DISCOVERY OF THE LAWS OF MOTION. 335 



happen, the thing thrown must have a certain proportion to the agent 

 which throws it ? Is it that what is thrown or pushed must react 13 

 against that which pushes it ; and that a body so large as not to yield 

 at all, or so small as to yield entirely, and not to react, produces no 

 throw or push ?" The same confusion of ideas prevailed after his 

 time ; and mechanical questions were in vain discussed by means of 

 general and abstract terms, employed with no distinct and steady 

 meaning ; such as impetus, power, momentum, virtue, energy, and the 

 like. From some of these speculations we may judge how thorough 

 the confusion in men's heads had become. Cardan perplexes himselt 

 with, the difficulty, already mentioned, of the comparison of the forces 

 of bodies at rest and in motion. If the Force of a body depends on 

 its velocity, as it appears to do, how is it that a body at rest has any 

 Force at all, and how can it resist the slightest effort, or exert any 

 pressure ? He flatters himself that he solves the question, by asserting 

 that bodies at rest have an occult motion. " Corpus movetur occulto 

 motu quiescendo." Another puzzle, with which he appears to distress 

 himself rather more wantonly, is this: "If one man can draw half 

 of a certain weight, and another man also one half; when the two 

 act together, these proportions should be compounded ; so that they 

 ought to be able to draw one half of one half, or one quarter only." 

 The talent which ingenious men had for getting into such perplexities, 

 was certainly at one time very great. Arriaga, 14 who wrote in 1639, 

 is troubled to discover how several flat weights, lying one upon another 

 on a board, should produce a greater pressure than the lowest one 

 alone produces, since that alone touches the board. Among other 

 solutions, he suggests that the board affects the upper weight, which it 

 does not touch, by determining its ubication, or whereness. 



Aristotle's doctrine, that a body ten times as heavy as another, will 

 fall ten times as fast, is another instance of the confusion of Statical 

 and Dynamical Forces : the Force of the greater body, while at rest, 

 is ten times as great as that of the other ; but the Force as measured 

 by the velocity produced, is equal in the two cases. The two bodies 

 would fall downwards with the same rapidity, except so far as they 

 are affected by accidental causes. The merit of proving this by ex- 

 periment, and thus refuting the Aristotelian dogma, is usually ascribed 

 to Galileo, who made his experiment from the famous leaning tower 

 of Pisa, about 1590. But others about the same time had not over- 



13 Avrcftlltiv. l * Eod. de Arriaga, Cursus Phllosophicus. Paris, 1639. 



