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

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

131107

THEOR. XXXIV. PROP. LXIII.

In quacunque coni-ſectione, etiam in triangulo, MAXIMA
diametro æquidiſtantium inter ſectionem, & quamcunque ordina-
tim applicatam interceptarum, eſt ipſa diameter; aliarum verò
ea, quæ propinquior eſt diametro, maior eſt remotiori.

ESto triangulum, vt in prima figura, vel circuli, aut Ellipſis, vel Parabo-
læ, vel tandem Hyperbolæ portio ABC, vt in ſecunda, quarum dia-
meter ſit BD, & ordinatim applicata ſit AC, ductiſque quotcunque EF,
GH, & c. parallelis ad BD. Dico BD eſſe _MAXIMAM_, diametro reliqua-
rum verò, propinquiorem EF, maiorem eſſe remotiori.

Nam ſi concipiatur ex B duci

96[Figure 96] quædam linea ordinatim appli-
catæ AC æquidiſtans quæ 1117. pri-
mi conic. cadet extra ſectionem, iungique
recta linea puncta E, B quæ 2210. pri.
conic. &
32. eiuſd. cadet intra, patet ipſam EB ad al-
teram partem productam (cum
ſecet in B eam, quæ ducta ſit ex
B parallela ad AC) conuenire
quoque cum CA ad partes A, & ſic BD maiorem eſſe recta EF, ſiue omnium
_MAXIMAM_. Quod primò, & c.

Item ſi puncta G, E, iungantur recta linea ipſa omnino cum 3322. pri.
conic. &
23. eiuſd. extra ſectionem conueniet, ac propterea ſecabit priùs eam, quæ ex B ducta
ſit ipſi A C ęquidiſtans; cum ergo GE ſecet vnam parallelarum, ſecabit quo-
que, ſi producatur, alteram CA ad partes A, & ſic EF erit maior ipſa GH.
Quod ſecundò, & c.

THEOR. XXXV. PROP. LXIV.

Ellipſium æqualium diametrorum, eidem angulo, vel Parabo-
læ, vel Hyperbolæ, aut portioni Ellipticæ, vel circulari, quæ non
ſit maior Ellipſis, vel circuli dimidio, inſcriptarum, ſe mutuò, ac
ſectionem contingentium, quæ propior eſt vertici, minor eſt re-
motiori.

ESto ABC, vel angulus rectilineus, vel Parabole, vel Hyperbole, aut por-
tio non maior dimidio ſemi-Ellipſis, vel ſemi-circuli, cuius vertex B,
diameter BD, & circa æqualia ipſius ſegmenta DE, EF adſcriptæ ſint dato
angulo, vel ſectioni Ellipſes DVE, ETF, ope diagonalium AG, IL, & ap-
plicatarum KHV, NMT, vt in præcedenti Scholio monuimus, quæ anguli
latera, vel ſectionem contingent in K, V, N, T, eique erunt inſcriptæ, & ſe
mutuò contingent in E (cum applicata LEG vtranque ſectionem contingat.)

Page concordance

Text layer

Text normalization

Search

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

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