The Liber de motu of Gerard of Brussels and the Origins of Kinematics in the West

but not applied to falling bodies) is found among the Oxford logicians of the first half of the fourteenth century: WILLIAM HEYTESBURY, RICHARD SWINESHEAD, and JOHN DUMBLETON. Furthermore, their description takes into account infinitesimal considerations and includes an interesting concept of instantaneous velocity, a sine qua non for any correct description of acceleration. It is rather interesting that both conclusions seem to be held simultaneously by some authors without realization of a contradiction (i.e., the velocity is both directly proportional to the time and distance of fall). In fact GALILEO at one time believed that he could deduce the conclusion that distance is directly proportional to the square of the time, from the " principle " that velocity of fall is directly proportional to the distance (which of course he could not). At any rate, one must realize that problem of the kinematic description of free fall has a much longer history than is customarily realized. LIBER DE MOTU OF GERARD OF BRUSSELS 95 fact weighing against such a translation is the absence of any extant manuscripts. Furthermore, the standard medieval library catalogues have no reference to such a translation. On the other hand, as HASKINS points out (i8), the celebrated emperor FREDERICH II in his De arte venandi cum avibus makes what appears to be a clear cut reference to the work, citing its author as ARISTOTLE and its title as Liber de ingeniis levandi pondera. The quotation given by FREDERICH clearly expresses a main cotention of the Mechanical Problems, " a larger circle is more effective in lifting a weight " (i9). Furthermore it is quite possible that the author of the celebrated thirteenth century statical treatise Liber de ratione ponderis had access to certain of the problems in the Mechanical Problems and had therefrom derived some of his propositions (20). However, I know of no other citation or use of the Mechanical Problems in the thirteenth or fourteenth century. In the early fifteenth century the Mechanical Problems appears to have been rendered from Greek. At least a license for the export of books from Bologna dated i8 August 1413 includes the title: Reportorium super mechanica Aristotelis (2I). The fact that a reportorium has been composed suggests certainly that the translation was made a long enough time before for it to have circulated, unless the Reportorium was prepared directly from the Greek text. Of course, it is by no means impossible that the earlier translation known to FREDERICH still survived in Italy, in spite of the apparent differences of title. Chapter One of the Mechanical Problems is a strange eulogy to the circle and circular movement. After his praise of the circle the Peripatetic mechanician takes up the case of the rotating radius, of which he notes that none of the points is moved equally fast as (I8) C. H. HASKINS, Studies in Medieval Science, Cambridge, 2nd Edit., 1927, pp. 3I6-17. (i9) Ibid., loc. cit. Cf. De arte venandi cum avibus, MS Vat. Pal. lat. 1071, I3C, ff. 23v-24r: " Portiones circuli quas faciunt singule penne sunt de circumferentiis equidistantibus, et illa que facit portionem maioris ambitus et magis distat a corpore avis iuvat magis sublevari aut impelli et deportari, quod dicit Aristoteles in libro de ingeniis levandi pondera dicens quod magis facit levari pondus maior circulus." (2o) E. MOODY and M. CLAGETT, Medieval Science of Weights, Madison, Wisconsin, 1952, PP. 205-2zi, and the discussions of Propositions R3.02, R3.o3,