Euclid Interactive Proofs

Step-by-step proof visualizations for Euclid's Elements, Book I

Proposition I.38

Triangles on Equal Bases

Triangles on equal bases and in the same parallels are equal in area.

Proposition I.39

Equal Triangles, Same Base

Equal triangles on the same base and on the same side are in the same parallels.

Proposition I.40

Equal Triangles, Equal Bases

Equal triangles on equal bases and on the same side are in the same parallels.

Proposition I.41

Parallelogram and Triangle

A parallelogram on the same base with a triangle and in the same parallels is double the triangle.

Proposition I.42

Construct a Parallelogram

To construct a parallelogram equal to a given triangle in a given rectilinear angle.

Proposition I.43

Complements About the Diameter

In any parallelogram the complements of the parallelograms about the diameter are equal to one another.