I'm fairly familiar with the normal recurve bow's history, but I'm not sure when takedown bows, which can be spilt apart for portability, were invented.
Thanks for any information provided! :)
The earliest takedown bows I know of are Indian steel bows. Most (if not all) are Mughal or later. Most of these steel bows are one piece, but a large minority are takedown bows, with either a screw joint in the middle of the grip, or one or two screw joints at the end(s) of the grip.
Steel bows were used in warfare, but were not as common as conventional composite bows. The steel bows are relatively sluggish, since they have heavy limbs compared to composite bows. Thus, they lack range. Their advantage is that they can be stored easily in armouries, and are much less susceptible to moisture.
Takedown bows were being used in Europe by about 1800. These were target bows. The earliest examples I have seen described are French, c. 1800. Typically, one or both limbs fits into a metal sleeve at the handle.
Japanese takedown bows of similar construction - one or both limbs fitting into a metal sleeve - are described in G. S. Stone, A Glossary of the Construction, Decoration and Use of Arms and Armor: in All Countries and in All Times, Dover, 1999 (reprint), pg 134. These are of quite low draw weight, and would have been useless in war.
While not strictly takedown bows, the Chinese made folding bows, with a hinge in the middle of the grip. Stone mentions these along with the Japanese takedown bows. All of the examples I have seen have been Qing Dynasty. Some examples:
These folding bows were low draw weight compared to military bows, and were not used in war.
The above examples of takedown and folding bows are from when these types became somewhat common in their respective countries/regions. There are multiple surviving examples; these are not unique one-off bows (there may have been earlier one-off bows, which have not survived and no record of has survived). With the exception of Indian steel bows, these takedown/folding bows were of low draw weight and unsuited for warfare; they were target/recreational bows. These all date from times when gunpowder weapons (including handheld firearms) were common on the battlefield. The Indian and Chinese examples date from times where archery was still used in battle (alongside guns).
One general difficulty with making militarily useful takedown/folding bows is that they tend to be (a) weaker, and thus must be made at much lower draw weights than military bows, or (b) more expensive (a wooden selfbow such as the European longbow could be very cheap; adding metal sleeves/hinges would add to the cost in materials and labour). The Indian steel bows are an exception to the first, since the steel handle is quite strong even with a screw joint, and might be an exception to the second (since adding a screw joint is a minor step compared with the rest of the task of making a steel bow, and the main military bow - the composite bow - was quite expensive).
