Halakha Imamat 24:19: Sefer HaChinukh

The root of this commandment is revealed to all, as “by justice a king sustains the land.” As were it not for the fear of judgment, people would kill one another. Therefore, God, blessed be He, commanded us to kill the murderer. And in His wisdom, blessed be He, He saw that it is fitting to punish him with the death penalty of strangulation. And the matter is beautiful, also according to our [understanding], since “as he has done, so shall it be done to him” — since the intention of the killer was to kill the murdered quickly, as from [the killer’s] fear of him, he will quicken his death with all of his might. And so too was the Torah lenient with his judgment to kill him with strangulation, which is a quick death penalty; and not with stoning and burning, which are with great pain. (In the other editions, it is written, “The truth is that the death penalty of the murderer is with the sword, [whereas] he who hits his father and mother has a death penalty of strangulation.”) However, with the statutes of licentiousness, in which the transgressors derived pleasure from the sin and the pleasure continued a bit, they sometimes get burning and sometimes stoning.

The commandment of the laws of penalties: That we were commanded about the law of one who injures his fellow to penalize that person, as it is written in the Torah in the section of “And if men fight” (Exodus 21:18). And this is called the laws of penalties. And in another verse, it includes all of the laws of penalties, and it is the verse, “as he did, so shall it be done to him” (Leviticus 24:19) — it means to say that what he pained [his fellow] should be taken away from his money, in accordance with that which he injured his fellow, as the tradition comes about it (Bava Kamma 83b). And even if he did not hit him, but only embarrassed him, the court must cause him pain through his money, that he should pay the one embarrassed, according to this amount. And these laws that are called the laws of penalties — for example, the laws of a man [who hurt another] man; an ox, an ox; an animal, a man; a man, an animal — must be judged in a court that has been ordained in the Land of Israel (Bava Kamma 84a).