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

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135111 datum punctum tranſeunte bifariam ſectæ, quod à lineis ad anguli verticem
non collimantibus conſequi minimè poſſet. Si verò inſcriptio, ac circumſcri-
ptio alĳs conditionibus confici iubeatur, aliæ item defintiones, & conſtru-
ctiones diuerſæ ad problematum ſolutiones requirerentur, quas omnes, licet
nobis fortuitò datum ſit Geometriæ legibus ſubĳcere, temporis tamen angu-
ſtĳs obſequentes, hic omittere neceſſe fuit; ſed aliàs forſan, Deo dante, ſi
quid vnquam ocĳ nacti fuerimus, hanc ipſam de MAXIMIS, & MI-
NIMIS doctrinam, & duplò, & triplò auctiorem denuò proferemus: inte-
rim varĳs ſtimulis, qui ad hæc edenda nos vrgent, obtemperantes, præſens
argumentum abſoluere properemus, vt citius (alteram huius tractationis
partem aggrediendo) ad noua pariter, & apprimè iucunda in conicis acciden-
tia deueniamus, & quod pluris eſt, præcipuè vtilitatis fundamenta iacien-
do, abſtruſionis doctrinæ myſteria perſpicacioribus ingenĳs aperiamus.

PROBL. XXVI. PROP. LXVIII.

Dato angulo rectilineo, per punctum intra ipſum datum, cum
dato ſemi-tranſuerſo latere, MAXIMAM Hyperbolen inſcribere.
Item.

Datę Hyperbolæ, per punctum extra ipſam datum, MINIMVM
angulum rectilineum circumſcribere.

Oportet autem, ad hoc vt anguli circumſcriptio fiat iuxta alla-
tam definitionem, ac præcedens monitum, datum punctum, vel
eſſe in centro, vel intra angulos, ab aſymptotis conſtitutos.

SIt, in tribus primis figuris, datus angulus rectilineus ABC, & datum in-
tra ipſum punctum ſit D: oportet per D _MAXIMAM_ Hyperbolen inſcri-
bere, cuius ſemi-tranſuerſum latus æquale ſit dato E.

Iungatur DB, & ſe-

101[Figure 101] cetur ex ipſa, DO ęqua
lis E. Iam, vel DO æ-
qualis eſt DB, vt in pri-
ma figura, vel minor vt
in ſecunda, vel maior
vt in tertia. Si primùm,
deſcribatur per D, 114. ſec.
conic. aſymptotis BA, BC
Hyperbole FDG: &
ipſa erit _MAXIMA_
quæſita.

Nam, quæ cum eo-
dem tranſuerſo, eidem angulo per D adſcribitur, cum recto, quod minus

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