Geometric Proofs Quotes

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

Plane geometry is sort of the key course where you learn about proving things and abstraction.

Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.

This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking.

I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.

Mathematics is the queen of the sciences.

The ludicrous state of solid geometry made me pass over this branch.

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning.

I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.

It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Geometry draws the soul towards truth.