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

9272GEOMETRIÆ quibus incidunt ad eundem angulum ex eadem parte, EO, MR, &
quę diuidunt ipſas, EO, MR, ſimiliter ad eandem partem exiſten-
tes parallelæ ipſis, BC, GN, ſunt vtipſæ, EO, MR, ad eandem
partem eodem ordine inter ipſas, & circuitum dictarum figurarum
compræhenſæ, quia quæ ſunt ex vna parte ſunt æquales ipſis, BO,
GR, & quæ ex alia ipſis, OC, RN, in triangulis autem ſunt, vt
ipſæ, BO, GR, vel, OC, RN, . i. vt, OE, RM, & ideo, earum
11B. defin.
10. incidentes, & oppoſitarum tangentium dictarum erunt ipſæ, EO,
MR, quę tangentes ſunt regulæ homologarum ſimilium figurarum,
AC, FN, vel, EBC, MGN. Vlterius, quia, BXC, GYN,
ſunt ſemicirculi, erunt figurę planę ſimiles iuxta meam definitionem,
quarum & tangentium, quæ per extrema, BC, GN, ducuntur e-
22Ex Lem.
ant. runt incidentes ipſi diametri, BC, GN, vt probatum fuit, veluti
idem patet de ſemicirculis, B ℟ C, GZN, & de quibuſcumq; alijs,
quæ diuident ipſas, EO, MR, ſimiliter ad eandem partem, & con-
ſequenter diuidunt etiam altitudines eorũdem reſpectu baſium ſum-
3317. Vnde-
cimi El. ptas ſimiliter ad eandem partem, & deijs, quæ per extrema, E, M,
ducuntur, habemus igitur cylindros, AC, FN, ſiue conos, BEC,
GMN, quorum ducta ſunt plana oppoſita tangentia dictorum ſo-
lidorum homologis figuris parallela, quæ ſunt plana, B ℟ CX, A
D; GYNZ, FH, quibus inciderunt duo plana ad ęquales angulos
ex eadem parte, illa nempè, in quibus ſunt ipſa parallelogramma,
AC, FN, vel triangula, BEC, quia ſunt recta ad baſes . i. ad dicta
tangentia, ipſæ autem ſiguræ . i. parallelogramma, vel triangula in-
uenta ſunt eſſe ſimilia, quarum homologarum regulæ oppoſitę tan-
gentes, AD, BC; FH, GN, quarum ſunt incidentes, EO, MR,
earum autem lineæ homologæ, ſumptæ regulis dictis tangentibus,
repertæ ſunt eſſe incidentes figurarum planarum ſimilium, quæ di-
uidunt altitudines dictorum ſolidorum iam dictas ſimiliter ad ean-
dem partem, & oppoſitarum tangentium, quæ omnes ijs, quæ du-
cuntur per extrema, BC, GN, tangentes circulos, B ℟ CX, GY
NZ, ſunt ęquidiſtantes, vt facilè conſideranti patebit, ergo cylin-
dri, AC, FN, vel coni, BEC, GMN, ſunt ſimiles iuxta meam defi-
44Defin. 11. nitionem generalem ſimilium ſolidorum, quod oſtendere opus erat.

THEOREMA XXIX. PROPOS. XXXII.

DEfinitio mea ſimilium conicorum, & cylindricorum
concordat cum definitione generali ſimilium ſolido-
rum.

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