A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page xi
... geometrical and harmonical progressions or 275 series order subtra CHAPTER VII . formed Theory of permutations and combinations 297 * Th CHAPTER VIII . as indica For On the formation of binomial products and powers .. 325 CHAPTER IX ...
... geometrical and harmonical progressions or 275 series order subtra CHAPTER VII . formed Theory of permutations and combinations 297 * Th CHAPTER VIII . as indica For On the formation of binomial products and powers .. 325 CHAPTER IX ...
Page 154
... geometrical representation of ratio , being the only one which is used in that science . Whatever modes , however , we may adopt in geometry for the representation of ratios , they must all of them be equally arbitrary and independent ...
... geometrical representation of ratio , being the only one which is used in that science . Whatever modes , however , we may adopt in geometry for the representation of ratios , they must all of them be equally arbitrary and independent ...
Page 156
... geometrical as well as other mag- nitudes . 262. The preceding observations will conduct us naturally to the following conclusions : ( 1 ) Magnitudes of the same kind , which admit of resolution into any numbers of parts or units ...
... geometrical as well as other mag- nitudes . 262. The preceding observations will conduct us naturally to the following conclusions : ( 1 ) Magnitudes of the same kind , which admit of resolution into any numbers of parts or units ...
Page 157
... geometrical mode of representing the division of one line by another , or the result of such a division : Reason why there for this result can bear no analogy to the quantities which pro- is no defini- duce it , being essentially ...
... geometrical mode of representing the division of one line by another , or the result of such a division : Reason why there for this result can bear no analogy to the quantities which pro- is no defini- duce it , being essentially ...
Page 161
... Geometrical magnitudes , being subject to the law of Lines may continuity , are capable of representing symbolically any mag- continuous nitudes of the same kind , and therefore also their ratios to each magnitude . other ; but when ...
... Geometrical magnitudes , being subject to the law of Lines may continuity , are capable of representing symbolically any mag- continuous nitudes of the same kind , and therefore also their ratios to each magnitude . other ; but when ...
Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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...
Page 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.
Page 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?
Page 34 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Page 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.
Page 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.
Page 173 - If the first has to the second the same ratio which the third has to the fourth...
Page 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.