THE VETERINARY PROFESSION 37 



equal to two right angles, then these two straight lines shall be 

 in one and the same straight line. 



ABCD is a rhombus ; 0,E,F are the mid-points of A C, 

 AB, CD, respectively : prove that FOE is a straight line. 



2. If one side of a triangle is greater than another, then the 

 angle opposite to the greater side shall be greater than the 

 angle opposite to the less. 



3. If two triangles have two angles of the one equal to two 

 angles of the other, each to each, and the sides adjacent to the 

 equal angles in each equal, then shall the triangles be equal in 

 all respects. 



4. The complements of the parallelograms about the diagonal 

 of any parallelogram are equal to each other. Apply the pro- 

 position to construct a parallelogram equal to a given one so 

 that one of its sides shall be twice a side of the given parallelo- 

 gram. 



5. If a straight line is divided into any two parts, the square 

 on the whole line is equal to the sum of the squares on the two 

 parts together with twice the rectangle contained by the two 

 parts. 



6. If one cord of a circle bisects another at right angles, 

 one of them must be a diameter. 



7. The straight line drawn perpendicular to a tangent to a 

 circle from the point of contact passes through the centre. 



8. AC, BD are two equal chords of a circle which cut one 

 another at right angles in E. Prove that the difference of the 

 squares on AB, CD is equal to twice the rectangle under the 

 sum of the chords i^AC, BD) and their distance from the centre. 



MECHANICS 



[Eight questions only to be answered.] 



1. Enunciate the Parallelogram of Forces. 



Determine the magnitudes of two forces acting at a 

 point at right angles to one another, such that the direc- 

 tion of their resultant SP makes an angle of 60° with the 

 direction of one of the forces. 



2. A uniform heavy bar 22 inches long, weighing 9 lbs., with 

 weights 5 lbs. and 8 lbs. hanging from the ends respectively, 



