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added addition algebra arithmetic becomes binomial called changed coefficient common difference common ratio compound consists contains cube root digit distance divided dividend division divisor double equal equation evident EXAMPLE EXERCISES expressed factors follows former four fourth fraction given quantities greater greatest common measure half happen Hence highest increased indices known latter least common multiple less lesser extreme means Method miles minus minutes multiplied negative number of terms obtained Omitting period permutations person placed positive probability problem proportion quadratic quan quotient raised Reason Reducing remainder represented result rule shillings sides signs square root Substituting these values Substituting this value subtracted taken third tities Transposing travelled trials twice unity unknown quantity value of y varies vinculum
Page 31 - The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second.
Page 32 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 208 - COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Page 32 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.
Page 76 - We have therefore the following rule for the multiplication of fractions : Multiply the numerators together for the numerator of the product, and the denominators for its denominator.
Page 255 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 209 - If four magnitudes constitute a proportion, the first will be to the sum of the first and second as the third is to the sum of the third and fourth.
Page 138 - We shall now show that every equation with one unknown quantity has as many roots as there are units in the highest power of the unknown quantity, and no more.