## Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies |

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### Common terms and phrases

added algebraic quantities apples arithmetical progression arithmetical series binomial bushels called cents a piece coefficient common difference complete equation Completing the square denotes Divide the number dividend division dollars entire quantity equal exactly divide exponent expression extract the square find the greatest Find the product Find the square Find the sum find the value following examples fourth fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence last term least common multiple lemon letter minus monomial negative quantities number of terms peaches perfect square polynomial positive quantity pound of coffee preceding prime factors principle proportion pupil quan question quotient ratio Reduce remainder represent the cost represent the number required the numbers required to find result rule second degree solution square root subtracted theorem three numbers tion tities transposing unknown quantity whole number

### Popular passages

Page 100 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 22 - Required the distance from A to B, from B to C, and from C to D.

Page 176 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 136 - In any proportion, the product of the means is equal to the product of the extremes.

Page 122 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.

Page 62 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

Page 78 - To find the greatest common divisor of three or more quantities, first find the greatest common divisor of two of them ; then, of that divisor and one of the other quantities, and so on. The last divisor thus found, will be the greatest common divisor sought.

Page 59 - 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 137 - A farmer has 2 horses, and a saddle worth 25 dollars ; now, if the saddle be put on the first horse, his value will be double that of the second ; but, if the saddle be put on the second horse, his value will be three times that of the first.

Page 219 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.