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Bøker Bok 1120 av 37The sum of the logarithms of any two numbers is equal to the logarithm of their product....
" 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. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 41
av Thomas Simpson - 1748 - 77 sider
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

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...
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The London encyclopaedia, or, Universal dictionary of science, art ...

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...
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Elements of Surveying: With the Necessary Tables

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...
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Elements of Surveying

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=—...
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The Theory and Practice of Surveying: Containing All the Instructions ...

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...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...
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Elements of Surveying: Including a Description of the Instruments and the ...

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....
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

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),...
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Elements of Surveying: With a Description of the Instruments and the ...

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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