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

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

11292GEOMETRIÆ& . Modòetiam ſi ad illa puncta non terminentur dico tamen, ls,
ad, E4, eſſe vt, 47, ad, ℟ & , etenim, ls, ad, 47, eſt vt, AC,
ad, FK, ideſt vt, LO, ad, uY, vel vt, E4, ad, ℟ & , vt probatum
eſt, ergo permutando, ls, ad, E4, erit vt, 47, ad, ℟ & , quod o-
ſtendere oportebat.

COROLLARIVM.

_E_T quoniam probatum eſt, l s, ad, 4 7, eſſe vt, E 4, ad, ℟ & , ſeu
vt, LO, ad, u γ, vt autem, LO, ad, u γ, ita duæ homologæ, QP,
ad, 83, ideò duæ homologæ, ls, 47, ſunt inter ſe, vt duæ homologæ,
QP, 8R, & cum oppoſitæ tangentes, DL, dO, pu, g γ, ductæ ſint vt-
cumque, licet ad eundem angulum cx eadem parte cum ipſis, E4, ℟ & ,
ideò duæhomologæ, ls, 4 7, erunt vt quæcumq; aliæ duæ homologæ qui-
buſuis regulis aſſimptæ, vel vt ecrum incidentes, immo & ipſæ inciden-
tes, crunt inter ſe, vt quæuis aliæ duæ incidentes, oſtenſum. n. eſt, A
C, ad, FK, eſſe vt, LO, ad, u γ.

THEOREMA XLV. PROPOS. XLVIII.

SI ſint duæ ſimiles figuræ planæ, quarum ſint ductæ oppo-
ſitæ tangentes, quæ ſunt homologarum earundem regu-
læ, per quas extendantur duo plana vtcumque inuicem pa-
rallela ęquè ad eandem partem ijſdem inclinata, deinde ſum-
ptis duabus quibuslibet homologis illæ deſcribere intelli-
gantur figuras planas ſimiles, ductis primò planis æquidi-
ſtantes, ita vt ſint ſimiliter deſcriptæ, & deſcribentes earum
lineæ, vel latera homologa, idem autem contingat cæteris
homologis, etiam ſi omnes figuræ deſcriptæ ſeorſim in vna-
quaque propoſitarum figurarum non eſſent ſimiles; Solida,
quę ab ijſdem tanguntur oppoſitis planis, in quibus ex traie-
ctione planorum præfatis oppoſitis tangentibus æquidiſtan-
tium eædem figuræ produci poſſunt, erunt ſimilia, & figuræ
deſcriptæ eorundem homologæ figuræ, & earum regulę ipſa
oppoſita tangentia plana, quorum & dictorum ſolidorum fi-
guræ incidentes erunt primò propoſitæ figuræ.

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110