Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000852">
                <pb pagenum="45" xlink:href="009/01/045.jpg"/>
                <figure id="id.009.01.045.1.jpg" place="text" xlink:href="009/01/045/1.jpg" number="13"/>
                <lb/>
              angulo recto C, ergo quadratum eius ex corol­
                <lb/>
              lario 47. primi, duplum erit quadrati B C, quare
                <lb/>
              etiam circulus B C D F, duplus erit circuli A B­
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              G C, per 2. duodecimi, & ſemicirculus B C D,
                <lb/>
              duplus erit ſemicirculi B A C: & quadrans B E­
                <lb/>
              C G, æqualis erit ſemicirculo B A C: ablato igi­
                <lb/>
              tur communi ſegmento B E C H, remanet lunu­
                <lb/>
              la B A C E, æqualis triangulo B C G, quod trian­
                <lb/>
              gulum ſi per vltimam ſecundi quadretur, erit lu­
                <lb/>
              nula B A C, conſequenter quadrata. </s>
              <s id="s.000853">
                <expan abbr="hucuſq;">hucuſque</expan>
              be­
                <lb/>
              nè procedit Hippocrates. </s>
              <s id="s.000854">ſed vt reliquum circu­
                <lb/>
              li quadret, ſic pergit, ponatur recta L M, dupla
                <lb/>
              ipſius B C, ſupra quam ſemicirculus deſcribatur
                <lb/>
                <figure id="id.009.01.045.2.jpg" place="text" xlink:href="009/01/045/2.jpg" number="14"/>
                <lb/>
              L O M, cui inſcribatur hexagoni
                <lb/>
              æquilateri dimidium L Q S M, & ſu­
                <lb/>
              per tribus hexagoni lateribus, ſint
                <lb/>
              tres ſemicirculi, vt in figura. </s>
              <s id="s.000855">&
                <expan abbr="quo-niã">quo­
                  <lb/>
                niam</expan>
              diameter L M, dupla eſt
                <expan abbr="vniuſ-cuiuſq;">vniuſ­
                  <lb/>
                cuiuſque</expan>
                <expan abbr="diametrorũ">diametrorum</expan>
              B C, L Q, Q S,
                <lb/>
              S M, erit ſemicirculus L O M, ęqua­
                <lb/>
              lis quatuor ſemicirculis prædictis
                <lb/>
              per 2. duodecimi, & per 4. ſecundi
                <lb/>
              ablatis igitur tribus
                <expan abbr="ſegmẽtis">ſegmentis</expan>
              com­
                <lb/>
              munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, æquale ſe­
                <lb/>
              micirculo B A C, & tribus lunulis L H Q N, Q R S O, S X M P, abſcindan­
                <lb/>
              tur
                <expan abbr="itaq;">itaque</expan>
              de trapezio tria triangula æqualia tribus lunulis, eo modo, quo ſu­
                <lb/>
              pra in prima figura factum eſt, & quod relinquetur æquale erit ſemicirculo
                <lb/>
              B A C. quod deinde quadretur per vlt. </s>
              <s id="s.000856">ſecundi, ſed aduerte, quod quando
                <lb/>
              ait, abſcindantur de trapezio tria triangula æqualia lunulis, eo modo, quo
                <lb/>
              ſupra, committit deceptionem, quia eodem modo, quo ſupra minimè id fa­
                <lb/>
              cere poſſumus, quia in ſuperiori figura triangula erant conſtituta ſuper la­
                <lb/>
              tus B C, quadrati B C D F, intra circulum deſcripti, qui circulus facit cum
                <lb/>
              B C, maius
                <expan abbr="ſegmentũ">ſegmentum</expan>
              , quam faciat ſemicirculus L O M, cum lateribus L Q,
                <lb/>
              Q S, S M. & propterea ſemicirculus iſte non habet eandem proportionem
                <lb/>
              ad vnamquamque lunularum ſuarum, quam habet ſemicirculus ſuperior
                <lb/>
              B C D, ad lunulam B A C E.
                <expan abbr="atq;">atque</expan>
              hæc eſt fallacia, quam authorem ſuum mi­
                <lb/>
              nimè latuiſſe putandum, cuius Ariſt. ſæpius mentionem in ſequentibus fa­
                <lb/>
              ciet : quì enim fieri poteſt, vt tam acutus inuentor, adeo manifeſtum erro­
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              rem non vidiſſet, verum propter adinuenti excellentiam, authori ſuo pla­
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              cuit paralogyſmus. </s>
              <s id="s.000857">mirabilis tamen ſemper habita eſt illa ſuperior lunulæ
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              quadratio. </s>
              <s id="s.000858">Ex quibus ſatis clara eſſe poſſunt ea, quæ ad
                <expan abbr="Mathematicũ">Mathematicum</expan>
              per­
                <lb/>
              tinent, ad locum hunc de Abductione declarandum. </s>
              <s id="s.000859">facta eſt igitur abdu­
                <lb/>
              ctio ab Hippocrate in quadratione trium poſteriorum lunularum, in qua­
                <lb/>
              rum quadratione diu immoratus, nunquam niſi cum paralogyſmo quadra­
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              re valuit. </s>
              <s id="s.000860">Hæc pluribus, vt ſequentibus etiam textibus, in quibus huius te­
                <lb/>
              tragoniſmi fit mentio ſatisfacere poſſimus. </s>
              <s id="s.000861">Hippocrates iſte Chius eſt alter </s>
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