## 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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4th power a-Ha acº Algebra arise arithmetical mean arithmetical series bers coefficient common denominator common index compound quantity consequently cube root cubic equation decimal denoted determine Diophantus divisor equa equal EXAMPLES FOR PRACTICE find the difference find the square find the sum find the value find two numbers frac geometrical progression geometrical series give given equation given number greatest common measure Hence infinite series last term letters loga logarithms natural number negative nth root number of terms number required perpendicular plane triangle PROBLEM proportion quadratic equation question quotient rational remainder required the numbers Required the product Required the sum required to convert required to divide required to find required to reduce result right angled triangle rithm rule second term simple form square number square root substituted subtracted sum required surd tion transposition triangle ABc unknown quantity Whence whole numbers

### Popular passages

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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...

Page 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.

Page 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.

Page 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.