Measurement of bases with rods.
Measurement of angles.—Description and use of the circle.—Use of the telescope to render the line of sight more precise.—Division of the circle.—Verniers.
Measurement and calculation of a system of triangles.—Reduction of angles to the centres of stations.
How to connect the secondary points to the principal system.—Use of the plane table and of the compass.
2. SPHERICAL TRIGONOMETRY.
Fundamental relations (cos.a = cos.b cos.c + sin.b sin.c cos.A) between the sides and the angles of a spherical triangle.
To deduce thence the relations sin.A : sin.B = sin.a : sin.b; cot.a sin.b - cot.A sin.C = cos.b cos.C, and by the consideration of the supplementary triangle cos.A = -cos.B cos.C + sin.B sin.C cos.a.
Right-angled triangles.—Formulas cos.a = cos.b cos.c; sin.b = sin.a sin.B; tang.c = tang.a cos.B, and tang.b = sin.c tang.B.
In a right-angled triangle the three sides are less than 90°, or else two of the sides are greater than 90°, and the third is less. An angle and the side opposite to it are both less than 90°, or both greater.
Resolution of any triangles whatever: