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

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        <div xml:id="echoid-div1047" type="section" level="1" n="631">
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            <s xml:id="echoid-s11414" xml:space="preserve">
              <pb o="442" file="0462" n="462" rhead="GEOMETRIÆ"/>
            poſitæ ex dictis trapezijs, & </s>
            <s xml:id="echoid-s11415" xml:space="preserve">triangulo, FIQ, quæ oſtenſa eſt eſſe
              <lb/>
            minor ſpatio reſiduo iam dicto circuli, ECDB, & </s>
            <s xml:id="echoid-s11416" xml:space="preserve">ideò figura com-
              <lb/>
            poſita ex dictis faſcijs erit minor ſpatio reſiduo iam dicto, cuita-
              <lb/>
            men circumſcribitur, quod eſt abſurdum, non eſt ergo trilineum,
              <lb/>
            FLHG, minus dicto ſpatio reſiduo circuli, ECDB, & </s>
            <s xml:id="echoid-s11417" xml:space="preserve">oſtenſum eſt
              <lb/>
            neq; </s>
            <s xml:id="echoid-s11418" xml:space="preserve">eſſe illo maius, ergo erit illi æquale, & </s>
            <s xml:id="echoid-s11419" xml:space="preserve">triangulus, FHG, eſt
              <lb/>
            æqualis circulo, ECDB, ergo triangulus, FHG, ad trilineum,
              <lb/>
            FLHG, erit vt circulus, ECDB, ad reſiduum ſpatium ab eo dem-
              <lb/>
            pto ſpatio ſub ſpirali, A53 MB, & </s>
            <s xml:id="echoid-s11420" xml:space="preserve">voluta, AB, ſed triangulus, FH
              <lb/>
            G, eſt ſexquialter trilinei, FLHG, ergo circulus, ECDB, erit ſex-
              <lb/>
            quialter ſpatij reſidui iam dicti, & </s>
            <s xml:id="echoid-s11421" xml:space="preserve">conſequenter erit triplus ſpatij,
              <lb/>
            quod comprehenditur ſub ſpirali, A53MB, & </s>
            <s xml:id="echoid-s11422" xml:space="preserve">voluta, AB, quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s11423" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1050" type="section" level="1" n="632">
          <head xml:id="echoid-head662" xml:space="preserve">COROLLARIVM</head>
          <p style="it">
            <s xml:id="echoid-s11424" xml:space="preserve">_H_Inc patet eductas à vertice parabolæ ad ſecantem quamcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s11425" xml:space="preserve">diametro eiuſdem parallelam, parabola, ac tangente ibidem
              <lb/>
            interceptam, ſimiliter ſecare eandem, actranſiens per punctum cur-
              <lb/>
            uæ parabolæ, in quo prædicta eam diuidit, eidemq; </s>
            <s xml:id="echoid-s11426" xml:space="preserve">parallela, ſecatip-
              <lb/>
            ſam tangentem, eſtenſum enim eſt, ex. </s>
            <s xml:id="echoid-s11427" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11428" xml:space="preserve">HG, ad GΓ, eſſe vt, GF, ad,
              <lb/>
            FQ. </s>
            <s xml:id="echoid-s11429" xml:space="preserve">ex quo nouus, ni fallor, ac pulcberrimus deſcribendi parabolam
              <lb/>
            elicitur modus.</s>
            <s xml:id="echoid-s11430" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1051" type="section" level="1" n="633">
          <head xml:id="echoid-head663" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11431" xml:space="preserve">_S_It deſcribendæ parabolæ diameter, A2, baſis, QX, cuiper, A, ſit
              <lb/>
            ducta parallela, LF, ſintque, AF, AL, æquales ipſis, 2X, 2Q, æ-
              <lb/>
            qualibus, ſecta autem, AF, in quotcunq; </s>
            <s xml:id="echoid-s11432" xml:space="preserve">partes æquales, vt in quin-
              <lb/>
            que, velutietiam, LA, in punctis, K, I, H, G, B, C, D, E, per ipſa du-
              <lb/>
            cantur diametro, A2, æquidiſtantes, ΚΣ, 19, H8, G7, B3, C4, D5, E6,
              <lb/>
            ſecantes ſi niliter baſim, QX, in æquas partes in punctis, Σ, 9, 8, 7, 3,
              <lb/>
            4, 5, 6, tandem iunctis,, LQ, FX, ipſæ ſimiliter ſecentur ac, AF, vel,
              <lb/>
            AL, ſcilicet in quinq; </s>
            <s xml:id="echoid-s11433" xml:space="preserve">partes æquales in punctis, R, S, T, V, M, N,
              <lb/>
            O, P, & </s>
            <s xml:id="echoid-s11434" xml:space="preserve">ad bæc puncta ducantur ab, A, rectæ lineæ, AR, AS, AT,
              <lb/>
            AV, AM, AN, AO, AP, necnon, AQ, AX, notentur autem pun-
              <lb/>
            cta, in quibus eductæ ab, A, ſecant parallelas diametro, A2, eatamẽ,
              <lb/>
            in quibus eductæ diuidunt eas parallelas, quæ viciſſim abſcindunt de
              <lb/>
            ipſis, AL, AF, verſus, A, eandem partem, quam ab ipſis, QL, XF, ab-
              <lb/>
            ſcindunt eductę, verſus tamen puncta, L, F, vt ex. </s>
            <s xml:id="echoid-s11435" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11436" xml:space="preserve">notabimus pun-
              <lb/>
            ctum, γ, in quo educta, AP, abſcindit {4/5}. </s>
            <s xml:id="echoid-s11437" xml:space="preserve">ipſius, QL, verſus, L, </s>
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