I haven't seen a Plat like this before, admitting to triangulating. I've seen some rough country Plats and they never admit to triangulating except minor things like crossing a river. They chained right up that 60% slope canyon wall according the notes.
The Geyser Hotel is shown just north of the east-west centerline of Section 13 and in the northeast quarter which was owned by Polack. Apparently in a Private Surveyor concluded that the Hotel was actually in the southeast quarter. Chapman owned the southeast quarter and sued to eject Polack from the hotel. It's not surprising there was confusion.
Chapman prevailed at trial and Polack appealed. The California Supreme Court reversed the trial court saying the original survey could not be impeached.
Chapman v. Polack, 70 Cal. 487 (1886)
The case is available here (free):
http://www.lexisnexis.com/clients/CACourts/
After agreeing to the terms and conditions, select citation on the right, 70 is the volume, Cal is the reporter, and 487 is the page number.