### Geometry and Algebra of the Meridian Ellipse

Ellipsoid of rotation:
`x*x*b*b + y*y*b*b + z*z*a*a = a*a*b*b`

 a: Major semi-axis (O-A), (F-B) b: Minor semi-axis (O-B) h: Ellipsoidal elevation (P-R) f: Semi-focal length (O-F) `f = a*a - b*b = (a + b)*(a - b)` Latitude and longitude: s: Sine latitude c: Cosine latitude p: Sine longitude q: Cosine longitude `s = kn` `c = SQRT(in*in + jn*jn)` `p = jn/c` `q = in/c` Normal direction cosines: `in = c*q` `jn = c*p` `kn = s` Prime vertical direction cosines: `ip = -s*q` `jp = -s*p` `kp = c` Geocentric latitude tangent: `z/x = (s*b*b)/(c*a*a)` t: Tangential plane free term (T-P) `t = -SQRT(a*a*c*c + b*b*s*s)` g: Normal interaxial segment (E-N) `g = f/t` o: Prime vertical free term (O-T) `o = g*s*c` n: Prime vertical radius (N-P) `n = (a*a)/t` l: Normal equatorial depth (E-P) `l = (b*b)/t` m: Meridian radius `m = (n*l)/t` r: Geometric mean of (n, n) `r = (n*b)/t` Coordinates of para-centre (T) `u = g*s*s*c*q` `v = g*s*s*c*p` `w = -q*s*c*c` Coordinates of surface point (P): `x = (n + h)*c*q = u - in*t` `y = (n + h)*c*p = v - jn*t` `z = -q*s*c*c = w - kn*t`
...