A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Dec 31, 07:32 -0800
Robin Stuart, you wrote:
"All this begs the the question as to how did Gerardus Mercator (1512-1594) construct his chart prior to the advent of calculus."
I think the short answer is that numerical integration was developed long before general, analytic integration. The idea of adding up arbitrarily small bits to get a sum of a variable function has been around since antiquity. I'm attaching an article that discusses some of the history of the "integral of the secant".