## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

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2d Rem 3d root 4th power 94 become zero approximate values arithmetical progression Binomial Theorem coefficient commensurable roots common denominator continued fraction continued product Corollary deficient terms denote dividend divisible Elimination by Addition equal to zero factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum fractional exponents free an Equation Free the equation gallons given equation given number gives greatest common divisor Hence highest power last term least common multiple logarithm monomials mth root number of terms places of decimals Polynomial Theorem Problem quantities in example quotient radical quantities radical signs ratio real root reduced remainder required root Scholium Second Degree second term Solution Solve the equation square root substituted term multiplied three equations tity unity unknown quan unknown quantity whence

### Popular passages

Page 47 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.

Page 149 - 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 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 54 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...

Page 110 - ... as many times as there are units in the exponent of the required power. Hence...

Page 68 - Ans. —j—. m-\-n 13. Divide the number 46 into two parts, so that when the one is divided by 7, and the other by 3, the sum of the quotients == 10. Ans. 28 and 18. 14. All my journeyings taken together, says a traveller, amount to 3040 miles; of which I have travelled 3£ times as much by water as on horseback, and 2.

Page 1 - ALGEBRA. CHAPTER I. FUNDAMENTAL PROCESSES OF ALGEBRA. SECTION I. Definitions and Notation. 1. Algebra, according to the usual definition, is that branch of mathematics in which the quantities considered are represented by the letters of the alphabet, and the operations to be performed upon them are indicated by signs. In this sense it would embrace almost the whole science of mathematics, elementary geometry alone being excepted. It is, consequently, subject in common use to some limitations, which...

Page 262 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.

Page 205 - A traveller sets out for a certain place, and travels 1 mile the first day, 2 the second, and so on. In 5 days afterwards another sets out, and travels 12 miles a day. How long and how far must he travel to overtake the first ? 6.

Page 203 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.