text: In 1861, Grassmann laid the groundwork for Peano's axiomatization of arithmetic in his Lehrbuch der Arithmetik. In 1862, Grassmann published a thoroughly rewritten second edition of A1, hoping to earn belated recognition for his theory of extension, and containing the definitive exposition of his linear algebra. The result, Die Ausdehnungslehre: Vollständig und in strenger Form bearbeitet (A2), fared no better than A1, even though A2 manner of exposition anticipates the textbooks of the 20th century.
  Response
  In the 1840s, mathematicians were generally unprepared to understand Grassmann's ideas. In the 1860s and 1870s various mathematicians came to ideas similar to that of Grassmann's, but Grassmann himself was not interested in mathematics anymore.
  Adhémar Jean Claude Barré de Saint-Venant developed a vector calculus similar to that of Grassmann, which he published in 1845. He then entered into a dispute with Grassmann about which of the two had thought of the ideas first. Grassmann had published his results in 1844, but Saint-Venant claimed that he had first developed these ideas in 1832.
  One of the first mathematicians to appreciate Grassmann's ideas during his lifetime was Hermann Hankel, whose 1867 Theorie der complexen Zahlensysteme.
  In 1872 Victor Schlegel published the first part of his System der Raumlehre, which used Grassmann's approach to derive ancient and modern results in plane geometry. Felix Klein wrote a negative review of Schlegel's book citing its incompleteness and lack of perspective on Grassmann. Schlegel followed in 1875 with a second part of his System according to Grassmann, this time developing higher-dimensional geometry. Meanwhile, Klein was advancing his Erlangen program, which also expanded the scope of geometry.