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

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[531.] COROLLARIVM XXVII.
Page: 383 (363)
[532.] SCHOLIV M.
Page: 384 (364)
[533.] Finis quarti Libri.
Page: 384 (364)
[534.] GEOMETRIÆ CAVALERII. LIBER QVINTVS. In quo de Hyperbola, Oppoſitis Sectionib us, ac ſolidis ab eiſdem genitis, babetur contemplatio. THEOREMA I. PROPOS. I.
Page: 385 (365)
[535.] THEOREMA II. PROPOS. II.
Page: 387 (367)
[536.] THEOREMA III. PROPOS. III.
Page: 388 (368)
[537.] THEOREMA IV. PROPOS. IV.
Page: 390 (370)
[538.] THEOREMA V. PROPOS. V.
Page: 391 (371)
[539.] PROBLEMA I. PROPOS. VI.
Page: 393 (373)
[540.] THEOREMA VI. PROPOS. VII.
Page: 394 (374)
[541.] THEOREMA VII. PROPOS. VIII.
Page: 395 (375)
[542.] THEOREMA VIII. PROPOS. IX.
Page: 396 (376)
[543.] THEOREMA IX. PROPOS. X.
Page: 398 (378)
[544.] THEOREMA X. PROPOS. XI.
Page: 399 (379)
[545.] THEOREMA XI. PROPOS. XII.
Page: 401 (381)
[546.] THEOREMA XII. PROPOS. XIII.
Page: 403 (383)
[547.] THEOREMA XIII, PROPOS. XIV.
Page: 404 (384)
[548.] SCHOLIVM.
Page: 406 (386)
[549.] THEOREMA XIV. PROPOS. XV.
Page: 406 (386)
[550.] THEOREMA XV. PROPOS. XVI.
Page: 407 (387)
[551.] COROLLARIVM.
Page: 407 (387)
[552.] THEOREMA XVI. PROPOS. XVII.
Page: 407 (387)
[553.] THE OREMA XVII. PROPOS. XVIII.
Page: 408 (388)
[554.] THEOREMA XVIII. PROPOS. XIX.
Page: 409 (389)
[555.] COROLLARIVM.
Page: 409 (389)
[556.] SCHOLIVM.
Page: 409 (389)
[557.] THEOREMA XIX. PROPOS. XX.
Page: 410 (390)
[558.] THEOREMA XX. PROPOS. XXI.
Page: 412 (392)
[559.] A@@ter ſupradictam rationem explicare.
Page: 414 (394)
[560.] COROLLARIVM:
Page: 415 (395)
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            OVX, ſimilia rectangulo, XOP, regula, OX, habebunt rationem
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            compoſitam ex ea, quam habetrectangulum ſub, MB, HI, adre-
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            ctangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s9807" xml:space="preserve">ex ea, quam habet parallelepipedum
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            ſub altitudine hyperbole, ADC, baſi quadrato, AC, ad parallele-
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            bipedum ſub altitudine hyperbole, OVX, baſi rectangulo, XOP,
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          <head xml:id="echoid-head569" xml:space="preserve">THEOREMA XI. PROPOS. XII.</head>
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            <s xml:id="echoid-s9809" xml:space="preserve">ASſumptis quibuſcunq; </s>
            <s xml:id="echoid-s9810" xml:space="preserve">hyperbolis, in vnaquaq; </s>
            <s xml:id="echoid-s9811" xml:space="preserve">re-
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            gula baſi, oſtendemus omnia quadrata vnius ad om-
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            nia quadrata alterius, habere rationem compoſitam ex ra-
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            tione rectanguli ſub compoſita ex ſexquialtera tranſuerſi
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            lateris, & </s>
            <s xml:id="echoid-s9812" xml:space="preserve">axi, vel diametro hyperbolæ primò dictæ, & </s>
            <s xml:id="echoid-s9813" xml:space="preserve">ſub
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            compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9814" xml:space="preserve">axi, vel diametro hyper-
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            bolæ ſecundò dictæ ad re ctangulum ſub compoſita ex trã-
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            ſuerſi lateris ſexquialtera, & </s>
            <s xml:id="echoid-s9815" xml:space="preserve">axi, vel diametro hyperbolæ
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            ſecundò dictæ, & </s>
            <s xml:id="echoid-s9816" xml:space="preserve">ſub compoſita ex tranſuerſo latere, & </s>
            <s xml:id="echoid-s9817" xml:space="preserve">axi
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            vel diametro hyperbolæ primò dictæ, & </s>
            <s xml:id="echoid-s9818" xml:space="preserve">ex ratione paral-
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            lelepipediſub altitudine hyperbolæ primò dictæ, baſiau-
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            tem quadrato baſis eiuſdem, ad parallelepipedum ſub al-
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            t tudine hyp rbolæ ſecundò dictæ, baſi pariter quadrato
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            b ſis eiuſdem. </s>
            <s xml:id="echoid-s9819" xml:space="preserve">Velſi comparentur omnia quadrata hy-
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            perbolæ primò dictæ, ad omnia rectangula hyperbolæ fe-
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            cundò dictæ ſimilia cuidam rectangulo, illa ad hæchabe-
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            buntrationem compoſitam exratione prædictorum rectã-
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            gulorum, & </s>
            <s xml:id="echoid-s9820" xml:space="preserve">exratione parallelepipedi primò dictiad pa-
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            rallelepipedum ſub altitudine hyperbolæ ſecundò, dictæ
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            baſirectangulo, cuiomnia dicta rectangula ſunt ſimilia.
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            <s xml:id="echoid-s9821" xml:space="preserve">Vel tandem ſi comparentur omnia rectangula primæ hy-
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            perbolæ ſimilia cuidam rectangulo ad omnia rectangula
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            ſecundæ hyperbolæ ſimilia pariter cuidam rectangulo, il-
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            la ad hæchabebunt rationem compoſitam ex ratione pa-
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            rallelepipedi ſub altitudine hyperbolæ primò dictæ baſi
              <lb/>
            rectangulo, cuiomnia eiuſdem rectangula ſunt ſimilia, ad
              <lb/>
            parallelepipedum ſub altitudine ecundæ hyperbolæ baſi
              <lb/>
            rectangulo, cuiomnia eiuſdem rectangula iam dicta </s>
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