Paul Tannery said of geometry of the eleventh century in Europe: "This is not a chapter in the history of science; it is a study in ignorance." Its level, he said, was equivalent to that in Greece before Pythagoras.
Quoted from N. Daniel in The Arabs and Mediaeval Europe; Edinburgh University Press; 1974:
Chapter 10; p. 263:
Paul Tannery said of geometry of the eleventh century in Europe: "This is not a chapter in the history of science; it is a study in ignorance." Its level, he said, was equivalent to that in Greece before Pythagoras. Scholars like Raimbaud of Cologne discussed the implications of the terms 'acute' and 'obtuse' angle. Arithmetic was not in such a bad way, and the use of the abacus was associated with Gerbert of Aurillac, Pope Sylvester II.
The revival of scientific learning is sometimes dated from his studies in Spain at the end of the tenth century. His writings on arithmetic and logic are his chief claim to honour… All the same, Europe was slow to adopt the algorithm, or decimal numeration; it was long a matter of academic knowledge rather than of practical use to men of business. In general, scientific studies had added little to the Etymologies of Isidore and the works of Bede. It was this gap in the European apparatus of learning that translation from Arabic in the twelfth century would fill. Medical knowledge at the beginning of that century was not in such a bad way, thanks to the work of Constantine the African at Monte Cassino, and associated with Salerno, which put Arab sources into a Latin form; and his influence was carried on into the twelfth century by his pupil, John Afflacius, whose history was, apparently similar to Constantine's.
The Salernitan experience included anatomical experimentation with pigs, which it did not owe to Arab links, but it foreshadowed twelfth-century attitudes, although it did not meet the high standards of translation that came to prevail. The explosion of scientific translation was the product, in practice, of military success.
The opening of much of Mediterranean culture to the people of the north of Europe was the result of the European conquest of southern Italy and Sicily, and of Toledo and other smaller centres in Spain. In the central area, the influence was more Greek than Arabic; in the west it was naturally exclusively Arabic.