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

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              <pb o="139" file="0159" n="159" rhead="LIBER II."/>
            neſque ipſorum ſolidorum, LDGF, 3687, ſimiliter ad eandem
              <lb/>
            partem diuidentibus, conceptę (vt probatum eſt) inter ſe ſimiles, vt
              <lb/>
            ipſæ, DEF, 647, necnon, MK {14/ }, 9 {10/ } {11/ }, & </s>
            <s xml:id="echoid-s3288" xml:space="preserve">omnium earundem
              <lb/>
            linearum homologarum regulæ duabus quibuſdam, nempe ipſis, O
              <lb/>
            E, Φ 4, æquid ſtantes, & </s>
            <s xml:id="echoid-s3289" xml:space="preserve">earum incidentes ipſæ, EF, 47, necnon,
              <lb/>
            K {14/ }, {10/ } {11/ }, quę omnes incidentes iacent in plano ſiminum figurarum,
              <lb/>
            LFG, 378, & </s>
            <s xml:id="echoid-s3290" xml:space="preserve">ſunt earum homologæ, æquidiſtantes ipſis, LQ,
              <lb/>
            3 {12/ }, communibus ſectionibus planorum incidentium figurarum, L
              <lb/>
            FG, 378, & </s>
            <s xml:id="echoid-s3291" xml:space="preserve">oppoſitorum tangentium, quarum quidem figurarum
              <lb/>
              <note position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">26. lib. 1.</note>
            plana ſunt ad plana tangentia, vt dictum eſt, æquè ad eandem par-
              <lb/>
            tem inclinata, & </s>
            <s xml:id="echoid-s3292" xml:space="preserve">cum ipſæ, inquam, figuræ, LFG, 378, ſint ſi-
              <lb/>
            miles interſe, nam ex. </s>
            <s xml:id="echoid-s3293" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3294" xml:space="preserve">eſt, EF, ad, 47, vt, OE, ad, Φ 4, ideſt
              <lb/>
              <note position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">A. Def. 10.
                <lb/>
              lib. 1.</note>
            vt, LG, ad, 38, quæ diuidunt ſimiliter ad eandem partem ipſas, L
              <lb/>
            G, 38, (quod etiam de cæteris probabitur) & </s>
            <s xml:id="echoid-s3295" xml:space="preserve">cum anguli, LGT,
              <lb/>
              <note position="right" xlink:label="note-0159-03" xlink:href="note-0159-03a" xml:space="preserve">26. lib. 1.</note>
            38 {13/ }, ſint etiam æquales ſuperius dictis conſequenter, & </s>
            <s xml:id="echoid-s3296" xml:space="preserve">ijs, quæ
              <lb/>
            lib. </s>
            <s xml:id="echoid-s3297" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">26. </s>
            <s xml:id="echoid-s3300" xml:space="preserve">oſtenia ſunt, ideò, inquam, & </s>
            <s xml:id="echoid-s3301" xml:space="preserve">ipſæ figuræ, LFG,
              <lb/>
              <note position="right" xlink:label="note-0159-04" xlink:href="note-0159-04a" xml:space="preserve">Defin. 11.
                <lb/>
              lib. 1.</note>
            378, & </s>
            <s xml:id="echoid-s3302" xml:space="preserve">ipſa iolida, LDGF, 3687, pariter ſimilia erunt.</s>
            <s xml:id="echoid-s3303" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3304" xml:space="preserve">Nunc ſolidum, 3678, planis, oppoſitis tangentibus parallelis,
              <lb/>
            in talia fruſta diuiſum intelligatur, vt quæ in ipſis ducuntur rectæ li-
              <lb/>
            neę ipſi, 38, æquidiſtantes, in ciſdem fruſtis ſingulę integrę habean-
              <lb/>
            tur .</s>
            <s xml:id="echoid-s3305" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3306" xml:space="preserve">ita vt ductarum ſic linearum, quæ ad fruſtorum ambientem ſu-
              <lb/>
            perficiem terminantur, pars quidein non ſit intra fruſta, pars verò
              <lb/>
            extra, ſed totæ intra, vel ſaltem nihil earum extra reperiatur, hanc
              <lb/>
            etenim ſectionem ſupponere ſieri poſſe nullam inuoluit repugnan-
              <lb/>
            tiam, cum hoc totum ſolidum ex duabus linearum translationibus re-
              <lb/>
            ſultans ſit interius integrum, enim vero ſi præfatum ſolidum in fru-
              <lb/>
            ſta quæcunque per dicta plana parallela icinderetur, nec in ipſis con-
              <lb/>
            tingeret, quod attentamus, denuò facta fruſta planis prædictis pa-
              <lb/>
            rallelis continuò reſecaremus, vt tandem omnis lmearum, ipſi, 38,
              <lb/>
            æquidiſtanter in d ctis fruſtis ducibilium, fractura tolleretur: </s>
            <s xml:id="echoid-s3307" xml:space="preserve">Eſto igi-
              <lb/>
            tur, quod hoc obtinuerimus per duo plana, 9 {10/ } {11/ }, 647, oppoſitis
              <lb/>
            plan@s tangentibus parallela, qu@bus ſolidum, 3678, intria fruſta,
              <lb/>
            3647, 6 {11/ }, &</s>
            <s xml:id="echoid-s3308" xml:space="preserve">, 9 {10/ } {11/ } 8, ſectum habeatur eius rationis, qualem di-
              <lb/>
            ximus, in his ergo ſingul s fruſtis ductæ quæcunque ipſi, 38, æqui-
              <lb/>
            diſtantes, & </s>
            <s xml:id="echoid-s3309" xml:space="preserve">ad eorum ſuperficiem terminatæ, integræ habebuntur.
              <lb/>
            </s>
            <s xml:id="echoid-s3310" xml:space="preserve">Sit vlterius in alio ſolido, LDFG, diuifa, LG, ſimiliter ac, 38, in
              <lb/>
            punctis, E, K, per quæ tranſeant plana, DEF, MK {14/ }, oppoſitis
              <lb/>
            planis tangentibus parallela, quibus ſolidum, LDFG, in tria fru-
              <lb/>
            ſta ſcindatur, LDEF, D {14/ }, MK {14/ } G, erunt ergo etiam hęc fruſta
              <lb/>
            eius rationis, qualem cupimus .</s>
            <s xml:id="echoid-s3311" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3312" xml:space="preserve">omnes ductę ipſi, LG, æquidiſtan-
              <lb/>
            tes, in ipſis fruſtis conceptæ, integræ erunt; </s>
            <s xml:id="echoid-s3313" xml:space="preserve">quodex eorum ſimili-
              <lb/>
            tudine facilè oſtendi poteſt, ſi enim aliqua ex. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3315" xml:space="preserve">in fruſto, </s>
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