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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N13B2C" type="main">
              <s id="N13BA3">
                <pb xlink:href="077/01/105.jpg" pagenum="101"/>
              CAB æqualis; reliquus igitur angulus LFD reliquo HAB
                <lb/>
              æqualis exiſtit. </s>
              <s id="N13BAB">& quoniam ita eſt CF ad FA, vt CL ad
                <arrow.to.target n="marg142"/>
                <lb/>
              cùm ſint FL AH ęquidiſtantes. </s>
              <s id="N13BB2">CF verò dimidia eſt ipſius
                <lb/>
              CA, erit & CL ipſius quo〈que〉 CH dimidia. </s>
              <s id="N13BB6">at CD ipſius
                <lb/>
              CB dimidia exiſtit; erit igitur DL ipſi BH ęquidiſtans. </s>
              <s id="N13BBA">
                <arrow.to.target n="marg143"/>
                <lb/>
              propterea angulus LDC eſt ipſi HBC ęqualis, & LDF
                <arrow.to.target n="marg144"/>
                <lb/>
              HBA ęqualis. </s>
              <s id="N13BC6">cùm ſittotus CDF toti CBA ęqualis; anguli
                <lb/>
              verò ACH & HCB tam ſunt trianguli ABC, quàm FDC.
                <lb/>
                <emph type="italics"/>
              Obeandem autem rationem trianguli EBD centrum grauitatis est
                <expan abbr="pũ-">pun-</expan>
                <emph.end type="italics"/>
                <arrow.to.target n="marg145"/>
                <lb/>
                <emph type="italics"/>
              ctum K.
                <emph.end type="italics"/>
              ſimiliter enim oſtendetur punctum K in triangu­
                <lb/>
              lo EBD eſſe ſimiliter poſitum, vt H in triangulo ABC.
                <lb/>
                <emph type="italics"/>
              Quare magnitudinis ex vtriſquè triangulis EBD FDC compoſitæ
                <lb/>
              centrum grauitatis eſt in medietate lineæ
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              L. cum triangula EBD
                <emph.end type="italics"/>
                <arrow.to.target n="marg146"/>
                <lb/>
                <emph type="italics"/>
              FDC ſint æqualia.
                <emph.end type="italics"/>
              ſunt enim in ęqualibus baſibus BD
                <arrow.to.target n="marg147"/>
                <lb/>
              & in ijſdem parallelis EF BC, ſiquidem eſt AE ad EB,
                <arrow.to.target n="marg148"/>
                <lb/>
              AF ad FC. quippè cùm latera AB AC ſint bifariam diui­
                <lb/>
              ſa.
                <emph type="italics"/>
              medium veròipſius
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              L eſt punctum N; cùm ſit
                <emph.end type="italics"/>
              KE ipſi AH
                <lb/>
              ęquidiſtans, & ob id ſit
                <emph type="italics"/>
              BE ad EA, vt B
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              ad
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              H.
                <emph.end type="italics"/>
              & vt
                <arrow.to.target n="marg149"/>
                <lb/>
              ad EA, ita CF ad FA;
                <emph type="italics"/>
              vt autem CF ad FA, ſic CL ad LH.
                <emph.end type="italics"/>
                <lb/>
              quare vt BK ad KH, ita CL ad LH.
                <emph type="italics"/>
              Si autem hoc. </s>
              <s id="N13C34">æquidi-
                <emph.end type="italics"/>
                <arrow.to.target n="marg150"/>
                <lb/>
                <emph type="italics"/>
              ſtans est BC ipſi
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              L, & iuncta est DH, erit igitur BD ad DC, vt
                <emph.end type="italics"/>
                <arrow.to.target n="marg151"/>
                <lb/>
                <emph type="italics"/>
              KN ad NL.
                <emph.end type="italics"/>
              D verò medium eſt ipſius BC. ergo &
                <arrow.to.target n="marg152"/>
              me­
                <lb/>
              dium eſt ipſius KL.
                <emph type="italics"/>
              Quare magnitudinis ex vtriſquè
                <expan abbr="dictorũ">dictorum</expan>
              trian
                <lb/>
              gulorum
                <emph.end type="italics"/>
              EBD & FDC
                <emph type="italics"/>
              compoſitæ centrum
                <emph.end type="italics"/>
              grauitatis
                <emph type="italics"/>
              est punctum
                <emph.end type="italics"/>
                <arrow.to.target n="marg153"/>
                <lb/>
                <emph type="italics"/>
              N. parallelogrammi verò AEDF centrum grauitatis eſt punctum M,
                <emph.end type="italics"/>
                <lb/>
              vbi ſimiliter diametri concurrunt,
                <emph type="italics"/>
              ac propterea magnitudinis ex
                <emph.end type="italics"/>
                <arrow.to.target n="marg154"/>
                <lb/>
                <emph type="italics"/>
              omnibus
                <emph.end type="italics"/>
              triangulis EBD FDC vna
                <expan abbr="cũ">cum</expan>
              parallelogramo AEDF
                <lb/>
                <emph type="italics"/>
              compoſitæ centrum grauitatis eſt in linea MN. Verùm
                <emph.end type="italics"/>
                <expan abbr="triangulorũ">triangulorum</expan>
                <lb/>
              EBD FDC, ſimulquè parallelogrammi AEDF, hoc eſt totius
                <lb/>
                <emph type="italics"/>
              trianguli ABC grauitatis centrum est punctum H; linea igitur MN pro
                <emph.end type="italics"/>
                <arrow.to.target n="marg155"/>
                <lb/>
                <emph type="italics"/>
              ducta tranſibit per punctum H. quod eſſe non poteſt.
                <emph.end type="italics"/>
              etenim cùm ſit
                <lb/>
              KN ipſi BD æquidiſtans; erit BK ad KH, vt DN ad
                <lb/>
              NH: vt autem BK ad KH, ita eſt BE ad EA, & vt BE ad
                <lb/>
              EA, ita eſt DM ad MA, cùm ſit EM ipſi BD æquidiſtans.
                <lb/>
              erit igitur DM ad MA, vt DN ad NH. quare MN ipſi AH
                <lb/>
              eſt ęquidiſtans; ideoquè MN numquam cùm AH conueni­
                <lb/>
              re poteſt.
                <emph type="italics"/>
              Non est igitur
                <emph.end type="italics"/>
              punctum
                <emph type="italics"/>
              H centrum grauitatis trianguli
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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