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

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        <div xml:id="echoid-div714" type="section" level="1" n="420">
          <head xml:id="echoid-head440" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7210" xml:space="preserve">_H_Inc apparet, ſi producatur, GO, btcunq; </s>
            <s xml:id="echoid-s7211" xml:space="preserve">in, E, & </s>
            <s xml:id="echoid-s7212" xml:space="preserve">circa ſemiaxes,
              <lb/>
            bel ſemidiametros, HO, OE, deſcribi intelligatur ſemicirculus,
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            vel ſemiellipſis, HEA, quod, ſi etiam producantur, ST, VX, in, N,
              <lb/>
            M, & </s>
            <s xml:id="echoid-s7213" xml:space="preserve">iungantur, HN, HM; </s>
            <s xml:id="echoid-s7214" xml:space="preserve">omnia quadrata trianguli, HXM, ad
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            omnia quadrata trianguli, HTN, regula, OE, erunt in ratione com-
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            poſita ex ea, quam habet quadratum, XM, ad quadratum, TN, . </s>
            <s xml:id="echoid-s7215" xml:space="preserve">i re-
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            ctangulum, AXH, ad rectangulum, ATH, & </s>
            <s xml:id="echoid-s7216" xml:space="preserve">ex ea, quam habet,
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            XH, ad, HT, . </s>
            <s xml:id="echoid-s7217" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7218" xml:space="preserve">erunt, bt parallelepipedum ſub altitudine, AX, baſt
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            quadrato, XH, ad parallelepipedum ſub altitudine, AT, baſi qua-
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            drato, TH.</s>
            <s xml:id="echoid-s7219" xml:space="preserve"/>
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        <div xml:id="echoid-div715" type="section" level="1" n="421">
          <head xml:id="echoid-head441" xml:space="preserve">THEOREMA X. PROPOS. XI.</head>
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            <s xml:id="echoid-s7220" xml:space="preserve">SI ad axim, vel diametrum datæ parabolæ ordinatim ap-
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            plicentur duę rectæ lineę eandem ſecantes, deinde ſum-
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            pto extremo puncto minoris dictarum ordinatim applicata-
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            rum, & </s>
            <s xml:id="echoid-s7221" xml:space="preserve">alio extremo puncto maioris dictarum, ſed non ad
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            eandem partem, iungantur dicta puncta recta linea; </s>
            <s xml:id="echoid-s7222" xml:space="preserve">hæc di-
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            uidet quadrilineum duabus ordinatim applicatis incluſum
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            in duo trilinea: </s>
            <s xml:id="echoid-s7223" xml:space="preserve">Trilineum igitur conſtitutum in maiori di-
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            ctarum linearum ad trilineum cõſtitutum in minori tanquam
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            in baſi erit, vt dicta maior ordinatim ductarum, ſimul cum
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            tertia proportionali duarum, quarum prima eſt tripla com-
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            poſitę ex minori, & </s>
            <s xml:id="echoid-s7224" xml:space="preserve">dimidia exceſſus maioris ſuper minorem,
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            ſecunda autem eſt dimidia dicti exceſſus, ad eandem mino-
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            rem, cum eadem tertia proportionali.</s>
            <s xml:id="echoid-s7225" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7226" xml:space="preserve">Sit ergo parabola, cuius baſis, BH, axis, vel diameter, NO, due
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            adipſam vtcunque ordinatim applicatæ ſint, BH, baſis, &</s>
            <s xml:id="echoid-s7227" xml:space="preserve">, AM,
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            minor ipſa, BH, abſcindens parabolam, ANM, ſumatur autem
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            vtcunque punctum, A, extremum minoris, AM, & </s>
            <s xml:id="echoid-s7228" xml:space="preserve">punctum, H,
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            ad aliam partem de duobus extremis maioris, BH, & </s>
            <s xml:id="echoid-s7229" xml:space="preserve">iungantur, A,
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            H, puncta recta linea, AH, deindeà punctis, A, M, demittantur
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            verſus, BH, parallelæipſi, NO; </s>
            <s xml:id="echoid-s7230" xml:space="preserve">AC, MG, erit ergo, BC, GH,
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            exceſſus, BH, ſuper, AM, &</s>
            <s xml:id="echoid-s7231" xml:space="preserve">, BC, æqualis ipſi, GH, dimidium
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            dicti exceſſus; </s>
            <s xml:id="echoid-s7232" xml:space="preserve">fiat etiam, vt tripla, HC, ad, BC, ita, BC, ad, </s>
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