Application of the Angular Analysis to the Solution of Indeterminate Problems of the Second Degree |
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Application of the Angular Analysis to the Solution of Indeterminate ... C. Gill No preview available - 2018 |
Application of the Angular Analysis to the Solution of Indeterminate ... Charles Gill No preview available - 2016 |
Common terms and phrases
2A COS 2B 2A sin 2B 2Au² 2B)+c² cos² 2B+ sin 2A 2R sin a(cos a(sin A)+cd(sin a² ƒ² by² c2 cos 2A cos 2A COS B COS cos B sin COS(A-B cos2 cosec cot 2B cot a cot cot B-1 cota equation becomes equation is x² equation of Prob equations x² Example expressed in rational find four numbers find three square given equations given number integers lower signs Math mp-nq mq+np number of angles plane triangle polygon positive numbers PROBLEM radius rational numbers roots sec 2A sin a cos sin a sin sin² Solution solve the equations substitution subtracting t{cos THEOREM three square numbers trigonometrical functions values whole numbers x² sin ²c y²+z² µ²
Popular passages
Page 15 - It is required to find three numbers in arithmetical progression, such, that the sum of every two of them may be a square.
Page 33 - Problems, the first of which finds "three square numbers, such that the sum of every two of them may be a square number;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths of the three lines from the angles to the middle of the opposite sides may be expressed by rational whole numbers ;
Page 17 - N-ab is a square number. 298. Find two integers such that if unity be added to each of them, as also to their sum and difference, the four results shall be squares. 299. If x = 1 +• n"1, shew that the sum of n terms of the series 1 + 2x + 3*
Page 52 - D may he assumed, so that the resulting values of v, w, x, &c., may be positive numbers ; but the complexity of the formulas do not encourage the attempt, and the object seems unworthy of the effort, which is one of mere labor.
Page 40 - To find three square numbers, such that the difference between twice the sum of any two of them and; the third, may be square numbers.
Page 22 - Find numbers, ad libitum, whose sum is a 4»th power, and such that, if the square of each be added to their sum, the several sums shall be all squares.
Page 11 - To find two square numbers, whose difference shall be equal to a given number (a = be).