An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 16
... whence by making this proposition general , as in the last , the sum of the isolated quantities 6a and -4a will be + 2a , and that of 4a and -6a will be 2a . 58. If two or more quantities be unlike , their sum can only be expressed by ...
... whence by making this proposition general , as in the last , the sum of the isolated quantities 6a and -4a will be + 2a , and that of 4a and -6a will be 2a . 58. If two or more quantities be unlike , their sum can only be expressed by ...
Σελίδα 72
... whence we infer that , if a number be divided into any two parts , the square of the number is equal to the square of the two parts , together with twice the product of those parts . Which may be demonstrated thus ; let the num- ber n ...
... whence we infer that , if a number be divided into any two parts , the square of the number is equal to the square of the two parts , together with twice the product of those parts . Which may be demonstrated thus ; let the num- ber n ...
Σελίδα 78
... whence we derive , dividing each side by b , α = mxv . b m ( 7 ) . 120. If a fraction is to be divided by m , it is the same whether the numerator be divided by m , or the de- nominator divided by it . For , from the equality ( 1 ) , we ...
... whence we derive , dividing each side by b , α = mxv . b m ( 7 ) . 120. If a fraction is to be divided by m , it is the same whether the numerator be divided by m , or the de- nominator divided by it . For , from the equality ( 1 ) , we ...
Σελίδα 80
... whence we might readily derive the rule for the addition and subtraction of fractions not re- duced to the same denominator . 124. It would be without doubt more simple to have recourse to property ( 4 ) in order to reduce to the same ...
... whence we might readily derive the rule for the addition and subtraction of fractions not re- duced to the same denominator . 124. It would be without doubt more simple to have recourse to property ( 4 ) in order to reduce to the same ...
Σελίδα 85
... whence A = mrDY B = nrD ' , SD = rD ' , 2d • C = qD ' ,, C = qD ' ; m and n are necessarily prime to one another , other- wise D would not be the greatest common divisor of A and B ; r and q are also prime to one another , in order that ...
... whence A = mrDY B = nrD ' , SD = rD ' , 2d • C = qD ' ,, C = qD ' ; m and n are necessarily prime to one another , other- wise D would not be the greatest common divisor of A and B ; r and q are also prime to one another , in order that ...
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...