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1) The Ming dynasty did not fall during 1644, the Ming captol fell during 1644. The Ming dynasty fell during 1664.
The last Southern Ming emperor was killed in Burma in 1661. Whether we should consider the Southern Ming rulers to be legitimate successors to the Chongzhen emperor is essentially a technicality; traditionally they were not (except by Ming loyalists and anti-Qing rebels/revolutionaries) because the Mandate of Heaven doctrine had the Mandate passing to the Qing in 1644, upon the suicide of the Chongzhen emperor. However, since we in the 21st century are not bound by the Mandate doctrine, we can just as well consider the Ming to last from 1368 to 1661.
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I find the quote also a bit too smooth to be believable.
1. I doubt that Ottoman muskets ever reached China in quantity.
2. I doubt Chinese could tell Europeans from Ottomans apart.
3. I wonder which Chinese manual could have been published the very same year the Ming dynasty fall? Too much turmoil IMHO.
The quote in question comes from a manual written in 1598 by the Ming official Zhao Shizhen, entitled the Shenqi Pu (Manual on Marvellous Weaponry). I was fortunate to get an electronic version from Thomas Chen some time ago.
The Ming army used muskets (niaochong, 'fowling guns') in large numbers in the late 16th century and early 17th century, and these were largely foreign designs that supplanted the indigenous but less effective Chinese handguns that had been used since the Yuan period. The Ottoman musket was known to the Chinese as the Lumi chong, after the word 'Rumi' (the Turkish/Arabic version of 'Rome' - the region of Turkey continued to be called Rumi by the Muslims even after Constantinople fell in 1453). The Shenqi Pu mentions that the Ming military first encountered the Lumi chong in 1472, at Hami in the Tarim Basin. The kingdom of Turfan was attacking Hami, and a Ming army was sent to aid Hami because it was a Ming tributary. Turfan 'borrowed' muskets from the Ottomans (probably via Central Asia), and used them to defeat the Ming army. However, the technology behind the Lumi chong remained unknown to the Ming for more than a century.
In 1597, Zhao Shizhen, the writer of the Shenqi Pu, managed to acquire a Lumi chong from Dosima, a Turk who had settled down in Beijing. Dosima was formerly an arsenal official for the Ottoman state, and had apparently come to China with his brother Babuli on a tribute mission to present a lion to the Ming court. The Ming emperor had appointed them to positions in the imperial court rather than send them back to Turkey, and Babuli's sons Bachen and Bazhong passed the military examinations and joined the Ming army. Through his acquaintance with Bachen and Bazhong, Zhao Shizhen met Dosima, who gladly gave him a Lumi chong and taught him everything he knew about the weapon as repayment for the kindness that the Ming government had shown to this Turkish family.
Zhao Shizhen found the Lumi chong to be far superior to the 'Japanese musket' (Wo chong - in other words, the Portuguese muskets copied by the Japanese) in ease of use, range, and power. He realized that the Ming army could use these new muskets to great effect against the Japanese in Korea - the Imjin War was then in its penultimate year. So he had the imperial arsenal produce copies of the Lumi chong, which Dosima inspected and declared to be satisfactory.
The Shenqi Pu has a detailed diagram of the Lumi chong, along with explanations and technical specifications. One distinctive addition that the Ming arsenal seems to have made to the Lumi chong is putting a blade at the end of the butt so that the musket could be used as a 'zhanmadao' (i.e. anti-cavalry sword) at close quarters.
Since the Imjin War ended in late 1598, some 8 months after the Shenqi Pu was published, it is unclear whether the Lumi chong was ever used by Ming units in Korea. I have also not seen any record of the Lumi chong being used against the Manchus, but if anyone has such information I would much appreciate a tip-off.