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

Table of contents

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[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
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            <s xml:id="echoid-s7872" xml:space="preserve">
              <pb o="327" file="0347" n="347" rhead="LIBER IV."/>
            guræ, CBDF, erunt vt, AF, ad parabolam, DBF, cum {@/2} {1/4}.
              <lb/>
            </s>
            <s xml:id="echoid-s7873" xml:space="preserve">parallelogrammi, AF; </s>
            <s xml:id="echoid-s7874" xml:space="preserve">parallelogrammum autem, AF, eſt ſex-
              <lb/>
            quialterum parabolæ, DBF, .</s>
            <s xml:id="echoid-s7875" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7876" xml:space="preserve">ad illam, vt 24. </s>
            <s xml:id="echoid-s7877" xml:space="preserve">ad 16. </s>
            <s xml:id="echoid-s7878" xml:space="preserve">ergo ſi nu-
              <lb/>
            mero 16. </s>
            <s xml:id="echoid-s7879" xml:space="preserve">iungatur {1/4}. </s>
            <s xml:id="echoid-s7880" xml:space="preserve">eiuſdem parallelogrammi, AF, fient 17. </s>
            <s xml:id="echoid-s7881" xml:space="preserve">
              <lb/>
            igitur omnia quadrata, AF, ad omnia quadrata figuræ, CBDF,
              <lb/>
            erunt vt 24. </s>
            <s xml:id="echoid-s7882" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s7883" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s7884" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div789" type="section" level="1" n="467">
          <head xml:id="echoid-head487" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7885" xml:space="preserve">_H_Inc patet omnia quadrata, AF, eſſe ſexquialtera omnium qua-
              <lb/>
            dratorum figuræ, CBDF, demptis omnibus quadratis trilinei, B
              <lb/>
              <note position="right" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">_1. huius._</note>
            CF, nam ſunt ad illa, vt, AF, ad parabolam, BDF, cuius parallelo-
              <lb/>
            grammum, AF, eſt ſexquialterum.</s>
            <s xml:id="echoid-s7886" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div791" type="section" level="1" n="468">
          <head xml:id="echoid-head488" xml:space="preserve">THEOREMA XXXI. PROPOS. XXXIII.</head>
          <p>
            <s xml:id="echoid-s7887" xml:space="preserve">IN eodem antec. </s>
            <s xml:id="echoid-s7888" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s7889" xml:space="preserve">Schemate oſten demus omnia
              <lb/>
            quadrata figuræ, CBDF, demptis omnibus quadratis,
              <lb/>
            BF, ad omnia quadrata, BF, demptis omnibus quadratis
              <lb/>
            trilinei, BCF, eſſe vt 11. </s>
            <s xml:id="echoid-s7890" xml:space="preserve">ad 5.</s>
            <s xml:id="echoid-s7891" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7892" xml:space="preserve">Nam omnia quadrata, AF, ad omnia quadrata figuræ, CBD
              <lb/>
            F, oſtenſa ſunt eſſe, vt 24. </s>
            <s xml:id="echoid-s7893" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s7894" xml:space="preserve">eadem verò ad omnia quadrata,
              <lb/>
            BF, ſunt vt 24. </s>
            <s xml:id="echoid-s7895" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s7896" xml:space="preserve">quia ſunt eorum quadrupla, ergo ad reſiduum
              <lb/>
            .</s>
            <s xml:id="echoid-s7897" xml:space="preserve">f. </s>
            <s xml:id="echoid-s7898" xml:space="preserve">ad omnia quadrata figuræ, CBDF, demptis omnib. </s>
            <s xml:id="echoid-s7899" xml:space="preserve">quadratis,
              <lb/>
              <figure xlink:label="fig-0347-01" xlink:href="fig-0347-01a" number="234">
                <image file="0347-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0347-01"/>
              </figure>
            BF, erunt vt 24. </s>
            <s xml:id="echoid-s7900" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s7901" xml:space="preserve">con-
              <lb/>
            uertendo omnia quadrata fi-
              <lb/>
            gurę, CBDF, demptis om-
              <lb/>
            nibus quadratis, BF, ad om-
              <lb/>
            nia quadrata, AF, erunt vt
              <lb/>
            11. </s>
            <s xml:id="echoid-s7902" xml:space="preserve">ad 24. </s>
            <s xml:id="echoid-s7903" xml:space="preserve">Item omnia qua-
              <lb/>
            drata, AF, ad omnia qua-
              <lb/>
            drata, BF, ſunt vt 24. </s>
            <s xml:id="echoid-s7904" xml:space="preserve">ad 6.
              <lb/>
            </s>
            <s xml:id="echoid-s7905" xml:space="preserve">omnia verò quadrata, BF,
              <lb/>
            ad omnia quadrata trilinei,
              <lb/>
            BCF, ſunt vt 6. </s>
            <s xml:id="echoid-s7906" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7907" xml:space="preserve">ergo omnia quadrata, AF, ad omnia qua-
              <lb/>
            drata trilinei, BCF, ſunt vt 24. </s>
            <s xml:id="echoid-s7908" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7909" xml:space="preserve">eadem verò ad omnia quadra-
              <lb/>
            ta, BF, ſunt vt 24. </s>
            <s xml:id="echoid-s7910" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s7911" xml:space="preserve">ergo omnia quadrata, AF, ad omnia qua-
              <lb/>
            drata, BF, demptis omnibus quadratis trilinei, BCF, erunt vt 24. </s>
            <s xml:id="echoid-s7912" xml:space="preserve">
              <lb/>
            ad 5. </s>
            <s xml:id="echoid-s7913" xml:space="preserve">erant autem omnia quadrata figuræ, CBDF, demptis </s>
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