The doctrine of ratios and proportion is introduced by Euclid as a part of his system of **geometry** ; and the student seldom fails to remark, that in the treatises on algebra, the same subject is presented under a considerably different form; though he is usually quite unable to determine wherein the essential difference consists; and would probably find but few teachers who could precisely point out the distinction to him.

— Rev. Baden Powell,

There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences . Many arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical , unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of **geometry**.

— ?"The Mathematical Preface" to Henry Billingsley's English translation of Euclid's

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.

— As quoted in "A Paper of Omar Khayyam" by A.R. Amir-Moez in

I need **geometry** to set the grammar of the image expressive language . The structural skeleton, the composition and the geometric layout provide a perspective from which one can read the image; otherwise we would do what Dadaists did when they put words in a little bag and then took them out at random in order to compose a poem.

— As quoted in: interview by Flavia Squarcio for

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

— As quoted in

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid a term used in this work to denote all of standard **geometry** Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

— As quoted in a review of

It is noteworthy that modern Platonists , almost without exception, are ignorant of mathematics, in spite of the immense importance that Plato attached to arithmetic and **geometry**, and the immense influence that they [these studies] had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have no time for the things that Plato thought important.

— Book One, Part II, Chapter XV, The Theory of Ideas, p. 132

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of **geometry** consists in these sense qualities.

—

How did it happen that the Reverend Charles Dodgson, thirty years of age, lecturer on **geometry** at Christ Church, Oxford, hitherto remarkable chiefly for his precision, on a single July afternoon, while rowing up the Isis with a brother don and three little girls, parthenogenetically gave birth to one of the most famous stories of all time?

— Page 23 (The Life of Lewis Carroll (1962))

The relationship of point to line bothered the Greeks and led Aristotle to separate the two. Though he admits points are on lines, he says that a line is not made up of points and that the continuous cannot be made up of the discrete. This distinction contributed also to the presumed need for separating number from **geometry**, since to the Greeks numbers were discrete and **geometry** dealt with continuous magnitudes.

— Morris Kline,

Plato's most enduring influence on science was his advice to approach the study of nature as an exercise in **geometry**. Through this "geometrization of nature," which could best be done in disciplines that could be suitably idealized, such as astronomy, one can formulate laws that are as "certain" as those in **geometry**. As Plato has Socrates remark in the Republic : "Let's study astronomy by means of problems, as we do in **geometry**, and leave the things in the sky alone."

— Note that Plato's influence in this regard, may be traced to the Pythagoreans.

— John Freely,

There is **geometry** in the humming of the strings, there is music in the spacing of the spheres.

— As quoted in

Sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt **geometry**, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art.

—

**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.

— As quoted in