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

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        <div xml:id="echoid-div706" type="section" level="1" n="415">
          <pb o="296" file="0316" n="316" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div708" type="section" level="1" n="416">
          <head xml:id="echoid-head436" xml:space="preserve">THEOREMA VIII. PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s7171" xml:space="preserve">SI ad baſim datæ parabolæ ordinatim applicetur recta li-
              <lb/>
            nea, ſub qua, & </s>
            <s xml:id="echoid-s7172" xml:space="preserve">ſub portione baſis abſciſſa, ac earum ex-
              <lb/>
            trema iungente, fiattriangulum, portio parabolæ abſciſſa ad
              <lb/>
            triangulum ſibi inſcriptum erit, vt ad reliquam baſis, dempta
              <lb/>
            abſciſſa, eadem reliqua cum, {1/3}, ipſius abſciſſæ.</s>
            <s xml:id="echoid-s7173" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7174" xml:space="preserve">Sit parabola, HGA, in baſi, HA, ad quam ordinatim applicetur
              <lb/>
            vtcunque recta linea, ST, fiat autem triangulum ſub, ST, & </s>
            <s xml:id="echoid-s7175" xml:space="preserve">vtrauis
              <lb/>
              <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="210">
                <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0316-01"/>
              </figure>
            duarum, HT, TA, vt ſub, HT, & </s>
            <s xml:id="echoid-s7176" xml:space="preserve">ſub, SH,
              <lb/>
            quod ſit, HST. </s>
            <s xml:id="echoid-s7177" xml:space="preserve">Dico portionem, HST, ad
              <lb/>
            triangulum, HST, eſſe vt compoſitam ex, A
              <lb/>
            T, &</s>
            <s xml:id="echoid-s7178" xml:space="preserve">, {1/3}, TH; </s>
            <s xml:id="echoid-s7179" xml:space="preserve">ad, AT, compleatur paralle-
              <lb/>
            logrammum, CT, eſt ergo parallelogrammum,
              <lb/>
              <note position="left" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">5. Huius.</note>
            CT, ad portionem, HST, vt, AT, ad com-
              <lb/>
            poſitam ex, {1/2}, AT, &</s>
            <s xml:id="echoid-s7180" xml:space="preserve">, {1/6}, TH, & </s>
            <s xml:id="echoid-s7181" xml:space="preserve">anteceden-
              <lb/>
            tium dimidia ſcilicet triangulum, HST, ad
              <lb/>
            portionem, HST, erit vt dimidia, AT, ad
              <lb/>
            compoſitam ex, {1/2}, AT, &</s>
            <s xml:id="echoid-s7182" xml:space="preserve">, {1/6}, TH, ideſt vt,
              <lb/>
            AT, ad, AT, cum, {1/3}, HT, & </s>
            <s xml:id="echoid-s7183" xml:space="preserve">conuertendo,
              <lb/>
            portio, HST, ad triangulum, HST, erit vt
              <lb/>
            compoſita ex, {1/3}, HT, & </s>
            <s xml:id="echoid-s7184" xml:space="preserve">tota, TA, ad, TA,
              <lb/>
            quod oſtendendum nobis erat.</s>
            <s xml:id="echoid-s7185" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div710" type="section" level="1" n="417">
          <head xml:id="echoid-head437" xml:space="preserve">SCHOLIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7186" xml:space="preserve">_P_Oteſt autem, & </s>
            <s xml:id="echoid-s7187" xml:space="preserve">dicta ratio ſic conſtitui, triplicatis terminis, ſcili-
              <lb/>
            cet, quod portio, HST, ad triangulum, HST, ſit bt bna, HA,
              <lb/>
            cum duabus, AT, ad tres, AT, bel ſic, quod ſit, bt dimidia, HA, cum,
              <lb/>
            AT, ad ipſam, AT.</s>
            <s xml:id="echoid-s7188" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div711" type="section" level="1" n="418">
          <head xml:id="echoid-head438" xml:space="preserve">PROBLEMA I. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s7189" xml:space="preserve">A Data parabola portionem abſcindere per lineam ab
              <lb/>
            eiuſdem baſim ordinatim ductam, quę ad triangulum
              <lb/>
            ſub eadem ordinatim ducta, & </s>
            <s xml:id="echoid-s7190" xml:space="preserve">abſciſſa per eandem à baſi pa-
              <lb/>
            rabolæ ad eandem partem, ad quam abſcinditur portio, ha-
              <lb/>
            beat datam rationem, dummodò hæc ſit maior ſexquialtera.</s>
            <s xml:id="echoid-s7191" xml:space="preserve"/>
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