## Mathematics: Compiled from the Best Authors, and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 1W. Hilliard, 1808 - Mathematics |

### From inside the book

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**denoted**by placing the dividend ov- er a line , and the divisor under it ; thus - 6 ÷÷ 2 = 3 . 10 = X 50 = L 100 C 500 D or 13 For every affixed , this becomes 10 1000 M or CIO 2000 = MM times as many . For every Cand , put one at each ... Page 135

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**denoted**by writing their indices above the first power ; so the second power of 3 may be**denoted**thus 32 , the third power thus 33 , the fourth pow er thus 3* , & c . and the sixth power of 503 thus 503* . Involution is the finding ... Page 136

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**denoted**by writing✓ before the power , with the index of the root against it : 8 so the third root of SO is✓ 50 , and the second root of it is ✓50 , the index 2 being omitted , which index is always un- derstood , when a root is ... Page 140

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**denoted**by that power of 2 ; that is , twice for the fourth root , thrice for the eighth root , and so on . 3d divisor 2a + 2b + c ) 2ac + 2bc + c2 2ac + 2bc + c2 Now the operation in each of these cases exactly agrees with the rule ... Page 143

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**denoted**by a aad b . Then a + 63a3 + 3a*b + Sab3 + 63 = No = given number , and to find the cube root of Nis the same as to find the cube root of a3 + 3u36 + 3ab2 + 63 ; the method of doing which is as follows : a3 + 3a*b + 3ab3 + b3 ...### Contents

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### Common terms and phrases

2qrs amount of 11 angle annuity annum answer required arithmetical called carats cent centre circle circumference coefficient common denominator completing the square compound interest cube root debt decimal denoted diameter discount Divide dividend division divisor equal equation EXAMPLES exponent figures Find the present fourth gallon geometrical progression geometrical series give given number greater greatest common measure improper fraction least common multiple less number logarithm manner Multiply natural number negative NOTE nth root number of combinations number of terms number of things payment perpendicular pound present worth PROBLEM proportion quotient radius ratio Reduce remainder repetend required to find rule of three sides simple interest sought square root subtract Suppose supposition surd taken tare triangle unknown quantity vulgar fraction Whence whole number yards