At the end of the paragraph, he repeats it even more explicitly: "By alternately using the aerofoil and hydrofoil, one could in principle reach arbitrarily large speeds and directions, as illustrated by the following diagram:"

Are you saying that he didn't mean "arbitrarily large" literally?

That was what I meant. And I see I was wrong. Sorry. It's such a shocking statement that I didn't take it seriously at first. In retrospect, the energy influx is continuous, so continuous acceleration is possible.