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

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        <div xml:id="echoid-div182" type="section" level="1" n="119">
          <p>
            <s xml:id="echoid-s1837" xml:space="preserve">
              <pb o="72" file="0092" n="92" rhead="GEOMETRIÆ"/>
            quibus incidunt ad eundem angulum ex eadem parte, EO, MR, & </s>
            <s xml:id="echoid-s1838" xml:space="preserve">
              <lb/>
            quę diuidunt ipſas, EO, MR, ſimiliter ad eandem partem exiſten-
              <lb/>
            tes parallelæ ipſis, BC, GN, ſunt vtipſæ, EO, MR, ad eandem
              <lb/>
            partem eodem ordine inter ipſas, & </s>
            <s xml:id="echoid-s1839" xml:space="preserve">circuitum dictarum figurarum
              <lb/>
            compræhenſæ, quia quæ ſunt ex vna parte ſunt æquales ipſis, BO,
              <lb/>
            GR, & </s>
            <s xml:id="echoid-s1840" xml:space="preserve">quæ ex alia ipſis, OC, RN, in triangulis autem ſunt, vt
              <lb/>
            ipſæ, BO, GR, vel, OC, RN, .</s>
            <s xml:id="echoid-s1841" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1842" xml:space="preserve">vt, OE, RM, & </s>
            <s xml:id="echoid-s1843" xml:space="preserve">ideo, earum
              <lb/>
              <note position="left" xlink:label="note-0092-01" xlink:href="note-0092-01a" xml:space="preserve">B. defin.
                <lb/>
              10.</note>
            incidentes, & </s>
            <s xml:id="echoid-s1844" xml:space="preserve">oppoſitarum tangentium dictarum erunt ipſæ, EO,
              <lb/>
            MR, quę tangentes ſunt regulæ homologarum ſimilium figurarum,
              <lb/>
            AC, FN, vel, EBC, MGN. </s>
            <s xml:id="echoid-s1845" xml:space="preserve">Vlterius, quia, BXC, GYN,
              <lb/>
            ſunt ſemicirculi, erunt figurę planę ſimiles iuxta meam definitionem,
              <lb/>
            quarum & </s>
            <s xml:id="echoid-s1846" xml:space="preserve">tangentium, quæ per extrema, BC, GN, ducuntur e-
              <lb/>
              <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">Ex Lem.
                <lb/>
              ant.</note>
            runt incidentes ipſi diametri, BC, GN, vt probatum fuit, veluti
              <lb/>
            idem patet de ſemicirculis, B ℟ C, GZN, & </s>
            <s xml:id="echoid-s1847" xml:space="preserve">de quibuſcumq; </s>
            <s xml:id="echoid-s1848" xml:space="preserve">alijs,
              <lb/>
            quæ diuident ipſas, EO, MR, ſimiliter ad eandem partem, & </s>
            <s xml:id="echoid-s1849" xml:space="preserve">con-
              <lb/>
            ſequenter diuidunt etiam altitudines eorũdem reſpectu baſium ſum-
              <lb/>
              <note position="left" xlink:label="note-0092-03" xlink:href="note-0092-03a" xml:space="preserve">17. Vnde-
                <lb/>
              cimi El.</note>
            ptas ſimiliter ad eandem partem, & </s>
            <s xml:id="echoid-s1850" xml:space="preserve">deijs, quæ per extrema, E, M,
              <lb/>
            ducuntur, habemus igitur cylindros, AC, FN, ſiue conos, BEC,
              <lb/>
            GMN, quorum ducta ſunt plana oppoſita tangentia dictorum ſo-
              <lb/>
            lidorum homologis figuris parallela, quæ ſunt plana, B ℟ CX, A
              <lb/>
            D; </s>
            <s xml:id="echoid-s1851" xml:space="preserve">GYNZ, FH, quibus inciderunt duo plana ad ęquales angulos
              <lb/>
            ex eadem parte, illa nempè, in quibus ſunt ipſa parallelogramma,
              <lb/>
            AC, FN, vel triangula, BEC, quia ſunt recta ad baſes .</s>
            <s xml:id="echoid-s1852" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">ad dicta
              <lb/>
            tangentia, ipſæ autem ſiguræ .</s>
            <s xml:id="echoid-s1854" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">parallelogramma, vel triangula in-
              <lb/>
            uenta ſunt eſſe ſimilia, quarum homologarum regulæ oppoſitę tan-
              <lb/>
            gentes, AD, BC; </s>
            <s xml:id="echoid-s1856" xml:space="preserve">FH, GN, quarum ſunt incidentes, EO, MR,
              <lb/>
            earum autem lineæ homologæ, ſumptæ regulis dictis tangentibus,
              <lb/>
            repertæ ſunt eſſe incidentes figurarum planarum ſimilium, quæ di-
              <lb/>
            uidunt altitudines dictorum ſolidorum iam dictas ſimiliter ad ean-
              <lb/>
            dem partem, & </s>
            <s xml:id="echoid-s1857" xml:space="preserve">oppoſitarum tangentium, quæ omnes ijs, quæ du-
              <lb/>
            cuntur per extrema, BC, GN, tangentes circulos, B ℟ CX, GY
              <lb/>
            NZ, ſunt ęquidiſtantes, vt facilè conſideranti patebit, ergo cylin-
              <lb/>
            dri, AC, FN, vel coni, BEC, GMN, ſunt ſimiles iuxta meam defi-
              <lb/>
              <note position="left" xlink:label="note-0092-04" xlink:href="note-0092-04a" xml:space="preserve">Defin. 11.</note>
            nitionem generalem ſimilium ſolidorum, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s1858" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div184" type="section" level="1" n="120">
          <head xml:id="echoid-head131" xml:space="preserve">THEOREMA XXIX. PROPOS. XXXII.</head>
          <p>
            <s xml:id="echoid-s1859" xml:space="preserve">DEfinitio mea ſimilium conicorum, & </s>
            <s xml:id="echoid-s1860" xml:space="preserve">cylindricorum
              <lb/>
            concordat cum definitione generali ſimilium ſolido-
              <lb/>
            rum.</s>
            <s xml:id="echoid-s1861" xml:space="preserve"/>
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