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Anthemius of Tralles (Greek: Ἀνθέμιος ὁ Τραλλιανός, Medieval Greek: [anˈθemios o traliaˈnos], Anthémios o Trallianós; c. 474 – 533 x 558)[1] was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capital of the Byzantine Empire. With Isidore of Miletus, he designed the Hagia Sophia for Justinian I.


Anthemius was one of the five sons of Stephanus of Tralles, a physician. His brothers were Dioscorus, Alexander, Olympius, and Metrodorus. Dioscorus followed his father's profession in Tralles; Alexander did so in Rome and became one of the most celebrated medical men of his time; Olympius became a noted lawyer; and Metrodorus worked as a grammarian in Constantinople.[2]

Anthemius was said to have annoyed his neighbor Zeno in two ways: first, by engineering a miniature earthquake by sending steam through leather tubes he had fixed among the joists and flooring of Zeno's parlor while he was entertaining friends and, second, by simulating thunder and lightning and flashing intolerable light into Zeno's eyes from a slightly hollowed mirror.[2] In addition to his familiarity with steam, some dubious authorities credited Anthemius with a knowledge of gunpowder or other explosive compound.[2]

Anthemius was a capable mathematician. In the course of his treatise On Burning Mirrors, he intended to facilitate the construction of surfaces to reflect light to a single point, he described the string construction of the ellipse[1] and assumed a property of ellipses not found in Apollonius of Perga's Conics: the equality of the angles subtended at a focus by two tangents drawn from a point. His work also includes the first practical use of the directrix: having given the focus and a double ordinate, he used the focus and directrix to obtain any number of points on a parabola.[2] This work was later known to Arab mathematicians such as Alhazen.

Eutocius's commentary on Apollonius's Conics was dedicated to Anthemius.[1]
Exterior of the Hagia Sophia, 2013

As an architect, Anthemius is best known for his work designing the Hagia Sophia.[2] He was commissioned with Isidore of Miletus by Justinian I shortly after the earlier church on the site burned down in 532 but died early on in the project. He is also said to have repaired the flood defenses at Daras.[3]
See also

Other Anthemiuses


Boyer (1991), p. 193.
Heath 1911, p. 98.



Boyer, Carl Benjamin (1991), A History of Mathematics (2nd ed.), John Wiley & Sons, ISBN 0-471-54397-7.


This article incorporates text from a publication now in the public domain: Heath, Thomas Little (1911), "Anthemius", in Chisholm, Hugh (ed.), Encyclopædia Britannica, 2 (11th ed.), Cambridge University Press, p. 93

Further reading

Baynes, T. S., ed. (1878), "Anthemius" , Encyclopædia Britannica, 2 (9th ed.), New York: Charles Scribner's Sons, p. 103
Editions of Anthemius's "On Burning-Glasses":

Dupuy, L. (1777), Περί παραδόξων μηχανημάτων [Perí Paradóxōn Mēkhanēmátōn; Concerning Wondrous Machines]. (in Greek)
Histoire de l'Academie des Instrumentistes, XLII. (in French)
Westermann, A. (1839), Παραδοξογράφοι [Paradoxográphoi; Marvel-Writers]. (in Greek)

External links

"Anthemius of Tralles", Complete Dictionary of Scientific Biography, 2008.
O'Connor, John J.; Robertson, Edmund F., "Anthemius of Tralles", MacTutor History of Mathematics archive, University of St Andrews.


Ancient Greek and Hellenistic mathematics (Euclidean geometry)
Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius's theorem
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Cyrene Library of Alexandria Platonic Academy
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction


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