The Elements of Algebra |
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Page 2
... greater or smaller than another ; thus ab is read a greater than 6 , and a < b is read a less than b . The opening being always turned to the larger quantity . 2. We now proceed to explain some algebraical abbre- viations . Instead of ...
... greater or smaller than another ; thus ab is read a greater than 6 , and a < b is read a less than b . The opening being always turned to the larger quantity . 2. We now proceed to explain some algebraical abbre- viations . Instead of ...
Page 5
... greater number the less number - S 2 - D = D , i.e. the greater = 1⁄2 the sum + 1⁄2 the difference of the numbers , the difference ; the less = the sum thus in the preceding example , S = 13 and D = 3 , + 13 then 2 13 and - 2 312 312 ...
... greater number the less number - S 2 - D = D , i.e. the greater = 1⁄2 the sum + 1⁄2 the difference of the numbers , the difference ; the less = the sum thus in the preceding example , S = 13 and D = 3 , + 13 then 2 13 and - 2 312 312 ...
Page 6
... a problem . And if we could shew that a and b being two numbers of which a is the greater a + b + α = 2 α - 2 we should have a theorem . CHAPTER I. ALGEBRAICAL DEFINITIONS . 9. EVERY quantity written in 6 INTRODUCTION .
... a problem . And if we could shew that a and b being two numbers of which a is the greater a + b + α = 2 α - 2 we should have a theorem . CHAPTER I. ALGEBRAICAL DEFINITIONS . 9. EVERY quantity written in 6 INTRODUCTION .
Page 7
... greater number of simple terms are connected by the signs + or - , as a + b , 7a2 + 5ab + 3bc , 4a2 - 6bc , & c . Also an algebraical expression consisting of one term , is called a Mononomial ; of two terms , a Binomial ; of three ...
... greater number of simple terms are connected by the signs + or - , as a + b , 7a2 + 5ab + 3bc , 4a2 - 6bc , & c . Also an algebraical expression consisting of one term , is called a Mononomial ; of two terms , a Binomial ; of three ...
Page 21
... greater . Thus a5 a2 = a3 . For a is the product of five a's and a2 of two a's , and therefore striking two from each we leave a × a × a or a3 in the numerator and unity in the denominator . Also for the same reason a2 1 = Hence in the ...
... greater . Thus a5 a2 = a3 . For a is the product of five a's and a2 of two a's , and therefore striking two from each we leave a × a × a or a3 in the numerator and unity in the denominator . Also for the same reason a2 1 = Hence in the ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.