A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 113
... consequently , by dividing both numerator and denominator = da ' b db = b of a fraction by the greatest common measure of the terms of the fraction , the resulting fraction will be simplified to its utmost extent , and thus the proposed ...
... consequently , by dividing both numerator and denominator = da ' b db = b of a fraction by the greatest common measure of the terms of the fraction , the resulting fraction will be simplified to its utmost extent , and thus the proposed ...
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 a = - b a ( 6. ) c — ef с cd - ef = ( 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 a = - b a ( 6. ) c — ef с cd - ef = ( 7. ) 1 ...
Page 137
... consequently is equal to -a . Next , let it be required to determine the product of √ — a by √ — ¿ ; by the rule , ( Art . 62. ) v = ax v = = = √ + ab ± √ab - The true result , however , is —√ab , so long as we suppose the radicals ...
... consequently is equal to -a . Next , let it be required to determine the product of √ — a by √ — ¿ ; by the rule , ( Art . 62. ) v = ax v = = = √ + ab ± √ab - The true result , however , is —√ab , so long as we suppose the radicals ...
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 159
... represent the integral part of the root of the numerator a b al , hence a 2 or 621 b is comprised between and 2 ° ( r + 1 ) 2 b2 2 b , consequently , the a root of is comprised between b 7 b and EXTRACTION OF ROOTS . 159.
... represent the integral part of the root of the numerator a b al , hence a 2 or 621 b is comprised between and 2 ° ( r + 1 ) 2 b2 2 b , consequently , the a root of is comprised between b 7 b and EXTRACTION OF ROOTS . 159.
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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