The fact that the earth is round was first discovered by ancient Greeks and was generally known ever since. That was true for the Christian world as well as for the Mulsim world. However, in China it was still believed that the earth was flat until the Jesuits convinced the imperial court to the contrary.
The ancient Greeks were aware that the earth was round. Erastosthenes calculated its circumference in the 200s BC and was off by about 16%.
Later Muslim scientists such as al-Khwarizmi in the 800s were also aware it was round. al-Khwarizmi's calculation done in Baghdad was off by about 4%.