A Treatise on Algebra: Arithmetical algebraJ. & J. J. Deighton, 1842 - Algebra |
From inside the book
Results 1-5 of 22
Page 8
... original number : thus if 7 be first added to 10 , makin by the signs and if the same number 7 be then subtracted from 17 result is 10 , which is the original number : or conversely , if first subtracted from 10 , leaving 3 , and if the ...
... original number : thus if 7 be first added to 10 , makin by the signs and if the same number 7 be then subtracted from 17 result is 10 , which is the original number : or conversely , if first subtracted from 10 , leaving 3 , and if the ...
Page 38
... original number 12 : and conversely , if the number 12 be first divided by 4 , and if their quotient 3 be then multiplied by 4 , the result will be the same original number 12. More generally if a number denoted by a be multiplied by a ...
... original number 12 : and conversely , if the number 12 be first divided by 4 , and if their quotient 3 be then multiplied by 4 , the result will be the same original number 12. More generally if a number denoted by a be multiplied by a ...
Page 54
... original dividend to be concrete , inasmuch as the mind cannot conceive the resolution of unity into parts , unless it represents a real magnitude . 93. There will occur cases in which the multiplier or di- multiplier visor will no ...
... original dividend to be concrete , inasmuch as the mind cannot conceive the resolution of unity into parts , unless it represents a real magnitude . 93. There will occur cases in which the multiplier or di- multiplier visor will no ...
Page 56
... original denominator of the improper fraction ; and conversely a mixed number becomes the improper fraction , whose numerator is the product of the integral part of the mixed number and of the denominator of the fraction , increased by ...
... original denominator of the improper fraction ; and conversely a mixed number becomes the improper fraction , whose numerator is the product of the integral part of the mixed number and of the denominator of the fraction , increased by ...
Page 75
... original and obvious meaning of the term . extension of terms from the 141. The use of symbols , whether digital or general , will Great lead to many other examples of the use of terms in senses ex- of the tremely remote from those ...
... original and obvious meaning of the term . extension of terms from the 141. The use of symbols , whether digital or general , will Great lead to many other examples of the use of terms in senses ex- of the tremely remote from those ...
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.