A deeper insight into the principles of navigation leads to the understanding of spheroid models, elliptic integrals etc. Thanks to sophisticated modern math software, these problems can easily be solved complying with navigational practise. In addition, some texts present navigation subjects mixing spherical and spheroid models which results in discrepancy been unexplained. Plane and Mercator sailings shall be based upon the spheroidal model or the spherical model without mixing them, thus resulting in error in calculated distance or mid-latitude. The difference in latitude parts must be used for spheroid, in place of the difference in latitude, to avoid inconsistency. Differential equation of a loxodrome on the spheroid presented here aims to understand mathematical postulates of navigation.