( H4 ) 
to a given Time, are the Meafures of Ratio’s, to a 
given Modulus of Time, whole Terms are the Sum 
and Difference of the ultimate Velocity and , 
the prefent Velocities that are acquired : that 
the Times of Afcent, taken from a given Time, 
are the Mealiires of Angles, to a given Modu* 
lus of Time, whofe Radius is to their Tangents in the 
Ratio of the ultimate Velocity to the prefent Ve- 
locities : and laftly, that the Spaces delcribed in De- 
Icent or Afcent, are the Meafures of Ratio’s to a given 
Modulus oi Space, whofe Terms are the ablblute ac- 
celerating andretarding Forces arifmgfrom Gravity and 
Refinance taken together at the Beginning and End of 
thofe Spaces. 
' This general Account may fuffice to illufirate what 
I am going to fay ; that fince the Magnitudes of Ra- 
tio’s (as well as their Terms) may be expounded by 
Quantities of any Kind, the Mathematician is at Li- 
berty upon all Occafions to chufe thofe which are fit- 
tefl for his Purpofe ; and fiich are they without doubt, 
that are put into his Hand by the Conditions of the 
Problem. He may indeed reprelent thefe Qiiantiries 
by an Hy^erbola^ or any other Logomerrical Syfiem, 
were not his Purpole anfwer’d with greater Simplicity 
by the very Syfiem itfelf, which occurs in each parti- 
cular Problem. And the fame may befaid for the Sy- 
Hems of Angular Meafures, inflead of recurring upon 
all Occafions to Elliptical or Circular Area’s. 
As to the Convenience of calculating from our Au- 
thor’s Conftrud:ions, he fliews that the Meafiires of 
any Ratio’s or Angles are always computed in the 
lame uniform Way ; by taking from the Tables the 
Logarithm of the Ratio, or the Number of Degrees in 
the Angle, and then by finding a fourth Proportional 
to three given Quantities ; for that will be the Meafure 
required 
