## 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 |

### From inside the book

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**the whole and one of the parts shall be equal to the square of the other**. Ans . 10 / 5-10 5. 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 ...### Other editions - View all

An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle No preview available - 2017 |

An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle No preview available - 2017 |

### Common terms and phrases

Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α

### 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 173 - 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 77 - 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 93 - 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 93 - 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 94 - 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.