A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1Gilberte and Rivington, 1841 - Mathematics |
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Page 77
... problems . PROBLEM I. Given the extremes , and the number of terms , to find the sum of all the terms . ADD the extremes together , multiply the sum by the number of terms , and divide by 2 . EXAMPLES . 1. The extremes being 3 and 19 ...
... problems . PROBLEM I. Given the extremes , and the number of terms , to find the sum of all the terms . ADD the extremes together , multiply the sum by the number of terms , and divide by 2 . EXAMPLES . 1. The extremes being 3 and 19 ...
Page 78
... PROBLEM III . Given one of the extremes , the common difference , and the number of terms ; to find the other extreme , and the sum of the series . MULTIPLY the common difference by 1 less than the number of terms , and the product will ...
... PROBLEM III . Given one of the extremes , the common difference , and the number of terms ; to find the other extreme , and the sum of the series . MULTIPLY the common difference by 1 less than the number of terms , and the product will ...
Page 79
In Two Volumes. For the Use of the Royal Military Academy Charles Hutton. PROBLEM VI . To find any number of arithmetical means between two given terms or extremes . SUBTRACT the less extreme from the greater , and divide the difference ...
In Two Volumes. For the Use of the Royal Military Academy Charles Hutton. PROBLEM VI . To find any number of arithmetical means between two given terms or extremes . SUBTRACT the less extreme from the greater , and divide the difference ...
Page 81
... PROBLEM I. To find one geometrical mean proportional between any two numbers . MULTIPLY the two numbers together , and extract the square root of the pro- duct , which will give the mean proportional sought . EXAMPLE . To find a ...
... PROBLEM I. To find one geometrical mean proportional between any two numbers . MULTIPLY the two numbers together , and extract the square root of the pro- duct , which will give the mean proportional sought . EXAMPLE . To find a ...
Page 101
... problem to discover . Thus , in the Rule of Three , if a , b , c taken in order be selected to designate generally the first , second , and third of the given terms taken in order , and which are all given in each actual case , and if ...
... problem to discover . Thus , in the Rule of Three , if a , b , c taken in order be selected to designate generally the first , second , and third of the given terms taken in order , and which are all given in each actual case , and if ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence