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1. ONE-TO-ONE CORRESPONDENCE 2. RELATIONS BETWEEN FUNDAMENTAL FORMS IN ONETO-ONE CORRESPONDENCE WITH EACH OTHER 3. COMBINATION OF TWO PROJECTIVELY RELATED FUNDAMENTAL FORMS 4. POINT-ROWS OF THE SECOND ORDER 5. PENCILS OF RAYS OF THE SECOND ORDER 6. POLES AND POLAHS 7. METRICAL PROPERTIES OF THE CONIC SECTIONS 8. INVOLUTION 9. METRICAL PROPERTIES OF INVOLUTIONS 10. ON THE HISTORY OF SYNTHETIC PROTECTIVE GEOMETRY161. Ancient results
This text An Elementary Course in Synthetic Projective Geometry by Derrick Norman Lehmer teaches the basics of projective geometry without using measurements or coordinates. It is the essentials of synthetic projective geometry. Enough examples have been provided to give the student a clear grasp of the theory. The student should have a thorough grounding in ordinary elementary geometry. Instead, it relies purely on drawing and logical relationships—like how points, lines, and planes connect and transform together. The book starts with easy ideas such as matching points on a line with rays from a point or planes through a line, and then builds up to important ideas like Desargues’s theorem, involution, and poles and polars. Lehmer keeps the explanations smooth and avoids complicated metric ideas, making his presentation especially clean and intuitive.
Title: Synthetic Projective Geometry by Derrick Norman Lehmer Publisher: Project Gutenberg Year: 1917 Pages: 146 Type: PDF Language: English ISBN-10 #: 1430495596 ISBN-13 #: 978-1430495598 License: Public Domain Work Amazon: Amazon
The author Derrick Norman Lehmer (1867–1938) was an American mathematician known for his work in number theory and his mechanical computational inventions. He earned his Bachelor’s (1893) and Master’s (1896) degrees from the University of Nebraska and completed his Ph.D. at the University of Chicago in 1900 under E. H. Moore. Lehmer is best known for creating large tables of prime numbers and inventing mechanical aids for calculations—most notably his “factor stencils” and the Lehmer sieve, developed with his son to find prime factors and solve number-theory problems efficiently.
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