## 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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**taken**for unity . Theoretic Arithmetic is the science of numbers . Practical Arithmetic is the art of numbering . In Arithmetic there are five principal or fundamental rules for its operations , namely , Notation , Addition ... Page 16

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**taken**, and the excess of nines also in the sum of these excesses , it is plain , the last excess must be equal to the excess of nines , contained in the sum of all the numbers ; the parts being equal to the whole . Α This rule was ... Page 17

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**taken**to- gether , make the true difference sought ; because , as the sum of the parts is equal to the whole , so must the sum of the dif rences of all the similar parts be equal to the difference of the wholes , or given numbers . 2 ... Page 18

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**taken**together , will evidently make up the difference of the given numbers . Q. E. D. The truth of the method of proof is evident ; for the differ- ence of two numbers , added to the less , is manifestly equal to the greater . 8. Sir ... Page 25

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**taken**as one number , according to the order , in which they are placed , is the true quotient of the whole dividend by the divisor , which may be thus demonstrated . Demon . The complete value of the first part of the dividend is , by ...### 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