Notes on algebra1885 |
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1)th term 3a²b a₂x abc2 algebraical definition arithmetical equality ay bx bz b₂ b² 4ac b₂c₁ b₂c₂ b₂c3 b₂y BINOMIAL THEOREM bracket c₂d coefficient cube root cubic equation d₁ d₂ degree divide both sides divisor equation ax² equations involving expression factors find the value Formula fraction ƒ q Hence incommensurable irrational letter multiply negative nth term number of Permutations positive integer Process proved quadratic equation quotient reciprocal equation Rule of Signs second term shew signs simple equation simultaneous equations Simultaneous Simple Solve the equations square root SURds symmetry take the equations theoretically Theory of Indices things taken three equations three unknown quantities UPPINGHAM SCHOOL xy³ zero
Popular passages
Page 74 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 74 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Page 25 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal.
Page 74 - Four quantities are said to be proportionals, when the first is the same multiple, part, or parts, of the second, that the third is of the fourth.
Page 41 - The sum of the roots of a quadratic equation in x is equal to the coefficient of x with its sign changed, divided by the coefficient ofx2.
Page 83 - The coefficient of the first term is unity ; the coefficient of the second term is the sum of the second terms of the binomial factors; the coefficient of the third term is the sum of the products of the second terms of the binomial factors taken two...
Page 74 - ... while the multiple of the first is equal to that of the second, the multiple of the third is less than that of the fourth. A proportion may consist of three or four terms (Defs. 8, 9, 10); 'corresponding' or 'homologous' terms are antecedents in relation to antecedents and consequents in relation to consequents (11).
Page 64 - Multiply both numerator and denominator of the fraction by such a quantity as will, make the denominator a perfect power of the same degree as the radical; Proceed as in Art.
Page 79 - The number of permutations of n things taken r together : the number of permutations taken r — 1 together :: 10 : 1, and the corresponding combinations :: 5 : 3.
Page 72 - This rule that you can multiply (or divide) both sides of an inequality by the same positive number maintaining the same direction of the inequality.