| Peter Nicholson - 1825 - 372 sider
...the exponent • From Napier, the invent' r of logarithms. X + Z is the logarithm of xz. Therefore, **the sum of the logarithms of any two numbers is equal to the** logarithms of their product. QED Cor. — Hence it is evident that the gum of the logarithms of any... | |
| Robert Simson - 1827 - 513 sider
...the powers of J +a, the numbers S, 4, 5, &.c., for the same reasons, will fall into the series. 6. **The sum of the logarithms of any two numbers is equal to the logarithm of the product of** the same two numbers. Thus if 1 +a raised to the wth power be equal to the number N, and if 1 +a raised... | |
| Thomas Curtis (of Grove house sch, Islington)
...multiplication, division, involution, and evolution, maybe performed with great facility. 12. For, since **the sum of the logarithms of any two numbers is equal to the logarithm of** their product, § 3, the product of any two numbers will be found in the table opposite to that logarithm... | |
| Charles Davies - 1830 - 306 sider
...at+n— nXwz. In this expression, x+y is the logarithm of n X m (2) ; from which we conclude, that tht **sum of the logarithms of any two numbers, is equal to the logarithm of** their product. ri. If the equation* ar=n, a»=m, be divided, member by member, - =- ; or oI~*=-. In... | |
| Charles Davies - 1830 - 300 sider
...or a*+»— nXm. In this expression, x+y is the logarithm of nXm (2) ; from which we conclude, that **the sum of the logarithms of any two numbers, is equal to** tht logarithm of 5. If the equations az=n, aP=m, be divided, member by member, — =— ; or az~'J=—... | |
| Robert Gibson - 1833 - 348 sider
...or «I+!'=nXm. In this expression, x+y is the logarithm of reX»i (2) ; from which we conclude, that **the sum of the logarithms of any two numbers, is equal to the logarithm of** their product. 5. If the equations ax=n, t&=^m, be divided, member by member, — =-; or ax~~y=-. In... | |
| Euclides - 1834
...the powers of 1+a, the numbers 3, 4, 5, &c. for the same reasons, will fall into the series. ART. 6. **The sum of the logarithms of any two numbers is equal to the logarithm of the product of** the same two numbers. Thus if 1 +a raised to the nth power be equal to the number N, and if 1+a raised... | |
| 1837 - 249 sider
...second, member by member, we have but since a is the base of the system, m+n is the logarithm MxN; hence, **The sum of the logarithms of any two numbers is equal to the logarithm of** their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.... | |
| Euclides - 1838
...the table for the number, NN', which has the sum a + x' for its logarithm. THEOREM II. The difference **of the logarithms of any two numbers is equal to the logarithm of the** quotient of those numbers. As before, let 10'= N and lO* = N'. Then, by dividing (Algebra, pa. 13),... | |
| Charles Davies - 1839 - 334 sider
...Logarithmic Sines, ........ 37 but since a is the base of the system, m+n is the logarithm JlfxJV; hence, **The sum of the logarithms of any two numbers is equal to the logarithm of** their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.... | |
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