You should consider, for example, the rate of progress in ancient Egypt or in China, where impressive accomplishments accumulated, but only very slowly and only over a long period of time
The Greek invention of rationality led to a sort of intellectual golden age, involving only part of the upper class in a slave society, but that golden age largely ended with the Roman invasion. The Library of Alexandria was perhaps first burnt accidentally by Julius Caesar as he tried to capture Pompey
Moreover, you'll have to look long and hard to find much Greek experimental work: most Greek reasoning was simply abstract and ideological, without experimental check. It was often impressive, but the emphasis on abstract and ideological work is precisely what we today dislike about medieval scholasticism -- which inherited its abstract and ideological bent from the Greek authors the scholastics so admired
Roman culture was scarcely interested in abstract thinking: it focused on pragmatic issues and barely had a useful notation for a few fractions (the uncia)
The Greek treasures passed to the Eastern Empire when Rome finally collapsed, and thus eventually they became an Islamic treasure, as Islam overtook the Eastern Empire. Islam also soon had the advantage of the Indic numerals, which Fibonacci began to advocate in Europe in the thirteen century. An Islamic golden age resulted and ideas percolated into Europe, probably from Spain
Perhaps the first clear indications of modern experimental philosophy come from the monk, Roger Bacon
It's impossible to imagine modern science without Greek rationality. But it's also impossible to imagine it without something like the Indo-Arabic numerals and algorithms. Subjecting reason to experimental tests is an idea that developed with late medieval disputes about Aristotelian texts. And of course the modern notion of a reproducible experiment leans very heavily on standardized mass production, which is a product of the industrial revolution.
... The works of Aristotle were made available in the Latin West in three clearly distinguishable stages. The first stage opened in the sixth century with Boethius's (c. 480–c. 524) translations of Aristotle's treatises on logic, along with some notions transmitted by Cicero (106–43 B.C.E.). Such works had but little effect upon the monastic life of the early Middle Ages. The second stage began in the twelfth century with the gradual translation of the entire corpus of Aristotle's works ... The condemnation in 1210 and 1215 of Aristotle's libri naturales (books of natural philosophy) at Paris was followed by an intense effort to axiomatize the quadrivial sciences ...
http://science.jrank.org/pages/8365/Aristotelianism-Medieval-Latin-Aristotelianism.htmlRoger Bacon (1214/1220–1292), Master of Arts, University of Paris, later Franciscan Friar was one of the earliest witnesses to the reception of Aristotle at Paris soon after the lifting of the Condemnations of 1210, 1215, 1231 ... Bacon in De scientia experimentali and in related works ... argues that logical argument alone, even when it originates from experience, is not sufficient for the ‘verification of things’ ... His aim is to provide a method for science, one that is analogous to the use of Logic to test validity in arguments. This new practical method consists of a combination of mathematics and detailed experiential descriptions of discrete phenomena in nature. It would be distinguished from the conjurations of Magic and from Moral and Religious Belief. It would also be different from Philosophy of Nature and from broad Optical Knowledge ... Bacon depends on the accounts handed on by Aristotle, Seneca and Avicenna. He is not uncritical of these accounts. His own important contribution is to be found in his calculation of the measured value of 42 degrees for the maximum elevation of the rainbow. This was probably done with an astrolabe, and in this, Bacon advocates the skillful mathematical use of instruments for an experimental science ...
http://plato.stanford.edu/entries/roger-bacon/#OpuMaiFouFivSixMatNatDeMulSpePerSciExp