Euclid of Alexandria

To truly know a shape, one must not only see it, but prove its properties. Otherwise, it's just a pretty picture.

The fifth postulate is not a suggestion, it's a challenge. And one that has kept many a mathematician awake at night.

Some seek to build empires. I seek to build logical structures. One is more enduring than the other.

If a figure is not congruent, it's simply not right. A principle I wish more people applied to their arguments.

The square on the hypotenuse is equal to the sum of the squares on the other two sides. A truth more reliable than any oracle.

To understand the universe, start with a point. Then add a line. Then a plane. It's all rather elementary, really.

A definition is not a suggestion; it is the bedrock upon which all else is built. Ignore it at your peril.

The sum of the angles in a triangle is two right angles. A fact that has never caused a war, unlike the sum of opinions in a forum.

Some truths are universal. Others are merely local opinions, disguised as fact.

If you cannot prove it, you cannot claim it. A simple rule that would silence many a demagogue.

The shortest distance between two points is a straight line. Unless you're trying to avoid your creditors, then it's a very winding path indeed.

A surface is that which has length and breadth only. Much like a politician's argument, broad but shallow.

The whole is greater than the part. A concept that seems to elude those who focus on trivialities while ignoring the grand design.

To understand the universe, one must first understand the triangle. It's more fundamental than any philosophy.

Some problems are unsolvable. Others merely require a different set of axioms. And a great deal of patience.

The beauty of geometry lies in its certainty. Unlike human affairs, where certainty is a fleeting illusion.

If a theorem is true, it is true everywhere, always. A comforting thought in a world of shifting sands.

To those who seek shortcuts, I offer only the long, winding path of rigorous proof. It's more rewarding in the end.

A solid is that which has length, breadth, and depth. Unlike some arguments, which have only length.

The elements are not a book of spells, but a guide to logical thinking. Though some might find the results equally magical.