I gave a book suggestion [Sibley's geometry] and a Wikipedia _link_ that mirrors what is said in Sibley, plus I already explained that there are undefined terms in geometry - and that 'point' is one of them. But a line made up of points is not one of them. and will you share with us your secret definition for points and lines or not? The specific problem I raised in connection with the definition for lines and points was whether ANY definition could satify the circular implication for lines constituted of points and points defined by the intersection of lines.That was the substance and direction of my post. However for what it's worth I'll be happy to share my take on the definition of geometric figures in general. Geometric figures are boundaries. That and nothing more. They're related to one another through the calculus and processes of derivation and integration but are not constituted or composed of one another. (Hmm although I'm beginning to wonder here whether that would include cubes composed of cubes etc.Oh well.Grist for another windmill to tilt at I daresay.) ~v~~