A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and Academies |
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added Algebra amount arithmetical arithmetical progression binomial breadth bushels coefficients common denominator common difference common index Completing the square compound interest contains courier cube root decimal distance divide both terms dividend divisor earth Evolving EXAMPLES exponent expressed Extract the square factor Find the sum find the value following RULE formula fraction gain geometrical geometrical mean geometrical progression geometrical series given number greater Hence infinity last term less lowest terms minus quantity number be divided number of terms number or quantity obtained oxen prefixed proportionals quadratic quadratic equation quan quantity or number quotient rate per cent ratio rational quantity remainder Required the numbers Required the sum required to find second term shillings simple form simple radical form square of half square rods square root subtracted surd THEOREM third power tity Transposing transposition twice unknown quantity value of x VERIFICATION
Popular passages
Page 54 - 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 39 - 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 235 - 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 61 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 263 - 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 267 - 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 193 - Multiply the difference of the two numbers, found by trial, by the least error, and divide the product by the difference of the errors, when they are alike, but by their sum, when they are unlike. Or say...
Page 100 - J- 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 oldest exceeded that of the youngest by $14.
Page 284 - Then, as the difference of these results is to the difference of the two assumed numbers, so is the difference between the true result, given...
Page 119 - 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.