Algebra for High Schools and Colleges: Containing a Systematic Exposition and Application of the Elementary and Higher Principles of the SciencePratt, Oakley & Company, 1859 - 306 páginas |
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Página xii
... IMAGINARY QUANTITIES . - 147 ... 166 . Perfect and Imperfect Powers , ( 229 ) .— A Rational Quantity - An Irrationa ... Imaginary Quantities - From what an Imaginary Quantity results , ( 246 ) .— Of the Cal- culus of Imaginary Quantities ...
... IMAGINARY QUANTITIES . - 147 ... 166 . Perfect and Imperfect Powers , ( 229 ) .— A Rational Quantity - An Irrationa ... Imaginary Quantities - From what an Imaginary Quantity results , ( 246 ) .— Of the Cal- culus of Imaginary Quantities ...
Página xiv
... Imaginary Roots , ( 292 ) .- Imaginary Roots of an Equation of an even degree , ( 293 ) .— Variations and Permanences of Signs , ( 294 ) .— STURM'S THEOREM - If the Equation has equal roots - Statement of the Theorem , ( 295 ) .— Limits ...
... Imaginary Roots , ( 292 ) .- Imaginary Roots of an Equation of an even degree , ( 293 ) .— Variations and Permanences of Signs , ( 294 ) .— STURM'S THEOREM - If the Equation has equal roots - Statement of the Theorem , ( 295 ) .— Limits ...
Página 147
... IMAGINARY QUANTITIES Perfect and Imperfect Powers . ( 229. ) A Perfect Power , of any degree , is a quantity which has an exact root of the same degree ; -otherwise , the quantity is called an Imperfect Power . Thus 4 and 9a2 are ...
... IMAGINARY QUANTITIES Perfect and Imperfect Powers . ( 229. ) A Perfect Power , of any degree , is a quantity which has an exact root of the same degree ; -otherwise , the quantity is called an Imperfect Power . Thus 4 and 9a2 are ...
Página 164
... . 22. Find the Square root of 23 + 81 / 7 , ( 245 ) . 23. Find the Square root of 194 8/3 , and of 7-2 / 10 . Ans . 4 + √7 . Ans . 4 + √3 , and √5 – √2 . IMAGINARY QUANTITIES . ( 246. ) An even root of 164 EXERCISES .
... . 22. Find the Square root of 23 + 81 / 7 , ( 245 ) . 23. Find the Square root of 194 8/3 , and of 7-2 / 10 . Ans . 4 + √7 . Ans . 4 + √3 , and √5 – √2 . IMAGINARY QUANTITIES . ( 246. ) An even root of 164 EXERCISES .
Página 165
... IMAGINARY QUANTITIES . ( 246. ) An even root of a negative quantity is impossible , and the symbol of such a root is therefore called an imaginary or impossible ... Imaginary Quantity may always be resolved IMAGINARY QUANTITIES . 165.
... IMAGINARY QUANTITIES . ( 246. ) An even root of a negative quantity is impossible , and the symbol of such a root is therefore called an imaginary or impossible ... Imaginary Quantity may always be resolved IMAGINARY QUANTITIES . 165.
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Términos y frases comunes
acres added Algebraic approximate value Arithmetical Progression Binomial Theorem cent common denominator common difference completing the square component factors Continued Fraction corresponding cube root denotes dividend divisor Equation containing example exponent extracting the square Find a number Find the cube Find the Product Find the Quotient Find the square Find the Sum Find the value Function Geometrical Progression given Equation given fraction given number greater greatest common measure Hence imaginary improper Fraction Inequality integral irrational last term least common multiple less letters logarithm lowest terms method miles monomial multiplied negative number of terms obtained polynomial positive preceding prefixed problem proportion quadratic Quadratic Equations ratio real roots Reduce remainder required root Resolve second equation second member second term side signs changed simplest form solution square rods square root substituted subtracting Surds unknown quantity value of x whole number yards
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Página 299 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the...
Página 209 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Página 105 - Three quantities are said to be 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.
Página 85 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 177 - A set out from C towards D, and travelled 7 miles a day. After he had gone 32 miles, B set out from D towards C, and went every day J^ of the whole journey; •and after he had travelled as many days as he went miles in a day, he met A. Required the distance from C to D.
Página 206 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Página 80 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Página 79 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Página 60 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Página 244 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log