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

Table of contents

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[351.] THEOREMA XXX. PROPOS. XXXI.
Page: 272 (252)
[352.] COROLLARIVM.
Page: 274 (254)
[353.] THEOREMA XXXI. PROPOS. XXXII.
Page: 274 (254)
[354.] COROLLARIVM.
Page: 275 (255)
[355.] THEOREMA XXXII. PROPOS. XXXIII.
Page: 275 (255)
[356.] COROLLARIVM.
Page: 276 (256)
[357.] THEOREMA XXXIII. PROPOS. XXXIV.
Page: 276 (256)
[358.] SCHOLIVM.
Page: 277 (257)
[359.] COROLLARIVMI.
Page: 279 (259)
[360.] COROLLARIVM II.
Page: 281 (261)
[361.] COROLLARIVM III.
Page: 282 (262)
[362.] COROLLARIVM IV.
Page: 282 (262)
[363.] COROLLARIVM V.
Page: 283 (263)
[364.] COROLL. VI. SECTIO PRIOR.
Page: 284 (264)
[365.] SECTIO POSTERIOR.
Page: 284 (264)
[366.] COROLLARIVM VII.
Page: 284 (264)
[367.] COROLLARIVM VIII.
Page: 285 (265)
[368.] COROLL. IX. SECTIO PRIOR.
Page: 285 (265)
[369.] SECTIO POSTERIOR.
Page: 285 (265)
[370.] COROLL. X. SECTIO PRIMA.
Page: 286 (266)
[371.] SECTIO II.
Page: 286 (266)
[372.] SECTIO III.
Page: 287 (267)
[373.] SECTIO IV.
Page: 287 (267)
[374.] SECTIO V.
Page: 287 (267)
[375.] COROLLARIVM XI.
Page: 287 (267)
[376.] COROLLARIVM XII.
Page: 288 (268)
[377.] COROLLARIVM XIII.
Page: 289 (269)
[378.] COROLLARIVM XIV.
Page: 289 (269)
[379.] COROLL. XV. SECTIO PRIMA.
Page: 290 (270)
[380.] SECTIO II.
Page: 291 (271)
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          <head xml:id="echoid-head447" xml:space="preserve">THEOREMA XV. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s7345" xml:space="preserve">INeadem ſupradicti Theorematis figura oſtendemus tri-
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            lineum, VNAI, ad trilineum, VNABX, eſſe vt pa-
              <lb/>
            rallelepipedum ter ſub, EI, & </s>
            <s xml:id="echoid-s7346" xml:space="preserve">quadrato, IA, cum cubo,
              <lb/>
            IA, ad parallelepipedum ter ſub, CX, & </s>
            <s xml:id="echoid-s7347" xml:space="preserve">quadrato, XB,
              <lb/>
            cum cubo, XB. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">Similiter trilineum, VEI, ad trilineum,
              <lb/>
            VECX, eſſe vt parallelepipedum ter ſub, AI, & </s>
            <s xml:id="echoid-s7349" xml:space="preserve">quadra-
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            to, IE, cum cubo, IE, ad parallelepipedum terſub, BX, & </s>
            <s xml:id="echoid-s7350" xml:space="preserve">
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            quadrato, XC, cum cubo, XC.</s>
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            <s xml:id="echoid-s7352" xml:space="preserve">Trilineum enim, VNAI, ad parabolam, ANE, eſt vt paral-
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              <note position="right" xlink:label="note-0325-01" xlink:href="note-0325-01a" xml:space="preserve">6.huius.</note>
            lelepipedum ter ſub, EI, & </s>
            <s xml:id="echoid-s7353" xml:space="preserve">quadrato, IA, cum cubo, IA, ad cu-
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            bum, AE, item parabola, ANE, ad parabolam, BNC, eſt vt
              <lb/>
            cubus, AE, ad cubum, BC, & </s>
            <s xml:id="echoid-s7354" xml:space="preserve">tandem parabola, BNC, ad trili-
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              <note position="right" xlink:label="note-0325-02" xlink:href="note-0325-02a" xml:space="preserve">2.huius.</note>
            neum, VABX, eſt vt cubus, CB, ad parallelepipedum ter ſub, C
              <lb/>
            X, & </s>
            <s xml:id="echoid-s7355" xml:space="preserve">quadrato, XB, cum cubo, BX, ergo, ex æquali, trilineum,
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            VNAI, ad trilineum, VNBX, erit vt parallelepipedum ter ſub,
              <lb/>
              <note position="right" xlink:label="note-0325-03" xlink:href="note-0325-03a" xml:space="preserve">6.huius.</note>
            EI, & </s>
            <s xml:id="echoid-s7356" xml:space="preserve">quadrato, IA, cum cubo, IA, ad parallelepipedum ter
              <lb/>
            ſub, CX, & </s>
            <s xml:id="echoid-s7357" xml:space="preserve">quadrato, XB, cum cubo, XB. </s>
            <s xml:id="echoid-s7358" xml:space="preserve">Eodem modo o-
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            ſtendemus trilineum, VIE, ad trilineum, VXC, eſſe vt paralle-
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            lepipedum ter ſub, AI, & </s>
            <s xml:id="echoid-s7359" xml:space="preserve">quadrato, IE, cum cubo, IE, ad pa-
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            rallelepipedum ter ſub, BX, & </s>
            <s xml:id="echoid-s7360" xml:space="preserve">quadrato, XC, cum cubo, XC,
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            quod, &</s>
            <s xml:id="echoid-s7361" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head448" xml:space="preserve">THEOREMA XVI. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s7363" xml:space="preserve">SI duæ intra curuam parabolicam ducantur rectæ lineæ
              <lb/>
            axem ſecantes, fuerint autem conſtitua@um ab eiſdem
              <lb/>
            parabolarum diametri, vel axis, & </s>
            <s xml:id="echoid-s7364" xml:space="preserve">diameter æquales, & </s>
            <s xml:id="echoid-s7365" xml:space="preserve">ipſe
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            parabolæ erunt æquales.</s>
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          <p>
            <s xml:id="echoid-s7367" xml:space="preserve">Sit curua parabolica, BAC, intra quam ducantur vtcunque duę,
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            DF, MC, axem ſecantes, ideſt non parallelæ axi, ſint autem, A
              <lb/>
            R, HO, diametri, vel axis, & </s>
            <s xml:id="echoid-s7368" xml:space="preserve">diameter inter ſe æquales. </s>
            <s xml:id="echoid-s7369" xml:space="preserve">Dico
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            parabolam, DAF, eſſe æqualem parabolæ, MHFC; </s>
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