The parametric latitude, also called the reduced latitude, is an auxiliary latitude denoted (Snyder 1987, p. 18), (Adams 1921), or (Karney 2023). It gives the latitude
on a sphere of radius for which the parallel has the same radius
as the parallel of geodetic latitude and the ellipsoid through
a given point. It is given by
(1)
(Snyder 1987, p. 18), where the eccentricity of an ellipsoid of rotation with equatorial radius and polar semi-axis is defined as
Adams, O. S. "Latitude Developments Connected with Geodesy and Cartography with Tables, Including a Table for Lambert Equal-Area
Meridional Projections." Spec. Pub. No. 67. U. S. Coast and Geodetic Survey,
1921.Karney, C. F. F. "On Auxiliary latitudes."
21 May 2023. https://arxiv.org/abs/2212.05818.Snyder,
J. P. Map
Projections--A Working Manual. U. S. Geological Survey Professional
Paper 1395. Washington, DC: U. S. Government Printing Office, p. 18, 1987.
(Snyder 1987, p. 18), 
(Adams 1921), or 
(Karney 2023). It gives the latitude
on a sphere of radius 
for which the parallel has the same radius
as the parallel of geodetic latitude 
and the ellipsoid through
a given point. It is given by
of an ellipsoid of rotation with equatorial radius 
and polar semi-axis 
is defined as
,
