An Elementary Treatise on Algebra: Theoretical and Practical ...Collins and Hannay, 1826 - 383 σελίδες |
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Σελίδα 46
... reduction is made by subtraction ; and every succeeding product is managed in like manner . In the follow- ing examples , the signs of all the terms of the product are changed in placing it under the dividend ; and then the re- duction ...
... reduction is made by subtraction ; and every succeeding product is managed in like manner . In the follow- ing examples , the signs of all the terms of the product are changed in placing it under the dividend ; and then the re- duction ...
Σελίδα 55
... reduced to a more simple expression . § I. Theory of Algebric Fractions . 116. It is evident ( Art . 103. ) that if we perform the same ope- ration on each of the two members of an equality , that is , upon two equivalent quantities or ...
... reduced to a more simple expression . § I. Theory of Algebric Fractions . 116. It is evident ( Art . 103. ) that if we perform the same ope- ration on each of the two members of an equality , that is , upon two equivalent quantities or ...
Σελίδα 58
... reduced to the same denomi- nator . 124. It would be without doubt more simple to have re- course to property ( 4 ) in order to reduce to the same deno- minator the fractions α a b b ' but our object is to show , that the principle of ...
... reduced to the same denomi- nator . 124. It would be without doubt more simple to have re- course to property ( 4 ) in order to reduce to the same deno- minator the fractions α a b b ' but our object is to show , that the principle of ...
Σελίδα 62
... reduce a A fraction to its most simple expression ; because that in di B viding A and B by their greatest common ... reduced unless that B ' ducible , because q is an integral quantity which is always ir- reducible ; or B being > R , the ...
... reduce a A fraction to its most simple expression ; because that in di B viding A and B by their greatest common ... reduced unless that B ' ducible , because q is an integral quantity which is always ir- reducible ; or B being > R , the ...
Σελίδα 63
... reduce B R ' R duce or which must reduce Ꭱ R " Ꭱ B or which must re- B R ' R ' R R " • R " or If , for example , R " = 0 , this quantity cannot be greater than R " ; R " is therefore the greatest quantity which can re- A B duce the ...
... reduce B R ' R duce or which must reduce Ꭱ R " Ꭱ B or which must re- B R ' R ' R R " • R " or If , for example , R " = 0 , this quantity cannot be greater than R " ; R " is therefore the greatest quantity which can re- A B duce the ...
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...