| Sir Isaac Newton - Calculus - 1745 - 479 pages
...the Logarithm of the compounded Ratio, and the reft eafily follows. Whence it follows that the Sum **of the Logarithms of two Numbers is equal to the Logarithm of** their Product, and the Difference of the Logarithms of two Numbers is the Logarithm of their Quotient,... | |
| William Trail - Mathematics - 1796 - 311 pages
...the fum of the logarithms of • b and f, is therefore, by the definition, the logarithm of 4f- ,' , **4. The difference of the logarithms of two numbers is equal to the logarithm of** their quotient For, if am-='b, and a"=c, f_=— , that is, am— "—— • m — n^ or the a" cc... | |
| Encyclopedias and dictionaries - 1816
...logarithms,^ X log. io = log. i'7i8»8i8, § 41 : Hence log, io XA = . XA is the logarithm of-; that is, **the difference of the logarithms of two numbers is equal to the logarithm of** their quotient. If we refume the equation r * =sa,vre have 1 A ' } I r —a*, therefore n A is the... | |
| Etienne Bézout, François Peyrard, Noble Heath - Arithmetic - 1825 - 236 pages
...of the logarithm of a number shows in what decade this number is comprised, number 222. 91. The sum **of the logarithms of two numbers is equal to the logarithm of** their product, number 227. 92. The logarithm of any power of a number is equal to the logarithm of... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...equal to the logarithms of the product of these numbers ; 2d. The difference of the logarithms of tw о **numbers is equal to the logarithm of the quotient of these numbers** ; 3d. The logarithm of any power of a number is equal lo the logarithm of the root multiplied by the... | |
| Thomas Curtis (of Grove house sch, Islington)
...table opposite to that logarithm which is the sum of the logarithms of ihe numbers. Again, because **the difference of the logarithms of two numbers is equal to the logarithm of** tlie quotient arising from the division of the one number by the other, § 4, that quotient will be... | |
| Silas Totten - Algebra - 1836 - 304 pages
...subtracting the exponent x from x, we have, а'-" =У or1.yl.y' =1Д; У У from which we see, that **the difference of the logarithms of two numbers, is equal to the logarithm of** their quotient. Hence, division is performed in logarithms by subtracting the logarithm of the divisor... | |
| Euclid - 1837 - 390 pages
...logarithms, which are called logarithmic sines, tangents, &c.* By the nature of logarithms, the sum **of the logarithms of two numbers is equal to the logarithm of** their product; and, conversely, if the logarithm of one number be taken from the logarithm of another,... | |
| James Thomson - Geometry - 1845 - 358 pages
...logarithms, which are called logarithmic sines, tangents, &c.* By the nature of logarithms, the sum **of the logarithms of two numbers is equal to the logarithm of** their product ; and, conTersely, if the logarithm of one number be taken from the logarithm of another,... | |
| Joseph Ray - Algebra - 1852 - 396 pages
...logarithms, x-\-x', the exponent of a, is the logarithm of NN' ; hence, we have PROPERTY I. — The sum **of the logarithms of two numbers is equal to the logarithm of** their product. It may be shown similarly that the sum of the logarithms of three or more factors, is... | |
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