—It is required to draw a line making with the line D E ([Fig. 8]) an angle equal to that contained by the lines B A C. From A, with any radius, draw an arc F G, and from D, with the same radius, draw the arc H I, and make H I equal F G; then a line drawn from D through I will make, with the line D E, an angle equal to the angle B A C.
Fig. 9.
To construct a Triangle, the length of the base and the angles at the base being given.
—It is required to construct a triangle whose base shall equal 1 inch, and the angles at the base be 30° and 45° respectively. Having made the base A B ([Fig. 9]) of the required length, make the angles at A and B of the required magnitude in the manner already described (see [Fig. 4]), and the continuation of these lines meeting in the point G will complete the construction of the required triangle.
Fig. 10.
To describe a Circle which shall pass through three given points.
—Let A B C ([Fig. 10]) be the points through which it is required to draw the circle. From each of these points, with any radius, describe arcs cutting each other in D and E; join the points D and E, and the point where these lines intersect will be the centre from which to describe the circle which will pass through the points A B C as required.
Fig. 11.