## 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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An Introduction to Algebra: With Notes and Observations: Designed for the ... John Bonnycastle,James Ryan, Fra No preview available - 2016 |

### Common terms and phrases

answer arise arithmetical mean arithmetical progression bers binomial coefficients consequently cube root cubic equation decimal denominator denoted determined divisor equa equal EXAMPLES FOR PRACTICE expression factors find the square find the sum find the value find two numbers former formula four roots frac fraction geometrical progression give given equation given number greatest common measure Hence infinite series integral last equation last term latter logarithms method multiplied negative nth root number of terms observed orders of differences perpendicular PROBLEM proportion quadratic equation quadratic surd question quotient rational remain Required the product Required the sum required to divide required to find required to reduce resolved result rule second term side simple form square number square root substituting subtracted taken third tion transposition unknown quantity value of x Whence whole numbers

### Popular passages

Page ii - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit...

Page 33 - 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 21 - 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 179 - ... and either of the former, to the correction of the number belonging to the result used ; which correction being added to that number when it is too little, or subtracted from it when it is too great, will give the root required nearly.

Page 125 - A shepherd being asked how many sheep he had in his flock, said, if I had as many more, half as many more, and 7 sheep and a half, I should have just 500; how many had he?

Page ii - In conformity to the Act of Congress of the United States, entitled " An Act for the encouragement of Learning, by securing the copies of Maps, Chart*, and Books, to the authors and proprietors of such copies, during the time therein mentioned.'' And also to an Act, entitled " An Act, supplementary to an Act, entitled an Act for the encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the...

Page 127 - 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 144 - 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 145 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal...

Page 97 - C = 2^V 10. Four quantities are in harmonical proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth.