An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
Contents
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Other editions - View all
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... Jeremiah Day No preview available - 2017 |
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... Jeremiah Day No preview available - 2016 |
Common terms and phrases
added algebraic antecedent applied arithmetical becomes binomial binomial theorem changed 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 inverted 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 substituted subtracted subtrahend supposed supposition theorem third tion tities Transposing triangle unit unknown quantity varies vulgar fraction whole number zero
Popular passages
Page 47 - 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 381 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Page 36 - This, according to the definition (Art. 90.) is taking the multiplicand as many times, as there are units in the multiplier.
Page 215 - 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. The consequent of each preceding ratio is, then, the antecedent of the following one.
Page 220 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 378 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Page 35 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Page 146 - Art. 257, 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.
Page 289 - After arranging the terms according to the powers of one of the letters, take the root of the first term, for the first term of the required root, and subtract the power from the given quantity.
Page 130 - MULTIPLY THE QUANTITY INTO ITSELF, TILL IT is TAKEN AS A FACTOR, AS MANY TIMES AS THERE ARE UNITS IN THE INDEX OF THE POWER TO WHICH THE QUANTITY IS TO BE RAISED.