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

Table of contents

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[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)
[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
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            go, vt quadratum, EY, ad quadratum, YS, ita rectangulum, TZ
              <lb/>
              <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">Ex 3. Co-
                <lb/>
              nic. p. 17.</note>
            S, ad rectangulum, BZA, eodem modo (ſumptoin, AB, vtcun-
              <lb/>
            quepuncto, M, & </s>
            <s xml:id="echoid-s5814" xml:space="preserve">per, M, ducta, CMG, parallela ipſi, BF,) ſe-
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            quetur rectangulum, GMC, ad rectangulum, BMA, eſſe vt qua-
              <lb/>
            dratum, EY, ad quadratum, YS, ergo rectangulum, TZS, ad re-
              <lb/>
            ctangulum, BZA, erit vt rectangulum, GMC, ad rectangulum,
              <lb/>
            BMA, & </s>
            <s xml:id="echoid-s5815" xml:space="preserve">ſic dereliquis oſtendemus .</s>
            <s xml:id="echoid-s5816" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5817" xml:space="preserve">rectangula ſub portione, AS
              <lb/>
            B, & </s>
            <s xml:id="echoid-s5818" xml:space="preserve">quadrilineo, AHTFB, adrectangula ſub omnibus abſciſſis,
              <lb/>
            AB, & </s>
            <s xml:id="echoid-s5819" xml:space="preserve">reſiduis abſciſſarum eiuſdem .</s>
            <s xml:id="echoid-s5820" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5821" xml:space="preserve">adrectangula ſub triangulis,
              <lb/>
            ABD, AVD, (ſunt .</s>
            <s xml:id="echoid-s5822" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5823" xml:space="preserve">rectangula ſub omnibus abſciſſis, AB, & </s>
            <s xml:id="echoid-s5824" xml:space="preserve">
              <lb/>
            reſiduis abſciſſarum eiuſdem, æqualia rectangulis ſub duobus triangu-
              <lb/>
              <note position="right" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">Coroll. 2.</note>
            lis, ABD, AVD,) erunt vt rectangulum, TZS, adrectangulum,
              <lb/>
              <note position="right" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">Prop. 19.
                <lb/>
              lib. 2.</note>
            AZB, ideſt vt quadratum, EY, ad quadratum, YS, vel vt quadra-
              <lb/>
            tum, SX, ad quadratum, XE, vel vt quadratum, ST, ad quadra-
              <lb/>
            tum, ER; </s>
            <s xml:id="echoid-s5825" xml:space="preserve">ergo rectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5826" xml:space="preserve">quadrilineo, A
              <lb/>
            HTFB, ad rectangula ſub triangulis, ABD, AVD, erunt vt qua-
              <lb/>
            dratum, ST, ad quadratum, ER; </s>
            <s xml:id="echoid-s5827" xml:space="preserve">quod oſtendere oportebat.</s>
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        <div xml:id="echoid-div577" type="section" level="1" n="341">
          <head xml:id="echoid-head358" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5829" xml:space="preserve">HINC patet, quoniam probauimus, omnia quadrata, AD, ſex-
              <lb/>
            cupla eſſe rectangulorum ſub triangulis, ABD, AVD, quod
              <lb/>
            in circulo eadem quadrat a ſint ſexcupla rectangulorum ſub portione,
              <lb/>
            ASB, & </s>
            <s xml:id="echoid-s5830" xml:space="preserve">quadrilineo, AHTFB. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">In ellipſi verò, quia pariter om-
              <lb/>
            nia quadrata, AD, rectangulorum ſub triangulis, ABD, AVD,
              <lb/>
            ſunt ſexcupla .</s>
            <s xml:id="echoid-s5832" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">ſunt ad illa, vt cubus, AB, ad ſui ipſius ſextam par-
              <lb/>
            tem, inſuper rectangula ſub triangulis, ABD, AVD, adrectangula
              <lb/>
              <note position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">Cor. 24.
                <lb/>
              lib. 2.</note>
            ſub portione, ASB, & </s>
            <s xml:id="echoid-s5834" xml:space="preserve">quadrilineo, AHTFB, ſunt vt quadra-
              <lb/>
            tum, ER, conuertendo ad quadratum, ST, .</s>
            <s xml:id="echoid-s5835" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5836" xml:space="preserve">vt ſexta pars cubi, AB,
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            ad eiuſdein talem partem, ad quam ipſa ſextapars ſit, vt quadratum, E
              <lb/>
            R, ad quadratum, ST, binc ex æquali omnia quadrata, AD, in elli-
              <lb/>
            pſi, ad rectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5837" xml:space="preserve">quadrilineo, AHTFB,
              <lb/>
            erunt vt cubus, AB, ad ſui ipſius eam partem, ad quam eiuſdem cubi,
              <lb/>
            AB, ſextapars ſit veluti quadratum, ER, ad quadratum, ST. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">Ve-
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            rum ſi in ellipſi diametri non ſint axes, vice cubi, AB, concludemus
              <lb/>
            omnia quadrata, AD, adrectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5839" xml:space="preserve">quadri-
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            lineo, AHTFB, eſſe vt parallelepipedum ſub altitudine, AB, baſi
              <lb/>
            rhombo quod ab ipſa, AB, deſeribitur, ad ſui ipſius eam partem, ad
              <lb/>
            quam eiuſdem parallelepipedi pars ſexta ſit veluti quadratum, ER, ad
              <lb/>
            quadratum, ST,</s>
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