Calendar: 1848-1849 Page 300

-yo THE SCHOOL Find the perimeter and area of the regular polygon of η sides inscribed in circle of given radius Show that the area of circle is π r3 where π is the length of semicircle whose radius is unity Apply De Moivre's theorem to find the cube roots of unity In the first proposition of the First Book of Euclid find the area common to the two circles in terms of the side of the equi- lateral triangle III taticsf Find the resultant of two parallel forces acting on rigid rod Determine the conditions of equilibrium of set of forces acting on rigid body in one plane '1 Find the ratio of the power to the weight in the screw State the laws of friction How are they proved body is placed on plane inclined at an angle of 30 to the horizon its weight is 10 lbs and it is found that horizontal force of lbs will just prevent it from slipping down the plane find the coefficient of friction Find the ratio of the power to the weight in the wheel and axle taking into account the friction of the axis round which the wheel and axle turns IV -DitTcvnittal iC ilculu Prove the following formulai sin χ tan log χ -- cos χ --- sec χ --- χ αχ α χ χ Expand by Maclaurin's Theorem ex sin χ in powers of or