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Euclid (fl. ca. 300 B.C.) mathematician. Encyclopedia of World Writers, Beginnings To 20th Century

Euclid lived in the time of the Egyptian king
Ptolemy I, who had been a general in the army of
Alexander the Great. Alexander’s conquests had
taken him to Egypt, where he founded the city of
Alexandria on the Nile Delta in 332 B.C. The metropolis
flourished, accumulating half a million
residents and becoming the world’s seat of scientific
and literary scholarship. Among its chief attractions
was the Alexandrian Library, which
boasted more than 500,000 Greek manuscripts
and translations.
Euclid,who probably received his mathematical
education in Athens from followers of PLATO, was
among the scholars drawn to Alexandria’s offerings,
and he established a school of mathematics
there. It is said that one of his pupils asked Euclid
what advantage he would gain by learning geometry.
Euclid instructed his slave to give the boy a
threepence, “since he must make gain out of what
he learns.”
The world’s most famous geometer did not discover
or invent the laws of geometry, as his theorems
and proofs came from the existing body of
Greek knowledge. Rather, his genius lay in organizing
and presenting them in a logical fashion.
Stoicheia, or Elements, totaling 13 books, is Euclid’s
masterpiece. The first six books cover plane geometry
(straight lines, intersection of lines, angles),
and the last three cover solid geometry (pyramids,
cones, cylinders, spheres). The middle books address
such subjects as ratios, proportions, magnitudes,
and prime numbers.
Euclid begins Elements with 25 definitions of
points, lines, plane surfaces, circles, parallels, and
other terms. This is followed by a list of five postulates,
which assume that it is possible, for instance,
to draw a line from one point to another; and five
axioms, such as “Things which are equal to the
same things are also equal to one another” and
“The whole is greater than the part.” From these
fundamentals, the first proposition—“On a given
finite straight line to construct an equilateral triangle”—
is demonstrated. From these elements
plus the proven first proposition, the second
proposition may be demonstrated, and so on. Each
new proposition can be traced to the previously
proven propositions on which it is based, all the
way back to Euclid’s initial descriptions of assumptions
and self-evident truths. There are a
total of 465 propositions. Ptolemy once wondered
whether there was a shorter way to reach these invaluable
conclusions, to which Euclid replied,
“There is no royal road to geometry.”
In addition to Elements, Euclid published several
other less-famous works. Fallacies, no longer
extant, provides methods for detecting illogical
conclusions; Data proves that if certain magnitudes
in a geometric figure are given, other magnitudes
may be deduced; Figures shows how to
divide figures proportionally; Surface-loci concerns
curved surfaces; Conics studies cones; Optics addresses
visual perspective; Elements of Music is
based on Phythagorean theory; and in his pioneering
work Phenomena, Euclid applies spheric geometry
to astronomy.
Through the centuries, Euclid’s Elements has
appeared in more than 2,000 different versions.
According to William Dunham, author of Journey
through Genius (1991),“This work had a profound
impact on Western thought as it was studied, analyzed,
and edited for century upon century, down
to modern times. It has been said that of all books
from Western civilization, only the Bible has received
more intense scrutiny than Euclid’s Elements.”
Great minds from Archimedes and CICERO
to Isaac Newton, Napoleon, and Lincoln have
studied this classic work, and it remains the definitive
geometry text in many classrooms.
English Versions of Works by Euclid
Euclid: The Thirteen Books of the Elements. Translated
by Sir Thomas L. Heath. New York: Dover Publications,
1908.
Euclid’s Phenomenon: A Translation and Study of a
Hellenistic Treatise in Spherical Astronomy. Translated
by Robert S. Thomas. Edited by J. L.
Berggren. New York: Garland, 1996.
Works about Euclid
Artmann, Benno. Euclid: The Creation of Mathematics.
New York: Springer-Verlag, 1999.
Mlodinow, Leonard. Euclid’s Window: The Story of
Geometry from Parallel Lines to Hyperspace. New
York: Simon & Schuster, 2002.

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