The Elements of Algebra |
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Page 3
... root being indicated by a small figure placed on the left of this sign ; thus Ja , is read the cube root , or third root of a , and √ , is read the fourth root of b ; but the square root of a is written √a and not Ja , the number in ...
... root being indicated by a small figure placed on the left of this sign ; thus Ja , is read the cube root , or third root of a , and √ , is read the fourth root of b ; but the square root of a is written √a and not Ja , the number in ...
Page 62
... cube or nth roots of any quantity as a , are derived from the methods by which the second , third , & c . powers of a are obtained . a is the square root ... cube root of a3 . .. a2 is the square root of a * . .. a * is the cube root of a12 ...
... cube or nth roots of any quantity as a , are derived from the methods by which the second , third , & c . powers of a are obtained . a is the square root ... cube root of a3 . .. a2 is the square root of a * . .. a * is the cube root of a12 ...
Page 63
... root of a represented by a3 , in the same manner Ja , might be written a3 , and the fourth root of a , a . So also the cube root of a3 , may be put a3 , and the fourth root of a3 may be written aa • These remarks are very important ...
... root of a represented by a3 , in the same manner Ja , might be written a3 , and the fourth root of a , a . So also the cube root of a3 , may be put a3 , and the fourth root of a3 may be written aa • These remarks are very important ...
Page 64
... cube root of a . And hence the third root of a1 and the fifth root of a may be written a and a respectively . And hence also , whenever we meet with a quantity as a having a fractional index , we must remember that the numerator of the ...
... cube root of a . And hence the third root of a1 and the fifth root of a may be written a and a respectively . And hence also , whenever we meet with a quantity as a having a fractional index , we must remember that the numerator of the ...
Page 66
... cube root of a positive number is + and of a negative number is - . A negative number has no square root ; for no number multiplied by itself can give a negative result ; and such a term as √9 or a is called an impossible root ...
... cube root of a positive number is + and of a negative number is - . A negative number has no square root ; for no number multiplied by itself can give a negative result ; and such a term as √9 or a is called an impossible root ...
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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.