Final answer:
The 19th-century project to discover the stages of human culture was part of the early development of anthropology, involving figures like Tylor and Morgan who proposed ethnocentric developmental stages culminating in European civilization.
Step-by-step explanation:
The 19th-century project to discover the stages of human culture and to arrange cultures in historical order is referred to as the development of anthropology and involves key figures like Edward Tylor and Lewis Henry Morgan. Tylor proposed that cultures progressed through stages from 'savagery' to 'barbarism' to 'civilization', a system further elaborated upon by Morgan who focused on technology as the primary driver of cultural evolution. Their theories reflected the ethnocentric and colonialist perspectives of the time, implying that European culture represented the pinnacle of societal development. These stages, although based on conjecture and lacking direct evidence, reflected the broader 19th-century worldview, where history was seen as a progression toward European-style democracy and civilization, and non-European societies were often viewed as less developed or 'stuck' in prior stages. This approach is characteristic of progressive history, which saw history unfolding in a linear fashion towards a predetermined end, typically defined by the standards of the European colonial powers.