 | Philip Ronayne - 1717 - Liczba stron: 478
...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 - 1748 - Liczba stron: 84
...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 - 1767 - Liczba stron: 266
...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 - 1799 - Liczba stron: 92
...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 - 1806 - Liczba stron: 234
...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 - Liczba stron: 816
...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 - 1811 - Liczba stron: 230
...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 - Liczba stron: 560
...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,... | |
 | 1816 - Liczba stron: 746
...* + 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 - Liczba stron: 588
...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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JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. 
