Why did European medical students study a Persian doctor's book for centuries?

Because it did what students needed: it put the medical knowledge of an entire world into one ordered book. The Canon of Medicine, an encyclopedia in five books, was completed in 1025 by Ibn Sina, known in the West as Avicenna, who was born around 980 to a Persian family in Transoxiana. It presents an overview of the medical knowledge of the Islamic world, shaped by Greco-Roman medicine (particularly Galen), Persian, Chinese and Indian traditions, and it served as a more concise reference than Galen's twenty volumes.

That tidy package is what Latin Europe wanted: its encyclopaedic content, systematic arrangement and combination of Galen's medicine with Aristotle's science and philosophy helped it enter European scholastic medicine. Translated into Latin as Canon medicinae by a Gerard of Cremona, it was used by medical scholars from the 13th century and by university courses from the 14th. Between the early 14th and the mid-16th century Avicenna was ranked with Hippocrates and Galen as one of the acknowledged authorities, the "prince of physicians". The first printed edition appeared in 1472, covering only book three, and 25 further Latin editions followed by 1608.

It was not just a list of cures. The Canon contains seven rules for experimenting with new drugs, taken partly from Galen. One says to test on a single condition, not a patient with several illnesses; another says to start with the weakest dose and raise it gradually until the potency is known.

Its reign ended slowly. In the 16th century humanists preferred ancient Greek and Roman authorities to Arabic ones, but the Canon was still being taught as background literature in Padua in 1715.