CONTENTS 
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ion to a curve 
urve 
r 
rrves 
hindex . 
mvers 
SYSTEMS 
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CHAPTER V 
NON-LINEAR SYSTEMS OE CURVES 
§ 1. General formulation 
General expression for a non-linear system .... 
Invariant numbers ........ 
Curves cut from a surface ....... 
§ 2. Singular points and the envelope 
Various arrangements of singular points ..... 
Analytic expression for the envelope ..... 
Determination of order of envelope . . 
§ 3. The inflexions 
Determination of the order of the curve of inflexions . 
§ 4. Projective theorems 
Properties of the index ........ 
Number of curves tangent to a given curve .... 
§ 5. Systems depending on more than one parameter 
Invariants for a two-parameter system ..... 
Number of curves in a two-parameter system which osculate a given 
curve .......... 
Number of curves in a /^-parameter system which touch k curves 
CHAPTER VI 
THE GENERAL CREMONA TRANSFORMATION 
§ 1. Fundamental properties 
Definitions and general principles ..... 
Fundamental points and fundamental curves 
§ 2. Nother’s factorization theorem 
Factorization of the general Cremona transformation 
Genesis of the fundamental curves ..... 
§ 3. Applications of the factorization theorem 
Fundamental points and curves, factors of the Jacobian 
Montesano’s theorem ....... 
§ 4. The identities of Clehsch 
Distribution of the fundamental points .... 
Coordinated groups of fundamental points 
Properties of unsymmetric transformations 
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