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

### From inside the book

Results 1-5 of 18

Page 110

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**shilling**; what were their re- spective shares ? Ans . Son 4007. , daughter 1607 . 16. There is a certain number ...**shilling**apiece less to pay , and if there had been two less , they would have had a**shilling**apiece more to pay ... Page 111

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**shilling**at the latter , that he had nothing left ; how much money had he at first ? Ans . 11d . 20. It is required to divide the number 75 into two such parts , that three times the greater shall exceed seven times the less by 15 . Ans ... Page 127

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**shilling**apiece less than they would other- wise have done ; what was their number at first ? • Ans . 16 persons . 18. It is required to find four numbers in geometrical pro- gression such , that their sum shall be 15 , and the sum of ... Page 171

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**shilling**, and have nothing about me but guineas , and he has nothing but louis - d'ors ; how must I contrive to acquit myself of the debt , the louis being valued at 17s . apiece , and the guineas at 21s . ? Ans . I must give him 13 ... Page 242

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**shillings**to two upon every deal , and after twenty deals found he had gained five**shillings**; how many deals did he win ? Ans . 13 . 5. A person wishing to enclose a piece of ground with palisades , found , if he set them a foot ...### 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...