Bibliography & Cited Sources

Primary Archival Editions, Historical Antecedents, and Sister GEOMETOR Codices

Every inline :cite: reference across the Euler (1765/1767) and Feuerbach (1822) codices links directly to its entry below.

Leonhard Euler — Solutio facilis problematum quorumdam geometricorum difficillimorum (1765/1767)

  • Citation Key: euler_1765 (Eneström E325)

  • Publication / Locus: Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, Tom. XI pro Anno MDCCLXV (Petropoli, 1767), pp. 103–123, Tab. II Fig. 1–9.

  • Context: Presented to the St. Petersburg Academy on 22 November 1765; establishes the six squared mutual distances among the four classical centers, proves the collinearity of the Euler line, and solves the inverse four-center reconstruction cubic. Public domain.

Karl Wilhelm Feuerbach — Eigenschaften einiger merkwürdigen Punkte des geradlinigen Dreiecks (1822)

  • Citation Key: feuerbach_1822

  • Publication / Locus: Mit einer Vorrede von Karl Buzengeiger. Nürnberg: Riegel und Wießner, 1822, pp. I–XVI, 1–62, Tab. I–II (Fig. 1–17).

  • Context: Composed at age twenty-two; establishes the nine-point circle, proves its internal tangency to the incircle and external tangency to the three excircles (§ 57), and appends nine pure Euclidean synthetic propositions (pp. 57–62). Public domain (BSB MDZ bsb10053455).

Giovanni Ceva — De lineis rectis se invicem secantibus statica constructio (1678)

  • Citation Key: ceva_1678

  • Publication / Locus: Mediolani: Ex Typographia Ludovici Montiae, 1678.

  • Context: Establishes the necessary and sufficient cyclic ratio criterion for cevian concurrency underlying the existence of the centroid, incenter, excenters, and orthocenter. Edited in sister repository geometor/ceva.

Menelaus of Alexandria — Sphaerica (c. 100 CE)

  • Citation Key: menelaus_sphaerica

  • Publication / Locus: Sphaerica, Book III, Lemma 1.

  • Context: Dual transversal collinearity theorem governing projective collinearity and harmonic cross-ratios along the Euler line. Edited in sister repository geometor/menelaus.

Euclid of Alexandria — Elements (Stoicheia)

  • Citation Key: euclid_elements

  • Publication / Locus: Books I–IV & VI, ed. T. L. Heath, Cambridge University Press, 1908.

  • Context: Axiomatic foundation for the circumcircle (IV.5), incircle (IV.4), and every synthetic step of Feuerbach’s Anhang (1.–9. Satz). Sister repositories geometor/euclid and geometor/elements.

Euclid of Alexandria — Data

  • Citation Key: euclid_data

  • Publication / Locus: Euclidis Data, Greek text of ancient geometric analysis.

  • Context: Praised by Karl Buzengeiger in the 1822 Vorrede (p. IV) as the classical model for analytical problem-reduction.

Simon Antoine Jean L’Huilier — Analogies entre les triangles plans et sphériques (1810)

  • Citation Key: lhuilier_1810

  • Publication / Locus: Annales de mathématiques pures et appliquées (ed. J. D. Gergonne), Tom. I, Nov. 1810, pp. 149–159.

  • Context: Cited by Feuerbach in § 2 (p. 2) for symmetric relations among the four tritangent radii \(r, r', r'', r'''\).

Giovanni Francesco Fagnano — Problemata quaedam ad methodum maximorum et minimorum spectantia (1775)

  • Citation Key: fagnano_1775

  • Publication / Locus: Nova Acta Eruditorum, Leipzig, 1775.

  • Context: Cited by Feuerbach in § 19 (p. 15) for the minimal-perimeter property of the orthic triangle \(\triangle MNP\).

Nicolaus Fuß — De quadrilateris quibus circulum tam inscribere quam circumscribere licet (1797)

  • Citation Key: fuss_1797

  • Publication / Locus: Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Tom. X (1797), pp. 103–125.

  • Context: Cited alongside Euler’s E325 by Feuerbach in § 49 (p. 34) on center-distance relations between inscribed and circumscribed circles.

Charles Julien Brianchon & Jean-Victor Poncelet — Recherches sur la détermination d’une hyperbole équilatère (1821)

  • Citation Key: brianchon_poncelet_1821

  • Publication / Locus: Annales de mathématiques pures et appliquées, Tom. XI (1820–1821), pp. 205–220.

  • Context: Independent projective proof that the circle through the altitude feet also passes through the side midpoints and the Euler midpoints.

Olry Terquem — Considérations sur le triangle rectiligne (1842)

  • Citation Key: terquem_1842

  • Publication / Locus: Nouvelles annales de mathématiques, Tom. I (1842), pp. 79–84, 196–200.

  • Context: Introduced the enduring name cercle des neuf points (“nine-point circle”) and gave an independent analytical proof of Feuerbach’s theorem.

Nathan Altshiller-Court — College Geometry (1952)

  • Citation Key: altshiller_court_1952

  • Publication / Locus: 2nd ed., New York: Barnes & Noble, 1952, Chapters IV–V.

  • Context: Modern synthetic exposition of the Euler line, nine-point circle, orthic triangle, and Feuerbach’s theorem. Sister repository geometor/altshiller-court.

Clark Kimberling — Encyclopedia of Triangle Centers (ETC)

  • Citation Key: kimberling_etc

  • Publication / Locus: Online & Book Codex in sister repository geometor/etc.

  • Context: Canonical indexing of X(1)–X(5) and the Feuerbach point X(11).

Norman J. Wildberger — Divine Proportions: Rational Trigonometry to Universal Geometry (2005)

  • Citation Key: wildberger_2005

  • Publication / Locus: Sydney: Wild Egg Books, 2005. Sister repository geometor/wildberger.

  • Context: Formulates metric geometry purely in rational quadrance and spread invariants.