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

Table of contents

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[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
[291.] THEOREMA XXXIX. PROPOS. XXXIX:
Page: 211 (191)
[292.] THEOREMA XL. PROPOS. XL.
Page: 212 (192)
[293.] COROLLARIVM.
Page: 212 (192)
[294.] THEOREMA XLI. PROPOS. XLI.
Page: 212 (192)
[295.] THEOREMA XLII. PROPOS. XLII.
Page: 213 (193)
[296.] COROLLARIVM.
Page: 214 (194)
[297.] SCHOLIVM.
Page: 215 (195)
[298.] Finis Secundi Libri.
Page: 215 (195)
[299.] CAVALERII LIBER TERTIVS. In quo de circulo, & Ellipſi, ac ſolidis ab eiſdem genitis, traditur doctrina.
Page: 217 (197)
[300.] THEOREMA I. PROPOS. I.
Page: 217 (197)
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              <pb o="251" file="0271" n="271" rhead="LIBER III."/>
            ta figuræ, BDMO, cum rectangulis bis ſub eadem ſigura, & </s>
            <s xml:id="echoid-s6252" xml:space="preserve">ſub
              <lb/>
            trilineis, BCO, ONM, erunt vt, AN, ad figuram, BDMO,
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            quod oſtendere opus erat.</s>
            <s xml:id="echoid-s6253" xml:space="preserve"/>
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        <div xml:id="echoid-div602" type="section" level="1" n="350">
          <head xml:id="echoid-head367" xml:space="preserve">THEOREMA XXIX. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s6254" xml:space="preserve">EXponatur figura Theor. </s>
            <s xml:id="echoid-s6255" xml:space="preserve">antecedentis, dimiſſis tamen re-
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            ctis lineis, DO, VR, & </s>
            <s xml:id="echoid-s6256" xml:space="preserve">ſit adhuc regula, EN, produ-
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            cantur autem ad eaſdem partes, AC, EN, in, HF, ita vt, C
              <lb/>
            H, ſit æqualis, NF, iuncta igitur, HF, erit, HF, parallela
              <lb/>
            ipſi, CN, quoniam, CH, NF, ſunt æquales, & </s>
            <s xml:id="echoid-s6257" xml:space="preserve">parallelæ,
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            & </s>
            <s xml:id="echoid-s6258" xml:space="preserve">erit parallelogrammum, AF, &</s>
            <s xml:id="echoid-s6259" xml:space="preserve">, CF. </s>
            <s xml:id="echoid-s6260" xml:space="preserve">Dico ergo omnia
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            quadrata, AN, cumrectangulis bis ſub, AN, NH, ad om-
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            nia quadrata figuræ, BDMO, cum rectangulis bis ſub ea-
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            dem, & </s>
            <s xml:id="echoid-s6261" xml:space="preserve">ſub quadrilineo, BOMFH, eſſe vt, AN, adfigu-
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            ram, BDMO.</s>
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            <s xml:id="echoid-s6263" xml:space="preserve">Omnia quadrata. </s>
            <s xml:id="echoid-s6264" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6265" xml:space="preserve">parallelogrammi, AN, ad omnia quadrata fi-
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            gurę, BDMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6266" xml:space="preserve">ſub trilineis, BC
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              <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Ex antec.</note>
            O, ONM, ſunt vt, AN, ad figuram, BDMO. </s>
            <s xml:id="echoid-s6267" xml:space="preserve">Item rectangula
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              <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2
                <unsure/>
              .</note>
            ſub, AN, NH, ad rectangula ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6268" xml:space="preserve">ſub, NH,
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            ſunt vt, AN, ad f
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            iguram, BDMO, & </s>
            <s xml:id="echoid-s6269" xml:space="preserve">eadem rectangula ſub, AN,
              <lb/>
            NH, bis ſumpta ad rectangula ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6270" xml:space="preserve">ſub, NH,
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            bis ſumpta erunt pariter, vt, AN, ad figuram, BDMO, . </s>
            <s xml:id="echoid-s6271" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6272" xml:space="preserve">vt omnia
              <lb/>
            quadrata, AN, ad rectangula bis ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6273" xml:space="preserve">ſub trili-
              <lb/>
            neis, BCO, ONM, cum omnibus quadratis eiuſdem figurę, BDM
              <lb/>
            O, ergo vt vnum ad vnum, ita omnia ad omnia. </s>
            <s xml:id="echoid-s6274" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6275" xml:space="preserve">vt omnia quadra-
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                <image file="0271-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0271-01"/>
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            ta, AN, ad omnia quadrata figuræ, BD
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            MO, cum rectangulis bis ſub eadem figu-
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            ra, & </s>
            <s xml:id="echoid-s6276" xml:space="preserve">ſub trilineis, BCO, ONM, ita om-
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            nia quadrata, AN, cum rectangulis bis ſub,
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            AN, NH, ad omnia quadrata figuræ, B
              <lb/>
            DMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6277" xml:space="preserve">
              <lb/>
            ſub trilineis, BCO, ONM, & </s>
            <s xml:id="echoid-s6278" xml:space="preserve">bis ſub ea-
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            dem, & </s>
            <s xml:id="echoid-s6279" xml:space="preserve">ſub, NH, .</s>
            <s xml:id="echoid-s6280" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6281" xml:space="preserve">ad rectangula bis ſub
              <lb/>
            eadem, & </s>
            <s xml:id="echoid-s6282" xml:space="preserve">ſub quadrilineo, BOMFH;
              <lb/>
            </s>
            <s xml:id="echoid-s6283" xml:space="preserve">ſunt autem omnia quadrata, AN, ad om-
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            nia quadrata figurę, BDMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6284" xml:space="preserve">ſub
              <lb/>
            trilineis, BCO, ONM, vt, AN, ad, BDMO; </s>
            <s xml:id="echoid-s6285" xml:space="preserve">ergo omnia qua-
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            drata, AN, cum rectangulis bis ſub, AN, NH, ad omnia quadrata
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            figurę, BDMO, cum rectangulis bis ſub, eadem, & </s>
            <s xml:id="echoid-s6286" xml:space="preserve">ſub </s>
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