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

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

Table of contents

[31.] VIII.

[32.] IX.

[33.] SCHOLIVM.

[34.] A. X.

[35.] B.

[36.] C.

[37.] D. IV.

[38.] E.

[39.] APPENDIX PRIOR Pro explicatione Definit. 10. antecedentis.

[40.] A. XI.

[41.] B.

[42.] C.

[43.] APPENDIX POSTERIOR Pro declaratione Definit. II.

[44.] SCHOLIVM.

[45.] XII.

[46.] XIII.

[47.] XIV.

[48.] XV.

[49.] POSTVLATA I.

[50.] II.

[51.] PROBLEMA I. PROPOS. 1.

[52.] COROLLARIVM.

[53.] PROBLEMA II. PROPOS. II.

[54.] PROBLEMA III. PROPOS. III.

[55.] SCHOLIVM.

[56.] THEOREMA I. PROPOS. IV.

[57.] COROLLARIVM I.

[58.] COROLLARIVM II.

[59.] THEOREMA II. PROPOS. V.

[60.] THEOREMA III. PROPOS. VI.

288GEOMETRIÆ ſimilium figurarum incidentes. Tales figuræ dicentur bi-
næ ſimiles, & ſimiliter inter ſe poſitę primò dictæ, ac ſecun-
dò dictæ, & earum, ac exremarum tangentium etiam dicen-
tur incidentes, quæ in tangentium extremas terminan-
tur.

APPENDIX PRIOR
Pro explicatione Definit. 10. antecedentis.

_S_Int duæ figuræ planæ. ABCD, KLγP, in quibus ſupponantur
ductæ oppoſitæ tangentes, AE, CG, in figura, ABCD, & KQ,
11_B.Def.1._ γ℟, in fig. KLγP, quibus incidant duæ rectæ lineæ, EG, Q℟, ad
eundem angulum ex eadem parte, ſiue ſecent figuras, ſiue non, du-
ctis autem vtcumq dictis tangentibus parallelis, BF, L& , quæ
in puctis F, & , diuidant ſimiliter ad eandem partem ipſas, EC,
Q℟, & circuitus figu-

6[Figure 6] rarum in punctis, B, I,
S, D, L, T, X, P. repe-
riamus, DF, ad, P& ,
eſſe vt, EC, ad, Q℟,
& ita eſſe, SF, ad, X& ,
IF, ad, T& , BF, ad
L& , ita nempè, vt, quæ
ſunt ad eandem partem
ipſarum, EG, Q℟, eo-
dem ordine ſumptæ, ſint,
vt ipſæ, EG, Q℟, ſic
etiam tangentes, AE, KQ, CG, γ℟, ſint vt, FQG, ℟, & ſic cæ-
teræ conſimiliter ſumptæ, tunc voco figuras, ABCD, KLγP ſimi-
22_A Def.10._ les, & ipſas, EG, Q℟, incidentes ſimiles figurarum, ABCD, KLγP,
33_B.Def.10._& oppoſitarum tangentium, AE, CG, KQ, γ℟; ipſas, BI, SD,
LT, XP, quæ clanduntur perimetris figurarum, & diuidunt pro-
ductæ, ſiopus ſit, ipſas, EG, Q℟. ſimiliter ad eandem partem,
voco, homologas earumdem figurarum, quarum dictæ oppoſitæ
44_C.Def.10_ tangentes dicuntur tangentes, ſiue regulæ.

Cum verò figuræ, ABCD, KLγP, fuerint in eodem plano,

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