An Elementary Course in Synthetic Projective Geometry

A scientific publication written in the early 21st century. This work focuses on the principles and fundamental concepts of synthetic projective geometry, aiming to present the topic in an accessible manner for both college students and potentially for secondary education. The text emphasizes the importance of understanding geometric relationships and structures without reliance on measurement, highlighting the significance of one-to-one correspondences and projective properties. The beginning of the course outlines the author's motivations and pedagogical approach, which departs from traditional methods to provide a clearer understanding of synthetic projective geometry. Lehmer explains the foundational concepts, such as one-to-one correspondence and the relationships among different geometric forms, like point-rows and pencils of rays. He stresses the necessity of a solid grounding in elementary geometry for students, suggesting that those with additional knowledge in analytical geometry and calculus will find the material easier to comprehend. This foundation prepares readers for a deeper exploration of projective relations, constructions, and theorems laid out in subsequent chapters.