Pedro Nunes · 1573
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The collected Latin works of Pedro Nunes (1502–1578), Cosmógrafo-Mor of Portugal and the leading mathematician of the age of discoveries, gathered at Basel in 1573 in an edition the author himself saw through the press. He was seventy-one, and this is the form in which he wanted his work to stand.
De arte atque ratione navigandi, in two books, is the centerpiece. Nunes asks what path a ship actually traces when it holds a constant compass bearing, and shows that it is not a great circle — not the shortest route — but a curve that crosses every meridian at the same angle and spirals in toward the pole without ever reaching it. The line was later named the loxodrome. From this follows his critique of the plane chart, which draws such a course as a straight line and so misrepresents both the distance sailed and the landfall.
The annotations on Peurbach’s Theoricae novae planetarum take up the standard university textbook of planetary theory and work through its constructions, correcting and extending as they go.
A short piece treats Aristotle’s mechanical problem of the rowed ship — why the oar, worked against the water, drives the hull forward — as a question about the lever.
De erratis Orontii Finaei is a demolition. Oronce Finé, royal mathematician at Paris, had published claimed solutions to squaring the circle, duplicating the cube and trisecting the angle. Nunes takes each in turn and shows exactly where the reasoning fails.
De crepusculis asks how long twilight lasts and why, at some latitudes and seasons, it never quite ends — a problem in spherical astronomy about the depression of the Sun below the horizon and the height of the atmosphere that scatters its light. It is accompanied by Alhazen’s own book on the causes of twilight. The treatise also introduced the nonius, Nunes’s method of reading fractions of a scale division by nested concentric arcs, the ancestor of the vernier that displaced it.
Nunes is where the Portuguese voyages meet mathematics. The problems he takes up were not academic exercises: what course to steer, what a chart can and cannot faithfully show, how to read an instrument more finely than its divisions allow. His analysis of the constant-bearing course posed the problem that Mercator’s projection of 1569 answers, and that Edward Wright later put on a rigorous footing — the chart on which a rhumb line is straight.
The twilight work belongs beside the astronomy in this corpus for the same reason: it treats the atmosphere as something with measurable extent, inferred from an observation any careful watcher can make.
The translated source is the 1573 Basel printing, the last and fullest gathering of Nunes’s Latin works and the one he prepared himself. The full title page runs to a paragraph, naming each treatise in turn; the volume is cited in the scholarship simply as his Opera.