“Proposition 2. If a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere.”

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

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Aristarchus of Samos16

ancient Greek astronomer and mathematician

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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)

“We deny the right of any portion of the species to decide for another portion what is and what is not their ‘proper sphere’. The proper sphere for all human beings is the largest and highest which they are able to attain to.”

Harriet Taylor Mill (1807–1858) British philosopher

Harriet Taylor Mill, The Enfranchisement of Women (1851)

“Thus it must be admitted that in the economic sphere, from the start, in all branches men are not of equal value or of equal importance. And once this is admitted it is madness to say: in the economic sphere there are undoubtedly differences in value, but that is not true in the political sphere. It is absurd to build up economic life on the conceptions of achievement, of the value of personality, and therefore in practice the authority of personality, but in the political sphere to deny the authority of personality and to thrust into this place the law of the greater number — democracy.”

Adolf Hitler (1889–1945) Führer and Reich Chancellor of Germany, Leader of the Nazi Party

Speech to the Industry Club (21 January 1932) as quoted in The Speeches of Adolf Hitler, April 1922 – August 1939 (1994) by Norman Hepburn Baynes, Oxford University Press, p.787
1930s

“A genius and an Apostle are qualitatively different, they are definitions which each belong in their own spheres: the sphere of immanence, and the sphere of transcendence.”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Source: 1840s, Two Ethical-Religious Minor Essays (1849), P. 90-91

“When it has been made a sphere, it continues a sphere.”

Marcus Aurelius book Meditations

VIII, 41
Meditations (c. 121–180 AD), Book VIII
Context: The things... which are proper to the understanding no other man is used to impede, for neither fire, nor iron, nor tyrant, nor abuse, touches it in any way. When it has been made a sphere, it continues a sphere.

“Proposition 11. The diameter of the moon is less than 2/45ths, but greater than 1/30th of the distance of the centre of the moon from our eye.”

Aristarchus of Samos ancient Greek astronomer and mathematician

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

“I propose to show that God, in creating the universe and arranging the spheres, had in view the five regular solids of geometry, and fixed by their dimensions the number, proportions and motions of the spheres. Take the sphere of the earth as a unit and circumscribe it with a regular dodecahedron. The sphere that contains this dodecahedron is the sphere of Mars.”

Johannes Kepler book Mysterium Cosmographicum

As Quoted in "The Discovery of Kepler's Laws," Scientific American: Supplement (Apr 29, 1911) Vol. 71, No. 1843, p. 278 https://books.google.com/books?id=ov4-AQAAMAAJ&pg=PA258. <br class="br">Mysterium Cosmographicum (1596)

“The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.”

Johannes Kepler book Mysterium Cosmographicum

Walter William Bryant, Kepler (1920), pp. 16–17
Mysterium Cosmographicum (1596)

“Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r2; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point—our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth's surface there is nothing beyond our own antipodes but there is no boundary there.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

p, 125
Space, Time and Gravitation (1920)

“And oft with holy hymns he charm'd their ears, And music more melodious than the spheres.”

John Dryden (1631–1700) English poet and playwright of the XVIIth century

“Proposition 2. If a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere.”

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