A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 65
... Extremes ; and the other terms , lying between them , the Means . The most useful part of arithmetical proportions , is contained in the following theorems : E THEOREM 1. - If four quantities be in arithmetical proportion 65 ...
... Extremes ; and the other terms , lying between them , the Means . The most useful part of arithmetical proportions , is contained in the following theorems : E THEOREM 1. - If four quantities be in arithmetical proportion 65 ...
Page 66
... extremes will be equal to the sum of the two means . Thus , of the four 2 , 4 , 6 , 8 , here 2 +84 + 6 = 10 . THEOREM 2. — In any continued arithmetical progression , the sum of the two extremes , is equal to the sum of any two means ...
... extremes will be equal to the sum of the two means . Thus , of the four 2 , 4 , 6 , 8 , here 2 +84 + 6 = 10 . THEOREM 2. — In any continued arithmetical progression , the sum of the two extremes , is equal to the sum of any two means ...
Page 67
... extremes , and the number of terms ; to find the common difference . RULE . - Subtract the less extreme from the greater , and divide the remainder by 1 less than the number of terms , for the common difference . EXAMPLES . 1. The extremes ...
... extremes , and the number of terms ; to find the common difference . RULE . - Subtract the less extreme from the greater , and divide the remainder by 1 less than the number of terms , for the common difference . EXAMPLES . 1. The extremes ...
Page 68
... extreme . 9 Or , 14 9 So that 9 is the mean required by both methods . PROB . V. To find two arithmetical means between two given extremes . RULE . - Subtract the less extreme from the greater , and divide the difference by 3 , so will ...
... extreme . 9 Or , 14 9 So that 9 is the mean required by both methods . PROB . V. To find two arithmetical means between two given extremes . RULE . - Subtract the less extreme from the greater , and divide the difference by 3 , so will ...
Page 69
... extremes , the quotient will give the other extreme . So , of the above numbers , the product of the means 12 ÷ 2 = 6 the one extreme , and 12 ÷ 6 2 the other extreme ; and this is the foundation and reason of the practice in the Rule ...
... extremes , the quotient will give the other extreme . So , of the above numbers , the product of the means 12 ÷ 2 = 6 the one extreme , and 12 ÷ 6 2 the other extreme ; and this is the foundation and reason of the practice in the Rule ...
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Common terms and phrases
algebraic axis bisected called centre circle circumference coefficient contained Corol cosec cosine cube root curve decimal denominator denote diameter difference differential co-efficient distance Divide dividend division divisor draw dy dx equal EXAMPLES exponent expression extract factors feet figure fraction given number greater greatest common measure Hence hyperbola inches latus rectum least common multiple logarithm manner monomial multiply negative nth root number of terms parallel parallelogram perpendicular plane polynomial positive Prob problem Prop proportional proposed equation quotient radius ratio rectangle Reduce remainder right angles rule sides sine square root straight line Substituting subtract tangent Taylor's theorem THEOREM unknown quantity VULGAR FRACTIONS whole number yards