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

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
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

21735

THEOR. XVII. PROP. XXV.

Rectorum laterum in Parabola, MINIMVM eſt rectum axis.

ESto Parabole A B C, cuius axis B D, rectum B E. Dico ipſum B E
reliquorum rectorum eſſe _MINIMVM_. Sit quælibet alia diameter
A F, quæ axi B D æquidiſtabit, ſitque ad A contingens A G, & B 11ex 46.
pr. conic. ipſi A G æquidiſtans, quæ diametro A F erit ordinatim applicata; tan-
dem axi applicetur A H, ſumaturque A I æqualis recto diametri A F.

Iam, ob contingentem A G, cum ſit
H B æqualis B G, & F A eidem B G ę-

178[Figure 178] qualis, erit H B ęqualis F A: rectan-
gulum ergo H B E ad F A I, vel qua-
dratum H A, ad quadratum B 22Coroll.
primæ 1.
huius. vel ad quadratum G A, erit vt B E
ad A I, ſed eſt quadratum A H minus
quadrato A G, ſiue recta A H minor
recta A G, cum acutus angulus A G B
minor ſit recto A H G, quare B E
rectum, minus erit recto A I: eadem-
que ratione demonſtrabitur B E quo-
cunque alio recto minus eſſe: quare
B E rectum axis, eſt _MINIMVM._
Quod erat oſtendendum.

COROLL.

HInc patet, data quacunque Parabolæ diametro, ſi quæratur ratio
inter eius rectum, rectumque axis, hanc ipſam reperiri inter qua-
dratum contingentis interceptæ, à vertice datæ diametri vſque ad axim,
& quadratum axi ſemi-applicatæ ab eodem vertice.

Verùm ſi omnium rectorum continuam proportionem, in lineis, &
veluti ipſorum quandam propagationem ante oculos ponere expetemus, id
à proximo Theoremate addiſcere liceat.

THEOR. XIIX. PROP. XXVI.

Recta latera diametrorum in Parabola, ſunt inter ſe in ratio-
ne linearum ex puncto axis remoto à vertice per quadrantem
ſui recti, ad ipſarum diametrorum vertices eductarum.

ESto Parabole A B C, cuius axis B D rectum B I, ac eius quarta pars
ſit B D, & quælibet aliæ diametri ſint A E, F G, & c. quarum ver-
tices iungantur rectis D B, D A, D F, & c. Dico, tùm axis, tùm prædi-
ctorum diametrorum latera eſſe inter ſe, vt ſunt ipſæ eductæ D B, D A,
D F, & c.

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
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

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
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

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
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