MOVING FOUCE. 
305 
rings, AB, AC, and AE, in the same plane, to be united at Cases 
A; tlie strings AB and AC to be prolonged to a leoglh j^Vrines of 
indefinitely great, when compared with the diagram, and the force] 
end of each of the three strings to pass over a vertical pulley. If 
tire parallelogram be completed, and if three weights m, n, and 
«, which are to each other as AD, AB, and AC respectively, be 
suspended by the respective strings AE, AB, and AC, they will 
balance each other, and the strings will coincide in direction 
with the diagonal and sides of the parallelogram. If the weights 
be set in mntion, by taking from m an indefinitely small part 
of its weight, n and o will descend raising m, and the point of 
junction of the strings will move in the direction AD. When 
that point has arrived at D, the weight m will have ascended a 
space equal to AD, n will have descended a space equal to AB, 
and 0 will have descended a space equal to AC. The (piantity 
of moving force, therefore, is, on one side m.AD, balanced on 
the other side by n.AB + o.AC ; (he moving force of each string 
being as the weight suspended to it multiplied into the space 
through which it has moved. So that in this case, where the 
parallelogram is right angled, the moving forces in the dif- 
ferent directions are as the squaies of the diagonal and the 
respective .sides of the parallelogram. 
When BAG is not a right angle, let the parallelogram be 
completed, and the weights suspended as before, and draw DF 
and DG (fig. 23) perpendiculars to AB and AC. If the weights 
be set in motion, the point of junction of the strings will move 
in the direction AD, and when that point has arrived at D, the 
weights w, n, and •, will bav’e moved through the spaces AD, 
AF, and AG respectively. Tlte moving force, therefore, is 
on one side m.AD balanced by n.AF + o.AG on the other side ; 
or the moving forces in the different direefione are respectively 
as the square of AD, the rectangle AB. AF, and the rectangle 
AC. AG. 
This conclusion, however, involves the geometrical proposi- 
tion, that the square of AD is equal to the sum of the rectangles 
AB. AF and AC AG, a property of the triangle which is 
demonstrated in the first prop, of the fourth book of Pappus j 
SuFft£MENT.-—VoL, XXXVI, No. I6S. Z and 
