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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            <s xml:id="echoid-s7647" xml:space="preserve">Sint intra curuam parabolicam, BAC, duæ vtcunquæ ductæ in
              <lb/>
            eandem terminatæ, DF, MC, quarum, DF, rectè, altera, MC,
              <lb/>
            obliquè ſecet axem, AP, ſit autem deſcripta linea, HR, vt ſit con-
              <lb/>
            ſtituta, HRC, figura diſtantiarum portionis, MFC, & </s>
            <s xml:id="echoid-s7648" xml:space="preserve">ab eodem
              <lb/>
            vertice, H, à quo ducitur linea, HR, ducatur, HQ, parallela
              <lb/>
            axi, AP, & </s>
            <s xml:id="echoid-s7649" xml:space="preserve">ſint diametri, AZ, HO, parabolarum, DAF, M
              <lb/>
            HC, inter ſeæquales. </s>
            <s xml:id="echoid-s7650" xml:space="preserve">Dico ergo omnia quadrata parabolæ, DA
              <lb/>
            F, regula, DF, eſſe æqualia rectangulis ſub parabola, MHC, re-
              <lb/>
            gula, MC, & </s>
            <s xml:id="echoid-s7651" xml:space="preserve">ſub, HRC, figura diſtantiarum eiuſdem parabolæ,
              <lb/>
            MHC. </s>
            <s xml:id="echoid-s7652" xml:space="preserve">Iungantur ergo, DA, AF, MH, HC, & </s>
            <s xml:id="echoid-s7653" xml:space="preserve">à puncto, M,
              <lb/>
            ducatur, MX, axi, AP, æquidiſtans, à puncto verò, C, perpendi-
              <lb/>
            cularis axi, AP, producta vſq; </s>
            <s xml:id="echoid-s7654" xml:space="preserve">in, B, tandem à puncto, H, ipſa, H
              <lb/>
            I, perpendicularis ipſi, MC: </s>
            <s xml:id="echoid-s7655" xml:space="preserve">Omnia ergo quadrata, DAF, para-
              <lb/>
            bolæ, regula, DF, adrectangula ſub parabola, MHC, regula, M
              <lb/>
            C, & </s>
            <s xml:id="echoid-s7656" xml:space="preserve">ſub trilineo, HRC, habent rationem compoſitam ex ea,
              <lb/>
            quam habent omnia quadrata parabolæ, DAF, regula, DF, ad
              <lb/>
              <note position="left" xlink:label="note-0338-01" xlink:href="note-0338-01a" xml:space="preserve">Defin.
                <lb/>
              12. 1. 1.</note>
            omnia quadrata parabolæ, MHC, regula, MC, & </s>
            <s xml:id="echoid-s7657" xml:space="preserve">ex ea, quam
              <lb/>
            habent omnia quadrata parabolę, MHC, regula, MC, adrectan-
              <lb/>
            gula ſub parabola, MHC, & </s>
            <s xml:id="echoid-s7658" xml:space="preserve">ſub trilineo, HRC, regula eadem,
              <lb/>
              <figure xlink:label="fig-0338-01" xlink:href="fig-0338-01a" number="228">
                <image file="0338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0338-01"/>
              </figure>
            MC: </s>
            <s xml:id="echoid-s7659" xml:space="preserve">Omnia verò quadrata para-
              <lb/>
            bolæ, DMF, regula, DF, ad om-
              <lb/>
            nia quadrata parabolæ, MHC, re-
              <lb/>
            gula, MC, ſunt vt omnia quadrata
              <lb/>
            trianguli, DAF, regula, DF, ad
              <lb/>
            omnia quadrata trianguli, MHC,
              <lb/>
            regula, MC, nam omnia quadrata
              <lb/>
            parabolarum ſunt ſexquialtera om-
              <lb/>
            nium quadratorum triangulorum in
              <lb/>
            eiſdem baſibus, & </s>
            <s xml:id="echoid-s7660" xml:space="preserve">circa eoſdem axes cum ipſis conſtitutorum, regu-
              <lb/>
              <note position="left" xlink:label="note-0338-02" xlink:href="note-0338-02a" xml:space="preserve">21. huius.</note>
            lis baſibus: </s>
            <s xml:id="echoid-s7661" xml:space="preserve">Omnia inſuper quadrata trianguli, DAF, regula, DF,
              <lb/>
            ad omnia quadrata trianguli, MHC, regula, MC, habent ratio-
              <lb/>
              <note position="left" xlink:label="note-0338-03" xlink:href="note-0338-03a" xml:space="preserve">D. Corol.
                <lb/>
              22. 1. 2.</note>
            nem compoſitam ex ratione altitudinum, & </s>
            <s xml:id="echoid-s7662" xml:space="preserve">quadratorum baſium
              <lb/>
            . </s>
            <s xml:id="echoid-s7663" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7664" xml:space="preserve">ex ratione, quam habet, AZ, ad, HI, & </s>
            <s xml:id="echoid-s7665" xml:space="preserve">ex rationẽ, quam ha-
              <lb/>
            bet quadratum, DF, ad quadratum, MC, vel quadratum, ZF,
              <lb/>
            ad quadratum, OC, eſt autem, AZ, æqualis ipſi, HO, ex hypo-
              <lb/>
            teſi, &</s>
            <s xml:id="echoid-s7666" xml:space="preserve">, ZF, ipſi, QC, ergo omnia quadrata trianguli, DAF, ad
              <lb/>
              <note position="left" xlink:label="note-0338-04" xlink:href="note-0338-04a" xml:space="preserve">Corol.
                <lb/>
              17. huius.</note>
            omnia quadrata trianguli, MHC, regulis iam dictis, habebunt ra-
              <lb/>
            tionem compoſitam ex ea, quam habet, OH, ad HI, & </s>
            <s xml:id="echoid-s7667" xml:space="preserve">ex ea,
              <lb/>
            quam habet quadratum, QC, ad qu adratum, CO, quia verò trian-
              <lb/>
            guli, HIO, OQC, ſunt æquianguli, ideò, OH, ad, HI, erit vt,
              <lb/>
            OC, ad, CQ, ergo illa habebunt rationem compoſitam ex ea, quam
              <lb/>
            habet, OC, ad, CQ, & </s>
            <s xml:id="echoid-s7668" xml:space="preserve">quadratum QC, ad quadratum, CO, </s>
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