Gauss, Carl Friedrich | Theoria Combinationis Observationum [and] Supplementum
The rare first edition of the “definitive exposition of Gauss’s mature ideas” on minimising observational errors in statistical analysis (DSB), together with the scarce supplement. Only two copies of the first volume, and one of the supplement, appear in auction records over the last two decades.
“The invention and development of the method of least squares provides a conceptually fascinating study in the early history of error analysis. The theory of errors consisted around 1800 of a collection of rules in astronomy and geodesy. (The discipline of mathematical statistics as such did not become established until the early twentieth century.) the method was first published by Adrien Marie Legendre in 1805 in a paper on the calculation of the orbits of comets. in 1808, in a major theoretical advance, Gauss presented a proof based on the assumption that the errors are distributed normally. The latter assumption was in turn deduced from the assumption that the arithmetic mean is the most likely value of a set of measurements. Gauss’s result stimulated Laplace to devise a new proof of least squares using a result later known as the central limit theorem, applied in this instance to measurements involving a large number of observations. Gauss’s primary achievement in his 1823 treatise was to take elements of Laplace’s analysis and produce yet another demonstration of the method, one valid for any number of observations. His proof was based on the postulate that among all linear combinations of the observations, the least-squares estimate has minimum variance. The treatise would provide an important source of ideas and techniques for later researchers in mathematical statistics” (review of a new translation by G. W. Stewart of Theoria Combinationis Observationum, ISIS volume 86, number 4, 1995).
Theoria Combinationis Observationum Erroribus Minimis Obnoxiae. [Together with] Supplementum Theoriae Combinationis Observationum... Gottingen: Heinrich Dietrich, 1823 & 1828.
2 volumes, quarto (240 x 200mm). Recent black and purple marbled boards, red morocco labels to spines, new endpapers. A few neat pencil notes in the margins, primarily in volume II. Light spotting to the contents of volume I. Excellent condition.