Cowper's "Task," published in 1784, twice mentions the umbrella:
"We bear our shades about us; self-deprived
Of other screen, the thin umbrella spread,
And range an Indian waste without a tree."
Book i.
In book iv., the description of the country girl, who dresses above her condition, concludes with the following lines—
"Expect her soon with footboy at her heels,
No longer blushing for her awkward load,
Her train and her umbrella all her care."
In both these passages of Cowper, the umbrella appears to be equivalent to what would now be called a parasol.