A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
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Page 54
... primary unit ) is divided into as many equal parts as there are units in the divisor or denominator and that as many of these subordinate units are taken as there are units in the numerator : it is for this reason that we are compelled ...
... primary unit ) is divided into as many equal parts as there are units in the divisor or denominator and that as many of these subordinate units are taken as there are units in the numerator : it is for this reason that we are compelled ...
Page 55
George Peacock. subordinate unit which is required to be expressed , the num ... units , three such units , and a times such b Ъ units , where a is the ... primary units only ; whilst the second gives = a pb Ђ a pb + c b pb C Ђ Ђ p ...
George Peacock. subordinate unit which is required to be expressed , the num ... units , three such units , and a times such b Ъ units , where a is the ... primary units only ; whilst the second gives = a pb Ђ a pb + c b pb C Ђ Ђ p ...
Page 56
... units such as 1 subordinate unit ī dinate unit 1 1 bc ' , compose one primary and if we take ac times the secondary subor- be forming the fraction bc ac be ( Art . 94. ) , it will evidently 1 be equivalent to a times the primary subordinate ...
... units such as 1 subordinate unit ī dinate unit 1 1 bc ' , compose one primary and if we take ac times the secondary subor- be forming the fraction bc ac be ( Art . 94. ) , it will evidently 1 be equivalent to a times the primary subordinate ...
Page 60
... primary b ' unit , that P and p ' cannot differ from each other by I or by any multiple of 1 . 109. LEMMA II . If two fractions be equal to one another , their reciprocals are also equal to one another . For if a a ' Ъ b = and if we ...
... primary b ' unit , that P and p ' cannot differ from each other by I or by any multiple of 1 . 109. LEMMA II . If two fractions be equal to one another , their reciprocals are also equal to one another . For if a a ' Ъ b = and if we ...
Page 66
... units , denominated the nume- by their denominators ( Art . 94. ) , as are expressed by their nume- rators , it follows ... primary unit ) by having their numerators and denominators multiplied or divided by the same number ( Art . 97 ...
... units , denominated the nume- by their denominators ( Art . 94. ) , as are expressed by their nume- rators , it follows ... primary unit ) by having their numerators and denominators multiplied or divided by the same number ( Art . 97 ...
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.