A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 120
... consequently the negative sign applies to the numerator alone ; and when the numerator is a polynomial , the negative sign extends to every term of the polynomial ; thus , ( 5. ) 1 - b a = α b a ( 6. ) c — ef – cd — ef - = d ( 7. ) 1 ...
... consequently the negative sign applies to the numerator alone ; and when the numerator is a polynomial , the negative sign extends to every term of the polynomial ; thus , ( 5. ) 1 - b a = α b a ( 6. ) c — ef – cd — ef - = d ( 7. ) 1 ...
Page 137
... consequently is equal to -a . - Next , let it be required to determine the product of V - a by V ; by the rule , ( Art . 62. ) v = a x v b H v - ax - b = = √ Fab ± √ab - The true result , however , is —√ab , so long as we suppose the ...
... consequently is equal to -a . - Next , let it be required to determine the product of V - a by V ; by the rule , ( Art . 62. ) v = a x v b H v - ax - b = = √ Fab ± √ab - The true result , however , is —√ab , so long as we suppose the ...
Page 154
... Consequently these two terms must form the two first terms of P Hence , if we extract the cube root of the first term of P , we shall obtain the first term of R , and then , dividing the second term of P by three times the square of the ...
... Consequently these two terms must form the two first terms of P Hence , if we extract the cube root of the first term of P , we shall obtain the first term of R , and then , dividing the second term of P by three times the square of the ...
Page 158
... consequently , the root of a is comprised between 2 r tween and ( r + 1 ) 2 n 2 2 9 n r 2 the roots of and ( r + 1 ) 2 n 2 222 that is , between and ጕ n r + n Thus , it ap- r pears , that 1 n represents the square root of a within of ...
... consequently , the root of a is comprised between 2 r tween and ( r + 1 ) 2 n 2 2 9 n r 2 the roots of and ( r + 1 ) 2 n 2 222 that is , between and ጕ n r + n Thus , it ap- r pears , that 1 n represents the square root of a within of ...
Page 159
... let r represent the integral part of the root of the numerator ab a b , hence or 12 , a 2 وح is comprised between ( r + 1 ) 2 and b2 " b2 consequently , the root of a is comprised between and b + ! EXTRACTION OF ROOTS . 159.
... let r represent the integral part of the root of the numerator ab a b , hence or 12 , a 2 وح is comprised between ( r + 1 ) 2 and b2 " b2 consequently , the root of a is comprised between and b + ! EXTRACTION OF ROOTS . 159.
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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