Footnote 76
Supp. Prop., §41-43.  I have mended the text as well as I could by inserting words, and adopting different readings. Nearly all the emendations rest on authority; see the Critical Notes.  The text is not a good one, but I do not see why these sections may not have been written by Chaucer.  For a definition of the terms `Urnbra Extensa' and `Umbra Versa' see sections 5 and 6 of the Practica Chilindri of John Hoveden, published by the Chaucer Society.  The umbra extensa or recta is the sliadow cast on a plain by any perfectly upright object; but the restriction is commonly introduced, that the altitude of the sun shall exceed 45°.  The umbra versa is the shadow cast perpendicularly downwards along a wall by a style which projects from the wall at right angles to it; the restriction is commonly introduced, that the sun's altitude shall be less than 45°.  The umbra versa is the one which appeared on the `chylindre'; hence John de Hoveden explains how to calculate the altitude of an object by it.