Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times." Volume 66 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 Excerpt: ...result shows that (OA, OA'), (OB, OB'), (OC, OC) are confocal. We get a similar result for any number n of straight lines OA, OB, OC, &c, the foci of the last ellipses being (2a2)', and therefore independent of the order in which the lines OA, OB, &c, are taken. OA3 = the difference of the squares of the semi-axes; /32 + 72 = their sum. 13186. (H. Orfeur.)--If the denominator of the penultimate convergent of a continued fraction be equal to tho numorator of the ultimate convergent, the partial quotients equidistant from the ends are equal. 13026. (Kov. T. Roach, II. A.)--On the Bedford Level three poles of equal height are set up in a straight lino at distances of 660 yards, and a man looks from tho top of the first polo at the top of the third. Show that, owing to the rotundity of the earth, the top of the second pole will be above his line of sight, and calculate the difference approximately, taking the radius of tho earth as 3960 miles. Solution by W. J. Doehs, M.A.; Rev. J. L. Kitchin; and others. The poles are normal to the surface; hence the tops lie on a circle whose centre is that of the earth. Tho chord A'C, the man's line of sight, thus falls below B'. 13208. (M. Brierley.)--Given a line drawn from the vertex to the middle of the base, and one of the angles at the base, to construct the triangle when the area is a maximum. Solution by Rev. T. Wiggins, S.J.; W. E. Jeffares, B.A.; and others. 13068. (Rov. T. Wiggins, S.J.)--A person in a boat w miles from the nearest point of the beach wishes to reach in the shortest time a place x miles from that point along the shore. Supposing he can walk y miles an hour, but pull only at the rate of z miles an hour, where must he land? Explain the absence of x in the answer, and the obvious discrepancy w...