[ SO ] 
Times, Velocities, &c. to become promifcuoufly the 
Subjects of geometrical or arithmetical Operations, 
I deltre, once, for all, to be underftood, not as fpeak- 
ing of thofe Quantities themfelves, but of Lines, or 
Numbers, proportional to them. 
Theorem. 
If a Spring of the Strength F 3 , and the Length 
CL, Fig. 4 , lying at full Liberty upon a horizon- 
tal Plane, reft with one End L againft an immove- 
able Support j and a Body of the Weight M, moving 
with the Velocity V, in the Direction of the Axis of 
rhe Spring, ftrike diredly upon the other End C, and 
thereby force the Spring inwards, or bend it through 
any Space C B ; and a middle Proportional, CG, be 
taken between the LineCAx^ and 2 a, a being 
the Height to which a heavy Body would afcend in 
vacuo with the Velocity V 5 and, upon the Radius 
R — C G } be ereded the Quadrant of a Circle G FAi 
I fay, 
1. When the Spring is bent thro’ any right Sine of 
that Quadrant, as C B, the Velocity v of the Body 
My is, to the original Velocity V, as the Co-fine to 
the Radius: That is, 
jK. 
2. The Time t of bending the Spring thro’ the 
fame Sine C B , is to T the Time of a heavy Body’s 
Afcending in vacuo with the Velocity V, as the cor - 
G F 
refponding Arch to 2 a: That is t — T x~ a • 
Demon 
