An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 206
... lues ( c ) , ( d ) , and ( e ) , of the equations ( Art . 214 ) , with three unknown quantities ; is sufficient to show that they deviate not at all froin this rule . With respect to their denominator , it requires a little more ...
... lues ( c ) , ( d ) , and ( e ) , of the equations ( Art . 214 ) , with three unknown quantities ; is sufficient to show that they deviate not at all froin this rule . With respect to their denominator , it requires a little more ...
Σελίδα 221
... lues of the unknown quantities , if one of the equa- tions , the third , for example , were comprised in the two others , and we would fall again into this case by the hypotheses a " -na + ma ' , b " = nb + mb ' , c " = nc + me ' , d ...
... lues of the unknown quantities , if one of the equa- tions , the third , for example , were comprised in the two others , and we would fall again into this case by the hypotheses a " -na + ma ' , b " = nb + mb ' , c " = nc + me ' , d ...
Σελίδα 233
... lues of x and y . [ 5x + 4y = 58 , ( 3x + 7y = 67 , S to find the va- Mult . the 2nd equation by 5 , then 15x + 35y = 335 ; 1st . 39 · 15x + 12y = 174 ; .. by subtraction , 23y = 161 , and y = = 7 ; 161 23 30 and .. x 6 . 5 whence , 5x ...
... lues of x and y . [ 5x + 4y = 58 , ( 3x + 7y = 67 , S to find the va- Mult . the 2nd equation by 5 , then 15x + 35y = 335 ; 1st . 39 · 15x + 12y = 174 ; .. by subtraction , 23y = 161 , and y = = 7 ; 161 23 30 and .. x 6 . 5 whence , 5x ...
Σελίδα 234
... lues of x and y . to find the va- Mult . the Istequation by 7 , then 77x + 219-700 , 2nd 3 , 12x - 21y 12 ; · .. by addition , 89x = 712 , 712 by division , x = 89 and .. x = 8 ; whence 3y = 100-11x - 100-11X8-100-88 12 ; 12 4 . Ex . 6 ...
... lues of x and y . to find the va- Mult . the Istequation by 7 , then 77x + 219-700 , 2nd 3 , 12x - 21y 12 ; · .. by addition , 89x = 712 , 712 by division , x = 89 and .. x = 8 ; whence 3y = 100-11x - 100-11X8-100-88 12 ; 12 4 . Ex . 6 ...
Σελίδα 236
... x and y . a + b By addition , 2x = a + b ; . • . x = 2 a- By subtraction , 2y - a - b , y = 2 Ex . 9. Given ( x + 2y = 12 , to find the va ( x - 2y = 4 , S lues of x and y . Mult . the 1st equation by 2 , then + 236 SIMPLE EQUATIONS .
... x and y . a + b By addition , 2x = a + b ; . • . x = 2 a- By subtraction , 2y - a - b , y = 2 Ex . 9. Given ( x + 2y = 12 , to find the va ( x - 2y = 4 , S lues of x and y . Mult . the 1st equation by 2 , then + 236 SIMPLE EQUATIONS .
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...