 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 - Trigonometry - 1827 - 546 pages
...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) - 412 pages
...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 - Surveying - 1830 - 318 pages
...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 - Surveying - 1830 - 390 pages
...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 - Surveying - 1833 - 436 pages
...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 - 518 pages
...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... | |
 | Charles Davies - Navigation - 1837 - 342 pages
...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 - 264 pages
...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 - Surveying - 1839 - 376 pages
...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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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. 
