“Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”
“From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a...”
Hermann Grassmann
“It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a prob...”
Hermann Grassmann
“I remain completely confident that the labour I have expended on the science presented here and which has demanded a significant part of my life as well as the most strenuous application of my powers,...”
Hermann Grassmann
“A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the ...”
Hermann Grassmann
“The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, no...”
Hermann Grassmann
