The Principles of Elementary Algebra |
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... surds , no special method is given for finding the square root of an expression which is a complete square , as the operation is only a case of factoring , and a simple case at that . For expressions which are not complete squares , the ...
... surds , no special method is given for finding the square root of an expression which is a complete square , as the operation is only a case of factoring , and a simple case at that . For expressions which are not complete squares , the ...
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... SURDS . 100 VIII . CONCRETE QUANTITY . GEOMETRICAL INTERPRETA- TIONS . THE GRAPH . 114 IX . THE QUADRATIC .. 136 X. INDETERMINATE AND SIMULTANEOUS EQUATIONS OF THE FIRST DEGREE . SIMULTANEOUS QUADRATICS . 153 XI . REMAINDER THEOREM ...
... SURDS . 100 VIII . CONCRETE QUANTITY . GEOMETRICAL INTERPRETA- TIONS . THE GRAPH . 114 IX . THE QUADRATIC .. 136 X. INDETERMINATE AND SIMULTANEOUS EQUATIONS OF THE FIRST DEGREE . SIMULTANEOUS QUADRATICS . 153 XI . REMAINDER THEOREM ...
Page 99
... 240,000 miles from the earth , and makes her circuit in 27 days . In what time would she complete her circuit if she were 10,000 miles distant ? CHAPTER VII . INDICES AND SURDS . 87. The index GENERALIZED PROPORTION , OR VARIATION . 99.
... 240,000 miles from the earth , and makes her circuit in 27 days . In what time would she complete her circuit if she were 10,000 miles distant ? CHAPTER VII . INDICES AND SURDS . 87. The index GENERALIZED PROPORTION , OR VARIATION . 99.
Page 100
Nathan Fellowes Dupuis. CHAPTER VII . INDICES AND SURDS . 87. The index law is the result of the convention that when Ρ is a positive integer , a a a ... •• to p factors shall be denoted by a " . And by this law a2 · a2 = ap + q , P ...
Nathan Fellowes Dupuis. CHAPTER VII . INDICES AND SURDS . 87. The index law is the result of the convention that when Ρ is a positive integer , a a a ... •• to p factors shall be denoted by a " . And by this law a2 · a2 = ap + q , P ...
Page 103
... surds . The expression 4 is an integer under a surd form . Many known incommensurables are not surds , and some of them are not , as far as we know , due to any finite combination of surds . As examples , we have 3.1415926 ... , which ...
... surds . The expression 4 is an integer under a surd form . Many known incommensurables are not surds , and some of them are not , as far as we know , due to any finite combination of surds . As examples , we have 3.1415926 ... , which ...
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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.