Elements of Algebra with ExercisesMacmillan Company, 1902 - 478 páginas |
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Página xi
... Roots Principal Roots Evolution Principles of Roots § 2. ROOTS OF MONOMIALS §3 . SQUARE ROOTS OF MULTINOMIALS §4 . CUBE ROOTS OF MULTINOMIALS $ 5 . HIGHER ROOTS §6 . ROOTS OF ARITHMETICAL NUMBERS Square Roots Cube Roots . 239 240 241 ...
... Roots Principal Roots Evolution Principles of Roots § 2. ROOTS OF MONOMIALS §3 . SQUARE ROOTS OF MULTINOMIALS §4 . CUBE ROOTS OF MULTINOMIALS $ 5 . HIGHER ROOTS §6 . ROOTS OF ARITHMETICAL NUMBERS Square Roots Cube Roots . 239 240 241 ...
Página xii
... Roots of Simple Binomial Surds 290 Approximate Values of Surd Numbers 291 CHAPTER XX . IMAGINARY AND COMPLEX NUMBERS . Imaginary Numbers Complex Numbers Complex Factors Square Root of a Complex Number 294 298 301 301 CHAPTER XXI ...
... Roots of Simple Binomial Surds 290 Approximate Values of Surd Numbers 291 CHAPTER XX . IMAGINARY AND COMPLEX NUMBERS . Imaginary Numbers Complex Numbers Complex Factors Square Root of a Complex Number 294 298 301 301 CHAPTER XXI ...
Página xiii
... Roots of a Quadratic Equation . Maxima and Minima Problems PAGE 305 • • 305 307 · 309 310 313 316 318 • 322 CHAPTER XXII . EQUATIONS OF Higher DegrEE THAN THE SECOND 327 CHAPTER XXIII . IRRATIONAL EQUATIONS . Special Devices 333 CHAPTER ...
... Roots of a Quadratic Equation . Maxima and Minima Problems PAGE 305 • • 305 307 · 309 310 313 316 318 • 322 CHAPTER XXII . EQUATIONS OF Higher DegrEE THAN THE SECOND 327 CHAPTER XXIII . IRRATIONAL EQUATIONS . Special Devices 333 CHAPTER ...
Página 82
... Root of the equation . E.g. , 3 and - 3 are roots of the equation x2 – 1 = 8 . - § 3. EQUIVALENT EQUATIONS . 1. We shall now give some principles upon which the solu- tion of integral equations depends . But it is to be kept in mind ...
... Root of the equation . E.g. , 3 and - 3 are roots of the equation x2 – 1 = 8 . - § 3. EQUIVALENT EQUATIONS . 1. We shall now give some principles upon which the solu- tion of integral equations depends . But it is to be kept in mind ...
Página 83
... root 9 . 2. Two equations are equivalent when every solution of the first is a solution of the second , and every solution of the second is a solution of the first . E.g. , equations ( 1 ) , ( 2 ) , ( 3 ) , and ( 4 ) of Art . 1 . 3. The ...
... root 9 . 2. Two equations are equivalent when every solution of the first is a solution of the second , and every solution of the second is a solution of the first . E.g. , equations ( 1 ) , ( 2 ) , ( 3 ) , and ( 4 ) of Art . 1 . 3. The ...
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Elements of Algebra with Exercises George Egbert Fisher,Isaac Joachim Schwatt Sin vista previa disponible - 2016 |
Términos y frases comunes
a₁ a²b a²b² a²x a²x² a³b ab² absolute value algebraic language ALGEBRAIC NUMBERS arithmetical arithmetical means assigned number ax² binomial coefficient Commutative Law complex number continued fraction convergent cube definition denominator digits divided divisor dollars equal number equivalent exactly divisible example illustrates EXERCISES exponent Find the values following expressions following principle given equation greater illustrates the following imaginary unit inequality integer irrational number less Let x stand logarithm miles minuend monomial multinomial multiplied negative numbers obtained parentheses positive integer positive number positive units powers quadratic equation quadratic surds r₁ radicand rational number remainder required numbers result second member Simplify solution Solve the equation square root summands symbolically unknown number whence wherein x²y xy² yards
Pasajes populares
Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - C„.r. That is, the number of combinations of n dissimilar .things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), etc., are functions of x; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.