(Bamidbar 35:19) "the avenger, he shall kill the murderer": The mitzvah is the avenger's. Whence is it derived that if he has no avenger, beth-din designates one for him? From "The avenger, he shall kill the murderer when he comes upon him" — in any event.
(Bamidbar 35:20) "And if in hatred he thrust him": What is the intent of this? From "And if with an iron implement," "And if with a hand-stone," "Or if with a wooden hand-implement," I might think that he is liable only if he killed him with these. Whence do I derive (the same for) other things? It follows by induction from all three, viz.: Stone is not like wood; wood is not like stone; and both are not like iron. And iron is not like both. What is common to all three is that they are potentially lethal, and if one killed (by them), it is a mitzvah for the avenger to kill him. This tells me only of his killing with these. Whence do I derive that he is likewise liable if he pushed him off the top of a roof and he fell and died? From "And if in hatred he thrust him" — in any event. — But perhaps even if he pushed him into water or fire or incited a dog or a snake against him? It follows (that this is not so) by induction from all three, viz.: Stone is not like wood and wood is not like stone and both are not like iron and iron is not like both. What is common to all three is that they are potentially lethal and he killed (by wielding them), in which instance he is liable — to exclude his thrusting him into fire or water or inciting a snare against him, in which instance his (the victim's) judgment is relegated to "Heaven." "or if he hurl aught at him in prey": (i.e.,) if he "hunted" him with intent to kill.