„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.“

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

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Aristarchus of Samos photo
Aristarchus of Samos16
ancient Greek astronomer and mathematician

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„Proposition 8. When the sun is totally eclipsed, the sun and the moon are then comprehended by one and the same cone which has its vertex at our eye.“

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

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„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 Danish philosopher and theologian, founder of Existentialism 1813 - 1855

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

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„Distance in a straight line has no mystery. The mystery is in the sphere.“

—  Thomas Mann German novelist, and 1929 Nobel Prize laureate 1875 - 1955

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

—  Marcus Aurelius, book Meditations

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„In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere“

—  Carl Friedrich Gauss German mathematician and physical scientist 1777 - 1855

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)
Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.

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„Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius.
Such an ellipse will be formed in our present case…“

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„If two right lines cut one another, they will form the angles at the vertex equal.“

—  Proclus Greek philosopher 412 - 485

...
This... is what the the present theorem evinces, that when two right lines mutually cut each other, the vertical angles are equal. And it was first invented according to Eudemus by Thales...
Proposition XV. Thereom VIII.

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„The centre and the radius of this auxiliary sphere are here quite arbitrary.“

—  Carl Friedrich Gauss German mathematician and physical scientist 1777 - 1855

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)
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„Too much has already been said and written about "women's sphere". Leave women, then, to find their sphere.“

—  Lucy Stone American abolitionist and suffragist 1818 - 1893

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„One of the commonest perversions of love is to limit it to the private sphere.“

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—  Thomas Moore Irish poet, singer and songwriter 1779 - 1852

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