*The Great Archimedes.*Waco: Baylor University Press, 2010. Pp. xvi, 116, 16 p. of plates. ISBN 9781602583115. $24.95 (pb). Contributors: Translated and edited by R. Alden Smith.

Reviewed by Anna Toscano, UniversitÃ degli Studi di Milano (toscano.anna@virgilio.it, anna.toscano@unimi.it)

In 2006, Mario Geymonat, a distinguished Latinist of the Ca' Foscari University of Venice, published for Sandro Teti Editore a delightful and richly illustrated biography of the great mathematician Archimedes—one of the most brilliant minds of antiquity—which included a preface by the classical philologist and historian Lucio Canfora as well as an introduction by Zhores Alferov, winner of the Nobel Prize in Physics in 2000.

In 2010 the Baylor University Press published the English edition of the book, edited by R. Alden Smith in an enriched format. This publication makes Geymonat's interesting work available to the international public, acknowledging his praiseworthy objective of offering an excellent example of high-level scientific popularization.

Boasting an extensive scientific background, especially as regards mathematics, Geymonat fluently translates both sources contemporary with Archimedes and the writings of this Syracusan mathematician, thus outlining for the readers, empathically involved in the narration, the image of a scientist with a free spirit and a sharp, open mind, whose thought, in the pages of this volume, is rendered with all its strength.

Geymonat deserves credit for having taken out of the "mouldy essays" for "specialists in the field" the recent achievements of the studies of history of science on the Syracusan scientist, making them accessible to a wider readership. Such research makes possible the redesign of the cultural panorama of the Alexandrian age, thus giving history a new awareness of the content of Archimedes' works, as well as the knowledge of what can be rightly considered the scientific revolution of the 3^{rd} century B.C., "erased" for over two millennia from the memory not only of European culture but of others as well.

The most important contributions to the reevaluation of Archimedes were made in the large number of studies carried out over the years on the *Palimpsest* containing little-known and unknown works by Archimedes, the so-called *Codex C*, found in Istanbul in 1906, then lost during the First World War and rediscovered in a high- priced auction at Christie's in New York in 1998.These studies added new elements to the comprehension of Archimedes' mathematical thought, and scholars have used the most recent technologies to enable a reading of new sections of the *Stomachion* and of the *Method on Mechanical Theorems* previously inaccessible. Thanks to modern techniques using X-rays and synchrotron light, it was possible both to understand the combinatorial nature of the problem dealt with in the *Stomachion* and to ascertain in theorems present in the *Method*, and never before read, a different use of the concepts of infinity and the infinitesimal from those adopted in the other known works by Archimedes.^{1}

Likewise, the reconstruction and decoding, concluded in 2005, of the charming Antikythera Mechanism, dating from the 1^{st} century B.C., which was found in a shipwreck off the coast of Antikythera in the Aegean Sea, confirmed the results achieved in 1974 by the historian Derek de Solla Price. He proved that the Greeks had attained an advanced level of technology that reached its height in the Antikythera Mechanism, which turned out to be a true astronomical "analogical calculator" operated by the advanced technology which next appeared in Europe in the 16^{th} century. The clockwork device had been one of the technological marvels of ancient Greece which came out of the cultural background inherited from Archimedes.

Furthermore, one of Archimedes' most admired technical achievements in antiquity was his Planetarium (Orrery). Detailed information on this object has been handed down to us through Cicero's writings, where he narrates that in the year 212 B.C., when Syracuse was sacked by the Roman troops, Consul Marcus Claudius Marcellus brought to Rome a device built by the Syracusan mathematician which reproduced the vault of heaven on a sphere and another device that represented the apparent motion of the Sun, Moon and Planets, hence the equivalent of a modern planetarium. In his report of the impressions of Gaius Sulpicius Gallus, who could personally observe the extraordinary object, Cicero^{2} remarks how Archimedes' genius was able to generate the motions of the planets, so different from each other, starting from a single rotation. Thanks to the account of Pappus of Alexandria, we know that Archimedes had described the construction of the planetarium in *On Sphere-Making*,^{3} a work now lost.

Attesting to the complexity of the early mechanisms built to represent the motion of the celestial bodies, the Antikythera Mechanism revived interest in Archimedes's Planetarium (Orrery). But a gear brought to light in Olbia in Sardinia in July 2006 especially aroused the attention of scholars, as it was probably to be identified with a device that belonged to the same Planetarium of the Syracusan mathematician.^{4} The first results of the studies on the object were presented to the public in a conference organized in April 2011 by the Ministero per i Beni e le AttivitÃ Culturali. According to a first reconstruction, the planetarium, which was presumably handed down to the descendants of the conqueror of Syracuse, might have been lost at Olbia before the wreck of the ship taking Marcus Claudius Marcellus to Numidia. The gear, dated from between the end of the 3^{rd} century and the mid-2^{nd} century B.C., although made at an earlier date than the other mechanisms discovered so far, shows gear teeth which are extraordinarily similar to that of the mechanical components of a contemporary device.^{5}

Such important finds testify to the high level of physical and mathematical skill as well as to the remarkable ability in technical design and implementation which Archimedes and contemporary Alexandrian science and technology had attained.

In his letter to Eratosthenes which opens his *Method*, Archimedes talks about his work, describing his innovative approach based on the ability to link theoretical considerations with practical achievements. He produced mechanical applications to solve concrete problems, on the basis of theoretical considerations connected to suggestions derived from experience and subsequently systematized, specified, and elaborated systematically.

This ability to avail himself of different methods showed both Archimedes' extreme mental agility and his new attitude towards research, that he considered a living element, very far from the idea of a mass of shackles and chains. As underlined by Geymonat in his book, Archimedes "among the ancient mathematicians must be thought of as the one who could avail himself of intuition with the most daring liberty, convinced of the free use of all of man's cognitive resources" (p. 7-8). Precisely for this ability, Archimedes's works were copied and circulated widely, not only in the Greek world, but also among the Arabs and Europeans one thousand years later. In the European culture of the Renaissance, his treatises, partially just rediscovered, led to an exponential development of mathematical and mechanical competences, triggering the process that would give rise to modern science.

The triumph of the great Syracusan mathematician at the height of the Renaissance attested to the revived interest in his work, brought about by the arrival in Florence of the Greek codex of his works, the *Codex A*, today kept in the Medicean-Laurentian Library. Between the late 16^{th} century and the early 17^{th} century the Apotheosis of Archimedes^{6} was actually painted, in Florence on the walls and ceilings of the *Stanzino delle Matematiche* in the Uffizi Gallery: next to the visual narrative of the Syracusan scientist's exploits, the frescoes in the *Stanzino* reproduced works by Pythagoras, Ptolemy, and Euclid surrounded by paintings of the numerous mathematical instruments showcased in the room at that time. Sixty years later, in the decorations of the eastern Corridor of the Gallery Galileo would be celebrated by Grand Duke Ferdinando II de' Medici and by Prince Leopoldo de' Medici as the "New Archimedes".

The figure of Galileo has a fundamental importance because of his central role in recovering the scientific method developed in the Hellenistic age, which later on had almost been forgotten. This rediscovery was due to his careful study, carried out "with infinite amazement",^{7} of some scientific works by Archimedes, admired and worshipped by all the scientists of the time for his daring inventions and taken as a model of rigour and whose research Method they tried in particular to reconstruct, deeming that Archimedes himself had concealed his secret from posterity.

With the rediscovery of the *Method*, it was possible to enter the philosophical-epistemological workshop of Archimedes where the physical and geometrical atomism of Democritus stands out as an important feature. For the Syracusan scientist there exists a close correspondence between physical and geometrical atomism; the same ratio existing between geometrical lines is also true for the physical lines, imagined as homogeneous, which balance each other in a lever. Indeed, it is possible to maintain that Archimedean physics and geometry were created in controversy with Plato,^{8} violating the prohibition against connecting mechanics and geometry, and even defying the Aristotelian veto according to which infinitesimal quantities of forces can, by adding up, overcome any finite resistance, no matter how strong, and introducing with his law of the lever the concept of the moment of a force. Archimedes, describing how a spiral originates from the movement of a point on a segment of a straight line moving in its turn in a circle around one of its fixed extremes, doubly contravened Aristotle's prohibition. He thus paved the way for a line of research that has allowed such progress in the technological use of mathematics as to send objects into space, besides providing the basis for the imaging science which is so essential today for deciphering the palimpsest with his works, as well as the Antikythera Mechanism and the device of Olbia.

Recently, the theme of the scientific and technological legacy of the Hellenistic culture and of its pedagogical value has regained importance thanks to theories of experimental education where classical geometrical and mathematical knowledge is substituted by branches of learning pertaining to financial and managerial themes in an attempt to devise educational paths more attuned to the trends of contemporary world aimed at training the younger generations.^{9} Geymonat's book, in its well-conceived literary form, stands in contrast to such a theory.

Having iconographic references, which partly reproduce some images taken from the frescoes of the *Stanzino* in the Uffizi Gallery, Geymonat's book consists of ten chapters ranging from *The Adventurous Life of a Remarkable Scientist* to *The Myth of Archimedes, Yesterday and Today*, through the testimony of the Latin poets Catullus and Virgil and Vitruvius's account.

The well-organized Notes, a short and up-dated Bibliography and an Index of Names complete the text.

**Notes:**

1. Stephanos Paipetis-Marco Ceccarelli, ed., *The Genius of Archimedes*, New York, Springer Publishing, 2010.

2. Cicero, *De re publica*, I, 14; *Tusculanae Disputationes*, I, 25; *De Natura Deorum,* II, 34.

3. *Collectio*, VIII, 1026.

4. Cicero, *Tusculanae disputationes* I, 63.

5. The restoration of the gear found in Olbia has revealed a very surprising feature: besides its very refined engineering workmanship, it is made of a brass alloy, a characteristic which had never been found so far in other metal artefacts with the same dating. Considering the perfect concordance between scientific evidence and historical, literary and archaeological outcomes, it was possible to consider the fragment from Olbia a mechanical component of the Planetarium of Archimedes. During the conference, all the reasons and scientific evidence were presented which led the engineer Giovanni Pastore, contract professor of Mechanical Construction at the University of Bari, to attribute the gear fragment found in Olbia to the Planetarium of Archimedes.

6. A. Toscano, Mathematics and physics in Tuscany.

7. G. Galilei, *Opere*, Utet, Torino, 1964, Vol. II, p. 613

8. Plutarchus, *Vitae Parallelae*, *Marcellus*

9. For example, this article from the Washington Post.

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