Citing a book vs citing the original paper
I think it can be appropriate to cite a book, exactly because they can provide a great overview of a topic. I can think of a some cases in which you can cite a book. First of all, you may want to point the reader to further background material of your field of research (say, in the introduction of a paper).

Another example: Say you are in -some research area- and you want to use something that is common knowledge in -other research area- citing a book may be helpful because they can contain more background and better explanations. 

Finally as you already mention, if the result is very old finding the original paper may be hard (for both you and the reader). Furthermore the exact phrasing of a results changes somewhat over time, so it may be more difficult to read.