文档介绍：Selected Topics in Three-Dimensional Synthetic Projective Geometry
Introduction, References, and Index
Renatus Ziegler
Preface
The following chapters are a contribution to visual geometry, mainly three-dimensional
projective geometry and line geometry. The development of flexible geometric thinking
seems to be somewhat neglected nowadays in the training of mathematicians and scientists
in general. But the need for engineers and scientists who fortable with the subtle-
ties of spatial geometry is apparent, even in spite of the now puter-aided
methods of graphic design. And there may be no better way to get deeply involved in spa-
tial geometry than in exercising the skills of visual representation by the means of synthetic
geometry. Thus I have adopted the synthetic method, which forms a characteristic feature of
this presentation.
Some experts identify the synthetic method with the axiomatic method, but I would rather
emphasize that the synthetic method deals directly with the properties of the geometric
objects themselves without representing them in terms of other objects, for example, in
algebraic equations. Of course, one often arrives much faster at geometric results or propo-
sitions by applying some kind of algebraic symbolism, but, during the process, the geomet-
ric object in question can disappear very easily from our imagination. – This approach
might be unfamiliar to many readers, but I know of nothing else that trains the geometric
intuition more effectively than synthetic geometry.
Another characteristic feature of this presentation is the approach to Euclidean geometry,
which is not conceived as a primitive space form but is consistently treated as a certain kind
of limiting case of general projective metric geometry. Not only can this be of practical
importance, but it will particularly refine and clarify the logical skills and the basic con-
cepts of geometry. In addition, it helps one