thro 5 which it was bent before the Body ftruck it, 
muft alfo be of an infinite Length ; and the Space 
B C D, thro 5 which the Spring will be further bent, 
muft be equal to the Height the Body can afcend 
to with the Velocity v, or & — s. 
For, by the laft, when p — s : : zl + s:2 l ; 
and the Refinances of the Spring at T> and B being 
refpe&ively as C *D and C B , that is, as / + s and /; 
fince thofe Refinances are now fuppofed equal to 
one another, we muft, upon that Suppofition, con- 
fider l + s as equal to / ; and adding / to each, 
2 / -f s — 2 /, that is, / muft be infinitely greater 
than s ; and then a : s : : 2 / : 2 /, or cc = s. 
Scholium IV. 
In this Propofition, and all its Corollaries, except 
the Four laft, we have confidered the Spring as being, 
at firft, wholly unbent, and then adied upon by a 
Body moving with the Velocity V, which bends it 
thro 5 fome certain Space : Bur, as we fuppofe the 
Spring to be perfectly elaftic, the Propofition and 
Corollaries will equally hold, if the Spring be fup- 
pofed to have been, at firft, bent thro 5 that fame Space, 
and, by unbending itfelf, to prefs upon a Body at 
Reft, and thereby to drive that Body before it, during 
theTimeofits Expanfion: Only, F”, inftead of being 
the initial Velocity, with which the Body ftruck the 
Spring, will now be the final Velocity, with which the 
Body parts from the Spring when wholly expanded,. 
Scholium V. 
If the Spring, inftead of being prefled inwards, be 
drawn outwards by the Action of the Body, we need 
