Geometry by Its Transformations: Lessons Centered on the History from 1800-1855

This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid’s Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration.

This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry. 

Christopher Baltus has degrees in history (BA), mathematics education (MAT), and mathematics (PhD). After three years of secondary mathematics teaching and two years in the Peace Corps, he taught college mathematics for 36 years. His article “Poncelet’s discovery of homology” appeared in Historia Mathematica, May 2023. In retirement, in Poughkeepsie, NY, he and his wife volunteer in an elementary school, he as an in-the-classroom mathematics aide.