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Elements of the Differential Calculus: With Examples and Applications, Volum 25
William Elwood Byerly
Uten tilgangsbegrensning - 1888
actual algebraic angle approaches approaches zero assumes axis becomes body called centre chord circle consider constant coördinates corresponding increments course curvature curve cycloid decreases definite derivative determine developed difference differential distance dividing easily equal equation evidently evolute EXAMPLES expression falling feet figure finite fixed formulas fraction function geometry give given given point greater hence higher order increases indefinitely increment independent variable indicated infinite infinitesimal instant integral length less limit maximum mean method moving multiplied nature negative normal notation obtained obviously parabola passing period plane polygon positive problems Prove quantity question radius ratio rectangle regard relation represent respect result seen Show sides sinx Substituting Suppose surface Take tangent Theorem tion true value variable velocity whole zero
Side 167 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Side 190 - Ja; = 0 185. We can now take up some new problems that could not be conveniently approached while the integral was treated merely as an inverse function, and we shall consider very briefly one connected with the subject of centre of gravity. The centre of gravity of a body is a point so situated that the body will remain motionless in any position in which it may be placed, provided this point is supported.
Side 252 - i a, the curves are said to have contact of the nth order at the point whose abscissa is a. Contact of a higher order than the first is called osculation. 238. The difference between the ordinates of points of the two curves having the same abscissa and infinitely near the point of contact, is an infinitesimal of an order one higher than the order of contact of the curves. Let x = o + Ja;, and y 2 y, =fa + Jxf'a + ~21 ; F"a + ..... 11...
Side 167 - If two right-angled triangles have the hypothenuse and a side of the one equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Side 260 - The book, in my opinion, is a model Algebra, distinguished for its clearness of explanation and the eminently practical nature of its matter. JC Glashan, Inspector of Public Schools, Ottawa, Canada : I am satisfied I can unqualifiedly recommend it. Henry Bay Warner, Prof. of Mathematics, Ml.