Is it possible to use the book translation of an author dead for more than two hundred years, and simply mentioning the author and the translator’s names without paying royalties to anyone?

The copyright over a written work lasts for the whole life of the author and, upon the heirs, for seventy years after his death, after which anyone could use the writing, make copies of it and reproduce it in any form he prefers. In this specific case, the copyright of the original author have indeed expired, as he has been dead for over two hundred years, but this must not lead you to think that there is nothing to be paid. You must bear in mind that the translation of a book is considered a work apart from the same book and there is a new copyright over it. It is also true that an author has the exclusive right of authorising the translation of his own book, this is not the case as the rights of the original author have expired for some time, but it is also true that, once translated, the translator has some real and definite claims over it. Therefore, if the translator is still alive or has been dead for less than seventy years, his authorisation for the use of the translation will need to be asked and the compensation due to him will need to be paid independently from anything owing to the original author. On the other hand, if it is in your own interest translating the work, then nothing will need to be asked to anyone and could be done without any problems as the original writing is freely available.