Biographical Register of Persons

Geometers, Algebraists, and Commentators in the Euler–Feuerbach Tradition

Every inline :person: reference resolves directly to its entry below.

Leonhard Euler (1707 – 1783)

Swiss Mathematician & Natural Philosopher

Author of Solutio facilis problematum quorumdam geometricorum difficillimorum (E325, 1765/1767), which inaugurated algebraic triangle-center geometry by computing all six mutual squared distances among the four classical centers, proving the collinearity of the Euler line, and reducing the inverse four-center problem to a cubic in the side lengths.

Karl Wilhelm Feuerbach (1800 – 1834)

German Geometer

Son of the jurist Paul Johann Anselm Ritter von Feuerbach and brother of the philosopher Ludwig Feuerbach. At age twenty-two, shortly after studying under Karl Buzengeiger at Freiburg, he published Eigenschaften einiger merkwürdigen Punkte des geradlinigen Dreiecks (Nürnberg, 1822), proving the fourfold tangency of the nine-point circle with the incircle and three excircles (§ 57).

Karl Heribert Ignaz Buzengeiger (1771 – 1835)

Professor of Mathematics at the University of Freiburg

Feuerbach’s university mentor at Freiburg im Breisgau; contributed the sixteen-page philosophical Vorrede (16 March 1822) contrasting ancient Greek geometric analysis with modern symmetric algebraic calculation.

Euclid of Alexandria (fl. c. 300 BCE)

Greek Geometer

Author of the Elements and the Data, furnishing both the axiomatic constructions of the incircle (IV.4) and circumcircle (IV.5) and the Book I, III, and VI propositions cited throughout Feuerbach’s synthetic Anhang.

Apollonius of Perga (c. 240 – c. 190 BCE)

Greek Geometer

Author of the Conics and the lost Tangencies (De Tactionibus); Apollonius’s median theorem in \(\triangle KOS\) is the decisive algebraic hinge of Feuerbach’s § 57 proof.

Pappus of Alexandria (c. 290 – c. 350 CE)

Greek Geometer

Author of Book VII of the Synagoge (Collection), preserving the treasury of Greek analysis discussed in Buzengeiger’s Vorrede and establishing projective harmonic division.

Menelaus of Alexandria (c. 70 – 140 CE)

Greco-Roman Mathematician & Astronomer

Author of the Sphaerica, establishing the transversal collinearity criterion dual to Ceva’s concurrency theorem.

Giovanni Ceva (1647 – 1734)

Italian Geometer

Author of De lineis rectis se invicem secantibus statica constructio (1678), grounding the concurrency of medians, bisectors, and altitudes in statics and cyclic side-division ratios.

Matthew Stewart (1717 – 1785)

Scottish Geometer

Successor to Colin Maclaurin at Edinburgh; published in Some General Theorems of Considerable Use in the Higher Parts of Mathematics (1746) the collinear cevian quadrance identity that governs Euler’s § 18 and Feuerbach’s § 60.

Giovanni Francesco Fagnano dei Toschi (1715 – 1797)

Italian Mathematician

Proved in 1775 that among all triangles inscribed in an acute triangle \(\triangle ABC\), the orthic triangle \(\triangle MNP\) minimizes perimeter—explicitly cited by Feuerbach in § 19 (p. 15).

Simon Antoine Jean L’Huilier (1750 – 1840)

Swiss Mathematician

Professor at Geneva; his November 1810 memoir in Gergonne’s Annales established symmetric identities among the four tritangent radii cited by Feuerbach in § 2 (p. 2).

Nicolaus Fuß (1755 – 1826)

Swiss-Russian Mathematician

Euler’s mathematical assistant and Permanent Secretary of the St. Petersburg Academy; cited alongside Euler by Feuerbach in § 49 (p. 34) for center-distance formulas of bicentric polygons.

Charles Julien Brianchon (1783 – 1864)

French Projective Geometer

Co-published with Jean-Victor Poncelet in Gergonne’s Annales (1820–1821) the theorem uniting the nine canonical points on a single circle of radius \(R/2\).

Jean-Victor Poncelet (1788 – 1867)

French Geometer & Engineer

Architect of modern projective geometry (Traité des propriétés projectives des figures, 1822) and co-discoverer with Brianchon of the nine-point circle.

Olry Terquem (1782 – 1862)

French Mathematician & Historian of Mathematics

Co-editor of the Nouvelles annales de mathématiques, who named the cercle des neuf points (“nine-point circle”) in 1842.

Nathan Altshiller-Court (1881 – 1968)

Polish-American Geometer

Author of College Geometry (1925; 2nd ed. 1952), standardizing the English pedagogy of modern synthetic triangle geometry.

Clark Kimberling (b. 1942)

American Mathematician

Creator of the Encyclopedia of Triangle Centers (ETC), assigning canonical center numbers X(1)–X(5) and X(11) (the Feuerbach point).

Norman J. Wildberger (b. 1956)

Canadian-Australian Mathematician

Developer of Rational Trigonometry (Divine Proportions, 2005), replacing transcendental distance and angle by algebraic quadrance and spread.