# An Introduction to Algebra: With Notes and Observations: Designed for the Use of Schools and Places of Public Education

Kimber and Conrad, and Joseph Crukshank; T. & G. Palmer, printers, 1811 - Algebra - 220 pages

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### Contents

 Definitions 13 Multiplication of algebra 21 Algebraic fractions 28 Involution or the raising of powers 43 Of irrational quantities or surds 52 Of infinite series 68 Of geometrical proportion 7 3 74 Of quadratic equations 99
 Of the nature and formation of equations in general 113 Of the resolution of equations by various methods 123 Of the resolution of biquadratic equations 18 1 136 To find the roots of exponential equations 143 Of diophantine problems 152 Of the summation and interpolation of infinite series 163 Of logarithms 190

### Popular passages

Page 26 - 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 ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 98 - 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 would it take each person to perform the same work alone ? Ans.
Page 61 - 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.
Page 164 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of differences.
Page 97 - 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 28 - 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 192 - For the same reason, if the logarithm of any number be multiplied by the index of its power, the product will be equal to the logarithm of that power.
Page 39 - 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 50 - ... 4. Divide the dividend by the divisor, and the quotient will be the next term of the root. 5. Involve the whole root...