# 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

Evert Duyckinck, Daniel D. Smith and George Long, 1818 - 260 pŕgines

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### Continguts

 Addition 8 Division 18 Algebraic Fractions 24 Involution or the raising of Powers 40 Of irrational Quantities or Surds 50 Of arithmetical Proportion and Progression 72 Of Equations 81 Miscellaneous Questions 98
 Of the Resolution of biquadratic Equations 130 To find the roots of Exponential Equations 140 Of the Binomial Theorem 143 Of the indeterminate Analysis 150 Of the Diophantine Analysis 162 Of the Summation and Interpolation of Series 173 Of Logarithms 200 Multiplication by Logarithms 213

### Passatges populars

Pŕgina 37 - 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.
Pŕgina 20 - 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.
Pŕgina 40 - ... 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.
Pŕgina 201 - From which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors.
Pŕgina 107 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare ? Let x be the number of leaps taken by the hound.
Pŕgina 121 - 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.
Pŕgina 107 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Pŕgina 108 - 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.
Pŕgina 121 - 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.
Pŕgina 31 - To reduce an improper fraction to a whole or mixed quantity. RULE. Divide the numerator by the denominator, for the integral part, and place the remainder, if any, over the denominator, for the fractional part; then the two, joined together, with the proper sign between them, will give the mixed quantity required.