Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTION A]

MAXIMUM AND MINIMUM POINTS

w.9

*205'381. F1: PPO CJ. rnaxp ctp = A.)`.cp =pcPpoLClU
Dent.
P t
F-.*205-38 ).: F: Hp.. p n p'P*',u A (1)
F.(1).*40-53. *24-37.
4 -F::Hp. x:. Xep'P*"p. e P. y. yP*x. ytx:
[*200-38] ly D. YPpoX:
4 -[*40-53] x E cp'P ",uc:: ) F. Prop
The three following propositions lead up to *205-42, which is used in
*261-26.
*205-4. F: CCP el.:).B'P = A. B'P=A
Dern.
F.-*56-381. *5515.:) F: Hp. (.(ax).D'P= t'xiAxLP = ffx.
[*93'101] ).B'P =A. B'P =A::) F.Prop
*205-401. F:g!B'P.. aA C'P e0 v.C'P a,,e 0v1
Dent.
F-.*205-4. Transp.:)F: Hp..C'PC a eI (1)
F. i*93-103. )F: Hp. D. j! C'PO a (2)
F -(1.(2. F: Hp. D. O'P CaaNe 0u 1 (3)
F.*37-41. D F. O'P C aC a P n Cip (4)
F.(4).*60-32-371. Transp. D F: C'PC aN O v1. I.a r CG'P - e 0 v1 (5)
F.(3).(5). )F.Prop
The following proposition, besides being required for *205-41, is used
in *250-151.
*205-41. F:Peconnex.aAC'Pr fs1.).mind'a=B'P a
Dent.
F. *20254. )F: Hp. ). CP r a = a nrC'P (1)
F. *37-41. )F. G'P r a =arAP"a (2)
F. (1). (2). *93-103. F F: Hp.:. B'P r a = a A C'P - (a A Pica)
[*22-93.*20511] = min'oC: D F. Prop
*205 42. F:Peconnex.E!B'Pa. ).B'P a=minp'a
Demn.
F. *205-401. ) F: IHp..a n G'P e.
[*205~-41. minpa = BIIP r a (- -
F.(1). *32-41. DF. Prop