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

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[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)
[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
[311.] THEOREMA VIII. PROPOS. IX.
Page: 230 (210)
[312.] COROLLARIVM.
Page: 231 (211)
[313.] THEOREMA IX. PROPOS. X.
Page: 231 (211)
[314.] COROLLARIVM.
Page: 232 (212)
[315.] THEOREMAX. PROPOS. XI.
Page: 233 (213)
[316.] COROLLARIVM I.
Page: 234 (214)
[317.] COROLL II. A. SECTIO I.
Page: 235 (215)
[318.] B. SECTIO II.
Page: 235 (215)
[319.] C. SECTIO III.
Page: 235 (215)
[320.] D. SECTIO IV.
Page: 235 (215)
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217197GEOMETRIÆ
CAVALERII
LIBER TERTIVS.
In quo de circulo, & Ellipſi, ac ſolidis ab
eiſdem genitis, traditur doctrina.
131[Figure 131]
THEOREMA I. PROPOS. I.
OMnia quadrata portionis circuli, vel El-
lipſis, ad omnia quadrata parallelo-
grammi in eadem baſi, & altitudine
cum portione conſtituti, regula baſi,
erunt, vt compoſita ex ſexta parte axis,
vel diametri eiuſdem, & dimidia reli-
quæ portionis, ad axim, vel diame-
trum reliquæ portionis: Eadem verò
ad omnia quadrata trianguli in ijſdem
exiſtentis erunt, vt compoſita ex dimidia totius, & reliquæ
portionis axi, vel diametro, ad axim, vel diametrum reliquæ
portionis.
Sit circulus, vel ellipſis, EDRP, cuius axis, vel diameter, ER,
ad quem ordinatim applicetur, DP, abſcindens vtcumque portio-
nem, DEP, quæ ſumatur quoq; pro regula, & centrum ſit, A, ac
parallelogrammum, FP, in eadem baſi, DP, cum portione, & ea-
dem altitudine; ſint autem primò, DF, PH, latera parallelogram-
mi, FP, parallela ipſi, ER. Dico ergo omnia quadrata portionis,
DEP, ad omnia quadrata parallelogrammi, FP, eſſe, vt compo-
ſita ex ſexta parte, EB, & dimidia, BR, adipſam, BR.

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