DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N16844" type="main">
              <s id="N16846">
                <pb xlink:href="077/01/172.jpg" pagenum="168"/>
              planè inſcriptæ eſſetinter puncta PH; vnde centrum ctiam
                <lb/>
              figurę in ABC ſimiliter planè inſcriptę inter KD eueniret;
                <lb/>
              eſſetquè centrum grauitatis portionis ABC vertici B propin­
                <lb/>
              quius, quam centrum figuræ planè inſcriptæ. </s>
              <s id="N16862">ideoquè
                <expan abbr="nullũ">nullum</expan>
                <lb/>
              accideret abſurdum. </s>
              <s id="N1686A">Quare ſi ſuppoſitum fuerit FP ad PH
                <lb/>
              eſſe, vt BK ad KD, tunc (vt eadem demonſtratio rei propo
                <lb/>
              ſitæ inſeruire poſſet) diuidenda eſſet diameter BD in
                <expan abbr="q;">〈que〉</expan>
              i­
                <lb/>
              ta vt BQ ad QD ſit, vt FL ad LH. & quoniam maio­
                <lb/>
                <arrow.to.target n="marg302"/>
              rem habet proportionem FL ad LH, quàm FP ad PH; ſiqui­
                <lb/>
              dem maior eſt FL, quàm FP, & PH maior, quàm LH. Vtverò
                <lb/>
              FL ad LH, ita eſt BQ ad QD; & vt FP ad PH. ita BK ad KD;
                <lb/>
              maiorem quo〈que〉 habebit proportionem BQ ad QD, quàm
                <lb/>
                <arrow.to.target n="marg303"/>
              BK ad KD. & componendo BD ad DQ maiorem, quàm ea
                <lb/>
                <arrow.to.target n="marg304"/>
              dem BD ad Dk. </s>
              <s id="N1688E">Quare maior eſt DK, quàm
                <expan abbr="Dq.">D〈que〉</expan>
              & ob id
                <lb/>
              punctum K propinquius erit vertici B, quàm
                <expan abbr="q.">〈que〉</expan>
              Deinde
                <lb/>
              planè inſcribenda eſſet figura in portione ABC, ita vt linea
                <lb/>
              inter centrum figuræ inſcriptæ, & centrum portionis minor
                <lb/>
              eſſet, quàm
                <expan abbr="Kq;">K〈que〉</expan>
              & reliqua quæ ſequuntur, ita tamen, vt quę
                <lb/>
              facta ſunt in EFG, fiant in ABC; & quæ in ABC,
                <expan abbr="fiãt">fiant</expan>
              in EFG.
                <lb/>
              oſtendeturquè centrum figurę inſcriptę in portione EFG pro
                <lb/>
              pinquius eſſe vertici F, quàm centrum grauitatis ipſius portio
                <lb/>
              nis EFG. quod quidem fieri non poteſt. </s>
              <s id="N168B0">Ex quibus perlpi­
                <lb/>
              cuum fit demonſtrationem eſſe vniuerſalem. </s>
              <s id="N168B4">& hanc
                <expan abbr="demõ">demom</expan>
                <lb/>
              ſtrationis partem Archimedem omiſiſſe, vt notam. </s>
              <s id="N168BC">Etvt an­
                <lb/>
              tea admonuimus, quòd centra grauitatis diametros in eadem
                <lb/>
              proportione diuidunt, omnibus parabolis competere intelli­
                <lb/>
              gendum eſt. </s>
              <s id="N168C4">ſiquidem omnes ſuntſimiles. </s>
              <s id="N168C6">quo demonſtrato,
                <lb/>
              in ſe〈que〉nti, quo in loco, & in qua diametri parte reperitur
                <expan abbr="cẽ">cem</expan>
                <lb/>
              trum grauitatis paraboles demonſtrat, quòd vt res perſpicua
                <lb/>
              reddatur; hæc priùs demonſtrabimus. </s>
            </p>
            <p id="N168D2" type="margin">
              <s id="N168D4">
                <margin.target id="marg302"/>
                <emph type="italics"/>
                <expan abbr="lẽma">lemma</expan>
              in
                <emph.end type="italics"/>
              4.
                <lb/>
                <emph type="italics"/>
              huius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N168E6" type="margin">
              <s id="N168E8">
                <margin.target id="marg303"/>
              28.
                <emph type="italics"/>
              quinti.
                <lb/>
              addi.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N168F3" type="margin">
              <s id="N168F5">
                <margin.target id="marg304"/>
              10.
                <emph type="italics"/>
              quinti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N168FE" type="head">
              <s id="N16900">LEMMA. I.</s>
            </p>
            <p id="N16902" type="main">
              <s id="N16904">Si magnitudo magnitudinis fuerit quadrupla, minorverò
                <lb/>
              magnitudo alterius magnitudinis ſit tripla, maior magnitu­
                <lb/>
              do vtrarum què ſimul magnitudinum tripla erit. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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