dd4 
ate Again, combining so with c'Bo, and with 8/cp, or with [1 12] and. 
[121], we get the two following other points, belonging to a fifth group 
of second construction, 
a™= (021); a,%=(012); 
whereof the first may be said to be a Seventh Typical Point. There are 
twenty points of this new group ®,,;, whereof each represents only one 
intersection, of the form A,-II,,.; for example, a = 3c ° c’B,B,. We 
are therefore to subtract 20 from the recent number 260 ; and thus there 
remain still 240 intersections to be accounted for, by new points P, upon 
the lines A,, ,,: since the lines A, as well as A,,, have been exhausted, 
as on examination will easily appear. 
[48.] The line x’c’ intersects the traces BB” and cc" of the fifth type 
[ 43, ] in the two following points, of a sixth group of second construction, 
a™=(121); a,"™=(112); 
whereof the former may be called an Highth Typical Point. There are 
siaty points of this new group, P,,., whereof each represents one inter- 
section, of the form A,,,- TI,,,; for example, a™is the intersection of the 
line b/c’ with the plane Bc,4,4,c,; there remain therefore 180 (=240 - 60) 
intersections A: II to be still accounted for, by other points P,, on the 
same set of lines Ag, >. 
[49.] The traces p,B”, p,c’”, which belong to the sixth type { 43. |, in- 
tersect the line n/c’ in two new points, namely, 
at (BOD); AP 2812); 
which belong to a seventh group 2,1, of second construction, and of which 
the former may be regarded as a Wenth Typical Pout. There are sixty 
points of this group, namely two on each of the 30 lines A,,.; and each 
is the intersection of one such line with éwo distinct planes II,,,; their 
group therefore represents a system of 120 such intersections; and only 
60 (= 180 — 120) intersections remain to be accounted for, by other points 
of this last form, Az, 2° Ma, 2. 
[50.] Accordingly, when we combine the line n/c’ with the traces 
4/Co, A'Bo, Which are of the seventh type [43.], we obtain, for the inter- 
sections of that line A,,. with two new planes II,,,,; namely with a/c,c, 
and a’B,B, (98), two new points, belonging to a new or eighth group P2,, 
of second construction, namely, 
A™ = (231); a,*=(218); 
whereof the former may be selected, as a Zenth (and, for our purpose, 
last) Typical Point: for the sixty points of this last group represent 
each one intersection, and thus account for a// the intersections which 
lately remained [49.], after all the preceding groups had been ex- 
hausted. 
