Book I · Orientation

Learn to see why.

Before any proposition, Euclid lays out what he will talk about, what he may draw, and what everyone must grant: definitions, postulates, common notions. The module keeps his order. Read the foundations, then construct each proposition with your own hand and answer for the proof.

The order of study

From first terms
to necessary conclusions.

First sequence

One growing art, from a line to a solid

Construction · transfer · subtraction · congruence · solid

Learn to see why.

From first terms
to necessary conclusions.

One growing art, from a line to a solid

The equilateral triangle

Placing a given length at a given point

Cutting off the lesser from the greater

Two sides and the angle between them

The angles at the base

Two sides, one meeting point

Three sides against three sides

Bisecting an angle

Bisecting a straight line

The perpendicular from a point on the line

The perpendicular from a point off the line

The angles on a straight line

A solid between two spheres

From first termsto necessary conclusions.

One growing art, from a line to a solid

The equilateral triangle

Placing a given length at a given point

Cutting off the lesser from the greater

Two sides and the angle between them

The angles at the base

Two sides, one meeting point

Three sides against three sides

Bisecting an angle

Bisecting a straight line

The perpendicular from a point on the line

The perpendicular from a point off the line

The angles on a straight line

A solid between two spheres

From first terms
to necessary conclusions.