A Treatise on the Differential and Integral Calculus: And on the Calculus of Variations |
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asymptote axis b²x² binomial theorem circle constant cosec coversin d²u d2u d2u d2u dx2 d³u d³u d³y determine differential coefficients dp dx dq dx du du dx dx dx dy dy dx dz dx² dx2 dy2 dx³ dxdy dy dz dz dx dz dy dz dz equal equation exponent expression F(x+h F₁x F₂x formula fraction function Hence increment h independent variable indeterminate form integrate intersect lines of curvature logarithms Maclaurin's maximum or minimum negative numerator obtain P₁ parabola plane curve power of h Prop quantities R₁ radius of curvature reduce to zero respect result rule for differentiating sec²x second differential coefficient sin x substitution subtan supposed surface tangent Taylor's Theorem u₁ u₂ versin x₁ y₁ Φια
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Page v - Brooklyn, NY* Mr. Courtenay was a mathematician of noble gifts and a great teacher. " His mind was quick, clear, accurate, and discriminating in its apprehensions, rapid and certain in its reasoning processes, and far-reaching and profound in its general views. It was admirably adapted both to acquire and use knowledge."t He was modest and unassuming in his manner, even to diffidence. He would never utter a harsh word to pupils or disparage their efforts. " His pleasant smile and kind voice, when...
Page 168 - At this point it may not be out of place to observe that an epicycloidal curve is a curve generated by the motion of a point on the circumference of a circle which rolls upon the convex side of a fixed circle...
Page 225 - Line. — The equation is (Art. 28), y = mx + b. (1) 1°. Let x = 0, then y = b. These are the coordinates of a point on the axis of y at a distance b from the origin. It is the point where the line intersects the axis of y, and the ordinate to this point is the intercept on that axis, (Art. 24). 2°.
Page 354 - ... each of which is therefore only a repetition of the first supposed complete primitive. Certain cases in which the equation Mdx + Ndy = 0 admits of finite solution. 4. The equation Mdx + Ndy = 0 can always be solved when the variables in M and N admit of being separated; ie when the equation can be reduced to the form Xdx + Ydy = 0 (8), in which X is a function of x alone, and Y a function of y alone.
Page 298 - B ^ sin A sin B cos A cos B = -[cos (A + B) + cos (A - B)] sin A sin B = -[cos (A - B) - cos (A + B)] sin A cos B...
Page 349 - Ndy = 0. A polynomial in x and y is said to be homogeneous when the sum of the exponents of those letters in each term is the same. Thus cu?
Page 61 - ... &c. But, according to the preceding Theorem, the terms involving the same powers of a; in the two members of the equation must be equal to each other. Therefore, A= 1, A+B = -1; hence B = -2. B+C= 0; " C = +2. C+D= 0;
Page iii - ... the mathematical chair was Edward H. Courtenay, from 1842 to 1853. He was the first regular occupant of this chair who was educated in this country. He was born in Baltimore, in 1803. After having been examined for admission to the US Military Academy at West Point, in 1818, the examiner remarked: " A boy from Baltimore, of spare frame, light complexion, and light hair, would certainly take the first place in his class.
Page 246 - ... where r. is a coefficient of torsion depending on the nature of the fibre. To determine A¿, the angle between the axis of x and the projection of the line of collimation on the plane of xz, fix the stirrup so that y is vertical and upwards, z to the north and x to the west, and observe the azimuth ¿ of the line of collimation. Then remove the magnet, turn it through an angle IT about the axis of z and replace it in this inverted position, and observe...
Page ii - Office of the District Court of th« United States, for the Southern District of New York.