A page opening from the editio princeps of Archimedes Opera (1544). This  is the Greek text of the Quadrature of the Parabola, Proposition 16, showing that the area of the parabola is one-third the area of the triangle formed by the base, the tangent, and the line joining the base and tangent, and Proposition 17, that the area of the parabola is four-thirds the triangle with the same base and equal height. Caltech Library.

A page opening from the editio princeps of Archimedes Opera (1544). This  is the Greek text of the Quadrature of the Parabola, Proposition 16, showing that the area of the parabola is one-third the area of the triangle formed by the base, the tangent, and the line joining the base and tangent, and Proposition 17, that the area of the parabola is four-thirds the triangle with the same base and equal height. Caltech Library.

A page openiong from the Archimedes Palimpsest.

A page openiong from the Archimedes Palimpsest.

Detail map of Alexandria Governorate, Egypt,Venezia, Veneto, Italy,Jerusalem, Jerusalem District, Israel,Roma, Lazio, Italy,Valdealgorfa, Aragón, Spain

A: Alexandria Governorate, Egypt, B: Venezia, Veneto, Italy, C: Jerusalem, Jerusalem District, Israel, D: Roma, Lazio, Italy, E: Valdealgorfa, Aragón, Spain

Survival of the Works of Archimedes was Dependent upon Three Manuscripts, Only One of Which Survived to the Present

1269 to 1544
This copy of the Moerbeke translation Archimedes

This copy of the Moerbeke translation Archimedes' Teragonismus edited by Giorgio Valla sold for 10,000 GBP at Sotheby's London on December 3, 2019.

In contrast to Euclid's Elements, which were written at the Royal Library of Alexandria, and widely disseminated, the writings of the Greek mathematician, physicist, engineer, inventor, and astronomer Archimedes were not widely known in antiquity. Survival of their texts was due to interest in Archimedes' writings at the Byzantine capital of Constantinople from the sixth through the tenth centuries.

"It is true that before that time individual works of Archimedes were obviously studied at Alexandria, since Archimedes was often quoted by three eminent mathematicians of Alexandria: Hero, Pappus, and Theon. But it is with the activity of Eutocius of Ascalon, who was born toward the end of the fifth century and studied at Alexandria, that the textual history of a collected edition of Archimedes properly begins. Eutocius composed commentaries on three of Archimedes' works: On the Sphere and the Cylinder, On the Measurement of the Circle, and On the Equilibrium of Planes. These were no doubt the most popular of Archimedes' works at that time. . . . The works of Archimedes and the commentaries of Eutocius were studied and taught by Isidore of Miletus and Anthemius of Tralles, Justinian's architects of Hagia Sophia in Constantinople. It was apparently Isidore who was responsible for the first collected edition of at least the three works commented on by Eutocius as well as the commentaries. Later Byzantine authors seem gradually to have added other works to this first collected edition until the ninth century when the educational reformer Leon of Thessalonica produced the compilation represented by Greek manuscript A (adopting the designation used by the editor, J. L. Heiberg).  Manuscript A contained all of the Greek works now known excepting On Floating Bodies, On the Method, Stomachion, and The Cattle Problem. This was one of the two manuscripts available to William of Moerbeke when he made his Latin translations in 1269.  It was the source, directly or indirectly, of all of the Renaissance copies of Archimedes. A second Byzantine manuscript, designated as B, included only the mechanical works: On the Equilibrium of Planes, On the Quadrature of the Parabola and On Floating Bodies (and possibly On Spirals).  It too was available to Moerbeke. But it disappears after an early fourteenth-century reference. Finally we can mention a third Byzantine manuscript, C, a palimpsest whose Archimedean parts are in a hand of the tenth century. It was not available to the Latin West in the Middle Ages, or indeed in modern times until its identification by Heiberg in 1906 at Constantinople (where it had been brought from Jerusalem)" (Marshall Clagett, "Archimedes," Dictionary of Scientific Biography I [1970] 223).

Transmission of Archimedes' writings to the west was largely dependent upon the translation into Latin of most of the Archimedean texts in manuscripts A and B by the Flemish Dominican William of Moerbeke (Willem van Moerbeke) in 1269.  These manuscripts had passed into the Pope's library from the collection of the Norman kings of the Two Sicilies.  Moerbeke's translations of the two manuscripts were not without errors, but they presented the texts in an understandable way. The holograph of Moerbeke's translation survives in the Vatican Library (MS Vat. Ottob. lat. 1850). It was not widely copied. Manuscripts A and B no longer survive.

"In the fifteenth century, knowledge of Archimedes in Europe began to expand. A new latin translation was made by James of Cremona in about 1450 by order of Pope Nicholas V. Since this translation was made exclusively from manuscript A, the translation failed to include On Floating Bodies, but it did include the two treatises in A omitted by Moerbeke, namely The Sand Reckoner and Eutocius' Commentary on the Measurement of the Circle. It appears that this new translation was made with an eye on Moerbeke's translation. . . . There are at least nine extant manuscripts of this translation, one of which was corrrected by Regiomontanus and brought to Germany about 1468. . . . Greek manuscript A itself was copied a number of times. Cardinal Bessarion had one copy prepared between 1449 and 1468 (MS E). Another (MS D) was made from A when it was in the possession fo the well-kinown humanist George [Giorgio] Valla. The fate of A and its various copies has been traced skillfully by J. L. Heiberg in his edition of Archimedes' Opera. The last known use of manuscript A occurred in 1544, after which time it seems to have disappeared.  The first printed Archimedean materials were in fact merely latin excerpts that appeared in George Valla's De expetendis et fugiendis rebus opus (Venice, 1501) and were based on his reading of manuscript A. But the earliest actual printed texts of Archimedes were the Moerbeke translations of On the Measurement of the Circle and On the Quadrature of the Parabola (Teragonismus, id est circuli quadratura etc.) published from the Madrid manuscript by L.[uca] Gaurico (Venice, 1503). In 1543 also at Venice N.[iccolo] Tartaglia republished the same two translations directly from Gaurico's work, and in addition, from the same Madrid manuscript, the Moerbeke translations of On the Equilbrium of Planes and Book I of On Floating Bodes (leaving the erroneous impression that he had made these translations from a Greek manuscript, which he had not since he merely repeated the texts of the Madrid manuscript, with virtually all their errors.) . . . The key event, however, in the further spread of Archimedes was the aforementioned editio princeps of the Greek text with the accompanying Latin translation of James of Cremona at Basel in 1544. . . ." Clagett, op. cit., 228-229).

For the editio princeps the editor Thomas Gechauff, called Venatorius (d. 1551), was able to use the above-mentioned manuscript of James of Cremona's (Jacopo da Cremona's) Latin translation corrected by Regiomontanus, which included the commentaries of Eutocius of Ascalon. For the Greek text Gechauff used a manuscript which had been acquired in Rome by humanist Willibald Pirckheimer, and is preserved today today in Nuremberg City Library.

Existence of a reliable Greek and Latin edition made the texts available to a wider range of scholars, exerting a strong influence on mathematics and physics in the sixteenth century. "One of the imortant effects of that influence can be seen in Kepler's Astronomia nova, in which Archimedes's so-called 'exhaustion procedure' was applied to the measurement of time elapsed between any two points in Mars's orbit" (Hook & Norman, Haskell F. Norman Library of Science and Medicine [1991] no. 61).

♦ After disappearing into a European private collection in the early twentieth century, the third key record of Archimedes' texts discussed above, the tenth century Byzantine manuscript C, known as the Archimedes Palimpsest, re-appeared at a Christie's auction in New York on October 28, 1998, where it was purchased by an anonymous private collector in the United States. Since then it has been made widely available to scholars, and has been the subject of much research.

Timeline Themes

Related Entries

Euclid's Elements:

Royal Library of Alexandria:





Pope Nicholas V:

Cardinal Bessarion:

Archimedes Palimpsest: