Calendar: 1853-1854 Page 400

390 THE SCHOOL Differential CalruIuS If χ I-a ץ dx ΪΞΙ2 1-x2' Expand esl x' according to the powers of χ as far as xy du If ץ sec χ where find Find the values of- -f cos χ sin xJ יי י χ sin χ י when χ יי Trace the curve y2 xa linear and hyperbolic asymptotes of xl a2 χ ft Λ Ii and CZ are arallels join AD Β intersecting in given AB AD and find CD when the sum of the triangles Α Ρ Β Ρ Β is maximum From what point of given straight line will another line of given magnitude and position appear to be the greatest Find the differential of the length of curve and apply the expression to the cycloid Define conjugate and multiple point and find the point at the origin of the first curve in question 10 Find the subtangent of the curve defined by 53 sec Θ SECOND CLASS MATHEMATICAL SCHOLARSHIP L-eueltD The complements of the parallelograms which are about the diameter of any parallelogram are equal to one another The diagonals of the complements being produced meet in the diagonal of the parallelogram