The Elements of Algebra and Trigonometry |
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Page 19
... appears with numerical coefficients ( 20 ) , as 5a , 3a , 7a , and thus presents two or more terms to be added ... appear with any coefficients , as a , 3b , 5c , their addition can only be left expressed by writing them in a line , a + ...
... appears with numerical coefficients ( 20 ) , as 5a , 3a , 7a , and thus presents two or more terms to be added ... appear with any coefficients , as a , 3b , 5c , their addition can only be left expressed by writing them in a line , a + ...
Page 31
... appear in the divisor and dividend , they can only be left with the division expressed . It could be effected only if the special values of the letters were assigned , to make a connection between them , which is not existing while the ...
... appear in the divisor and dividend , they can only be left with the division expressed . It could be effected only if the special values of the letters were assigned , to make a connection between them , which is not existing while the ...
Page 64
... appear that this value is not a root or does not satisfy the equation . For in this case x 4-8 + = + 2 x2 - 8 = - • 1 + 1 = 0 , 4 2 4 2 + -3x + II 2- = 2 = 3 + 2+ II = - 7 4 7 4 + 13 7 4 9 so that the two members of the equation are not ...
... appear that this value is not a root or does not satisfy the equation . For in this case x 4-8 + = + 2 x2 - 8 = - • 1 + 1 = 0 , 4 2 4 2 + -3x + II 2- = 2 = 3 + 2+ II = - 7 4 7 4 + 13 7 4 9 so that the two members of the equation are not ...
Page 65
... appears with the same sign in both members of an equation , it may be cancelled in both , and the remaining quantities are equal still . Ex . If x3 + 2x2 + 3 = 2x2 + 4 , .. cancelling 2x2 + 3 from each member we have x3 = I. If x2 - 3x ...
... appears with the same sign in both members of an equation , it may be cancelled in both , and the remaining quantities are equal still . Ex . If x3 + 2x2 + 3 = 2x2 + 4 , .. cancelling 2x2 + 3 from each member we have x3 = I. If x2 - 3x ...
Page 66
... appears , let each member be multiplied by its denominator . Thus , if x + 3 + 3 + x 4 + x = x2 + 3 , then when both members are multiplied by 4 , x + 3 + 4x = 4x2 + 12 , 1 no fraction appears . If there be several fractions , let each ...
... appears , let each member be multiplied by its denominator . Thus , if x + 3 + 3 + x 4 + x = x2 + 3 , then when both members are multiplied by 4 , x + 3 + 4x = 4x2 + 12 , 1 no fraction appears . If there be several fractions , let each ...
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Common terms and phrases
a²+b² added algebraic quantity angle BAC angle PAQ arithmetic called cent circle circumference coefficient complement compound interest computed containing denominator denote difference digits divided dividend division divisor equal Euclid Examples for Practice expressed Find the number former fraction gallons gives goniometrical Hence hypotenuse inches instance integer known latter length less logarithm magnitude means measured method miles an hour minutes monomial multiplied negative sign observed perpendicular places of decimals positive problem prop proper fraction proportional quadratic quadratic equation quotient radius ratio result right angle right-angled triangle Science Examination shillings simple equation sine solution solved square feet square root subtracted Suppose symbols tables taken tangent tion triangle ABC triangle wherein Trigonometry unknown quantity vertical whence yards zero ΙΟ
Popular passages
Page 174 - A farmer bought some sheep for £72, and found that if he had received 6 more for the same money, he would have paid £1 less for each. How many sheep did he buy ? 13. A and B distribute £60 each among a certain number of persons : A relieves 40 persons more than B does, and B gives to each 5*.
Page 178 - When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second.