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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N140F0" type="main">
              <s id="N1414A">
                <pb xlink:href="077/01/113.jpg" pagenum="109"/>
                <emph type="italics"/>
              nea OX. dicti autem trapezii centrum gauitatis est etiam in li­
                <lb/>
              nea EF, quare trapezii ABCD centrum grauitatis est punctum
                <lb/>
              P. At verò triangulum BCD ad ABD proportionem habet eam,
                <arrow.to.target n="marg176"/>
                <lb/>
              OP ad P
                <emph.end type="italics"/>
              X. cùm ſint puncta OX triangulorum centla graui
                <lb/>
              tatis, ac punctum P vtrorum〈que〉 commune centrum.
                <emph type="italics"/>
              Sed vt
                <lb/>
              triangulum BDC adtriangulum ABD, ita eſt
                <emph.end type="italics"/>
              quo〈que〉 baſis
                <emph type="italics"/>
              BC
                <emph.end type="italics"/>
                <arrow.to.target n="marg177"/>
                <lb/>
                <emph type="italics"/>
              ad
                <emph.end type="italics"/>
              baſim
                <emph type="italics"/>
              AD.
                <emph.end type="italics"/>
              cùm triangula eandem habeant altitudinem,
                <lb/>
              ſiquidem ſunt in ijsdem parallelis AD BC. quare vt BC ad
                <lb/>
              AD, ita OP ad PX.
                <emph type="italics"/>
              Sed
                <emph.end type="italics"/>
              quoniam anguli RPO SPX
                <arrow.to.target n="marg178"/>
              ver­
                <lb/>
              ticem ſunt ęquales, & angulus PRO ipſi PSX, veluti
                <arrow.to.target n="marg179"/>
                <lb/>
              ROP angulo PXS eſt ęqualis, erit triangulum OPR triangu
                <lb/>
              lo XPS ſimile; quare
                <emph type="italics"/>
              vt OP ad PX, ſic PR ad PS.
                <emph.end type="italics"/>
              eſt
                <arrow.to.target n="marg180"/>
                <lb/>
              BC ad AD, vt OP ad PX
                <emph type="italics"/>
              ; vt igitur BC ad AD, ita RP ad PS.
                <emph.end type="italics"/>
                <arrow.to.target n="marg181"/>
                <lb/>
              & antecedentium dupla, duæ ſcilicet BC ad AD, vt duæ PR
                <lb/>
              ad PS. & componendo duæ BC cum AD ad AD; vt
                <arrow.to.target n="marg182"/>
                <lb/>
              PR cum PS ad PS. & ad conſe〈que〉ntium dupla, vt ſcilicet
                <lb/>
              duæ BC cum AD ad duas AD, ita duæ PR cum PS ad duas
                <lb/>
              PS. dictum eſt autem BC ad AD ita eſſe, vt PR ad PS. quare
                <lb/>
              conuerrendo AD ad BC erit, vt PS ad PR. &
                <arrow.to.target n="marg183"/>
                <lb/>
              dupla. </s>
              <s id="N14232">hoc eſt duæ AD ad BC, vt duæ PS ad PR. Ita〈que〉 in
                <lb/>
              eadem ſunt proportione duç BC cum AD ad duas AD, vt
                <lb/>
              duę PR
                <expan abbr="cũ">cum</expan>
              PS ad duas PS. ſicut verò duę AD ad BC, ita duę
                <lb/>
              PS ad PR. antecedentes igitur ad ſuas ſimul conſe〈que〉ntes
                <arrow.to.target n="marg184"/>
                <lb/>
              eadem erunt proportione.
                <emph type="italics"/>
              Quare ſicut duæ BC cum AD ad duas
                <lb/>
              AD cum BC, ita duæ RP cum PS ad duas P S cum PR,
                <lb/>
              verùm duæ quidem RP cum PS eſt vtra〈que〉 ſimul SR RP.
                <emph.end type="italics"/>
              bis
                <lb/>
              enim aſſumitur PR, ſemel verò PS. Cum autem lineæ DH ES
                <lb/>
              à lineis diuidantur ęquidiſtantibus ED OT HM, erit DK
                <arrow.to.target n="marg185"/>
                <lb/>
              KH, vt ER ad CS; kD verò eſt æqualis KH, erit ER ipſi
                <lb/>
              RS ęqualis. </s>
              <s id="N14258">erit igitur ER cum RP,
                <emph type="italics"/>
              hoc est PE
                <emph.end type="italics"/>
              ipſis SR RP
                <lb/>
              ęqualis.
                <emph type="italics"/>
              duæ verò PS cum PR eſt vtra〈que〉 PS SR.
                <emph.end type="italics"/>
              bis enim aſ­
                <lb/>
              ſumitur PS, ſemel què PR. & quoniam FS eſt ęqualis ipſi SR.
                <lb/>
              quod quidem eodem modo oſtendetur, cùm ſit FS ad SR, vt
                <lb/>
              BH ad Hk. </s>
              <s id="N1426E">erit FS cum SP,
                <emph type="italics"/>
              hoc est PF
                <emph.end type="italics"/>
              ipſis PS SR æqualis.
                <lb/>
              Quare ita ſehabet PE ad PF, vt duæ BC cum AD ad duas
                <lb/>
              AD cum BC. Centrum igitur grauitatis P trapezij ABCD
                <lb/>
              in linea eſt EF, quæ
                <expan abbr="cõiungit">coniungit</expan>
              parallelas AD BC bifariam di </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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