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 condition constant corresponding deduce definition degree denote derive determine divided dividend divisor equal equivalent exactly divisible example EXERCISES expressed factor factorisation Find the coefficient Find the number finite geometric 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 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 272 - Find the external radius of the single bowl (the volume of a sphere is proportional to the cube of its radius).
Page 260 - 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 119 - 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. From...
Page 265 - ... 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 201 - Confining ourselves to the case of integral functions of a single variable x, let us investigate what are the essential factors of every common multiple of two given integral functions A and B. Let G be the GCM of A and...
Page 121 - 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 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 327 - A farmer bought some sheep for £72, and found that if he had received 6 more for the same money, he would have paid £1 less for each. How many sheep did he buy ? 13. A and B distribute £60 each among a certain number of persons : A relieves 40 persons more than B does, and B gives to each 5*.
Page 271 - ... threepenny tickets for the whole journey it loses 10 per cent. It then divides the route into two parts, selling twopenny tickets for each part, thereby gaining 4 per cent, and selling 3300 tickets every week. How many persons used the cars weekly under the old system ? 12. The price of a passenger's ticket on a French railway is proportional to the distance he travels ; he is allowed 25 kilograms of luggage free, but on every kilogram beyond this amount he is charged a sum proportional to the...
Page 357 - We have already seen (§ 58) that the graph for this equation is a straight line passing through the origin. The graph will run to an infinite distance in the first and third quadrants, or in the second and fourth quadrants, according as a is positive or negative. It should be observed that in passing through its zero, which corresponds to...