Development of the mathematics resembles usually a growing tree - from old branches grow new ones. However sometimes domains of mathematics which were separated for the long time are fused together at one point starting a new domain.
Surely the most famous example (and probably the most fruitful) is the fusion of geometry and algebra into analytic geometry made by Descartes.
Are there also other known fusions in history of mathematical domains which merged into one subject after many years of distinct development?
If it is known to MSE users please give some examples with the most appropriate date of fusion and specific event which could be regarded as the starting point (as Descartes' La Géométrie 1637) and approximate years of separate developments...
Probably it is hard to find other example when such unconnected mathematical developmental processes were so long as in the case of analytic geometry.. but anyway it's interesting what fusion could take the second and the third place in this ranking counting the years of independent development?