Instrument lying on the plane


Pedro Nunes (1502 - 1578)

Mathematics, Cosmography and Nautical Science in the 16th century.


                                                                                                                                                                              Science ╗ instrument lying on the plane


Nautical Chart.

Loxodromic Curve.

Width of the "clime" zones.

Minimum twilight.

Height of the atmosphere.

Extra meridian methods for latitude determination.

Dial of Achaz.

"Annotation on the Moon".

Nonius scale.

Shadow instrument.

Instrument lying on the plane.

Nautical ring.

Mathematical diagrams/graphic solutions.

Archimedes' calculation of pi.

Copernicus errors in trigonometry.

Solution of higher order equations.

Contact angle.

Libro de Algebra: Letter to the Reader.

Rowing: Annotation to Aristotle'sMechanica.


The instrument lying on the plane allowed an observer to obtain the height of the sun without having to point directly to it.

The basic concept was that of a gnomon. The problem of vertical shadows is that the length of the shadow projected by the gnomon is proportional to the co-tangent of the angular height, which introduces a non-linearity to the scale.

Pedro Nunes devised this solution in order to convert the reading of the angle into a circular scale.


The base of the instrument could be a wood plate. In this base a circle, and a tangent to this circle, were drawn. Then, a triangular plate made of wood or brass would be attached to the base in the position seen in the figure:






The height (altura) of the sun, that is the shadow abc (or alternatively the zenith distance), could be read in the circular scale cd.


This instrument was in fact used aboard by JoŃo de Castro in a expedition to the Red Sea. In spite of the good readings obtained by Castro, this instrument was not welcome among mariners. The main reason was that, in order to give good readings, the instrument should lay on a stable, horizontal surface, which was only possible in calm days or when in land.



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