Newton (early 18th century) and Gauss (early 19th century) both developed, among others in that time, iterative methods to find solutions to computational problems. Today these methods are immediately associated with numerical analysis. That is to say, computer-aided mathematics. Since these methods are useful to us when we can tell a computer to do the many calculations necessary quickly in sequence.
I'd like to see some light shed on this pre-computer era of problem solving by use of algorithms. Do I need to imagine Newton, when confronted with a problem which is hard to solve analytically, sitting by candlelight doing one tedious numerical computation after another, working through his iterative algorithm?