A Treatise on AlgebraHarper & brothers, 1855 - 316 páginas |
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Página vi
... solved by Subtraction and Addition . Equations solved by Division and Multiplication . Equations cleared of Fractions ............ ... Solution of Problems SECTION VIII . EQUATIONS WITH TWO OR MORE UNKNOWN QUANTITIES . Elimination by ...
... solved by Subtraction and Addition . Equations solved by Division and Multiplication . Equations cleared of Fractions ............ ... Solution of Problems SECTION VIII . EQUATIONS WITH TWO OR MORE UNKNOWN QUANTITIES . Elimination by ...
Página viii
... - Common Logarithms . 316 Exponential Equations solved 320 Compound Interest . - Increase of Population 321 MISCELLANEOUS EXAMPLES .. 325 ALGEBRA . SECTION I. PRELIMINARY DEFINITIONS AND NOTATION ( Article viii CONTENTS .
... - Common Logarithms . 316 Exponential Equations solved 320 Compound Interest . - Increase of Population 321 MISCELLANEOUS EXAMPLES .. 325 ALGEBRA . SECTION I. PRELIMINARY DEFINITIONS AND NOTATION ( Article viii CONTENTS .
Página 2
... solved by Arith- metic , and we obtain an answer , which is applicable only to this problem . But in the solution of a general Algebraic problem we em- ploy letters , to which any value may be attributed at pleasure . The results ...
... solved by Arith- metic , and we obtain an answer , which is applicable only to this problem . But in the solution of a general Algebraic problem we em- ploy letters , to which any value may be attributed at pleasure . The results ...
Página 3
... solved Arith- metically , these solutions are generally much more tedious than the Algebraic . This advantage which is possessed by Algebra is partly due to the representation of the unknown quantities by letters , and their ...
... solved Arith- metically , these solutions are generally much more tedious than the Algebraic . This advantage which is possessed by Algebra is partly due to the representation of the unknown quantities by letters , and their ...
Página 59
... solving equations depends upon their de- gree , and the number of unknown quantities . We will begin with the most simple case . SIMPLE EQUATIONS CONTAINING BUT ONE UNKNOWN QUAN- TITY . ( 98. ) The various operations which we perform ...
... solving equations depends upon their de- gree , and the number of unknown quantities . We will begin with the most simple case . SIMPLE EQUATIONS CONTAINING BUT ONE UNKNOWN QUAN- TITY . ( 98. ) The various operations which we perform ...
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Términos y frases comunes
according to Art algebraic arithmetical progression binomial Binomial Theorem coefficients Completing the square continued fraction contrary sign cube root Divide the number dividend divisible equa equation whose roots example exponent expression extracting the square factors figure Find the square find the values following RULE four quantities fourth power fourth root geometrical progression given equation greater greatest common divisor Hence inequality infinite series last term less letters taken method miles monomial multiplied negative nth root number of combinations number of permutations number of terms obtain original equation polynomial preceding Prob problem QUADRATIC EQUATIONS quotient radical quantities ratio real roots Reduce remainder represent Required the cube Required the number Required the square Required the sum result second degree second term square root subtract surd Theorem three numbers tion tities unity unknown quantity values of x Whence whole number zero
Pasajes populares
Página 229 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 28 - 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 231 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5. Double the whole root already found for a new divisor, and continue the operation as before, until all the periods are brought down.
Página 76 - 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 141 - 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 308 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 13 - Add all the positive coefficients together, and oho all those that are negative ; subtract the least of these results from the greater ; to the difference annex the common letter or letters, and prefix the sign of the greater sum. Thus, instead of 7a— 4a, we may write 3a, since these two expressions obviously have the same value.
Página 196 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of the series required.
Página 334 - The number of deaths in a besieged garrison amounted to 6 daily ; and allowing for this diminution, their stock of provisions was sufficient to last 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the...
Página 28 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.