The Elements of Algebra |
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Page 4
... question : " If the sum of two numbers be 13 , and their difference 3 , what are the numbers ? " First , if the smaller of the two numbers were known , the larger would be found by adding 3 to it . Let therefore the smaller be called x ...
... question : " If the sum of two numbers be 13 , and their difference 3 , what are the numbers ? " First , if the smaller of the two numbers were known , the larger would be found by adding 3 to it . Let therefore the smaller be called x ...
Page 5
... questions , but investigates rules by which all questions of the same kind may be solved ; i.e. S D it arrives at a general answer , such as + which will suit 2 2 , every question , whatever numbers consistent with the question we put ...
... questions , but investigates rules by which all questions of the same kind may be solved ; i.e. S D it arrives at a general answer , such as + which will suit 2 2 , every question , whatever numbers consistent with the question we put ...
Page 6
Thomas Grainger Hall. There are two kinds of questions in Algebra - Problems and Theorems . In the problem , we have to ... question , " To find two numbers whose sum is 13 , and difference 3 " , is a problem . And if we could shew that a ...
Thomas Grainger Hall. There are two kinds of questions in Algebra - Problems and Theorems . In the problem , we have to ... question , " To find two numbers whose sum is 13 , and difference 3 " , is a problem . And if we could shew that a ...
Page 75
... questions must be expressed in algebraic terms ; and the equality between any two such expressions , is termed an equation . The two algebraical expressions are called mem- bers of the equation : Thus if 2x + 4 = x + 10 ; such an ...
... questions must be expressed in algebraic terms ; and the equality between any two such expressions , is termed an equation . The two algebraical expressions are called mem- bers of the equation : Thus if 2x + 4 = x + 10 ; such an ...
Page 103
... question are incapable of being fulfilled . As , for instance , if it were proposed to find two numbers whose sum = 6 and product = 12 , we should have p = -6 , and q = -12 ; for the equation arising would be x2 - 6x = -12 , and p2 · q ...
... question are incapable of being fulfilled . As , for instance , if it were proposed to find two numbers whose sum = 6 and product = 12 , we should have p = -6 , and q = -12 ; for the equation arising would be x2 - 6x = -12 , and p2 · q ...
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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.