Practical Treatise on the Differential and Integral Calculus: With Some of Its Applications to Mechanics and Astronomy |
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Common terms and phrases
abscissa algebraic sum altitude angle Applying Arithmetic Assume the equation ax² binomial binomial formula body bx² Calculus centre of gravity co-ordinates constant cosx curvature curve whose equation cycloid cylinder d³y Davies day dx2 denoted distance dx² dy dx dy² ellipse equal EXAMPLES exponent expression factor find the maximum Find the value fractions Hence hyperbola infinitely small infinitesimal Integrating by Formula Let dy limits logarithm Mathematics MAXIMA AND MINIMA method minimum moment of inertia multiplying negative ordinate parabola partial fractions Peck's perpendicular plane point of inflexion quantity radius vector reducing result revolution second differential coefficient sinx sphere Substituting successive differential coefficients surface surface of revolution tangent tanx tion triangle trigonometry value of dy velocity versin vertex volume whence whole number
Popular passages
Page 17 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 9 - ... is equal to, the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by the square of the denominator.
Page 206 - practical," because the author believes the Theory cannot be studied with advantage until the pupil has acquired a certain facility in combining numbers, which can only be had by practice. 3. Peck's Complete Arithmetic, The whole subject— theory and practice— presented within very moderate limits. This author's most remarkable faculty of mathematical treatment is comprehended in three words : System, Conciseness, Lucidity. The directness and simplicity of this work cannot be...
Page 186 - In other words, if a point move in a curve, whether with a uniform or a varying velocity, its change of direction is to be regarded as constituting an acceleration towards the centre of curvature, equal in amount to the square of the velocity divided by the radius of curvature. The whole acceleration will, in every case, be the resultant of the acceleration, thus measuring change of direction, and the acceleration of * actual velocity along the curve.
Page 204 - Many of the series of to-day, built upon a similar basis, and described as "modern books," are destined to a similar fate ; while the most far-seeing eye will find it difficult to fix the time, on the basis of any data afforded by their past history; when these...
Page 208 - These are crowded with interesting matter that is not strictly a part of history proper. They may be learned or not, at pleasure. They are certain in any event to be read. 9.
Page 207 - Peck's Manual of Algebra. Bringing the methods of Bourdon within the range of the Academic Course. Peck's Manual of Geometry. By a method purely practical, and unembarrassed by the details which rather confuse than simplify science. Peck's Practical Calculus. Peck's Analytical Geometry. Peck's Elementary Mechanics. Peck's Mechanics, with Calculus. The briefest treatises on these subjects now published. Adopted by the great Universities : Yale, Harvard, Columbia, Princeton, Cornell, &c.