A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 144
... substituting for z 2 and 2 z b their values , we find , 2 ( x + a + b ) 2 = x2 + a2 + b2 + 2xa + 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 ...
... substituting for z 2 and 2 z b their values , we find , 2 ( x + a + b ) 2 = x2 + a2 + b2 + 2xa + 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 ...
Page 173
... ... ( x + a ) " . Example VII . Required the 7th term of the expansion of ( x + a ) 12 . Here n = 12 ) .: n - p + 2 = 7 , p = 75 p - l = 6 , n - p + 1 = 6 Substituting these values in the general expression , we find BINOMIAL THEOREM . 173.
... ... ( x + a ) " . Example VII . Required the 7th term of the expansion of ( x + a ) 12 . Here n = 12 ) .: n - p + 2 = 7 , p = 75 p - l = 6 , n - p + 1 = 6 Substituting these values in the general expression , we find BINOMIAL THEOREM . 173.
Page 174
Composed for the Use of the Royal Military Academy Charles Hutton William Ramsay. Substituting these values in the general expression , we find that the term sought is , 12. 11. 10.9.8.7 • · 1 2 3 4 5 6 x6 a , or 924 x5 a6 ...
Composed for the Use of the Royal Military Academy Charles Hutton William Ramsay. Substituting these values in the general expression , we find that the term sought is , 12. 11. 10.9.8.7 • · 1 2 3 4 5 6 x6 a , or 924 x5 a6 ...
Page 175
... substituting for n in the series . ( x + a ) ; = xi ( 1 + 2 ) ; ra S + ↑ - S S 1 ) 2 α Ꭶ S ( − 1 ) ( − 2 ) a 3 + 3 X Ꮖ = x2 ( 1 + x + 1.2 + 2 ° ¦ ( − 1 ) ( − 2 ) ( − 3 ) - 1.2 3.4 • S · s ) a 7 - s r ( r + 1 X Or reduced , = x2 ...
... substituting for n in the series . ( x + a ) ; = xi ( 1 + 2 ) ; ra S + ↑ - S S 1 ) 2 α Ꭶ S ( − 1 ) ( − 2 ) a 3 + 3 X Ꮖ = x2 ( 1 + x + 1.2 + 2 ° ¦ ( − 1 ) ( − 2 ) ( − 3 ) - 1.2 3.4 • S · s ) a 7 - s r ( r + 1 X Or reduced , = x2 ...
Page 201
... substituting the value of this unknown quantity in either of the equations containing the two unknown quantities , we shall arrive at the value of the other unknown quantity . The process which most naturally suggests itself for the ...
... substituting the value of this unknown quantity in either of the equations containing the two unknown quantities , we shall arrive at the value of the other unknown quantity . The process which most naturally suggests itself for the ...
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algebraic algebraic quantities altitude axis base bisected body centre chord circle circumference co-ordinates Corol cosec cosine cube curve decimal denominator diameter difference differential co-efficient distance divide divisor draw equal equation Example exponent expression extract feet figure force fraction given gravity Hence hyperbola inches latus rectum least common multiple length logarithm manner monomial multiply nth root number of terms parabola parallel parallelogram perpendicular polynomial positive Prob PROBLEM PROP proportional quotient radius ratio rectangle reduced right angles rule sides sine specific gravity square root straight line Substituting subtract tangent THEOREM triangle ABC unknown quantity velocity VULGAR FRACTIONS weight whole number yards