Changes in Paradox table don't get posted

I'm trying to add some records to an empty table. The code I'm using
looks right, but no matter what I do the only record that actually
gets posted is the last one I try to post. Here's a sample of code:

with Table1 do
begin
   Active := true;
   First;
   for i := 1 to 10 do
   begin
      Edit;
      Table1Field1.AsInteger := i;
      Next;
   end;
end;

After running this code when I use Database Explorer or Database
Desktop to look at the contents of the table there is only one record,
and its value = 10. Is there something I'm failing to do here?