Tag Archives: Ptolemy

Ptolemy and Pythagoras in Ulm

Photography by Carlos Dorce

Photography by Carlos Dorce

The cathedral is one of the main attractions of Ulm because its tower is the tallest in the World (more than 161 metres!). However, one of the most interesting work of art which can be admired inside the church is the 15th century choir stalls crafted by Jörg Syrlin the Elder. There are 89 seats arranged in two rows with 90 busts of saints, Old Testament figures and classical philosophers and scholars as Ptolemy…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and Pythagoras:

Photography by Carlos Dorce

Photography by Carlos Dorce

We must remember that Ptolemy represent the Astronomy in the Liberal Arts and Pythagoras usually represents the Arithmetic although his bust here is related with the Music.

Most of the people who visit the cathedral don’t know that this is one of the most wonderful medieval work of art which can be seen in Germany although this beautiful picture woul remain in their minds in a lot of years.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Cathedral of Ulm (map)

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Johannes Kepler Monument in Weil der Stadt

kepler0

Photography by Carlos Dorce

Weil der Stadt is located near Stuttgart. Johannes Kepler was born in this very veautiful town on December 27, 1571 and his memory is still there: this big statue is in the middle of the Market Square…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and Copernicus, Mästlin, Tycho Brahe and Jobst Bürgi are with him in this monumental sculpture.

Photography by Carlos Dorce

Photography by Carlos Dorce

The four scientists are in the corners of the base of the statue and the words “Astronomia”, “Optica”, “Mathematica” and “Physica” are graved on each of the four sides.

Photography by Carlos Dorce

Photography by Carlos Dorce

I must say that here we have the first (imaginary) bust of Bürgi that I know. Bürgi was one of the originators of the logarithms because Kepler said that he had seen Bürgi using logarithms in astronomical calculus (Rudolphine Tables (1627)) before their “official” first occurrence in Napier’s  Mirifici Logarithmorum Canonis Descriptio (1614). Furthermore, Bürgi published his logarithms in his Aritmetische und Geometrische Progreß tabulen (1620) but his “red numbers” and “black numbers” couldn’t never win the “logarithms” which were the first calculator in all history.

Photography by Carlos Dorce

Photography by Carlos Dorce

Notice that this statue is not very similar to this other portrait from 1620:

Joost_buergi

J.Bürgi at the age of 67. Drawing by Aegidius Sadeler (1619)

The base of the statue also have four graved images representing moments in Kepler’s life like thispicture with Kepler in the middle explaining the Copernican system…

Photography by Carlos Dorce

Photography by Carlos Dorce

… with Hipparchus and Ptolemy watching how a central Sun brights in the middle of the universe.

kepler7

Can you imagine Kepler investigating about his elliptical orbits?

Photography by Carlos Dorce

Photography by Carlos Dorce

Next to Market Square there is his bithplace which hosts… no, no, no! Tomowwor will be another day!

Location: Weil der Stadt (map)

Abû al-Wafâ’ al-Buzjanî’s doodle

1075 aniversari del naixement d'Abu al-Wafa al-Buzjani

This beautiful doodle was published by google in the Persian and Arabic countries last 10th June because in 10th June 940 the great Abû al-Wafâ’ al-Buzjanî was born in Persia. Since 959, he worked in the Caliph’s court in Baghdad among other distinguished mathematicians and scientists who remained in the city after Sharâf al-Dawlâh became the new caliph in 983. He continued to support mathematics and astronomy and built a new observatory in the gardens of his palace in Baghdad (June 988) which included a quadrant over 6 metres long and a sextant of 18 metres.

Abû al-Wafâ’ wrote commentaries on works of Euclid, Ptolemy, Diophantus and al-Khwârizmî, and his works were very important in the developement of Trigonometry and Astronomy.

Museum of Nicolaus Copernicus, Frombork

Photography by Carlos Dorce

Photography by Carlos Dorce

In a previous post I began to talk about this museum located inside Frombork castle. You can learn almost everything about him, his life and his works on medicine, economies and, of course, astronomy, including the replicas of his instruments (we saw them also in Warsaw). For example, it’s possible to see some facsmile editions of his works and also a recreation of his desk:

Photography by Carlos Dorce

Photography by Carlos Dorce

Among the references about his publication of his works, we can find this engraving showing Copernicus in a lecture for the Cracovian scientists in 1509:

Photography by Carlos Dorce

Photography by Carlos Dorce

Or this other wonderful one (1873) with Copernicus in he middle of the picture talking about his heliocentric system:

Photography by Carlos Dorce

Photography by Carlos Dorce

How proud he is of his heliocentric theory!

Photography by Carlos Dorce

Photography by Carlos Dorce

And who are his guests? First of all, Hipparcus (with the armillar spher) and Ptolemy (with his geocentric system) are listening the theory which will finish theirs. Ptolemy looks askance at Tycho Brahe meanwhile Newton is looking at Laplace:

Photography by Carlos Dorce

Photography by Carlos Dorce

Galileo Galilei is behind Copernicus looking at him with great reverence:

Photography by Carlos Dorce

Photography by Carlos Dorce

And Hevelius, the other great Polish astronomer, agrees Copernicus’ theories although he never had the telescope to check them.

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, Johannes Kepler seems to be bored of listening this obvious theory although his ellipses will be the curves which will change the astronomy.

Photography by Carlos Dorce

Photography by Carlos Dorce

A beautiful picture for a beautiful museum. Next step: the cathedral!

Location: Frombork castle (map)

The Long Market in Gdansk

Source: Wikimedia Commons

The Long Market (Długi Targ) is one of the most important touristic attractions of Gdansk. It was a merchant road in the 13th century. After the massacre of Gdansk citizens on 13 November 1308 by Teutonic Knights, the place became the main street of the city and is name “Longa Platea” was first written in 1331. Nowadays it’s a very beautiful long square full of typical shops and restaurants which are the soul of this cosmopolutan city. One of its most representative houses is the town hall from the 16th century and Neptune’s Fountain, the main symbol of the city, is also there. This fountain was constructed in 1617 from Abraham van den Blocke’s designs.

Photography by Carlos Dorce

Photography by Carlos Dorce

Thus, if you visit Gdansk, you must have time to take a beer or a coffee in one of the cafes or have a typican Polish dinner in one of the restaurants which fill all the beautiful houses which can be admire in the square.

Among all these houses we also find a lot of mathematical symbols which allow me to talk of them in this new post. For example, Radisson Blue hotel is located in number 19 and the allegorical paintings of the facade are a joy for the mathematical freak:

Photography by Carlos Dorce

Photography by Carlos Dorce

On both sides we have some of the most important men in the history of astronomy like Hipparcus of Rhodas,

Photography by Carlos Dorce

Photography by Carlos Dorce

Ptolemy:

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus:

Photography by Carlos Dorce

Photography by Carlos Dorce

Galileo Galilei:

Photography by Carlos Dorce

Photography by Carlos Dorce

and Hevelius:

Photography by Carlos Dorce

Photography by Carlos Dorce

Approaching the town hall, there is another red house which is full of artists ans it’s coronated by a replica of Aristotle and Plato from Raffaello’s “School of Athens”:

Photography by Carlos Dorce

Photography by Carlos Dorce

In another house there also are the allegorical Astronomia rounded by Cellarius’ heliocentric systems:

Photography by Carlos Dorce

Photography by Carlos Dorce

And finally we find other allegories like the Architecture, the Geometry or the Geography in the opposite side of the square:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example…

Photography by Carlos Dorce

Photography by Carlos Dorce

…or:

Photography by Carlos Dorce

Photography by Carlos Dorce

As you can see, this is an excuse to admire the beautiful facades of the houses in this square which I never tire of walking through it.

By the way, there is a beautiful sundial in the town hall:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Długi Targ in Gdansk (map)

An astrolabe in Berlin

Photography by Carlos Dorce

The first object which you can see in the second floor of the Pergamon Museum in Berlin is this Iraqi astrolabe made by the astronomer and poet Hibât Allâh al-Bagdâdî and designed by the great Abû Jacfâr al-Khâzin (c.900-c.970). This bronze piece is unique!

Al-Khâzin was a very important Persian mathematician and astronomer who worked in Ray and wrote a Commentary on the Almagest. He also wrote one of the most important work on the construction of astrolabes which was very appreciated by his colleagues.

Location: Pergamon Museum (map)

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)

Immortal Books, essential instruments (I)

Photography by Carlos Dorce

Photography by Carlos Dorce

This post is about a very interesting exhibition about 26 selected scientific books which I visited in Madrid in August and it can be visited now in A Coruña (from the 17th October). There are explanation of the 26 books and their authors and I am going to talk about the mathematical ones (of course!). Furthermore, there are Eulogia Merle‘s drawings of every scientist exhibited here so this is another interesting attraction to visit it.

The first great mathematician is Euclid (c.295 BC).

Photography by Carlos Dorce

Photography by Carlos Dorce

[In Spanish:] Es difícil precisar datos de la biografía del más destacado matemático de la antigüedad grecolatina, considerado el Padre de la Geometría. Solo se conocen con certeza dos hechos indiscutibles: vivió en una época intermedia entre los discípulos de Platón y los de Arquímedes, y formó una gran escuela de matemáticas en Alejandría. Según el filósofo bizantino Proclo, Euclides enseñó en esta ciudad del delta del Nilo durante el mandato de Ptolomeo I Sóter, es decir, entre los años 323 y 285 a.C. Murió en torno al año 270 a.C. Su fama radica en ser el autor de los Elementos, un tratado de geometría que ha servido de libro de tecto en la materia hasta comienzo del siglo XX. Está compuesto por trece libros que tratatn de geometría en dos y tres dimensiones, proporciones y teoría de números. Presenta toda la geometría basándose en teoremas que pueden derivarse a partir de cinco axiomas o postulados muy simples que se aceptan como verdaderos.

There are two different digital editions of the Elements and a compass from the 16th or 17th century with all this information:

Photography by Carlos Dorce

Photography by Carlos Dorce

The next Greek mathematician is Archimedes (287-212 BC) although his book here is On the floating bodies which is less mathematical than phisician.

Photography by Carlos Dorce

Photography by Carlos Dorce

Ptolemy (2nd century) is the next and his Almagest was the most important astronomical book since the 16th century.

Photography by Carlos Dorce

Photography by Carlos Dorce

There is also an interesting wooden astrolabe from 1630 (“Claudii Ricchardi”):

Photography by Carlos Dorce

Photography by Carlos Dorce

Arsitotle, Hippocrates and Pliny the Younger are the other three Greek scientists represented in the exhibition.

Location: MUNCYT in Madrid (map) and MUNCYT in A Coruña (map)

Whipple Museum of the History of Science (III)

Photography by Carlos Dorce

Photography by Carlos Dorce

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Indian astrologer’s celestial globe from the 19th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

This celestial globe is extremely unusual in being inscribed in Arabic, Persian and Urdu, representing a blending of traditions. It was probably designed for astrological use.

English Ptolemaic armillary sphere, by Richard Glynne (c. 1715)

Photography by Carlos Dorce

Photography by Carlos Dorce

Ptolemy’s cosmology placed the moon along with Mercury, Venus, the sun, Jupiter and Saturn in orbit around the Eart, which stood at rest at the centre of the universe. Although a sun-centred universe was more widely accepted among astronomers in the 18th century, Ptolemaic armillary spheres such as this one continued to be made and sold.

Upstairs there is another exhibition related to globes and armilar spheres and we can find some terrestial globes and Copernican and more Ptolemaic spheres. Here you have one Ptolemaic one dated in 1790:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, I must point to two delicatessen. The first one is this little ivory plaque showing astronomers working with their instruments:

Photography by Carlos Dorc

Photography by Carlos Dorce

The other is this picture showing a figure pointing to a globe from a section of the Roman mosaic from mid-2nd century (Museo Nacional de Arte Romano):

WM28

LocationWhipple Museum of the History of Science in Cambridge (map)

The British Museum

Photography by Carlos Dorce

Photography by Carlos Dorce

Today we’ve been in the British Museum. If you visit London you must go there to understand the history of the World. t has been my third time there but I love it as our first time together! I am going to write two or three posts about it but today I am only going to talk about the Islamic astronomical instruments which are exhibited in floor -1 because in the frontispiece of the main entrance you can see an armilar sphere above which everybody must walk to enter the museum.

Some aspects of science in the Islamic world developed in the service of religion. The obligatory five daily prayers, performed facing Makka, and the times for fasting in the holy month of Ramadan for example, require accurate knowledge of time and direction. For many centuries Muslims used instruments, mathematical tables and certain practices of folk-astronomy to find this important information. In this way Muslim scholars reached a level of sophistication unparalleled in Europe until well into the modern age.

We have an example in this astrolabe by Abd al-Karim al-Misri (1241):

Photography by Carlos Dorce

Photography by Carlos Dorce

Another important object is this astrolabe quadrant engraved by the timekeeper (muwaqqit) of the Umayyad mosque at Damascus (1334/4):

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, we find this brass celestial globe with constellations by Muhammad ibn Hilal al-Munajjim al-Mawsili (Mosul, 1275/6):

Photography by Carlos Dorce

Photography by Carlos Dorce

Celestial globes are representations of the night sky. They were already known in Ancient Greece. The 48 constellations described by the astronomer Ptolemy in the 2nd century AD were adopted by Islamic scholars, who then influenced European knowledge of the stars and their names. Constellations on globes are always shown in ‘globe-view’, as if seen from the outside of the sphere. In the Islamic tradition this means that human figures are represented from the front, but left-handed:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationBritish Museum in London (map)