Octants, Quadrants, and Sextants are all so closely related that we will discuss them as if they were a single instrument. There are important differences between them, but they are closely related for our purposes. We will refer to this general class of instruments as "sextants".
Sextants measure the angle between objects. They can be used vertically, such as to find the angle between the horizon and the sun. This is useful for determining one's latitude. They can also be used horizontally, to determine the distance between (for example) two mountains on a shoreline. This is useful for determining one's distance from shore.
Cross-Staff and Backstaff
Quadrant 1460-1700s, Octant 1742-present, Sextant 1730-present