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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N135C9" type="main">
              <s id="N1361E">
                <pb xlink:href="077/01/099.jpg" pagenum="95"/>
              KC ad R. ac propterea lineæ OPQR inter ſe ſunt æquales.
                <lb/>
              Atverò quoniam ita eſt AC ad AG, vt AG ad O, & vt
                <lb/>
              AC ad GH, ita GH, hoc eſt AG ipſi ęqualis, ad P. rurſus
                <lb/>
              vt AC ad HK, ita HK, hoc eſt AG ad
                <expan abbr="q.">〈que〉</expan>
              ac tandem vt
                <lb/>
              AC ad KC, ita KC, hoc eſt AG ipſi ęqualis, ad R. erit
                <arrow.to.target n="marg119"/>
                <lb/>
              ad omnes conſe〈que〉ntes ſimul ſumptas AG GH HK KC,
                <lb/>
              hoc eſt erit AC ad eandem AC, vt AG ad omnes ſimul
                <lb/>
              OPQR. vnde ſequitur omnes ſimul OPQR ipſi AG ęqua
                <lb/>
              les eſſe. </s>
              <s id="N1364F">Ita〈que〉 quoniam ſimilia triangula in dupla
                <arrow.to.target n="marg120"/>
              pro­
                <lb/>
              portione laterum homologorum, erit triangulum ABC ad
                <lb/>
              ALG, vt AC ad O. eodemquè modo erit triangulum ABC
                <lb/>
              ad GMH, vt AC ad P. rurſus ABC ad HNK, vt AC ad
                <lb/>
              Q, & vt idem ABC ad KFC, ita AC ad R. triangulum
                <lb/>
              igitur ABC ad omnes conſe〈que〉ntes, videlicet ad omnia
                <expan abbr="triã">triam</expan>
                <arrow.to.target n="marg121"/>
                <lb/>
              gula ſimul ſumpta ALG GMH HNK KFC, eritvt AC ad
                <lb/>
              omnes ſimul OPQR. hoc eſt ad AG. oſtenſum eſt igitur,
                <lb/>
              quod propoſitum fuit. </s>
            </p>
            <p id="N1366C" type="margin">
              <s id="N1366E">
                <margin.target id="marg114"/>
              2.
                <emph type="italics"/>
              ſexti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N13677" type="margin">
              <s id="N13679">
                <margin.target id="marg115"/>
              1.
                <emph type="italics"/>
              lemma.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N13682" type="margin">
              <s id="N13684">
                <margin.target id="marg116"/>
              29.
                <emph type="italics"/>
              primi.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1368D" type="margin">
              <s id="N1368F">
                <margin.target id="marg117"/>
              76.
                <emph type="italics"/>
              primi.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N13698" type="margin">
              <s id="N1369A">
                <margin.target id="marg118"/>
                <emph type="italics"/>
              ex
                <emph.end type="italics"/>
              17
                <emph type="italics"/>
                <expan abbr="quĩi">quini</expan>
              .
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N136AB" type="margin">
              <s id="N136AD">
                <margin.target id="marg119"/>
                <emph type="italics"/>
              ex
                <expan abbr="præcedẽ">præcedem</expan>
                <lb/>
              ti lemmate
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N136BB" type="margin">
              <s id="N136BD">
                <margin.target id="marg120"/>
              19.
                <emph type="italics"/>
              ſexti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N136C6" type="margin">
              <s id="N136C8">
                <margin.target id="marg121"/>
                <emph type="italics"/>
              ex
                <expan abbr="præcedẽ">præcedem</expan>
                <lb/>
              ti lemmate
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.077.01.099.1.jpg" xlink:href="077/01/099/1.jpg" number="61"/>
            <p id="N136DA" type="head">
              <s id="N136DC">PROPOSITIO. XIII.</s>
            </p>
            <p id="N136DE" type="main">
              <s id="N136E0">Omnis trianguli centrum grauitatis eſt in recta
                <lb/>
              linea ab angulo ad dimidiam baſim ducta. </s>
            </p>
            <p id="N136E4" type="main">
              <s id="N136E6">
                <emph type="italics"/>
              Sit triangulum ABC. & in ipſo ſit AD
                <emph.end type="italics"/>
              ab angulo A
                <emph type="italics"/>
              ad dimi­
                <lb/>
              diambaſim BC ducta. </s>
              <s id="N136F2">oſtendendum est, centrum grauitatis trianguli
                <lb/>
              ABC eſſe in linea AD. Non ſit quidem, ſed ſi fieri potest ſit punctum
                <lb/>
              H. & ab ipſo ducatur HI æquidiſtansipſi BC,
                <emph.end type="italics"/>
              quæ ipſam AD
                <arrow.to.target n="marg122"/>
                <lb/>
              in I.
                <emph type="italics"/>
              Deinde diuiſa DC bifariam, idquè ſemper fiat, dones relinqua­
                <lb/>
              tur linea
                <emph.end type="italics"/>
              D
                <foreign lang="grc">ω</foreign>
                <emph type="italics"/>
              minor ipſa HI. Diuidaturquè ipſarum vtra〈que〉 BD DC
                <lb/>
              in partes æquales
                <emph.end type="italics"/>
              D
                <foreign lang="grc">ω</foreign>
              ; parteſquè in DC exrſtentes ſint D
                <foreign lang="grc">ω ωβ
                  <lb/>
                β</foreign>
              Z ZC; quibus reſpondeant æquales partes D
                <foreign lang="grc">ααζζ</foreign>
              O OB.
                <emph type="italics"/>
              &
                <lb/>
              a ſectionum punctis ducantur
                <emph.end type="italics"/>
              OE
                <foreign lang="grc">ζ</foreign>
              G
                <foreign lang="grc">α</foreign>
              L
                <foreign lang="grc">ω</foreign>
              M
                <foreign lang="grc">β</foreign>
              K ZF
                <emph type="italics"/>
              æquidictan
                <lb/>
              tes ipſi AD. & connectantur EF G
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              LM quæ nimirum ipſi BC
                <lb/>
              æquidistantes erunt.
                <emph.end type="italics"/>
              cùm enim ſint BD DC interſe equales, iti­
                <lb/>
              dem OB ZC æquales; erit DO ipſi DZ ęqualis. </s>
              <s id="N1374C">quare DO
                <lb/>
              ad OB eſt, vt DZ ad ZC. Quoniam autem EO FZ ſunt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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