As soon as I say something, I must revise it. I stand by what I said before, actually, that a 7-strutted parasol was odd and surprising to me. I will maintain that 8 or 6 is what I see the most, so it is reasonable to wonder if an a-typical number of struts and segments might not be an artistic issue rather than an actual phenomenon. But here is a physical object rather than a drawing - an umbrella (not totally the same thing, but close cousin of the parasol), sold by August Auctions here. They dated it to 1790-1810. Here is the description and the pictures, but pay special attention to the picture of the inside, where you can see the struts. Count them. I see nine, an odd and unusual number. Isn't that fascinating?
"Umbrella with dark blue-green cotton cover, striped with beige around edges, ivory or bone points, metal framing, baleen canopy ribs, tortoise colored crooked handle, possibly horn, brass cylindrical slide and tip, stenciled green and tan cotton drawstring case, (small dents in brass, minor stains and wear to wood handle) excellent."