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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N14F2F" type="main">
              <s id="N14F79">
                <pb xlink:href="077/01/137.jpg" pagenum="133"/>
              tur KN FL IM, quæ diametrum BD ſecent in punctis
                <lb/>
              STV. oſtendendum eſt, lineas KN FL IM baſi AC ęqui
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              diſtantes eſſe. </s>
              <s id="N14F87">deinde diametrum BD lineas KN FL IM
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              bifariam in punctis STV diuidere poſtremo lineas KN F
                <gap/>
                <lb/>
              IM ita diametrum BD diſpeſcere, vt poſito vno BS, linea ST
                <lb/>
              ſit tria, TV quin〈que〉; & VD ſeptem. </s>
              <s id="N14F90">Producantur FE KH
                <lb/>
              ad RX. quoniam enim FR eſt æquid
                <gap/>
              tans BD, erit AE
                <arrow.to.target n="marg211"/>
                <lb/>
              EB, vt AR ad RD; eſt〈que〉 AE ipſi EB æqualis ergo AR i­
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              pſi RD æqualis exiſtit. </s>
              <s id="N14F9D">eodem què modo oſtendetur FX æ­
                <lb/>
              qualem eſſe XT. quandoquidem eſt FX ad XT, vt FH ad
                <lb/>
              HB. ſimiliterquè ad alteram partem, exiſtentibus LO NP i­
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              pſi BD æquidiſtantibus, erit DO ipſi OC æqualis, & TP
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              ipſi PL. quod quidem eodem prorſus modo demonſtrabi­
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              tur. </s>
              <s id="N14FA9">Quoniam autem AC bifariam à diametro diuiditur in
                <lb/>
              puncto D, erit DR ipſi DO æqualis, cùm vnaquæ〈que〉 ſit
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              dimidia ipſarum AD DC æqualium. </s>
              <s id="N14FAF">eſt igitur RD dimidia
                <lb/>
              ipſius AD, quæ dimidia eſt baſis AC. quod idem euenit ipſi
                <lb/>
              DO. quare BD ſeſquitertia eſt ipſius FR, & ipſius LO, ex de­
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              cimanona Archimedis de quadratura paraboles. </s>
              <s id="N14FB7">ac propterea
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              eandem habet proportionem BD ad FR, quam ad LO.
                <arrow.to.target n="marg212"/>
                <lb/>
              ſequitur FR æqualem eſſe ipſi LO. & obid FL ipſi AC
                <expan abbr="æ-quidiſtantẽ">æ­
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                quidiſtantem</expan>
              eſſe. </s>
              <s id="N14FC6">& FT ipſi RD, & TL ipſi DO ęqualem.
                <lb/>
              vnde FT ipſi TL ęqualis exiſtit. </s>
              <s id="N14FCA">eadem quèratione prorſus in
                <lb/>
              portione FBL oſtendetur KN ipſi FL, ac per conſe〈que〉ns i­
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              pſi AC ęquidiſtantem eſſe. </s>
              <s id="N14FD0">& KS ipſi SN æqualem exiſte­
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              re. </s>
              <s id="N14FD4">Producatur IG ad Z, quæ ipſam AB ſecet in 9. linea ve­
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              rò LO ſecet BC in
                <expan abbr="q;">〈que〉</expan>
              ductaquè MY ipſi BD æquidiſtans
                <lb/>
              ipſam ſecet BC in
                <foreign lang="grc">α</foreign>
              . & quoniam IZ eſt æquidiſtans FR, e­
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              rit AG ad GF, ut A9 ad 9E, & AZ ad ZR. & eſt AG
                <arrow.to.target n="marg213"/>
                <lb/>
              GF æqualis, erit igitur A9 ipſi 9E, & AZ ipſi ZR æquaiis.
                <lb/>
              Eodemquè modo oſtendetur C
                <foreign lang="grc">α</foreign>
              ipſi
                <foreign lang="grc">α</foreign>
              Q, & CY ipſi YO ę­
                <lb/>
              qualem eſſe. </s>
              <s id="N14FF5">quo niam autem in portione AFB a dimidia baſi
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              ducta eſt LF, à puncto autem 9, hoc eſt à dimidia dimidię ba
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              ſis AB (eſt enim E9 dimidia ipſius AE, quæ dimidia eſt baſis
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              AB) ducta eſt 9I diametro æquidiſtans, erit EF ſeſquitertiai­
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              pſius I9 pari〈que〉 ratione oſtendetur QL ſeſquitereiam eſſe i­
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              pſius M
                <foreign lang="grc">α</foreign>
              quare vt FE ad I9, ita LQ ad M
                <foreign lang="grc">α</foreign>
              . obſimilitudinem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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