Generic trademark acquired substantial market dominance or mind share, such that the primary meaning of the genericized trademark becomes the product or service itself rather than an indication of source for the product or service. A trademark thus popularized has its legal protection at risk in some countries such as the United States and United Kingdom, as its intellectual property rights in the trademark may be lost and competitors enabled to use the genericized trademark to describe their similar products, unless the owner of an affected trademark works sufficiently to correct and prevent such broad use. Thermos, Kleenex, ChapStick, Aspirin, Dumpster, Band-Aid,
Lune of Hippocrates circle. He proved that the lune bounded by the arcs labeled "E" and "F" in the figure has the same area as triangle "ABO". This afforded some hope of solving the circle-squaring problem, since the lune is bounded only by arcs of circles. Heath concludes that, in proving his result, Hippocrates was also the first to prove that the area of a circle is proportional to the square of its diameter. Hippocrates' book on geometry in which this result appears, "Elements", has been lost, but may have formed the model for Euclid's "Elements". Hippocrates' proof was preserved through the "History