How obtain the code?

What are the commands to get the images in this article?

Your question relates to this Library entry:

Analytical Cartography

which is dated 2000. Since then Wolfram Language got updated with full maps and GeoGraphics functionality: Maps & Cartography. That includes various types of projections.

If you are still interested in the code for the Library notebook - it has contact information of the authors - you should just email them.