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

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            <s xml:id="echoid-s9706" xml:space="preserve">
              <pb o="377" file="0397" n="397" rhead="LIBER V."/>
            HR, ad quadratum, SX, & </s>
            <s xml:id="echoid-s9707" xml:space="preserve">rectangulum, BVC, ad rectangulum:
              <lb/>
            </s>
            <s xml:id="echoid-s9708" xml:space="preserve">AVO, quæ eſt compoſita pariter ex duabus .</s>
            <s xml:id="echoid-s9709" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9710" xml:space="preserve">ex ea, quam habet,
              <lb/>
              <note position="right" xlink:label="note-0397-01" xlink:href="note-0397-01a" xml:space="preserve">5. 1. 2.</note>
            CV, ad, VO, & </s>
            <s xml:id="echoid-s9711" xml:space="preserve">ex ea, quam habet, BV, ad, VA, vt autem, BV,
              <lb/>
            ad, VA, ſic eſt, ſumpta, OV, communi altitudine, rectangulum,
              <lb/>
            BVO, ad rectangulum, AVO, quodſerua. </s>
            <s xml:id="echoid-s9712" xml:space="preserve">Sumatur nunc harum
              <lb/>
            rationum componentium ea, quam habet quadratu, HR, ad qua-
              <lb/>
            dratum, SX, quæ eſt eadem el, quam habet quadratum, HV, ad
              <lb/>
              <note position="right" xlink:label="note-0397-02" xlink:href="note-0397-02a" xml:space="preserve">5. 2. Elem.</note>
            quadratum, VS, quia verò rectangulum, HSR, cum quadrato, SV,
              <lb/>
              <note position="right" xlink:label="note-0397-03" xlink:href="note-0397-03a" xml:space="preserve">10. 2. Cõ.</note>
            eſt æquale quadrato, HV, ideò quadratum, VS, eſt exceſſus, quo
              <lb/>
            quadratũ, HV, ſuperat rectang. </s>
            <s xml:id="echoid-s9713" xml:space="preserve">HSR, & </s>
            <s xml:id="echoid-s9714" xml:space="preserve">quia rectangul. </s>
            <s xml:id="echoid-s9715" xml:space="preserve">HSR, eſt
              <lb/>
            æquale quadrato, EO, ideò, vt quadratum, HV, ad rectaugulum,
              <lb/>
              <note position="right" xlink:label="note-0397-04" xlink:href="note-0397-04a" xml:space="preserve">4. 6. Elem.</note>
            HSR, ita erit idem quadratum, HV, ad quadratum, EO, & </s>
            <s xml:id="echoid-s9716" xml:space="preserve">ita
              <lb/>
            erit quadratum, VC, ad quadratum, CO, quia triangula, CEO,
              <lb/>
            CHV, ſunt ſimilia, ergo, per conuerſionem rationis, quadratum,
              <lb/>
            HV, ad exceſſum ſui ſuper quadratum, EO, .</s>
            <s xml:id="echoid-s9717" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9718" xml:space="preserve">ad quadratum, VS,
              <lb/>
            erit vt quadratum, VC, ad exceſſum ſui ſuper quadratum, CO, .</s>
            <s xml:id="echoid-s9719" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s9720" xml:space="preserve">ad rectangulũ bis ſub, CO, OV, cum quadrato, OV, .</s>
            <s xml:id="echoid-s9721" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9722" xml:space="preserve">ad rectan-
              <lb/>
            gulum ſemel ſub, BO, OV, cum quadrato, OV, .</s>
            <s xml:id="echoid-s9723" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9724" xml:space="preserve">ad integrum
              <lb/>
            rectangul@, BVO; </s>
            <s xml:id="echoid-s9725" xml:space="preserve">erit ergo, vt quadratum, HV, ad quadratum,
              <lb/>
            VS, ita quadratum, CV, ad rectangulum, BVO, hæc ergo ratio,
              <lb/>
            quam nempè habet quadratum, CV, ad rectangulum, BVO, ſum-
              <lb/>
            pta vice eius, quam habet quadratum, HV, ad quadratum, VS,
              <lb/>
            vel quadratum, HR, ad quadratum, SX, (quæ erat vna rationum
              <lb/>
            componentium) componit rationem omnium quadratorum triã-
              <lb/>
            guli, HCR, ad omnia quadrata hyperbolæ, SOX, ſimul ſumpta
              <lb/>
            cum ea, quam habet rectangulum, BVO, ad rectangulum, AVO,
              <lb/>
            & </s>
            <s xml:id="echoid-s9726" xml:space="preserve">cum ea, quam habet, CV, ad, VO; </s>
            <s xml:id="echoid-s9727" xml:space="preserve">harum autem trium rationũ
              <lb/>
            componentium ea, quam habet quadiatum, CV, ad rectangulum,
              <lb/>
            BVO, & </s>
            <s xml:id="echoid-s9728" xml:space="preserve">quam habet hoc rectangulum, BVO, ad rectangulum,
              <lb/>
            AVO, componunt rationem quadrat, CV, ad rectangulum, AV
              <lb/>
            O, illas ergo tres in has duas rationes reiolutas habemus .</s>
            <s xml:id="echoid-s9729" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9730" xml:space="preserve">in eam,
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            quam habea quadratum, CV, ad rectangulum, AVO, & </s>
            <s xml:id="echoid-s9731" xml:space="preserve">in eam,
              <lb/>
            quam habet, CV, ad, VO, porro iſtæ duæ rationes componunt
              <lb/>
            rationem parallelepipedi ſub, CV, & </s>
            <s xml:id="echoid-s9732" xml:space="preserve">quadrato, CV, .</s>
            <s xml:id="echoid-s9733" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9734" xml:space="preserve">cubi, CV,
              <lb/>
            ad parallelepipedum ſub, OV, & </s>
            <s xml:id="echoid-s9735" xml:space="preserve">rectangulo, AVO, .</s>
            <s xml:id="echoid-s9736" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9737" xml:space="preserve">parallele-
              <lb/>
            pipedi ſub, AV, & </s>
            <s xml:id="echoid-s9738" xml:space="preserve">quadiato, VO, .</s>
            <s xml:id="echoid-s9739" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9740" xml:space="preserve">parallelepiped ſub, AO, & </s>
            <s xml:id="echoid-s9741" xml:space="preserve">
              <lb/>
            quadrato, OV, cum cubo, OV, i. </s>
            <s xml:id="echoid-s9742" xml:space="preserve">parallelepipedi ter ſub, CO, & </s>
            <s xml:id="echoid-s9743" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0397-05" xlink:href="note-0397-05a" xml:space="preserve">36. 1. 1.</note>
            quadrato, OV, cum cubo, OV; </s>
            <s xml:id="echoid-s9744" xml:space="preserve">ergo omnia quadrata trianguli,
              <lb/>
            HCR, ad omnia quadrata hyperbolæ, SOX, erunt vt cubus, CV,
              <lb/>
            ad parallelepipedum ter ſub, CO, & </s>
            <s xml:id="echoid-s9745" xml:space="preserve">quadrato, OV, cum cubo, O
              <lb/>
            V, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s9746" xml:space="preserve"/>
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