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

Table of contents

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[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
[311.] THEOREMA VIII. PROPOS. IX.
Page: 230 (210)
[312.] COROLLARIVM.
Page: 231 (211)
[313.] THEOREMA IX. PROPOS. X.
Page: 231 (211)
[314.] COROLLARIVM.
Page: 232 (212)
[315.] THEOREMAX. PROPOS. XI.
Page: 233 (213)
[316.] COROLLARIVM I.
Page: 234 (214)
[317.] COROLL II. A. SECTIO I.
Page: 235 (215)
[318.] B. SECTIO II.
Page: 235 (215)
[319.] C. SECTIO III.
Page: 235 (215)
[320.] D. SECTIO IV.
Page: 235 (215)
[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)
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            GH, vel quadratum, EC, ad quadratum, IM, vel ad quadratum,
              <lb/>
              <note position="left" xlink:label="note-0306-01" xlink:href="note-0306-01a" xml:space="preserve">Ex 38. &
                <lb/>
              Schol. 40.
                <lb/>
              lib. 1.</note>
            CN, vt, GC, ad, CI,.</s>
            <s xml:id="echoid-s6968" xml:space="preserve">. vt, ON, ad, NM, eſt autem, CH, pa-
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            rallelogrammum in eadem baſi, & </s>
            <s xml:id="echoid-s6969" xml:space="preserve">altitudine cum trilineo, CMH
              <lb/>
            E, & </s>
            <s xml:id="echoid-s6970" xml:space="preserve">punctum, N, vtcunq; </s>
            <s xml:id="echoid-s6971" xml:space="preserve">ſumptum, per quod acta eſt ipſi, CG,
              <lb/>
            parallela, NO, repertumque eſt, vt quadratum, EC, ad quadra.
              <lb/>
            </s>
            <s xml:id="echoid-s6972" xml:space="preserve">tum, CN, itaeſſe, ON, ad, NM; </s>
            <s xml:id="echoid-s6973" xml:space="preserve">ergo horum quatuor ordinum
              <lb/>
              <note position="left" xlink:label="note-0306-02" xlink:href="note-0306-02a" xml:space="preserve">Coroll. 3.
                <lb/>
              26. lib. 2.</note>
            magnitudines erunt proportionales ſcilicet omnia quadrata maxi-
              <lb/>
            marum abſciſſarum, EC, magnitudines primi ordinis collectæ iuxta
              <lb/>
            quadratum, CE, ad quadrata omnium abſciſſarum ipſius, CE, ſiue
              <lb/>
            ambo ſint recti, vel eiuſdem obliqui tranſitus, quæ ſunt magnitudi-
              <lb/>
            nes ſecundi ordinis collectæ, iuxta quadratum, CN, erunt vt om-
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              <figure xlink:label="fig-0306-01" xlink:href="fig-0306-01a" number="200">
                <image file="0306-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0306-01"/>
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            nes lineæ parallelogrammi, CH, ma-
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            gnitudines tertij ordinis collectæ, iux-
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            ta, NO, ad omnes lineas trilinei, CM
              <lb/>
            HE, magnitudines quarti ordinis col.
              <lb/>
            </s>
            <s xml:id="echoid-s6974" xml:space="preserve">lectas, iuxta, NM, regula pro his om-
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            nibus lineis exiſtenteipſa, EH; </s>
            <s xml:id="echoid-s6975" xml:space="preserve">vt au-
              <lb/>
              <note position="left" xlink:label="note-0306-03" xlink:href="note-0306-03a" xml:space="preserve">3. Lib. 2.</note>
            tem ſunt omnes lineæ parallelogram-
              <lb/>
            mi, CH, ad omnes lineas trilinei, CM
              <lb/>
            HE, ita eſt parallelogrammum, CH,
              <lb/>
            ad trilineum, CMHE, ergo paralle-
              <lb/>
            logrammum, CH, ad trilineum, CMHE, eſt vt quadrata maxi-
              <lb/>
            marum abſciſſarum ipſius, CE, ad quadrata omnium abſciſſarum ip-
              <lb/>
            ſius, CE, verum illa quadrata ſuntiſtorum tripla, ergo erit paralle-
              <lb/>
              <note position="left" xlink:label="note-0306-04" xlink:href="note-0306-04a" xml:space="preserve">Color. 25
                <lb/>
              lib. 2.</note>
            logrammum, CH, triplum ipſius trilinei, CMHE, ergo idem pa-
              <lb/>
            rallelogrammum, CH, erit ſexquialterum ſemiparabolæ, GCM
              <lb/>
            H, ideò etiam parallelogrammum, AH, erit parabole, FCH, ſex-
              <lb/>
            quialterum. </s>
            <s xml:id="echoid-s6976" xml:space="preserve">Quoniam verò triangulum, CFH, eſt dimidium pa-
              <lb/>
            rallelogrammi, AH, ideò quarum partium parallelogrammum, A
              <lb/>
            H, erit ſex, & </s>
            <s xml:id="echoid-s6977" xml:space="preserve">parabola, FCH, conſequenter ea undem quatuor,
              <lb/>
            triangulum, CFH, erit tria, & </s>
            <s xml:id="echoid-s6978" xml:space="preserve">ideò erit ad parabolam, FCH, vt
              <lb/>
            tria ad quatuor, & </s>
            <s xml:id="echoid-s6979" xml:space="preserve">idcircò erit eiuſdem ſubſexquitertium, quæ oſten-
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            dere oportebat.</s>
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          <head xml:id="echoid-head426" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s6981" xml:space="preserve">HInc patet ductas in trilineo, CMHE, æquidiſtantes axi, bel dia-
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            metro, CG, eſſe inter ſe, bt quadrata abſciſſarumper eaſdem d
              <lb/>
            tangente, CE, berſus berticem parabolæ, quieſt punctum, C; </s>
            <s xml:id="echoid-s6982" xml:space="preserve">nam oſten-
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            ſum eſt, ON, ſiue, HE, ad, NM, eſſe bt quadratum, EC, ad quadra-
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            tum, CN, & </s>
            <s xml:id="echoid-s6983" xml:space="preserve">punctum, N, ſumptum eſt btcunque, ideo, &</s>
            <s xml:id="echoid-s6984" xml:space="preserve">c.</s>
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