88 
Proceedings of the Eoyal Society of Edinburgh. [Sess. 
particular curves, and the general development of the theory. Prominent 
among such works may be mentioned Loria’s Ebene Kurven , Wieleitner’s 
Spezielle Kurven, in German ; and Teixeira’s Gourbes algebriques, in French 
or Spanish. These works, compiled with great care, are indispensable to 
the geometer in the study of his subject, but a perusal of the early rare 
treatise of Maclaurin on the Geometria Organica reveals the fact that the 
claims of the latter geometer have frequently been entirely overlooked. 
For example, Teixeira himself, in a note on the Researches of Maclaurin 
on Circular Cubics ( Proc . Edinburgh Math. Soc., 1912), points out that 
many of the classic properties connected with these curves are due to 
Maclaurin, although his name does not even appear in the list of writings 
on the Strophoid published by Tortolini and Gunther. 
Again, the whole theory of Pedals, and more particularly the Pedals of 
the Conic Section, is given in the Geometria Organica — a theory to be 
rediscovered and named in the nineteenth century, more than a hundred 
years after the publication of Maclaurin’s work. In this connection it may 
be pointed out that Maclaurin invented the term, the Radial Equation of a 
Curve (for its p — r equation), long before the term Radial came to be 
applied to another purpose by Tucker. 
These two examples sufficiently illustrate my contention that Maclaurin’s 
treatise has been strangely overlooked. It is the business of the present 
note to indicate others, to point out how fully he has in many cases antici- 
pated writers of comparatively recent times, and to vindicate his claims 
to a far more careful consideration than has of late been the fashion. It 
may here be remarked that Poncelet in his magistral Traite gives full 
credit to the importance of Maclaurin’s two geometrical treatises, the 
Geometria Organica and the Proprietates Linear um Cur varum, pub- 
lished as an appendix to his posthumous Treatise on Algebra. In fact, the 
French school generally does more justice to the Scottish geometers of the 
eighteenth century than do English writers in the sister kingdom. 
§ 2. The Geometria Organica is the first great treatise of Maclaurin, 
and appeared in London, in 1720, under the royal imprimatur (1719) of 
Newton, to whom the work is dedicated. At the time the youthful 
Maclaurin (for he was only twenty-one years of age) held the Chair of 
Mathematics in the New College* in Aberdeen. The work expands and 
develops two earlier memoirs published in the Philosophical Transactions 
of the Royal Society : — 
(i) Tractatus de Gurvarum Gonstructione et Mensura, etc., 1718, giving 
the Theory of Pedals : (ii) Nova Methodus Universalis Curvas Omnes 
* i.e. Marischal College. 
