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

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11490

PROBL. XVII. PROP. LI.

Datæ Parabolæ per punctum intra ipſam datum MAXIMAM
Parabolen inſcribere, & è contra.

Datæ Parabolæ per punctum extra ipſam datum MINIMAM
Parabolen circumſcribere.

SIt data Parabole ABC, & oporteat primò per punctum D intra ipſam da-
tum _MAXIMAM_ Parabolen inſcribere.

Ducatur diameter

79[Figure 79] BDE, cuius rectum
latus ſit BF, (quod
in poſterùm intelli-
gatur ſemper ex ver-
tice cõtingenter ap-
plicatum ſectioni,
prout in prę; cedenti-
bus factum eſt, & in
quinta primarũ defi-
nitionũ monuimus)
& per verticem D,
circa diametrũ D E
adſcribatur datæ Parabolæ ABC Parabole GDH, cuius rectum DI 115. huius. le ſit recto BF; nam ipſa erit congruens datæ Dico hanc eſſe _MAXIMAM_
in ſcriptam quæſitam.

Nam cum ipſæ ſint congruentes Parabolæ per diuerſos vertices ſimul ad-
ſcriptæ erunt inter ſe nunquam coeuntes: quare GDH datæ ABC erit 2242. h. datum punctum D inſcripta.

Ampliùs, quælibet alia Parabole per verticem D adſcripta cum recto,
quod minus ſit ipſo DI minor eſt Parabola GDH, quæ verò cum recto 332. Co-
roll. 19. h. quod excedat ipſum DI, qualis eſt MDN, eſt quidem maior GDH, 44ibidem. omnino ſecat circumſcriptam ABC. Nam ſi fiat vt LI ad ID, ita BD ad DE,
& per E applicetur EMA ſecans BA in A, & DM in M. Cum ſit BD ad DE,
vt Li ad ID, erit componendo BE ad ED, vt LD ad DI; vnde rectangulum
ſub extremis BE, & DI, ſiue BF, hoc eſt quadratum applicatæ AE in 55Coroll.
1. huius. rabola ABC, æquale erit rectangulo ſub medijs ED, DL ſiue quadrato 66ibidem. plicatę; ME in Parabola MDN, ac ideò AE, ME ſunt æquales, quapropter
Parabole DN occurrit ſibi adſcriptæ BA, per diuerſos vertices in puncto M,
& ob id in eodem occurſu, & ad alteram quoque partem ſe mutuò ſecabũt: 7750. h. Itaque congruens Parabole GDH erit _MAXIMA_ inſcripta quæſita. Quod
primò, & c.

IAM datæ Parabolæ GDH, oporteat per punctum B extra ipſam datam
_MINIMAM_ Parabolen circumſcribere.

Ducatur BDE diameter datę; GDH, cuius rectum ſit DI, & ei adſcribatur
per B, cum recto BF, quod æquet ipſum DI, congruens Parabole ABC:

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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
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135	111
136	112
137	113
138	114
139	115
140	116