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

Sargent, Wilson & Hinkle, 1848 - 240 σεκΏδερ

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### Ργλοωικό αποσπήσλατα

”εκΏδα 60 - 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.
”εκΏδα 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
”εκΏδα 178 - 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.
”εκΏδα 235 - In any proportion the product of the means is equal to the product of the extremes.
”εκΏδα 124 - 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.
”εκΏδα 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
”εκΏδα 64 - That is, 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.
”εκΏδα 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
”εκΏδα 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.