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

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138114 BGL erit diameter, tum datæ Hyperbolæ, tum deſcripti anguli; & cum GH,
GI, per punctum G, in Hyperbola ſumptum, ductæ ſint aſymptotis æquidi-
ſtantes, ipſæ, ad partes B productæ, Hyperbolæ occurrent, cum aſymptotos
ſecent, ſed ad partes H, I, nunquam cum ſectione conuenient, at 11Coroll.
11. huius. que ducatur ex G extra angulum HGI, ſecabit producta alteram aſympto-
ton (cum ſecet in G ipſi parallelam GH) ac ideò priùs Hyperbolen datam:
eſt igitur HGI _MAXIMV S_ inſcriptus angulus, vti quærebatur. Quod primò
erat, & c.

IAM ſit datus angulus HGI, & datum punctum ſit B, in angulo tamen, qui
ei eſt ad verticem: oportet per B _MINIMAM_ Hyperbolen circumſcribe-
re, cum dato ſemi- tranſuerſo R.

Iungatur GB, & producatur, ſu-

104[Figure 104] maturque B D æqualis R; & per D
agantur DE, DF, ipſis GH, GI pa-
rallelæ, & per B cum afymptotis
DE, DF deſcribatur 224. ſec.
conic. ABC, Dico hanc eſſe _MINIMAM_
circumſcriptam quæſitam.

Nam eadem ratione, vt ſupra. ,
oſtendetur DBGL eſſe diametrum
ſectionis, & dati anguli, & rectas
GH, GI, ad partes H, I productas (cum aſymptotis æquidiſtent) nunquam
cum ſectione conuenire; ideoque Hyperbolen ABC dato angulo eſſe circũ-
ſcriptam: ſed eſt quoque _MINIMA_, quoniam, quæ cum eodem tranſuerſo
adſcribitur, ſed cum recto maiori, maioreſt ipſa ABC; quæ verò cum 332. Co-
roll. 19. h. cto minori, qualis eſt MBN, eſt quidem minor ABC, ſed omnino ſecat 44ibidem. tera dati anguli: quoniam ducta DO, quæ ſit aſymptotos inſcriptæ MBN,
ipſa cadet infra DE, ſed eam ſecat in D, quare producta, alteram 55ex 37. h. lam ſecabit GH, ſed DO tota cadit extra BM, vnde occurſus DO cum GH
erit extra BM; ſiue GH neceſſariò ſecabit priùs ſectionem BM. Eſt igitur ſe-
ctio MBN _MINIMA_ circumſcripta quæſita dato angulo HGI, per datum
punctum B, & cum dato ſemi-tranſuerſo R. Quod vltimò faciendum erat.

PROBL. XXVIII. PROP. LXX.

Dato angulo rectilineo, per punctum intra ipſum datum, cum
dato tranſuerſo latere, MAXIMAM Ellipſim inſcribere: & è con-
tra.

SIt datus angulus ABC, & punctum intra ipſum ſit D, per quod ei opor-
teat, cum dato tranſuerſo R, _MAXIMAM_ Ellipſim inſcribere.

Sumatur DE ęqualis R, & per D, & E in angulo ABC applicentur 6666. h. HEL, & iungatur HG diametrum ſecans in M, per quod applicetur AMD,
& circa diametrum DE, ac per terminos applicatæ AC, deſcribatur 77Coroll.
57. h. DAEC. Dico hanc eſſe _MAXIMAM_ quæſitam. Quoniam, ipſa ADCE eſt
menſali HFGL, ſiue dato angulo inſcripta, & quælibet alia Ellipſis 88Schol.
62. h.

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