Geometric Principles Quotes

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

Geometry is the art of correct reasoning from incorrectly drawn figures.

We cannot ... prove geometrical truths by arithmetic.

Music is the arithmetic of sounds as optics is the geometry of light.

When Moses was alive, these pyramids were a thousand years old. Here began the history of architecture. Here people learned to measure time by a calendar, to plot the stars by astronomy and chart the earth by geometry. And here they developed that most awesome of all ideas - the idea of eternity.

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

Geometry enlightlens the intellect and sets one's mind right

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

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.

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

Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.

And therefore in geometry (which is the only science that it hath pleased God hitherto to bestow on mankind), men begin at settling the significations of their words; which settling of significations, they call definitions, and place them in the beginning of their reckoning.

Experience proves that anyone who has studied geometry is infinitely quicker to grasp difficult subjects than one who has not.

... preliminary accounting, banking and surveying (known as arithmetic, algebra and 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.

The only royal road to elementary geometry is ingenuity.

Rightness expresses of actions, what straightness does of lines; and there can no more be two kinds of right action than there can be two kinds of straight lines.

Many statements about God are confidently made by theologians on grounds that today at least sound specious. Thomas Aquinas claimed to prove that God cannot make another God, or commit suicide, or make a man without a soul, or even make a triangle whose interior angles do not equal 180 degrees. But Bolyai and Lobachevsky were able to accomplish this last feat (on a curved surface) in the nineteenth century, and they were not even approximately gods.

Hippocrates is an excellent geometer but a complete fool in everyday affairs.

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.

Projective geometry is all geometry.

We think of Euclid as of fine ice; we admire Newton as we admire the peak of Teneriffe. Even the intensest labors, the most remote triumphs of the abstract intellect, seem to carry us into a region different from our own-to be in a terra incognita of pure reasoning, to cast a chill on human glory.

Geometry is to the plastic arts what grammar is to the art of the writer.

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.