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There are not very many pictures showing parasols, but they are certainly there. This isn't a surprise, because when the Dutch started colonising the East Indies they came across these convenient items and surely brought them back over to Europe. Apart from this parasols have been known throughout the ages but with different impact on different societies.
By the late 1690s there is an English advert for parapluis, and this French word means an umbrella in contrast to a parasol, which is a proof for parasols having bee adapted quickly for rain. Not only that, in this advert collapsible umbrellas are praised. The shape of those later umbrellas or parasols is more like the modern ones.

1660 Minister Seguier waded by black silk parasols carried by his pages. The edge is adorned with a deep gold brush fringe. The shape of the parasol is that of Asian ones still.	1662 Page carrying his Lady's closed parasol.
1675 A little later, but it still has the shape of the parasols in the 1660s and this one has a fringe as well, which seems to be obligatory.	Late 17th Later parasol, Italian probably 1690s. It is made from silk and embroidered with coloured silks and gold thread.
The parasol I had made in Thailand. It was made from a thick blue silk and I had the handle lengthened, using a nicely turned banister. The gold metal brush fringe was added by myself.	The fringe is so heavy that it pulls the parasol down into a more domed shape.