## Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry |

### From inside the book

Page 126

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

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 . 10 V 5 - 10 , and 30 10 , and 30 – 10 V 5 . 5.### What people are saying - Write a review

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Bonnycastle's Introduction to Algebra: Containing the ..., Pages 1-283 J. Bonnycastle,J. Ryan,J. F. Jenkins No preview available - 2017 |

### Common terms and phrases

according added Algebra answer appears arise arithmetical assumed base become coefficients common consequently consisting contained continued cube root denominator denoted determined difference divided division divisor equal equation evident EXAMPLES expression extracting factors find the sum find the value find two numbers former formula four fourth fraction gallons geometrical give Given greater greatest half Hence hour infinite integral kind known last term latter least less logarithms manner means method miles multiplied negative Note observed obtained person positive PRACTICE PROBLEM proportion proposed quadratic question quotient rational reduced remain Required the sum required to divide required to find resolved respectively result rule shillings side simple square number square root substituted subtracted surd taken taking third triangle unknown quantity usual value of x Whence whole numbers yards

### Popular passages

Page 43 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.

Page 45 - ... required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.

Page 27 - 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 111 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.

Page 29 - In the case here given, the operation of division may be considered as terminated, when the highest power of the letter, in the first, or leading term of the remainder, by which the process is regulated, is less than the...

Page 112 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the the same work alone ? Ans.

Page 12 - Q/~\—C = equal to, the sign of equality; signifying that the quantities between which it is placed are equal to each other. Thus...

Page 52 - ... and the quotient will be the next term of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before...

Page 126 - 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 109 - A labourer engaged to serve for 40 days, on condition that for every day he worked he should...