The Science of Mechanics in the Middle Agesby Marshall Clagett

The Science of Mechanics in the Middle Ages by Marshall ClagettReview by: Curtis WilsonIsis, Vol. 51, No. 2 (Jun., 1960), pp. 234-237Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/226874 .

Accessed: 15/06/2014 19:58

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize,preserve and extend access to Isis.

http://www.jstor.org

This content downloaded from 185.2.32.96 on Sun, 15 Jun 2014 19:58:30 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=ucpress

http://www.jstor.org/action/showPublisher?publisherCode=hss

http://www.jstor.org/stable/226874?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


234 BOOK REVIEWS

Stoics discarded the notion of surface, and conceived of an infinite sequence of boundaries defining a figure. Time was the "measure of swiftness and slowness" and consequently related to particulars and flux.

Translations of the most important passages used are included at the end of the book.

Sambursky has treated Stoicism as one school, and has made no attempt to separate the opinions of the various philosophers. This, I believe, is a funda- mental weakness of the book. Radical changes in Stoic physics are evident. Chrysippus, we know, differed from Cleanthes in his treatment of presentation (p. 25) and of the lemma of Dio- genes (p. 78). And Posidonius' work is by no means orthodox (pp. 28 and 42).

Sambursky pays too much attention to parallels between the Stoics and the Presocratics. The antecedents of Stoi- cism are to be found in the maze of opinions that belong to the Post-Aristo- telian period and particularly to the Me- garians. I take exception to the importance which he attaches to Diogenes of Apollonia, a Presocratic philosopher who lived in the last half of the 5th century B.C. In discussing the Stoic theory of sense perception (p. 25), Sambursky refers to the fact that presentation for Cleanthes was an impression (typosis) on the soul but that for Chrysippus it was a modification (heteroiosis). The parallel for this passage is surely Plato's Theaetetus (191 D ff.), not Diogenes.

There appears to be important bibli- ography with which Sambursky is not familiar. For instance, on page two he finds parallels between the Stoic pneuma and Alcmaeon and the Hippocratic corpus, but fails to mention its connec- tion with the pneuma described in the writings of Diocles of Carvstus, a Sici- lian physician who was a younger con- temporary of Aristotle. The problem has been discussed by W. Jaeger in Diokles von Karystos (Berlin, 1938), pp. 216-8, and by F. Solmsen, "The Vital Heat, the Inborn Pneuma and the Aether," The Journal of Hellenic Studies, 1957, 77: 119-123.

It is unfortunate that Sambursky did not equate his references with the frag-

ments of the Stoics in von Arnim's Stoi- corurm veterum fragmenta (Leipzig, 1921). Most of his readers would have found this edition easily accessible and a miore convenient way of studying the passages cited. Perhaps also a chronol- ogy of the Stoic philosophers and late sources would have been useful.

The weaknesses in Sambursky's book are due to the fact that scholarship has barely touched the surface of Stoic phil- osophy. Much work needs to be done before the contributions of individual Stoics can be assessed and the philos- ophy of the different schools recon- structed. Sambursky's book is an important step in such a reconstruction.

MARGARET E. REESOR

University of North Carolina * * *

MARSHALL CLAGETT: The Science of Mechanics in the Middle Ages. xxix + 711 pp., figs., plates, bibl. Madison: The University of Wisconsin Press, 1959. $8.00.

Serious and scholarly study of the history of mechanics in the Middle Ages began, little more than a half century ago, with the monumental investigations of Pierre Duhem (Les Origines de la statique, 1905-6; J:tudes sur Leonard de Vinci, 1906-13; Le Systeme du monde, 1913-16, 1954-57). Duhem's extensive research into manuscript and early printed sources provided a starting-point and reference for all subsequent work in this field. More recent scholars-Anne- liese Maier, Alexander Koyre, Ernest Moody, Marshall Clagett, and others- have extended Duhem's findings, cor- rected errors in detail, and modified his occasionally extravagant claims for the modernity of medieval theories. A ma- ture analysis and evaluation of the medieval writings on mechanics has now become possible. This task is carried out for the first time in English, and mag- nificently, in the present volume by Clagett.

Lucid organization and thorough in- dexing make the book eminently useable. It is divided into four main parts, of which the first three deal respectively with statics, kinematics, and dynamics, and the last is a summary, outlining the scope of medieval mechanics and its fate



BOOK REVIEWS 235

as it was transmitted into early modern times. Each of the chapters in the first three parts is accompanied by extensive excerpts from the relevant medieval or early modern documents in English translation (more than 200 pages worth all told); in cases in which the manuscript sources are rare and inaccessible, the original Latin text is also included. Each document presented is followed by detailed commentary.

The story which emerges from this combination of source book, analytical commentary, and evaluation, is complex, an interlacing of continuity and novelty. The development of modern mechanics in the seventeenth century can no longer be regarded as a creatio ex nihilo. Nor can the medieval innovations in mechanics be regarded simply as anticipating the work of Galileo and Newton. In Clagett's words (p. xix), "anyone who is honestly interested in the enormously complex historical process of the forma- tion of modern science must examine in detail the germinal concepts of the pre- ceding periods. Such an examination will reveal the elements of continuitv (and thereby also of novelty) in the new science. This examination will give some insight into how a protoscientific theory was criticized and emended uitil it was no longer a cogent whole. It will also show how the very points of criticism of the older system became points of de- parture for the new. It will show, in short, how medieval mechanics-largely Aristotelian with some traces of Archi- medean character - was continually modified to the point where it was seri- ously undermined, thus requiring a new mnechanical system-and it was the Gali- lean-Newtonian system of the seventeenth century that fulfilled that require- ment."

The first section of Clagett's book sur- veys in detail the medieval tradition in statics, its Greek and Arabic antecedents and its early modern continuation. Edi- tions and translations of many of the documents relevant to this account were previously published by Moody and Clagett in their volume entitled The Medieval Science of Weights. In the present work, however, Clagett presents and analyzes ten documents not covered

in the earlier volume; and the two intro- ductory chapters, together with the com- mentaries, provide a connected history of statics down to the time of Galileo.

The medieval work in statics, as Cla- gett shows, combined two traditions: the idealized, axiomatic, and purely static manner of treatment stemming from Archimedes, and a dynamic approach stemming from Aristotle. The dynamic approach to static equilibrium, deriving from the Aristotelian tradition and in particular from the Mechanica attributed to Aristotle, led to two major medieval innovations: (1) the use of the concept of "positional gravity" or grazitas secun- dum situm, whereby the weight of a body in a constraint system was in effect resolved into components; and (2) the use of the principle of virtual velocities as an axiom in deductive proofs of laws of equilibrium. By the use of these prin- ciples the thirteenth-century mathemati- cian Jordanus de Nemore was able, three centuries before Galileo, to arrive at a correct solution of the problem of the conditions of equilibrium of two weights on diversely inclined planes; also, he solved the problem of the conditions of equilibrium for the bent lever, thus giv- ing evidence of an understanding of the principle of static moment. Jordanus' Liber de ratione ponderis, which em- bodies these results, was printed twice during the sixteenth century; it was known to Tartaglia and to J.-B. Bene- detti, and as Clagett shows (p.159), there is a good chance that Galileo was also familiar with it. In all likelihood, the fruitful interlocking of dynamic and static considerations in Galileo's work, and his frequent use of the principle of virtual velocities, derive directly or in- directly from the medieval tradition.

Part II of Clagett's book, on kinematics, outlines and analyzes the medieval work which formed the background for the emergence of the law of free fall -Theorem I of the treatise on naturally accelerated motion in the Third Day of Galileo's Discorsi. This theorem, which states that the distance traversed in a uniformly accelerated motion starting from rest is equal to the distance traversed in a uniform motion in which the velocity is half the final velocity in the



236 BOOK REVIEWS

accelerated motion, had already been stated and proved by the schoolmen of Merton College, Oxford, in the thirties of the fourteenth century; and Clagett therefore refers to it as "the Merton theorem of uniform acceleration." The Mertonians did not apply their theorem to the case of freely falling bodies, and although such application was made by Domingo Soto in the sixteenth century, the schoolmen never made the transition from free fall to fall down inclined planes-the transition which in Galileo's work led to the possibility of empirical verification.

The development of the Merton theorem depended on the prior development of the notion of speed as a quantity or Euclidean magnitude. Aristotle had been restricted to qualitative definitions of the comparative adverbs "faster" and "slower." As Clagett stresses, the Greek (and particularly Euclidean) insistence that only magnitudes of the same kind could have a ratio to one another pre- vented the ancients and the medieval schoolmen from defining speed in the modern manner, as the number of the distance divided by the number of the time. The lack of such a metric definition of speed, in fact, is responsible for the prolixity and the logical lapses in the treatise on uniform motion which begins the Third Day of Galileo's Discorsi (the second theorem of that treatise, for instance, is a petitio principii). The medieval schoolmen, however, starting with Gerard of Brussels in the thirteenth century, took long strides toward a quanti- tative treatment of velocity. Thus Ger- ard states that two uniform velocities are to one another as the corresponding distances traversed in the same time. Moreover, the notion of the instantaneous intensity of a motion, that is, its velocity at an instant, emerged in the work of the fourteenth-century Merto- nian Thomas Bradwardine, and played a considerable role in the later medieval discussion of the "intension and remis- sion of forms," the intensity of a quality at a spatial point or instant of time being treated as a quantity. The fourteenth- century definitions of instantaneous velocity and uniform acceleration are the same as those used later by Galileo.

Clagett gives a full account of the vari-

ous fourteenth-century proofs of the Merton theorem; a further chapter deals with the introduction by Oresme and his successors of the technique of graphing the instantaneous velocity of a motion against time, whereby the proof assumes the form in which it is given by Galileo. Neither the schoolmen nor Galileo, however, approach the logical precision of Isaac Beeckman, who in 1618 realized that a correct proof requires a limiting process, that is, an integration in the sense of the integral calculus.

Part III of Clagett's study, entitled "Medieval Dynamics," deals in the main with two medieval developments: (1) the introduction by Bradwardine of a law relating the velocity of a motion to the impelling force and the resistance, as a replacement for the Aristotelian law of motion; and (2) the elaboration of the impetus theory, particularly by Buri- dan, to account causally for projectile motion and the acceleration of free fall. Aristotle had held that the velocity of a body varies directly as the impelling force and inversely as the resistance; be- cause of an internal mathematical diffi- culty in this theory, Bradwardine re- placed it by an equally erroneous theory, according to which the velocity is a loga- rithmic function of the ratio of force to resistance. Despite its mistakenness, Bradwardine's law was of importance in focussing attention on the concepts of functionality and instantaneous velocity. Buridan's impetus theory, in abandon- ing the Aristotelian explanation of pro- j ectile motion in terms of the air as mover, and introducing an internal cause for the continuation of the projectile's motion, was even more important as an intermediate stage and link between Aristotelian dynamics and the in- ertial mechanics of Galileo and Newton. Galileo's early work De Motu affirms a variant of the scholastic impetus theory; and in his later work Galileo continues to use the term "impetus," although with changed meaning-the term has come to signify an effect rather than a cause.

The last chapter of Part III deals with several miscellaneous problems of importance to mechanics in the fourteenth century, including the question of the motion of the earth and the perceptual



BOOK REVIEWS 237

relativity of motion, the notion of a closed mechanical system, and the possibility of a plurality of worlds as it con- nects with the discussion of centers of gravity. Part IV then describes in detail the spread of the fourteenth-century Mertonian kinematics and Parisian dynamics through Europe during the suc- ceeding centuries up to 1600, and con- cludes with a summary of the medieval achievements.

The Science of Mechanics in the Mid- dle Ages is a long and complex work, based on the most painstaking scholarship. Without doubt, Clagett has here provided the standard documentary studv and reference work on the medieval mechanical doctrines.

CURTIS WILSON St. John's College, Annapolis, Maryland

A. M. GOICHON: Le Recit de Havv ibn Yaqzdn commente' par des textes d'A7ni- cenne. Avant-propos, traductions, expli- cations et notes. 254pp. Paris: Desclee de Brouwer, 1959.

Verdaderamente el tema de Avicena es central en la filosofia 'arabe y aun diriamos que en la filosofia medieval. En los u'ltimos anios, sobre todo en ocasion de las fiestas del milenario de Avicena, se han remozado notablemente los estu- dios avicenianos. En particular, es un deber notar la nueva edicion y traduc- cion por Mr. H. Corbin de uno de los Tratados misticos de Avicena: el Recit de Hayy ibn Yaqzan, cuyo texto mejora el anterior de A. F. Mehren, pues esta organizado en capitulos, a tenor del comentario persa, inedito hasta entonces, atribuido muy verosimilmente al compa- nero y secretario de Avicena, Juzjani (cf. A7Aicenne et le Re'cit visionnaire. I. Le Re'cit de Hayy ibn Yaqadn, texte arabe, ancienne version et commentaire en persan, traduction franqaise et avant- propos. Teheran, 1952). A esta edicion hizo seguir Mr. Corbin su etude sur le cycle des Recit azicenniens y las Notes et gloses de la traduction du Re'cit de Hayy ibn Yaqzan (Teheran, 1954). Sin embargo, la posicion tipica de Mr. Cor- bin en su obra es seguir muy fielmente el citado comentario persa y pretender explicar la doctrina de nuestra obra avi-

ceniana en funcion, principalmente, de la tradicion gnostica e irania.

Dicha tendencia de la exegesis de Mr. Corbin no ha parecido normalmente ob- jectiva a una persona tan tecnica y espe- cializada en doctrina aviceniana como es Mlle A.-M. Goichon, cuyo solo nombre representa una vida de dedicacion a elu- cidar los problemas de la filosofia de Avicena. Y fruto de esta reaccion es la obra que reseinamos. En contra de la posicion de Mr. Corbin, la autora se esfuerza en comentar la doctrina del IJayy ibn Yaqzan a base de los puros textos de Avicena, en especial su Poema sobre el alma, su Epistola sobre el amor, su gran obra Sifa', especialmente la parte psicologica o Kitab al-Nafs, y tambien del Kitab al-isardt wa-l-tanbihat, tradu- cido anteriormente por la autora.

Despues del cotejo con tales fuentes, la autora cree que el relato de Hayy ibn Yaqzan no representa ni un simbolo, ni una alegoria, ni un relato batin o esote- rico, ni un arquetipo, segun las diversas hipotesis que se podrian considerar y que examina Mr. Corbin, ni tampoco el relato de una "iniciacion que no podria ser dada ni contada sino solo en sim- bolos," ni menos la propia "novela espi- ritual del autor," ni tampoco un sue-no o perspectiva de un "visionario .. . en un estado intermedio entre la vigilia y el sueno," soluciones presentadas por Mr. Corbin en Le cycle des recits avicen- niens. Para Mlle Goichon nuestro relato de Hayy ibn Yaqzan representa un resu- men de la doctrina avicenista del conoci- miento, comprendiendo sus perspectivas mas elevadas, presentadas bajo un cafna- mazo de imagenes, la mayor parte de las cuales tienen una fuente perfectamente precisa en obras filosoficas y cientificas o presumidas como tales. Mejor podria decirse que siguiendo Avicena una prac- tica eminentemente platonica, ha querido proyectar su doctrina con una serie de imagenes o metaforas que le dieran un mayor prestigio. Pero, desde luego, no hay que inscribir tal relato de Hayy ibn Yaqzan en el cuadro de una filosofia israqui "oriental," alimentada del esote- rismo gnostico, pues el mismo Sohra- wardi, tan conocido por Mr. Corbin, confiesa repetidamente que Avicena no puede inscribirse normalmente en tal



Documents

The Science of Mechanics in the Middle Agesby Marshall Clagett