As pointed out by brianpck and Shootforthemoon above, there is a general explanation for your apparently specific question on Ancient Greek.
To put it in cognitive linguistic terms (e.g., in Lakoff & Johnson's (1980, 1999) famous theory of conceptual metaphors), the explanation of the polysemy involved in your question is explained by the following conceptual metaphor: CAUSES ARE SOURCES (i.e., the abstract cognitive domain of CAUSES is {understood/expressed} in terms of the more physical domain of SOURCES).
Some examples and comments from Lakoff & Johnson (1999: 213) follow: "She got rich from her investments. He got a sore arm from pitching too many innings. Harry died from pneumonia. I'm tired from working all day (...). In the most basic kind of causation, a physical force is applied to move something or change its appearance. In such cases, typically whatever exerts the force must move from an initial source location to a position in which force is exerted. In such a situation, there is a correlation between the application of the causal force and motion from an initial location. This correlation is the basis of a metaphor for causation in which causes are conceptualized as sources and the word from expresses source".
(e.g. "A cause is that from which an effect proceeds."