256 _On the Measure of 
is demonstrated in the first prop. of the fourth 
book of Pappus; and that prop. unfolds, as he 
observes, a general principle, including the 
properties demonstrated in the 1.47, and VI. 31, 
of Euclid. For the following concise demon- 
stration, [am indebted to my friend Dr. Roget. 
Draw BH and CI petpendiculars to AD. 
Then the triangles ABH and ADF being 
similar, AB: AD:: AH: AF. Also ACT and 
ADG being similar, AC:AD :: AI(=HD):AG, 
from these proportions we obtain the following 
equations AB.AF=AD.AH and AC.AG= 
AD.FID, which being added together, give 
AB.AF+AC.AG=AD.AH+AD. HD=AD. 
(AH+HD)=AD>.* 
Various other interesting and useful exam- 
ples might be given of the application of the 
measure of moving force, which consists of the 
pressure multiplied into the space through 
which it acts; but I believe I have already 
exceeded the proper limits of a dissertation of 
this kind, and doubtful as I must be of the 
favourable reception of the reasoning which I 
have adopted, I am more disposed to curtail 
than to lengthen it. 
By way of recapitulation, however, I Irish 
briefly to observe, that we appear to derive all 
* The same proposition is demonstrated in the IL. 19. of 
Professor Leslie’s Elements of Geometry. 
