Mollweid formulas
The minor grazing rule formulas , named after the German mathematician and astronomer Karl Mollweide are trigonometric formulas for arbitrary triangles apply. Isaac Newton discovered these relationships a century earlier.
Derivation |
Sine law :
Sine addition theorem for double angles :
Angle sum in the triangle and transition to the complementary angle :
Addition of (1) and (2), application of (3) and (5), truncation using (6): Subtract (1) - (2), apply (4) and (5), truncate using (7): Multiplication with the common denominator gives the formulas given. The other two formulas, which contain a sum or a difference between two sides, are created through cyclic substitution of the side and angle names |
source
- CB Mollweide: Additions to plane and spherical trigonometry. In: Monthly correspondence for conveyance of the earth and sky customer, 1808, pages 394–400.