A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 43
... quantities are integers , or mixed numbers , or compound fractions , they must be reduced , by their proper rules , to the form of simple fractions . * The truth of this rule may be shown as follows : Let the compound fraction be of ...
... quantities are integers , or mixed numbers , or compound fractions , they must be reduced , by their proper rules , to the form of simple fractions . * The truth of this rule may be shown as follows : Let the compound fraction be of ...
Page 88
... quantities into one term or sum , and the connecting of dissimilar quantities by their respective signs . The rule of addition may be divided into two cases : - ( 1 ) When the quantities are similar , and have the same signs . ( 2 ) ...
... quantities into one term or sum , and the connecting of dissimilar quantities by their respective signs . The rule of addition may be divided into two cases : - ( 1 ) When the quantities are similar , and have the same signs . ( 2 ) ...
Page 90
... quantities can only be collected by writing them in suc- cession , and prefixing to each its respective sign . Thus 9xy , — 5 c d , and 3 a b , are dissimilar quantities , and their sum is 9 xy + 3 ab - 5 cd . In like manner 2 a b , 3 a ...
... quantities can only be collected by writing them in suc- cession , and prefixing to each its respective sign . Thus 9xy , — 5 c d , and 3 a b , are dissimilar quantities , and their sum is 9 xy + 3 ab - 5 cd . In like manner 2 a b , 3 a ...
Page 94
... QUANTITIES WITH LITERAL COEFFICIENTS . ( 1 ) From ax2 + byx + cy2 Take dx2 - hxy + ky Rem . ( a ― d ) x2 + ( b + h ) xy + ( c − k ) y3 . ( 2 ) From ( a + b ) + y2 + ( a + c ) ( a + x ) 3 Take ( a - b ) x2 + y2 + c ( a + x ) 3 Rem ...
... QUANTITIES WITH LITERAL COEFFICIENTS . ( 1 ) From ax2 + byx + cy2 Take dx2 - hxy + ky Rem . ( a ― d ) x2 + ( b + h ) xy + ( c − k ) y3 . ( 2 ) From ( a + b ) + y2 + ( a + c ) ( a + x ) 3 Take ( a - b ) x2 + y2 + c ( a + x ) 3 Rem ...
Page 95
... quantities . CASE I. 10. When both multiplicand and multiplier are simple quantities . To the product of the coefficients affix that of the letters . Thus , to multiply 5 a x by 4 a xy , we have 5 x 4 = 20 ; ax × axy = = a2x2 y ; .. 5ax ...
... quantities . CASE I. 10. When both multiplicand and multiplier are simple quantities . To the product of the coefficients affix that of the letters . Thus , to multiply 5 a x by 4 a xy , we have 5 x 4 = 20 ; ax × axy = = a2x2 y ; .. 5ax ...
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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