School of Athens. Perspective: Central Vanishing Point
art, any method employed to represent three-dimensional
space on a flat surface or in relief sculpture.
Vanishing Point: the
point in linear perspective at which all imaginary lines
of perspective converge.
School of Athens was painted by Raphael Sanzio or
Raffaello Santi (1483-1520) for Pope Julius II
(1503-1513). In this fresco,
Raphael depicts the great
philosophers and mathematicians of ancient Greece
colleagues in a timeless academy:
Plato is in the center pointing his finger to the
heavens while holding the Timaeus, his treatise on the
origin of the world. Next to him, his younger pupil
Aristotle holds a copy of his Ethics while
describing the earth and the wide realm of moral
teaching with his extended hand in an elegant horizontal
Pythagoras contemplates his system of proportions at
the lower left and Euclid draws a circle on a
slate at the lower right.
To the Greeks mathematics
was essentially geometry, and it was in Elements,
Euclid's treatise on the subject, that the notion of an
axiomatic system was first laid out In this system
certain self-evident statements called axioms are
assumed to be true and new statements called theorems
are derived from them using the Aristotelian rules of
The Fresco of Raphael's
School of Athens is a masterpiece of Art. However, over
the centuries it has posed many problems to know all
details of the persons who are depicted. Unfortunately Raphael did not leave any personal
notes on this work but some of the persons can be
The identity of some of the
philosophers in the picture, such as Plato or Aristotle,
is uncontroversial, but scholars disagree on many of the
other figures. According to Lahanas, they are usually
identified as follows:
Zeno of Citium or Zeno of
Frederik II of Mantua?
Anicius Manlius Severinus
Boethius or Anaximander or Empedocles
Alcibiades or Alexander the
Antisthenes or Xenophon?
Hypatia — (Francesco Maria
della Rovere or Raphael's mistress Margherita.)
Aeschines or Xenophon?
Heraclitus — (Michelangelo)
Plato holding the Timaeus —
( Leonardo da Vinci)
Aristotle holding the
Diogenes of Sinope?
Euclid or Archimedes with
students ( Bramante)?
Strabo or Zoroaster? (Baldassare
Castiglione or Pietro Bembo)
Ptolemy? - Apelles —
Protogenes — (Il Sodoma or
The American Heritage Dictionary. Wikipedia. Houghton
Mifflin Company: Scientist. Columbia University Press:
Encyclopedia. Encyclopedia Britannica.
and Geometric Art.