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

Si datum punctum F ſit in axe intra ſectionem, vt in ſecunda figura,
quod tamen diſtet à vertice per interuallum non maius dimidio recti B E: item F B erit _MINIMA_.

9. huius
ad nu. 1.

Cum verò, in eadem figura,
ſegmentũ F B excedet prædictum
recti dimidium: dematur B I ęqua-
lis ſemi-recto B E, & tunc habe-
bit H B ad B I maiorem rationem
quàm ad B F: ſi ergo H F ſecetur
in L, ita vt H L ad L F, ſit vt H B
ad B I, punctum L omnino cadet
inter B & F; itaque ducta A L C
ordinatim axi applicata, iunctaq; F A. Dico ipſam F A eſſe _MINI-_
_MAM_ quæſitam.

243.1.

0209-01

Ducta enim ex A contingente A M, quæ axi occurret in M. Erit rectangulum H L M ad quadratum L A, vt tranſuerſum latus ad rectum, vel vt G B ad B E; vel ſumptis ſubduplis, vt H B ad B I; vel, ob conſtructionem, vt H L ad L F; vel,
ſumpta communi altitudine L M, vt idem rectangulum H L M ad rectan-
gulum F L M: ergo quadratum L A æquabitur rectangulo F L M, ſed eſt
A L ipſi F M perpendicularis: quare angulus F A M rectus erit, ſed A M ſectionem contingit in A: ergo F A eſt _MINIMA_ ducibilium ex F ad
Hyperbolæ peripheriam A B C, eſt autem F C ęqualis F A: vnde in hoc caſu duę erunt _MINIMAE_, & c.

243.1.

2. pr. h.
24. pri-
mi conic.
37. ibid.
203. Se-
pt. Pappi.
11. h. ad
num. 1.

At ſi datum punctum F fuerit in axe coniugato H F, vt in tertia figu-
ra. Diuidatur F H in I, ita vt F I ad I H ſit vt tranſuerſum G B ad rectũ
B E, & per I agatur I A axi æquidiſtans, quæ in vno tantùm puncto A
Hyperbolæ occurret. Dico iunctam F A eſſe _MINIMAM_ quæſitam.

26. pri-
mi conic.

Producatur F A axi occurrens
in L, cui applicetur A M, duca-
turque ex A contingens A N, quę axi occurret in Q. Erit in trian- gulo F L H, ob parallelas, H M ad
ad M L, vt F A ad A L, vel vt F I
ad I H; vel vt tranſuerſum ad re-
ctum per conſtructionem; vel vt re-
ctangulum H M N ad quadratum M A, ſed eadem H M ad M L, (ſum-
pta communi altitudine M N) eſt
vt idem rectangulum H M N ad re-
ctangulum L M N; vnde quadratum
M A, æquabitur rectangulo N M L, & eſt A M ipſi L N perpendicularis: quare angulus L A N, & qui ei deinceps eſt F A N rectus erit, ſed A N ſectionem contingit, ergo F A eſt _MINIMA_ quæſita.

243.1.

0209-02
2. pr. h.
24. primi
conic.
37. ibid.
203. Se-
pt. Pappi.
10. h.

Si autem datum punctum F ſit extra Hyperbolen inter axem coniuga-
tum S H T, & ſectionis peripheriam, vt in quarta, & quinta figura, vel

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