A History of Mathematics |
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Page xv
... proved to be useless . The chemist smiles at the childish efforts of alchemists , but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of to - day . He is ...
... proved to be useless . The chemist smiles at the childish efforts of alchemists , but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of to - day . He is ...
Page xvi
... proved in 1761 that the ratio of the circumference of a circle to its diameter is incom- mensurable . Some years ago , Lindemann demonstrated that this ratio is also transcendental and that the quadrature of the circle , by means of the ...
... proved in 1761 that the ratio of the circumference of a circle to its diameter is incom- mensurable . Some years ago , Lindemann demonstrated that this ratio is also transcendental and that the quadrature of the circle , by means of the ...
Page 12
... proved at all , but were known to be true merely from observation or as matters of fact . The second great defect was their inability to bring the numerous special cases under a more general view , and thereby to arrive at broader and ...
... proved at all , but were known to be true merely from observation or as matters of fact . The second great defect was their inability to bring the numerous special cases under a more general view , and thereby to arrive at broader and ...
Page 21
... proved by the Pythagoreans after the manner of Euclid . They demonstrated also that the plane about a point is completely filled by six equilateral triangles , four squares , or three regular hexagons , so that it is possible to divide ...
... proved by the Pythagoreans after the manner of Euclid . They demonstrated also that the plane about a point is completely filled by six equilateral triangles , four squares , or three regular hexagons , so that it is possible to divide ...
Page 27
... proving that if magnitudes are infinitely divisible , motion is impossible . Zeno argues that Achilles could not overtake a tortoise ; for while he hastened to the place where the tortoise had been when he started , the tortoise crept ...
... proving that if magnitudes are infinitely divisible , motion is impossible . Zeno argues that Achilles could not overtake a tortoise ; for while he hastened to the place where the tortoise had been when he started , the tortoise crept ...
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Common terms and phrases
Abel Abelian functions algebra Almagest analysis analytical angles Apollonius applied Arabic Archimedes arithmetic astronomical became Berlin Bernoulli born calculus Cauchy Cayley century circle Clebsch coefficients conic contains convergent Crelle's Journal cubic curve degree Descartes determine developed differential equations Diophantus Dirichlet discovery elasticity elliptic functions Euclid Euler Felix Klein Fermat fluxions fractions Gauss gave geometry given Göttingen Greek Hindoo important integrals invention investigated Jacobi John Bernoulli Lagrange Laplace later Legendre Leibniz linear lines logarithms mathe mathematicians mathematics matical mechanics memoir method motion Newton notation paper Paris partial differential equations plane Poincaré Poisson polygon principle problem professor proof published pupil Pythagoreans quadratic quadrature quantities quaternions researches Riemann Riemann's surfaces roots solution solved square surface Sylvester symbols synthetic synthetic geometry tangents theorem theory of functions theory of numbers theta-functions Thomson tion treatise triangle trigonometry University variable velocity Vieta Weierstrass writings wrote