Diagram No 3. 
[To face page 640. 
Roots 
Bases 
Sums. 
Trigonal 
Rumbers. 
Sums. 
Square 
Numbers. 
Sums. 
4 
4 
4 
5 = 17 
10 
10 
10 
15 = 
: 45 
16 
16 
16 
25 = 73 
2 
3 
5 
6 = 16 
3 
6 
15 
21 = 
45 
4 
9 
25 
36 = 74 
3 
4 
5 
5 = 17 
6 
10 
15 
15 = 
46 
9 
16 
25 
25 = 75 
3 
3 
3 
7 = 16 
6 
6 
6 
28 = 
46 
9 
9 
9 
49 = 76 
3 
4 
4 
6 = 17 
6 
10 
10 
21 = 
47 
9 
16 
16 
36 = 77 
2 
3 
4 
7 = 16 
3 
6 
10 
28 = 
47 
4 
9 
16 
49 = 78 
3 
3 
5 
6 = 17 
6 
6 
15 
21 = 
48 
9 
9 
25 
36 = 79 
2 
2 
6 
6 = 16 
3 
3 
21 
21 = 
48 
4 
4 
36 
36 = 80 
2 
4 
5 
6 = 17 
3 
10 
15 
21 = 
49 
4 
16 
25 
36 = 81 
2 
2 
5 
7 = 16 
3 
3 
16 
28 =j 
49 
4, 
4 
25 
49 — 82 
3 
3 
4 
7 = 17 
6 
6 
10 
28 = 
50 
9 
9 
16 
49 = 83 
1 
3 
5 
7 = 16 
1 
6 
15 
28 = 
50 
1 
9 
25 
49 = 84 
2 
4 
4 
7 = 17 
3 
10 
10 
28 = 
51 
4 
16 
16 
49 = 85 
2 
3 
3 
8 = 16 
3 
6 
6 
36 = 
51 
4 
9 
9 
64 = 86 
2 
3 
5 
7 = 17 
3 
6 
15 
28 = 
52 
4 
9 
25 
49 - 87 
2 
2 
4 
8 = 16 
3 
3 
10 
36 = 
52 
4 
4 
16 
64 = 88 
1 
4 
6 
6 = 17 
1 
10 
21 
21 = 
53 
1 
16 
36 
36 = 89 
1 
3 
4 
8 = 16 
1 
6 
10 
36 = 
53 
1 
9 
16 
64 = 90 
J 1 
4 
5 
7 = l 17 
J 1 
10 
15 
28 l = l 
"541 
1 
16 
25 
491= 91 
U 
5 
5 
5 =ll9 
lio 
15 
15 
15/=1 
.55J 
16 
25 
25 
25J= 91 
3 
3 
5 
7 = 18 
6 
6 
15 
28 = 
55 
9 
9 
25 
49 = 92 
Pentagonal 
Numbers. Sums. 
22 22 35 = 101 
28 
Hexagonal 
Numbers. 
28 28 
Sums. 
45 = 129 
34 
Heptagonal 
Numbers. Sums. 
34 34 55 = 157 
12 
35 
51 = 103 
6 
15 
45 
66 = 132 
7 
18 
55 
81 = 161 
22 
35 
35 = 104 
15 
28 
45 
45 = 133 
18 
34 
55 
55 = 162 
12 
12 
70 = 106 
15 
15 
15 
91 = 136 
18 
18 
18 
112 = 166 
22 
22 
51 = 107 
15 
28 
28 
66 = 137 
18 
34 
34 
81 = 167 
12 
22 
70 = 109 
6 
15 
28 
91 = 140 
7 
18 
34 
112 = 171 
12 
35 
51 = 110 
15 
15 
45 
66 = 141 
18 
18 
55 
81 = 172 
5 
51 
51 = 112 
6 
6 
66 
66 = 144 
7 
7 
81 
81 = 176 
22 
35 
51 = 113 
6 
28 
45 
66 = 145 
7 
34 
55 
81 = 177 
5 
35 
70 = 115 
6 
6 
45 
91 = 148 
7 
7 
55 
112 = 181 
12 
22 
70 = - 116 
15 
15 
28 
91 = 149 
18 
18 
34 
112 = 182 
12 
35 
70 = 118 
1 
15 
45 
91 = 152 
1 
18 
55 
112 = 186 
22 
22 
70 = 119 
.6 
28 
28 
91 = 153 
7 
34 
34 
112 = 187 
12 
12 
92 = 121 
6 
15 
15 
120 = 156 
7 
18 
18 
148 = 191 
12 
35 
70 = 122 
6 
15 
45 
91 = 157 
7 
18 
55 
112 =192 
5 
22 
92 = 124 
6 
6 
28 
120 = 160 
7 
7 
34 
148 = 196 
22 
51 
51 = 125 
1 
28 
66 
66 = 161 
1 
34 
81 
81 = 197 
12 
22 
92 = 127 
1 
15 
28 
120 = 164 
1 
18 
34 
148 = 201 
22 
35 
701 = 128 
J 1 
28 
45 
91]= 165 
/ 1 
34 
55 
1121= 202 
35 
35 
35 J= 127 
128 
45 
45 
45J= 163 
134 
55 
55 
55l= 199 
12 
35 
70 = 129 
15 
15 
45 
91 = 166 
18 
18 
55 
112 = 203 
22 
5 
12 
12 
12 
5 
12 
5 
5 
5 
12 
1 
5 
5 
5 
5 
1 
1 
.( 1 
1 22 
12 
