Die Hauptsächlichsten Theorien Der Geometrie

A historical monograph written in the late 19th century. The work aims to present a comprehensive overview of the development of geometric theories, examining their evolution from ancient times to modern advancements. As a scholarly text, it reflects on the historical milestones and key figures in the field of geometry, intended for an audience looking to deepen their understanding of the subject's progression through history. At the start of the monograph, the author expresses a desire to fulfill the need for a retrospective on geometric advancements given the rapid progress in mathematics. Loria introduces his intention to provide a ''chronicle'' that acts as a precursor to a more extensive history of geometry in the current century. He notes the considerable challenge of writing such a historical account, emphasizing that a successful narrative would help both novices and experienced mathematicians grasp the solutions to pressing geometric problems. Although Loria acknowledges the difficulties in achieving a complete study, he outlines the foundational topics he plans to cover, including the history of geometry before the mid-19th century, theories of curves and surfaces, and the implications of differential geometry.