Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div902" type="section" level="1" n="539">
          <p>
            <s xml:id="echoid-s9626" xml:space="preserve">
              <pb o="374" file="0394" n="394" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0394-01" xlink:href="fig-0394-01a" number="269">
                <image file="0394-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0394-01"/>
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            diuidendo minor ea, quam habet,
              <lb/>
            AC, ad, CE, eandem ergo, quam
              <lb/>
            habet, HL, ad, LR, habebit, AC, ad
              <lb/>
            maiorem, CE, ſit illa, CO, & </s>
            <s xml:id="echoid-s9627" xml:space="preserve">per,
              <lb/>
            O, ducatur, SV, parallela ipſi regu-
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            læ, FG, iunganturque, SE, EV: </s>
            <s xml:id="echoid-s9628" xml:space="preserve">Om-
              <lb/>
            nia ergo quadrata hyperbolæ, SEV,
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            ad omnia quadrata trianguli, SEV,
              <lb/>
            ſunt vt, AO, ad, OC, quia verò, AC,
              <lb/>
            ad, CO, eſt vt, HL, ad, LR, compo-
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            nendo, AO, ad, OC, erit vt, HR, ad,
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            RL, ergo omnia quadrata hyperbo-
              <lb/>
            læ, SEV, ad omnia quadrata triangu-
              <lb/>
            li, SEV, erunt vt, HR, ad, RL, .</s>
            <s xml:id="echoid-s9629" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9630" xml:space="preserve">in
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            ratione data, quod facere opus erat.</s>
            <s xml:id="echoid-s9631" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div904" type="section" level="1" n="540">
          <head xml:id="echoid-head564" xml:space="preserve">THEOREMA VI. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s9632" xml:space="preserve">SI circa datam hyperbolam deſcribantur aſymptoti,
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            eiuſdem autem baſis vſq; </s>
            <s xml:id="echoid-s9633" xml:space="preserve">ad aſymptotos producatur,
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            quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s9634" xml:space="preserve">O nnia quadrata hyperbolæ ad
              <lb/>
            omnia quadrata trianguli aſymptotis, & </s>
            <s xml:id="echoid-s9635" xml:space="preserve">baſi comprchen-
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            ſi, habebunt rationem compoſitam ex ea, quam habet
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            quadratum baſis hyperbolæ ad quadratum baſis trianguli,
              <lb/>
            & </s>
            <s xml:id="echoid-s9636" xml:space="preserve">ex ea, quam habet rectangulum ſub compoſita ex ſex-
              <lb/>
            quialtera tranſuerſi lateris, & </s>
            <s xml:id="echoid-s9637" xml:space="preserve">axi, vel diametro datæ hy-
              <lb/>
            perbolæ, ſub eodem axi, vel diametro, ad rectangulum
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            ſub compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9638" xml:space="preserve">axi, vel diametro
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            eiuſdem hyperbolæ; </s>
            <s xml:id="echoid-s9639" xml:space="preserve">& </s>
            <s xml:id="echoid-s9640" xml:space="preserve">ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9641" xml:space="preserve">tranſuerſi late-
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            ris, & </s>
            <s xml:id="echoid-s9642" xml:space="preserve">eodem axi, vel diametro.</s>
            <s xml:id="echoid-s9643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9644" xml:space="preserve">Sit igitar data hyperbola, cuius baſis, SX, circa axim, vel dia-
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            metrum, OV, cuius tranſuerſum latus ſit, BO, bifariam in C, di-
              <lb/>
            uiſum, ſit autem illi in directum adiuncta, AB, æqualis, BC, de-
              <lb/>
            inde ducta per, O, tangente hyperbolam, quæ ſit, ED, cui erit
              <lb/>
            parallela baſis, SX, abicindantur, EO, OD, ita vt quadratum, E
              <lb/>
            O, & </s>
            <s xml:id="echoid-s9645" xml:space="preserve">quadratum, OD, ſeorſim ſint æqualia quartæ parti rectan-
              <lb/>
            guli ſub, BO, latere tranſuerſo, & </s>
            <s xml:id="echoid-s9646" xml:space="preserve">ſub eiuſdem recto latere, ſi ergo
              <lb/>
            iunctis, CE, CD, ipsæ producantur indefinitè verſus baſim, SX,
              <lb/>
              <note position="left" xlink:label="note-0394-01" xlink:href="note-0394-01a" xml:space="preserve">1.2. Con.</note>
            cui productæ occurant in punctis, H, R, erunt, CH, CR, </s>
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