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

568

SERIES

[PART V

The above proposition is of great importance in the theory of maxima and
mini ma.
*205-31. F:P Econnex. ).minp,nmaxp El1-) Cls [*205-3.*71,12]
*205-32. F:. P e connex. _i! minp'a.=E Yminp'a.-.a e I'Minp
[*205-31. *71-163. *33-41]
*205-33. F: PEconnex. K CU'TMinp.. Minp KEE 6&'K
Dem.
F.-*205-31.)F:Hp.).Minp K EI1-+ CIS (1)
F.*205-1.:)F:llp.:).minypr tc e (2)
F.-*35-65.:)F:Hp. ). I'Minp rIC== I (3)
F. (i).(2). (3). *80-14. DF. Prop
*205-34. F:P econnex./ KC EL'minp. ).K eCIS2 Mult [*205-33. *88'2]
The following proposition is used in *260'17.
*205-35. F:: P2 CJ. Pcconnex.):
x = Minp'ca x e a n G'P:y E a rA CGP - tfx.:)y. xPy
Dem.
F.*205-31. *71P36. )FP:: Hp. x:. = minp'a.x minp a
[*205-1.*37-265] xWe a A G'P - P"(a AiCP
[*37-105] xe:xa iC'P: ye a ACOP. Dy. " (yPX):
[*51-221]=r:xariC GP y=x.:)y. (yPx):yeaAC'P-t'x.Dx. c(yPx) (1)
F.*200-36. D F:.llp. ):yPz. z,,y. y z:
[Transp.*10O1] ):y= X.:)Y.., (yPx) (2)
F. (1). (2). ) F:: Hp.)D:.
= minp'a. -: xea nG'P:y e cIAG'P - t'x. DY. )(yPW):
[*202-5] =-:xEaA C'P:ycaAG'6P-t'x.:)y.xPy::) F. Prop
*205-36. F: P E trans A connex.).minp'a Cp'P*""(a A G'P)
Dem.
F.*205 -2. *20118.)DF:.IIHp.wx=rni np'a.D: y e(a nG'P). y. xP*Y:. ) F. Prop
The above proposition is used in *230-53.
*205'37. F: PEtrans. maxp'a= A.:). P*"a=Plla [*201-52.*205-123]
The following proposition is used in *257-21.
*205-38. F:Pp C-J.:).,a AP'P*",LLC mmD(Pp.)'1g
Dem.
F. *200-381. )F:: Hp.:):. x. ),u. x~P*x: ): x p. ). -(xPp0y):.
[*40-51.*37-105] ): 'D ~ C ~" 1
F. *24-12. ) ej.)tC (J'P (3)
F.- (1). (2). (3).:)F Hp. p. PIaPP*"IcpC,LLA C'p - Pp
[*205-11.*91P504] C min (PO)'~ ) F. Prop