Tag Archives: Ibn Qurra

Aljafería Palace (Qasr al-Jaʿfariya)

Aljaferia Palace Photgraphy by Carlos Dorce

Aljaferia Palace
Photography by Carlos Dorce

Aljaferia Palace is one of the most beautiful Islamic palaces which can be visited in Spain. It was built in the second half of the 11th century in the Moorish taifa os Saraqusta (present day Zaragoza) by the King al-Muqtâdir Bânû Hûd.

Source: Wikimedia Commons

I’m sure that you are wondering why I am talking about this building now. The building is wonderful but this is not the reason. Do you know who King al-Mu’tamân is? No? King al-Mu’tamân (1081-1085) grew in this palace and was educated under teachers and philosphers. Before 1081, he began to write an encyclopaedic work about Mathematics (Kitâb al-Istikmâl or Book of the Perfection) with his collaborators’ contributions. Al-Mu’tamân wanted to write the most important mathematical treatise until that time. Only four hundred propositions about Classic Geometry have survived: some results from Euclid’s Elements and Data, Apollonius’ Conics, Archimedes’ On the sphere and the cylinder, Theodosius’ Spherics, Menalaus’ Spherics and Ptolemy’s Almagest. There also are Arabic contributions as Thâbit b. Qurra’s treatise on amicable numbers, some of the Bânû Mûsâ’s works, Ibrâhim b. Sinân’s The Quadrature of the Parabola and Ibn al-Haytham’s Optics, On the Analysis and the Synthesis and On the given things. One of the most interesting results is the demonstrarion of Ceva’s Theorem (attributed to the Italian mathematician Giovanni Ceva (d. 1734) ). Unfortunately, al-Mu’tamân became King of Saraqusta in 1081 and the Book of Perfection was never finished so the sections about Astronomy and Optics weren’t writen. The Book of Perfection was commented by Maimonides (1135-1204) some years later.

Photography by Carlos Dorce

Photography by Carlos Dorce

In 1118 King Alfonso I of Aragon conquered Zaragoza and after a lot of years, the palace became the royal residence. Nowadays, we can visit most of its rooms included Catholic Monarchs‘s throne room. Can you imagine young al-Mu’tamân playing with his friends in this idilic place?

Photography by Carlos Dorce

Photography by Carlos Dorce

Or praying in the octogonal Oratory?

Photography by Carlos Dorce

Photography by Carlos Dorce

Visiting the Palace, we can see a very good quotation about the importance of the Geometry in the Islamic art:

The preference of the Islamic culture for abstract art developed a type of decoration based on geometric order, its main argument being repeated themes and the objective of suggesting infinity. Of great importance in this concept was the development of mathematics in the Muslim civilization, which were then skillfull applied to construction and decoration. Starting off with a few examples of symmetry, Hispano-Muslim and then Mudejar art was capable of developing complex decorative themes that were always based on repetition.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Aljaferia palace in Zaragoza (map)

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Van Gent’s Claudius Ptolemy

Portrait of Claudius Ptolemy (c. 1475)
Justus van Gent (c.1410 – c.1480)
Louvre Museum. Font: Wikimedia Commons

This is not the first time in which I talk about Justus van Gent’s paintings. Indeed, the first post of this blog was dedicated to the portrait of Euclid of Alexandria made by this Dutch painter. This portrait is in Louvre Museum and it’s part of the serie of portraits of some important people made by Van Gent.

Claudius Ptolemy lived and worked in the IInd century AD in Alexandria. We know little about him and we can place his life from his own astronomical observations recorded in his great work entitled Mathematical Collection. His first observation was an eclipse of the Moon made in Alexandria in the 5 April of 125 AD and the last one was the observation of the maximum elongation of Mercury made in the 2 February of 141 AD. This recorded data mean that Ptolemy worked in his astronomical book in the period 125-141 AD. Furthermore, we know that in the year 147/148 AD he erected a stele in the town of Canopus about 25 Km East of Alexandria. we can also observe that his name Claudius Ptolemy is a good definition of his life: Claudios is a Greek name whereas Ptolemaios could indicate that he came from one of the various Egyptian towns named after the Ptolemaic kings.

Ptolemy’s Mathematical Collection was the most important Greek astronomical work. Later the Arabs called it with the superlative Al-Majistî (Almagest)  and with this name the Latin Europe adopted as the referencial astronomical handbook. In the IVth century, Pappus of Alexandria (c.290-c.350) made a Commentary on it and part of the commentary on Book V (the Almagest is divided in 13 Books) as well as his commentary on Book VI are actually extant in the original. Theon of Alexandria (c.335–c. 405) wrote another commentary on the Mathematical Collection in 11 books incorporating as much as was available of Pappus’ work. Theon was assisted by his daughter Hypatia of Alexandria (c.360–March 415) and the whole text was published at Basel by Joachim Camerarius (April 12, 1500 – April 17, 1574) in 1538.

Joachim Camerarius (1500-1574)
Font: Wikimedia Commons

The Mathematical Collection arrived at the Muslim World and it was translated into Arabic, first by translators unnamed at the instance of Yahyâ b. Khâlid b. Barmak, then by al-Hajjâj, the translator of Euclid (c.786-835), and again by Ishaq b. Hunain (d.910) whose translation was improved by Thâbit b. Qurra (c.826–February 18, 901). The first edition to be published (Venice, 1515) was the Latin translation made by Gherard of Cremona from the Arabic, which was finished in 1175. Although there was a previous Latin translation from the Greek, the first Latin translation from the Greek to be published was that made by Georgius of Trebizond in 1451 and the editio princeps of the Greek text was brought out by Grynaeus at Basel in 1538.

According to Sir Thomas Heath in his A History of Greek Mathematics (II, 275), the Almagest is most valuable for the reason  that it contains very full particulars of observations and investigations by Hipparchus, as well as of the earlier observations recorded by him. The indispensable preliminaries to the study of the Ptolemaic system, general explanations of the different motions of the heavenly bodies in relation to the Earth as centre, propositions required for the preparation of Tables of Chords, the Table itself, some propositions in spherical trigonometry,… are in Books I and II; Book II deals with the length of the year and the motion of the Sun on the eccentric and epicycle hypotheses; Book IV is about the length of the months and the theory of the Moon; in Book V we find the construction of an astrolabe and the theory of the Moon continued, the diameters of the Sun, the Moon and the Earth’s shadow, the distances between them and their dimensions; the conjunctions and oppositions of Sun and Moon, the solar and lunar eclipses and their periods are studied in Book VI; Books VII and VIII are about fixed stars and the precession of the equinoxes and Books IX-XIII are devoted to the movements of the planets.

Illustration of the Ptolemic system
Harmonia Macrocosmica by Andreas Cellarius (1661). Font: Wikimedia Commons.

Location: Louvre Museum in Paris (map)