f ii 6 q ) 
it meet A W m W. So is A W the Radius of the Curva- 
ture at A* - 
VIII. This Curve tttay be continued on infinitely above 
the point F f but by a different and more operofe way of 
Conftru&ion ) whofe Properties will be tbefe. i. The 
Difference of its Tangent and Subtangent ( taking the 
Subtangent in the Line H S ) will be always equal to the 
Tame given Line F H or a. That is, as t -p s = a, below 
F, fo t — * s == a above F. 2 . As below F the Curve Line 
is equal to the Sum ot its Ordinate and Subtangent. fo a* 
bove, it is equal to their Difference or — S — y. 3. As below 
F, 3 a y =1 L M, fo above 2 a y = I a t* . All which 
(and its other Properties) may be demonftrated as the Pre- 
cedent mutatis mutandis. 
TX. With a little variation in the precedentConftru&ioh 
may the Logarithmick Curve be conftru&ed, which is alfo a 
£ iuadrairix to the Hyperbola. In Fig. 1. omitting the 
String M R P, let the diftance M R be equal to the Subtan*- 
gent of the intended Logarithmick Curve (which, as ’tis 
known, is invariable.) Stick a Pin at R in the RularC D* 
to which apply the Rular E F, fo that the edge of the lit- 
tle Quadrant k l, reiling upon the Rular A B, the diftance 
M i be equal to M R. Then keeping the Rular E F tight 
to the Pin R and Rular A B, Hide the Rular C D along in 
a ftraight Line ( by the Rular or Line S Q._) So will the 
Wheel g ^defcribe a part of the Logarithmick Curve T V, 
whofe Snbumgent is every where M R. 
X. Fig. 2. Let F AEreprefent the Logarii hmick. Curve, 
whofe Subtangent Is equal to FH. LI a is an Equilater 
Hyperbola ( &c. as before § III.) Let F G — x, G a ~ 
y. F H ( = B P ) = a. G'H ( = L S ) = a — x. A C = 
% C a ss y .Then A C :€a : : AB : BD. that is x ::: a 
