A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 |
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Σελίδα
George Peacock. fr ti P de ld of an A TREATISE ON ALGEBRA . VOL . I. ARITHMETICAL ALGEBRA . BY GEORGE PEACOCK , D.D. F.R.S. F.G.S. F.R.A.S. PRESIDENT OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY , LOWNDES'S PROFESSOR OF ASTRONOMY , DEAN OF ELY ...
George Peacock. fr ti P de ld of an A TREATISE ON ALGEBRA . VOL . I. ARITHMETICAL ALGEBRA . BY GEORGE PEACOCK , D.D. F.R.S. F.G.S. F.R.A.S. PRESIDENT OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY , LOWNDES'S PROFESSOR OF ASTRONOMY , DEAN OF ELY ...
Σελίδα iv
... arithmetical algebra , we consider symbols as repr senting numbers , and the operations to which they a submitted as included in the same definitions ( whether e pressed or understood ) as in common arithmetic : the sig + and denote the ...
... arithmetical algebra , we consider symbols as repr senting numbers , and the operations to which they a submitted as included in the same definitions ( whether e pressed or understood ) as in common arithmetic : the sig + and denote the ...
Σελίδα v
... arithmetical algebra are Thus we generalizations of reasoning , and not of form . conclude that ( a + b ) is equivalent to a2 + 2ab + b2 , for all homogeneous values of a and b , inasmuch as it may be easily shewn that their specific ...
... arithmetical algebra are Thus we generalizations of reasoning , and not of form . conclude that ( a + b ) is equivalent to a2 + 2ab + b2 , for all homogeneous values of a and b , inasmuch as it may be easily shewn that their specific ...
Σελίδα vi
... algebra adopts the rules of arithmetica algebra , but removes altogether their restrictions : thu symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations o value of the symbols ...
... algebra adopts the rules of arithmetica algebra , but removes altogether their restrictions : thu symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations o value of the symbols ...
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ arith arithmetical algebra arithmetical series coefficient complete quotient consequently considered continued fraction continued product converging fractions corresponding cube denoted determined divided dividend division divisor equal equation expressed final digit finite number following are examples geometrical given greater greatest common measure identical inasmuch indeterminate equations involve known terms last Article last term least common multiple less magnitudes means metical minuend modulus multiplicand number of combinations number of days number of terms operation ordinary preceding primary unit primitive problem proposition quadratic quadratic equations quadratic surds quantities ratio recurring decimal reduced replace represent resolvend respectively result rule scale shewn similar manner square root subordinate units subtract subtrahend surds Symbolical Algebra third tion Transposing unknown numbers unknown symbols whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 266 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Σελίδα 272 - A and B can do a piece of work in 6 days ; A and C can do it in 9 days, and A, B, C can do 8 times the same work in 45 days.
Σελίδα 177 - 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...
Σελίδα 166 - COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Σελίδα 256 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Σελίδα 34 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Σελίδα 34 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second.
Σελίδα 269 - In wh.it time could each do it separately? Ans. A in 24, B in 48 days. 19. A and B drink from a cask of beer for 2 hours, after which A falls asleep, and B drinks the remainder in 2 hours and 48 minutes; but if B had fallen asleep and A had continued to drink. it would have taken him 4 hours and 40 minutes to finish the cask. In what time could each singly drink the whole? Ans. A in 10 hrs., B in 6 hrs.
Σελίδα 173 - If the first has to the second the same ratio which the third has to the fourth...
Σελίδα 167 - When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth, to their difference.