Die kleine Speyerer Basis oder Beweis dass man mit einem geringen Aufwand an Zeit, Mühe und Kosten durch eine kleine genau gemessene Linie die Grundlage einer grossen Triangulation bestimmen kann. GAUSS'S COPY WITH HIS SIGNATURE

Schwerd, Friedrich Magnus

Verlag: Speier: J.C. Kolb, 1822

First edition, very rare, CARL FRIEDRICH GAUSS'S COPY WITH HIS SIGNATURE, of this important early work of geodesy. "The derivation of the length of a terrestrial arc first requires a measurement of a line [of a base] on the surface of the Earth which is the only operation in which a measure of length itself is applied. That line becomes a side of a triangle whose angles are measured by proper instruments and the other sides of the triangle are trigonometrically calculated. A second triangle is adjoined to the first one and its elements become known in a similar way, then a third triangle is added etc. A chain of triangles extending from one point on the surface of the Earth to another on the same meridian is thus formed and the distance between them becomes known. To measure that distance directly without forming triangles will always be time-consuming and only possible if the measured line does not pass through hills or water [hardly ever possible]" (Sheynin). Schwerd (1792-1871) became professor at the gymnasium in Speyer in 1817 and, on the establichment of a Lyceum in Speyer in 1836, was made professor of mathematics and physics there, a position he held for the rest of his life. In 1820, Schwerd and his students measured the distance Speyer to Oggenheim using a short base of 860m, connecting it with the line Speyer-Oggenheim using a trigonometric net. This led to the present publication, 'The small Speyer basis or proof that with a small investment of time, effort and expense one can determine the basis of a large triangulation by a small precisely measured line,' in which Schwerd showed that the use of a short base line led to more accurate results when determining distances by triangulation. Schwerd's technique was quickly adopted by surveyors and continued to be used until it was replaced by today's surveying by satellites. This was probably an important work for Gauss. His preoccupation with surveying began in 1817 and continued for the next eight years. "The triangulation of Hannover was not officially approved until 1820, but already in 1818 Gauss began an arduous program of summer surveying in the field followed by data reduction during the winter . . . the period of preoccupation with geodesy was in fact one of the most scientifically creative of Gauss's long career. Already in 1813 geodesic problems had inspired his 'Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodus nova tractata,' a significant early work on potential theory. The difficulties of mapping the terrestrial ellipsoid on a sphere and plane led him in 1816 to formulate and solve in outline the general problem of mapping one surface on another . . . Surveying problems also motivated Gauss to develop his ideas on least squares and more general problems of what is now called mathematical statistics" (DSB). Poggendorff II, 878. COPAC lists Cambridge only. 4to, pp. 99 with 4 folding engraved plates. Contemporary plain pink wrappers with title in manuscript on upper wrapper. Signature of Gauss inside front wrapper, stamp of Gauss Bibliothek and of Göttingen University library on title, release stamp on verso of front wrapper indicating that the book was sold as a duplicate in 1951. Bestandsnummer des Verkäufers ABE-1668105145172

Bibliografische Details

Titel: Die kleine Speyerer Basis oder Beweis dass ...
Verlag: Speier: J.C. Kolb
Erscheinungsdatum: 1822
Einband: Soft cover
Zustand: Near Fine
Auflage: 1st Edition