80 NOTES ON TRIGONOMETRICAL PROPOSITIONS.
Logarithms. | ||||||
Propor- tion |
Sine compl. ½ sum of angles | 53° | 11′ | 58″ | 2222368 | |
Sine compl. ½ diff. of angles | 84° | 18′ | 3″ | 49553 | ||
Tangent ½ base | 34° | 30′ | 0″ | 3750122 | ||
Tangent ½ sum of sides | 40° | 30′ | 0″ | 1577307 |
Another Example.
Let there be given
the angle 47°, | |||||
the sides containing it | 50° | 35′ | 11″ | ||
31° | 6′ | 5″ | |||
| 90° | 41′ | 16″ | sum. | |
45° | 20′ | 38″ | half sum. | ||
44° | 39′ | 22″ | compl. of half sum. | ||
28° | 29′ | 6″ | difference. | ||
14° | 14′ | 33″ | half difference. | ||
28° | 29′ | 6″ | compl. of half diff. |
Logarithms. | ||||||
Propor- tion 1. |
Sine compl. ½ sum of sides | 44° | 39′ | 22″ | 3526118 | |
Sine compl. ½ diff. of sides | 75° | 45′ | 27″ | 312192 | ||
Tan. compl. ½ vert. angle | 66° | 30′ | 0″ | −8328403 | ||
Tan. ½ sum of angs. at base | 72° | 30′ | 0″ | −11452329 | ||
Propor- tion 2. |
Sine ½ sum of sides | 45° | 20′ | 38″ | 3406418 | |
Sine ½ diff. of sides | 14° | 14′ | 33″ | 14023154 | ||
Tan. compl. ½ vert. angle | 66° | 30′ | 0″ | −8328403 | ||
Tan. ½ diff. of angs. at base | 38° | 30′ | 0″ | 2288333 |
72° | 30′ | ||
38° | 30′ | | |
111° | 0′ | angles at the base. | |
34° | 0′ |
And these relations are all uniformly maintained,
whether