Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000956">
                <pb pagenum="52" xlink:href="009/01/052.jpg"/>
              ſeparatim oſtendit, aut vtens diuerſis demonſtrationibus, vna pro æquila­
                <lb/>
              tero, altera pro Iſoſcele, tertia pro Scaleno, oſtendens, quod
                <expan abbr="vnumquodq;">vnumquodque</expan>
                <lb/>
              illorum habet tres angules æquales duobus rectis angulis; iſte nondum no­
                <lb/>
              uit triangulum omne habere talem affectionem, niſi modo ſophiſtico, quia
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              non cognoſcit hanc affectionem illis
                <expan abbr="cõpetere">competere</expan>
              propter naturam illam com­
                <lb/>
              munem trianguli, cui primo, & per ſe competit; & neque vniuerſaliter co­
                <lb/>
              gnoſcit triangulum omne eſſe tale, etiam ſi nullum aliud reperiatur trian­
                <lb/>
              gulum, præter illud æquilaterum, vel illud Iſoſceles, vel illud Scalenum, de
                <lb/>
              quibus ſeparatim
                <expan abbr="demõſtrauit">demonſtrauit</expan>
              , & ſecundum numerum, ideſt de vnoquoque,
                <lb/>
              quatenus eſt vnum numero. </s>
              <s id="s.000957">non nouit autem ſecundum ſpeciem, idest fecun­
                <lb/>
              dum naturam, & formam communem illis tribus indiuiduis, quæ eſt natu­
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              ra trianguli. </s>
              <s id="s.000958">hoc autem eſſe exemplum primi erroris manifeſtè conuincitur,
                <lb/>
              tum ex verbis illis, quando nihil ſit ſuperius, præter ſingulare, tum ex hu­
                <lb/>
              ius textus verbis illis
                <emph type="italics"/>
              (Singulum triangulum)
                <emph.end type="italics"/>
              & ex illis
                <emph type="italics"/>
              (Niſi ſecundum nume­
                <lb/>
              rum)
                <emph.end type="italics"/>
              ideſt, niſi de vno, quod ſit vnum numero. </s>
              <s id="s.000959">propterea nos de ſingulari
                <lb/>
              triangulo omiſſa Zabarellæ ſententia explicauimus tandem in confirma­
                <lb/>
              tionem noſtræ expoſitionis in hæc tria errata illud non omittendum, ſatius
                <lb/>
              eſſe dicere, Ariſt. attuliſſe pro tribus erratis tria exempla ordine retrogra­
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              do, quàm, quod facit Zabarella, primum eſſe pro tertio, ſecundum pro pri­
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              mo, tertium verò pro ſecundo; eo enim modo, Ariſt. confuſionem nulla ra­
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              tione, imò contra omnem rationem imponimus.</s>
            </p>
            <p type="main">
              <s id="s.000960">
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            <p type="margin">
              <s id="s.000961">
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              31</s>
            </p>
            <p type="main">
              <s id="s.000962">Textu 14. continet quidem quædam mathematica, ſed ferè eadem cum
                <lb/>
              ſuperioribus, quæ quia tum ex prædictis facile intelligi poſſunt, tum quia
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              benè ab expoſitoribus explicantur, ne actum agamus, prætermittimus.</s>
            </p>
            <p type="main">
              <s id="s.000963">
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              </s>
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            <p type="margin">
              <s id="s.000964">
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              32</s>
            </p>
            <p type="main">
              <s id="s.000965">Tex. 20.
                <emph type="italics"/>
              (Niſi magnitudines numeri ſint)
                <emph.end type="italics"/>
              hoc eſt, niſi magnitudines ſint di­
                <lb/>
              feretæ, ita vt cadant ſub numerum, vt ſi linea quæpiam diuidatur in partes
                <lb/>
              decem, vel duodecim, tunc euadit quantitas diſcreta, ſiue numerus. </s>
              <s id="s.000966">& tunc
                <lb/>
              linea numerus eſt. </s>
              <s id="s.000967">idem de ſuperficie, ac ſolido intelligendum.</s>
            </p>
            <p type="main">
              <s id="s.000968">
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              </s>
            </p>
            <p type="margin">
              <s id="s.000969">
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              33</s>
            </p>
            <p type="main">
              <s id="s.000970">Ibidem
                <emph type="italics"/>
              (Propter hoc Geometriæ non licet monſtrare, quod contrariorum vna
                <lb/>
              eſe ſcientia, ſed neque quod duo cubi cubus)
                <emph.end type="italics"/>
              quo ad verba illa, duo cubi cubus,
                <lb/>
              quæ ad nos pertinent, vult Ariſt. docere, quod non debet Geometra oſten­
                <lb/>
              dere numerorum affectiones (per cubos enim intelligit numeros quoſdam
                <lb/>
              ſic dictos, vt paulo poſt oſtendam) vt ſi quis vellet geometricè oſtendere id,
                <lb/>
              quod oſtenditur in 4. noni Elem. ſcilicet, ſi cubus numerus cubum numerum
                <lb/>
              multiplicauerit, productus numerus erit pariter cubus. </s>
              <s id="s.000971">nonnulli latinorum
                <lb/>
              perperam textum hunc expoſuerunt putantes reperiri ſolummodo cubos
                <lb/>
              geometricos, at Euclides definit. </s>
              <s id="s.000972">19. ſeptimi, ſic arithmeticum cubum de­
                <lb/>
              finit, cubus numerus eſt, qui ſub tribus numeris æqualibus continetur, qua­
                <lb/>
              lis eſt. </s>
              <s id="s.000973">8. qui eſt ad inſtar cubi geometrici, & continetur ſub tribus binarijs
                <lb/>
              multiplicatis inuicem, quæ multiplicatio ſic inſtituitur, exponuntur tres bi­
                <lb/>
                <figure id="id.009.01.052.1.jpg" place="text" xlink:href="009/01/052/1.jpg" number="21"/>
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              narij, 2, 2, 2, primus ducitur in ſecundum, & producitur.
                <lb/>
              </s>
              <s id="s.000974">4. qui eſt numerus quadratus huius figuræ,
                <figure id="id.009.01.052.2.jpg" place="text" xlink:href="009/01/052/2.jpg" number="22"/>
              , deinde
                <lb/>
              tertius binarius ducitur in prædictum quadratum 4. & pro­
                <lb/>
              ducitur 8. qui dicitur cubus, quia ſi intelligantur duo qua­
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              ternarij, vnus ſupra alterum, vt in præſenti figura refe­
                <lb/>
              runt cubicam figuram, cuius tam longitudo, quam </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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