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

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            <s xml:id="echoid-s4580" xml:space="preserve">
              <pb o="187" file="0207" n="207" rhead="LIBER II."/>
            ſe extendit, quot ſunt figurarum planarum variationes, quæ nulto aſſi-
              <lb/>
            gnato coarctantur numero, cuius modi demonſtrationis vniuerſalitatem
              <lb/>
            in alijs figuris quoque in poſterum conſiderandis proſequemur, vt am-
              <lb/>
            plius infra patebit.</s>
            <s xml:id="echoid-s4581" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div468" type="section" level="1" n="283">
          <head xml:id="echoid-head299" xml:space="preserve">N. SECTIO XIII.</head>
          <p style="it">
            <s xml:id="echoid-s4582" xml:space="preserve">_I_N Prop. </s>
            <s xml:id="echoid-s4583" xml:space="preserve">29. </s>
            <s xml:id="echoid-s4584" xml:space="preserve">& </s>
            <s xml:id="echoid-s4585" xml:space="preserve">eius Corollario tandem edocemur ſolida ſimilaria
              <lb/>
            genita ex parallelogrammo, vel triangulo eodem, iuxta duas regu-
              <lb/>
            las latera angulum continentia, ideſt cylindricos ab eodem parallelo-
              <lb/>
            grammo, & </s>
            <s xml:id="echoid-s4586" xml:space="preserve">conicos ab eodem triangulo genitos, iuxta dictas regulas,
              <lb/>
            eſſe inter ſe, vt eaſdem regulas.</s>
            <s xml:id="echoid-s4587" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div469" type="section" level="1" n="284">
          <head xml:id="echoid-head300" xml:space="preserve">THEOREMA XXXV. PROPOS. XXXV.</head>
          <p>
            <s xml:id="echoid-s4588" xml:space="preserve">PArallelepipedum ſub baſi rectangulo quodam, altitu-
              <lb/>
            dine autem quadam recta linea æquatur parallelepipe-
              <lb/>
            dis ſub baſi eodem rectangulo, & </s>
            <s xml:id="echoid-s4589" xml:space="preserve">ſub quotcumq; </s>
            <s xml:id="echoid-s4590" xml:space="preserve">paitibus,
              <lb/>
            in quas altitudo vtcumq; </s>
            <s xml:id="echoid-s4591" xml:space="preserve">diuidui poteſt. </s>
            <s xml:id="echoid-s4592" xml:space="preserve">Et ſi rectangulum,
              <lb/>
            quod eſt baſis, intelligatur vtcumq; </s>
            <s xml:id="echoid-s4593" xml:space="preserve">diuiſum in quotcumq;
              <lb/>
            </s>
            <s xml:id="echoid-s4594" xml:space="preserve">rectangula, dictum parallelepipedum æquatur parallelepi-
              <lb/>
            pedis ſub ſingulis partibus altitudinis, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">ſingulis partibus
              <lb/>
            bafis.</s>
            <s xml:id="echoid-s4596" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4597" xml:space="preserve">Sit parallelepipedum rectangulum, AP, cuius baſis rectangulum,
              <lb/>
            TH, ſupponatur pro nunc indiuiſa, & </s>
            <s xml:id="echoid-s4598" xml:space="preserve">altitudo, DT, diuiſa vtcum-
              <lb/>
            quein quotcumq; </s>
            <s xml:id="echoid-s4599" xml:space="preserve">partes, DS, ST. </s>
            <s xml:id="echoid-s4600" xml:space="preserve">Dico parallelepipedum, AP,
              <lb/>
            æquari parallelepipedis ſub, DS, TH, & </s>
            <s xml:id="echoid-s4601" xml:space="preserve">ſub, ST, TH. </s>
            <s xml:id="echoid-s4602" xml:space="preserve">Duca-
              <lb/>
            tur per, S, planum æquidiſtans baſi, TH, quodin eo producet re-
              <lb/>
              <note position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">Corol. 12.
                <lb/>
              lib. I.</note>
            ctangulum, vt, SG, ſuntigitur, AM, NP, parallelepipeda, &</s>
            <s xml:id="echoid-s4603" xml:space="preserve">, A
              <lb/>
            M, eſt ſub, DS, SG, vel, IH, (quia, SG, TH, ſunt figuræ ſi-
              <lb/>
              <note position="right" xlink:label="note-0207-02" xlink:href="note-0207-02a" xml:space="preserve">Corol. 12.
                <lb/>
              lib. I.</note>
            mdes, & </s>
            <s xml:id="echoid-s4604" xml:space="preserve">æquales) NP, vero ſub, ST, TH, continetur, eit autem
              <lb/>
            parallelepipedum, AP, contentum ſub, DT, TH, æquale paral-
              <lb/>
            lelepipedis, AM, NP, ſuis partibus ſimul ſumptis, ergo parallele-
              <lb/>
            pipedum ſub, DT, TH, æquatur parallelepipedis ſub, DS, TH,
              <lb/>
            & </s>
            <s xml:id="echoid-s4605" xml:space="preserve">ſub, ST, TH.</s>
            <s xml:id="echoid-s4606" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4607" xml:space="preserve">Sit nunc bafis, TH, diuiſa vtcumque in quotcumque rectangula,
              <lb/>
            TV, VP. </s>
            <s xml:id="echoid-s4608" xml:space="preserve">Dico parallelepipedum ſub, DT, TH, æquari paral-
              <lb/>
            lelepipedis ſub, DS, TV, ſub, DS, VP, ſub, ST, TV, & </s>
            <s xml:id="echoid-s4609" xml:space="preserve">ſub,
              <lb/>
            ST, VP. </s>
            <s xml:id="echoid-s4610" xml:space="preserve">Ducatur per rectam, QV, planum æquidiſtans </s>
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