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

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

Table of contents

[131.] THEOREMA XXXVII. PROPOS. XL.

[132.] SCHOLIVM.

[133.] THEOREMA XXXVIII. PROPOS. XLI.

[134.] THEOREMA XXXIX PROPOS. XLII.

[135.] THEOREMA XL. PROPOS. XLIII.

[136.] THEOREMA XLI. PROPOS. XLIV.

[137.] THEOREMA XLII. PROPOS. XLV.

[138.] THEOREMA XLIII. PROPOS. XLVI.

[139.] THEOREMA XLIV. PROPOS. XLVII.

[140.] COROLLARIVM.

[141.] SCHOLIVM.

[142.] LEMMA.

[143.] COROLLARIVM.

[144.] THEOREMA XLV. PROPOS. XLVIII.

[145.] COROLLARIVM.

[146.] THEOREMA XLVI. PROPOS. XLIX.

[147.] THEOREMA XLVII. PROPOS. L:

[148.] COROLLARIVM I.

[149.] COROLLARIVM II.

[150.] SCHOLIVM.

[151.] Finis Primi Libri.

[152.] CAVALER II LIBER SECVNDVS.

[153.] DIFINITIONES. I.

[154.] COROLLARIVM.

Page: 120 (100)

[155.] II.

Page: 120 (100)

[156.] COROLLARIVM.

Page: 120 (100)

[157.] III.

Page: 120 (100)

[158.] COROLLARIVM.

Page: 121 (101)

[159.] IV.

Page: 121 (101)

[160.] V.

Page: 121 (101)

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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