A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 10
... proposed . Thus , if it is required to find the interest of a thousand dollars for three months at six per cent . the question may be solved by Arithmetic , and we obtain an answer , which is applicable only to this problem . But in the ...
... proposed . Thus , if it is required to find the interest of a thousand dollars for three months at six per cent . the question may be solved by Arithmetic , and we obtain an answer , which is applicable only to this problem . But in the ...
Página 25
... proposed to be subtracted , is less than 5a by 3b , too much has been taken away by 36 ; and therefore , the true remainder will be greater than 8a + 56-5a by 3b , and will hence be expressed by 8a + 5b5a + 3b , where the signs of the ...
... proposed to be subtracted , is less than 5a by 3b , too much has been taken away by 36 ; and therefore , the true remainder will be greater than 8a + 56-5a by 3b , and will hence be expressed by 8a + 5b5a + 3b , where the signs of the ...
Página 26
... proposed . From EXAMPLES . 5a2 - 2b 5xy + 8x - 2 10-8x - 3xy 4√ ax - 2x2y Subtract 2a2 + 5b 3xy - 8x - 7 -x + 3xy 3√ ax - 5xy2 Remainder 3a2 , 76 From 5a4b2c + 7d Take 3a + 2b + c + 5d 6aby4yx + 4zx 3aby + 5zx + 3yx From 6aby Take ...
... proposed . From EXAMPLES . 5a2 - 2b 5xy + 8x - 2 10-8x - 3xy 4√ ax - 2x2y Subtract 2a2 + 5b 3xy - 8x - 7 -x + 3xy 3√ ax - 5xy2 Remainder 3a2 , 76 From 5a4b2c + 7d Take 3a + 2b + c + 5d 6aby4yx + 4zx 3aby + 5zx + 3yx From 6aby Take ...
Página 34
... proposed to multiply a- b by c d . By this we understand that the quantity a ab is to be repeated as many times as there are units in c- d . If we multiply a - bc . But a by c we obtain ac b was only to be taken c times ; therefore in ...
... proposed to multiply a- b by c d . By this we understand that the quantity a ab is to be repeated as many times as there are units in c- d . If we multiply a - bc . But a by c we obtain ac b was only to be taken c times ; therefore in ...
Página 41
... proposed polynomials are homogeneous , and of the second degree . Hence the product must be homogeneous , and of the fourth degree . The powers of a must decrease successively by unity , beginning with the first term , while those of x ...
... proposed polynomials are homogeneous , and of the second degree . Hence the product must be homogeneous , and of the fourth degree . The powers of a must decrease successively by unity , beginning with the first term , while those of x ...
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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.