Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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        <body>
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            <p type="main">
              <s id="s.002080">
                <pb pagenum="119" xlink:href="009/01/119.jpg"/>
              linea N P L, cuius extrema puncta ſunt L, N, quæ data erunt, cum ſint ex­
                <lb/>
              trema lineæ K M, circumlatæ; & quemadmodum dabatur ſuperius punctum
                <lb/>
              M. eadem ratione ex Datis, dabitur punctum N, & L. quare etiam ſectio
                <lb/>
              N P L, quæ inter data puncta continetur, data erit ex 26. Datorum.</s>
            </p>
            <p type="main">
              <s id="s.002081">Illud nunc in memoriam
                <expan abbr="reuocãdum">reuocandum</expan>
              , quod paulò ante probaui, nimirum
                <lb/>
              proportionem linearum G M, K M, non poſſe ſeruari in alijs lineis, quæ ſint
                <lb/>
              in eodem plano trianguli G M K, ſi ducantur ab ijſdem punctis G, K. poteſt
                <lb/>
              tamen ſeruari in alijs duabus, quæ cadant in prædictum ambitum, ſiue
                <expan abbr="cir-cunferẽtiam">cir­
                  <lb/>
                cunferentiam</expan>
              L M N,
                <expan abbr="quæq́">quæque</expan>
              ; ſint in alio plano,
                <expan abbr="quã">quam</expan>
              in plano trianguli G M K,
                <lb/>
              quod tamen tranſeat per axem G K O,
                <expan abbr="ſitq́">ſitque</expan>
              ; vnum ex planis illis, de quibus
                <lb/>
              ſupra dictum eſt. </s>
              <s id="s.002082">Verumenimuerò ad quid probatio hæc? </s>
              <s id="s.002083">non poſſe duas
                <lb/>
              alias lineas in eodem plano, &c.? exiſtimo Ariſt. idcircò hoc probaſſe, quia
                <lb/>
              ſi aliæ duæ lineæ habentes eandem rationem, poſſent collocari in eodem
                <lb/>
              plano; eſſent
                <expan abbr="permutãdo">permutando</expan>
              illæ duæ (in priori figura) G R, R K.
                <expan abbr="vtraq;">vtraque</expan>
                <expan abbr="vtriq;">vtrique</expan>
                <lb/>
              æquales prioribus G M, M K, per quas videtur Iris, cum enim K R, ſit æqua­
                <lb/>
              lis ipſi K M, erit, & G M, æqualis ipſi G R, per 7. 5. & in eius ſcholio. </s>
              <s id="s.002084">qua­
                <lb/>
              re natura ageret tam per lineas breuiſſimas
                <expan abbr="agẽdo">agendo</expan>
              per has, quam per illas,
                <lb/>
                <expan abbr="hocq́">hocque</expan>
              ; pacto per has etiam Iris videri poſſet. </s>
              <s id="s.002085">cum ergò conſtet non poſſe has
                <lb/>
              eſſe prioribus proportionales, ſed maiorem, vel minorem, alteram illarum,
                <lb/>
              quàm ſit G M, ſequitur, quod non faciunt angulum æqualem angulo G M K,
                <lb/>
              ſub quo videtur Iris,
                <expan abbr="nimirũ">nimirum</expan>
              angulum G R K, qui ſit æqualis angulo G M K;
                <lb/>
              habet enim Iris hunc angulum determinatum, ita vt ſub maiori, vel mino­
                <lb/>
              ri videri nequeat; ex 10. Baptiſta Porta. </s>
              <s id="s.002086">ſi autem punctum R, eſſet infra M,
                <lb/>
              angulus G R K, eſſet minor angulo Iridis G M K, ſi verò ſupra eſſet maior
                <lb/>
              eodem, quod vel ad ſenſum patere poteſt in quouis circulo,
                <expan abbr="idq́">idque</expan>
              ; ſufficiat, ne
                <lb/>
              longior euadat hæc tractatio. </s>
              <s id="s.002087">Fortè etiam addi poteſt, quod alibi exiſten­
                <lb/>
              te puncto R, quàm in M, non poſſent anguli incidentiæ, & reflexionis eſſe
                <lb/>
              æquales, quæ cauſa eſſet cur ſub alio angulo, quam prædicto G M K, Iris
                <lb/>
              non appareret.</s>
            </p>
            <p type="main">
              <s id="s.002088">Prædicta omnia ſunt ſecundum Ariſtot. diſcurſum, & figurationem dicta,
                <lb/>
              nam ſecundum veritatem poſſunt in eadem nube conſtitui plures anguli
                <lb/>
              æquales, nec tamen in eodem orbe, ſed vnus ſupra
                <expan abbr="alterũ">alterum</expan>
              ; vt in figura præ­
                <lb/>
                <figure id="id.009.01.119.1.jpg" place="text" xlink:href="009/01/119/1.jpg" number="61"/>
                <lb/>
              ſenti, ſi nubes eſſet vbi B D.
                <lb/>
              oculus in C, Sol in A. eſſent
                <lb/>
              duo anguli A B C, A D C, æ­
                <lb/>
              quales per 33. 3. qui tamen
                <lb/>
              non ſunt in gyrum conſtituti,
                <lb/>
              poſſet igitur, per
                <expan abbr="illorũ">illorum</expan>
              vtrun­
                <lb/>
              que Sol Iridem efficere. </s>
              <s id="s.002089">atque
                <lb/>
              animaduerſio hęc videtur ma­
                <lb/>
              gni
                <expan abbr="momẽti">momenti</expan>
              eſſe, ad Iridis
                <expan abbr="de-monſtrationẽ">de­
                  <lb/>
                monſtrationem</expan>
              conſtituendam:
                <lb/>
              cum hinc vſitatæ demonſtra­
                <lb/>
              tiones infringatur. </s>
              <s id="s.002090">Fortè confugiendum eſt ad illud, quod Maurolycus, &
                <lb/>
              10. Baptiſta Porta obſeruarunt; debere
                <expan abbr="nimirũ">nimirum</expan>
              diſtantiam ab oculo ad cen­
                <lb/>
              trum Iridis eſſe æqualem altitudini, ſiue ſemidiametro Iridis. </s>
              <s id="s.002091">Ita vt non </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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