PRELUDE TO THE EPOCH OF GALILEO. 321 



after the moving power had ceased to act ; and that he had ascribed 

 it to the effect of the air or other medium in which the stone moves. 

 Tartalea, whose Nuova Scienza is dated 1550, though a good pure 

 mathematician, is still quite in the dark on mechanical matters. One 

 of his propositions, in the work just mentioned, is (B. i. Prop. 3), 

 " The more a heavy body recedes from the beginning, or approaches 

 the end of violent motion, the slower and more inertly it goes ;" which 

 he applies to the horizontal motion of projectiles. In like manner 

 most other writers about this period conceived that a cannon-ball 

 goes forwards till it loses all its projectile motion, and then falls down- 

 wards. Benedetti, who has already been mentioned, must be con- 

 sidered as one of the first enlightened opponents of this and other 

 Aristotelian errors or puzzles. In his Speculationum Liber (Venice. 

 1585), he opposes Aristotle's mechanical opinions, with great expres- 

 sions of respect, but in a very sweeping manner. His chapter xxiv. is 

 headed, " Whether this eminent man was right in his opinion con- 

 cerning violent and natural motion." And after stating the Aristote- 

 lian opinion just mentioned, that the body is impelled by the air, he 

 saj s that the air must impede rather than impel the body, and that 5 

 " tin; motion of the body, separated from the mover, arises by a certain 

 natural impression from the impetuosity (ex impetuositate) received 

 from the mover." He adds, that in natural motions this impetuosity 

 continually increases by the continued action of the cause, — namely, 

 the propension of going to the place assigned it by nature ; and that 

 thus the velocity increases as the body moves from the beginning of 

 its path. This statement shows a clearness of conception with regard 

 to the cause of accelerated motion, which Galileo himself was long 

 in acquiring. 



Though Benedetti was thus on the way to the First Law of Motion. 

 — that all motion is uniform and rectilinear, except so far as it is 

 affected by extraneous forces ; — this Law was not likely to be either 

 generally conceived, or satisfactorily proved, till the other Laws of 

 Motion, by which the action of Forces is regulated, had come into 

 view. Hence, though a partial apprehension of this principle had 

 preceded the discover}' of the Law r s of Motion, w r e must place the 

 establishment of the principle in the period when those Laws were 

 detected and established, the period of Galileo and his followers. 



5 P. 1S4. 

 Vol. I.— 21 



