Join question

I have a table that is set up like this

table A:
First_name,Last_name,login

I have another table that is set up like this

table B:
date,date,person1,person2,person3

where the person1,2,3 is the login name from the first table.

I need to get the first_name and last_name of all 3 persons using one select (well I don't have to do it in one.. but I
thoughtit would be cleaner).. I can do one person using a join select like this: 

select A.First_name,A.Last_name from A,B where B.person1 = A.login

I tried adding an or statement like "or B.person2 = A.login" but that returns 2 entrys for each row.. where I'm trying
toget all the information back in one.   

Thanks in advance,

Travis