| Philip Ronayne - Algebra - 1717 - 408 pages
...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, one... | |
| Thomas Simpson - Logarithms - 1748 - 77 pages
...of them ; fince one Half of the Terms will be intirely deftroyed thereby. Therefore, becaufe the Sum **of the Logarithms of any two Numbers is equal to the Logarithm of** the Product of thofe Numbers, (fee Article i.) it is manifeft that zx -f ^JL JT^JL &c. will truly exprefs... | |
| John Rowe - Calculus - 1767 - 218 pages
...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. Corollary.... | |
| Thomas Simpson - Trigonometry - 1799 - 79 pages
...either of them ; fince one half of the terms will be jntireiy deilroyed thereby. Therefore, becaufe the **fum of the logarithms of any two numbers is equal to the logarithm** pf the produft of thofe numbers, (jee Article I.) it is mani2A?3 fed that zx + —-+ - &c. will truly... | |
| John Bonnycastle - Algebra - 1806 - 208 pages
...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 numbers,... | |
| John Bonnycastle - Algebra - 1811 - 220 pages
...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 express... | |
| 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 N,... | |
| Encyclopedias and dictionaries - 1816
...* + 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 - Euclid's Elements - 1816 - 528 pages
...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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