Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools and Academies, Book 1 |
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Common terms and phrases
1st Bk added affected quadratic equation algebraic quantities arithmetical progression arithmetical series binomial cents coefficient common denominator common difference Completing the square cube decimal Define denotes dividend division entire quantity equal EQUATIONS CONTAINING exponent expressed extract the square Find a number find the G.C.D. Find the product Find the square Find the sum find the value following examples fourth geometrical progression geometrical series gives greater greatest common divisor Hence illustrate infinite series last term least common multiple letter minus mixed quantity monomial multiplicand multiply both terms negative quantity number of places number of terms perfect square polynomial prime factors problem proportion Proposition question quotient ratio Reduce remainder represented required the numbers required to find Rule second degree SIMPLE EQUATIONS solving square root taken Theorem tion tity Transposing trinomial units unknown quantity whole number x²-y²
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.