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### Contents

 Section 1 1 Section 2 4 Section 3 16 Section 4 25 Section 5 27 Section 6 29 Section 7 47
 Section 8 52 Section 9 61 Section 10 70 Section 11 73 Section 12 77 Section 13 91

### Popular passages

Page 65 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.
Page 84 - The fore-wheel of a carriage makes six revolutions more than the hind-wheel in going 120 yards ; but if the circumference of each wheel be increased one yard, it will make only four revolutions more than the hind-wheel in going the same distance.
Page 64 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Page 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.
Page 48 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Page 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.
Page 70 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 45 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.
Page 48 - Take the root of the first term, for the first term of the required root...
Page 44 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive \$ '75, and, for every day he was idle, he should forfeit \$ '25 ; at the expiration of the time, he received \$ 27'50 ; how many days did he work...