Isaac hadn't studied Euclid that much, and hadn't cared enough to study him well. If he wanted to work with a curve he would instinctively write it down, not as an intersection of planes and cones, but as a series of numbers and letters: an algebraic expression. That only worked if there was a language, or at least an alphabet, that had the power of expressing shapes without literally depicting them, a problem that Monsieur Descartes had lately solved by (first) conceiving of curves, lines, et cetera, as being collections of individual points and (then) devising a way to express a point by giving its coordinates – two numbers, or letters representing numbers, or (best of all) algebraic expressions that could in principle be evaluated to generate numbers. This translated all geometry to a new language with its own set of rules: algebra. The construction of equations was an exercise in translation. By following those rules, one could create new statements that were true, without even having to think about what the symbols referred to in any physical universe. It was this seemingly occult power that scared the hell out of some Puritans at the time, and even seemed to scare Isaac a bit.