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

Table of contents

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[221.] COROLLARIVM II.
Page: 167 (147)
[222.] LEMMA.
Page: 168 (148)
[223.] THE OREMA XX. PROPOS. XX.
Page: 168 (148)
[224.] COROLLARIVM.
Page: 169 (149)
[225.] THE OREMA XXI. PROPOS. XXI.
Page: 169 (149)
[226.] COROLLARIVM.
Page: 170 (150)
[227.] THE OREMA XXII. PROPOS. XXII.
Page: 170 (150)
[228.] A. COROLLARII SECTIO I.
Page: 174 (154)
[229.] B. SECTIO II.
Page: 174 (154)
[230.] C. SECTIO III.
Page: 174 (154)
[231.] D. SECTIO IV.
Page: 174 (154)
[232.] E. SECTIO V.
Page: 175 (155)
[233.] F. SECTIO VI.
Page: 175 (155)
[234.] THEOR EMA XXIII. PROPOS. XXIII.
Page: 175 (155)
[235.] A. COROLLARII SECTIO I.
Page: 176 (156)
[236.] B. SECTIO II.
Page: 177 (157)
[237.] C. SECTIO III.
Page: 177 (157)
[238.] D. SECTIO IV.
Page: 177 (157)
[239.] E. SECTIO V.
Page: 177 (157)
[240.] F. SECTIO VI.
Page: 177 (157)
[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
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            lineæ erunt interſe, vtrectangula ſub partibus baſis ab ei-
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            ſdem æquidiſtantibus conſtitutis.</s>
            <s xml:id="echoid-s7005" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7006" xml:space="preserve">Sit ergo parabola, FCH, circa axim, vel diametrum, CG, ad
              <lb/>
            quam ordinatim applicetur recta linea vtcunq; </s>
            <s xml:id="echoid-s7007" xml:space="preserve">FH, ducantur dein-
              <lb/>
            de intra parabolam axi, vel diametro, CG, parallelæ vtcunque, A
              <lb/>
            N, MO, baſim, FH, in punctis, N, O, diuidentes. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">Dico igitur re-
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            ctam, AN, ad rectam, MO, eſſe vt rectangulum, FNH, ad re-
              <lb/>
            ctangulum, FOH; </s>
            <s xml:id="echoid-s7009" xml:space="preserve">ducatur per, M, ipſi, FH, parallela, MI; </s>
            <s xml:id="echoid-s7010" xml:space="preserve">eſt
              <lb/>
            ergo, GC, ad, CI, vt quadratum, GH, ad quadratum, IM, vel
              <lb/>
              <note position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">38. EtSch.
                <lb/>
              40. lib. 1.</note>
            ad quadratum, GO, ergo, perconuerſionem rationis, GC, ad, G
              <lb/>
              <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a" number="202">
                <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0308-01"/>
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            I, vel ad, MO, erit vt quadratum, H
              <lb/>
            G, ad ſuireliquum, dempto quadrato,
              <lb/>
            GO, hoc autem reſiduum eſt rectan-
              <lb/>
            gulum ſub, GOH, bis, vna cum qua-
              <lb/>
            drato, OH, quod eſt æqualerectan-
              <lb/>
            gulo, FOH, nam rectangulum, GO
              <lb/>
            H, cum quadrato, OH, æquatur re-
              <lb/>
            ctangulo, GHO, .</s>
            <s xml:id="echoid-s7011" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7012" xml:space="preserve">rectangulo ſub,
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            FG, OH, cui ſi iunxeris rectangulum
              <lb/>
            ſub, GO, & </s>
            <s xml:id="echoid-s7013" xml:space="preserve">eadem, OH, conſurget
              <lb/>
            integrum rectangulum, FOH, æqualerectangulis ſub, GOH, bis,
              <lb/>
              <note position="left" xlink:label="note-0308-02" xlink:href="note-0308-02a" xml:space="preserve">4. 2. Elem.</note>
            vna cum quadrato, OH, ergo, CG, ad, MO, erit vt quadratum,
              <lb/>
              <note position="left" xlink:label="note-0308-03" xlink:href="note-0308-03a" xml:space="preserve">3.2. Elem.</note>
            GH, .</s>
            <s xml:id="echoid-s7014" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7015" xml:space="preserve">vt rectangulum, FGH, ad rectangulum, FOH, & </s>
            <s xml:id="echoid-s7016" xml:space="preserve">con-
              <lb/>
              <note position="left" xlink:label="note-0308-04" xlink:href="note-0308-04a" xml:space="preserve">1. 2. Elem.</note>
            uertendo, MO, ad, CG, erit vtrectang. </s>
            <s xml:id="echoid-s7017" xml:space="preserve">HOF, ad rectangulum, H
              <lb/>
            GF; </s>
            <s xml:id="echoid-s7018" xml:space="preserve">codem modo oſtendemus, CG, ad, AN, eſſe vt idem rectan-
              <lb/>
            gulum, HGF, ad rectangulum, FNH, ergo ex æquali, & </s>
            <s xml:id="echoid-s7019" xml:space="preserve">conuer-
              <lb/>
            tendo, AN, ad, MO, erit vt rectangulum, FNH, ad rectangulum,
              <lb/>
            FOH, quod oſtendere oportebat. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">Poſſunt autem vocari &</s>
            <s xml:id="echoid-s7021" xml:space="preserve">, AN,
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            MO, ordinatim applicatæ ad baſim parabolæ, FCH, ſcilicet ad
              <lb/>
            ipſam, FH.</s>
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          <head xml:id="echoid-head429" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
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            <s xml:id="echoid-s7023" xml:space="preserve">SI ad baſim parabolæ ordinatim applicetur vtcunque re-
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            cta linea, ſiat autem parallelogrammum, & </s>
            <s xml:id="echoid-s7024" xml:space="preserve">triangulum
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            habentia circa communem angulum dictam applicatam, & </s>
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            abſciſſam à baſiab vtrauis extremitatum eiuſdem, vel ſint
              <lb/>
            duæ ad baſim vtcunque ordinatim applicatæ, ſub alterutra
              <lb/>
            quarum, & </s>
            <s xml:id="echoid-s7026" xml:space="preserve">ſub in cluſa ab ijſdem portione baſis ſiat paralle-
              <lb/>
            logrammum, & </s>
            <s xml:id="echoid-s7027" xml:space="preserve">triangulum; </s>
            <s xml:id="echoid-s7028" xml:space="preserve">dicti parallelogrammi, vel </s>
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