Tag Archives: Napier

Kepler’s last home in Regensburg

Photography by Carlos Dorce

Photography by Carlos Dorce

Kepler’s last home is this orange house located in Keplerstrasse 5 in Regensburg. Reading the famous Kepler’s biography written by Max Caspar:

[…] On November 2 [1630] he rode, tired, on a skinny nag, over The Stone Bridge into Regensburg. He took up quarters in Hillebrand Billj’s house in the street now named after him. This acquaintance was a tradesman and later an innkeeper.

Only a few days after his arrival Kepler came down with an acute illness. His body was weakened by much night study, by constant worry, and also by the long journey at a bad time of year. In the beginning he attributed no significance to his being taken ill. He had often before suffered from attacks of fever. He believed that his fever originated from “sacer ignis”, fire-pustules. As the illness became worse, an attempt was made to help him by bleeding. But soon he began to lose consciousness and became delirious. Several pastors visited him and “refreshed him with the vitalizing water of consolation”. It is not said anywhere that holy communion was afforded him. In the throes of death Pastor Christoph Sigmund Donauer rendered him aid. When, almost in the last moment of his life, he was asked on what he pinned his hope of salvation, he answered full of confidence: only and alone on the services of Jesus Christ; in Him is based, as he wanted to testify firmly and resolutely, all refuge, all his solace and welfare. At noon on November 15 this pious man breathed his last. […].

A plaque on the facade says that this is the house which I was looking for when I have arrived at Regensburg:

Photography by Carlos Dorce

Photography by Carlos Dorce

Bad luck! This small museum is only open in the weekends and it’s possible to rent a guided visit only for groups! I’ve not arrived here to give up! Finally, I’ve been able to visit it and the first thing that I’ve seen… the magnificent bust of the last owner of the house…

Photography by Carlos Dorce

Photography by Carlos Dorce

… over a plaque in German language where it’s possible to read a little part of this story:

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum located in the house is very small and explains Kepler’s life and works focussing the interest in his astronomical discoveries and his three laws.

Photography by Carlos Dorce

Photography by Carlos Dorce

There is also a representation of the barrels whose volume was calculated precisely by Kepler in 1615:

Photography by Carlos Dorce

Photography by Carlos Dorce

Another bust representing the great mathematician is in the room of the first floor next to some information about his commemorative monument also in Regensburg.

Photography by Carlos Dorce

Photography by Carlos Dorce

There are a lot of Kepler’s works (which seem to be original) and this wonderful German edition of Napier’s logarithms (1631) which couldn’t be used by Kepler but exemplifies the great impact that this powerful calculator had in the beginning of the 17th century.

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course, his Astronomia Nova, his Harmonices mundi,… and his Tabula Rudolphinae are also exhibited.

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are explanation about his relation with Tycho Brahe and the Copernican system and a lot of astronomical instruments like sextants, globes, compasses,…

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, I want to say goodbye looking at this famous portrait. This man discovered the elliptical orbits of the palnets and his obsession with numbers let him find the second and the third law. Copernicus was right and Newton will be confirm all this theories. The World was explained (Wait Einstein, wait!).

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Kepler’s museum in Regensburg (map)

Kepler-Museum in Weil der Stadt

Photography by Carlos Dorce

Photography by Carlos Dorce

This building is the theorical Kepler’s bithplace in Weil der Stadt which hosts a very small museum about Kepler’s life and work:

At the age of six Kepler attends the German school. Continuing with Latin school he has to interrupt his attendance several times to help his parents with their work in the fields and at their inn. As a result he requires five years to complete the usual three school years.

The sickly child shows more enthusiasm at school than for hard work in the fields. His parents decide to send him to monastery school: First to the Adelberg monastery school (lower seminary) and then to Maulbronn (higher seminary).

His school comrades and teachers give him a hard time: At an early stage he starts to have his own ideas of church doctrine. His main struggle is with the meaning of Predestination and Communion.

Two celestial phenomena arouse his interest in astronomy: His mother shows him a comet, his father a lunar eclipse. Both phenomena remain in his mind for a long time. On the other hand, he never mentions his astronomy lessons in his written work.

Furthermore…

During the Age of Reformation the University of Tübingen, founded in 1477, forms the intellectual centre for Southern German Lutheran and for the Duchy of Württemberg. In 1536, Duke Ulrich orders the accomodation of poor students in Tübingen’s Stift. His aim is to ensure more graduates for loyal service in church and administration.

Coming from a humble background, Kepler wins a scholarship at the Stift. In 1589, he takes up his studies at the Faculty of Arts providing a general education, where the talented student receives many important stimuli. In particular, he studies the works of the Neoplatonists, whose ideas of a harmonically built creation make a deep impact on him.

However, his Professor of astronomy, Mästlin, influences him the most. Like a fatherly friend he familiarizes him with the ideas of Copernicus. Kepler sees an analogy in the central position of the sun to God’s omnipotence and consequently becomes a convinced advocate of the heliocentric view.

Kepler passes the baccalaureat exam at the Faculty of Arts as the second best in his class. […]. Before graduating, he accepts the position as provincial mathematician in Graz.

These were the first steps in Kepler’s life and the first thing that you see after entering the museum is the bust of this great mind:

Photography by Carlos Dorce

Photography by Carlos Dorce

Since 1594, as a provincial mathematician in Graz, Kepler…

[…] has to teach at the Lutheran seminary and write astrological calendars. His enthusiasm for astronomy inspires him to do his own research, and in 1596 he publishes his first work on astronomy Mysterium Cosmographicum.

He attempts to prove that a harmonic creation allows for only six planets. He regards the five regular Platonic polyhedra as elements of the planetary system, which, nested in the proper order, should determine the planet’s distance to the sun. As this approximately corresponds with the Copernican planetary distances, the work catches the attention of such important astronomers as Galileo Galieli and Tycho Brahe.

In spite of his fame, Kepler has to worry about his position in Graz. The Counter-Reformation creates great tension between the Lutheran inhabitants and the Catholic authorities. To recommend himself to the archduke Kepler dedicates a treatise to him on the solar eclipse of July 10th, 1600.

However, this does not prevent his expulsion from Graz one month later.

Photography by Carlos Dorce

Photography by Carlos Dorce

So these years in Graz were the period in which Kepler dreamt of his Mysterium cosmographicum and the possibility of the God’s design for the universe based in the regular polyhedra:

Photography by Carlos Dorce

Photography by Carlos Dorce

After Graz, Kepler became Tycho Brahe’s assistnat in Prague. After Tycho’s death, he assumed his position as imperial mathematician for Emperor Rudolph II:

[…] The quality of the [astronomical] data depends on the exactness of the particular orbit theory. Since all tables used around 1600 are inaccurate, Emperor Rudolph commissions Brahe and Kepler with the creation of the Tabulae Rudolphinae in 1601. When Brahe dies in the same year Kepler has to continue the work on his own.

It takes 22 years to complete the final version of the tables. Alone, the development of the elliptical orbits takes Kepler eight years. When he hears about the development of Napier’s logarithm, he integrates this into his tables and manages to simplify the calculation of orbital positions […]

Kepler discovered his first law and published it in his Astronomia nova (1609) and ten years later, he publishes his Harmonice mundi with the second and the third laws. Furthermore, Kepler had also time to wpork on infinitesimal calculus to compute the volume of some tonnels of wine:

Photography by Carlos Dorce

Photography by Carlos Dorce

I could follow explaining more things about Kepler’s life and works but this museum is very small so you must visit it. And Weil der Stadt is a very beautiful town!

Location: Kepler-Museum in Weil der Stadt (map)

The Collegius Maius of the Jagiellonian University

Photography by Carlos Dorce

Photography by Carlos Dorce

Copernicus studied in the Collegius maius between 1491 and 1495. On the list of 69 students matriculated in 1491 at the Cracok Academy were “Nicolaus Nicolai de Thuronia” and aslso his brother “Andreas Nicolai”. The Jagiellonian University consisted offour faculties at the time (the Theological Faculty, the Canonical La Faculty, the Medical Faculty and the Liberal Arts Faculty). Copernicus began his studies learning the grammar of Latin, poetry and rhetoric but he early started to attend lectures on Euclidean geometry and astronomy. During the 15th and early 16th centuries, the University gained importance in Central Europe as a scientific center due to the high level of astronomical and mathematical sciences: the distinguished professors of the time included Marcin Hrol (c.1422-c.1453), Wojciech of Brudzewo (1445-1495), Jan of Glogow (c.1445-1507) and Maciej of Miechow (1453-1523). In the second semester of 1493 he attended lectures of Jerzy Peürbach, with the comments of Wojciech of Brudzewo, and the lectures about Aristotle’s De Caelo. It’s unknown when Copernicus brothers finished their studies n Cracow but they surely didn’t receive their degrees. Perhaps their mother’s death in 1495 caused their return to Prussia.

Thus one of the required mathematical visits that must be done in Cracow is this College:

Photography by Carlos Dorce

Photography by Carlos Dorce

The building hosts an interesting museum with a lot of old objects which are not directly related to the College but I must recognize that it’s possible to imagine how the academical life was in the 15th century. The first room is a big hall full of shelves with books, statutes, quadrants, portraits, maps and spheres:

Photography by Carlos Dorce

Photography by Carlos Dorce

Everything takes you back to a ‘kitsch’ Renaissance:

Photography by Carlos Dorce

Photography by Carlos Dorce

There is space for our Copernicus, of course,…:

Photography by Carlos Dorce

Photography by Carlos Dorce

…and also for Galileo:

Photography by Carlos Dorce

Photography by Carlos Dorce

There is a special small room dedicated exclusively to Copernicus with astrolabes, charts, books and copies of some interesting documents:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, look at this interesting torquetum made by Hans Dorn in 1480 (the astrolabe was also made by Dorn in 1486)…:

Photography by Carlos Dorce

Photography by Carlos Dorce

…or this portrait of Kepler from the 18th century:

Portrait of Johannes Kepler

Portrait of Johannes Kepler

Furthermore, a bust of Isaac Newton…

Photography by Carlos Dorce

Photography by Carlos Dorce

… is on the top of the door through which you enter a room full of astronomical and mathematical instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

Can you see this little Aechimedes screw?

Photography by Carlos Dorce

Photography by Carlos Dorce

Before ending the visit, Newton (again!) says goodgye to the visitors in a very modern picture:

Photography by Carlos Dorce

Photography by Carlos Dorce

And Kepler too!

Photography by Carlos Dorce

Photography by Carlos Dorce

One thing more… Go to the ticket office and you will see some mathematical objects more like these English Napier Rods from the 17th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Collegius Maius (map)

Kircher’s Organum Mathematicum

Photography by Carlos Dorce

Photography by Carlos Dorce

Yesterday I didn’t remember to show Kircher’s Organum Mathematicum:

Organum Mathematicum was invented in 1661 by the Jesuit astronomer and mathematician Athanasius Kircher. This device is a comprehensive portable encyclopedia and is designed for the following disciplines: arithmetic, geometry, fortifications, chronology, gnomonics (sundials), astronomy, astrology, steganography (encoding) and music. The case contains tables for calculations without ‘tiring the mind’. Each of the nine disciplines contains 24 flat boards of different colours, with definitions and information.

This is Athanasius Kicher:

Athanasius Kircher (1602-1680) pictured in the book Mundus Subterraneus (1664) by Cornelius Bloemart (1603-1680). Source: Wikimedia Commons

Of course, in the exhibition you can also find compasses, rules, abacus, slide rules, the Napier bones,…

Photography by Carlos Dorce

Photography by Carlos Dorce

…and calculators from the 20th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

Whipple Museum of the History of Science (and V)

Photography by Carlos Dorce

Photography by Carlos Dorce

The last post dedicated to Whipple Museum is for the calculators and their predecessors. All these objects are located in the next room which contains a lot of things in shelves and drawers as if they were in a store. There are calculators and a drawer dedicated to the Napier’s rods or bones:

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are some interesting abacus like this one:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, different slide rules fill some drawers. You must be very patient and it’s a pity that this museum isn’t located in a larger building. 

WM27

Photography by Carlos Dorce

I have more pictures but you must go there if you want to have a real idea of the exhibition. It’s impossible to summarize it in some photos!

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

Whipple Museum of the History of Science (IV)

Photography by Carlos Dorce

Photography by Carlos Dorce

Some mathematical objects also exhibited here like this Gunter’s square made in 1567. Gunter also invented his scale for computing adapting the new logarithms invented by Napier in 1614. Hence, it’s time to start our visit to all the Napier’s rods and slide rules of the exhibition. Let’s have a look to a couple of them, like these English Napier’s rods from 1720…

Photography by Carlos Dorce

Photography by Carlos Dorce

or this other ivory set made from the 17th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

From Gunter scales the slide rules were invented and this spiral logarithmic scale by John Holland (1650) is a very good example of the great inventions of the men from the Renaissance:

Photography by Carlos Dorce

Photography by Carlos Dorce

After the slide rules and before the computers, ihis fragment of the ‘Difference Engine No. 1’ by Charles Babbage (1832-3)  assembled by his son Henry Babbage (c.1880) must also be exhibited:

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, a very curious mathematical object: this magic cube made by A. H. Frost in 1877:

Photography by Carlos Dorce

Each row, each column and each diagonal have the same sum!

Photography by Carlos Dorce

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

The Science Museum in London (IV)

Photography by Carlos Dorce

Photography by Carlos Dorce

John Napier invented published his Mirifici Logarithmorum Canonis Descriptio in 1614 and the invention of the logarithms was the beginning of a new method of computing. Henry Briggs met Napier in Edimburg in the summer of 1615 and 1616 and these two men together decided to improve the invention creating the decimal logarithms which were published by Briggs some years later. In 1620 Edmund Gunter published his Canon Triangulorum where he described one of the first attempts to create a slide rule:

Photography by Carlos Dorce

Photography by Carlos Dorce

After the Gunter’s scale was invented, some other descriptions of the rule appeared like the one made by Wingate in paris in 1624. Gunter’s scale was very popular because all the trigonometrical resolutions of the triangles were reduced to additions and substractions on the rule:

Photography by Carlos Dorce

Photography by Carlos Dorce

The slide rule was invented by William Oughtred who designed both a circular and a straight form of slide rule in about 1621 but did not publish his work until much later. Richard Delamain, one of his former pupils, published a description of a circular slide rule in 1630, and claimed priority of invention although he copied Oughtred’s ideas. In 1660’s Thomas Browne invented the spiral slide rule consisting in fixed scales and moveable index arms similar to Oughtred’s circles of proportion:

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

The Science Museum in London (III)

Photography by Carlos Dorce

Photography by Carlos Dorce

A lot of calculating machine from different times are on display and John Napier and his arithmatic inventions are part of this trasure. There is his Rabdologia (1617) where he described his famous Napier’s bones or rods and we have also some examples of them.

Photography by Carlos Dorce

Photography by Carlos Dorce

The box located in the bottom of the picture is Napier’s own Napier’s bones. There other sexagessimal bones are also very curious:

Photography by Carlos Dorce

Photography by Carlos Dorce

Napier’s bones were very popular and they were used until the 19th century as we can see them in this wooden box:

Photography by Carlos Dorce

Photography by Carlos Dorce

The exhibiion continues with “The Art of reckoning”:

As the level of trade increased throughout the Renaissance, the European counting boards and abacusses were gradually replaced by the use of pen and paper. Merchants andgentlemen taught themselves and their sons the new method.

In England, during the 16th and 17th centuries, many books were written encouraging people to learn arithmetic, and many gadgets invented to aid the beginner. By the 18th century, ready reckoners, devices to simplify calculation, were available to many tradesmen.

These words introduces all the calculating machines world but it’s also the moment of the former counting methods. For example, what do you think about this replica of a 16th century counting cloth?

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

The Museum of the History of Science (III)

Photography by Carlos Dorce

Photography by Carlos Dorce

The mathematicalinstruments are also part of the collection. For example, there is a 17th-century box with some wooden polyhedra and some models for the study of Spherical Trigonometry:

Photography by Carlos Dorce

Photography by Carlos Dorce

And more wooden models in this mathematical box:

Photography by Carlos Dorce

Photography by Carlos Dorce

John Rowley was one of the leading London instrument makers in the late 17th and early 18th centuries and there are some mathematical compasses and instruments made by him in the collection:

Photography by Carlos Dorce

Photography by Carlos Dorce

Object number 1 is a proportional compass meanwhile number 5 is a ruler with pencil and dividers and number 6 is a slide rule.

Of course, if we are in a museum where the History of the Mathematics is exhibited, Napier’s rods must be here:

Photography by Carlos Dorce

Photography by Carlos Dorce

Unsigned, English, c. 1679

Photography by Carlos Dorce

Photography by Carlos Dorce

Unsigned, English, 17th century?

Photography by Carlos Dorce

Photography by Carlos Dorce

Charles Cotterel’s Arithmetical Compendium, Unsigned, English, c.1670

As in the Pitt Rivers Museum, the abacus also have their space in the showcases:

Oriental abacuses use beads on rods to represent numbers. Addition and substraction can be quickly performed by flicking the beads to and fro. Rather than ten beads in each column, the Chinese abacus uses five ‘unit’ beads and two ‘five’ beads (1 and 2). The Japanese abacus has just four ‘unit’ beads and one ‘five’ in each column (3).

Photography by Carlos Dorce

Photography by Carlos Dorce

The next Arithmetical instrument was made in the 18th century for counting. Addition was performed by turning the brass discs but since there isn’t no mechanism it was up to the user to carry tens:

Photography by Carlos Dorce

Photography by Carlos Dorce

I am going to finish this post with this reproduction of the Measurers by the Baroque painter Van Balen (1575 – 17 July 1632) which can be seen upstairs:

The Measurers. Hendrick van Balen

Location: The Museum of the History of Science (map)