Ladies' Diary/Largest Cylinder from given Cone/Historical Note

David Wells informs us in his Curious and Interesting Puzzles of $1992$ that the solution as given here is "something of a cheat", as it refers the reader to to one of Mr. Hutton's texbooks.
This is puzzling, however, as this problem is cited as appearing in $1714$, and Charles Hutton was not born until $1737$.