Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.000943">
                <pb pagenum="51" xlink:href="009/01/051.jpg"/>
              dum quid ſit alterna proportio. </s>
              <s id="s.000944">Alternam igitur proportionem definit Eu­
                <lb/>
              clides definitione 12. quinti, ſic, eſt ſumptio antecedentis ad
                <expan abbr="antecedẽtem">antecedentem</expan>
              ,
                <lb/>
                <figure id="id.009.01.051.1.jpg" place="text" xlink:href="009/01/051/1.jpg" number="20"/>
                <lb/>
              & conſequentis ad conſequentem. </s>
              <s id="s.000945">Explico, exponantur qua­
                <lb/>
              tuor quantitates proportionales, v.g. vt 6. ad 3. ita ſint 4. ad
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              2. ſi igitur argumentemur ſic, vt 6. ad 3. ita 4. ad 2. ergo al­
                <lb/>
              ternatim erit, vt 6. ad 4. ita 3. ad 2. ſiue dixerimus, vt pri­
                <lb/>
              mum ad ſecundum, ita tertium ad quartum, igitur alterna­
                <lb/>
              tim erit, vt primum ad tertium, ita ſecundum ad quartum: valebit conſe­
                <lb/>
              quentia; quæ quidem probatur deinde propoſitione 16. quinti de magnitu­
                <lb/>
              dinibus, hoc eſt in vniuerſum de lineis, ſuperficiebus, & ſolidis. </s>
              <s id="s.000946">quando igi­
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              tur Ariſt. ait, monſtramus proportionale, ideſt, quaſuis quatuor quantita­
                <lb/>
              tes proportionales, habere hanc proprietatem, vt ſint etiam alternatim
                <lb/>
              proportionales, & non monſtramus vnica demonſtratione de omni quouis
                <lb/>
              proportionali, ſed ſeparatim de magnitudinibus in 16. quinti, de numeris
                <lb/>
              in 13. ſeptimi, & ſeorſum de temporibus in aſtronomia, vel phyſica; hoc
                <lb/>
              modo non oſtendimus vniuerſaliter de primo ſubiecto, quia talis affectio
                <lb/>
              conuenit ſingulis, non vt numeri, aut magnitudines, aut tempora ſunt, ſed
                <lb/>
              ſecundum quandam naturam illis omnibus communem, cui primò illa paſ­
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              ſio debetur; quæ quidem natura communis nomine caret, & propterea eſt
                <lb/>
              cauſa erroris.</s>
            </p>
            <p type="main">
              <s id="s.000947">
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              </s>
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            <p type="margin">
              <s id="s.000948">
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              29</s>
            </p>
            <p type="main">
              <s id="s.000949">
                <emph type="italics"/>
              Nunc autem vniuerſaliter demonſtratur)
                <emph.end type="italics"/>
              nuſquam apud Mathematicos in­
                <lb/>
              uenio hanc demonſtrationem vniuerſalem de illo communi omnibus præ­
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              dictis, quare dicendum cum Zabarella, illud, nunc, eſſe intelligendum ſic,
                <lb/>
              nunc autem, ideſt, in præſentia autem deberet vniuerſaliter demonſtrari,
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              quod tamen cum non fiat, contingit nos decipi putantes vniuerſaliter de­
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              monſtraſſe. </s>
              <s id="s.000950">vel dicendum iſtud verificari tantum de lineis, ſuperficiebus, &
                <lb/>
              ſolidis, de quibus ſimul in vnica natura communi, quæ eſt magnitudo, de­
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              monſtratur in 16. quinti vniuerſaliter. </s>
              <s id="s.000951">
                <expan abbr="atq;">atque</expan>
              hoc modo explicatum eſt exem­
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              plum ſecundi erroris, qui verbis illis
                <emph type="italics"/>
              (Vel ſit quidem, ſed innominatum ſit in
                <lb/>
              rebus ſpecie differentibus)
                <emph.end type="italics"/>
              continebatur.</s>
            </p>
            <p type="main">
              <s id="s.000952">
                <arrow.to.target n="marg30"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000953">
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              30</s>
            </p>
            <p type="main">
              <s id="s.000954">Ibidem
                <emph type="italics"/>
              (Propter hoc ſi quis monſtrauerit ſingulum triangulum. </s>
              <s id="s.000955">demonſtratio­
                <lb/>
              ne aut vna, aut altera, quod duos rectos habet vnumquodque,
                <expan abbr="æquilateiũ">æquilaterum</expan>
              ſeorſum,
                <lb/>
              & ſcalenum, & æquicrus: nondum nouit triangulum, quod duobus rectis, niſi ſo­
                <lb/>
              phiſtico modo,
                <expan abbr="neq;">neque</expan>
              vniuerſaliter triangulum,
                <expan abbr="neq;">neque</expan>
              ſi vllum eſt præter prædicta
                <lb/>
              triangulum alterum. </s>
              <s id="s.000956">non enim ſecundum quod triangulum,
                <expan abbr="neq;">neque</expan>
              omne triangulum,
                <lb/>
              niſi ſecundum numerum, ſecundum ſpeciem autem non omne; & ſi nullum eſt, quod
                <lb/>
              non nouit)
                <emph.end type="italics"/>
              vltimo loco ponit exemplum primi erroris, quem ſupra verbis il­
                <lb/>
              lis
                <emph type="italics"/>
              (Quando vel nihil ſit accipere ſuperius, præter ſingulare)
                <emph.end type="italics"/>
              expreſſerat, quod,
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              vt benè intelligamus, opus eſt ea, legere, quæ libro primo Priorum ſecto 3.
                <lb/>
              cap. 1. ſcripſimus de proprietate illa trianguli, quod ſcilicet habet tres an­
                <lb/>
              gulos æquales duobus rectis angulis, quibus præmiſſis, ſic deinde locum
                <lb/>
              hunc interpretaberis; Propter hoc, quod præcedenti textu dictum eſt; no­
                <lb/>
              tandum in primo errore vniuerſale, tanquam ſi non eſſet vniuerſale oſten­
                <lb/>
              ditur de ſingulari, ſi quis igitur monſtrauerit ſingillatim de
                <expan abbr="vnoquoq;">vnoquoque</expan>
              trian­
                <lb/>
              gulo in ſingulari, ſcilicet de vno æquilatero, tantum, & de vno Scaleno, &
                <lb/>
              de vno Iſoſcele, ſeparatim, vtens aut eadem demonſtratione dum de
                <expan abbr="vnoq́">vnoque</expan>
              ; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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