General Observations

Now here is a double edge sword to what you are saying.First and foremost alot of Roman inventions were based on greek knowledge,the catapult, Crossbow,Water Mill,Aqueducts,etc were based on knowledge of the greeks. Archimededes,Hero,and Pythagorus were studied extensively by the Romans later on.Later on the Romans such capitulated a vast majority these ideas and knowledge and disperesed to other lands they conqured in Europe.Most of which relatively didn't have a establishments.

Before Hadrian conquered Brtiain  most the inhabitants were living relatively simple,after he built Hadrians Wall,the ancestors of the Scottish were considered to be inferior to that of the new Roman citizens of Brittania,this Roman impact still reverberates to this day.   During the Laws of Conquest English and Irish were forbade to marry because of the  outlook of Brtainians to Irish.After the fall of the Roman empire did the Varangians Vikings,Saxons,Jutes,Anglos,Suevi,Goths build up a civilzation right away ,No. They wre gradullay christanized and brought into the old roman culture.The forst Post Roman in old Roman structures such as St.Angelos ,the Collessium and so on. The encastellions  and absolutism would be the rise of Europe.Europe in the Medieval times did not really sprout up their own advance societes until the end of Medieval times. They were basically living on the vestiges of the past.

The Vedic math,ALgebra,and Technolgical innovations in the east were all transported to Europe. They were stil later on able to rule over most of the people that created it would you those were inferior.

Inventions and technological development is also a matter of time. At different times the initiative of important inventions was in different parts of the world.