-
1
-
2
Euclidean geometry : a guided inquiry approach /
Berkeley, Calif. : Providence. R.I. : Mathematical Sciences Research Institute ; American Mathematical Society, 2012Format: Book
-
3
-
4
Non-Euclidean geometry.
Toronto, University of Toronto Press, 1957Table of Contents: “…The Historical Development of Non-Euclidean Geometry -- 1.1 Euclid -- 1.2 Saccheri -- 1.3 Gauss, Wachter, Schweikart, Taurinus -- 1.4 Lobatschewsky -- 1.5 Bolyai -- 1.6 Riemann -- 1.7 Klein --2. …”
3d ed.
Format: Book
-
5
Projective and Euclidean geometry.
New York, Wiley 1962Table of Contents: “…Euclid reexamined : Undefined terms ; Problems of existence ; Problems of congruence ; Problems of order ; Other axiom systems -- Hilbert's axioms : Axioms of existence and incidence ; Axioms of order ; Axioms of congruence ; Axioms of continuity and completeness ; Hilbert's axioms for solid geometry -- The growth of geometry : The Greek era ; The development of non-Euclidean geometries ; The development of projective geometry -- Projective geometry : The projective plane ; The basic incidence relations ; The content of projective geometry ; The principle of duality ; Projective space ; Space duality -- Fundamentals of synthetic projective geometry : The theorem of Desargues ; Harmonic sequences ; Functions and relations ; Projective transformations ; The theorem of Pappus -- Natural homogeneous coordinates : Coordinates for the projective plane ; Line coordinates; duality ; Homogeneous equations ; Space coordinates -- Vectors and matrices : Real vector spaces ; Linear independence ; Matrix algebra ; Rank of a matrix ; Bases for vector spaces ; Nonsingular matrices -- Fundamentals of analytic projective geometry : Dependent and independent points ; Applications of the dependence relation ; Change of coordinates; general homogeneous coordinates ; Projective transformations between lines ; Cross ratio ; Projective transformations of a line onto itself; involutions ; Other projective transformations ; Synthetic introduction to the conics ; Pascal's theorem ; Tangents and points of contact ; Analytic representation of a conic ; Polarities -- Axiomatic projective geometry : Axioms for the projective plane ; Introduction of coordinates on a line ; Coordinates in the plane ; The seven-point plane ; Complex projective geometry ; The real projective plane -- Descendants of real projective geometry : Groups and subgroups of transformations ; Affine geometry ; Similarity geometry ; Equiareal geometry ; Euclidean geometry ; Non-Euclidean geometries -- Appendix : Permutations ; Theory of determinants ; Systems of linear equations.…”
Format: Book
-
6
-
7
-
8
-
9
-
10
Non-Euclidean geometry; or, Three moons in mathesis.
Brooklyn, Galois Institute of Mathematics and Art 1966
[2d ed.].Format: Book
-
11
Non-Euclidean geometry : a critical and historical study of its development /
LaSalle, Ill. : Open Court Publishing Co., 1938
2nd rev. ed.Format: Book
-
12
Non-Euclidean geometry ; or, Three moons in mathesis /
[Lancaster, Pa.] : [The Science Press Printing Company], 1940Format: Book
-
13
Non-Euclidean geometry : a critical and historical study of its development /
[New York] Dover Publications 1955Table of Contents: “…The attempts to prove Euclid’s parallel postulate : The Greek geometers and the parallel postulate ; The Arabs and the parallel postulate ; The parallel postulate during the renaissance and the 17th century -- The forerunners of non-Euclidean geometry : Gerolamo Saccheri (1667-1733) ; Johann Heinrich Lambert (1728-1777) ; The French geometers towards the end of the 18th century ; Adrien Marie Legendre (1752-1833) ; Wolfgang Bolyai (1775-1856) ; Friedrich Ludwig Wachter (1792-1817) ; Bernhard Friedrich Thibaut (1776-1832) -- The founders of non-Euclidean geometry : Karl Friedrich Gauss (1777-1855) ; Ferdinand Karl Schweikart (1780-1832) ; Franz Adolf Taurinus (1794-1874) -- The founders of non-Euclidean geometry (cont.) : Nicolai Ivanovitsch Lobatschewsky (1793-1856) ; Johann Bolyai (1802-1860) ; The absolute trigonometry ; Hypotheses equivalent to Euclid’s postulate ; The spread of non-Euclidean geometry -- The later development of non-Euclidean geometry : Differential geometry and non-Euclidean geometry : Geometry upon a surface ; Principles of plane geometry on the ideas of Riemann ; Principles of Riemann’s solid geometry ; The work of Helmholtz and the investigations of lie.Projective geometry and non-Euclidean geometry : Subordination of metrical geometry to projective geometry ; Representation of the geometry of Lobatschewsky-Bolyai on the Euclidean plane ; Representation of Riemann’s elliptic geometry in Euclidean space ; Foundation of geometry upon descriptive properties ; The impossibility of proving Euclid’s postulate -- The fundamental principles of statics and Euclid’s postulate : On the principle of the lever ; On the composition of forces acting at a point ; Non-Euclidean statics ; Deduction of plane trigonometry from statics -- Clifford’s parallels and surface, sketch of Clifford-Klein’s problem : Clifford’s parallels ; Clifford’s surface ; Sketch of Clifford-Klein’s problem -- The non-Euclidean parallel construction and other allied constructions : The non-Euclidean parallel construction ; Construction of the common perpendicular to two non-intersecting straight lines ; Construction of the common parallel to the straight lines which bound an angle ; Construction of the straight line which is perpendicular to one of the lines bounding an acute angle and parallel to the other ; The absolute and the parallel construction -- The independence of projective geometry from Euclid’s postulate : Statement of the problem ; Improper points and the complete projective plane ; The complete projective plane ; Combination of elements ; Improper lines ; Complete projective space ; Indirect proof of the independence of projective geometry from the fifth postulate ; Beltrami’s direct proof of this independence ; Klein’s direct proof of this independence -- The impossibility of proving Euclid’s postulate, an elementary demonstration of this impossibility founded upon the properties of the system of circles orthogonal to a fixed circle : The system of circles passing through a fixed point ; The system of circles orthogonal to a fixed circle -- The science of absolute space -- The theory of parallels.…”
Format: Book
-
14
-
15
-
16
The foundations of Euclidean geometry /
Cambridge [England] : The University press, 1927“…Euclidean geometry.…”
Format: Book
-
17
Computing in Euclidean geometry /
Singapore ; River Edge, N.J. : World Scientific, 1995
2nd ed.Format: Book
-
18
Euclidean geometry and transformations /
Reading, Mass. : Addison-Wesley Pub. Co., 1972Format: Book
-
19
-
20
Computing in Euclidean geometry /
Singapore ; River Edge, N.J. : World Scientific, 1992Format: Book