What commonality do Desargues, Monge and Poncelet share?

zbeckabee

"There is no "objective pull" (to use the phrase from Quine recently employed by rbrt tragesser) to points and lines at infinity, however. That is what their inventors (Desargues and Monge) and their chief developer and justifier (Poncelet) intended to mark by calling them 'imaginary' or 'improper' elements. Poncelet took such "beings of thought" (etres de raison, ens rationes) to typify the algebraic approach to things and he saw the justification of introducing imaginary objects in geometry as the same as the use of imaginary objects (e.g. complex numbers)in algebra." http://www.cs.nyu.edu/pipermail/fom/1998-January/000820.html Apr 05 07, 11:14 AM