An Elementary Treatise on the Calculus: With Illustrations from Geometry, Mechanics and Physics |
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Common terms and phrases
a₁ abscissa absolutely convergent algebraically angle approximation arc PQ argument asymptote ax+b axes axis calculation called centre chord circle conic constant continuous function coordinates corresponding cosines curvature curve definite number denote derivative ellipse equal example EXERCISES expression finite function f(x geometrical given gradient graph greater Hence hyperbola increases increment independent variable infinite infinitesimal integral curve integrand inverse function latus rectum limit magnitude Mean Value Theorem notation ordinate parabola parallel perpendicular plane point moves polar polar coordinates positive integer positive number positive or negative proper fraction prove radius ratio represents respect root straight line student suppose surface symmetry tangent Taylor's Theorem theorem turning value value of f(x varies volume x-axis x₁ y₁ zero ди ди др дх
Popular passages
Page 47 - A parabola is a curve which, is the locus of a point that moves in a plane so that its distance from a fixed point in the plane is always equal to its distance from a fixed line in the plane.
Page 369 - Cycloid is traced by a point on the circumference of a circle which rolls without slipping along a straight line.
Page 179 - The lower corner of a leaf, whose width is a, is folded over so as just to reach the inner edge of the page : find the width of the part folded over when...
Page 81 - The limit of the quotient of two functions is equal to the quotient of their limits, provided the limit of the denominator is not 0.
Page 348 - If an arc of a plane curve revolve about an axis in its plane, not intersecting it, the surface generated is equal to the length of the arc multiplied by the length of the path of its mean centre.
Page 179 - From a given circular sheet of metal it is required to cut out a sector so that the remainder can be formed into a conical vessel of maximum capacity ; prove that the angle of the sector removed must be about 66°.
Page 177 - Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is -»- cm.
Page 14 - A variable y is said to be a function of another variable x, if, when x is given, y is determined.
Page 178 - ... wall. 25. At what distance above the centre of a circle of radius a must an electric light be placed in order that the brightness at the circumference of the circle may be the greatest possible ? (Assume that the brightness of a small surface A varies inversely as the square of the distance r from a source of light, and directly as the cosine of the angle between r and the normal to the surface at A.) (Gibson's Calculus.) 78. Points of inflexion: rectangular coordinates. As a point moves along...
Page 178 - The stiffness of a rectangular beam varies as the product of the breadth and the cube of the depth. Find the...