# Euclid Biography

**
Born: c. 335
B.C.E.
Greece
Died: c. 270
B.C.E.
Alexandria, Egypt
**

*Greek mathematician*

The Greek mathematician (math expert) Euclid wrote the
*
Elements,
*
a thirteen-volume set of textbooks of geometry (the study of points,
lines, angles, and surfaces)—the oldest major mathematical work
existing in the Western world.

##
*
Unknown background
*

Almost nothing is known of Euclid personally. It is not even known for
certain whether he was really a creative mathematician or was simply
good at collecting and editing the work of others. Most of the
information about Euclid comes from Proclus (411–485 C. E.), a
fifth-century Greek scholar. Some believed Euclid was the son of a Greek
man who was born in Tyre and lived in Damascus. His mathematical
education may have been obtained from students of Plato (c. 427
B.C.E.
–347
B.C.E.
) in Athens, Greece, since most of the earlier mathematicians upon whose
work the
*
Elements
*
is based had studied and taught there.

##
*
The
*
Elements

No earlier writings similar to the
*
Elements
*
have survived. One reason is that the
*
Elements
*
expanded on all previous writings of this type, so keeping any earlier
texts around was thought to be unnecessary. For example, about 600
B.C.E.
the Greek mathematician
Thales (c. 625–c. 546
B.C.E.
) is said to have discovered a number of theorems (statements that can
be demonstrated or proved) that appear in the
*
Elements.
*
Early mathematics dealt only with concrete problems, such as
determining areas and volumes. By Euclid's time, mathematics had
become more of an intellectual occupation for philosophers (thinkers, or
seekers of wisdom) rather than for only scientists.

The
*
Elements
*
consists of thirteen books. Each book contains a number of theorems,
from about ten to one hundred, which follow a series of definitions. The
usual elementary course in Euclidean geometry is based on "Book
I." "Book V" is one of the finest works in Greek
mathematics, a masterful description of the theory of proportions (the
relation of one part to another part or the sum of all parts) originally
discovered by Eudoxus. "Book VI" applies the statements of
"Book V" to the figures of plane geometry (the study of
flat surfaces and the relationships of figures lying within the
surfaces). In "Book VII" a prime number is defined as that
which is measured by a unit alone (a prime number can be divided only by
itself and the number 1). "Book IX" contains
Euclid's proof that there are infinitely many prime numbers,
which is still used in current algebra textbooks.

The
*
Elements
*
were translated into Latin and Arabic, but it was not until the first
printed edition, published in 1482, that they became important in
European education. The first complete English version was printed in
1570. It was during the most active mathematical period in England,
about 1700, that Greek mathematics was studied most closely.
Euclid's writings were used by

##
*
Euclid's other works
*

Some of Euclid's other works are known only because other writers
have mentioned them. The book
*
Data
*
discusses plane geometry and contains propositions (problems to be
demonstrated) in which certain data are
given about a figure and from which other data can be figured out.
Euclid's
*
On Division,
*
also dealing with plane geometry, is concerned with more general
problems of division. A work by Euclid that has survived is
*
Phaenomena.
*
This is what today would be called applied mathematics, concerning the
geometry of spheres for use in astronomy.

Another surviving work, the
*
Optics,
*
corrects the belief held at the time that the sun and other heavenly
bodies are actually the size they appear to be to the eye. This work
discusses the relationship between what the eye sees of an object and
what the object actually is. For example, the eye always sees less than
half of a sphere, and as the observer moves closer to the sphere, the
part of it that is seen is decreased, although it appears larger.

Another lost work is the
*
Porisms.
*
A porism is somewhere between a theorem and a problem; that is, rather
than something to be proved or something to be constructed, a porism is
concerned with bringing out another feature of something that is already
there. To find the center of a circle or to find the greatest common
divisor of two numbers are examples of porisms. This work appears to
have been more advanced than the
*
Elements,
*
and perhaps if it still existed it would give Euclid a higher place in
the history of mathematics.

##
*
For More Information
*

Artmann, Benno.
*
Euclid: The Creation of Mathematics.
*
New York: Springer, 1999.

Burton, David M.
*
Burton's History of Mathematics.
*
Dubuque, IA: Wm. C. Brown Publishers, 1995.

Mlodinow, Leonard.
*
Euclid's Window.
*
New York: Free Press, 2001.

Scott, Joseph Frederick.
*
A History of Mathematics: From Antiquity to the Beginning of the
Nineteenth Century.
*
London: Taylor & Francis, 1958.

Simmons, George F.
*
Calculus Gems: Brief Lives and Memorable Mathematics.
*
New York: McGraw-Hill, 1992.