10 HISTORY OF MECHANICS. 



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

 De Proportionibus Numerorum, Motuum, Ponde- 

 rum, &c., was published in 1545) asserts that the 

 force is double when the angle of inclination is 

 double, and so on for other proportions; this is pro- 

 bably a guess, and is an erroneous one. Guido 

 Ubaldi, of Marchmont, published at Pesaro, in 1577, 

 a work which he called Mechanicorum Liber, in 

 which he endeavours to prove that an acute wedge 

 will produce a greater mechanical effect than an 

 obtuse one, without determining in what propor- 

 tion. There is, he observes, " a certain repugnance" 

 between the direction in which the side of the 

 wedge tends to move the obstacle, and the direc- 

 tion in which it really does move. Thus the Wedge 

 and the Inclined Plane are connected in principle. 

 He also refers the Screw to the Inclined Plane 

 and the Wedge, in a manner which shows a just 

 apprehension of the question. Benedetti (1585) 

 treats the Wedge in a different manner ; not exact, 

 but still showing some powers of thought on me- 

 chanical subjects. Michael Varro, whose Tractatus 

 de Motu was published at Geneva in 1584, deduces 

 the Wedge from the composition of hypothetical 

 motions, in a way which may appear to some per- 

 sons an anticipation of the doctrine of the Com- 

 position of Forces. 



There is another work on subjects of this kind, 

 of which several editions were published in the 

 sixteenth century, and which treats this matter in 



