Music is **geometry** in time.

—

Since **geometry** is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world (for what is there in God which is not God?), and he with his own image reached down to humanity.

— Book IV, Ch. 1, as quoted in "Kepler's Astrology"in

"Some fool has put the head of this nail on the wrong end." "You idiot, it's for the opposite wall!" To be sure, if the space of physical objects allowed motions of translation only, and not also rotations. That space has such **geometry** is a fantasy; experience shows otherwise. It is only experience that makes this complaint and the rejoinder a dialogue of madmen.

— p.35 ("The Conduct of Inquiry")

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean **geometry**.

— Book 1, Chapter 2, Section 4, p. 16

Neither natural ability without instruction nor instruction without natural ability can make the perfect artist. Let him be educated, skilful with the pencil, instructed in **geometry**, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens.

— Chapter I, Sec. 3

Variant translation (by Frank Granger): "For neither talent without instruction nor instruction without talent can produce the perfect craftsman."

Everything one invents is true, you may be perfectly sure of that. Poetry is as precise as **geometry**.

— Letter to Madame Louise Colet (14 August 1853).

Since **geometry** is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art.

— Albrecht Dürer

Various relations being established in **geometry** between lines constituted under given conditions, as parts of geometrical figures, if we choose to adopt the idea of expressing these lines by numerical measures , we are then brought to the distinction of such lines being in some cases commensurable in their numerical values, in others not so. Their geometrical relations however are absolutely general, and do not refer to any such distinction.

— Rev. Baden Powell,

It is worthy of notice that Apollonius nowhere introduces the notion of directrix for a conic, and that, though he incidentally discovered the focus of an ellipse and hyperbola, he did not discover the focus of a parabola. Conspicuous in his **geometry** is also the absence of technical terms and symbols, which renders the proofs long and cumbrous.

—

It is a remarkable fact in the history of **geometry** , that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.

— Florian Cajori,

**geometry** is to sculpture what grammar is to the art of the writer.

— 1913 Les Peintres cubistes; Me ditations esthe tiques,'Sur la peinture, 3'.

**geometry** is that part of universal mechanics which accurately proposes
and demonstrates the art of measuring.

— 1687 Philosophiae Naturalis Principia Mathematica (translated by Andrew Motte,1729).