There is no royal road to geometry.

What has been affirmed without proof can also be denied without proof.

QED – Quod erat demonstrandum.

QED - Quod erat demonstrandum.

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

Things which are equal to the same thing are also equal to one another.

Sire, there is no royal road to geometry.

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 the angles are less than two right angles.

A line is length without breadth.

Give him threepence, since he must make a gain out of what he learns.