Trigonometric functions, developed in the 16th century, and logarithms, introduced by John Napier in 1614, brought spectacular advances in astronomy… and hence in navigation, since sailors at the time found their bearings by observing celestial bodies. Between two known values of these functions, linear interpolation was used: the function was treated as linear (a line segment) between those two values. It is, of course, no such thing.

John Napier (1550–1617).

Left: Isaac Newton (1643–1727). Right: René Descartes (1596–1650).