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

Table of contents

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[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)
[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)
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          <p>
            <s xml:id="echoid-s7529" xml:space="preserve">
              <pb o="313" file="0333" n="333" rhead="LIBER IV."/>
            omnia quadrata, AH, ſunt dupla omnium quadratorum parabo-
              <lb/>
              <note position="right" xlink:label="note-0333-01" xlink:href="note-0333-01a" xml:space="preserve">Exa@. tec.</note>
            læ, FCH, & </s>
            <s xml:id="echoid-s7530" xml:space="preserve">omnia quadrata, RM, ſunt dupla omnium quadra-
              <lb/>
            torum parabolę, OCM, ideò omnia quadrata parabolę, FCH, ad
              <lb/>
            omnia quadrata parabolę, OCM, erunt vt omnia quadrata; </s>
            <s xml:id="echoid-s7531" xml:space="preserve">AH,
              <lb/>
            ad omnia quadrata, RM: </s>
            <s xml:id="echoid-s7532" xml:space="preserve">Omnia vero quadrata, AH, ad omnia
              <lb/>
            quadrata, RM, habentrationem compoſitam ex ea, quam habet
              <lb/>
            quadratum, FH, ad quadratum, OM, ideſt ex ea, quam habet,
              <lb/>
            GC, ad, CI, & </s>
            <s xml:id="echoid-s7533" xml:space="preserve">ex ea, quam habet, HE, ad, NM, quiaillę cum
              <lb/>
              <note position="right" xlink:label="note-0333-02" xlink:href="note-0333-02a" xml:space="preserve">11. 1. 2.</note>
            baſibus, OM, FH, continent angulos ęquales, duę autem ratio-
              <lb/>
            nes, ſcilicet, quam habet, GC, ad, CI, &</s>
            <s xml:id="echoid-s7534" xml:space="preserve">, HE, ad, NM, . </s>
            <s xml:id="echoid-s7535" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7536" xml:space="preserve">G
              <lb/>
            C, ad, CI, componuntrationem quadrati, GC, ad quadratum, C
              <lb/>
            I, ergo omnia quadrata, AH, ad omnia quadrata, RM, vel om-
              <lb/>
            nia quadrata parabolę, FCH, ad omnia quadrata parabolę, OC
              <lb/>
            M, erunt vt quadratum, GC, ad quadratum, CI, quod oſtende-
              <lb/>
            re opus erat.</s>
            <s xml:id="echoid-s7537" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div750" type="section" level="1" n="442">
          <head xml:id="echoid-head462" xml:space="preserve">THEOREMA XXII. PROPOS. XXIII.</head>
          <p>
            <s xml:id="echoid-s7538" xml:space="preserve">IN figura Prop. </s>
            <s xml:id="echoid-s7539" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7540" xml:space="preserve">ſumpta regula ipſa, BH, oſtendemus
              <lb/>
            omnia quadrata, PH, ad omnia quadrata fruſti, ABH
              <lb/>
            M, eſſe vt, ON, ad compoſitam ex, NR, & </s>
            <s xml:id="echoid-s7541" xml:space="preserve">@. </s>
            <s xml:id="echoid-s7542" xml:space="preserve">RO: </s>
            <s xml:id="echoid-s7543" xml:space="preserve">Omnia
              <lb/>
            verò quadrata fruſti, ABHM, ad omnia quadrata triangu-
              <lb/>
            li, RBH, eſie vt compoſitam ex, ON, dupla, NR, et @. </s>
            <s xml:id="echoid-s7544" xml:space="preserve">R
              <lb/>
            O, ad ipſam, NO.</s>
            <s xml:id="echoid-s7545" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7546" xml:space="preserve">Sumatur in, RO, vtcunq; </s>
            <s xml:id="echoid-s7547" xml:space="preserve">punctum, X, per quod regulę, BH,
              <lb/>
            paralleia ducatur, XT, ſecans curuam parabolę in, I, eſt ergo qua-
              <lb/>
            dratum, OH, vel quadratum, TX, ad quadratum, XI, vt, ON,
              <lb/>
              <figure xlink:label="fig-0333-01" xlink:href="fig-0333-01a" number="224">
                <image file="0333-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0333-01"/>
              </figure>
            ad, NX, eſt autem parallelogram-
              <lb/>
            mum, RH, in eadem bafi, & </s>
            <s xml:id="echoid-s7548" xml:space="preserve">alti-
              <lb/>
            tudine cum quadrilineo, ROHM,
              <lb/>
            & </s>
            <s xml:id="echoid-s7549" xml:space="preserve">punctum, X, ſumptum eſt vt
              <lb/>
            cunque, ductaque, XT, regulæ
              <lb/>
            parallela, repertum eſt quadratum,
              <lb/>
            TX, ad quadratum, XI, eſſe vt,
              <lb/>
            ON, ad, NX, ergo horum quatuor ordinum magnitudines erunt
              <lb/>
              <note position="right" xlink:label="note-0333-03" xlink:href="note-0333-03a" xml:space="preserve">Coroll. @.
                <lb/>
              26. 1. 2.</note>
            proportionales. </s>
            <s xml:id="echoid-s7550" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7551" xml:space="preserve">omnia quadrata, RH, magnitudines primi ordinis
              <lb/>
            collectę iuxta primam. </s>
            <s xml:id="echoid-s7552" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7553" xml:space="preserve">iuxta quadratum, TX, ad omnia quadrata
              <lb/>
            quadrilinei, RMHO, magnitudines ſecundi ordinis collectas iuxta fe-
              <lb/>
            cundã. </s>
            <s xml:id="echoid-s7554" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7555" xml:space="preserve">iuxta quadratum, XI, erunt vt maximę abſciſlarum, OR,
              <lb/>
            adiunctal, RN, ad omnes abiciſſas, OR, adiuncta, RN, quę </s>
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