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

Table of contents

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[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)
[481.] THEOREMA XLI. PROPOS. XLIII.
Page: 357 (337)
[482.] THEOREMA XLII. PROPOS. XLIV.
Page: 358 (338)
[483.] THEOREMA XLIII. PROP. XLV.
Page: 358 (338)
[484.] THEOREMA XLIV. PROP. XLVI.
Page: 359 (339)
[485.] THEOREMA XLV. PROP. XLVII.
Page: 360 (340)
[486.] THEOREMA XLVI. PROPOS. XLVIII.
Page: 361 (341)
[487.] THEOREMA XLVII. PROPOS. XLIX.
Page: 362 (342)
[488.] THEOREMA XLVIII. PROPOS. L.
Page: 364 (344)
[489.] THEOREMA XLIX. PROPOS. LI.
Page: 365 (345)
[490.] SCHOLIVM.
Page: 365 (345)
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            <s xml:id="echoid-s11491" xml:space="preserve">
              <pb o="446" file="0466" n="466" rhead="GEOMETRIÆ"/>
            producta, AC, vſq; </s>
            <s xml:id="echoid-s11492" xml:space="preserve">ad circumferentiam circuli, DG, cui incidat
              <lb/>
              <figure xlink:label="fig-0466-01" xlink:href="fig-0466-01a" number="320">
                <image file="0466-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0466-01"/>
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            in, O, portio igi-
              <lb/>
            tur circuli, CAV
              <lb/>
            N, ad portionem
              <lb/>
            circuli, DAEGO,
              <lb/>
            habet rationem
              <lb/>
            compoſitá ex ea,
              <lb/>
            quam habet por-
              <lb/>
              <note position="left" xlink:label="note-0466-01" xlink:href="note-0466-01a" xml:space="preserve">Deſin. 12.
                <lb/>
              1. 1.</note>
            tio, CAVN, ad
              <lb/>
            portionem, OAE
              <lb/>
              <note position="left" xlink:label="note-0466-02" xlink:href="note-0466-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              3. huius.</note>
            G, ideſt ex ratio-
              <lb/>
            ne quadrati, VA,
              <lb/>
              <note position="left" xlink:label="note-0466-03" xlink:href="note-0466-03a" xml:space="preserve">33. Sexti.
                <lb/>
              Elem.
                <lb/>
              7. huius.</note>
            ad quadratum, A
              <lb/>
            E, & </s>
            <s xml:id="echoid-s11493" xml:space="preserve">ex ratione
              <lb/>
            portionis, OAEG, ad portionem, DAEGO, ideſt ex r@tione cir-
              <lb/>
            cumferentiæ, EGO, ad circumferentiam, EGD, ideſt ex ratione,
              <lb/>
            VA, ad, AE, duæ autem rationes quadrati, VA, ad qua lratum, A
              <lb/>
            E, & </s>
            <s xml:id="echoid-s11494" xml:space="preserve">ipſius, VA, ad, AE, componunt rationem cubi, VA, ad cu-
              <lb/>
            bum, AE, ergo portio, CAVN, ad portionem, DAEGO, erit vt
              <lb/>
            cubus, VA, ad cubum, AE, ſunt autem ſpatia, AXC, AXCD, ter-
              <lb/>
            tiæ partes dictarum portionum, ergo ſpacium, AXC, ad ſpatium,
              <lb/>
            AXCD, erit vt cubus, VA, ad cubum, AE, quoderat oſtenden-
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              <note position="left" xlink:label="note-0466-04" xlink:href="note-0466-04a" xml:space="preserve">Exantec.</note>
            dum.</s>
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          <head xml:id="echoid-head666" xml:space="preserve">THEOREMA XII. PROPOS. XII.</head>
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            <s xml:id="echoid-s11496" xml:space="preserve">COmpræhenſum ſpatium ſub ſpirali, q æ eſt minor
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            ea, quæ ſub prima reuolutione fit, nec abet termi-
              <lb/>
            num initium ſpiralis, & </s>
            <s xml:id="echoid-s11497" xml:space="preserve">rectis, quæ à terminis ipſius in ſpi-
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            ralis initium ducuntur, ad ſectorem habentem radium æ-
              <lb/>
            qualem maiori earum, quæ à termino ad initium ſpiralis
              <lb/>
            ducuntur, arcum verò, qui intercipitur inter duas rectas
              <lb/>
            ſecundum eaſdem partes ſpiralis, habet eandem rationem,
              <lb/>
            quam rectangulum compræhenſum ſub rectis à terminis
              <lb/>
            in principium ſpiralis ductis, vna cum. </s>
            <s xml:id="echoid-s11498" xml:space="preserve">quadrati exceſſus,
              <lb/>
            quo maior dictarum linearum ſuperat minotẽ, ad quadra-
              <lb/>
            tum maioris linearum à terminis ad initium ſpiralis coniũ-
              <lb/>
            ctarum.</s>
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