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

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141117

PROBL. XXIX. PROP. LXXIII.

Dato angulo rectilineo, per punctum in qualibet eius diametro
datum, MAXIMAM Ellipſim inſcribere, cuius latera datam ha-
beant rationem.

SIt datus angulus ABC, diameter BD, & datum punctum D, per quod
oporteat Ellipſim inſcribere, cuius tranſuerſum latus ad rectum, datam
quamcunque habeat rationem E ad F, & ſit _MAXIMA_.

Applicetur per D, ordinatim GDH, & 1166. h.

108[Figure 108] per H ducatur HIL diametrum ſecans in I, &
BA in L, ita vt ex I, & L ductis A I, LM ipſi
DH parallelis, rectangulum DIM, ad quadra-
tum AI, rationem habeat E ad F, & cum 2272. h. uerſo DM, per extrema applicatæ AC, Elli-
pſis deſcribatur DAMC. Dico hanc 33Coroll.
57. h. _MAXIMAM_ quæſitam.

Eſt enim LB ad BG, ſiue MB ad BD, 4471. h. LA ad AG, ſiue vt MI ad ID, quare BA, BC
Ellipſim contingent, ideoque ipſa erit 5534. pri.
conic. lo inſcripta, eritque _MAXIMA_, vt in præce-
dentibus oſtenſum fuit. Quod erat, & c.

LEMMA X. PROP. LXXIV.

Datis medijs proportionalibus, Arithmetica nempe, & Geo-
metrica inter eaſdem ignotas extremas; ipſas extremas inuenire.

SIt AB media arithmetica, & AC media

109[Figure 109] geometrica inter duas eaſdem ignotas
extremas, quarum idem ſit terminus A, &
ſimul congruere intelligantur: patet primò
AB ſuperare ipſam AC, cum media ari-
thmetica ſit maior media geometrica. Iam
oporteat datis AC, AB ignotas extremas
proportionales inuenire.

Fiat centro A interuallo A C circulus
CF, cui ex puncto B contingens ducatur
BF, quæ eum radio FA rectum efficiet an-
gulum, vnde ſubtenſa BA erit maior ipſa
BF; ſi ergo cum centro B, interuallo BF
deſcribatur ſemi- circulus DFE, ipſæ ſeca-
bit BA infra A, ſed tamen vltra C (cum ſit
BC minor BF, eo quod AC æquatur AF,
& tota AB minor eſt duobus AF, FB) ſecabitque productam AB in E;

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117	93
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120	96
121	97
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123	99
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125	101
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135	111
136	112
137	113
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Scan	Original
111	87
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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
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116

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
130	106
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116