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

### From inside the book

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**Fractions**, Simple Equations , and Quadratics , I have added a great variety of practical examples , as being essentially necessary to exercise young students in the elementary principles . Several new rules are introduced , those of ... Page 10

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**Fractions**, # Involution , or the Raising of Powers , Evolution , or the Extraction of Roots , Of Irrational Quantities , or Surds , # Of Arithmetical Proportion and Progression , Of Geometrical Proportion and Progression , Of Equations ... Page 12

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**fraction**b Thus , ba and both signify the quotient of b divided by a ; and a + c . ab a + c P a signifies that a - b is to be divided by equal to , the sign of equality ; signifying that the quan- tities between which it is placed are ... Page 13

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**fraction**. 1 2 Thus , a is the square root of a ; a3 is the cube root of a ; 1 and an is the nth root of a , or a root denoted by any num- ber n . In like manner , a2 is the square of a ; a3 is the cube of a ; and am is the mth power of ... Page 25

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**fraction**, and reduce it to its simplest form , by cancelling the letters and figures that are common to each term . * I would advise the learner to perform the calculation of this ex- ample several ways ; viz . First , by multiplying ...### Other editions - View all

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

Algebra answer arise arithmetical arithmetical mean ax² ax³ binomial bx² coefficients consequently cube root cubic equation decimal denominator denoted divisor equal EXAMPLES FOR PRACTICE expression find a number find the square find the sum find the value find two numbers former formula fraction gallons geometrical give given number Given x² greater greatest common measure Hence infinite series last term less logarithms method multiplied negative nth root number of terms perpendicular PROBLEM proportion quadratic equation quadratic surd question quotient rational remain Required the number Required the sum required to divide required to find resolved result rule shillings side square number square root substituted subtracted surd third unknown quantity 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...