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

Table of contents

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[171.] POSTVLATA I.
Page: 128 (108)
[172.] II.
Page: 128 (108)
[173.] THEOREMA I. PROPOS. I.
Page: 128 (108)
[174.] SCHOLIVM.
Page: 131 (111)
[175.] THEOREMA II. PROPOS. II.
Page: 132 (112)
[176.] COROLLARIV M.
Page: 133 (113)
[177.] THEOREMA III. PROPOS. III.
Page: 133 (113)
[178.] COROLLARIVM.
Page: 135 (115)
[179.] THEOREMA IV. PROPOS. IV.
Page: 135 (115)
[180.] COROLLARIVM.
Page: 136 (116)
[181.] THEOREMA V. PROPOS. V.
Page: 137 (117)
[182.] THEOREMA VI. PROPOS. VI.
Page: 138 (118)
[183.] THEOREMA VII. PROPOS. VII.
Page: 139 (119)
[184.] THEOREMA VIII. PROPOS. VIII.
Page: 140 (120)
[185.] COROLLARIVM.
Page: 140 (120)
[186.] THEOREMA IX. PROPOS. IX.
Page: 140 (120)
[187.] COROLLARIVM.
Page: 141 (121)
[188.] THEOREMA X. PROPOS. X.
Page: 141 (121)
[189.] COROLLARIVM.
Page: 143 (123)
[190.] THEOREMA XI. PROPOS. XI.
Page: 143 (123)
[191.] COROLLARIVM.
Page: 144 (124)
[192.] THEOREMA XII. PROPOS. XII.
Page: 144 (124)
[193.] COROLLARIVM.
Page: 145 (125)
[194.] THEOREMA XIII. PROPOS. XIII.
Page: 145 (125)
[195.] COROLLARIVM.
Page: 146 (126)
[196.] THEOREMA XIV. PROPOS. XIV.
Page: 146 (126)
[197.] COROLLARIVM.
Page: 147 (127)
[198.] THEOREMA XV. PROPOS. XV.
Page: 147 (127)
[199.] A. DEMONSTRATIONIS SECTIO I.
Page: 148 (128)
[200.] B. SECTIO SECVNDA.
Page: 149 (129)
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            <s xml:id="echoid-s2848" xml:space="preserve">Sint igitur parallelogramma, AM, MC, in eadem altitudine. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">Di-
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">A. Deſ. 8.
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              huius.</note>
            co omnia quadrata parallelogrammi, AM, ad omnia quadrata pa-
              <lb/>
            rallelogrammi, MC, regula, GH, eſſe vt quadratum, GM, ad
              <lb/>
            quadratum, MH. </s>
            <s xml:id="echoid-s2850" xml:space="preserve">Sit intra parallelogramma, AM, MC, ducta
              <lb/>
            vtcunque, DI, parallela ipſi, GH, cuius portio, DE, maneat in,
              <lb/>
              <figure xlink:label="fig-0141-01" xlink:href="fig-0141-01a" number="81">
                <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0141-01"/>
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            AM, &</s>
            <s xml:id="echoid-s2851" xml:space="preserve">, EI, in, BH, quoniam ergo, D
              <lb/>
            E, eſt æqualis ipſi, GM, figurę autem pla-
              <lb/>
            næ ſimiles deicriptæ à lateribus, vel lineis
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">25. lib. 1.</note>
            homologis æqualibus ſunt æquales, & </s>
            <s xml:id="echoid-s2852" xml:space="preserve">ideò
              <lb/>
            quadratum, DE, erit æquale quadrato, G
              <lb/>
            M, & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">quadratum, EI, quadrato, MH,
              <lb/>
            ergo, vt quadratum, GM, ad quadratum,
              <lb/>
            MH, ita erit quadratum, DE, ad quadratum, EI, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">quia, DI, vt-
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            cunq; </s>
            <s xml:id="echoid-s2855" xml:space="preserve">ducta eſt parallela ipſi, GH, ideò, vt vnum ad vnum, ita om-
              <lb/>
              <note position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            nia ad omnia idelt vt quadratum, GM, ad quadratum, MH, ita
              <lb/>
            erunt omnia quadrata parallelogrammi, AM, ad omnia quadrata
              <lb/>
            parallelogrammi, MC, regula, GH, quod erat oſtendendum.</s>
            <s xml:id="echoid-s2856" xml:space="preserve"/>
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        <div xml:id="echoid-div301" type="section" level="1" n="187">
          <head xml:id="echoid-head202" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s2857" xml:space="preserve">_H_Inc patet, ſi vice quadratorum ſumamus alias quaſcunque figuras
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            ſimiles, quod eodem pacto oſtendemus omnes figuras ſimiles pa-
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              <note position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">_A. Def. 8._
                <lb/>
              _huius._</note>
            rallelogrammi, AM, ad omnes ſimiles figuras parallelogrammi, MC,
              <lb/>
            vt ex. </s>
            <s xml:id="echoid-s2858" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2859" xml:space="preserve">omnes circutos parallelogrammi, AM, ad omnes circulos pa-
              <lb/>
            rallelogrammi, MC, eſſe vt ſimiles ſiguras ab ipſis b ſibus, GM, MH,
              <lb/>
            d@ſcriptas, nam fi uræ planæ ſimiles quæcunq; </s>
            <s xml:id="echoid-s2860" xml:space="preserve">vt dictum eſt, deſcriptæ à
              <lb/>
            lateribus, vel lineis homologis æqualibus ſunt æquales; </s>
            <s xml:id="echoid-s2861" xml:space="preserve">omnibus pari-
              <lb/>
              <note position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">_25. lib. 1._</note>
            ter aſſumptis figuris ſimilibus, regula eadem, GH.</s>
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          <head xml:id="echoid-head203" xml:space="preserve">THEOREMA X. PROPOS. X.</head>
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            <s xml:id="echoid-s2863" xml:space="preserve">PArellelogrammorum in eadem baſiexiſtentium omnia
              <lb/>
            quadrata, regula ipſa baſi, ſunt vt altitudines, vel vt la-
              <lb/>
            tera, quę æqualiter baſi ſunt inclinata, ſi illa ſint ęquiangula.</s>
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          <p>
            <s xml:id="echoid-s2865" xml:space="preserve">Sint parallelogramma, AD, BD, in eadem b ſi, CD, exiſten-
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            tia, quorum ſint altitudines iuxta baſim, CD, ſumptæ, AO, CN.
              <lb/>
            </s>
            <s xml:id="echoid-s2866" xml:space="preserve">Dico omnia quadrata parallelogrammi, AD, adomnia quadrata
              <lb/>
            parallelogrammi, BD, regula, CD, eſſe vt, AO, ad, CN, vel
              <lb/>
            etiam vt, AC, ad, CB, ſi parallelogramma, BD, DA, fuerint æ-
              <lb/>
            quiangula, producantur autem, CA, CB, indefinitè ad partes </s>
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