Chapter summary:
Before Toscanelli met the Chinese Ambassador, Europe’s knowledge of the universe was wrongly based on Ptolomey. To believe that the earth was merely one planet among many revolving round the sun required a radical change in thought. This intellectual revolution was led by Nicholas of Cusa. While at Padua, where he graduated in 1424, Nicholas became a close friend and devoted follower of Toscanelli, with whom he frequently collaborated on new ideas. In 1444, Nicholas possessed one of the two known torquetum based upon the Chinese equatorial system. By measuring the angular distance between the moon and a selected star that crossed the local meridian, and by knowing the equation of time of the moon and the declination and right ascension of a selected star, longitude could be calculated. During Nicholas’s era, the alphonsine tables based on Ptolomey were the standard work on positions of the sun, moon and planets. Nicholas realized these tables were highly inaccurate, a finding he published in 1436 in his Reparatio Calendari. This realization led him to his revolutionary theory that the earth was not at the centre of the universe, was not at rest and had unfixed poles. His work had a huge influence on Regiomontanus.
Regiomontanus was born Johan Mueller and was recognised as a mathematical and astronomical genius when young. He became a pupil of the celebrated astronomer and mathematician Peurbach. Peurbach and Regiomontanus collaborated to make detailed observations of Mars which showed that the Alphonsine tables (which were based upon the earth being at the centre of the universe) were seriously in error. This was confirmed when the two observed an eclipse of the moon which was later than the tables predicted. From that time, Regiomontanus realised as Nicholas of Cusa had done that the old Ptolemaic systems of predicting the courses of the moon and planets did not stand up to serious investigation. Although Regiomontanus was some forty years younger than Toscanelli, Nicholas of Cusa and Alberti, there are numerous references in Regiomontanus’s writing to the influence which Toscanelli and Nicholas of Cusa had on his work
Regiomontanus’s legacy was his 1474 Calendarum and Ephemeris tables – his ephemeris tables, 800 pages long and containing 300,000 calculations, were of monumental importance in enabling European mariners to determine latitude and longitude and their position at sea. So accurate were these tables – for a period of thirty years from 1475 – that Navigators could calculate their latitude and longitude at sea without using clocks. They could therefore, for the first time, find their way to the New World, accurately chart what they had found and return home in safety. Coupled with the Chinese world maps, European exploration could now start in earnest – which it did, Dias, for example calculated the true latitude of the Cape of Good Hope using Regiomontanus’s tables. He reported this to the King of Portugal who knew for the first time how far the Captains had to travel south to get into the Indian Ocean. Columbus, Vespucci and others also used Regiomontanus’s ephemeris tables to predict eclipses, latitude and longitude for years after Regiomontanus died. Regiomontanus’s ephemeris tables in 1474 had created a revolution in exploration.
After the torquetum was introduced to Europe, Astrolobes, on which Arabic and European astronomers had lavished all their mathematical art, passed out of favour. Guo Shou Jing’s torquetum –forerunner of modern European instruments such as the astrocompass – lived on.
From there on, European Astronomers followed Chinese methods.
Further reading:
Regiomontanus’ Astronomical Tables:
http://www.hps.cam.ac.uk/starry/regiotables.html
Regiomontanus and Calendar reform:
http://www.hps.cam.ac.uk/starry/regiocalen.html
Almagest Ephemeris Calculator:
http://www.phys.uu.nl/~vgent/astro/almagestephemeris.htm
The torquetum, by Richard A. Paselk
http://www.humboldt.edu/~rap1/EarlySciInstSite/Instruments/Torquetum/Turq.html
Applications of the Chinese remainder theorem:
http://findarticles.com/p/articles/mi_qa3926/is_199904/ai_n8847320
On Ancient Chinese Cryptography and other Cryptography-related anecdotes
By Victor K. Wei
http://dsns.csie.nctu.edu.tw/iwap/proceedings/proceedings/invited_speeches/Wei.pdf
The Jiuzhang Suanshu (Nine Chapters on the Mathematical Art) is the longest surviving and one of the most important in the ten ancient Chinese mathematical books.
http://www.chinaculture.org/gb/en_madeinchina/2005-08/18/content_71980.htm
Pre-Copernican Astronomical Activity, by Lynn Thorndike
http://www.jstor.org/pss/3143515
The Copernican Revolution:
http://physics.ucr.edu/~wudka/Physics7/Notes_www/node41.html
http://www.phys-astro.sonoma.edu/PEOPLE/FACULTY/TENN/COPERNICANREVOLUTION.HTML
Nicholas of Cusa: an introduction
http://www.newadvent.org/cathen/11060b.htm
Nicholas of Cusa and the Infinite:
http://www.integralscience.org/cusa.html
