'If one would understand the Greek genius fully, it would be a good plan to begin with their geometry.' As early as the sixth century BCE, Thales of Miletus used geometrical principles to calculate distance and height. Within a few hundred years, Euclid had produced his seminal Elements, which was still used as a textbook when this two-volume work was first published in 1921. A distinguished civil servant as well as an expert on ancient Greek mathematics, Sir Thomas Little Heath (1861–1940) includes here sufficient detail for a modern mathematician to grasp ancient methodology, alongside explanatory sections aimed at classicists. This remains a rigorous and essential exposition of a vast topic. Volume 1 includes an introduction and a section on numerical notation and arithmetical operations. The coverage begins with Thales and ends with Euclid. Volume 2 focuses on post-Euclidian mathematics, beginning with the work of Aristarchus of Samos and extending to that of Diophantus of Alexandria.