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3d root 94 become zero arithmetical progression Binomial Theorem coefficient commensurable roots common difference continued fraction continued product Corollary deficient terms denote dividend divisible equal roots equation becomes factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots integer last term least common multiple letter logarithm monomials negative roots number of real number of terms obtained places of decimals polynomial positive roots preceding article Problem proportion quantities in example Questions into Equations quotient radical quantities ratio real root reduced remainder required equation required root Scholium Second Degree Solution Solve the equation square root subtracted tained term multiplied unity unknown quantity whence
Page 149 - subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. Double the root now found for a new divisor and continue the operation as before, until all the periods are brought down. EXAMPLES. 1.
Page 203 - One hundred stones being placed on the ground, in a straight line, at a 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. 11 miles, 840 yards.
Page 157 - Find three numbers such, that the product of the first and second is 6, that of the first and third is 10, and the sum of the squares of the second and third is 34. Ans. 2, 3, 5.
Page 262 - that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 50 - A merchant adds yearly to his capital one third of it, but takes from it at the end of each year $1000 for his expenses. At the end of the third year, after deducting the last
Page 69 - A father gives to his five sons $1000, which they are to divide according to their ages, so that each elder son shall receive $20 more than his next younger brother. What is the share of the youngest? Ans. $160.
Page 95 - C compare their fortunes. A says to B, 'give me $700 of your money, and I shall have twice as much as you retain; ' B says to C, ' give me $1400, and I shall have thrice as much as you have remaining ;
Page 53 - A work is to be printed, so that each page may contain a certain number of lines, and each line a certain number of letters. If we wished each page to contain 3 lines more, and each line 4 letters more, then there would be 224 letters more on each page; but if