A Treatise on AlgebraHarper & brothers, 1852 - 334 σελίδες |
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
75 cents according to Art Algebra arithmetical arithmetical progression binomial coefficients common denominator Completing the square continued fraction contrary sign cube root denotes Divide the number dividend divisible equa equation whose roots exponent expression extracting the square factors figure Find the square find the values following RULE fourth power fourth root geometrical geometrical progression given equation greatest common divisor Hence inequality infinite series last term least common multiple less letters taken Loomis method monomial multiplied Muslin negative nth root number of terms obtain polynomial principles Prob problem proportional quadratic equations quan quotient ratio real roots Reduce remainder represent Required the cube Required the number Required the square Required the sum result second term Sheep extra solved square root substitute subtract surd THEOREM third three numbers tion tities unity unknown quantity Whence whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 329 - is engaged for n days, on condition that he receives p pence for every day he works, and pays q pence for every day he is idle. At the end of the time he receives a pence. How many days did he work, and how many was he idle? Ans» He worked — - — , and was idle — ¡ — days*
Σελίδα 27 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, if we multiply a + b By a
Σελίδα 28 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second, Thus, if we multiply a — b By a- b a?— ab
Σελίδα 33 - Hence, for the division of monomials, we have the following RULE. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2. Subtract the exponent of each letter in the divisor from the exponent of the same letter in the dividend. EXAMPLES 1. Divide
Σελίδα 236 - 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. 6.
Σελίδα 306 - The logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. Hence we see that if it is required to multiply two or more numbers by each other, we have only to add their logarithms ; the sum will be the logarithm of their product. We
Σελίδα 128 - that the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. Ex.
Σελίδα 176 - Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes^ and the other two the means of a proportion. Let ad=bc. Then will
Σελίδα 182 - Three quantities are said to be in harmonical proportion when the first is to the third as the difference between the first and second is to the difference between the second and third» Thus, 2, 3, 6 are in harmonical proportion
Σελίδα 192 - One hundred stones being placed on the ground in a straight line, at the distance of two yards from each other, how far will a person travel who shall bring them one by one to a basket which is placed two yards from the first stone ? Ans.