A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 192
... prop . VIII . = and hence subtracting these a equal quantities from unity , b Or , Or , 1 -- a a - a = b C = C α с ... Prop . IX . a + b c + d b d And , - a b By Prop . X. = 192 ALGEBRA .
... prop . VIII . = and hence subtracting these a equal quantities from unity , b Or , Or , 1 -- a a - a = b C = C α с ... Prop . IX . a + b c + d b d And , - a b By Prop . X. = 192 ALGEBRA .
Page 290
... ( Prop . I , p . 280 ) , we have the following process , viz .: 1 + A + A + · • " B1 B11 r B1 r C1 rC1 C11 A - 2 + A + A , ( ~ rB 7B - 2 A - 3 B - 1 B1 - 2 C - 3 rCn - 2 C1 - 2 CA - 1 rB - 1 Bo Whence C1_1 = A „ -1 + rB „ ¬2 290 ALGEBRA .
... ( Prop . I , p . 280 ) , we have the following process , viz .: 1 + A + A + · • " B1 B11 r B1 r C1 rC1 C11 A - 2 + A + A , ( ~ rB 7B - 2 A - 3 B - 1 B1 - 2 C - 3 rCn - 2 C1 - 2 CA - 1 rB - 1 Bo Whence C1_1 = A „ -1 + rB „ ¬2 290 ALGEBRA .
Page 291
... ( Prop . IV , p . 277 ; ) hence we have C1 - 1 = ( r — a1 ) ( r — a2 ) ( r — a3 ) + ( r − a1 ) ( r — a2 ) ( r — a1 ) . + ( r — a1 ) ( r — a3 ) ( r — a ; ) · + ( r − a2 ) ( r − a3 ) ( r — a1 ) · • to ( n - 1 ) factors do . do . ( 2 ) do .
... ( Prop . IV , p . 277 ; ) hence we have C1 - 1 = ( r — a1 ) ( r — a2 ) ( r — a3 ) + ( r − a1 ) ( r — a2 ) ( r — a1 ) . + ( r — a1 ) ( r — a3 ) ( r — a ; ) · + ( r − a2 ) ( r − a3 ) ( r — a1 ) · • 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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axis become x becomes bisected called centre chord circle circumference co-ordinates Corol cosec cosine curve decimal denominator determine diameter difference differential co-efficient distance Divide divisor draw dx dy dy dx equal EXAMPLES expression feet figure formula fraction function greatest common measure Hence hyperbola inches latus rectum least common multiple logarithm manner monomial multiplied negative nth root opposite P₁ parallel parallelogram perpendicular polynomial positive Prob problem Prop proportional quotient radius ratio rectangle remaining right angles rule sides sine square root straight line Substituting subtract tangent Taylor's theorem THEOREM triangle ABC unknown quantity whence whole number yards