A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 95
... hence in either case the product ab must be affected with the sign , and is therefore — a b . • Let N represent either a number or any quantity whatever , and put a = + N ; b = N Then , since a = + a , and b = + b , we shall have + a + ...
... hence in either case the product ab must be affected with the sign , and is therefore — a b . • Let N represent either a number or any quantity whatever , and put a = + N ; b = N Then , since a = + a , and b = + b , we shall have + a + ...
Page 99
... hence , 2 + 0 - 3+ 5 2 + 0 5 4 + 06 + 10 -10 + 0 + 15-25 4 + 0 −16 + 10 + 15 — 25 Hence 4a3 - 16a3 b2 + 10 a2 b3 + 15ab1 . - 2565 = product . The coefficient of a1 being zero in the product , causes that term to dis- appear . - ( 4 ...
... hence , 2 + 0 - 3+ 5 2 + 0 5 4 + 06 + 10 -10 + 0 + 15-25 4 + 0 −16 + 10 + 15 — 25 Hence 4a3 - 16a3 b2 + 10 a2 b3 + 15ab1 . - 2565 = product . The coefficient of a1 being zero in the product , causes that term to dis- appear . - ( 4 ...
Page 100
... hence a3 - a3 a5 = a3 - 5 = a - 2 ; but = 1 .. = a Similarly , And 1 a + x = 1 a ( a + x ) ' ; ( x + y ) = ( x + y ) ... hence we may conclude , ( 1. ) That if the term of the dividend have the sign + , and that of the divisor the sign + ...
... hence a3 - a3 a5 = a3 - 5 = a - 2 ; but = 1 .. = a Similarly , And 1 a + x = 1 a ( a + x ) ' ; ( x + y ) = ( x + y ) ... hence we may conclude , ( 1. ) That if the term of the dividend have the sign + , and that of the divisor the sign + ...
Page 107
... hence , by writing 4 for n in formula ( 1 ) , we have at - b4 a- -b = a3 + b . a3 - b3 a - b = a3 + b ( a2 + ab + b2 ) by ( 3 ) = a3 + a2b + a b2 + b3 . ... ..... ( 4 ) . Hence , generally , aa — ba will always be exactly divisible by a ...
... hence , by writing 4 for n in formula ( 1 ) , we have at - b4 a- -b = a3 + b . a3 - b3 a - b = a3 + b ( a2 + ab + b2 ) by ( 3 ) = a3 + a2b + a b2 + b3 . ... ..... ( 4 ) . Hence , generally , aa — ba will always be exactly divisible by a ...
Page 110
... Hence a3 - 3a2 x + 3a x2 - x3 = quotient . - - - - 1 are In this example the coefficients of the dividend are ... Hence x2 - 3x + 5 = quotient required . ( 3. ) Divide a3 + 2a1b + 3a3 b2 — a2b3 — 2a b1 — 3b5 by a2 + 2ab + 3b2 . -2 -3 1 + ...
... Hence a3 - 3a2 x + 3a x2 - x3 = quotient . - - - - 1 are In this example the coefficients of the dividend are ... Hence x2 - 3x + 5 = quotient required . ( 3. ) Divide a3 + 2a1b + 3a3 b2 — a2b3 — 2a b1 — 3b5 by a2 + 2ab + 3b2 . -2 -3 1 + ...
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Common terms and phrases
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