Definition:Euclid's Definitions - Book VI

Euclid's Definitions: Book $\text{VI}$

These definitions appear at the start of Book $\text{VI}$ of Euclid's The Elements.

1. Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional.
2. Two figures are reciprocally related when there are in each of the two figures antecedent and consequent ratios.
3. A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
4. The height of any figure is the perpendicular drawn from the vertex to the base.

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.) ... (previous) ... (next): Book $\text{VI}$. Definitions