The Principles of Elementary Algebra |
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Page 8
... power of a , read a nth - power , ' or ' a - to - the - nth , ' and denotes that a is to be taken n times as a factor ... powers of the same subject is that power of the subject which is denoted by the sum of the exponents . Thus , a1 ...
... power of a , read a nth - power , ' or ' a - to - the - nth , ' and denotes that a is to be taken n times as a factor ... powers of the same subject is that power of the subject which is denoted by the sum of the exponents . Thus , a1 ...
Page 11
Nathan Fellowes Dupuis. Herein lies the advantage of algebraic symbolization , its great powers being due to two things : ( 1 ) The universal significance of the quantitative symbol , and ( 2 ) That the operations performed , unlike ...
Nathan Fellowes Dupuis. Herein lies the advantage of algebraic symbolization , its great powers being due to two things : ( 1 ) The universal significance of the quantitative symbol , and ( 2 ) That the operations performed , unlike ...
Page 12
... power of 2 is 2 " × 22 × 21 - n × 2 ? 11. What power of a is am - n · аo · an ― р · ap¬m ? • 12. According to the index law at x a - 1a4-1 = a3 . Hence interpret a - 1 . 22. The symbols = and = . The symbol = 12 SYMBOLS , DEFINITIONS ...
... power of 2 is 2 " × 22 × 21 - n × 2 ? 11. What power of a is am - n · аo · an ― р · ap¬m ? • 12. According to the index law at x a - 1a4-1 = a3 . Hence interpret a - 1 . 22. The symbols = and = . The symbol = 12 SYMBOLS , DEFINITIONS ...
Page 25
... is arranged according to the powers of x . With three factors we readily see that taking the from every factor gives 3 ; taking it from every factor but one , and taking the other letter from that MULTIPLICATION . 25.
... is arranged according to the powers of x . With three factors we readily see that taking the from every factor gives 3 ; taking it from every factor but one , and taking the other letter from that MULTIPLICATION . 25.
Page 27
... powers are exhibited in the following table , which may be extended at pleasure - The coefficients form the diagonals , up to the 8th power . 1 1 ----- --1 -15- 7 ----- -21-- -28- -35 -1 -28 -56- Ex . 4. ( x + a − b ) ( x + b − c ) ...
... powers are exhibited in the following table , which may be extended at pleasure - The coefficients form the diagonals , up to the 8th power . 1 1 ----- --1 -15- 7 ----- -21-- -28- -35 -1 -28 -56- Ex . 4. ( x + a − b ) ( x + b − c ) ...
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Common terms and phrases
a₁ ab² arithmetic ax² b₁ becomes binomial binomial theorem c₁ coefficients complete square continued fraction convergent cube root decimal denominator denote diagonal difference dimensions Divide divisor elementary algebra equal equate coefficients equation EXERCISE expansion expression find the L. C. M. find the nth Find the value finite geometric geometric series given gives graph Hence imaginary independent term integer integral function inversions letters linear factors logarithms mantissa matrix miles monomial Multiply negative nth root nth term number of terms numerical quantity operation permutations positive integers proper fraction quadratic quantitative symbol R₁ rationalizing factor recurring series relation remainder result sides signs Similarly solution square root substituting subtract suffixes surd theorem tion triangle U₂ variable Whence zero
Popular passages
Page 90 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 254 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 336 - ... University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc. "Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions...
Page 254 - ... that the logarithm of the product of two numbers is the sum of the logarithms of the numbers.
Page 74 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.