45 ^ Mr. T. Muir on the first Extension of the term Area, 



Lastly, we have 



Descriptio figurarum per motum rectce quemcunque. 



This, though more interesting and requiring more elucida- 

 tion than the others, is treated very briefly. The motion con- 

 sidered is that compounded of the motions of the two prece- 

 ding sections. The describing line is now subject simultaneously 

 to translation and rotation ; that is, it rotates round a variable 

 centre. In certain of the cases as many as three circuits must 

 be attended to, the third (not hitherto mentioned) being the 

 locus of the centre of rotation. As an instance of this the 

 author's thirteenth figure is given (see fig. 3). 



Fig- 3. 



The remainder of the paper, comprising seven sections, does 

 not treat de genesi figurarum, and need not, therefore, be referred 

 to unless in the most cursory manner. It may be said to deal 

 in the first place with cognate subjects, e. g. the angles of 

 rectilineal figures having autotomic perimeters, multiple circles 

 (i. e. circles of N x 360 degrees) and the figures inscribed in 

 them, stellate regular polygons (i. e. regular polygons with auto- 

 tomic perimeters), and in the second place with applications 

 of the new ideas to the extension of known geometrical theorems. 



