p. 146, Landen's Lucub.ations) which being called A, that of be 3 A, and confequently the whole fluent of 2 a3 x Anfwers were given by Mers. Bell, Bulmer, and Culler Coatfienfis, 1 XXXII. By Mr. BELL, Howdon-dock. FROM the fecond equation fubtrast three times the first, there remains 3 yy - - 2 x x = 10, for y fubftiture its value, reduced, become; x4 + 10x2 = 20, Hence x = and y = 211474. 1'30692, Anfavers were given by Mers. Ariftarchus, Bulmers Cuftin, Dixon, Dubfon, Marskienfis, Savill, and Walters. XXXIII. LET x =x Anfwere by CUSTIN, Newcale. the length of the piece broken off, d = 250, = piece ftanding, and c 70. Then, in the rightangled triangle, are given, the bafe (c) perpendicular (d and hypothenufe (x). Hence x2 + ce = xx, or x 2 x) = Mers. Addifon, Ariftarchus, Artuofo, Baron, Bell, Bulmer, Chapman, Dixon, Prudah, Savill, and Walters, fa voured us with Solutions. XXXIV. Anfwered by Mr. W. WALTERS, Darlington. diameter; and by Hutton's Measurer, p. 131, 2x2 +x2 + 42:2 x 2168 x 108 282 404 2638. Whence x 24 inches, the lefs diameter, and 48 inches the greater. Solutions were given by Meffis. Addifon, Ariftarchus, Artuofa, Baron, Bell, Bulmer, Chapinan, Cuftin, Dixon, Evanthus Markienfis, and Savill. New New QUESTIONS. XXXV. By Mr. W. SAVILI. HOW many deals may a perfon play at the game of whift, without ever holding the fame cards twice. XXXVI. By Mr. BARON, South-Shields. A PERSON being asked the hour of the day, answered 'tis past five: the bour and minute hands have coincided, fince the clock laft truck, and the angle fubtended by the hands is now one third of the angle between the hour-hand and the 12 o'clock line. I demand the time, without the help of algebra. XXXVII. By Mr. CHAPMAN, Sunderland. THERE is a rectangular field, whofe content is 20 acres; the angle at the bafe is 25 degrees: query the length of the hypotheaufe and base?. XXXVIII. By Mr. H. BELL, Howden-dock. SUPPOSE a ball carried up into the air, to the heighth of 10560 feet, there to be let fail, and to ftrike an inclined plane whofe angle of incidence is equal to 45°, with a force of 60lb. required the weight of the ball, when at reft on the surface of the earth, and when fufpended in the air at its greatest distance. ACKNOWLEDGEMENTS. Mers. Addifon, Baron, Nicholson, and fome other correfpondents remark, that the mathematical queftions in general are not adapted to the capacities of boys: que bave inferted nearly all the Questions we have been fovoured with, because we thought it contrary to the respect due to our mathematical Correfpondents to check their ardour in the pursuit of knowledge. It is in contemplation to propofe a Prize for the mathematical 'Department. TRIS. ECTION's Effay is received. |