A Treatise on AlgebraHarper & brothers, 1855 - 316 páginas |
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Página 15
... consider negative as well as positive quantities ; and by the sum of two quantities , we mean their aggregate , regard being paid to their signs . Thus the sum of +7 and −5 is +2 , which is numerically less than either 7 or 5. So ...
... consider negative as well as positive quantities ; and by the sum of two quantities , we mean their aggregate , regard being paid to their signs . Thus the sum of +7 and −5 is +2 , which is numerically less than either 7 or 5. So ...
Página 19
... consider easterly motion + , westerly motion must be regarded as - , and vice versa . And generally , when quantities which are estimated in differ- ent directions enter into the same algebraic expression , those which are measured in ...
... consider easterly motion + , westerly motion must be regarded as - , and vice versa . And generally , when quantities which are estimated in differ- ent directions enter into the same algebraic expression , those which are measured in ...
Página 21
... c represent any three numbers , we shall have abc equal to bca or cab . It is convenient to consider the subject of multiplication un- der three Cases . CASE I. ( 49. ) When both the factors are SECTION IV MULTIPLICATION.
... c represent any three numbers , we shall have abc equal to bca or cab . It is convenient to consider the subject of multiplication un- der three Cases . CASE I. ( 49. ) When both the factors are SECTION IV MULTIPLICATION.
Página 31
... consider the properties of coefficients by themselves , and pre- pare him for some investigations which are to follow , particu- larly in Section XX . The beginner , however , in attempting to apply the method , must be cautious not to ...
... consider the properties of coefficients by themselves , and pre- pare him for some investigations which are to follow , particu- larly in Section XX . The beginner , however , in attempting to apply the method , must be cautious not to ...
Página 60
... consider these different cases in succession . I. The unknown quantity may be combined with knowu quantities by addition . Let it be required to solve the equation x + 6 = 24 . If from the two equal quantities , x + 6 and 24 , we ...
... consider these different cases in succession . I. The unknown quantity may be combined with knowu quantities by addition . Let it be required to solve the equation x + 6 = 24 . If from the two equal quantities , x + 6 and 24 , we ...
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Términos y frases comunes
according to Art algebraic arithmetical progression binomial coefficients common denominator Completing the square continued fraction cube root difference Divide the number dividend divisible dollars equa equation containing EXAMPLES exponent expression extracting the square factors figure Find the square find the values following RULE four quantities fourth power fourth root geometrical progression greater greatest common divisor Hence infinite series last term less letters taken logarithm 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 radical sign ratio Reduce remainder represent Required the cube Required the fourth Required the number Required the square Required the sum second degree second term simple form 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.