An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 87
... lowest terms . 137. It may also be shown , that the greatest com- mon measure of two quantities will , in no respect , be altered , by multiplying or dividing either of them by any quantity which is not a divisor of the other , or that ...
... lowest terms . 137. It may also be shown , that the greatest com- mon measure of two quantities will , in no respect , be altered , by multiplying or dividing either of them by any quantity which is not a divisor of the other , or that ...
Σελίδα 94
... lowest terms ; this observation is applicable to numbers , and as in algebraic quantities , the greatest simple divisor may be readily found by inspection . Now , it only remains to discover , if compound algebraic quantities can admit ...
... lowest terms ; this observation is applicable to numbers , and as in algebraic quantities , the greatest simple divisor may be readily found by inspection . Now , it only remains to discover , if compound algebraic quantities can admit ...
Σελίδα 110
... lowest terms , or most simple expression . RULE . 150. Observe what quantity will divide all the terms both of the numerator and denominator with- out a remainder : Divide them by this quantity , and the fraction is reduced to its lowest ...
... lowest terms , or most simple expression . RULE . 150. Observe what quantity will divide all the terms both of the numerator and denominator with- out a remainder : Divide them by this quantity , and the fraction is reduced to its lowest ...
Σελίδα 111
... lowest . Now 21x2 and 7x 2x + ax + 4 terms is 3x 30a2b2c- · 6abc2 12a2c2b Ex . 2. Reduce to its 36abcx lowest terms . Here the quantity which divides both the nume- rator and denominator without a remainder is evi- 30a2 b2c - 6abc2 ...
... lowest . Now 21x2 and 7x 2x + ax + 4 terms is 3x 30a2b2c- · 6abc2 12a2c2b Ex . 2. Reduce to its 36abcx lowest terms . Here the quantity which divides both the nume- rator and denominator without a remainder is evi- 30a2 b2c - 6abc2 ...
Σελίδα 112
... lowest a2 + b2 Ex . 4. Reduce x4-3ax3-8a3x2 + 18a3-8a1 x3 - ax2 - 8a2 x + 6α3 to its lowest terms . Here , by proceeding according to the method of ( Art . 141 ) , we find the greatest common measure of the numerator and denominator to ...
... lowest a2 + b2 Ex . 4. Reduce x4-3ax3-8a3x2 + 18a3-8a1 x3 - ax2 - 8a2 x + 6α3 to its lowest terms . Here , by proceeding according to the method of ( Art . 141 ) , we find the greatest common measure of the numerator and denominator to ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² added adfected algebraic quantities becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root difference digits divi dividend division enunciation equa equal example exponent expressed extracting the root factors find the values formula fourth gives greater greatest common divisor greatest common measure Hence least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative observed operation positive preceding Prob problem proportion proposed equation quadratic equations quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations solution square root substituting subtracted third tion tity transposition travelled unity unknown quantity values of x whence whole number
Δημοφιλή αποσπάσματα
Σελίδα iv - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Σελίδα 498 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Σελίδα 57 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 162 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples...
Σελίδα 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 503 - THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to CF.
Σελίδα 496 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Σελίδα 318 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 7 - NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...