# A Theoretical and Practical Treatise on Algebra: In which the Excellencies of the Demonstrative Methods of the French are Combined with the More Practical Operations of the English and Concise Solutions Pointed Out and Particularly Inculcated : Designed for Schools, Colleges and Private Students

Ivison, Phinney & Company, 1863 - Algebra - 360 pages

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Page 34 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 29 - 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 54 - Any term may be transposed from one member of an equation to the other by changing its sign; (1, 2).
Page 90 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to I.
Page 204 - 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 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 150 - There is a stack of hay whose length is to its breadth as 5 to 4, and whose height is to its breadth as 7 to 8. It is worth as many cents per cubic foot as it is feet in breadth ; and the whole is worth, at that rate, 224 times as many cents as there are square feet on the bottom. Required the dimensions of the stack.
Page 11 - If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Page 11 - If the same quantity or equal quantities be added to equal quantities, their sums will be equal. 2. If the same quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal.
Page 44 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.