Biancani, Giuseppe, Aristotelis loca mathematica, 1615
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              rum, ſiue dicas quadrata
                <expan abbr="quoq;">quoque</expan>
              earum eſſe commenſurabilia, v. g. linea dua­
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              rum vnciarum, & linea trium vnciarum ſunt
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              commenſurabiles longitudine, & potentia,
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              quia potentia lineæ duarum vnciarum, ſiue
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                <expan abbr="quadratũ">quadratum</expan>
              , eſt quatuor vnciarum ſuperficia­
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              lium: & quadratum lineæ trium vnciarum,
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              eſt nouem vnciarum quadratarum, vt patet
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              in figuris, quorum quadratorum communis
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              menſura eſt vncia vna quadrata. </s>
              <s id="s.003411">atque hanc
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              illi nullo modo diuidi poſſe contendebant.</s>
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              279</s>
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              <s id="s.003414">Tertius locus
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              (Præterea ſi quis communem ſtatam, ac determinatam menſu­
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              ram faciat diuiduam, non erit amplius in rerum natura linea vlla rationalis, aut
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              irrationalis, reſpectu expoſitæ, ac determinatæ lineæ; neque aliarum vlla erit, de
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              quibus modo dictum eſt, veluti quam Apotomen vocant ex duobus nominibus. </s>
              <s id="s.003415">Ve­
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              rùm neque ſecundum ſe aliquam definitam naturam habebunt, ſed collatæ ſibi ipſis
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              tam rationales, quàm irrationales erunt omnes.
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              <s id="s.003416">Hæc eſt alia eorumdem ratio ad idem comprobandum: quam, vt benè
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              percipiamus, nonnulla prius ex definitionibus 10. Elem. ſunt explicanda:
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              vt quæ nam ſint lineæ rationales, quæ irrationales, quæ ex binis nomini­
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              bus, quæ Apotomæ.</s>
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              <s id="s.003417">Propoſita igitur linea quapiam, v. g. trium palmorum qualis eſt linea A,
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              poſſunt inueniri quamplurimæ lineæ, quarum aliæ ſint illi longitudine com­
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              menſurabiles, ſiue quæ cum expoſita A, ha­
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              beant communem menſuram. </s>
              <s id="s.003418">v. g. linea B,
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                <expan abbr="quinq;">quinque</expan>
              palmorum eſt commenſurabilis lineæ
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              A, quia vtramque communis menſura vnius
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              palmi metitur: aliæ verò ſint eidem A, lon­
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              gitudine incommenſurabiles, qualis eſſet diameter C D, quadrati lineæ A,
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              quæ eſt cum latere A, incommenſurabilis ex vltima 10.</s>
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              <s id="s.003419">Cæterum lineam primò expoſitam, vt eſt in præ­
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              ſentia A, quod eſſet notæ quantitatis, Græci appella­
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              runt
                <foreign lang="grc">Ρήτην,</foreign>
              ideſt rationalem, quemadmodum Latini
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              eam appellant.</s>
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              <s id="s.003420">Linearum autem longitudine
                <expan abbr="incommẽſurabilium">incommenſurabilium</expan>
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              cum expoſita rationali A, aliæ ſunt, quæ tamen ſunt
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              commenſurabiles eidem potentia, ideſt conſtituunt
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              quadrata, quæ ſunt commenſurabilia quadrato ra­
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              tionali A, vt linea C D, cum ſit diameter quadrati li­
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              neæ A, quadratum exhibet, quod eſt duplum quadrati lineæ A, ex 47. primi,
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              quadratum autem lineæ A, eſt nouem, igitur quadratum eius duplum erit
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              octodecim, quadratum ſcilicet lineæ C D. octodecim autem, & nouem ſunt
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                <expan abbr="cõmenſurabilia">commenſurabilia</expan>
              communi vnitatis menſura, huiuſmodi lineæ dicuntur com­
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              menſurabiles potentia tantum, potentia. </s>
              <s id="s.003421">n. </s>
              <s id="s.003422">lineæ dicuntur
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              illius.</s>
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              <s id="s.003423">Quæ igitur rationali propoſitæ ſunt commenſurabiles aliquo modo, ſiue
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              longitudine, & potentia (
                <expan abbr="quæcunq;">quæcunque</expan>
              enim commenſurabilis eſt longitudine,
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              eſt etiam potentia) ſiue potentia ſolùm, rationales ipſæ quoque </s>
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