Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001441">
                <pb pagenum="78" xlink:href="009/01/078.jpg"/>
              ſphæram in plana vlla reſoluere,
                <expan abbr="neq;">neque</expan>
              in alias plures ſuperficies, quia ſphæ­
                <lb/>
              ra ambitur vnica tantum ſuperficie ſphærica. </s>
              <s id="s.001442">quando verò ex planis corpo­
                <lb/>
              ra generant, vt facit Plato in Timæo, accipíunt primò triangulum æquila­
                <lb/>
              terum, & ex quatuor triangulis æquilateris ſimul compactis conficiunt py­
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              ramidem; & hoc modo alia ſolida à pluribus ſuperficiebus ambita conſti­
                <lb/>
              tuunt: verum hac ratione nullo modo poſſunt ſphæram componere, quia
                <lb/>
              vnica tantum,
                <expan abbr="eaq́">eaque</expan>
              ; ſphærica ſuperficie compræhenditur:
                <expan abbr="atq;">atque</expan>
              hoc pacto iſti
                <lb/>
              diuidentes, & componentes corpora fidem faciunt, ſphæram, cum ex nullis
                <lb/>
              componatur, ſolidorum eſſe primam.</s>
            </p>
            <p type="main">
              <s id="s.001443">
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            <p type="margin">
              <s id="s.001444">
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              106</s>
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            <p type="main">
              <s id="s.001445">Tex. 25.
                <emph type="italics"/>
              (Est autem, & ſecundum numerorum ordinem aſſignantibus, ſic po­
                <lb/>
              nentibus rationabiliſſimam, circulum quidem ſecundum vnum; triangulum autem
                <lb/>
              ſecundum dualitatem, quoniam duo recti. </s>
              <s id="s.001446">ſi autem ſecundum triangulum, vnum.
                <lb/>
              </s>
              <s id="s.001447">circulus non erit figura)
                <emph.end type="italics"/>
              In ordine figurarum conueniens eſt, inquit, primam
                <lb/>
              facere circulum propter ſimpliciſsimam ipſius naturam, cum vnica, ac per­
                <lb/>
              fecta circulari linea comprehendatur:
                <expan abbr="Triangulũ">Triangulum</expan>
              verò ſecundam, quoniam
                <lb/>
              duo anguli recti, ideſt, quia triangulum habet tres angulos æquales duobus
                <lb/>
              rectis angulis; quod fusè explicatum eſt lib. 1. Priorum, ſecto 3. cap. 1. De­
                <lb/>
              mum ſi primum locum dederimus triangulo, nullus alius remanet pro cir­
                <lb/>
              culo, quod eſt inconueniens, ergo circulus prima figura erit.</s>
            </p>
            <p type="main">
              <s id="s.001448">
                <arrow.to.target n="marg107"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001449">
                <margin.target id="marg107"/>
              107</s>
            </p>
            <p type="main">
              <s id="s.001450">Tex. 31.
                <emph type="italics"/>
              (At verò, quod aquæ ſuperficies talis ſit, manifeſtum eſt hac ſuppoſi­
                <lb/>
              tione ſumpta, quod apta natura eſt ſemper confluere aqua ad magis concauum: ma­
                <lb/>
              gis autem concauum eſt, quod centro propinquius est. </s>
              <s id="s.001451">ducantur ergo ex centro A,
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.009.01.078.1.jpg" place="text" xlink:href="009/01/078/1.jpg" number="43"/>
                <lb/>
                <emph type="italics"/>
              linea A B, & linea A C, & producatur, in qua B C,
                <lb/>
              ducta igitur ad baſim linea, in qua A D, minor eſt eis,
                <lb/>
              quæ ex centro. </s>
              <s id="s.001452">magis igitur concauus locus eſt, quare
                <lb/>
              influet aqua, donec
                <expan abbr="vtiq;">vtique</expan>
              æquetur. </s>
              <s id="s.001453">æqualis eſt autem eis,
                <lb/>
              quæ ex centro linea A E, quare neceſſe eſt apud eas, quæ
                <lb/>
              ex centro, eſſe aquam, tunc enim quieſcet. </s>
              <s id="s.001454">linea autem,
                <lb/>
              quæ eas, quæ ex centro tangit, circularis eſt, ſphærica
                <lb/>
              igitur aquæ ſuperficies eſt, in qua B E C.)
                <emph.end type="italics"/>
              toto hoc
                <lb/>
              textu lineari demonſtratione probat aquæ manen­
                <lb/>
              tis ſuperficiem eſſe ſphæricam: quæ demonſtratio
                <lb/>
              perſpicua euadit, ſi figura, quæ in codicibus tam
                <lb/>
              græcis, quam latinis,
                <expan abbr="atq;">atque</expan>
              etiam in commentarijs deſideratur, quemadmo­
                <lb/>
              dum fecimus, reſtituatur. </s>
              <s id="s.001455">ſit igitur in præcedenti figura A, centrum mundi,
                <lb/>
              ex quo educantur duæ rectæ lineæ æquales A B, A C, quæ deinde alia recta
                <lb/>
              B C, coniungantur. </s>
              <s id="s.001456">educatur
                <expan abbr="quoq;">quoque</expan>
              recta alia ex centro A, quæ pertingat
                <lb/>
              ad B C, quæ baſis eſt trianguli B A C, & producatur vlterius quantumlibet
                <lb/>
              in E. intelligatur demum circumferentia tranſire per puncta B, & C, quia
                <lb/>
              illæ duæ lineæ A B, A C, ſunt æquales, quæ circumferentia alteram A D, quæ
                <lb/>
              fuit protracta, ſecet in E. </s>
              <s id="s.001457">Iam ſic argumentatur: aqua natura ſua ſemper
                <lb/>
              defluit ad locum magis concauum, ideſt, ad loca centro A, terræ propin­
                <lb/>
              quiora, quale eſſet in figura locus D, reſpectu locorum B, & C, quia A D,
                <lb/>
              linea minor eſt ijs, quæ ex centro eductæ ſunt A B, A C. quapropter aqua
                <lb/>
              debet defluere ex B, ad D, vel ex C, ad idem D, donec pertingat ad E. qui
                <lb/>
              locus non eſt decliuior punctis B, & C. quare cum loca B, E, C, quæ ſunt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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