MR. H. M TAYLOR OX A SPECIAL FORI\[ OF THE 
nn 
and similarly, if we select the triangle 
2 , 
o 1 
" i 5 
22, 
we must take also 
11 , 
23 , 
26 
and 
15 , 
20 , 
27. 
We can see that if we were to choose the triang^le 
o 
1 
17 
00 
we must also take 
12 
5 
19 
, 24, 
and 
14 
9 
16 
, 25 
9 
and if we 
select the triangle 
2 
5 
20 
, 23 
9 
we must take also 
11 
9 
22 
, 27, 
and 
15 
J 
21 
, 26 
• 
Hence we see that the three 
groups 
4 6 5 
1 
16 
19 
2 
21 
22 
9 8 7 
• 
17 
14 
24 
• 
20 
15 
27 
13 10 3 
18 
25 
12 
23 
26 
11 
form three sets such that the triangle obtained by reading any row or column is of 
the type we have considered above, with respect to the triangles obtained by reading 
the other two rows or columns, and also that there is but one way of completing the 
second and third sets when the first is chosen. 
§ 21. Two triple tangent planes, which do not pass through the same line, intersect 
in a straight line which cuts the two triangles in the same three points, these points 
being intersections of pairs of lines on the surface. 
There are 45.16 = 720 such pairs of triple tangent planes; there are, therefore, 
720 straight lines which run through three of the points of contact of the triple 
tangent planes, and no more. 
