quadrans

Latin quadrans meant a quarter, one-fourth — from quattuor (four). A quadrant was the quarter of a circle — the 90-degree arc. As a navigational instrument, the quadrant measured the angle between a celestial body and the horizon, allowing a navigator to determine latitude by measuring the sun's altitude at noon or Polaris's altitude at night. The instrument was a quarter-circle arc with degree markings, a plumb line to establish vertical, and sights along one edge.

The quadrant's history as a navigational instrument spans from the Islamic world to the European age of exploration. Arab astronomers developed precision quadrants in the 9th-10th centuries at the House of Wisdom in Baghdad; Al-Battani (858-929 CE) used a mural quadrant — a quadrant mounted on a wall aligned to the meridian — to measure the sun's path with extraordinary precision. His measurement of the obliquity of the ecliptic was accurate to within a few arcseconds.

European navigators used smaller, portable quadrants from the 13th century onward. The quadrant was superseded by the cross-staff, then the astrolabe, then the back-staff, and finally by Hadley's reflecting quadrant (1731) — which became the sextant, the most accurate navigational instrument before GPS. Each improvement used the same quarter-circle principle.

Coordinate geometry divides the Cartesian plane into four quadrants — the four areas defined by the x and y axes. The quadrant I (positive x, positive y), II (negative x, positive y), III (negative x, negative y), and IV (positive x, negative y) are the navigational quadrant's mathematical descendants. The four-part division of the circle became the four-part division of the plane.