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

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6. IN quarta autem figura Ellipſis
circa minorem axim BR, in

133[Figure 133] qua prædictæ contingentibus
perpendiculares ipſi BR occur-
runt: dico AC, quæ à remotiori
contactu educitur minorem eſſe
DG, quæ à propinquiori. Nam
cum ſit DO ad DG, vt I L ad IG,
vel vt tranſuerſum latus ad 113. Co-
roll. 90. h. ctum, vel vt HL ad HC, vel vt
AN ad AC, erit DO ad DG, vt
AN ad AC, & permutando, vt
DO ad AN, ita DG ad AC, ſed
eſt DO maior AN, vt ſupra ad numerum 5. oſtenſum eſt, ergo, & DG maior
erit ipſa AC. Quod ſecundò oſtendere propoſitum fuit.

PROBL. XXXIV. PROP. XCIV.

Dato angulo rectilineo, ad punctum in eius latere datum MA-
XIMVM circulum inſcribere.

SIt datus angulus rectilineus ABC, & punctum in eius latere datum ſit A,
ad quod oporteat _MAXIMVM_ circulum inſcribere.

Bifariam ſecetur angulus à recta BD, & ex A ipſi AB perpendicularis eri-
gatur AE, occurrens BD in E; & centro E, interuallo EA deſcribatur circu-
lus. Dico hunc eſſe _MAXIMVM_ quæſitum.

Nam ſumpta BC ipſi BA æquali, iunctiſque AC, EC; cum latera AB,
BE, æqualia ſint lateribus CB, BE, & anguli ad B æquales, erit EA æqualis
EC. Inſuper ſunt BA, AE, ipſis BC, CE æqualia, vtrunque vtrique, & ba-
ſis BE communis, ergo angulus BAE angulo BCE æqualis, nempe rectus
quare circulus ex EA per C tranſibit, contigetque latera BA, BC, ſiue erit
angulo ABC inſcriptus. Dico hunc eſſe _MAXIMVM_ quæſitum.

Nam ſi centra circulorum ad A pertinen-

134[Figure 134] tium, fuerint in portione perpendicularis
AE, inter A, & E; ipſi, vt ſatis conſtat, erũt
quidem angulo inſcripti, cum circulo quo-
que inſcripti ſint; ſed minores erunt circulo
ADC cum ſint minoris radij; illi verò quo-
rum centra ſunt in producta AE, vt in F, ſunt
quidem maiores, ſed latus BC omnino ſecát:
quoniam ducta F G parallela ad E C, quæ
productæ A C occurrat in G, cum ſit AF ad
FG, vt AE ad EC, ſitque AE ipſi EC æqua-
lis, erit quoque AF æqualis FG: quare cir-
culus ex FA tranſibit per punctum G, quod
eſt extra angulum; ideoque in ſe remeans ſecabit omnino latus BC, quod
eſt infinitæ extenſionis. Si verò centrum ſumatur extra prædicta

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Scan	Original
101	77
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106	82
107	83
108	84
109	85
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113	89
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