Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003423">
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              Aliæ verò (quarum permultæ in decimo reperiun­
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              tur) quæ nec longitudine, nec potentia illi ſunt
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              commenſurabiles, irrationales appellantur, qua­
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              lis eſſet media proportionalis E F, inter duas A,
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              & C D, in præſenti figura ex 11. 10.</s>
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            <p type="main">
              <s id="s.003424">Sciendum præterea ex 37. 10. & ſequentibus,
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              quod ex duabus lineis rationalibus reſpectu rationalis expoſitæ. </s>
              <s id="s.003425">v. g. A, com­
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              menſurabilibus inuicem tantum potentia, componitur linea, quæ cum ea­
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                <figure id="id.009.01.204.2.jpg" place="text" xlink:href="009/01/204/2.jpg" number="125"/>
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              dem expoſita eſt irrationalis,
                <expan abbr="vocaturq́">vocaturque</expan>
              ; ex
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              duobus nominibus, ſiue Binomium, vt ſi ex
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              latere A, & diametro C D, componatur li­
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              nea A C D, erit irrationalis cum rationali
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              A,
                <expan abbr="diceturq́">diceturque</expan>
              ; binomium. </s>
              <s id="s.003426">Amplius ex 74. 10. & ſequentibus, ſi prædictum
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              minus nomen, ſiue minor linea A, detrahatur ex maiori nomine C D, vt re­
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              linquatur B D linea, erit ipſa reliqua B D, irrationalis, quam poſtea appel­
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              lant Apotomen, ſiue latinè Reſiduum.</s>
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            <p type="main">
              <s id="s.003427">Poſtremò, & hoc non ignorandum ex 43. 10. lineam, ſiue
                <expan abbr="binomiũ">binomium</expan>
              A C D,
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              non poſſe diuidi in alio puncto, præter C, in duas lineas, quæ ſint rationales
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              expoſitæ, & potentia tantum inuicem commenſurabiles.</s>
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              <s id="s.003428">His præmiſſis textum, ac rationem illorum explicabo in hunc modum.</s>
            </p>
            <p type="main">
              <s id="s.003429">Si quis faciat diuiduam lineam illam, quæ eſt communis
                <expan abbr="mẽſura">menſura</expan>
              omnium
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              commenſurabilium, ſequetur hoc abſurdum contra demonſtrationes 10.
                <lb/>
              quod nulla erit amplius linea rationalis, nec irrationalis, quia ſi communis
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              menſura diuidatur, tolletur ea de rerum natura; vnde non erit amplius in­
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              ter lineas ſymetria vlla, quare neque vllæ erunt rationales, eſſe enim ratio­
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              nale oritur ex commenſurabilitate. </s>
              <s id="s.003430">quare
                <expan abbr="neq;">neque</expan>
              extabit illa rationalis expo­
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              ſita, ad quam cæteræ relatæ dicuntur rationales, vel irrationales: quapro­
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              pter etiam irrationales nullæ erunt,
                <expan abbr="neq;">neque</expan>
              vlla alia erit ex prædictis, veluti
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              nec irrationalis illa, quam vocant Apotomen ex Binomio, ſiue ex duobus
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              nominibus, de qua Euclides propoſ. </s>
              <s id="s.003431">74. 10. & ſequentibus pertractat.</s>
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              <s id="s.003432">Notandum in verſu illo
                <emph type="italics"/>
              (Apotomen ex duobus nominibus compoſitam)
                <emph.end type="italics"/>
              vni­
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              ca voce illa
                <emph type="italics"/>
              (Compoſitam)
                <emph.end type="italics"/>
              addita ab Interprete Iatino, quæ non extat in tex.
                <lb/>
              græco, magnum Ariſtoteli imponi erratum, cum hac ratione dicat apoto­
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              men ex duobus nominibus eſſe compoſitam, quod falſiſſimum eſt. </s>
              <s id="s.003433">Apotome
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              enim, vt ſupra dictum eſt, ne dum ex duobus nominibus conſtat, verum ip­
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              ſa eſt reſiduum lineæ maioris, ſi minor ab ipſa detrahatur. </s>
              <s id="s.003434">Verumenimuero
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              vox illa
                <emph type="italics"/>
              (Compoſitam)
                <emph.end type="italics"/>
              in nullo codice reperitur, quare pro arbitrio, atque
                <lb/>
              ex Geometriæ inſcitia addita, tolli debet, ne tantæ inſcitiæ Ariſt. ipſe re­
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              darguatur. </s>
              <s id="s.003435">hæc in hunc locum ſufficiant.</s>
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              280</s>
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              <s id="s.003438">Quartus locus
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              (Quod verò de commenſurabilibus lineis poſtremò dicunt, om­
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              nes vna quadam, & eadem menſura oportere menſurari, falſum eſt admodum, &
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              nequaquam Mathematicorum ſuppoſitionibus concordat. </s>
              <s id="s.003439">non enim ita ſupponunt
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              Geometræ,
                <expan abbr="neq;">neque</expan>
              vtile ipſis iſtud foret, imò potius aduerſaretur, lineas omnes com­
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              menſurabiles eſſe, & omnium commenſurabilium linearum communem menſuram
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              exiſtimare. </s>
              <s id="s.003440">quamobrem ridiculum eſt eos, qui dicunt ſe demonstrare ex Geometra­
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              rum decretis, & ex quibus Mathematici docent in contentioſam pariter, ac falla­
                <emph.end type="italics"/>
              </s>
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          </chap>
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