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

Table of contents

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[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
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          <head xml:id="echoid-head484" xml:space="preserve">E. SECTIO V.</head>
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            <s xml:id="echoid-s7811" xml:space="preserve">_T_Andem, quòd, ſi dictorum trilineorum ſecantes ád tángentes eán-
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            demrationem habuerint, omnia quadrata eorundem erunt in tri-
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            plaratione tangentium, vel ſecantium.</s>
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        <div xml:id="echoid-div784" type="section" level="1" n="465">
          <head xml:id="echoid-head485" xml:space="preserve">THEOREMA XXIX. PROPOS. XXXI.</head>
          <p>
            <s xml:id="echoid-s7813" xml:space="preserve">EXponatur figura Theor. </s>
            <s xml:id="echoid-s7814" xml:space="preserve">antecedentis, & </s>
            <s xml:id="echoid-s7815" xml:space="preserve">intra paralle-
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            logrammum, AC, ducatur vtcunq; </s>
            <s xml:id="echoid-s7816" xml:space="preserve">recta, EF, pa-
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            rallelaipſi, BC, quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s7817" xml:space="preserve">Oſtendemus. </s>
            <s xml:id="echoid-s7818" xml:space="preserve">n.
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            </s>
            <s xml:id="echoid-s7819" xml:space="preserve">om@ia quadrata, AC, demptis omnibus quadratis ſemipa-
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            rabolæ, ABC, ad omnia quadrata, EC, demptis omni-
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            bus quadratis quadrilinei, MEBC, eſſe vt quadratum, A
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            B, ad quadratum, BE.</s>
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            <s xml:id="echoid-s7821" xml:space="preserve">Omnia. </s>
            <s xml:id="echoid-s7822" xml:space="preserve">n. </s>
            <s xml:id="echoid-s7823" xml:space="preserve">quadrata, AC, ad omnia quadrata, EC, demptis
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            omnibus quadratis quadrilinei, EMCB, habent rationem compo-
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            ſitam ex ea, quam habent omnia quadrata, AC, ad omnia qua-
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            drata, EC, ideſt ex ea, quam habet, AB, ad, BE, & </s>
            <s xml:id="echoid-s7824" xml:space="preserve">ex ea,
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              <note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">10. l. 2.</note>
            quam habent omnia quadrata, EC, ad reſiduum, demptis ab ijſdem
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                <image file="0345-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0345-01"/>
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            omnibus quadratis quadrilinei, MEBC,
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            .</s>
            <s xml:id="echoid-s7825" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7826" xml:space="preserve">ex ea, quam habet, AB, ad {1/2}, BE,
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              <note position="right" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">23. huius.</note>
            duæ autem hæ rationes .</s>
            <s xml:id="echoid-s7827" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7828" xml:space="preserve">quàm habet,
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            AB, ad, BE, &</s>
            <s xml:id="echoid-s7829" xml:space="preserve">, AB, ad {1/2}. </s>
            <s xml:id="echoid-s7830" xml:space="preserve">BE, com-
              <lb/>
            ponunt rationem quadrati, AB, ad re-
              <lb/>
            ctangulum ſub, EB, & </s>
            <s xml:id="echoid-s7831" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s7832" xml:space="preserve">BE, .</s>
            <s xml:id="echoid-s7833" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7834" xml:space="preserve">ad
              <lb/>
            dimidium quadrati, BE, ergo omnia
              <lb/>
              <note position="right" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">21. huius.</note>
            quadrata, AC, ad omnia quadrata, E
              <lb/>
            C, demptis omnibus quadratis quadrili-
              <lb/>
            nei, MEBC, erunt vt quadratum, AB,
              <lb/>
            ad dimidium quadrati, BE, ſunt autem omnia quadrata, AC,
              <lb/>
            demptis omnibus quadratis ſemiparabolæ, ABC, dimidium
              <lb/>
            omnium quadratorum, AC, quia omnia quadrata, AC, ſunt du-
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            pla omnium quadratorum ſemiparabolæ, ABC, ergo omnia qua-
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            drata, AC, demptis omnibus quadratis ſemiparabolæ, ABC, ad
              <lb/>
            omnia quadrata, EC, demptis omnibus quadratis quadrilinei, E
              <lb/>
            MCB, erunt vt dimidium quadrati, AB, ad dimidium quadrati,
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            BE, ideſt vt quadratum, AB, ad quadratum, BE, quod erat
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            demonſtrandum.</s>
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