Now, since the angle of the satellite on the circumference must be half the angle of the adjacent primary triangle at the centre, it follows that in constructing a list of satellites and their angles, the angles of the corresponding primary triangles can be found. For instance—
Satellite 8, 3, contains 20° 33′ 21·76″
Satellite 2, 7, contains 15° 56′ 43·425″
Each of these angles doubled, gives the angle of a "primary" triangle as follows, viz.:—
The 48, 55, 73 triangle = 41° 6′ 43·52″
The 28, 45, 53 triangle = 31° 53′ 26·85″
The angles of the satellites together must always be 45°, because the angle at the circumference of a quadrant must always be 135°.
From the Gïzeh plan, as far as I have developed it, the following order of satellites begins to appear, which may be a guide to the complete Gïzeh plan ratio, and to those "primary" triangles in use by the pyramid surveyors in their ordinary work.
| 1, | 2 | 2, | 3 | 3, | 4 | 4, | 5 | 5, | 6 | 6, | 7 | 7, | 8 | 8, | 9 |
| 1, | 3 | 2, | 5 | 3, | 5 | 4, | 7 | 5, | 7 | 7, | 9 | ||||
| 1, | 4 | 2, | 7 | 3, | 7 | 4, | 9 | 5, | 8 | ||||||
| 1, | 5 | 2, | 9 | 3, | 8 | 5, | 9 | 7, | 1 | ||||||
| 1, | 6 | 5, | 11 | ||||||||||||
| 1, | 7 | 3, | 11 | 5, | 13 | ||||||||||
| 1, | 8 | 3, | 13 | ||||||||||||
| 1, | 9 | ||||||||||||||
| 1, | 11 | ||||||||||||||
| 1, | 13 | ||||||||||||||
| 1, | 15 | ||||||||||||||
| 1, | 17 |
Primary triangles may be found from the angle of the satellite, but it is an exceedingly round-about way. I will, however, give an example.
Let us construct a primary triangle from the satellite 4, 9.
| Rad. × 4 | = ·4444444 = Tangt. < 23° 57′ 45·041″ |
| 9 | |
| ∠ 23° 57′ 45·041″ × 2 = 47° 55′ 30·083″. | |
| therefore the angles of the "primary" are 47° 55′ 30·083″. | |
| and 42° 4′ 29·917″. | |
| The natural sine of 42° 4′ 29·917″ = ·6701025. | |
| The natural co-sine 42° 4′ 29·917″ = ·7422684. | |