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KF5JRV > TECH 20.09.16 13:34l 62 Lines 3017 Bytes #999 (0) @ WW
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Subj: The Sector
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Sent: 160920/1115Z 2248@KF5JRV.#NWAR.AR.USA.NA BPQ1.4.65
The Sector
The rise of instrumentation in medieval natural philosophy was intimately
bound to the study of the heavens. However, the revival of geometry also
served practical aims, in construction and in war. A new instrument, the
sector, allowed for calculations to be made based on the proportions between
triangles.
The stars and the land
Astrolabes and quadrants were instruments first devised in antiquity and
developed in the Middle Ages to chart the movements of stars, and they also
became very useful tools for surveying.
One could use sightlines and angles to calculate unknown distances from known
ones. Leonard Digges (c. 1515-c. 1559) is also credited with inventing the
theodolite, a specialist surveying tool that used a refracting lens to help
calculate angles.
Though helpful for observation, tools such as the astrolabe, quadrant, and
theodolite required their user to have a good knowledge of arithmetic. Only a
select few had the ability to carry out complex calculations, and especially
in the context of war, it became clear that a tool dedicated to calculations
was needed.
Reading the book of nature
Little known at the time, Galileo Galilei (1564-1642) was a lecturer at the
University of Padua, where he taught courses on practical subjects such as
military architecture. During this time, behind closed doors, he set an
instrument maker to work on a device based on the proportional compass, a
drawing tool, to aid in artillery calculations.
Galileo was probably not the first to 'invent' such a device, which became
known as a sector. He may have gotten the idea from a friend, and London
mathematician Thomas Hood was already familiar with a version of the
instrument at the time. However, Galileo's writings did much to publicize the
device. He became known for his view of mathematics as the core of natural
philosophy, which was novel in the strength of his insistence:
"[The book of nature] is written in the language of mathematics, and its
characters are triangles, circles, and other geometric figures without
which it is humanly impossible to understand a single word of it; without
these, one wanders about in a dark labyrinth." Galileo Galilei, Il
Saggiatore, 1626
We might say that Galileo saw the sector as a way to become better acquainted
with nature through simplified calculations.
Sectors had different sets of rulings for different types of calculations,
identical on each arm. A pair of dividers was used to match points along the
rulings, and it could also be used as a protractor to measure angles. Some
sectors even included a clamp, to suit their role as an artillery compass.
While it might seem to us like only a ruler, its design was revolutionary in
that it portrayed measurement lines alongside 'artificial lines': sines,
tangents, and logarithms. Combined with knowledge of proportions between
triangles, the sector was a powerful instrument.
73 Scott kf5jrv
KF5JRV @ KF5JRV.#NWAR.AR.USA.NA
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