# Calendar: 1852-1853 Page 335

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GENERAL LITERATURE AND SCIENCE 381 II Given two numbers and the difference of their logarithms find the base of the system If η he prime number prime to and then -1 η is an integer η Three balls revolve in circles round common centre in 24 22 and 20 hours respectively they start from points in the same straight line wdien will they be in straight line again Find two fractions whose denominators are prime to each 68 other and sum ό If η be any number show that η -1 sin sin sin to η factors If log 12440 55 0048204 log 12441 0948553 find log 12440 345 Transform γ 53 into continued fraction and find the first four converging fractions If be in harmonic progression and מ be positive integer a" cn bn Find the coefficient of xn in the expanision of 10 Solve the equation cos χ sin 11 If be an approximate root of show that v- iV an מ Ν η a" 12 nCr being the combination of η things taken together prove that nCr nCn

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