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

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128104 cum quadrato intermediæ partis DC; rectangulum ergo ACB ſuperat re-
ctangulum ADB; & hoc ſemper; ergo rectangulum ACB, ſub æqualibus
partibus compræhenſum, eſt _MAXIMV M._ Quod primo, & c.

Item, quadrato dimidiæ A C æquatur

93[Figure 93] rectangulum A D B, vna cum quadrato
DC, & eidem quadrato AC æquatur re-
ctangulum AED vna cum quadrato EC,
ergo rectangulum A D C cum quadrato
DC, æquale erit rectangulo AEB, cum
quadrato EC, eſt autem quadratum DC
minus quadrato EC, cum ſit linea DC mi-
nor EC, ex hypoteſi; ergo rectangulum
ADC maius erit rectangulo AEB. Quod ſecundò, & c.

THEOR. XXXII. PROP. LXI.

Si fuerint duæ quæcunque coni-ſectiones, non excepto circulo,
eiuſdem, vel diuerſi nominis per diuerſos vertices ſimul adſcriptæ,
quæ in eiuſdem communis ordinatim ductæ extremis punctis ſimul
conueniant, è quorum altero eadem recta linea vtranque ſectionem
contingat, ea coni-ſectio cuius vertex cadit infra verticem alterius
erit alteri inſcripta, & in ijſdem tantùm applicatæ extremis ſe con-
tingent.

SInt duæ quælibet coni-ſectiones ABC, ADC non excepto circulo, eiuſ-
dem, vel diuerſi nominis per diuerſos vertices B, D ſimul adſcriptæ,

94[Figure 94] quarum communis diameter ſit BH, communiſq; applicata ſit AC, in cuius
extremis A, C, ſectiones ſimul occurrant, & ex eorum altero veluti ex

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116	92
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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
130	106
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116