Ch. 4 Medieval Latin Astronomy

Ch. 4
Medieval Latin Astronomy
Chronology of Medieval Latin Astronomy
400 AD
Burning of library at Alexandria
Sack of Rome
Martianus Capella, Nuptials Philology & Mercury
Macrobius, Commentary on Dream of Scipio
Boëthius, Consolation of Philosophy
Venerable Bede, On the Divisions of Time; computus
Fall of Toledo to Christians
Bologna first university
Gerard of Cremona: Latin trans. Almagest, Toledo Tables
Sacrobosco, Treatise on Sphere
Anon., Theory of the Planets
Profatius Judaeus: astrolabe quadrant
University of Paris
Thomas Aquinas, Summa
Buridan, Oresme: impetus
Gutenberg Bible (movable type)
Peurbach, Regiomontanus: New Theory of the Planets, Epitome
Bernhard Walther: observatory
Fall of Constantinople to Turks
Copernicus, On the Revolutions
Reinhold, Prutenic Tables
Early Latin Astronomy
Early Latin Astronomy
Martianus Capella, Nuptials of Philology and Mercury
• Elaborate allegory from early fifth century AD about the
courtship of Philology (personifying learning and having
been made immortal by the gods) by Mercury (personifying
intelligent and profitable pursuit)
• First two books accompanied by seven more dedicated to
the liberal arts, handmaidens to the bride:
Dialectics (metaphysics and logic)
Music (including poetry)
Early Latin Astronomy
Martianus Capella, Nuptials of Philology and Mercury
• Referred to by one modern commentator as “… an
immense mass of learning, but the materials are ill-selected,
ill-arranged, and ill-digested, though from amidst much that
is dull and frivolous, we can occasionally extract curious
and valuable information ...”
• Was much admired during the Middle Ages and frequently
copied (by hand, of course!)
• Consequently accumulated a vast number of copying
errors, with sometimes interesting results (next slide)
• Originally included idea attributed to Heraclides that
Mercury and Venus go around Sun, not Earth; quoted by
Early Latin Astronomy
Martianus Capella, Nuptials of Philology and Mercury
Mercury and Venus’s orbits
Early Latin Astronomy
Macrobius, Commentary on Cicero’s ‘Dream of Scipio’
• Included handbook on astronomy
• Cosmology presented based on Plato and
Pythagoreans – number as basis
• Spherical Earth with size according to
Eratosthenes, seven planetary spheres, celestial
• Placement of Sun ambiguous
Early Latin Astronomy
Macrobius, Commentary on Cicero’s ‘Dream of Scipio’
Universe with Earth at center, seven planetary spheres, and
celestial sphere divided into twelve houses of
Latin Astronomy
Macrobius, Commentary on Cicero’s ‘Dream of Scipio’
Diagram of solar eclipse
Diagram of lunar eclipse
Early Latin Astronomy
Boëthius, Consolation of Philosophy
• Written while under house arrest just prior to his
execution for treason by order of Theodoric the
Great, King of the Ostrogoths
• Is dialogue between author and Philosophy,
personified as wise and compassionate lady
• Has themes of transitory nature of fame and
wealth, wheel of Fortune affecting everyone;
consolation found in things of the mind, knowledge
that God is the source of all good
Early Latin Astronomy
Boëthius, Consolation of Philosophy
• Has been described as “the single most important
and influential work in the West on Medieval and
early Renaissance Christianity, and is also the last
great Western work that can be called Classical”
• Was widely copied, edited, translated, and
commented upon throughout the Middle Ages
Early Latin Astronomy
• Apart from Consolation, aimed at preserving
classical knowledge and especially Aristotle and
Plato by translating Greek into Latin with comments
• Plan largely unfulfilled; covered mostly
mathematics and logic  influenced Scholastics in
• Organization of mathematical studies into what
later became the quadrivium – arithmetic, harmony,
geometry, and astronomy (not much about latter)
Early Latin Astronomy
Date of Easter
• Historically tied to Jewish observance of
Passover – beginning 15th day of month Nisan
• Early church: Pascha (Easter) on Nisan 14
• Independent of local Jewish observances, same
for entire Church – First Council of Nicaea (325
Date = first Sunday after first ecclesiastical full
Moon following “vernal equinox” (actually Mar.
21; equinox often on Mar. 20)
Early Latin Astronomy
Date of Easter
• Ecclesiastical full Moon ≠ astronomical full
Moon; based on day number for Moon’s age (14)
with months of 29 or 30 days (synodic month) –
see rightmost column in Farmer’s Almanac (+1)
• Like Jewish calendar, based on Metonic 19-year
cycle -- lunisolar
• Look for cycle that includes both lunisolar cycle
and the day of the week (Easter must be Sunday)
Early Latin Astronomy
Date of Easter
• Solution in Venerable Bede, On the Divisions of
• Julian calendar: common years 365 days ÷ 7 = 52
remainder 1  day of week advances by one each
year (Jan 1. on Mon. – next year on Tues.)
• Leap years every fourth year: remainder 2 instead
of 1  every four years add 5 days
• In seven cycles of four years go through exactly 5
weeks, end up same day of week (28 years)
Early Latin Astronomy
Date of Easter
• Metonic cycle for tropical year and lunar phase,
28-year cycle for day of week  19 × 28 = 532
• (Western Christianity later switched to Gregorian
calendar; more complicated – three of four century
years omitted)
• Latin name for calculation of date: computus
Early Latin Astronomy
Translations from Arabic to Latin
• Gerbert of Aurillac (later Pope Sylvester I)
studied astrology at Barcelona, wrote book on
astrolabe (ca. 1000 AD)
• Athelhard of Bath went to Middle East;
translated zij of al-Khwarizmi (1126), introduced
ideas of algebra to West
• Translations often had awkward combinations
of Latin and Arabic words
Islamic Influence
Translations from Arabic to Latin
• After Toledo captured by Christians (1085),
numerous works translated into Latin, spread
through Europe
• Gerard of Cremona: Toledo Tables; later
Almagest (1175; other translations elsewhere,
some from Greek)
• Gerard’s other translations included Aristotle’s
On the Heavens, Euclid’s Elements, and alKhwarizmi’s Algebra – 87 works in all!
Islamic Influence
Astrology in the Christian West
• Astrology in precarious position, as in Islam –
regarded by some as superstitious
• At same time, established as part of medicine,
based on Aristotle’s microcosm-macrocosm
analogy (Chaucer quote in Hoskin)
• Aristotle’s ideas themselves initially considered
heathen, banned at University of Paris
Medieval Astronomy
Astrology in the Christian West
• Later, astrology reconciled with Christianity to
some degree: influence of stars not rigidly
deterministic but only tendency
• Man imbued with free will by the Creator,
capable of resisting influence
• Aristotle’s ideas themselves were completely
reconciled with Church doctrine by Thomas
Aquinas at University of Paris in Summa
Theologica (1274)
Medieval Astronomy
• Some grown from cathedral schools; all tied to
Church -- faculty clerical (some minor orders);
faculty and students all under canon (church)
law, not civil law
• First chartered university Bologna (1088);
second Oxford (1096)
• Most distinguished medieval university Paris
Medieval Astronomy
Organization of faculty in descending order of status:
• Theology
• Medicine
• Law
• Arts (liberal arts)
Function of university originally was teaching,
not research.
Students of Arts were very young, typically 13 or
14 and sometimes younger.
Medieval Astronomy
Medieval Arts Curriculum
Theology or Metaphysics
Moral Philosophy, Natural Philosophy
Quadrivium: Arithmetic, Harmony (Music),
Geometry, Astronomy
Trivium: Grammar, Rhetoric, Logic
(Hoskin, Cambridge Illustrated History)
Medieval Astronomy
Medieval Christian Cosmology
• Illustration from Nuremberg
Chronicles (1493)
• Aristotelian with added
Christian features
• Earth at center with four
elements, planetary spheres,
sphere of fixed stars =
firmament (precession),
crystalline sphere (trepidation),
and Prime Mover (daily)
• Empyreum = Heaven with God
and angels on outside of all
Medieval Christian Cosmology
• Illustration from Peter Apian’s
Cosmographia (1539)
• Aristotelian with added
Christian features
• Earth at center with four
elements, planetary spheres,
sphere of fixed stars =
firmament (precession),
crystalline sphere (trepidation),
and Prime Mover (daily)
• Empyreum = Heaven with God
and angels on outside of all
Astronomy Textbooks
• Need for simplified textbooks on astronomy for
Arts students – Almagest far too hard!
• Sacrobosco (John of Holywood) in 13th century:
 Computus – introduction to time-reckoning
 Algorismus – arithmetic used in astronomy
 Tractatus de sphaera = Treatise on the Sphere –
celestial sphere (stuff we did at beginning of course);
comprised four parts:
Celestial sphere with Earth at center, daily motion
Celestial equator, ecliptic and zodiac, meridian,
altitude of celestial pole
III. Rising and setting of celestial bodies, length of day
and night at different latitudes
IV. Motions of Sun, Moon, planets; outline of eclipses
Medieval Astronomy
Astronomy Textbooks
• Part IV completely unsatisfactory
• Most popular replacement: anonymous Theory of
the Planets fairly soon (later 13th century)
 Hipparchus’s model for Sun
 Ptolemaic-like models for Moon, Mars, Jupiter, and
 Models for Venus and Mercury
 Treatment of eclipses not entirely satisfactory
Medieval Astronomy
Beginning of new thought – research? -- in
universities, not just teaching ancients
University of Paris in 14th century – concept of
impetus in connection with Aristotle’s theory of
violent or forced motion
Medieval Astronomy
• Sublunary (terrestrial) region:
 everything consisting of varying proportions of four
elements (taken from Empedocles) – earth and water
(heavy) and air and fire (light)
 mutability (change) is endemic
 natural motions are vertical – down (heavy elements)
and up (light elements)
• Superlunary (celestial) region:
 only one element = “fifth” element or quintessence
 immutability = no change
 natural motion is uniform circular motion
Motion other than natural is “violent/forced motion”
Development of impetus concept -• Jean Buridan: effect of air resistance on motion
• Nicole Oresme: impetus as “incorporeal force” (like
fuel) initially infused into body, then used up (also
anticipated Descartes with analytic geometry)
• Albert of Saxony: projectile’s trajectory in three
stages: impetus dominates; impetus exhausted and
gravity becomes important; gravity dominates
Medieval Astronomy
Oresme, Commentary on Aristotle’s On the Heavens
• Impetus allows one to evade the argument of
fall against the Earth’s rotation
• Arrow is imparted impetus in forward direction
by Earth’s rotation before it is released
• Arrow moves eastwards as it rises and falls
• Conclusion: One cannot tell if Earth rotates or is
at rest.
Medieval Astronomy
• Earth does not rotate around an axis:
Argument of fall: If Earth rotates, an
arrow shot vertically will fall to the west of
the archer; instead it falls on the archer’s
head unless he moves away.
(Actually, the arrow does fall to the west, but by an
extremely small amount.)
Instruments of Late Medieval
Old Quadrant
curves for finding time of day
angular scale for altitude
plumb line
(Hoskin, Cambridge Illustrated History)
Medieval Instruments
Instruments of Late Medieval
New Quadrant = Astrolabe Quadrant
ecliptic from rete of astrolabe, folded twice
angular scale
for altitude
Medieval Instruments
Instruments of Late Medieval
New Quadrant = Astrolabe Quadrant
• Invented by Profatius Judaeus (Jacob ben
• Both quadrants more efficient than
astrolabe: for given size, baseline is twice as
long for angular scale (radius vs. diameter)
• Like astrolabe, new quadrant is both
demonstration instrument and measuring
Medieval Instruments
Instruments of Late Medieval
Medieval Instruments
Instruments of Late Medieval
• Invented by Levi ben Gerson = Gersonides in
first half of 14th century
• Observer sights across top of cross-piece at one
object, then across bottom at the other, adjusting
the position of the cross-piece to do so
• Long piece is marked so that distance of crosspiece from eye can be measured
Medieval Instruments
Instruments of Late Medieval
• Cross-staff (also known as Jacob’s staff) had two
1. Measuring angular separation between two
objects, as with the star and the Moon in the
2. Measuring the altitude of an object as angular
distance above the horizon; if Polaris, estimates
latitude for navigation
• (Could also be used to measure Sun’s altitude
with eye protection, but was replaced by
backstaff, which uses a shadow, and later sextant)
Medieval Instruments
Instruments of Late Medieval
Little Dipper
sighting hole
Big Dipper
pivot arm
• Sight through hole on Polaris
• Line up pivot arm on pointer stars – Big or Little
Instruments of Late Medieval
1) Use reading to correct for displacement
of Polaris from true North Celestial Pole
1) Use reading to tell sidereal time of night;
correct to solar time by using scale for
days of year
Medieval Instruments
Instruments of Late Medieval
Mechanical Clock
(Hoskin, Cambridge Illustrated
Instruments of Late Medieval
Mechanical Clock
• Mechanical clocks for time of observation -not yet accurate enough for precision time
• Richard of Wallingford – astronomical clock
replica medieval universe: Moon’s phases and
eclipses, variable motion in longitude
• Giovanni de Dondi – astrarium at Padua;
geared Ptolemaic mechanism (Remember
Antikythera Mechanism?)
Medieval Instruments
Instruments of Late Medieval
Astrarium of de Dondi (1364)
Moon dial
Modern reproduction from detailed plans
Venus dial
Medieval Instruments
Prague Astronomical Clock (1410)
Medieval Instruments
Instruments of Late Medieval
Prague Astronomical Clock,
complete view
astrolabe face
calendar face
Medieval Instruments
Instruments of Late Medieval
Astronomical Clock of
Strasbourg Cathedral (1354)
astrolabe face
Medieval Instruments
Astronomy Textbooks
• Printing using moveable type introduced to Europe
by Gutenberg, 1450 – two major effects:
 More rapid and wider dissemination of ideas
 Elimination of copying errors (but more important to
• Georg Peurbach (sometimes Purbach), professor at
University of Vienna; gave private lectures on
Ptolemaic system
• Lecture notes written up, published posthumously
20 years later by protegé Johannes Müller, known as
Regiomontanus – New Theory of the Planets (1474)
New Theory of the Planets (1474)
• Peurbach self-taught in astronomy (professor of
• Studied Almagest and Alhazen’s On the
Configuration of the World among others
• Sufficiently knowledgeable to be appointed
mathematicus (court astrologer) to King of Bohemia
and Hungary, later to Holy Roman Emperor
Renaissance Textbooks
• Elementary but thorough treatment of Ptolemaic
• Based on planets embedded in crystalline spheres;
system resembles aspects of al-Tusi’s work –
• Most widely used textbook of sixteenth century
New Theory of Planets
• Spheres rolling within spheres – 3-d Tusi couple?
New Theory of Planets
• Prodigy – almanac at 11 superior to Gutenberg’s!
• Cardinal Bessarion from Constantinople met
Peurbach, Regiomontanus; invited to Italy to study
Almagest in Greek, critique translation by George of
• Result was Epitome of the Almagest (1462), a
clarification of Ptolemaic system read by Copernicus
and Galileo
• Finished after Peurbach’s death
• Wrote textbooks on trigonometry and algebra
• Moved to Nuremberg 1471 – center of trade,
learning, publishing – for two reasons:
1. Recruit highly qualified observers to obtain more and
better observational data  improve planetary tables
2. Print books – key element in advancing astronomy and
mathematics (dissemination, eliminate copying errors)
• Published Ephemerides (almanacs) for years 14751506 -- day-by-day tables
 Left-hand page: positions Sun, Moon, planets, nodes for
 Right-hand page: positions of Sun w.r.t. Moon, times of
new and full Moon, Moon w.r.t. planets, planets w.r.t.
each other (conjunctions)
 Feast days, Sunday dominical letters
• Ephemerides famously used by Christopher
Columbus in 1504 to frighten natives of Jamaica into
giving him provisions
• Called to Rome by Pope Sixtus IV – calendar
• Died shortly thereafter, reform didn’t happen;
rumor poisoned by George of Trebizond’s relatives –
more likely plague
• Calendar reform postponed until much later
Bernhard Walther
• Wealthy merchant of Nuremberg; humanist, friend
of Albrecht Dürer
• Trained by Regiomontanus
• Converted part of house into observatory
• Acquired Regiomontanus’s instruments after death;
observed over 30 years
Observatory located on roof
Albrecht Dürer House (museum)
• First long European series of accurate observations
• Recognized and allowed for atmospheric refraction
• Most accurate observations until Tycho Brahe (1’
for Sun, 5’ for Moon and planets)
• Used mechanical clock in astronomical observation
• Three Mercury observations used by Copernicus
• Born Niklas Koppernigk in Thorn (Torun in
modern Poland), 1473
• Name spelled differently in vernacular at
various times, as was customary
• In Latin Nicolaus Copernicus; only last used
• Thorn in German-speaking region  both
Germans and Poles claim Copernicus!
• Born in Thorn (Torun in modern Poland)
• Birthplace is house at left (not
too shabby!)
• Father was well-to do merchant;
died when Copernicus 10; mother
• Taken under care of maternal
uncle; priest, later Bishop of
Warmia – political as well as
spiritual authority
• Uncle planned for career in Church = canon
• Entered University of Cracow at 18 (had been in
several schools previously)
• Studied astronomy with Brudzewski; Peurbach’s
New Theory of the Planets and Aristotle’s On the
Heavens among others
• Early opposition to uncle’s plan  Copernicus
sent to Italy
• Matriculation University of Bologna (uncle’s
alma mater) as member of the German nation (one
of four)
• Studies for degree in canon (church) law;
• Also learned more astronomy from Domenico
Maria Novara; boarded, observed with him
• Ended up taking degree later on at Ferrara
(cheaper than Bologna)
• After brief trip home permitted return to Italy,
study medicine – physician to uncle and chapter of
• Studied medicine two years at Padua
• Returned to Poland to take up position as canon
at Frauenberg (Frombork) cathedral
Frauenberg (Frombork) Cathedral, 2010
Spent rest of life carrying out his duties in Frombork …
… while pursuing his understanding of planets ...
… and, of course, observing them.
• According to account much later, invited to
lecture on astronomy at Jubilee in Rome (1500,
before degree)
• Early statement of ideas – Commentariolus =
Brief Commentary (1512); circulated in
Brief Commentary
Seven theses:
1. Celestial bodies do not all revolve around the same
2. Earth’s center is only the center of the Moon’s orbit
and the center of gravity (tendency of things to
3. All planets revolve around the Sun, which is the
center of the Universe.
4. The Earth-Sun distance is extremely small
compared to the distances of the stars  no
5. The stars are immobile; their apparent motion is
caused by Earth’s rotation.
Seven theses (cont’d):
6. Earth revolves around the Sun, causing Sun’s
apparent motion around the ecliptic, in addition to
other motions.
7. Earth’s revolution around Sun causes the retrograde
motion of the other planets
• Reception among those who saw it not
• Interest on part of high Church officials,
including Pope Clement VII and several cardinals
• Observed especially from 1512 through 1529,
accumulating data to prove his theses
• Situation changed with 1539 visit by Rheticus,
professor of astronomy and mathematics at
Wittemberg University (Protestant).
• Rheticus spent two years with Copernicus,
learned about results.
• Rheticus wrote Brief Narration describing
Copernicus’s work.
• Lack of controversy persuaded Copernicus to
publish complete heliocentric system.
On the Revolutions, Six Books
• Above is original title given by Copernicus,
translated from Latin De revolutionibus, libri VI
• Dedicated to Pope Paul III
• Printed Nuremberg; originally Rheticus oversaw
• Oversight turned over to Andreas Osiander,
Lutheran minister and theologian, who saw it through
to completion in 1543
On the Revolutions of
the Heavenly
Spheres, Six Books
• Above is translation of
title given by Osiander
(next slide)
• Osiander made two unauthorized changes, probably
with the best of intentions:
1) Title changed to On the Revolutions of the Heavenly
Spheres, Six Books
2) Preface added without Osiander’s name attached
• First suggests Earth excluded, especially to reader of
that time (Aristotle’s cosmology) – immobile?
• Second contradicts Copernicus’s main point
Osiander’s Preface
• No consultation with
Copernicus or Rheticus
• Admitted contents
• Denied models are
real; confused reader
about Copernicus’s
Why did Osiander make these changes?
He was afraid of the reaction of the Protestants!
He was right, too:
Martin Luther himself referred to Copernicus as “that fool
[or possibly ‘that fellow’] who would overturn all of
Philipp Melanchthon, one of the foremost Lutheran
intellectuals, denounced Copernicanism.
Why were the Protestants opposed?
• They believed that each man could and should
interpret the Bible for himself.
• There are passages that seem to be contradicted
by Copernicanism – Sun standing still in Joshua,
other plain references to Sun going around Earth.
Why was the Roman Catholic Church not opposed?
• The bishops and cardinals thought the work
interesting and encouraged him.
• Church officials saw no threat to Church
doctrine – Church’s theologians interpreted Bible.
• Copernicus was one of their own.
Church’s opposition came later, with Galileo’s challenge.
On the Revolutions, Six Books
Outline of Copernican system and arguments for
it, plus two chapters on plane and spherical
Spherical astronomy
Earth’s motions: rotation, trepidation, precession
Moon’s motions
Planetary motions in (celestial) longitude
Planetary motions in (celestial) latitude
Arguments for Copernican system – two kinds:
1. Citations from ancients – Philolaus, Heraclides,
and others, but not Aristarchus (struck out in
MS); also, idea of Sun as “hearth of the
2. Criticisms of Ptolemy – equant, celestial sphere
rotating more rapidly than Earth; also, Sun’s role
“Escape clause” from argument of parallax (as in
Brief Commentary)
• In Book I, sketch of
heliocentric model, no
• Orbital periods given
• Orbital periods
calculated from separate
formulae for inferior,
superior planets
Formulae for sidereal (orbital) period P using
synodic period S, which is the observed quantity:
Inferior planet: assuming circular orbit, size of orbit in
astronomical units (AU) = sine of greatest elongation
Superior planet: knowing planet’s orbital period,
calculate angle P’SE’ and find length SP’ = distance.
Distances mostly pretty good except Saturn, most
distant (Earth doesn’t count – 1 AU by definition)
• Model for Earth’s
• T is Earth (Terra), S is
Sun, E is “mean Sun”
(Note that Earth’s orbit isn’t centered on the
real Sun!)
• Circle with small
circle going around it is
primary epicycle; much
smaller circle is
secondary epicycle,
both moved near center
• Model for superior
planet orbit
• T is Earth (Terra), E is
mean Sun, P is planet
• Model for inferior
planet orbit
• T is Earth (Terra), E is
mean Sun, Q is planet
• Epicycle moved to
center from outside
• Model for Moon’s
• T is Earth (Terra), E is
mean Sun, M is Moon
• Identical to al-Shatir’s
lunar model
Several misconceptions about Copernicus’s work:
• Won adherents because Copernican system much
simpler than Ptolemaic
Actually at least as complicated – eliminated
separate epicycles for retrograde motion, but
added secondary epicycles to eliminate equant
 ended up with roughly as many as Ptolemy
Several misconceptions about Copernicus’s work:
• Proved Sun at center and Earth rotating,
Only presented arguments, no proof; proof of
Earth’s revolution around Sun in 1728, rotation
a century later
Several misconceptions about Copernicus’s work:
• Hardly read by anyone – few could understand it
There were at least 500 copies, many of which
were marked with comments, especially about
the mathematical models if not the arguments
for the Sun being at the center. Also, it went to
a second edition (see next slide).
On the Revolutions, Six Books
• Title page from second edition
(yes, there was one!).
• Published in Basel (Switzerland)
in 1566
In some ways Copernicus’s work was of the past
– epicycles and uniform circular motion.
However, the one “big idea” in it – heliocentrism - was to have an enormous impact. It led to an
understanding of the planets’ actual orbits and, in
the process, to the establishment of the foundations
of modern physics. That is really what the
Copernican Revolution is all about.
That idea was also a giant first step in
understanding our true place in the Universe.
• Approached by Vatican about calendar reform
(remember Regiomontanus)
• Opined that time wasn’t ripe – needed more and
better data before undertaking
• Reform followed his death by a few decades
Prutenic Tables (1550)
• Erasmus Reinhold, professor of astronomy and
mathematics at Wittenberg, author
• Based on On the Revolutions, used models
• Superseded Alfonsine Tables
• Somewhat better, partly because much newer
• Replaced in turn by Kepler’s Rudolphine Tables
about 80 years later (much better)
End Ch. 4

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