I am reading the Essay of the title written by Beltrami in Italian and I found a specific point of the essay which in my opinion could be fully clarified only if compared with its translations. At the moment, I do not have access to Stillwell's translation for example, so I am asking here in case someone has it.
I am looking for the translation of the little paragraph just after Beltrami computes the formula for the geodetic arch $\sigma$, which you can find at page 7 in its Italian version here.