
The Elements

Euclid, also called "Euclid of Alexandria" (to distinguish him from the Socratic philosopher Euclid of Megara) is considered the founder of Geometry, often referred to as the "elementer" (στοιχειωτής). He was active in Alexandria during the reign of Ptolemy 323–283 BCE. The Elements is one of the most influential works in Mathematics, and was used for teaching Mathematics from its appearance until the beginning of the 20th century; and although it was written so early, it is an exemplar of Mathematical rigour.
His name (Euclid) means "renowned", "glorious". We
don't know much about his life. According to Arabic sources, he
was born in Tyre around 325 BCE. Proclus briefly refers to
Euclid in his commentary work on the Elements. According
to Proclus, Euclid belonged to Plato's circle, and he composed
the Elements from the works of various students of Plato such as
Eudoxus of Cnidus, Theaetetus and Philip Opundius. Euclid died
around 270 BCE in Alexandria.
Although the
Elements are composed from various earlier works, Euclid's great
contribution is that he integrated them very well in one work with
an absolute commitment to mathematical rigor, a rigor that has
remained the basis of Mathematics to this day.
In todays Greece, several books on Euclidean
"Geometry" are available, on which the teaching of geometry in
secondary education is based. In our view, although several of
these are very worthy efforts, none has the mathematical beauty,
charm, and rigor that the Elements themselves have.
Unfortunately the Elements are not available to Greek
Mathematicians and we hope that this edition will fillin this
gap. The text does not target the Historians of Mathematics, but
the Mathematician colleagues who have to teach geometry in
today's modern school classroom.
We firmly believe that Euclid's text is unsurpassed,
and it is in our opinion unfortunate that it is not taught
verbatim in secondary education. Typical is the example of the
Pythagorean Theorem (Book 1, Proposition 47) which is taught
with various proofs, such as that of similar triangles,
preferring a fast way to prove it, over the deeper understanding
one gets from Euclid's beautiful proof.
The following pdf contains a release of the Elements
in modern Greek using modern mathematical notation but following
the essence of Euclid's proofs. It also contains the ancient
text at the end of the file, while each Proposition in the
modern Greek text is connected with a hyperlink to the
corresponding Proposition in the ancient Greek from the
original.
The comments added are minimal, so as not to affect
the flow of the text, but to provide necessary the
clarifications so that the text can be understood by modern
Mathematicians.
The source code of the book is available under
restrictions.
We also find it helpful to take a detour when
studying Book 12 Proposition 2. Because in this proposition it
is proved that the area of the circle of radius r is equal to
the area of the circle of radius 1 times r^{2}. In
order for this part to be complete, we recommend the study of
Archimedes' Measurement of a Circle, which estimates the
area of a circle of radius 1, i.e. π, which he finds to be 3.14.