Can you solve this Russian nested doll problem?

Nested dolls are a traditional Russian toy and have common metaphorical use. This problem highlights an interesting property that they have due to an important mathematical result.

Suppose that a given set of Russian dolls are all the same shape, though different in size, and have identical height ratios between top and bottom parts. The bases of these dolls are a bit thicker than the rest of them. When the tops are all removed, as well as the innermost doll (which traditionally is all one piece), the edges of the bottoms are all flush with one another. In order for this to hold, what can we conclude about the relative heights of the tops and bottoms of each doll?