The Historical Exploration Of Staudt's Synthetic Projective Geometry Thought

Synthetic method uses pure geometry method to solve geometric problems.Before the birth of analytic geometry,it is the only way geometers used.Synthetic method was in a disadvantage position in the 18 th century,but it revived at the beginning of the 19 th century.The revival of synthetic method brought the prosperous development of the synthetic projective geometry,its representative men included Poncelect,Chasles,Steiner and Staudt etc.Staudt made projective geometry break away from measurement,his synthetic projective geometry thought holds the pivotal position in projective geometry.This dissertation makes a historical exploration of Staudt's synthetic projective geometry thought on the basis of studying a large number of documents.The details include the background,the core content and the later generations' improvement of Staudt's thought.The main results are as follows:1.This dissertation illuminates the background of Staudt's synthetic projective geometry thought.Projective geometry originated from the ancient Greek,developed in the 17 th century by Desargues and other people.Poncelect's founding work with Chasles and Steiner's study of cross ratio made projective geometry mature in 19 th century.2.This dissertation explores the core content of Staudt's synthetic projective geometry thought.Staudt's synthetic projective geometry thought mainly reflected in his two worksGeometrie der Lage and Beitr?ge zur Geometrie der Lage.Staudt published Geometrie der Lage in 1847,in this wok he firstly defined the projective relationship of figures which do not depend on any measure concepts.On this basis,he also gave the particular definition of conic sections by means of involution and polarity.Staudt published Beitr?ge Geometrie der Lage in 1856-1860,in this work he introduced "wurf" to redefine the cross ratio and used involution to define imaginary elements.3.This dissertation analyzes the later generations' improvement of Staudt's synthetic projective geometry thought.Staudt got Staudt Theorem from his non-metric projective definion,but there are some theoretical defects.Klein and Pieri respectively improved the defects from continuity and axiomatization.