CHAPTER XII. 



OF THE POSITIONS OF EQUILIBRIUM. 



PROBLEM LVI. 



373. Suppose that a solid homogeneous triangular prism, 

 floats upon the surface of a fluid of greater specific gravity 

 than itself, with only one of its edges immersed : 



It is required to determine in what position it will rest, 

 when it has attained a state of perfect equilibrium. 



Let ABC be a vertical transverse section, at right angles to the axis 

 of the homogeneous prism, floating A 

 in a state of equilibrium on the fluid 

 whose horizontal surface is IK. 



Bisect AB, BC the sides of the tri- 

 angle in the points r and n, and D E, 

 D c in the points H and m ; draw the 

 straight lines CF and AH, intersecting 

 one another in the point G, and CH, 

 EWI intersecting in g ; then is G the 

 centre of gravity of the whole triangle 

 ABC, and g the centre of gravity of 

 the triangle DEC, which falls below 

 DE the plane of floatation. 



Join the points G, g by the straight 

 line G # ; then, according to the prin- 

 ciple announced and demonstrated in the sixth proposition, the straight 

 line gc, is perpendicular to DE the surface of the fluid. 



Draw FH, and because CF and CH the sides of the triangle CFH, 

 are cut proportionally in the points G and g, it follows from the prin- 

 ciples of geometry, that the straight lines Gg and F H are parallel to 

 one another ; but we have shown that gG is perpendicular to the hori- 



