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

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        <div xml:id="echoid-div1156" type="section" level="1" n="692">
          <p>
            <s xml:id="echoid-s12848" xml:space="preserve">
              <pb o="503" file="0523" n="523" rhead="LIBER VII."/>
            cabunt, tertia verò hanc periphęriam diuidet in duobus punctis,
              <lb/>
            quę ſunt ab ambas partes plani, ILM, nempè vnum ſupra alterum
              <lb/>
            infra ipſum, quare non ad aliud punctum, quam ad, H, concurrẽt
              <lb/>
            tres rectæ lineæ, AE, AF, AG, ad eandem partem plani, ILM, cum
              <lb/>
            ipſis, HI, HL, HM, conſtitutæ, ergo, AF, cadet in, HL, AE, in,
              <lb/>
            HI, &</s>
            <s xml:id="echoid-s12849" xml:space="preserve">, AG, in, HM, quibus pręoſtenſis, reliquum demonſtratio-
              <lb/>
            nis, vt ibi, proſequemur.</s>
            <s xml:id="echoid-s12850" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1159" type="section" level="1" n="693">
          <head xml:id="echoid-head726" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s12851" xml:space="preserve">PArallelogramma in eadem altitudine exiſtentia inter
              <lb/>
            ſe ſunt vt baſes.</s>
            <s xml:id="echoid-s12852" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12853" xml:space="preserve">Sin in ſigura Prop. </s>
            <s xml:id="echoid-s12854" xml:space="preserve">5. </s>
            <s xml:id="echoid-s12855" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12856" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12857" xml:space="preserve">parallelogramma, AM, MC, in ea-
              <lb/>
            dem altitudine. </s>
            <s xml:id="echoid-s12858" xml:space="preserve">Dico eadem eſſe inter ſe, vt baſes, GM, MH.
              <lb/>
            </s>
            <s xml:id="echoid-s12859" xml:space="preserve">
              <note position="right" xlink:label="note-0523-01" xlink:href="note-0523-01a" xml:space="preserve">Ex 2. hu-
                <lb/>
              ius.</note>
            Hoc autem manifeſtum eſt, ſunt enim dicta parallelogramma figu-
              <lb/>
            rę proportionaliter analogę, iuxta ipſas baſes, cum ſit, GM, ad,
              <lb/>
            MH, vt, DE, ad, EI, &</s>
            <s xml:id="echoid-s12860" xml:space="preserve">, DI, ducta ſit vtcumque, vnde patet pro-
              <lb/>
            poſitum etiam independenter à methodo Indiuiſibilium.</s>
            <s xml:id="echoid-s12861" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1161" type="section" level="1" n="694">
          <head xml:id="echoid-head727" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s12862" xml:space="preserve">PRopofitionis 5. </s>
            <s xml:id="echoid-s12863" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s12864" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12865" xml:space="preserve">prior pars pendet quidem ab Indiuiſi-
              <lb/>
            bilium methodo, verum pars poſterior, necnon Prop. </s>
            <s xml:id="echoid-s12866" xml:space="preserve">6.</s>
            <s xml:id="echoid-s12867" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12868" xml:space="preserve">& </s>
            <s xml:id="echoid-s12869" xml:space="preserve">
              <lb/>
            8. </s>
            <s xml:id="echoid-s12870" xml:space="preserve">abſq; </s>
            <s xml:id="echoid-s12871" xml:space="preserve">illa methodo, vt intuenti apparebit, oſtenduntur, qua-
              <lb/>
            propter, cum ab eadem exemptę ſint, non indigent vt reſtauren-
              <lb/>
            tur, ſed illas tamquam ſtylo veteri demonſtratas, vt veras in hoc
              <lb/>
            libro quoq; </s>
            <s xml:id="echoid-s12872" xml:space="preserve">vſurpabimus, quod etiam de alijs Propoſitionibus fiet,
              <lb/>
            quę a methodo Indiuiſibilium immediatę pendere non conſpicien-
              <lb/>
            tur, etiamſi mediatè ab eadem vtiq; </s>
            <s xml:id="echoid-s12873" xml:space="preserve">dependere competiantur, ſuffi-
              <lb/>
            ciet enim illas Prop. </s>
            <s xml:id="echoid-s12874" xml:space="preserve">de nouo oſtendere, quę immediatè ab ipſa
              <lb/>
            methodo Indiuiſibilium fidem ſumpſiſſe videbuntur. </s>
            <s xml:id="echoid-s12875" xml:space="preserve">Cum verò
              <lb/>
            ſubſequentes Propoſitiones, in quibus parallelogrammorum om-
              <lb/>
            nia quadrata, ſeu omnes figurę ſimiles, regulis baſibus, examinan-
              <lb/>
            tur, ſint in gratiam cylindricorum, prima verò tantum pendeat ex
              <lb/>
            methodo Indiuiſibilium, propterea illa erit denuo oſtendenda,
              <lb/>
            quam nunc ſubiungo.</s>
            <s xml:id="echoid-s12876" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1162" type="section" level="1" n="695">
          <head xml:id="echoid-head728" xml:space="preserve">THEOREMA V. PROPOS. V.</head>
          <p>
            <s xml:id="echoid-s12877" xml:space="preserve">CYlindrici in eadem altitudine exiſtentes inter ſe ſunt
              <lb/>
            vt baſes.</s>
            <s xml:id="echoid-s12878" xml:space="preserve"/>
          </p>
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