I need a diagram. I'll use the one on wikipedia's visual angle page.
At 11 inches, 1 inch has a visual angle of about 5.2 degrees. But the exact number doesn't much matter. You can set two instances of the visual angle equation equal (one for the unknown distance and one for the definition of retinal, an inch long at 11 inches distance), and simplify to give you what similar triangle ratios would too. A length, s=D/11, for the side of the similar triangle opposite the eye, which by the operating definition of "retinal" has 300pixels along it. So, we can use s as a scaling factor, 300ppi/(D/11)="ppi you need at distance D to be retinal". Solve for D instead if you wish.
That might not even be clear with the diagram, sorry.
At 11 inches, 1 inch has a visual angle of about 5.2 degrees. But the exact number doesn't much matter. You can set two instances of the visual angle equation equal (one for the unknown distance and one for the definition of retinal, an inch long at 11 inches distance), and simplify to give you what similar triangle ratios would too. A length, s=D/11, for the side of the similar triangle opposite the eye, which by the operating definition of "retinal" has 300pixels along it. So, we can use s as a scaling factor, 300ppi/(D/11)="ppi you need at distance D to be retinal". Solve for D instead if you wish.
That might not even be clear with the diagram, sorry.