Greek Geometry, Rational Trigonometry, and the Snellius – Pothenot Surveying Problem

Abstract

Pythagoras’ theorem, Euclid’s formula for the area of a triangle as one half the base times the height, and Heron’s or Archimedes’ formula are amongst the most important and useful results of ancient Greek geometry. Here we look at all three in a new and improved light, replacing distance with quadrance, and angle with spread. As an application of this simpler and more elegant rational trigonometry, we show how the famous surveying problem of Snellius and Pothenot, also called resection, can be simplified by a purely algebraic approach.