masterpiece. The first six books cover plane geom-
etry (straight lines, intersection of lines, angles),
and the last three cover solid geometry (pyramids,
cones, cylinders, spheres). The middle books ad-
dress such subjects as ratios, proportions, magni-
tudes, 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 postu-
lates, 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 tri-
angle”—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 as-
sumptions and self-evident truths. There are a
total of 465 propositions. Ptolemy once wondered
whether there was a shorter way to reach these in-
valuable conclusions, to which Euclid replied,
“There is no royal road to geometry.”
In addition to Elements, Euclid published sev-
eral other less-famous works. Fallacies, no longer
extant, provides methods for detecting illogical
conclusions; Data proves that if certain magni-
tudes in a geometric figure are given, other mag-
nitudes may be deduced; Figures shows how to
divide figures proportionally; Surface-loci concerns
curved surfaces; Conics studies cones; Optics ad-
dresses visual perspective; Elements of Music is
based on Phythagorean theory; and in his pioneer-
ing work Phenomena, Euclid applies spheric geom-
etry 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, ana-
lyzed, 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 re-
ceived more intense scrutiny than Euclid’s Ele-
ments.” Great minds from Archimedes and CICERO
to Isaac Newton, Napoleon, and Lincoln have
studied this classic work, and it remains the defin-
itive 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 Publi-
cations, 1908.
Euclid’s Phenomenon: A Translation and Study of a
Hellenistic Treatise in Spherical Astronomy. Trans-
lated by Robert S. Thomas. Edited by J. L.
Berggren. New York: Garland, 1996.
Works about Euclid
Artmann, Benno. Euclid: The Creation of Mathemat-
ics. New York: Springer-Verlag, 1999.
Mlodinow, Leonard. Euclid’s Window: The Story of
Geometry from Parallel Lines to Hyperspace. New
York: Simon & Schuster, 2002.
Euripides (ca. 484–406 B.C.) playwright
Euripides was born on the Greek island of Salamis
near Athens into a reasonably prosperous family.
He made his home there, most likely on an estate
owned by his father, and it is said he penned many
of his dramas in a seaside cave. He was married
twice, both times unhappily, and had three sons. A
scholar and an intellectual, Euripides counted
among his friends some of the leading philosophers
of the day, including
SOCRATES, an admirer of his
plays; and the Sophist Protagoras, who debuted his
agnostic work “Of the Gods” at Euripides’ home.
Euripides saw roughly 88 of his plays produced,
but he was honored at the Greek drama festivals
only four times.Visionary and avant-garde, Euripi-
des’ plays reflected his unorthodox views, which
were not shared by the general public during his
lifetime. He was soundly ridiculed, and the comic
playwright ARISTOPHANES parodied his plays in The
Thesmophoriazousai (411 B.C.), which includes a
Euripides 101