This does what you want. Passing the desired start index as a parameter prevents Groovy from using a default of 1 for the line number.
The eachLine method is defining the second argument to be the line number. It ignores any requests you make of i. For example, if you change i++ to i+=2, you get the same behavior 1-6 as before because eachLine is helpfully setting i to the line number for you.