The creator or owner of a piece of software does not in general have any copyright over the output when others run the software, unless that output is itself a derivative work of input supplied by the copyright owner, or forming part of the software.
In this case the translation is a derivative work of the 19th century original, but that is assumed to be in the public domain. SAo google has no copyright on the resulting translation. But copyright protection is only available for "original works of authorship". (See 17 USC 102 in the US, and similar laws elsewhere.) A machine-produced translation is not an original work, and it is surely not then work of the author of the overall book.
However, the author would still have a copyright on the book as a whole. The legal situation is no different than if the author had simply quoted a 19th century work. One may incorporate public domain works into a later work, and that later work is still protected by copyright, provided that there is enough original contentr to make the work as a whole "an original work of authorship". Others may use the PD [arts, or the original from which they are taken, but not the rest of the work (beyond what fair use would allow in any case).
For example, I have made a number of posts here on LAW.SE. In several,of those I quoted sections from one of the numbers of The Federalist. That 19th century work is in the public domain. Anyone else may re-quote the passages I quoted from it. But that gives them no rights to use the rest of my work, except as the CC-BY-SA license or fair use permits.
So the author would retain copyright on the book as a whole. But soemoen who merely quotes or uses the translated 19th century article but none of the original parts of the book would not be infringing that copyright.
I say probably in the header, because I do not have any actual case-law to cite here. It is possible that some court has rules otherwise on the subject of the copyright on the output of a software tool, but I strongly doubt it.