Diameter, width and thickness in the hyperbolic plane

Abstract In hyperbolic geometry there are several concepts to measure the breadth or width of a convex set. first part paper we collect them and compare their properties. Than introduce new concept thickness body. Correspondingly, define three classes bodies, bodies constant with, diameter having shadow property, respectively. We prove that property follows fulfilment both stronger as width. last this paper, body variant Blaschke’s theorem on larger circle inscribed plane-convex given diameter.