I'm not familiar with capillarity but if you are, and you have the time, I'm sure that fermat's library would love to add it with some historical remarks and annotations
He's just using it as a synonym for "Consider..." or "Assume we have...", which is a really common way to start. I didn't find this paper to read very differently from a contemporary paper in Physical Review Letters, except that there's no introduction that gives context within the rest of the literature.
Using the word "imagine" isn't that unusual. Here's some examples in just the past couples of years:
"We might then imagine other starting points which..."
To me it read more like a math text than a physics text, in which "let there be X...", "imagine Y...", and similar phrases, are usually found. Yet I agree, it seems the physics community has grown a slight alergy to that kind of writing, and it probably would be received with a bit of skpeticism/disdain nowadays.
Nothing special about the "imagine" portion; plenty of research in theoretical Computer Science takes an even more informal.approach in the introduction.
This thesis actually describes a scheme Monotype developed to replace the older hand-setting approach (used through WWII). Nice intro to the subject though.
