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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              <pb o="199" file="0219" n="219" rhead="LIBER III."/>
            eſſe vt, BR, ad compoſitam ex, {1/2}, BR, &</s>
            <s xml:id="echoid-s4889" xml:space="preserve">, {1/6}, BE, ideò omnia
              <lb/>
            quadrata trianguli, DEP, cum ſint, {1/3}, omnium quadratorum pa-
              <lb/>
              <note position="right" xlink:label="note-0219-01" xlink:href="note-0219-01a" xml:space="preserve">24.Lib.2</note>
            rallelogrammi, FP, erunt ad omnia quadrata portionis, DEP, vt,
              <lb/>
            {1/3}, RB, ad compoſitam ex, {1/2}, RB, &</s>
            <s xml:id="echoid-s4890" xml:space="preserve">, {1/6}, BE, ideſt vt tota, RB,
              <lb/>
            ad compoſitam ex, {3/2}, RB, &</s>
            <s xml:id="echoid-s4891" xml:space="preserve">, {3/6}, BE, ſed, {1/2}, RB, .</s>
            <s xml:id="echoid-s4892" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">{3/6}, RB, cum,
              <lb/>
            {3/6}, BE, conſtituunt, {3/6}, integrę, ER, ſcilicet, {1/2}, eiuſdem, ER, quę
              <lb/>
            ideò cum, {2/2}, ipſius, BR, .</s>
            <s xml:id="echoid-s4894" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">cum, BR, ad ipſam, BR, erit, vt om-
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            nia quadrata (conuertendo) portionis, DEP, ad omnia quadrata
              <lb/>
            trianguli, DEP.</s>
            <s xml:id="echoid-s4896" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4897" xml:space="preserve">Quoniam verò, ſi in parallelogrammi, vel trianguli dicti, baſi, D
              <lb/>
              <note position="right" xlink:label="note-0219-02" xlink:href="note-0219-02a" xml:space="preserve">9. Lib. 2.</note>
            P, ſit parallelogrammum, vel triangulum, & </s>
            <s xml:id="echoid-s4898" xml:space="preserve">in eadem altitudine,
              <lb/>
              <note position="right" xlink:label="note-0219-03" xlink:href="note-0219-03a" xml:space="preserve">Per B. Co
                <lb/>
              roll. 22.
                <lb/>
              lib. 2.</note>
            omnia quadrata dictorum parallelogrammorum inter ſe æquantur,
              <lb/>
            ficut etiam omnia quadrata triangulorum, regula eorundem baſi,
              <lb/>
            ideò oſtenſum eſt omnia quadrata portionis, DEP, ad omnia qua-
              <lb/>
            drata parallelogrammi in eadem baſi, & </s>
            <s xml:id="echoid-s4899" xml:space="preserve">altitudine cum ipſa conſti-
              <lb/>
            tuti eſſe, vt compoſita ex, {1/6}, BE, &</s>
            <s xml:id="echoid-s4900" xml:space="preserve">, {1/2}, BR, ad eandem, BR, ad
              <lb/>
            omnia verò quadrata trianguli in ijſdem poſiti, vt compoſita ex, B
              <lb/>
            R, & </s>
            <s xml:id="echoid-s4901" xml:space="preserve">dimidia, RE, ad ipſam, BR, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s4902" xml:space="preserve"/>
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        <div xml:id="echoid-div499" type="section" level="1" n="301">
          <head xml:id="echoid-head318" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s4903" xml:space="preserve">_H_INC patet in figura, in qua baſis portionis conſtitutæ per cen-
              <lb/>
            trum circuli, vel ellipſis tranſeat, quoniam omnia quadrata pa-
              <lb/>
            rallelogrammi, FP, ad omnia quadrata portionis, DEP, ſunt vt,
              <lb/>
            A R, ad compoſitam ex, {1/2}, AR, &</s>
            <s xml:id="echoid-s4904" xml:space="preserve">, {1/6}, AE, ſcilicet, {1/6}, AR, quia,
              <lb/>
            E A, eſt æqualis ipſi, AR, {1/2}, AR, autem, &</s>
            <s xml:id="echoid-s4905" xml:space="preserve">, {1/6}, AR, conſtituunt,
              <lb/>
            {4/6}, vel, {2/3}, ipſius, AR, ideò omnia quadrata parallelogrammi, FP, eſ-
              <lb/>
            ſe ad omnia quadrata portionis, DEP, vt, AR, ad, {2/3}, AR, ideſt eſſe
              <lb/>
            eorundem ſexquialtera; </s>
            <s xml:id="echoid-s4906" xml:space="preserve">quia verò omnia quadrata trianguli, DEP,
              <lb/>
              <note position="right" xlink:label="note-0219-04" xlink:href="note-0219-04a" xml:space="preserve">_24.Lib.2._</note>
            ſunt, {1/3}, omnium quadratorum parallelogrammi, FP, ideò omnia qua-
              <lb/>
            drata trianguli, DEP, ad omnia quadrata portionis, DEP, ſunt vt 1.
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            </s>
            <s xml:id="echoid-s4907" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s4908" xml:space="preserve">& </s>
            <s xml:id="echoid-s4909" xml:space="preserve">conuertendo omnia quadrata portionis, DEP, ſunt dupla om-
              <lb/>
            uium quadratorum trianguli, DEP, & </s>
            <s xml:id="echoid-s4910" xml:space="preserve">ſub ſexquialtera omnium qua-
              <lb/>
            dratorum parallelogrammi, FP, dummodo in eadem baſi, & </s>
            <s xml:id="echoid-s4911" xml:space="preserve">altitudine
              <lb/>
            cum portione ſint conſtituti parallelogrammum, & </s>
            <s xml:id="echoid-s4912" xml:space="preserve">triangulum, vt pau-
              <lb/>
            lò ſupr a in fine demonſtrationis ſubiunximus.</s>
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