44 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



2.295 Intrinsic Equation of a plane curve. An intrinsic equation of a plane 

 curve is one giving the radius of curvature, p, as a function of the arc, s, 



If T is the angle between the #-axis and the positive tangent (2.271) : 

 ds 



dT= ) 



/ s ds 

 .A3 



x = 







cos T-ds 

 sin T'ds. 



2.300 The general equation of the second degree: 



A = flu 0i 2 013 



021 022 023 

 031 032 033 



A ^ = Minor of hk- 

 Criterion giving the nature of the curve: 



= O 



(Pascal: Repertorium der hoheren Mathematik, II, i, p. 228) 



