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

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            <s xml:id="echoid-s3409" xml:space="preserve">
              <pb o="144" file="0164" n="164" rhead="GEOMETRIÆ"/>
            F, ad ſolidum, 3467, habebit rationem compoſitam ex duabus ra-
              <lb/>
            tionibus ipſius, LE, ad, 34, quod etiam ſerua.</s>
            <s xml:id="echoid-s3410" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div350" type="section" level="1" n="214">
          <head xml:id="echoid-head229" xml:space="preserve">G. SECTIO VII.</head>
          <p>
            <s xml:id="echoid-s3411" xml:space="preserve">SI igitur inter ſolida, LEDF, 3467, medium ſumamus ſoll-
              <lb/>
              <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">Deſin. 12.
                <lb/>
              lib. 1.</note>
            dum, OEDF, habebit ſolidum, LEDF, ad ſolidum, 3467,
              <lb/>
            rationem compoſitam ex ratione ſolidi, LEDF, ad ſolidum, OE
              <lb/>
            DF, .</s>
            <s xml:id="echoid-s3412" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3413" xml:space="preserve">ex ratione ipſius, LE, ad, 34, & </s>
            <s xml:id="echoid-s3414" xml:space="preserve">ex ratione ſolidi, OED
              <lb/>
            F, ad ſolidum, 3467, .</s>
            <s xml:id="echoid-s3415" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3416" xml:space="preserve">compoſitam ex duabus rationibus ipſius,
              <lb/>
            LE, ad, 34, igitur ſolidum, LEDF, ad ſolidum, 3467, habe-
              <lb/>
            bit rationem compoſitam ex tribus rationibus ipſius, LE, ad, 34,
              <lb/>
            .</s>
            <s xml:id="echoid-s3417" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3418" xml:space="preserve">triplam rationem habebit eius, quam habet, LE, ad, 34, quia
              <lb/>
              <note position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">Def. Vnd.
                <lb/>
              6. Elem.</note>
            verò, LE, 34, ſunt homologæ partes integrarum incidentium, L
              <lb/>
            G, 38, quæ ſunt in prima huius Propoſ. </s>
            <s xml:id="echoid-s3419" xml:space="preserve">figura, ideò his fruſtis ibi-
              <lb/>
            dem conſpectis iam oſtenſum erit fruſtum, LEDF, ad fruſtum, 34
              <lb/>
            67, triplam rationem habere eius, quam habet, LE, ad, 34, ideſt,
              <lb/>
            LG, ad, 38.</s>
            <s xml:id="echoid-s3420" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div352" type="section" level="1" n="215">
          <head xml:id="echoid-head230" xml:space="preserve">H. SECTIO VIII. ET VLTIMA.</head>
          <p>
            <s xml:id="echoid-s3421" xml:space="preserve">EOdem modo ſumptis alijs duobus fruſtis, D {14/ }, 6 {11/ }, oſtendemus
              <lb/>
            eadem habere triplam rationem duarum, LG, 38, & </s>
            <s xml:id="echoid-s3422" xml:space="preserve">ſimiliter
              <lb/>
            reliqua fruſta pariter triplam rationem habere duarum, LG, 38, & </s>
            <s xml:id="echoid-s3423" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0164-03" xlink:href="note-0164-03a" xml:space="preserve">12. Quin.
                <lb/>
              Elem.</note>
            vt vnum ad vnum, ſic omnia ad omnia .</s>
            <s xml:id="echoid-s3424" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">vt fruſtum, LEDF, ad
              <lb/>
            fruſtum, 3467, ita eſſe omnia fruſta ſolidi, LG, ad omnia fruſta
              <lb/>
            ſolidi, 38, ſed fruſtum, LEDF, ad fruſtum, 3467, triplam ratio-
              <lb/>
            nem habere oſtenſum eſt eius, quam habet, LG, ad, 38, ergo ſo-
              <lb/>
            lidum, LG, ad ſolidum, 38, triplam rationem habebit eius, quam
              <lb/>
              <note position="left" xlink:label="note-0164-04" xlink:href="note-0164-04a" xml:space="preserve">B. Huius
                <lb/>
              Propoſ.</note>
            habet, LG, ad, 38, eſt autem ſolidum, LG, æquale ſolido, AP,
              <lb/>
            &</s>
            <s xml:id="echoid-s3426" xml:space="preserve">, 38, ipſi, V &</s>
            <s xml:id="echoid-s3427" xml:space="preserve">, ergo ſolidum, AP, ad, V &</s>
            <s xml:id="echoid-s3428" xml:space="preserve">, triplam rationem
              <lb/>
            habebit eius, quam, LG, ad, 38, quia verò, LG, 38, ſunt inci-
              <lb/>
            dentes ſimilium planarum figurarum, H {00/ }, Σ 2, & </s>
            <s xml:id="echoid-s3429" xml:space="preserve">oppoſitarum
              <lb/>
            tangentium, HL, {00/ } G, Σ 3, 28, ideò, vt, LG, ad, 38, ita erunt
              <lb/>
            lineæ homologæ figurarum, H {00/ }, Σ 2, ſumptæ regulas, HL, Σ 3,
              <lb/>
            ex. </s>
            <s xml:id="echoid-s3430" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">ita, OX, ad, ΦΛ, iſtæ verò ſunt incidentes ſimilium figura-
              <lb/>
              <note position="left" xlink:label="note-0164-05" xlink:href="note-0164-05a" xml:space="preserve">Ex diffin.
                <lb/>
              linearum
                <lb/>
              incident.</note>
            rum, BC, ΠΩ, & </s>
            <s xml:id="echoid-s3432" xml:space="preserve">oppoſitarum tangentium, BO, CX, ΠΦ, ΩLamp;</s>
            <s xml:id="echoid-s3433" xml:space="preserve">,
              <lb/>
            ideò, vt ipſæ, OX, ΦΛ, ita erunt quælibet homologæ figurarum,
              <lb/>
            BC, ΠΩ, ſumptę regulis ipſis, CX, ΩΛ, at ſolidum, AP, ad, V &</s>
            <s xml:id="echoid-s3434" xml:space="preserve">,
              <lb/>
              <note position="left" xlink:label="note-0164-06" xlink:href="note-0164-06a" xml:space="preserve">Vt patet
                <lb/>
              in A. hu-
                <lb/>
              ius.</note>
            triplam rationem habet eius, quam, LG, ad, 38, ergo etiam tri-
              <lb/>
            plam rationem habebit eius, quam, OX, ad, ΦΛ, & </s>
            <s xml:id="echoid-s3435" xml:space="preserve">conſequenter
              <lb/>
            etiam triplam rationem eius, quam habebit quælibet in figura, </s>
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