306 
MOVING FORCE. 
cB*lty*in^tl!e^ prop, unfolds, as he observes, a general principre, 
doctrines of including the properties demonstrated in tlie I. 47, and VI. 31,. 
morii^ foice, Euclid. For the following concise demonstration, I am 
indebted to my friend Dr. Roget. Draw BH and Cl perpen- 
diculars to AD. Then the triangles ABH and ADI' being 
similar, AB : AD : : AH ; AF. Alro ACT and ADG being 
similar, AC : AD : : AI (=HD) : AG. From these propor- 
tions we obtain the following equations AB.AF = AD. AH 
and AC.AG = AD.HD, which being added together, give 
AB.AF+AC.AG = AD.AH+AD. HD = AD, (AH+HD) 
= AD**. 
t 
Various other interesting and useful examples might be given 
of the application of the measure of moving force, which con- 
sists/ 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 wish briefly to observe, 
that we appear to derive all our notions of force from pressure as 
it is perceived by the sense of touch, and that in all cases where 
neither the velocity nor the figure of the body pressed is changed 
by the pressure, we have only simple pressure balanced by 
pressure, the various combinations of which have long ago been 
explained and demonstrated in the most satisfactory manner. 
But in all cases where either the velocity or the figure of the 
body pressed is changed by the pressure, we have examples of 
moving force, which may be properly represented by a 
rectangle j of which the pressure forms one side, and the space, 
through which it acts, the other side : and however various and 
complicated the changes of velocity and of figure may appear, 
they must all be derived from determinate quantities of moving 
force. We may have changes of rectilineal velocity in various 
directions, changes of rotatory velocity, and changes of figure, 
• The same proposition is demonstrated in the II. 19. of Profe.csor 
Leslie’s Elements of Geoxuetiy. 
all 
