A Complete Course of Pure Mathematics, Volume 2W. P. Grant, 1830 - Mathematics |
Common terms and phrases
1st order 1st term 2nd degree 2nd order 2nd side angle arbitrary assume axis becomes binomial calculation CHIG co-ordinates coefficients consequently constant contain continued fraction convergents cosine curve cycloid deduce denominator denoting derivative determine differential differential calculus divided divisor dx² eliminating equa exact differential example exponent expression factor x factors formula function given gives Hence hyperbola imaginary integer integral lastly letters limits logarithms manner multiplying negative obtain osculating circle perpendicular plane polynomial positive preceding proposed equation quantity quotient radius reduced render roots Similarly singular solution straight line substitute Suppose surface tangent Taylor's theorem theorem tion transformed equation triangle UNIV values variable whence whilst
Popular passages
Page 185 - In every spherical triangle the sines of the angles are proportional to the sines of the opposite sides.
Page 184 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 237 - The derivative of a quotient is equal to the denominator multiplied by the derivative of the numerator minus the numerator multiplied by the derivative of the denominator, all divided by the square of the denominator.
Page 185 - sin В sin C' sin С sin A cos a = cos b cos с + sin 6 sin с cos A, with similar formulae for cos b and cos c. cos A = — cos В cos С + sin В sin С cos a, with similar formulae for cos В and cos C.
Page 182 - ... be so applied to each other as to coincide throughout. The sides and angles of a figure are in such intimate and dependent relation, that from the equality of some of them we may infer the equality of the rest. For example, if of two triangles we know that three parts are mutually equal — either the three sides, or two sides and the included angle, or two sides and the angle which is opposite the greater of the two, or two angles and the included side — then may we conclude from this that...
Page 314 - What is the tangent of the angle made with the axis of x by the perpendicular from the origin on 3z — '2y — 6 = 0?
Page 303 - R is equal to the cube of the normal divided by the square of the semiparameter, R= _ ___ ?, since N = 2/w sec w.
Page 325 - R -\-r; consequently, the value of a is the tangent of the angle made with the axis of x by the tangent drawn from the centre B to the circle described from A with radios R — r, or R + r.
Page 89 - ... may be expressed by an independent equation ; that is, an equation not produced by any combination of the others of the system. If, on the contrary, the number of independent equations exceeds the number of unknown quantities involved in them, the conditions which they express cannot be fulfilled. For example, let it be required to find two numbers such that their sum shall be 100, their difference 80, and their product 700. The equations expressing these conditions are, x— y= 80 and Now, the...
Page 323 - Q*', s'R, is [N°. 753] the quotient of its base ]>(}]{$ divided by the cosine of the angle which it makes with the plane .TJ/, vi/.