A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the object's altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight and it is an essential part of celestial navigation. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart. Common uses of the sextant include sighting the sun at solar noon and sighting Polaris at night, to find one's latitude (in northern latitudes). Sighting the height of a landmark can give a measure of distance off and, held horizontally, a sextant can measure angles between objects for a position on a chart. A sextant can also be used to measure the lunar distance between the moon and another celestial object (e.g., star, planet) in order to determine Greenwich time which is important because it can then be used to determine the longitude.
The scale of a sextant has a length of ⅙ of a turn (60°); hence the sextant's name (sextāns, -antis is the Latin word for "one sixth"). An octant is a similar device with a shorter scale (⅛ turn, or 45°), whereas a quintant (⅕ turn, or 72°) and a quadrant (¼ turn, or 90°) have longer scales.
Sir Isaac Newton (1643–1727) invented the principle of the doubly reflecting navigation instrument (a reflecting quadrant—see Octant (instrument)), but never published it. Two men independently developed the octant around 1730: John Hadley (1682–1744), an English mathematician, and Thomas Godfrey (1704–1749), a glazier in Philadelphia. John Bird made the first sextant in 1757. The octant and later the sextant, replaced the Davis quadrant as the main instrument for navigation.
Johann Carl Friedrich Gauß (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. He referred to mathematics as "the queen of sciences".