On a remarkable application of Cotes's theorem

Abstract

These theorems, however simple their algebraic expressions, it must immediately be seen, become for the most part complicated and unintelligible when geometrically enunciated. They are indeed (if we may in any case be allowed to consider a curve as unidentified with its equation_ properties rather of the equations of the conic sections, than of the curves themselves, -- of a limited number of disjoined points determined according to a certain law, rather than a series of consecutive ones composing a line.