90 Proceedings of the Royal Society of Edinburgh. [Sess. 
Cramer in his Courbes algebriqnes expressly quotes the Geometria Organica 
as his authority. 
For the sake of brevity I have, in what follows, restricted my attention 
to what would seem of modern interest, and have on this account omitted 
entirely the discussion of asymptotes to curves and the exhaustive 
enumeration of cubic curves as based on Newton’s work. The nomenclature 
is also modern, save where the curves were already familiar to mathema- 
ticians in Maclaurin’s day. Maclaurin rarely attempts to give names 
to the hosts of new curves generated by his methods. A remarkable 
feature of interest lies in the fact that many of the methods employed only 
require an obvious generalisation to furnish standard methods of generating 
unicursal cubics and quartics supposed to have been invented during the 
latter half of the nineteenth century. It will be my special object to indicate 
these at the proper time and place. In order to emphasise Maclaurin’s own 
work I have followed the order of his Propositions, and the numbers 
attached to these are taken from the Geometria Organica. 
It has been found necessary, however, to use a more convenient notation 
for the figures. 
o 
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