„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 photo
Hans Reichenbach
1891 - 1953
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Giuseppe Peano photo

„Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.“

—  Giuseppe Peano Italian mathematician 1858 - 1932
Geometric Calculus (1895) as translated by Lloyd C. Kannenberg (2000) "The Operations of Deductive Logic'" Ch. 1 "Geometric Formations"

Shiing-Shen Chern photo
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Donald Judd photo

„The main virtue of geometric shapes is that they aren't organic, as all art otherwise is. A form that's neither geometric or organic would be a great discovery.“

—  Donald Judd artist 1928 - 1994
Donald Judd (1967), quoted in: Alexander Alberro, ‎Blake Stimson (1999) Conceptual Art: A Critical Anthology. p. 204

Martin Gardner photo

„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

Albrecht Dürer photo

„Whoever … proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.“

—  Albrecht Dürer German painter, printmaker, mathematician, and theorist 1471 - 1528
Vier Bücher von menschlicher Proportion (1528).

Isaac Newton photo

„But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one.“

—  Isaac Newton British physicist and mathematician and founder of modern classical physics 1643 - 1727
Context: The Antients, as we learn from Pappus, in vain endeavour'd at the Trisection of an Angle, and the finding out of two mean Proportionals by a right line and a Circle. Afterwards they began to consider the Properties of several other Lines. as the Conchoid, the Cissoid, and the Conick Sections, and by some of these to solve these Problems. At length, having more throughly examin'd the Matter, and the Conick Sections being receiv'd into Geometry, they distinguish'd Problems into three Kinds: viz. (1.) Into Plane ones, which deriving their Original from Lines on a Plane, may be solv'd by a right Line and a Circle; (2.) Into Solid ones, which were solved by Lines deriving their Original from the Consideration of a Solid, that is, of a Cone; (3.) And Linear ones, to the Solution of which were requir'd Lines more compounded. And according to this Distinction, we are not to solve solid Problems by other Lines than the Conick Sections; especially if no other Lines but right ones, a Circle, and the Conick Sections, must be receiv'd into Geometry. But the Moderns advancing yet much farther, have receiv'd into Geometry all Lines that can be express'd by Æquations, and have distinguish'd, according to the Dimensions of the Æquations, those Lines into Kinds; and have made it a Law, that you are not to construct a Problem by a Line of a superior Kind, that may be constructed by one of an inferior one. In the Contemplation of Lines, and finding out their Properties, I like their Distinction of them into Kinds, according to the Dimensions thy Æquations by which they are defin'd. But it is not the Æquation, but the Description that makes the Curve to be a Geometrical one.<!--pp.227-228

Isaac Newton photo

„Geometrical Speculations have just as much Elegancy as Simplicity, and deserve just so much praise as they can promise Use.“

—  Isaac Newton British physicist and mathematician and founder of modern classical physics 1643 - 1727
Context: Geometrical Speculations have just as much Elegancy as Simplicity, and deserve just so much praise as they can promise Use.<!--p.232

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