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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N15D7F" type="main">
              <s id="N15D85">
                <pb xlink:href="077/01/156.jpg" pagenum="152"/>
              BG ad GC, vt LT ad TN, & KS ad SM. & ut EH ad HF ita
                <lb/>
              PX ad XR, & OV ad
                <expan abbr="Vq.">V〈que〉</expan>
              Deinde erunt AG DH à lineis KM
                <lb/>
              LN OQ PR in eadem proportione diuiſæ; ſiquidem ita eſt
                <lb/>
              AS ST TG, ut DV VX XH. cùm ſint, ut expoſitæ propor­
                <lb/>
              tiones AK KL LB, & DO OP PE. Præterea erit ſpacium,
                <lb/>
              BN ad LM, vt ER ad PQ, & LM ad triangulum AK M,
                <lb/>
                <arrow.to.target n="fig71"/>
                <lb/>
              vt PQ ad triangulum
                <expan abbr="DOq.">DO〈que〉</expan>
              Nam quoniam triangulu AEC
                <lb/>
              ſimile eſt triangulo ALN, oblatus LN ipſi BC æquidiſtans;
                <lb/>
              erit ABC ad ALN, ut AB ad AL duplicata. </s>
              <s id="N15DB9">eodemquè modo
                <lb/>
              erit DEF ad DPR, vt DE ad DP duplicata; eandem aut
                <gap/>
              m,
                <lb/>
              habet proportionem AB ad AL, quam DE ad DP: quadoqui
                <lb/>
              dem latera AB DE in eadem ſunt proportione diuiſa; erit igi­
                <lb/>
              tur triangulum ABC ad ALN, vt triangulum DEF ad DPR.
                <lb/>
              ſimiliterquè oſtendetur ALN ad AkM ita eſſe, ut DPR ad
                <lb/>
                <expan abbr="DOq.">DO〈que〉</expan>
              Quoniam autem ABC eſt ad ALN, ut DEF ad DPR,
                <lb/>
                <arrow.to.target n="marg268"/>
              diuidendo erit BN ad ALN, ut ER ad DPR. Atverò
                <expan abbr="quoniã">quoniam</expan>
                <lb/>
              ALN ad AKM eſt, vt DPR ad
                <expan abbr="DOq;">DO〈que〉</expan>
              erit per conuerſio­
                <lb/>
              nem rationis ALN ad LM, vt DPR ad
                <expan abbr="Pq.">P〈que〉</expan>
              qua­
                <lb/>
                <arrow.to.target n="marg269"/>
              re ex ęquali BN eſt ad LM, ut ER ad
                <expan abbr="Pq.">P〈que〉</expan>
              Cùm au
                <gap/>
              em ſit
                <lb/>
              ALN ad AKM, ut DPR ad
                <expan abbr="DOq;">DO〈que〉</expan>
              erit diuidendo LM ad
                <lb/>
              AKM, vt PQ ad
                <expan abbr="DOq.">DO〈que〉</expan>
              Quocirca erit ſpacium BN ad
                <lb/>
              LM, vt ER ad PQ, & LM ad triangulum AKM,
                <lb/>
              vt PQ ad triangulum
                <expan abbr="DOq.">DO〈que〉</expan>
              Ex quibus perſpicuum
                <lb/>
              eſt omnia triangula aliquam inter ſe habere ſimilitudinem,
                <lb/>
              ex qua poſſibile fuit determinare in omnibus ſitum, vb
                <gap/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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