I killed Septimus before I got the Oghma Infinium. Is there another way to get the item?
According to the UESP wiki there is a bug where Septimus will not die when approaching the altar, making it impossible to complete the quest, although you might be able to kill him yourself at that point to trigger the next scene. There is also another bug where a bandit marauder enters the cave and kills Septimus, making it impossible to complete. Taking these into account, I would assume that you would not be able to complete the quest without Septimus alive until the end.