What is a birth certificate?
A birth certificate will tell you the date and place of birth of a named child. It will also give you the names of the parents and the parental residence, possibly. And the father's occupation. So the birth certificate will give you two generations for the price of one. And it will give you the mother's maiden name, or her former name, so that you can then look for their marriage certificate. And a sequence of these birth, marriage, birth, marriage certificates will take the family tree back in time and will provide proof of relationship.