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-s7596" xml:space="preserve">
              <pb o="315" file="0335" n="335" rhead="LIBER IV."/>
            ita erit alia prædictæ parallela ad diſtantiam parallelarum
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            ductarum ab eiuſdem extremitate ſecundò dictæ.</s>
            <s xml:id="echoid-s7597" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7598" xml:space="preserve">Sit ergo intra curuam parabolicam, ABCDF, ducta vtcunque,
              <lb/>
            BF, obliquè ſecans axem, NR, in eandem curuam terminata,
              <lb/>
            agatur deinde intra portionem, BNF, reſectam à, BF, recta, C
              <lb/>
            D, parallela ipſi, BF; </s>
            <s xml:id="echoid-s7599" xml:space="preserve">ducantur inſuperà punctis, B, C, D, F, axi,
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            NR, parallelæ, BO, CV, DG, FH, & </s>
            <s xml:id="echoid-s7600" xml:space="preserve">à puncto, F, cadat
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              <figure xlink:label="fig-0335-01" xlink:href="fig-0335-01a" number="225">
                <image file="0335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0335-01"/>
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            ipſi, NR, perpendicularis, F
              <lb/>
            A, ſecans parallelas, DG
              <lb/>
            R, CV, BO, in punctis, G,
              <lb/>
            R, V, O, poterunt ergo dicta-
              <lb/>
            rum parallelarum diſtantiæ iumi
              <lb/>
            in ipſamet, AF, nam ipſa per-
              <lb/>
            pendiculariter dictas parallelas
              <lb/>
            ſecat, erit ergo, OF, diſtantia
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            parallelarum, BO, FH, ab
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            extremis punctis rectæ, BF, ductarum; </s>
            <s xml:id="echoid-s7601" xml:space="preserve">pariter, VG, erit diſtan-
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            tia parallelarum, CV, DG, ab extremis punctis, CD, ducta-
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            rum. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">Dico ergo, BF, ad, FO, eſſe vt, CD, ad, VG: </s>
            <s xml:id="echoid-s7603" xml:space="preserve">Ducan-
              <lb/>
            tur a puncto, D, ipſi, CV, perpendicularis, DX, ſecans, BF, in,
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            M, quoniam ergo anguli, BOF, CXD, ſunt recti, ideò iuntin-
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            terſe æ quales, item anguius, OBF, eſt æqualis angulo, VIF, & </s>
            <s xml:id="echoid-s7604" xml:space="preserve">V
              <lb/>
            IF, ipſi angulo, XCD, ergo angulus, OBF, erit æqualis angulo, X
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              <note position="right" xlink:label="note-0335-01" xlink:href="note-0335-01a" xml:space="preserve">46. Elem.</note>
            CD, & </s>
            <s xml:id="echoid-s7605" xml:space="preserve">ideò reliquus, OFB, reliquo, XDC, æqualis erit, & </s>
            <s xml:id="echoid-s7606" xml:space="preserve">trian-
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            guli, BOF, CXD, ſimiles erunt, vnde, BF, ad, FO, erit vt, C
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            D, ad, DX, . </s>
            <s xml:id="echoid-s7607" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7608" xml:space="preserve">ad, VG, quod oſtendere opus erat.</s>
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          <head xml:id="echoid-head465" xml:space="preserve">PROBLEMA II. PROPOS. XXV.</head>
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            <s xml:id="echoid-s7610" xml:space="preserve">A Sſumpta iterum ſuperioris figura, dimiſſa axi, & </s>
            <s xml:id="echoid-s7611" xml:space="preserve">ei-
              <lb/>
            dem parallelis, BO, CV, DG, FH, & </s>
            <s xml:id="echoid-s7612" xml:space="preserve">ipſa, DX,
              <lb/>
            ſiguram plènam deſcribere cum portione, BCDF, com-
              <lb/>
            munem habens angulum mixtum ſub, BF, & </s>
            <s xml:id="echoid-s7613" xml:space="preserve">curua, FD
              <lb/>
            C, quifit ad punctum, F, ita vt quælibet in deſctipta figu-
              <lb/>
            ra recta linea ipſi, BF, æquidiſtanter ducta, ſit diſtantia pa-
              <lb/>
            rallelarum axi, quæ ab extremis punctis eiuſdem rectæ li-
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            neæ, productæ vſque ad curuam parabolicam, duci poſſunt:
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            </s>
            <s xml:id="echoid-s7614" xml:space="preserve">Vocetur autem hæc deſcripta figura; </s>
            <s xml:id="echoid-s7615" xml:space="preserve">figura diſtantiarum
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            portionis, ſiue parabolæ, BCDF.</s>
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