Use of the formula cos.p+cos.q = 2cos.½(p + q)cos.½(p - q), to render logarithms applicable to the sum of two trigonometrical lines, sines or cosines.—To render logarithms applicable to the sum of two tangents.
Construction of the trigonometric tables.
Use in detail of the tables of Callet.—Appreciation, by the proportional parts, of the degree of exactness in the calculation of the angles.—Superiority of the tangent formulas.
Resolution of triangles.
Relations between the angles and the sides of a right-angled triangle, or of any triangle whatever.—When the three angles of a triangle are given, these relations determine only the ratios of the sides.
Resolution of right-angled triangles.—Of the case in which the hypothenuse and a side nearly equal to it are given.
Knowing a side and two angles of any triangle, to find the other parts, and also the surface of the triangle.
Knowing two sides a and b of a triangle and the included angle C, to find the other parts and also the surface of the triangle.—The tang.½(A - B) may be determined; or tang.A and tang.B directly.
Knowing the three sides a, b, c, to find the angles and the surface of the triangle.—Employment of the formula which gives tang.½A.
Application to surveying for plans.