This paper takes as its point of departure two striking incongruities between scientific practice and trends in modern history and philosophy of science. (1) Many modern historians of science are so preoccupied with local scientific practices that they fail to recognize important non-local elements. (2) Many modern philosophers of science make a sharp distinction between explanation and evidence, whereas in scientific practice explanatory power is routinely used as evidence for scientific claims. I draw attention to one specific way in which scientists in disparate fields, periods, and locales have used the explanatory power of their ideas as evidence. Scientists such as Copernicus, Kepler, Newton, Darwin, and Einstein all availed themselves of a pattern of reasoning that I have dubbed common-origin inferences (or COIs). A COI traces some striking coincidences back to a common origin (typically some causal structure or mechanism). This then provides an explanation for these coincidences, which is counted as evidence for the explanation.