PHYSICS
52
PHYSICS
The conditions manifested in this hypothetic mill-
stone are realized in the celestial orbs, as in these
neither friction nor gravity impedes motion; hence
it may be admitted that each celestial orb moves in-
definitely by v-irtue of a suitable impetus communi-
cated to it by God at the moment of creation. It is
useless to imitate Aristotle and his commentators by
attributing the motion of each orb to a presiding spirit.
This was the opinion proposed bj- Buridan and adopted
by Albert of Saxony; and whilst formulating a doctrine
from which modern dynamics was to spring, these
masters understood that the same dynamics governs
both celestial and sublunary bodies. Such an idea
was directly opposed to the essential distinction estab-
lished by ancient physics between these two kinds of
bodies. Moreover, following William of Occam, the
masters of Paris rejected this distinction; they ac-
knowledged that the matter constituting celestial
bodies was of the same nature as that constituting
sublunary bodies and that, if the former remained
perpetually the same, it was not because they were, by
nature, incapable of change and destruction, but sim-
ply because the place in which they were contained
no agent capable of corrupting them. A century
elapsed between the condemnations pronounced by
Etienne Tempier (1277) and the editing of the
"Traite du Ciel et du Monde" by Oresme (1377) and,
within that time, all the essential principles of Aris-
totle's physics were undermined, and the great con-
trolling ideas of modern science formulated. This
revolution was mainly the work of Oxford Franciscans
hke Richard of JSIiddletown, Duns Scotus, and Wil-
liam of Occam, and of m.isters in the School of Paris,
heirs to the tradition inaugurated by these Francis-
cans; among the Parisian masters Buridan, Albert of
Saxony, and Oresme were in the foremost rank.
X. Prop.\g.\tion of the Doctrines of the School of P.\ris in Germ.wy .\nd It.\ly — Purbach
AND REGIOMONTANr.S — NICHOLAS OF CuS.\ — ViNCI. —
The great \\'estern Schism in\-olved the University of Paris in politico-religious quarrels of extreme violence; the misfortunes brought about by the conflict between the Armagnacs and Burgundians and by the Hundred Years' War, completed what these quarrels had begun, and the wonderful progress made by science during the fourteenth century in the University of Paris sud- denly ceased. However, the schism contributed to the diffusion of Parisian doctrines by driving out of Paris a large number of brilliant men who had taught there with marked success. In 1386 Marsile of Inghem (d. 1396), who had been one of the most gifted pro- fessorsof theUniversity of Paris,became rectorof the in- fant University of Heidelberg, where he introduced the dynamic theories of Buridan and Albert of Saxony.
About the same time, another master, reputedly of Paris, Heinrich Heimbuch of Langenstein, or of Hesse, was chiefly instrumental in founding the Uni\-ersity of Vienna and, besides his theological knowledge, brought thither the astronomical tradition of Jean des Linieres and John of Saxony. This tradition was carefully preserved in Vienna, being magnificently developed there throughout the fifteenth century, and paving the way for Gcorg Purbach (1423-61) and his disciple Johann Miillcr of Konig.-iberg, surnamed Regiomon- tanus (1436-76). It was to the writing of theories calculated to make the Ptolemaic sj'stem known, to the designing and constructing of exact instruments, to the multiplying of observations, and the preparing of tables and almanacs (ephemerides), more accurate than those used by astronomers up to that time, that Purbach and Regiomontanus devoted their prodig- ious energy. By perfecting all the details of Ptolemy's theories, which they never called in question, they were most helpful in bringing to light the defects of these theories and in preparing the materials by means of which Copernicus was to build up his new astron- omy.
Averroism flourished in the Italian Universities of
Padua and Bologna, which were noted for their ad-
herence to Peripatetic doctrines. Still from the be-
ginning of the fifteenth century the opinions of the
School of Paris began to find their way into these insti-
tutions, thanks to the teaching of Paolo Nicoletti of
Venice (flourished about 1420). It was there de-
veloped by his pupil Gaetan of Tiene (d. 1465).
These masters devoted special attention to propaga-
ting the dynamics of impetus in Italy.
About the time that Paola of Venice was teaching at Padua, Nicholas of Cusa came there to take his doctorate in law. Whether it was then that the latter became initiated in the physics of the School of Paris matters little, as in any event it was from Pari- sian physics that he adopted those doctrines that smacked least of Peripateticism. He became thor- oughly conversant with the dynamics of impetus and, like Buridan and Albert of Saxony, attributed the motion of the celestial spheres to the impetus which God had communicated to them in creating them, and which was perpetuated because, in these spheres, there was no element of destruction. He admitted that the Earth moved incessantly, and that its motion might be the cause of the precession of the equinoxes. In a note discovered long after his death, he went so far as to attribute to the Earth a daily rotation. He imag- ined that the sun, the moon, and the planets were so many systems, each of which contained an earth and elements analogous to our Earth and elements, and to account for the action of gravity in each of these sys- tems he followed closely the theory of gra\'ity ad- vanced by Oresme.
Leonardo da Vinci (1452-1519) was perhaps more thoroughly convinced of the merits of the Parisian physics than any other Italian master. A keen ob- server, and endowed with insatiable curiosity, he had studied a great number of works, amongst which we may mention the various treatises of the School of Jordanus, various books by Albert of Saxony, and in all likelihood the works of Nicholas of Cusa; then, profiting by the learning of these scholars, he formally enunciated or else simply intimated many new ideas. The statics of the School of Jordanus led him to dis- cover the law of the composition of concuiTent forces stated as follows: the two component forces have equal moments as regards the direction of the resultant, and the resultant and one of the components have equal moments as regards the direction of the other com- ponent. The statics derived from the properties which Albert of Saxony attributed to the centre of gra\'ity caused Vinci to recognize the law of the polygon of support and to determine the centre of gravity of a tetrahedron. He also presented the law of the equi- librium of two liquids of different density in commu- nicating tubes, and the principle of virtual displace- ments seems to have occasioned his acknowledgement of the hydrostatic law known as Pascal's. Vinci con- tinued to meditate on the properties of impetus, which he called impeto or forza, and the propositions that he formulated on the subject of this power very often showed a fairly clear discernment of the law of the con- servation of energy. These propositions conducted him to remarkably correct and accurate conclusions concerning (he impossibility of perpetual motion. Un- fortunately he misunderstood the pregnant explana- tion, afforded by the theory of impetus, regarding the acceleration of falling bodies, and like the Peri- patetics attributed this acceleration to the impulsion of the encompassing air. However, by way of com- pensation, he distinctly asserted that (he velocity of a body (hat falls freely is proportional to the time occu- pied in the fall, and he understood in what way this law extends to a fall on an inclined plane. When he wished to determine how the path traversed by a fall- ing body is connected with the time occupied in the fall, he was confronted by a difficulty which, in the
