Sweden used the streck and the USSR used . Being based on the milliradian, the NATO mil subtends roughly 1 m at a range of 1000 m (at such small angles, the curvature is negligible). Prefixes smaller than milli- are useful in measuring extremely small angles. Microradians (μrad, ) and nanoradians (nrad, ) are used in astronomy, and can also be used to measure the beam quality of lasers with ultra-low divergence. More common is the arc second, which is rad (around 4.8481 microradians). History Pre-20th century The idea of measuring angles by the length of the arc was in use by mathematicians quite early. For example, al-Kashi (c. 1400) used so-called diameter parts as units, where one diameter part was radian. They also used sexagesimal subunits of the diameter part. Newton in 1672 spoke of "the angular quantity of a body's circular motion", but used it only as a relative measure to develop an astronomical algorithm. The concept of the radian measure is normally credited to Roger Cotes, who died in 1716. By 1722, his cousin Robert Smith had collected and published Cotes' mathematical writings in a book, Harmonia mensurarum. In a chapter of editorial comments, Smith gave what is probably the first published calculation of one radian in degrees, citing a note of Cotes that has not survived. Smith described the radian in everything but name, and recognized its naturalness as a unit of angular measure. In 1765, Leonhard Euler implicitly adopted the radian as a unit of angle. Specifically, Euler defined angular velocity as "The angular speed in rotational motion is the speed of that point, the distance of which from the axis of gyration is expressed by one." Euler was probably the first to adopt this convention, referred to as the radian convention, which gives the simple formula for angular velocity . As discussed in , the radian convention has been widely adopted, and other conventions have the drawback of requiring a dimensional constant, for example . Prior to the term radian becoming widespread, the unit was commonly called circular measure of an angle. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson (brother of Lord Kelvin) at Queen's College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, vacillated between the terms rad,