206 Prof. Gauss on the Representation of the Parts 

 Table F. (continued.) 



Reduction of Decimetres, Centimetres, and Millimetres, to 



English Inches. 



XXXV. General Solution of the Problem : to represent the 

 Parts of a given Surface on another given Surface, so that the 

 smallest Parts of the Representation shall be similar to the cor- 

 responding Parts of the Surface represented. By C. F. Gauss. 

 Answer to the Prize Question proposed by the Royal Society 

 of Sciences at Copenhagen. 



[Concluded from p. 113.] 



12. AS a fourth example, we will consider the represen- 

 •*•"■ tation of the surface of an ellipsoid of revolution in 

 a plane. Let a and b be the two principal semiaxes of the el- 

 lipsoid, so that we may put x — a cos / sin u, y=a sin / sin u, 

 z —b cos u. We shall then have 



& = a 2 sin u* dt 2 + (a 2 cos u 2 -\- b 2 sin «*) d u 2 

 and the differential formula w = gives, if we put for brevity 



*/(l ^\ = s (b being supposed <a), 



= dt + idu >v/(cotang w 2 +l— e 2 ). 



Putting 



