## Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools and Academies, Book 1 |

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added addition affected algebraic arithmetical becomes binomial called cents changed coefficient common common divisor consists contains decreasing Define denominator denotes difference distance Divide dividend division divisor elimination entire equal equation evident exactly examples exponent expressed extract the square factors figures Find Find the square Find the sum find the value four fourth fraction given gives greater half Hence illustrate increased known less letter manner means measure method minus monomial Multiply negative NOTE number of terms operation perfect square places polynomial positive preceding principle problem progression proportion quadratic equation quan question quotient radical ratio Reduce remainder represented result REVIEW Rule second degree separated sides similar simple solution solving square root Substituting subtracted taken third tion tity Transposing travels twice units unknown quantity whole

### Popular passages

Page 83 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 238 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 10 - X. is read into, or multiplied by. It denotes that the quantities between which it is placed, are to be multiplied together.

Page 43 - 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 233 - In any proportion the product of the means is equal to the product of the extremes.

Page 92 - To solve an equation, is to find the value of the unknown quantity ; or, to find a number, which being substituted for the unknown quantity, will render the two members identical.

Page 90 - Every equation is composed of two parts, separated from each other by the sign of equality. The First Member of an equation is the quantity on the left of the sign of equality. The Second Member is the quantity on the right of the sign of equality. Each member is composed of one or more terms. 147. There are generally two classes of quantities' in an equation, the known and the unknown.

Page 105 - 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 94 - Hence, Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Page 111 - What two numbers are as 3 to 4, to each of which, if 4 be added, the sums will be as 5 to 6 ? Ans. 6 and 8.