A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Yves Robin-Jouan
Date: 2015 Feb 26, 03:13 -0800
Just a remark about your answer:
Indeed, I consider that the explicit introduction of plane equations with x y z as variables by Yvon-Villarceau was the settlement of a linear solution of the problem (1877). Please read again his original text (in French), you will realize how clever it is!
Solving a big linear system has been made much earlier par Carl Friedrich Gauss.
Linear algebra (with definitions of matrix and vectors) has been founded on 1855 by Cayley and Sylvester. It took some time for the navigation specialists to assimilate such mathematics... Franz Brunnow proposed a full spherical trigonometric solution on 1860, and a lot of followers continued during more a century (till 1997 to my knowledge) to invent new trigonometric methods... They were sure that such solutions were better that simply inversing a matrix. I have discussed with a few of them. May be there are right !
To show to my students how simple can be the linear solution, I am used to do a complete hand computation in a well chosen example in the middle of Atlantic.
Thanks to you, Antoine or Kermit,
Yves or Ulyves