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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              <pb o="373" file="0393" n="393" rhead="LIBER V."/>
            dempto quadrato, ME, quia verò tripla, BE, eſt compoſita ex, E
              <lb/>
            X, & </s>
            <s xml:id="echoid-s9597" xml:space="preserve">dupla, EN, ſi a rectangulo ſub compoſita ex, EX, & </s>
            <s xml:id="echoid-s9598" xml:space="preserve">dupla,
              <lb/>
            EN, & </s>
            <s xml:id="echoid-s9599" xml:space="preserve">ſub, EM, abſtuleris quadratum, ME, .</s>
            <s xml:id="echoid-s9600" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9601" xml:space="preserve">rectangulum ſub,
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            MF, &</s>
            <s xml:id="echoid-s9602" xml:space="preserve">, ME, remanebit rectangulum ſub compoſita ex ipſa, XE,
              <lb/>
            EN, NM, & </s>
            <s xml:id="echoid-s9603" xml:space="preserve">ſub, EM, illas ergo tres componentes rationes in has
              <lb/>
            duas reſolutas habemus, ſcilicet in eam, quam habet rectangulũ
              <lb/>
            ſub, XEN, integra, & </s>
            <s xml:id="echoid-s9604" xml:space="preserve">ſub, EN, ad rectangulum ſub integra, XE,
              <lb/>
            EN, NM, & </s>
            <s xml:id="echoid-s9605" xml:space="preserve">ſub, ME, & </s>
            <s xml:id="echoid-s9606" xml:space="preserve">in eam, quam habet, NE, ad, EM, quæ
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            duæ rationes componunt rationem parallelepipedi ſub, NE, & </s>
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              <lb/>
            ſub rectangulo integræ, XEN, ductæ in, EN, ideſt parallelepipe-
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              <note position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">3.6. .1.</note>
            di ſub integra, XEN, & </s>
            <s xml:id="echoid-s9608" xml:space="preserve">quadrato, NE, ad parallelepipedum ſub,
              <lb/>
            ME, & </s>
            <s xml:id="echoid-s9609" xml:space="preserve">rectangulo integræ, XE, EN, NM, ductæ in, ME, .</s>
            <s xml:id="echoid-s9610" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9611" xml:space="preserve">ad
              <lb/>
            parallelepipedum ſub integra, XE, EN, NM, & </s>
            <s xml:id="echoid-s9612" xml:space="preserve">quadrato, ME,
              <lb/>
            ergo omnia quadrata, AF, demptis omnibus quadratis hyperbo-
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            læ, DNF, ad omnia quadrata, SF, demptis omnibus quadratis
              <lb/>
            fruſti, HDFG, erunt vt parallelepipedum ſub integra, XEN, & </s>
            <s xml:id="echoid-s9613" xml:space="preserve">
              <lb/>
            quadrato, NE, ad parallelepipedum ſub integra, XE, EN, NM,
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            & </s>
            <s xml:id="echoid-s9614" xml:space="preserve">quadrato, ME, quod erat oſtendendum.</s>
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          <head xml:id="echoid-head563" xml:space="preserve">PROBLEMA I. PROPOS. VI.</head>
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            <s xml:id="echoid-s9616" xml:space="preserve">A Data hyperbola portionem abſcindere per lineam
              <lb/>
            ad eiuſdem axim, vel diametrum ordinatim appli-
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            catam, cuius omnia quadrata, regula propoſitæ hyperbo-
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            læ baſi, ad omnia quadrata trianguli in eadem baſi, & </s>
            <s xml:id="echoid-s9617" xml:space="preserve">cir-
              <lb/>
            ca eundem axim, vel diametrum cum portione, ſiue hyper-
              <lb/>
            bola abſciſſa, exiſtentis, habeant datam rationem, quam
              <lb/>
            oportet eſſe quidem maioris inæqualitatis, ſed tamen mi-
              <lb/>
            norem ſexquialtera.</s>
            <s xml:id="echoid-s9618" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s9619" xml:space="preserve">Sit ergo data hyperbola, FEG, cuius axis, vel diameter, E M & </s>
            <s xml:id="echoid-s9620" xml:space="preserve">
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            larus tranſuerſum, CE, cuius ſit, AE, ſexquialtera, baſis, & </s>
            <s xml:id="echoid-s9621" xml:space="preserve">regu-
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            la, FG, data ratio, quam habet, HR, ad, RL, maioris inæquali-
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            tatis, ſed minor ſexquialtera, oportet ergo ab hyperbola, FEG,
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            per lineam ad, EM, ordinatim applicatam .</s>
            <s xml:id="echoid-s9622" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9623" xml:space="preserve">baſi, fiue regulæ,
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            FG, parallelam, portionem, ſiue hyperbolam abſcindele, cuius
              <lb/>
            omnia quadrata ad omnia quadrata trianguli in eadem baſi, & </s>
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              <lb/>
            circa eundem axim, vel diametrum cum ipſa habeant rationem,
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            quam habet, HR, ad, RL; </s>
            <s xml:id="echoid-s9625" xml:space="preserve">quia ergo ratio, HR, ad, RL, eſt mi-
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            nor ſexquialtera, erit minor ea, quam habet, AE, ad, EC, & </s>
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