If n is Triangular then so is 9n + 1/Historical Note

Historical Note on If $n$ is Triangular then so is $9 n + 1$
, in his of $1980$, reports that the result If $n$ is Triangular then so is $9 n + 1$ was published by  in $1775$.

He published this along with If $n$ is Triangular then so is $25 n + 3$ and If $n$ is Triangular then so is $49 n + 6$.

There is an obvious pattern.