## An Elementary Text-book on the Differential and Integral Calculus |

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### Contents

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### Common terms and phrases

absolutely convergent algebraic angle arbitrary assigned asymptote axis Calculus called chord circle circular sectors cone constant continuous function coordinates corresponding cusp cuts cylinder definite integral degree determinate difference-quotient differential equation dx dy dy dx elementary functions ellipse equal evaluated EXAMPLES Find the area Find the envelope formula geometrical Hence hyperbola independent variable infinite inflexion intersection interval limit mean value minimum values negative neighborhood normal one-valued ordinate origin parabola parallel parameter partial derivatives perpendicular point of contact polynomial primitive quadratic quotient radii radius of curvature rational rational function rectangle represented respect revolution revolving roots Show sin'x singular point singular solution slope solution Solve sphere straight line subinterval substitution surface symbol tangent plane theorem tion total derivative Trace the curve tractrix

### Popular passages

Page 411 - The order of a differential equation is the order of the highest derivative which occurs.

Page 163 - Cycloid is traced by a point on the circumference of a circle which rolls without slipping along a straight line.

Page 328 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.

Page 487 - So 4- 104 pp. $1.10. The Tables, which are to five places of decimals, are regularly supplied to the United States Military Academy and to Princeton University and Yale University for the entrance examinations.

Page 321 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.

Page 417 - Find the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact.

Page 239 - To find the locus of the foot of the perpendicular drawn from the origin to a tangent plane to any surface.

Page 415 - Determine the curve in which the polar subtangent is proportional to the length of the radius vector.

Page 177 - The limit of the sum of a finite number of functions is equal to the sum of their limits.

Page 362 - ... partly on one side, and partly on the other side of the principal railway, and that without reference to the title under which...