standardizing and preserving Christian dogma

• scriptoria

• herbaria (cultivating herb and vegetable gardens)

• vivaria (husbanding useful animals)

• valetudinaria (maintaining good health)

• founded by Holy Roman Emperor, Charlemagne (742-814) with the aim of training teachers and creating a literate aristocracy

• most notable cathedral schools:
• Paris
• Chartres

• served similar purpose to monastery schools, but were directed to include instruction in secular as well as sacred subjects -- reading, writing, speaking, mathematics, natural philosophy

• but these schools were unable to meet the growing needs of an increasingly secular society

• some (like Chartres) died out

• others (like Paris) began to assume modern form of universities

The Nestorians

From time to time, leaders in the early Christian Church gathered in what they called "ecumenical councils":  meetings at which bishops from all of Christendom could consider, discuss and (it was hoped) come to universal agreement on disputed or unclear points of scripture and church doctrine. The first of these councils was held in the city of Nicaea (ny-SEE-ah) near Constantinople in 325 CE.  Soon afterward, academies modeled after that in Alexandria were founded in Antioch and Nisibis. 

Greek served as the lingua franca for scholars at all the Alexandrian-style schools, but Syriac was the native language of students at Nisibis and many texts were translated there from Greek into Syriac.  When the school moved to Edessa in 363, the Syriac tradition moved with it.

At the third council, held in Ephesus in 431 CE, delegates condemned the bishop of Constantinople, Nestorius (381-451), as a heretic for questioning Mary's status as Mother of God.  Nestorius and his followers were exiled and settled in Edessa.  Religous conflicts in Edessa prompted the Nestorians to move further east in 457.

Around 560, the Persian leader, Khosru I, established an Alexandrian academy in Jundishapur where instruction would be conducted in Syriac.

The Bactrians

For centuries after the dissolution of Alexander's empire, Greek culture continued to influence the people of Bactria.  Cities like Bactra and Merv were crossroads on the Silk Road (c. 100 BCE) that helped introduce new commodities and technologies from the East, such as paper and paper-making in the 750s.

India

Alexander's empire had extended to the Indus River valley.  Despite the enormous distances separating Alexandria and India, communication and trade continued over the centuries via land and sea (Alexandria-Medina-Aden-Cambay; Alexandria-Antioch-Basra-Cambay).

Astronomical records from Alexandria found their way to observatories like those in Pataliputra and Ujjain.  Indian astronomers added their own observations to the old but replaced the old-fashioned sexagesimal system of notation (base 60) which dated back to Babylonian times with a decimal system that included a symbol for "nothing" to help keep track of place values.  They called this symbol sunya, the Hindi word meaning "the void."  When this was translated into Arabic, scholars used the word sifr, meaning "empty."  Italians transliterated this word as zefirum, zefiro, and zefro, which eventually became zero.

• wrote Al Kitab al-Mukhtasar fi Hisab al-Jabr Wal-Muqabalah (The Compendious Book on Calculation by Completion and Balancing)

• traveled among rulers of central Asia
• wrote on all sciences
• medical textbook used until 1650 in European universities

• translated Aristotle

• discovered movement of the sun's apogee
• evaluated the ecliptic's obliquity with great precision
• proved the variation of the apparent angular diameter of the sun
• suggested possibility of annular solar eclipses
• introduced spherical astronomy
• first to use expressions "sine" and "cosine"
• quoted by Copernicus

• predicted three lunar eclipses within an half hour's accuracy

• Persian; worked in Baghdad
• compiled star catalogue of 1,018 stars
• wrote Kitab su-war al-kawakib (Book on the Constellations of Fixed Stars, 964)
• described boundaries of constellations

The constellation Sagittarius as it would appear to an observer examining a celestial globe.

• member of Baghdad School
• noted the irregularity of the Moon's highest altitude

• studied optics, human vision
• his work was translated into Latin
• critiqued aesthetic of Ptolemy's equant-deferent system
• felt that off-center circles and off-center motion violated spirit of uniform circular motion
• inspired the mathematical constructs of Al-Tusi and Al-Shatir

• determined earth's circumference
• carried out geodetic measurements
• determined latitudes and longitudes
• measured specific gravity of precious stones
• wrote clear account on India and its people
• wrote best medieval treatise on Hindu numerals

• considered Ptolemy's system to be mathematical not physical regarding the order of the inferior planets (Mercury and Venus)

• best known works in astronomy are the Ilkhani Tables and the Tadhkirah fi ilm al-Haya  (Memoir on Astronomy)
• placed the Earth at the center of motion and orbits
• to account for non-uniform motions and eliminate the equant, invented a geometrical device called the "Tusi couple"
• only new mathematical model of planetary motion to appear in medieval times
• replaced Ptolemy's epicycle
• center of large circle moves around Earth on regular orbit
• planet is attached to inner circle
• inner circle rolls around inside larger circle
• failed to improve upon the accuracy of the predictions made by the Ptolemaic system
• Copernicus experimented with the "Tusi couple"
• constructed observatory at Maragheh in western Persia
  • operational in 1262

Page from al-Tusi's Memoir on Astronomy.  "Tusi couple" is illustrated on right-hand page.

• placed Earth at the center of planetary orbits
• added extra epicycles to the motions of the planets
• system was extraordinarily complex
• not an improvement compared to accuracy of Ptolemy's system
• wrote a book entitled Kitab Nihayat al-Sul fi Tashih al-Usul (A Final Inquiry Concerning the Rectification of Planetary Theory)--departs largely from the Ptolemaic system

• ruler of Samarkand
• initiated construction of observatory there
• compiled catalogue of 1,012 stars with positions measured to high precision
• catalogue not based on the work of Ptolemy.

The Fakhri sextant at Ulugh Beg's observatory is a 60° arc of stone with a 40 m radius.  Because of its large size, observers could measure star positions with a very high precision.  Many scholars were attracted to work and study at the observatory from 1420 to 1437.

• Southern Spain--Arabic to Latin
• Cordova
• Toledo
• Seville

• Southern Italy and Sicily--Arabic and some Greek to Latin
• Salerno
• Monte Cassino (monastery founded by St. Benedict in 529)
• Palermo
• Syracuse

Universities:

• were products of guild system
• Paris:  guild of masters
• Bologna:  guild of students

• were structured around four faculties:  Arts, Theology, Law, Medicine

• offered instruction in the seven liberal arts:

Greatest happiness comes from contemplation of knowledge already derived.

• Differences between what is written and what is seen today may be due to current inability to fully understand either what is written or what is seen.
• Task of the scholar is to find ways to reconcile these differences.

"By doubting we come to inquiry; by inquiring we perceive the truth."--Peter Abelard (1079-1142)

• Use systematic doubt and question everything.
• Learn the difference between statements of rational proof and those merely of persuasion.
• Be precise in the use of words; expect precision from others.
• Watch for error, even in Holy Scripture.

"You will find more in forests than in books.  Woods and stones will teach you more than any master."--St. Bernard of Clairvaux (c. 1090-1153)

• Don't bother reading words written by fallible men.
• Study the Book of Nature directly.

The telescope is a relatively modern invention.  Before 1610, the naked eye was the only optical instrument available to skywatchers.  Pre-telescope astronomers, navigators, surveyors, calendar makers, and timekeepers made use of a variety of other tools that evolved so gradually over such a long period of time that we cannot identify their origins.

Instruments like the astrolabe, alidade, cross-staff, quadrant, and sextant were all designed to guide the observer's eye along a particular line of sight to a target object thus enabling him to measure its position compared to some point of reference.  Knowing these positions with some confidence was key to determining local time and/or position, and creating accurate celestial and terrestrial maps.

One man holds a quadrant while another sights the eclipsed sun.  An assistant tracks the time with a portable sundial.
______________

Student navigators practice using the cross-staff.

Sacrobosco (? - 1256)

• also known as John Halifax, John of Holywood, or Johannes de Sacre Bosco
• born in Yorkshire, England
• educated at Oxford
• taught mathematics at University of Paris
• first European to write about Ptolemy's system (Sphæra Mundi)

• one of the first astronomy books printed
• the principal elementary textbook on astronomy for 400 years
• Johannes Gutenberg (c.1397-1468) introduced movable type around 1440
• 25 editions of Sphæra Mundi printed between 1472-1500, and 40 more by 1650

Sacrobosco writing (literally) "On the Sphere", from a 1537 edition of Sphæra Mundi.

In the border at the top are instruments for measuring space:  square (upper left corner) and diopter (upper right corner); and for measuring time:  hourglass (left of center) and pocket sundial (right of center). 

Scattered around the border are icons representing other mathematical studies including music and perspective drawing.  Also shown are symbols for the celestial poles:  "Acticus" (upper left, should read "Arcticus") and "Antar" (upper right, abbreviation for "Antarcticus".  These are accompanied by small drawings of Ursa Major.

On the wall behind Sacrobosco hang his observing instruments (quadrant and astrolabe) and his drafting tools (compass and square).

Even if readers could not understand all or most of the text, they could learn from studying the book's many illustrations.

Later editions included movable illustrations called volvelles which readers could turn to better understand changing celestial phenomena.

A volvelle from a 16th c edition of Sphæra Mundi that illustrates a lunar eclipse.

Georg Peurbach (1426-1461) initiated the challenging task of translating the Almagest directly from Greek into Latin. 

After Peurbach's untimely death, the project was carried out by his pupil, Johannes Müller of Königsberg (1436-1476), who was known by his latinized name, Johannes de Regiomontanus (Königsberg, or King's Mountain).

The book, The Epitome of Ptolemy, published in 1496:

• systematized and clarified Ptolemy's Almagest

• became popular textbook; used by Columbus and Copernicus

• didn't improve the predictive power of Ptolemy's system

• didn't resolve problems with calendar

• prompted Copernicus to conclude that something was fundamentally wrong with Ptolemy's system

Gerard of Cremona's Latin translation of Almagest from 1175 appeared in print in 1518.

The first edition of Almagest in the original Greek was published in 1538.