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

Table of contents

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[231.] D. SECTIO IV.
Page: 174 (154)
[232.] E. SECTIO V.
Page: 175 (155)
[233.] F. SECTIO VI.
Page: 175 (155)
[234.] THEOR EMA XXIII. PROPOS. XXIII.
Page: 175 (155)
[235.] A. COROLLARII SECTIO I.
Page: 176 (156)
[236.] B. SECTIO II.
Page: 177 (157)
[237.] C. SECTIO III.
Page: 177 (157)
[238.] D. SECTIO IV.
Page: 177 (157)
[239.] E. SECTIO V.
Page: 177 (157)
[240.] F. SECTIO VI.
Page: 177 (157)
[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)
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        <div xml:id="echoid-div541" type="section" level="1" n="324">
          <head xml:id="echoid-head341" xml:space="preserve">THEOREMA XII. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s5276" xml:space="preserve">SI circulum, vel ellipſim duæ rectæ lineæ in terminis
              <lb/>
            coniugatarum diametrorum tetigetint inter ſe conue-
              <lb/>
            nientes, eiſdem diametris ductis. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">Omnia quadrata conſti-
              <lb/>
            tuti parallelogrammiad omnia quadrata trilinei à dictis tan-
              <lb/>
            gentibus, & </s>
            <s xml:id="echoid-s5278" xml:space="preserve">ab incluſa curua comprehenſi, regula altera
              <lb/>
            diametrorum, erunt vt dictum parallelogrammum ad ſui
              <lb/>
            reliquum, dempto quadrante circuli, vel ellipſis iam dictæ,
              <lb/>
            quod inſcribitur prædicto parallelogrammo, ſimul cum ex-
              <lb/>
            ceſſu dicti quadrantis ſuper duas tertias iam dicti parallelo-
              <lb/>
            grammi, quæ ratio erit proximè, vt 21. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">ad 2.</s>
            <s xml:id="echoid-s5280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5281" xml:space="preserve">Sit circulus, vel ellipſis, ABCD, cuius diametri coniugatæ, A
              <lb/>
            C, BD, in quorum terminis, C, D, duæ rectæ lineę ipſum tangen-
              <lb/>
            tesinter ſe conueniant in, V. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">Dico ergo (ſumpta regula qualibet
              <lb/>
            diametrorum, vt, BD,) quod omnia quadrata parallelogrammi, O
              <lb/>
            V, ad omnia quadrata trilinei, DCV, duabus tangentibus, DV,
              <lb/>
            VC, & </s>
            <s xml:id="echoid-s5283" xml:space="preserve">ab ijs incluſa curua, DC, comprehenſi ſunt, vt idem paral-
              <lb/>
              <figure xlink:label="fig-0237-01" xlink:href="fig-0237-01a" number="148">
                <image file="0237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0237-01"/>
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            lelogrammum, OV, ad ſui reliquum
              <lb/>
            dempto quadrante, OCD, circuli,
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            vel ellipſis, ABCD, ſimul cum eo
              <lb/>
            ſpatio, quo idem quadrans excedit
              <lb/>
            duas tertias parallelogrammi, OV.
              <lb/>
            </s>
            <s xml:id="echoid-s5284" xml:space="preserve">Sumatur intra, OC, vtcunque pun
              <lb/>
            ctum, E, & </s>
            <s xml:id="echoid-s5285" xml:space="preserve">per, E, ducatur ipſi, B
              <lb/>
            D, parallela, EF, ſecans curuam, D
              <lb/>
            C, in, I. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Omnia ergo quadrata pa-
              <lb/>
            rallelogrammi, OV, ad rectangula
              <lb/>
            ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s5287" xml:space="preserve">ſemi-
              <lb/>
            portione, OCD, ſunt vt parallelo
              <lb/>
              <note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">Coroll.1.
                <lb/>
              26.lib.2.</note>
            grammum, OV, ad eandem ſemiportionem, OCD; </s>
            <s xml:id="echoid-s5288" xml:space="preserve">ſed eadem ad
              <lb/>
              <note position="right" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">Coroll.1.
                <lb/>
              huius.</note>
            omnia quadrata ſemiportionis, OCD, ſunt ſexquialtera, ergo ad
              <lb/>
            reſiduum erunt vt parallelogrammum, OV, ad reſiduum ſemipor-
              <lb/>
            tionis, OCD, demptis ab ea, {2/3}, parallelogrammi, OV, quarum
              <lb/>
            idem parallelogrammum, OV, eſt ſexquialterum; </s>
            <s xml:id="echoid-s5289" xml:space="preserve">reſiduum autem
              <lb/>
            rectangulorum ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s5290" xml:space="preserve">ſemiportione, OC
              <lb/>
            D, demptis omnibus quadratis ſemiportionis, OCD, ſunt rectan-
              <lb/>
              <note position="right" xlink:label="note-0237-03" xlink:href="note-0237-03a" xml:space="preserve">Vide ibid.
                <lb/>
              dicta.</note>
            gula ſub ſemiportione, OCD, & </s>
            <s xml:id="echoid-s5291" xml:space="preserve">trilineo, CDV, nam veluti </s>
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