A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 |
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Página viii
... factors of a product ' , of the rule fo the multiplication and division of fractions , of the rule for finding the greatest common measure of two quantities , whether numbers or algebraical expressions3 , of the form of the product of ...
... factors of a product ' , of the rule fo the multiplication and division of fractions , of the rule for finding the greatest common measure of two quantities , whether numbers or algebraical expressions3 , of the form of the product of ...
Página 21
... factors , and ab is expressed by a.b : but it may be considered as a general principle in Algebra , amongst different modes of repre- sentation which possess the same meaning and which are equally distinct and unambiguous , to adopt ...
... factors , and ab is expressed by a.b : but it may be considered as a general principle in Algebra , amongst different modes of repre- sentation which possess the same meaning and which are equally distinct and unambiguous , to adopt ...
Página 22
... factors are different from each other . In Algebra , however , the product of two symbols is exhibited only and no operation , like arithmetical multiplication , is performed ; and consequently it is not necessary , in the case of ...
... factors are different from each other . In Algebra , however , the product of two symbols is exhibited only and no operation , like arithmetical multiplication , is performed ; and consequently it is not necessary , in the case of ...
Página 23
... factor or multiplicand is repeated . In all such cases it is usual , for greater brevity , to express the same ... factors , a2 and a3 , of the symbol . product . In the same manner when a1 is multiplied into a the result a a7 is ...
... factor or multiplicand is repeated . In all such cases it is usual , for greater brevity , to express the same ... factors , a2 and a3 , of the symbol . product . In the same manner when a1 is multiplied into a the result a a7 is ...
Página 24
... factors which are multiplied together , and it will therefore be correctly represented by a single power of a , whose index is equal to the sum of the indices of all the component factors of the product : for it is obvious that the ...
... factors which are multiplied together , and it will therefore be correctly represented by a single power of a , whose index is equal to the sum of the indices of all the component factors of the product : for it is obvious that the ...
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.