A Course of Mathematics: Composed for the Use of the Royal Military Academy |
From inside the book
Results 1-5 of 100
Page 192
... prop . VIII . = and hence subtracting these a с equal quantities from unity , b 1 = 1 a C Or , α b с d = α C Or , a ... Prop . IX . + b = c + d d 7 And , a By Prop . X. a - b 192 ALGEBRA .
... prop . VIII . = and hence subtracting these a с equal quantities from unity , b 1 = 1 a C Or , α b с d = α C Or , a ... Prop . IX . + b = c + d d 7 And , a By Prop . X. a - b 192 ALGEBRA .
Page 280
... Prop . V ) . Hence the permanencies in the proposed equation will be replaced by variations in the changed equation , and the variations in the former by permanencies in the latter ; and since the changed equation cannot have a greater ...
... Prop . V ) . Hence the permanencies in the proposed equation will be replaced by variations in the changed equation , and the variations in the former by permanencies in the latter ; and since the changed equation cannot have a greater ...
Page 291
... ( Prop . IV , p . 277 ; ) hence we have C1 - 1 = ( r — a1 ) ( r — a2 ) ( r — a3 ) + ( r − a1 ) ( r — a2 ) ( r — a1 ) + ( r − a 、) ( r — a3 ) ( r — aş ) · + ( r − α2 ) ( r − ɑ3 ) ( 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 − a 、) ( r — a3 ) ( r — aş ) · + ( r − α2 ) ( r − ɑ3 ) ( 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 297
... ( Prop . VI . Cor . 3 , p . 292 ) , that if ( x — a1 ) ( x — a2 ) 2 be the greatest common measure of X and X1 , then X is divisible by ( x - a1 ) 2 ( x — a1⁄2 ) 3 , and the depressed equation furnishes the distinct and separate roots of ...
... ( Prop . VI . Cor . 3 , p . 292 ) , that if ( x — a1 ) ( x — a2 ) 2 be the greatest common measure of X and X1 , then X is divisible by ( x - a1 ) 2 ( x — a1⁄2 ) 3 , and the depressed equation furnishes the distinct and separate roots of ...
Other editions - View all
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