The first is taught universally (as far as I can make out) at school and university, that Galileo discovered that all bodies (at least in vacuum) fall at the same rate. He didn't. He read it in Lucretius' great work of Roman science "De Rerum Natura" published about 60 BC. Lucretius followed Epicurean atomic theory and derived the fact from first principles. Since he was aware that different bodies eg feather and stone, fall at different rates, he went on to recognise air resistance. I believe that Galileo's contribution was to demonstrate the fact experimentally (not using the Tower of Pisa) but by using the inclined plane to slow down gravity. I've never been able to find a good reference (in English) to Galileo's experimental work to confirm this. The second is Darwin and "survival of the fittest" (SoF). Darwin's theory was about "natural selection" (NS) about which he was delightfully vague - and correctly so given the state of science in his day - and not about SoF. I'm pleased to see that modern texts are moving away from reference to SoF although "fitness" seems more intractable to removal. To put it crudely, in Heisenbergian terms, NS is to Speciation what quantum theory is to classical physics. SoF was invented by a railway engineer turned philosopher, Herbert Spencer. To be fair, most of his work seems to have been quite sensible. When he read "Origins" he immediately sided with Huxley as one of Darwin's great defenders and attempted to explain NS with SoF drawing on his deterministic railway engineering experience. He got it hopelessly wrong and has misled the world ever since. There is no such thing as "survival of the fittest" anywhere - except perhaps in sorting machines. In writing this, as an engineer, I like to think that "it takes one to know one".