Calendar: 1857-1858 Page 434

436 THE SCHOOL Triangles upon equal bases and between tbe same parallels are equal to one anotber Let ABC Β be two equal triangles on the same base AB and on opposite sides of it join CO cutting Β in Έ then shall CE ΈΏ 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 If two triangles have one angle of the one equal to one angle of the other and the sides about the equal angles pro- portionals the triangles shall be equiangular and shall have those angles equal which are opposite to the homologous sides 10 If two triangles which have two sides of the one propor- tional to two sides of the other be joined at one angle so as to have their homologous sides parallel to one another the re- maining sides shall be in straight line 11 If ABC Ό be parallelogram and Ρ and two points in line parallel to AB and if FA QB meet in and ΡD QC in prove that RS is parallel to AD 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 II -algebra If four quantities be proportionals according to Euclid's definition prove that they will be so according to the algebraic definition If ev &c &c then shall am bη -cp f- &c αλΜ bxn &c Two clocks point to 12 at the same instant one of them gains 7" and the other loses 6'' in 12 hotys AVhen will one have gained half-an-hour on the other and what time will it show If ץ -f 15 find