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Danilo Capecchi (Rome, Italy) WEIGHT AS ACTIVE OR PASSIVE PRINCIPLE in the LATIN and ARABIC SCIENTIA DE PONDERIBUS 1. Introducti

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Danilo Capecchi (Rome, Italy) WEIGHT AS ACTIVE OR PASSIVE PRINCIPLE in the LATIN and ARABIC SCIENTIA DE PONDERIBUS 1. Introducti ORGANON 43:2011 Danilo Capecchi (Rome, Italy) WEIGHT AS ACTIVE OR PASSIVE PRINCIPLE IN THE LATIN AND ARABIC SCIENTIA DE PONDERIBUS 1. Introduction The various studies regarding the natural motion, movement and equi- librium of bodies, today unified under modern mechanics, belonged in the past to different sciences, including physics, astronomy, geometry and mechanics . According to Aristotle, physics was the study of being in movement , particularly the motion of bodies, according to nature (natural motion) and against nature (violent motion) 1. The former occurs because bodies tend, by themselves, to reach their natural state (the centre of the World for heavy bodies); the latter occurs as the result of a motive power. For both classes of motion Aristotle suggests mathematical laws which, while still vague on the metric of many quantities, represent an early formulation of dynamics. Mechanics was developed mainly by mathematicians. In ancient Greece the term mechanics was used when referring to machines and devices in gen- eral 2. To be more exact, it was intended to mean the study of simple machines (winch, lever, pulley, wedge, screw and inclined plane) with reference to motive powers and displacements of bodies. Historically works considering 1 See I. E. Drabkin, Notes on the laws of motion in Aristotle in: The American Journal of Philology 59, 1/1938, pp. 60–84, A. Stinner, The story of force from Aristotle to Einstein in: Physics Education 29, 1994, pp. 77–85. 2 Aristotle defines mechanics as the part of the art which helps us to work against nature. See Aristotle, Mechanical problems in: Aristotle, Minor works , (ed.) W. S. Hett, William Heinemann, Cambridge 1955, p. 333: For in many cases nature produces effects against our advantage; for nature always acts consistently and simply, but our advantage changes in many ways. When, then, we have to produce an effect contrary to nature, we are at a loss, because of the difficulty, and require skill. Therefore we call that part of skill which assists such difficulties, a device [...]. Of this kind are those in which the less master the greater, and things possessing little weight move heavy weights, and all similar devices which we term mechanical problems . Pappus Alexandrinus considers mechanics as a useful and deep science and underlines the use of machines. See: Pappus Alexandrinus, Mathematical Collection , Book 8, transl. D. Jackson, The Arabic version of the mathematical collection of Pappus Alexandrinus Book VIII , Ph.D. dissertation, University of Cambridge, 1970, p. 1: The science of Mecha- nics, Hermodorus my son, in so far as it is useful in many great affairs of men, has become a worthy subject for philosophers’ interest and a worthy object of aspiration for all those concerning themselves with the mathematical sciences. This is because this science is almost the first to approach knowledge of the nature of the matter of what is in the world. For, since the stability and decay of bodies together with their movements, fall into the category of universals, this science establishes with reasons such of them as are in their natural state, and compels some of them to move from the natural places peculiar to them, imparting to them movements contrary to their own by means of the devices which lie within its scope, and which are reached through ideas derived from matter itself. 50 Danilo Capecchi these arguments were referred to as Mechanics (from Aristotle, Heron 1, Pap- pus 2 to Galileo). None of the treatises entitled Mechanics avoided theoretical considerations on its object, particularly on the law of lever. Indeed certain treatises reduced their role to proving this law; to mention but The book on the balance by Euclid 3 or On the equilibrium of planes by Archimedes 4. It is an axiom of modern historiography that, since its origins, mechanics has followed two routes, Aristotelian and Archimedean 5. The Aristotelian route is associated with Mechanical problems by Aristotle 6. Its principles, particularly the law of lever, are proved dynamically , as a balance of tendencies of weights suspended from the arms of a lever or a balance going downwards. The level of formalization and rigor varies from author to author. The Archimedean route is associated with On the equilibrium of planes (and, to a lesser extent, with the The book on the balance ) and dynamics is, instead, reduced to a minimum. Weights are considered as plane figures (geometrical instead of physical entities) with the main concern being the evaluation of center of gravity; and more attention is given to rigorous proof than to physical aspects 7. Recent studies by Jaouiche and Knorr 8 suggest a different interpretation. According to these authors, while it is certain that there are two different approaches in mechanics, the assumption that one is derived from Aristotle’s 1 See Heron, Mechanics , Arabic text and French transl. Carrà de Vaux, Les mécaniques ou l’élévateur de Héron d’Alexandrie in: Journal Asiatique series IX, 1, 1893, pp. 386–472 and Heron, Mechanics , transl. by J. Miller, web edition, http://archimedes.mpiwg-berlin.mpg.de/cgi.bin/toc/toc.cgi 1999. 2 See Pappus Alessandrinus (4th AD), whose elements of mechanics are contained in book 8 of the Mathe- matical Collections . Two versions of the Mathematical Collections survived, one in Greek – Mathematica collectiones a Federico Commandino urbinate in latinum conversae , Pisauri, apud Hieronimum concordiam, 1588 – , the other in Arabic – D. Jackson, The Arabic version of the mathematical collection of Pappus Alexan- drinus Book VIII . Arabic version is more complete than the Greek one and probably more close to the original. Greek version contains fragments of Heron’s Mechanics . 3 The attribution of this book to Euclid is controversial. It is known only in the Arabic language and has been made available just recently by F. Woepcke, Journal asiatique , series IV, 18, 1851, pp. 217–232. 4 See Archimedes, On the equilibrium of planes in: The works of Archimedes , (ed.) T. L. Heath, Dover, New York 2002, pp. 189–220, Archimedis, Opera Omnia cum commentari Eutocii , (ed.) J. L. Heiberg, vol. 2, Leipzig, Teubner 1881. 5 See M. Clagett, The science of mechanics in the Middle Ages , University of Wisconsin Press, Madison 1959, chap. 1, G. Galilei, Le Mecaniche , (ed.) R. Gatto, Olschki, Firenze 2002, p. IX. 6 During the Middle Ages and Renaissance the attribution of the Mechanical problems to Aristotle was substantially undisputed. For the attributions in more recent periods see Aristotle, Problemi Meccanici , (ed.) M. E. Bottecchia Dehò, Rubbettino, Catanzaro 2000. It is worth mentioning that F. Kraft, Dynamische und statische Betrachtungsweise in der antiken Mechanik , Franz Steiner, Wiesbaden 1970 considers the Mechanical problems to be an early work by Aristotle, when he had not yet fully developed his physical concepts. See also P. L. Rose and S. Drake, The Pseudo–Aristotelian Questions of Mechanics in: Renaissance culture, Studies in the Renaissance 18, 1971, pp. 65–104. A recent paper by T. N. Winter, The Mechanical problems in the corpus of Aristotle , University of Nebraska, Lincoln, Digital publication 2007 considers Archytas of Tarentum as the author of Mechanical problems . 7 These aspects of the Archimedean route will be enhanced by mathematicians of the Renaissance – Com- mandino, Luca Valerio, Galilei – who consider theoretical mechanics to be pure geometry. 8 See K. Jaouiche, Le livre du Qarastun de Thabit Ibn Qurra , E. J. Brill, Leiden 1976, pp. 42–63, W. R. Knorr, Ancient sources of the medieval tradition of mechanics: Greek, Arabic and Latin studies of the balance. Istituto e museo di storia della scienza, Firenze 1982, pp. 107–117. Weight as Active or Passive Principle in The Latin and Arabic ... 51 writing and the other from Archimedes’s, is yet to be proved. For example, Knorr observes that the principles of the so–called Aristotelian mechanics express but a diffuse knowledge which is not unique to Aristotle 1. This holds true, for example, for the law of violent motion according to which a displace- ment of a body is proportional to the force applied. This law is formulated by Aristotle in his On the Heaven and Physics 2, but it is not difficult to accept that he simply formalized what was but a diffuse kind of knowledge. According to Knorr, most of the so–called Aristotelian mechanics could be found in Archimedes’ work also 3. Archimedean mechanics would represent simply the more formalized approach adopted by a mature Archimedes, avoiding, in the proofs, physical concepts like force, for example, whose meaning is difficult to grasp with certainty. Indeed there is a general change in attitude among historians of ancient science, especially those educated in mathematics and physics. They now tend to believe that the development of mathematics and mechanics was independent of the development of philosophy, and that these, at best, influenced each other. Therefore, the labels Aristotelian , Platonic , etc. probably used to be less important to ancient scientists than usually supposed 4. The theses by Jaouiche and Knorr would explain why, in nearly all the medieval technical writings on mechanics, both Latin and Arabic, there is no explicit reference to the name or to the works of Aristotle. Not even in the historical periods when theoretical works, Physics and On the Heaven , were widely circulated. This holds true also for those medieval mathematicians who were familiar with Aristotle’s philosophical works, Bradwardwine among them. They seem to be moving on two levels. On the one hand, the mathema- tician, working on a technical text and organizing more geometrico ; on the other hand, the philosopher working on a philosophical text, involving more or less the same arguments. In the article, for simplicity and in keeping with tradition, I will continue to use the labels Aristotelian and Archimedean ; the former when the principles are proved per causas , where weight is treated as a motive power (active principle) or a resisting effect (passive principle) and the concept of center of gravity is not relevant; the latter when the centre of gravity and the rules of their evaluation are dominant concepts.
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