Mishnah/Seder Nezikin/Tractate Sanhedrin/Chapter 1/5
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Seder Nezikin, Tractate Sanhedrin
Chapter 1, Mishnah 5
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Sanhedrin deals primarily with the court. It presents three courts, a Bet Din of 3, a court of 23, and a larger court known as the "sanhedrin" made up of 71 judges in capital cases. The first chapter of Sanhedrin is focused on how many judges are needed for different cases, capital and non-capital.
The fifth mishnah of this chapter categorizes cases that require 71 judges. The number 71 is found in the Torah, when Moses appoints a court of 70 judges in the desert. (70+Moses=71) There is little evidence, however, that such a court ever actually existed.
Hebrew Text 
- אין דנין לא את השבט ולא את נביא השקר ולא את כהן גדול, אלא על פי בית דין של שבעים ואחד.
- ואין מוציאין למלחמת הרשות, אלא על פי בית דין של שבעים ואחד.
- אין מוסיפין על העיר ועל העזרות, אלא על פי בית דין של שבעים ואחד.
- אין עושין סנהדריות לשבטים, אלא על פי בית דין של שבעים ואחד.
- אין עושין עיר הנדחת, אלא על פי בית דין של שבעים ואחד.
- ואין עושין עיר הנדחת בספר, ולא שלש , אבל עושין אחת או שתים.
English Translation 
There is no judgment for a tribe, or a false prophet, or a high priest, except by a court of 71. (The nation) cannot send [declare] to a war of free choice, except by a court of 71. Cannot add [annex] to a city or region, except by a court of 71. Cannot make a Sanhedrin for tribes except by a court of 71. Cannot proclaim a city of idolatry, except by a court of 71, and there cannot be a city of idolatry on the border, and there cannot be three cities of idolatry, only one or two.
This is a list of cases requiring 71 judges, each of which alludes to biblical laws. Here is a brief explanation of these laws:
A tribe - This refers to the suspicion that a whole tribe of people is committing idolatry. If they are found guilty, the whole tribe would be killed, so 71 judges are needed.
A false prophet or a high priest - The rules for how to determine a false prophet are found in the Torah. In addition, a high priest who commits a capital sin must be tried by a court of 71.
War of free choice - Some wars are required, such as the biblical order to destroy Amalek, but wars that are not required must be declared by a Sanhedrin, not by a king or priest or smaller court.
City of idolatry - The Torah explains that a city of idolatry must be burned completely to the ground and nothing in it (human, animal, or property) must survive. This mishnah restricts the use of such a verdict, disallowing any city on the border or any group of three cities to be proclaimed as cities of idolatry.