## A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies |

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added Algebra amount arithmetical progression B's gain binomial breadth bushels Clearing of fractions common denominator common difference common index Completing the square compound interest contain couriers cube root decimal denoted distance dividend divisor earth equal quantities Evolving EXAMPLES expressed Extract the square factor Find the sum find the values following RULE formula fourth power gentleman geometrical geometrical progression Hence horse infinity last term least common multiple less miles minus quantity Multiply number of terms number or quantity obtained oxen prefixed proportionals quadratic equation quotient rate per cent ratio rational quantity remainder Required the number Required the sum required to find second power second term shillings simple form square of half square rods square root Substituting subtract surd THEOREM third power Transposing transposition twice unknown quantity value of x VERIFICATION yards

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Page 56 - RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.

Page 40 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 196 - 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 ? All equations of the second degree may be reduced to one of the following forms.

Page 278 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.

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 133 - 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. 5th. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down. NOTE.

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 197 - 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.