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

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            <s xml:id="echoid-s1716" xml:space="preserve">
              <pb o="67" file="0087" n="87" rhead="LIBER I."/>
            uX, oſtenderemus figuras his ductis comprehenſas, quales fuerunt,
              <lb/>
            LPIK, YdXu, eſſe ſimiles, ex quo propoſitum quoque noſtrum
              <lb/>
            haberemus. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Similiter ſi anguli ſolidi, Q, f, pluribus, quam tribus
              <lb/>
            angulis planis contineantur, currit tamen demonſtratio, cum trian-
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">Ex Lem.
                <lb/>
              4. & 1.</note>
            gula, GOo, 8fs, licet non ſint in ambitu ſolidorum ſint tamen ſi-
              <lb/>
            milia, & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">ęquè ad eandem partem inclinata figuris, cum quibus con-
              <lb/>
            currunt, etenim ex. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">pyramides, SGOo, p8fs, ſi eorum latera
              <lb/>
            iungerentur, ſimiles eſſent, quapropter ipſius demonſtrationis vis
              <lb/>
            non eneruatur. </s>
            <s xml:id="echoid-s1721" xml:space="preserve">Similiter ſi, oOS, sfp, non eſſent triangula, ſed
              <lb/>
            aliæ quæcumque figuræ ſimiles, pro, oS, sp, acceptis lateribus ip-
              <lb/>
            ſis, Oo, fs, adiuncta, os, conterminantibus, & </s>
            <s xml:id="echoid-s1722" xml:space="preserve">planis ad hæc la-
              <lb/>
            tera pariter terminantibus, eodem modo demonſtratio abſoluere-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s1723" xml:space="preserve">hæc omnia autem ſingillatim proſequi nimis longum, ac ſche-
              <lb/>
            matibus rem aperire, res tricis plena eſſet, quapropter Lectoris in-
              <lb/>
            duſtriæ hoc relinquo, ſi enim ea rectè percepcrit, quę ſuperius expli-
              <lb/>
            cata ſunt, circa huius veritatem minimè hæſitabit, infinita autem ſi-
              <lb/>
            milium ſolidorum planis contentorum varietas efficit, vt ægrè ip-
              <lb/>
            ſius demonſtrationis vniuerſalitatem oculis ſubijcere poſſim, quod
              <lb/>
            Lector æqui, bonique faciat, hæc verò oſtendenda proponebantur.</s>
            <s xml:id="echoid-s1724" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div175" type="section" level="1" n="115">
          <head xml:id="echoid-head126" xml:space="preserve">THEOREMA XXVII. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s1725" xml:space="preserve">POſita definit. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">vndec. </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">ſimilium ſolidarum figura-
              <lb/>
            rum, ſequitur, & </s>
            <s xml:id="echoid-s1730" xml:space="preserve">mea definitio generalis ſimilium ſo-
              <lb/>
            lidorum.</s>
            <s xml:id="echoid-s1731" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1732" xml:space="preserve">Aſſumptis denuò antec. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">figuris, ſint adhuc ſimilia ſolida
              <lb/>
            iuxta Euclidem ipſa, AGS, T8p. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">Dico eadem eſſe etiam ſimilia
              <lb/>
            iuxta definit. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">huius, quam de ſimilibus ſolidis generaliter attuli.
              <lb/>
            </s>
            <s xml:id="echoid-s1738" xml:space="preserve">Sint autem ducta eadem oppoſita tangentia plana, vt ibi, ita vt duę
              <lb/>
            ſimiles figurę, GFSO, f8 & </s>
            <s xml:id="echoid-s1739" xml:space="preserve">p, ſint plana contactuum ex vna par-
              <lb/>
            te, ex alia verò ſint plana tangentia, AC, TR, captis autem alijs
              <lb/>
            duabus ſimilibus figuris cum baſibus concurrentibus, ipſis nempè, O
              <lb/>
            So, fps, illarum plana extendantur, ita vt ſecent oppoſita tangen-
              <lb/>
            tia plana, in rectis nempè, BC, OD; </s>
            <s xml:id="echoid-s1740" xml:space="preserve">QR, f℟; </s>
            <s xml:id="echoid-s1741" xml:space="preserve">extenſis autem vl-
              <lb/>
            terius planis, GOo, 8fs, quęnunc ſint in ambitibus ſolidorum ipſa
              <lb/>
            ſecent oppoſita tangentia plana in rectis, AB, TQ; </s>
            <s xml:id="echoid-s1742" xml:space="preserve">GO, 8f, & </s>
            <s xml:id="echoid-s1743" xml:space="preserve">
              <lb/>
            plana figurarum, OSO, fps, producta in rectis, BO, Qf, ſecen-
              <lb/>
            tur verò hęc ſolida duobus planis oppoſitis tangentibus parallelis vt-
              <lb/>
            cumque, & </s>
            <s xml:id="echoid-s1744" xml:space="preserve">ſint illa eadem, quę in ſolidis produxerunt figuras, LH
              <lb/>
            MP, YVZd, iſtæ ergo ſimiles erunt, & </s>
            <s xml:id="echoid-s1745" xml:space="preserve">earum homologæ, ſi </s>
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