“Had the acute-angled rabble been all, without exception, absolutely destitute of hope and of ambition, they might have found leaders in some of their many seditious outbreaks, so able as to render their superior numbers and strength too much even for the wisdom of the Circles. But a wise ordinance of Nature has decreed that, in proportion as the working-classes increase in intelligence, knowledge, and all virtue, in that same proportion their acute angle (which makes them physically terrible) shall increase also and approximate to the comparatively harmless angle of the Equilateral Triangle. Thus, in the most brutal and formidable of the soldier class — creatures almost on a level with women in their lack of intelligence — it is found that, as they wax in the mental ability necessary to employ their tremendous penetrating power to advantage, so do they wane in the power of penetration itself.

How admirable is this Law of Compensation! And how perfect a proof of the natural fitness and, I may almost say, the divine origin of the aristocratic constitution of the States in Flatland! By a judicious use of this Law of Nature, the Polygons and Circles are almost always able to stifle sedition in its very cradle, taking advantage of the irrepressible and boundless hopefulness of the human mind. Art also comes to the aid of Law and Order. It is generally found possible — by a little artificial compression or expansion on the part of the State physicians — to make some of the more intelligent leaders of a rebellion perfectly Regular, and to admit them at once into the privileged classes; a much larger number, who are still below the standard, allured by the prospect of being ultimately ennobled, are induced to enter the State Hospitals, where they are kept in honourable confinement for life; one or two alone of the more obstinate, foolish, and hopelessly irregular are led to execution.”

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Preface (March 30, 1807)
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

this harmonic proportion may be expressed as <math>\frac{12}{6}=\frac{12-8}{8-6}</math> or inversely.
Nicomachus of Gerasa: Introduction to Arithmetic (1926)

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter I, Sec. 16
Context: As for men upon whom nature has bestowed so much ingenuity, acuteness, and memory that they are able to have a thorough knowledge of geometry, astronomy, music, and the other arts, they go beyond the functions of architects and become pure mathematicians. Hence they can readily take up positions against those arts because many are the artistic weapons with which they are armed. Such men, however, are rarely found, but there have been such at times; for example, Aristarchus of Samos, Philolaus, and Archytas of Tarentum, Apollonius of Perga, Eratosthenes of Cyrene, and among Syracusans Archimedes and Scopinas, who through mathematics and natural philosophy discovered, expounded, and left to posterity many things in connection with mechanics and with sundials.

Robert Layton Sibelius (London: J. M. Dent, [1965] 1971), ch. 16, p. 153.
Criticism

From the book De divina proportione

Source: Flatland: A Romance of Many Dimensions (1884), PART I: THIS WORLD, Chapter 5. Of Our Methods of Recognizing One Another

As quoted in Mishima : A Life in Four Chapters (1985).
Context: All my life I have been acutely aware of a contradiction in the very nature of my existence. For forty-five years I struggled to resolve this dilemma by writing plays and novels. The more I wrote, the more I realized mere words were not enough. So I found another form of expression.

Part I, ch. 1.
The Compleat Angler (1653-1655)