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

Table of figures

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            <s xml:id="echoid-s13778" xml:space="preserve">
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            idem probabimus circa alias quaſcumque applicatas. </s>
            <s xml:id="echoid-s13779" xml:space="preserve">In ellipſi
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            verò oſtendemus rectangula, ℟XB, QDC, eſſe vt quadrata, BP, C
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            N, ſicut rectangula, ℟XB, QZC, vt quadrata, BP, CM. </s>
            <s xml:id="echoid-s13780" xml:space="preserve">Ergo ſi
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            intelligamus ſolidum rectangulum fieri ſub parallelogrammis, GX,
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              <figure xlink:label="fig-0552-01" xlink:href="fig-0552-01a" number="362">
                <image file="0552-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0552-01"/>
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            XE, & </s>
            <s xml:id="echoid-s13781" xml:space="preserve">quadratum ſolidum, EP,
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            communi regula, BP, erunt hæc
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            ſolida inter ſe æqualiter, vel pro-
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            portionaliter, analoga, cum ſint
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            in eiſdem planis parallelis, nem-
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            pè tranſeuntibus per lineas, ℟P,
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            GH, & </s>
            <s xml:id="echoid-s13782" xml:space="preserve">quæcunq; </s>
            <s xml:id="echoid-s13783" xml:space="preserve">plana his pa-
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            rallela præfata ſolida ſecantia,
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            producant in ipſis æquales figu-
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            ras planas, vel ſaltem proportionales, ſicut patuit de rectangulo, Q
              <lb/>
            ZC, æquali quadrato, CM; </s>
            <s xml:id="echoid-s13784" xml:space="preserve">vel ad idem exiſtente, vt rectangulum,
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            ℟XB, ad quadratum, BP. </s>
            <s xml:id="echoid-s13785" xml:space="preserve">Eadem ratione, quia probauimus re-
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            ctangulum, QDC, æquari quadrato, CN, vel ad idem eſſe vt re-
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            ctangulum, ℟XB, ad quadratum, BP, concludemus ſolidum rectã-
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            gulũ ſub trapezio, EG℟X, & </s>
            <s xml:id="echoid-s13786" xml:space="preserve">triangulo, EXB, eſſe ęqualiter, vel pro-
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            portionaliter, analogum quadr. </s>
            <s xml:id="echoid-s13787" xml:space="preserve">ſolido, EBP, iuxta communem re-
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            gulam, BP, igitur rectangulum ſolidum, ſub GX, XF, æquabitur qua-
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            drato ſolido, EP, & </s>
            <s xml:id="echoid-s13788" xml:space="preserve">rectangulum ſolidum ſub, EG℟X, EXB, ęqua-
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            bitur quadrato ſolido, EBP, vel ſaltem erunt proportionalia in el-
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            lipſi, ergo quadratum ſolidum, EP, ad quadr. </s>
            <s xml:id="echoid-s13789" xml:space="preserve">ſolidum, EBP, erit
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              <note position="left" xlink:label="note-0552-01" xlink:href="note-0552-01a" xml:space="preserve">1. huius.</note>
              <note position="left" xlink:label="note-0552-02" xlink:href="note-0552-02a" xml:space="preserve">3. huius.</note>
            vt rectangulum ſolidum ſub, GX, XE, ad rectangulum ſolidum
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            ſub, EG℟X, &</s>
            <s xml:id="echoid-s13790" xml:space="preserve">, EXB, hoc eſt, vt, ℟X, ad compoſitam ex {1/2}. </s>
            <s xml:id="echoid-s13791" xml:space="preserve">℟X,
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            & </s>
            <s xml:id="echoid-s13792" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s13793" xml:space="preserve">XB, ideſt, vt, RB, ad compoſitam ex {1/2}. </s>
            <s xml:id="echoid-s13794" xml:space="preserve">RB, & </s>
            <s xml:id="echoid-s13795" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s13796" xml:space="preserve">BE, ergo,
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            iterum conſpecta figura prop. </s>
            <s xml:id="echoid-s13797" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13798" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13799" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13800" xml:space="preserve">quadratum ſolidum portio-
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              <note position="left" xlink:label="note-0552-03" xlink:href="note-0552-03a" xml:space="preserve">16. huius.</note>
            nis, DEP, ad quadratum ſolidum, EP, erit vt compoſita ex {1/6}. </s>
            <s xml:id="echoid-s13801" xml:space="preserve">BE,
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            & </s>
            <s xml:id="echoid-s13802" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13803" xml:space="preserve">BR, ad ipſam, BR, cum enim ſemiportiones, DEB, BEP,
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            ſint homologę ſecundum regulam planum tranſiens per regulam,
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            BP, cuiæquidiſtant plana ſolida ſecantia, ſicut etiam, FB, BH, & </s>
            <s xml:id="echoid-s13804" xml:space="preserve">
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            cum quadratum ſolidum figuræ, FP, diuiſæ per lineam, EB, æque-
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              <note position="left" xlink:label="note-0552-04" xlink:href="note-0552-04a" xml:space="preserve">Cor. 3. 15.
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              huius.</note>
            tur quadratis ſolidis, FB, BH, & </s>
            <s xml:id="echoid-s13805" xml:space="preserve">duobus rectangulis ſolidis ſub, FB,
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            BH, ideſt quatuor quadratis ſolidis, BH, ideò quadratum ſolidum,
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            FP, quadruplum erit quadrati ſolidi, BH, ſicut etiam patebit qua-
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            dratum ſolidum portionis, DEP, quadruplum eſſe quadrati ſolidi
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            ſemiportionis, EBP, ergo, vt quadratum ſolidum, EBP, ad qua-
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            dratum ſolidum, BH, ita eſt quadratum ſolidum portionis, DEP, ad
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            quadratum ſolidum, DH, ideſt vt compoſita ex {1/6}. </s>
            <s xml:id="echoid-s13806" xml:space="preserve">BE, & </s>
            <s xml:id="echoid-s13807" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13808" xml:space="preserve">BR, ad
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            ipſam, BR, quod oſtendendum erat.</s>
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