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 75
... means , that 4 is to 2 , as 6 is to 3 ; or thus , 4 : 2 6 3 , or thus , § , both which mean , that the ratio of 4 to 2 , is equal to the ratio of 6 to 3 * . = = * The test of equal ratios in arithmetic is that the quotients of the ...
... means , that 4 is to 2 , as 6 is to 3 ; or thus , 4 : 2 6 3 , or thus , § , both which mean , that the ratio of 4 to 2 , is equal to the ratio of 6 to 3 * . = = * The test of equal ratios in arithmetic is that the quotients of the ...
Page 76
... Means . The most useful part of arithmetical proportion is contained in the following theorems : THEOREM 1. When four quantities are in arithmetical proportion , the sum of the two extremes is equal to the sum of the two means . Thus ...
... Means . The most useful part of arithmetical proportion is contained in the following theorems : THEOREM 1. When four quantities are in arithmetical proportion , the sum of the two extremes is equal to the sum of the two means . Thus ...
Page 78
... means . EXAMPLE . To find two arithmetical means between 2 and 8 . 8 -2 Here = 2 common difference . 3 Then 2 + 24 = the one mean , and 26 the other mean . PROBLEM VI . To find any number of arithmetical means 78 ARITHMETIC .
... means . EXAMPLE . To find two arithmetical means between 2 and 8 . 8 -2 Here = 2 common difference . 3 Then 2 + 24 = the one mean , and 26 the other mean . PROBLEM VI . To find any number of arithmetical means 78 ARITHMETIC .
Page 79
... mean terms required . EXAMPLE . To find five arithmetical means between 2 and 14 . Here 14 2 2 common difference . Then by adding this common difference continually , the means are found to be 4 , 6 , 8 , 10 , 12 . See more of ...
... mean terms required . EXAMPLE . To find five arithmetical means between 2 and 14 . Here 14 2 2 common difference . Then by adding this common difference continually , the means are found to be 4 , 6 , 8 , 10 , 12 . See more of ...
Page 80
... means , an operation which is denoted by the word Alternando . This will give 6 : 14 :: 3 : 7 or 7 : 3 : 14 6 or 7 14 :: 3 : 6 . Or , 2dly , we may put the extremes in the places of the means , called Invertendo . Thus 3 6 : 7 : 14 . Or ...
... means , an operation which is denoted by the word Alternando . This will give 6 : 14 :: 3 : 7 or 7 : 3 : 14 6 or 7 14 :: 3 : 6 . Or , 2dly , we may put the extremes in the places of the means , called Invertendo . Thus 3 6 : 7 : 14 . Or ...
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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