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

Table of contents

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[311.] THEOREMA VIII. PROPOS. IX.
Page: 230 (210)
[312.] COROLLARIVM.
Page: 231 (211)
[313.] THEOREMA IX. PROPOS. X.
Page: 231 (211)
[314.] COROLLARIVM.
Page: 232 (212)
[315.] THEOREMAX. PROPOS. XI.
Page: 233 (213)
[316.] COROLLARIVM I.
Page: 234 (214)
[317.] COROLL II. A. SECTIO I.
Page: 235 (215)
[318.] B. SECTIO II.
Page: 235 (215)
[319.] C. SECTIO III.
Page: 235 (215)
[320.] D. SECTIO IV.
Page: 235 (215)
[321.] E. SECTIO V.
Page: 236 (216)
[322.] F. SECTIO VI.
Page: 236 (216)
[323.] THEOREMA XI. PROPOS. XII.
Page: 236 (216)
[324.] THEOREMA XII. PROPOS. XIII.
Page: 237 (217)
[325.] COROLLARIVM.
Page: 239 (219)
[326.] THEOREMA XIII. PROPOS. XIV.
Page: 239 (219)
[327.] COROLLARIVM.
Page: 242 (222)
[328.] THEOREMA XIV. PROPOS. XV.
Page: 242 (222)
[329.] ALITER.
Page: 244 (224)
[330.] THEOREMA XV. PROPOS. XVI.
Page: 244 (224)
[331.] THEOREMA XVI. PROPOS. XVII.
Page: 247 (227)
[332.] COROLLARIVM I.
Page: 248 (228)
[333.] COROLLARIVM II.
Page: 249 (229)
[334.] THEOREMA XVII. PROPOS. XVIII.
Page: 249 (229)
[335.] COROLLARIVM.
Page: 251 (231)
[336.] THEOREMA XVIII. PROPOS. XIX.
Page: 251 (231)
[337.] COROLLARIVM.
Page: 252 (232)
[338.] THEOREMA XIX. PROPOS. XX.
Page: 252 (232)
[339.] COROLLARIVM.
Page: 254 (234)
[340.] THEOREMA XX. PROPOS. XXI.
Page: 254 (234)
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          <head xml:id="echoid-head442" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7257" xml:space="preserve">_H_Inc patet triangulum, ABH, ad portionculam, ASB, eſſe bt,
              <lb/>
            BH, ad, CE.</s>
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          <head xml:id="echoid-head443" xml:space="preserve">THEOREMA XI. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s7259" xml:space="preserve">ASſumpta figura Propoſ. </s>
            <s xml:id="echoid-s7260" xml:space="preserve">ant. </s>
            <s xml:id="echoid-s7261" xml:space="preserve">dimiſſa recta, AG, & </s>
            <s xml:id="echoid-s7262" xml:space="preserve">con-
              <lb/>
            ſtituto parallelogrammo ſuper, BH, circa axim, vel
              <lb/>
            diametrum, RO, quod ſit, PH, iunctiſque, BR, RH, o-
              <lb/>
            ſtendemus parallelogrammum, PH, ad fruſtum parabolæ,
              <lb/>
            ASBHIM, eſſe vt, BH, ad, HC, cum, CE; </s>
            <s xml:id="echoid-s7263" xml:space="preserve">& </s>
            <s xml:id="echoid-s7264" xml:space="preserve">trian-
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            gulum, RBH, ad idem fruſtum eſſe vt, BH, ad duplam,
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            HC, CE.</s>
            <s xml:id="echoid-s7265" xml:space="preserve"/>
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            <s xml:id="echoid-s7266" xml:space="preserve">Parallelogrammum enim, PH, eſt ad triangulum, ABH, vt
              <lb/>
            dupla, BH, ad ipſam, BH, triangulum verò, ABH, ad ſection-
              <lb/>
            culam, ASB, eſt vt, BH, ad, CE, ergo, ex æquali, parallelo-
              <lb/>
            grammum, PH, ad ſectionculam, ASB, eſt vt dupia, BH, ad,
              <lb/>
              <note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">Gorol. 11
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              huius.</note>
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            CE, & </s>
            <s xml:id="echoid-s7267" xml:space="preserve">ad duas portionculas, AS
              <lb/>
            B, MIH, erit vt dupla, BH, ad
              <lb/>
            duplam, CE, ideſt vt, BH, ad, C
              <lb/>
              <note position="left" xlink:label="note-0320-02" xlink:href="note-0320-02a" xml:space="preserve">O. 1. 2.</note>
            E. </s>
            <s xml:id="echoid-s7268" xml:space="preserve">Item parallelogrammum, PH,
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            ad trapezium, ABHM, eſt vt, B
              <lb/>
            H, ad, AM, cum dimidio exceſſus,
              <lb/>
            BH, ſuper, AM, . </s>
            <s xml:id="echoid-s7269" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7270" xml:space="preserve">ad, AM, vel,
              <lb/>
            CG, GH, ergo, colligendo, pa-
              <lb/>
            rallelogrammum, PH, ad ſectionculas, ASB, MIH, cum trape-
              <lb/>
            zio, ABHM, . </s>
            <s xml:id="echoid-s7271" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7272" xml:space="preserve">ad fruſtum parabolæ, ASBHIM, erit vt, BH,
              <lb/>
            ad, HC, cum, CE. </s>
            <s xml:id="echoid-s7273" xml:space="preserve">Quia verò triangulum, RBH, eſt dimidium
              <lb/>
            parallelogrammi, PH, ideò ad fruſtum, ASBH'IM, erit vt di-
              <lb/>
            midia, BH, ad, HC, cum, CE, . </s>
            <s xml:id="echoid-s7274" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">vt, BH, ad duplam, HC, C
              <lb/>
            E, quod erat oſtendendum.</s>
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