## An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry |

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Page 121

It is required to divide a line , of 20 inches in length , into two such parts that the rectangle of

It is required to divide a line , of 20 inches in length , into two such parts that the rectangle of

**the whole and one of the parts shall be equal to the square of the other**. Ans . 105 - 10 5. It is required to divide the number 60 ...### What people are saying - Write a review

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according added addition Algebra answer arise arithmetical assumed base bers changed coefficient common denominator compound consequently consisting contained continued cube root decimal denoted determined difference dividend division divisor equal equation EXAMPLES expression factors find the square find the sum find the value former four fourth fraction geometrical give Given greater Hence infinite series integral kind known least less letters logarithms manner means method mixed quantity multiplied natural negative Note observed operation performed person placed positive PRACTICE PROBLEM progression proper proportion quadratic question quotient rational remainder represented Required the difference Required the sum required to divide required to find required to reduce resolved result rule second term side simple sought square number square root substituted subtracted surd taken taking third tion triangle unknown quantity usual value of x Whence whole numbers

### Popular passages

Page 10 - 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 20 - 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 27 - 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 167 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...

Page 69 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Page 85 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.

Page 85 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.

Page 86 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.

Page 30 - 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.