i. Similar Rectilineal Figures are those whose several angles are equal, each to each, and whose sides about the equal angles are proportional.
Similar figures agree in shape; if they agree also in size, they are congruent.
1. When the shape of a figure is given, it is said to be given in species. Thus a triangle whose angles are given is given in species. Hence similar figures are of the same species.
2. When the size of a figure is given, it is said to be given in magnitude; for instance, a square whose side is of given length.
3. When the place which a figure occupies is known, it is said to be given in position.
ii. A right line is said to be cut at a point in extreme and mean ratio when the whole line is to the greater segment as the greater segment is to the less.
iii. If three quantities of the same kind be in continued proportion, the middle term is called a mean proportional between the other two.
Magnitudes in continued proportion are also said to be in geometrical progression.
iv. If four quantities of the same kind be in continued proportion, the two middle terms are called two mean proportionals between the other two.