Arithmetic Prize Papers

W. P. Workman
1895 Mathematical Gazette  
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more » ... unction Eyz as the sum of three positive or three negative squares. W. J. GREENSTREET. 60. To inscribe three mutually tangent circles in an isosceles triangle. PROF. D. S. WRIGHT. 61. In the trapezoid ABCD the parallel sides AB, CD are constants, and meet the variable base BD at right angles: prove that the perpendicular to BD from the intersection of the diagonals AD, BC is constant. PROF. D. S. WRIGHT. REVIEWS AND NOTICES. A Treatise on Computation. By E. M. LANGLEY. (Longmans, 1895.) Great attention has of late years been paid to quick methods of performing numerical calculations, and not a few papers and leaflets been written on the subject, but these have of necessity reached but a limited circle of readers. The present book presents in a systematic form the latest results of these endeavours, and should be welcomed by all good teachers of arithmetic. It is divided into four sections, the first being devoted to the best methods of performing arithmetical operations (including Homer's method of finding cube roots), and the second to abbreviated means of obtaining approximate results, attention being called to the fact that in scientific calculations the data are only approximately accurate, and that no calculated results can be more accurate than the data. The third section is on logarithmic work, and is worthy of most careful attention by every student and teacher. The fourth section works out some practical examples, illustrating the methods of the book. It is a book that cannot be read in junior classes, but should be in the hands of every teacher, who should use its methods in such classes, and it should be worked through by the students as soon as they are sufficiently advanced. The book hardly deals at all with mercantile computation, except so far as that is decimal. The following two misprints have been noticed. P. 7, Ex. (5), 1985673 should be two separate numbers, viz. 1985 and 673. P. 183, No. 32. The fraction 4 should be -47.
doi:10.2307/3604728 fatcat:hkx56z4zszasjcjfa5uxsdvs2e