Samuel Daniel, The Whole Works of Samuel Daniel, London, 1623. Collection David Kasten.
Seeing someone’s name, or a list of names, in a book is not unusual. It is still practiced to indicate ownership, prevent theft, and possibly to add value depending on the name. Names when accompanied by dates are often useful for establishing family history and can aid in dating bindings and repairs.
Earlier books sometimes posit the locus of identity to the book itself; “I belong to Peachey” for example. Sometimes a name is followed by the phrase, “this is my book”.  This has always seemed a bit strange to me—why would someone sign a book that wasn’t theirs?  Doesn’t the name alone signify ownership?
In this case, perhaps it doesn’t. Did Thomas Sedgewick sign a book that wasn’t his? The writing appears to be from the same hand; the ink color and degree of corrosion are quite similar, and the handwriting looks similar to me, especially the heavy “k”‘s at the end. Another possibility is that after reading the book he no longer wanted to be associated with it. Or maybe someone else added the second line, to deny Thomas Sedgewick ownership, or simply as a joke?
Peachey Conservation 