649 
clear from what precedes that every point e.g. S,,, can only be 
part of one configuration, which we can easily construct, starting 
from that point. 
With a view to this we join S,, O; the intersection of this 
line with y, is 7,,; we draw s,,, the polar line of S,, with regard 
to B, which cuts y, besides in 7,, in S,,, S,, and S,,; the polar 
lines of these 3 points cut y, in the 6 other points of the configu- 
ration and 7, 7,,, 7,,. Yet each point, e.g. S,,, though belonging 
to only one configuration, is twice a base point of the pencil (3); 
for we can as well produce this pencil and also y by starting from 
a pencil (3) with the base points S,,,.S,,,.S,,,.S,, as from one with 
the base points SS. S,,, Sas 
Any point of a harmonical curve y, belongs to one configuration 
(10,,10,) of Dersarcurs; if we consider y, as given we can easily 
construct these configurations from one of their points. 
Moreover it has appeared from the way in which we produced 
y, that: 
Lf a configuration (10,,10,) of Desaraurs and a point O are 
given, we can produce a harmonical curve y, circumscribed to this 
configuration, with its node in O, while the conic of Burtini connected 
to it coincides with the come relative to which the configuration is 
self-conjugated. 
43 
Proceedings Royal Acad. Amsterdam. Vol. XXII. 
