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

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22745

LEMMA X. PROP. XXXV.

Si duæ rectæ lineæ terminatæ A B, C D bifariam ſectæ fue-
rint in E, F, & proportionaliter producantur, vt in prima figu-
ra; vel diuidantur, vt in ſecunda, in G, H, ita vt ſit A B ad B G,
vt C D ad D H, parteſq; adiectæ, vel demptæ B G, D H iterum
proportionaliter ſecentur in I, L, ita vt B I ad I G, ſit vt D L ad
L H. Dico rectangulum A G B ad rectangulum A I B, eſſe vt re-
ctangulum C H D ad rectangulum C L D.

NAm cum ſit A B ad B G, vt C D ad D H, erit in prima figura com-
ponendo, in ſecunda verò diuidendo A G ad G B, vt C H ad H D,

190[Figure 190]& eſt B G ad G I, vt D H ad H L (cum diui-
dendo factum ſit B I ad I G, vt D L ad L H)
ergo ex æquo A G ad G I erit vt C H ad H L,
& in prima figura per conuerſionem rationis,
in ſecunda verò, componendo, per conuer-
ſionem rationis, & conuertendo, erit G A ad
A I, vt H C ad C L: & cum ſuperiùs demon-
ſtratum ſit eſſe B G ad G I, vt D H ad H L,
erit, per conuerſionem rationis, G B ad B I,
vt H D ad D L. Iam rectangulum A G B ad
A I B habet rationem compoſitam ex ratione
G A ad A I, vel ex H C ad C L, & ex ratio-
ne G B ad B I, vel ex H D ad D L, ſed ex ijſ-
dem rationibus H C ad C D, & H D ad D L
componitur ratio rectanguli C H D ad rectan-
gulum C L D, quare vt rectangulum A G B ad
A I B, ita rectangulum C H D ad C L D. Quod erat, & c.

THEOR. XXI. PROP. XXXVI.

Quælibet Portiones eiuſdem, vel diuerſarum Parabolarum
ſunt Acuminata Proportionalia.

Item, Portiones eiuſdem, vel diuerſarum Hyperbolarum,
Ellipſium, aut Circulorum; quarum tamen ſegmenta diametro-
rum in ijſdem portionibus intercepta ad ſuas ſemi-diametros
eandem homologam habeant rationem, ſunt pariter inter ſe
Acuminata proportionalia.

SInt primò duę portiones A B C, D E F eiuſdem, vel diuerſarum Pa-
rabolarum in prima figura, quarum baſes ſint A C, D F. Dico

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120	96
121	97
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123	99
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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

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