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

Scan	Original
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46
71	47
72	48
73	49
74	50
75	51
76	52
77	53
78	54
79	55
80	56
81	57
82	58
83	59
84	60
85	61
86	62
87	63
88	64
89	65
90	66

125101

COROLL. I.

EX quinque proximè præcedentibus problematibus ſatis conſtat, _MAXI-_
_MAM_, vel _MINIMAM_ Hyperbolen, inſcriptam, vel circumſcriptam
cuilibet datæ per punctum intra, vel extra Hyperbolen datũ in locis poſſibili-
bus, ad eandem regulam, aut concentricè adſcriptam, vel cuius centrum pro
inſcripta cadat infra centrum datæ, & pro circumſcripta cadat vltra, ſemper
eidem datæ Hyperbolæ ſimilem eſſe.

COROLL. II.

PAtet quoque, _MAXIMAM_ Hyperbolarum datæ Hyperbolæ ſimilium,
per datum intra ipſam punctum inſcriptarum, eſſe concentricam, cum
hæc, inter ſimiles, ſit _MAXIMORVM_ laterum. Item _MINIMAM_ Hyperbola-
rum datæ Hyperbolæ ſimilium per datum extra ipſam punctum in angulo
aſymptotali, circumſcriptarum, eſſe pariter concentricam, cum eadem, in-
ter ſimiles, ſit _MINIMORV M_ laterum.

PROBL. XXIII. PROP. LVII.

Datis magnitudine, & poſitione cuiuslibet coni- ſectionis dia-
metri ſegmento, & vna applicatarum, & pro Hyperbola, & Ellipſi
dato etiam tranſuerſo latere; imperatam coni-ſectionem deſcri-
bere.

SIt in qualibet ſigura, pro quacunque coni-ſectione, datum magnitudine,
& poſitione diametri ſegmentum AB, & vna applicatarum CD, & pro
Hyperbola, & Ellipſi in ſecunda, & tertia, datum ſit quoque rectum latus
AF, quod pro Hyperbola in ſecunda vltra BA ipſi in directum ponatur, & in
tertia, ex A ad partes B: oportet circa diametrum AB, ſuper applicatam
CD, quæſitam coni-ſectionem deſcribere.

Fiat in ſingulis figuris, vt

90[Figure 90] AB ad BC, ita BC ad BE
ipſi BC in directum poſitã,
& per E, in prima figura,
ducta EG parallela ad BA,
vel in ſecunda, & tertia iun-
cta FE, occurrat AG, (quæ
ipſi CD æquidiſtet) in G, &
per verticem A cum data
diametro AB, datiſque la-
teribus AF, A G deſcriba-
tur quæſiti nominis 115. 6. 7.
huius. CAD, cuius ordinatim du-
ctæ ad angulum ABD

Page concordance

Text layer

Text normalization

Search

Scan	Original
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46
71	47
72	48
73	49
74	50
75	51
76	52
77	53
78	54
79	55
80	56
81	57
82	58
83	59
84	60
85	61
86	62
87	63
88	64
89	65
90	66

Scan	Original
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46
71	47
72	48
73	49
74	50
75	51
76	52
77	53
78	54
79	55
80	56
81	57
82	58
83	59
84	60
85	61
86	62
87	63
88	64
89	65
90	66

Scan	Original
61
62
63	39
64	40
65	41
66	42
67	43
68	44
69	45
70	46
71	47
72	48
73	49
74	50
75	51
76	52
77	53
78	54
79	55
80	56
81	57
82	58
83	59
84	60
85	61
86	62
87	63
88	64
89	65
90	66