A Treatise on AlgebraHarper & brothers, 1846 - 346 σελίδες |
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Σελίδα iv
... Proposition is distinctly enunciated , and illustrated by appropriate examples . It is believed that Sturm's Theorem is here exhibited in so simple a form , that youth of ordinary abilities may learn to apply it with facility and pleas ...
... Proposition is distinctly enunciated , and illustrated by appropriate examples . It is believed that Sturm's Theorem is here exhibited in so simple a form , that youth of ordinary abilities may learn to apply it with facility and pleas ...
Σελίδα 12
... propositions . ( 9. ) A determinate problem is one which admits of a certain or definite answer . An indeterminate problem commonly admits of an indefinite number of solutions ; although when the answers are required in positive whole ...
... propositions . ( 9. ) A determinate problem is one which admits of a certain or definite answer . An indeterminate problem commonly admits of an indefinite number of solutions ; although when the answers are required in positive whole ...
Σελίδα 71
... proposition which declares the equality of two quantities expressed algebraically . Thus x 4b - x , is a proposition expressing the equality of the quantities x — 4 and b — x . - The quantity on the left hand side of the sign of ...
... proposition which declares the equality of two quantities expressed algebraically . Thus x 4b - x , is a proposition expressing the equality of the quantities x — 4 and b — x . - The quantity on the left hand side of the sign of ...
Σελίδα 127
... proposition may be rigorously demon- strated . It is easy to perceive that this rule for a polynomial includes the preceding rule for a trinomial , and that in Art . 60 for a binomial . SECTION XI . EVOLUTION AND RADICAL QUANTITIES ...
... proposition may be rigorously demon- strated . It is easy to perceive that this rule for a polynomial includes the preceding rule for a trinomial , and that in Art . 60 for a binomial . SECTION XI . EVOLUTION AND RADICAL QUANTITIES ...
Σελίδα 200
... Proposition above demonstrated , from which it appears that 16 is the greatest product which can be obtained by decomposing 8 into two parts , and multiplying them together . ( 197. ) When q is negative , and numerically equal to 22 ...
... Proposition above demonstrated , from which it appears that 16 is the greatest product which can be obtained by decomposing 8 into two parts , and multiplying them together . ( 197. ) When q is negative , and numerically equal to 22 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 332 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Σελίδα 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.
Σελίδα 138 - The nth root of the product of any number of factors is equal to the product of the nth roots of those factors.
Σελίδα 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.
Σελίδα 31 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Σελίδα 4 - A Grammar of the Greek Language, for the Use of Schools and Colleges. By Charles Anthon, LL.D.
Σελίδα 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.