A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 107
... substituting particular numbers for n , in the formulas ( 5 ) , ( 6 ) , ( 7 ) , we may deduce various algebraical formulas , several of which will be found in the following deductions from the rules of multiplication and division ...
... substituting particular numbers for n , in the formulas ( 5 ) , ( 6 ) , ( 7 ) , we may deduce various algebraical formulas , several of which will be found in the following deductions from the rules of multiplication and division ...
Page 146
... substituting for z and 2 z b their values , we find , ( x + a + b ) 2 = x2 + a2 + b2 + 2 x a + 2xb + 2ab Hence it appears , that the square of a trinomial is composed of the sum of the squares of all the terms , together with twice the ...
... substituting for z and 2 z b their values , we find , ( x + a + b ) 2 = x2 + a2 + b2 + 2 x a + 2xb + 2ab Hence it appears , that the square of a trinomial is composed of the sum of the squares of all the terms , together with twice the ...
Page 177
... Example VII . Required the 7th term of the expansion of ( x + a ) 12 . Here.n p = 12 } . : n - p + 2 = 7 , 7 S p — 1 = 6 , n - p + 1 6 M Substituting these values in the general expression , we find BINOMIAL THEOREM . 177.
... Example VII . Required the 7th term of the expansion of ( x + a ) 12 . Here.n p = 12 } . : n - p + 2 = 7 , 7 S p — 1 = 6 , n - p + 1 6 M Substituting these values in the general expression , we find BINOMIAL THEOREM . 177.
Page 178
Composed for the Use of the Royal Military Academy Charles Hutton William Rutherford. Substituting these values in the general expression , we find that the term sought is , 12. 11. 10.9.8.7 1 2 • • x6 as , 3 4. 5 6 or 924 x6 a ...
Composed for the Use of the Royal Military Academy Charles Hutton William Rutherford. Substituting these values in the general expression , we find that the term sought is , 12. 11. 10.9.8.7 1 2 • • x6 as , 3 4. 5 6 or 924 x6 a ...
Page 179
... substituting for n in the series . ( + a ) i = x ( 1 + % ) : : ( − 1 ) γα S S - = x2 ( 1 + 2 + 1.2 : . 2 : ( − 1 ) ( − 2 ) a - 3 α 3 2 a X + S ? ( − 1 ) ( − 2 ) ( − 3 ) - • 1.2 3 4 • - 1 2. 3 a1 α X 4 4 S + & c . } S + Or reduced ...
... substituting for n in the series . ( + a ) i = x ( 1 + % ) : : ( − 1 ) γα S S - = x2 ( 1 + 2 + 1.2 : . 2 : ( − 1 ) ( − 2 ) a - 3 α 3 2 a X + S ? ( − 1 ) ( − 2 ) ( − 3 ) - • 1.2 3 4 • - 1 2. 3 a1 α X 4 4 S + & c . } S + Or reduced ...
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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