540 
but also the second (or congruent) symbol for a’ shows, by (19), that 4’ 
is in the plane ape; we may therefore write the formula of intersection, 
A’ = BC * ADE, (51) 
whereby this point a’ is entirely determined ; and then the point a”, as 
being its harmonic conjugate with respect to B and c, or as satisfying 
the equation (50), is to be considered as being itself a known point. We 
have thus assigned the three first points Po, P), Po, of the group (47), 
namely the points c, a’, B; and if we denote by 1 the point Be « II in 
which the variable plane H, or [/.. s |, intersects the given line zc, so that 
L= (0, n,—m, 0, 0), or briefly, .=(0” m 00), (52) 
writing m for — m, then the fourth point P,; is 1; and the required for- 
mula of interpretation for the quotient m:n becomes, 
= = (ca/’3). (53) 
In like manner, if we write 
z/ = (10100), c/=(11000), 8” =(10100), o””=(11000), (54) 
and 
at = (710100), w = (mi000), (55) 
in which 7 =- 7, and /=— J, so that w= ca + I, n=an- I, and 
B/= CA‘ BDE, 0/ = AB‘ CDE, (cB/AB’’) = (ac’BC’”’) = — 1, (56) 
is aie have these two other formule of interpretation, analogous to 
’ 
= (aB/cm), - = (Bc//AN) ; (57) 
~|] 8 
and therefore, 
(48cm) . (BC’AN) . (cA”/BL) = 1. (58) 
[15.] Again, if we denote by a, 8, s the intersections pa - IJ, px - I, 
pe ° II, so that 
a = (700/70), x = (070m0), s = (007n0), (59) 
where 7=~-71; if also we introduce seven new points syntypical [9 .] 
with the three points a’p/c’, and seven others syntypical with a//3/c’’, 
as follows : 
A, = (10001), B, = (01001), c,=(00101), ,=(00011); (60) 
A, = (10010), B,= (01010), c,= (00110); (61) 
a/, = (10001), 8’; = (01001), o’;=(00101), v’,=(00011); (62) 
a’, = (10010), 3’,=(01010), oc’, = (00110); : (63) 
so that, by principles already established, we shall have the seven rela- 
tions of intersection, 
