436 
EUCLID 
laquelle on demande de démontrer qu’une chose ou plusieurs 
choses sont données, qui, ainsi que l’une quelconque d’une 
infinité d’autres choses non données, mais dont chacune est 
avec des choses données dans une même relation, ont une 
propriété commune, décrite dans la proposition,’ We need 
not follow Simson’s English or Scottish successors, Lawson 
(1777), Playfair (1794), W. Wallace (1798), Lord Brougham 
(1798), in their further speculations, nor the controversies 
between the Frenchmen, A. J. H. Vincent and P. Breton (de 
Champ), nor the latter’s claim to priority as against Chasles ; 
the work of Chasles himself (Les trois livres des Pariâmes 
d’Euclide rétablis . . . Paris, 1860) alone needs to be men 
tioned. Chasles adopted the definition of a porism given by 
Simson, but showed how it could be expressed in a different 
form. ‘ Porisms are incomplete theorems which express 
certain relations existing between things variable in accord 
ance with a common law, relations which are indicated in 
the enunciation of the porism, but which need to be completed 
by determining the magnitude or position of certain things 
which are the consequences of the hypotheses and which 
would be determined in the enunciation of a theorem properly 
so called or a complete theorem.’ Chasles succeeded in eluci 
dating the connexion between a porism and a locus as de 
scribed by Pappus, though he gave an inexact translation of 
the actual words of Pappus : ‘ Ce qui constitue le porisme est 
ce qui manque à l’hypothèse d’un théorème local (en d’autres 
termes, le porisme est inférieur, par l’hypothèse, au théorème 
local ; c’est à dire que quand quelques parties d’une proposi 
tion locale n’ont pas dans l’énoncé la détermination qui leur 
est propre, cette proposition cesse d’être regardée comme un 
théorème et devient un porisme) ’ ; here the words italicized 
are not quite what Pappus said, viz. that ‘a porism is that 
which falls short of a locus-theorem in respect of its hypo 
thesis ’, but the explanation in brackets is correct enough if 
we substitute £ in respect of ’ for £ par 5 ( £ by ’). The work of 
Chasles is historically important because it was in the course 
of his researches on this subject that he was led to the idea of 
anharmonic ratios ; and he was probably right in thinking 
that the Porisms were propositions belonging to the modern 
theory of transversals and to projective geometry. But, as a