An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 14
... tion , 5a will represent five times that thing , and 7a seven times the same thing , whatever may be the denomination or numeral value of a ; and conse- quently , if the quantities 5a and 7a are to be in- corporated , or added together ...
... tion , 5a will represent five times that thing , and 7a seven times the same thing , whatever may be the denomination or numeral value of a ; and conse- quently , if the quantities 5a and 7a are to be in- corporated , or added together ...
Σελίδα 16
... tion of algebraic quantities , taken in a general sense , or without any regard to their particular values , means only the uniting of them together , by means of the arithmetical operations denoted by the signs and ; and as these are ...
... tion of algebraic quantities , taken in a general sense , or without any regard to their particular values , means only the uniting of them together , by means of the arithmetical operations denoted by the signs and ; and as these are ...
Σελίδα 17
... tion of algebraic quantities , which is generally di- vided into three cases , are readily deduced from them . CASE I. When the quantities are like and have like signs . RULE . 59. Add all the numeral coefficients together , to their ...
... tion of algebraic quantities , which is generally di- vided into three cases , are readily deduced from them . CASE I. When the quantities are like and have like signs . RULE . 59. Add all the numeral coefficients together , to their ...
Σελίδα 26
... tion in Laplace's manner . Thus , we can write , a = a + b - b .... ( 1 ) , a - ca - cb - b ... . ( 2 ) ; -b , or so that if from a we are to subtract + b or which is the same , if in a we suppress + b , or b , the remainder , from ...
... tion in Laplace's manner . Thus , we can write , a = a + b - b .... ( 1 ) , a - ca - cb - b ... . ( 2 ) ; -b , or so that if from a we are to subtract + b or which is the same , if in a we suppress + b , or b , the remainder , from ...
Σελίδα 31
... tion , that the product contains either of the factors as many times as the other contains an unit . There- fore , the product ab contains a as many times as contains an unit , that is , 6 times . α And the same quantity ab , contains b ...
... tion , that the product contains either of the factors as many times as the other contains an unit . There- fore , the product ab contains a as many times as contains an unit , that is , 6 times . α And the same quantity ab , contains b ...
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...