PRELUDE TO THE EPOCH OF GALILEO. 313 



chanics, any more than the notions of square and round make a Geom- 

 etry, or the notions of months and years make an Astronomy. The 

 unfolding these Notions into distinct Ideas, on which can be founded 

 principles and reasonings, is further requisite, in order to produce a 

 science ; and, with respect to the doctrines of Motion, this was long in 

 coming to pass; men's thoughts remained long entangled in their 

 primitive and unscientific confusion. 



We may mention one or two features of this confusion, such as we 

 find in authors belonging to the period now under review. 



We have already, in speaking of the Greek School Philosophy, no- 

 ticed the attempt to explain some of the differences among Motions, 

 by classifying them into Natural Motions and Violent Motions ; and 

 we have spoken of the assertion that heavy bodies fall quicker in pro- 

 portion to their greater weight. These doctrines were still retained : 

 vet the views which they implied were essentially erroneous and un- 

 sound; for they did not refer distinctly to a measurable Force as the 

 cause of all motion or change of motion ; and they confounded the 

 causes which produce, and those which Reserve, motion. Hence such 

 principles did not lead immediately to any advance of knowledge, 

 though efforts were made to apply them, in the cases both of terrestrial 

 Mechanics and of the motions of the heavenly bodies. 



The effect of the Inclined Plane was one of the first, as it was one 

 nf the most important, propositions, on which modern writers employed 

 themselves. It was found that a body, when supported on a sloping 

 surface, might be sustained or raised by a force or exertion which 

 would not have been able to sustain or raise it without such support. 

 And hence, The Inclined Plane was placed in the list of Mechanical 

 Powers, or simple machines by which the efficacy of forces is increased : 

 ili • question was, in what proportion this increase of efficiency takes 

 place. It is easily seen that the force requisite to sustain a body is 

 smaller, as the slope on which it rests is smaller ; Cardan (whose work, 

 De Proportionibus Numerorum, Motuum, Ponderum, &c, was pub- 

 lished in 1545) asserts that the force is double when the angle of 

 inclination is double, and so on for other proportions : this is probably 

 a guess, and is an erroneous one. Guido Ubaldi, of Marchmont, pub- 

 lished at Pesaro, in 1577, a work which he called Mechanicorum 

 Liber, in which he endeavors to prove that an acute wedge will pro- 

 duce a greater mechanical effect than an obtuse one, without deter- 

 mining in what proportion. There is, he observes, " a certain repug- 

 nance" between the direction in which the side of the wedge tends to 



