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We are all familiar with Rebbi Yishmael's 13 principles for expounding the torah, however there are other systems not included in his list. I remember once hearing a shiur that there are over 40 ways to expound the torah. Is there an authoritative list of every way that is used by chazal to expound the torah?

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Bamidbar Rabba 2:3 explains that there are 49 ways to expound the torah, but does not list them

4

I suspect you are referring to the famous teaching of Rabbi Eliezer the son of Rabbi Yosi HaGlili that enumerates 32 middos (principles) for interpreting the Torah. A detailed discussion of these 32 principles can be found in the back of Tractate Brachos in standard editions of the Vilna Shas, a few pages after the Mevoh HaTalmud.

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