A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 |
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Página iv
... definitions ( whether e pressed or understood ) as in common arithmetic : the sig + and denote the operations of addition and subtractio in their ordinary meaning only , and those operations a considered as impossible in all cases where ...
... definitions ( whether e pressed or understood ) as in common arithmetic : the sig + and denote the operations of addition and subtractio in their ordinary meaning only , and those operations a considered as impossible in all cases where ...
Página v
... definition of the power of a symbol , and therefore in no other case can we appeal to it in determining the form of the product : the series for ( a + b ) " is also a necessary result of the same definition , and subject therefore to ...
... definition of the power of a symbol , and therefore in no other case can we appeal to it in determining the form of the product : the series for ( a + b ) " is also a necessary result of the same definition , and subject therefore to ...
Página vi
... definitions upo which that science is founded . Symbolical algebra adopts the rules of arithmetica algebra , but ... definition upon which those rules in arithmetical algebra are founded we are thus enabled to subtract a + b as well ...
... definitions upo which that science is founded . Symbolical algebra adopts the rules of arithmetica algebra , but ... definition upon which those rules in arithmetical algebra are founded we are thus enabled to subtract a + b as well ...
Página vii
... definitions of arithmetical algebra , as far as they proceed in common , and by the " principle of the permanence of equivalent forms " in all other cases , which those definitions cannot comprehend : it will follow therefore that in ...
... definitions of arithmetical algebra , as far as they proceed in common , and by the " principle of the permanence of equivalent forms " in all other cases , which those definitions cannot comprehend : it will follow therefore that in ...
Página viii
... definitions which are totally inapplicable in such cases . It is quit true indeed that writers on algebra have not hithert remarked the character of the transition from one class of results to the other , and have treated them both a ...
... definitions which are totally inapplicable in such cases . It is quit true indeed that writers on algebra have not hithert remarked the character of the transition from one class of results to the other , and have treated them both a ...
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.