Introduction

The Hellenistic scientific revolution was forgotten precisely because that scientific method was abandoned in antiquity and its recovery was exceedingly slow. For example, coming back to mathematics, Newton was still far below the Hellenistic level of rigor, as evident from comparing his argument about the ratio of infinitesimal quantities (Principia, I.I) with Archimedes’ work On Spirals, where infinitesimals of different orders are introduced: in essence, Newton lacked the limit concept which Archimedes possessed. The full recovery of the Hellenistic way of doing mathematics had to wait for Cauchy and Weierstrass...

What about the general and steady (on the average) impoverishment of Hellenistic science under the Roman empire? This is a major historical problem, strongly tied to the even bigger one of the decline and fall of the antique civilization itself. I would summarize the author’s argument by saying that it basically represents an application to science of a widely accepted general theory on decadence of antique civilization going back to Max Weber. Roman society, mainly based on slave labor, underwent an ultimately unrecoverable crisis as the traditional sources of that labor force, essentially wars, progressively dried up. To save basic farming, the remaining slaves were promoted to be serfs, and poor free peasants reduced to serfdom, but this made trade disappear. A society in which production is almost entirely based on serfdom and with no trade clearly has very little need of culture, including science and technology. As Max Weber pointed out, when trade vanished, so did the marble splendor of the ancient towns, as well as the spiritual assets that went with it: art, literature, science, and sophisticated commercial laws. The recovery of Hellenistic science then had to wait until the disappearance of serfdom at the end of the Middle Ages. To quote Max Weber: “Only then with renewed vigor did the old giant rise up again.”

The same scientific method characterizes the investigations in biomedical sciences (here the main For example, Scholia, related to the various writing stages of Philisophiae Naturalis Principia Mathematica; figure is Herophilus of Chalcedon, who developed a theory, very much like our modern ones, of human anatomy and physiology, discovered the nervous system, and made a distinction between sensors and motors), in economics and mass production techniques, in architecture and urban development, and in cognitive sciences. Taken as a whole, the scientific methods characterized Hellenistic civilization, which underwent a major crisis in 145–144 B.C. (under Roman pressure after the subjugation of Macedonia and the destruction of Carthage) and later a slow but steady decline during its forced integration into the Roman state, concluded in 30 B.C. with the reduction of Egypt to a Roman province. However, Alexandria maintained its role as the scientific capital of antiquity (with a partial recovery in the second century A.D., the time of the mathematician and mechanical engineer Heron, the physician Galenus, and the astronomer Claude Ptolemy) well into the fifth century A.D. To fix the time scale, note that the rise, decline, partial recovery, and fall of Alexandrine science took more than seven centuries. Before turning to the question of the decline of Hellenistic science, I come back to the new light shed by the book on Euclid’s Elements and on pre-Ptolemaic astronomy. Euclid’s definitions of the elementary geometric entities—point, straight line, plane—at the beginning of the Elements have long presented a problem. Their nature is in sharp contrast with the approach taken in the rest of the book, and continued by mathematicians ever since, of refraining from defining the fundamental entities explicitly but limiting themselves to postulating the properties which they enjoy. Why should Euclid be so hopelessly obscure right at the beginning and so smooth just after? The answer is: the definitions are not Euclid’s. Toward the beginning of the second century A.D. Heron of Alexandria found it convenient to introduce definitions of the elementary objects (a sign of decadence!) in his commentary on Euclid’s Elements, which had been written at least 400 years before. All manuscripts of the Elements copied ever since included Heron’s definitions without mention, whence their attribution to Euclid himself. The philological evidence leading to this conclusion is quite convincing.

Review by Sandro Graffi of “ La Rivoluzione Dimenticata” (The Forgotten Revolution) Lucio Russo Feltrinelli, Milan, 1996 (

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