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

Scan	Original
31	11
32	12
33	13
34	14
35	15
36	16
37	17
38	18
39	19
40	20
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40

3515LIBER I. tinget figuram, ABC, contingatin ſitu ipſius, FG, & in pun-
cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
11A. Def. 1. C, à nobis inuentus, qui in huius Problematis priori parte inue-
niendus proponebatur.

Sit nunc figura ſolida, ſiue ſolidum, ADE, in quo reſpectu
plani, BECD, ſit vertex inueniendus, ſumpto igitur exrra pla-
num figuræ, vtcumque puncto, N, per ipſum agatur planum, K
HVX, ipſi, BECD, æquidiſtans, quod vel continget ſolidum,
BAC, vel non, ſi autem non contingat, moueatur accedendo,
22Poſtul. 2. velrecedendo, à plano, BECD, tandem igitur contingetipſum,
tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
33A. Def. 2. E, reſpectu plani, BECD, qui inueniendus proponebatur.

COROLLARIVM.

_H_Inc manifeſtum eſt, ſi recta, BC, tangat planam figuram, AB
44_B. Def. 1._ C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
55_B. Def. 2._ pè, BC; & ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
66_A. Def. 2._ quibus puncta contactuum erunt oppoſiti vertices earumdem figura-
rum, boc pacto inuenti: Siverò recta linea, BC, ſecaret figuran, A
BC, vel planum, BECD, ſecaret ſolidum, ADE, eodem pacto ex
alia parte lineæ, BC, vel plani, BDCE, inueniemus verticem, vn-
de inuenti erun@ propoſitæ figuræ planæ oppoſiti vertices, & ductæ op-
poſitæ tangentes reſpectu datæ lineæ BC; & in ſolido iuuenti erunt
oppoſiti vertices, & ducta oppoſita tangentia plana reſpectu dati
plani, BDCE, quæ cum tangunt in figuris planis, figuræ contactuum
77_C. Def. 2._ vocantur etiam oppoſitæ baſes, & earum ſingulæ baſes, & baſes li-
neares, ſi contactus fieret in lineis: binc ergo diſcimus inuenire op-
88_A. B. Def._
_1. & 2._ poſitos vertices figuræ planæ, vel ſolidæ cuiuſcumque, & eorum op-
poſita tangentia ducere reſpectu datæ in figura plana rectæ lineæ, &
dati plani par@ter in ſolida figura.

PROBLEMA II. PROPOS. II.

CVilibct figuræ planæ parallelogrammum circumſcri-
bere, cuius latera duabus datis rectis lineis, in pro-
poſitæ figuræ plano ſe ſecantibus, ſint parallela.

Page concordance

Text layer

Text normalization

Search

Scan	Original
31	11
32	12
33	13
34	14
35	15
36	16
37	17
38	18
39	19
40	20
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40

Scan	Original
31	11
32	12
33	13
34	14
35	15
36	16
37	17
38	18
39	19
40	20
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40

Scan	Original
31	11
32	12
33	13
34	14
35	15
36	16
37	17
38	18
39	19
40	20
41	21
42	22
43	23
44	24
45	25
46	26
47	27
48	28
49	29
50	30
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40