# Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times Volume 59

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 edition. Excerpt: ...others. Let M be the mass of bucket or counterpoise, and m the mass of the ball. Velocity of ball just before first impact is (2gh)i. The velocity of the ball relative to the bucket has to be gradually destroyed by impacts. Therefore total time between ball starting from rest and settling down to rest on bucket is Loss of kinetic energy by an impact = iii (1--e5) (rel. vel. before By the equation of energy, total energy imparted to the system = K.E. at end + K. E. lost; therefore 11530, (Rev. C. L. DonosoN, M.A.)--Required a general investigation of the following trigonometrical formula, which is useful in calculating limits for the value of 1r. The problem which I set myself was to break up tan'1 1/It into two angles of the same form. Let.Brit" Art. " Algebra" (Ed. 7, Vol. 11., p. 497, Ed. 8, Vol. 11., p. 557, as = as, and so on, the disadvantage of the use of any given formula varying with the suflix pertaining to that formula. From the remarks at the end of the second volume of the Werke, it appears that GAUss had obtained a formula, of this class, which fully deserves the epithet " remarkable." We have be integral. Thus we give at, a value, and then, by means of a table of " prime factors of aa+1," we can find suitable values for a, and hence for b. G/1Uss's Editor, SciiEnmo, to whom we owe the abstraction and preservation of these manuscript remains, gives (Werke, Bd. 11., p. 525) the following examples of the use of the formula: (2): --we may very readily "expand " a relation in A cots; thus we have, for 11r, the several values: --6582, (R. A. R0BsnTs, M.A.)--If a bicircular quartic meet a conic, show that the sum of the eccentric angles of the eight points of intersection is...show more

## Product details

• Paperback | 30 pages
• 189 x 246 x 2mm | 73g
• United States
• English
• black & white illustrations
• 1236993934
• 9781236993939