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Europe Science Revolution Part 4


The Recovery of the Ancient Learning


Astrology  & Astronomy in the Middle Ages.


By Michael Johnathan McDonald.


Analysis of Latitude of Form

  1. Cultivated in Paris and Oxford in the 14th Century.

  2. On the list of Tempier's restrictions.

  3. Outlined in a letter to Galileo's teacher Paolo Sarpe.

  4. Two paragraphs: The first is recognized as medieval; graph tow is modern

  5. Topic Rate of fall. The motion.

  6. Significance: The understanding of motion away from Aristotelian motion to modern motion.


  • Applied mathematician

  • " The Starry Messenger:" Galiileo's telescope discoveries

  • Courtier and combatant: Challenging the Society of Jesus

  • First brush with the Inquisition

  • Two chief world systems

  • Unwilling martyr: Galileo's condemnation and its consequences

  • Two new sciences

The Age of Descartes

  • "Plus Utlra:" Francis Bacon's method

  • "Cogito ergo um:" René Descartes' method

  • The Cartesian system (1): A universal physics

  • The Cartesian system (2): A quasi-mathematical physics

  • The spread of Cartesianism

  • The naturalization of comets and the decline of astrology

  • Astronomy in the academics

Age of Newton

  • A disagreeable genius

  • From Descartes' pushes to Newton's pulls

  • The raw data from the Principia

  • Add Galileo and Kepler...

  • Newton's world system

  • Chronology and prophecy

  • The last of the Magi



Galileo Galilei


Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was an Italian physicist, astronomer, and philosopher who is closely associated with the scientific revolution. His achievements include improvements to the telescope, a variety of astronomical observations, the first law of motion, the second law of motion, and effective support for Copernicanism. He has been referred to as the "father of modern astronomy", as the "father of modern physics", and as "father of science". His experimental work is widely considered complementary to the writings of Francis Bacon in establishing the modern scientific method. Galileo's career coincided with that of Johannes Kepler. The work of Galileo disagreed with Aristotle's work is considered to be a significant break from that of Aristotle. In addition, his conflict with the Roman Catholic Church is taken as a major early example of the conflict of authority and freedom of thought, particularly with science, in Western society (wikipedia).


Path: Florence - Pisa - Venice - Padua.

Galileo Bio.


Galileo was Born in Pisa on February 15, 1564.  Galileo was the son of Vincenzio Galilei (1520-1591), by trade a cloth merchant who moved the family to Pisa in hopes of improving their fortunes. Galileo's mother's name was Giulia Ammannati (1538-1620). "An old and distinguished Florentine family from which Galileo was descended had originally been called Bonajuti. His great-grandfather had changed the family name to Galilei in honor of a brother, a noted physician of the fifteenth century whose given name was Galileo. " (Drake). "Vincenzio was an accomplished musician, composer and music theorist who wrote several books on the subject that reveal some traits later characteristic of his son  ― a good knowledge of mathematics, distrust and even contempt of reliance upon authority, and a pugnacious temper" (Drake).


Early Years:

  1. No focus

  2. Disinterested in geometry and mathematics.

The Astrology sign of Aquarius, has many fame-lasting stars connected to it.

  1. trivia: His leading disciple wrote the wrong birthday, February 18, so he could be linked spiritually ( same souls) as Michelangelo who died on this date - therefore their souls merged.

  2. Coincidence, Galileo was born a few days later. 


Accademia de Disegno

  1. Trade tech school, not a major university. Like a community college or technology school. This school was funded by Cosomo de' Medici.

  2. Teacher Ostilio Ricci saved Galileo's life by directing his focus of study to something he understood and was good at.

  3. Ricci's teacher was Niccolo Tartaglia.

Galileo's works

  • Two New Sciences 1638 Lowys Elzevir (Louis Elsevier) Leiden (in Italian, Discorsi e Dimostrazioni Matematiche, intorno á due nuoue scienze Leida, Appresso gli Elsevirii 1638)

  • Letters on Sunspots

  • The Assayer (In Italian, Il Saggiatore)

  • Dialogue Concerning the Two Chief World Systems 1632 (in Italian, Dialogo dei due massimi sistemi del mondo)

  • The Starry Messenger 1610 Venice (in Latin, Sidereus Nuncius)

  • Letter to Grand Duchess Christina

Courtier and combatant: Challenging the Society of Jesus


The Society of Jesus

The Soldiers of the Christian Church

The Most Important Agent in The Catholics Church


The Society of Jesus (Societas Iesu (S.I. or S.J.) in Latin) is a Christian religious order of the Roman Catholic Church in direct service to the Pope. Its members, known as Jesuits since the Protestant Reformation, have been called "Foot soldiers of the Pope" in part because the Society's founder, Saint Ignatius of Loyola, was a soldier before he began to follow God as a monk and eventually a priest. Today, Jesuits number almost 20,000 and comprise the largest single religious order in the Catholic Church. Jesuit priests and brothers are engaged in ministries in 112 nations on six continents. Their work is focused on education and intellectual contributions, primarily at colleges and universities, as well as missionary work and ministry in human rights and social justice (wiki).


In Spain about the 1540s, a small group of individuals helped the poor and sick.. Pope Paul III decided to make them a legitimate group in the Church and they began to take a more wider and prominent role in the Church's activities.


In 1610-1611, Galileo travels to Rome to try to persuade  the Jesuits of his grand strategy to convince them of adopting the Copernicus system. Galileo had a little bit of a genial temporal disposition that made him disagreeable after a while. Many genius have this trait, usually in reaction to the less informed who take a long periods of coaxing to convince them (Jesuits) or get one's point across to them. The Copernicus system is not an easy application to understand.  Therefore, Galileo invited there wrath. To understand the other outside factors that may not have anything to do with understanding the Copernicus system, the Church's reaction to Martin Luther and the Protestants was complex as well as complicated. The Council of Trent ( beginning in the 1540s lasting 20 years)  was set up not only to wade on issues of what to do about Luther and the Protestants, but also reform the Church, in ways of public relations. The Church had long been attacked upon general issues of infidelity, moral degradation, scheming ( indulgences) the public, and misrepresentation of the ethics of Christianity. At first there were many Bishops and Cardinals in attendance. However, over time the attendance dwindled and many forums ended in disagreement. However, St. Thomas was adopted as the doctor of the Church, as we as the Eucharist later agree upon in general which both will have significance consequences for Galileo in the upcoming years of his life. When the Council of Trent first began De Rev. was making its slow but weighty appearance on the academic scene. The second phase of the Council of Trent, occurred in the 1550s where the doctrine of the Eucharist was adopted. This second effort was the codification of laws mentioned above which came into law.


The Council of Trent Objectives: Engines for the reformation of the Latin Church.

1. Create Roman Inquisition

2. To bring the Society of Jesus into political arena, and infiltrate them into schools. Jesuits actually create great academic standards.

3. Create and Index, where books must be corrected to pass publishing standards reckoned by the Church's oversight.


The Index of Prohibited Books, or simply "Index." The codex entitled "Index librorum prohibitorum." The Index was a peer review, and employed many people. This is where the term censorship came into the Middle Ages and Renaissance. The readers were censors and it was like getting a free book review, which included suggestions. Catchphrase, donec corrigatur, Prohibited until corrected. The stigma surrounding this censorship does remains negative. This can remind us of the Ulema in the Ottoman Empire that censored scientific books for about 100 years. The Pope issues a Bull or a Brief and ones work is in contention to the Church (in formâ communi). A place to report was the  Sacred Congregation of the Roman Inquisition, of the Sacred Office.


  • How did Galileo get into trouble? Galileo had a problem with deference and intolerance. This made the Jesuits mad at him. With Urban VIII, he long time friend, he made a mistake in editing and place unfavorable words in one of his fictional characters, which were Urban's favorite quotes. One can only guess if it was intentional or not. However, the fact in significance was his beginning downfall in his relationship with the Pope and the Church and which cost him his freedom and therefore he spent the later part of his life under house arrest which was not common. Most people who broke the Index rules had eight-year terms in prison at most. It was unusual for a person to remain under any type of arrest for the rest of their lives as like Galileo.



1620s The Index comes out.


(Saint Robert Bellarmine, Montepulciano, October 4, 1542 – Rome, September 17, 1621), Robert Bellarmine, S. J. now a saint.  J. L was against the literal meaning of scriptures, but not heretical.


In 1616, Cardinal Bellarmine notified Galileo Galilei of the decree of the Tribunal of the Inquisition against the Copernican hypothesis. When Galilei complained of rumors to the effect that he had been forced to abjure and do penance, Bellarmine wrote him a courteous letter describing what had been said, which was used in Galilei's defense at his trial in 1633.

In reply to a posthumous treatise of William Barclay, the celebrated Scottish jurist, he wrote another Tractatus de potestate summi pontificis in rebus temporalibus, which reiterated his strong assertions on the subject, and was therefore prohibited in France, where it agreed with the sentiments of neither the king nor the bishops. He was among the theologians consulted on the teaching of Galilei when it first made a stir at Rome (Wikipedia).

1616, the proofs were circulated in manuscripts


Il Saggiatore,  satire 1623 The Masterpiece of Satire Book.

1. The scientific model of repeated experiments is a main part of this work. we know these procedures as the modern scientific method.
2. Galileo supports Copernicus instead of Kepler, so his model uses the mean, instead of the true, sun which show us exactly more of a Ptolemy thematic, and a little graduated theme than Tyco's universe.

Galileo Galilei
Il Saggiatore (The Assayer)
Rome, 1623

This quietly polemical text puts the case for a pared-down scientific conception of matter and a mathematical basis for science.

Excerpt: How the mind's intuitions lead me to conceive of matter

"So I tell you, as soon as I conceive of a corporeal material or substance, I clearly feel pulled out of necessity to conceive that it is bounded or having this or that shape, that it is large or small in relation to others, that it is in this or that location, at this or that time, that it moves or is still, that it touches or does not touch another body, that it is one, few, or many, nor by any imagination can I separate it from these conditions; but that it be white or red, bitter or sweet, sounding or mute, of a pleasant or unpleasant smell, I do not feel compelled in the mind to apprehend it necessarily accompanied by such conditions." In Galileo (1929-39), VI:347-8 (my translation). <UCLA > .


Galileo Downfall with The Pope

The Church was not in a feud with Galileo. It was him and Pope that had a falling out due to a misshapen on a popular phrase the Pope was know to use and was placed in one of Galileo's less intelligent characters in one of his books that enraged his friend which led to his downfall.

Book: Dialogue Concerning the Two Chief World Systems, 1632 (in Italian, Dialogo dei due massimi sistemi del mondo)

Characters: conversation takes place for four days.

Sagredo (great independent and open mind who always agrees with Galileo's character)

Salviate (Galileo)

Simplicio (The quizer a fan of Aristotle, but not a good exponent of him)

The Jesuits and Galileo get into heated matches after Il Saggiatore comes out. Pope Urban VIIl liked the attack on the Jesuits, just as long as he personally was never attacked. They were friends and used to have dinner together.  Pope Urban VIIl's sublime doctrine or  favorite saying was something like 'God does it different and one never knows'. Pope says we need equal treatment. This way he didn't need to say if one person was correct on a new scientific finding or not. This helped please all sides anyway. Pope and Galileo initially agreed at dinner, " just leave the question open." No one really knows God's plans.  There were friends up until the 1630s. Galileo places possible by mistake a passage of the Pope's sublime doctrine into the simple man's voice. To the Pope it is a gratuitous insult.

On the section of the tides the censures say we need editing. This was before publishing, when the manuscript was presented to the censure council. Pietro Redondi, Galileo is a heretic. His research showed his attack on the Jesuits.  A plea barging is settle and it is only a material heresy, in the authors head.

Galileo also made other decision that were in conflict with the Church. He wrote about how Copernicus was correct and the Church was wrong.

Galileo and his pupil Mario Guiducci

Day 1) Aristotle's physics of problems.  Discussion of separating physics from math.

Day 2) Diurnal motion and defeat of Copernicus.

Day 3) Annual motion, easily repeated  and discussion on retrogression.

Day 4) The tides, and not well received by the Jesuits, but shows Copernicus is correct.

Now to explain tides simplistically, in the middle aged mind,  we look at like a cord on a pendulum, and a ball representing the earth is on point of the cord while another ball is either above or below the ball of the earth. The moon ball closer to the top part of the cord representing the sun and its subsequent relationship with its position below the earth ball at furthest distance from the sun, determines the distance of the swing of the pendulum. Therefore the moon position on the cord closest to  the sun moves the fastest and the  moon position on the cord at furthest position is the slowest motion. 

The Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) was Galileo's comparison of the Copernican system, in which the Earth and other planets orbit the Sun, with the traditional Ptolemaic system, in which everything in the Universe circles around the Earth. The book was published in Florence in 1632 under a formal license from the Inquisition. In 1633 Galileo was convicted of "grave suspicion of heresy" based on the book, which was then placed on the Index of forbidden books, from which it was not removed until 1822. In an action that was not announced at the time, the publication of anything else he had written or ever might write was also banned.

While writing the book, Galileo referred to it as his Dialogue on the Tides; and this was its title when the manuscript went to the Inquisition for approval: Dialogue on the Ebb and Flow of the Sea. He was ordered to remove all mention of tides from the title and to change the preface, because granting approval to such a title would look like approval of his theory of the tides, which attempted to prove the motion of the Earth physically. As a result, the formal title on the title page is Dialogue, which is followed by Galileo's name and academic posts, followed by a long subtitle. The name by which the work is now known is extracted from deep within the subtitle. This must be kept in mind when discussing Galileo's motives for writing the book.

The book is presented as a series of discussions, over a span of four days, among two philosophers and a layman:

Salviati argues for the Copernican position and presents some of Galileo's views directly, calling him the "Academician" in honor of Galileo's membership in the Accademia dei Lincei. He is named after Galileo's friend Filipo Salviati (1582 - 1614).
Sagredo is an intelligent layman who is initially neutral. He is named after Galileo's friend Giovanfrancesco Sagredo (1571 - 1620).
Simplicio is a dedicated follower of Ptolemy and Aristotle, who presents the traditional views and the arguments against the Copernican position. He is modeled after Ludovico delle Colombe (1565 - 1616?) and Cesare Cremonini (1550 - 1631), both of whom were conservative philosophers. The character's name is not "Simpleton", but is taken from the sixth-century philosopher Simplicius, who wrote notable commentaries on Aristotle. ( wikipedia).


Book: Dialogue Concerning the Two Chief World Systems, 1632 (in Italian, Dialogo dei due massimi sistemi del mondo)

Characters: conversation takes place for four days.

Sagredo (great independent and open mind who always agrees with Galileo's character)

Salviate (Galileo)

Simplicio (The quizer a fan of Aristotle, but not a good exponent of him)


The social changes had many levels. Copernicus was set on the problems of the equant, and Luther was set on the problems of the indulgences, which both affected the reforming of science and religion.


Luther wants to go back to natural living, back to the justification of St. Augustine and live by the faith. His reasoning is that God chose you but we cannot decipher God's mind. This was what he thought the Church was doing. Kepler in the same sense, being a Protestant understood this as well. God made the universe the way he did, but man's observation is not in contention with God's ultimate meaning. The Church was stuck upon the old scholarship of Thomas and Aristotle, Ptolemy and others that believed the Earth was the center of the Universe, so therefore, man was at the center of God's plan.


Trivia: What does it mean to be a Humanist in the Middle Ages? One had to know the languages of Greek, Latin and Hebrew.


Galileo's Laws


Centripetal acceleration


The property of the motion of a body traversing a circular path. The acceleration is directed radially toward the centre of the circle and has a magnitude equal to the square of the body's speed along the curve divided by the distance from the centre of the circle to the moving body. The force causing this acceleration is directed also toward the centre of the circle .




Centrifugal acceleration

This is basic physics, independent of cosmology, that was well known:

A centrifugal = velocity x velocity / 'distance from the center.'

Therefore, objects don't fly off a spinning Earth because the downward acceleration of gravity is 300 times more powerful than the outward acceleration due to the spinning of the Earth.


Newton took this idea further.  He could calculate the centrifugal forces experienced by the planets.  He used Kepler's third law for the periods of the planets and found that the forces varied as the inverse square of the distances from the Sun.

He then asked, what about the Moon?  If it behaves like the planets, then the centrifugal force that it feels should be proportional to the inverse square of its distance from the (center of) the Earth.  But what can Newton compare the Moon too?

He compared the centrifugal acceleration of the Moon (at a distance of 60 Earth radii from the center of the Earth) to the force felt by something near the surface of the Earth (at a distance of one Earth radius from the center of the Earth):


1/2 acc.· t2


The theorum of Galileo on Mechanical inventions.


the circle sweeps out the angle...

The time of an object to fall is the same in respect to anywhere on the circle. However, the cords at the bottom is a contradiction with an isosceles circle and Galileo observes that  bigger amplitudes ( we need to speed it up to make an equal swing of a pendulum).


isosceles triangle, the angle in a semicircle being a right angle, formulas for the circumference and area of a circle


Claudius shiner.




François d'Aguilon, was  Jesuit Church authority for the mathematical department. He also was an architect, and conduced many natural science projects on Optics, which are included in his work with pictorial representation called Opticorum libre sex (published in Antwerp 1613).





François d'Aguilon (also d'Aguillon or Aguilonius) (1546 – 1617) was a Belgian mathematician and physicist. He was born in Brussels, Belgium and became a Jesuit in 1586. In 1611, he started a special school of mathematics, in Antwerp, which intended to perpetuate the mathematical research and study in the Jesuit society. This school produced geometers like André Tacquet and Jean-Charles de la Faille. His book, Opticorum Libri Sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike), published in Antwerp in 1613, was illustrated by famous painter Peter Paul Rubens. Furthermore, it inspired the works of Desargues and Christiaan Huygens and was notable for containing the principles of stereographic projection. He died in Antwerp ( Wiki) .


Stages Outline





1)     1634   - 1670


2)     1670   - 1710


3)     1710   - 1760






1)     1634   - 1670


The separation of  thought to whom  is correct? Aristotle's physics or Copernicus physics?


Giambattista Ricciole, Novum Almagestum, 1651. All knowledge summed up into an encyclopedia. Hundreds of arguments of philosophy and physics.


Galileo was not accused of vehemence suspicion, a serious crime. These were crimes of a person giving assistance to heretics, or opposing the holy office, or violation on an injunction. Galileo wrote a book saying the Church was wrong about Copernicus. So this was the excuse the Church took him to court. He said " Do with me what you will." After one year of imprisonment , he was moved to his house and place under house arrest for the rest of his life. Galileo was a lay person and he never remitted and this is why he remained in his condition. This became the buzz of Europe, and possibly this facilitated scientific research. The Pope sent out diplomats to spread the word to all mathematicians to show Galileo was incorrect. Copernicus' book had only a few pages of corrections and nothing to do with math. The Attitude was mixed. Some said in 1634 reformable judgment, others in 1632 said maybe this is heresy.  It was a stupid decree some said, and didn't hurt the Church what was in the Copernican book.  Up until 1820 the Church didn't drop the decree.




2)     1670   - 1710


We can only depend upon the guidance of the Church. Fictionalization of Copernicus work is the byword in academia - this pleased the Church. The Jesuits were apologetic, but taught Copernicus' system anyway.

Lorenzo Ciccarelli, lawyer, and printed index books on his printer for fun. Copernicus comes off his press.



3)     1710   - 1760


Church still had to point out the fictionalization of Copernicus' work.  Benedict XIV (14th) had a sincere interest in science but as with the Church a Pope cannot overrule without much consternation a rule of a previous Pope. Galileo words seemed to change with added essays telling the reader math cannot give us the truth. Also some of Galileo's dialogue was changed. Jesuits attacked Enrico and this facilitated his rise to a cardinal position by the favoritism of the Pope.



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

Modern Thought: J. L Heilbron, tells us "the artifacts move to the north " where Protestant revolution is taking place. Freedom of thought significantly loosely governed than in Italy. Luther and Copernicus came from the north, both Protestants.  Protestants more tolerant of Copernicus' ideas, even a snide but non-direct comment by Luther on the falsities of people who promote different universes.


1758 a New Index is published minus Copernicus inclusion. However, Galileo remains. Popes do not undermined their predecessors.

Cosmic egg, George Lemaître (Expanding Universe).

Fr. Lemaître proposed what became known as the Big Bang theory of the origin of the Universe, although he called it his 'hypothesis of the primeval atom'. He based his theory, published in 1935 on the laws of relativity set forth by Einstein, among others, as well as ancient cosmological-philosophical traditions, although at the time Einstein believed in an eternal universe and had previously directed derogatory comments at Fr. Lemaître's mathematical competence. (Wikipedia).



4)      1760 - 1820



More math investigators ignore, and nobody says nothing.

Giuseppe settles everything.

Pope Pius  VII, 1820.


Filippo Anfossi, an Italian Dominican, Master of the Sacred Palace and chief theologian of Rome ,  is considered way to the right by Heilbron.

These are doctrinal fights about math and astronomy which were to have no restrictions. However, the corrections as discussed before were not the math or the physics of in Copernicus's work but his theology commentary in his work. Yet, Protestant toward the end of the 19th Cnetury enjoyed kidding the Catholics over their treatment of Galileo. " You should apologize" was the sentiment.


1835 The Latin Church finally recognized Copernicus.


Setting the record strait!

1992 a commission established to achieve this goal - trouble reaching a decision of why things happened the way they did in history when speaking of suppression of some of the commentary of Galileo and Copernicus. Many came together but no one could make up their mind on how things happens. There was not enough record keeping.


Pope John Paul, 20th Century, wanted to apologize for past deeds of the Church which is not their way because the persons invovled should be the ones who apologize, not the ones who were not there.


Books for convincing the people often employed things they could understand coupled with the less understood physic equations and high-tech math. Therefore, in 1616 Galileo combined physiology and philosophy which  shouldn't be combined according to the Council of Trent. One remembers that Einstein combined energy and matter, two things that said were not meant to go together as a formula concept,  to figure out the theory of relativity. The Council of Trent doesn't think that philosophy and physics can go hand in hand. Who knows?


It was true the Churches exhibited some responsibility but one need to look at what the Church was trying to accomplish. That is to say, the job of the Latin Church was the protection of the European people. That was their first job, and sometimes these bizarre treatments in physics coupled with philosophy were just as they proclaimed hypotheses and not laws. For all the correct judgments the Church made against so many on the Index it was only  responsible to see that some people such as Copernicus and Galileo would be unduly censored with the rest that were truly wrong in retrospect. It is hard to censor most of the wrong theories and not let a few correct ones slip through. In 1992 Pupard, we use the phrase,"" tragic ,mutual incompetence," is correct but a harsh judgment of ourselves. In retrospect it was not like Galileo and Copernicus were not utilized in academia wich is the main point of progressing the learning for the advancement of western civilization. Things turned out in the commission to change sides in that some said Galileo had the Bible right, but not the science, and other said we just couldn't interpret correctly the philosophical statements of him. Therefore, the Church concluded that it had the science right but didn't have the correct interpretation of the Bible. The Commission apology was impossible in this way. Why? Pio Paschine, prepared 300 years of history and the test was suppressed. The commission resurrected this text and found out that the Jesuits didn't do their part in all of this censorship of history, according to Heilbron. Job promotion is one followed the Pope's decisions in the past to promote Jesuits who followed the censorship squad.  The Jesuits were placed in a negative light in this regard. Lets resurrect Pashine's work and show how the Church was unable to make faith and science compatible thus leading to censorship in the middle ages and the renaissance. If we cannot face ourselves we must try to understand what happened at least. Maybe what came out of all of this is that Galileo received a tonsure in 1620  to receive Urban's VIII's presents, and that to show a promotion of Galileo above the Pope Uraban's magnanimity will one day turn Galileo into a saint. Galileo was not against the Church as we Urban, but Galileo's actions of  placing the Pope's favorite saying into the simpleton character made history which turned into something else with all his other writings on Copernicus' promotions.



Edit section for Apirl 5, 2005 ( Need to work on this)

Torricelli's work in physics

Evangelista Torricelli (October 15, 1608 - October 25, 1647) was an Italian physicist and mathematician.

After Galileo's death Torricelli was nominated grand-ducal mathematician and professor of mathematics in the Florentine academy. The discovery of the principle of the barometer which has perpetuated his fame ("Torricellian tube", "Torricellian vacuum") was made in 1643. The torr, a unit of pressure is named after him. Torricelli is also famous for the discovery of an infinitely long solid now called Gabriel's horn, whose surface area is infinite, but whose volume is finite. This was seen as an "incredible" paradox by many at the time (including Torricelli himself, who tried several alternative proofs), and prompted a fierce controversy about the nature of infinity, involving the philosopher Hobbes. It is supposed by some to have led to the idea of a "completed infinity".

Torricelli was also a pioneer in the area of infinite series. In his De dimensione parabolae of 1644, Toricelli considered a decreasing sequence of positive terms and showed the corresponding telescoping series necessarily converges to a0 − L, where L is the limit of the sequence, and in this way gives a proof of the formula for the sum of a geometric series ( wikipedia).


Torricelli stayed with Galileo.


Weights falling down in every direction as if a ball was released at the same time then thesame time to get to the tangent described in a circle is the same. It takes twice as long to get there from  a reflection.




All associated with an entire foreign way of thinking.


  • Robert Boyle & Robert Hooke

  • Francis Bacon

  • René Descartes


North of the Alps.


South of the Alps.


Tops of barometers.


Accademia del Cimento 1657-1667.


Founded by Prince Leopoldo de’ Medici and the Grand-duke Ferdinando II in 1657, the Academy resolved to test a series of principles of natural philosophy which up till then had been commonly accepted solely on the basis of the authority of Aristotle. They proposed to follow Galileo's example, and use only rigorous experimentation as their guide. ( Website)



Robert Boyle and Robert Hooke working together and finish around 1660.

Air Pump. The Airpump goes north to England about 1660s. The Jesuits bring it to the Lutherans. Hooke excelled in mechanics and Boyle was able to pay him for the time and effort. Later they turns things around and make a compressed air device. This leads to Boyle law. hH=constant. Pressure in space and time & Volume in a space was a constant. pV=constant. The use of quantitative rules was in importance and useful for life, Prior this was just a Aristotelian theory of quantitative ideas. He expressed his law into anagram in the language of Latin to hid from everyone the law. This was the only form of copyright that existed in those days and most philosophers ( Scientists during this period in terms of physical science) used them.

This was a guard against undermining. Before quantitative axioms were useless to the old Latin and Geek masters, but these laws changed them. However, vacuums and pumps were long ago postulated there physical application was never put together. This is the two things into one. The ideas and the physical application of the two becoming one.


Cosomo short lived Academe.



Medici, after Urban VIII's death decided to form an academy dedicated to Galileo and they employed 10 physicists or professors to invent, do science and to performs proofs of scientific experiments. They ran experiments of can electricity survive in a vacuum or barometer. Filling a barometer tube with mercury, then wiggling an amber fixture attacked to a rod against a fir fixture while a leather sleeve kept out most of the air was produced. They really wanted to see what happened in a vacuum. Bells didn't ring, bugs dies, etc.. The problem was it was for the Medici's to see only. They didn't want to publish anything, and fear of the Church they claimed everything was of hypotheses and never a theory or law. This academic only lasted ten-years. All experiments were given no credit to the professors and no explanation was given in their book that they published. The Great book the Medici called it headed with the statement that " we do not stand behind any theoretical statement in the book" (a paraphrase). When Piero Medici, the weak leader rose to power, things fell apart. However the major influence from this academia wound-up being Francis Bacon.



Francis Bacon worked for Elizabeth & James I of England. He was trained as a lawyer who fell in love with the high-life. He became James' chief layer, garnering power. He desired more money than he actually was making which was a good deal anyway. He lost a bribery case involving him that ruined him and he fell from influence around 1620s. Before in 1605 he published a book in English. He was looking for a replacement of scholastic philosophy for higher learning. He wanted to do away with the old philosophers because he thought they bogged down men's' minds. We must remember that after the establishment of the printing press, Aristotle's enemies printed pamphlets and books attacking his theories. This was, of course, a reaction to the Church's adherence of his ways over the centuries from the recovery period of learning all ready spoken about in part I.


"This was an old vision, a vision with a history. In the 17th century, the English statesman and "Father of Modern Science, Francis Bacon (1561-1626), believed that natural philosophy (what we call science) could be applied to the solution of practical problems, and so, the idea of modern technology was born. For Bacon, the problem was this: how could man enjoy perfect freedom if he had to constantly labor to supply the necessities of existence? His answer was clear -- machines. These labor saving devices would liberate mankind, they would save labor which then could be utilized elsewhere. "Knowledge is power," said Bacon, and scientific knowledge reveals power over nature" (Keris).


After he fell from influence he went back to work.


James started the initiative of the National Science Foundation.

Theme was changing thought and advancement.


Bacon published the work entitled " Novum Organum ( 1620).


"Idols of the Tribe"

  • Bacon's idols of though as he called it were the old philosopher's outdated thoughts and theories, He said we should avoid:

  • Anthropomorphism - looking at ourselves

  • wishful thinking

  • idol in a cave - individual prejudices.

  • idols of theater - systems of thought of Aristotle and Plato.

For example, William Gilbert, who was fascinated with the magnet and wrote De Magete (1600) was a target of Bacon. He belived everyithing in the world was connected to magnets. He belonged to the idol of the cave, because he had one focus on everything.


I guess instead we should have Bacon as the new idea mater?


Bacon - The Solution in the tribe book as goes - Patience - "put weights on thought no wings"


Everything is complicated. and therefore in teaching, one must investigate something thoroughly before one writes about it.


Developing philosophy was his major goal and he suggested (Albeit like Aristotle did so long ago) one should investigate all sources of the material before publishing or claiming the knowledge of a particular subject. His keyword was " Patience." He therefore wrote a comprehensive book on teh " Natural history of Wind" which was so convoluted and clumsy that no-one could understand it. " What was he trying to say."


Bacon wrote a book called the, New Atlantis, and this was about the reliance of the state. He needed money so he enlisted the king's help in writing about Utopia. There was this island of Bensalem and its institution was called Solomon's house. Everyone who became shipwreck on this island fell in love with the Utopia and never left, except for Bacon's informant, of course.  There were three-dozen Solomon industrial spies that went about the earth collecting the scientific inventions - they were the ants of the scheme. The bees were the research institutes and offered there tests to the spies. These three-dozen extracted information and material for experiments on the island. They were not there just to get info. Experiments created the English term 'crossing,' implying that two experiments were treated together to see which one was the better outcome ( Which held better). All inventions were free of charge. The three dozen upheld the bad experiments that would harm the public on the island. Therefore they were the overlords of protection for this society. Bacon spends alot of time explaining their lifestyles and how they were rich - in fact it was physiologically his own self-wishing of becoming rich as he once was back during his lawyer days. Soloman's house was not received until the Medici acted as sponsors.





René Descartes (1596–1650)


Significance: He wanted to change the relationship between philosophy and theology - he was no anti-religious.


"René Descartes was born in a village near Tours in France in 1596. At the age of eight years he entered the Jesuit college La Flèche in Anjou, where he would study classics, logic, and Aristotelian philosophy, as well as mathematics from the books of Clavius. On account of his fragile health he was allowed the privilege of sleeping until 11 o'clock every morning, a habit he kept for his entire life. Descartes studied at the college until 1612, and despite his Jesuit education, would maintain the importance of separating reason and faith" (European).


"Descartes went on to obtain a degree in law from Poiter, then enlisted in the Dutch military. Military service was tradition in his family, and when the Thierty [sic] Years' War began he was encouraged to volunteer under the Count de Bucquoy in the Bavarian army. In his leisure time he studied mathematics, having been influenced by the Dutch mathematician and scientist Beeckman. Descartes dates his first new philosophical ideas and his analytical geometry from three dreams that he had while campaigning on the Danube. He saw November 19, 1619, the date of these dreams, as a landmark moment in his life. It was around 1619 that he may have started Rules for the Direction of Mind, his first major philosophical treatise, which would remain unfinished. This work discusses the proper method for engaging with science and rational theology"(European).


He wandered around Paris for a while.

"From 1620 to 1628 Descartes traveled through Europe, moving from Bohemia, to Hungary, Germany, Holland and France. In 1623 he was is Paris where he met Mersenne, a connection who would keep him in contact with his contemporaries in science. After Paris, he spent time in Venice, returning to France in 1625. In 1628 he met the Cardinal de Berulle, the founder of the Oratorians. Berulle was impressed by his conversation with Descartes, and he encouraged Descartes to devote his life to the study of truth. In 1629 Descartes moved to Holland where he would live in seclusion for 20 years. Occasionally during this time he would visit France, and he changed his address frequently to maintain his privacy" (European).

"During his first four year in seclusion he wrote Le Monde, a thesis on physics defending a [Copernican] heliocentric view of the universe. 1633 was the year that Galileo's Dialogue was condemned by the Catholic Church, and although Descartes book was ready, he put off its publication out of concern that his views might too be censured. The incomplete manuscript of Le Monde was finally published in 1664. In 1637 Descartes published Optics, Meteorology, and Geometry, a collection of essays. The preface to the collection is titled Discourse on the Method of Rightly Conducting the Feason and Seeking Truth in the Sciences, and was written for the most part before 1633. A conclusion to the preface, added later, explained that he would publish despite of the risks because he needed readers to help confirm his scientific theories. In Discourse Descartes insists on the use of deductive reasoning, countering Francis Bacon's induction as introduced in Novum Organum from 1620. The work from these years forms the basis of some of Descartes most important contributions to mathematics and physics, including the introduction of what is now known as analytic geometry" (European).

Hw was nervous about publishing Le Mond, and Galileo was censored  with the new unintelligent non-tolerant Church leaders at that time. The best way to spread the truth in a Jesuit school is to get bunch of friends. He remained quite.

1637 He wrote a paper and it was a discourse essay called Discourse of Method, 1637, in which he discussed ancient geometry ( Not do all the math), Optics, which was not practical and meteors ( replaced teaching of the schools). Common sense was his biggest wit in his books. His method: It was doubting, and doubting everything until there was nothing left to doubt. " I think therefore, I am." H was always a devout Catholic, however he understood that old dogma of remaining loyal to outdated science like Aristotle needed to go in order to further the western civilization.


"In 1644 Principia Philosophiae was published in Amsterdam. Its four 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. The book concentrates on physical science, specifically the laws of motion and theory of vortices. In 1647 the French court granted Descartes a pension to honor his work"



Descartes always refused the Aristotelian and Scholastic traditions that had been the dominant shape of philosophy throughout the Medieval times, and he rejected religious influence in his scientific and philosophical studies. Throughout his life and afterwards his work was condemned by the Catholic Church, and was officially prohibited in 1663. Nonetheless, Descartes was a devout Catholic, and influenced by the Reformation's challenge of Church authority, and he often uses a vocabulary influenced by scholastic thought. As long as he felt an idea was in line with his thoughts on clear reasoning he was glad to borrow it. He saw reason as the foundation and guide in the pursuit of truth, and he was relentless in his search for absolute certainty" (European).



Anything you perceive, is true, he like to note.

How does one know it to be true?

  1. Because it has to be God

  2. Consequences - the supreme being would not deceive.


Points of his reason: He thinks he knows how to test a truth claim,

  1. by balance and clarity.

  2. Ground it ultimately in God.

His thinking substance was radical.

Res Extensa, is like the force all around us.

  • extension and substance was the same thing.

  • it was colorless, odorless and characterless.

  • Only notion of shape and mobility builds the universe.

For Copernicus Descartes  doesn't like only that he showed the results of the universe, " He is built without foundations."  Descartes  wanted to break the old Aristotlean system and make a new updated version of the universe.


Cartesian System

Analytical of Cartesian Geometry.

This was the unification of Algebra and Geometry. This was well used until the 19 century, as a major force. Today we have variables of this system we learn in school.



Cartesian Geometry

Conic sections, shows advantages, orthogonal lines.


The Princess of Bohemia, Elizabeth, daughter of the Kind of Bohemia, nice of Charles of England was tutored by René.  Correspondence between then about geometric and algebra problems. She said I can solve the problem. René  was not really up to doing the math himself, but the Princess used his system, and they had letters back and forth. She did all the calculations, he didn't like calculations - he liked the big picture.


Snell's law of refraction, and lenses shapes (grinding).


Refraction is the bending of the path of a light wave as it passes across the boundary separating two media. Refraction is caused by the change in speed experienced by a wave when it changes medium.


Rainbow and Refraction


Descartes also made contributions in the field of optics; for instance, he showed by geometrical construction using the Law of Refraction that the angular radius of a rainbow.

In the 13th Century it was known that 42° is a constant = α+ b of light diffracting. He described this process in the form of a water droplet with light-ray bouncing around in the droplet and ricocheting off the sides to flow outward at a 42°  angle. Then the eye perceives the wavelength. The droplet bends the light-ray to the 42° . Here is a example from a website.


Descartes Universe



Descartes believed that God created the universe as a perfect. However he needed to show everyone how it came about.


The program of René entails an independence of the Aristotelian Universe system.

  • Why? The entire Aristotelian system should be replaced by this primal chaotic universe system.

  • He wanted to replace it with the Cartesian System.

  • He wanted to present things that were familiar to the readers. This meant beginning with first principles then proceeding to the mathematical concepts until one reaches a series of reductions, reducing physics to mathematics.

  • He didn't show laws of motion, because the average reader couldn't grasp its concepts. .

  • His most famous phrase was "Cogito ergo sum," (I think, therefore I am). He derived his philosophy and his belief of God from this utterance.

  • A fundamental force of motion René worked on with inertia, accelerations and variations of collisions ( exchanges) of velocity and mass gave Newton his thoughts which led him to his discourses and laws of motion.

  • A Simple collision rule, V+v/2 >v.

  • What happens if the bodies are the same size? V12 = v/4 =  ½(0 + v/2),  V11 = 3v/4 =  ½(0 + v/2). Therefore, he stated, ' everything exclusively is a  plenum' (the antithesis of a vacuum; in other words, completely filled space).

  • René deemed  mass times velocity (today known as momentum).

Descartes also believed that colors were caused by the rotation of "spheres" of light, using the tennis ball as a model of a spinning sphere. Unlike Newton, Descartes believed that white light was the pristine form. Descartes gave the first formulation of what is now known as Snell's law of refraction. Descartes believed that God created the universe as a perfect clockwork mechanism of vortical motion that functioned deterministically thereafter without intervention.



René Descartes' Universe


  • Descartes was the first to make a graph, allowing a geometric interpretation of a mathematical function and giving his name to Cartesian coordinates

Number one motive is 'Motion.'


  1. Beginning. The void is black

  2. God: " Let there be motion.

  3. Orange like balls first appear. These are ultimately little balls of knowledge and this is at the stage 1.5. This is the undifferentiated universe.

  4. Next, balls squeeze out matter.

  5. Next the balls stack upon each other.

  6. channel particles emerge between the balls.

  7. Struggling in inertia or weight, a process of orange-sized balls faster then some channel particles that emerge.

  8. Quantity motion is converted to a universe full of vortices. This becomes stage two.

  9. The orange -like balls become suns and channel particles flow between them in a screw like motion and some screw into the oranges.

  10. Each vortices has one ball in the center with the particles swishing around.

  11. The ones that screw into the sun become sun-spots.

  12. The vortices swirl around. And if too many channel particles chaotically start flying around then,

  13. Things break free and comet-like things fly-loose from the vortices.

  14. Neighboring vortices capture the comet-like things and they become a planet.

  15. When many happen then they knock into another sweeping planets all over the vortices.

  16. The orange, or now identified as a sun captures these planets, and eventually more of the same until we have our solar system.

  17. So our Earth retained its nature of its origins of vortex.

  18. This also caused the tides. This is a notion on attraction and gravity.  Note: Newton later gets his ideas of quantitative idea from this and Descartes. 



Magnetic Fields


The twisting of the Earth Particles caused it to line up. The magnetic field was important to establishing forces and his main field of concentration that the prime motive is motion. He also discussed poles of magnetisms.


Huygens Christian


Huygens Christian,    b. 1629-95. He came from a  prominent family in the new independent Holland. His father  taught him a little of the Cartesian system, and he learned more at Paris University. He believed in only sound physics should be used and was used in Descartes system. Descartes though is taking chances in kinematics. He had a variety of responses to Descartes' Universe. He was welcomed in Paris Academia and was there when Rohault was there. He could grind a telescope lenses better than anyone else. This helped with his universe findings. He discovered Titan and Saturn's rings. His father taught him the Cartesian system when he was young and he learned more when he studied in Paris. Huygens was against Descartes but he used much of his work in his own. Galileo has blurred vision from a short telescope, called chromatic aberration, and his lenses were not ground well enough to distinguish the details of Saturn. Therefore, a couple hundred foot telescopes solved this problem, but they were hard to manage. One could only look a small bits of the sky. Very few people were able to work these. It was like catching a fish in the sky.

Giuseppe Campani, a principle lens maker in Rome, made new powerful telescopes and was an excellent lens maker. Huygen's solution was to tie a string to a pole and therefore, one man could operate the telescope by themselves. These long scopes were called boon telescopes.




For Huygens, Descartes treatment of light was the worst of the worst. 'Light must be a motion, because fire is a motion', he thought. He thought how does light come to our eyes? The balls of light would collide in our eyes making everything fuzzy , he thought, 'Light must become kind of wave, ' he concluded.  He states that light is a pulse (correct) and it has a vibration. One of his experiments involves metal balls hanging together and the ends are swung and the as the ball's on the end smash into a line of balls ( the locus of eather - must have subtle matter to propagate) the other end swings upward and repeats the process and the middle balls vibrate - this showed that light was not a indefinite velocity because the atoms (balls) would interfere with each other. This was an experiment on subtle matter and a demonstration on refraction. The double refraction is what he shows for the progressive motion of light. Light continues, says Descartes, but Huygens had a tip from the University of Paris where people were conducting viewings to see if light travels great distances, does if have a terminus? " We just proved it at the academy that light takes time to move," Huygens says. The questions people were now asking was: " If light was always everywhere then what makes a shadow?" The concept of the speed of light was born. To prove this the Moon and satellites of Jupiter were studied with observations of progressive motions. They looked at the shadow of the Moon or Satellite and kept time and then waited to the Earth moved to another position around the the Sun to take another observation. This was done to prove light was not an infinite velocity. Once there was the two positions of the Earth recorded with the observations then they were calculated together to see if distance equaled time for both positions looking for the constant and measuring against it.




Christiaan Huygens (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. He studied law at the University of Leiden and the College of Orange in Breda before turning to science. Historians commonly associate Huygens with the scientific revolution.

He also examined Saturn's planetary rings, and in 1656 he discovered that those rings consisted of rocks. In the same year he observed the Orion Nebula. Using his modern telescope he succeeded in subdividing the nebula into different stars. (The brighter interior of the Orion Nebula bears the name of the Huygens Region in his honour.) He also discovered several interstellar nebulae and some double stars. Huygens generally receives minor credit for his role in the development of modern calculus. He also achieved note for his arguments that light consisted of waves. (wikipedia).


Huygens Galileo similarities.


Huygens Galileo
Worked in pieces and polished them, there was no complete theory of a universe.

Mathematician, and a little better than Galileo

Made improvements to telescopes to and found  at Saturn's rings and Titian, the satellite.

Improves on the pendulum clock of Galileo. and makes improvements in an order of magnitude.

Both usually waited a long time to have their stuff published - were relectant.

He always polished his work usually waiting 15-30 years before publishing.

Worked in pieces and polished them, there was no complete theory of a universe.


Made telescopes to look at Jupiter's satellites.

Studies the  pendulum clock.

Both usually waited a long time to have their stuff published.


With these new telescopes, as one will see with the new science universities ( academies) small portion of sky brings out allot of detail. The Jovian system with its moons appears flat on the poles and bulging at the middle.

Huyges during the 1640s to 1670s look for the flattening of the poles and observed the flatness of the poles on Jupiter.  With the new Cartesian principles the an argument erupted between what people believed the deformities of Earth were. It looks like a lemon, it looks like a peanut, or Newton's view of a pumpkin. This had a little play in those days. Finally it was a fight of a pumpkin to a lemon.


Cassini found the first spots on Jupiter and that Jupiter had flat plaes. He found four more moons and gave the period of the rotations using Kepler's third law. He noted miniature-like solar systems, of the orbits of the moons around planets and so surveyed the our solar system using Kepler's third law.

Giovanni Domenico Cassini (June 8, 1625–September 14, 1712) was an Italian astronomer and engineer. Cassini was born in Perinaldo, Imperia, at that time in the Republic of Genoa. Cassini was an astronomer at the Panzano Observatory, from 1648 to 1669. He was a professor of astronomy at the University of Bologna and became, in 1671, director of the Paris Observatory. He thoroughly adopted his new country, to the extent that he became interchangeably known as Jean-Dominique Cassini. Along with Robert Hooke, Cassini is given credit for the discovery of the Great Red Spot on Jupiter (ca. 1665). Cassini was the first to observe four of Saturn's moons; he also discovered the Cassini Division (1675). Around 1690, Cassini was the first to observe differential rotation within Jupiter's atmosphere. In 1672 he sent his colleague 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 (wikipedia).


Bologna, a second type city of the Papel States becomes involved in the astronomy and science. They do not want to fall behind the rest of the countries in Europe.


Donato Crete a painter whose paintings still hanging in the Vatican displayed all the current discoveries in his work and the new instruments, albeit the objects were out of scale. Inhis work one sees Saturn with its Huygens' rings. The objective of the paintings were to communicate to the public that the pope needed support for the funding of a science university. Pope Clement XI (Giovanni Francesco Albani ) oversaw Astronomy Eustachio Manfredo


etym. Eustachio de Divinis


Francesco Bianchini (December 13, 1662 – March 2, 1729) was an Italian philosopher and scientist. He worked for the curia of many popes, including being secretary of the commission for the reform of the calendar, working on the method to calculate the correct date for Easter in a given year. 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 noonHe published many books, including A Universal History, and Hesperi et Phosphori nova Phaenomena in which he deduced a rotational period from the observation of the surface of Venus. Today, we know that this is impossible, because of the thick cloud cover on this planet. He also worked on the parallax of Venus, and he measured the precession of the Earth's rotational axis.

As part of 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. His point of view on the Copernican system is not evident, but it was noted that the picture of the planetary system in his book about Venus has an empty center (wikipedia)

Francesco Bianchini became Pope Clement XI's  lieutenant and minister of culture. Looking at Venus he discovered features on Venus. He must have not seen his own spots in his retina with his long telescope.  However, Venus is covered with clouds. He saw cracks on the moon, and stated that if one could not see the crack then their telescope lenses and in general scope were not up to par. With Venus he began to name Portugal names to places on Venus. He published a book in 1720s.



Eustachio Divini and Cassini ground there lenses into spherical surfaces therefore created  aberration. (Heilbron, Sun 246). Short scopes with technology for good convex lenses were not available. Therefore, the math said go long. According to Bianchini, who preferred Campani's test bed, a 50-foot telescope was needed to view the disks and diameters of the planets, the spots on Jupiter, and Saturn's rings, and one of a hundred feet to see all the satellites of Saturn; whereas people content with observing nothing more exotic than the eclipses of Jupiter's moons could do with something between 15 and 25 feet" (Heilbron, Sun 249). The big scopes were impractical for one man and even difficult for two. But Cassini made a pulley to adjust his lenses to the height and rotation of a fork carried by the frame riding on the pulley to work the azimuth positions (Heilbron, Sun 254).


17th Century

Scientific Revolution


Long (Boon) Telescopes solved Chromatic Aberration.


Giuseppe Campani (1635-1715) was an Italian optician and astronomer who lived in Rome during the latter half of the 17th century.

His brother, Matteo Campani-Alimenis, and he were experts in grinding and polishing lenses, especially those of great focal length and slight curvature. These lenses were used in long telescopes of considerable power. The astronomer Cassini made his discoveries with these lenses.

Campani also made many observations himself. Cassini called his attention to the spots on Jupiter, and he disputed with Eustachio Divini, an Italian optician, the priority of their discovery. His astronomical observations and his descriptions of his telescopes are detailed in the following papers: Ragguaglio di due nuovi osservazioni, una celeste in ordine alla stella di Saturno, e terrestre l'altra in ordine agl' instrumenti (Rome, 1664, and again in 1665); Lettere di G. C. al sig. Giovanni Domenico Cassini intorno alle ombre delle stelle Medicee nel volto di Giove, ed altri nuovi fenomeni celesti scoperti co' suoi occhiali (Rome, 1666).

His brother, mentioned above, is also noted as a mechanician for his work on clocks. He was a priest in charge of a parish in Rome. Louis XIV of France ordered several long-focus lenses (86, 100, 136 feet respectively) for Cassini, who discovered with their aid additional satellites of Saturn (wikipedia).

"The long telescope could not replace the meridianna as a precise chronicler of the movement of the sun" (Heilbron, Sun 255). The long scope could not be moved well enough to follow the horizon in respect to the meridian, as for keeping of time, but for observing the stars this was a good invention.

King Louis XIV from pleading with the new Royal Academy gents, builds an observatory, with these long telescopes. This was after the 30 Years War, and people wanted not to fight anymore and this became an opportune time to start to progress into the sciences. ( See below).

  • The propagation of the Cartesian system in the  second half of the17th century.


1660s Academics Change




Henri  Régnier

Henfi Le Roy (Regius)


Utrecht  University, established March 26, 1636. (Utrecht  is a municipality and the capital city of the Dutch province of Utrecht). It is one of the oldest universities in the Netherlands. Henri  Régnier a professor of philosophy taught the Cartesian system. Le Roy succeeded Henri  Régnier. Studying medicine and Cartesian , the young doctors were trying to incorporate the  Harvey circulation of blood methods, and include studies of the the heart pump which fit nicely into the Cartesian system. (Harvey, William  (1578-1657), English physician, the discoverer of the circulation of the blood). The significance is that young doctors are fighting with the old doctors over traditional methods, and it is these young ones that are experimenting with the Harvey heart pumps. Young doctors were adopting the modern ways, i.e. the non-Galen ideas. This showed free-thinking.


Descartes begins to argue with Le Roy because he was not disseminating his system the way Descartes  wanted. Le Roy placed certainty back into the front pages of a pocket book for the Cartesian System, and this law Descartes  thought to be the most important and in this way he made changes to the physics of the system and René said that this stood in the way of his own progress of the Cartesian system. In the 1650s Descartes moved to Sweden and tutored Queen Christina of Sweden  as her private philosopher, It was cold and his body didn't manage well in the climate at that age. He died there of pneumonia.






Henri de Montmor

Jacques Rohault (e. 1620-1672).

Pierre - Sylvan Régis

Bernard le Bouvier de Fontenelle ( 1675-1757).



The decuples of the Cartesian system flocked to the University of Paris, and his system was taught at the university. This was cells of his followers advocated his teachings be included in the curriculum.

Rohault  asked to go back to the basics, and wanted no more matters on metaphysical treatments. He was schooled in a Jesuit school then took this MA from Paris. He lectured as a professor in Paris on Natural Philosophy. His fame came from his weekly lectures at  his house and was an advocated advocate of Descartes' work. His work Traité de physique (1671) 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.


Pierre - Sylvan Régis broiught Cartesian system big crowds and was nick-named the silver tongue. The King closed his public lectures in the 1680s, and said that he could conduct them in his private space. But there was an affected opposition of lay positions to the Cartesian teachings beginning in the 1640s. A chancellor in Germany banned the teachings, but one some aspects of it. These teachings were a very integral part on free speech and free thought and did cause concern. Some these of Descartes like his doctrine of the Eucharist were placed on the Index around 1633. The Jesuits came out in numbers to condemn the Cartesian system, first around 100, then 50, 40, 30, 20 and the only around 10 of them as the system proved vital for real application to help western civilization.


In the17thcentury the Cartesian system conquered France. The system only had a few principles, it was applicable and could be associated with categories. However, the best argument for its acceptance was its easy grasping of the figures, like the shapes of these systems. It explained the working views of a possible understanding of magnetism, gravity and one could make inferences.


Bernard Le Bouvier de Fontenelle (1657-1757) went to Paris and he was a mild Cartesian follower. Fontenelle was born in Rouen, Normandy. He died in Paris. His Conversations of the Plurality of the Worlds was a best seller.

" He wrote extensively on the nature of the universe: Behold a universe so immense that I am lost in it. I no longer know where I am. I am just nothing at all. Our world is terrifying in its insignificance. He led the French Academy of Sciences for a significant amount of time and is noted for the accessibility of his work - particularly its novelistic style. This allowed non-scientists to appreciate scientific development in a time where this was unusual. His object was to popularize the astronomical theories of René Descartes, whose greatest exponent he is sometimes considered" ( This story took place in a garden where beautiful girls learned about the universe and the entire Cartesian system of vortices. It was laid-out so that it seemed that we learn general cosmology from a female persona. It was very influential for the first forty-years until the 18th century.


Bernard Le Bouvier de Fontenelle's Histoire des oracles (1687) attacked priests or practices of pagan religions - things really haven't changed since that is a popular method of attack today. Another approach was to emphasized similarities in religions, refuting the uniqueness f any religion, including Christianity.....Fontenelle's De l'orignine des fables (1724




Leibniz sees measure of a body's "force" was the product of mass times velocity squared. We call this proportion today kinetic energy.


Gresham College.

Sir Thomas Gresham , born in 1518 was a London merchant, the founder of the Royal Exchange and of Gresham College in which he designed  in 1596, in London. A group went to London associated to the college to petition the royal society for a private college in which to experiment with new ideas of the people we been speaking about here. This was the Anti-University idea. Universities up until this period were regulated by who so ever was in charge of the curriculum, be it the Catholic Church or an arm like the Jesuits or even the newly Protestants. Gresham College taught only practical things  opposed to scholastic philosophy of the universities. This Anti-University thought pursuits were best folowed outside of these regulations and therefore, the group petitioned the King and received an OK to have and own their college. This was quite a change for western civilization.


Royal Scientific Academies


The two Main Royal Scientific Academies, England's private, and France's public,  changed the outlook of what a Middle Aged University did and what it could do. The later seventeenth century saw the rise of organizations of scientists and others interested in natural philosophy. Paris, Royal Academy of Sciences, its initial name, was founded in Paris in 1666 and a little time before this Europe saw the Royal Society founded in London in 1660 ( initially called the Royal Society of London or the more popular title of Royal Society of London for the Improvement of Natural Knowledge). Later the Paris, Royal Academy of Sciences is called the French Academy of Sciences (Académie des sciences)  and initially was credited due to the pleading  of Jean-Baptiste Colbert, and was from the beginning deemed by the king under pressure as a public institution. The academy continued at the forefront of scientific developments in Europe in the 17th and 18th centuries. The English academy still operates today and is still privately operated. These academies had the distinction of claiming as for the body of members the distinction of ' the learned society.'

King Louis XIV, as a  counterweight against the English and with pleading from the new scientific gents, builds an observatory, with these long telescopes. This was after the 30 Years War, and people wanted not to fight anymore and this became an opportune time to start to progress into the sciences. In England,  beginning in 1660 when the English monarchy was restored under King Charles II (who said lets all get along) after the English Civil War, a group of  several hundred gentlemen and scientists approached the king. John Evelyn (October 31, 1620 – February 27, 1706) was an English writer, gardener and diarist, in 1660, was one of the members of the group that founded the Royal Society. There was Patrick Hook's job every week to bring in a new experiment. two-hundred people in a crowed stood around and suggested improvements, and it was Hook's job to figure out which suggestion was the better. There slogan was Nullius in Verba [ iurare, to swear in other words] - trust no one. There were interesting people like Boyle, and Christopher Rien, who built a cathedral.


What did the English start out with? Dissections ( medical); pumps, blood transfusions ( sheep blood into man); temperatures on everything; antidotes on everyone; mechanics, collisions of bodies.  These, sometimes bizarre experiments brought lampoons and parodies from the Academy watchers. Gulliver's Travels satire on human nature  lessoned when the scientists began providing benefits for humankind from their experiments, Therefore these science academies had not be closed in history ever sense and its phenomena is still with us today. 


French Royal Academia develops where Henri de Montmor, a Cartesian lawyer discussed the merits of the Huygens, Descartes progressions on science searches for the cost effectiveness of starting a Royal Academy for science (only). When King Louis XIV tells his cabinet, including Colbert ( Minister) the proposition and possible benefits, word gets out and two camps form calling for free money, because Louis was not going to make his academy private like the British because he wanted autonomous control over the business conducted for national interests. Therefore, natural knowledge would be regulated by the state. Also this academy leaves out medicine, while the British Academy doesn't. The huge government bureaucracy creates a finance problem so only 50 people are hired instead of the 200 private citizens or so of the English system. The English system was a pay-to-play proposition, allowed by the King, and freedom was the price paid, and therefore no royal oversight was the benefit. They scientists could work on what they wanted. However, to get into this system, which still applies today, one has to pay to become a member.


What did the French start out with? The French began with an order by the king to map France. This was thought to help the taxmen and the Army. This was of course a lose of freedom of action ( limiting the scope of inquiry) , setting back the French from the English who were doing all sorts of experiments. Jean Picard, measured the distances from triangles and the French scientists used this method going from church-roof-tops to church-roof-tops triangulating areas of France then taking a foot measure of one triangle and using this as the standard and calculating the earth for maps. The easiest way to map was to make a strait line and measure on both sides connecting triangles, and hope that the church-roof-tops were not far out of angle to the standard. Trigonometry used in the survey was ascertained by finding two zenith stars on the meridian as two points on a line and then triangulating separate triangles hoping they added up to 180° . This method gets the distance. The hard part was to use the toise, a French yard-stick that was about 2.2 meters. They placed then one-by-one to measure from the ground while they surveyed the  stars at night. To get equal and accurate distance, they needed to build flat scaffolding-like structures to lay out the toise. When churches couldn't be found they had to build scaffolding-towers and lay the planks on them. The other order of business was to get a flat piece of land to use as the measured standard. This was accomplished in sandy-flat places. The other places that had to go were on tops of mountains.

Jean  Picard, theFrench astronomer,  was close to an accuracy as one could get at that time. He was about 20'' of acr off. In the first survey, instead of getting the desired boundaries they wanted, the lost some land of about 150 kilometers on the coastlines from the previous map. Therefore, it was said that the Geometers lost more land for the French then losses to Germany, Italy or Britain. To convert the Erath portion they had to get out their stars. The formula was

ΔФ = Za +Zb. Therefore the points A and B on the earth were the angles of the Z primes of the parallaxes of the stars. 20 minuets of arc is equal to 20 nautical miles. It was important to survey the correct coordinates. The Meter measurement originally came from this eventual Royal endeavor of mapping France then getting the northern hemisphere correct.  A meter was deemed 1/10 millionth of the equator to the north pole. Therefore the toise was deemed later as 107 = 90°, 1m =1/9·10~ 1.1 ·105  

5 ·104 Ts =1.1 ·105 m,

Ts = 2.2 meters


This was a big stick. It was decided to measure the meridian spanning the Mediterranean and Dunkirk which was within French territory by Jacques Cassini in 1719. The toise was used and placing the sticks level which meant building the running scaffolds.  ( see Sun in the Church)


It took seven years  to measure baseline, equator to north pole. The best level places was a frozen medium like a lake or a river. The Artic circle was frozen and did the job. It was an incredible act by Jacques. TheArc between the stars had an acr value of the degree of the meridian and only was off one toise length, in 50,000 places matching the differences with Picard. (verify see Sun in the Church) .


" No telescope existing in1665 could be relied upon to determine the diameter of the solar disk to within a minuet of arc" (Heilbron, Sun 256)


So they sought to measure the earth by dividing up the southern and northern hemispheres from the equator.



Copernicus was off by about 18' of arc. Richer whittled it down to 1' of arc. This was important for declination and calculating the speed of light later on. Since this project needed a  correct solar theory, we look to Danish astronomer Richer.


Jean Richer who like to observe the planet Mars from Cayenne, French Guyana, and in 1671–73 he contributed to both astronomy and geodesy. The French astronomer observed that the clocks beat of seconds in Paris was slower than in the tropics. Accuracy of the Clock. Why is it important? Time is critical on the ocean and when one doesn't want to drift into a coral reef cited from a map because  seconds-off of an hour from a clock can  create a disaster - throw-off the measurement of distance-to-time. So, The theorem of Galileo, of course utilized by Huygen's was a Pendulum bob between two metal plates called cheeks ( Jowls) to shorten the cord so that the pendulum swings equally. One can see a reflector on a wheel when it is in motion make the same design as a cycloid inverse which is the same theory of the shortening of the cords at certain places to increase the accuracy of the clock. Time is to fall in the same place in respect to the angles of the circle. This helped correct the clock.


Jean Picard, a French astronomer who first accurately measured the length of a degree of a meridian (longitude line) and from that computed the size of the Earth,  became professor of astronomy at the Collège de France, Paris, in 1655. His measurement of the Earth was used by Sir Isaac Newton to verify his theory of gravitation.


The English Academy began to publish a monthly periodical. Sometimes the articles were not of the academies findings but of other people's and other places in the known world's findings. This sparked interest in the speed of dissemination of knowledge. Therefore the magazine became a popular image of communication of the western civilization. Previously it was the annual almanac that held the most coveted ownership parcel of the sophisticated ( the ones who could afford them)  in Europe during the middle ages during the early periods of the printing press. The popularity of the magazine led to subscriptions, noting a  new money making vehicle - good for commerce, and regular reporting on learning. The web of knowledge facilitated the progress of western civilization. In 1665 the magazine published a new moon around Saturn.


The important things going on at this time about planets and timekeeping.

  1. Jupiter and Moons, and figuring out their orbits for corrections of clocks.

  2. knowing starts and where they are in the sky.

  3. This method proved good on land, but on the bumpy sea this method was useless.


Therefore, another method for the sea needed to come into play for the west.

The Building of the Greenwich Observatory & Longitude for the Success of Navigation at Sea


Sir John Flamstead, the Astronomer Royal and namesake of the  Flamstead House at the Royal Naval Observatory Greenwich succeeded in measuring Longitude at sea with use of a chronometer in a Parish at Port Royal. He measured star positions as the job for his new appointment at Greenwich, but was given no instruments. ( See Jean Richer). His findings helped to correct the clock.

The Royal Observatory, Greenwich (formerly the Royal Greenwich Observatory or RGO) was commissioned in 1675 by King Charles II. At this time the King also created the position of Astronomer Royal, to serve as the director of the observatory and to "apply himself with the most exact care and diligence to the rectifying of the tables of the motions of the heavens, and the places of the fixed stars, so as to find out the so much desired longitude of places for the perfecting of the art of navigation." It is situated on a hill in Greenwich Park in Greenwich, London, overlooking the River Thames (wikipedia).

Greenwich Mean Time (GMT) is mean solar time at the Royal Greenwich Observatory in Greenwich, London, England, the United Kingdom, which by convention is at 0 degrees geographic longitude. Noon Greenwich Mean Time is not necessarily the moment when the Sun crosses the Greenwich meridian (and reaches its highest point in the sky in Greenwich) because of Earth's uneven speed in its elliptic orbit and its axial tilt. This event may be up to 16 minutes away from noon GMT (this discrepancy is known as the equation of time). The fictitious mean sun is the annual average of this nonuniform motion of the true Sun, necessitating the inclusion of mean in Greenwich Mean Time. As the United Kingdom grew into an advanced maritime nation, British mariners kept their timepieces on GMT in order to calculate their longitude "from the Greenwich meridian". This did not affect shipboard time itself, which was still solar time (wikipedia).

Italian Academics


Accademia Fisico Malematica , Romana., G.G. Ciampini

or Fisica Matematica

Improving the carriages because Italy's road were rough on the back. They wanted to make shock-absorbers.


According to every comet since Julius Caesar.

Accademi Chimento

Telling time on the public squares of Italy. (verify see Sun in the Church) .




Bologna  17th-18thCentury


Geminiano Montanari (Sun in the Church).


Montanari: Hypsometry



Academe 1690:        Eustaschio Manfrede ( now, Degli Inquieti)

Bologna  schools fell into a despair over the professors, now professors would teach and no students went to class. At the time there was ration of 1:2 of professor to student. Including holidays, festivals, a religious days-off meant that not all the professors could find positions to teach the students as by law they were to teach consistently. There was too many of them.  Fights broke out over who lectures, so everyone just quit. The new scientific style school, the Degli Inquieti replaced the school system, needing a new focus, people like Luigi F. donated his world travel writings on condition that only a few teachers would teach at the school.


First Research Instatution

Pope Benedict XIV's School system replicated ever since.


Pope Clemet XI loves art so Donato Creti, Marsili had commissions to give to the pope and this winds his heart to help finance some of the schools. Therefore, the Pope says, go ahead with scientific schools but we must have art schools in the same institutions.. One of, or possibly the most expensive part of these schools were the astronomy departments. He gives money to start the astronomy departments, but fails to pay salaries for the teachers and the old ways return. Next, Benedict XIV dropped the prohibition of heliocentricism, and paid 24 teachers full time in which half of them were just researchers. This became our modern system of western style Universities. In these new types of schools we have the stereotype dormitories of cramped spaces and overcrowdedness.


First Women to become Professor


Laura Basse becomes the first women in the Italian schools to make a professorship (of Physics | Depicted in art of the period). Women had to get a hold of books, and this was difficult as it was somewhat restricted to young women. However, secret retrievals of scholastic material was not unknown.





From the 13th Century the astronomy devices were the astrolabe and the naked eye, and the schools in the 14th century were tables in private homes, with emphasis of pious writings. 14th Century , Dissection was allowed but not with Bologna  citizens and including their relatives.




Work Cited: , Bernard Le Bouvier de Fontenelle, <>2006.


Drake, Stillman trans.,  Discoveries and Opinions of Galileo,  (Garden City, New York: Doubleday & Company, INC.,1957).


European Graduate School EGS, René Descartes, ( New York: New York, 1997) <> 2006.


Galileo Galilei, "The Institute and Museum of  The History of Science "


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).


Heilbron, J. L. The Sun and the Church. 4th ed., (Boston: Harvard University Press, 1999),


Keris, Steven, Lecture 17: The Origins of the Industrial Revolution in England,  History Guide, 2001 <> 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. 30,32.


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


UCLA, Galileo, Francis F. Steen,  Early Modern Studies,<> 2006.


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Wikipedia, Dialogue Concerning the Two Chief World Systems, Free open-source  Encyclopedia. (wikipost Mar 2006)  <> 2006.


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Galileo Galilei



April , 2006






Born in Pisa on February 15, 1564, Galileo was the son of Vincenzo Galilei (1520-1591), a music scholar, and Giulia Ammannati (1538-1620). He studied at the University of Pisa, where he held the mathematics chair from 1589 to 1592. He was then appointed to the chair of mathematics at the University of Padua, where he remained until 1610. In the Padua years, he conducted studies and experiments in mechanics, built the thermoscope, and invented and built the geometric and military compass. In 1594, he patented a water-lifting machine. In 1609, he developed the telescope, with which he performed the observations that led him to the discovery of Jupiter's moons. In 1610, he was appointed mathematician and philosopher to the Grand Duke of Tuscany. He studied the peculiar appearances of Saturn and observed the phases of Venus. In 1611, he went to Rome, where he joined the Accademia dei Lincei and observed sunspots. In 1612, opposition arose to the Copernican theories, which Galileo supported. In 1614, from the pulpit of Santa Maria Novella, Father Tommaso Caccini (1574-1648) denounced Galileo's opinions on the motion of the Earth, judging them dangerous and close to heresy. Galileo went to Rome to defend himself against these accusations. However, in 1616, Cardinal Roberto Bellarmino (1542-1621) personally handed Galileo an admonition enjoining him to neither advocate nor teach Copernican astronomy, because it was contrary to the accepted understanding of the Holy Scriptures. In 1622, Galileo wrote the Saggiatore [The Assayer], which was approved and published in 1623. In 1624, he developed the first known example of the microscope. In 1630, he returned to Rome to apply for a license to print the Dialogo dei Massimi Sistemi [Dialogue on the Great World Systems], published in Florence in 1632. But in October of that year, he was ordered to appear before the Holy Office in Rome. The court issued a sentence of condemnation and forced Galileo to abjure. He was confined in Siena and eventually, in December 1633, he was allowed to retire to his villa in Arcetri. In 1634, he was deprived of the support of his beloved daughter, Sister Maria Celeste (1600-1634), who died prematurely. In 1638, when he was almost totally blind, the Discorsi e dimostrazioni intorno a due nuove Scienze [Discourses and demonstrations on two new Sciences] was published in Leiden. Galileo died in Arcetri on January 8, 1642. ( Galileo Galilei, The Institute and Museum of  The History of Science ).


V.2 Galileo’s telescope

Inventor and maker: Galileo Galilei
Date: Late 1609 - early 1610
Place: Italian
Materials: Wood, leather
Dimensions: Length 980 mm
Current inventory: 2428


Galileo Galilei, The Institute and Museum of  The History of Science

Original telescope made by Galileo consisting of a main tube with separate housings at either end for the objective and the eyepiece. The tube is formed by strips of wood joined together. It is covered with red leather (which has become brown with the passage of time) with gold tooling. The plano-convex objective, with the convex side facing outward, has a diameter of 37 mm, an aperture of 15 mm, a focal length of 980 mm, and a thickness at the center of 2.0 mm. The original eyepiece was lost and was replaced in the nineteenth century by a biconcave eyepiece with a diameter of 22 mm, a thickness at the center of 1.8 mm, and a focal length of -47.5 mm (the negative focal length means that the lens is diverging). The instrument's magnification is 21 and its field of view 15'. It is registered in the 1704 inventory of the Uffizi Gallery as "A telescope of Galileo 1 2/3 braccia [973 mm] long in two pieces to lengthen it, covered with leather of several colors and gold tooling, with two lenses, of which the eyepiece is at an angle": the eyepiece was thus still present, but loose in its housing. By the end of the eighteenth century, it was missing. In 1611, Prince Federico Cesi, founder of the Accademia dei Lincei, suggested calling this instrument telescopio [from the Greek tele ("far") and scopeo ("I see")].

Galileo designed ingenious accessories for the telescope's various applications. One of the most important was the micrometer, an indispensable device for measuring distances between Jupiter and its moons. Another was the helioscope, which made it possible to observe sunspots through the telescope without risking eye damage. ( Galileo Galilei, The Institute and Museum of  The History of Science ).

Galileo's mechanical studies were deeply influenced by two historical precedents. The first was the investigative model of Archimedes, characterized by rigorously geometric analytical methods. The second was the detailed interpretative work of Archimedes's legacy performed by humanists with geometrical expertise, such as Federico Commandino and Guidobaldo del Monte. In his Mathematical discourses and demonstrations, Galileo inaugurated the science of the resistance of physical bodies. For the first time, strict methods were proposed for theoretically predicting the breaking point of bodies subjected to traction and of bodies to which weights had been applied. Galileo also made major contributions in the field of statics, through innovative analyses on the problems of equilibrium and the operation of simple machines. In hydrostatics, we should note his reconstruction of the method used by Archimedes to expose the craftsman who had sold the tyrant of Syracuse a crown in gold and silver alloy, passing it off as a crown of solid gold. And there are his ingenious reflections and demonstrations on the phenomena of floating IMSS - Multimedia Catalogue - Galileo and mechanics.




European Institute of Protestant Studies Interesting side notes on Galileo and the period of his wars with the Jesuits.


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