7 
Geminus, which Petavius describes as “ nondum editus,” yet 
exists in some English library. One of two strange things 
must have happened (see He Morgan, ib. p. 450), viz. either 
the minute Petavius omitted the title of the work, if it were 
given : or Heilbronner preserved a title from some other 
source, if it were not. I am not aware that the manuscript 
has been discovered. 
4. Lagrange, at page 2 of vol. i of his “ Mecanique Anali- 
tique” (1.811), observes that the laws of statics are founded 
on general principles which may be reduced to three ; that 
of the lever, that of the composition of forces, and that of 
virtual velocities. He says (ib. p. 18, No. 14) that the 
principle of the lever is the only one which has the advan- 
tage of being founded on the nature of equilibrium consi- 
dered in itself, and as a state independent of motion. 
5. Lagrange (ib. p. 20) says that it does not appear that 
the ancients knew of the law of virtual velocities. From 
what is said by Whewell in his “ History of the Inductive 
Sciences” (1837, vol. ii, pp. 39 and 42; vol. i, pp. 69, 81, 82 
and 94) it seems that the law, so far as it relates to the 
lever, was known to Aristotle. Whewell considered the 
physical philosophy of Aristotle (ib. i, 25) and of the Greeks 
(ib. 33) as an utter failure. He apparently regarded the 
doctrine of the lever (see vol. ii, p. 59 ; vol. i, chap. I, sect. 1, 
p. 91) with greater favour than that of virtual velocities (see 
vol. ii, chap. II, sect. 4, p. 39), in connection with which he 
makes no special mention of Lagrange (see vol. ii, p. 120). 
Professor Cayley (Messenger, N. S., vol. iii, p. 1) has given a 
dissertation “ On the general equation of virtual velocities.” 
6. There are two modes of approaching the parallelogram 
of forces. First, we may from the composition of motions, 
through the second law of motion, pass to the composition 
of forces. Thomson and Tait, fortified by the example of 
Newton (see their ‘Treatise,’ &c., vol. i, pp. 181, 182, 
§ 255 — 257) have followed this mode, which they believe 
