A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 |
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Página iv
... replaced by digital numbers : thus expressions , such as a + b , we must suppose a and b to quantities of the same kind : in others , like ab , we mu suppose a greater than b , and therefore homogeneous wit a it in products and ...
... replaced by digital numbers : thus expressions , such as a + b , we must suppose a and b to quantities of the same kind : in others , like ab , we mu suppose a greater than b , and therefore homogeneous wit a it in products and ...
Página 9
... replaced by the vinculum , which is a line drawn er the symbols which are required to be connected together : thus , b + c is used nstead of ( b + c ) : a - b - c instead of a- ( b − c ) ; and similarly in other cases . B Rule for the ...
... replaced by the vinculum , which is a line drawn er the symbols which are required to be connected together : thus , b + c is used nstead of ( b + c ) : a - b - c instead of a- ( b − c ) ; and similarly in other cases . B Rule for the ...
Página 14
... replacing c - 10 + d + 8 , by its equivalent expression c + d2 , and also 14 + d - 9 - e by its equivalent expression de + 5 , when the remaining opera tions may be exhibited as follows : c + d - 2 d - e + 5 c + d - 2 - d + e −5 = c + ...
... replacing c - 10 + d + 8 , by its equivalent expression c + d2 , and also 14 + d - 9 - e by its equivalent expression de + 5 , when the remaining opera tions may be exhibited as follows : c + d - 2 d - e + 5 c + d - 2 - d + e −5 = c + ...
Página 16
... replaced by a , and if the symbol into which it is to be multiplied ( or which is to be repeated in addition as often as unity is contained in a ) be b , then the product or result will be denoted by ab ( Art . it will necessarily ...
... replaced by a , and if the symbol into which it is to be multiplied ( or which is to be repeated in addition as often as unity is contained in a ) be b , then the product or result will be denoted by ab ( Art . it will necessarily ...
Página 17
... replace expressions such as a +2 a by 3a : appears . x + 7x + 9x by 17x : ab - cd - 9 cd by ab - 10 cd . other co- combina- one . 31. If two or more like ( Art . 28 ) terms present themselves Rule for the in a compound expression with ...
... replace expressions such as a +2 a by 3a : appears . x + 7x + 9x by 17x : ab - cd - 9 cd by ab - 10 cd . other co- combina- one . 31. If two or more like ( Art . 28 ) terms present themselves Rule for the in a compound expression with ...
Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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...
Página 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.
Página 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?
Página 34 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Página 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.
Página 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.
Página 173 - If the first has to the second the same ratio which the third has to the fourth...
Página 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.