## 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 |

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Page viii

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**Problems**Construction of the Plane Scale ( Prob . L. ) PLANE TRIGONOMETRY . Definitions**Problems**MENSURATION OF SUPERFICIES .**Problems**relating to 340 349 380- 387 391 the areas of right lined figures . 406-425 certain lines belonging ... Page 55

... greater measures the less , which is absurd . Therefore 54 is the greatest common measure . In the very same manner , the demonstration to 3 or more numbers . may be applied

... greater measures the less , which is absurd . Therefore 54 is the greatest common measure . In the very same manner , the demonstration to 3 or more numbers . may be applied

**PROBLEM**II . To find the least common multiple of ARITHMETIC . 55. Page 152

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**PROBLEM**1 . The first term , the last term , and the number of terms being given , to find the sum of all the terms . RULE . * Multiply the sum of the extremes by the number of terms , and half the product will be the answer . EXAMPLES ... Page 153

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**PROBLEM**II . The first term , the last term , and the number of terms being given , to find the common difference . RULE 3. * Divide the difference of the extremes by the number of terms less 1 , and the quotient will be the common ... Page 154

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**PROBLEM**III . Given the Jlrst term , the last term , and the common difference , to find the number of terms . RULE . * Divide the difference of the extremes by the common dif- ference , and the quotient , increased by 1 , is the number ...### 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