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

Table of contents

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[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
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          <head xml:id="echoid-head467" xml:space="preserve">THEOREMA XXIV. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s7635" xml:space="preserve">INeadem antecedentis figura oſtendemus omnia quadra-
              <lb/>
            ta portionis, BSF, ad rectangula ſub eadem portione,
              <lb/>
            BSF, & </s>
            <s xml:id="echoid-s7636" xml:space="preserve">ſub figura, SEF, regula communi, BF, eſſe vt, B
              <lb/>
            F, ad, FE.</s>
            <s xml:id="echoid-s7637" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7638" xml:space="preserve">Eſt enim quadratum, BF, ad rectangulum ſub, BF, FE, vt, B
              <lb/>
            F, ad, FE; </s>
            <s xml:id="echoid-s7639" xml:space="preserve">ſimiliter ducta vtcunque, CD, parallela regulę, BF,
              <lb/>
            oſtendemus quadratum, CD, ad rectangulum, ſub, CD, DZ,
              <lb/>
            eſſe vt, CD, ad, DZ, eſt autem vt, BF, ad, FE, ita, CD, ad,
              <lb/>
            DZ, ergo quadratum, BF, ad rectangulum, BFE, erit vt qua-
              <lb/>
            dratum, CD, ad rectangulum, CDZ, ſic oſtendemus quamlibet
              <lb/>
            ductam intra portionem, BSF, parallelam regulę, BF, ad eiuſdem
              <lb/>
              <note position="right" xlink:label="note-0337-01" xlink:href="note-0337-01a" xml:space="preserve">Corol.
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              4. 1. 2.</note>
            portionem incluſam figura, SFE, eſſe vt quadratum, BF, ad re-
              <lb/>
            ctangulum ſub, BF, FE, ergo quadratum, BF, ad rectangulum
              <lb/>
            ſub, BF, FE, erit vt omnia quadrata portionis, BSF, ad rectan-
              <lb/>
            gula ſub portione, BSF, & </s>
            <s xml:id="echoid-s7640" xml:space="preserve">ſub figura, SEF, vt autem quadratum,
              <lb/>
            BF, ad rectangulum ſub, BF, FE, ita, BF, ad, FE, ergo omnia
              <lb/>
            quadrata portionis, BSF, ad rectangula ſub portione, BSF, & </s>
            <s xml:id="echoid-s7641" xml:space="preserve">fi-
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            gura, ESF, erunt vt, BF, ad, FE, quod oſtendere opus erat.</s>
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          <head xml:id="echoid-head468" xml:space="preserve">THEOREMA XXV. PROPOS. XXVII.</head>
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            <s xml:id="echoid-s7643" xml:space="preserve">SI intra curuam parabolæ duæ vtcunque ducantur rectæ
              <lb/>
            lineę in eandem @terminatæ, quarum vna rectè, altera
              <lb/>
            obliquè axim ſecet, ſint autem conſtitutarum ab eiſdem pa-
              <lb/>
            rabolarum diametri inter ſe æquales: </s>
            <s xml:id="echoid-s7644" xml:space="preserve">Omnia quadrata pa-
              <lb/>
            rabolæ per eam, quæ rectè axim ſecat, conſtitutæ, regula
              <lb/>
            eadem, erunt æqualia rectangulis ſub parabola per obli-
              <lb/>
            quam ad axem conſtituta, regula eadem, & </s>
            <s xml:id="echoid-s7645" xml:space="preserve">ſub figura di-
              <lb/>
            ſtantiarum eiuſdem parabolæ per obliquam ad axem con-
              <lb/>
            ſtitutæ.</s>
            <s xml:id="echoid-s7646" xml:space="preserve"/>
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