The poverty of his parents meant that he had to work for his living, and until 1808 he was a farm labourer, horse driver, and quarryman, obtaining at intervals some education and private study.
Having saved a little money he left Wales, and, arriving in London on 15 September 1809, attended a school to perfect himself in writing and grammar, but took no special interest in any subject except arithmetic.
In January 1810 he obtained an engagement at Mr. Rainhall's school as teacher of arithmetic, at a salary of 20l., and there commenced calculating the times of the eclipses and exhibiting their mode of occurrence by diagrams.
Meanwhile, he corrected the press of a Welsh magazine then published, and wrote his ‘Key to Bonnycastle's Trigonometry’ (1814), which established his character as a mathematician.
Sir John Franklin came to Davies after many years of service at sea to increase his knowledge of some of the higher branches of the science of navigation.