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

SECTION C]

PROGRESSIONS

259

*122-23. F:REProg. aC D'R.3g!ca )D
E! min (R0)'a. a - RP "at 'minl (RP,)'6a
Dent.
F. (1).(2). *32-4. *93-111.DIF-. Prop
This proposition shows that every existent class contained in a progression
has a fitrst, tertm, i.e. that a progression is a well-ordered series (cf. *250).
*122-231. F:1?e Prog.a C R a. D.ca= A
Dem.

F. *91-504.DF::Hp.)D.ca CUIR
F.(1). (2). *1 22-23141. Transp.)D F. Prop
*122-24. F:1? eProg. PEPot'R. ). D'P=-P*"B'P= s'gen'P
Dem.
F. *1 22-1. *92-102. ) F: Hp.) Pc6 I1-+1I
[*93-42] )p'IG"Pot'P = 1"PpEiG"Pot'P.
[*122-231] ).p '"Pot'P = A
F.(1).*93-37-36. ) F: Hp.). C'P=:P*"B'P-s'gen'P
F. (2). *122-143. DF. Prop
Except when P= R, B'P will not reduce to a single term. In
P = RV) B'P = IR (IR vJ), i.e. B'P consists of the first v terms
progression.
*122-25. F: RePro. P ePot'R.xeD'R.)

(1)
(2)
(1)
(2)
fact, if
of the

C3~~~~~~~~~4
(P*'(x) 1 P c Prog. x = B'{(P*'x) 1 PI

Dem.

F.*122-1.*92-102.:) F: Hp -).(P*'x)lPe Il-+1
F *122-143. ) F: Hp. D. P*'xC D'P.
[*35-62] D. D'{ (P*'x) 1 PI = 4 -F. *37-4.*91-52.:)F. U'[{(P*'x)1 P1 4-oc
F.*122-16.*91-6. )F:HpD.)x'-~ep0'x
F. *91-542. D)F: YeP*'X.Y + X.D. Ye PPO'X
F.(2).(3).(4).(5). )F: Hp.D).x-B'1(P*'x)1PI
F.(1).(2).(6).*96-131.)F.Prop

(1)
(2)
(3)
(4)
(5)
(6)

17-2