A treatise on algebra, in theory and practice |
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a²+ab added algebra Arith arithmetic binomial theorem common denominator common difference common ratio cube root decimal period deno descending series divided dividend equal equation contains EXAMPLE 1.-Find EXERCISES exponent Find the greatest fraction greater extreme greatest common measure greatest simple common Hence highest digit highest power indices integer inverse last divisor latter leading quantity least common multiple lesser extreme lowest power means miles minator Minuend minus multiplicand Multiplying extremes negative quantity number of terms numerical coefficient numerical quantities obtained ounces permutations positive proportion quadratic quan quotient Reason Reduce remainder required greatest common required number result rule Rule.-It second term shillings sides signs simple common measure simple quantity square root Substituting these values Substituting this value subtracted Subtrahend third tiple tities Transposing unity unknown quantity value of y vinculum x²y
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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 210 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
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.
Page 228 - ... progression, is equal to the sum of the first and last terms multiplied by half the number of terms; therefore, the sum of the moments about R, is 5,000 X 5!L±.§!