Systematic Bibliography

Primary Public-Domain Editions, Historical Treatises, and Philosophical Debates

[poincare-1902] — Henri Poincaré (1902)

La Science et l’Hypothèse. Bibliothèque de Philosophie scientifique, pp. 1–284 (Introduction & Parts I–IV, Chs. I–XIII). Ernest Flammarion, Éditeur, Paris.

Primary French public-domain witness. Synthesizes Poincaré’s foundational essays from 1891–1901 into a unified treatise on arithmetic induction, the continuum, non-Euclidean geometries, conventionalism, classical mechanics, and electrodynamics; later Flammarion printings include the section ‘Les Géométries de Hilbert’ (pp. 63–64).

[poincare-1905-greenstreet] — Henri Poincaré (trans. W. J. Greenstreet, preface by J. Larmor) (1905)

Science and Hypothesis. xxvii + 244 pp.. Walter Scott Publishing Co., Ltd., London and Newcastle-on-Tyne.

Authorized British public-domain English translation, collated in this codex against the 1902 Flammarion French edition and Halsted’s 1905 American translation.

[poincare-1905-halsted] — Henri Poincaré (trans. George Bruce Halsted, special preface by H. Poincaré, intro. by Josiah Royce) (1905 / 1913)

Science and Hypothesis (reprinted in The Foundations of Science, 1913). xxxii + 196 pp.. The Science Press, New York and Garrison, N.Y..

Authorized American public-domain translation preserving strict non-Euclidean terminology (‘Bolyai and Lobachevski’, ‘reasoning by recurrence’) and Poincaré’s special English preface clarifying the limits of convention in science.

[poincare-1882] — Henri Poincaré (1882)

Théorie des groupes fuchsiens. Acta Mathematica, Vol. 1, pp. 1–62. Beijer / F. & G. Beijer, Stockholm.

Memoir introducing the conformal hyperbolic disk and upper half-plane models, orthogonal-circle geodesics, and Fuchsian automorphic tessellations.

[poincare-1891] — Henri Poincaré (1891)

Les géométries non euclidiennes. Revue générale des sciences pures et appliquées, Vol. 2, pp. 769–774. Georges Carré, Paris.

Original essay introducing the Lobachevsky–Euclidean Translation Dictionary and the conventionalism thesis (‘Les axiomes géométriques ne sont donc ni des jugements synthétiques a priori ni des faits expérimentaux. Ce sont des conventions’).

[poincare-1894] — Henri Poincaré (1894)

Sur la nature du raisonnement mathématique. Revue de Métaphysique et de Morale, Vol. 2, pp. 371–384. Armand Colin, Paris.

Foundational paper defending complete mathematical induction (reasoning by recurrence) as the paradigmatic synthetic a priori judgment of pure mathematics (expanded into Ch. I of La Science et l’Hypothèse).

[poincare-1895-espace] — Henri Poincaré (1895)

L’espace et la géométrie. Revue de Métaphysique et de Morale, Vol. 3, pp. 631–646. Armand Colin, Paris.

Introduces the distinction between perceptual/motor space and geometric space along with the Heated-Disk optical world (expanded into Ch. IV of La Science et l’Hypothèse).

[poincare-1899-russell] — Henri Poincaré (1899)

Des fondements de la géométrie : à propos d’un livre de M. Russell. Revue de Métaphysique et de Morale, Vol. 7, pp. 251–279. Armand Colin, Paris.

Poincaré’s incisive review of Bertrand Russell’s 1897 Essay on the Foundations of Geometry, challenging Russell’s claim that projective geometry is wholly a priori and demanding an operational criterion of spatial congruence.

[russell-1897] — Bertrand Russell (1897)

An Essay on the Foundations of Geometry. xvi + 201 pp.. Cambridge University Press, Cambridge.

Russell’s neo-Kantian treatise arguing that projective geometry expresses the a priori form of externality while constant-curvature metrical axioms encompass empirical elements (digitized in geometor/bertrand-russell).

[russell-1899-reponse] — Bertrand Russell (1899)

Sur les axiomes de la géométrie. Revue de Métaphysique et de Morale, Vol. 7, pp. 684–707. Armand Colin, Paris.

Russell’s French reply to Poincaré defending the irreducibility of absolute distance and spatial relations against Poincaré’s group-theoretic conventionalism.

[poincare-1900-replique] — Henri Poincaré (1900)

Sur les principes de la géométrie : réponse à M. Russell. Revue de Métaphysique et de Morale, Vol. 8, pp. 73–86. Armand Colin, Paris.

Poincaré’s rejoinder to Russell on disguised definitions, solid-body displacements, and the meaninglessness of absolute spatial scale.

[poincare-1902-hilbert] — Henri Poincaré (1902)

Les fondements de la géométrie (Review of D. Hilbert, Grundlagen der Geometrie). Bulletin des Sciences Mathématiques, 2e série, Vol. 26, pp. 249–272. Gauthier-Villars, Paris.

Detailed technical review of Hilbert’s 1899 Grundlagen, directly informing the ‘Les Géométries de Hilbert’ section in Flammarion printings of La Science et l’Hypothèse.

[hilbert-1899] — David Hilbert (1899)

Grundlagen der Geometrie (Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen). Chs. I–VII, 92 pp.. B. G. Teubner, Leipzig.

Formal axiomatization of Euclidean geometry and construction of non-Archimedean and non-Pascalian geometries (bilingual codex in geometor/hilbert).

[hoenen-1954] — Petrus Hoenen, S.J. (1954)

De Noetica Geometriae: Origine Theoriae Cognitionis. Analecta Gregoriana, Vol. 63, 293 pp.. Pontificia Università Gregoriana, Rome.

Systematic epistemological critique of Poincaré’s conventionalism and Hilbert’s formalism grounded in Aristotelian–Thomistic intelligible matter and intellectual nexus judgment (bilingual codex in geometor/hoenen).

[lobachevsky-1840] — Nikolai Ivanovich Lobachevsky (1840)

Geometrische Untersuchungen zur Theorie der Parallellinien. 61 pp., 2 plates. G. Fincke, Berlin.

Concise German exposition of hyperbolic geometry (translated into English by G. B. Halsted, 1891).

[bolyai-1832] — János Bolyai (1832)

Appendix scientiam spatii absolute veram exhibens. Supplement to Farkas Bolyai, Tentamen juventutem studiosam in elementa matheseos purae introducendi, 26 pp.. Typis Collegii Reformatorum, Maros-Vásárhely.

Independent creation of absolute and hyperbolic geometry.

[riemann-1867] — Bernhard Riemann (1854 / 1867)

Über die Hypothesen, welche der Geometrie zu Grunde liegen. Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Vol. 13, pp. 133–152. Dieterichsche Buchhandlung, Göttingen.

Establishes Riemannian manifolds, metric tensors, and constant-positive-curvature geometry.

[beltrami-1868] — Eugenio Beltrami (1868)

Saggio di interpretazione della geometria non-euclidea. Giornale di Matematiche, Vol. 6, pp. 284–312. Pellerano, Naples.

First projective disk and pseudospherical models demonstrating the relative consistency of Lobachevsky’s plane geometry.

[klein-1872] — Felix Klein (1872)

Vergleichende Betrachtungen über neuere geometrische Forschungen (Erlanger Programm). 48 pp.. Andreas Deichert, Erlangen.

Unifies Euclidean, projective, and non-Euclidean geometries as invariant theories of transformation groups (codex in geometor/klein).

[casey-1888] — John Casey (1888 / 1892)

A Sequel to the First Six Books of the Elements of Euclid. 5th ed., Books I–VI & Supplementary Chapter. Hodges, Figgis, & Co., Dublin / Longmans, Green, & Co., London.

Synthetic theory of coaxial circles, inversion, and orthogonal circles underpinning Euclidean constructions in the Poincaré disk (codex in geometor/casey).

[lemoine-1902] — Émile Lemoine (1902)

Géométrographie, ou Art des constructions géométriques. Collection Scientia, Phys.-Math. n° 18, 88 pp.. C. Naud, Paris.

Quantitative complexity calculus of ruler-and-compass and circle-inversion constructions (codex in geometor/lemoine).

[euclid-heath-1908] — Euclid (trans. Sir Thomas Little Heath) (1908)

The Thirteen Books of Euclid’s Elements. 3 vols. (esp. Vol. I, Postulate 5 & Props. I.1–I.32). Cambridge University Press, Cambridge.

Definitive commentary on the parallel postulate and Book VI circle-similarity theorems (folio codex in geometor/euclid and constructive DAG in geometor/elements).

[wildberger-2005] — Norman J. Wildberger (2005 / 2013)

Divine Proportions: Rational Trigonometry to Universal Geometry (and Universal Hyperbolic Geometry I–IV, Geometriae Dedicata, 2010–2013). 300 pp. / Geometriae Dedicata Vol. 163, pp. 215–274. Wild Egg Books, Sydney / Springer.

Algebraic formulation of Euclidean and hyperbolic geometry via rational quadrance and spread without transcendental functions (formalized in geometor/wildberger).