An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα vii
... of algebraic fractions , VI . Multiplication and division of algebraic frac- VII . Resolution of algebraic fractions or quotients into infinite series , 104 122 129 135 · CHAPTER III . Page On Simple Equations involving only one.
... of algebraic fractions , VI . Multiplication and division of algebraic frac- VII . Resolution of algebraic fractions or quotients into infinite series , 104 122 129 135 · CHAPTER III . Page On Simple Equations involving only one.
Σελίδα 135
... INFINITE SERIES . 160. An infinite series is a continued rank , or pro- gression of quantities , connected together by the signs or ; and usually proceeds according to some regular , or determined law . Thus , ++++++++ , & c . 1 Or ...
... INFINITE SERIES . 160. An infinite series is a continued rank , or pro- gression of quantities , connected together by the signs or ; and usually proceeds according to some regular , or determined law . Thus , ++++++++ , & c . 1 Or ...
Σελίδα 139
... infinite series ; which is , 1 + a + a2 + a3 + a1 + a3 + a® + a + a3 + ao + a1o + a11 + a 12+ , & c . to infinity : and there are sufficient grounds to maintain that the value of this infinite series is⚫ the same as that of the ...
... infinite series ; which is , 1 + a + a2 + a3 + a1 + a3 + a® + a + a3 + ao + a1o + a11 + a 12+ , & c . to infinity : and there are sufficient grounds to maintain that the value of this infinite series is⚫ the same as that of the ...
Σελίδα 141
... infinite , or become terminated , in re- storing to it these six terms , it should be composed of a definite or assignable number of terms , which it is not . Therefore the surplus of the series must have the same sum as the total . We ...
... infinite , or become terminated , in re- storing to it these six terms , it should be composed of a definite or assignable number of terms , which it is not . Therefore the surplus of the series must have the same sum as the total . We ...
Σελίδα 151
... infinite series . α into an a - X α ax -OC ४ x2 α x2 α Quotient . OC x2 1 + - + 8/88/8 。 x2 α OC 3 a2 203 α a2 ast , & c . X3 a2 , & c . In this example , if x be less than a , the series is convergent , or the value of the terms ...
... infinite series . α into an a - X α ax -OC ४ x2 α x2 α Quotient . OC x2 1 + - + 8/88/8 。 x2 α OC 3 a2 203 α a2 ast , & c . X3 a2 , & c . In this example , if x be less than a , the series is convergent , or the value of the terms ...
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
according added algebraic quantities arithmetical becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root DEMONSTRATION difference digits divi divided dividend division equa equal exponent expressed extracting the root factors find the values formula fourth given equation greater greatest common divisor Hence integral least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative number of terms observed positive Prob problem proportionals 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 square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number
Δημοφιλή αποσπάσματα
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...
Σελίδα 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
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 323 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...
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 452 - There are four numbers in arithmetical progression : the sum of the squares of the two first is 34 ; and the sum of the squares of the two last is 130. What are the numbers?
Σελίδα 493 - Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the same ratio to the second and fourth...
Σελίδα 501 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...
Σελίδα 285 - A cask, which held 146 gallons, was filled with a mixture of brandy, wine, and water. In it there were 15 gallons of wine more than there were of brandy, and as much water as both wine and brandy. What quantity was there of each...
Σελίδα 490 - 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...