From a commercial photographer, commercial prepress person, and amateur genealogy hack, I can add my two cents worth if it's still needed. I'm sure you've figured out by now that what's happening is your scanner is reacting (badly) to the printing screen angles used when the book was printed. Under casual viewing, our eyes adjust to the dot patterns and we see the image, not the dots themselves. When this image is viewed by equipment that has its own screening issues (like a scanner), they can conflict and the noise either gets enhanced or, worse, a moire' pattern is created. It can get really ugly.

I agree wholeheartedly with the thread on copyright issues and want to repeat that it's illegal to copy someone else's work (whether written or photo...it doesn't matter). That being said, I can tell you that your best bet for duplication may be a good old fashioned film camera (35mm type). Using film to duplicate the image can have a softening effect on the printing dots. When this is enlarged from the film to print, the dots will get softer. If you're wanting a digital copy, then it can be scanned. It's several steps and generations from the original but this is one of those rare cases when it can help to have multiple generations.

I can also tell you that when we ran into this problem in the commercial prepress dept., we'd skip using the high-end drum scanner (it only makes the problem worse) and went to the low-end flatbed scanner. The optics aren't as good and it tends to soften the screening pattern. Wish I could tell you that there was a simple, magical button to push but there really isn't. Good luck!