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

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              <pb o="143" file="0163" n="163" rhead="LIBER II."/>
            ſibus æquidiſtante, eo nempè, quod producit figuram, CNX, er-
              <lb/>
              <note position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" xml:space="preserve">Corol. 12.
                <lb/>
              hb. 1.</note>
            go, CNX, erit æqualis ipſi, BVG, quod cum alijs adhuc ſerua.</s>
            <s xml:id="echoid-s3388" xml:space="preserve"/>
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        <div xml:id="echoid-div348" type="section" level="1" n="213">
          <head xml:id="echoid-head228" xml:space="preserve">F. SECTIO VI.</head>
          <p>
            <s xml:id="echoid-s3389" xml:space="preserve">QVia verò, LE, ad, EO, eſt vt, BH, ad, HC, .</s>
            <s xml:id="echoid-s3390" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3391" xml:space="preserve">vt, VE,
              <lb/>
            ad, EN, permutando, & </s>
            <s xml:id="echoid-s3392" xml:space="preserve">diuidendo, LV, ad, VE, erit vt,
              <lb/>
            ON, ad, NE, .</s>
            <s xml:id="echoid-s3393" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3394" xml:space="preserve">vt, 35, ad, 54, ergo, LE, 34, ſunt ſimi-
              <lb/>
            liter ad eandem partem diuiſæ a figuris, BVG, RSP, ergo ſunt ip-
              <lb/>
            ſæ figuræ inter ſe ſimiles, quarum latera homologa ipſæ, VG, SP,
              <lb/>
              <note position="right" xlink:label="note-0163-02" xlink:href="note-0163-02a" xml:space="preserve">Ex diffin.
                <lb/>
              Emilium
                <lb/>
              ſolid.</note>
            lineæ homologę figurarum ſimilium, LFE, 374, quarum inciden-
              <lb/>
            tes ſuntipſę, LE, 34, vnde eſt, EF, ad, 47, vt, LE, ad, 34, .</s>
            <s xml:id="echoid-s3395" xml:space="preserve">ſ.
              <lb/>
            </s>
            <s xml:id="echoid-s3396" xml:space="preserve">vt, VG, ad, SP, ſunt verò figuræ, DEF, 647, quia ſimiles, in
              <lb/>
            dupla ratione ipſarum, EF, 47, & </s>
            <s xml:id="echoid-s3397" xml:space="preserve">ipſæ, BVG, RSP, in dupla
              <lb/>
              <note position="right" xlink:label="note-0163-03" xlink:href="note-0163-03a" xml:space="preserve">Ex antec.</note>
            ratione ipſarum, VG, SP, ergo vt figura, DEF, ad figuram, 64
              <lb/>
            7, ita erit figura, BVG, vel, CNX, eidem æqualis ad figuram, R
              <lb/>
            SP, Quoniam verò ſolida, LEDF, 3647, ſunt ſimilia, vt facilè
              <lb/>
            oſtendi poreſt, & </s>
            <s xml:id="echoid-s3398" xml:space="preserve">eorum figuræ incidentes, & </s>
            <s xml:id="echoid-s3399" xml:space="preserve">oppoſitorum plano-
              <lb/>
            rum tangentium (quorum ex vna parte duo ſunt ipſa, 647, DEF,)
              <lb/>
            ſunt figuræ, LEF, 347 quarum lineæ incidentes, LE, 34, ideò
              <lb/>
            plana ipſis, DEF, 647, æquidiſtantia, quæ ſimiliter ad eandem
              <lb/>
            partem diu dunt incidentes, LE, 34, diuidunt etiam altitudines di-
              <lb/>
            ctorum ſolidorum reſpectu dictorum tangentium ſumptas ſimiliter
              <lb/>
              <note position="right" xlink:label="note-0163-04" xlink:href="note-0163-04a" xml:space="preserve">17. Vnd.
                <lb/>
              Elem.</note>
            ad eandem partem (hocdico quotieſcunque, non contingat, LE,
              <lb/>
            34, eſſe perbendiculares ipſis, DEF, 647, tunc enim ſiunt eædem
              <lb/>
            incidentes altitudines dictorum ſolidorum) cum igitur, vt, LE, ad,
              <lb/>
            34, .</s>
            <s xml:id="echoid-s3400" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3401" xml:space="preserve">ad, EO, ita ſit altitudo ſolidi, LEDF, tum adabſciſſam al-
              <lb/>
            titudinem per planum tangens in, O, ipſi, DEF, æquidiſtans .</s>
            <s xml:id="echoid-s3402" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">ad
              <lb/>
            altitudinem ſolidi, OEDF, tum ad altitudinem ſolidi, 3467, ideò
              <lb/>
            ſolida, OEDF, 347, erunt in eadem altitudine ſumpta reſpectu
              <lb/>
            baſium, DEF, 647, & </s>
            <s xml:id="echoid-s3404" xml:space="preserve">plana ipſis baſibus æquidiſtantia partes æ-
              <lb/>
            quales ab ipſis, OE, 34, abſcindentia, et am ab eorum altitudini-
              <lb/>
            bus abſcindent partes æquales, oſtendimus autem figuras, quę ab ip-
              <lb/>
            ſis, OE, 34, abſcindunt partes æquales, eſſe proportionales, ergo
              <lb/>
            in ſolidis, OEDF, 3467, in eadem altitudine exiſtentibus ſumpta
              <lb/>
            reſpectu baſium, DEF, 647, figuræ, quę ab eiſdem altitudinibus
              <lb/>
            vtcunque abſcindunt partes æquales, ſunt ſemper, vt ipſæ baſes, er-
              <lb/>
            go vt vna ad vnam, ſic omnes ad omnes, & </s>
            <s xml:id="echoid-s3405" xml:space="preserve">ſic ſolida ad ſolida .</s>
            <s xml:id="echoid-s3406" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">vt
              <lb/>
              <note position="right" xlink:label="note-0163-05" xlink:href="note-0163-05a" xml:space="preserve">4. huius.</note>
            baſis, DEF, ad baſun, 647, ita erit ſolidum, OEDF, ad ſolidum,
              <lb/>
              <note position="right" xlink:label="note-0163-06" xlink:href="note-0163-06a" xml:space="preserve">Ex antec.</note>
            3467, eſt autem, DEF, ad, 647, in ratione dupla eius, quam
              <lb/>
            habet, EF, ad, 47, .</s>
            <s xml:id="echoid-s3408" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">in ratione compoſita ex duabus rationibus
              <lb/>
              <note position="right" xlink:label="note-0163-07" xlink:href="note-0163-07a" xml:space="preserve">Deſin. 12.
                <lb/>
              lib. 1.</note>
            ipſius, EF, ad, 47, velipſius, LE, ad, 34, ergo ſolidum, </s>
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