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

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          <p>
            <s xml:id="echoid-s435" xml:space="preserve">
              <pb o="10" file="0030" n="30" rhead="GEOMETRIÆ"/>
            deinde inter eadem plana tangentia eiſdem æquidiſtantia
              <lb/>
              <note position="left" xlink:label="note-0030-01" xlink:href="note-0030-01a" xml:space="preserve">D. Def.2.</note>
            vtcumque plana ducta fuerint, altitudines ſolidorum, re-
              <lb/>
            ſpectu dictorum tangentium ſumptas, ſimiliter ad eandem
              <lb/>
            partem diuidentia, reperiamus figuras exhis planis in di-
              <lb/>
              <note position="left" xlink:label="note-0030-02" xlink:href="note-0030-02a" xml:space="preserve">A.Def.10.</note>
            ctis ſolidis conceptas eſſe ſimiles, vel ſi plures producan-
              <lb/>
            tur, tot numero in vno, quot in alio ſolido produci, quæ
              <lb/>
              <note position="left" xlink:label="note-0030-03" xlink:href="note-0030-03a" xml:space="preserve">E.Def.10.</note>
            fint binæ ſimiles, & </s>
            <s xml:id="echoid-s436" xml:space="preserve">quæ ſunt vnius ſolidi ſimiliter inter ſe
              <lb/>
            diſpoſitę, ac quę ſunt alterius, & </s>
            <s xml:id="echoid-s437" xml:space="preserve">omnium homologas dua-
              <lb/>
            bus quibuſdam rectis lineis communiter, tamquam earum-
              <lb/>
            dem regulis, æquidiſtare. </s>
            <s xml:id="echoid-s438" xml:space="preserve">(ſic.</s>
            <s xml:id="echoid-s439" xml:space="preserve">n. </s>
            <s xml:id="echoid-s440" xml:space="preserve">earum homologæ cum
              <lb/>
            quibuſuis alijs duabus regulis angulos æquales cum præ-
              <lb/>
            dictis facientibus, vt infra Prop. </s>
            <s xml:id="echoid-s441" xml:space="preserve">23. </s>
            <s xml:id="echoid-s442" xml:space="preserve">huius oſtendetur, e-
              <lb/>
            tiam haberi poterunt) Vnde ſiregulæ homologarum acci-
              <lb/>
            piantur cum incidentibus planis concurrentes, & </s>
            <s xml:id="echoid-s443" xml:space="preserve">conce-
              <lb/>
            ptarum in ſolidis ſimilium figurarum ductæ in ſingulis op-
              <lb/>
            poſitæ tangentes præfatis regulis Parallelę producantur, ſt
              <lb/>
            opus ſit, quouſq; </s>
            <s xml:id="echoid-s444" xml:space="preserve">prædictis incidentibus planis occurrant,
              <lb/>
            & </s>
            <s xml:id="echoid-s445" xml:space="preserve">binarum quarumcumque oppoſitarum tangentium pun-
              <lb/>
            cta occurſuum iungantur rectis lineis, etiam has iungentes
              <lb/>
            reperiamus ſingulas eſſe incidentes ſuarum ſimilium figu-
              <lb/>
            rarum, & </s>
            <s xml:id="echoid-s446" xml:space="preserve">oppoſitarum tangentium, ac omnes dictas inci-
              <lb/>
            dentes concipi in figuris ſimilibus, quarum, & </s>
            <s xml:id="echoid-s447" xml:space="preserve">ipſæ inci-
              <lb/>
            dentes ſint homologæ, & </s>
            <s xml:id="echoid-s448" xml:space="preserve">omnium regulæ communes ſe-
              <lb/>
            ctiones planorum incidentium, & </s>
            <s xml:id="echoid-s449" xml:space="preserve">oppoſitorum planorum
              <lb/>
            tangentium. </s>
            <s xml:id="echoid-s450" xml:space="preserve">Has omnes, inquam, conditiones ſimilia ſo-
              <lb/>
            lida in vniuerſum habere ſuppono.</s>
            <s xml:id="echoid-s451" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div48" type="section" level="1" n="41">
          <head xml:id="echoid-head51" xml:space="preserve">B.</head>
          <note position="left" xml:space="preserve">B</note>
          <p>
            <s xml:id="echoid-s452" xml:space="preserve">IPſæ autem figuræ planæ ſimiles, quæ capiunt omnes di-
              <lb/>
            ctas incidentes, vocentur. </s>
            <s xml:id="echoid-s453" xml:space="preserve">Figuræ incidentes dictorum
              <lb/>
            ſimilium ſolidorum, & </s>
            <s xml:id="echoid-s454" xml:space="preserve">oppoſitorum tangentium iam du-
              <lb/>
            ctorum.</s>
            <s xml:id="echoid-s455" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div49" type="section" level="1" n="42">
          <head xml:id="echoid-head52" xml:space="preserve">C.</head>
          <note position="left" xml:space="preserve">C</note>
          <p>
            <s xml:id="echoid-s456" xml:space="preserve">FIguræ verò ex planis dictis tangentibus Parallelis in
              <lb/>
              <note position="left" xlink:label="note-0030-06" xlink:href="note-0030-06a" xml:space="preserve">D.Def.2.</note>
            eiſdem ſolidis conceptæ, quotcumque ſint, altitudi-
              <lb/>
            nes eorumdem reſpectu dictorum tangentium ſumptas ſi-
              <lb/>
            militer ad eandem partem diuidentes, quæ ſimiles eſſe </s>
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