A simple equation of state for dense fluids is used to investigate some empirically known regularities and also to explore some new ones. The known regularities predicted by the EOS are (i) there is a common bulk modulus point at which bulk modulus versus density of different isotherms of any fluid intersect at that single point and (ii) for each isochore with density greater than the Boyle density pressure versus temperature is linear. The new regularities explored by the EOS are (iii) there is a common compression point at which the compression factor against density of different isotherms of any dense fluid intersects at that single point and (iv) (B-r - 1)v(2) varies Linearly with rho(2) for each isotherm of any dense fluid, where B-r is the reduced bulk modulus and rho = 1/v is the molar density of the fluid. Experimental data were used to show the validity of the new regularities. A physical interpretation for each regularity is given.