The Nautical Chart
The nautical chart
was a very important instrument used in navigation. It was a natural
evolution of the portolan chart, used mainly in Mediterranean
navigations. This "evolution" introduced many geometrical problems,
unnoticed by the pilots of the ships. Pedro Nunes identified the
main geometrical problems of the square nautical chart and provided
solutions. His work was a precursor of Mercator's.
See his
work in: Obras, Vol. I; Obras, Vol. IV.
The Loxodromic
Curve
A
loxodrome is a curve in the surface of a globe, made by following a
constant bearing course, so it cuts all meridians with the same
angle. Pedro Nunes referred to this curve as a rhumb line but
it was the Dutch mathematician Willebrord Snell who named it
loxodromic curve.
The
origin of the loxodromic curve is deeply related with the problems
of the nautical chart, principally with the confusion between what
was a great circle and a constant bearing course. The rhumb line was
misinterpreted as a straight line in the common nautical chart.
The loxodromic curve is a
straight line in a WrightMercator chart.
See his
work in: Obras, Vol. I;
[Manuscrito de Florença];
Obras,
Vol. IV (Chapter. 1).
Cosmographic and
astronomical topics
The width of the
"clime" zones.
The notion of
klimata was introduce in classical antiquity (as far as we now
by Aristotle). It was used to divide the Earth in parallels
(usually seven). Two consecutive parallels had a difference of half
hour for the length of the longest day of the year.
As far as we know,
no classical, Arabic or medieval author left a mathematical method
to find the length of the climes. Pedro Nunes was the first to
present a geometrical method to find out this values. He included it
in a commentary to the climes' chapter of Sacrobosco's Sphaera,
published in his Tratado da sphera (1537). His
Annotatio
in extrema verba capitis de climatibus
is certainly his most published text since it was included in many
editions of
Élie
Vinet's editions of
Sacrobosco's Sphaera.
The minimum
twilight.
Nunes adressed the
question in the book De crepusculis (1542).
In it Nunes
answered a question by a pupil  Prince Henrique, one of the king’s
brothers and future king  about the problem concerning the length
of twilights for different regions. In this book, Nunes showed how
an atmospheric phenomenon could be explained using the “most certain
and evident mathematical principles”.
The height of the
atmosphere.
Extra meridian
methods for latitude determination.
The dial of Achaz.
A geometric
solution of a biblical miracle. Nunes dealt with the problem in his
Tratado da sphera (1537) and later in his Opera (1566).
"Annotation on the
Moon".
Instruments
The Nonius scale.
Nunes
devised this graphical procedure as a solution to enhance
instruments’ precision and presented it for the first time in
De crepusculis (propositio III).
The shadow
instrument.
The
instrument
lying on the plane.
A simple solution that
enabled a observer to obtain the height of the sun. Due to the needs
of a steady plane in which the instrument should lie it was never
much used aboard.
The
nautical ring.
Another interesting and
simple proposal of an instrument destined to obtain the height of
the sun.
Mathematical
diagrams/graphic solutions.
Other
Mathematical Topics
Archimedes'
calculation of pi.
Copernicus errors
in trigonometry.
Pedro Nunes was an early
reader of Copernicus' De revolutionibus (1543). In his
Opera (1566) Nunes presents some mathematical reflections on
Copernicus' text. Nunes was aware of the physical implications of
Copernicus theory but he left that discussion to the “philosophers”.
His main concern was the mathematical consistency of Copernicus'
work: Nunes pointed some trigonometrical errors in it.
Solution of higher
order equations.
Nunes dealt with this
question in his Libro de Algebra (1567).
The contact angle.
Nunes dealt with
this problem in his Libro de Algebra. The debate was
originated in the III book of Euclides' Elements, and registed many
commentaries until the 16th century.
Nunes refuted
Jacques Peletier demonstrations and concluded that the contact (or
contingence) angle is a quantity.
He also used some
of Jordanus arguments (proposition II, De ponderibus)
establishing an interesting use of an example from "natural
philosophy" to sustain mathematical ideas.
Libro de Algebra:
Letter to the Reader.
This important text
included in the Libro de Algebra is an important example of the
well known disputes around the resolution of third degree equations.
It was also important to legitimate algebra as a mathematical field.
Rowing: Annotation
to Aristotle's Mechanica.
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