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

Table of contents

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[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
[291.] THEOREMA XXXIX. PROPOS. XXXIX:
Page: 211 (191)
[292.] THEOREMA XL. PROPOS. XL.
Page: 212 (192)
[293.] COROLLARIVM.
Page: 212 (192)
[294.] THEOREMA XLI. PROPOS. XLI.
Page: 212 (192)
[295.] THEOREMA XLII. PROPOS. XLII.
Page: 213 (193)
[296.] COROLLARIVM.
Page: 214 (194)
[297.] SCHOLIVM.
Page: 215 (195)
[298.] Finis Secundi Libri.
Page: 215 (195)
[299.] CAVALERII LIBER TERTIVS. In quo de circulo, & Ellipſi, ac ſolidis ab eiſdem genitis, traditur doctrina.
Page: 217 (197)
[300.] THEOREMA I. PROPOS. I.
Page: 217 (197)
[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
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        <div xml:id="echoid-div672" type="section" level="1" n="393">
          <head xml:id="echoid-head410" xml:space="preserve">COROLLARIVM XXV.</head>
          <p>
            <s xml:id="echoid-s6859" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s6860" xml:space="preserve">28. </s>
            <s xml:id="echoid-s6861" xml:space="preserve">aſſumitur adhuc antecedentis figura, hic autem
              <lb/>
            colligimus nos, ſuperiores aſpicientes figuras pro noſtro exem-
              <lb/>
            plo, ſolidum ſimilare genitum ex portione circuli, vel ellipſis, TC
              <lb/>
            FEY, ad ſolidum ſimilare genitum ex circulo, velellipſi, iuxta com-
              <lb/>
            munem regulam, FH, (comparatis tamen genitis vel ambo ex ijs,
              <lb/>
            quæ ſunt circuli, vel ex ijs, quæ ſunt ipſius ellipſis) eſſe vt cylindri-
              <lb/>
            cum ſub altitudine, MI, baſi portione, TCFEY, vna cum, {1/6}, cu-
              <lb/>
            bi, TY, (quod tamen ſolum in circuli figu a contingit) in figura au-
              <lb/>
            tem ellipſis illud commutamus in hoc. </s>
            <s xml:id="echoid-s6862" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6863" xml:space="preserve">vna cum ea parte cubi, TY,
              <lb/>
            vel parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">rhombo, RZ, ad quam eiuſdem cu-
              <lb/>
            bi, vel parallelepipedi ſexta pars ſit, vt quadratum primi axis ad qua-
              <lb/>
            dratum ſecundi ad, {2/3}, parallelepipedi ſub, AD, & </s>
            <s xml:id="echoid-s6865" xml:space="preserve">parallelogram-
              <lb/>
            mo, AQ,. </s>
            <s xml:id="echoid-s6866" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6867" xml:space="preserve">in figura circuli, ad, {2/3}, cubi, FH. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">Dictam igitur ra-
              <lb/>
            tionem in ſuprapoſitis exemplis habet Malum Roſeum, ad ſphęram
              <lb/>
            genitam ex circulo, ex cuius portione maiori Malum Roſeum dici-
              <lb/>
            tur genitum iuxta regulam, FH; </s>
            <s xml:id="echoid-s6869" xml:space="preserve">& </s>
            <s xml:id="echoid-s6870" xml:space="preserve">eandem habet Malum Coto-
              <lb/>
            neum ad ſphæroides genitum ex ellipſi reuoluta circa axem, CE, pa-
              <lb/>
            rallelam axi, TY, circa quem reuoluitur portio, TCFEY, ad ge-
              <lb/>
            nerandum Malum Cotoneum, quam rationem pariter diximus ha-
              <lb/>
            bere ſupradicta ſimilaria ſolida, &</s>
            <s xml:id="echoid-s6871" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6872" xml:space="preserve"/>
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        <div xml:id="echoid-div673" type="section" level="1" n="394">
          <head xml:id="echoid-head411" xml:space="preserve">COROLLARIVM XXVI.</head>
          <p>
            <s xml:id="echoid-s6873" xml:space="preserve">IN Propoſit. </s>
            <s xml:id="echoid-s6874" xml:space="preserve">29. </s>
            <s xml:id="echoid-s6875" xml:space="preserve">habetur ſolidum ſimilare genitum ex, AN, ad
              <lb/>
              <figure xlink:label="fig-0298-01" xlink:href="fig-0298-01a" number="193">
                <image file="0298-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0298-01"/>
              </figure>
            ſolidum ſimilare genitum ex figu-
              <lb/>
            ra, CBDMN, demptis ſolidis ſimila-
              <lb/>
            ribus genitis ex trilineis, ſiue figuris, B
              <lb/>
            CO, ONM, eſſe vt, AN, ad figuram,
              <lb/>
            BDMO. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">Apponatur hie illa figura,
              <lb/>
            &</s>
            <s xml:id="echoid-s6877" xml:space="preserve">, vt fiat noſtrum exemplum, reuol-
              <lb/>
            uatur, AN, quod ſupponamus eſſe pa-
              <lb/>
            rallelogrammum rectangulum conue-
              <lb/>
            nienter ipſi reuolutioni, circa axim, C
              <lb/>
            N, manentem, fiet igitur ex, AN, cy-
              <lb/>
            lindrus, ex reuolutione verò figuræ, B
              <lb/>
            DMO, fiet ſolidum totupliciter varia-
              <lb/>
            bile, quotupliciter figura, BDMO,
              <lb/>
            variari poteſt, vocabimus autem ſolida
              <lb/>
            genita à figuris inſcriptis rectangulo, AN, genita inquam per </s>
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