( m ) 
( se Rr a Degree or Particle of the Equator :) to Mm 
the Fluxion or correlpondent Particle of the Meridian Line 
R M . Whence, and from what is premifed concerning 
the Nature of this Nautical Proje&ion, tis evident that 
R Mi s the meridional Part anfvvering to the Latitude whofe 
Cofmeis G R. Or thus ; With Center R and Radius 
A R defcribe the Quadrant A * *, in which let the Arc 
A y. be equal to the given Lat. From k draw x. C paral- 
lel to K R, and interfering the Curve in C, fo is C x the 
Meridional Part defir’d being equal to R M, as is eafy 
to fhew. 
As to the other Properties of this Curve, tis evident, 
from its ConftrudUon, that its Tangent (as CM) is a Con- 
fiant Line every where equal to A R ; the Curve being 
generated by the Motion of the Wheel at the End of 
the Rular which is its Tangent. And from hence the 
Curve ACB may, for diftindHon, be call'd the Equi - 
tangential Curve. ; 
7 . The Fluxion of the Area A R MC is the little Se- 
&or or Triangle MC d, which fame is alfo the Fluxion 
of the Sedtor CD M r whence the Areas ARMC, 
C D M are equal, and the whole Area A C B Arc, K MR 
being infinitely continued, is equal to the Quadrant^# a; 
8 - To find the Radius of Cutvature of any Particle, 
as C c, from Cdraw an indefinite Line C T perpendicular 
to C M , (on the concave fide of the Curved and from c 
another Line perpend icular to c m, which Lines, (becaufe 
of the Inclination of C M to c m,) will lomewhere meet 
as at T, making an Angle CTc— MCm. Thefe Angles 
being equal, their Radii are proportional to their Arcs.* 
therefore, M d : C c :: M C : C f. Butd c — dm (be- 
caufe o £ C M = c fo thztMd : dm ( : : 0 D • D E) 
i: CM : C f. But CD=C M, therefore. CT^DE- 
Tangent of the Arl J jft : * ‘ 
