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Bøker Bok 110 av 30JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm...
" JJ/xJV; 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. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 43
av Thomas Simpson - 1799 - 79 sider
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1717 - 408 sider
...the Logarithm of of the Product of the faid two (natural ) Numbers : And confequently the Remainder of the Logarithms of any two Numbers, is equal to the Logarithm of the Quotient of the " faid two Numbers ; as alfo twice three times, four times, &c. or one half,...
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An Introduction to the Doctrine of Fluxions

John Rowe - 1767 - 218 sider
...how a Ci/oid is generated, art. 34. note. t> a—x-\-ca> x Hyp. Log. of a = (becaufe the Difference of the Logarithms of any two numbers is equal to the Logarithm of their ._ . L . 2 Quotient,) — cxxHyp. Log. of - = the Content of the J a — x Solid ABH required....
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Elements of Algebra for the Use of Students in Universities: To which is ...

William Trail - 1796 - 311 sider
...oi~ ' ;-'-<' '-,••',;- --'-I": 3. Hence the properties of logarithms are eafily deduced. I*''The fum of the logarithms of any two numbers is equal to the logarithm of their product. Le-t b and c be the numbers, m and M their logarithms,^ that am—ti^ and a" =<r,...
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An Introduction to Algebra: With Notes and Observations; Designed for the ...

John Bonnycastle - 1806 - 208 sider
...either of them, as one half of the terms will, in that cafe, be entirely deftroyed. Since, therefore, the fum of 'the logarithms of any two numbers is equal to the logarithm of the produit of thofe numbers, it is manifeft that 2_r+ — ц -- &c. will truly exprefs the logarithm...
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Encyclopædia Britannica: or, A dictionary of arts and sciences, compiled by ...

Encyclopaedia Britannica - 1810
...logarithms of all numbers within certain limits may be applied to Amplify calcular tions : for (ince the fum of the logarithms of any two numbers is equal to the logarithm of their produit ; it follows, that as often as we have occafion to find the produit of two or more...
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1811 - 220 sider
...them, as one half of the terms will, in that case, be entirely destroyed. Since, therefore, the sum of the logarithms of any two numbers is equal to the logarithm of the product of those numbers, it is manifest that 2x + M«3 Q-r5 1 I 3.' ^— -4 , &c. will truly...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...powers of 1 + a, the numbers 3, 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 riroduct of the same two nnmbm Thus if 1 + a raised to the w th power be equal to the number...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volum 13

1816
...therefore r * + r," =•: «*,;, but r AX r * == r A + i; therefore A ^- B Is the logarithm of at; that is, the fum of the logarithms of any two numbers is equal to the logarithm of the produft. Again, A. • A i A' A A' * »•' = a; therefore r = r> , andrp = f. Thus it appears...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...powers of 1 -t. a, the numbers 3, 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 ntb power be equal to the number...
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Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volum 12

1823
...logarithms of all numbers within certain limits may be applied to simplify calculations ; for since the sura of the logarithms of any two numbers is equal to the logarithm of their product, it follows, that as often as we have occasion to find the product of two or more...
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