Euclid's Elements
Interactive exploration of the foundational work of geometry. Learn through hands-on constructions with compass and straightedge.
Fundamentals of plane geometry: triangles, parallels, and area
The fundamental assumptions upon which all of Euclidean geometry is built.
To draw a straight line from any point to any point.
To produce a finite straight line continuously in a straight line.
To describe a circle with any center and radius.
That all right angles are equal to one another.
That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Self-evident truths that apply to all sciences, not just geometry.
Things which are equal to the same thing are also equal to one another.
If equals be added to equals, the wholes are equal.
If equals be subtracted from equals, the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.
Ready to Begin?
Start with Proposition 1: constructing an equilateral triangle on a given line segment.