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

Table of contents

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[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
[251.] COROLLARIVM II.
Page: 186 (166)
[252.] COROLLARIVM III.
Page: 186 (166)
[253.] THEOREMA XXVII. PROPOS. XXVII.
Page: 187 (167)
[254.] THEOREMA XXVIII. PROPOS. XXVIII:
Page: 188 (168)
[255.] COROLLARIVM.
Page: 189 (169)
[256.] THEOREMA XXIX. PROPOS. XXIX.
Page: 190 (170)
[257.] COROLLARIVM.
Page: 190 (170)
[258.] THEOREMA XXX. PROPOS. XXX.
Page: 191 (171)
[259.] COROLLARIVM.
Page: 192 (172)
[260.] THEOREMA XXXI. PROPOS. XXXI.
Page: 193 (173)
[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
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            <s xml:id="echoid-s8748" xml:space="preserve">
              <pb o="348" file="0368" n="368" rhead="GEOMETRI Æ."/>
            enim eodem modo demonſtratio his figuris aſſumptis) omnes fi-
              <lb/>
            guras ſimiles portionis, BSF, ad figuras vice rectangulorum ſum-
              <lb/>
            ptas eſſe pariter, vt, BF, ad, EF, & </s>
            <s xml:id="echoid-s8749" xml:space="preserve">pariter ſoliudm, quorum omnes
              <lb/>
            dictæ figuræ ſimiles vice quadratorum ſumptæ ſunt omnia plana,
              <lb/>
            ad ſolidum, quorum figuræ vice rectangulorum ſumptæ ſunt om-
              <lb/>
            nia plana, eſſe, vt, BF, ad, FE; </s>
            <s xml:id="echoid-s8750" xml:space="preserve">quæ quidem ſolida non ſunt ſolida
              <lb/>
            ad inuicem ſimilarià, quia vtriuſque ſolidi figuræ non ſunt inter ſe
              <lb/>
            fimiles, ſed tantum ſunt ſimiles inter ſe, quæ ſunt in vnoquoque
              <lb/>
            horum ſolidorum ſingillatim ſumpto.</s>
            <s xml:id="echoid-s8751" xml:space="preserve"/>
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        <div xml:id="echoid-div838" type="section" level="1" n="495">
          <head xml:id="echoid-head515" xml:space="preserve">COROLL. V. SECTIO I.</head>
          <p>
            <s xml:id="echoid-s8752" xml:space="preserve">IN Prop 27. </s>
            <s xml:id="echoid-s8753" xml:space="preserve">ſimiliter aſſumpta eiuſdem ſigura, vt fiat noſtrum
              <lb/>
            exemplum reuoluatur parabola, BAC, circa AP, axem, vt fiat
              <lb/>
              <figure xlink:label="fig-0368-01" xlink:href="fig-0368-01a" number="251">
                <image file="0368-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0368-01"/>
              </figure>
            cono des parabolicum, BAC, à quo
              <lb/>
            per planum à, DZ, deſcriptum in re-
              <lb/>
            uolutione abſcindetur conoides para-
              <lb/>
            bolicum, DAF, cuius baſis rectè axim,
              <lb/>
            AP, ſecat, & </s>
            <s xml:id="echoid-s8754" xml:space="preserve">eſt circulus, intelligatur
              <lb/>
            autem etiam per, MC, planum ex-
              <lb/>
            tendi rectũ ad planũ parabolæ, BAC,
              <lb/>
            per hoc igitur abſcindetur pariter co
              <lb/>
            noides parabolicum, cuius baſis erit ellipſis, cuius maior diameter,
              <lb/>
            MC, minor autem erit, CR. </s>
            <s xml:id="echoid-s8755" xml:space="preserve">Dico nunc hæc duo conoidea eſſe
              <lb/>
            inter ſe æqualia, cum diametri eorundem, AZ, HO, ſint æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s8756" xml:space="preserve">ſi enim intellexerimus conoides, DAF, planis parallelis baſi ſecari,
              <lb/>
            & </s>
            <s xml:id="echoid-s8757" xml:space="preserve">pariter conoides, MHC, ſecari planis parallelis ſuæ baſi, fient,
              <lb/>
              <note position="left" xlink:label="note-0368-01" xlink:href="note-0368-01a" xml:space="preserve">45. l. 1.</note>
            ductis omnibus eorundem planis, in conoide, DAF, dicta omnia
              <lb/>
            plana, omnes figuræ ſimiles inter ſe .</s>
            <s xml:id="echoid-s8758" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8759" xml:space="preserve">omnes circuli figuræ geni-
              <lb/>
            tricis, quæ eſt parabola, DAF; </s>
            <s xml:id="echoid-s8760" xml:space="preserve">in conoide verò, MHC, dicta omnia
              <lb/>
            plana fient omnes figuræ ſimiles genitricis, MHC, .</s>
            <s xml:id="echoid-s8761" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8762" xml:space="preserve">omnes ellipſes
              <lb/>
            eiuſdem, quarum coniugatæ diametri erunt inter ſe, vt, MC, ad, C
              <lb/>
            R, maiores diametros in figura genitrice, MHC, ſitas habentes.
              <lb/>
            </s>
            <s xml:id="echoid-s8763" xml:space="preserve">Intelligantur nunc circa illas maiores diametros deſcribi circuli in
              <lb/>
            planis ellipſium iacentes, erit ergo quilibet circulus ad ellipſim ab
              <lb/>
            eo comprehenſam, vt maior diameter ad minorem, & </s>
            <s xml:id="echoid-s8764" xml:space="preserve">quia iſtę con-
              <lb/>
              <note position="left" xlink:label="note-0368-02" xlink:href="note-0368-02a" xml:space="preserve">10. l. 3.</note>
            iugatæ diametri ſunt omnes inter ſe, maiores .</s>
            <s xml:id="echoid-s8765" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8766" xml:space="preserve">ad minores, vt M
              <lb/>
            C, ad, CR, .</s>
            <s xml:id="echoid-s8767" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">vt quadratum, MC, ad rectangulum, MCR, & </s>
            <s xml:id="echoid-s8769" xml:space="preserve">vt
              <lb/>
            vnum ad vnum, ſic omnia ad omnia .</s>
            <s xml:id="echoid-s8770" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8771" xml:space="preserve">vt omnes circuli figuræ ge-
              <lb/>
            nitricis, MHC, ad omnes eiuſdem ſimiles ellipſes, ita circulus circa,
              <lb/>
            MC, ad ellipſim circa, MC, .</s>
            <s xml:id="echoid-s8772" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">ſic quadratum, MC, ad </s>
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