Citing a book vs citing the original paper Books often have great overviews of topics and can cite dozens of papers in a single section or chapter and the book author typically cites the original discoveries of many others besides himself.

Is it ever appropriate to cite a book alone, or should I always cite the original papers?

Does it matter if my use of the the material is a brief reference to a broad topic I'm building on vs a specific paper? 

Is the number of years that have passed, or perhaps how common the knowledge is in the field a factor when deciding to cite the book or the original paper?

Does the answer vary by field? If so, in my case I'm typically working with robotics and computer vision papers.
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.