What was the first Japanese book translated and published in one of the European languages?
By "first" I mean the date of translation, not the original.
Not often I get to upstage Semaphore on his own turf, but here it goes...
One of the first translators of Japanese works was the brilliant German polymath, Julius Klaproth. He made several translations from the Japanese in the 1830s, the first of which was of the Sangoku Tsūran Zusetsu in 1832. This important book, first published in 1785 in Japan, had been brought to Europe by Isaac Titsingh who had made a manuscript translation from which Klaproth worked.
Now, this, of course, was not the first Japanese book translated into a western language, but in terms of fame is perhaps the most notable. The actual earliest book is hard to determine, but one candidate is the Osacka Monogattari published in Yedo (Tokyo) in 1668. I believe this is a translation into Latin. There is a copy of this incredibly rare book in the British Museum.