Concept
Geometry
Overview
branch of mathematics regarding geometric figures and properties of space
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Geometry is discussed.
The distinctive mark of the spaces represented by both is that, like the surface of a sphere, they are finite but unbounded. The reduction of metrical to projective properties, as will be proved hereafter, has only a technical importance; at the same time, projective Geometry is able to deal directly with those purely descriptive or qualitative properties of space which are common to Euclid and Metageometry alike…
Bertrand Russell, An essay on the foundations of geometry
names the idea; states what it is; the book is about it
Then, by certain speculative and "play" impulses, there arose elementary arithmetical problems which began to be of interest in themselves. Geometry here also comes into consideration, and, in connection with positional number symbols, begin those interactions between arithmetic and geometry that result in the forms of our contemporary mathematics. The complex quantities represented by number symbols are no longer…
John Dewey, Creative Intelligence
names the idea; a chapter is titled for it; states what it is; opens on it
_Relatively to geometry_, we must remark that the equations are as yet adapted to represent only entire geometrical loci, and not at all determinate portions of those loci. It would, however, be necessary, in some circumstances, to be able to express analytically a part of a line or of a surface, or even a _discontinuous_ line or surface, composed of a series of sections belonging to distinct geometrical figures…
Auguste Comte, The philosophy of mathematics
names the idea; a chapter is titled for it; states what it is; opens on it
The geometer takes any set of axioms that seem interesting, and deduces their consequences. What defines Geometry, in this sense, is that the axioms must give rise to a series of more than one dimension. And it is thus that Geometry becomes a department in the study of order.
Bertrand Russell, Mysticism and Logic and Other Essays
names the idea; states what it is; opens on it
If we deny the relation between the practically-rigid body and geometry, we shall indeed not easily free ourselves from the convention that Euclidean geometry is to be retained as the simplest. Why is the equivalence of the practically-rigid body and the body of geometry--which suggests itself so readily--denied by Poincare and other investigators?
Albert Einstein, Sidelights on Relativity
names the idea; a chapter is titled for it; states what it is; opens on it
Philosophers who discussed Geometry
- Anaximander
- Ernest Nagel
- Xenocrates
- Ammonius Hermiae
- Nicolas Malebranche
- Simone Weil
- Alcmaeon of Croton
- Plato
- Philip K. Dick
- Protagoras
- Archytas
- William Kingdon Clifford
- Aristippus
- René Descartes
- Al-Kindi
- Pavel Florensky
- Thomas Hobbes
- Thales of Miletus
- The School of Athens
- Gottlob Frege
- Melissus of Samos
- Rudolf Carnap
- Alfred Tarski
- Charles Sanders Peirce
Related ideas
- Force
- Book of Optics
- General relativity
- Golden ratio
- Springer Science+Business Media
- Ancient Greek mathematics
- Johannes Kepler
- Ibn al-Haytham
- Method of exhaustion
- Latin
- Leonardo da Vinci
- University of St Andrews
- Archimedes
- Indian mathematics
- Algebra
- Mathematics
- Middle Ages
- Group (mathematics)
- Classical mechanics
- Mechanics
- Mesopotamia
- Velocity
- Real number
- Manifold
Opposing perspectives
Place in the tradition
Part of Analytic philosophy.