14 SIR J. COCKLE ON MATHEMATICAL HISTORY. 



" matter of obvious and universal experience/' says : — 

 " This general fact is obvious, when we possess in our minds 

 the ideas which are requisite to apprehend it clearly. 

 When we are so prepared, the truth appears to be manifest 

 independent of experience, and is seen to be a rule to which 

 experience must conform.''^ 



He seems {ib. ii, 25) to reiterate this opinion, which, 

 if '' ajDpears to be manifest " be taken to mean " is self- 

 evident,'' will hardly pass unquestioned. 



12. Lagrange (Mec. An. i. 4, 5) tells us, in words 

 which I translate as follows, to " imagine a triangular plane 

 loaded with two equal weights at the two ends of its base, 

 and with a double weight at its vertex. This plane will 

 evidently be in equilibrium when supported by a straight 

 line or fixed axis which passes through the middle of the 

 two sides of the triangle ; for we may regard each of these 

 sides as a lever loaded at its two ends with two equal weights, 

 and which has its fulcrum on the axis which passes through 

 its middle. Now we may contemplate this equilibrium 

 in another manner, by regarding the base itself of the 

 triangle as a lever of which the ends are loaded with two 

 equal weights — and by imagining that there is a trans- 

 verse lever which joins the vertex of the triangle and the 

 middle of its base in the form of a T, and of which 

 one end is loaded with the double weight placed at the 

 vertex, and the other serves as the fulcrum of the lever 

 Avhich forms the base. It is evident that this last lever 

 will be in equilibrium on the transverse lever which sus- 

 tains it at its middle, and that the transverse lever will 

 consequently be in equilibrium on the axis on which the 

 plane is already in equilibrium. But since the axis passes 

 through the middle of the two sides of the triangle, it will 

 necessarily pass also through the middle of the straight line 



