A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 192
... prop . VIII . = b d and hence subtracting these a equal quantities from unity , 1 -- b a Or , -- a b с = a C Or , α ... Prop . IX . a ‡ 1 - © ‡ d a + b c + www . d And , By Prop . X. ab - = b 192 ALGEBRA .
... prop . VIII . = b d and hence subtracting these a equal quantities from unity , 1 -- b a Or , -- a b с = a C Or , α ... Prop . IX . a ‡ 1 - © ‡ d a + b c + www . d And , By Prop . X. ab - = b 192 ALGEBRA .
Page 273
... Prop . 26. To find a number such that its square may be to the product of the differences of that number , and two other given numbers , a and b , in the given ratio , p : q . Ans . ( a + b ) p + ( ab ) 2p2 + 4abpq 2 ( p - g ) Prob . 27 ...
... Prop . 26. To find a number such that its square may be to the product of the differences of that number , and two other given numbers , a and b , in the given ratio , p : q . Ans . ( a + b ) p + ( ab ) 2p2 + 4abpq 2 ( p - g ) Prob . 27 ...
Page 291
... ( Prop . IV , p . 277 ; ) hence we have C1- = ( r — a1 ) ( r — a2 ) ( r — α3 ) - + ( r − a1 ) ( r − α2 ) ( r — αs ) + ( r — a1 ) ( r — α3 ) ( ṛ — α1 ) + ( r − α2 ) ( r − α3 ) ( r — aş ) · · to ( n - 1 ) factors do . do . ( 2 ) do ...
... ( Prop . IV , p . 277 ; ) hence we have C1- = ( r — a1 ) ( r — a2 ) ( r — α3 ) - + ( r − a1 ) ( r − α2 ) ( r — αs ) + ( r — a1 ) ( r — α3 ) ( ṛ — α1 ) + ( r − α2 ) ( r − α3 ) ( r — aş ) · · to ( n - 1 ) factors do . do . ( 2 ) do ...
Page 296
... ( Prop . VI . Cor . 4 ; ) but when- ever p in its continuous progress towards q , arrives at a root of any of the derived equations , that function becomes zero , and neither the preceding nor succeeding function can vanish for the same ...
... ( Prop . VI . Cor . 4 ; ) but when- ever p in its continuous progress towards q , arrives at a root of any of the derived equations , that function becomes zero , and neither the preceding nor succeeding function can vanish for the same ...
Page 419
... PROP . 1 . A straight line cannot be partly in a plane , and partly out of it . For , by def . ( 1 ) , when a straight line has two points common to a plane , it lies wholly in that piane . PROP . II . If two planes cut each other ...
... PROP . 1 . A straight line cannot be partly in a plane , and partly out of it . For , by def . ( 1 ) , when a straight line has two points common to a plane , it lies wholly in that piane . PROP . II . If two planes cut each other ...
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algebraic axis bisected centre chord ciphers circle circumference co-ordinates coefficient contained Corol cosec cosine cube root curve decimal denominator denotes 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 quotient radius ratio rectangle Reduce remainder right angles rule sides sine square root straight line substitute subtract tangent THEOREM unknown quantity VULGAR FRACTIONS whole number yards