Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Scan	Original
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
60
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46

4929

COROLL. I.

HInc patet, quod ſi recta linea in Parabola vtcunque applicata ex
11Vni-
uerſalius
quàm in
4. prop.
exerc. 6.
Caual. vtraque parte ſectioni occurrens cum diametro, vel intra, vel extra
ſectionem conueniat, atque ex ipſius terminis cum ſectione, ad diametrum
ducantur ordinatæ, erunt ab his abſciſſa diametri ſegmenta ex vertice ſum-
pta, extremæ, & abſciſſum ab applicata, erit media trium continuè propor-
tionalium. Demonſtratum eſt enim in figuris Theorematis quando AH dia-
metrum ſecat in M, & ſectionem in A, H, quod ordinatim applicatis AF,
HI, eſt FB ad BM, vt BM ad BI.

COROLL. II.

EX quo etiam elicitur, quod ſi in Parabola ABC ducta AH diametrum
ſecans in M producatur vſque ad occurſum cum contingente ex verti-
ce B in S, ſemper rectangulum ſub ſegmentis AS, & SH, inter ſectionem, &
contingentem interceptis æqua†@ quadrato ſegmenti SM inter contingẽtem,
ac diametrum intercepti. Nam cum ſit vt FB ad BM, ita BM ad BI erit quo-
que ob parallelas, AS ad SM, vt SM ad SH, quare rectangulum ASH æqua-
bitur quadrato SM.

COROLL. III.

HInc etiam eſt, quod, ſi ijſdem poſitis,
interior Parabole ADG habuerit ver-

26[Figure 26] ticẽ in D puncto medio rectæ AB, ipſa quo-
que tranſibit per F medium punctum baſis
AC, & quæcunque educta ex contactu A,
qualis eſt AH, bifariam ſecabitur in O ab in-
terna ſectione; quare ſi ex O ducatur OLM
diametro BF æquidiſtans, ipſa erit diameter
portionis ALH, & AH vna applicatarum,
AO verò ſemi-applicata. Cumque ſit AP
contingens ABC in A, erit OL in trilineo
mixto ADFB, æqualis LM in trilineo mixto
ALBP, & ſic de omnibus vbicunque inter-
ceptis in ijſdem trilineis.

THEOR. VI. PROP. XIV.

Parabolæ æqualium altitudinum inter ſe ſunt vt baſes.

SInt duæ Parabolæ ABC, DEF æqualium altitudinum, hoc eſt concipian-
tur diſpoſitæ inter eaſdem parallelas BE, AF: dico eſſe vt baſis AC
vnius, ad baſim DF alterius, ita Parabole ABC ad Parabolen DEF.

Page concordance

Text layer

Text normalization

Search

Scan	Original
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
60
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46

Scan	Original
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
60
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46

Scan	Original
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
60
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46