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Note: the example in Map Projections - A Working Manual by John P. Snyder of the USGS, Page 4, may be interpreted as saying that circles of equal area (equal radii) on the map denote equal areas on the surface the map depicts. (I have more reading to do but I'm not sure any projection could be equal-area for arbitrary shapes of the same area.)

Further note: above is also citation for these words: homolographic, homalographic, authalic and equiareal.[1]