## The elements of algebra, tr. from the first three chapters of the Algebra of m. Bourdon, by A. De Morgan |

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added ALGEBRAIC FRACTIONS algebraical language algebraical quantities algebraical translation arithmetical bb'x becomes x binomial called cleared of fractions coefficient common factor composed contain contrary signs couriers denominator difference divide dividend and divisor division ells enunciation equal equation becomes equations ax evidently exact quotient example find a number given numbers given polynomial given quantities gives greater greatest common divisor greatest common measure highest exponent leaps least common multiple method monomial multiplicand nomials numerical value obtained original equation partial products perfect square performed positive terms preceding primitive equation principal letter principle problem radical sign rate of interest remainder result rule rule of signs second degree second side second term similar terms simple polynomial simplified solution solved square root substituted subtraction suppose tain Take the equation third tiply transformations trinomial twice the product unknown quantity verified whence whole number write

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Page 28 - 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 56 - How many days did he work and how many was he idle ? Ans. he worked 48 days, and was idle 22.

Page 28 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.

Page 21 - Write in the quotient, after the co-efficient, all the letters common to the dividend and divisor, and affect each with an exponent equal to the excess of its exponent in the dividend over that in the divisor.

Page 91 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.

Page 114 - ... the sum of the roots is equal to the coefficient of the second term with its sign changed, and the product of tlte roots is equal to the last term. For the roots of ax...

Page 5 - ... the product multiply the number of tens by one more than itself for the hundreds, and place the product of the units at the right of this product, for the tens and units. Thus...

Page 99 - The sum of two numbers multiplied by their difference, is equal to the difference of their squares.

Page 18 - From the rules for multiplication, which have been laid down, it follows, mogenrous, and the degree of each term of the product will be equal to the sum of the degrees of any two terms whatever of the multiplier and multiplicand.

Page 72 - A second person has $ 35,000, on which he gains the second rate of interest; but he owes $24,000, for which he pays the first rate of interest. The sum which he receives is greater than that which he pays by $310. What are the two rates of interest ? 27. A says to B and C, give me half of your money, and I shall have $ 55.