The Elements of Algebra |
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Page 2
... added , the sign of inequality > , by which we shew that one quantity is 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 ...
... added , the sign of inequality > , by which we shew that one quantity is 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 ...
Page 3
... 5b , it may also be written 5 ( a - b ) or 5.a - b . 6 . These are the chief signs and abbreviations made use of in Algebra ; and to them may be added .. therefore , and since . Also is to ; thus ab expresses 1-2 INTRODUCTION . 3.
... 5b , it may also be written 5 ( a - b ) or 5.a - b . 6 . These are the chief signs and abbreviations made use of in Algebra ; and to them may be added .. therefore , and since . Also is to ; thus ab expresses 1-2 INTRODUCTION . 3.
Page 4
... adding 3 to it . Let therefore the smaller be called x , then the larger is x + 3 , and their sum will be x + x + 3 , or 2x + 3. But this sum is by the question equal to 13 , and thus we have an equality or as it is technically termed ...
... adding 3 to it . Let therefore the smaller be called x , then the larger is x + 3 , and their sum will be x + x + 3 , or 2x + 3. But this sum is by the question equal to 13 , and thus we have an equality or as it is technically termed ...
Page 10
... added the quantity so changed to a . Next , had we to subtract a nega- tive quantity from another asb , from a : what is the re- sult ? It is clear that the difference between the two quantities will be unaltered , if we add the same ...
... added the quantity so changed to a . Next , had we to subtract a nega- tive quantity from another asb , from a : what is the re- sult ? It is clear that the difference between the two quantities will be unaltered , if we add the same ...
Page 14
... added to a , the result is algebraically expressed by a + b : and that when b is to be subtracted from a the result is written a - b : and thus the signs + and are the marks of the opposite - MULTIPLICATION AND DIVISION OF ALGEBRAIC ...
... added to a , the result is algebraically expressed by a + b : and that when b is to be subtracted from a the result is written a - b : and thus the signs + and are the marks of the opposite - MULTIPLICATION AND DIVISION OF ALGEBRAIC ...
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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.