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

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133109 Cipſius latera BA, BC eum contingant; & erit _MAXIMVS_: Nam licet fa-
cta ſupra EF eadem penitùs, conſtructione nempe ſumpta FG æquali ad FE,
& ducta GH perpendiculari ad GA, oſtendetur pariter H eſſe centrum alte-
rius circuli dato angulo inſcripti, ſed is erit minor circulo ex DE, cum ob
parallelas GH, AD, ſit AB ad BG, vt DA ad HG, ſed eſt AB maior BG, vn-
de radius DA erit maior radio HG, ſiue circulus AEC maior circulo ex HE.
Iam quilibet alius circulus per E, dato angulo adſcriptus, cuius diameter
minor ſit EI, minor eſt ipſo AEC, & quilibet alius, cuius diameter ſit maior
ipſa EI, eſt quidem maior AEC, ſed omnino ſecat dati anguli latera, cum
hæc circulum contingant: ex quo circulus ex DE erit _MAXIMVS_ inſcriptus
quæſitus. Quod erat primò, & c.

SIverò ad datum punctum B extra circulum AEC, cuius ſit centrum D, ſit
ei circumſcribendus _MINIMVS_ angulus rectilineus; iam per ſe patet
angulum ABC, à ductis contingentibus ex B, eſſe _MINIMVM_ quæſitum.
Quod vltimò faciendum, ac demonſtrandum erat.

LEMMA VII. PROP. LXVI.

In dato angulo, à recta linea per verticem vtcunque ſecto, lineas
applicare, quæ à prædicta diuidantur in data ratione.

SIt datus angulus ABC, vtcunque ſectus à re-

99[Figure 99] cta BD, punctum in eo ſit D, ex quo opor-
tet rectam, qualis eſt ADC, applicare ita vt ip-
ſius partes AD, DC ſint in data ratione, veluti
E ad F.

Ducatur DG parallela ad alteram linearum,
angulum continentium, vt ad AB; & fiat vt E ad
F, ita BG ad GC, iungaturque CD, quæ cum
BA conueniat in A. Dico factum eſſe, quod
proponebatur.

Et enim, ob parallelas, vt AD ad DC, ita BG
ad GC, vel E ad F. Quod, & c.

SCHOLIVM.

SI data ratio E ad F, fuerit ratio æqualitatis, tunc BD, licet præter morem,
vocetur dati anguli diameter, & ſi bifariam, & ad rectos angulos ipſas
applicatas ſecuerit, dicatur axis.

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Scan	Original
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
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131	107
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135	111
136	112
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