„We can… treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.“

—  Hans Reichenbach, The Philosophy of Space and Time (1928, tr. 1957)
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Hans Reichenbach
professor académico alemão 1891 - 1953
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„In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.“

—  Martin Gardner recreational mathematician and philosopher 1914 - 2010
"Mathematical Games", in Scientific American (October 1973); also quoted in Roger B. Nelson, Proofs Without Words: Exercises in Visual Thinking (1993), "Introduction", p. v

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„The Circle is a Geometrical Line, not because it may be express'd by an Æquation, but because its Description is a Postulate. It is not the Simplicity of the Æquation, but the Easiness of the Description, which is to determine the Choice of our Lines for the Construction of Problems.“

—  Isaac Newton, Arithmetica Universalis
Arithmetica Universalis (1707), Context: The Circle is a Geometrical Line, not because it may be express'd by an Æquation, but because its Description is a Postulate. It is not the Simplicity of the Æquation, but the Easiness of the Description, which is to determine the Choice of our Lines for the Construction of Problems. For the Æquation that expresses a Parabola, is more simple than That that expresses a Circle, and yet the Circle, by reason of its more simple Construction, is admitted before it. The Circle and the Conick Sections, if you regard the Dimension of the Æquations, are of the fame Order, and yet the Circle is not number'd with them in the Construction of Problems, but by reason of its simple Description, is depressed to a lower Order, viz. that of a right Line; so that it is not improper to express that by a Circle that may be expressed by a right Line. But it is a Fault to construct that by the Conick Sections which may be constructed by a Circle. Either therefore you must take your Law and Rule from the Dimensions of Æquations as observ'd in a Circle, and so take away the Distinction between Plane and Solid Problems; or else you must grant, that that Law is not so strictly to be observ'd in Lines of superior Kinds, but that some, by reason of their more simple Description, may be preferr'd to others of the same Order, and may be number'd with Lines of inferior Orders in the Construction of Problems.<!--p.228

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