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3d root accented applied approximate values arithmetical becomes binomial called changed coefficient consequently contain continued product Corollary corresponding Demonstration denote difference Divide dividend divisible Elimination equal EXAMPLES exponent expressed extract factor figure Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum follows fourth fraction Free given equation gives greater greatest common divisor Hence imaginary increased integer known last term least less letter limit logarithm means method monomials multiplied negative obtained period places places of decimals polynomial preceding Problem progression proportion quotient radical quantities ratio real root reduced remainder represented result reverse rule second term Solution Solve the equation square root substitution subtract successive suppressed tained taken Theorem third true units unity unknown quantity whence written
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 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.