Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001013">
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              Mathematicas facultates habere demonſtrationes perfectiſſimas, quod
                <lb/>
              ageometreti negare ſolent, ſed audacter aiunt exempla Ariſt. non eſſe vera:
                <lb/>
                <expan abbr="neq;">neque</expan>
              requiri veritatem exemplorum; in
                <expan abbr="quorũ">quorum</expan>
                <expan abbr="vtroq;">vtroque</expan>
              peccant, nam dictum
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              illud vſurpari ſolet, & debet de exemplis moralibus. </s>
              <s id="s.001014">at vero requiri confor­
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              mitatem exemplorum cum regulis traditis, nemo ſanæ mentis dubitabit.
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              </s>
              <s id="s.001015">Verum iſti confundunt conformitatem cum veritate. </s>
              <s id="s.001016">Veritas exemplo tunc
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              ineſt, quando illud, quod in exemplo narratur, verè extitit, vt ſi quis in
                <lb/>
              exemplum pudicitiæ afferret hiſtoriam Ioſephi,
                <expan abbr="verũ">verum</expan>
              iſtud eſſet exemplum.
                <lb/>
              </s>
              <s id="s.001017">quæ veritas in exemplis moralibus non ſemper eſt neceſſaria, talia exempla
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              ſunt ſæpè parabolæ, & fabulæ, quæ nunquam extiterunt, v. g. narratur ab
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              Ariſt. de quodam filio, qui patrem crudeliter traxerat, qui poſtea grandior
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              factus, cum filium procreaſſet, ab eodem pariter raptatus eſt ipſe, vſque ad
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              eundem locum, quo ipſe patrem ſuum impiè raptauerat. </s>
              <s id="s.001018">non eſt neceſſe, ta­
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              lem extitiſſe filium,
                <expan abbr="neq;">neque</expan>
              patrem. </s>
              <s id="s.001019">Verumtamen ſemper conformitas exem­
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              pli cum regulis, & præceptis, quæ traduntur neceſſaria eſt, alioquin exem­
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              pla deſtruerent id, quod præceptio conſtruit,
                <expan abbr="illiq́">illique</expan>
              contraria eſſet, quod om­
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              nino abſurdum foret. </s>
              <s id="s.001020">non ſecus, ac ſi quis vellet alium docere characteres
                <lb/>
              latinos,
                <expan abbr="illiq́">illique</expan>
              ; barbaros, quos Gothicos vocant in exemplum proponeret. </s>
              <s id="s.001021">re­
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              quiritur igitur ſemper in omni exemplo conformitas cum eo, quod doce­
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              tur; in moralibus tamen non ſemper requiritur veritas, vti diximus; Alij
                <lb/>
              verò dicunt non requiri in exemplis determinatam veritatem, ſed ſatis eſſe,
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              ſi exemplum verum ſit ſecundum opinionem aliquorum:
                <expan abbr="quorũ">quorum</expan>
              ſententiam
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              non improbamus. </s>
              <s id="s.001022">Exempla igitur ab Ariſt. paſſim ex mathematicis allata,
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              congrua,
                <expan abbr="conformiaq́">conformiaque</expan>
              ; omninò ſunt ipſius doctrinæ, aliter ipſum perpetuò
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              mentientem facimus. </s>
              <s id="s.001023">Poſtremò illud etiam eſt aduertendum, fortè Ariſt. in
                <lb/>
              præſenti textu ſpectaſſe
                <expan abbr="nõ">non</expan>
              ad hanc Euclidianam demonſtrationem, ſed po­
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              tius ad Pithagoricam. </s>
              <s id="s.001024">Pithagorei enim eam aliter, quamuis per idem me­
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              dium, ſcilicet à cauſa materiali, demonſtrabant; conſtruebant enim aliter,
                <lb/>
                <expan abbr="neq;">neque</expan>
              vlla vtebantur diuiſione. </s>
              <s id="s.001025">quod dictum velim propter nonnullos, qui ab
                <lb/>
              huiuſmodi diuiſionibus abhorrent,
                <expan abbr="timentq́">timentque</expan>
              ; ne demonſtrationis perfectio­
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              ni per eas plurimum derogetur. </s>
              <s id="s.001026">Pithagoreorum demonſtrationem vide
                <lb/>
              apud Clauium in ſcholio 32. primi Euclidis, quam ex Eudemo etiam Pro­
                <lb/>
              clus in comm. eiuſdem recitat.</s>
            </p>
            <p type="main">
              <s id="s.001027">
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              <s id="s.001028">
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              37</s>
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            <p type="main">
              <s id="s.001029">Ibidem
                <emph type="italics"/>
              (Sed quemadmodŭm harmonica per Arithmeticam)
                <emph.end type="italics"/>
              vide ſupra tex. 20.</s>
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              38</s>
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            <p type="main">
              <s id="s.001032">Ibidem
                <emph type="italics"/>
              (Demonſtratio autem non computatur in aliud genus; niſi, vt dictum
                <lb/>
              eſt geometricæ demonſtrationes in Perſpectiuas, aut Mechanicas, & arithmeticæ in
                <lb/>
              harmonicas)
                <emph.end type="italics"/>
              exempla ſubalternationis Perſpectiuæ, & Muſicæ in tex. 20. at­
                <lb/>
              tulimus; nunc Mechanicæ ſubalternationis, quam hic Ariſt. inſinuat, exem­
                <lb/>
              plum ſit illud, quod Archimedes prop. 14. primi Aequep. demonſtrat, ni­
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              mirum centrum grauitatis omnis trianguli eſſe punctum illud, in quo rectæ
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              lineæ ab angulis trianguli ad dimidia latera oppoſita ductæ concurrunt. </s>
              <s id="s.001033">ſit
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              triangulum A B C, à cuius angulis A, & B, ducantur duæ rectæ A D, B E, ita
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              vt bifariam ſecent latera A C, B C, in punctis D, & E, & concurrant in F.
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              </s>
              <s id="s.001034">Dico F, eſſe centrum grauitatis propoſiti trianguli. </s>
              <s id="s.001035">Quoniam enim in 13.
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              Aequep. probauit centrum grauitatis eſſe in ea linea, quæ ducta ab angulo
                <lb/>
              quouis ſecat oppoſitum latus bifariam, crit in linea A D,
                <expan abbr="centrũ">centrum</expan>
              </s>
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          </chap>
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    </archimedes>
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