# 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

Jacob Ernst, 1858 - Algebra - 360 pages
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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 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 199 - 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.
Page 199 - Three lines are 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 ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 190 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 147 - It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.
Page 11 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the 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 by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal....
Page 212 - The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to their product as 34 to 15. What are the numbers?
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.
Page 23 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.