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Page 172 - 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 231 - 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 21 - 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 69 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 35 - Give him threepence, since he must make gain out of what he learns.
Page 167 - 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 39 - The area of a triangle equals half the product of its base by its altitude.
Page 122 - 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 243 - 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.