Art of Archery (1515)
"And if you wish to know if a string is good, untwist the middle of it, and if the three strands are separate and distinct, it is a good one, provided always that when the string is twisted up again, it is hard and firm, for the harder it is, the better it will be."
Toxophilus 1545
"Now what a string ought to be made on, whether of good hemp, as they do now-a-days, or of flax, or of silk, I leave that to the judgement of stringers, of whom we must buy them. Eustathius, upon this verse of Homer,"
It goes on to say
"Eustathius, upon this verse of Homer, doth tell, that in old time, they made their bow-strings of bullocks' thermes, which they twined together as they do ropes" this is talking about the ancient Greeks not the middle ages.
Thats is the only reference to construction, its not concrete.