Calendar: 1857-1858 Page 401

GENERAL LITERATURE AND SCIENCE 403 of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle If from point in the diameter Β of circle Ρ Ρ be drawn to the extremities of the chord QR which is parallel to AB then shall AP2 PB2 PQ2 PR1 Sum cos sin β -J- cos sin cos s'n &c to η terms If be the length of line drawn from to bisect AB 1c the base of the triangle ABC then area of the triangle I2 c2 tan The elevation of tower at place due south of it is 30 and at place due west of and feet from is 18 show 111 jT1 tL1-Ml fl1 πι 111 וווד Τ that the tower's height -7 Let ABC ABB be two equal triangles on the same base AB but on opposite sides of it join CD cutting AB in then shall CE ED 10 Triangles upon equal bases and between the same parallels are equal to one another 11 In circle the angle in semicircle is right angle but the angle in segment greater than semicircle is less than right angle and the angle in segment less than semicircle is greater than right angle 12 lamp elevated 32 feet from the ground is just seen by man six feet high at the distance of 10 miles determine the earth's radius 13 If two triangles which have two sides of the one pro- portional to two sides of the other be joined at one angle so as to have their homologous sides parallel to one another the remain- ing sides shall be in straight line 14 If Β CD be parallelogram and Ρ anil two points in line parallel to AB and if PA QB meet in and PD in prove that RS is parallel to AD 15 If two straight lines be parallel and one of them is ai