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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              <pb o="299" file="0319" n="319" rhead="LIBER IV."/>
            E, & </s>
            <s xml:id="echoid-s7233" xml:space="preserve">iungatur, AG. </s>
            <s xml:id="echoid-s7234" xml:space="preserve">Dico trilineum, ABH, ad trilineum, AM
              <lb/>
            H, eſſe vt, BH, cum, CE, ad ipſam, AM, cum, CE: </s>
            <s xml:id="echoid-s7235" xml:space="preserve">Prius au-
              <lb/>
            tem dico portionculam, ASB, eſſe æqualem portionculæ, MIH,
              <lb/>
            & </s>
            <s xml:id="echoid-s7236" xml:space="preserve">enim trapezium, ABOR, æquatur trapezio, ROHM, & </s>
            <s xml:id="echoid-s7237" xml:space="preserve">
              <lb/>
            quadrilineum, RASBO, ipſi quadrilineo, RMIHO, cum, A
              <lb/>
            O, axis, vel diameter bifariam diuidat omnes æquidiſtantes ipſi, B
              <lb/>
            H, & </s>
            <s xml:id="echoid-s7238" xml:space="preserve">ideò omnes lineæ quadrilinei, RASBO, æquentur omni-
              <lb/>
            bus lineis quadrilinei, RMHO, vnde dicta quadrilinea etiam ſunt
              <lb/>
            ęqualia, & </s>
            <s xml:id="echoid-s7239" xml:space="preserve">ideo portionculæ, ASB, MIH, inter ſe ſunt æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s7240" xml:space="preserve">
              <note position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">3.2.</note>
            Quoniam vero portio, ASBC, ad triangulum, ABC, eſt vt com-
              <lb/>
            poſita ex {1/3}, BC, & </s>
            <s xml:id="echoid-s7241" xml:space="preserve">ex, CH, ad, CH, ideò, diuidendo, portion-
              <lb/>
              <note position="right" xlink:label="note-0319-02" xlink:href="note-0319-02a" xml:space="preserve">8. huius.</note>
            cula, ASB, ad triangulum, ABC, erit vt {1/3}, BC, ad, CH, vel
              <lb/>
            vt, BC, ad triplam, CH, . </s>
            <s xml:id="echoid-s7242" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7243" xml:space="preserve">ſumpta, BC, communi altitudine, vt
              <lb/>
            quadratum, BC, ad rectangulum ſub, BC, & </s>
            <s xml:id="echoid-s7244" xml:space="preserve">tripla, CH; </s>
            <s xml:id="echoid-s7245" xml:space="preserve">eſt au-
              <lb/>
              <note position="right" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">5. l. 2.</note>
            tem triangulum, ABC, ad triangulum, ABH, vt, CB, ad, BH,
              <lb/>
            ideſt (ſumpta communi altitudine tripla, CH,) vt rectangulum
              <lb/>
            ſub, BC, & </s>
            <s xml:id="echoid-s7246" xml:space="preserve">tripla, CH, ad rectangulum ſub, BH, & </s>
            <s xml:id="echoid-s7247" xml:space="preserve">tripla, CH,
              <lb/>
              <figure xlink:label="fig-0319-01" xlink:href="fig-0319-01a" number="212">
                <image file="0319-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0319-01"/>
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            ergo ex æquali portioncula, ASB,
              <lb/>
            ad triangulum, ABH, erit vt qua-
              <lb/>
            dratum, BC, ad rectangulum ſub,
              <lb/>
            BH, & </s>
            <s xml:id="echoid-s7248" xml:space="preserve">tripla, HC, quoniam vero,
              <lb/>
            BC, eſt media proportionalis inter
              <lb/>
            triplam, HC, & </s>
            <s xml:id="echoid-s7249" xml:space="preserve">ipſam, CE, ideò
              <lb/>
              <note position="right" xlink:label="note-0319-04" xlink:href="note-0319-04a" xml:space="preserve">Elicitur
                <lb/>
              ex 12. 1. 2.</note>
            quadiatum, BC, æquatur rectan-
              <lb/>
            gulo ſub tripla, HC, & </s>
            <s xml:id="echoid-s7250" xml:space="preserve">ſub, CE,
              <lb/>
            vnde portioncula, ASB, ad triangulum, ABH, erit vt rectangu-
              <lb/>
            lum ſub, CE, & </s>
            <s xml:id="echoid-s7251" xml:space="preserve">tripla, CH, ad rectangulum ſub, BH, & </s>
            <s xml:id="echoid-s7252" xml:space="preserve">tripla,
              <lb/>
            CH, ideſt erit, vt baſis, CE, ad baſim, BH, ergo, componendo,
              <lb/>
            trilineum, ASBH, ad triangulum, ABH, erit vt, CE, cum, B
              <lb/>
            H, ad ipſam, BH, triangulum verò, ABH, ad triangulum, AC
              <lb/>
            G, vel ad triangulum, AGM, eſt vt, BH, ad, CG, vel ad, AM,
              <lb/>
            eſt vero triangulum, AGM, æquale triangulo, AHM, ergo tri-
              <lb/>
            lineum, ASBH, ad triangulum, AMH, erit vt, CE, cum, BH,
              <lb/>
            ad, AM, eſt verò trilineum, ASBH, ad portionculam, ASB,
              <lb/>
            vel, MIH, illi æqualem, per conuerſionem rationis, vt, BH,
              <lb/>
            cum, CE, ad ipſam, CE, ergo, colligendo, trilineum, ASBH,
              <lb/>
            ad triangulum, AHM, & </s>
            <s xml:id="echoid-s7253" xml:space="preserve">portionculam, MIH, . </s>
            <s xml:id="echoid-s7254" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7255" xml:space="preserve">ad trilineum,
              <lb/>
            AMIH, erit vt, BH, cum, CE, ad ipſam, AM, cum, CE,
              <lb/>
            quod oſtendere oportebat.</s>
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