| 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,... | |
| 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.... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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