An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesH.C. Peck, 1866 |
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Common terms and phrases
added algebraic antecedent applied arithmetical becomes binomial binomial theorem called co-efficients common difference Completing the square compound quantity containing continued fraction contrary sign cube root cubic equation degree denominator diminished dividend division divisor dollars equa Euclid example exponents expression factors figure fourth geometrical geometrical progression given equation given quantity greater greatest common measure Hence infinite series integral last term less manner mathematics method Mult multiplicand negative quantity notation nth power nth root number of terms obtain original equation parallelogram positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio Reduce the equation remainder rule second term sides square root Sturm's Theorem substituted subtracted subtrahend supposed supposition theorem third tion tities Transposing triangle unit unknown quantity varies vulgar fraction whole number zero
Popular passages
Page 43 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 214 - If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS OF BOTH COUPLETS, MAY BE INVERTED, WITHOUT DESTROYING THE PROPORTION. If a : b'.'.c :d ) .-, And 12:8::6:4$then
Page 385 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 31 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Page 44 - ... 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 51 - 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 194 - A gentleman bought a number of pieces of cloth for 675 dollars, which he sold again at 48 dollars by the piece, and gained by the bargain as much as one piece cost him. What was the number of pieces? Ans. 15.
Page 142 - Required the second root of x". 14. Required the fifth root of d3. 15. Required the 8th root of a3. 210. a. The rule in the preceding article may be applied to every case in evolution. But when the quantity whose root is to be found, is composed of several factors, there will frequently be an advantage in taking the root of each of the factors separately. This is done upon the principle that the root of the product of several factors, is equal to the product of their roots. Thus ^/a6=^/ax Vb.
Page 213 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 211 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.