Nunes's Loxodrome and Nonius

Timeline

1. 1537Lisbon · LisbonIn the Defense of the Sea Charts and Certain Navigational Doubts appended to On the Sphere, Nunes pointed out that drawing meridians as parallel straight lines on a plane chart introduces error; the loxodrome of a constant compass course meets meridians at a constant angle yet is not the shortest great-circle path on the sphere, but a curved equiangular line approaching the poles.
2. 1542Lisbon · LisbonBeyond discussing the duration of twilight, the 1542 On Twilight described engraving on a quadrant a set of concentric arcs divided into progressively decreasing equal parts, used to read the remainder of an angle less than one degree. This device, later called the nonius, improved the precision of altitude and angle measurements for navigation and astronomical observation.
3. 1566–1569Lisbon and Low Countries cartographic circles · Low CountriesNunes had already required charts to represent the loxodrome on the sphere as a straight line. A 1566 Latin work strengthened the spherical-trigonometric formulation, and the 1569 Mercator projection achieved this cartographic goal, allowing rhumb-line courses to be plotted with a ruler on a plane chart.