Editing Exsecant (section)

== Etymology ==

The word ''secant'' comes from Latin for "to cut", and a general [[secant line]] "cuts" a circle, intersecting it twice; this concept dates to antiquity and can be found in Book 3 of [[Euclid's Elements|Euclid's ''Elements'']], as used e.g. in the [[intersecting secants theorem]]. 18th century sources in [[Neo-Latin|Latin]] called ''any'' non-[[tangent]]ial line segment external to a circle with one endpoint on the circumference a ''secans exterior''.{{r|Latin}}

The trigonometric [[secant function|''secant'']], named by [[Thomas Fincke]] (1583), is more specifically based on a line segment with one endpoint at the center of a circle and the other endpoint outside the circle; the circle divides this segment into a radius and an external secant. The external secant segment was used by [[Galileo Galilei]] (1632) under the name ''secant''.{{r|galileo}}