Calendar: 1859-1860 Page 444

GENERAL LITERATURE AND SCIENCE 445 dx xh dx AT -r -X-X2 X2 14 Also the following differentials χ log dx xKe-' dx 3j 1' si5 Mcos0 W7rLre 15 Find the length of an arc of the common parabola 16 Prove that xm-1 Α may be rationalized when either or I--1- is an integer η qj Ex x-3dx dx bx2 III -EroblitnS With point in the circumference of circle as centre an equal circle is described find the area of the intercepted figure Any whole number of the form a2 b2 where is greater than may be divided into three others in Harmonic Progression of which the sum of the squares shall be β4 -j- Of all rectangles inscribed in given right-angled isosceles triangle and having common angle with it the greatest is that which has its sides equal Find the ratio of this square to that which is inscribed in the same triangle with one side in the hypothenuse tan2 θ tan2φ sin θ sin φ If -ΓΖ and show that tan' י tan' β sin sin β cos cos β If pairs of normals are drawn to parabola at right angles to one another their points of intersection will lie on another