What ideas did the church and Muslim scholars preserve?

Answer 1

This excerpt might help (It's from my History book by the way):

"Scholars in Muslim lands saved much of the learning of the ancient world. Europeans in the West had lost this knowledge after the Western Roman Empire fell. Through Muslim scholars ,western Europeans found out about Aristotle and other ancient Greek thinkers."

Answer 2

The answer you are looking for is GREEK AND ROMAN WORKS OF MATH, SCIENCE, LITERATURE, AND PHILOSOPHY, but the phrasing of the question is odd.

Muslim Scholars in the 9th-12th centuries translated these texts from Greek and Latin into Arabic and kept them in their own libraries, most prominently the Bait al-Hikma (House of Wisdom) in Baghdad, Iraq. They were translated by Muslims for their own technological and social development; they were not done for the Europeans, on behalf of the Europeans, or with the foresight that they would be later used by Europeans.

These documents finally got back to Europe through translations made primarily by Jews and Mozarabic Christians in Iberia. These two minority groups within Islamic Spain retained a knowledge of Arabic an access to the sources in the Islamic Libraries. Once Toledo and other cities of Islamic Spain fell into European hands, these individuals were tasked with re-translating the texts from Arabic into Latin, so that European Rulers could the texts themselves. Muslims, by and large, were absent from this transfer of the texts back to Europe.

Answer 3

by translating works of Aristotle and Plato

Answer 4

they critically analyzed, collated, corrected and supplemented substantially the Greek science and philosophy.