The word 'Mahogony' is sometimes used rather loosely for anything vaguely reddish rather than in its botanical sence, but I wouldn't want to be definite without touching it.
Whatever, it's a nice door. Just rub a little linseed oil into it and it should look fine.
It looks like the same timber that I've got in several doors and floorboards, which based on information given on this forum ages ago I decided was probably elm.
Doesn't mahogany have a closer grain than timber shown in the picture?
I have a quantity of rough sawn mahogany tucked away for future projects and yes, the photo does look like them. My guess is that this is reused from something else. Front doors (even in 1730) if made of high quality wood would have been panelled, not ledge and brace. However during the early nineteenth some useful planks lying around somewhere would have been just right for knocking up a cellar door.
My daughters cottage , 17th c., has a three ledged and a bit plank door, one plank and the bit is mohogany the rest pine held together with slotted head screws. ( obviously a made up effort possibly late 19th early 20th cent).
If you check on the type of hingies and the way the ledges are put together it will give you more information.