History of Fencing question

[Scottgun]

At the library I picked up Pirates Terror on the High Seas- From the Caribbean to the South China Sea. In it was a picture of a rapier from around 1605:

http://wallacelive.wallacecollection...=Simage%2Fjpeg

In the note for the picture it says (my bold), "Rapier fencing was a two-handed art; the other hand being used to parry and defend or to carry a dagger for attack"

That seems confusing.

1). If they didn't carry a dagger, with what would you parry and defend? An armored glove perhaps?

2). When I think of fencing, I think of foil fencing--sport swords with "blades" no thicker than a coat hanger and the primary attack is thrusting with no slashing which I know is a criticism of the fencing style in the game. Yet, this rapier looks like it has a robust blade that could have sharpened edges and could indeed accomodate a slashing attack. Did some weapons and fencing styles have slashing in their repertoire? Or is "fencing" being used generically?

P.S. Enjoying the book so far if anyone is looking for a general introduction to pirate history.