From the preceding it is manifest that—
| sine² | + ver-s = dia. |
| ver-s |
The formula to find the "primary triangle" to any satellite is as follows:—
Let the long ratio line of the satellite or sine be called a, and the short ratio line or versed-sine be called b. Then—
| (1) | a | = sine. |
| (2) | a² + b² | = radius. |
| 2b | ||
| (3) | a² - b² | = co-sine. |
| 2b |
Therefore various primary triangles can be constructed on a side DB (Fig. 64) as sine, by taking different measures for AD as versed-sine. For example—
| From Satellite 5, 1. | ||
| ||
| 5 | = sine. | = 5 |
| 5² + 1² | = radius. | = 13 |
| 2 × 1 | ||
| 5² - 1² | = co-sine. | = 12 |
| 2 × 1 |
| From Satellite 5, 2. |
|
|
| × 4 |
|
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