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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <pb xlink:href="077/01/088.jpg" pagenum="84"/>
            <p id="N12F72" type="head">
              <s id="N12F74">PROPOSITIO. X.</s>
            </p>
            <p id="N12F76" type="main">
              <s id="N12F78">Omnis parallelogrammi centrum grauitatis
                <lb/>
              eſt punctum, in quo diametri coincidunt. </s>
            </p>
            <p id="N12F7C" type="main">
              <s id="N12F7E">
                <emph type="italics"/>
              Sit parallelogrammum
                <lb/>
              ABCD. & in ipſo ſit li­
                <lb/>
              nea EF
                <emph.end type="italics"/>
              bifariam
                <emph type="italics"/>
                <expan abbr="ſecãs">ſecans</expan>
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="fig35"/>
                <lb/>
                <emph type="italics"/>
              latera AB CD. itidem­
                <lb/>
              què ſit KL
                <expan abbr="ſecãs">ſecans</expan>
              AC BD
                <emph.end type="italics"/>
                <lb/>
              bifariam. </s>
              <s id="N12FA3">conueniant­
                <lb/>
              què EF kL in H.
                <emph type="italics"/>
              est
                <lb/>
              vti〈que〉 parallelogrammi
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg85"/>
                <emph type="italics"/>
              ABCD centrum grauita
                <lb/>
              tis in linea EF. hoc enim
                <lb/>
              oſtenſum eſt. </s>
              <s id="N12FBB">eadem verò de cauſa
                <emph.end type="italics"/>
              centrum grauitatis ipſius AD
                <emph type="italics"/>
              est
                <lb/>
              etiam in linea
                <emph.end type="italics"/>
              K
                <emph type="italics"/>
              L. quare punctum H
                <emph.end type="italics"/>
              parallelogrammi AD
                <emph type="italics"/>
              cen­
                <lb/>
              trum grauitatis existit. </s>
              <s id="N12FD3">Verùm in puncio H diametri parallelogram­
                <lb/>
              mi concurrunt.
                <emph.end type="italics"/>
              ductis enim lineis AH HB CH HD; quoniam
                <lb/>
              lineæ AE EB EF FD inter ſe ſunt ęquales. </s>
              <s id="N12FDC">ſimiliter quo〈que〉
                <lb/>
              AK KC BL LD inter ſe ęquales; erit EH ipſi HF ęqua
                <lb/>
              lis, cùm ſint ipſis BL LD ęquales. </s>
              <s id="N12FE2">duæ igitur AE EH dua
                <lb/>
                <arrow.to.target n="marg86"/>
              bus DF FH ſunt æquales, & angulus AEH angulo DFH
                <lb/>
                <arrow.to.target n="marg87"/>
              ęqualis; erit triangulum AEH triangulo DFH ęquale. </s>
              <s id="N12FF0">ac
                <lb/>
              propterea angulus EHA angulo FHD æqualis. </s>
              <s id="N12FF4">cùm igitur
                <lb/>
              ſit EHF recta linea, eruntangnli EHA FHD adverticem,
                <lb/>
              & obid AHD recta exiſtit linea. </s>
              <s id="N12FFA">ac per conſe〈que〉ns diame­
                <lb/>
              ter parallelogrammi AD. pariquè ratione oſtendetur BHC
                <lb/>
              rectam eſſe lineam. </s>
              <s id="N13000">ex quibus patet in puncto H
                <expan abbr="vtrã〈que〉">vtran〈que〉</expan>
              dia
                <lb/>
              metrum conuenire. </s>
              <s id="N13008">centrum igitur grauitatis parallelogram­
                <lb/>
              mi AD eſt
                <expan abbr="pũctum">punctum</expan>
              , in quo diametri concurrunt.
                <emph type="italics"/>
              Quare demon
                <lb/>
              stratumeſt, quod propoſitum fuit.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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