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

Scan	Original
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60

5838GEOMETRIÆ bus, quæ ſunt regulæ homologarum earundem, poſſunt reperiri duæ in-
cidentes earundem, quarum altera ſit iam ducta; veluti, acta, HP, vt-
cumque inuentæ ſunt duæ incidentes, KN, HP, quarum altera fuit,
HP. Et quia bomologarum in eaſdem incidentes productarum, & ad
eas terminatarum, portiones, eodem ordine ſumpcæ, ſunt proportiona-
les, ſunt enim, vt ipſæ incidentes, ideò per homologarum productarum,
talia extremaſemper tranſeunt aliquæ incidentes.

THEOREMA XVII. PROPOS. XX.

SI conicus ſecetur quomodocumq; planis parallelis, cum
omnibus eiuſdem lateribus coincidentibus, conceptæ
in ipſo figuræ erunt inter ſe ſimiles, & ſimiliter poſitæ.

Sit conicus, cuius baſis, FHG, ver-

29[Figure 29] tex, A, ſecetur autein vtcumque planis
parallelis, quæ cum omnibus eiuſdem la-
teribus coincidant, & ſint conceptæ in
ipſo figuræ, DME, BNC. Dico has
eſſe ſimiles, & ſimiliter poſitas: Nam
quia planum figuræ, DME, coincidit
omnibus lateribus conici, AFHG, ideo
1117. Huius. eſt etiam conicus ipſe, ADME, ſecatur
autem plano eius baſi, DME, æquidi-
22Exantec. ſtante, eo ſcilicet, quod producit figu-
ram, BNC, ergo figura, BNC, erit ſi-
milis baſi, DME, & eidem ſimiliter po-
ſita, quod erat demonſtrandum.

THE OREMA XVIII. PROPOS. XXI.

SI quilibet conicus ſecetur plano per verticem, ſiue ab
eodem tangatur in plano, nempe in triangulo, veltrian-
gulis, ſecetur autem alijs planis vtcumq; baſi parallelis, com-
munes ſectiones, quæ ab eodem plano ſecante ſiunt in dictis
planis baſi parallelis, erunt homologę lineę, vel latera figu-
rarum, quæ ab eiſdem æquidiſtantibus planis in eodem co-
nico producuntur.

Page concordance

Text layer

Text normalization

Search

Scan	Original
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60

Scan	Original
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60

Scan	Original
51	31
52	32
53	33
54	34
55	35
56	36
57	37
58	38
59	39
60	40
61	41
62	42
63	43
64	44
65	45
66	46
67	47
68	48
69	49
70	50
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60