What We Have Discussed

The three building blocks of geometry are Points, Lines, and Planes, which are undefined terms.

Ancient mathematicians, including Euclid, tried to define these undefined terms.

Euclid developed a system of thought in his “The Elements” that serves as the foundation for the development of all subsequent mathematics.

Some of Euclid’s axioms are:

Things which are to the same things are equal to one another.

If equals are added to equals, the wholes are also .

If equals are subtracted from equals, the remainders are also .

Things which coincide with one another are to one another.

The whole is than the part.

Things which are double of the same things are to one another.

Things which are halves of the same things are to one another.

Euclid’s postulates are:

Postulate 1: To draw a straight line from any point to any .

Postulate 2: A terminated line can be produced infinitelyonly finitely.

Postulate 3: To describe a circle with any centre and radius.

Postulate 4: That all right angles to one another.

Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together is less than two right angles, then the two straight lines, if produced infinitely, meet on that side on which the of the angles is less than two right angles.