A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página vi
... UNKNOWN QUANTITIES . Elimination by Substitution · By Comparison . - By Addition and Subtraction Equations containing three unknown Quantities Equations containing m unknown Quantities SECTION IX . DISCUSSION OF EQUATIONS OF THE FIRST ...
... UNKNOWN QUANTITIES . Elimination by Substitution · By Comparison . - By Addition and Subtraction Equations containing three unknown Quantities Equations containing m unknown Quantities SECTION IX . DISCUSSION OF EQUATIONS OF THE FIRST ...
Página viii
... unknown Coefficients . - Rule SECTION XIX . GENERAL THEORY OF EQUATIONS . Definitions . - General Form of Equations ... Quantity The second Term of an Equation taken away The Limits of a Root determined Derived Polynomials . - Equal ...
... unknown Coefficients . - Rule SECTION XIX . GENERAL THEORY OF EQUATIONS . Definitions . - General Form of Equations ... Quantity The second Term of an Equation taken away The Limits of a Root determined Derived Polynomials . - Equal ...
Página 13
Elias Loomis. The first letters of the alphabet are commonly used to represent known quantities , and the last letters those which are unknown . ( 13. ) The sign — ( a horizontal line ) is called minus , and indi- cates that one quantity ...
Elias Loomis. The first letters of the alphabet are commonly used to represent known quantities , and the last letters those which are unknown . ( 13. ) The sign — ( a horizontal line ) is called minus , and indi- cates that one quantity ...
Página 71
... quantity on the right , the second member . Equations are usually composed of certain quantities which are known , and others which are unknown ... unknown quantities by the last letters , x , y , z , & c . An identical equation , is one in ...
... quantity on the right , the second member . Equations are usually composed of certain quantities which are known , and others which are unknown ... unknown quantities by the last letters , x , y , z , & c . An identical equation , is one in ...
Página 72
Elias Loomis. Those which contain only the first power of the unknown . quantity , are called simple equations , or equations of the first degree . As ax + b = cx + d . Those in which the highest power of the unknown quantity is a square ...
Elias Loomis. Those which contain only the first power of the unknown . quantity , are called simple equations , or equations of the first degree . As ax + b = cx + d . Those in which the highest power of the unknown quantity is a square ...
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Términos y frases comunes
according to Art algebraic arithmetical binomial Charles Anthon coefficient common denominator Completing the square contrary sign cube root cubic equation deduce denotes Divide the number dividend divisible equation containing equation whose roots equation x³ exponent expression Extracting the root extracting the square factors find the values following RULE fourth power fourth root given equation greatest common divisor Hence inequality infinite series last term less logarithm method miles monomial multiplied negative nth root number of terms obtain order of differences original equation polynomial positive Prob problem PROPOSITION quadratic equations quotient radical quantities ratio real roots remainder Required the cube Required the fourth Required the square Required the sum result second degree second term Sheep extra simple form solved square root Sturm's Theorem subtract surd Theorem unknown quantity variation Whence whole number
Pasajes populares
Página 38 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Página 37 - THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Página 91 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Página 332 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 33 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Página 138 - The nth root of the product of any number of factors is equal to the product of the nth roots of those factors.
Página 168 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 31 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Página 4 - A Grammar of the Greek Language, for the Use of Schools and Colleges. By Charles Anthon, LL.D.
Página 213 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.