## A Treatise on the Elements of Algebra |

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### Common terms and phrases

1st equation 4th power A=log algebraic quantities ANSW ANSWER arithmetic means arithmetic progression arithmetic series coefficient common denominator common difference common ratio Complete the square compound interest cube root decimal digits divide the number dividend divisible by 9 divisor equal expressed Extract the square Find the sum Find the value foregoing four quantities fraction required geometric progression geometric series given number greatest common measure Hence increase inversely last term least common multiple least number lesser number Let the number lowest terms means mixed quantity multiply each side number of terms number required numerator and denominator population Quadratic Equations quadratic surds quantity varies question quotient radical sign Reduce remainder RULE solution square number square root Subtract surd quantity THEOR Theorem three numbers transposition unknown quantities whole number

### Popular passages

Page 189 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.

Page 12 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.

Page 34 - MOMENTUM, from moveo, to move ; the product of the numbers which represent the quantity of matter and the Velocity of a body, is called its momentum or quantity of motion. MUCILAGINOUS ; resembling mucilage or gum. MULTIPLE, from multiplico, to render manifold ; a quantity is said to be a multiple of another when it contains that other quantity a certain number of times without a remainder. N.

Page 154 - A COMMON MULTIPLE of two or more numbers, is any number which is divisible by each of the given numbers; thus, 48 is a common multiple of 4, 6, and 8.

Page 47 - ... root, &c. and the quotient will be the next term of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before. Proceed in the same manner, for the next following term of the root ; and so on, till the whole is finished.

Page 108 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 101 - From this mode of estimating the magnitude of a ratio, it appears that when the consequent of a ratio is not an aliquot part of the antecedent, the value of the ratio must be expressed by a fraction whose numerator is the antecedent, and denominator the consequent, of that ratio. Thus, the magnitude of the ratio of 15 : 7 is expressed by the fraction — , and of the ratio 4 : 13, by...

Page 46 - Arrange the terms according to the powers of some letter, beginning with the highest, and set the square root of the first term in the quotient. Subtract the square of the root thus found from the first term, and bring down the next two terms for a dividend.

Page 85 - A and B start at the same time to travel 150 miles; A travels 3 miles an hour faster than B, and finishes his journey 8$ hours before him ; at what rate per hour did each travel? Ans. 9 and 6 miles per hour. 19. A company at a tavern had 1 dollar and 75...

Page 102 - If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth. (Alg. 364.) Thus, if a : b : : c : d, then |=|, and"=^.