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

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            <s xml:id="echoid-s12813" xml:space="preserve">
              <pb o="502" file="0522" n="522" rhead="GEOMETRIÆ"/>
            T, & </s>
            <s xml:id="echoid-s12814" xml:space="preserve">cęteris vt ibidem conſtructis, eodem modo prius oſtende-
              <lb/>
            mus vt ibitriangula, AFE, KZT, necnon, AFG, KZY, EFG, TZ
              <lb/>
            Y, & </s>
            <s xml:id="echoid-s12815" xml:space="preserve">AGE, KYT, eſſe inter ſe ſimilia, & </s>
            <s xml:id="echoid-s12816" xml:space="preserve">angulum, PGE, æquari
              <lb/>
            angulo, XYT. </s>
            <s xml:id="echoid-s12817" xml:space="preserve">Hoc ſuppoſito, cum, PG, ad, GA, ſit vt, XY, ad,
              <lb/>
            YK, &</s>
            <s xml:id="echoid-s12818" xml:space="preserve">, AG, ad GE, vt, KY, ad, YT, exæquali, PG, ad GE, erit vt, X
              <lb/>
            Y, ad, YT, & </s>
            <s xml:id="echoid-s12819" xml:space="preserve">ſunt circa æquales angulos, PGE, XYT, ergotrian-
              <lb/>
              <note position="left" xlink:label="note-0522-01" xlink:href="note-0522-01a" xml:space="preserve">6. Sex. Ele.</note>
            gula, PGE, XYT, ſunt ſimilia, ergo, PE, ad, EG, eſt vt, XT, ad,
              <lb/>
            TY, &</s>
            <s xml:id="echoid-s12820" xml:space="preserve">, GE, ad, EA, vt, YT, ad, Tk, ergo, PE, ad, EA, eſt vt, X
              <lb/>
            T, ad, TH, & </s>
            <s xml:id="echoid-s12821" xml:space="preserve">ſunt circa rectos, PEA, XTK, ergo triangula, PEA,
              <lb/>
              <note position="left" xlink:label="note-0522-02" xlink:href="note-0522-02a" xml:space="preserve">6. Sex. Ele.</note>
            XTk, ſunt ſimilia, ergo, AP, ad, PE, erit vt, KX, ad, XT, ſed &</s>
            <s xml:id="echoid-s12822" xml:space="preserve">,
              <lb/>
            PE, ad, PG, eſt vt, XT, ad, XY, ergo, AP, ad, PG, erit vt, KX, ad,
              <lb/>
            XY, &</s>
            <s xml:id="echoid-s12823" xml:space="preserve">, PG, ad, GA, eſt vt, XY, ad, Yk, ergo triangula, APG, kXY,
              <lb/>
              <note position="left" xlink:label="note-0522-03" xlink:href="note-0522-03a" xml:space="preserve">5. Sex. Ele.</note>
            ſunt ſimilia, rectus autem eſt angulus, AGP, cum rectus ponatur,
              <lb/>
            AGV, ergo, kYX, &</s>
            <s xml:id="echoid-s12824" xml:space="preserve">, ΚΥΔ, rectus erit, vnde anguli, AGV, κΥΔ ę-
              <lb/>
            quales erunt. </s>
            <s xml:id="echoid-s12825" xml:space="preserve">Cum verò quadratum, PA, ęquetur quadratis, PG,
              <lb/>
              <note position="left" xlink:label="note-0522-04" xlink:href="note-0522-04a" xml:space="preserve">47. Primi
                <lb/>
              Elem.</note>
            GA, ſeu quadratis, PG, GE, EA, & </s>
            <s xml:id="echoid-s12826" xml:space="preserve">quadratum PA, ęquetur etiam
              <lb/>
            quadratis, PE, EA, duo quadrata, PE, EA, æ quabuntur tribus
              <lb/>
            quadratis, PG, GE, EA, & </s>
            <s xml:id="echoid-s12827" xml:space="preserve">ablato communi quadrato, EA, erit
              <lb/>
            quadratum, PE, æquale quadratis, PG, GE, vnde angulus, PGE,
              <lb/>
              <note position="left" xlink:label="note-0522-05" xlink:href="note-0522-05a" xml:space="preserve">48. Primi
                <lb/>
              Elem.
                <lb/>
              Deſin. 6.
                <lb/>
              Vnd, Ele.</note>
            rectus erit, & </s>
            <s xml:id="echoid-s12828" xml:space="preserve">conſequenter etiam rectus ipſe, XYT, vnde anguli,
              <lb/>
            AGE, kYT, erunt inclinationes ſecundorum planorum, AV, ΚΛ,
              <lb/>
            cum ſubiectis planis, HV, &</s>
            <s xml:id="echoid-s12829" xml:space="preserve">Δ, & </s>
            <s xml:id="echoid-s12830" xml:space="preserve">inter ſe ęquales, per quę ſuppo-
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            ſito caſui ſatisfieri maniſeſtum eſt.</s>
            <s xml:id="echoid-s12831" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12832" xml:space="preserve">In Lemmate 5. </s>
            <s xml:id="echoid-s12833" xml:space="preserve">poſt Prop. </s>
            <s xml:id="echoid-s12834" xml:space="preserve">8. </s>
            <s xml:id="echoid-s12835" xml:space="preserve">prętermiſſa fui demonſtratio prę-
              <lb/>
            ſentis caſus, cum eadem facilis exiſtimaretur, nempè quando, FE,
              <lb/>
            FG, cum, AE, AG, &</s>
            <s xml:id="echoid-s12836" xml:space="preserve">, LI, LM, cum, HI, HM, concurrere mini-
              <lb/>
            me poſſe contingat, vt cum angulos, EAF, GAF, IHL, MHL, re-
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            ctos, vel recto maiores acciderit eſſe: </s>
            <s xml:id="echoid-s12837" xml:space="preserve">Sic autem tum hic, tum ſup-
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            poſitus ibi caſus poterit vniuerſaliter demonſtrari. </s>
            <s xml:id="echoid-s12838" xml:space="preserve">Intelligantur
              <lb/>
              <note position="left" xlink:label="note-0522-06" xlink:href="note-0522-06a" xml:space="preserve">4. Primi
                <lb/>
              Elem.</note>
            ipſę, AE, AF, AG, HI, HL, HM, inter ſe ęquales, & </s>
            <s xml:id="echoid-s12839" xml:space="preserve">iungantur,
              <lb/>
            EF, FG, EG, IL, LM, IM: </s>
            <s xml:id="echoid-s12840" xml:space="preserve">Cum ergo anguli, FAG, LHM, ſup-
              <lb/>
            ponantur ęquales, & </s>
            <s xml:id="echoid-s12841" xml:space="preserve">latera, FA, LH, &</s>
            <s xml:id="echoid-s12842" xml:space="preserve">, AG, HM, ęqualia, erunt
              <lb/>
            pariter baſes, FG, LM, æquales: </s>
            <s xml:id="echoid-s12843" xml:space="preserve">Sic autem probabimus tum, EF,
              <lb/>
              <note position="left" xlink:label="note-0522-07" xlink:href="note-0522-07a" xml:space="preserve">7. Primi
                <lb/>
              Elem.</note>
            IL, tum, EG, IM, inter ſe æquales eſſe. </s>
            <s xml:id="echoid-s12844" xml:space="preserve">Rurſus ſuſpenſa pyrami-
              <lb/>
            de, AEFG, ponatur, F, in, L, demittaturq; </s>
            <s xml:id="echoid-s12845" xml:space="preserve">FG, ſuper, LM, cui cõ-
              <lb/>
            gruet, & </s>
            <s xml:id="echoid-s12846" xml:space="preserve">triangulo, EFG, cadente ſuper, ILM, punctum, E, pari-
              <lb/>
            ter erit in, I; </s>
            <s xml:id="echoid-s12847" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s12848" xml:space="preserve">punctum, A, dico fore in, H, tres enim ſphæ-
              <lb/>
            ricæ ſuperficies ſuper centris, I, L, M, radijs inuicem ſe ſecantibus
              <lb/>
            deſcriptæ, nempè radijs, HI, HL, HM, ſeu, AE, AF, AG, in duo-
              <lb/>
            bus tantum punctis ſeſe decuſſare poſſunt, vt facile oſtendi poteſt,
              <lb/>
            duę enim quęlibet ſphæricæ ſuperficies in circuli periphæria ſe </s>
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