Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="head">
              <s id="s.005606">APPENDIX.</s>
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            <p type="main">
              <s id="s.005607">
                <emph type="italics"/>
              Placet nunc demum, vt melius àdhuc Mathematica­
                <lb/>
              rum natur a pateat, locaqué Arist. Mathematica ma­
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              gis illustrentur, Demonſtrationes primi Elemento­
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              rum Euclidis breuiter expendere, atque vnamquamque
                <lb/>
              ad ſuum demonſtrationis genus referre.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.005608">Prima igitur Demonſtratione Euclides oſtendit Triangulum il­
                <lb/>
              lud eo modo
                <expan abbr="cõſtrnctum">conſtructum</expan>
              eſſe æquilaterum, hoc proximo medio,
                <lb/>
              quia ſcilicet habet tria latera æqualia, quod medium eſt ipſius
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              ſubiecti demonſtrationis, ſiue trianguli æquilateri definitio:
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              quare hæc demonſtratio erit per cauſam formalem.</s>
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            <p type="main">
              <s id="s.005609">Secunda Demonſtratione oſtendit duas lineas eſſe æquales, quoniam am­
                <lb/>
              bæ ſunt vni tertiæ æquales, quæ ratio nititur illi axiomati, quæ ſunt æqualia
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              vni tertio, ſunt etiam inter ſe. </s>
              <s id="s.005610">eſt quidem demonſtratio oſtenſiua, ſed non
                <lb/>
              per cauſam, verum à ſigno: eſſe enim æquales vni tertiæ, eſt ſignum æquali­
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              tatis earum.</s>
            </p>
            <p type="main">
              <s id="s.005611">Tertia Demonſtratio eodem medio vtitur, quo ſecunda.</s>
            </p>
            <p type="main">
              <s id="s.005612">Quarta Demonſtratio oſtendit, primò de illis duobus triangulis, quod
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              habent baſes æquales, quia baſes congruunt ſibi mutuo. </s>
              <s id="s.005613">ſecundò, oſtendit
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              alios duos angulos eſſe æquales alijs duobus
                <expan abbr="vtrumq́">vtrumque</expan>
              ;
                <expan abbr="vtriq́">vtrique</expan>
              ; eadem ratione,
                <lb/>
              quia nimirum ſibi mutuò congruunt. </s>
              <s id="s.005614">ſi dixeris igitur, quod ſibi mutuò con­
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              gruere ſit definitio æqualis, erit demonſtratio per cauſam formalem; ſi au­
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              tem dixeris eſſe ſignum æqualitatis, erit à ſigno, & à poſteriori.</s>
            </p>
            <p type="main">
              <s id="s.005615">5. Oſtendit de Triangulo Iſoſcele, primò, quod Anguli, qui ſunt ad ba­
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              ſim, ſunt æquales, ratio eſt, quia ablatis æqualibus ab æqualibus ipſi ſunt
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              reliqui. </s>
              <s id="s.005616">Quæ quidem ratio etiam Ariſt. teſte, eſt per cauſam materialem;
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              nam eſſe dimidium, tertiam partem, duplum, reliquum, alicuius totius, &
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              ſimilia, nihil aliud eſt, quàm eſſe partes reſpectu totius; partes autem ſunt
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              materia, vt apertè docet Ariſt. tex. 3. lib. 5. Metaph. quem ſupra
                <expan abbr="cũ">cum</expan>
              alijs
                <expan abbr="ex-plicatũ">ex­
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                plicatum</expan>
              habes. </s>
              <s id="s.005617">ſecundò, demonſtrat de eodem Iſoſcele, angulos infra baſim
                <lb/>
              eſſe æquales, ratio, quia opponuntur ęqualibus lateribus
                <expan abbr="triangulorũ">triangulorum</expan>
              quar­
                <lb/>
              tæ præcedentis, quæ ratio videtur ſignum quoddam æqualitatis eorum eſſe.</s>
            </p>
            <p type="main">
              <s id="s.005618">6. Probat duo illa latera illius trianguli eſſe æqualia, ab impoſſibili, quia
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              ſequeretur partem eſſe æqualem toti.</s>
            </p>
            <p type="main">
              <s id="s.005619">7. Duas poſteriores lineas cum duabus prioribus neceſſariò coincidere
                <lb/>
              demonſtrat, quia aliter ſequeretur, vel partem eſſe æqualem toti: vel angu­
                <lb/>
              los lſolcelis ſub baſi eſſe inæquales, vel etiam eos, qui ſupra baſim, contra
                <lb/>
              quàm oſtenſum eſt in quinta.</s>
            </p>
            <p type="main">
              <s id="s.005620">8. Probat angulos illos fore æquales, quia congruunt: per 8. ſcilicet
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              axioma: videtur à ſigno.</s>
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          </chap>
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