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-s11500" xml:space="preserve">Sit ſpiralis ex prima reuolutione@@o, OP℟QX, primus circu-
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            lus, ΩkXF, cuius, radius, & </s>
            <s xml:id="echoid-s11501" xml:space="preserve">voluta ſit, OX, ſpiralis, ℟Q, minor
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            ea, quæ ſub prima reuolutione fit, nec habet terminum initium
              <lb/>
            ſpiralis, iunctis autem, OA, OQ, & </s>
            <s xml:id="echoid-s11502" xml:space="preserve">ijs vſque ad circumferentiam,
              <lb/>
            FΩΚΧ, productis, cui incidant in, Ω, F. </s>
            <s xml:id="echoid-s11503" xml:space="preserve">Dico trilineum, ℟OQ,
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            ad ſectorem, AOQ eſſe vt rectangulum, AO℟, cum {1/3}. </s>
            <s xml:id="echoid-s11504" xml:space="preserve">quadrati,
              <lb/>
            A℟, ad quadratum, AO. </s>
            <s xml:id="echoid-s11505" xml:space="preserve">Exponatur parallelogrammum rectan-
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            gulum, ED, cuius latus, CD, ſit æqualeipſi, OX, &</s>
            <s xml:id="echoid-s11506" xml:space="preserve">, BD, circum-
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            ferentiæ, FΩΚΧ, & </s>
            <s xml:id="echoid-s11507" xml:space="preserve">ſit iuncta, BC, &</s>
            <s xml:id="echoid-s11508" xml:space="preserve">, CT, ſit æqualis circumferẽ-
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            tiæ, XkΩ, TM, circumferentiæ, ΩF, &</s>
            <s xml:id="echoid-s11509" xml:space="preserve">, ME, circumferentiæ, FX,
              <lb/>
            & </s>
            <s xml:id="echoid-s11510" xml:space="preserve">per puncta, M, T, ducanturipſi, CD, parallelæ, MH, TN,
              <lb/>
            quarum, MH, ſecet, BC, in, I, & </s>
            <s xml:id="echoid-s11511" xml:space="preserve">per, I, ipſi, EC, parallela duca-
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            tur, IG, erit ergo, MC, æqualis circumferentiæ, XkΩF, & </s>
            <s xml:id="echoid-s11512" xml:space="preserve">quia
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            circumferentia, ΧFΩκ, ad circumferentiã, FΩkX, eſt vt, XO, ad,
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              <note position="right" xlink:label="note-0467-01" xlink:href="note-0467-01a" xml:space="preserve">7. huius.
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              4. Sexti
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              Elem.</note>
            OQ, ideſt, EC, ad, CM, eſt vt, XO, ad, OQ, eſt autem, EC, ad,
              <lb/>
            CM, vt, EB, ad, MI, ergo, EB, ad, MI, erit vt, XO, ad, OQ, ſunt
              <lb/>
            autem ipſæ, XO, EB, æquales, ergo etiam æquales eruntiplæ, </s>
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