Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001215">
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              quod tamen non obſtat, quominus probare poſſit, aliquando poſſe
                <expan abbr="cõſtrni">conſtrui</expan>
              ,
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              & eſſe aliquod particulare triangulum, vt fit in prædicta demonſtratione,
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              Euclidis.</s>
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              71</s>
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              <s id="s.001218">Tex. 11.
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              (Manifeſtum autem, & ſic, propter quid eſt rectus in ſemicirculo)
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              affert exemplum demonſtrationis per cauſam materialem,
                <expan abbr="idq́">idque</expan>
              ; vti ſolet ex
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              Mathematicis petitum, eſt enim apud Euclidem 31. demonſtratio 3. Elem.
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              vbi ipſe oſtendit angulum in ſemicirculo eſſe rectum. </s>
              <s id="s.001219">Vbi aduertendum eſt
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              propoſitionem hanc 31. ab Euclide demonſtrari duobus modis; ex quibus
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              ſecundum innuit hoc loco Ariſt. cui aſcripta eſt figura ſimilis huic noſtræ;
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              in editione Clauiana. </s>
              <s id="s.001220">quod fortè non benè aduertens Iacobus Zabarella,
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              alioquin in his ſatis oculatus incidit in errorem, dicens, ſe nullo pacto vi­
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              dere medium Euclidianæ demonſtrationis eſſe cauſam materialem; quod
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              tamen nos mox aperiemus. </s>
              <s id="s.001221">per angulum in ſemicirculo intelligas eum, qui
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              fit à lineis ductis ab extremitatibus diametri, & ſimul in quoduis punctum
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                <figure id="id.009.01.065.1.jpg" place="text" xlink:href="009/01/065/1.jpg" number="32"/>
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              circumferentiæ coeuntibus, vt in figura
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              præſenti vides lineas A C, B C, ad C, pun­
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              ctum conuenire,
                <expan abbr="ibiq́">ibique</expan>
              ; facere angulum,
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              A C B, qui dicitur angulus in ſemicircu­
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              lo, quia deſcriptus eſt in ſemicirculo A­
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              C B.
                <expan abbr="eſtq́">eſtque</expan>
              ; ſanè mirabilis hæc ſemicirculi
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              proprietas, cum
                <expan abbr="vbicunq;">vbicunque</expan>
              punctum C, in
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              periphæria ſumptum fuerit, ſemper ta­
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              men angulus A C B, fiat rectus. </s>
              <s id="s.001222">quod Euclides eodem prorſus medio, quod
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              Ariſt. hic innuit, hoc modo demonſtrat. </s>
              <s id="s.001223">ducta enim recta D C, à centro D,
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              ad punctum C, exurgunt duo lſoſcelia triangula A D C, C D B, ergo per
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              5. primi, anguli D C A, D A C, ſunt æquales: pariter anguli D C B, D B C,
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              æquales ſunt. </s>
              <s id="s.001224">& quia per 32. primi, anguli D A C, D C A, ſimul ſunt æqua­
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              les angulo externo C D B, & inter ſe æquales, erit angulus A C D, dimidium
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              anguli C D B. eadem ratione probatur angulus D C B, eſſe dimidium an­
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              guli C D A. ergo totus angulus A C B, dimidium erit duorum angulorum
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              A D C, C D B, qui per 13. primi, ſunt vel recti, vel duobus rectis
                <expan abbr="æquiualẽt">æquiualent</expan>
              .
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              </s>
              <s id="s.001225">Sequitur igitur, angulum A C B, in ſemicirculo eſſe dimidium duorum re­
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              ctorum; & quia omnes recti ſunt æquales, ſequitur dimidium duorum re­
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              ctorum, nihil aliud eſſe, quam vnum rectum angulum, ergo angulus in ſe­
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              micirculo, cum ſit ſemiſſis duorum
                <expan abbr="rectorũ">rectorum</expan>
              , erit vnus rectus angules; quod
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              erat probandum. </s>
              <s id="s.001226">ex quibus vides medium illud, quod Ariſt. aſſumpſit, eſſe
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              omnino idem cum eo, quo Euclides vtitur, ſcilicet, eſſe dimidium duorum
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              rectorum, & propterea eſſe rectum: quod etiam medium in toto demon­
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              ſtrationis decurſu eſt vltimum, & principale, quod proximè concluſionem
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              attingit, & propterea dici meretur eſſe medium huius demonſtrationis.
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              </s>
              <s id="s.001227">Cæterum, quod medium iſtud ſit in genere cauſæ materialis, patet ex eo,
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              quod eſt, eſſe dimidium; nam eſſe dimidium, vel eſſe tertiam partem, & ſi­
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              milia, nihil aliud eſt, quam eſſe partem; eſſe autem partem eſt eſſe materiam
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              totius, etiam ex ſententia ipſius Ariſt. ex hac præterea materia conflatur
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              definitio minoris extremi, vel ſubiecti; dum dicitur, angulus in ſemicircu­
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              lo eſt dimidium duorum rectorum. </s>
              <s id="s.001228">ſyllogiſmus enim reducitur tandem ad </s>
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