Summation over k of Floor of x plus k over y/Historical Note

Historical Note on Summation over $k$ of $\left \lfloor{x + k / y}\right \rfloor$
The summation over $k$ of $\left \lfloor{x + \dfrac k y}\right \rfloor$ is attributed to, who published this result in $1809$.

Little biographical information can be found about him.