Tag Archives: Quadrant

A plaque in the Cloth Hall in Krakow

Photography by Carlos Dorce

Photography by Carlos Dorce

In the ground floor of the Cloth Hall of Krakow there is this modern plaque (2007) designed by Czeslaw Dźwigaj and the selection of the text was made by Jerzy Wyrozumski and Alexander Kravchuk:

1257 Krakow city rights advocates by the German tradition and the situation of the market and the houses and affected courts

It was Bolesław V, “the Chaste One”, (1226–1279), Duke of Sandomierz in Lesser Poland from 1232 and High Duke of Poland from 1243 until his death, who introduced in 1257 the city rights modelled on the Magdeburg law allowing for tax benefits and new trade privileges for the citizens and this plaque was designed to conmemmorate the 750th anniversary of this moment.

The Cloth Hall is one of the most emblematic symbols of Krakow because is probably the oldest shopping mall in the World:

Source: Wikimedia Commons

It’s in the middle of the main square of Krakow and everybody visit it and buy something in the shops of the ground floor.

Photography by Carlos Dorce

Photography by Carlos Dorce

So next time that you visit Krakow look at the floor to this conmemorative plaque:

Location: The Cloth Hall in Krakow (map)

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Monument to Hevelius

Photography by Carlos Dorce

Photography by Carlos Dorce

This monument was designed by Jan Szczypka on 2006 and was unveiled on January 28 to conmemmorate the 395th anniversary of his birth. It’s opposite the Old Town Hall and near the church where he was buried which tower can be seen behind the monument.

Photography by Carlos Dorce

Photography by Carlos Dorce

Hevelis was the last great astronomer who worked without telescopes so he is working with a quadrant in spite of the 17th century modern devices.

Next to him there is a stellar map painted on a large wall waiting to be observed by this great astronomer.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Monument to Hevelius in Gdansk (map)

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)

Copernicus and Hevelius in the Museum of Technology

Photography by Carlos Dorce

Photography by Carlos Dorce

My trip to Poland and Praghe finished yesterday and I remember that in my first post about the Museum of Technology of Warsaw I didn’t talk about the astronomical room in the second floor of the museum. It has some telescopes, reproductions of satellites and a lot of information about the space and we can also find the corner dedicated to Copernicus and his De Revolutionibus Oribium Coelestium and Hevelius.

Photography by Carlos Dorce

Photography by Carlos Dorce

There are three reproductions of Copernicus’s astronomical instruments which we can imagine in the hands of this Polish astronomer. First of all, the armillary sphere…

Photography by Carlos Dorce

Photography by Carlos Dorce

…the paralactic triangle (triquetum) for measuring the angular heigh of the Moon…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and the solar quadrant used by Copernicus in 1510-1520 in order to watch the Sun:

Photography by Carlos Dorce

Photography by Carlos Dorce

Johannes Hevelius’ instruments are represented by some old images…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and there is a representation of his observatory in Gdansk:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Museum of Techonolgy in Warsaw (map)

The National Technical Museum in Prague

Photography by Carlos Dorce

Photography by Carlos Dorce

This is one of the Top 10 Museums in Prague! The museum was founded in 1908 and has been in its current location since 1941. It’s a very big building and the collection exhibited is so big although the exhibition about transports is its main attraction:

Photography by Carlos Dorce

Photography by Carlos Dorce

But for me, the exhibition about Astronomy has been the interesting part of the museum and I have been able to visit it on my own meanwhile my children were playing in another room with some technical toys. The astronomical rooms are very dark so it has been very difficult to take good pictures although I’ve tried to do my best. The collections has sundials, armilar spheres, quadrants, astrolabes,… and a lot of other astronomical instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, the polyhedrical sundials are so beautiful like this constructed on a cube by German David Beringer around 1750:

Photography by Carlos Dorce

Photography by Carlos Dorce

Or… what about this other constructed by Mathias Karl Krausler in 1691?

Photography by Carlos Dorce

Photography by Carlos Dorce

The oldest exhibited astrolabe is this unsigned one from around 1450:

Photography by Carlos Dorce

Photography by Carlos Dorce

And there also is an unsigned torquetum from the late 16th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

One of the instruments which have surprised me has been Joost Bürgi’s sextant for measuring the angles of celestial bodies (I knew that Bürgi, one of the inventor of logarithms, had constructed a lot of clocks and astronomical instruments but I didn’t expect to find one here!). Kepler used it to measure two consecutive oppositions of the planet Mars in 1602 and 1604.

There also is Habermel’s sextant, built by Erasmus Habermel (1538 – 15th of November of 1606 in Prag) who was  mechanic at the court of Emperor Rudolph II:

Photography by Carlos Dorce

Photography by Carlos Dorce

The prevailing opinion for a long time was that the instrument belonged to Brahe and so it was called the “Tychonian sextant”.

Habermel was specialised in small devices and portable sundials and one example is this sundial in the form of a book (c.1600)…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and another is this equinoctial sundial (1585):

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, look at this armilar sphere from the second half of the 16th century! It’s a piece of art!

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

Copernicus’ House in Torun

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus’ house was built in the 14th/15th century in the Gothic style of the Hanseatic towns. It has a high entrance hall with an open kitchen on the ground floor and the merchant’s office. The rooms are upstairs.

Photography by Carlos Dorce

Photography by Carlos Dorce

The building was the property of Copernicus’ family in the years 1463-1480 and it may well be here that he was born in 1473.  In an old picture it’s possible to see Napoleon Bonaparte walking in front of the present Copernicus Street nr 40. Till the end of the 19th century there was the wrong opinion that Copernicus had been born there although it seems to be the present numbers 15 and 17 the right houses. In the end of the 15th century, Copernicus’ father owned these three houses and another one in 36 and 37 Old Market Square.

Nowadays, there is a restaurant in 40 Copernicus Street…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and a new building is a department store (“Dom Towarowy”):

Photography by Carlos Dorce

Photography by Carlos Dorce

The interior of the house (17 Copernicus Street) is reconstructed and the imagination is the only way to see Copernicus familiy in it.

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum is full of portraits (I’m going to write another post about them!), the replicas of the instruments, scultures about the heliocentric system… and information about Copernicus’ life and works. For example, here you have a very modern design for Copernicus’ office:

Photography by Carlos Dorce

Photography by Carlos Dorce

And the room dedicated to his De Revolutionibus:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, hthe replicas of Copernicus’ instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

A few days ago I went to Frombork where Copernicus died and today I’ve been in the house where he was born. I’ve been in Olsztyn too so… what about going to Krakow where he studied? Thus… next step: Krakow!

Location: Copernicus’ house in Torun (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)

Pythagoras in Temple Bar Moument

Photography by Carlos Dorce

Photography by Carlos Dorce

The Temple Bar Memorial (1880) stands in the middle of the road opposite Street’s Law Courts marking the place where Wren’s Temple Bar used to stand as the entrance to London from Westminster.

The monument has two standing statues dedicated to Queen Victoria and the Prince of Wales because both were the last royals to pass through the old gate in 1872.

Photography by Carlos Dorce

Photography by Carlos Dorce

The reliefs round Queen Victoria contains some allegories which includes the first picture about the Euclidean demonstration of the theorem of Pythagoras. We also find a ruler and a globe with the ecliptic.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Temple Bar (map)

The National Maritime Museum

The National Maritime Museum is another of the touristic attractions which can be visited in Greenwich. Of course, you can see boats, ships, maps,… and all the things related to the sea and the English glorious past. Therefore… what can the mathematical tourist visit here? Navigators used charts, maps, astrolabes, globes,… in their adventures so we can start our mathematical visit with all these mathematical objects!

Photography by Carlos Dorce

Photography by Carlos Dorce

Brass celestial globe. German, about 1725

This is one of a pair with a terrestial globe. It shows constellations, the Milky Way and the Magellanic Clouds. It contains some mistakes, indicating that it was a luxury item that could adorna wealthy home rather than an up-to-date scientific instrument. Nevertheless, with its calendar ring, it could be used to identify what was seen in the night sky.

There also are terrestial globes which were used by navigators to measure distances on the terrestial surfaces:

Photography by Carlos Dorce

Photography by Carlos Dorce

The first golden globe is from 1600 and the globe at its right is a French globe from 1625. Behind it there is a German terrestial globe by Johann Reinhold (1588). Of course, sundials also are shown in the exhibition! The first one (left) is an inclining dial for use in Japan before 1872 and the second is an equinoctial dial fou use in Huangzou, China, in the 19th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

We can also find astrolabes, compasses, quadrants, telescopes, rulers,…

Photography by Carlos Dorce

Photography by Carlos Dorce

Look at this astrolabe from Islamic Spain (c.1230) by an unknown maker! It’s a jewel!

Photography by Carlos Dorce

Photography by Carlos Dorce

I am sure that you can find out more mathematical objects if you have enough time to enjoy all the exhibition!

Location: National Maritime Museum in Greenwich (map)

The Royal Observatory in Greenwich (and III)

Source: Wikimedia Commons

The third step in the visit to the Royal Observatory of Greenwich is Flamsteed House.

The Royal Observatory of Greenwich was founded in 1675 when Charles II ordered that a small observatory be built in Greenwich Park and appointed John Flamsteed as his ‘astronomical observator’. Flamsteed’s task was to make observations that would improve astronomical navigation, in particular providing a means of finding longitude at sea.

Photography by Carlos Dorce

Photography by Carlos Dorce

The ceiling of the first room is painted with a map of the night sky and there are portraits of the ten Astronomers Royal who lived here between 1676 and 1948:

Photography by Carlos Dorce

Photography by Carlos Dorce

Christopher Wren was responsible for building the Observatory. He later said that it was designed ‘for the Observator’s habitation & a little for Pompe’. The following four rooms were Flamsteed’s living quarters. They were incorporated into the enlarged home of the Astronomer’s Royal over the next two and a half centuries. Beyond these, upstairs, is the magnificient Great Star Room, or Octagon Room.

ROG14

The Octagon Room by Francis Place (c. 1760)

The Octagon Room is one of the few surviving interiors designed by Wren and it was used mainly for observing eclipses, comets and other unusual celestial events.

The 32-inch Astronomical Quadrant is located in this room. It is signed by John Bird but the telescope which was once attached is missing.

Photography by Carlos Dorce

Photography by Carlos Dorce

The engraving of the Octagon Room by Francis Place shows a similar, earlier quadrant standing on a wheel-tripod platform, which allowed the astronomer to roll it from window to window.

On the wall behind the quadrant we can see three replicas of the clocks which were made in 1676 by Thomas Tompion and sold by Flamsteed’s widow some years later. There is also a replica telescope tube of the kind used here until 1765. Will my daughter be able to discover a new planet?

Photography by Carlos Dorce

Photography by Carlos Dorce

If we go downstairs now we’ll discover an exhibition about the determination of the longitude at sea:

Where am I?

At sea, navigation is a matter of life and death. Out of sight of land, how can you tell where you are?

By 1700, skilled seamen could find their position north or south (their latitude), but still lacked accurated instruments or methods to calculate their east-west position, known as longitude.

With growing international trade, the lives and valuable cargoes lost in shipwrecks made solving this ‘Longitude Problem’ urgent for all sea-going nations.

Photography by Carlos Dorce

Photography by Carlos Dorce

The exhibition starts with these two 17th-century globes from North Africa (left) and Persia (right) and then you meet the star of the ‘Longitude Problem’:

John Harrison Photography by Carlos Dorce

John Harrison (1693-1776) by Thomas King (c. 1766)
Photography by Carlos Dorce

Finding longitude – the timekeeper method

One solution to the Longitude Problem was an accurate and portable sea-going clock. By 1726, news of the Longitude Prize had reached John Harrison, a carpenter and self-taught clockmaker from Lincolnshire. Harrison was already making highly accurate land-based clocks and had solved major problems to do with temperature change and friction.

Harrison spent the next 45 years of his life developing portable sea-going timekeepers that would accurately, in spite of a ship’s motion and temperature changes. Each timekeeper represented years of obsessive labour.

By 1760, Harrison had solved the Longitude Problem with his fourth marine timekeeper, now known as H4. It is one of the most important machines ever made.

Photography by Carlos Dorce

Photography by Carlos Dorce

Harrison’s first timekeeper [H1]

This timekeeper took five years to build. In 1736, it was tested on a sea voyage to Lisbon and back. Harrison was very seasick, but the timekeeper worked. It was the most accurate sea-going clock then known, though not quite accurate enough to win the 20.000 pounds prize.

This prize was offered in 1734 by the British government for a ‘practical and useful’ method enabling ships to determine their longitude at sea.

In the exhibition there are also some timekeepers more and the portraits of some of the most important scientific men which lived in the same time as Harrison: Halley succeeded Flamsteed as Astronomer Royale and his major programme was to replace all the astronomical instruments which were sold by Flamsteed’s widow, and to chart the Moon’s 19-year cycle.

Edmund Halley Photography by Carlos Dorce

Edmund Halley by George White after G.Kneller (c.1721)
Photography by Carlos Dorce

Newton advised the Parliamentary committee that established the Longitude Prize and became a member of the Board of Longitude:

Sir Isaac Newton Photography by Carlos Dorce

Sir Isaac Newton by Jacobus Houbraken after G.Kneller (18th century)
Photography by Carlos Dorce

Finally, apart of the camera obscura, we can find outside the Family Tombstone of Halley which was moved to the Observatory from the churchyard of St. Margaret’s in Lee when Halley’s tomb was restored in 1854. The tomb itself is still located at St. Margaret’s with a replica tombstone in place:

Photography by Carlos Dorce

Photography by Carlos Dorce

As you have seen, you must visit the Royal Observatory in Greenwich if you visit London: it’s only a few metro stops from the center of the city!

LocationGreenwich Observatory (map)