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

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        <div xml:id="echoid-div750" type="section" level="1" n="442">
          <p>
            <s xml:id="echoid-s7555" xml:space="preserve">
              <pb o="314" file="0334" n="334" rhead="GEOMETRIE"/>
            magnitudines collectæ iuxta tertiam, & </s>
            <s xml:id="echoid-s7556" xml:space="preserve">quartam. </s>
            <s xml:id="echoid-s7557" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7558" xml:space="preserve">iuxta, ON, ter-
              <lb/>
            tiam, &</s>
            <s xml:id="echoid-s7559" xml:space="preserve">, NX, quartam, ijſdem recti, vel eiuſdem obliqui tranſitus
              <lb/>
            ſumptis: </s>
            <s xml:id="echoid-s7560" xml:space="preserve">Quia verò datæ rectæ lineæ, OR, adiungitur, RN, ideò
              <lb/>
            maximæ abſciſſarum, OR, adiuncta, RN, ad omnes abſciſſas, OR,
              <lb/>
            adiuncta, RN, recti, vel eiuſdem obliqui tranſitus, ſunt vt, ON, ad
              <lb/>
            compoſitam ex, NR, & </s>
            <s xml:id="echoid-s7561" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s7562" xml:space="preserve">RO, ideò omnia quadrata, RH, ad om.
              <lb/>
            </s>
            <s xml:id="echoid-s7563" xml:space="preserve">
              <note position="left" xlink:label="note-0334-01" xlink:href="note-0334-01a" xml:space="preserve">Corol.
                <lb/>
              20. 1. 2.</note>
            nia quadrata quadrilinei, RMHO, vel eorum quadrupla. </s>
            <s xml:id="echoid-s7564" xml:space="preserve">. </s>
            <s xml:id="echoid-s7565" xml:space="preserve">omnia
              <lb/>
            quadrata. </s>
            <s xml:id="echoid-s7566" xml:space="preserve">PH, ad omnia quadrata fruſt, ABHM, erunt vt, ON,
              <lb/>
            ad compoſitamex, NR, & </s>
            <s xml:id="echoid-s7567" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s7568" xml:space="preserve">RO; </s>
            <s xml:id="echoid-s7569" xml:space="preserve">Et conuertendo omnia quadrata
              <lb/>
            fruſti, ABHM, ad omnia quadrata, PH, erunt vt compoſita ex,
              <lb/>
            NR, & </s>
            <s xml:id="echoid-s7570" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">RO, ad, NO, omnia verò quadrata, PH, omnium qua-
              <lb/>
            dratorumtrianguli, RBH, ſunt tripla. </s>
            <s xml:id="echoid-s7572" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7573" xml:space="preserve">ſunt vt, NO, ad {1/3}. </s>
            <s xml:id="echoid-s7574" xml:space="preserve">eiuſ-
              <lb/>
              <note position="left" xlink:label="note-0334-02" xlink:href="note-0334-02a" xml:space="preserve">24. 1. 2.</note>
            dem, NO, ergo, ex æquali, omnia quadrata fruſti, ABHM, ad
              <lb/>
            omnia quadrata trianguli, BRH, erunt vt compoſita ex, NR, & </s>
            <s xml:id="echoid-s7575" xml:space="preserve">{1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s7576" xml:space="preserve">RO, ad {1/3}. </s>
            <s xml:id="echoid-s7577" xml:space="preserve">NO, vel vt horum tripla. </s>
            <s xml:id="echoid-s7578" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7579" xml:space="preserve">vt compoſita ex tribus, NR,
              <lb/>
            & </s>
            <s xml:id="echoid-s7580" xml:space="preserve">ſexquialtera, RO, adipſam, NO, porrò ſi iunxerimus vnam,
              <lb/>
            NR, cum, RO, fiet integra, ON, cum duabus, NR, & </s>
            <s xml:id="echoid-s7581" xml:space="preserve">dimidia,
              <lb/>
            RO, æqualistriplæ, NR, & </s>
            <s xml:id="echoid-s7582" xml:space="preserve">ſexqualteræ, RO; </s>
            <s xml:id="echoid-s7583" xml:space="preserve">ergo omnia qua-
              <lb/>
            drata fruſti, ABHM, ad omnia quadrata trianguli, RBH, erunt
              <lb/>
            vt compoſita ex dupla, NR, & </s>
            <s xml:id="echoid-s7584" xml:space="preserve">dimidia, RO, cum, NO; </s>
            <s xml:id="echoid-s7585" xml:space="preserve">ad ipſam,
              <lb/>
            NO; </s>
            <s xml:id="echoid-s7586" xml:space="preserve">quæ oſtendere oportebat.</s>
            <s xml:id="echoid-s7587" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div752" type="section" level="1" n="443">
          <head xml:id="echoid-head463" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7588" xml:space="preserve">_O_Via autem probatum fuit omnia quadrata, PH, ad omnia quã-
              <lb/>
            drata fruſti, ABHM, eſſe vt, NO, ad dimidiam, OR, cum,
              <lb/>
            RN, ſunt autem omnia quadrata, PH, ad omnia quadrata parallelo-
              <lb/>
            grammi, AG, vt quadratam, HO, ad quadratam, RM, . </s>
            <s xml:id="echoid-s7589" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7590" xml:space="preserve">vt, ON,
              <lb/>
            ad NR, ideò omnia quadrata, PH, ad omnia quadrata fruſti, AB
              <lb/>
            HM, ab ijſdem demptis omnibus quadratis, AG, erunt vt, NO,
              <lb/>
            ad dimidiam ipſius, OR.</s>
            <s xml:id="echoid-s7591" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div753" type="section" level="1" n="444">
          <head xml:id="echoid-head464" xml:space="preserve">THEOREMA XXIII. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s7592" xml:space="preserve">SI intra curuam parabolæ ducatur vtcunq; </s>
            <s xml:id="echoid-s7593" xml:space="preserve">recta linea in
              <lb/>
            eandem terminata, & </s>
            <s xml:id="echoid-s7594" xml:space="preserve">ad axem obliqua, deinde intra
              <lb/>
            portionem ab ipſa reſectam ducatur alia vtcunq; </s>
            <s xml:id="echoid-s7595" xml:space="preserve">prædictæ
              <lb/>
            parallela, agantur autem ab extremitate harum parallela-
              <lb/>
            rum lineæ axi æquidiſtantes: </s>
            <s xml:id="echoid-s7596" xml:space="preserve">Vt baſis reſectæ portionis ad
              <lb/>
            diſtantiam parallelarum ab eiuſdem extremitate </s>
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