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

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134110

PROBL. XXV. PROP. LXVII.

Dato angulo rectilineo, per punctum intra ipſum datum MA-
XIMAM Parabolen inſcribere: & è contra.

SIt datus angulus rectilineus ABC, & datum, intra ipſum, punctum ſit D.
Oportet per D _MAXIMAM_ Parabolen inſcribere.

Sumatur DE æqualis DB, & per E in angulo ABC applicetur, 1166. h. AEC, quæ à diametro AE ſit bifariam ſecta in E, & per verticem D circa
2257. h. diametrum ED, & applicatam AC magnitudine, & poſitione datam de- ſcribatur Parabole ADC. Dico ipſam eſſe quæſitam.

Quoniam cum ſint DE, DB æquales, rectæ

100[Figure 100]332. huius. AB, CB ſectionem contingent, vnde Parabo- le erit dato angulo inſcripta; eritque _MAXIMA_
quoniam quælibet Parabole per D ipſi ADC
adſcripta cum recto, quod eius recto ſit minus
ipſa ADC minor eſt, quęlibet verò 442. Co-
roll. 19. h. cum recto, quod prædictum excedat licet ea-
dem ſit maior, ſecat tamen latera dati anguli. 55ibidem. Quare Parabole ADC eſt _MAXIMA_. Quod
primò, & c.

SI verò data ſit Parabole ADC, & extra ip-
ſam datum ſit pũctum B, per quod ei opor-
teat _MINIMVM_ angulum rectilineum circum-
ſcribere. Ducta BE parabolæ diametro, & ſumpta DE æquali DB applica-
taque AEC, iunctiſque BA, BC, Erit angulus ABC _MINIMVS_ quæſitus,
662. huius. vt ſatis perſpicuè patet. Nam cum ipſæ BA, BC ſectionem contingant om- nes aliæ ex B ductæ minorem angulum dato ABC adſcriptum conſtituentes,
ſectionem ſecabunt, quare, & c. Quod vltimò, & c.

MONITVM.

MOnendus hìc Lector eſt, quod dum in hoc, & in ſequentibus
problematibus; dato angulo, per datum punctum adſcribitur,
velinſcribi, aut circumſcribi proponitur, quæſita coni-ſectio,
vel circulus; & è contra, dum datæ com-ſectioni, vel circulo
per datum punctum adſcribitur, velinſcribitur, aut circumſcribitur quæſi-
tus angulus; id ſemper à nobis accipi intelligitur in eodem ſenſu quintæ ſe-
cundarum definitionum huius, qua in præcedentibus hactenus vſi ſumus;
nempe lineam, quæ per datum punctum educta diameter eſt datæ, vel quæſitæ
ſectionis, eſſe quoque diametrum dati, vel quæſiti anguli, ſiue eius verti-
ci occurrere; ita vt quæ in angulo ducuntur æquidiſtantes ordinatim appli-
catis com-ſectionis, velcirculi, ſint quoque ab eadem ſectionis diametro

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111	87
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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
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136	112
137	113
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139	115
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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
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