Geometric Reasoning Quotes

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

Geometry enlightlens the intellect and sets one's mind right

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

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.

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

But it is the bane of psychology to suppose that where results are similar, processes must be the same. Psychologists are too apt to reason as geometers would, if the latter were to say that the diameter of a circle is the same thing as its semi-circumference, because, forsooth, they terminate in the same two points.

We are perpetually moralists, but we are geometricians only by chance. Our intercourse with intellectual nature is necessary; our speculations upon matter are voluntary, and at leisure.

There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.