An Elementary Treatise on Algebra: Theoretical and Practical ...Collins and Hannay, 1826 - 383 σελίδες |
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Σελίδα vii
... common divisor of two or more quantities 60 III . Method of finding the least common multiple of two or more quantities - 72 IV . Reduction of algebraic fractions V. Addition and subtraction of algebraic fractions VI . Multiplication ...
... common divisor of two or more quantities 60 III . Method of finding the least common multiple of two or more quantities - 72 IV . Reduction of algebraic fractions V. Addition and subtraction of algebraic fractions VI . Multiplication ...
Σελίδα 62
... common divisor of A and B ; r and are also prime to one another , in order that D ' may be the greatest common ... least quotients possible ; admitting this enunciation , and supposing AB . The greatest common divisor of A and B , cannot ...
... common divisor of A and B ; r and are also prime to one another , in order that D ' may be the greatest common ... least quotients possible ; admitting this enunciation , and supposing AB . The greatest common divisor of A and B , cannot ...
Σελίδα 72
... common divisor , consequently a - c is the greatest common divisor of the pro- posed quantities . Ex . 8. Required the greatest common divisor of y1 - x1 and y3 — y2x — yx2 + x3 . Ans . y2 ... least common multiple of or more quantities -
... common divisor , consequently a - c is the greatest common divisor of the pro- posed quantities . Ex . 8. Required the greatest common divisor of y1 - x1 and y3 — y2x — yx2 + x3 . Ans . y2 ... least common multiple of or more quantities -
Σελίδα 73
... least common multiple is therefore 22 X3Xa * x3 = 12α2x3 . Ex . 3. Required the least common multiple of 12a2y ( a + b ) , 6a3y2 + 12a3by3 + 6ab2 y3 , and 4a2 y2 . These quantities resolved into their simplest factors become 22 X3 Xay ...
... least common multiple is therefore 22 X3Xa * x3 = 12α2x3 . Ex . 3. Required the least common multiple of 12a2y ( a + b ) , 6a3y2 + 12a3by3 + 6ab2 y3 , and 4a2 y2 . These quantities resolved into their simplest factors become 22 X3 Xay ...
Σελίδα 80
... common divisor of two algebraic quan- tities , it may not be improper to ... ordinary methods , to the lowest expression possible . Thus , fractions that have ... least compounded , and rising therein to a single dimension only ; I divide ...
... common divisor of two algebraic quan- tities , it may not be improper to ... ordinary methods , to the lowest expression possible . Thus , fractions that have ... least compounded , and rising therein to a single dimension only ; I divide ...
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...