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 76
... ratio of the consequent of one couplet , and the antecedent of the next couplet , is not the same as the common difference or ratio of the couplets , the proportion is discontinued . So , 4 , 2 , 8 , 6 , are in discontinued arithmetical ...
... ratio of the consequent of one couplet , and the antecedent of the next couplet , is not the same as the common difference or ratio of the couplets , the proportion is discontinued . So , 4 , 2 , 8 , 6 , are in discontinued arithmetical ...
Page 79
... ratios , as those of 6 to 3 , and 14 to 7 , which , by what has been already said , ( p . 50 , 75 , ) may be expressed fractionally , § and 4 ; to judge whether they are equal or unequal , we must reduce them to a common denominator ...
... ratios , as those of 6 to 3 , and 14 to 7 , which , by what has been already said , ( p . 50 , 75 , ) may be expressed fractionally , § and 4 ; to judge whether they are equal or unequal , we must reduce them to a common denominator ...
Page 80
... ratio of the series raised to the power denoted by 1 less than the number of the terms . So , of the ten terms 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , 512 , 1024 , the common ratio is 2 , one less than the number of terms 9 ; then the ...
... ratio of the series raised to the power denoted by 1 less than the number of the terms . So , of the ten terms 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , 512 , 1024 , the common ratio is 2 , one less than the number of terms 9 ; then the ...
Page 81
... ratio . So , the sum of 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , 512 , 1024 , ( whose ratio is 2 , ) is 1024 + 1024 2 2 - - 1 1024 1022 2046 . This subject will be resumed in the algebraic part of this work . A few examples may here be ...
... ratio . So , the sum of 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , 512 , 1024 , ( whose ratio is 2 , ) is 1024 + 1024 2 2 - - 1 1024 1022 2046 . This subject will be resumed in the algebraic part of this work . A few examples may here be ...
Page 82
... ratio . Then 3 x 2 = 6 , and 6 × 2 = 12 , and 12 x 2 = 24 , and 24 x 2 = 48 . Or 962 48 , and 48 ÷ 2 = 24 , and 24 ÷ 2 = = 12 , and 12 ÷ 2 = 6 . That is , 6 , 12 , 24 , 48 , are the four means between 3 and 96 . OF HARMONICAL PROPORTION ...
... ratio . Then 3 x 2 = 6 , and 6 × 2 = 12 , and 12 x 2 = 24 , and 24 x 2 = 48 . Or 962 48 , and 48 ÷ 2 = 24 , and 24 ÷ 2 = = 12 , and 12 ÷ 2 = 6 . That is , 6 , 12 , 24 , 48 , are the four means between 3 and 96 . OF HARMONICAL PROPORTION ...
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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