Euclid

On the same base and on the same side of it, there cannot be two triangles having the sides which extend from the extremities of the base equal to one another toward the same point.

If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they will also have the angles which are contained by the equal straight lines equal.

To bisect a given rectilineal angle.

To bisect a given finite straight line.

To draw a straight line at right angles to a given straight line from a given point on it.

To draw a straight line perpendicular to a given infinite straight line from a given point not on it.

If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles.

If with any straight line, and at a point on it, two straight lines not lying on the same side make the adjacent angles equal to two right angles, the two straight lines will be in a straight line with one another.

If two straight lines cut one another, they make the vertical angles equal to one another.

In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.

In any triangle, two angles taken together in any manner are less than two right angles.

In any triangle the greater side subtends the greater angle.

In any triangle the greater angle is subtended by the greater side.

In any triangle two sides taken together in any manner are greater than the remaining one.

If from the ends of one of the sides of a triangle two straight lines be constructed meeting within the triangle, the straight lines so constructed will be less than the remaining two sides of the triangle but will contain a greater angle.

Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one.

On a given straight line and at a point on it, to construct a rectilineal angle equal to a given rectilineal angle.

If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the equal straight lines greater than the other, they will also have the base greater than the base.

If two triangles have the two sides equal to two sides respectively, but have the base greater than the base, they will also have the one of the angles contained by the equal straight lines greater than the other.

If two triangles have two angles equal to two angles respectively, and one side equal to one side, namely, either the side adjoining the equal angles, or that subtending one of the equal angles, they will also have the remaining sides equal to the remaining sides and the remaining angle to the remaining angle.