Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

tam AC deſcribatur Ellipſis ALCN. Dico hanc eſſe _MAXIMAM_ inſcriptã quæſitam.

174.1.

Coroll.
57. h.

Nam, in qualibet figura, cum
ſit rectangulum DHE, ſiue NGL
æquale quadrato HI, ſiue GF,
erit NG ad GF, vt GF ad GL, & componendo NG cum GF, hoc
eſt NK, erit ad GF, vt FG cum
GL, ſiue vt KL ad GL, & permu-
tando NK ad KL, vt GF ad GL,
vel vt NG ad GF, vel vt NF ad FL, quæ ſunt differentiæ, trium
proportionalium NG, GF, GL; ergo recta KAM tanget Elli- pſim ALCN, ſiue hæc angulo
ABC erit inſcripta, ſed in alijs fi-
guris, ipſa KAM tangit quoque
datã ei ſimul adſcriptam ſectio-
nem ABC, (ex conſtructione)
adūdem terminum cõmunis ap-
plicatæ AC, quapropter Ellipſis ALCN datæ ſectioni, vel circulo erit inſcripta.

174.1.

0152-01
Coroll.
12. h.
4. h.
61. h.

Dico demum hanc eſſe _MAXIMAM_: quoniam quæ ipſi adſcribitur per
eoſdem terminos applicatæ AC, & cum tranſuerſa diametro æquali ipſi LN,
_licet minor fuerit eadem ALCN_, ſecat contingentem KAM, in A, atque aliò ad partes AK, ſi nempe vertex nouiter adſcriptæ cadat ſupra L; vel ad par-
tes AM, ſi cadat infra, vt ex ipſa 81. huius facilè elicitur: cum ergo inouiter
adſcripta Ellipſis ſecet contingentem KAM, in ſe ipſam rediens, ſecabit om-
nino datam ſectionem ABC, quare Ellipſis ALCN, eſt _MAXIMA_ dato an-
gulo, vel ſectioni ABC inſcripta, circa datam applicatam, & cum data
tranſuerſa diametro DE, immo potiùs ipſa ALCN eſt vnica huiuſmodi con-
ditionibus inſcriptibilius. Quod faciendum, & demonſtrandum erat.

174.1.

81. h.

175. COROLL.

EX hac conſtat interceptum diametri ſegmentum inter quamlibet appli-
tam, & verticem, æquale eſſe (in Parabola) intercepto ſegmento eiuſ-
dem diametri inter verticem, & occurſum contingentis, ductæ ex termino
applicatæ, cum diametro: in Hyperbola, verò maius, ſed in Ellipſi, vel cir-
culo minus eſſe.

Demonſtratum eſt enim, in ſecunda figura, KB æ qualem eſſe BF, in ter-
tia verò KB, minorem BF, & in quarta KB maiorem BF.

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