556 
[54.] The points on the first typical line ze [238.] are, in 1 number, 
eight; their literal symbols being, by what precedes, 
TBs CARY AU AY eA Alas ZAn\iars 
the ternary symbols corresponding to which have been shown to be, 
(010), (001), (011), (011), (021), (012), (021), (012). 
In fact, that these eight points are all on the line zc, is evident on mere 
inspection of their symbols, which are all of the common form, 
(Oyz) [23.]. 
[55.] The points on the second typical line, aa’ | 30.], are in number 
seven: their literal symbols being, 
7 m Iv Iv. 
A, A’, Dy, A , Ao, A > Ad ? 
and their ternary symbols being, 
(100), (011), (111), (211), (111), (211), (811). 
In fact, each of these seven symbols is evidently of the form (twu), or 
(zyy) (80. ]. 
[56.] The points on the third eypioal line, Bc’ [31.], are in number 
ten; namely the points, 
B’ , Cc, INGA TNL Gs Aura Doe IN Aes A oe 
of which the ternary symbols are, 
(101), (110), (011) (211), (121), (112), (321), (312), (281), (213); 
each of these ten symbols being of the form (ctw) [81.], with «=¢+ u, 
as before. 
[57.] These three typical lines, in the plane anc, which may be de- 
noted by the ternary symbols, [100], [011], [111], and represent a sys- 
tem of nine lines 4,, A, in that plane II,, are also three typical traces [ 43. | 
of other planes thereon; and the remaining traces of such planes are in 
number thirteen, represented by four other lines, as types : of which lines, 
considered as such traces, the ternary symbols have been found [43. | to 
be, 
[111], [011], [211], [211]; 
answering to the literal symbols, 
alla! nat Da”, AC, 
and serving as abridged expressions for the four equations of ternary 
form, 
ew+y+2=0, yt+s=0, Qr=yts, Ww=y-2 
