## A History of Elementary Mathematics |

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abacus Abel Abelian functions algebra Almagest analysis analytical angles Apollonius applied Arabic Archimedes arithmetic astronomical became Berlin Bernoulli Boethius born calculus called Cauchy Cayley century circle Clebsch coefficients conic sections contains convergent Crelle's Journal cubic curve degree Descartes determine developed differential equations Diophantus discovery Egyptian elliptic functions equal Euclid Euler expressed Fermat fluxions formula fractions Gauss gave geometry given gives Greek Hindoo important integral invention investigations Jacobi John Bernoulli known Lagrange Laplace later Legendre Leibniz linear lines logarithms mathe mathematicians mathematics matical maxima and minima mechanics memoir method motion Newton notation paper Pappus Paris plane polygon principle problem professor progress proof published pupil Pythagoreans quadratic quadrature quantities ratio researches Riemann roots sexagesimal solution solved spherical square surface Sylvester symbol synthetic geometry tangents theorem theory of numbers theta-functions tion treatise triangle trigonometry variable velocity Vieta Wallis writings wrote

### Popular passages

Page 222 - QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY TO EQUALITY, AND BEFORE THE END OF THAT TIME APPROACH NEARER THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL.

Page 310 - THEOREM. If a straight line falling on two other straight lines, make the exterior angle equal to the interior and opposite...

Page 285 - M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator.

Page 25 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 104 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.

Page 41 - Give him threepence, since he must make gain out of what he learns.

Page 217 - I consider mathematical quantities in this place not as consisting of very small parts, but as described by a continued motion. Lines are described, and thereby generated, not by the apposition of parts, but by the continued motion of points...

Page 45 - The area of a triangle equals half the product of its base by its altitude.

Page 172 - He spoke of imaginary quantities ; inferred by induction that every equation has as many roots as there are units in the number expressing its degree ; and first showed how to express the sums of their powers in terms of the coefficients.

Page 297 - Euler) and discovered between the theory of surfaces and the integration of partial differential equations, a hidden relation which threw new light upon both subjects. He gave the differential of curves of curvature, established a general theory of curvature, and applied it to the ellipsoid.