“It is impossible to trisect an arbitrary angle.” We (the mathematical community) have been certain of this for the past 170 years. Missing in that statement is the qualifying phrase“... using a straightedge and compass.” But if we are clumsy enough to scratch our straightedge in two places, we can in fact trisect an arbitrary angle, a result that was known to Archimedes. We are equally confident in the much more modern assertion: “There is no algorithm to solve an arbitrary quintic,” where the oft omitted qualifying phrase is “... using the extraction of roots.” In this talk, we will give an example of a quintic whose roots are not expressible using the extraction of roots, but whose real roots are constructible using a compass and twice-notched straightedge. We will also analyze the power and limitations of these tools, and present some open questions.