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

Table of contents

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[531.] COROLLARIVM XXVII.
Page: 383 (363)
[532.] SCHOLIV M.
Page: 384 (364)
[533.] Finis quarti Libri.
Page: 384 (364)
[534.] GEOMETRIÆ CAVALERII. LIBER QVINTVS. In quo de Hyperbola, Oppoſitis Sectionib us, ac ſolidis ab eiſdem genitis, babetur contemplatio. THEOREMA I. PROPOS. I.
Page: 385 (365)
[535.] THEOREMA II. PROPOS. II.
Page: 387 (367)
[536.] THEOREMA III. PROPOS. III.
Page: 388 (368)
[537.] THEOREMA IV. PROPOS. IV.
Page: 390 (370)
[538.] THEOREMA V. PROPOS. V.
Page: 391 (371)
[539.] PROBLEMA I. PROPOS. VI.
Page: 393 (373)
[540.] THEOREMA VI. PROPOS. VII.
Page: 394 (374)
[541.] THEOREMA VII. PROPOS. VIII.
Page: 395 (375)
[542.] THEOREMA VIII. PROPOS. IX.
Page: 396 (376)
[543.] THEOREMA IX. PROPOS. X.
Page: 398 (378)
[544.] THEOREMA X. PROPOS. XI.
Page: 399 (379)
[545.] THEOREMA XI. PROPOS. XII.
Page: 401 (381)
[546.] THEOREMA XII. PROPOS. XIII.
Page: 403 (383)
[547.] THEOREMA XIII, PROPOS. XIV.
Page: 404 (384)
[548.] SCHOLIVM.
Page: 406 (386)
[549.] THEOREMA XIV. PROPOS. XV.
Page: 406 (386)
[550.] THEOREMA XV. PROPOS. XVI.
Page: 407 (387)
[551.] COROLLARIVM.
Page: 407 (387)
[552.] THEOREMA XVI. PROPOS. XVII.
Page: 407 (387)
[553.] THE OREMA XVII. PROPOS. XVIII.
Page: 408 (388)
[554.] THEOREMA XVIII. PROPOS. XIX.
Page: 409 (389)
[555.] COROLLARIVM.
Page: 409 (389)
[556.] SCHOLIVM.
Page: 409 (389)
[557.] THEOREMA XIX. PROPOS. XX.
Page: 410 (390)
[558.] THEOREMA XX. PROPOS. XXI.
Page: 412 (392)
[559.] A@@ter ſupradictam rationem explicare.
Page: 414 (394)
[560.] COROLLARIVM:
Page: 415 (395)
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              <figure xlink:label="fig-0394-01" xlink:href="fig-0394-01a" number="269">
                <image file="0394-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0394-01"/>
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            diuidendo minor ea, quam habet,
              <lb/>
            AC, ad, CE, eandem ergo, quam
              <lb/>
            habet, HL, ad, LR, habebit, AC, ad
              <lb/>
            maiorem, CE, ſit illa, CO, & </s>
            <s xml:id="echoid-s9627" xml:space="preserve">per,
              <lb/>
            O, ducatur, SV, parallela ipſi regu-
              <lb/>
            læ, FG, iunganturque, SE, EV: </s>
            <s xml:id="echoid-s9628" xml:space="preserve">Om-
              <lb/>
            nia ergo quadrata hyperbolæ, SEV,
              <lb/>
            ad omnia quadrata trianguli, SEV,
              <lb/>
            ſunt vt, AO, ad, OC, quia verò, AC,
              <lb/>
            ad, CO, eſt vt, HL, ad, LR, compo-
              <lb/>
            nendo, AO, ad, OC, erit vt, HR, ad,
              <lb/>
            RL, ergo omnia quadrata hyperbo-
              <lb/>
            læ, SEV, ad omnia quadrata triangu-
              <lb/>
            li, SEV, erunt vt, HR, ad, RL, .</s>
            <s xml:id="echoid-s9629" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9630" xml:space="preserve">in
              <lb/>
            ratione data, quod facere opus erat.</s>
            <s xml:id="echoid-s9631" xml:space="preserve"/>
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        <div xml:id="echoid-div904" type="section" level="1" n="540">
          <head xml:id="echoid-head564" xml:space="preserve">THEOREMA VI. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s9632" xml:space="preserve">SI circa datam hyperbolam deſcribantur aſymptoti,
              <lb/>
            eiuſdem autem baſis vſq; </s>
            <s xml:id="echoid-s9633" xml:space="preserve">ad aſymptotos producatur,
              <lb/>
            quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s9634" xml:space="preserve">O nnia quadrata hyperbolæ ad
              <lb/>
            omnia quadrata trianguli aſymptotis, & </s>
            <s xml:id="echoid-s9635" xml:space="preserve">baſi comprchen-
              <lb/>
            ſi, habebunt rationem compoſitam ex ea, quam habet
              <lb/>
            quadratum baſis hyperbolæ ad quadratum baſis trianguli,
              <lb/>
            & </s>
            <s xml:id="echoid-s9636" xml:space="preserve">ex ea, quam habet rectangulum ſub compoſita ex ſex-
              <lb/>
            quialtera tranſuerſi lateris, & </s>
            <s xml:id="echoid-s9637" xml:space="preserve">axi, vel diametro datæ hy-
              <lb/>
            perbolæ, ſub eodem axi, vel diametro, ad rectangulum
              <lb/>
            ſub compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9638" xml:space="preserve">axi, vel diametro
              <lb/>
            eiuſdem hyperbolæ; </s>
            <s xml:id="echoid-s9639" xml:space="preserve">& </s>
            <s xml:id="echoid-s9640" xml:space="preserve">ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9641" xml:space="preserve">tranſuerſi late-
              <lb/>
            ris, & </s>
            <s xml:id="echoid-s9642" xml:space="preserve">eodem axi, vel diametro.</s>
            <s xml:id="echoid-s9643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9644" xml:space="preserve">Sit igitar data hyperbola, cuius baſis, SX, circa axim, vel dia-
              <lb/>
            metrum, OV, cuius tranſuerſum latus ſit, BO, bifariam in C, di-
              <lb/>
            uiſum, ſit autem illi in directum adiuncta, AB, æqualis, BC, de-
              <lb/>
            inde ducta per, O, tangente hyperbolam, quæ ſit, ED, cui erit
              <lb/>
            parallela baſis, SX, abicindantur, EO, OD, ita vt quadratum, E
              <lb/>
            O, & </s>
            <s xml:id="echoid-s9645" xml:space="preserve">quadratum, OD, ſeorſim ſint æqualia quartæ parti rectan-
              <lb/>
            guli ſub, BO, latere tranſuerſo, & </s>
            <s xml:id="echoid-s9646" xml:space="preserve">ſub eiuſdem recto latere, ſi ergo
              <lb/>
            iunctis, CE, CD, ipsæ producantur indefinitè verſus baſim, SX,
              <lb/>
              <note position="left" xlink:label="note-0394-01" xlink:href="note-0394-01a" xml:space="preserve">1.2. Con.</note>
            cui productæ occurant in punctis, H, R, erunt, CH, CR, </s>
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