Hippocrates of Chios
Encyclopedia
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
mathematician, (geometer), and astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
, who lived c. 470 – c. 410 BCE
Common Era
Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...
.
He was born on the isle of Chios
Chios
Chios is the fifth largest of the Greek islands, situated in the Aegean Sea, seven kilometres off the Asia Minor coast. The island is separated from Turkey by the Chios Strait. The island is noted for its strong merchant shipping community, its unique mastic gum and its medieval villages...
, where he originally was a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
, possibly for litigation. There he grew into a leading mathematician.
On Chios Hippocrates may have been a pupil of the mathematician and astronomer Oenopides
Oenopides
Oenopides of Chios was an ancient Greek mathematician and astronomer, who lived around 450 BCE. He was born shortly after 500 BCE on the island of Chios, but mostly worked in Athens.- Astronomy :...
of Chios. In his mathematical work there probably was some Pythagorean
Pythagorean
Pythagorean means of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras. See:-Philosophy:* Pythagoreanism is a term used for the esoteric and metaphysical beliefs purported to have been held by Pythagoras....
influence too, perhaps via contacts between Chios and the neighbouring island of Samos
Samoš
Samoš is a village in Serbia. It is situated in the Kovačica municipality, in the South Banat District, Vojvodina province. The village has a Serb ethnic majority and its population numbering 1,247 people .-See also:...
, a center of Pythagorean thinking: Hippocrates has been described as a 'para-Pythagorean', a philosophical 'fellow traveler'. The Reductio ad absurdum
Reductio ad absurdum
In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...
argument (or proof by contradiction) has been traced to him.
Mathematics
The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometryGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
textbook, called Stoicheia Elements, that is, basic theorems, or building blocks of mathematical theory). From then on, mathematicians from all over the ancient world could, at least in principle, build on a common framework of basic concepts, methods, and theorems, which stimulated the scientific progress of mathematics.
Only a single, and famous, fragment of Hippocrates' Elements is existent, embedded in the work of Simplicius
Simplicius
Simplicius may refer to:* Pope Simplicius * Simplicius of Cilicia , philosopher* Simplicius, Constantius and Victorinus , Roman martyrs and saints* Simplicius, Faustinus and Beatrix , Roman martyrs and saints...
. In this fragment the area is calculated of some so-called Hippocratic lunes
Lune (mathematics)
In geometry, a lune is either of two figures, both shaped roughly like a crescent Moon. The word "lune" derives from luna, the Latin word for Moon.-Plane geometry:...
— see Lune of Hippocrates
Lune of Hippocrates
In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of circles, one of which passes through the center of the other and has half the area of the other...
. This was part of a research programme to achieve the "quadrature of the circle
Squaring the circle
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge...
", that is, to calculate the area of the circle, or, equivalently, to construct a square with the same area as a circle. The strategy apparently was to divide a circle into a number of crescent-shaped parts. If it were possible to calculate the area of each of those parts, then the area of the circle as a whole would be known too. Only much later was it proven (by Ferdinand von Lindemann
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i.e., it is not a root of any polynomial with rational coefficients....
, in 1882) that this approach had no chance of success, because the factor pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
(π) is transcendental
Transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
. The number π is the ratio of the circumference to the diameter of a circle, and also the ratio of the area to the square of the radius.
In the century after Hippocrates at least four other mathematicians wrote their own Elements, steadily improving terminology and logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
's Elements (c. 325 BC) that was to remain the standard geometry textbook for many centuries. Hippocrates is believed to have originated the use of letters to refer to the geometric points and figures in a proposition, e.g., "triangle ABC" for a triangle with vertices at points A, B, and C.
Two other contributions by Hippocrates in the field of mathematics are noteworthy. He found a way to tackle the problem of 'duplication of the cube', that is, the problem of how to construct a cube root. Like the quadrature of the circle this was another of the so-called three great mathematical problems of Antiquity. Hippocrates also invented the technique of 'reduction', that is, to transform specific mathematical problems into a more general problem that is more easy to solve. The solution to the more general problem then automatically gives a solution to the original problem.
Astronomy
In the field of astronomy Hippocrates tried to explain the phenomena of cometComet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
s and the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
. His ideas have not been handed down very clearly, but probably he thought both were optical illusions, the result of refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
of solar light by moisture that was exhaled by, respectively, a putative planet near the sun, and the stars. The fact that Hippocrates thought that light rays originated in our eyes instead of in the object that is seen, adds to the unfamiliar character of his ideas, which belong to the realm of speculative philosophy.