Introduction to Algebra: For the Use of Secondary Schools and Technical Colleges |
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a+b+c algebraic quantity algebraic sum approximation arithmetical ax² beginner bracket calculation co-ordinates commensurable common constant corresponding deduce definition degree denote derive determine divided dividend divisor equal equivalent exactly divisible example EXERCISES expressed factorisation factors Find the coefficient Find the number finite given graph Hence identity infinity integer integral equation integral function law of association law of distribution laws of Algebra linear equation means monomial multiplying negative nth root obviously operands operations partial fractions partial products permutations positive integers positive quantity problem proper fraction proportion quadratic quadratic function quadratic surds quotient radicand rational function reduced remainder respectively result Show sides solution straight line subtraction suppose symmetric theorem tion triangle variables whence x-axis x²+1 x²+x+1
Popular passages
Page 262 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 209 - The product of two or more fractions produces a fraction whose numerator is the product of the numerators of the given fractions and whose denominator is the product of the denominators of the given fractions.
Page 121 - AC.BD, etc., absolute areas. § 90. The fundamental theorem in the mensuration of plane areas is the proposition that the area of any parallelogram is equal to the area of a rectangle contained by its base and its altitude ; or the proposition, immediately derivable therefrom, that the area of a triangle is equal to half the area of the rectangle contained by its base and its altitude. If, therefore, a denote the base and h the altitude of a triangle, the symbolic expression for its area is ^ah....
Page 97 - ... equations in two variables x and, y is in general inconsistent. This is merely a particular case of the general principle that we cannot in general determine two variables so as to satisfy more than two independent conditions. In the particular case of a linear system, say — ax + by + c = 0, a'x + b'y + c = 0, a"x + b"y + c
Page 267 - ... 12. Insert four mean proportionals between 6 and 192. 13. Given the third and fifth of a series of quantities in continued proportion, find the first and fourth of the series. 14. Find two numbers such that their sum, their difference, and the sum of their squares are in the ratio 5 : 3 : 51.
Page 366 - FIG. 3-10. is positive when x is positive, and negative when x is negative.
Page 123 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 327 - The bill of a party at a restaurant was £10 ; but three of the party were unable to pay. The rest divided the bill equally among them, and each had 3s. 4d. more than his proper share to pay. How many were there in the party ? 12. A grazier bought a certain number of oxen for £240. After losing 3 he sold the remainder for £8 a head more than they cost him, thus gaining £59 by his bargain. How many oxen did he buy ? 13. A merchant bought a number of barrels of herrings for £15. Twenty were lost...
Page x - In mathematics he was greater Than Tycho Brahe, or Erra Pater: For he, by geometric scale, Could take the size of pots of ale; Resolve, by sines and tangents straight, If bread or butter wanted weight; And wisely tell what hour o' th' day The clock doth strike, by Algebra.
Page 82 - ... for division amongst the holders of the rest of the stock, being a dividend at the rate of 4 per cent per annum. Find the capital and the receipts.