A Theoretical and Practical Treatise on Algebra: In which the Excellencies of the Demonstrative Methods of the French are Combined with the More Practical Operations of the English and Concise Solutions Pointed Out and Particularly Inculcated : Designed for Schools, Colleges and Private Students |
Common terms and phrases
3d power 3d term 4th power algebraic algebraic quantities apply arithmetical arithmetical progression assumed binomial square binomial theorem cent Clearing of fractions coefficients common measure Completing the square containing couriers cube root cubic equation decimal denominator distance dividend division dollars equa equal roots equation becomes EXAMPLES Expand exponents expressed factors Find the sum find the values following RULE geometrical progression give greater Hence last term least common multiple less letter logarithm lower terms method Multiply negative number of terms observe operation primitive equation problem Prod proportion quadratic quadratic equations quotient real roots Reduce remainder represent resolved result second power second term solution specific gravity square root substitute subtract suppose surd theorem third three numbers tion transformed equation Transpose trial divisor unity unknown quantity values of x variations of signs whole numbers
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Page 24 - ... 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 29 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 34 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 90 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to 1.
Page 44 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 23 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 89 - Two persons, A and B, can perform a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 and B in 48 days.
Page 202 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 185 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Page 11 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal....