There have been some lively debates on the web over the exact way to roll for character hit points per level.The original D&D rules were vague about it. Many have tried to figure it out. This hyper analysis of a simple text seems to have spawned some bizzare interpretations. I see only two variations on this each supported by a passage from a different rulebook.
Type 1- pg 11 D&D blue book;
As a character goes up a level he increases his hit dice. The new die is rolled and the score is added to his current number of hits.
If the new level has the same number of hit dice but adds points (ie +1) do not roll but add the number to the characters current hit point total. This is the method I used when I started playing AD&D back in the early 80's.The advantge of this method is that characters can always increase their total number of hit points when going up a level.
Type 2- pg 5 Swords&Wizardry Whitebox 1st print;
Characters re-roll their HD each time they advance a level to obtain a number of hit points. (If you roll poorly, those hit points don't go down, however)
With this method you roll the hit dice total for the new level and compare the result to your current hit point score and use whatever is greater as your hit point total.
The difference with this method is that characters are not guaranteed an increase in hit points with each new level. I now prefer this way as it can limit the characters to lower hit point totals.
Interestingly I could not find any referance to the type 2 method in the older rulebooks I have.