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Recovery Western Civilization


The Recovery of the Ancient Learning

Beginning 13th Century



Astrology  & Astronomy in the Middle Ages.

Astronomy & Astrology part 1




Chronoloyg Short & Important


3000-1200 BCE. Sumerian and Egyption observations of the universe.

Greek writing on system of Universe, the first complete systems.

427 Plato, b. 427.

384 Aristotle, b. 384, complete system.

90 ADE., Claudius Ptolemaeus, b. 90 ADE., Ptolemy.


1203 Universities begin, but Aristotle is not taught in them right away.

Dante, (b . 1265), Christianization of Aristotle’s universe.

1277 Condemnation (Paris bishop, Tempier, 219 proposals) 

1280 c. Thomas Aquinas :The double tension is the Christian belief and what the Greek believed.

1391 Chaucer, wrote on the Astrolabe - first scientific treaties in English.


1436 b. Rigiomontanus, Summoned by Pope Sixtus IV, calendar reform.

1492, Maps: Martin Behaim, the globe of the world of with Japan included. Aided Columbus in support scheme.


1450s, The Great Period of Change


1450s onward saw the emergence of new things such technology, such as the printing press, and new ideas and events that changed western civilization.


The Reconquest of Spain.

The Fall of the Eastern Roman Empire

The Northern Renaissance takes place

The Printing Press begins, A New Media World

The Reformation, A New Religious world

Columbus, A New Terrestrial World

Copernicus, A New Celestial World



1470s, Almanacs the most important book to own outside of the bible.

1473 Nicolaus Copernicus (born February 19, 1473 – died May 24, 1543) was a Polish astronomer of German origin, who is remembered for providing the first modern formulation of a heliocentric (Sun-centered) theory of the solar system in De revolutionibus orbium coelestium. Attached geometrics to the principle of uniform circular motion which included the earth creating a new field of thought of a natural motion of the spheres.

1492 Martin Behaim, Globe of the world.

1518 b. Sir Thomas Gresham , b. 1518, founder 1596 of the Royal Exchange and of Gresham College .


Nicolaus Copernicus, b. 1473. Places Sun at center of solar system. Copernicus Revolution.

1540s, The Council of Trent, reformation of the Latin Church.


1543, Copernicus presents a theory that Earth revolves around Sun, which is placed on the Papal Index of forbidden books until 1835.

1545, At Council of Trent, the Church condemns judicial astrology.

1546 b. Tycho Brahe, Uraniborg and observations, and data for study, helped Kepler. The Tychonic system is very similar to the Copernican one, except that it has a static earth instead of a static sun.

1546, François d'Aguilon, Jesuit, began school of mathematics, in Antwerp.

1540s Council of Trent continues, establishes Jesuits as arm of the church.

1651 Giambattista Ricciole , Novum Almagestum, All knowledge summed up into an encyclopedia.

1564 Galileo Galilei (b. Pisa, February 15,). Medici Moons, Telescope, centrifugal studies, Copernicus defender.

1570s-80s Accademia de Disegno, tech schoolfunded by Cosomo de' Medici ( Galileo attnd.).

1571 Johannes Kepler (b. December 27,). Three laws of motion, Newton uses these for his studies on gravity and this inverse law.

1570s Ostilio Ricci saves Newton’s life by directing to an academic path.

1571 Johannes Kepler (December 27, 1571 – November 15, 1630), University of Tübingen as a theology student ( Studies, in Graz Sothern Austria), a key figure in the scientific revolution and the true founder of the New Astronomy. Kepler's elliptical orbit law: The planets orbit the sun in elliptical orbits with the (true) sun at one focus.

Kepler's equal-area law: The line connecting a planet to the sun sweeps out equal areas in equal amounts of time.

Kepler's law of periods: The time required for a planet to orbit the sun, called its period, is proportional to the long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets. 

1571 Sacred Congregation of the Index, organized independently, donec corrigatur ( until corrected).

1580 Publishing, House of Elzevir was founded in 1580 in Leiden by Lowys (Louis) Elzevir, after William the Silent established the first Dutch university there in 1575. Published Galileo’s work.

1582 standardize the calendar, Pope Gregory XIII., the Gregorian calendar, current use.

1586 Plus Ultra (“More beyond”) Bacon is said to have published the book (Two pillars)

1596 (Gresham College, Anti-University idea) Sir Thomas Gresham , b. 1518 founder of the Royal Exchange and of Gresham College in which he designed. 

1596 b. René Descartes, ( b. village near Tours in France) new & total mechanical Universe system, influences wide & Newton in early life. The Mechanics of Motion is everything in the universe.

1610-1611, Galileo travels to Rome to try to persuade  the Jesuits of his grand strategy to convince them of adopting the Copernicus system.

1613 François d'Aguilon, b. 1546 , Set up Jesuit schools, published Opticorum libre sex (Antwerp).

1616, Cardinal Bellarmine notified Galileo Galilei of the decree of the Tribunal of the Inquisition against the Copernican hypothesis.

1619cogito ergo sum”, spiritual experience on the 10th of November 1619, Rene Descartes became enthusiastic about what he called the admirable scientific method – to serve mankind.

1620s Francis Bacon’s (1561-1626) fall from grace with court of Elizabeth & James I of England. Wanted to do away with the old philosophers because he thought they bogged down men's minds. Machines will save mankind. Idea of modern technology.

1620 e. Jacques Rohault (d.1672).

1621 Index is published.

1622 b. Francesco Bianchini, A gnomon in the south wall of the Santa Maria degli Angeli e dei Martiri projects the sun's image onto Bianchini's line every solar noon., claimed to see cracks on the moon.

1623, Il Saggiatore (The Assayer), Jesuits and Galileo get into heated matches.

1629 Huygens Christian, b. 1629, Best telescope grinder in Paris, discovered Titan and Saturn's rings. Competition Galileo. Disputed speed of light with Descartes system.

1625 Giovanni Domenico Cassini (b. June 8, 1625), Mars -parallax to determine its distance, true dimensions of the solar system, Longitude accuracy., utilized Jupiter’s system for more accurate clock.

1623 Il Saggiatore (The Essayer) Rome. Polemic, mathematical basis for science.

1632, Dialogue Concerning the Two Chief World Systems, Florence, Galileo, under formal license of Inquisition.

Day 1, Aristotle’s physics of problems, Day 2 Diurnal motion, Day 3 Annual Motion, retrogression, tides and defending of Copernicus – not well accepted by the Jesuits.

1633 Galileo’s trial; convicted of "grave suspicion of heresy" based on the book, the Dialogue.

1634 Elzevir visits Galileo in Arcetri and agrees to publish Dialogue… Two New Sciences. d=1/2gt2

1630s Pope Urban VIII’s sublime doctrine is noticed in Simplico’s voice in Dialogue, ends Galileo friendship.

Giuseppe Campani b.1635, working with long boon telescopes.

1625 Giuseppe Campani (d.1715) was an Italian optician and astronomer, His brother, Matteo Campani-Alimenis, and he were experts in grinding and polishing lenses. Cassini used his lenses to see spots on Jupiter.

1636, Utrecht  University, established, Holland. Henri  Régnier a professor of philosophy taught the Cartesian system. Le Roy succeeded Henri  Régnier.

1637 Discourse on Method, La Géométrie, introduces Descartes mechanical system.

1638 Galileo's final book Discourses and Mathematical Demonstrations Relating to Two New Sciences, and a sort of scientific testament covering much of his work in physics over the preceding thirty years.

1643 Evangelista Torricelli (b. 1608) discovery of the principle of the barometer, professor of mathematics in the Florentine academy.

1644 Descartes, Principia Philosophiae (pub. Amsterdam), sections, titled The Principles of Human Knowledge, The Principles of Material Things, Of the Visible World and The Earth, are a study of mechanics, developing a mathematical foundation of the universe.

1644 Torricelli, De dimensione parabolae, pioneer in the area of infinite series.

1640s Galileo, Torricelli, weights falling down in every direction as if a ball was released at the same time.

1651, Giambattista Ricciole, Novum Almagestum, All knowledge summed up into an encyclopedia.

Francis Bacon, b. 1561, natural philosophy (plus ultra) practical problems., Machines will solve hard labor and sorrow.

1656 Huygens’ discovered Saturn’s rings consisted of rocks.

1657-1667, Accademia del Cimento, Italy., Prince Leopoldo de’ Medici and the Grand-duke Ferdinando II founded. To prove Galileo’s work. Studies, electricity.

Bernard Le Bouvier de Fontenelle b.1657, refutes uniqueness, the method of personal attack.

1660 Robert Boyle and Robert Hooke working together and finish around… quantitative rules…useful for life.

1660s The Airpump goes north to England. This leads to Boyle law. hH=constant.

1660, Royal Society of London for the Improvement of Natural Knowledge, founded (See Gresham College).

1662 b. Francesco Bianchini (He saw cracks on the moon; name Portugal names to places on Venus) his efforts to improve the accuracy of the calendar, Bianchini constructed several important meridian lines, devices for calculating the position of the sun and stars. The most notable of these are in the cathedral church of San Petronio in Bologna, and in the basilica of Santa Maria degli Angeli e dei Martiri in Rome.

1666  Paris, Royal Academy of Sciences, founded in Paris. King Louis XIV funded. State controlled. First order to map France. Initially was credited due to the pleading of Jean-Baptiste Colbert.

1667, Geminiano Montanari (b. 1633) registers star Algol varied brightness. 1660s , The Airpump goes north to England. he moved to Bologna, where he drew an accurate map of the Moon using an ocular micrometer of his own making. He also made observations on capillarity and other problems in statics, and suggested that the viscosity of a liquid depended on the shape of its molecules. In 1669 he succeeded Giovanni Cassini as astronomy teacher at the observatory.

1740s Benedict XIV, School system replicated ever since, research institutes, pays for astronomy department, paid 24 teachers full time in which half of them were just researchers.

1670s Lorenzo Ciccarelli, lawyer, and printed index books, Copernicus( In Italy).

1671  Traité de physique  system of Jacques Rohault was founded entirely upon Cartesian principles. Lectured at Paris. Became the leading authority on natural philosophy and was translated into Latin  in 1674 and used as a university textbook. His focus of experiments were on the weight of air, and magnetism.

1672 Giovanni Domenico Cassini (1625–1712) Italian astronomer & Engineer sent Jean Richer to Cayenne, French Guiana, while he himself stayed in Paris. The two made simultaneous observations of Mars and thus found its parallax to determine its distance, thus measuring for the first time the true dimensions of the solar system. Cassini was the first to make successful measurements of longitude by the method suggested by Galileo, using eclipses of the satellites of Jupiter as a clock.

1675, The Royal Observatory, Greenwich. Commission by King Charles II, Sir John Flamstead, the first Astronomer Royal, 0 degrees geographic longitude (GMT), 16 minutes annual discrepancy.

1677 Benedict de Spinoza, a rationalist metaphysics, promoter of Descartes, (Ethics) in mathematical-deductive.

1687 Principia, published in 1687 (Philosophiae Naturalis Principia Mathematica), Newton’s’ natural Philosophy. These were philosophies on matters on force of universal attraction, forces between bodies, and particles of matter; particles, meaning atoms

1690 Academe, Eustaschio Manfrede ( now, Degli Inquieti), Bologna  schools fell into a despair over the professors.

1695 Enrico Noris (b.1631-1704), Jesuits opposed his book Historica Palagiana (1673), now considered a millstone in history of dogmatics ( Sun, Heilbron), result got  promoted. curator of the Vatican Library (1695) later promoted to Cardinal.

1700 England.

1740 Laura Bassi, received license to read Descartes (Italy, academia), becomes first Italian women professor.

1740 Benedict XIV, born Prospero Lorenzo Lambertini, traditional practices codified, gives books benefit of doubt if written by Catholics. Galileo was Catholic, sincere interest in science.

1815 ― 25  Filippo Anfossi d. 1825 Vicar-General of the Order of Preachers and later Master of the Sacred Palace, doctrinal fights about math and astronomy which were to have no restrictions.

1822, Dialogue of the Two Chief World Systems, removed from Index.


1935 George Lemaître, Big Bang Theory published, b. 1894, (Expanding Universe).


(date?)Robert K. Merton, his thesis was the connection of the Protestant's ethic to capitalism.






  • Homemade astrolabe see part II.

By Michael Johnathan McDonald.


Recap on the major events of the middle ages, and the recovery of learning.

These are a short recap on the set of developments of the recovery of the learning which ultimately changes western civilization from the dark depths of ignorance to the light of information and knowledge.


  • This is all about information which leads to knowledge which leads to a civilization which leads to progress.

  1. Rome falls and due to constant wars and all learning is lost for the western civilization. Books to monasteries and hidden places – book worms, and fire destroy many works.

  2. Rise of Islam in the 7th century takes over a large area of the known world.

  3. Islamic civilization grows which signifies the expanse of learning and gathering of knowledge.

  4. They start a program to translate Greek and Roman works into Arabic.

  5. They comment on these books which lead to investigations and sometimes improvements, including the ancient concepts of the astrolabe, in which they make and employ many of them.

  6. Meanwhile western civilization, where all ancient knowledge has been lost, some postulate if a triangle can be measured with a formula of 180° degrees? This is truly the dark-ages of learning for the western civilization.

  7. The conquests to the middle east open up avenues of international discourse. Westerners see Islamic states at an advanced state of civilization, and they desire to have their own.

  8. 12-13th century, slowly the heritage of ancient learning comes to the west by rediscovery ancient books, of  translated  back from Arabic to Latin and Greek by a few scholars, including monks.

  9. Some of these books, are discovered in Spain, during the later courses of the reconquest, and  are translated from libraries in Spain where the Umayyad and various administrations of Islamic rule kept the western books. 

  10. The Role of the Latin Church in the middle ages kept western peoples together, under Christianity. The unifying forces of the Christian churches, mainly the Roman Latin Church, expelled attempts by Islam to conquer Europe.


The double tension.

The double tension is the Christian belief and what the Greek believed. When these books were translated from Arabic to Latin or Greek apparently the westerners now understood they were in the dark compared to the Islamic civilization. So the result was a major push to get up to speed. First and foremost was the Pope allowing universities to be established. This elementary step placed a learning institution back into western civilization.


Arabs to Europeans: The translations form Spain.

Commentaries on mathematics: trigonometry tables, star charts, and the ephemerides.  

Almanacs, an Arabic word, are the ingredient to passing information that leads to knowledge.

Astrolabes, and working sets of problems due to which direction to pray to the Quiba (Kaaba)  on the earth.


1203 Universities begin, but Aristotle is not taught in them right away. His works eventually are accepted but this is a war with theology. The double tension arises in that these ancient books do not speak of a Christian universe, but a widely range of topics counter to theology and cosmology of the Latin Church.

Condemnation of 1277 


The Paris bishop, Tempier, with the help of theologians,  backed 219 proposals ( propositions)  for these universities. Therefore , Aristotle work is condemned because it is against scriptures (at least some parts of his work).  The significance was a great blow to academic freedom. This could be seen as a step backwards, where Aristotle doesn’t fully come back into the picture in totality until the 16th century.


Dante, (b . 1265) a  poet and intellectual, writes on the universe in his work The Divine Comedy. Here we see the use of dates appealed by the positions of the planets. Dante’s universe creates a major structure with a theme. The planets, the sun and the stars are incorruptible, while the terrestrial, which includes the four elements are corruptible.  This was a major divide line of distinction. 


Distinction or forming boundaries of thought creates a building block for knowledge. This new information becomes a disciplinary normality where the next person can build a thought-structure from this foundation. Dante’s universe is geocentric, dividing lines of upper and lower parts of the globe and universe, the concepts of purgatory, paradise, and the four terrestrial elements and the one incorruptible celestial element, created a universe that was irreducible by things in full. Are there atoms under the sun? No. Nothing was irreducible in Dante’s universe.  Why would Dante suggest such?  Dante’s universe came from Aristotle, but he doesn’t want the religious people to understand this. Many people say why are no footnote’s taking place in people’s work? Well this was a scheme to get around the religious authorities. Aristotle was banned so why mention it was him where one received their ideas. Also, place one’s thoughts in poetry and people think that this is fiction. But the learned can understand and they did. The learned knew who said what and where. But the common authorities had no clue.


Double tensions continues until the great events of the 15th-16th  Centuries.


1450s - Onwards is a turning point in western civilization. Why?


  1. The fall of Byzantine to the Turks distracts the Church from the new religious movements arising in the north.

  2. The Voyages of Columbus, opens up new information that is contrary to Aristotle by the discovery of new worlds.

  3. Copernicus, creates a new universe.

  4. Luther and Reformation crack the academic dominance of the church which leads to more freedom of thought and expression.

  5. The ‘new’ printing press churns out new the banned knowledge, including the translations of Aristotle’s rivals,  and mass communication which brings information which creates knowledge for the era is slowing beginning.

  6. The reconquest of Spain from Islam and the recapture of the libraries.


The break form Aristotle – no more Aristotelian grand synthesis.

Humanist now translates and uses Aristotle’s rivals, which finally defeat the Aristotelian model and its dominance in learning, and his universe.


Church loses power to enforce, because too much information is flooding into the system. The Church is fighting the Turks and the Protestants benefit by the distraction.


These changes create in the theme of double tension, a breakage of philosophy and physics with the new control of applied mathematics. The spiritual and the non-spiritual separate into categories.


Copernicus, although apprehensive till his death about his new concepts of the universe and the Church’s power to destroy anyone who differs, finally gets his heliocentric work published with the key-word hypothesis used as safety outlet against the Church's ever watchful eyes. It was heretical to claim that humans on the  geocentric earth were not the center of all existence.


The new religious world, the new universe world and the Columbus new discoveries of a new terrestrial world, all help create the foundation where a Kepler could flourish. Without these there is no Kepler.


Tycho Brahe 's religiosity and firm belief in astrology including the desires to reform astronomy by these methods inspires to calculate more accurate positions for the planets. He uses strict and constant physical observation. He divides the universe again, with the induction of what are comets and paths of the tail. Therefore the unchanging and changing are trimmed down a little as comments link the corruptible to the incorruptible - the changing and the unchanging.


1600-1750 The battle of Astrology and the Church ignites, because they have no other issue now that the new of the knowledge of the universe is allowed to be taught in schools. The Church actually battles something they had no problem, and actually promoted, with prior to this time. Galileo, Kepler, Tycho, Thomas Aquinas (Star’s influence on a person)  Copernicus and so many others actually taught astrology to students and people. The significance of the battle creates mathematicians, while the other significance is the free-will ( Greeks now influencing western civilization again) and predestination argument.


Rudolphian tables, Kepler’s later work, yielded the best predictions so far in astronomy. He was able to whittle down the errors of degree(s) from Copernicus and Ptolemy's estimates to one minuet of arc in this book, which is astounding. In 1631, a year after his death he predicted a rare event that Mercury would pass the solar disc and leave a shadow, which it did.  By this time western civilization began to roar.


  • Astrology changed how western civilization moved from the dark ages of learning to the new ages of enlightenment and by discovery  of ancient teachings. Without astrology, Copernicus, Kepler,  and many other astronomers could not have figured out much of the complexities of the known universe in the middle ages to the renaissance. Astrology became ingrained in society and of how society thought and discovered it s various mysteries of God and the Universe. Johannes Kepler, employed as imperial astrologer by two  prominent kings, discovered his theories by understanding and teaching when younger of an astrology concept called the trigon periods. This led to the Platonic solid theories and his universe structure. Astrology's etymological definition relies on its concepts of understanding celestial bodies, space, and stars.  Today it is regulated to a pseudo-science with limited scope. Therefore astronomy/astrology is closely linked as a field of study in the ancient days, and the medieval universities of Europe.

  • The ultimate debate upon destiny verses chance takes center stage in the argument between what is astrology during the middle ages? Finally the branch breaks into two divisions which  both are no more compatible with each other than the next hair brained theory. The evolution decreed by social norms saw its citing the reemergence of ancient knowledge. About 1700s Astrology fell to the way side. Many governments backed a ban on this type of learning. At least the archaic forms of Judicial Astrology, predicting victories of battles, the fall of leaders and social changes. Much of the reason for the demise stemmed from the Almanacs which utilized Judicial Astrology. These Almanacs became political and physiological warfare methods, as pamphlets bearing the predictions passed back and forth between political enemies. ( See William Lily and England's civil war periods for  a great example of a statistical spike in astrology pamphlets).

  • Some of the discussions themes...

  • Beatrice: The antipedies, Dante, and the concepts of purgatory.

  • Columbus knew the earth was round. How was he able to know and then to navigate?

  • The Four Elements are  Earth, Air ,Fire, Water .

  • Aristotle argues a spiracle world. His astro-biology universe remained a stable theory up until the 1500s.

  • Astrolabes: The height of the pole of your horizon is your latitude. In the Middle Ages Latitude was easier to calculate. Homemade astrolabe.

  • Know why and how to place one circle in another position. Find where you are on the earth.  Use it to find direction, time, and other wonderful stuff.

  • Calendar reforms: Regiomontanus' ephemerid states that the 12th of February is actually two days before the month of February. For example, the 28th of February is actually two days before the month of March.

  • Roman New Year was March 25th.  In 325 the Council of Nicea made its important fixation of the Vernal Equinox. So the first full moon after the Vernal Equinox follows with the upcoming Sunday in which the Church chose to celebrate Easter. By the 13th Century the vernal equinox was falling on week prior to March 21st. This was a world problem and started with the a solution in the 13th century with the recovery of the ancient learning.

  • The Julian Year did not begin on the first day of the year. The conversions of the Roman times conflict with the other dates because they naturally run backwards.

  • Late in the 17th Century until the early 18th Century England for 70 years began their new year written as  April 8/18..(1719/20) (c. 1720s). The taxable year for England was on April 6 to the following April 15th. This meant that 10 days were alive in England, giving more reasons to revise the calendar.

  • March 25th was the new year.

  • Why did the Calendar change when it did? The Reformation cracked the Church's dominance which had a stranglehold on keeping the old system in place. Protestants wrote books and had them published by way of the new printing press complaining of the errors of the Latin Church's Calendar.

  • Maps: Martin Behaim, the globe of the world of 1492 with Japan included. The authoritative scholars believed him but he was discredited by the judges, which seems to be the case with all new revelations of this sort.

  • 9th-10th centuries described in the diary of a Noblewomen of Heian Japan ( See: Kagerō (no) Nikki) astrology  and as told in the work appears as the extreme functionality in all of the people's lives. Significance, is that astrology is world wide phenomenon during this era.

  • A medieval board-game, using dice, turns into the astrology square-chart house system. The turn meaning of the horoscope is not the birth-chart itself but the horizon.

  • Medical Practices: Melathesia, otherwise known as medical astrology drives the middle age industry. The Moon's position is the signifier of the diagnosis. Wherever the moon governed on the body that hour the patient's problem lay there. No bleeding if the moon was in a water sign. The moon spelt trouble, but this also minimized the days for bleeding which actually didn't do anything positive anyway. But bleeding was a middle age fad and people bleed themselves even when they were not sick. They just cut their veins. Signs governed parts of the body. Aries was the top of the head and of course, Pisces was the feet.

  • Universities taught astrology for this purpose - from the 13th until the 17th century.

  • Symbolism: Saturn depicted (In art or writ) as a warrior as well as Mars in the middle ages. Today it is more Greek traditional.

  • Farnesina (Rome) is a horoscope painted by Perruzzi Chige.

  • Architecture: San Lorenzo (Filippo Brunelleschi architect) , a famous building in Italy commemorates a political event of 1439 by Sagretia Vecchia. This commemoration is a piece of artwork on one of the ceilings of San Lorenzo.

  • As for the correct calculations and recording of birth charts, only the wealthy retained this privilege. Around the expected time the nobles would call in their people to record what was happening in the skies at the time of birth.  Keeping an accurate time of birth remained nearly impossible without modern necessities such as wristwatches or walled clocks. The main clocks of the towns resided in the main church on the inside, so people usually had to guess at their children's birth times. This is why many people during the middle ages have their times of birth recorded on the half-an-hour intervals. This, of course, for the common people meant they could never have true reading of their chart. This is why Nostradamus never cared to read or cast charts of people, contrary to outcries of scholars who cite him not capable of understanding the technicalities of charts. He just didn't care. He used whatever ephemeris was available and read the noon-time figures for the day in question. He only started to receive requests late in his life after he became famous and still in his letters he is congenial and tries to persuade his admires that he has no time to do a chart for them. The scholars that actually make this their crying claim to an inability do not see that Nostradamus actually decried the use of astrology ( See: C6Q100 of his Les Propheties)  and therefore could not beheld accountable for the profession. His own claim that he practiced Judicial Astrology for 40 years remains a blinding spot for scholars who have no understanding what his other practice held in antiquity. This is astro-astrology.  It appears nothing like a normal astrology horoscope (birth chart) would look like or the interpretations of judicial astrology.

  • The Science of Astrology: "Rotation of the Trigon of Great Conjunctions." Any one of the corners of the triangle or trigon will move through 30 degrees in about 200 years and completely around the Zodiac in 2400 years. The 20-year conjunction points are roughly one-third of the Zodiacal Circle around from each other. If the points are connected, they form a near equilateral triangle within the circle. Each successive 60-year Great Conjunction occurs an average of about nine degrees farther down the track, in the forward direction through the Zodiac, from the previous one. Therefore, the entire triangle can be thought of as rotating in the forward direction through the Zodiac in increments of nine degrees every 60 years.  (Terry).

  • Religion and the Latin Church.

  • Note the clock indications and the Sumerian mathematical base system for their society. Note that some of Nostradamus' judicial astrological applications use 800 year occurrences, indicating 1/3 around the circle or 120° any one of the corners of the triangle or trigon will move.

  • The procession of the equinoxes ( the wobble of  the earth around its axis) thought to take 24,000 years by medieval references, whereas today, and in antiquity, we know it is roughly about 25,920 years. Still this figure is divisible by three; each sign is 2,160, representing a 30° part of the circle. So ever 2,400 years we get three 800-year 120° harmonic trigon cycles that Nostradamus used.

  • The leading astro-scientists that changed the fields of our universe.

  • Basic significance of science in the Middle Ages to the beginnings of the enlightenment.

  • Why is Chaucer important to Astronomy and Astrology?

"About 1391 Chaucer wrote his Treatise on the Astrolabe for his son. All scientific texts were written in Latin, so that scholars everywhere could read them. But Chaucer's son was too young at 10 to read Latin, so Chaucer's instructions to his son became the first scientific text written in English" (Green ).


Important Figures and Themes.

Dante's truth claim: The way to Heaven (Paradiso)  can only be achieved through feminism.

Dante's childhood love evanescence never subdued : "La Commedia (1321)— the greatest love poem about the soul's ascent from Inferno to Purgatory to Paradise. Beatrice,"

  • Solstice meaning a standing still of the Sun.

  • Tropical means moving back into.

  • The sensible horizon is tangent to the earth at any place.

  • The Horizon is your personal own tangent to the horizon.

  • Danti " Your on the other side of the horizon plane".

Sacrobosco, Johannes de (yōhän′ əs də săkrōbŏs′ kō), or John of Hollywood, c.1200–1256, English mathematician and astronomer. He wrote several widely read and influential books: Algorismus, a study of arithmetic; a treatise on the calendar; and the most popular medieval introductory textbook on astronomy, the Tractatus de sphaera.  (The Columbia).

  • "Sacrobosco wrote a computus (" The science that considers time from the motions of the sun and moon") that had many versions down into the sixteenth century" (Heilbron)

  • Sacrobosco, John of Hollywood, viewed as second to Euclid.

Sacrobosco's importance in the history of astronomy stems from his authorship of some of the most popular and enduring textbooks of the middle ages. His Algorismus, perhaps his first work, was a treatise on numerals and arithmetic. The most famous of his works, De Sphaera, a basic account of the spherical geometry underpinning the mathematical astronomy of Ptolemy and his Arabic commentators, was composed c. 1230. It rapidly achieved popularity, and was reproduced and commented upon even into the seventeenth century. The Compotus or De anni ratione, a treatise on the calendar and calendrical computation, can be dated to c. 1235, while the Tractatus de quadrante, which describes the construction and use of the so-called quadrans vetus or old quadrant, was composed after 1239. Other works, including commentaries upon Aristotle, have been ascribed to Sacrobosco, but these attributions are considered dubious (Starry 2).

                    Roger Bacon's  Δ = 1 day in 125 years=11.52 minuets/year.





                                Dream of Macrobious (a 5th century scholar).


Macrobious: The Chart of the eleven circles - where did they come from? "The Dream of Scipio, Somnium Scipionis, was studied by the Roman philosopher Macrobius (395 - 423); his Commentary upon Scipio's Dream was valued throughout the Middle Ages. Chaucer was also acquainted with it, referencing the work explicitly in his Parliament of Foules. This dream-vision by the Roman philosopher Cicero describes Scipio's inter-planetary journey through the cosmos.


  1. 11 Circles of interest.

  • There are eleven spheres  (see: Macrobious). The first seven are the planets. The eight sphere is the zodiac; the tenth sphere is the 26,000 year cycle and the eleventh sphere is the elect.

  • The North Pole penetrates the eight's sphere.

                    Martianus Capella: The marriage of mercury and philosophy.

Understanding the earth was round and the literacy of the European peoples' all was forgotten. Cosmology took a twist to the unknown. Cosmology comes back with Danti

The Great Paschal Cycle of Victorius.



" Around 455 Pope Saint Leo I, [...] commissioned Victorius of Aquitaine to look into the matter. " He looked into the discrepancies of the cycles and the Saltus, in the date of the equinox, and the difference in allowed terminal dates for Easter Sunday ( The Roman 16-22 Luna against the Alexandrian 15-21). He suggested that Rome set the equinox earlier then 25th of March and adopt the19 year cycle. He calculated that Christ died during the fourth year of the 275th cycle. He found a fact that " After 532 years everything repeated itself, the moons, the dates, the days, the Sundays, the Easters." ( Predieri, AS, Bol., Mem., 3(1851), 131-2.; Heilbron 30).

Early midlevel astronomy.




  • Aristotle became the first person to discuss and write upon the universe and astronomy. His cosmology would gain much acceptance up until the 1500’s, where Copernicus. Kepler and Galileo began to figure out that the earth is not the center of the universe.

  • From the 3rd century to the 1500s, the dominant view held that the earth was the center of the universe. The Tychonic universe even had a geostatic structure, in lieu of Kepler's coaxing Tycho.

  • Aristotle knew that the World was spiracle by the earth's s shadow on the moon during a lunar eclipse. Ptolemy even had better arguments.

  • Tactile qualities.

  • Terrestrial elements go downward, water and earth and fire and air go upward. Dante's cosmology says that the fifth element, the ether was unattainable, and was unchangeable, and or was incorruptible. The four terrestrial elements, seen below are all corruptible, and belong to the earth. The theme of the dual tension and the duality of the division ever widening, or receding to one's point of view is what is at stake in the middle ages.

The four elements blend:

Generation implies change.

Aristotle believes motion equals change. This is called his doctrine of motion. Also, he is against reducing everything to atoms.

Hot Fire Dry

Hot Air Moist

  • These elements go upward.

He didn't like molecules, and to him nothing was irreducible. Each thing had its own uniqueness.

Dry Earth cold

Moist Water Cold

  • These elements go downward.


  • Corruption & Generation equals themes.

  • Early questions about if the earth could rotate around the sun. How does a rock know how to fall? If a rock understands that it is out in the air, suspended, then it knows it has to go down. But there is no vacuum. See Copernicus and the violent motion' part II.

  • Ptolemy views seven planets in the universe; this includes the Moon. Kepler, said I cannot place seven planets in the five known three- dimensional geometric shapes so I need to get rid of the moon as a planet. Therefore, six planets become the solution.

  • Celestial 5th element. The quintessence. Math

  • The physics of heaven is different then the physics of earth. What distinguishes the different things in the heavens? It is the planets, the unchanging stars, and the unchanging Sun.

  • Aristotle's answer is the Intelligence. He associated each a sphere with a disembodied intelligence. Thomas Aquinas  associates them with angels.

  • These concepts also have a duality referred too as the  movers and the unmoved concept.

  • What connects the terrestrial with the celestial?  Comets - see Tycho.

  • Heavens are eternal and unchanging. Meteorological Aristotle's book.

  • The sublunary phenomenon.


Ptolomey's astronomical universe doesn't constitute a system: The mechanism of planetary motion are independent of each other...  (Koyré 101)

"Ptolemy did, however, know that the earth was spherical. He pointed out that people living to the east saw the sun rise earlier, and how much earlier was proportional to how far east they were located. He also noted that, though all must see a lunar eclipse simultaneously, those to the east will see it as later, e.g. at 1 a.m., say, instead of midnight, local time. He also observed that on traveling to the north, Polaris rises in the sky, so this suggests the earth is curved in that direction too. Finally, on approaching a hilly island from far away on a calm sea, he noted that the island seemed to rise out of the sea. He attributed this phenomenon (correctly) to the curvature of the earth." (Fowler).


Earth Flat or Circular Argument in Antiquity.

  • Phi = Alpha. Lets say Alpha is the altitude. It is the measurement between the horizon and the North Pole.

  • Argument in medieval texts describes an argument of the Greeks by the shadow on the moon representing a spherical shadow cast by the earth on the surface of the moon. Examples of squares, triangles, and circles make up the argument in Medieval texts which seem quite laughable considering what we know today.

  • Religious problems with changing the paradigm? Saint Thomas Aquinas: He invented what is called the " double truth" and just uttering it was heretical.

  • Fights against the new learning: 1230: Logic comes into play but metaphysics is not allowed. It was considered opposition against the faith. 

One of the major theses of Aristotle who was against breaking things down to the atom level is creationism. Intelligent design is a revival of Aristotle's old idea: that animals seem designed, and this could not be by chance. Then you would tie it to a period where Universities begun to reach social importance and its re-beginnings in western civilization. The 13th century emerges as a point of debate over the importance of these new revelations (that is to say the recovery of Aristotle's Universe)  Tempier and the sixteen theologians assemble to speak and discuss theologies. , then turn to Averroes the Arabic commentator, then onto Siger of Brabant who always ends with Aristotle's Universe was eventually expelled form academia. You will probably find 1277 a key date as Tempier, the Paris Bishop and his theologians, create 219 proposals to regulate Aristotle and other non-Church doctrinal teachings in the universities. They place overseers at these universities to monitor them tightly. The significance is the stagnation of progression for western civilization for roughly four-hundred years of literature regulation persists. 

Tomas Aquinas had his own group of theologians and intellects that sided with the  Latin Church.  Arabs take Aristotle's universe over Plato's universe and call him not by name but as “the Philosopher”, spiting neo-Platonists who disagreed vehemently with Aristotle's universe. Intelligent design is a powerful force in the world, not only today, but yesterdays, as well.  One is never going to get rid of God in academia or society fully. God represents a solace from an otherwise a cruel and violent existence, and death and the afterlife is seen as a happy occurrence, more or less Herodotus’s famous observation. Thomas Aquinas  and his band of twelve preached against mystics. Bonaventure was the leader of the second group of twelve. These people regulated along with Church direction what was allowed taught and what was not. The Latin Church controlled for its own regulative purposes to keep society functioning and healthy. One can make an argument that their intentions were good, but they didn't understand the consequences. Dante's hopes are recorded in his work that although academic wars exist on planet earth in paradise everyone gets along together.


Again: The significance is the stagnation of progression ( learning) for western civilization for a few hundred years.

  • The Aristotle universe is that everything is governed by one single light. The goal is that everyone has their own particular place in the world. This eventually is apart of Luther's doctrine of talent.

  • Students who had economic clout from groups to learn. Previously learning took place by wandering teachers.


                    1201: Universities Europe

Universities: Students form a type of union ( called a guild) and rule the schools. They hire and maintain the faculty. They formed a legal basis for universities and the Pope granted permission. The determination was free from local jurisdiction.  The levels are as today, the undergraduate B. A. (baccalaureate means commencer or beginner) , the graduate programs. Exams to move on. and  a banquet that the students pays for, usually sandwiches and drinks. Students must pay for their degrees. If one became a doctor of his field ( example: P. H. D.) , they could teach anywhere is the world. The teachers and the students often warred against each other. IT was less of a crime to shoot and arrow at a professor then to break curfew. Often teachers were fined or removed depending upon the satisfaction of the students. Oxford, Cambridge and Paris are universities and offer B.As and P. H. Ds. Most classes are oriented toward Law, theology, and medicine. The medical degree was much shorter a period and this is why many students often went toward this direction.

Art curriculum is about four years and consists of sixteen to twenty year-olds. To become a master of theology it took sixteen -years and this is why most profession, that of doctor or medicine, or other technical positions were preferred. Theologians took on civil and cannon responsibilities and was connected to Law.


To start your degree in the classroom one will hear books read to them. This is where lecture came from as the professor would read the book to the class. The class takes notes and will debate issues for inter-testing. The students break up into groups and pair off on the issues. Disputations were given in Latin.  Books were expensive and this is why the students listened to a lecturer  rather then having to own a book themselves. If a student wanted to check-out a book the student would have to put a down payment as a surety. These payments were expensive and we know that sometimes entire vineyards became collateral for checking out books.


Footnotes were commentary usually annotated on the sides of a page in the middle ages. But there was not concept of a footnote during these times. There was no official citing of sources as arose in the 1700s. When the translations were done,  usually one person would read and the other would write. This was quicker process. Often commentary placed on each page to rectify  the translation process and commentary notes linking historical arguments.


Church's Overlords of the University to Keep watch. Although not in control, their presence is like a interest group as a whole in a political process. A dual notion also consists of a recruiting apparatus for the Church.


Fryers: Dominicans and Franciscans take positions on campuses and influence the Universities. They live in monastic houses. A Benedictine, thus is called for the title of the position.


The Trends: conservative to the Church's positions. This would oscillate between left and right politics and these  were the theologians. They have to represent the church. In general, the artists were liberal or more accurately open to novelty ( This tends to be a historical trend in all cultures) . However, until the proto- Renaissance the art was defiantly two-dimensional and church regulated, when the pieces were displayed for public prominence only. Otherwise personally the rule applies to artistic freedom.


How Arabs preserved western knowledge.


The Arabs rounded up Cyriac Christians and forced them to  help translate western books. They moved them to Baghdad, just like the Soviets moved German scientists to Russia after World War II. Event period from 750-900 approximately. The Cyriac Christens kick started The Islamic science programs.

12th century is the beginning of the recovery of learning in the west. Letters from the 9th-10th centuries show basic questions to mathematics indicating it was  indeed a dark age for learning, in which the middle ages takes its adjective from.  For example, what is the external angle of a triangle? was a question posed in a letter of deep concentration. Also, what was the sum of a triangle that makes a strait line? The west was really lost.

  1. There are seven liberal arts: They will eventually marry, so to speak.

  • Quadrivium: Arithmetic, geometry, astronomy, and Music. ( higher studies)

  • Trivium: grammar, logic and theory. ( where we get the term trivial).

How do we get Aristotle and Plato's universes? They survived. During the eleventh century our civilization is infantile compared to the Muslim civilization. Libraries in Spain controlled by the Muslims and places in Sicily, where the Normandy kingdom existed, which was semi-autonomous depending upon the leaders. Depending upon which Muslim leaders ruled the promotion of western thought was regulated or allowed to some extent. It was cyclic and not a constant measure. The Normandy Sicily Kingdom  was a polyglot administration both Arabs and Normans.

Al·ma·gest Arabic renames Ptolemy's treaties on astronomy, and mathematics called al-majisti , translated the greatest.  He lived about 150 A.D. and is often confused in renaissance art as a leader of the Egyptian kingdom. He also wrote on fixt stars and astrology, a type of method seldom used, but Nostradamus employed his paran method with interpretations.  This is an often criticized prophetic method by traditional astrologers because it displaces the object of free will and promotes predestination whereas astrology in its popular purpose promotes choices and only likely destiny and not absolute judgments. 

  1. Some popular words from Arabic that the west has adopted are artichoke, alcohol, alchemy, syrup, apricot, tariff, jasmine, zenith, nadir, algebra, algorithm, many star names, Arabic numbers.

  2. The Arabs passed on he concept of zero to the west in which they took from India who were great math technicians of antiquity. cipher: The mathematical symbol (0) denoting absence of quantity; zero.

  3. The Arabs were interested in the applications of astronomy and navigation. The Arabs gave back to the west  scientific astronomy and even improved on things.  Things usually transferred during war

  4. Arabs made tables out of everything. They continued to improve on the Hellenistic astrolabe. They make them out of metal which gives them sturdiness. By this time they had perfected machines for engraving and movable parts. This was relatively novel for them.


                    Dante Alighieri                             cosmology continued......

  • Significance: Dante Christianized the Greek Cosmology.

    Dante message to western civilization by way of interpreting his writings is to find a higher  and greater purpose in life. We need to find paradise and hard work such as learning language and studying will make us as one community. This process appears in the unity of the systematical universe which makes up his great works.

    Dante's significance to middle age astrology and astronomy can be described as:  Beatrice leads Dante to paradise, and she beings to ascend to paradise , leaving Virgil, the aspiration of Dante in purgatory, because he is Greek ( traditional) thus a polytheist, and cannot travel to God's Christian realm, to show him the perfection of God. This work signified the first celestial unifying model of the universe. The unity of the Universe is what Dante was after. He often tried to placate both sides of the doctrinal positions. However the cultural relevance is a division emerging in metaphysics and physical science.


Opening sonnet of La Vita Nuova, remains one of Dante great works. His celestial mechanics and looking for paradise led to understanding our universe a little grater than Middle Age thought had before attempted.

"Durante degli Alighieri, better known as Dante, (c. June 1, 1265 – September 13/14, 1321) was an Italian Florentine poet. His greatest work, La divina commedia (The Divine Comedy), is considered the greatest literary statement produced in Europe in the medieval period, and the basis of the modern Italian language.


When he was nine years old he met Beatrice Portinari, the daughter of Folco Portinari, with whom he fell in love "at first sight", and apparently without even having spoken to her. He saw her frequently after age 18, often exchanging greetings in the street, but he never knew her well. It is hard to decipher of what this love consisted, but something extremely important for Italian culture was happening: as it is in the sign of this love that Dante gave his imprint to the Stil Novo and would lead poets and writers to discover the themes of Love (Amore), which had never been so emphasized before. Love for Beatrice (as in a different manner Petrarca would show for his Laura) would apparently be the reason for poetry and for living, together with political passions.

When Beatrice died in 1290, Dante tried to find a refuge in Latin literature. From the Convivio we know that he had read Boethius's De consolatione philosophiae and Cicero's De amicitia. He then dedicated himself to philosophical studies at religious schools like the Dominican one in Santa Maria Novella. He took part in the disputes that the two principal monastic orders (Franciscan and Dominican) publicly or indirectly held in Florence, the former explaining the doctrine of the mystics and of San Bonaventura, the latter presenting Saint Thomas Aquinas' theories. " ( wikipost).

                    Dante's Accent to Paradise.



"Astronomy and philosophy remained tightly integrated within the liberal arts of the first universities Oxford and Paris. This was the astronomy of Ptolemy, preserved by the works of Arab astronomers.

     Dante who started his journey in the northern hemisphere expects to see the sun moving to his right, to the south of the meridian. Within the works that Dante studied was a reverence for the fact (considered highly philosophical in a world without satellites) that the heavens appear to behave differently from different vantage points on a spherical earth. What Dante is coming to terms with is that his subterranean journey across hell took him straight through the earth, past its center, and up into the southern hemisphere.

     Virgil asks Dante to remember all that he studied, then work out the significance of what he is seeing. In a sudden flash of understanding any amateur astronomer knows well, Dante "gets it:" he is seeing the motion of the sun from the other side of the world! As soon as Dante turns his mental worldview upside-down, it all makes sense. Dante brings to life the power of astronomy to transform our worldview (the very foundation of our experience of life on planet Earth) through poetry" ( Lord).

The day is 24 hours, however, the Sun's movement is 23.56 hours. This equals roughly about one degree a day. However, there are 235 days a year and the sun speeds up during winter and slows down during the summer due to gravitational pull of the Sun. The path of the Earth is not a perfect circle but a ellipse and is closer to the Sun by about 200,000 during the northern hemisphere's winter season. Still the Greeks understand only that the sun speeds up during the period it is under the tropics of Capricorn and slows down during the period of the tropics of Cancer. The furthest north the sun travels is the point called the tropic of Cancer. The furthest south the Sun travels is called the Tropic of Capricorn.



  • Trivia: If someone is at 37 Latitude in the Northern Hemisphere, the path of the Tropic of Cancer has a greater arc then the Tropic of Capricorn. Therefore the Sun appears longer in in the sky during summer then winter.

  • Seven degrees on each side appear most of the Zodiac stars.

  • The Babylonians used base 60 as their mathematical functions. They even knew of the ellipse of the earth's path around the sun noting the differential in speed. 

  • Apogee and the Perigee was measured by the Greeks when they observed the Sun's annual path by calculating and the off-center of the point of observance. The inequality is measured if we used the radius of one and the eccentricity is 0338.

Turks are conquering parts of Anatolia and many flee Constantinople understanding the inevitable.


The Latin Language deemed by some as Barbaric and the path back to enlightenment is by studying and knowing Greek.


Manuel (or Emmanuel) Chrysoloras (c. 1355 – April 15, 1415), one of the pioneers in introducing Greek literature to western Europe.
 Chrysoloras became famous as a translator of Homer and Plato (The Republic), his works circulated in manuscript in his lifetime; two were eventually printed, his Erotemata (Questions). first published at Venice in 1484, and then widely reprinted, which was the first basic Greek grammar in use in Western Europe, and Epistolae III de comparatione veteris et novae Romae (Three Letters Comparing Ancient and Modern Rome). Many of his treatises on morals and ethics and other philosophical subjects came into print in the 17th and 18th centuries, because of their antiquarian interest. (Wikipedia).


Johannes Bessarion, or Basilius (c. 1395-1472), was a Roman Catholic Cardinal-Bishop and the titular Patriarch of Constantinople. He was one of the illustrious Greek scholars who contributed to the great revival of letters in the 15th century, and was born at Trebizond. Bessarion was one of the most learned scholars of his time. Besides his translations of Aristotle's Metaphysics and Xenophon's Memorabilia, his most important work is a treatise directed against George of Trebizond, a violent Aristotelian, entitled In Calumni atorem Platonis. Bessarion, though a Platonist, is not so thoroughgoing in his admiration as Gemistus Pletho, and rather strives after a reconciliation of the two philosophies. His work, by opening up the relations of Platonism to the main questions of religion, contributed greatly to the extension of speculative thought in the department of theology (Wikipedia).


Why the Greek language and not just use the Latin translated from Arabic sources? The Latin translations were full of mistakes, so the Europeans decided to make a club to get their hands on any Greek manuscripts, in the original by any Arab that would sell them or other trader of manuscripts. "Lets get our hands on a Greek original copy of Ptolemy?"



The Great Period Of Change

1450s onward saw the emergence of new things such technology, such as the printing press, and new ideas and events that changed western civilization.

  • The Reconquest of Spain.

  • The Fall of the Eastern Roman Empire

  • The Northern Renaissance takes place

  • The Printing Press begins, A New Media World

  • The Reformation, A New Religious world

  • Columbus, A New Terrestrial World

  • Copernicus, A New Celestial World


Well known to Columbus is the earth is round. We know this by his own logs and writings.

  • Ironic events: Islam forces the West to go Further West and facilitates the founding of Europeans on Americas soils inadvertently dominating one large part of the globe.

1450s were a busy time. The Turks took Byzantine 1453 and ended the eastern Roman empire. This shifted the shipping dominance in the eastern Mediterranean ocean in the advantage for the Turks. The Genoese, the community that our Columbus was born into grew up in what is now a diminished shipping dominance along with other Mediterranean shipping companies like the Venetians and the  Portuguese.  This shift in regional power created a need to look elsewhere for trade which had flourished with goods such as  spices for food preservation and prized commodities from various cultures in Africa, and Arabia. Genoa is nested on a hill and is a prime shipping area in which Columbus grew up at and he decided not to go into the weaving business of his father, but to become a sailor who watched the great Genoese companies work from the ports and docks on the Mediterranean.  He was born in 1451, and was blessed that around the same time the printing press will emerge disseminating local knowledge. He sat along on voyages to England and traveled possibly as far north as Iceland. He was shipwrecked at Portugal once and also took voyages south to the 10° degrees looking for the passage around the Cape of Good Hope, Africa. This way he was exposed to the best geography and navigation of his time. Also around this time the Portuguese discovered Cape Verde Islands a future launching pad for the new world. As far as Columbus is concerned the most important aspect of the period is the reconquest of Spain. He will have to wait to propose his ideas to Queen Isabella. who has sold her jewels for the financing of the war. Meanwhile...


                   Columbus Fudging of the Numbers.

  • To the Europeans of this age, all land east of the Indus River (India) was “the Indies.” 

  • Fudging the numbers somehow workout for Columbus.

  1. Columbus wants to become famous and rich. He needs to make a sales pitch to the Queen as the judges understand little but enough  geographical knowledge to make arguments against a voyage.

  2. Columbus needed to wait for the war in Spain to subside before he could look for financing for his journey. Meanwhile he began to fudge the number to make a sales pitch to the Queen. Pierre d'Ailly job consisted of a chancellorship at the University of Paris. While Columbus waited he read his book titled " Imago Mundi' (1410) which was published in the 1470s. In the sides of the pages, Columbus used commentary to support his cause. First he turned his attention of Ptolemy's work on Geography.

  • Cathay (fabled cities of Cathay (China) ) to Cape Saint Vincent, Portugal.

Ptolemy  divided up the world sensibly as 50% water and 50% land, and he also out of frustration called Martinus of Tyre an idiot because he stated that Cathay's distance was actually 45 degrees shorter than his own calculations,  of 180 degrees, However, Columbus's mission was to shorten the distance in whatever way he could to make his case against the naysayer judges, at that time. Columbus' point was to get funding.  Therefore, he cited Marco Polo who stated that he walked   to Cathay and it was 28 degrees shorter than Tyre's measurements. Polo also stated that there were no less then 1378 islands around Japan. This was in part why many maps prior to Columbus's mission showed a batch of islands to the west of Spain in the far reaches of the Atlantic. Then from Cathay to  Capangu Japan, the distance of 30 degrees to Cathy was finally added to the distance of St. Vincent's Island. Therefore seventy-seven degrees remained. Yet, Columbus considered the latitude with the earths circumference which  gave a 10 %  leeway taking the degrees down to 61°. "If we leave form the Canary Islands then it will be even shorter".  Not liking odd numbers, Columbus then shortened this number to a nice round number of 60° degrees. Then taking the shortest ancient mile numbers the Italian ( Roman, 1,524 meters, or 5,000 feet) instead of nautical miles, Columbus fudged the numbers.  Columbus most likely said, " Look it is easy and not as far as you think. Just a few day's sailing, The ancient geographers show us the world is much smaller then we think." His estimate clearly showed a small number of about 2800 nautical miles while the earth was thought to be about 10,000 ( Canary Islands to Japan est. 10,600)(19,600 km) nautical miles. The Queen and her judges didn't believe him. They thought he was crazy and that they world starve to death. Another factor is Columbus wanted fame and 50% of the spoils. However, some bankers thought it was a good risk. Why? The Turks control of the east and the recent the expulsion of the Muslims and Jews showed that a competitive edge ruled the conversations of Europe and Spain at that time. What was Christendom to do? They took the risk and the rest is history. It was sink or swim, so to speak.

Columbus' Voyages One-to-Four

1st. Departed 6th of September, 1492 from the Canary Islands. The Canary Islands have a continual wind current blowing toward the west in which Columbus knew about and composed a wind map, and this knowledge allowed him to make the trip in 36 days ( arrived October 12, 1492) , and even 33 days was  his own personal estimates which meant he was not far-off in his estimates. The first trip comprised three vessels, Pinta; the Santa Clara but known as the Niña and Santa Maria. The Santa Maria was shipwrecked and Columbus could not take all the passengers with him back to Spain so he set up a colony he name La Navidad. 39 men stayed behind.  He became a hero. He didn't bring much back with him the first trip.  The natives on this trip were friendly. The natives on the next trip turned out to be cannibals which will get Columbus in trouble for mistreatment from the crown. Getting to the new world was easy as others had postulated, however they didn't know how to sail back to Spain with the winds traveling toward the west. However, Columbus knew and understood currents and the northerly wind patterns and the others didn't know. When he left the new world, in which he also discovered Cuba, he sailed home in a northerly pattern and passed the Azores. This rout had the winds to his back ( going east) and was able with relative ease to sail home.

2nd. 21 days and 17 vessels.  Columbus met up with indigenous cannibals and he mistreated them and also fought with the colonizers. He also found La Navidad gone and his men. He is sent back to  face charges of abuses against the indigenous natives of the new world. Makes his fellow sign documents that he indeed found the Indies. This made them mad because there were no oriental clothing or oriental women to meet them as promised. The Spanish colonizers that sail with Columbus knew they were nowhere near the east or the Indies. Columbus took back with him a few natives, who died shortly after arriving in Spain.


3d. Left from Cape Verde Islands. It was a tough voyage. He goes to Orinoco river in Brazil, called at that time, now called Venezuela. Over 1330 miles long, and the third largest river system in the world. Columbus thought he discovered Paradise spoken about in the literature of the middle ages. 

Amerigo Vespucci , was a businessman, and left to venture out after knowledge of Columbus's discoveries. He is cited with the naming of the Americas but was not the first to set eyes on south America, but was the first to explore some inner river systems and some lands of South America, in Venezuela and Brazil. Columbus' trying to find a new way to routs further east set his eyes on the South America river system that spans from Venezuela to Brazil called the Orinoco river with its four tributaries and was a place he though constituted the fabled Paradise on Earth. He found mild mannered native in canoes and some gold. " I think I found the terrestrial paradise."

Columbus's temper and treatment of the natives got him sent back to Spain in chains. He pleads with the Queen that he could find a passage out of the isthmuses ( later called Central America) and to the real Indies, although he himself believed adamantly that he already had found it. By this time other voyages are set up to explore the new world. Soon an onslaught and planning to colonize the new world is the talk of Papal states, Portugal and Spain.


4th. This time Columbus butts up against the isthmuses and takes a long time to search for a passage and then the bottom of his boat rots and he becomes marooned. He still has a disagreeable demeanor ( most geniuses do).   Regiomontanus tables provided Columbus with an escape plan out of subversion of the natives. Although the natives had seen eclipses before, they could not predict them. With the  Regiomontanus book of astronomical time-tables of the 19 year cycles of the new moon, the years for eclipses were drawn-out in picture form along with the intensity and beginning times. Columbus being his brash self managed to fight once more with the natives and colonizers who then decided to not feed him and work against him. He began to starve and things looked bad. His last hope was too proclaim that he had direct communication with God and that he would block-out the sun if treatment toward him continued, in which it did. " I will cause the sun to darken." He just referred to this book, unbeknownst to them, and scared them half-to- death. Columbus knew he was about 75° latitude, as it was easy to calculate with a book of declinations which he also had with him. The eclipse began in Nuremburg, Germany in the early stages of the afternoon at 1:30 pm. and reached where Columbus was marooned in Jamaica about 7:30 p.m.


He gets back to Spain, a rich man from bringing back some gold, he writes his will - still believes to his death that he found the Indies and not the new world. In the late period of his life he becomes more religious, a saintly figure, and tries to signify what his name really meant. Christopher Columbus, a man that started a revolution of journeys and colonies. Before he was sailing the world the going parading with everyone including the church thought the world would surely end soon. In fact many thought the world would end about 150 years after Columbus's death ( about 1666). Therefore the reason the crown took a stance on treating the natives correctly was that one cannot convert and do God's duty  by maltreatment of another. The Church's job consisted of converting as many as possible to Christ before the end of the world.


Columbus set up a bank account in his birth town of Genoa to fund a future crusade to take back Jerusalem. In 1517, the Ottomans had taken over Palestine from the Mamluks and dominated the area for the next few hundred years. The Ottomans became too strong.  He also set up a trust fund for four missionaries to be installed and kept-up the colonies in the Indies ( the New World) , he still believed, otherwise known to everyone else as the new world, to convert people to the teachings of Christ.

side not:" What seems to be the greatest injustice of all is that the new lands that the Great Navigator, Admiral of the Ocean Seas, Governor and Viceroy discovered were never given his name. That honor fell to a fellow Italian, Amerigo Vespucci, from the city of Florence, considered by some as the heart and soul of the Renaissance. As an agent of the Medici family in Seville, Amerigo, like everyone else, was caught up in the excitement of the discoveries. On two separate occasions he sailed to the Indies and, initially, believed that this was part of the Old World. After extensive travel through the littoral of Brazil and northern South America, as well as visits to several of the islands, Vespucci reached a different conclusion than Columbus. To Amerigo Vespucci this was empirically a “New” World, hitherto unknown to the ancients. Amerigo’s letters were widely circulated, and it was through his writing that Europe came to know about the lands to the west. In 1507, when a group of geographers working on a new edition of an atlas, the word “America” was written across the newly discovered lands.   By the time they realized their mistake it was too late to correct it. (Thomas C. Tirado, Ph.D, Reprint permission granted by Encarta Encyclopedia, 2000 )"

...end of Columbus's discussions.



           Maps in the middle age and the age of the renaissance.

Here are examples of maps before the time of Columbus and the understanding of the sphere of the world by numerous people all who didn't think the world was flat. These maps before Columbus indicated a spherical earth with various measurements of scientific data accompanying the content. Ptolemy's  geography-world remained a predominate theory that half the world was land the other half was water. What the maps show represents the majority of the land and the water is assumed outside the boundaries of the circumference. Ptolemaic maps were of equal space with the summer solstice in a prominent position and zones in square grids. These were compass zone-maps and were composed by cartographers who made good money, paid by the shipping companies, of course. Columbus's brother was involved in such a profession.

By the time we get the Magellan map the world looks really detailed. Other trivia: The gulf of California was actually thought to be a separate Island for some time.

Cartography, T-O map; Periods: Middle Age & Renaissance

The TO maps for education purposes attained the most widely used maps in this regard and appeared in what are called T. O. maps because their design  informally represented a recognizable   circle as the symbol  O. and the T symbols.  Within the circle representing the three great divisions that often also represented, not only Moses three sons who were supposed to have populated the three major regions of the earth, but the three major regions themselves. Actually lines of the T symbols themselves represented the Mediterranean Ocean separating Europe to the north, Africa to the south west and Asia to the  east and the Atlantic Ocean to the west. However, over time different regions within the sphere evolved to represent different criteria by efforts of from different authors.

The T and O map or T-O map, is a type of medieval world map, representing the physical world as described by the 7th century scholar Isidore of Seville in his Etymologiae (chapter 14, de terra et partibus):

Orbis a rotunditate circuli dictus, quia sicut rota est [...] Undique enim Oceanus circumfluens eius in circulo ambit fines. Divisus est autem trifarie: e quibus una pars Asia, altera Europa, tertia Africa nuncupatur.
            "The world is called 'round' after the roundness of a circle, because it is like a wheel [...] Because of this, the Ocean flowing around it is contained in a circular limit, and it is divided in three parts, one part being called Asia, the second Europe, and the third Africa." (Crosby).




          The above right photo is the earliest printed example of a classical T and O map (by Guntherus Ziner, Augsburg, 1472), illustrating the first page of chapter XIV of the Etymologiae.


        The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England. A classic "T-O" map with Jerusalem at center, east toward the top, Europe the bottom left and Africa on the right.

Click for high-resolution of the map (here).





How to find latitude

How was Columbus able to sail the oceans? As mentioned before, his early voyages helped him become acquainted with known cartography, navigation and currents of his day. Also, the understanding of how to know where one is on the earth at any given point was the most important. In order to do this one needs to know how to pin point one's latitude at any given area on the globe: The use of an astrolabe; carry a book of declination or understand how to utilize some mathematical systems. To do this we turn to line-geometry and forms of trigonometry.


 Δ = 1 day in 125 years=11.52 minuets/year.


                    The formula for Latitude: Alpha = 90° - Phi + Delta.

  • How to check for accuracy? Phi should always be complimentary to Alpha because of the right triangle. Delta is a variable, unless placed on the autumnal and vernal equinoxes in which its value represents zero. Without using trigonometry on the high-seas, Columbus just used his declination book to factoring in Delta. To achieve this, his day-calendar needed to be accurate. For basic astronomical data, he brought Regiomontanus's ephemeris  and lunar cycles (See voyage four). In this case alpha is our latitude. Longitude is a more complicated business for the medieval navigators. However, it was possible and done.

                    Working with Circles & Inequality.

  •   Apogee and Perigee.

  • Counter diurnal, the motion against the stars. 1° per day.

  • Diurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis. The time for one complete rotation is 23 hours, 56 minutes and 4.09 seconds (1 sidereal day).

The sun appears to move slower in the summer months (actually a few days longer) , and start to speed up in the fall accelerating to the winter and begin slowing once again around the vernal equinox. The ancients didn't know that the earth's rotation around the sun actually moved in a ellipse and was actually the earth which was 200,000 miles closer to the sun into the northern hemisphere during the winter months, but they were privy to differential speeds of the sun. The Greeks measured this by by placing the observant outside the central point of the circle. If we have a strait line of PCA, C being the center, and placing B a parameter point between Summer and the autumnal equinox and placing P another parameter point between winter and the vernal equinox then we place a second line calling it PA at the points of the summer solstice and, for example, point P at the winter solstice.  The Greeks could then start their observation. If we use the radius of the circle and call it a whole number of ' one' then the observer would move off the center which achieves a different perspective and will call this point O.  From here the Greek observer would watch all year and see that calculating the angle A, the winter solstice appears from the vantage point of  O to which becomes .0338. What happens when the observer moves-off the center is the angle appears to increase and become larger. Therefore, we see the sun moving faster around P at Perigee and slower around A at apogee. Therefore the Greeks though the sun moved in an ellipse. This became known as the AP the line of Apsides, the major axis of an elliptical orbit. However, if did not explain an ellipse and the true positions of the planets.

  • AP: the line of Apsides.

  • OC: eccentricity.

The Sun travels to directions all at the same time.

The motion of the Sun  appears from the vantage point of earth to move forward and backwards at the same time. How can this be? Surely the sun cannot move in two directions at once? Well it does.  As the earth rotates the sun appears to rise in the east and set in the west. However, everyday the sun appears to move from the west to the east approximately 1° degree. This is actually the orbit of the Earth around the sun. This measure is linked to the 3 minuets and 56 seconds of celestial movement against the back drop of fix-stars. This constant aberration appears to us when the sun goes down or rises later or earlier throughout the year. The reason that the sun appears to move backwards one degree each day is not the sun, but the apparent motion of the sun. The earth is actually moving around the sun approximately at one degree a day, so it appears the sun is moving backwards as we travel around the sun. To the ancients they didn't know what was happening. The earth was the center to them. This is part of the calendar's investigations that lasted millennia and gave people headaches. The fact that no-other than investigations into atomic physics  in history, no other world human mass-effort took so much energy and time trying to figure out the motions of the sun and moon and fix them to a standard calendar. So, in part, people all over the world, and or different time-zones,  could all celebrate festivals and religious functions of the same day.

  • Why is the ecliptic call such? An eclipse happens when the sun and the moon's are on the same path and form an eclipse of one another.

  • The ecliptic runs through the zodiac, which is a bunch of zodiacal  stars of 7° degrees on both sides of the ecliptic which make up the astrological constellations familiar to most people.

  • The ecliptic is our celestial equator, but is not the stellar equator.

                        Diurnal motion


Diurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis. The time for one complete rotation is 23 hours, 56 minutes and 4.09 seconds (1 sidereal day).

Direction of the motion in the Northern hemisphere:

  • looking to the north, below the North Star: left-right, west-east

  • looking to the north, above the North Star: right-left, east-west

  • looking to the south: left-right, east-west

Thus northern circumpolar stars move anti-clockwise around the North Star.

At the North Pole, north, east and west are not applicable, the motion is simply left-right, or looking vertically upward, anti-clockwise around the zenith. For the southern hemisphere, interchange north/south and left/right, and replace North Star by southern celestial pole. The circumpolar stars move clockwise around it. East/west are not interchanged. At the equator both celestial poles are at the horizon and motion is anti-clockwise (i.e. to the left) around the North Star and clockwise (i.e to the right) around the southern celestial pole. All motion is from east to west, except for the two stationary points.

The daily path of an object on the celestial sphere, including the possible part below the horizon, has a length proportional to the cosine of the declination. Thus the speed of the diurnal motion of a celestial object is this cosine times 15 °/hr = 15'/min = 15"/s, i.e. (compare angular diameter):

up to a Sun or Moon diameter every two minutes
ca. four seconds for the largest planet
2000 diameters of the largest stars per second


latitudes (almucantars) and longitudes (azimuths)

The azimuths

  1. The azimuths can be described as the directions on the globe. These are the longitudes positions.

  2. 'The horizontal angular distance from a reference direction, usually the northern point of the horizon, to the point where a vertical circle through a celestial body intersects the horizon, usually measured clockwise. Sometimes the southern point is used as the reference direction, and the measurement is made clockwise through 360°.' (The American Heritage® Dictionary of the English Language, Fourth Edition
    Copyright © 2000 by Houghton Mifflin Company.



Latitude of a place is equal to the height of the pole.

  • What is the minimum northern latitude on a mid-summer's day?  Put the sun at the Zenith at the mid-summer day and now measure the latitude. From the equator to the tropical positions, this is 23°.

  • If you're at the equator observing the Sun on the mid-summer's day the sun is north of the Zenith.

  • The Sun is at the equinox when it is at the zenith if you are at the equator.

  • At the vernal equinox at the north pole, the sun never sets. However, at the winter solstice at the north pole the sun never rises.


Astrology in the middle ages




The sun in the  zodiacal signs affects life on earth regardless if one believes in astrology or not. In the summer signs of the 'Northern Hemisphere' the weather is hot and it is opposite for the winter signs. The moon cycles affect the tides on the earth.  Also, the planets, the very ancient concept of astrology, had a large impact on life. Astrology dominated the middle ages and all the big names taught it and wrote on it. During Sumerian times, astrology was practiced in what is called Regional Astrology. Basically this was one of the practices (applications) of different methods of astrology that Michel Nostredame practiced in France in the 16th century. He used this system mainly in his almanacs. He was criticized, because at this period, astrology had morphed into a personal and free-will concept opposite of the ancient regional traditions and Judical Astrology was nothing like Regional Astrology.  Practitioners  in the Sumerian and Babylonian times had kings, princes as nobles as their clients. Regional forecasts usually were the fairing of the leader when planets were in certain constellations. This had nothing to do with birth charts and a reading of judicial outcomes by a birth chart. By the 6th century B.C.E. we start to see horoscopes. The word horoscope is actually meant to mean the term horizon in astrology and its significance is heavily shown in ancient as well as in medieval times through the renaissance. Today it just means astrology chart, usually a birth chart of some type of chart drawn-up and connected to predictions or  'now' suggestions, according to the washed-out version of astrology that we saw promoted in the renaissance and very significantly agreed upon by most professional astrologers for public and political reasons. The practice of regional astrology, is much or almost totally opposite of what astrology came to be known from the time of the renaissance-till-today.


In the middle ages until about mid-sixteenth century, astronomy and astrology were sort-of linked as one concept. However, with the onset of the printing press and the dissemination of the ancient knowledges already translated, waiting for print and wider production, astrology broke-off from astronomy and we see this beginning to take shape early in the sixteenth century. The break in history is described in other sections here. We will also begin to see arguments emerge from the Almanac authors who used regional astrology and the professional astrologers who broke off to free-will physiological astrology. By the end of the sixteenth century, Rome and other magistrates will forcefully suggest that stoppage of all Regional and Judicial Astrology. So by the years 1610 we begin to see the almanac change forms from regional predictions to the forms we currently see in the 20th century. The moon cycles and weather forecasts still existed in the almanacs, but there were no more predictions on country's politics and leader's fates issued for each annual volume.


After the beginning of the sixth century, gradually astrology and horoscopes become crafted to individual people and regional astrology takes on a less significant role. By Jesus' time, Babylonian stars astrology and Roman Kal astrology made horoscopic news. Astrology became a big industry as it was shifting to individuals who wanted to know some type of physiological or physical traits about themselves. Stars and planets were often used together, which will go out of style in the renaissance period. If a good astrologer during the Roman times made an astrological hit, they became famous and garnered the attention of the ruling elite. This also meant a good job. There was always a love-hate relation between the two and both were considered necessary for each other's public relations. Astrologers more or less considering the region, time and ruler,  became a Roman phenomenon. Personal astrologers became an industry as such the industry is today - connected to recent U.S. presidents and C.E.Os. of large companies to a thriving phone industry. Roman Caesars used and  saw their fair share of fame connections with astrologers. When an important person was correct it made the buzz cycles.


Many naysayer's believe astrology is a self-fulfilling industry. No more of a prime example is the story of Domitian, the Roman Caesar who lived during the bulk of Roman's bad leaders.


Titus Flavius Domitianus (24 October 51 – 18 September 96), commonly known as Domitian, was a Roman emperor of the gens Flavia and received a warning by the buzz patrol that a good astrologer had predicted his death at 5:00 a.m. the morning of 18 September 96 ADE. His birth chart was made public and many astrologers cast their predictions of his fate and rule. The astrologer that called out his death prediction was summons and told that he would die instead of Domitianus ( himself). The astrologer also said the method of death was the emperor,  he predicted , would also see dogs  devour his corps. The astrologer was then put on the torch-bed to be burned to prove the prediction the other way around, but a rainstorm put the fire out, and in fact dogs came and devoured his corps. Still scared of the prediction, as the day approached, Domitianus  began to sleep on top of his sword, and on the night before the astrological prediction, he locked his door to his room and tried hopelessly to fall asleep. When Domitianus  called out to a servant guard, he asked through the door what time it was? The guard told him it was 6:00 a.m. ( the morning of 18 September). Feeling relived he opened the door and went out where he was stabbed to death and died. The prediction came true. The guard had lied and told Domitianus it was  6:00 a.m. in the morning when it really was 5:00 a.m. This was a self-fulfilling prophecy according to skeptics, as naysayer would say that because his chart was public they knew when to kill him to blame astrology instead of the plot to kill him for his constant persecution of peoples in the regions of Rome. Whatever view one wants to take,  the significance is that all soothsayers were banned from these public predictions by the following Roman leaders. This will happen in the beginning of the 17th century in Europe as well as laws passed to stop the production of astrology based Almanacs. Astrology does have power regardless if one believes in it or not. It quite ran the middle ages and provided clues for the famous astronomers in which we will be talking about the findings of their great laws and astronomical achievements.




Houses and the Drawing up of the famed square chart


How a board game became the outline for the medieval astrology chart format.



The board game included rolling of dice over four equal regions, like a equilateral cross, of which all cardinal points represented the celestial directions at the games latitude, creates the foundation of the boxed astrology chart. The Mid-Heaven was the place of the meridian. This represented mature. The western point of the cross was the horizon and represented birth, and this is where we get the term horoscope, the term for the birth chart. The eastern point of the cross represented death and was the setting of the sun on the horizon. The lower meridian horizon was the nadir of the board game. This was a flat surfaced game where the players rolled the dice. As more sections were determined, the houses became involved in what we know as the twelve divisions of the chart. Out of this dice chart becomes the written house systems. The first house represents Life.


The houses

1. Life

2. Inheritance

3. Siblings

4. parents

5. children

6. sickness

7. marriage

8. death

9. travels

10. honors

11. favorable

12. unfavorable. 

One will notice that marriage house is located close to the descendant indicating the death point of the chart. The marriage house  is also 180° opposite life. At 150° Life and death houses aspect each other. However, death was often related to the 7th house at 180° opposite the house of life, the first house. So marriage and death were often related themes.


Calendar Sections




During his years in Vienna, Regiomontanus composed a tract on the construction and use of the astrolabe (Starry).

Peurbach and Regiomontanus showed how to find the real moon's positions using the Ptolemaic principles.

Suggestions for repairing the calendar were suggested at the Lateran Council in 1511. Pope Leo X and the Holy Roman Emperor Maximilian asked the universities  to send in suggestions. The vernal equinox could not be agreed upon. Was it the 10th of March or the 25 of March? Copernicus thought is was too dangerous to travel. Some believe he didn't go because the true time of the vernal equinox was not agreed upon and that any Calendar reform became futile because of it.



Regiomontanus (1436-1476). Johannes Müller von Königsberg (June 6, 1436 – July 6, 1476), known by his Latin pseudonym Regiomontanus, was an important German mathematician, astronomer and astrologer. He was born in the Franconian village of Unfinden near Königsberg, Bavaria (not to be confused with the East Prussian city of Königsberg, now known as Kaliningrad). He is also called Johannes Müller, der Königsberger (Johannes Müller of Königsberg). His full Latin name was Joannes de Regio monte, which abbreviated to Regiomontanus (from the Latin for "Königsberg"—"King's Mountain"). Summoned by Pope Sixtus IV, Regiomontanus went to Rome in 1475 to assist in reforming the calendar and was made bishop of Regensburg. He was very active in Nüremberg. Ephemerides 1475-1506. Nürnberg: Regiomontan, 1474, and his work, Megale syntaxis" des Klaudios Ptolemaios: Epitoma in almagestum Ptolemei. Venedig: Joh. Hamman, 1496 were staples of Christopher Columbus. (wikipost)


Regiomontanus's ephemeredes show the Roman Kal dating system which didn't match up to the European dating system. Often the Julian year didn't start on the first of the year. In the third column the numbering system ran backwards, as was the Roman system. This is how the Roman's kept time. So when looking at the dating system, one sees in the tables that the 12th of February is actually two-days before the month of February itself. One looking at the 28th of February sees this day was two days before the month of March. The columns of letters consisted of dominical lettering after the Sunday. A-G. The Solis ( sun) column shows degrees and minuets of the sun's position per-day. The Lunae ( moon) only shows degrees and signs but no minuets. For example, on the French calendar there was 31 days of January and lunar month, but the moon actual synodic month is 29.503 of lunation. Therefore calendars often needed changing from the months of cycles of 30 lunar months, then 29 day lunar months, and then placing in an extra month later to make up the needed 10 or 11 days. The calendars were not uniform in Europe until Pope Gregory decided to force the needed changes that were in fact proposed hundreds of  years earlier, but never adopted for various reasons. The lunar 19 year cycle was figured out long before and could have been instituted but the Church's control on the calendar and their stubbornness' allowed the mis-data to continue. It would be the splitting up of the church, as the real reason the calendar gets corrected and no other real reason, even though their are many conspiracy reasons promoted even till this day. The Protestant and the printing press meet up to issue pamphlets showing the needed change of the calendar.


The Fifth Council held at the Lateran Palace in Rome was summoned by Julius II (Pope: 1503-13) and continued by Leo X (1513-21), and lasted between 1512 and 1517. Paul of Middelburg presided over the commission to reform the calendar and sought advice from experts all over Europe, including Copernicus. Copernicus wrote in a response, which is now lost, but probably stated something along the position stated in the preface to his Revolutions, that reform of the calendar was premature because the precise length of the tropical year was not yet known with sufficient accuracy ( Starry 3).


Ptolemy and Calendar Reform


Ptolemy did not directly contribute to calendar reform, but his work proved essential for the study of historical chronology, the establishment of the exact period of time elapsed between two dates, when those dates might be given in different calendar systems, as a consequence, for example, of calendar reform.  To achieve an absolute chronology, it is necessary to have dates in a local calendar that is continuous (without interruptions) and precisely known, tied to observations of astronomical events (such as lunar eclipses) to provide fixed points. Such circumstances existed in Mesopotamia and Egypt. In dating astronomical observations, Ptolemy employed the Egyptian administrative year. This was of unvarying length: twelve months of thirty days, and five extra days at the end to total 365. The numbers of individual years could be given with reference to a standard epoch (defining some particular event as occurring at year 1), or to the reign of a particular ruler. In the latter case, an unbroken list of kings would also be required. Ptolemy provided such a list, which was maintained and extended by the Byzantines well into the Middle Ages.

(Starry 4).


Pope Gregory XIII: He wants to standardize all Calendars because many other civilizations were laughing at the west because the printing press provided a wide media to show western civilizations' mathematical errors in regards to astronomy within the functions of a calendar.  October 4th, 1582 was followed by October 15th, 1582. People acted strangely, to say the least. Much art shows drinking parties, some felt they lost part of their lives. However, western civilization made it through the ordeal.


1543: Copernicus presents theory that Earth revolves around Sun, which is placed on the Papal Index of forbidden books until 1835.
1545: At Council of Trent, the Church condemns judicial astrology.

1550: Catherine de Medici consults astrologers Gauric, Ruggieri and Nostradamus.
1552: Martin Luther supports astrology by writing preface to work by prominent astrologer Johannes Lichtenberger.
1555: Nostradamus gains fame in Europe. His famous prophetic work 'Seven Centuries' is published in 1555. He works in
Henry II's court and publishes almanacs.
1560: Girolamo Cardano, physician, philosopher, mathematical genius and astrologer. He writes commentary on Tetrabiblos.

1570: John Dee is astrologer for Queen Elizabeth I and helps to arrange Gregorian calendar (1583) and dabbles in alchemy and magic. (History).








Continued on part II



The angular distance north or south of a planet's equator, measured in degrees, as on a map or globe.


Angular distance on a planet's surface, measured east or west from the prime meridian (Greenwich, England, on Earth) to the meridian passing through a position, expressed in degrees.

right ascension

The angular distance, measured in hours, minutes, and seconds of time, eastwards from the zero point which is the intersection of the celestial equator and the ecliptic; one of two coordinates used to define position in the sky--equivalent of longitude on Earth. One hour of right ascension is equivalent to 15 degrees of arc--the angle through which the celestial sphere appears to turn in 1 hour as the Earth rotates.


the angular distance, measured in degrees north or south of the celestial equator; one of two coordinates used to define position in the sky--equivalent of latitude on Earth.

  1. Stereographic Projection preserves circles

  2. Stereographic Projection preserves angles

This means that circles on a sphere (i.e. latitudes on the Earth) are represented as circles on a plane and the angles between lines are retained when the lines are projected. This is how the climates of the astrolabe are created. The lines of latitude, almucantar, azimuth, and hour angles are represented stereographically onto a plane (usually taken is the equatorial plane) and the climates are merely a scaled-down representation of this (Jamieson,).


  1. First map out the Universe. This is the three dimensional image that will use to transfer onto a two dement ional image.

The Vernal Equinox is the first point of Aries.

Zenith: The point on the celestial sphere that is directly above the observer.

Meridian: Archaic, noon; An imaginary great circle passing through the two poles of the celestial sphere and the zenith of a given observer.

All circles project as circles through the horizon.



  1. Almucantars are used every 10°.

  2. Almucantar is a  circle or parallel of altitude.

  3. Example: Two stars which have the same almucantar have the same altitude.

  4. 0° Almucantar is the horizon.

  5. 90° Almucantar is the zenith.

  6. Almucantars help you determine the height of an object from the horizon.


1. The horizontal angular distance from a reference direction.




Question? You are at the south pole and you look up and find what intersection? ( Na′)

Where is the vernal equinox projected at the ecliptic?

Diurnal motion goes clockwise, so the sun goes counter-clockwise?

Divide Tympan into equal 15° segments. ( Clock/Hours/Degrees)

Hours are 1-12,- 1-12. Not 1-24

Declination, a deviation, latitudes.

Rule for projections: Any point x projects onto the celestial equator where the line of sight of the pole crosses the equator.

Degree above the equator are called declination.

Casting star points on a rete. The vernal equinox is a point on the celestial equator.

Project through the right ascension ( Counter clockwise)

Use cord to measure star to rete outside of tropic.

Star  OX = (cos Ф/1+Sin Ф)

Put in ruler and clock.


Locus of centers of projected azimuths are Z′ B = B Nadir.

To find the horizon on the Tympan, bisect the perpendicular line of the horizon from the calculation of your zenith. First label your directions, for example, K, and H. and then find their primes. All primes are figured from the South Pole threw the line of the equator. Label them K′, & H′. From your North Pole NP line to the South Pole SP the equator intersects also as a perpendicular line and where they meet call it 0. Find your radii of your tropics of Capricorn and Cencer. The photo indicates how to do this. Pick whatever zenith latitude one wants  - preferably where you live.

Since the orientation of the ecliptic to the horizon is continually changing, the ecliptic cannot be fixed on the tympan. ( Astrolabe/23 J. L. Heilbron)

σ = 90° - Δ + Ф

Make zodiac signs out-side of the ecliptic band.


The rule:

The rule is marked off at declination intervals or the angular distance of an object from the celestial equator.

The Front of an Astrolabe

The latitude plate:



Work Cited:

Alden, Terry. The Mill of Time: 'Celestial Cycles and the Ancient Mythological Sciences'.  see fig. 2. <> Feb. 2006.


The Columbia Electronic Encyclopedia , 2004, Columbia University Press. <> 2006.


Crosby, Alfred W. The Measure of Reality : Quantification in Western Europe, 1250-1600. Cambridge: Cambridge University Press,1996.

    Retrieved from "". February. 2006 ( See section on T-O maps where referenced).


Fowler , Michael How the Greeks Used Geometry to Understand the Stars. University of Virginia  1995.

    <> 2006.


Green, Norman   Astrolabes.  <> 2006.


Khun S. Thomas. The Copernican Revolution 'Planetary Astronomy in the Development of Western Thought'. by the President of Fellows of Harvard. 1957. r. 1985.

    Lord, Peter. Dante's Astronomy. San Jose Astronomical Association. 2002. <> Jan2006.



Heilbron, J. L. Astronomy and Astrology in Medieval and Early Modern Europe. Represented in University of California Berkeley Reader. History 181A. January 2006.

    ( Astrolabe/23 J. L. Heilbron).


History of Astrology, Kopernicus and Nostradamus , (UK)    <> 2006.


Koyré, Alexander , The Astronomical Revolution: Copernicus-Kepler- Borelli 2nd ed. ( Ithaca: Dover Publications, Inc, New York),1992.


Jamieson, Laura  and Maria Montero. Stereographic Projection, Chaucer and the Astrolabe.  <> 2006.


Starry Messenger, Regiomontanus and the Astrolabe . Department of History and Philosophy of Science.  1999, 2000. Cambridge University, England. <> Feb. 2006.

    2. Johannes de Sacrobosco <> 2006.


    3. Copernicus and Calendar Reform <> 2006.


    4. Ptolemy and Calendar Reform <> 2006.


The Devine Comedy. The Digital Dante . Project Columbia University's Institute for Learning Technologies. <> Jan. 2006.


Wikipedia, Regiomontanus, Free open-source  Encyclopedia. (wikipost Feb 2006) < > 2006.


Wikipedia, Dante, Free open-source  Encyclopedia. (wikipost Feb 2006) < > 2006.


Wikipedia, Manuel Chrysoloras, Free open-source  Encyclopedia. (wikipost Mar 2006) < > 2006.


Wikipedia, Johannes Bessarion, Free open-source  Encyclopedia. (wikipost Mar.  2006) < > 2006.




Starry Messenger

Astrolabe Resources



March 10th, 2006


Copyright © 2006 Michael Johnathan McDonald. . All rights reserved.

Chronology: History 181A, notes U.C. Berkeley, Spring 2006. 

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