Biographical Register of Geometers & Scholars

Prosopographical Apparatus (67 Historical Geometers, Editors, and Contemporaries)

Synthesizes Altshiller-Court’s List of Names (pp. 307–309), Historical and Bibliographical Notes (pp. 295–306), and Frontmatter acknowledgments.

Altshiller-Court, Nathan (1881–1968)

Polish-born, Belgian-educated mathematician (D.Sc., University of Ghent, 1911) who taught at the University of Oklahoma for over thirty years. His College Geometry (1925; 2nd ed. 1952) and Modern Pure Solid Geometry (1935) established the standard English-language synthesis of modern synthetic triangle and circle geometry.

Apollonius of Perga (c. 262 – c. 190 BC)

  • Role: Hellenistic Geometer (‘The Great Geometer’)

  • Articles in College Geometry: § 11, § 61, § 506, § 516, § 597, § 599

  • Principal Works: Conics; Plane Loci (τόποι ἐπίπεδοι); Tangencies (ἐπαφαί)

  • Edition Loci: f. 0034 (p. 15) · f. 0326 (p. 307)

Author of the Conics and lost treatises Plane Loci (reconstructed by Robert Simson, 1749) and Tangencies (On Contacts, reconstructed by Viète, 1600). Namesake of the Apollonian circle of constant distance ratio (§ 11, Locus 11), the three Apollonian circles of a triangle (Ch. X, § 597), and the Problem of Apollonius on circles tangent to three given circles (Ch. VIII, §§ 506–517).

Archimedes of Syracuse (c. 287 – 212 BC)

  • Role: Greek Mathematician, Physicist & Engineer

  • Articles in College Geometry: § 141, § 469

  • Principal Works: Book of Lemmas (Liber Assumptorum); Measurement of a Circle; On Spirals

  • Edition Loci: f. 0326 (p. 307)

Greatest mathematician of antiquity, cited by Altshiller-Court for theorems on chords, circles, the arbelos (shoemaker’s knife), and precursors to harmonic and metric relations.

Bernhart, Arthur (1908–1996)

  • Role: Mathematician, University of Oklahoma

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: Curves of Pursuit (Scripta Mathematica, 1954–1959)

  • Edition Loci: f. 0008 (p. ix)

Colleague of Nathan Altshiller-Court in the Department of Mathematics at the University of Oklahoma; acknowledged in the 1952 Preface/Acknowledgments (p. ix) for reading the proofs of the Second Edition.

Bobillier, Étienne (1798–1840)

  • Role: French Geometer & Mechanician

  • Articles in College Geometry: § 155, § 259

  • Principal Works: Mémoires in Annales de Gergonne

  • Edition Loci: f. 0326 (p. 307)

Early contributor to projective and metric triangle geometry, abbreviated geometry of polars, and pedal/circumcircle properties.

Brahmagupta (598 – c. 668)

  • Role: Indian Mathematician & Astronomer

  • Articles in College Geometry: § 261, § 265, § 266

  • Principal Works: Brāhmasphuṭasiddhānta (628)

  • Edition Loci: f. 0326 (p. 307)

Formulated the area formula and orthogonality/median-altitude theorem for cyclic quadrilaterals with perpendicular diagonals (Brahmagupta’s theorem, Ch. IV).

Brianchon, Charles Julien (1783–1864)

  • Role: French Projective Geometer

  • Articles in College Geometry: § 207, § 224, § 381, § 449

  • Principal Works: Recherches sur la détermination d’une hyperbole équilatère (with Poncelet, 1820–1821)

  • Edition Loci: f. 0326 (p. 307)

Student at the École Polytechnique under Monge. With Poncelet (1821), published the first complete proof of the Nine-Point Circle theorem and discovered Brianchon’s hexagram theorem.

Brocard, Henri (1845–1922)

  • Role: French Meteorologist & Army Officer-Geometer

  • Articles in College Geometry: § 606, § 618, § 650, § 654, § 658, § 661, § 665, § 667, § 668, § 669, § 670, § 672, § 673, § 677

  • Principal Works: Étude d’un nouveau cercle du plan du triangle (1881); Notes de bibliographie des courbes géométriques

  • Edition Loci: f. 0326 (p. 307)

Co-founder (with Lemoine and Neuberg) of the late-19th-century revival of triangle geometry. Investigated the Brocard points Ω, Ω’, Brocard angle ω, Brocard circle, and Brocard triangles (Ch. X, §§ 649–683).

Butchart, John Harvey (1907–1997)

  • Role: Professor of Mathematics, Arizona State College

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: Some Properties of the Limaçon and Cardioid (Amer. Math. Monthly, 1945)

  • Edition Loci: f. 0008 (p. ix)

American geometer and contributor to The American Mathematical Monthly; acknowledged by Altshiller-Court (p. ix) for carefully reading both the manuscript and the proofs of the 1952 Second Edition and contributing important suggestions and additions.

Carnot, Lazare Nicolas Marguerite (1753–1823)

  • Role: French Mathematician & Statesman (‘Organizer of Victory’)

  • Articles in College Geometry: § 133, § 146, § 175, § 185, § 224, § 310, § 314

  • Principal Works: Géométrie de position (1803); Essai sur la théorie des transversales (1806)

  • Edition Loci: f. 0326 (p. 307)

Pioneered the systematic use of signed geometric quantities and transversals in Géométrie de position (1803); proved Carnot’s Theorem relating circumradius, inradius, and signed distances from circumcenter to triangle sides (§ 146).

Casey, John (1820–1891)

  • Role: Irish Geometer, Catholic University of Ireland

  • Articles in College Geometry: § 362, § 471, § 475, § 587, § 661

  • Principal Works: A Sequel to the First Six Books of the Elements of Euclid (1881; 6th ed. 1892)

  • Edition Loci: f. 0326 (p. 307)

Author of A Sequel to the First Six Books of the Elements of Euclid (1881), one of the primary English precursors to College Geometry. Formulated Casey’s Theorem (§ 471), generalizing Ptolemy’s theorem to four circles tangent to a fifth circle, leading to an elegant proof of Feuerbach’s theorem.

Castillon, Johann (Salvemini, Giovanni Francesco) (1709–1791)

  • Role: Italian-Swiss Geometer, Berlin Academy

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: Sur un problème de géométrie plane (Nouveaux Mémoires de l’Académie de Berlin, 1776)

  • Edition Loci: f. 0027 (p. 8)

Solved in 1776 the celebrated Cramer-Castillon Problem of inscribing in a given circle a triangle whose sides pass through three given points—a projective-constructive counterpart to Chapter I’s incidence problems (§ 9, § 14).

Catalan, Eugène Charles (1814–1894)

  • Role: Franco-Belgian Mathematician, University of Liège

  • Articles in College Geometry: § 160, § 290, § 353, § 381, § 496

  • Principal Works: Théorèmes et problèmes de géométrie élémentaire (6th ed., 1879)

  • Edition Loci: f. 0326 (p. 307)

Author of Théorèmes et problèmes de géométrie élémentaire (Cn. in Altshiller-Court’s bibliography), a rich treasury of constructive problems, harmonic division, and coaxal systems.

Ceva, Giovanni (1647–1734)

  • Role: Italian Mathematician & Hydraulic Engineer

  • Articles in College Geometry: § 326, § 328

  • Principal Works: De lineis rectis se invicem secantibus statica constructio (1678)

  • Edition Loci: f. 0326 (p. 307)

Discovered Ceva’s Theorem (1678) governing the concurrency of triangle cevians via products of signed ratios on the sides (Ch. VI, § 326).

Chapple, William (1718–1781)

  • Role: English Surveyor & Mathematician

  • Articles in College Geometry: § 152, § 175

  • Principal Works: An Essay on the Properties of Triangles Inscribed in and Circumscribed about Given Circles (1746)

  • Edition Loci: f. 0326 (p. 307)

Published in 1746 (twenty years before Euler) the formula d² = R(R - 2r) for the distance between the circumcenter and incenter of a triangle (§ 152).

Chasles, Michel (1793–1880)

  • Role: French Geometer & Historian of Geometry

  • Articles in College Geometry: § 306, § 316, § 343, § 356, § 650

  • Principal Works: Aperçu historique sur l’origine et le développement des méthodes en géométrie (1837); Traité de géométrie supérieure (1852)

  • Edition Loci: f. 0326 (p. 307)

Master of projective geometry, cross-ratios (anharmonic ratio), homography, and the history of synthetic methods (Chl. in Altshiller-Court’s bibliography).

Coolidge, Julian Lowell (1873–1954)

  • Role: American Geometer, Harvard University

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: A Treatise on the Circle and the Sphere (1916)

  • Edition Loci: f. 0326 (p. 307)

Author of A Treatise on the Circle and the Sphere (1916), synthesized by Altshiller-Court in Chapters VIII–X.

Court, Arnold (1914–1999)

  • Role: Climatologist & Professor of Geography, UCLA / CSUN

  • Articles in College Geometry: Frontmatter / Apparatus

  • Edition Loci: f. 0003 (p. [iv])

Son of Nathan and Sophie Altshiller-Court; renewed the copyright of the 1952 Second Edition of College Geometry in 1980 (p. [iv]).

Crelle, August Leopold (1780–1855)

  • Role: German Mathematician & Journal Founder

  • Articles in College Geometry: § 650, § 654, § 661

  • Principal Works: Über einige Eigenschaften des ebenen geradlinigen Dreiecks (1816)

  • Edition Loci: f. 0326 (p. 307)

Early investigator (1816) of the Brocard points and angle inside a triangle sixty years before Brocard’s 1875–1881 rediscovery.

d’Ocagne, Philbert Maurice (1862–1938)

  • Role: French Geometer & Founder of Nomography

  • Articles in College Geometry: § 558, § 567, § 568, § 576, § 581, § 599

  • Principal Works: Sur un élément du triangle rectiligne: la symédiane (1883)

  • Edition Loci: f. 0326 (p. 307)

Introduced the term symmedian (‘symédiane’, § 558) and established fundamental properties of symmedians, the Lemoine point, and antiparallels.

Desargues, Girard (1591–1661)

  • Role: French Architect & Founder of Projective Geometry

  • Articles in College Geometry: § 343, § 345, § 374

  • Principal Works: Brouillon project d’une atteinte aux événemens des rencontres du cône avec un plan (1639)

  • Edition Loci: f. 0326 (p. 307)

Introduced points and lines at infinity, involution, polar reciprocity, and Desargues’ Two-Triangle Perspective Theorem (§ 343).

Descartes, René (1596–1650)

  • Role: French Philosopher & Mathematician

  • Articles in College Geometry: § 516

  • Principal Works: La Géométrie (1637)

  • Edition Loci: f. 0326 (p. 307)

Founder of analytic geometry; contrasted by Altshiller-Court with pure synthetic and Greek geometric analysis.

Euclid of Alexandria (fl. c. 300 BC)

  • Role: Author of the Elements

  • Articles in College Geometry: § 2, § 11, § 23, § 68, § 87, § 111, § 175, § 251, § 410

  • Principal Works: Elements (Στοιχεῖα); Data (Δεδομένα); Porisms (lost)

  • Edition Loci: f. 0326 (p. 307)

Compiler of the thirteen books of the Elements, whosecompass-and-straightedge postulates and Books I–VI propositions form the explicit axiomatic bedrock of College Geometry.

Euler, Leonhard (1707–1783)

  • Role: Swiss Mathematician & Natural Philosopher

  • Articles in College Geometry: § 93, § 134, § 152, § 175, § 201, § 207, § 246, § 255, § 307

  • Principal Works: Solutio facilis problematum quorumdam geometricorum difficillimorum (1765)

  • Edition Loci: f. 0326 (p. 307)

Initiated modern triangle geometry in his 1765 St. Petersburg memoir: proved the collinearity of the orthocenter H, centroid G, and circumcenter O on the Euler line (§ 201), established OI² = R² - 2Rr (§ 152), Euler’s collinear four-point identity (§ 307), and quadrilateral median relations (§ 246).

Fagnano, Giovanni Francesco Toschi di (1715–1797)

  • Role: Italian Mathematician & Cleric

  • Articles in College Geometry: § 188, § 194

  • Principal Works: Problemata quaedam ad methodum maximorum et minimorum spectantia (1775)

  • Edition Loci: f. 0326 (p. 307)

Posed and solved Fagnano’s problem (1775): among all triangles inscribed in an acute triangle, the orthic triangle has minimum perimeter (§ 194).

Feuerbach, Karl Wilhelm (1800–1834)

  • Role: German Geometer

  • Articles in College Geometry: § 134, § 136, § 207, § 215, § 224, § 540

  • Principal Works: Eigenschaften einiger merkwürdigen Punkte des geradlinigen Dreiecks (1822)

  • Edition Loci: f. 0326 (p. 307)

Published in 1822 at age twenty-two one of the crown jewels of elementary geometry: Feuerbach’s Theorem (§ 215, § 540), proving that the nine-point circle of a triangle is internally tangent to the incircle (at the Feuerbach point X(11)) and externally tangent to the three excircles.

Fuhrmann, Wilhelm (1833–1904)

  • Role: German Mathematician

  • Articles in College Geometry: § 155, § 215, § 639

  • Principal Works: Synthetische Beweise planimetrischer Sätze (1890)

  • Edition Loci: f. 0326 (p. 307)

Author of Synthetische Beweise planimetrischer Sätze (1890) and discoverer of the Fuhrmann circle and Fuhrmann triangle.

Gallatly, William (c. 1850 – c. 1928)

  • Role: English Geometer

  • Articles in College Geometry: § 639, § 690, § 697

  • Principal Works: The Modern Geometry of the Triangle (2nd ed., 1913)

  • Edition Loci: f. 0326 (p. 307)

Author of The Modern Geometry of the Triangle (Gy., 2nd ed. 1913), frequently cited by Altshiller-Court on Lemoine, Brocard, Tucker, and orthopole theorems.

Gauss, Carl Friedrich (1777–1855)

  • Role: German Mathematician & Astronomer

  • Articles in College Geometry: § 175, § 353

  • Principal Works: Disquisitiones Arithmeticae (1801)

  • Edition Loci: f. 0326 (p. 307)

Proved the collinearity of the midpoints of the three diagonals of a complete quadrilateral (the Gauss-Newton line) and studied triangle altitudes and inversion precursors.

Gergonne, Joseph Diaz (1771–1859)

  • Role: French Mathematician & Founder of Annales de Mathématiques

  • Articles in College Geometry: § 331, § 374, § 421, § 505, § 517

  • Principal Works: Annales de mathématiques pures et appliquées (1810–1832); Recherche du cercle qui en touche trois autres sur une sphère ou sur un plan (1816)

  • Edition Loci: f. 0326 (p. 307)

Formulated projective duality, discovered the Gergonne point X(7) where cevians to the incircle contact points concur (§ 331), and devised Gergonne’s celebrated master solution to the general Problem of Apollonius using poles, polars, and the radical center (§ 517).

Grebe, Ernst Wilhelm (1804–1874)

  • Role: German Mathematician

  • Articles in College Geometry: § 572, § 573

  • Principal Works: Das geradlinige Dreieck in Bezug auf die Quadrate der Perpendikel (1847)

  • Edition Loci: f. 0326 (p. 307)

Studied the symmedian point in 1847 (hence called the Grebe point in German literature, § 572).

Heron of Alexandria (fl. c. 60 AD)

  • Role: Graeco-Egyptian Mathematician & Engineer

  • Articles in College Geometry: § 12, § 132

  • Principal Works: Metrica; Catoptrica

  • Edition Loci: f. 0327 (p. 308)

Formulated Heron’s area formula for a triangle in terms of its semiperimeter and solved the shortest-path reflection problem on a line (§ 12).

Jacobi, Carl Friedrich Andreas (1797–1845)

  • Role: German Geometer (Schulpforta)

  • Articles in College Geometry: § 626, § 650, § 654

  • Principal Works: De triangulorum rectilineorum proprietatibus quibusdam nondum satis cognitis (1825)

  • Edition Loci: f. 0327 (p. 308)

Early investigator of isogonal conjugates, Brocard angles, and triangle centers in De triangulorum rectilineorum proprietatibus (1825).

Johnson, Lee Wayne (1906–1991)

  • Role: Professor & Head of Mathematics, Oklahoma A. and M. College

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: Introduction to Linear Algebra (with R. D. Riess & J. T. Arnold)

  • Edition Loci: f. 0008 (p. ix)

Head of the Department of Mathematics at Oklahoma A. and M. College (now Oklahoma State University); acknowledged by Altshiller-Court (p. ix) for reading the 1952 manuscript with great care and contributing important suggestions and additions.

Johnson, Roger Arthur (1889–1954)

  • Role: American Geometer, Brooklyn College

  • Articles in College Geometry: § 229

  • Principal Works: Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle (1929)

  • Edition Loci: f. 0327 (p. 308)

Contemporary of Altshiller-Court and author of Modern Geometry (1929), discoverer of Johnson’s three-circle theorem.

Kimberling, Clark (b. 1942)

  • Role: American Mathematician & Creator of the Encyclopedia of Triangle Centers (ETC)

  • Articles in College Geometry: Frontmatter / Apparatus

  • Principal Works: Triangle Centers and Central Triangles (1998); Encyclopedia of Triangle Centers (ETC)

  • Edition Loci: f. 0327 (p. 308)

Founder of the Encyclopedia of Triangle Centers (ETC), indexing X(1), X(2), … via homogeneous trilinear and barycentric coordinates, systematically citing Altshiller-Court’s College Geometry as a canonical synthetic reference.

L’Huilier, Simon Antoine Jean (1750–1840)

  • Role: Swiss Mathematician, Geneva

  • Articles in College Geometry: § 131, § 134, § 136, § 138, § 142, § 160, § 265

  • Principal Works: Éléments d’analyse géométrique et d’analyse algébrique appliquées à la recherche des lieux géométriques (1809)

  • Edition Loci: f. 0327 (p. 308)

Author of Éléments d’analyse géométrique et d’analyse algébrique (LHr., 1809), a key source for Altshiller-Court on tritangent radii, exradii identities, and geometric analysis.

La Hire, Philippe de (1640–1718)

  • Role: French Geometer & Astronomer

  • Articles in College Geometry: § 292, § 345, § 374

  • Principal Works: Sectiones Conicae (1685)

  • Edition Loci: f. 0327 (p. 308)

Student of Desargues’ projective school; author of Sectiones Conicae (1685), founder of polar reciprocity in the plane, and namesake of De la Hire’s Problem (§ 292).

Lemoine, Émile Michel Hyacinthe (1840–1912)

  • Role: French Civil Engineer & Geometer

  • Articles in College Geometry: § 136, § 565, § 572, § 573, § 576, § 588, § 591, § 593, § 616

  • Principal Works: Note sur un point remarquable du plan du triangle (1873); La Géométrographie ou l’art des constructions géométriques (1902)

  • Edition Loci: f. 0327 (p. 308)

Sparked the modern geometry of the triangle with his 1873 Lyon paper on the symmedian (Lemoine) point K = X(6), Lemoine circles (first and cosine circles), Lemoine axis, and geometrography (quantitative measure of construction simplicity, Ch. X, §§ 558–596).

Menelaus of Alexandria (c. 70 – 140 AD)

  • Role: Graeco-Roman Mathematician & Astronomer

  • Articles in College Geometry: § 310, § 313

  • Principal Works: Sphaerica

  • Edition Loci: f. 0327 (p. 308)

Proved Menelaus’ Theorem on collinearity of three points on the sides of a triangle via signed segment ratios (Sphaerica Book III; Ch. VI, § 310).

Miquel, Auguste (1816–1851)

  • Role: French Mathematician

  • Articles in College Geometry: § 282, § 650

  • Principal Works: Théorèmes de géométrie (Journal de Liouville, 1838)

  • Edition Loci: f. 0327 (p. 308)

Discovered Miquel’s pivot theorem (1838) on the concurrency of circles through triangle vertices and side points, as well as the Miquel point of a complete quadrilateral.

Monge, Gaspard (1746–1818)

  • Role: French Geometer & Founder of the École Polytechnique

  • Articles in College Geometry: § 405, § 406, § 421

  • Principal Works: Géométrie descriptive (1799)

  • Edition Loci: f. 0327 (p. 308)

Creator of descriptive geometry and teacher of Carnot, Poncelet, Brianchon, and Dupin. Proved Monge’s Theorem that the external centers of similitude of three circles taken in pairs are collinear (§ 405).

Möbius, August Ferdinand (1790–1868)

  • Role: German Mathematician & Astronomer

  • Articles in College Geometry: § 306, § 518

  • Principal Works: Der barycentrische Calcul (1827)

  • Edition Loci: f. 0327 (p. 308)

Introduced homogeneous barycentric coordinates (Der barycentrische Calcul, 1827), signed areas/segments, and circular Möbius transformations.

Nagel, Christian Heinrich von (1803–1882)

  • Role: German Geometer (Ulm)

  • Articles in College Geometry: § 160, § 196, § 333, § 626

  • Principal Works: Untersuchungen über die wichtigsten zum Dreiecke gehörigen Kreise (1836)

  • Edition Loci: f. 0327 (p. 308)

Investigated the tritangent centers, the Nagel point X(8) where cevians to the excircle contact points concur (§ 333), and isogonal/isotomic relations (1836).

Neuberg, Joseph Jean Baptiste (1840–1926)

  • Role: Luxembourgish-Belgian Geometer, University of Liège

  • Articles in College Geometry: § 606, § 616, § 654, § 677, § 679, § 680, § 690, § 693

  • Principal Works: Sur le point de Steiner (1886); Mémoire sur le tétraèdre (1884); Sur les projections d’une droite sur les côtés d’un triangle (orthopole)

  • Edition Loci: f. 0031 (p. 12) · f. 0327 (p. 308)

Co-founder (with Mansion) of Mathesis and co-architect (with Lemoine and Brocard) of modern triangle geometry; discovered the isodynamic points, Neuberg circles, and the orthopole (§ 690).

Newton, Isaac (1642–1727)

  • Role: English Mathematician & Natural Philosopher

  • Articles in College Geometry: § 244, § 269, § 506

  • Principal Works: Philosophiae Naturalis Principia Mathematica (1687); Arithmetica Universalis (1707)

  • Edition Loci: f. 0327 (p. 308)

Author of Principia Mathematica and Arithmetica Universalis; proved Newton’s theorem on quadrilaterals circumscribed about a circle (§ 269).

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

  • Role: Hellenistic Geometer

  • Articles in College Geometry: § 4, § 84, § 308, § 345, § 355, § 506, § 545

  • Principal Works: Synagoge / Mathematical Collection (Books I–VIII)

  • Edition Loci: f. 0022 (p. 3) · f. 0030 (p. 11) · f. 0327 (p. 308)

Author of the Mathematical Collection (Συναγωγή), Book VII (‘Treasury of Analysis’) of which codifies ancient Greek geometric Analysis and Synthesis (§ 4), preserves lemmas to Apollonius and Euclid, states the invariance of harmonic cross-ratios (§ 355), the Problem of Pappus (§ 84), and Pappus’ arbelos chain (§ 545).

Peaucellier, Charles-Nicolas (1832–1913)

  • Role: French Military Engineer

  • Articles in College Geometry: § 518, § 533

  • Principal Works: Note sur le compas composé (Nouvelles Annales, 1864 / 1873)

  • Edition Loci: f. 0327 (p. 308)

Invented Peaucellier’s Cell (1864), the first exact planar linkage converting circular motion into rectilinear motion via geometric inversion (§ 533).

Petersen, Julius Peter Christian (1839–1910)

  • Role: Danish Mathematician

  • Articles in College Geometry: § 4, § 11, § 15, § 23, § 31

  • Principal Works: Methods and Theories for the Solution of Problems of Geometrical Constructions (1879)

  • Edition Loci: f. 0026 (p. 7) · f. 0327 (p. 308)

Author of Methods and Theories for the Solution of Problems of Geometrical Constructions (Pt., 1866; English ed. 1879), the direct methodological ancestor of Altshiller-Court’s Chapter I and Chapter II (Method of Loci, Similitude, Rotation, Translation).

Plato (c. 427 – c. 347 BC)

  • Role: Athenian Philosopher & Founder of the Academy

  • Articles in College Geometry: § 2, § 4

  • Principal Works: Meno; Republic; Timaeus

  • Edition Loci: f. 0327 (p. 308)

Credited in ancient tradition with codifying the method of geometric Analysis (regressive resolution to known truths) and restricting canonical constructions to straightedge and compass.

Plücker, Julius (1801–1868)

  • Role: German Geometer & Physicist

  • Articles in College Geometry: § 421, § 440, § 518

  • Principal Works: Analytisch-geometrische Entwicklungen (1828–1831)

  • Edition Loci: f. 0327 (p. 308)

Introduced trilinear coordinates, line geometry, and algebraic formulations of the radical axis and coaxal circles.

Poncelet, Jean-Victor (1788–1867)

  • Role: French Engineer & Architect of Projective Geometry

  • Articles in College Geometry: § 31, § 207, § 358, § 374, § 394, § 440, § 447, § 460, § 463, § 518

  • Principal Works: Traité des propriétés projectives des figures (1822)

  • Edition Loci: f. 0327 (p. 308)

Wrote Traité des propriétés projectives des figures (1822), initially drafted as a prisoner of war at Saratov (1813–1814). Established continuity, ideal chords, limiting points of coaxal circles (Poncelet’s coaxal theorems, Ch. VIII.G), homothecy, and (with Brianchon) the Nine-Point Circle.

Ptolemy, Claudius (c. 100 – c. 170 AD)

  • Role: Graeco-Egyptian Astronomer & Geometer

  • Articles in College Geometry: § 255, § 536

  • Principal Works: Almagest (Μαθηματικὴ Σύνταξις)

  • Edition Loci: f. 0327 (p. 308)

Proved Ptolemy’s Theorem in Almagest Book I, Ch. 10: in a cyclic quadrilateral, the product of the diagonals equals the sum of the products of opposite sides (§ 255; generalized by inversion in § 536).

Rouché, Eugène (1832–1910)

  • Role: French Mathematician

  • Articles in College Geometry: § 84, § 215, § 310, § 440, § 506, § 558, § 650, § 677

  • Principal Works: Traité de géométrie (with Ch. de Comberousse, 7th ed., 1900)

  • Edition Loci: f. 0327 (p. 308)

Co-author with Charles de Comberousse of Traité de géométrie (Rouché., 7th ed. 1900, with Neuberg’s appendix on triangle geometry), Altshiller-Court’s single most frequently cited French reference.

Servois, François-Joseph (1767–1847)

  • Role: French Mathematician & Artillery Professor

  • Articles in College Geometry: § 282, § 284, § 287, § 374

  • Principal Works: Solutions peu connues de différens problèmes de géométrie-pratique (1804)

  • Edition Loci: f. 0327 (p. 308)

Introduced the term ‘pole’ in projective geometry (1811) and studied the Wallace-Simson line independently.

Simson, Robert (1687–1768)

  • Role: Scottish Geometer, University of Glasgow

  • Articles in College Geometry: § 11, § 282, § 308

  • Principal Works: Apollonii Pergaei Locorum Planorum Libri II (1749); The Elements of Euclid (1756)

  • Edition Loci: f. 0328 (p. 309)

Restorer of Euclid’s Elements (1756), Euclid’s Data, and Apollonius’s Plane Loci (1749; cited by Altshiller-Court in § 11). Though the ‘Simson line’ (Ch. V, § 282) bears his name through Poncelet/Servois attribution, it was first published by William Wallace in 1799.

Spieker, Theodor (1823–1913)

  • Role: German Geometer (Potsdam)

  • Articles in College Geometry: § 333

  • Principal Works: Lehrbuch der ebenen Geometrie (1862)

  • Edition Loci: f. 0327 (p. 308)

Author of Lehrbuch der ebenen Geometrie (1862); investigated the incircle of the medial (complementary) triangle—the Spieker circle, centered at the Spieker point X(10), center of mass of the triangle’s perimeter.

Steiner, Jakob (1796–1863)

  • Role: Swiss Geometer, University of Berlin

  • Articles in College Geometry: § 207, § 215, § 282, § 299, § 412, § 440, § 470, § 506, § 518, § 626, § 679

  • Principal Works: Einige geometrische Betrachtungen (Crelle’s Journal, Vol. 1, 1826); Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander (1832)

  • Edition Loci: f. 0327 (p. 308)

Regarded as the purest synthetic geometer since Apollonius. Introduced the ‘power of a point’ with respect to a circle (1826, Ch. VIII.E, § 412), proved fundamental theorems on the Simson line envelope (Steiner deltoid, § 299), complete quadrilaterals, inversion, the Problem of Apollonius, and the Steiner point R = X(99) on the circumcircle (§ 679).

Stewart, Matthew (1717–1785)

  • Role: Scottish Geometer, University of Edinburgh

  • Articles in College Geometry: § 308

  • Principal Works: Some General Theorems of Considerable Use in the Higher Parts of Mathematics (1746)

  • Edition Loci: f. 0327 (p. 308)

Student of Robert Simson and Colin Maclaurin; published Stewart’s Theorem (1746) relating the length of any cevian to the side lengths and divided base segments (Ch. VI.B, § 308).

Tarry, Gaston (1843–1913)

  • Role: French Mathematician

  • Articles in College Geometry: § 680, § 681

  • Principal Works: Sur les figures semblablement associées à un triangle (1886)

  • Edition Loci: f. 0328 (p. 309)

Discovered the Tarry point X(98) on the circumcircle, diametrically opposite the Steiner point X(99) (§ 680).

Taylor, Henry Martyn (1842–1927)

  • Role: English Mathematician, Trinity College, Cambridge

  • Articles in College Geometry: § 689

  • Principal Works: On a Six-Point Circle Connected with a Triangle (Messenger of Mathematics, 1882)

  • Edition Loci: f. 0328 (p. 309)

Investigated the six projections of the feet of the altitudes onto the other two sides, proving they lie on a special Tucker circle: the Taylor circle (§ 689).

Thales of Miletus (c. 624 – c. 546 BC)

  • Role: Ionian Natural Philosopher & Geometer

  • Articles in College Geometry: § 11, § 23

  • Edition Loci: f. 0328 (p. 309)

Founder of deductive Greek geometry; credited with Thales’ theorem that a diameter subtends a right angle at any point on the circle (§ 11, Locus 5; Euclid III.31) and proportional intercepts on parallel lines.

Thébault, Victor (1882–1960)

  • Role: French Geometer

  • Articles in College Geometry: § 239, § 690

  • Principal Works: Les récréations mathématiques (1952)

  • Edition Loci: f. 0328 (p. 309)

Prolific 20th-century problemist and close correspondent of Altshiller-Court in the American Mathematical Monthly and Mathesis; contributed numerous theorems and problems to the 1952 Second Edition.

Tucker, Robert (1832–1905)

  • Role: English Mathematician & Honorary Secretary of the LMS

  • Articles in College Geometry: § 588, § 684, § 685

  • Principal Works: The ‘Triplicate-Ratio’ Circle (1883); Some Properties of a Quadrilateral in a Circle and of Circles Linked with a Triangle (1885)

  • Edition Loci: f. 0328 (p. 309)

Discovered the family of six-point Tucker circles generalizing the first Lemoine, cosine, and Taylor circles (Ch. X.F, §§ 684–689).

Varignon, Pierre (1654–1722)

  • Role: French Mathematician & Mechanician

  • Articles in College Geometry: § 240

  • Principal Works: Élémens de mathématique (1731)

  • Edition Loci: f. 0328 (p. 309)

Proved Varignon’s Theorem (published posthumously 1731) that the midpoints of the sides of any quadrilateral form a parallelogram (§ 240).

Viète, François (1540–1603)

  • Role: French Mathematician

  • Articles in College Geometry: § 506, § 516

  • Principal Works: Apollonius Gallus (1600)

  • Edition Loci: f. 0328 (p. 309)

Reconstructed Apollonius’s lost Tangencies in his Apollonius Gallus (1600), solving the ten cases of the Problem of Apollonius sequentially via centers of similitude and inversion precursors (§§ 506–516).

Wallace, William (1768–1843)

  • Role: Scottish Mathematician, University of Edinburgh

  • Articles in College Geometry: § 282

  • Principal Works: Mathematical Repository, Vol. II (1799), p. 111

  • Edition Loci: f. 0328 (p. 309)

First published in Thomas Leybourn’s Mathematical Repository (1799) the collinearity of the pedal projections of a circumcircle point onto the three sides of a triangle—now known as the Wallace-Simson line (§ 282).