John of Saxony (also Johannes de Saxonia, John Danko or Dancowe of Saxony) was a medieval astronomer. Although his exact birthplace is unknown it is believed he was born in Germany, most likely Magdeburg. His scholarly work is believed to date from the end of the 13th century into the mid 14th century. He spent most of his active career, from about 1327 to 1355, at the University of Paris. [1]
John of Saxony is quoted in various medieval manuscripts and referenced as the author of various astronomical or astrological treatises, even though his authorship in some cases is questionable.
A computus dating back to 1297 is attributed to John of Saxony even though the author is listed as Iohannes Alemanus. The fact that the geographical longitudes of Paris and Magdeburg, considered John's birthplace, among other facts is why some historians consider him the author.
Viewed with less suspicion is his commentary on Liber Introductorius ad Magisterium Idiciorum Astrorum written by al-Qabisi (Alcabitius), an Arab scholar from the late 10th century. John of Saxony's commentary on this treatise is preserved in many manuscripts, several incunabula and old prints, the latest of which dates from the middle of the 16th century. [1]
Among his other contributions were a commentary on Alcabitius's Introduction to the art of astrology, [2] which went through eleven printed editions, and an Almanach for the years 1336 to 1380 that he computed for the meridian of Paris using the Alfonsine tables. [3]
John of Saxony was of the opinion that astronomers of that time wrote their works in such a confusing manner that those who weren't trained in the field couldn't comprehend nor use them appropriately. Under the tutelage of his master, John of Ligneres, he sought to write tables that accounted for any situation and could be put to practical use. As he puts it: "Therefore to the praise of glorious God, the honor of my master, and the profit of scholars who wish to learn the workings of astronomical tables, I, John of Saxony, with God's aid intend to give examples of all the operations which are commonly performed with tables so that there may be no one henceforth who will shrink from the use and employment of tables of the stars because of the difficulty working with them." [4]
The more widely recognized work by John of Saxony is his Canons on the Alfonsine Tables. The Alfonsine Tables are the mathematical calculations from Ptolemy's Almagest with limited modifications. [5] These tables for calculating planetary positions, prepared under the auspices of Alfonso X, were originally in Castillian. [6] They were also used to derive ecliptic longitudes for planets for any chosen time and observer's position, lunar phases, lunar and solar eclipses, as well as calendar dates. Like the 11th century Toledan Tables before them, the Alfonsine Tables were based on the geocentric model of the planetary system as described in Ptolemy's Almagest. Around 1320, the Alfonsine Tables appeared in Paris where they were studied at the University of Paris by astronomers John of Ligneres, John of Saxony, and later Johannes de Muris. [1]
In order to study the tables, they were translated from Castillian into Latin, which was the scholarly language of the day. This is due in large part to the Catholic upbringing of the day in medieval Europe. This act alone allowed greater access and understanding of astronomical work to that point. In 1327 he added an influential set of explanations and instructions (Canons) to the revision of the Alfonsine Tables by his master, John of Ligneres. His intent was to allow students at the University of Paris to utilize the astronomical tables.
The canons of John of Saxony explained how one could find the planetary position (longitudes) at any given time. One would have to calculate the length of time between the basic year and the year sought. They would then divide them by mean figures of the planetary orbits, and add/subtract values to adjust for hours and minutes. To expedite these calculations he had an accompanying table of sexagesimal multiplication. [7] In addition to this, he divided the day into sixty parts rather than 24 hours, consistently representing time by sexagesimal fractions and multiples of a day. It is in this form that the Alfonsine tables circulated in Western Europe for the next three centuries. [8]
After translation and Canons were added to the Alfonsine Tables, they were disseminated from Paris to the rest of medieval Europe. As they were received, the tables were converted to the local meridians for proper use. Although widely used, a published print version of the tables and John of Saxony's Canons didn't exist. It wasn't until 1483 when Erhard Ratdolt in Venice published both. To date neither John of Ligneres' or Johannes de Muris' canons have been published in print. [1]
Hipparchus was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.
Claudius Ptolemy was an Alexandrian mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathēmatikē Syntaxis or Mathematical Treatise, and later known as The Greatest Treatise. The second is the Geography, which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika but more commonly known as the Tetrábiblos, from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite.
The zodiac is a belt-shaped region of the sky that extends approximately 8° north and south of the ecliptic, which is the apparent path of the Sun across the celestial sphere over the course of the year. The orbital paths of the Moon and major planets are within the belt of the zodiac.
Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy in Koine Greek. One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy.
In astronomy and celestial navigation, an ephemeris is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position over time. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available.
Georg von Peuerbach was an Austrian astronomer, poet, mathematician and instrument maker, best known for his streamlined presentation of Ptolemaic astronomy in the Theoricae Novae Planetarum. Peuerbach was instrumental in making astronomy, mathematics and literature simple and accessible for Europeans during the Renaissance and beyond.
Gerard of Cremona was an Italian translator of scientific books from Arabic into Latin. He worked in Toledo, Kingdom of Castile and obtained the Arabic books in the libraries at Toledo. Some of the books had been originally written in Greek and, although well known in Byzantine Constantinople and Greece at the time, were unavailable in Greek or Latin in Western Europe. Gerard of Cremona is the most important translator among the Toledo School of Translators who invigorated Western medieval Europe in the twelfth century by transmitting the Arabs' and ancient Greeks' knowledge in astronomy, medicine and other sciences, by making the knowledge available in Latin. One of Gerard's most famous translations is of Ptolemy's Almagest from Arabic texts found in Toledo.
Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī, usually called al-Battānī, a name that was in the past Latinized as Albategnius, was an astronomer, astrologer and mathematician, who lived and worked for most of his life at Raqqa, now in Syria. He is considered to be the greatest and most famous of the astronomers of the medieval Islamic world.
Johannes de Sacrobosco, also written Ioannes de Sacro Bosco, later called John of Holywood or John of Holybush, was a scholar, monk, and astronomer who taught at the University of Paris.
The Toledan Tables, or Tables of Toledo, were astronomical tables which were used to predict the movements of the Sun, Moon and planets relative to the fixed stars. They were a collection of mathematic tables that describe different aspects of the cosmos including prediction of calendar dates, times of cosmic events, and cosmic motion.
Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī was a Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetic for businessmen contains the first instance of using negative numbers in a medieval Islamic text.
Abu al-Saqr Abd al-Aziz ibn Uthman ibn Ali al-Qabisi, generally known as Al-Qabisi,, and sometimes known as Alchabiz, Abdelazys, Abdilaziz, was a Muslim astrologer, astronomer, and mathematician.
The Alfonsine Tables, sometimes spelled Alphonsine Tables, provided data for computing the position of the Sun, Moon and planets relative to the fixed stars.
Johannes de Muris, or John of Murs, was a French mathematician, astronomer, and music theorist best known for treatises on the ars nova musical style, titled Ars nove musice.
Campanus of Novara was an Italian mathematician, astronomer, astrologer, and physician who is best known for his work on Euclid's Elements. In his writings he refers to himself as Campanus Nouariensis; contemporary documents refer to him as Magister Campanus; and the full style of his name is Magister Campanus Nouariensis. He is also referred to as Campano da Novara, Giovanni Campano or similar. Later authors sometimes applied the forename Johannes Campanus or Iohannes Campanus.
During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The collection of ancient scientific texts began in earnest at the start of the 15th century and continued up to the Fall of Constantinople in 1453, and the invention of printing allowed a faster propagation of new ideas. Nevertheless, some have seen the Renaissance, at least in its initial period, as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. More recently, however, scholars have acknowledged the positive influence of the Renaissance on mathematics and science, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the study of language and the correct reading of texts.
The Prutenic Tables, were an ephemeris by the astronomer Erasmus Reinhold published in 1551. They are sometimes called the Prussian Tables after Albert I, Duke of Prussia, who supported Reinhold and financed the printing. Reinhold calculated this new set of astronomical tables based on Nicolaus Copernicus' De revolutionibus orbium coelestium, the epochal exposition of Copernican heliocentrism published in 1543. Throughout his explanatory canons, Reinhold used as his paradigm the position of Saturn at the birth of the Duke, on 17 May 1490. With these tables, Reinhold intended to replace the Alfonsine Tables; he added redundant tables to his new tables so that compilers of almanacs familiar with the older Alfonsine Tables could perform all the steps in an analogous manner.
Johannes Stadius or Estadius, was a Flemish astronomer, astrologer, and mathematician. He was one of the important late 16th-century makers of ephemerides, which gave the positions of astronomical objects in the sky at a given time or times.
John of Lignéres or Johannes de Lineriis was a French astronomer who wrote several works on the calculation of moon, sun, and planetary positions. Many of his works are confounded with the works of similar named Parisian astronomer collaborators and students including Johns of Murs, John of Sicily, John of Saxony, and John of Montfort. His works were important in importing Arabic astronomical calculations into European traditions.