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Geometry Geometry: Euclid and Beyond by Hartshorne

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  1. Jan 24, 2013 #1

    Table of Contents:
    Code (Text):

    [*] Euclid's Geometry
    [*] A First Look at Euclid's Elements
    [*] Ruler and Compass Constructions
    [*] Euclid's Axiomatic Method
    [*] Construction of the Regular Pentagon
    [*] Hilbert's Axioms
    [*] Axioms of Incidence
    [*] Axioms of Betweenness
    [*] Axioms of Congruence for Line Segments
    [*] Axioms of Congruence for Angles
    [*] Hilber Planes
    [*] Intersection of Lines and Circles
    [*] Euclidean Planes
    [*] Geometry over Fields
    [*] The Real Cartesian Plane
    [*] Abstract Fields and Incidence
    [*] Ordered Field and Betweenness
    [*] Congruence of Segments and Angles
    [*] Rigid Motions and SAS
    [*] Non-Archimedean Geometry
    [*] Segment Arithmetic
    [*] Addition and Multiplication of Line Segments
    [*] Similar Triangles
    [*] Introduction of Coordinates
    [*] Area
    [*] Area in Euclid's Geometry
    [*] Measure of Area Functions
    [*] Dissection
    [*] Quadratura Circuli
    [*] Euclid's Theory of Volume
    [*] Hilbert's Third Problem
    [*] Construction Problems and Field Extensions
    [*] Three Famous Problems
    [*] The Regular 17-Sided Polygon
    [*] Constructions with Compass and Marked Ruler
    [*] Cubic and Quartic Equation
    [*] Appendix: Finite Field Extensions
    [*] Non-Euclidean Geometry
    [*] History of the Parallel Postulate
    [*] Neutral Geometry
    [*] Archimedean Neutral Geometry
    [*] Non-Euclidean Area
    [*] Circular Inversion
    [*] Digression: Circles Determined by Three Conditions
    [*] The Poincaré Geometry
    [*] Hilbert's Arithmetic of Ends
    [*] Hyperbolic Trigonometry
    [*] Characterization of Hilbert Planes
    [*] Polyhedra
    [*] The Five Regular Solids
    [*] Euler's and Cauchy's Theorems
    [*] Semiregular and Face-Regular Polyhedra
    [*] Symmetry Groups of Polyhedra
    [*] Appendix: Brief Euclid
    [*] Notes
    [*] References
    [*] List of Axioms
    [*] Index of Euclid's Propositions
    [*] Index
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 24, 2013 #2


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    Outstanding guide to Euclid. This opens up Euclid and makes one see why that is such a great book. And goes much further. Enough beautiful material for years of self study.
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