drawing on the face of a quadrant for measuring
angles 45 concentric arcs, one of which was divided into 90
equal parts or degrees, and the remainder into 89, 88, 87, 86,
etc., successively, the last being divided into 46 equal parts.
When the index did not exactly cut one of the divisions of the arc of
degrees, it passed through or near to one of the divisions of one or
other of the other arcs; and by noting the place of that division the
fractional parts of a degree were calculated.