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

[141.] SCHOLIVM.

Page: 109 (89)

[142.] LEMMA.

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[143.] COROLLARIVM.

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[144.] THEOREMA XLV. PROPOS. XLVIII.

Page: 112 (92)

[145.] COROLLARIVM.

Page: 113 (93)

[146.] THEOREMA XLVI. PROPOS. XLIX.

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[147.] THEOREMA XLVII. PROPOS. L:

Page: 115 (95)

[148.] COROLLARIVM I.

Page: 117 (97)

[149.] COROLLARIVM II.

Page: 117 (97)

[150.] SCHOLIVM.

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[151.] Finis Primi Libri.

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[152.] CAVALER II LIBER SECVNDVS.

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[153.] DIFINITIONES. I.

[154.] COROLLARIVM.

[155.] II.

[156.] COROLLARIVM.

[157.] III.

[158.] COROLLARIVM.

[159.] IV.

[160.] V.

[161.] COROLLARIVM.

[162.] VI.

[163.] COROLLARIVM.

[164.] VII.

[165.] A. VIII.

[166.] B.

[167.] C.

[168.] D.

[169.] E.

[170.] APPENDIX. Pro antecedentium Definitionum explicatione.

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150130GEOMETRIÆ MZP, adomnes lineas figuræ, OZP, regula, MP, & ideò vt, M
11Goroll. 4.
huius. P, ad, PO, vel ad, Ω & , ita figura, MZP, ad figuram, OZP,
224. huius. quod etiam ſerua.

D. SECTIO IV.

VLterius ab ipſis, OP, Ω & , abſcindantur partes æquales, O
R, ΩΥ, & per puncta, R, Y, ducantur ipſis, ZP, ℟ & , æ-
quidiſtantes, SR, VY, & per, S, vbi, RS, ſecat lineam, ZO, du-

88[Figure 88] catur, HC, æquidiſtans ipſi, M
P, & per, C, vbi, HC, ſecat li-
neain, ZM, ducatur, CN, pa-
rallelaipſi, ZP, ſecans, MP, in,
N; eſt igitur vt, MP, ad, PO,
ita, CH, ad, HS, per conſtru-
ctionem . i. ita, NP, ad, PR, &
permutando, vt, MP, ad, PN,
ita, OP, ad, PR, diuidendo, vt,
MN, ad, NP, ita, OR, ad, R
P, . i. ita, ΩΥ, ad, Y & , igitur ip-
ſæ, CN, VY, æquidiſtant regu-
lis homologarum, quę ſunt, ZP,
℟ & , & diuidunt ad eandem par-
tem ſimiliter ipſas incidentes, M
P, Ω & , (ſi . n. ZP, ℟ & , ſtatue-
33Corollar.
123. lib. 1. ris regulas homologarum ipſę, M
P, Ω & , ſunt incidentes, ſi verò
has ſtatueris regulas, illæ erunt in-
cidentes, ambę . n. terminant in
oppoſitas tangentes, quæ ſunt re-
gulæ homologarum earundem) ergo, CN, ad, VY, erit vt, MP,
ad, Ω & , . i. vt, ZP, ad, ℟ & , & ſunt, CN, SR, æquales, & , S
R, VY, vtcunque ductæ ipſis, ZP, ℟ & , æquidiſtantes, ergo ve,
ZP, ad, ℟ & , ita, SR, ad, VY, ergo vt, ZP, ad, ℟ & , ita erit
444. huius. figura, OZP, ad figuram, Ω ℟ & , quod pariter ſerua.

E. SECTIO V. ET VLTIMA.

QVoniam verò figura, MZP, ad figuram, Ω ℟ & , habet ratio-
55Defin. 12.
lib. 1. nem compoſitam ex ratione figuræ, MZP, ad figuram, O
ZP, . i. ex ratione, MP, ad, Ω & , & ex ratione figuræ, OZ
P, ad figuram, Ω ℟ & , . i. ex ratione ipſius, ZP, ad, ℟ & a . i. ex

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