Almagest

Almagest (in Greek μαθηματική σύνταξις, Arabic المجسطي, DMG al - maǧisṭī ) is called one of the masterpieces of ancient astronomy, which dates back to the Hellenistic Greek scholar Claudius Ptolemy.

Basics

The most comprehensive and most competent representation of the astronomical system of the Greeks gave us Claudius Ptolemy with his created around the middle of the 2nd century textbook Mathematike syntaxis (Eng. "Mathematical Compilation "). Later copies of this highly respected work bore the title Megiste syntaxis ( "The Greatest compilation " ), which was adopted as the al - madschisti in the Arabic translations and went from there as Almagest in today's parlance. In contrast to other works of the time the text of the Almagest is fully preserved.

The Almagest is based on the geocentric Ptolemaic worldview and works its astronomical Details. In contrast to the more physically based work Hypotheseis ton ( " hypotheses on the planet " ) planomenon of Ptolemy in the Almagest is the mathematical description of the orbits of individual celestial bodies in the foreground. Because of its exact mathematical modeling of celestial movements and the resulting possibility provided this fairly accurately predict, it became the standard work of mathematical astronomy from the 2nd to the 17th century.

The Almagest repressed because of its qualities very early on all other Greek astronomical writings. Ptolemy

• Systematized in the whole of ancient knowledge about the objects in the sky
• Took advantage of this high level of Greek mathematics and
• Embedded his system in the Aristotelian physics.

Today, the plant is considered to be the climax and conclusion of ancient astronomy.

In addition to the work itself also ancient comments on it have survived, especially Pappus and Theon of Alexandria.

The content and structure of the Almagest was for more than 1500 years for all astronomical handbooks the model. As Euclid's Elements is also the Almagest of 13 books:

• Book 1-2: Introduction to the Ptolemaic system and the mathematical lemmas
• Book 3: Theory of sun
• Book 4-5: Theory of the Moon
• Book 6: lunar and solar eclipses
• Book 7-8: Stars and star catalog (List of Constellations )
• Book 9-13: theory of the planets (Saturn, Jupiter, Mars, Venus and Mercury)

Content

As a " preliminary " Ptolemy provides some principles:

• The sky building has a spherical shape and turns like a ball.
• Your shape after the earth, considered as a whole, also spherical.
• Your location after she takes as a center in the middle of the whole sky.
• Their size and distance to it is in relation to the sphere of fixed stars as a point.
• The earth takes turn any local changes causing movements.

However, the simple ideas of spheres and circles were not in accordance with the observational data. Two difficulties were striking:

• The first inequality - planets traverse the path segments with non-uniform speed,
• The second inequality - planets move partially in the opposite direction, their movements resemble a kind of loop.

To explain these phenomena, there have been various models. Ptolemy took over in his work the epicycle of Apollonius of Perge with its epicycles and deferent, as this theory had the advantage compared to the older spherical shells model of Eudoxus of Cnidus that you could expand it ( epicycles higher order). From Hipparchus of Nicaea was the idea of the eccentric position of the deferent came ( Exzentertheorie ). Because of the uneven speed of Ptolemy needed in addition also a balance point, the so-called equant: from this point the movement of the planets appeared to turn smoothly.

The solar theory of Hipparchus, Ptolemy took over unchanged, but was of the opinion that the moon theory should be portrayed more accurately because of the complex motion of the Moon. Thanks to the very precise, handed by those same Hipparchus data of the lunar motions, Ptolemy determined in his lunar theory values ​​that could be significantly improved only by Tycho Brahe.

The Almagest contains, among other things, a systematic review of the art to measure from the measurement of angles and distances Distances ( triangulation). It later developed trigonometry ( triangulation ). In Book 1 you will find the famous table of chords, a forerunner of trigonometric tables, of ½ ° to 180 ° in increments of ½ ° (this corresponds essentially to the table of sines of ¼ ° to 90 ° in ¼ ° increments ). The following are additional sets of plane and spherical trigonometry.

Also the Almagest contains a catalog of celestial objects. This inventory consists of the information about 1025 stars in 48 constellations. This catalog was the next 15 centuries, then as influential for the structure, terminology, and the coordinate data of all his successors.

Criticism

With the epicyclic model, namely the planetary motions in the context of then- measurement accuracy could predict very reliable, but at the price of some contradictions with the principles of Aristotelian physics:

• The motion of the planet was no longer the center of the world (due to an eccentric position of the deferent ),
• The uniformity of planetary motion was to ensure only by mathematical tricks.

Therefore, they spoke very early by saving the phenomena. By this was meant that astronomy should be seen rather as a branch of geometry than as a branch of physics. You would be responsible only for the exact mathematical representation of the movements of the stars.

A fundamental criticism on the Almagest - namely that this handle to a grotesque falsification - practiced in the 1970s, the American astrophysicist Robert Russell Newton.

Tradition

In the 9th century, many Greek writings were known to the Arabs, especially the Almagest. This has now been translated several times and commented on. He became the basis of astronomical observing and calculating the Arab world. The first and best translation we owe to the Christian Arab scholar Ibn Ishaq Hunain. Other early translations are from Al- Hajjaj ibn Yusuf ibn Matar Sahl ibn Bishr and ( Sahl al -Tabari ) and later simplified edition of Abu l - Wafa.

Since you hardly had access to Greek sources of antiquity during the Early Middle Ages in Western Europe, also the Almagest was unknown. Although astronomy was part of the quadrivium, the knowledge in this field were rather low. That changed, however, with the increasing interest in astrology, because that accurate data of astronomy were in demand. In the second half of the 12th century, several astronomy works were finally available, including Thabit ibn Qurra of the next and Abu Ma'shar al Balkhi ( Albumasar ) and the Almagest. This was translated from Arabic by Gerard of Cremona into Latin.

From the middle of the 13th century, the Almagest strong competition got in the astronomical lectures of universities by the Theorica planetarum ( "Planet Theory" ), an anonymous treatise, which was probably written by a teacher of the University of Paris. The planetary theory described the basic Ptolemaic theory for each planet and supplemented this description by further drawings.

In the 15th century, the Greek scholar George of Trebizond created from Greek sources, a translation into Latin, which has been criticized as inadequate, including Cardinal Bessarion Basilius .. The astronomer Georg von Peuerbach and then Regiomontanus worked on better translations, but died early. A summary of Regiomontanus, the " epitome ", was printed only twenty years after his death, in 1496 as " Epytoma Ioa [n ] nis de Mo [n ] te Regio in Almagestu [m ] Ptolomei ". This Bessarion work was dedicated for two decades one of the most important foundations of astronomy, Copernicus also belonged to the owners of a copy. In a complete Latin text of the Almagest was not published until 1515 in Venice. The pressure of the first Greek original version followed in 1538 in Basel, where in 1543 the Latin works of Regiomontanus and Peuerbach on the Almagest appeared, " Ioannis de Monte Regio et Georgii Purbachii Epitome in Cl. Ptolomaei magnam compositionem ... ". In the same year appeared in Nuremberg in the work " De Revolutionibus " of Nicolaus Copernicus, which built in the shape of the Almagest, and that caused the one shown in the Almagest geocentric worldview was replaced by the Copernican heliocentric. The biggest proponent of the new world were over half a century later, Galileo Galilei and Johannes Kepler. Kepler's laws then initiated also the development of modern astronomy. Erasmus Reinhold published in 1549 about the Almagest as a Greek - Latin juxtaposition, and in 1551 his Prutenischen tables with data from Copernicus.