53 6 
for then A — ' +c J <£ 2 and AS 2 — 
Mr. Wild bore on 
A x cof. AZ* 
vi a* 
B x cof. BZ 1 
m'b 4 
C(£ 2 - c x ccf -. C — . 
2 4 . 
m c 
Suppofe W to be the point of CA and V that of CB which 
comes under Z; then at W cof. BZ = o, and cof. AZ = ma 1 
= f. CW ; and at V, cof. AZ = o, and cof. BZ = ml z % yj~ = 
f. C V = f. CW CV and CW being a kind of femi- 
a y B 
tranfverfe and femiconjugate axes to the elliptic track on the 
fpherical furface that paffes under Z. And the gnomonical 
projection of the track on a plane touching the lphere at C, or 
the orthographical on the plane of the great circle BA (fig. 
so.) becomes known; for here YZ = col. BZ = CX ; CY = 
XZ = cof. AZ, and Asf - CY 1 x 4-, = ZY 2 x -4 is the 
m a 
vrb 4 
equa- 
tion of the curve VZW which is the projection of the track 
on this plane, being an ellipfis whofe femi-axes are f. CV and 
f. CW or and becaufe a -^- x ZY 2 = — 
y B 0 r A 
CY 2 . Moreover, the perpendicular to the plane of the pro- 
jection from Z on the plane to Z on the fpherical furface itfelf 
*= cof. CZ = <r -gx ZY r2 = v/i -CZ 2 = v/i-ZX 2 , 
ZY" a ; and the fluxion of the track at Z upon the fpherical fur- 
face = V cof. AZ 2 + cof. BZ 2 + cof. CZ 2 = m>S cCx + by 1 -f c*z% 
and fince i 
Ax 
y z 
= = - we thence obtain x 1 -^^, z 2 = 
%X *■ A * 
Cs 
B 2 ., 2 . • 2 
_ y y 
xy 
AV 
YLL and the fluxion of the track = wy \J^ 4+^ + 
2 > 
which divided by i gives m 
R 
C 
-va 
CV 
the velocity 
with 
