A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 95
... substitute the values of a and b from the first two equa- tions , we have + ( + N ) = + N ; + ( −N ) = — N − ( + N ) = — N ; — ( — N ) = + N. Now , in each of these formulas , the sign of the second number is what is named the product ...
... substitute the values of a and b from the first two equa- tions , we have + ( + N ) = + N ; + ( −N ) = — N − ( + N ) = — N ; — ( — N ) = + N. Now , in each of these formulas , the sign of the second number is what is named the product ...
Page 169
... substitution in the three preceding equations , we have Va11— √√ / a1 — 2 + Vaa — 3b2¬WV√ / a11b3 + a - b = √ / a11 + " √a " —2b + " / aa — 3b2 + " / a ” —4b3 + Va - √b a - b Va + b a + b Ja + b ... + √√√⁄b11 . ( 1 ) • • - ( 2 ) ...
... substitution in the three preceding equations , we have Va11— √√ / a1 — 2 + Vaa — 3b2¬WV√ / a11b3 + a - b = √ / a11 + " √a " —2b + " / aa — 3b2 + " / a ” —4b3 + Va - √b a - b Va + b a + b Ja + b ... + √√√⁄b11 . ( 1 ) • • - ( 2 ) ...
Page 185
... substitute -a for a in the expression for Vita , we have √x — a = x * ( 1 — a 1 n - 1 2 α 1 n -1 2n -1 a · · • • n X n 2 n x n 2 n 3 n If we put x64 , a 8 , we shall obtain a series of terms which will decrease with great rapidity ...
... substitute -a for a in the expression for Vita , we have √x — a = x * ( 1 — a 1 n - 1 2 α 1 n -1 2n -1 a · · • • n X n 2 n x n 2 n 3 n If we put x64 , a 8 , we shall obtain a series of terms which will decrease with great rapidity ...
Page 196
... substitute for a , b , c , d , the known quantities which they represent , the equality subsisting between the two members will be self - evident . In each of the above cases the equation is called an identical equation . 4. Finally ...
... substitute for a , b , c , d , the known quantities which they represent , the equality subsisting between the two members will be self - evident . In each of the above cases the equation is called an identical equation . 4. Finally ...
Page 205
... substitute this expression in the other equation . We shall see that the elimination may be effected by different methods , which are more or less simple according to the nature of the question proposed . Example 1 . Let it be proposed ...
... substitute this expression in the other equation . We shall see that the elimination may be effected by different methods , which are more or less simple according to the nature of the question proposed . Example 1 . Let it be proposed ...
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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