“Archimedes is said to have requested his friends and relatives to place upon his tomb a representation of a cylinder circumscribing a sphere within it, together with the inscription giving the ratio (3/2) which the cylinder bears to the sphere; from which we may infer that he himself regarded the discovery of this ration as his greatest achievement.”

p, 125
Achimedes (1920)

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Thomas Little Heath46

British civil servant and academic 1861–1940

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“Proposition 1. Two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or of the cone, touches the spheres.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“Eudoxus was perhaps the greatest of all Archimedes's predecessors, and it is his achievements, especially the discovery of the method of exhaustion, which interest us in connexion with Archimedes.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
Achimedes (1920)

“The Sphere would willingly have continued his lessons by indoctrinating me in the conformation of all regular Solids, Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I ventured to interrupt him. Not that I was wearied of knowledge. On the contrary, I thirsted for yet deeper and fuller draughts than he was offering to me.”

Edwin Abbott Abbott book Flatland

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 19. How, Though the Sphere Showed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It

“Real greatness has nothing to do with a man’s sphere. It does not lie in the magnitude of his outward agency, in the extent of the effects which he produces. The greatest men may do comparatively little.”

William Ellery Channing (1780–1842) United States Unitarian clergyman

Source: Self-Culture (1838)

“The Earth is cylindrical, three times as wide as it is deep, and only the upper part is inhabited. But this Earth is isolated in space, and the sky is a complete sphere in the center of which is located, unsupported, our cylinder, the Earth, situated at an equal distance from all the points of the sky.”

Anaximander (-610–-547 BC) pre-Socratic Greek philosopher

As quoted in "Science Attests the Accuracy of the Bible" in The Watchtower (1 October 1980)

“Treat nature in terms of the cylinder, the sphere, and the cone, the whole put into perspective so that each side of an object, or of a plane, leads towards a central point. Lines parallel to the horizon give breadth, whether a sections of nature, or, if you prefer, of the spectacle which Pater omnipotens aeterne Deus unfolds before your eyes. Lines perpendicular to this horizon give depth... Everything I am telling you [ Joachim Gasquet ] about - the sphere, the cone, cylinder, concave shadow – on mornings when I'm tired these notions of mine get me going, they stimulate me, I soon forget them once I start using my eyes.”

Paul Cézanne (1839–1906) French painter

Source: Quotes of Paul Cezanne, after 1900, Cézanne, - a Memoir with Conversations, (1897 - 1906), pp. 163-164, in: 'What he told me – I. The motif'

“We voluntaryists believe that no true progress can be made until we frankly recognize the great truth that every individual, who lives within the sphere of his own rights, as a self-owner, and has not himself first aggressed upon others by employing force or fraud in his dealings with them [and thus deprived himself of his own rights of self-ownership by aggressing upon these same rights of others], is the only one true owner of his own faculties, and his own property.”

Auberon Herbert (1838–1906) British politician

The Principles of Voluntaryism and Free Life

“No man is liberated from fear who dare not see his place in the world as it is; no man can achieve the greatness of which he is capable until he has allowed himself to see his own littleness.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Dreams and Facts (1919)
1910s

“Cézanne made a cylinder out of a bottle. I start from the cylinder to create a special kind of individual object. I make a bottle — a particular bottle — out of a cylinder.”

Juan Gris (1887–1927) Spanish painter and sculptor

Response to questionnaire circulated to the Cubists by Amédée Ozenfant and Le Corbusier, editors of L'Esprit Nouveau # 5 (February 1921), pp. 533-534; trans. Douglas Cooper in Daniel-Henry Kahnweiler, Juan Gris, His Life and Work (1947)

“Eudoxes… not only based the method [of exhaustion] on rigorous demonstration… but he actually applied the method to find the volumes (1) of any pyramid, (2) of the cone, proving (1) that any pyramid is one third part of the prism which has the same base and equal height, and (2) that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them (which no doubt means, not that he gave no sort of proof, but that he was not able to establish the propositions by the rigorous methods of Eudoxes. Archimedes adds that we must give no small share of the credit for these theorems to Democritus… another testimony to the marvellous powers, in mathematics as well as in other subjects, of the great man who, in the words of Aristotle, "seems to have thought of everything"…. Democritus wrote on irrationals; he is also said to have discussed the question of two parallel sections of a cone (which were evidently supposed to be indefinitely close together), asking whether we are to regard them as equal or unequal… Democritus was already close on the track of infinitesimals.”

Thomas Little Heath (1861–1940) British civil servant and academic

Achimedes (1920)

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Thomas Little Heath46

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