An Elementary Treatise on Algebra: Theoretical and Practical ...Collins and Hannay, 1826 - 383 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 18.
Σελίδα 63
... fraction will therefore itself be the B greatest expression , that is , it will be irreducible . Reciprocal- ly , the last divisor being unity , we may conclude that the frac- tion proposed is irreducible , or in its lowest terms . 137 ...
... fraction will therefore itself be the B greatest expression , that is , it will be irreducible . Reciprocal- ly , the last divisor being unity , we may conclude that the frac- tion proposed is irreducible , or in its lowest terms . 137 ...
Σελίδα 67
... + b2 ) ( a2 + ab + b2 ) . 142. It has been remarked ( Art . 136 ) , that if the last divi- sor be unity , and the remainder nothing ; then the fraction is already in its lowest terms ; this observation is applicable ALGEBRAIC FRACTIONS .
... + b2 ) ( a2 + ab + b2 ) . 142. It has been remarked ( Art . 136 ) , that if the last divi- sor be unity , and the remainder nothing ; then the fraction is already in its lowest terms ; this observation is applicable ALGEBRAIC FRACTIONS .
Σελίδα 68
... lowest terms . Ex . 4. Required the greatest common divisor of a2 + ax + x2 and a3 + 2a2x + 3ax2 + 4x3 . It is plain by inspection that they do not admit of any simple divisor ; then the operation according to the rule will stand thus ...
... lowest terms . Ex . 4. Required the greatest common divisor of a2 + ax + x2 and a3 + 2a2x + 3ax2 + 4x3 . It is plain by inspection that they do not admit of any simple divisor ; then the operation according to the rule will stand thus ...
Σελίδα 78
... lowest terms , or most simple expression . RULE . 149. Observe what quantity will divide all the terms both of the numerator and denominator without a remainder : Di- vide them by this quantity , and the fraction is reduced to its ...
... lowest terms , or most simple expression . RULE . 149. Observe what quantity will divide all the terms both of the numerator and denominator without a remainder : Di- vide them by this quantity , and the fraction is reduced to its ...
Σελίδα 79
... lowest terms . a2 + b2 x4 . -3ax3 - 8α2x2 + 18a3 . - 8a4 Ex . 4. Reduce to its lowest terms . x3 - ax2 - 8a2x + 6α3 Here , by proceeding according to the method of ( Art . 141 ) , we find the greatest common measure of the numerator and ...
... lowest terms . a2 + b2 x4 . -3ax3 - 8α2x2 + 18a3 . - 8a4 Ex . 4. Reduce to its lowest terms . x3 - ax2 - 8a2x + 6α3 Here , by proceeding according to the method of ( Art . 141 ) , we find the greatest common measure of the numerator and ...
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...