fixed-width compass (i.e. a rusty compass). Motivated by Mascheroni's result, in 1822 Jean Victor Poncelet conjectured a variation on the same theme. He proposed that any construction possible by straightedge and compass could be done with straightedge alone. The one stipulation though is that a single circle with its center identified must be provided. This statement, now known as the Poncelet-Steiner theorem, was proved by Jakob Steiner eleven years later. A proof later provided in 1904 by Francesco Severi relaxes the requirement that one full circle be provided, and shows that any small arc of the circle, so long as the center is still provided, is still sufficient. Additionally, the center itself may be omitted instead of portions of the arc, if it is substituted for something else sufficient, such as a second concentric or intersecting circle, or a third circle, or a non-intersecting second circle provided a point on either the centerline or the radial axis between them is given. The compass equivalency theorem shows that in all the constructions mentioned above, the familiar modern compass with its fixable aperture, which can be used to transfer distances, may be replaced with a "collapsible compass", a compass that collapses whenever it is lifted from a page, so that it may not be directly used to transfer distances. Indeed, Euclid's original constructions use a collapsible compass. See also Napoleon's problem Geometrography Inversive geometry Notes References Further reading External links Construction with the Compass Only Compass and straightedge constructions Theorems in plane geometry