Galileo Galilei
(Pisa, February 15, 1564 - Arcetri, January 8, 1642)
 It 'was a physicist, philosopher, astronomer and Italian mathematician,

considered the father of modern science.
 "Philosophy is written in this grand book which stands continually open to our gaze
 (I mean the universe), but can not be understood unless you first learn to understand the language, and to know the characters,  I 'which is written.
 It is written in the language of mathematics, and its characters are triangles,
 circles, and other geometrical figures, without which it is humanly impossible to understand a word;
 without these one is wandering around in a dark labyrinth. '
 (Galileo Galilei, The Assayer, Chapter VI)
 His name is associated with important contributions in dynamic and astronomy
 including the improvement of the telescope, which allowed important astronomical observations
 and the introduction of the scientific method

(often called the Galilean method or experimental scientific method).
 Of primary importance was its role in the astronomical revolution and its support for the heliocentric system and the Copernican theory.
 Suspected of heresy and accused of trying to subvert the natural philosophy of

Aristotle and the Holy Scriptures,  Galileo was tried and condemned by the Holy Office,

 as well as forced, June 22, 1633,  abjuration of his astronomical concepts and to confinement

in his villa in Arcetri.
 This process was canceled 359 years later, October 31, 1992, by Cardinal Poupard
 who writes that the condemnation of 1633 was unfair and backward, to an undue admixture of theology
 and pseudo-scientific cosmology and Pope John Paul II, in his address to the participants
 at the plenary session of the Pontifical Academy of Sciences.


Youth (1564-1588)
Teaching in Pisa (1589-1592)
The Paduan period (1592-1610)

The telescope
In Florence
Around sunspots

The letters Copernican
Biblical exegesis and heliocentrism
The dispute with the Church's

The complaint of the Dominican Tommaso Caccini
Galileo in Rome
The controversy on the comets
Il Saggiatore
Letter to Francis Ingoli
Dialogue Concerning the Two Chief World Systems
The process, the abjuration and sentence
Discourses and Mathematical Demonstrations Concerning Two New Sciences
The last few years

An affectionate correspondence
After the death
Galilei's rejection of essentialism and science
The "language" mathematics
The scientific method
Experimental apparatus and measurement
Parabolic motions, circular motions and squaring the circle
The principle of inertia
The pendulum
The hydrostatic balance
Inclined planes, acceleration of gravity and energy conservation
The speed of light
Science and theology

Galileo Galilei and the art

Galileo and music


Youth (1564-1588)         

Galileo Galilei was born February 15, 1564 in Pisa,
The eldest of seven children of Vincenzo Galilei and Giulia Ammannati.
The Ammannati originating in the lands of Pistoia and Pescia, boasted prestigious origins:
a Thomas Ammannati (ca 1345-1396), was made a cardinal by Pope Clement VII in 1385,
while his brother Boniface (ca. 1350 to 1399) was awarded the purple in 1397 as a successor of Clement,
the antipope Benedict XIII, and as for James Ammannati Piccolomini (1422 - 1479),
Cardinal since 1477, was a humanist,
continuation of the Commentaries of Pius II and author of a Life of Galileo Galilei popes House
which has been lost.
It is understandable how Giulia Ammannati not lack to detect the difference in origins to Vincenzo
as the ancestors of her husband had belonged to the middle-class Florentine
Thomas remembers a Bonaiuti, which was part of the government of Florence after the expulsion of the Duke of Athens in 1343,
and Galileo Bonaiuti (1370 - ca 1450), medically known in his time and standard-bearer of justice,
whose tomb in the Basilica of Santa Croce became the grave of his descendants;
from Galileo Bonaiuti the family name was changed to Galilei.
But Vincent was born in Santa Maria a Monte in 1520, by which time his family had fallen and he
musician value, had to move to Pisa joining to need more money,
students for the profession of music commerce.
On July 9, 1563 Vincenzo rents a house in Via dei Mercanti in Pisa by Giuseppe Bocca while
among those with whom he was in business, stands the name of the patrician Jacopo della Seta Pisa,
member of the Wake.
Lute teacher and music theorist - had been part of the Florentine Camerata dei Bardi,
was in conflict with the classical tradition supported by his teacher Zarlino,
which attributed the harmony between all sounds the control of numerical proportions and
with his Discourse around Messer Opera Gioseffo Zarlino of Chioggia and the
Dialogue of early music and modern
had proposed to return to the monodic melody against the prevailing contrapuntal polyphony.
Of the other six children of Vincenzo and Julia, were some news of Peter Paul
of Virginia, born in 1573, Michelangelo, born in 1575, and Livia, born in 1578,
Like his brother Michelangelo, in Florence, where the Galilei family had returned in 1574.
The young Galileo made his first studies in Pisa under Muzio Tedaldi, customs officer of the city,
and Florence, first with his father, then a master of dialectics, and finally in the school of
convent of Santa Maria di Vallombrosa, where he took the habit of a novice up to the age of fourteen.

          Vincenzo, September 5, 1581, the son enrolled at the University of Pisa with

the intention to make him study medicine,  
as if to Galileo ripercorresse the tradition of his glorious ancestor and above
embark on a career that could reserve lucrative earnings;
Despite his interest in experimental progress in those years,
Galileo's attention was soon drawn to mathematics, which he began to study in the summer of 1583, advantage of the opportunity of knowledge at Florence

of Ostilio Ricci da Fermo, a follower of the school of mathematics Niccolo Tartaglia.
              Ricci was characteristic of the setting that he gave the teaching of           

   Ostilio Ricci

not an abstract science, but a science that would serve to solve practical problems
mechanics and engineering techniques.
It is likely to Pisa Galileo has also followed the physics courses required dall'aristotelico
Francesco Bonamico:
I testify the coincidence of arguments between the Juvenilia, Ostilio Ricci
notes of physics by Galileo sketched in this period, and the ten books of the De motu Bonamico.
During his stay in Pisa, which lasted until 1585, Galileo arrived at his first, personal discovery,
the isochronism of the pendulum swings.                 

And so, after four years, the young Galileo resigned to pursue further studies
of medicine at Pisa, and went to Florence,
where he developed his new scientific interests, dealing
              meccanicae of hydraulics; Courtyard of the University of Pisa                     

 Cortile dello Studio di Pisa

                        in 1586 invented a tool for the determination of the hydrostatic density of bodies:                  
describes the details in brief treatise The bilancetta, first circulated among his acquaintances
and published posthumously in 1644.
The influence of Archimedes and the teaching of the Ricci was also observed in his studies

on the center of gravity of solids, expressed in theoremata about centrum gravitatis solidorum, published only in 1638 in the appendix to the Speeches and mathematical demonstrations concerning two new sciences, and found a solution to the problem of the crown of Heron.
Meanwhile, Galileo tried a regular budget accommodation:
as well as private lessons in mathematics in Florence and Siena, in 1587 he went to Rome to ask
a recommendation to enter the University of Bologna to the famous mathematician Christoph Clavius, but to no avail, Bologna because they preferred to the chair of mathematics at Padova

Giovanni Antonio Magini.
At the invitation of the Florentine held in 1588 two lessons about the shape,

location and size of Dante's Inferno, defending the assumptions already made by Antonio Manetti on the topography of Hell until Dante imagined, in 1589, recommended by Cardinal Francesco Maria Del Monte, brother of the mathematician Guidobaldo, obtained from
Grand Duke Ferdinand I, a three-year contract to hold the chair of mathematics at the University of Pisa.


Teaching in Pisa (1589-1592)   

Pisa is the result of teaching the manuscript De Motu antiquiora,
which contains a series of lessons
in which he tries to give an account of the problem of the movement.
Basis of her research is the treatise, published in Turin in 1585,
Diversarum speculationum mathematicarum liber Giovanni Battista Benedetti,
one of the supporters of the physical
theory of '"surge" as the cause of "violent motion."
Although not known to define the nature of such an impetus imparted to the body, this theory,
prepared for the first time in the sixth century by John Philoponus and then supported by physicists

 in Paris, despite not being able to solve the problem, opposed to the traditional

Aristotelian explanation of the movement as a product of the medium in which the bodies

themselves move.
In Pisa, Galileo did not confine himself to scientific pursuits:
date back to this period his Considerations on the rate that will be followed up with Apostilles Ariosto:
it is scattered notes on sheets and notes in the margins on the pages of his books
Jerusalem and the Orlando Furioso where, while reproving the rate
"The shortage of imagination and the slow monotony of image and verse, what he loves nell'Ariosto
is not only the multimillion pleasant dreams, the rapid change his situation,

 the living elasticity of rhythm, but the harmonious balance of this, the coherence of the

 organic unity, despite the variety, Ghost poetic. " In the summer of 1591, the father Vincenzo passed away, leaving Galileo with the burden of keeping the whole family:
for the wedding of her sister Virginia, who married that same year, Galileo had to provide a dowry,
contracting of debts, as well as will have to do for the wedding of her sister Livia in 1601 and more

money will have to spend to help the needs of the large family of his brother Michelangelo.
Not enough the modest salary of sixty crowns a year, and in view of the expiry of his contract,
Galileo turned again influential friend Guidobaldo Del Monte, who recommended him to the

 prestigious University of Padova, where it was still vacant chair in mathematics after his death,

 in 1588, by Professor Giuseppe Moleti.
On 26 September 1592 the authorities of the Republic of Venice enacted a decree

of appointment, with a contract, extendable to four years with a salary of 180 florins a year.
On December 7, Galileo held in Padova introductory speech and a few days later began a training course to have a large following among students.
Will remain for 18 years, which will define "best them eighteen years of my age."


         The Paduan period (1592-1610)   

In the dynamic environment of the University of Padova, also a result of the climate of relative religious tolerance ensured
from the Republic of Venice, Galileo conducted cordial relations with personality orientation
philosophical and scientific away from her, as the professor of natural philosophy Cesare Cremonini,
strictly Aristotelian philosopher.
He also attended the learned circles and environments Senate of Venice,
where he made friends with the noble Giovan Francesco Sagredo, Galileo will make the protagonist of his
Dialogue Concerning the Two Chief World Systems, and Paolo Sarpi, theologian and expert also in mathematics and astronomy.
It is contained in its letter dated 16 October 1604 the friar served formulation
the law of falling bodies:

"The spaces passed by the natural motion proportione be in double time,
and consequently the spaces passed in times
be equal as ab unitate, et alia.
And the principle is this:
that the mobile natural vadia growing speed with that which deviates proportione
from the beginning of its motion;
v. g., falling from the grave to term for the line abcd,
suppose that the degree of speed that has to c to the degree

      of speed  
it had in
b be the distance as the distance ca ba,
and so in consequence of having degree
speed greater than at
second that is greater than the radius of approx.
ca '

   Paolo Sarpi

Galileo was required to Padova lessons mechanics since 1598:
his Treatise of mechanical, printed in Paris in 1634, should be the result of his courses,
that had originated from the mechanical issues of Aristotle.
Unlike the greek philosopher, for which there are two motions 'natural', that is spontaneous,
dependent on the substance of the bodies, one directed downward, typical of the bodies of land

and water, and one upward, typical of bodies of air and fire, for Galileo any body tends to fall down,
in the direction of the center of the Earth.
If there are bodies that rise upwards is because the medium in which they are located,

having a higher density, pushes them up, according to the well-known principle already

expressed by Archimedes:
the law of falling bodies Galileo, regardless of medium, is therefore valid for all bodies,
whatever their nature.
At the University of Padova Galileo rigged, with the help of Marcantonio Mazzoleni,

an artisan who lived in the same house, a small laboratory in which experiments performed and manufactured instruments sold to supplement their income.
It is the machine of 1593 to bring the water to a higher level, for which he obtained a patent from the Venetian Senate twenty years for its public use.
Also gave private lessons, his students were, among others, Vincenzo Gonzaga,

Prince of Alsace John Frederick,
future cardinal Guido Bentivoglio and Federico Cornaro and received salary increases:
received annually from 320 florins in 1598, passed the 1,000 achieved in 1609.
Around 1594 wrote two treatises on fortifications, the Brief Introduction
military architecture and fortification of the Treaty;
around 1597 Galileo built a compass, which he described in the pamphlet The operations of the
geometric compass et military, published in Padova in 1606 and dedicated to Cosimo II.
The compass tool was already known and, in different forms and for different purposes, already in use, or Galileo claims due special merits for his invention:
but the Milanese Baldassarre Capra (ca 1580 - 1626), a pupil of Simon Mayr, in his paper
Usus et fabrica circini cuiusdam proportionis, accused him of having plagiarized a previous invention.
On April 9, 1607 Galileo overturned the charges Capra, obtaining the condemnation of the Reformers Study Padova and published in its turn a defense against the calumnies et impostures of

Belshazzar Capra.

La Supernova di Keplero      
                                                                                                            Giovanni Keplero



Capra had already argued with Galileo in 1604 about a "new star", given on October 9 by the

astronomer between 'Ilario Altobelli, which he informed Galileo.
Bright was also observed on October 17 by Kepler, who made it the subject of a study,
De Stella nova in pede Serpentarii, so that the star is now known as Kepler's Supernova.
Of this astronomical phenomenon Galileo held three lectures, the text of which is not known, but his arguments against wrote the Aristotelian Antonio Lorenzini, probably at the suggestion of

Cesare Cremonini,
and also intervened against both the Goat.
From them we know that Galileo had interpreted the phenomenon as evidence of the mutability of the heavens, on the grounds that, not presenting the "new star" no change of parallax, it should be beyond the orbit of the Moon.
Galileo responded to criticism with a scathing book where, hiding under the pseudonym of de

Cecco Ronchitti, defenses the validity of the parallax method to determine the distances,

or at least the minimum distance, also of objects
only visually accessible to the observer, which are celestial objects.
The appearance of the supernova created great concern in society and Galileo did not hesitate

 to take advantage of time to prepare, on commission, personal horoscopes for the price of

60 pounds Veneto.
Moreover, in the spring of the same year, 1604, Galileo was put on trial by the Inquisition
Padova as a result of a complaint by one of its former employee, who accused him precisely
of making horoscopes and have argued that the stars determine the choices of man.
The process, however, was strongly blocked by the Senate of the Venetian Republic and the file
investigation was covered up, so that it never got any news the Roman Inquisition,
that the Holy Office.
It does not appear that, in the years of controversy over the "new star", Galileo had already publicly pronounced in favor of the Copernican theory: it is believed that although he was deeply convinced Copernican thought of not having even evidence strong enough to obtain the consent of

 the invincibly universality of scholars.
He had, however, privately expressed their adherence to Copernicanism

as early as 1597:                
in that year, Kepler, who had recently published his   
Prodromus dissertationum cosmographicarum, wrote of being

Copernican for many years and have evidence
(But not exposed)
in support of
Copernicus, "praeceptoris us."


                     The telescope      

 Nicolaus Copernico

The evidence in support of the Copernican theory could be offered only after meticulous observations
and the instrument that would have made possible had just been invented.
Optics were employed Giovanni Battista Della Porta in his Magia naturalis (1589) and
De refractione (1593), Nicolaus Copernicus
and Kepler in Vitellionem For paralipomena, 1604, works from which it was possible to
reach the construction of the telescope:
but the instrument was built for the first time, regardless of those studies in the early

seventeenth century
Lippershey by the craftsman Hans, also known as Johann Lippershey or Lipperhey (Wesel, 1570 - Middelburg, September 1619) a German optician naturalized Dutch.
Galileo had news, and maybe even a specimen, in the spring of 1609 and was rebuilt and

strengthened empirically August 21 introduced him as his invention to the Venetian government that, appreciating the '' invention ', doubled the salary and offered him a contract lifetime of teaching.


Il Sidereus Nuncius             

For the rest of that year, Galileo undertook in astronomical observations:
gained more precise information on the lunar mountains, on the composition of the Milky Way and discovered the four largest satellites of Jupiter.
The new findings were published March 12, 1610 in
Sidereus Nuncius
a copy of which Galileo sent the Grand Duke of Tuscany, Cosimo II, who had been his pupil, together with a copy of his telescope and the dedication of the four satellites,
baptized by Galileo at first and then Cosmic Sidera Medici Sidera
("Medicean Planets").
Clearly the intention of Galileo to earn the gratitude of the Casa Medici, most likely not only
for the purposes of its intent to return to Florence, but also to obtain an influential protection in view of the presentation, before an audience of scholars, those innovations, which certainly would not fail to raise controversy.
On 5 June 1610 the Florentine government communicated to the successful employment as a scientist
"Primary Mathematics of the University of Pisa and Philosopher to the Grand Duke senz'obbligo to read and reside either in the studio or in the city of Pisa, and the salary of a thousand crowns a year, Florentine money. "
Galileo signed a contract on July 10 and September reached Florence.
Here he took care to give to Ferdinand II, son of the Grand Duke Cosimo, who had the best optical lens
made in his workshop organized when he was in Padova, where, with the help of master glassmakers of Murano packaged "Glasses" more perfect and in such quantity to export, as he did with the telescope voter mandate Cologne which in turn lent it to Kepler, who made good use and, grateful, he concluded his work Narratio de observatis if a quartet from Jovis satellibus erronibus of 1611, as saying:
"Vicisti Galilaee," acknowledging the truth of the discoveries of Galileo.
The young Ferdinand or someone else broke the lens, and then Galilei gave him

something less fragile:
a magnet "armed", that is wrapped in a sheet of iron, when properly positioned,
which increased the force of attraction in such a way that, yet weighs only six ounces the magnet
"Raised fifteen pounds of wrought iron in the form of tomb"
When transferring Galilei in Florence left his partner, the Venetian Marina Gamba (1570-1612)
known in Padova, by whom he had three children:
Virginia (1600-1634) and Livia (1601-1659), never legitimate, and Vincenzo, who recognized in 1619.
Galileo in Florence gave her daughter to her grandmother Livia, who already lived with the other daughter Virginia, and left his son Vincenzio in Padova in the care of his mother and then,

after the death of this, such a Marina Bartoluzzi.
Later, that became difficult coexistence of the two girls with Giulia Ammannati
Galileo ushered the girls in the convent of San Matteo in Arcetri (Florence), in 1613,
forcing them to take the vows made as soon as the rituals sixteen Virginia took
the name Sister Maria Celeste and Livia to Sister Arcangela, and while the first resigned
his condition and remained in constant correspondence with his father,
Livia never accepted the imposition father.

In Florence 
The publication of Sidereus Nuncius appreciation but also caused several controversies.
In addition to the charge that he possessed, with the telescope, a discovery that did not belong,
was put in doubt the reality of what he claimed to have discovered.
Both the famous Padovan Aristotelian Cesare Cremonini, both the mathematical

Bologna Antonio Magini,         
that would be the inspiration for libel antigalileiano.
Short pilgrimage against Nuncium Sidereum written by Martin Horký,
while accepting the invitation of Galileo
to look through the telescope that he had built, believed that he saw no
supposed satellite of Jupiter.
            Only later did the Magini changed his mind and with him the

Vatican astronomer  Christoph Clavius,
which initially took the view that the satellites of Jupiter discovered by

Galileo were only illusion produced by the lenses of the telescope.                      

 Cesare Cremonini

             Cesare Cremonini              
It was this latter objection difficult to refute in 1610-1611, due to both the low quality
of the optical system of the first telescope of Galileo, is the assumption that the lens could
not only improve vision but also distort it.
A very important support was given to Galileo to Kepler, who, after an initial skepticism and once built a
telescope sufficiently efficient, verified the existence of actual satellites of Jupiter,
published in Frankfurt in 1611 the Narratio de observatis if a quartet from Jovis satellibus erronibus.
As the Jesuit professors at the Collegio Romano were among the most scientific authorities of the time,
March 29, 1611 Galileo went to Rome to present his findings.
He was received with full honors by Pope Paul V, the cardinal Francesco Maria Del Monte

and Maffeo Barberini, and Prince Federico Cesi, who enrolled in the Academy of the Lincei,

he founded eight years earlier.                   
On April 1, Galileo could already write to the ducal secretary Belisario Vinta the Jesuits             
"Having finally know the truth of the new Medicean Planets, have made two months
here in continuous observations, which are continuing, and the aviamo

found with mine, and respond quite correct. " Galileo, however, at that time

       did not know that the enthusiasm with which

he was spreading   and defending their findings and theories would

   have provoked resistance and suspicion precisely in the ecclesiastical sphere.              
On April 19, Cardinal Robert Bellarmine instructed mathematicians Vatican approntargli of a report on the new discoveries made by "a mathematician for mezo of an instrument called cannon ochiale overo "and Congregation of the Holy Office, the following May 17, precaution churches of the Inquisition Padova
if it had never been opened, locally, any process against Galileo.                     


Evidently, the Roman Curia was already beginning to glimpse the consequences "could have
these unusual developments in science on the general conception of the world and thus, indirectly,
on the sacred principles of traditional theology. "



Around sunspots   

In 1612 Galileo wrote his Discourse on the things that are in the water, or in the move
in which relying on the theory of Archimedes showed, against that of Aristotle, that the bodies floating or
sink in water depending on their specific weight not of their shape, causing the response of the controversy          
Apologetic discourse of speech around the letters of Galileo Galilei and Aristotle Florentine

Ludovico delle Colombe.
On October 2, the Pitti Palace, attended by the Grand Duke and the Grand Duchess Cristina, and Cardinal Maffeo Barberini, then his great admirer, gave public experimental demonstration of the assumption, definitively refuting the Doves.
Galileo also mentioned in his speech to sunspots, which he claimed to have already observed in
Padova in 1610, but did not give notice:
wrote again the following year, the Story and demonstrations around the sunspots and their accidents,
published in Rome by the Lincei, in response to three letters of the Jesuit Christoph Scheiner that
addressed at the end of 1611 to Mark Welser, announced his discovery of sunspots.
Apart from the question of the priority of discovery, Scheiner claimed erroneously that the stains consisted of swarms of stars rotating around the Sun, while Galileo considered the fluid matter belonging to the same surface of the Sun and rotating around it Roberto Bellamino precisely because of the rotation of the star.
The astronomical discoveries corroborate the heliocentric theory:
the existence of the phases of Venus and also those of Mercury, also observed by Galileo,

showed that those planets revolved around the Sun
Galileo, by writing to Giuliano de 'Medici on 1 January 1611, stated that "Venus necessarissimamente
turns around the sun, as well as Mercury and all the other planets, which is well believed by all Pittagorici,
Copernicus, Kepler and me, but not sensibly felt, as now in Venus and Mercury. "
On May 12, 1612 to Federico Cesi reiterated his Copernican view writing as the Sun was talking
"In itself in a lunar month with similar revolution all'altre of the planets, that is, from the west to the east
around the poles of the ecliptic:
which I doubt he wants to be the new funeral or rather the ultimate and final judgment of pseudofilosofia,
having already seen signs in the stars, the moon and the sun;
and I'm waiting to see great things arise from Peripato for maintaining the immutability of the heavens,
which I do not know where it can be saved and hidden. "
In March 1614 he carried out studies on the method for determining the weight of the air, calculating its minimum weight However, different from zero.
The air is in fact about 760 times lighter than water: the scholars of the time, on the contrary,

 they thought, no experimental support, that the air had no weight.

          The letters Copernican             

The so-called "Copernican letters" are those written by Galileo to defend the Copernican system
and to clarify his conception of science.
The letters are four: one to Father Benedetto Castelli, two Monsignor Pietro Dini, one at a Grand Duchess mother Christine of Lorraine.

 Biblical exegesis and heliocentrism      
Convinced of the correctness of the Copernican cosmology, Galileo was well aware of course
that this did not fit with different statements of the Bible and the Church Fathers,
that show instead a geocentric universe.
And because the Church saw the Holy Scriptures inspired by the Holy Spirit,

the heliocentric theory could be accepted, at most, only as a simple mathematical model without any relevance to the real position of celestial bodies.
Right under this condition, the book of Copernicus, De revolutionibus orbium coelestium
had not yet been condemned by the ecclesiastical authorities.
Galileo, Catholic scientist, believes he can solve the problem by reversing the current solution,

then: the Copernican theory is true, are the Scriptures to be written, when appropriate,
no correspondence with reality, using a language that expresses a useful model and
understandable to humans.             
 On 21 December 1613 it wrote to the student and friend

             Benedictine Benedetto Castelli,                         
mathematical Copernican player then in Pisa, that "if good Scripture can not err,
may nevertheless sometimes err no de 'its interpreters and exhibitors,

                Benedetto Castelli in various ways:
among which one would be very serious and frequent, when they

wanted to stay forever in the pure meaning of the words, because then you apparirebbono not only different contradictions,  

 Benedetto Castelli

but still serious heresies and blasphemies;
then it would be necessary to give God and feet and hands and eyes, and no less with physical and human as anger, repentance, hatred, and yet sometimes the oblivion of things past

and ignorance of the future »


It must be then that many propositions of the Bible are accommodated to
be understood by simple illiterate:
between these compromises must be within the well-known episode of the request
Joshua God to stop the sun to prolong the day:
Joshua stops the Sun

  Giosuè ferma il sole

       (Gustave Dorè)

"I say that this site shows us clearly the falsity and impossibility of                          

Aristotelian and Ptolemaic system mundane,                  
and the meeting well s'accomoda co 'the Copernican. "                    

He explains that if Galileo s'interpretasse the letter of the passage, it would be that according to the Ptolemaic system, stopping the sun, the day would not be extended but, on the contrary, shortened:
"Since, therefore, absolutely impossible in costituzion of Ptolemy and Aristotle stop the motion of the Sun and lengthen the day, even as the Scripture says have happened, or should, therefore, that the movements they be not ordered as does Ptolemy, or should alterar the meaning of words, and say that when Scripture says that God stopped the sun, it meant that stopped 'the first piece of furniture, but that the ability to sit of those who are barely capable of comprehending the rise and 'the setting of the sun, she said the opposite of what he said, speaking to men sensible. "
On the contrary, by adopting the interpretation heliocentric Universe, to prolong
'Space and' the time of day lighting, it was enough that he stopped the sun,
com'appunto them sound the words of the sacred text. "
Similar considerations played Galileo in Florence letters to Monsignor Piero Dini
and to the Grand Duchess Christina of Lorraine, which aroused concern in conservative
for innovative ideas and the polemical character and the courage with which the scientist suggested that
some passages of Scripture were reinterpreted in the light of the Copernican system.
There is a famous phrase: "understood by a person constituted in ecclesiastical eminent degree,
the intention of the Holy Spirit be to teach us how to go to heaven, not how the heavens vadia "
normally attributed to Cardinal Baronius.

The dispute with the Church's    

In the Church, there were two more orders guardians of scientific and theological
the Jesuit Order, which boasted in its ranks many mathematicians and physicists,
and the Dominican faithful to doctrine of St. Thomas, and therefore suspicious of anything new that metaphysical could in any way oppose.
While the Jesuits, in the first instance, it showed open face of the new astronomical discoveries,
the Dominicans were the strongest opponents of Galileo, denouncing the dangers that the

 theories of Galileo could make to the traditional doctrine of the Church. Trial of Galileo
However, the attitude of the two orders in against Galileo will spill two decades later:

the Jesuits in 1633 will be to denounce the Dialogue Concerning the

 Two Chief World Systems, involving the allegations also the Dominicans who

               had authorized the publication of the work.
On 1 November 1612, the Dominican Niccolò Lorini denounced in

                    a sermon given in the

  Processo a Galilei

convent of San Matteo Florence theories of Copernicus, which not even know the name well, except apologize Nov. 5 with a letter Galileo, in which he wrote that it did not accuse the scientist,

 protected by the Grand Duke, but               
"Not to strain opinion one dead, being by others started the argument, I said two words to be alive,

 and said, as I say, that the opinion of quell'Ipernico, or as you call it, it appears that

precludes the Holy Scriptures.                   

The complaint of the Dominican Tommaso Caccini   


Two years later, December 21, 1614, from the pulpit of Santa Maria Novella in Florence,

the Dominican friar Tommaso Caccini (1574 - 1648) launched against some modern mathematicians, and in particular against Galileo, the prosecution to contradict the Holy Scriptures with their

astronomical concepts inspired by the theories of Copernicus.
His sermon ended with a guessed pun, taken from the Acts of the Apostles:
"Viri Galilaei, quid statis aspicientes in coelum?». To this was added the still Lorini,
by sending the Cardinal Paolo Emilio Sfondrati, prefect of the Congregation of the Index in Rome
February 7, 1615, on behalf of the whole community of the convent of San Marco in Florence, a copy
the letter of Galileo to Castelli.
The Lorini noted that the letter, which claimed be his "happened to be in the hands"
and described as "a writing, the current here in the hands of all, made by those who ask Galileisti"
contained "many propositions that seem suspicious or reckless or."


The Letter of the Foscarini       

Tommaso Caccini arrived in Rome, March 20, 1615, and in the palace of the Holy Office, in front of the Cardinals Bellarmine, Galamini, Millini, Sfondrati, Taverna,

Verallo and Zapata denounced Galileo as a supporter
the Earth's motion around the Sun, and also because the brother Ferdinando Ximenes had heard
by some disciples of Galileo that "God is not otherwise Substance, but damn, God is sensitive,
because in him are under divinali, really, the miracles that are said to be made from 'Saints
are not true miracles. " Required of the Catholic faith of Galileo, Caccini replied mischievously
that he "was held by many good Catholic, as is required for other suspect in matters of faith,
because they say, be very close to that between Paul served, so famous in Venice for his impiety,
et yet to say that this pass letters between them. " Meanwhile,
 Naples had been published the book of the Carmelite theologian Paolo Antonio Foscarini

Letter opinion on the de 'Pittagorici and Copernicus, dedicated to Galileo, Kepler and all
academic Lincei, which intended to grant the biblical passages with the

Copernican theory interpreting
"So that contradicano not at all."
But you could give Bible and Copernicus did not believe Cardinal Robert Bellarmine,

 former judge, as the Sfrondati and the Taverna, in the process of Bruno, which April 12
wrote to Foscarini
"First, I say that V. P. et Signor Galileo do prudently to be content to speak ex suppositione
and not absolutely, as I have always believed that Copernicus spoke habbia. Why say,
which assumed that the Earth moves and the Sun is stationary you save all

appearances better than to put eccentrics and epicycles, that is fine, and has no danger,

 and that is enough to mathematician:
but really want to say that the Sun is at the center of the world and only turned himself in
without running from east to west, and that the Earth is in the 3rd heaven and turns with great speed
around the Sun, it is very dangerous not only to irritate the philosophers and theologici school
but yet to harm the Holy Faith by rendering Holy Scripture false
Second, I say that, as you know, the Council prohibisce writings against the

Common consent of 'the Holy Fathers;
and if the P. V. I do not say they only want to read the Holy Fathers, but like modern commentaries

 on Genesis, Psalms, on Ecclesiastes, and Joshua, he will find that all agree in exhibiting

at literam that the sun is in the sky and turns
around the Earth with great speed, and that the Earth is farthest from the sky and lies in the

center of the world, still.
Consider hora her, his prudence, whether the Church can support you give to
Scripture a sense contrary Fathers et alli them all exhibitors Greek and Latin [...]
Third, I say that when we Fusse demostratione true that the sun is at the center of the universe

and the earth in the third heaven, and that the sun does not circle the earth but the earth

around the sun it would be necessary allhora with great circumspection
unfold in the scriptures that seem contrary, and rather to say that we do not understand

that it is false to say that which proves. But I do not believe that there is such dimostratione

since that I have not shown:
nor is the show that istesso supposed that the sun is at the center and the earth in the sky, to be saved appearances, and show that indeed the sun is at the center and the earth in the sky, because the first dimostratione I think there might be, but the second I have great doubt, and in case of doubt one must not leave the Holy Scripture expounded by 'Fathers'
In fact, the Foscarini will, for a short time, imprisoned the following year and his Letter prohibited.
Meanwhile, the Inquisition settled, November 25, 1615, to examine the Letters on Sunspots
Galileo and decided to come to Rome to defend himself in person, supported by the

Grand Duke Cosimo:
"The mathematician Galileo in Rome" - Cosimo II wrote to Cardinal Scipione Borghese
- 'Et comes spontaneously to give an account of himself to some charges, or rather lies,
that have been placed by 'his followers. "


        Galileo in Rome     

The ambassador of the Medici Court, Piero Guicciardini, excellent knowledge of the environment Roman was well aware of the dangers looming on the scientist: "I know that some friars of St. Dominic,
which have largely in the Holy Office, and others, have the evil spirit upon him;
and this is not the country to come to play on the moon, nor of the will, in the century runs,
support either bring new doctrines. "
On 24 February 1616, requested by the Holy Office, theologians unanimously answered that the proposition "The sun is the center of the world and of all property of local motion," was "foolish and absurd in philosophy, and formally heretical, "as it contradicted many passages of Holy Scripture

and the opinions of Fathers of the Church that the proposition

"the Earth is not the center of the world, nor immovable, but from self moves also diurnal motion,

 "was" reprehensible in philosophy with regard to theological truth
at least erroneous in faith. " As a result, on February 25 the Pope ordered Cardinal Bellarmine
"Summon Galileo and admonish him to abandon the said opinion, and if he refused to obey,
Father Commissioner, before a notary and witnesses, to make him abandon the commandment

 of all that doctrine and not to teach, not to defend it and not treat it.

" A document dated 26 February attest happened the precept of Bellarmine and obedience

 while Galileo was made on March 5 public the decree of the Congregation of the Index prohibiting

 and suspended "respectively writings of Nicolaus Copernicus' De revolutionibus orbium coelestium,
of Didaco Stunica of Job and Paolo Antonio Foscarini, a Carmelite friar. " 
At the sight of the defeat of the followers of Copernicus' theories,

                     seems unjustified   satisfaction
shown by Galileo, writing to Picchena, March 6, that the complaint by Caccini
"Has not been matched in the Holy Church, to only those books are banned them
which ex professo wanted to say that she is not divided by Scripture.

Villa Medici, The work of Copernicus himself will rise 10 verses

                           of the preface to Paul III,            

 Roma Vills Medici

Rome where not mention the opinion that this doctrine repugni to the Scriptures, and,
as mean, you could raise a word here and there, where he calls 2 or 3 times, the land sidus [...] I,
as from the nature of shop you can see, I've no interest or point I'd be busy, if, as I said,
my enemies I will havessero interfered [...] a saint haverebbe the Treaty or more
reverence or with greater zeal towards the Holy Church: which perhaps have not made my enemies,
who have not forgiven machine, to slander et every diabolical suggestion [...]
know V. S. with as much coolness and temperance I is governed. "
Instead the ambassador Guicciardini did not find him or phlegmatic or tempered
March 4 if you already wrote to Cosimo II Galilei "s'infuoca in its openioni, has extreme passion inside,
et little fortress et caution to know how to win, "and prophetically understood that Galileo
"Does not see et not see what should be, so that, as it has done since a hora, there remain inside deceived, et take him in danger. "
Galilei was still in Rome for three months to discuss and try to convince of his opinions,
so that Guicciardini wrote to May 13 Picchena, that Galileo "has a fixed mood of the friars scaponire
et struggle with who he can not lose if you do not [...] be the absente of this country we would
of great benefit & service. "
It so happened that rumors spread that Galileo had recanted his views of Copernicus,
so that the scientist, before finally returning to Florence, he felt the need to ask,
May 26, 1616, a statement autograph Cardinal Bellarmine thus:
"We Roberto Cardinal Bellarmine, havendo understood that Mr. Galileo Galilei is slandered
or charged with havere abjured in our hands, et yet to have been for this penitenziato of penances healthy et being sought for the truth, say that the said Mr. Galileo has not abjured in our hands
or other here in Rome, no less than any other place we know, any of its opinion or doctrine,
neither healthy nor penances not even received the other lots, but he was denounced in the Declaration
made by Our Lord [Paul V] publicata by the Sacred Congregation of the Index, which is contained
that the doctrine attributed to Copernicus, that the earth moves around the sun and that the sun is in
center of the world without moving from east to west, is contrary to Holy Scripture, and therefore not
can be defended or held. And in witness whereof this habbiamo writing and signed by our own hand,
this day May 26, 1616. The same as above, Roberto Cardinal Bellarmine. "
The cardinal insisted that the prohibition of supporting Copernicus, perhaps the honors and
courtesies received in spite of everything, Galileo did fall into the illusion that he was allowed to
that it was forbidden to others, "the contradictions and distinctions and tradeoffs born during the
first process is the source of future complications of the second trial of Galileo. "         


The controversy on the comets  

Orazio Grassi: De tribus cometis
However, Galileo did not answer the De situ et contra quiet Terrae Copernici systema disputatio the
Secretary of the Congregation of Propaganda Fide Ingoli Francis had sent in January
previous refutation of heliocentrism, based on the "modern" model of Tycho Brahe:
sign that the censorship of the Holy Office had recommended Galileo effect and prudence,
desist from which, however, eight years later, when it considers erroneously that

 the cultural climate had changed.
In November 1618 three comets appeared in the sky, that attracted the attention and stimulated

 the studies astronomers across Europe. Among them, the Jesuit Orazio Grassi,

 a mathematician at the Collegio Romano, held a successful lesson that was widely reported, the astronomical Disputatio de tribus cometis years
with it, based on some direct observation and a logical-school he supported the hypothesis

 that comets were bodies located beyond the "heaven of the Moon"
and used to validate the model of Tycho Brahe, according to which the Earth is at the

center of the universe, with the other planets in orbit around the Sun instead, against the

heliocentric hypothesis.
Galileo decided to respond in defending the validity of the Copernican model.

 Answered in an indirect way, through the written discourse of the comets of his friend and disciple,

 Mario Guiducci, but in which the master's hand was certainly present. Galileo argued in its reply
erroneously that comets were celestial objects, but pure optical effects produced by sunlight
elevatisi of vapors from Earth, but also indicated the contradictions of reasoning Fat
and its erroneous deductions from the observations of comets with the telescope.
The Jesuit responded with a paper entitled Libra astronomical ac philosophica,
signed with the pseudonym Lothario Sarsi anagrammatico of direct attack

Galileo and Copernicus. 

Galileo felt so compelled to respond directly, only in 1622 the treaty was ready Basic Books.
Written in the form of a letter was sent in October 1622 examination of academic Lincei,
which approved it: dedicated to Galileo academician and teacher of the Pope Room Virginio Cesarini,
after having been given the imprimatur by the Dominican theologian Nicholas Riccardi,

 was published in May 1623 in Rome.
On August 6, after the death of Pope Gregory XV, under the name of Urban VIII ascended

the papal throne Maffeo Barberini, For years a friend and admirer of Galileo.

It seemed that a new era and promising to be opened, "the hope rises again,
that hope which was almost completely buried. We are about to witness the return of the precious
know from long exile in which he had been forced, "wrote Galileo to papal nephew

Francesco Barberini. But mistaken.



Galilei: Il Saggiatore       

Against Libra astronomical ill-chosen title by Grassi, because he derived from the mistaken
opinion that comets had appeared in the constellation Libra,
when in fact it had been observed that in the Scorpio, 
Galileo brilliantly exercised his irony in naming his answer, to highlight its accuracy
compared to the coarseness of the arguments of Fats, Basic Books,
in which, with exquisite balance and right you ponder the things contained in Pound,

wanting also to imply that the empirical observations be measured
with a precision instrument such as the tester, which is there to measure the Assayer
the weight of gold dust and not by the pound, the imprecise and rough scales.

   In his work, the self-styled Lothario Sarsi argued his demonstrations by bringing eggs,    slingshots,

 Il Saggiatore

Babylonians, topics on which Galilei expressed himself thus claiming the superiority of observations
empirical arguments on unproven "If Sarsi wants me to believe that Babilonii cocesser
the eggs with fast turn them in the sling, I believe, but to us this is not the case [...]
Now we do not miss eggs or slings, or strong men that the tadpole, and while not cuocono [...].
And since we do not miss anything but be of Babylon, therefore, be the Babilonii causes

 dell'indurirsi eggs, and the attrition of the air. "
The Assayer, however, remains a work wrong, because it develops a theory of comets

 without foundation.
On the positive side, there are hints of correct scientific solutions, such as the demonstration that the heat is not developed from mere movement of bodies, but by the friction of the medium, or as considerations adherence and water on the bodies, or the controversy sull'improprio use of common language big, small, near, far - in an area that should be strictly scientific.
Of particular importance in the book is the claim - polemic against the fat that was invoked
the authority of the masters of the past to ascertain the truth in matters of natural
according to which 'Philosophy is written in this grand book that continually
we are open before in my eyes (I mean the universe), but can not be understood unless you first

learn to understand the language, and to know the characters, it 'which is written. It is written in the language of mathematics, and its characters are triangles,
circles and other geometrical figures, without which it is humanly impossible to understand a word;
without these one is wandering around in a dark labyrinth. "


Letter to Francis Ingoli  

 On April 23, 1624 Galilei arrived in Rome to pay homage to the pope and snatch the granting of tolerance of the Church against the Copernican system, but in the six hearings granted to him by

Pope Urban VIII
not obtained from these no definite commitment in this sense: as he wrote on

June 8 to Federico Cesi, Cardinal Hohenzollern had spoken of the Copernican theory with

 the pope, who had answered
"How are all the heretics of his opinion and have it for most certain and, therefore, is to go very
cautious in coming to any determination. " In any case, the Church "had damned nor was it for
dannarla for heretical, but only for rash. "
With no insurance but with the vague encouragement that came from having been honored

by Pope Urban that granted a pension to his son Vincenzo - Galileo thought he could finally answer,
In September 1624, the Disputatio Francis Ingoli.       
Galileo knows he can not afford, with the powerful secretary of the Congregation of Propaganda Fide
and for his past, no open irony:
prudently, pressed so did not want to "support the position that has already been declared for suspect and repugnant "to the doctrine of the Church, and adds that" a confusion of heretics,
between those who feel the most cry all be of the opinion of Copernicus'
will demonstrate to them that "we Catholics not for lack of natural speech [...]
remain in the old certainty taught by 'sacred authors,

but the reverence that we bring to  the scriptures. "   

 Urbano VIII

This reverence, according to Galileo, however, should not prevent a Catholic to understand

and explain correctly the problems of astronomical sciences and natural so that those heretics Copernican "will tax us for men in our constant oppenione, but not for blind or ignorant

dell'umane disciplines. " Urban VIII
Made formal homage to Catholic orthodoxy, in its reply Galileo will refute the arguments
anticopernicane dell'Ingoli without proposing that astronomical model,

or to respond to theological arguments:
so, the argument that the center of the universe is the place "lower end" and must be occupied

by the Earth because this is the body "more crass" than any other celestial body,

Galileo argues that there is in the universe one place lower, but as many as the centers of each body: "we Aremo University of world many centers and many places upper and lower those globes worldly

and orbi that around at different points will radiate ».
As for the idea that the Earth is the most "large intestine" of the heavenly bodies,
"Neither I nor you know, and we can not definitely know," since no experience proves it.
These allegations of a multiplicity of centers and the well-known passage: "It is still undecided
(And I think will always be between the humanities) if the universe is finite or infinite well [...]
My mind is not known accommodate conceive neither finite nor infinite, "did discuss the
scholars on the real opinion had by Galileo. It is possible that Galileo, knowing the fate
Bruno suffered from a few decades earlier and that of De revolutionibus Copernicus - and, of course,
his own story, later, in 1633 - has been pushed "to practice the virtue of prudence.
Giordano Bruno is not what he never mentioned, either in written or in the letters.
However, it is also possible that this problem, like those of cosmology in general and also of

celestial mechanics, he had a great interest for him. "
In the Letter Galileo states for the first time what will be called the principle of Galilean relativity:
the common objection brought by supporters of the immobility of the Earth, consisting of observation
that the serious fall perpendicularly on the surface, rather than obliquely, as apparently
should happen if the earth moved, Galileo responds bringing the experience of the ship in which,
it is in uniform motion or is stationary, the phenomena of falling or, in general, of the motions of the bodies contained in it, occur in exactly the same way, because "the universal motion of the ship,
being communicated to the air and all the things contained in it,
and not contrary to the natural inclination of those in their indelibly is preserved. "


      Dialogue Concerning the Two Chief World Systems   

In that same 1624 Galileo began his new job, a dialogue that
comparing the different views of stakeholders, would allow him to expose the various current theories
on cosmology - and therefore also the Copernican - without showing personal commitment
in favor of any of them.
Reasons of health and family prolonged the preparation work:
had to take care of the large family of his brother Michelangelo, while his son Vincenzo,
graduated in law at Pisa in 1628, married the following year with Sestilia Bocchineri, sister of

Geri Bocchineri, one of the secretaries of Duke Ferdinand, and Alessandra, who will have some

 part in the last years of the life of our.
To fulfill the desire of his daughter Maria Celeste, a nun in Arcetri, to have closer,
rented a cottage near the convent "The Jewel."
It was expected that the dialogue, the title should have been The ebb and flow,
was published in Rome by the Academy of the Lincei and Galileo, completed the work

 in January 1630, went there in March to get the ecclesiastical imprimatur.
Departed from Rome on June 26, with insurance assessors, the Dominican Nicholas Riccardi

and Raffaello Visconti, approved for printing with few substantial changes.
On 1 August, however, died Federico Cesi, the patron of the Accademia dei Lincei
and this declined to publish his work, so he decided to publish Galileo in Florence:
here quickly got permission from the Dominican Giacinto Stefani, but also needed permission

 from Rome, that was slow in coming.
Finally, in July 1631, Father Riccardi sent the inquisitor of Florence
permission to print a draft preface and the order to change the title on the expected flow
and ebb this title, recalling what Galileo saw the proof of the correctness of the
Copernican system was changed in Dialogue of Galileo Galilei Lynceus, where he congresses

of four days, they talk on the Two Chief World Systems, Ptolemaic and Copernican, and the work

could be published February 21, 1632 in Florence.



The two main systems are the Ptolemaic and the Copernican  


Galileo thus excludes from discussion the hypothesis recent Tycho Brahe - three are

the protagonists of the dialogue:
two are real people, friends of Galileo, and which was already dead, the

Florentine Filippo Salviati (1582-1614) 
and the Venetian Gianfrancesco Sagredo (1571-1620), in whose house pretending held

conversations, while the third, Simplicio, calls in the name of a well-known, ancient


 of Aristotle, in addition to imply his simplicity science.
He is a supporter of the Ptolemaic system, while the opposition is supported by the

Copernican Salviati, performing a function as neutral as the Sagredo, however, ends up

who sympathize with the hypothesis Copernican.
Dialogue takes place in four days: unfounded or insufficiently In the first, 


 is criticized for old theses

of Aristotelian physics, Ptolemy based on observation and
experimental verification and without a rigorous mathematical support:
of course, the human intellect can not remotely match the infinite sum of divine knowledge,
but even a few human knowledge of mathematics and geometry equal the divine knowledge
as they reach the "objective certainty."
In the second and third day refute the objections to the motion of rotation and revolution Earth:
"Here is another force esclamar time and enhance the ammirabil perspicuity of

Copernicus and together compiagner his misfortune, because he does not live in our time when,

 tor by the apparent absurdity movement preserved the Earth and the Moon, we see Jupiter almost another Earth, not retain a moon, but accompanied by four moons go around the sun in 12 years. "
On the fourth day it exposes the subject of the tides, as evidence of the Earth's motion:
erroneous test, especially since the dialogue is criticism about the right intuition of Kepler

and other astronomers it was the pull of the moon causing the tides.
Almost at the end are the words of Simplicio "Your well thought parermi more ingenious  than others I felt n'abbia me, but not, however, the
I respect true and conclusive: indeed, thinking always ahead of his

                mind's eye a steadfast doctrine,
which for most learned person and Eminent learned and

                which is force subside [...] 

 Dialogo sui Massimi Sistemi

God in His infinite power and wisdom could give the element of water, the reciprocal movement [...]
in many ways and yet our intellect inescogitabili [...] excessive boldness would be if other
wanted to limit and coerce the divine power and wisdom to his particular fancy. "
Was, this, exposure of '"argument of the end" or "topic of Urban VIII"
so called because he led a cardinal, in Galileo:
God, "in His infinite power, can anything that does not involve contradiction [...], and if God

could have known these things and otherwise how it has been devised [...] we must not bind in this way the divine power and knowledge. " In this way science is conceived not already in its value

 of explanation of the phenomena on the basis of a absolute principle, but as descriptive of sensible appearances traced to principles hypothetical not expect to obtain the true knowledge of

 physical reality.
Galileo certainly never shared such a position, but it was thought that those words made say
Simplicio intended to be a mockery of the Pope: in fact, Galileo considered it necessary,
precisely at the end of the dialogue, it shows the position of Urban VIII, the three protagonists,
logically only non-Copernican Simplicio, when pressed by the participants could expose it,
wanting Galileo - according to the provisions of the Decree of 1616 - deny or at least

 mitigate the feeling that the Copernican system was that he intended to be the sole basis of any proper cosmological interpretation.


The work received many accolades, including those of Benedetto Castelli, Fulgenzio Micanzio,
collaborator and biographer Paolo Sarpi, and Tommaso Campanella, but already in August spread
rumors of a ban on the book:  
Master of the Sacred Palace Nicholas Riccardi wrote on July 25 inquisitor of Florence
Clement Egidi by order of the Pope's book was no longer to be widespread;
August 7 asked him to track down and confiscate copies already sold.
For its part, the Florentine ambassador Francesco Niccolini

                             Sept. 5 referring to the court of
consulting with the Pope who "broke into a lot of anger, and suddenly I said ch'anche
our warp of enter where Galileo had not ought, and materials in the most serious

          and the most 

 Giovanni Ciampoli

 pericolose che in these times, Had Power arouse.
I replied that the Sr Galilei had not printed without an endorsement of his ministers [...]

I replied with the same outburst that he and Ciampoli
had circumvented [...] that in these matters the Office had no more than censure,
and then call to retract. "
On September 23, the Roman Inquisition urged to notify the Florentine Galileo order
to "appear in Rome before the end of October before the Commissioner-General of the Holy Office."
Several were his attempts to refrain from presenting in Rome:
on 1 January 1633, Cardinal Antonio Barberini wrote Florentine inquisitor Clemente Egidi
that the Holy Office did not want to "tolerate these fintioni nor dissemble his coming here," threatening to
"Et take him take him to the prison of this Supreme Court, also linked with irons."
Without the protection of the Grand Duke of Tuscany, who did not intend to get into conflict with the Church, February 13, 1633 Galilei arrived in Rome.
Ambassador Niccolini was allowed to host the scientist, waiting for the trial started,
and learned from the Pope himself Galileo that, "although he declares its intention to deal hypothetically
the earth's motion, however, to report on the actual arguments, and they talked and talked about
alleged and conclusively, and ch'anche had contravenuto order datoli in 1616 by

Cardinal Bellarmine Sr. "
For the first time you become aware of an order - or precept - that Bellarmine would
summoned Galileo in that now distant 1616. Galileo did not seem worried indeed,
as he wrote to Geri Bocchineri March 5, had the conviction that "the charges go and falling,
and some yet to be completely gone too obvious for their vanity, which you can believe that adversely
lightening all'altre that still exist in the foot, so I hope these are still to
terminate in the same way. "
The ambassador had the opposite view and urged Galileo to not make the mistake of defending in front
the Court its views of Copernicus, "in order to finish it as soon as possible."


The process, the abjuration and sentence   

The trial began on April 12, with the first interrogation of Galileo,
which the Commissioner inquisitor,
the Dominican Vincent Maculano, confronted him that he had received 26 February 1616,

a "precept" with which Cardinal Bellarmine would notice to quit the Copernican theory,
not to support it in any way and do not teach it. 
That precept, if it was ever actually shown to Galileo in

   February 1616 and if it is not even a false artfully constructed,

 does not bear any signature or of Bellarmine, or witnesses,
or Galileo himself, who denied having read them, but had only received a

                        voice in front of the

 Inquisition Bellarmine from the notification of the

                     Congregation according to which  

 Davanti all'Inquisizione

the opinion of the motion of the Earth "To be repugnant to the Holy Scriptures and only admitted

 former suppositione 'and' ex suppositione is could pigliar and servirsen. "

The following May he received the note in the letter of Bellarmine
which "contains the doctrine attributed to Copernicus, that the earth moves around the sun and
that the sun is at the center of the world without moving from east to west, contrary to the Holy Scriptures,
and therefore can not be defended or held. " The letter does not specifically mention the prohibition against teaching the Copernican doctrine, even within the limits of a mere scientific hypothesis and, thanks to this indirect authorization, as well as the explicit, but only verbal, received in February,

 he had written his Dialogue Concerning the Two Chief World Systems, not surprisingly getting the prescribed by ecclesiastical imprimatur.
The inquisitor, however, pressed, asking if there were any witnesses present at the time of notification
the "precept" and Galileo, responding not to remember, made the mistake of mentioning the word precept, arguing that "we have in any way contravenuto to that precept."
The inquisitor, verbalizing, he took to the notice of the alleged obligation and asked him if he remembered how and by whom he had been ordered and Galileo: "I fitting that the precept was that I could not keep nor defend, and may be you still Fusse or teach. "
For the inquisitor it was time to establish that Galileo published Dialogue, had circumvented
ordered not to treat the Copernican hypothesis, deceiving the ecclesiastical censors:
When asked if he had shown the precept to the Master of the Sacred Palace before being given 'imprimatur, Galileo not only admitted not to have said "any thing sodetto precept"
since, came to support, "in that book I show the opposite of that opinion of Copernicus,
and that the reasons for it Copernicus are invalid and inconclusive. "
With this obvious lie, ended the first interview:
Galileo was detained, "though under strict surveillance," in three rooms of the palace of the Inquisition,
"With full and free right to walk."
The Congregation of the Holy Office, which met on April 21, stated that in Galileo's Dialogue
"Defend itself, and s'insegni opinion riprouata, and damned by the Church, et, however,

 that the author makes suspect yet to keep. "
Galileo, again questioned April 30, said he had re-read in those
day his Dialogue "almost like writing nova and another author," admitting that a reader who does not
knew intimately the author would have had the impression that he wanted to confirm
the Copernican theory. Apologizing for the inquisitor 'a mistake so alien from my intentione "
offered to "ripigliar arguments already made in favor of that false opinion and damned,
and confutargli in the most effective way that God blessed me will be given. "
The full submission and poor health of the scientist made him get permission to leave the palace
Inquisition and return to the embassy in Florence. Constituted in the next 10 May explained
that the letter of Bellarmine - where it was not prescribed the prohibition to teach the Copernican doctrine
had made him forget the precept where instead the ban was ordered, and justified the "worsening"
of his dialogue as due solely to the "vain ambition and pleasure to appear witty in addition to the common de 'popular writers, inavertentemente scorsomi from the pen, "declaring himself ready

again to correct his book.
To finish the process, the Inquisition was to test the sincerity of the statement of
Galileo 'Do not hold the damn review »: for this purpose, June 16, the Congregation established
that "Galileo was asked about his plans, even comminandogli torture and if he had sustained,
after abjuration de vehementi in front of the congregation, was sentenced to prison arbitrarily
the Holy Congregation, with the injunction not to wax, either verbally or in writing,
on the mobility of the Earth and immobility of the Sun. "
On June 21, Galileo was interrogated for the last time, when asked if still held, or had held
in the past, and for how long, the theory of the centrality of the Sun, Galileo replied that he had once
considered the views of Ptolemy and Copernicus both "disputable,

because either one or the other could be true in nature, "but after the ban in 1616, claimed to hold,

 since then, and still is," very true for and the undoubted opinion of Ptolemy. "

Asked to explain why he had then defended the opinion of Copernicus in his Dialogue,

Galileo said that he wanted only to explain the reasons for both opinions,
convinced that he had no probative force, so that "to proceed with safety
dovessere resort to the determination of the most sublime doctrines. "

At the insistence of the Inquisitor to tell the truth, otherwise he would have acted "against him with

 the appropriate remedies law and fact, "Galileo denied that he had never supported the opinion of Copernicus," moreover, I'm here in their hands, face what he likes. " Explicit threat of torture,
Galileo replied only: "I am here to make the obedience, and I have held this opinion after
determination made, as I said. " The minutes of the constituted concludes that 'not being able to
have nothing in execution of the decree, had his signature, was sent back to his place. "
The next day, June 22, in the chapter room of the Dominican convent of Santa Maria sopra Minerva,
This kneeling and Galileo, the sentence was rendered by the cardinals Gaspare Borgia, happy Centini,
Guido Bentivoglio, Desiderio Scaglia, Antonio and Francesco Barberini, Laudivio Zacchia,

 Berlinghiero Gessi Fabrizio Verospi and Marzio Ginetti,

"Inquisitors general against heretical depravity," in which he summed up
the long history of conflict between Galileo and the Church's teaching, which began in 1615 with

the written Of sunspots and the letter to Castelli, which the "qualifiers theologians" had the opposite:
"That the Sun is the center of the world and imobile of local motion, is the proposition absurd

and false in philosophy, and formally heretical, for being explicitly contrary to Holy Scripture;
that the Earth is not the center of the world nor imobile, but it moves eziandio of diurnal motion,

 is equally proposition absurd and false in philosophy, and considered in theology ad

 minus erroneous fide "
The ruling then handed version of the warning received in February 1616 after being the Bellarmine
"Kindly advised and admonished, I was the Father Commissary of the Holy Office of that time that precept, with notary and witnesses, which omninamente had to leave the false opinion, and that in the future you could not keep,
neither defend nor teach in any way, either in voice or in writing: and since you have

 promised to obey him, you were fired. "
Recalled that he then wrote his Dialogue "without meaning to those who gave you such power,
you had precept not to hold, defend, or teach in any such doctrine, "
in the judgment emphasizes that the book
teach the Copernican doctrine, as to the personal beliefs of Galileo, the process was considered
"Must be against you to rigorous examination, in which [...] you answered a Catholic."
Having made so "vehemently suspected of heresy," Galileo had incurred the censures and penalties
set "against such offenders."
Set the abjuration "with a sincere heart and unfeigned faith" and prohibited the Dialogue,
Galileo was sentenced to "formal imprisonment at the pleasure ours" and
"Punishment greet" the recitation of the seven penitential psalms weekly for three years,
reserving the Inquisition "moderate, alter or rising of all or part of" the pain and penance.


             Discourses and Mathematical Demonstrations Concerning Two New Sciences   

Discourses and Mathematical Demonstrations
After the trial in 1633 Galileo wrote and published in the Netherlands in 1638 his greatest treatise
Scientific Discourses and mathematical demonstrations concerning the two new sciences mecanica
and local motions by which we consider the father of modern science.
On the first day, Galileo is the strength of materials: different resistance must be
linked to the structure of the particular matter and Galileo, while not pretending to achieve a
explanation of the problem, deals with the interpretation of atomism of Democritus,

considering a hypothesis able to explain physical phenomena. In particular, the possibility of the existence of vacuum provided by Democritus - is considered a serious scientific hypothesis and in a vacuum - ie into nonexistence of any other means to resist - Galileo rightly maintains that all bodies
"Descend with equal velocity," in contrast with contemporary science that he considered it impossible
of motion in a vacuum.
After treating the static and the lever on the second day,
in the third and fourth deals with the dynamic, establishing uniform laws of motion,
of naturally accelerated motion and uniformly accelerated motion and vibration of the pendulum.
If the legend of the sentence of Galileo, "And yet it moves", pronounced just after the abjuration,
serves to suggest its intact belief in the validity of the Copernican model,
the conclusion of the trial marked the defeat of its program for the dissemination of new scientific methodology,
strictly based on the observation of the facts and their experimental verification
against the old science that produces' experiences as made and responsive to its needs without

having neither made nor ever seen "- and against the prejudices of common sense, which often suggests real any appearance: a program of scientific renewal, which taught "not to have more trust in authority, in tradition and common sense, "he wanted to" teach to think. "


            The last few years   
The sentence included a term of imprisonment at the discretion of the Inquisition and the obligation
to act for three years, once a week, the penitential psalms. The literal rigor was mitigated in practice:
imprisonment consisted of forced stay for five months at the Roman residence of the Grand Duke of Tuscany, Francesco Niccolini, at the Spanish Steps and here, in the house of the

 Archbishop Ascanio Piccolomini in Siena,
at the request of these. As for the penitential psalms, Galileo instructed to recite,
with the consent of the Church, his daughter Maria Celeste. In Siena the Piccolomini favored

Galileo allowing it to meet the city's personality and to discuss scientific issues.
Following an anonymous letter that denounced the actions of the archbishop and Galileo himself,
the Holy Office provident, receiving the same request made earlier by Galileo,
to confine the isolated villa ("The Jewel") that the scientist had in the countryside of Arcetri.
The order of 1 December 1633 he enjoined Galileo to "stand alone, do not call nor
receive anything, for the time at the discretion of His Holiness. " Only family members could visit him,
with the prior authorization: for this reason he was particularly painful loss
daughter Sister Maria Celeste, the one with which he maintained links, which took place April 2, 1634.
He could, however, maintain correspondence with friends and admirers, even outside Italy: to Elia Diodati, in Paris, wrote March 7, 1634, consolation of his misfortunes that "envy and malice me
machinato against "with the statement that" the shame lies above the traitors and made the most sublime degree of ignorance. " From the King James Version knew the Latin translation that

Matthias was doing Bernegger in Strasbourg in his Dialogue, which was released the following

year in the Netherlands, and told of a "Rocco Antonio this [...]
pure peripatetic and remotest dall'intender nothing of mathematics or astronomy »
who wrote in Venice "and biting insults" against him.
This, and other letters, show how little Galileo had renounced their beliefs Copernican
but now he was involved in the drafting of a new work, which will be the last and his best,
published in Leiden, Holland, Discourses and Mathematical Demonstrations Concerning Two New Sciences.
It is still a dialogue that takes place between the three protagonists of the same previous

Dialogue of Two Chief World Systems Sagredo, Salviati and Simplicio - again in four days.
It is in 1640 the decisive contribution of Galileo who encouraged his pupil Bonaventura Cavalieri

 to develop the ideas the teacher and others on the indivisible assembling them in a

geometrical method (method of indivisible)
to determine areas and volumes: This method represented a milestone for the future development

of calculus.
With blindness and the worsening state of health, in 1639 he was allowed to Galileo the assistance of
young pupil Vincenzo Viviani and, since October 1641, also of Evangelista Torricelli.


An affectionate correspondence   

  The last years of Galileo are marked by an affectionate correspondence with Alessandra Bocchineri,
Sestilia sister, the wife of his son Vincenzo.
When Galilei, now sessantaseienne, Alessandra knows, this is a beautiful woman of 33 who has been refined and has cultivated his intelligence in the court life of the

Duchess Eleonora Gonzaga of Mantova.
The young intellectual is made known to Galileo by his son Vincenzo who boasted of beautiful
and intelligent sister-goers admired the European courts.
Alessandra July 28 of 1630 calls for the villa of "S.Gaudenzio" hills Sofignano,
Galilei guest of her husband Giovanni Francesco Buonamici, the good friend who sends
Galilei wine of their "Vineyard of Venus", particularly appreciated by the scientist.
"I am satisfied was so very kind of conversation V. S. and so attached to its quality
merits and that I can not forget from time to time to say hello and ask you to be pleased

 to let me know new his health, and keep with the memory of desire I hold to be honored

by any of its commandment.
And if it were not that V. S. I think that people here take for the affection V. S. brings them compel
to come support our parts, I would have taken courage to beg VS he wanted to console
by his presence it 'the next few days of the beginning of August, but because I promise to enjoy

 it at all so I reserve for another time to ask for this grace, which will be yet common to Mr.
Knight my husband look at each point lathes Bisenzio Valley and in the name of his

greeting V. S.It is, and all core I kiss your hands and rest slave to his virtues. '
Galileo replied with a long letter of 8 August 1630 where it is justified for not having responded
time not his fault but for the delay in her letter was delivered to the:
"Very Mrs. I could not be attributed to anything but my bad luck,
that I always cross the things you want, so a waste of time because it is interposed
between the date of his courteous letter and 'the Ricapito in the distance not exceeding 10 miles;
that it was there on July 28, and they were seven in August, interval of 11 days and 11 nights and the
that troubles me most is the absence in which I will be, all this time, incurred in the soul
of V. S., which, knowing havermi written response from not seeing me havera sentenced to a solemn villain;
where I, not knowing, or hoping hip or demanding, as a favor, I have not heard in those days
affliction other than that of his absence: but I swear right to V. S. that 'the taste et sudden unexpected
rewarded more than the extension of rad '11 days. God grant that 'the return of my response is not as
slowly to the left of my concept rudeness face outlet in this' mind of V. S.,
malagevolmente that can eradicarsi. When I heard the heroic resoluzione taken in Rome et made
I formed this to her, the concept of its value, that nothing more I wanted to see it, and Believe me that '
this was one of the primary causes that hastened my return, which perhaps Harei extended

 a few months more:
but because in addition to a simple view havevo adding the hope of gustar of his conversation,
estimating that she Fusse to allocate in Florence, judge hora V. S. which I find myself,
defrauded of such an assignment, and I see this in his absence, and I fear the continuation,
as flinch from the words that he collects from its head. Here 's how human judgment often err.
Far less serious was its distance of 500 miles, and I did not haveva presence known,
this of 10, after 'haverla seen and heard. This I say to V. S., has' the same respect
to S. his wife, it still returned to these parts desired than expected,
to which an excess of courtesy and affezzione obviously shown me, I haveva strongly bound,
Even as perpetually keep me, from the conversation of which I promised useful and particular delight.
Hora I can only consolation other than what I hear in serving both, while I come Honorato
of their commandments, of which the effectiveness plead with equal readiness that they will find

 in me esequirgli; which will know infinite, although in a very feeble forces.

Favoriscami to kiss his hands in my
the very name I. S. Ca.r her husband, much to R. S. his brother, S.ra to his mother,
et all to his house: and the Holy grant him full of happiness. From Bellosguardo them August 8, 1630.

Of V. S. very I. '
There are traces of a later match between the two until a letter of Galileo's May 24, 1640
where praises, while women 's intelligence Alessandra, "so rare that women are so sensibly
discorrino as she does. "
In the following years Alessandra responding to a letter of 27 March 1641 Galilei

assures him that would accept his invitation but is forced to reject them for fear of giving

scandal while the renewed his desire to see it:
"I often between me vo stipolando in the same way that I could do to find the way
before I die to boccarmi with your lordship and stay a day in his conversation,
without giving scandal or jealousy to those people who have amused by this will.
If I thought that V. S. you could find cho good health, and do not give him trouble
the viagiare in caroza, I would like to send my mares and find a carozino lest VS
favorisi me to come and stay with us dua days, now that they are 'good tenpi.
But the supprico to want to help and answer me, for I will send to you soon,
and may come slowly, and I do not think she patissi ... '
The now senior scientist in the regret of not being able to accept an additional call
Alessandra visit her in Prato replied that he could not reach, "not only for
the many ailments that keep me in this oppressed my most grievous age, but because they are
considered still in prison, for those cases which are very well known ", but calls itself
to come in Arcetri oblivious of any malignant consequences:
"Nor do I oppose any respect or suspicion or fear that I may come to this
some turbulence:
because it is in any way by other people received this meeting or interview,
or is joyful or is disagreeable, little care, since I am addicted to suffer and support
as very light weights much more serious charges. '
She could console him in these last days before his death day "for long
continuous idleness and short for the relationship to the months and years elapsed,

 or anything else left for me to consolation that the memory of past friendships,

of which a few things I have left. "
Will write again Galilei, in reply to a letter of Alessandra lost,
renewing his affection:
'Molt' Mrs. I received my most grateful letter V. S, very time
I was much consolation, havendomi found seriously ill in bed for several weeks in here.
Rendo cordialisssime gratie to V. S. of 'affection so kind that she shows towards my person,
and of 'office condoglienza with whom she visits me in my misery and disgratie.
For now I do not need to prevalermi canvas: rest well with increased obbligationi
the kindness of V. S., which delights in to watch over my interests.
I beg you to forgive this my involuntary brevity the gravity of the evil;
and kiss with love friendlier hands, as I do yet to Sr her husband.
On Arcetri, 20 Xbre 1641. '
This letter of 20 December 1641 of "involuntary brevity" is the announcement of the death of Galileo
which cometh upon 15 days after the night of 8 January 1642 in Arcetri, assisted by Viviani and Torricelli.


   After the death  

       Place of burial, the Basilica of Santa Croce, Florence                            
Galilei was buried in the Basilica of Santa Croce in Florence,                         

 together with the other major                        
                   Florence such as Machiavelli and Michelangelo,        

 but it was not possible innalzargli 's "august and sumptuous deposit"

desired by the disciples, because on January 25th the nephew of Pope Urban VIII,

Cardinal Francesco Barberini, wrote the Inquisitor of Florence Giovanni Muzzarelli

of "pass the ears of the Grand Duke It is not good to frabricare mausoleums corpse of the man who was penitentiato in the Tribunal of the Holy Inquisition,

 and died while it lasted penance [...]    

 Santa Croce Firenze

nell'epitaffio or iscrittione that will arise in the tomb, you read these words that may

offend reputatione of the Tribunal. Holy Cross                
The same warning even though she will have with those who recite the Lord's Prayer funeral [...]. "Florence
The Church held the surveillance also against the students of Galileo:
when they gave birth to 'Accademia del Cimento,  
it intervened with the Grand Duke and the Academy was dissolved in 1667.



 Tomba di Galileo in S.Croce


Galilei and science   

The fundamental importance of the figure of Galileo plays regards its role in the recovery of

the method science developed in the Hellenistic period and then almost forgotten, thanks to its

careful study some scientific works, particularly those of Archimedes.
Its importance to the revival of science in general and physics in particular is attributable
the discoveries that made ​​by means of experiments, such as, for example, the principle of relativity,
the discovery of Jupiter's four main moons, called the Galilean satellites
(Io, Europa, Ganymede and Callisto), the principle of inertia and the speed of falling bodies
is the same for all bodies, regardless of the mass or from the material (an idea, the latter,
which actually dates back to John Philoponus, but had apparently been forgotten).
Galileo also became interested in the problem of measuring the speed of light:
In fact, he realized that this could not be infinite, but his attempts to measure it were fruitless.
Reflecting on the motions along inclined planes discovered the problem of minimum time in the fall of material bodies, and studied various trajectories, including the spiral paraboloid and the cycloid.
As part of his mathematical research discovered the first property of infinity:
a part is equal to the whole.
Also led his student, Bonaventura Cavalieri, to study the indivisible,
realizing the consequences of the infinitesimal calculus in the study of motion


       Galilei's rejection of essentialism and science  

         Premise to the understanding of the Galilean method may be considered to be the critical
essentialism that Galileo track in 1613, in his letters to Welser.
What, you ask Galilei, the man in his quest want to get to know?
"Either we want specolando attempt to penetrate the true essence and intrinsic sustanze natural;
or we want to be content to be in news for some of their affections. "
For knowledge we intend to grasp the first principles of the phenomena
or how they grow? Galileo responds:
"The attempt of the essence, the company does not have to be impossible and less fatigue

for no less vain in the next sustanze elementary and in the remotest heavenly and I seem

 to be equally ignorant of Substance of the Earth's Moon, clouds elementary spots of the sun,

nor do I see that nell'intender these substances near aviamo Another advantage that the

copy of 'detail, but all equally unknown
for which we go wandering, passing with little or no one purchase from one to another. '
The search for first principles essential therefore involves an endless series of questions for each
answer raises a new question: if we were to ask what is the substance of the clouds,
a first response would be that it is water vapor, but then we must ask what is this phenomenon
and we say that it is water, to ask after what water, responding
which is the fluid that flows in the rivers but this "news water" is only "nearest
dependente and more under "richer variety of different information, but does not bring us some
knowledge of the substance of clouds, which we know exactly how much before.
But if we want to understand the "affections", the particular characteristics of the bodies,
we know both those bodies that are distant from us, like the clouds, and in those closest
such as water.
It must therefore be understood in a different way the study of nature.
"Some strict defenders of each minutia peripatetic"
brought up in the worship of Aristotle, believed that "philosophy is neither to be other than
to a large practice on the texts of Aristotle "that lead as the only proof of their theories.
And not wanting to "never rouse eyes off those cards," refuse to read "this great book of the world"
(Ie directly observing the phenomena),
as if "it were written by nature to not be read by anyone other than Aristotle,
and that her eyes had to see to all his posterity. "


         The "language" mathematics   

The question of mathematics as a tool for investigating the nature, wrote:
"... this great book [of nature] which stands continually open before our eyes
(I mean the universe), can not be understood unless you first learn to understand the language,

and to know the characters or what is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly

impossible to understand a word;
without these one is wandering around in a dark labyrinth. '

(Galileo Galilei, Works VI)

Galileo mathematics is therefore the supreme tool in the investigation of nature.
In this regard, he distinguished between primary qualities of bodies, objects precisely survey
science as they apply to the math, and secondary qualities
(eg, smells, tastes, judgments of taste etc.), who can not be studied scientifically.

The scientific method  

The Galilean method consists of two main aspects:
sensible experience, namely the experiment, which can be done practically or only abstractly
("mental experiences"), but must always follow a careful theoretical formulation,
or to hypotheses that are able to drive the experience so that it is not providing results arbitrary;
required proof, which is a rigorous mathematical analysis and the results of experience,
which is able to draw from this any consequence in a necessary and not objectionable,
and that further evaluation, with further experience, or the so-called trial,
which is the real experiment which is always verified the outcome of any theoretical formulation.

  Experimental apparatus and measurement   

Phases of the Moon designed by Galileo in 1616
Therefore fundamental for the mathematical analysis of the phenomena the use of measuring instruments.
In the course of his life, Galileo proposed originally or reworked on the basis of existing ideas
different experimental setups and measurement of great importance in the evolution of science and technology:
the inclined plane to study the motion of bodies;
the hydrostatic balance to measure the density of the bodies;
the thermoscope for measuring variations in air density as a function of temperature;
a car driven by animal power to lift water from deep wells;
the proportional compass to solve problems in mathematics and geometry;
the celatone, a tool for measuring longitude at sea using satellites of Jupiter;
the jovilabe, a tool to calculate the relative positions of Earth and Jupiter;
the helioscope, a tool that allows you to observe the Sun
the micrometer a device mounted on the telescope possible to measure,
simultaneous observations with the telescope, how far it each satellite from the planet.


  Parabolic motions, circular motions and squaring the circle  

Studies of parabolic motion, and commuters along inclined planes allowed to Galileo

 to discover the universality of motion.
Studies on the motion of the ball polished stones along the inclined planes and measures

of how objects.
Moving increase and decrease their speed allowed Galileo to discover that their trajectories
were parables. Processing data with a mathematical discovered that, wanting to launch a

cannonball as far as possible, the inclination of the barrel should be 45 °.

By varying up or down the inclination, for identical values, the range is the same:

the trajectory at 40 ° to 50 ° and that have the same range.
Studying, yet as fluctuate stones if linked along a string, or as they move along a plane falling
inclined, Galileo discovered that it was examples of the same physical quantity: the motion.

 Thus was born, the first example of universality in physics: all movements of material bodies are

due to a single source. It comes from the life-giving force to the motion and friction that it opposes.
The sum of these two forces come velocities and accelerations, with strictly conserved quantities as,
For example, the amount of linear motion.
The rectilinear movement and the circular one may be composed and decomposed in

different ways.
It is then possible to produce a wide variety of movements parabolic: all examples of motion.
The universality of the motion, however, put in crisis the squaring of the circle,

 a concept that has deep roots.
The circle is the perfect geometric figure and was associated with the sky, while the lines

and thus the geometric figure
square of the natural world was so obvious, before Galileo, considered impossible to obtain a
square from a circle and vice versa. Galileo, however, designed the "proportional compass"
the realization of which is assigned to the artisan of his confidence, Marcantonio Mazzoleni,
with which it is able to transform any length of circle in the four sides of a square.
The instrument consisted of two rulers metal joined by a hinge.
The obvious conclusion was that there was nothing in the preferred circular motion or no difference
all other types of motion, despite what Galileo was convinced that the planetary orbits were circles
and ellipses, as discovered by Kepler - God, to the world, has chosen the orbits perfect

geometric figures:
and these are the circles ellipses.

 The material bodies move because there is a net force acting on them.
The velocities and accelerations are determined by the sum of the positive and negative forces,
generally friction, which, having regard to all the conservation laws, determines the

observed motion.

                  The principle of inertia       


By experimenting with the pendulum and the inclined plane,

Galileo arrived at the discovery of the role of
friction in the motion of bodies and the formulation of the principle of inertia,

then encoded by Isaac Newton
or even, in a system without friction, a body will remain in its state

of motion or of rest if there are no external forces on it are involved.





Il lampadario che dal 1587 sostituisce la "Lampada di Galileo" nel Duomo di Pisa

     The pendulum                            

Another discovery Galileo implemented in 1583 is the isochronism of

small oscillations of a pendulum.                      
On this subject, there is also a legend, according to which the idea would

come to mind looking at the oscillations of a lamp suspended in the nave of the Cathedral of Pisa. The lamp is commonly
lamp is indicated as Galileo, it is not the sight of the young scientist,
as she was built in 1587 by Domenico Vincenzo Possenti, then a few years after

Galileo's insight on the pendulum.
The lamp instead was seen swinging, most small and spartan, is now kept in close
       Monumental Cemetery Chapel in Aulla.   

 Pendolo di Galilei a Pisa

This tool is simply composed of a stone tied to a thin and inextensible:
if this has a length of one meter, is obtained by an oscillation of the duration of about two seconds. 
                         The frequency of the pendulum's motion was not the only point of Galileo: Pisa
noticed, in fact, that for the same length of wire, and regardless of the weight of the stone,
the oscillation takes the same amount of time to vary the amplitude, as long as this is not excessive.
The periodic law of the pendulum for small oscillations and neglecting the effects of friction, is in fact:

where T is the period of oscillation, I  the length of the wire and g the acceleration of gravity.
It can be noted that the period of oscillation is independent of the mass and
(in the approximation valid for small oscillations) maximum amplitude
oscillation same, ie the angle between the initial position and the central minimum.
For oscillation of a pendulum is defined as the movement of the pesetto of the

pendulum from the initial point of oscillation
(from which the pendulum part with zero velocity)

 at the same point of departure via the other end,        
then the movement from one extreme to the other is a half-




 Schema del Pendolo


     The hydrostatic balance  

The Bilancetta was written by Galileo in 1586, when he was still awaiting assignment

university in Pisa.
The work, printed posthumously, describes the invention of the hydrostatic balance:
For fabricar therefore the scale, piglisi a straight edge at least two arms,

and how much more will be long the more accurate the instrument;
and divide in the middle, where you put the perpendicular [the heart], then aggiustino arms that are
balance, with the thin one to weigh more, and one of the arms above the note the terms
[where return] dwarf the counterweights of the simple metals when they are weighed nell'aqqua,
warning to weigh the purest metals are. (The Works)
It also describes how you get the PS specific gravity of a body with respect to water:

In The Bilancetta are, then, two tables that list thirty-nine specific weights of precious metals

and genuine he determined experimentally with a rigorous mathematical method: the

measurements are very accurate and comparable with modern values​​.
This is the first detailed list of specific weights derived analytically and experimentally.


Inclined planes, acceleration of gravity and energy conservation   

Galileo was able to determine the value of the acceleration of gravity, that is the size that
regulates the motion of bodies falling towards the center of the Earth,

studying the fall of spheres well-polished down an inclined plane, which is also very smooth.

Since the motion of the sphere depends on the angle of inclination of the plane, with simple measurements at different angles was able to obtain a value only
slightly lower than that of Padova
(9.82 m/s2), despite the systematic errors due to friction,
that could not be completely eliminated. ball on the inclined plane
Said v the velocity of the sphere along the inclined plane, the speed parallel to the

 horizontal plane is given by v cos?
while the perpendicular, which is that useful in the determination of the gravity,

resulting v sin?    
With these studies, Galileo discovered a phenomenon that is a direct consequence

of the conservation of mechanical energy:
placing another inclined plane next to the first of which date back to the ball, it was discovered that
this would stop at the same height of departure. However, the concept of energy is not yet
present in the physics of the seventeenth century, and only with the development, over a century later,
of classical mechanics of Newton will come to a precise formulation of this concept.


  The speed of light  

Galileo was certainly among the first to realize that the speed of light was not infinite,
and first devised an experiment to obtain the measurement.
His idea was to bring on a hill with a lantern covered with a cloth and then raise
the drape sending a signal to a friend instead of another hill a kilometer and a half away.
His friend as soon as he saw the signal, he then lifted her drape allowing Galileo
to record the time taken by light to reach the other hill and back.
A precise measurement of this time would allow to measure the speed of light. However,
the attempt was unsuccessful: Consider it takes light only
one hundred thousandth of a second to travel a distance of 3 km.
The first measurement of the speed of light was the work in 1675, Danish astronomer Rømer,
based on the accurate measurement of delays of the eclipses of Jupiter's moon, Io.


           Science and theology   

Galilei in the early years of his astronomical discoveries, not explicitly poses the problem
the theological consequences of the discoveries made with his telescope and how that

universe immense, full of irregularities, corruptible, not perfect spheres and no center could

be in conflict with the worldview defense by the Catholic Church. Note for example as in

"Sidereus Nuncius",
in which these findings were reported for the first time ever, the problem between science and faith
was not even mentioned or discussed.
This question was posed to Galileo by the strong reactions and controversies that over

 the years were raised by his discoveries and his way to investigate, based on the direct

reading of the book of nature, without recourse to authority, it was Aristotle or theological.
He was forced to address the question of the relationship between science and faith,

the concept of truth, with the main purpose to defend its autonomy as a scientist and also

 to warn the Church of the harm that would come to the Christian religion if he insisted

on using the Bible in matters of natural science that scientific progress would show clearly false.
The first document in which Galileo faced this issue was a letter to Father Benedetto Castelli,
written in 1613, where it was also that of the biblical Joshua stopped the sun's course.
In this letter Galilei clarified his position as a Christian and a scientist who championed the

 autonomy of science from religion, concluding that science and faith did not interfere at all

with each other, since worked on separate floors:
Faith spoke and worked on the metaphysical plane, while the science of the physical.

Astronomy has nothing to do with the Bible

"[...] Which propositions, as being, dictating the Holy Spirit, were uttered in such a manner
by the sacred writers to sit down to the ability of the common people very rude and unruly [...]. '
(Galileo Galilei, "Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany")
Ie, Scripture, inspired by the Holy Spirit, which therefore can not lie,
spoke in the ancient language of that time to understand. But
"[...] In the disputes of the natural problems you should begin by the authority of places of Scripture,
but by sensible experiments and demonstrations necessary, because,

proceeding equally from the divine Word
Sacred Scripture and nature, as dictated by the Holy Spirit, as a very faithful executor
of the orders of God [...]. '
(Galileo Galilei, "Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany")
Therefore, "... it seems that what the effects of natural or sensible experience places

before our eyes or necessary demonstrations conclude, should not in any circumstances be

 called into question for places.
Scripture avesser different words semblant, then said that not every of

Scripture is bound to obligations as severe com'ogni effect of nature. "
Hence, the Galilean vision according to which there are two "books", that are capable of

 detecting the same truth that comes from God: one is the Bible,

 which has essentially salvific value and redemption of the soul,
written in terms corresponding to the vision spread throughout the populace,

 and therefore requires careful interpretation
As to the claims relating to the description of natural phenomena that are described in it a little.
The other is the "great book of nature written in mathematical characters."
The universe, which should be read in a scientific and therefore should not be postponed

to the first but to be well interpreted, must be studied with the tools that the same

God of the Bible has given us:
"Senses", "discourse" and "intellect".

"[...] I believe that the authority of Scripture had only aim to persuade
men in those articles and propositions that are Needed to their health,

and overcoming all human speech, I could not for other science or other means to get used

credible, that the mouth of the Holy Spirit.
But that the same God who has endowed us with senses, speech and intellect, wanted,

 postponing the use of these, give us in any other way the news that we can achieve those,

I do not think it is necessary to believe it, and highest in those sciences of which a

minimum particle conclusions and divided it says the Scripture;
What exactly is astronomy, of which there is something so small part, that there are not even

named the planets.
But if the first sacred writers had car thought to persuade the people of the provisions

and movements of bodies celestial, avrebero not treated so little, that is nothing in comparison

to the infinite high and admirable conclusions which in this science are competing. '

(Galileo Galilei, "Letter to Father Benedetto Castelli") 

The letter to Father Castelli aroused controversy, however violent and sarcastic by the Florentine clergy, totally conservative, such that Galileo was forced to make public displays of Catholicism
and even to hasten to Rome to defend his curial environment by believing scientist.
After decades of controversy and a process, the Church forced Galileo to recant, censured and condemned his findings index the works of Copernicus and Galileo until 1823.
Over the centuries that followed the Church changed its position with respect to Galilei:
In 1734 the Holy Office granted the erection of a mausoleum in his honor in the church of

 Santa Croce in Florence;
Benedict XIV in 1757 took the Index books that taught the motion of the Earth, thereby

formalizing the in fact already had Pope Alexander VII in 1664 with the withdrawal

of the decree of 1616.        
The final authorization to the teaching of motion of the Earth and the immobility of the

Sun came with a decree of the Sacred Congregation of the Inquisition approved by Pope Pius VII September 25, 1822.


Beyond the historical judgment on the legal and moral condemnation of Galileo,
the epistemological questions and biblical hermeneutics that were at the center of the process were
object of reflection by many modern thinkers, who often cited the story of Galileo
to exemplify - sometimes deliberately paradoxical in terms
their thinking on these issues.
For example, the Austrian philosopher Paul Feyerabend, a supporter of anarchist theory

of knowledge, wrote:
"The Church from the time of Galileo held to the reason than Galileo himself,

and also take into account the ethical and social consequences of Galileo's doctrine.

 Its verdict against Galileo was rational and just, and only for reasons of political

expediency if they can justify the review »
(P. Feyerabend, Wider den Methodenzwang, FrankfurtM / Main 1976, p. 206.)
In 1968, Pope Paul VI gave start the review process and with the intention to create a definitive
about this controversy Pope John Paul II July 3, 1981, called for it to be taken
interdisciplinary research on the difficult relations with the Church and Galileo established,
a Pontifical Commission for an examination of the Ptolemaic-Copernican

of the sixteenth and seventeenth centuries, in which the Galileo fits.
After thirteen years of trial, October 31, 1992, the Church clarified its interpretation
on the theological question Galilean scientific recognizing that the condemnation

of Galileo Galilei was due his stubbornness in not wanting to accept the invitation of the

Church to consider its findings as mere ypothesis is not proven and, on the other hand, the

 "lack of insight", that intelligence and foresight, theologians who condemned him.:
"Like most of his opponents, Galileo does not distinguish between what is
the scientific approach to natural phenomena and reflection on the nature of philosophical,
it generally calls for.
That's why he rejected the suggestion that he had been given to present system as a hypothesis
Copernicus, as long as it is not confirmed by irrefutable proof. That was, however,
requirement of the experimental method of which he was the inspired founder. [...]
The problem posed by the theologians of the time, therefore, was that of compatibility between heliocentrism and Scripture Thus the new science, with its methods and the freedom of research which they implied, obliged theologians to examine their own criteria of scriptural interpretation.
Most could not do it. Paradoxically, Galileo, a sincere believer, showed himself on this
point most insightful theologians who opposed him. '
The mistake of the Church was, therefore, to not being able to
"[...] At the same time to overcome habits of thought and to devise a pedagogy capable of illuminating
God's people say, in general, that the pastor ought to show a genuine boldness,
avoiding the double trap of uncertain and of hasty judgment, and the other one could do much harm. '
(John Paul II to members of the Pontifical Academy of Sciences, October 31, 1992)


Galileo Galilei and the art     

Statue of Galileo in the portico of the Uffizi Gallery
(Works XI)
Lodovico Cardi, called Cigoli, Florence, was a painter at the time of Galileo;
at some point in his life, to defend his actions, asked for help to his friend Galileo:
had, in fact, defend against attacks than those who believed the sculpture to painting,
as has the gift of three-dimensionality, at the expense of just two-dimensional painting.
Galileo responded with a letter dated June 26, 1612. He, first of all, provides an incredible
anticipation of the modern distinction between optical and tactile values​​:
The statue, with its three dimensions, deceives the sense of touch, while painting, in two dimensions,
deceives the sense of sight. From what Galilei gives the artist a greater expressive power than to the
sculptor, since the former is capable of producing emotions much better than the second.
"To what then say that the sculptors that nature makes men of sculpture and painting,
I say that she makes him no less sculpted paintings, because she's scolpe and colors, ... '
He adds:
"For unto as the means, co 'which mimics, are far away from the things to be imitated,
more imitation is marvelous. '
In art, as in poetry and music, said Galileo, that the emotional power that is able to convey.
And this description ignores the harsh reality.


Galileo and music    

Galileo's father was a musician (lutenist and composer) and music theorist well known in his day.
Indirectly, Galileo provided a major contribution to the understanding of acoustic phenomena,
having first understood the importance of oscillatory phenomena and the concept of frequency.
In the aforementioned letter of Galileo to Lodovico Cardi is this sentence:
"I do not ammireremmo us a musician, who sang and rappresentandoci the complaints and passions
a lover we moved to compassionarlo, much more than if crying what to do? ...

And much more so ammireremmo,
if silence, with only one instrument, with crudities et pathetic musical accents, what did ... '

(Works XI)

To understand its meaning, we must consider that at the end of the sixteenth century had opened
in the Italian music a dispute between the proponents of the so-called
"Second practice" or "new practice" music that would later gave birth to the genre of melodrama
and oratory and those of the "first practice" of which Palestrina was considered the exponent
more typical. For these, the relationship between music and text was realized especially

 in so-called madrigalisms, onomatopoeic effects or variously alluding to words like "murmur",

"shake", "down", "breath" and the like.
According to the musicians of the second practice, however, the music itself

was designed to evoke the emotions and the feelings of the soul:
each had a specific musical interval evocative, and between text and music should exist a perfect
correspondence of effects at much easier to be realized in monody and in polyphony.
The sentence of Galileo testify so its adherence to the new musical aesthetic, according to which

a melody
(Well-composed, and effectively performed) is able to elicit in the listener lives even emotions
in the absence of a text.
In fact, this position was held by the group of musicians who belonged to his father, Vincenzo Galilei.
The idea that instrumental music should be just as expressive of vocal music

was exposed some years later also by Girolamo Frescobaldi in the introduction to the

First Book of Touch and Games (1637).
It should be noted, however, that the authenticity of the letter to Lodovico Cardi,

of which there is only one copy, back several decades, is uncertain, and furthermore the occasional reference to the music serves only as an argument of support for the view that painting

is not less than the sculpture.