Plato and His Followers
Geometry and the Geocentric Universe
Name: Michael Hong
Student Number: 994776417
Instructor: Professor W. H. Clarke
Date: October 31,2005
Plato is
considered to be one of the greatest philosophers in history he was also a
mathematician. Plato believed in the idea of mathematical harmony, the
perfection of the Creator’s original plans (Plato,2005).This premise along with
a second premise that the most perfect object is a sphere led Plato to believe
that the universe was spherical, therefore it had perfect volume (Plato,2005). This
idea of perfect objects being spherical expanded to the idea that the motion of
planets should be circular and uniform (Plato 2005). With all these assumptions
Plato concluded that the Earth was located in the centre of the universe (Plato,
2005). The Greeks created an approximate model of the order of the planets from
observation, and they came to the conclusion that the following planets orbited
the Earth in the following order: Moon, Mercury, Venus, the Sun, Mars, Jupiter
and Saturn. This model of the universe first conceived by Plato with the Earth
located in the centre is known as the geocentric model.
The
geocentric model has been analyzed and refined over centuries by many Greek mathematicians
and astronomers. A general overview will look at the major Greek mathematicians
and astronomers who followed from Plato, and who also contributed to the
geocentric model when the Greeks were at their intellectual height.
Eudoxus
of Cnidus (c.400 – c.350
BC) was a pupil of Plato who developed a model of planetary motions with
his mentor (Eudoxus of Cnidus, 2003). His model stated that 27 Earth-centered
spheres carried the Sun, Moon and planets around the Earth (Eudoxus of Cnidus,
2003). These spheres were believed to be heavenly spheres guiding the heavenly
celestial bodies (Eudoxus of Cnidus, 2003). His ideas seem to be based on Eudoxus’s
assumptions and not on any scientific observation.
Aristotle,
(c. 384 – c. 322 BC) Plato’s most famous pupil and another one of the most
famous philosophers in history continued his mentor’s model by strengthening
it. Aristotle was able to prove that the Earth was spherical by his observation
of the Earth casting a circular shadow on the moon during a lunar eclipse
(Aristotle 2, 2005). Another method that Aristotle carried out to prove that
the Earth was spherical was the observation of stars when an individual
traveled north or south (Aristotle, 2005).
He mentioned that the individual would see stars in different positions
which demonstrated the Earth was a sphere as opposed to it being flat
(Aristotle, 2005). Aristotle’s geocentric model was based on Eudoxus and
Callipus’s model with some modifications to the number of spheres. Aristotle
increased the numbers of spheres to 49 from Callipus’s 34 to account for the
movement of the rest of the celestial bodies (Aristotle 2, 2003). Aristotle
even went as far as creating new laws of motion, which stated that the bodies
would move in a vertical straight line motion (Aristotle, 2005). He also
created a fifth element known as ether, the name for the natural circular
movement of an object (Aristotle, 2005)
Callippus
(c.370 – c.300 BC) was
the first individual to modify Eudoxus’s planetary model by increasing the
number of Earth-centered spheres from 27 to 34 (Callippus,2005).His reason for the increase of spheres was
due to the fact that he believed that Eudoxus’s model didn’t account for all
the planetary movements(Callippus,2005). He also created a method to determine the lengths of seasons through
his precise measurements (Callippus, 2005).
The main
problem with the geocentric model at this time was that it could not explain
the retrograde motion of planets. Retrograde motion is the movement of a planet
from east to west when observed from Earth (Retrograde motion, 2000). This
phenomenon occurs when Earth catches up to a planet and overtakes it (Retrograde
motion, 2000).
Apollonius of Perga (c.262 – c.190 BC) is primarily known for
his geometric work on conic sections, but also further expanded on the
geocentric model (Apollonius of Perga, 2005). He created the terms: ellipse,
parabola and hyperbola by cutting different angles into a cone to create
different sections (Apollonius
of Perga, 2005). His addition to the geocentric model was the introduction of
the epicycle, created to help explain planetary and retrograde motion (Apollonius of Perga, 2005). An
epicycle is the orbit of a planet along the circumference of a larger circle
known as a deferent (Epicycle, 2003). The deferent is the larger circle around
the Earth in which the planets move along (Deferent, 2003).This idea of epicycles was vaguely conceived by
Eudoxus when he spoke of heavenly spheres but was not deeply thought about
until Apollonius further analyzed the model.
Hipparchus (c.
170 BC – c. 120 BC) worked in
All the
Greek astronomers and mathematicians mentioned have demonstrated that geometry
is vital to support astronomical observations or theories. Beginning with Plato
and ending with Ptolemy in this essay, the evolution of mathematics and
astronomy has led to more accurate models of the universe whether the models
were refined from older models or if they were newly created ones. The
transition from the geocentric model to the heliocentric model shows how new
models are created as technology and civilization advances. Plato will always
be remembered as the great thinker who created an initial model of how our
solar system is structured.
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