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

Table of contents

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[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
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          <pb o="297" file="0317" n="317" rhead="LIBER IV."/>
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            <s xml:id="echoid-s7192" xml:space="preserve">Hoc Problema ſoluetur methodo Propoſ. </s>
            <s xml:id="echoid-s7193" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7194" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7195" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">propterea circa
              <lb/>
            ipſum non immoror.</s>
            <s xml:id="echoid-s7197" xml:space="preserve"/>
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        <div xml:id="echoid-div712" type="section" level="1" n="419">
          <head xml:id="echoid-head439" xml:space="preserve">THEOREMAIX. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s7198" xml:space="preserve">SI ad baſim datæ parabolæ ordinatim applicentur vtcun-
              <lb/>
            que rectæ lineæ, triangula ſub ipſis, & </s>
            <s xml:id="echoid-s7199" xml:space="preserve">portionibus baſis
              <lb/>
            abijſdem abſciſſis, erunt vt parallelepipeda ſub baſibus qua-
              <lb/>
            dratis abſciſſarum à baſi, altitudinibus autem reſiduis ipſius
              <lb/>
            baſis demptis abſciſſis.</s>
            <s xml:id="echoid-s7200" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7201" xml:space="preserve">Sit parabola, HGA, cuius baſis, HA, axis, vel diameter, GO,
              <lb/>
            ſint autem ductæ duæ vtcunq; </s>
            <s xml:id="echoid-s7202" xml:space="preserve">ordinatim applicatæ adipſam baſim,
              <lb/>
            HA, ipſæ, ST, VX, & </s>
            <s xml:id="echoid-s7203" xml:space="preserve">iungantur, SH, VH. </s>
            <s xml:id="echoid-s7204" xml:space="preserve">Dico triangulum,
              <lb/>
            VHX, ad triangulum, HST, eſſe vt parallelepipedum ſub altitudi-
              <lb/>
            ne, AX, baſi quadrato, XH, ad parallelepipedum ſub altitudine, A
              <lb/>
            T, baſi quadrato, TH. </s>
            <s xml:id="echoid-s7205" xml:space="preserve">Quoniam enim triangula vnum angulum
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              <figure xlink:label="fig-0317-01" xlink:href="fig-0317-01a" number="211">
                <image file="0317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0317-01"/>
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            vni angulo æqualem habentia ratio-
              <lb/>
              <note position="right" xlink:label="note-0317-01" xlink:href="note-0317-01a" xml:space="preserve">6. Lib. 2.</note>
            nem habent ex ratione laterum illis
              <lb/>
            angulis circumſtãtium compoſitam,
              <lb/>
            ideò triangulum, VHX, ad triangu-
              <lb/>
              <note position="right" xlink:label="note-0317-02" xlink:href="note-0317-02a" xml:space="preserve">3. Huius.</note>
            lum, SHT, habebit rationem com-
              <lb/>
            poſitam ex ea, quam habet, VX, ad,
              <lb/>
            ST, ideſt rectangulum, AXH, ad
              <lb/>
              <note position="right" xlink:label="note-0317-03" xlink:href="note-0317-03a" xml:space="preserve">G. D Cor.
                <lb/>
              4. Gen. 34,
                <lb/>
              lib. 2.</note>
            rectangulum, ATH, & </s>
            <s xml:id="echoid-s7206" xml:space="preserve">ex ea, quam
              <lb/>
            habet, XH, ad, HT, ſed iſtæ duæ
              <lb/>
            rationes componunt rationem paral-
              <lb/>
            lelepipedi ſub altitudine, HX, baſi
              <lb/>
            rectangulo, AXH, ad parallelepi-
              <lb/>
            pedum ſub altitudine, HT, baſi re-
              <lb/>
            ctangulo, HTA, . </s>
            <s xml:id="echoid-s7207" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7208" xml:space="preserve">parallelepipedi
              <lb/>
              <note position="right" xlink:label="note-0317-04" xlink:href="note-0317-04a" xml:space="preserve">Schol. 35.
                <lb/>
              lib. 2.</note>
            ſub altitudine, AX, baſi quadrato, XH, ad parallelepipedum ſub
              <lb/>
            altitudine, AT, baſi quadrato, TH, ergo triangulum, VHX, ad
              <lb/>
            triangulum, SHT, erit vt parallelepipedum ſub altitudine, AX, baſi
              <lb/>
            quadrato, XH, ad parallelepipedum ſub altitudine, AT, baſi qua-
              <lb/>
            drato, TH, quod erat oſtendendum.</s>
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