Systematic Bibliography

Primary Treatises, Archival Editions & Constructive Literature

August Adler (1890 / 1906) — Zur Theorie der Mascheronischen Constructionen / Theorie der geometrischen Konstruktionen

Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, Math.-Naturwiss. Classe, Bd. 99, Abt. IIa, pp. 910–916; Sammlung Göschen Nr. 301. K.-K. Hof- und Staatsdruckerei, Vienna / G. J. Göschen, Leipzig.

Unified proof of Mascheroni’s theorem via circle inversion (5C_1 + 3C_3) alongside comparative expositions of Steiner’s constructions and Lemoine’s Géométrographie.

Nathan Altshiller-Court (1952) — College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle

2nd ed., Chapters IV–X (Similitude, Harmonic Division, Inversion, Recent Geometry of the Triangle). Barnes & Noble, New York.

Modern synthetic reference connecting antiparallels, symmedians, Brocard geometry, radical axes, and circle inversion.

Antoine-Michel Carette (trans.) (1798) — Géométrie du compas, par L. Mascheroni

xvi + 263 pp., 14 folding plates. Duprat, Libraire pour les Mathématiques, Paris.

French translation through which Lemoine and French geometers cited Mascheroni’s problem numbering and compass-only methods.

Euclid (trans. Sir Thomas L. Heath) (1908 / 1926) — The Thirteen Books of Euclid’s Elements

3 vols. (Books I–XIII); GEOMETOR Digital Scriptorium Edition (geometor/euclid & geometor/elements). Cambridge University Press.

Standard English philological reference and axiomatic proposition benchmark for Lemoine’s Euclidean comparisons.

Lorenzo Mascheroni (ed. Gaetano Fazzari) (1901) — La Geometria del Compasso: Nuova edizione con prefazione e note

Prefazione pp. v–xvi; Testo pp. 1–152. Casa Editrice ‘Era Nova’, Palermo.

Scholarly Italian edition whose preface (p. xi) explicitly compares Mascheroni’s constructions with Euclidean methods via ‘il metodo della Geometrografia del Lemoine’.

David Hilbert (1899) — Grundlagen der Geometrie

Siebentes Kapitel: Die geometrischen Konstruktionen auf Grund der Axiome I–IV (§§ 36–39). B. G. Teubner, Leipzig.

Algebraic characterization (pythagorean vs. euclidean quadratic fields) of constructions executable with straightedge and unit-segment transferrer.

Peter H. J. Hoenen, S.J. (1954) — De Noetica Geometriae: Origine Theoriae Cognitionis

Analecta Gregoriana, Vol. 63. Pontificia Università Gregoriana, Rome.

Epistemological investigation of geometric phantasia, intelligible matter, and constructive intuition.

Clark Kimberling (1998–) — Encyclopedia of Triangle Centers (ETC)

X(1) Incenter, X(2) Centroid, X(3) Circumcenter, X(6) Symmedian/Lemoine Point, X(7) Gergonne, X(8) Nagel, X(10) Spieker, X(98) Tarry, X(99) Steiner. University of Evansville / GEOMETOR ETC Codex.

Canonical trilinear/barycentric indexing of the triangle centers benchmarked in Lemoine Problems XXI, XXVII, and L–LXIII.

Émile Lemoine (1873) — Sur quelques propriétés d’un point remarquable du triangle

Association Française pour l’Avancement des Sciences (Congrès de Lyon), Comptes Rendus, pp. 90–95. Secrétariat de l’AFAS, Paris.

Foundational memoir introducing the symmedian point K = X(6), the Lemoine line, and the first Lemoine circle.

Émile Lemoine (1888) — De la mesure de la simplicité dans les sciences mathématiques (Note sur une manière d’évaluer la simplicité des constructions géométriques)

AFAS, Compte Rendu de la 17e Session (Congrès d’Oran, 30 mars 1888), Première Partie, p. 161; tirage à part pp. 1–12. Masson / AFAS, Paris.

First public announcement of quantitative construction measurement, initially employing an eight-symbol notation (ρ_1..γ’_2) and introducing the set-square (équerre) operations.

Émile Lemoine (1892 / 1893) — La Géométrographie ou l’Art des constructions géométriques

AFAS, Compte Rendu de la 21e Session (Congrès de Pau, septembre 1892), Seconde Partie, pp. 36–100; tirage à part pp. 1–66. Gauthier-Villars et Fils / Secrétariat de l’AFAS, Paris.

Canonical Pau memoir establishing the five elementary operations R_1, R_2, C_1, C_2, C_3, the coefficients S and E, and Problems I–LXIII.

Émile Lemoine (1895) — Étude sur le triangle et sur certains points de Géométrographie

Proceedings of the Edinburgh Mathematical Society, Vol. 13, pp. 2–25. Williams & Norgate, Edinburgh.

Extends Géométrographie to continuous families of triangle configurations and restricted-instrument comparisons.

Émile Lemoine (1902) — Géométrographie, ou Art des constructions géométriques

Collection Scientia, Série Physico-Mathématique, n° 18, 88 pp.. C. Naud, Éditeur, Paris.

Definitive monograph synthesizing the Pau ruler-and-compass canon with Géométrographie de l’équerre, Géométrographie Mascheronienne (compass alone), and Géométrographie Steinerienne (straightedge with fixed circle).

John Sturgeon Mackay (1893 / 1894) — The Geometrography of Euclid’s Problems

Proceedings of the Edinburgh Mathematical Society, Vol. 12, pp. 2–16. Williams & Norgate, Edinburgh.

First systematic English-language exposition of Lemoine’s Pau memoir applied across Euclid’s Elements.

Lorenzo Mascheroni (1797 (Anno V della Repubblica Francese)) — La Geometria del Compasso

Libri I–XII, §§ 1–213, 18 plates (Figs. 1–108). Eredi di Pietro Galeazzi, Pavia.

Classic compass-only treatise proving constructively that every ruler-and-compass point determination can be carried out with the compass alone.

Georg Mohr (1672) — Euclides Danicus, Bestaende udi Too Deele

Parts I–II, 36 pp. (republished with German translation by J. Hjelmslev, Copenhagen: Høst & Søn, 1928). Jacob van Velsen, Amsterdam.

Earliest complete proof of compass-only Euclidean constructibility, anticipating Mascheroni by 125 years.

Pappus of Alexandria (c. 340 CE) — Synagoge (Mathematical Collection), Book VII: On the Domain of Analysis

ed. Friedrich Hultsch (1876–1878); ed. & trans. Alexander Jones (Springer, 1986). Weidmann, Berlin / Springer, New York.

Source of complete-quadrilateral harmonic division and projective incidence lemmas underlying Lemoine’s zero-circle constructions.

Jean-Victor Poncelet (1822) — Traité des propriétés projectives des figures

Tome I, Section III, Chapitre III, §§ 351–358. Bachelier, Paris.

First statement of the theorem that a single circle traced with its center suffices for all ruler-and-compass constructions using the straightedge alone.

Proclus Diadochus (c. 470 CE) — In primum Euclidis Elementorum librum commentarii

ed. Gottfried Friedlein (1873); trans. Glenn R. Morrow (Princeton University Press, 1970). B. G. Teubner, Leipzig.

Classical philosophical commentary on postulates, instruments, and the problem/theorem distinction.

Jakob Steiner (1833) — Die geometrischen Constructionen, ausgeführt mittelst der geraden Linie und Eines festen Kreises, als Lehrgegenstand auf höheren Unterrichts-Anstalten und zur praktischen Benutzung

§§ 1–22, [1]–[110]; Ostwald’s Klassiker der exakten Wissenschaften Nr. 60, ed. A. J. von Oettingen (1895). Ferdinand Dümmler, Berlin (Wilhelm Engelmann, Leipzig, 1895).

Systematic demonstration of straightedge-only constructibility with one fixed circle and its center across eight canonical fundamental problems (§ 18, [68]–[85]).