Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
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... Interest 257 LI . Of the Nature of Equations of the Second Degree 269 LII . Of Pure Equations of the Third Degree 273 LIII . Of the Resolution of Complete Equations of the Third Degree 276 LIV . Of the Rule of Cardan 283 LV . Of the ...
... Interest 257 LI . Of the Nature of Equations of the Second Degree 269 LII . Of Pure Equations of the Third Degree 273 LIII . Of the Resolution of Complete Equations of the Third Degree 276 LIV . Of the Rule of Cardan 283 LV . Of the ...
Page 257
... INTEREST . 410. INTEREST is a consideration paid for the use , or for the forbearance of the payment of money . It is usual to express the interest of any principal by per cents , by which is meant the annual interest paid for 100 ...
... INTEREST . 410. INTEREST is a consideration paid for the use , or for the forbearance of the payment of money . It is usual to express the interest of any principal by per cents , by which is meant the annual interest paid for 100 ...
Page 258
... interest for the time required , so that representing this amount by M , we shall have the equation , MP + nrP = P ... interest is become due , it be added to the principal , and upon the principal so continually increased , at the end ...
... interest for the time required , so that representing this amount by M , we shall have the equation , MP + nrP = P ... interest is become due , it be added to the principal , and upon the principal so continually increased , at the end ...
Page 259
... interest at 5 per cent . , we have seen that a principal of 201. amounts to 217. at the end of one ycar ; and the ... interest being 5 per cent . But if the interest were reckoned at 6 per cent . , the fraction would be . S 2 414. Ge ...
... interest at 5 per cent . , we have seen that a principal of 201. amounts to 217. at the end of one ycar ; and the ... interest being 5 per cent . But if the interest were reckoned at 6 per cent . , the fraction would be . S 2 414. Ge ...
Page 260
... interest for a year be represented by R , we shall have the amount , or M≈ RP , and hence we have = M R P = and R = M1 P " . These equations are easily resolved by logarithms , when the numbers are large , for if R , n , and P be given ...
... interest for a year be represented by R , we shall have the amount , or M≈ RP , and hence we have = M R P = and R = M1 P " . These equations are easily resolved by logarithms , when the numbers are large , for if R , n , and P be given ...
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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.