3d power 4th power added affected quadratic algebraic arithmetical binomial BINOMIAL THEOREM co-efficient common denominator common difference common index completing the square compound quantities contains cube root denoted Divide the number dividend division divisor dollars equal factors equal quantities evolution EXAMPLES FOR PRACTICE expressed Find the square find two numbers following GENERAL RULE fractional index gallons geometrical given quantity greater greatest common measure Hence improper fraction integer involution involved last term less letter lowest power merator Mult multiplicand multiplying the equation negative quantity nth root number of terms numerator and denominator positive Prob proportion quadratic equation quan QUEST.-How QUEST.-What quotient radical quantities radical sign ratio Reduce the equation remainder Required the cube Required the nth sides square of half square root Substitute subtracted subtrahend third tion tity Transposing twice unknown quantity whole yards
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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 232 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 198 - 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.
Page 94 - Hence any odd power has the same sign as its root. But an even power is positive, whether its root is positive or negative.
Page 65 - To multiply a fraction by a fraction. Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 58 - To reduce fractions of different denominators to a common denominator. Multiply each numerator into all the denominators except its own for a new numerator ; and all the, denominators together^ for a common denominator. 8. Reduce -r, and -,, and — to a common denominator. 6
Page 21 - One quantity is said to be a measure of another, when the former is contained in the latter any number of times, without a remainder.
Page 228 - 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 183 - The same method which is employed for the reduction of three equations, may be extended to 4, 5, or any number of equations, containing as many unknown quantities. The unknown quantities may be exterminated, one after another, and the number of equations may be reduced by successive steps from five to four, from four to three, from three to two, &c. !' I"*! *t y t