Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000803">
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              Ex Libro ſecundo Priorum.
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              12</s>
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              <s id="s.000806">Ex cap. 21.
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              (Quod faciunt, qui coalternas putant ſcribere, latent enim ipſe
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              ſe ipſos talia accipientes, quæ non est poſſibile monstrare uon exiſtentibus
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              coalternis)
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              Vult Ariſt. exemplo mathematico explicare, quid ſit pe­
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              titio principij. </s>
              <s id="s.000807">vbi per coalternas intelligit parallelas lineas, vox
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              enim græca
                <foreign lang="grc">παραλληλος,</foreign>
              idem ſignificat, ac mutuus, & coalternus. </s>
              <s id="s.000808">quoad
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              exempli explicationem vtor figura textibus apponi ſolita, quæ eſt præſens.
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                <figure id="id.009.01.042.1.jpg" place="text" xlink:href="009/01/042/1.jpg" number="11"/>
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              probat Euclides in 28. primi Elem. quod ſi
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              linea recta quædam, vti E F, cadens ſuper
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              duas rectas, vti ſunt A B, C D, fecerit angu­
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              los alternos ęquales, angulos
                <expan abbr="nimirũ">nimirum</expan>
              A G H,
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              G H D, ij enim dicuntur alterni; ſiue alios
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              duos, nimirum B G H, G H C, hi enim ſunt
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                <expan abbr="quoq;">quoque</expan>
              alterni; probat inquam has duas li­
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              neas A B, C D, eſſe inuicem parallelas. </s>
              <s id="s.000809">Iam ſi quis vellet probare, ſe duas
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              parallelas duxiſſe, hac ratione, quia ſcilicet faciunt prædictos angulos al­
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              ternos æquales; & probaret facere angulos alternos æquales, quia ſunt pa­
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              rallelæ, hic peteret principium, ideſt, illud, quod principio
                <expan abbr="probandũ">probandum</expan>
              erat,
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              afferret pro ratione, & cauſa, quod dicitur peti principium, quia tunc pe­
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              timus, vt concedatur nobis, id, quod principio, & primo omnium demon­
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              ſtrare propoſueramus. </s>
              <s id="s.000810">aduerte, quod characteres, qui ſunt in ſequentibus
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              verbis huius loci, non appellant characteres figuræ appoſitæ; in quo quidam
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              decepti, nullo pacto poterant locum hunc intelligere.</s>
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              13</s>
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              <s id="s.000813">Ex cap. 22. lib. 2. Priorum
                <emph type="italics"/>
              (Vt ſi volens monſtrare, quod diameter eſt incom­
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              menſ. argueret Zenonis rationem, quod non eſt moueri)
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              ſuperius ſecto 3. lib. 1.
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              fusè explicauimus hanc aſymmetriam, quam ſi quis vellet demonſtrare ea­
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              dem illa ratione, qua Zeno motum impugnabat, quia ſcilicet
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              com­
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              munis, quæ debet vtramque, quantitatem menſurare, debet in menſurando
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              infinitas partes pertranſire, nimirum medietates medietatum in infinitum,
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              eſt autem impoſſibile pertranſire infinitas huiuſmodi partes, & propterea
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              non poterit metiri,
                <expan abbr="neq;">neque</expan>
              vnam,
                <expan abbr="neq;">neque</expan>
              alteram ex
                <expan abbr="quãtitatibus">quantitatibus</expan>
              , quæ putaban­
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              tur commenſurabiles, afferret hic, inquit Ariſt. non cauſam pro cauſa.</s>
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              14</s>
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              <s id="s.000816">Ex eodem cap.
                <emph type="italics"/>
              (Quoniam idem
                <expan abbr="vtiq;">vtique</expan>
              falſum per plures petitiones accidere
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              nihil fortaſſe inconueniens, veluti coalternas coincidere; & ſi maior eſt extrinſecus
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              angulus intrinſeco; & ſi triangulus habet plures rectos duobus)
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              per plures poſi­
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              tiones ſubaudi falſas. </s>
              <s id="s.000817">per coalternas intellige lineas æquidiſtantes, ſeu pa­
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              rallelas, vt in ſuperiori cap. monuimus. </s>
              <s id="s.000818">Cæterum Euclides propoſ. </s>
              <s id="s.000819">28. pri­
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              mi Elem. oſtendit, quod ſi fuerint duæ parallelæ veluti in præcedenti figura,
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              A B, C D, ſuper quas alia recta E F, incidat, neceſſario faciet angulum ex­
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              trinſecum E G B, v. g. æqualem interno, & oppoſito, & ad eaſdem partes,
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              angulo videlicet G H D. ſi ergo inquit Ariſt ſupponamus iſtud falſum, an­
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              gulum ſcilicet E G B, externum eſſe maiorem angulo interno G H D, ſequi­
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              tur etiam falſum, videlicet lineas
                <expan abbr="æquidiſtãtes">æquidiſtantes</expan>
              A B, C D, concurrere. </s>
              <s id="s.000820">& pro­
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              batur conſequentia hoc modo, quia ſi angulus E G B, maior eſt angulo </s>
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