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

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165141

THEOR. XLVI. PROP. XCII.

Si Parabolen, vel Hyperbolen, aut Ellipſim circa maiorem
axim recta linea, præter ad verticem contingat, cui à tactu ducta
ſit perpendicularis axi occurrens; circulus, cuius centrum ſit idem
occurſus, radius verò ſit ipſa perpẽdicularis erit ſectioni inſcriptus.

Si autem Ellipſis fuerit circa minorem axim, cui prædicta per-
pendicularis occurrat, circulus ex ea tanquam radio, at centro fa-
cto ipſo occurſu, erit eidem Ellipſi circumſcriptus.

ESto ABC, Parabole, vel Hyperbole, in prima figura, aut Ellipſis in ſe-
cunda, circa maiorem axim BO; vel circa minorẽ, vt in tertia, quarum
vertex B, & ad aliud punctum quædam contingens EF, cui ducta ſit perpen-
dicularis ED, quæ axi occurret in D, quo facto centro, & interuallo 1188. h. circulus EGHI deſcribatur. Dico primùmhunc, in prima, & ſecunda figu-
ra, datæ ſectioni eſſe inſcriptum.

130[Figure 130]

Applicata enim EH, ſecans axim in L, & iuncta DH. Cum in triangulis
ELD, HLD anguli ad L ſint recti, & latera EL, LD æqualia lateribus HL,
LD, erit baſis DE æqualis DH, exquo circulus ex DE tranſibit omnino per
H, ideoque coni-ſectio, & circulus, ſunt binæ ſectiones ſimul adſcriptæ
(cum earum diametri, & applicatæ ſimul congruant) quæ in ijſdem extre-
mis communis applicatæ EH ſimul conueniunt, atque ad eorum alterum E,
eadem recta EF vtranque ſectionem contingit, nempe ſectionem ABC, ex
ſuppoſitione, & circulum EGHI, cum EF ſit ad extremum ſemi-diametri
ED perpendicularis, atque vertex circuli G cadit infra B verticem ſectionis,
cum ſit DB maior DE, ſiue maior DG, quare circulus ex DE erit 22ibideni.33@ 1. h. inſcriptus. Quod primò erat, & c.

AMpliùs, dico in tertia figura, prædictum circulum EGHI eſſe datæ El-
lipſi ABCO circumſcriptum.

Nam facta eadem conſtructione, ac ſupra oſtendetur pariter

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101	77
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105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106