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

10379

THEOR. XXIV. PROP. XXXXV.

Similes Hyperbolæ per diuerſos vertices ſimul adſcriptæ, &
quarum eadem ſit regula, ſunt inter ſe nunquam coeuntes, & in in-
finitum productæ ad ſe propiùs accedentes, ſed ad interuallum
nunquam perueniunt æquale cuidam dato interuallo.

SInt duæ Hyperbolæ ABC, DEF per diuerſos vertices B, E ſimul adſcri-
ptæ, quarum eadem ſit regula GH (ſic enim ſimiles erunt, 116. ſecúd.
defin. ductis contingentibus BI, EL; eſt tranſuerſum GB ad rectum BI, vt tranſuer-
ſum GE ad rectum EL.) Dico primùm, has in infinitum productas, nun-
quam ſimul conuenire.

71[Figure 71]

Protracta enim contingente LE, ſectionem ABC ſecane in M, N, quæ
erit ipſi ordinata, cum ſectiones ponantur ſimul adſcriptæ; patet ſectionem
DEF totam cadere infra contingentem MN. Iam ſumpto in ſectione DEF
quolibet puncto D, per ipſum ordinatim applicetur ADOH alteram ſectio-
nem ſecans in A, regulam verò in H: erit quadratum AO, ad quadratum
DO, vt rectangulum BOH ad rectangulum EOH (ob ęqualitatem) vel 22Coroll.
1. huius. altitudo BO ad altitudinem EO, ſed eſt BO maior EO, quare quadratum
AO maius erit quadrato DO, ex quo punctum D cadit intra Hyperbolen
ABC; & ſic de quibuſcunque alijs punctis Hyperbolę DEF: quare huiuſmo-
di ſectiones inter ſe nunquam conueniunt. Quod primò, & c.

Iam ſi datæ Hyperbolæ, per verticem E, adſcribatur Hyperbole P E Q
cuius latera ER, ES æqualia ſint lateribus BG, BI, vtrunque vtrique, ipſæ
Hyperbolæ ABC, PEQ, congruentes erunt, eritque, (ob 331. Co-
roll. 19. h. RE ad ES, vt GB ad BI, vel vt GE ad EL, quare Hyperbolæ DEF,

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