(1) FOURTH CLASS.
1. Draw a right line tangent to two circles. (fig. 1.)
Take either of the right lines in fig. 1. The circles
may be placed more or less distant from each other, and may even intersect or cut each other. A radius drawn from the centre to the point of contact will be perpen- dicular to the tangent.
2. Draw four tangents to two circles. (fig. 1.)
There may be two interior and two exterior tan- gents. The right line which joins the centres is also the point where the tangents must intersect each other.
3. Add two squares. (fig. 2.)
This figure and figure 3, present two rectangular tri- angles, on whose sides three squares are constructed. The two small squares have this peculiarity, that one of their sides is exactly one side of the triangle, and anoth- er is merely a prolongation of the other side of the right angle. If a semicircle be drawn on the greatest side of the triangle, it must touch the apex of the triangle.
It is a fact in geometry, that the . greatest of these three squares, contains a surface equal to the other two added together.
