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

Table of contents

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[321.] E. SECTIO V.
Page: 236 (216)
[322.] F. SECTIO VI.
Page: 236 (216)
[323.] THEOREMA XI. PROPOS. XII.
Page: 236 (216)
[324.] THEOREMA XII. PROPOS. XIII.
Page: 237 (217)
[325.] COROLLARIVM.
Page: 239 (219)
[326.] THEOREMA XIII. PROPOS. XIV.
Page: 239 (219)
[327.] COROLLARIVM.
Page: 242 (222)
[328.] THEOREMA XIV. PROPOS. XV.
Page: 242 (222)
[329.] ALITER.
Page: 244 (224)
[330.] THEOREMA XV. PROPOS. XVI.
Page: 244 (224)
[331.] THEOREMA XVI. PROPOS. XVII.
Page: 247 (227)
[332.] COROLLARIVM I.
Page: 248 (228)
[333.] COROLLARIVM II.
Page: 249 (229)
[334.] THEOREMA XVII. PROPOS. XVIII.
Page: 249 (229)
[335.] COROLLARIVM.
Page: 251 (231)
[336.] THEOREMA XVIII. PROPOS. XIX.
Page: 251 (231)
[337.] COROLLARIVM.
Page: 252 (232)
[338.] THEOREMA XIX. PROPOS. XX.
Page: 252 (232)
[339.] COROLLARIVM.
Page: 254 (234)
[340.] THEOREMA XX. PROPOS. XXI.
Page: 254 (234)
[341.] COROLLARIVM.
Page: 256 (236)
[342.] THEOREMA XXI. PROPOS. XXII.
Page: 257 (237)
[343.] THEOREMA XXII. PROPOS. XXIII.
Page: 261 (241)
[344.] THEOREMA XXIII. PROPOS. XXIV.
Page: 262 (242)
[345.] THEOREMA XXIV. PROPOS. XXV.
Page: 264 (244)
[346.] THEOREMA XXV. PROPOS. XXVI.
Page: 265 (245)
[347.] THEOREMA XXVI. PROPOS. XXVII.
Page: 267 (247)
[348.] THEOREMA XXVII. PROPOS. XXVIII.
Page: 268 (248)
[349.] THEOREMA XXVIII. PROPOS. XXIX.
Page: 269 (249)
[350.] THEOREMA XXIX. PROPOS. XXX.
Page: 271 (251)
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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-
              <lb/>
            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-
              <lb/>
              <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>
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            <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
              <lb/>
            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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