An Elementary Treatise on Algebra: Theoretical and Practical ...Collins and Hannay, 1826 - 383 σελίδες |
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Σελίδα 22
... means that the sum of rx and mx is to be subtracted , that negative sum is to be express- ed by ( rx + mx ) = — ( r + m ) x . For the same reason , the multinomial quantity - my + n2y - aby " ry2 + 6y2 , when put into a parenthesis ...
... means that the sum of rx and mx is to be subtracted , that negative sum is to be express- ed by ( rx + mx ) = — ( r + m ) x . For the same reason , the multinomial quantity - my + n2y - aby " ry2 + 6y2 , when put into a parenthesis ...
Σελίδα 50
... means of certain signs , renders both the language and al- gorithm of this science extremely simple and commodious . Besides the advantages which the algebraic method of nota- tion possesses over that of numbers , it may be observed ...
... means of certain signs , renders both the language and al- gorithm of this science extremely simple and commodious . Besides the advantages which the algebraic method of nota- tion possesses over that of numbers , it may be observed ...
Σελίδα 74
... means that the whole of that fraction is to be hence the improper fraction required is a2 — y2 —a2 + y3 x - mixed quantity 23 X 2 x x Or , as ; ( Art . 67 ) , the proposed , may be put under the form x2 + which is reduced as Ex . 1 ...
... means that the whole of that fraction is to be hence the improper fraction required is a2 — y2 —a2 + y3 x - mixed quantity 23 X 2 x x Or , as ; ( Art . 67 ) , the proposed , may be put under the form x2 + which is reduced as Ex . 1 ...
Σελίδα 116
... means . Because , if a : b :: x : d ; then α X b d ' ( Art . 187 ) , ad = bx , by clearing of fractions . ( Art . 24 ) , and ... Let 3x 5x : 2x : 7 ; then 7X3x = 2x × 5x , or 21x = 10x2 : and..21 = 10x . Again , let 5x + 20 : 4x + 4 : 5 ...
... means . Because , if a : b :: x : d ; then α X b d ' ( Art . 187 ) , ad = bx , by clearing of fractions . ( Art . 24 ) , and ... Let 3x 5x : 2x : 7 ; then 7X3x = 2x × 5x , or 21x = 10x2 : and..21 = 10x . Again , let 5x + 20 : 4x + 4 : 5 ...
Σελίδα 123
... means , we have 2 ( 3x - 2 ) = 4 ( 5x - 9 ) , or 6x - 4 = 20x - 36 , by transposition , 6x - 20x = -36 + 4 . or - 14x = -32 , by changing the signs , 14x = 32 , by division , 14x 32 - 14 14 ; .. x = 24 . Ex . 2. Given 3a : x :: b + 5 ...
... means , we have 2 ( 3x - 2 ) = 4 ( 5x - 9 ) , or 6x - 4 = 20x - 36 , by transposition , 6x - 20x = -36 + 4 . or - 14x = -32 , by changing the signs , 14x = 32 , by division , 14x 32 - 14 14 ; .. x = 24 . Ex . 2. Given 3a : x :: b + 5 ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
1st equation a²+ab+b² according added algebraic quantities becomes binomial changing the signs coefficients common denominator completing the square compound quantity consequently cube root demonstrated denoted difference divided dividend division equa equal equations Art example exponent expression extracting the root factors find the values formula gives greater greatest common divisor Hence improper fraction least common multiple letter lowest terms lues magnitudes manner miles mixed quantity multiplied number of terms numbers or quantities observed operation positive preceding prefixed Prob problem proportion proposed equations quadratic quadratic equation 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 square root substituting subtracted surd third tion tities transposition unity unknown quantities values of x whence whole number
Δημοφιλή αποσπάσματα
Σελίδα iv - 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 time therein mentioned." And also to an act, entitled, " an act, supplementary to an act, 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, and extending the benefits thereof...
Σελίδα 146 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 336 - 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 341 - XX. THEOR. IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less...
Σελίδα 339 - If the whole be to the whole, as a magnitude taken from the first is to a magnitude taken from the other ; the remainder...
Σελίδα 340 - 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 31 - 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 329 - 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, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Σελίδα 335 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.
Σελίδα 331 - 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 whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...