the In-(tnd-circumscribcd Polygon. 



345 



considered as touching in the circular points at infinity j and 

 consequently, when the concentric circles are replaced by two 

 conies having- double contact, the circular points at infinity are 

 replaced by the points of contact of the two conies. 



Thus, in the figure (which is simply Sir W. R. Hamilton's 



figure 81 put into perspective), the system of relations 



F, G( .. )ABCI 

 G,II(-)BCDK 

 H,I(..)CDEF 

 I, K(..)DEAG 

 K,F(-)5^ABH 



will mean, F, G( •• )ABCI, that there is a conic inscribed in the 

 quadrilateral ABCI such that the tangents to this conic through 

 the points F and G ])ass two and two through the points of con- 

 tact of the circumscribed and the inscribed conies, and simi- 

 larly for the other relations of the system. As the figure is 

 drawn, the tangents in question are of course (as the tangents 

 through the foci in the case of the two concentric circles) ima- 

 ginary. 



2 Stone Buildings, 

 March 7. l.'<54. 



