Daf: Nazir 5a-10b

Get a gemara, or this will likely be unintelligible…

5a
We are consistently taught that a Gezeirah Shavah (or pleonasm, as Rabbi J. David Bleich translates it) is a received tradition, such that logic is ineffective in analyzing it. This is a message reiterated all through the gemara. Nonetheless, the middle passage on this page – היכא דאיכא דדמי לה etc – certainly sounds like there is logic at work here!

The gemara seems to counsel shaving on Friday afternoon, which is problematic given the gemara elsewhere warning not to shave on Friday afternoon! See the Aruch haShulchan Orach Chaim 251:3, who has everyone from Rif and Rambam to Arizal and GRA.
Perhaps in this case one has davened earlier. Alternatively, see the Rosh here, who may be solving precisely this problem with his "לאו דוקא פניא" statement.

It is rare that we use Gematria for halachah, but for another example see Rashi on אך-חלק in the beginning of Pesachim.
See also the Rosh here, who seems to be disturbed by the use of Gematria for halachah, such that he decides it’s only an asmachta.

6b
The Rosh decides that Rav Masna has been defeated.

8a
I cannot understand why everyone insists that ימות הלבנה refers to a lunar year. There is no such thing, astronomically or halachically, as a lunar year; the gemara in Rosh HaShanah is explicit on this point; our “lunar year” is simply a collection of twelve lunar months.

8b
A “digon” house seems to be brought up simply for the sake of fitting in with the trigon and tetragon house.
For those who don’t have a gemara in front of them – trigon is a triangle, a shape with three angles. You can have a house with three angles between its walls. Ditto for tetragon/square/four angles. But there is no such thing as a house – or any shape – with only two angles.
The only possibility I can imagine is one put forth at our Daf shiur, of a house with two canoe-shaped walls – but I don’t think this is what the gemara means.

10a
See the Rosh on the cow here being the korban of a nazir.

10b
The word תורף is interesting here.
Rosh takes it like מקום התורף to refer to that which is revealed, or which reveals. Tosafos seems to do the same.
To me, another possibility is that this is like תורף הגט in Gittin – the term תורף is used to refer to the essence of a legal document, the part with the actual names and contract-specific information, as opposed to the טופס which is the boilerplate language.
That would fit with the use here very nicely; the תורף is the essence.