“… spread on a plane the surface of a sphere in such a way that the positions of all places shall correspond on all sides with each other both in so far as true direction and distance are concerned and as concerns true longitudes and latitudes.”

Legend on 1569 map

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Gerardus Mercator3

cartographer, philosopher and mathematician 1512–1594

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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…”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

“Nothing makes the earth seem so spacious as to have friends at a distance; they make the latitudes and longitudes.”

Henry David Thoreau (1817–1862) 1817-1862 American poet, essayist, naturalist, and abolitionist

“The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes…. but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“All you have to do is put all other concerns aside and your fondest desire will come true. Unfortunately, 'all other concerns' includes your health, financial well-being, interpersonal relationships, and often any inkling of why you had this desire in the first place. Good luck!”

Jack Terricloth (1970)

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“In war, theory is all right so far as general principles are concerned; but in reducing general principles to practice there will always be danger. Theory and practice are the axis about which the sphere of accomplishment revolves.”

Napoleon I of France (1769–1821) French general, First Consul and later Emperor of the French

Napoleon : In His Own Words (1916)

“Allow me to repeat what I said when you were here: deal with nature by means of the cylinder, the sphere and the cone, all placed in perspective, so that each side of an object or a plane is directed towards a central point. Lines parallel to the horizon give breadth, a section of nature, or if you prefer, of the spectacle spread before our eyes by the 'Pater Omnipotens Aeterne Deus'. Lines perpendicular to that horizon give depth. But for us men, nature has more depth than surface, hence the need to introduce in our vibrations of light, represented by reds and yellows, enough blue tints to give a feeling of air.”

Paul Cézanne (1839–1906) French painter

Quote from Cézanne's letter to Émile Bernard, 15 April 1904; as quoted in Letters of the great artists – from Blake to Pollock, Richard Friedenthal, Thames and Hudson, London, 1963, p. 180
Quotes of Paul Cezanne, after 1900

“…the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i. e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. …such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“As far as the surface is concerned – oil on canvas, conventionally applied – my pictures have little to do with the original photograph. They are totally painting (whatever that may mean). On the other hand, they are so like the photograph that the thing that distinguished the photograph from all other pictures remains intact.”

Gerhard Richter (1932) German visual artist, born 1932

Notes, 1964-65; as cited on collected quotes on the website of Gerhard Richter: on 'Photo-paintings' https://www.gerhard-richter.com/en/quotes/subjects-2/photo-paintings-12 <br class="br">1960's

“… two thirds of all sorrow is homemade and, so far as the universe is concerned, unnecessary.”

Aldous Huxley book Island

Source: Island

“So far as the religion of the day is concerned, it is a damned fake … Religion is all bunk.”

Thomas Edison (1847–1931) American inventor and businessman

As quoted in What on Earth is an Atheist! (1972) by Madalyn Murray O'Hair, p. 251.
Date unknown

“… spread on a plane the surface of a sphere in such a way that the positions of all places shall correspond on all sides with each other both in so far as true direction and distance are concerned and as concerns true longitudes and latitudes.”

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Gerardus Mercator3

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