&ugrave;m autem po&longs;&longs;it <lb/>in infinitum augeri &amp; minui, laterum illorum pro&shy;<lb/>portio, po&longs;&longs;unt etiam duorum illorum <expan abbr="extremor&utilde;">extremorum</expan> <lb/>motus in data ratione con&longs;titui. Quanta enim erit <lb/>BC ad AB, tantus erit motus vis D ad motum vis E: <lb/>ergo &amp; in hoc medio primum lemma no&longs;trum de&shy;<lb/>mon&longs;tratum e&longs;t. </s>
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 <s>In hoc autem medij genere hoc diuer&longs;um ab <lb/>aliis mediis accidit, qu&ograve;d non tam facil&egrave; vtrin&shy;<lb/>que motus eo cietur, ac in illis, in quibus &longs;i virium <lb/>proportio momento vel &longs;uperet, vel minor &longs;it pro&shy;<lb/>portione motus <expan abbr="extremor&utilde;">extremorum</expan> medij, tum motus hinc <lb/>vel inde cietur. Atqui in hoc propter &longs;uperficie&shy;<lb/>rum contactum, quarum pori vel a&longs;peritates &longs;e&shy;<lb/>&longs;e mutu&ograve; &longs;ubingrediuntur, &amp; ita inuicem adh&aelig;&shy;<lb/>rent, fit vt &aelig;gri&ugrave;s cieatur motus, facili&ugrave;s ve- <s>In hoc autem medij genere hoc diuer&longs;um ab <lb/>aliis mediis accidit, qu&ograve;d non tam facil&egrave; vtrin&shy;<lb/>que motus eo cietur, ac in illis, in quibus &longs;i virium <lb/>proportio momento vel &longs;uperet, vel minor &longs;it pro&shy;<lb/>portione motus <expan abbr="extremor&utilde;">extremorum</expan> medij, tum motus hinc <lb/>vel inde cietur. Atqui in hoc propter &longs;uperficie&shy;<lb/>rum contactum, quarum pori vel a&longs;peritates &longs;e&shy;<lb/>&longs;e mutu&ograve; &longs;ubingrediuntur, &amp; ita inuicem adh&aelig;&shy;<lb/>rent, fit vt &aelig;gri&ugrave;s cieatur motus, facili&ugrave;s ve-

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