This he treated synthetically, to the total exclusion of analysis, which he hated, and he is said to have considered it a disgrace to synthetic geometry if equal or higher results were obtained by analytical geometry methods.
32.
Therefore, the proof of the first part in synthetic geometry, and the proof of the third part in terms of linear algebra both are fundamental steps of the proof of the equivalence of the two ways of defining projective spaces.
33.
Complex projective space was first introduced by as an instance of what was then known as the " geometry of position ", a notion originally due to Lazare Carnot, a kind of synthetic geometry that included other projective geometries as well.
34.
These figures were all involved in algebraic geometry, rather than the pursuit of projective geometry as synthetic geometry, which during the period under discussion was a huge ( in volume terms ) but secondary subject ( when judged by its importance as research ).
35.
The alternative approach consists in defining the projective space through a set of axioms, which do not involve explicitly any field ( incidence geometry, see also synthetic geometry ); in this context, collineations are easier to define than homographies, and homographies are defined as specific collineations, thus called " projective collineations ".
36.
At the beginning of the 1930s, Adams published a series of articles and essays about projective, synthetic geometry and its relationship to physics, to Goethe s theory of metamorphosis and to anthroposophical spiritual science, particularly the pioneering work " Of Etheric Space " in the magazine " Natura " of the Goetheanum s Medical Section.
37.
After a period as a teacher in A�dz he became professor of synthetic geometry at Dresden where his growing interest in kinematics culminated in his " Lehrbuch der Kinematik, Erster Band, Die ebene Bewegung " ( Textbook of Kinematics, First Volume, Planar Motion ) of 1888, developing the approach to the theory of degree of freedom.
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