After I found that the plan of the Gïzeh group was a system of "primary" triangles, I had to work out the rule for constructing them, for I had never met with it in any book, but I came across it afterwards in the "Penny Encyclopedia," and in Rankine's "Civil Engineering." The practical utility of these triangles, however, does not appear to have received sufficient consideration. I certainly never met with any except the 3, 4, 5, in the practice of any surveyor of my acquaintance. (For squaring off a line nothing could be more convenient than the 20, 21, 29 triangle; for instance, taking a base of 40 links, then using the whole chain for the two remaining sides of 42 and 58 links.) Table of Some Primary Triangles and their Satellites. ANGLE OF PRIMARY PRIMARY SATELLITE. ANGLE OF SATELLITE DEG. MIN. SEC. RAD. CO.-S. SINE. DEG. MIN. SEC. 2 47 39·70 841 840 41 41 1 1 23 49·85 6 43 58·62 145 144 17 17 1 3 21 59·31 8 47 50·69 85 84 13 13 1 4 23 55·34 10 23 19·89 61 60 11 11 1 5 11 39·94 12 40 49·37 41 40 9 9 1 6 20 24·68 14 14 59·10 65 63 16 8 1 7 7 29·55 16 15 36·73 25 24 7 7 1 8 7 48·36 18 55 28·71 37 35 12 6 1 9 27 44·35 22 37 11·51 13 12 5 5 1 11 18 35·75 25 3 27·27 85 77 36 9 2 12 31 43·63 25 59 21·22 89 80 39 13 3 12 59 40·61 28 4 20·94 17 15 8 4 1 14 2 10·47 30 30 36·49 65 56 33 11 3 15 15 18·24 31 53 26·85 53 45 28 7 2 15 56 43·42 36 52 11·65 5 4 3 3 1 18 26 5·82 41 6 43·52 73 55 48 8 3 20 33 21·76 42 4 30·08 97 72 65 13 5 21 2 15·04 43 36 10·15 29 21 20 5 2 21 48 5·07 46 23 49·85 29 20 21 7 3 23 11 54·92 47 55 29·92 97 65 72 9 4 23 57 44·96 48 53 16·48 73 48 55 11 5 24 26 38·24 53 7 48·35 5 3 4 2 1 26 33 54·17­ 58 6 33·15 53 28 45 9 5 29 3 16·57 59 29 23·51 65 33 56 7 4 29 44 41·75 61 55 39·06 17 8 15 5 3 30 57 49·53 64 0 38·78 89 39 80 8 5 32 0 19·39 64 56 32·73 85 36 77 11 7 32 28 16·36