Mathematical Questions with Their Solutions Volume 73; From the Educational Times. (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. 1900 Excerpt: ...Dans le quadrilatere inscriptible ABCC, Gi est le point de coupe des paires de cotes opposes. Il en resulte que le triangle FH, est' autopolaire par rapport a la circonference; Gi se trouvant sur BC, sa polaire Fit passe par le pole A' de BC. En outre OG est perpendiculaire sur FiH ce qui demontre les deux dernieres parties. 14317. (G. H. Hardy, B.A.)--Prove FRULLANi's theorem J-- (-)-- (fa) _ (oo (0)j loga/J) extending it to apply to the eases in which (1) p (x), while possessing a determinate integral near any value of x, has a discrete set of infinities in the range (0, oo); (2) only the principal value of the integral is deter 14239. (B. N. Cama, M.A. In continuation of Quests. 14177 and 14207.)--If OPiP2 OCQs... be two vectors including a right angle, meeting an equiangular spiral (pole 0) in the points P P2. Q1, Qj, Bhow that the parabolas drawn to touch the curve at PiQi, P2Q2, and having the chords of contact for their focal chords are in geometrical progression; further, that their axes are parallel to a fixed line. The perpendicular from o on AB equals half the difference, or half the sum, of the perpendiculars from b and c on AB, and the ratio of perpendiculars from a on AB and AC can he proved equal to (sin B--cos B) and (sin C--cos C). Therefore Aa, Bfl, C7 are concurrent. 14388. (Rev. T. Roach, M.A.)--A circle is inscribed in the sector of a clock face formed by the hands at 4 o'clock, and perpendiculars are drawn from the centre to both clock hands, forming a sector of the smaller circle. Find the ratio of the larger sector to the smaller. 9964. (Capitaine De Rocquigny.)--Trouver des solutions entieres de liquation x'" + ym--1 = M (xy). 9890. (R-W. D. Christie.)--Fi...