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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              <pb o="404" file="0424" n="424" rhead="GEOMETRIÆ"/>
            nem rectanguli, DC, CE, vel ſub, RZ, EC, ad quadratum, AV,
              <lb/>
            cum {1/3}. </s>
            <s xml:id="echoid-s10497" xml:space="preserve">quadrati, kI, ergo omnia quadrata, FC, demptis omnibus
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              <figure xlink:label="fig-0424-01" xlink:href="fig-0424-01a" number="287">
                <image file="0424-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0424-01"/>
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            quadratis oppoſitarum hyperbola-
              <lb/>
            rum, FAD, EVC, regula, EC, ad
              <lb/>
            omnia quadrata figuræ, FADCVE,
              <lb/>
            regula, DC, vel, AV, habebunt ra-
              <lb/>
            tionem compoſitam ex ractione re-
              <lb/>
            ctanguli, AOZ, bis cum {2/3}. </s>
            <s xml:id="echoid-s10498" xml:space="preserve">quadra
              <lb/>
            ti, KI, ad rectangulum, AZO, & </s>
            <s xml:id="echoid-s10499" xml:space="preserve">ex
              <lb/>
            ratione rectanguli ſub, RZ, EC, ad
              <lb/>
            quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10500" xml:space="preserve">quadrati,
              <lb/>
            KI, .</s>
            <s xml:id="echoid-s10501" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10502" xml:space="preserve">cum {4/12}. </s>
            <s xml:id="echoid-s10503" xml:space="preserve">quadrati, KI, quæ
              <lb/>
            ſunt {4/3}. </s>
            <s xml:id="echoid-s10504" xml:space="preserve">quadrati, LI, .</s>
            <s xml:id="echoid-s10505" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10506" xml:space="preserve">rectanguli,
              <lb/>
              <note position="left" xlink:label="note-0424-01" xlink:href="note-0424-01a" xml:space="preserve">Corol, 21.
                <lb/>
              huius.</note>
            AZV, vnde rectangulum ſub, AZ,
              <lb/>
            & </s>
            <s xml:id="echoid-s10507" xml:space="preserve">ſexquitertia, ZV, erit æquale ter-
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            tiæ parti quadrati, kI, erit igitur di-
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            cta ratio compoſita ex ratione pri-
              <lb/>
            mò dicta, & </s>
            <s xml:id="echoid-s10508" xml:space="preserve">ex ratione fectanguli
              <lb/>
            ſub, RZ, EC, ad quadratum, AV,
              <lb/>
            cum {1/3}. </s>
            <s xml:id="echoid-s10509" xml:space="preserve">quadrati, kI, ſiue cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s10510" xml:space="preserve">ſexquitertia,
              <lb/>
            ZV, quod oſtendere propoſitum erat.</s>
            <s xml:id="echoid-s10511" xml:space="preserve"/>
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          <head xml:id="echoid-head593" xml:space="preserve">THEOREMA XXVI. PROPOS. XXVII.</head>
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            <s xml:id="echoid-s10512" xml:space="preserve">SI in eadem anteced. </s>
            <s xml:id="echoid-s10513" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s10514" xml:space="preserve">figura intelligantur de-
              <lb/>
            ſcriptæ ſectiones, quæ ab Apollonio coniugatæ vo-
              <lb/>
            cantur, quæ ſint, Y & </s>
            <s xml:id="echoid-s10515" xml:space="preserve">B, HTN, coniugatæ prædictis, FAD,
              <lb/>
            EVC, habentes ſcilicet quadratum tranſuerſi lateris, & </s>
            <s xml:id="echoid-s10516" xml:space="preserve">T,
              <lb/>
            æquale rectingulo ſub alio tr anſuerſo latere, AV, & </s>
            <s xml:id="echoid-s10517" xml:space="preserve">linea
              <lb/>
            iuxta qua n poſſunt, ſiue latere recto oppoſitarum ſectionũ,
              <lb/>
            FAD, EVC, & </s>
            <s xml:id="echoid-s10518" xml:space="preserve">regula ſit DC, latus parallelogrammi, FC,
              <lb/>
            expoſitis primò ſectionibus oppoſiti, FAD, EVC, circum-
              <lb/>
            ſcriptum, æquidiſtans earu nlateri tranſuerſo, AV: </s>
            <s xml:id="echoid-s10519" xml:space="preserve">Om-
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            nia quadrata, FC, ad omnia quadrata figuræ, FADCVE,
              <lb/>
            demptis omnibus quadratis oppoſitarum hyperbolarum,
              <lb/>
            Y & </s>
            <s xml:id="echoid-s10520" xml:space="preserve">B HTN, quæ portionibus laterum, FE, DC, inter op-
              <lb/>
            poſitas ſectiones, Y & </s>
            <s xml:id="echoid-s10521" xml:space="preserve">B HTN, exiſtentium conſtituuntur,
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            erunt vt parallelepipedum ſub dimidia baſis primò expoſi-
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            tarum alterutrius, hyperbolarum, vt ſub, ZC, & </s>
            <s xml:id="echoid-s10522" xml:space="preserve">ſub </s>
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