I am very sorry, but you are very wrong.
It's dark ages in Europe but it's really golden age in Islamic Empires which far surpassed the Greek and Roman. The epitome was the Baitul Hikmah or House of Wisfom established at the time of Abassid Caliphate [1].
>Between the fall of Rome (476 AD) and the Carolingian empire (~800 AD)
During this time Al-Khwarizmi was born and House of Wisdom was established. His contributions in algebra (book Al-Jabr) and many others, and the word algorithm literally originated from his name [2].
Many Greek and Indian books translated to Arabic during this myth so called dark age by the Islamic Scholars.
Many many more new books were written that improved and innovated the prior knowledge. These books greatly expanding the state-of-the-art centered both in Baghdad, Iraq and Toledo, Spain.
The book Almagest by Ptolemy studied by Galileo was the Arabic translation of the Ptolemy works. Of course at the time of Galileo, Islamic astronomers knowledge and contributions have already far surpassed the Greek and the Indian.
The Islamic scholars not only translating (that it self is a progress) but also contributing to the body and foundations of knowledge not only in astronomy, but in many others in mathematics, sciences (physics, chemistry, biology), medicine, engineering, geography, psychology, politics, economy, architecture, etc.
There are numerous other polymath scholars like Al-Khwarizmi, for examples Al-Haitham, Ibnu-Sina, Ibnu-Rusd to name just a few. But European community has been in denial for so long time and in addition unfairly supressing these Islamic scholars contributions. They even literally changed the scholars name and Latinized them with lousy names like Alhazen, Avicennia, Averroes to hide the fact that they are Islamic scholars. Imagine if now people changed name of the scholar like Newton to Nawab in the literature.
Heck, even Copernicus copied diagrams from the Islamic earlier astronomers' books without proper citations, that in the modern will be plagiarism [3]. If this happen today, the university president (if plagiarised his/her book/thesis/paper) will be asked to resign.
[1] House of Wisdom:
https://en.wikipedia.org/wiki/House_of_Wisdom
[2] Al-Khwarizmi:
https://en.wikipedia.org/wiki/Al-Khwarizmi
[3] Islamic Astronomy and Copernicus [pdf]:
Islamic Astronomy and Copernicus [pdf]