A Theoretical and Practical Treatise on Algebra: In which the Excellencies of the Demonstrative Methods of the French are Combined with the More Practical Operations of the English and Concise Solutions Pointed Out and Particularly Inculcated : Designed for Schools, Colleges and Private Students |
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Page viii
... Logarithms . Compound Interest 231 Exponential Equations and Logarithms 233 244 246 Annuities 247 SECTION VII . General Theory of Equations . 251 Binomial Equations 260 Newton's Method of Divisors ( Art . 167 ) 264 Equal Roots 267 ...
... Logarithms . Compound Interest 231 Exponential Equations and Logarithms 233 244 246 Annuities 247 SECTION VII . General Theory of Equations . 251 Binomial Equations 260 Newton's Method of Divisors ( Art . 167 ) 264 Equal Roots 267 ...
Page 231
... , will convert that series into regular powers of y , which was the object to be accomplished . As every term contains y , we can reduce the REVERSION OF A SERIES . 231 Reversion of a Series Application of Logarithms Compound Interest.
... , will convert that series into regular powers of y , which was the object to be accomplished . As every term contains y , we can reduce the REVERSION OF A SERIES . 231 Reversion of a Series Application of Logarithms Compound Interest.
Page 233
... logarithm of the number b ; and to every variation of x , there will be a corresponding variation to b ; a is constant , and is 20 LOGARITHMS . 233 Exponential Equations and Logarithms.
... logarithm of the number b ; and to every variation of x , there will be a corresponding variation to b ; a is constant , and is 20 LOGARITHMS . 233 Exponential Equations and Logarithms.
Page 234
... logarithm of the base of any system is unity . If we suppose x = 0 , the equation becomes ao = 1 ; hence , the logarithm of 1 is 0 , in every system of logarithms . ( Art . 146. ) The logarithms of two or more numbers added together ...
... logarithm of the base of any system is unity . If we suppose x = 0 , the equation becomes ao = 1 ; hence , the logarithm of 1 is 0 , in every system of logarithms . ( Art . 146. ) The logarithms of two or more numbers added together ...
Page 235
... logarithm . On this principle we may approximate to the logarithm of any proposed number . For example , we propose to find the lo- garithm of 2 . This number is between 1 ... logarithm of 3 be required . The equation LOGARITHMS . 235.
... logarithm . On this principle we may approximate to the logarithm of any proposed number . For example , we propose to find the lo- garithm of 2 . This number is between 1 ... logarithm of 3 be required . The equation LOGARITHMS . 235.
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Popular passages
Page 18 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 28 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 23 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 191 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Page 82 - It is required to divide the number 24 into two such parts, that the quotient of the greater part divided by the less, may be to the quotient of the less part divided by the greater, as 4 to 1.
Page 196 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 191 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 198 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page vii - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal....
Page 55 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.