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G. Waldo Dunnington in his biography of Gauss states (on p. 165):"only a portion of his results in the field of curved surfaces was presented in the Disquisitiones generalis, and a second memoir on the subject was planned." I must mention in adddition that i found an enormous amount of material on these subjects in volumes 8 and 9 of his works - the titles of the various manuscripts range from geodesic lines on ellipsoid, the figure of the earth ("erdellipsoid"), and lots of kinds of conformal mappings. It came as a surprise to me that i didn't find any summaries of these writings, and as far as i know Gauss, the probability that the importance of these writings is neglible is pretty small. I didnt even find a concise evaluation of his work in theoretical geodesy (like his memoirs from 1843 and 1846). So my questions is mainly to get sources - if anyone knows good articles about the subjects mentioned, please add it.

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  • $\begingroup$ An obvious place to start would be Bühler's Gauss, chapter 9 and appendix B. $\endgroup$ Commented Jun 25, 2017 at 10:40

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Here is a review of Vol. 8 of Gauss's works: https://projecteuclid.org/euclid.bams/1183417390

As for his works in earthly geodesy, i.e. the adjustment of triangulations, which forms a part of Vol. 4 and Vol. 9, the best introduction to it is in chapter 3 of "Numerical analysis of symmetric matrices" by Schwarz, Rutishauser and Stiefel: https://books.google.de/books?id=j8O7AAAAIAAJ&q=adjustment+%22constrained+fitting%22

A more thorough exposition is in chapters 5 and 6 of Wright/Hayford: https://archive.org/stream/adjustmentobser01hayfgoog#page/n6/mode/2up

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