Shocking Sayings

A straight line is a line which lies evenly with the points on itself.

A plane surface is a surface which lies evenly with the straight lines on itself.

A plane angle is the inclination of the lines to one another, when two lines meet one another, but are not in the same straight line.

And when the lines containing the angle are straight, the angle is called rectilineal.

Rectilineal figures are those which are contained by straight lines...

Trilateral figures are those contained by three straight lines, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has only two of its sides equal, and a scalene triangle that which has its three sides unequal.

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite side…

Let the following be postulated:

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 centre and radius.

That all right angles are equal to one another.

A quantity is said to be a part of a quantity, the less of the greater, when it measures the greater.

And the greater is a multiple of the less when it is measured by the less.

The only purpose of the 'Elements' is to demonstrate mathematically certain fundamental propositions.

For the things of the world cannot be made manifest without the knowledge of mathematics.

Proof by contradiction is a powerful tool.

The prime numbers are more than any assigned multitude of prime numbers.

If a straight line be cut in extreme and mean ratio, the greater segment is also cut in extreme and mean ratio by the lesser segment.