Sentence:  He next treats of the properties of the <WSD>Conchoid</WSD>, which Nicomedes invented for doubling the cube; applying it to the solution of certain problems concerning Inclinations, with the finding of two mean proportionals, and cubes in any proportion whatever. 
Meaning of the word marked with <WSD> tags:  Any of a family of curves defined as the locus of points "p", such that each "p" is on a line that passes through a given fixed point "P" and intersects a given curve, "C", and the distance from "p" to the point of intersection with "C" is a specified constant (note that for nontrivial cases two such points "p" satisfy the criteria, and the resultant curve has two parts).