How did Dalton advance the atomic philosophy proposed by Democritus?
Quite possibly not at all.
Dalton was a natural philosopher, a true scientist, and an accomplished polymath. His extensive experiments led him to propose an early atomic theory, for which today we would have to work hard to find exceptions:
Dalton proposed that,
Elements are made of small particles called atoms. Atoms of a given element are identical in size and mass; atoms of different elements differ in size, mass, with respect to atoms of other elements. Atoms cannot be subdivided, created, or destroyed. Atoms of different elements combine in simple whole-number ratios to form chemical compounds. In chemical reactions, atoms are thus combined, separated, or rearranged.
All of these proposals were advanced on the basis of extensive experiment. His work could be repeated by other researchers, and new results incorporated in this atomic theory.
By contrast, Democritus was a Greek philosopher of the 5th century BC. As far as we know, he did no experimental work, and NONE of his writings survive. He proposed that the stuff of matter was a single indivisible element, called an atom; the very name comes from the Greek,