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="390" file="0410" n="410" rhead="GEOMETRIÆ"/>
            eorum notitia in ſuppoſitione eiuſdem byperbolæ qudaraturæ deficiat;
              <lb/>
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            <s xml:id="echoid-s10061" xml:space="preserve">ſi quis tamen adbuc voluerit aliacirca eandem contemplari, metbo-
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            dum tenere poterit Lib. </s>
            <s xml:id="echoid-s10062" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10063" xml:space="preserve">& </s>
            <s xml:id="echoid-s10064" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10065" xml:space="preserve">à me proſequutam, mibi verò poſt
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            byperbolarum ſpeculationem ad oppoſitas ſectiones, & </s>
            <s xml:id="echoid-s10066" xml:space="preserve">coniugatas
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            Appolonij opportunè videtur tranſeundum.</s>
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        <div xml:id="echoid-div933" type="section" level="1" n="557">
          <head xml:id="echoid-head581" xml:space="preserve">THEOREMA XIX. PROPOS. XX.</head>
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            <s xml:id="echoid-s10068" xml:space="preserve">SI ad axim, vel diametrum vtriuſq; </s>
            <s xml:id="echoid-s10069" xml:space="preserve">oppoſitarum ſectio-
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            num ordinatim applicentur rectæ lineæ in eaſdem
              <lb/>
            terminatæ, ita vt abſciſſæ per eaſdem ab axibu, vel dia-
              <lb/>
            metris verſus vertices ſint æquales erũt iſtæ applicatæ pa-
              <lb/>
            rallelogrammi oppoſita latera, quod parallelogrãmum ſi
              <lb/>
            compleatur, regula applicatarum altera ſumpta, omnia
              <lb/>
            quadrata parallelogrammi conſtituti ad reliquum, dem-
              <lb/>
            ptis ab ijſdem omnibus quadratis oppoſitarum hyperbo-
              <lb/>
            larum iam ſer dictas ordinatim applicatas conſtitutarum,
              <lb/>
            erunt vt rectangulum ſub compoſita ex tranſuerſo latere,
              <lb/>
            & </s>
            <s xml:id="echoid-s10070" xml:space="preserve">axi, vel diametro alterutrius oppoſitarum hyperbola-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s10071" xml:space="preserve">ſub compoſita ex hoc axi, vel diametro, & </s>
            <s xml:id="echoid-s10072" xml:space="preserve">. </s>
            <s xml:id="echoid-s10073" xml:space="preserve">tran-
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            ſuerſi lateris, ad rectangulum bis ſub . </s>
            <s xml:id="echoid-s10074" xml:space="preserve">tranſuerſi lateris,
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            & </s>
            <s xml:id="echoid-s10075" xml:space="preserve">ſum compoſita ex. </s>
            <s xml:id="echoid-s10076" xml:space="preserve">eiuſdem tranſuerſi lateris, & </s>
            <s xml:id="echoid-s10077" xml:space="preserve">axi,
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            vel diamerro alrerutrius oppoſitarum hyperbolarum, cum
              <lb/>
            {2/3}. </s>
            <s xml:id="echoid-s10078" xml:space="preserve">quadrati eiuſdem axis, vel diametri.</s>
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            <s xml:id="echoid-s10080" xml:space="preserve">Sint oppoſitæ ſectiones, AMC, BND, quarum latus tranſuer-
              <lb/>
            ſum ſit, NM, communis axis, vel diameter earundem, ad quam
              <lb/>
            hincinde productam ordinatim applicẽtur, BD, AC, in fectiones
              <lb/>
            terminatæ, abicindentes verſus vertices, NM, axes, vel diame-
              <lb/>
            tros, FN, ME, hyperbolarum, BND, AMC, (quas pariter oppo-
              <lb/>
            ſitas voco) quæ ſint inter ſe æquales, iunganturque, BA, DC, & </s>
            <s xml:id="echoid-s10081" xml:space="preserve">
              <lb/>
            ſit, O, centrum oppoſitarum ſectionum, BND, AMC: </s>
            <s xml:id="echoid-s10082" xml:space="preserve">Quoniam
              <lb/>
            ergo, FN, ME, ſunt æquales, erunt etiam æquales, BD, AC, & </s>
            <s xml:id="echoid-s10083" xml:space="preserve">
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            ſunt equidiſtantes, quia ad eandem diametrum, velaxim, FE, ſunt
              <lb/>
              <note position="left" xlink:label="note-0410-01" xlink:href="note-0410-01a" xml:space="preserve">Blicitur
                <lb/>
              ex 29. Pri.
                <lb/>
              Con.</note>
            ordinatim applicate, ergo, BA, DC, erunt ęquidiſtantes, &</s>
            <s xml:id="echoid-s10084" xml:space="preserve">, BC,
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            parallelogrammum. </s>
            <s xml:id="echoid-s10085" xml:space="preserve">Dico ergo (regula ſumpta altera applica-
              <lb/>
            tarum, AC, BD, vt, AC,) omnia quadrata, BC, ad reliquum eo-
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            rundem demptis omnibus quadratis oppoſitarum hyperbolarum,
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            BND, AMC, eſſe vt rectangulum, NEO, ad rectangulum, </s>
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