Index of Persons

Prosopographical Registry of Geometers & Commentators

Amédée Mannheim (1831–1906) — Professor of descriptive geometry at the École Polytechnique; inventor of the modern slide rule layout

Raised classical descriptive-geometry objections to Géométrographie answered by Lemoine on pp. 57–58, where Mannheim’s common-tangent construction of the radical axis (S = 58) is contrasted with the two-secant-circle construction (S = 17).

Antoine-Michel Carette (1772–1855) — French officer of engineers and translator of Mascheroni

Translated Mascheroni’s treatise into French as Géométrie du compas (Paris: Duprat, 1798), transmitting compass-only geometry to the École Polytechnique generation of Poncelet, Brianchon, and Cauchy.

August Adler (1863–1923) — Czech-Austrian geometer and Privatdozent in Vienna and Prague

In Zur Theorie der Mascheronischen Constructionen (1890) and Theorie der geometrischen Konstruktionen (1906), gave the conceptual proof of the Mohr–Mascheroni theorem via circle inversion (Lemoine’s Problem XXXVIII: 5C_1 + 3C_3) and systematically integrated Lemoine’s Géométrographie with restricted-instrument theory.

Auguste Gouzy (fl. 1888–1895) — French geometer and contributor to Journal de Mathématiques Élémentaires

Co-discoverer with Lemoine of the S = 14 three-circle construction of the mean proportional (Problem XXXV), cutting the classical cost S = 24 by ten operations.

Charles-Ange Laisant (1841–1920) — French mathematician, politician, and co-founder of L’Intermédiaire des Mathématiciens

Lifelong collaborator and biographer of Lemoine; co-edited the Scientia series and promoted Géométrographie across French and international mathematical societies.

Christian Heinrich von Nagel (1803–1882) — German geometer in Ulm

Investigated the exterior contact triangle and the Nagel point X(8) where cevians to opposite excircle touchpoints concur (Lemoine Problem LXI, S = 16).

Clark Kimberling (1942–) — American geometer; creator of the Encyclopedia of Triangle Centers (ETC)

Professor of mathematics at the University of Evansville whose Encyclopedia of Triangle Centers (ETC) canonizes trilinear and barycentric indexing for 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, and X(99) Steiner.

David Hilbert (1862–1943) — German mathematician; author of Grundlagen der Geometrie (1899)

In Chapter VII (§§ 36–39) of Grundlagen der Geometrie, complemented Steiner’s fixed-circle ruler constructions with algebraic criteria characterizing exactly which problems are solvable with straightedge and segment-transferrer (Eichmaß) alone.

Euclid of Alexandria (fl. c. 300 BCE) — Alexandrian mathematician; author of the Elements

Codified deductive geometry from three constructive postulates (joining points, extending segments, describing circles). As Lemoine observes, Euclid’s constructions optimize speculative deductive economy—minimizing auxiliary theorems invoked in proof—rather than minimizing operational hand movements of ruler and compass.

Eugène Charles Catalan (1814–1894) — Franco-Belgian mathematician at the University of Liège

Devised the ingenious four-circle construction of a square on a given base AB analyzed by Lemoine in Problem XLVII (S = 19 fully traced vs. S = 21 classical).

Gaetano Fazzari (1856–1935) — Italian mathematician and historian of mathematics in Palermo; founder of Il Pitagora

Edited the critical 1901 Palermo edition of Mascheroni’s La Geometria del Compasso, explicitly evaluating Mascheroni’s constructions by ‘il metodo della Geometrografia del Lemoine’ in his historical preface (p. xi).

Gaston Tarry (1843–1913) — French amateur mathematician in Algeria; discoverer of the Tarry point X(98)

Stationed in Algiers, Tarry collaborated closely with Lemoine, contributing the two optimal S = 9 parallel constructions (Problem XVII: two-circle equal-radius method and single-aperture rhombus method) and studying the circumcircle point X(98) antipodal to the Steiner point X(99) (Problem LVII).

Georg Mohr (1640–1697) — Danish mathematician; author of Euclides Danicus (1672)

Published Euclides Danicus in Dutch and Danish at Amsterdam in 1672—125 years before Mascheroni—proving that all constructions of the first six books of Euclid can be carried out with a compass alone; the treatise remained overlooked as an optical-perspectival work until Johannes Hjelmslev’s rediscovery in 1928.

Henri Brocard (1845–1922) — French army meteorologist and geometer; co-founder of modern triangle geometry

Rediscovered the bicentric Brocard points ω, ω’ and Brocard angle in 1875. In Lemoine’s Géométrographie (Problems LIV–LV and pp. 58–59), Brocard’s own classical construction of ω, ω’ (S = 74) serves as a celebrated benchmark reduced by Lemoine to S = 38.

Jakob Steiner (1796–1863) — Swiss-born synthetic projective geometer; professor of geometry at the University of Berlin

Following Systematische Entwickelung der Abhängigkeit geometrischer Gestalten (1832), Steiner published Die geometrischen Constructionen, ausgeführt mittelst der geraden Linie und Eines festen Kreises (1833), proving via harmonic ranges, centers of similitude, and radical axes that a single fixed circle drawn with its center suffices to execute all Euclidean constructions by straightedge alone.

Jean-Victor Poncelet (1788–1867) — French military engineer and founder of modern projective geometry

In his Traité des propriétés projectives des figures (1822, §§ 351–358), first stated that all ruler-and-compass problems can be solved by straightedge alone when a single circle and its center are given in the plane—a theorem rigorously carried out and organized into eight canonical problems by Jakob Steiner in 1833.

John Casey (1820–1891) — Irish geometer; author of A Sequel to the First Six Books of the Elements of Euclid

Synthesized Anglo-Irish and Franco-Belgian triangle and circle geometry; cited by Lemoine in Problem LVI on the Steiner point X(99).

Joseph Diaz Gergonne (1771–1859) — French mathematician; founder of Annales de Mathématiques Pures et Appliquées

Formulated projective principle of duality and identified the Gergonne point X(7) where lines joining triangle vertices to opposite incircle contact points concur (Lemoine Problem LIX, S = 27).

Joseph Jean Baptiste Neuberg (1840–1926) — Luxembourgish-Belgian geometer at the University of Liège; co-editor of Mathesis

Alongside Lemoine and Brocard, one of the three founders of modern triangle geometry; Lemoine analyzes Neuberg’s circle and radical point Φ in Problem LXII (S = 37).

Lorenzo Mascheroni (1750–1800) — Italian mathematician and poet; professor of algebra and geometry at the University of Pavia

Author of Adnotationes ad calculum integralem Euleri (1790, introducing the Euler–Mascheroni constant γ) and La Geometria del Compasso (Pavia, 1797), dedicated in verse to Napoléon Bonaparte, proving constructively across twelve books that every ruler-and-compass problem solvable by point determinations can be executed with the compass alone.

Maurice d’Ocagne (1862–1938) — French engineer and mathematician; creator of nomography

Correspondent of Lemoine on practical graphical precision, nomographic alignment, and the distinction between geometric exactitude (E) and physical drafting error (pp. 60–62).

Michel Chasles (1793–1880) — French projective geometer and historian of geometry

Author of Aperçu historique (1837) and Traité de géométrie supérieure (1852), formalizing signed cross-ratios, homography, and involution invoked in Lemoine’s projective problems.

Napoléon Bonaparte (1769–1821) — French general and member of the Institut National

Met Lorenzo Mascheroni during the 1797 Italian campaign, received the poetic dedication of La Geometria del Compasso, and famously proposed Mascheroni’s compass-only circle-quadrisection problem to Laplace and Lagrange in Paris.

Pappus of Alexandria (c. 290–c. 350 CE) — Late antique Greek geometer; author of the Synagoge (Mathematical Collection)

Preserved the Treasury of Analysis in Book VII of the Synagoge, establishing cross-ratio invariance, harmonic division by the complete quadrilateral, and pole-polar relations that underpin Lemoine’s zero-circle projective constructions (XXXIX, XLVI) and Steiner’s First Chapter.

Proclus Diadochus (412–485 CE) — Neoplatonic philosopher and commentator on Book I of Euclid’s Elements

Distinguished problems (genesis of geometric figures in phantasia) from theorems (demonstration of eternal attributes) and preserved classical Greek debates on postulated instruments and minimal postulates.

Theodor Spieker (1823–1913) — German geometer in Potsdam

Introduced the Spieker center X(10)—incenter of the medial triangle and center of mass of a uniform wire perimeter—analyzed in Lemoine Problem LX (S = 29).

Émile Michel Hyacinthe Lemoine (1840–1912) — French geometer, civil engineer, and polymath; co-founder of modern triangle geometry and creator of Géométrographie

Educated at the Prytanée National Militaire and the École Polytechnique (1860), Lemoine introduced the symmedian point X(6) and Lemoine circles at the 1873 Lyon congress of the Association Française pour l’Avancement des Sciences (AFAS), inaugurated the quantitative science of geometric simplicity at Oran (1888) and Pau (1892), co-founded L’Intermédiaire des Mathématiciens with C.-A. Laisant (1894), and published the definitive monograph Géométrographie in Collection Scientia No. 18 (1902).