Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
From inside the book
Results 1-5 of 60
Page
... Square Root of Binomial Surds 238 XLVIII . Of Logarithms in general 244 XLIX . On the Application of Logarithms to Arith- metical Calculations 254 L. Of the Calculation of Interest 257 LI . Of the Nature of Equations of the Second ...
... Square Root of Binomial Surds 238 XLVIII . Of Logarithms in general 244 XLIX . On the Application of Logarithms to Arith- metical Calculations 254 L. Of the Calculation of Interest 257 LI . Of the Nature of Equations of the Second ...
Page 53
... square root . For example , if we multiply 12 by 12 , the product 144 is a square , of which 12 is the square root . The origin of this term is taken from geometry , where the contents of a square are found by multiplying its side by ...
... square root . For example , if we multiply 12 by 12 , the product 144 is a square , of which 12 is the square root . The origin of this term is taken from geometry , where the contents of a square are found by multiplying its side by ...
Page 54
... square of the numerator by the square of the denominator , and the fraction which ex- presses that division is the square of the given fraction . Thus is the square of , and reciprocally is the square root of ft . 140. If we wish to find ...
... square of the numerator by the square of the denominator , and the fraction which ex- presses that division is the square of the given fraction . Thus is the square of , and reciprocally is the square root of ft . 140. If we wish to find ...
Page 55
... square will be aa or a2 ; if the root be 2a the square is 4 a a or 4a2 ; from which we learn that if the root be doubled , the square will be four times as great . Thus also if the root be 3a the square will be 9 a2 , & c .; but if the root ...
... square will be aa or a2 ; if the root be 2a the square is 4 a a or 4a2 ; from which we learn that if the root be doubled , the square will be four times as great . Thus also if the root be 3a the square will be 9 a2 , & c .; but if the root ...
Page 56
... square root of a given number is a number such that its square is equal to the number pro- posed , and that we may prefix to such roots either a positive or a negative sign . 145. Thus , when a square number is given , and we can retain ...
... square root of a given number is a number such that its square is equal to the number pro- posed , and that we may prefix to such roots either a positive or a negative sign . 145. Thus , when a square number is given , and we can retain ...
Contents
1 | |
4 | |
8 | |
12 | |
16 | |
19 | |
22 | |
28 | |
101 | |
115 | |
133 | |
137 | |
138 | |
140 | |
142 | |
148 | |
32 | |
36 | |
40 | |
43 | |
46 | |
49 | |
50 | |
51 | |
52 | |
53 | |
64 | |
66 | |
69 | |
74 | |
76 | |
88 | |
152 | |
157 | |
167 | |
173 | |
183 | |
189 | |
195 | |
204 | |
249 | |
254 | |
269 | |
276 | |
298 | |
301 | |
305 | |
311 | |
Common terms and phrases
already seen arithmetic means arithmetic series arithmetical progression assume binomial cent CHAP coefficient common difference Completing the square consequently consider contains cube root decimal determine divided dividend divisible equal equation evident example exponent expressed Extracting the root factors find the greatest Find the sum find the values formula four roots fourth term geometric means geometrical progression given number gives greater number greatest common divisor greatest common measure Hence infinite series infinitum instance integer irrational last term less letters logarithm manner method multiplied negative numbers number of permutations number of terms obtain quadratic surds quotient radical sign ratio reduced remainder represented required to find rule second degree second term square root subtracted suppose third degree three numbers tion transposition unity unknown quantity whence whole number
Popular passages
Page 46 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 24 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 228 - There are three numbers in geometrical progression ; the sum of the first and second of which is 9, and the sum of the first and third is 15.
Page 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Page 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 58 - We call this new species of numbers, irrational numbers ; they occur whenever we endeavour to find the square root of a number which is not a square. Thus, 2 not being a perfect square, the square root of 2, or the number which, multiplied by itself, would produce 2, is an irrational quantity. These numbers are also called surd quantities, or incommensurables.
Page 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Page 77 - any quantity may be transferred from "one side of the equation to the other, by changing its sign ;" and and it is founded upon the axiom, that " if equals be added to " or subtracted from equals, the sums or remainders will be
Page 113 - Ans. 3 and 7 8. The difference of two numbers is 2, and the difference of their cubes is 98; required the numbers. Ans. 5 and 3 9.
Page 37 - If the numerator and denominator are both, multiplied or both divided by the same number, the value of the fraction will not be altered.