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

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        <div xml:id="echoid-div338" type="section" level="1" n="207">
          <p style="it">
            <s xml:id="echoid-s3147" xml:space="preserve">
              <pb o="133" file="0153" n="153" rhead="LIBER II."/>
            ac voluntas, pulchras demonſtrationes etſi difficiles, ac longas infracto
              <lb/>
            quodam animi vigore ſuperandi, potius quam ab ipſis ſuperari velint.
              <lb/>
            </s>
            <s xml:id="echoid-s3148" xml:space="preserve">Poterat quidem in plures Propoſitiones commodius diſtribui, ſed cum-
              <lb/>
            illæ omnes in hanc ſimpliciſſimam eſſent conſpiraturæ, eas omnes ſub
              <lb/>
            hac vna Propoſit. </s>
            <s xml:id="echoid-s3149" xml:space="preserve">colligaui, quamtamen in Sectiones ceu in tot mem-
              <lb/>
            bra distinguere placuit, ne Lectoris mens nimium defatigaretur. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">Porrò
              <lb/>
            quanti hæc Propoſitio ſit momenti, ſicut & </s>
            <s xml:id="echoid-s3151" xml:space="preserve">præcedens Propoſ. </s>
            <s xml:id="echoid-s3152" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3153" xml:space="preserve">atten-
              <lb/>
            ta præcipuè earum vniuerſalitate, neminem, qui eaſdem intellex erit,
              <lb/>
            fore puto, qui itidem non agnoſcat; </s>
            <s xml:id="echoid-s3154" xml:space="preserve">quid enim fuit, quo ad figuras pla-
              <lb/>
            nas, Euclidem lib. </s>
            <s xml:id="echoid-s3155" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3156" xml:space="preserve">Elementorum in Propoſ 19. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">demonſtraſſe ſimilia-
              <lb/>
            triangula, & </s>
            <s xml:id="echoid-s3158" xml:space="preserve">in Propoſ. </s>
            <s xml:id="echoid-s3159" xml:space="preserve">20. </s>
            <s xml:id="echoid-s3160" xml:space="preserve">ſimilia Polygona eſſe in dupla ratione la-
              <lb/>
            te um homologorum, necnon lib. </s>
            <s xml:id="echoid-s3161" xml:space="preserve">12. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3163" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3164" xml:space="preserve">Circulos eſſe, vt diame-
              <lb/>
            trorum quadrata, hoc eſt in dupla ratione diametrorum? </s>
            <s xml:id="echoid-s3165" xml:space="preserve">Similiter in eo,
              <lb/>
            quod ſpectat ad ſolida, quid fuit ipſum nobis in lib. </s>
            <s xml:id="echoid-s3166" xml:space="preserve">12. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3169" xml:space="preserve">oſten-
              <lb/>
            diſſe ſimiles Pyramides eſſe in tripla ratione laterum homologorum, & </s>
            <s xml:id="echoid-s3170" xml:space="preserve">
              <lb/>
            in Prop. </s>
            <s xml:id="echoid-s3171" xml:space="preserve">12. </s>
            <s xml:id="echoid-s3172" xml:space="preserve">ſimiles conos, & </s>
            <s xml:id="echoid-s3173" xml:space="preserve">cylindros eſſe in triplaratione diametro-
              <lb/>
            rum quæ ſunt in baſibus, & </s>
            <s xml:id="echoid-s3174" xml:space="preserve">in Propoſ. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">18. </s>
            <s xml:id="echoid-s3176" xml:space="preserve">Sphæras itidem eſſe in tri-
              <lb/>
            pla proportione diametrorum? </s>
            <s xml:id="echoid-s3177" xml:space="preserve">Quid tandem fuit alios quoq; </s>
            <s xml:id="echoid-s3178" xml:space="preserve">demonſtraſ-
              <lb/>
            ſe, quædam alia ſimilia ſolida, vt portiones Sphærarum, necnon Sphæ-
              <lb/>
            roidearum, & </s>
            <s xml:id="echoid-s3179" xml:space="preserve">Conoide arum figurarum, eſſe in tripla ratione linearum,
              <lb/>
            vel laterum homologorum? </s>
            <s xml:id="echoid-s3180" xml:space="preserve">Præ huius comparatione, quod in his duabus
              <lb/>
            tantum Propoſitionibus edocemur; </s>
            <s xml:id="echoid-s3181" xml:space="preserve">omnes .</s>
            <s xml:id="echoid-s3182" xml:space="preserve">n. </s>
            <s xml:id="echoid-s3183" xml:space="preserve">ſimiles figuras planas in
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s3184" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3185" xml:space="preserve">& </s>
            <s xml:id="echoid-s3186" xml:space="preserve">omnes ſolidas in ſubſequenti Propoſ. </s>
            <s xml:id="echoid-s3187" xml:space="preserve">17. </s>
            <s xml:id="echoid-s3188" xml:space="preserve">comprebendimus,
              <lb/>
            quod mebercle conſideratione dignum videtur.</s>
            <s xml:id="echoid-s3189" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div339" type="section" level="1" n="208">
          <head xml:id="echoid-head223" xml:space="preserve">THEOREMA XVII. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s3190" xml:space="preserve">OMnia ſimilia ſolida ſunt in tripla ratione linearum, vel
              <lb/>
            laterum homologorum, quę ſunt in eorundem homo-
              <lb/>
            logis figuris.</s>
            <s xml:id="echoid-s3191" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div340" type="section" level="1" n="209">
          <head xml:id="echoid-head224" xml:space="preserve">A. DEMONSTRATIONIS SECTIO I.</head>
          <p>
            <s xml:id="echoid-s3192" xml:space="preserve">SInt duo vtcunq; </s>
            <s xml:id="echoid-s3193" xml:space="preserve">ſimilia ſolida, V &</s>
            <s xml:id="echoid-s3194" xml:space="preserve">, AP. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">Dico hæc eſſe in tri-
              <lb/>
            pla ratione linearum, ſiue laterum homologorum, quæ ſunt in
              <lb/>
            eorundem homologis figuris. </s>
            <s xml:id="echoid-s3196" xml:space="preserve">Quia ergo dicta ſolida ſunt ſimilia, po-
              <lb/>
            terunt duci duo plana oppoſita tangentia in vnoquoque propoſito-
              <lb/>
            rum ſolidorum (quæ in ſolido, AP, repræſententur peripſas, AH,
              <lb/>
              <note position="right" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              lib. 1.</note>
            P {00/ }, & </s>
            <s xml:id="echoid-s3197" xml:space="preserve">in ſolido, V &</s>
            <s xml:id="echoid-s3198" xml:space="preserve">, peripſas, V Σ, & </s>
            <s xml:id="echoid-s3199" xml:space="preserve">2,) homologis eorundem
              <lb/>
            figuris æquidiſtantia, inter quæ etiam ducibilia erunt alia duo plana
              <lb/>
              <note position="right" xlink:label="note-0153-02" xlink:href="note-0153-02a" xml:space="preserve">Defin. 11.
                <lb/>
              lib. 1.</note>
            æqualiter ad ipſa, & </s>
            <s xml:id="echoid-s3200" xml:space="preserve">ad eandem partem inclinata, in quibus </s>
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