A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 690
... dy thus in the dx y = ax2 dy dx ~ 213 > 313 dy dx = 2ax = 23 = 3x2 * In this treatise the principles of Lagrange have been almost exclusively adopted , but although that writer has with great propriety denominated this branch of ...
... dy thus in the dx y = ax2 dy dx ~ 213 > 313 dy dx = 2ax = 23 = 3x2 * In this treatise the principles of Lagrange have been almost exclusively adopted , but although that writer has with great propriety denominated this branch of ...
Page 691
... dx in like manner if u = ƒ ( z ) the first differential co - efficient of u ... dx dy = 0 . CHAPTER II . ON FINDING THE FIRST DIFFERENTIAL CO - EFFICIENT OF ... dy dx = nx2 - 1 n ( n - 1 ) 1.2 n ( n - 1 ) ( n - 2 ) 3 1.2.3 -x13 h3 + & r ...
... dx in like manner if u = ƒ ( z ) the first differential co - efficient of u ... dx dy = 0 . CHAPTER II . ON FINDING THE FIRST DIFFERENTIAL CO - EFFICIENT OF ... dy dx = nx2 - 1 n ( n - 1 ) 1.2 n ( n - 1 ) ( n - 2 ) 3 1.2.3 -x13 h3 + & r ...
Page 692
... dy dx - = a . p = log . a . a * 2 p 122 + ... - ╈ 1.2 1 ) 2 + † ( a — 1 ) ' — . . . = log . a In the system of logarithms whose base is « , p = 1 . If y = € 1 dy dx Let 3. To find the first differential co - efficient of log . x . y ...
... dy dx - = a . p = log . a . a * 2 p 122 + ... - ╈ 1.2 1 ) 2 + † ( a — 1 ) ' — . . . = log . a In the system of logarithms whose base is « , p = 1 . If y = € 1 dy dx Let 3. To find the first differential co - efficient of log . x . y ...
Page 693
... dx Cos . x . From this it appears that the first differential co - efficient ... dy = - sin . x dx . ) — sin.x h h3 ( 4-1.2.3 + 1.2.3.4.5- ) h5 COS . x 1.2 ... dx dy y = ax = p . a * = log . a.ax dx y = log . x dy = cy y = sin . x dx dy ...
... dx Cos . x . From this it appears that the first differential co - efficient ... dy = - sin . x dx . ) — sin.x h h3 ( 4-1.2.3 + 1.2.3.4.5- ) h5 COS . x 1.2 ... dx dy y = ax = p . a * = log . a.ax dx y = log . x dy = cy y = sin . x dx dy ...
Page 694
... dx y = ax + b y = e + b y = log . x b y = log..x + b y = sin x +6 y = cos x + b 213 91 91 98 98 98 93 dy then dx dy dx dy dx dy dx dy dx = ex - - 1 dy = log . a . ax y = ca * y = c.ex y = c log . x log . a X 118 y = c log..x dy = cos ...
... dx y = ax + b y = e + b y = log . x b y = log..x + b y = sin x +6 y = cos x + b 213 91 91 98 98 98 93 dy then dx dy dx dy dx dy dx dy dx = ex - - 1 dy = log . a . ax y = ca * y = c.ex y = c log . x log . a X 118 y = c log..x dy = cos ...
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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