A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies |
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A's gain acres added Algebra amount arithmetical progression arithmetical series binomial bushels coefficient common denominator common difference Completing the square compound interest contain cube root cubic decimal denotes distance Divide dividend divisor Evolving EXAMPLES exponent expressed Extract the square factor feet Find the logarithm find the sum find the values following RULE formula fraction gentleman geometrical mean geometrical progression geometrical series given number greater Hence infinity last term less letters lowest terms miles minus mixed quantity Multiply negative number of terms obtain prefixed proportionals quadratic quotient rate per cent ratio Reduce remainder Required the number Required the sum required to find second power second term shillings side simple form square rods square root subtract surd third power Transposing transposition twice unknown quantity values of x VERIFICATION whole number yards
Popular passages
Page 241 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 190 - A square court-yard has a rectangular gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the gravel-walk ; and the number of square yards in the walk exceeds the number of yards in the periphery of the court by 164. Required the area of the court.
Page 122 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.
Page 84 - ... to that of the second and third ; but if I put it with the second horse, it will make the value double that of the first and third ; and if I put it with the third horse, it will make the value triple that of the first and second. What is the value of each horse ? 8. A laborer agreed to serve for 36 days on these conditions : that for every day he worked he was to receive $1.25, but for every day he was absent he was to forfeit $0.50. At the end of the time he received $17. Required how many...
Page 103 - ... of the sum of the shares of the other three, the share of the second ^ of the sum of the other three, and the share of the third ^ of the sum of the other three; and it was found that the share of the...
Page 274 - N : so that the common log. of any number 10° or N, is n the index of that power of 10 which is equal to the said number. Thus 100, being the second power of 10, will have 2 for its logarithm : and 1000, being the third power of 10, will have 3 for its logarithm: hence also, if 50 be = lo>">»<"", then is 1-69897 the common log.
Page 120 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 199 - A and B engaged to reap a field for 90 shillings. A could reap it in 9 days, and they promised to complete it in 5 days. They found, however, that they were obliged to call in C, an inferior workman, to assist them the last two days, in consequence of which B received 3s.
Page 284 - BY LOGARITHMS. RULE. FROM the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Page 339 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.