The short version of these chapters is that you need to think very carefully before concluding either that one culture got an idea from another, or that a culture really developed an idea from its own heritage rather than contact with another culture. For instance, both the ancient Greeks and the ancient Chinese had an idea of atoms. But modern Europe did far more to develop atomic theory in its current form than China did. Therefore, one could not credit the Chinese with developing a scientific understanding of atoms free from European influence. While there is an understandable desire to give due credit to non-European civilizations, credit for our modern understanding of atoms rests with Europe.
On the other hand, the Europeans and the Arabs both read the ancient Greeks, but the Europeans did not do much to build on Greek physics until they had contact with the Arabs, who had done a lot to further develop the subject. Therefore, the Arabs deserve a share of credit for Europe moving physics forward.