A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |
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Page 76
... extremes is equal to the sum of the two means . Thus , with regard to the four , 2 , 4 , 6 , 8 , we have 2 + 8 = 4 + 6 = 10 . THEOREM 2. In any continued arithmetical progression , the sum of the two extremes is equal to the sum of any ...
... extremes is equal to the sum of the two means . Thus , with regard to the four , 2 , 4 , 6 , 8 , we have 2 + 8 = 4 + 6 = 10 . THEOREM 2. In any continued arithmetical progression , the sum of the two extremes is equal to the sum of any ...
Page 77
... extremes is 20 2 18 , and 2 x 9 18 also . Consequently the greatest term is equal to the least term added to the ... extremes multiplied by the number of terms , and divided by 2 ; or the sum of the two extremes multiplied by the number ...
... extremes is 20 2 18 , and 2 x 9 18 also . Consequently the greatest term is equal to the least term added to the ... extremes multiplied by the number of terms , and divided by 2 ; or the sum of the two extremes multiplied by the number ...
Page 78
... 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 be the difference of the extremes ...
... 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 be the difference of the extremes ...
Page 79
... extremes . SUBTRACT the less extreme from the greater , and divide the difference by 1 more than the number of means required to be found , which will give the com- mon difference ; then this being added continually to the least term ...
... extremes . SUBTRACT the less extreme from the greater , and divide the difference by 1 more than the number of means required to be found , which will give the com- mon difference ; then this being added continually to the least term ...
Page 80
... extremes in the places of the means , called Invertendo . Thus 3 6 : 7 : 14 . Or , 3dly , we may multiply or divide ... extreme terms of a geometrical progression is equal to the common ratio of the series raised to the power denoted by ...
... extremes in the places of the means , called Invertendo . Thus 3 6 : 7 : 14 . Or , 3dly , we may multiply or divide ... extreme terms of a geometrical progression is equal to the common ratio of the series raised to the power denoted by ...
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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