An Introduction to Algebra: Being the First Part of a Course of Mathematics Adapted to the Method of Instruction in the American Colleges |
Common terms and phrases
12 rods abscissa added algebraic angle antecedent applied arithmetical arithmetical progression become binomial calculation co-efficients common difference Completing the square compound quantity consequent contained cube root cubic equation curve diminished Divide the number dividend division divisor dollars equa Euclid exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multi multiplicand negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tities Transposing triangle twice unit unknown quantity varies
Popular passages
Page 59 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 154 - The equality of the two sides is not affected by this alteration, because we only change one quantity x for another •which is equal to it. By this means we obtain an equation which contains only one unknown quantity.
Page 215 - Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 231 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 33 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Page 163 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 49 - The value of a fraction, is the quotient of the numerator divided by the denominator.
Page 20 - ... 6. If a quantity be both multiplied and divided by another, the value of the former will not be altered.
Page 122 - ... 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 109 - Whenever, therefore, we meet with a quantity of this description, we may know that its square root is a binomial ; and this may be found, by taking- the root of the two terms which are complete powers, and connecting them by the sign -|-. The other term disappears in the root.