Euclid

In any right-angled triangle the square which is described on the side opposite the right angle is equal to the squares described on the sides which contain the right angle.

If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend.

The sum of the angles of any triangle is equal to two right angles.

If a straight line fall on parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.

A unit is that by virtue of which each of the things that exist is called one.

A prime number is that which is measured by a unit alone.

Any composite number is measured by some prime number.

If a straight line be cut in extreme and mean ratio, the whole is to the greater segment as the greater segment is to the lesser.

Similar rectilineal figures are those which have their angles severally equal and the sides about the equal angles proportional.

In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.

To describe a circle about a given triangle.

To construct a regular pentagon in a given circle.

To construct a regular hexagon in a given circle.

To construct a regular 15-gon in a given circle.

The diameter is the greatest chord in a circle.

If a straight line touch a circle, and from the point of contact there be drawn across through the circle a straight line cutting the circle, the angles which it makes with the tangent will be equal to the angles in the alternate segments of the circle.

If two straight lines cut one another within a circle, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other.

If from an external point two straight lines be drawn to a circle, and one of them cut the circle and the other touch it, the rectangle contained by the whole line which cuts the circle and the segment of it outside the circle is equal to the square on the tangent.

The five regular solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

To construct a tetrahedron and comprehend it in a sphere.