The Elements of Algebra and Trigonometry |
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Page 19
... presents two or more terms to be added together , the addition of these is effected by adding the numerical co- efficients , and making their sum the coefficient of the literal symbol . Thus : 5a + 3a = 8a , 5a + za + 7a = 15a . To see ...
... presents two or more terms to be added together , the addition of these is effected by adding the numerical co- efficients , and making their sum the coefficient of the literal symbol . Thus : 5a + 3a = 8a , 5a + za + 7a = 15a . To see ...
Page 24
... present , with a view to the purposes of this book , it will not be demonstrated further than with indices which are positive integers . It has been seen that a2 means a × a , a3 means a xa xa , and so on , and if m be any integral ...
... present , with a view to the purposes of this book , it will not be demonstrated further than with indices which are positive integers . It has been seen that a2 means a × a , a3 means a xa xa , and so on , and if m be any integral ...
Page 38
... present no difficulty , being the multiplication of an algebraic quantity by itself as many times as the exponent ( 30 ) prescribes . 84. The following formulæ , which can be readily verified , deserve to be retained in the memory on ...
... present no difficulty , being the multiplication of an algebraic quantity by itself as many times as the exponent ( 30 ) prescribes . 84. The following formulæ , which can be readily verified , deserve to be retained in the memory on ...
Page 39
... present , though not so readily , the squares and cubes of multinomials . They must first , by means of brackets , be regarded as binomials . For example , ( x2 — 2x + 1 ) 2 = { ( x2 — 2x ) + 1 } 2 . If in i . x2-2x be regarded as ...
... present , though not so readily , the squares and cubes of multinomials . They must first , by means of brackets , be regarded as binomials . For example , ( x2 — 2x + 1 ) 2 = { ( x2 — 2x ) + 1 } 2 . If in i . x2-2x be regarded as ...
Page 57
... present viewed , is nothing but a repetition of multiplication , a \ 2 3 a a = - ( 9 ) 3 = b b - a2 ( 1 ) a X = a2 a - a3 b2b 639 and generally when n is any positive integer , an ( 3 ) * === bn 121. Evolution again , being the ...
... present viewed , is nothing but a repetition of multiplication , a \ 2 3 a a = - ( 9 ) 3 = b b - a2 ( 1 ) a X = a2 a - a3 b2b 639 and generally when n is any positive integer , an ( 3 ) * === bn 121. Evolution again , being the ...
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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.