When is a quadrant not a quadrant?
The octant ('eighth of a circle') fits a full quadrant into an arc of only 45 degrees.
The instrument was used most often at sea to measure the height of the sun. Observations were made not directly but by reflection. The mirror pivoted at the top needs to turn through only half the angle of the sun to reflect an image down to coincide with the horizon. The index arm rotates the mirror and directly indicates degrees of elevation.