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Marino Ghetaldi in the Palace of Rector of Ragusa

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Marino ou, en Dalmate [ first ] Marin Ghetaldi . Ghetaldus, Ghetalde (EN Latin Marinus Ghetaldus ) or in Croatian Marin Getaldić is a mathematician, physicist and politician of the Republic of Ragus [ Note 1 ] or 1566 in Ragusa (today Dubrovnik in Croatia), died on or 1627 [ Note 2 ] in the same town.

He is one of the very few students of François Viete with Nathanael Tarportley, Jean de Beaugrand, Jacques Aleaume and the Scottish Alexander Anderson [ 2 ] with whom he is in close contact. Surveyor among mathematicians at the origin of the emergence of new algebra, he is also one of the first to make his contribution to analytical geometry [ 3 ] . In correspondence with Galileo and Clavius, he communicates to Italian mathematicians, Paolo Sarpi, Antonio Santini, Carlo Renaldini, etc. This new way of noting the algebraic questions and implements it itself in the reconstruction of the works of Apollonios de Perga. In physics, he leaves a study of parabolic mirrors, and one of his achievements (71 cm in diameter, 146 cm height) is at the Marine Museum in London [ 4 ] . Latin Croatian Writer [ 5 ] , his memory remains present in the streets of the current Dubrovnik, where he is presented as the ‘Apollonios de Perga’ Croatian [ 6 ] .

The youth [ modifier | Modifier and code ]

Born in a patrician and numerous family, originally from Taranto [ 7 ] In Italy, Marino Ghetaldi is one of the six children of Maro Marino Jacques Ghetaldi and Ana Andrée Resti [ 8 ] . His four brothers, André, Simon, Jacques and Martolicu, as well as his sister Niki, live behind the Saint-Blaise church, near the palace of the rector, seat of the government of the Republic of Ragusa. Despite its nobility, it is a little fortunate family and Niki becomes a religious in his majority [ 8 ] . Ghetaldi is first of all the student of the Franciscans of Ragusa, whose school is located at the western door of the city. The priest Ivan Simunov (Jean Siméon) teaches him grammar and literature there. Later, Andreas Gallus, Nicolas Di Matteo, Ivan Hristoforov (Jean Christophore) and Victor Basaljic teach him mathematics [ 9 ] , [ 8 ] . He then frequented the university circles grouped around Flora Zuzori, a beauty that is sung by many poets, where the astronomer Nicolas Nalješković, the philosopher Nicolas Gučetić, the poets Victor Beselji and Didacus Pyrrhus as well as the historian Pan Pan Pan -Slave Mavro Orbin.

At the age of eighteen, Ghetaldi enters the Grand Council, the legislative body of the Republic, as a clerk, and therefore leads his administrative and scientific careers. His work essentially concerns arms and the sale of salt, including six months on the Janjina peninsula, where he is suspended for a time for having ignoring the laws [ 8 ] .

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Travel time [ modifier | Modifier and code ]

In 1597, he abandoned his responsibilities from the district of Sabbioncello and accompanied his friend Marino Gucetic (Di Gozzi), the nephew of the English banker Nicolas Gozzi [ Note 3 ] , in his travels. They go to Rome where Ghetaldi is the pupil of Clavius; In England, where he remains two years in the company of Marino Gucetic and binds with Francis Bacon; Then in 1599 in Antwerp where he completed his training with Michel Coignet and Federico Saminiati [ Note 4 ] of Lucca.

Proposed to a position as a mathematics professor at the University of Louvain, which he declines, he came to Paris (around 1600) and meets François Viete of whom he became the friend. The Parthenay mathematician communicates to him some of his works, including his Harmonicon Celeste [ ten ] And as the master of the requests of Henri IV lacks time to deal with his own mathematical work, Ghetaldi publishes with David Leclerc his Apollonius Gallus (the English Apollonsius) eton The numerous power [ 11 ] , [ twelfth ] , [ 13 ] .

A letter from Marino Ghetaldi’s hand, dated , and intended for his master, Michel Coignet, illustrates the respect he has to the French surveyor.

“Finding myself in Paris for other personal things, I wanted, before leaving for Italy, to visit him. His knowledge proved to me that he was no less affable than scholar. Not only did he show me a lot of his still unpublished works, but he entrusted them to me, so that I can screw them to my house and my convenience. I was able to study several treaties from his new algebra, which opened a such light to me that I seem to see a host of things without which I would consider myself blind. »»

– Letter to Coignet, February 15, 1600 [ 14 ] .

Subsequently, Ghetaldi becomes a follower of this way of writing mathematics, which makes it possible to move from the study of specific cases to the general resolution of whole families of problems, put into equations according to the process described by Viete.

The following year (1601), he returned to Ragusa by Italy [ Note 5 ] And stays in Padoue, where he binds with Paolo Sarpi [ 15 ] chez lesbian librichilile GIAN Vincenzie Pescelo Peselli (EN company’s Pessot [ 7 ] ). He meets Galileo with which he then remains in regular correspondence [ 16 ] , [ 17 ] . He follows his teaching and Galileo reveals his compass to him, which Ghetaldi proposes to copy. After a year, he left Padua, and ended up arriving in Rome around 1602. He notably met there the mathematician-Jesuite Luca Valerio, member of the Academy of Lyncusians, friend of Galileo, and Neapolitan and anti-copernican Jesuit.

First publications [ modifier | Modifier and code ]

His first work, the only one as a physicist, the Promoted Archimedes or of various types of gravity and size comparable (not Latin: Archimedes’ presentation relating to the density of heavy bodies and the comparison of their size ) (abbreviated Promoted to Archimedes ), is printed in 1603. Dedicated to Cardinal Olivario, he relates to the serious and under the pretext of presenting Archimedes’ physics, Ghetaldi gives his own measures of the densities of gold, mercury, silver, Copper, iron, tin … but also water, wine, oil, wax and honey [ 18 ] . He does it with great precision, demonstrating with the help of the specious algebra of proposals on the mixtures of gold and silver (the called problem of the crown of Heron II) which until then have only been treated rhetorically [ 19 ] . His second work, Do no proposals about the parabola (On the parable), dedicated to the Jesuit of Bamberg, was released in Rome the same year (1603). Ghetaldi defines parables there as sections of a revolution cone.

The return to Ragusa [ modifier | Modifier and code ]

View of Ston from the ramparts. Overview of the saltworks in the background

Towards the end of the year 1603, he nevertheless experienced some troubles with justice without the cause being known. His biographers do not know the origin of his resources either (a rich heritage in England is assigned to him [ 6 ] ), nor the role with him of Marino Gučetić of Gozzi, who seems to have accompanied him in each of his trips for six years. Ghetaldi escapes himself from Rome via Venice and then returns to Ragusa, where he resumes his place in the Great and the Petit Council of the Republic. Appointed judge at the Court of Appeal in 1604, he was in this period in charge by the Senate to ensure the inhabitants of the city of Ston with malaria. This city, a source of important income for Ragusa thanks to the saltworks of the Neretva and the Pelješac peninsula, is protected from threats from the Ottoman and Venice Empire, by external ramparts over 5 kilometers, and interiors on 900 meters [ Note 6 ] . He undertakes the consolidation of the semi-circular tower, Pozvizd [ 20 ] , which dominates the fortifications of Ston. His appointment to the reconstruction of Ston’s ramparts was acquired two years earlier by 22 votes against 12 and one abstention [ 21 ] . Ghetaldi cannot, however, escape the disease. After a period of care, he was among the envoys of the Senate of the Republic with Constantinople in 1606. This mission was deemed perilous, and the rumor runs that he left life there. This rumor runs still several years after this trip [ 22 ] . Again in Ragusa, and in correspondence with the mathematicians Christopher Grienberger, Clavius [ 23 ] , Galileo and Paul Guldin, he finds himself, according to his own words:

“In a corner of the world where you never see a mathematical gazette [ 24 ] . »

Paul Guldin, who appreciates his work, tries to persuade him to edit Viete’s complete works in Munich [ 6 ] .

  • Remparts de Ston
  • Remparts de Ston
  • Fort Kaštio
  • Les salines de Ston

Second publications [ modifier | Modifier and code ]

In 1607, he published in Venice L’Apollonius recycling or restored Apollonius Pergaei inclinations geometry (Restoration of the book by Apollonios de Perga on the inclination), again dedicated to Cardinal Olivario [ 7 ] , and the APOLLONIUM reinforced the French or exsuscripta Apollonius Pergaei tactis part of the rest of the geometry (held English Apollon from François Vète), demading to Paolo Emilio has been acquainted by Paolo Emilio Cesi [ 7 ] , Era, Marquis de Riano and Within Cardinally Killays Cesu [ 25 ] , as well as a small book, Various problems collection (collection of various problems), dedicated to Marino Gozzi [ 7 ] and containing 42 geometry problems and their solutions. Marino Ghetaldi written [ 26 ] :

“I dedicate this book to you, to you with which I crossed for six years almost all of Europe. And to tell the truth, I don’t know if no one knows the concerns of my mind better than you. »»

In 1613, he published Apollonius reconstructed or restored Apollonius Pergaei himself inclinations of Geometry Book (The second book of inclinations of Apollonios de Perga), and has a controversy for some time with Clément Cyriaque de Mangin, in which his Scottish friend Alexander Anderson also participates and in which it is a question of defending the memory of François Viete.

The mage and the consul [ modifier | Modifier and code ]

The Palace of the Raguse Rector

After his stay in Constantinople, where he sought in vain for manuscripts translated from Greek to Arabic, Ghetaldi specializes in the development of optical instruments, parabolic mirrors and telescopes. He leads his experiences in a cave that remained famous today [ 27 ] . The people and the sailors then take it for a slightly crazy “mage”. In a letter to Clavius, he flattered himself in 1608 to be able to melt under the sun lead, money, and steel at the hearth of his mirror, which supposes a temperature of 1 200 °C [ 28 ] , [ 29 ] . The same year (1608), the , he writes to Galileo that he is as buried living in Ragusa:

‘ I am here as a buried [ 30 ] . »

In charge of the Wine Office, then wool, and finally consul for civil disputes and again judge at the Court of Appeal, he is authorized to return to Rome in 1620.

He saw a year there, and was elected the following year (without ever sitting there official because the academy does not know where he is lodging [ thirty first ] ) to the Lycèse Academy. At that time the members of the Academy were closely monitored by the Holy Office and Ghetaldi left for Ragus [ 32 ] .

In 1625, in a letter dated , he writes to “Older friend who has left” , the Jesuit mathematician Christopher Grienberger, how he proposes to measure the diameter of the earth using calculations on the spherical triangles. He dies as he is preparing a new trip to Rome [ 33 ] In order to realize this dream of surveyor.

Wedding, friendships and currencies [ modifier | Modifier and code ]

Marino Ghetaldi married Marijom (or Maria) Sorkočević, died in diapers, of which he had three daughters: Anica, Franica and Maria.

Its friends also has the Jesuit mathematician Théodose Rubeo [ 34 ] Other Rossi, élève of the Clavius [ 35 ] , [ Note 7 ] , The Sichissimime Rotaniste Gian Vincenzo pinna et Matthantianen-omnronanta paan labi de lui cultrait [ 36 ] : “Angel for costume (manners), demon for mathematics. »»

The Ghetaldi house in Ragusa

It is also linked to Cardinal Serafino Olivario, prelate of French origin, legal and confidant advisor of the pope [ 7 ] . Among his friends is the Orientalist Scottish poet George Stracchan [ 37 ] , which came to Paris in 1592, then to Rome, and pushed its linguistic journeys [ 38 ] Until Anah (only her is kept White friends ).

Some authors including Montucla then Maximilien Marie [ 39 ] in his History of mathematical and physical sciences wrongly claim that the mission of which he was charged near the Sultan interrupted his work and that he did not return to Constantinople.

A districted is attributed to him, engraved on the property of the ghetaldi:

” Stay away. Do not worry about jealousy, arguments, or vanity. Peace and tranquility adorn the cave, gardens and rocks. »»

Finally, in his preface to Promoted , he modestly affirms [ 40 ] :

‘ It is I am who I would rather know how to know how to learn how to teach. »

A work between two centuries [ modifier | Modifier and code ]

Ghetaldi’s work extends in many directions. It is located at the hinge [ 41 ] Between the time of major innovations at the end of XVI It is century and the one where the tools of algebra and mechanics will truly settle. Ghetaldi is one of these intermediate generations, with whom he corresponds, those of Johannes Kepler, Paul Guldin, Willebrard Snell, Jacques Aleaume, Albert Girard but also Jean de Beaugrand and Alexander Anderson or Paolo Sarpi, generations who continue the work of Copernicus, Viete, Harriot or Tycho Brahe, but which do not see their efforts. If Galileo is distinguished from them by its longevity, it is the only one that can collect a share of the benefit of so many works, whose coronation is the work of the next two generation, with Wallis, Fermat, Girard Desargues, Descartes, Frans Van Schooten, Christian Huygens, Newton and finally Leibniz [ 42 ] . There is therefore something unfinished and peripheral in the work of the mathematician and Ragusain physicist. And this is not surprising because his work was born in Ragusa, in a city that declined, located far from all mathematical centers, so that, several times in his life, Ghetaldi manifests the awareness of this isolation. If he publishes, it is in Paris, Padua, Rome, Venice, not in Ragusa. As for her latest work, significantly, she is published by her daughters posthumously via the Apostolic Chamber, in Rome, under the protection of Cardinal Francesco Barberini, the one who, three years later, tries in vain to protect Galileo.

Because Ghetaldi’s work develops in the shadow of the Company of Jesus and his best supporters, the two pontifical mathematicians, Christopher Clavius ​​and Christopher Grienberger, far from the innovation home that is at that time Protestant Holland [ 43 ] . Its impossible affiliation to the Lycéen Academy also marks the difficulty for Italian mathematicians and physicists of the first half of the XVII It is century to work freely, without accounting in Rome. Did Sarpi and Galileo know, in the 1610s, the same type of difficulty in making their discoveries admitted? It seems that Ghetaldi has folded better than them.

In a more particular way, Ghetaldi sets an internal limitation in his approach to science, that of restoring – in Latin, his native language – the works of the ancient Greeks, and to do it mainly using the geometric tool . While other European scholars, a little younger, further from Rome, like Albert Girard or his friend Anderson embarked on the search for new inventions in algebra, Ghetaldi tries to remain faithful to his first masters, Clavius ​​and Coignet, Only appealing in the last resort of the new algebra of Viete. He then does it with great dexterity; so great that it has sometimes been considered the precursor of analytical geometry [ 41 ] .

Physicist ghetaldi [ modifier | Modifier and code ]

The Foyer of the parabolic mirror

In physical sciences, Ghetaldi performs several experiences on the density of materials, leaving excellent measures of these densities; It is also known for its tinted glasses manufacturing [ 44 ] ; His manifest interest in mirrors and in particular parabolic mirrors, whose home he describes have remained in the memories; In addition to his political works, he is also known for his attempts to measure the terrestrial department.
Thirty years after nearly his death his works are still estimated and his density scales (published in the Promoted to Archimedes ) are still resumed, notably by Gaspar Schott, who integrates them as they are in his Magic universal of 1658.

Mathematician ghetaldi [ modifier | Modifier and code ]

In mathematics, Ghetaldi’s work is even more considerable. Student of Michel Coignet and Christopher Clau [ 45 ] , correspondent for Galileo Galilée and friend of Alexander Anderson, he is a patient emulator of Apollonios de Perga and writes two pounds to his glory. But above all, he publishes, popularized [ forty six ] And continues the work of Viete, which he completes by numerous works announcing the discoveries of Pierre de Fermat and Girard Desargues.

Ghetaldi’s most important contribution to mathematics is its application of algebra to geometry, particularly in its The resolution of the composition of mathematics, five , posthumously published by her daughters, Anna Francesca and Maria (they published this book while respecting the will of their father to dedicate him to Cardinal Francesco Barberini). In this work, Ghetaldi announces, ten years before, the geometry of the philosopher of The Hague, and, eight years before, Pierre Hérigone and his mathematical courses . This publication was sometimes considered the first book of analytical geometry [ 47 ] never published.

On page 240 of this latest publication [ 48 ] , appears in particular in writing

F i n A + G i n A – – A Q {Displaystyle Fina+Gina-Aq}

aequabitur

WITH Q {displaystyle ZQ}

The equation of a conical [ Note 8 ] . Also remarkable in this work the particular form of the symbol ”

′ + ′ {Displaystyle ‘+’}

», Close to a pattered cross or a Malta cross. It was already found at DE HORTEGA (in its Treatando subtillissimo de arithmetic y geometry , in 1552 and 1563), Guillaume Klebitius (in 1565) and Adrien Romain (in 1593), and it was found in René Descartes (in 1637) [ 49 ] .

In the years following his disappearance, the mathematical work of Ghetaldi particularly influences Paolo Sarpi, Antonio Santini [ 50 ] , Jean de Beaugrand [ forty six ] , Giovanni Camillo Glorioso et Carlo Renaldini [ 51 ] One of the last Italians to adopt the language of new algebra, as well as the English mathematician William Oughtred, who takes up part of his results in his Brochures mathematics .

A moving work [ modifier | Modifier and code ]

Marino Ghetaldi (Gallery of illustrious Ragusans)

Whether for lack of time, because of his charges in the Republic or the little importance that he attaches to delimit the field of his proposals, the work of Ghetaldi is not free from incorrections or errors [ 52 ] . In addition, he remains a prisoner of the desire to reconstruct the books of Antiquity. This quest dominates the mathematics of the late Renaissance (up to Hérigone), and Ghetaldi does not escape it. Like his predecessors, Francesco Maurolico or Marule, Viete, or Snellius, Ghetaldi innovates by believing to find the true algebraic language of Pappos, Diophante, Theon of Alexandria or Apollonios of Perga. Through this rediscovery, in a whole new style, of the analysis of Apollonios, thereby exceeding it singularly in the words of Jean Itard [ 53 ] , Ghetaldi suggests in his latest work, posthumously published, the first developments in analytical geometry.

However, this evolution is not without hesitation or fight. It began in 1603, when, in its Of the various , Ghetaldi solves three kinds of problems with purely geometric methods. He does not always give the conditions under which his resolutions apply.

In Some proposals from the parabola , Ghetaldi also failed to perfectly demonstrate the identity of the parables obtained by section of an oblique cone and those obtained by section of a cone of revolution [ 52 ] .

Later, in Supplement Apollonius French , it only resolves imperfectly the fifth problem of Apollonios.

This last error caused the publication in 1612 by Alexander Anderson of his Supplement Apollonius [ 52 ] . The Treaty of the Scottish is then brought to Ragusa by the Orientalist George Strachan and gives rise to a correction of Ghetaldi in 1613 in his Apollonius recycling or restored Apollonü Pergaei de inclinations of the geometry, the second book . Although their methods of resolving this fifth Apollonios problem are different, Ghetaldi marks in his preface all the respect he owes to the work of the Scottish. Anderson, for his part, dedicated to Ghetaldi the publication in 1615 of his Zetetics of Apollonius problems . A mathematical friendship is formed around the heritage of Viete.

But, in 1616, Ghetaldi attracted the wrath of the Burgundian mathematician Clément Cyriaque de Mangin [ 54 ] For his work of 1603. Mangin (then Jacob Christmann and later of Michelangelo Ricci) particularly criticizes him for his errors in the resolution of a problem due to Regiomontanus: The triangles of the planes and a spheresh ( Plans and spherical triangles , first edition 1533).

Then, in 1617, it was Alexander Anderson who defended Ghetaldi and the honor of the school of François Viete (namely cited by de Mangin), by publishing an answer, scathing, CYRIACO VIETAM CYRIACO CYRIACO Cyriaco recently short Διακρισις , against Cyriaque. Anderson also completed its resolution, in 1619, in Exercises of mathematician decas first .

When at the end of his life, Ghetaldi returns to this defective demonstration one last time, he does so with the desire to resolve this difficult question by new methods. This is indeed found in his latest work, the The resolution of the composition of mathematics, five , which opens with the list of proposals to demonstrate and gives the algebraic solutions to some problems of Apollonios of Perga [ 55 ] that Ghetaldi has already resolved geometrically (without specifying the limits of the quantities in play) in his first publications. Ghetaldi then resumed the fifth problem of Apollonios there by the methods of new algebra (without citing the work that Anderson devoted to this subject in 1619, failing to have received them according to Ronald Calinger [ 52 ] Because probably, the Scottish died in the meantime). This innovative work, in which the first traces of analytical geometry appear, was the subject of in -depth studies by Eugène Gelcich in 1882 [ Note 9 ] .

Publications [ modifier | Modifier and code ]

Various problems collection , 1607

During his lifetime Ghetaldi publishes six works but his main work is posthumously published:

We also owe him the construction of a parabolic mirror preserved until XIX It is century in the collections of the Barbarini family, then at the London Maritime Museum [ 56 ] as well as in 1604 the construction of a tower Pozvizd , part of the Ragusa fortification system.
A publication of sees was carried out for the 400th anniversary of his birth, we will consult for this purpose the analysis devoted to him by Jean Grisard [ 57 ]

Resounding [ modifier | Modifier and code ]

The coat of arms of the Ghetaldi family

Ghetaldi is recognized very early as one of the best surveyors and algebraists of his time. As early as 1603, Henry Percy, the protector of Thomas Harriot and ninth count of Northumberland heard of him [ 58 ] . A certain competition is also established around Harriot about the measures of densities. In France, less than four years after his disappearance, Pierre Hérigone gives, at the end of the first volume of his Mathematician , four problems under the title of Apollonius Pergeus’s inclinations of inclinations, returned by Marinus Ghetaldus (Pergaei inclination of geometry, a marine Ghetaldo restored). CET EMPRUNT who VA de la Page 905 à 914 n’est autre que l ‘ Apollonius recycling or restored Apollonius Pergaei inclination of the geometry , or at least 4 problems of this treaty. As for Johannes Kepler, he took him, according to his letters, like the equal of Galileo. He is also appreciated by Mersenne and Claude Mydorge [ 59 ] , [ 60 ] .

At the end of XVII It is A century, the work of Marino Ghetaldi was still held in great esteem by many scholars, notably the Englishman Edmond Halley and the Dutch Christian Huygens. French Montucla still quotes it in its history, but gives Descartes all the glory of the invention of analytical geometry. In the following century, Charles Bossut and Joseph-Louis Lagrange almost scratched him in their history of sciences [ 58 ] . The Germans nevertheless pay tribute to him [ 58 ] , notably Abraham Gotthelf Kästner. In fact, its influence is maintained at XVIII It is century through the English, John Lawson [ sixty one ] , Samuel Horsley [ 62 ] , Reuben Burrow [ 63 ] which borrow a lot from his work [ 6 ] . They are followed in the following century by Johann Wilhelm Camerer [ sixty four ] et Daniel Schwenter [ 52 ] .

At XIX It is A century, Michel Chasles seems to ignore its importance and speak of it only in the margins of Viete [ 65 ] . I am The ITALY Francesco Maria APENDINI [ 66 ] and G. Barbieri paid tribute to him in 1802 then 1840, in their illustrious Ragusan galleries. They are followed sixteen years later by the Croatian Simeone Gliubich. In 1868, the publisher of the Penny Encyclopedia, Charles Knight, devoted a few pages to him in his biographies [ sixty seven ] But we will have to wait until the end of XIX It is century, with Antonio Favaro, Heinrich Wieleitner (1874-1931) [ 68 ] And Croatian Eugène Gelcich (a teacher at the Naval School of Pola, Austria) so that his role is fully recognized. However, his works have still not been translated from Latin.

Michael Sean Mahoney evokes in The beginnings of algebraic thought [ 69 ] the importance of The resolution of mathematics ; He pays him a vibrant tribute in The mathematical career of Pierre de Fermat, 1601-1665 [ 70 ] , specifying with what Ghetaldi care performs the ztetic and poristic stages of the geometric problems he has in sight, but also the vigilance with which he follows in their exegesis, the stages of Poristic. Mahonney judges for example that he is particularly useful in understanding theorems that Fermat leaves, a few years later, to the sagacity of his reader [ 71 ] . More recently, his work has been fully reissued, and commented on, by Croatian astronomer Zarko Dadic [ 72 ] .

In his homeland, the fame of Marino Ghetaldi has long remained in the spotlight: at XIX It is , Ragusa still gives its name to a ship and, nowadays, He is one of the few mathematicians to have his Facebook page [Ref. necessary] , while he is still making the headlines of the local weekly on the anniversary of his death (the 7th or the ) [ Note 10 ] .

As for the cave, located at the foot of Mont Bergato, in which he worked on his optical experiences, this ragous cave, where he led his experiences on the mirrors, and linked to his villa by a staircase stolen according to the writer Andrew Archibald Paton [ seventy three ] , this cave which gave her the reputation of a hermit and a mage to her, she has bears from her nickname beast [ 74 ] .

Notes [ modifier | Modifier and code ]

  1. ↑ No arguments seem to decide between the date of 1568, more modern, cited by žarko Dadić and Saltykov in Memories concerning the yugoslavic surveyor Marinus Ghetaldi (1968) and the date of 1566, older, cited by John Gardner Wilkinson, Maximilien Marie or Andrew Archibald Paton
  2. ↑ 1627 According to Antonio Favaro, Wilkinson and Patton but 1626 after Michel Chasles, Johann Christoph Heilbronner, the Dictionary of Scientific Biography (New York 1970-1990) et H Wieleitner, Marino Ghetaldi, Marino Ghetaldi and the beginnings of coordinate geometry, 1915, in Bibliotheca Mathematica.
  3. ↑ (in) L’A article d’Adam S. eterovich, On the Croats in England in the time of Ghetaldi , on the site Croatians.com is the only source available on the tribulations of the two friends in England and the reason for this trip, linked to the inheritance that the nephew of the banker Nicolas Gozzi must collect [ read online (page consulted on September 23, 2010)]] .
  4. ↑ Federico Samminiati (1573? -1632) studied in Antwerp with Michel Coignet, and published in 1599 in this city (which he considers his homeland) a collection of astronomical tables where are verses of Michel Coignet, as well as extracts from Letters from Coignet to Mercator and some glowing comments by Marino Ghetaldi on the work of Saminiati. (it) Cesare Lucchesini, Memoirs and documents to serve at the Istory of the Principality of Lucca, Volume 9 (Memoirs and documents to serve the history of the Principality of Lucca), 1825, Presses Francesco Bertini, 268 p. [ read online (page consulted on September 23, 2010)]] .
  5. ↑ A notarial act gives it there the as a witness to (hr) Nicolas Gucetic Testament (article by Ivica Martinovic, published on the site Science in Croats – Science in Croatia [ read online (page consulted on September 23, 2010)]]
  6. ↑ A photograph of interior fortifications is available on photos-voyages.com and a photograph of Ston’s ramparts, Naru Kenji work is available on panoramino , by 42 ° 50 ‘8.84 “N and 17 ° 41’ 33.75” E.
  7. ↑ Theodosius of Rossi is quoted by Johannes Kepler after Three imperial mathematicians d’Edward Rosen, Abaris Books, 1986 (ISBN  0898352428 ) , p. 204 [ read online (page consulted on September 20, 2010)]] . He is a papal bouclier carrier; he remains his his necessary for drawings (on the site of the Paris Observatory), as well as a solar clock (on the Site Italy devoted to gnomonic).
  8. ↑ There is also direct parentage between the algebraic notations of Ghetaldi and those of his former friend, François Viete. Unlike Ghetaldi, Blaise Pascal uses for example, some 30 years later, the notation equated (present) in place and d’aequbitur (future), as did before Viete Francesco Maurolico [ read online ] .
  9. ↑ A list of works by Eugène Gelcich is available at this address on Abe.Book .
  10. ↑ Anniversary of the death of Ghetaldi reported on the first page of the Dubrovacki List (the Dubrovnik sheet) [ read online (page consulted on September 23, 2010)]] .

References [ modifier | Modifier and code ]

  1. ↑ (in) Harriet Bjelovucic, The Ragusan Republic: victim of Napoleon and its own conservatismHarriet Bjelovučić , Brill Archive, , 192 p. ( read online )
  2. ↑ Egidio Festa, Vincent Jullien, Maurizio, Geometry, atomism and empty in the Galileo school , Publié from Florence, Fontenay and Saint-Cloud of Science and the History of Science Museum of Science [ read online (page consulted on September 20, 2010)]] . p. 82 (ISBN  2902126514 ) .
  3. ↑ Pierre Boutroux, The principles of mathematical analysis , Bookstore in Hermann and Files, first edition 1919, [ read online (page consulted on March 9, 2011)]] .
  4. ↑ National Maritime Museum, Park Row, Greenwich, Londres
  5. ↑ (in) Latin Croatian writers Extract from an article by Branko Franolic, Works of croatian latinists recorded in the British library general catalogue (Works of Croatian Latinists kept in the general catalog of British libraries), Croatian Information Center (December 1998) (ISBN  953-6058-26-X ) [ read online (page consulted on September 20, 2010)]] .
  6. ↑ A B C and D (in) NEPRINAJSTIC, The Great Men of Croatian Science (“The great men of Croatia”, 1996), article available on the site Sciences and Croatia [ read online (page consulted on September 20, 2010)]]
  7. ↑ a b c d e and f (it) G. Barbieri, Gallery of Ragusei illustrious] (Portrait of illustrious Ragusans), section XVII, Martecchini, 1841, 208 pages, not paginé [ read online (page consulted on September 20, 2010)]] .
  8. ↑ A B C and D (hr) Ivan Drazic , Marino Ghetaldi; Life and work of a Croatian mathematician (Marino Ghetaldi- Life and Work of the Father of Croatian Mathematics), Publié a couple Mathematics and schools , Journal of Mathematics Teaching (1332-0327) VI (2004), 27, p. 78-83 [ read online (page consulted on September 20, 2010)]]
  9. ↑ Article Ghetaldi de Mactor [ read online (page consulted on January 21, 2011)]]
  10. ↑ (in) Christine Jones Schofield evokes the celestial Harmonicon, in Tychonic and semi-Tychonic world systems (world systems according to Tycho-Brahé) Note 110, p. 326 . Ayer Publishing, 1981 (ISBN  0405138598 ) [ read online (page consulted on September 23, 2010)]] .
  11. ↑ Florian Cajori, a history of arithmetical method (1907) [ read online (page consulted on September 23, 2010)]] .
  12. ↑ (in) Francis Masseres, a specimen of vieta’s method of resolving algebraic equations by approximation , London (an example of Viete methods for the approximated resolution of the algebraic equations), 1800, ex. at BRISTISH MUSEUM
  13. ↑ Bulletin of the Archaeological Society of Touraine, volume IL], Tours 2003, p. 152 . [ read online (page consulted on September 23, 2010)]] .
  14. ↑ An extract from Ghetaldi’s letter on the Jean Paul Guichard site [ read online (page consulted on September 20, 2010)]] .
  15. ↑ (it) Aurelio Angelo Bianchi-Giovini, Biography of Fà Paolo Sarpi: Theologian and State Consultor of the Venetian Republic] (Paolo Sarpi, theologian and expert in the Republic of Venice), Zürich, 1836; D.G. Bellini, 1847, p. 322 [ read online (page consulted on September 20, 2010)]] (Book put in the index [ read online (page consulted on September 20, 2010)]] ).
  16. ↑ (in) Mordechai Feingold, The new science and Jesuit science: seventeenth century perspectives (modern science and the Jesuits, prospects for XVII It is century) Springer, 2003 [ read online (page consulted on September 20, 2010)]] , p. 119 (ISBN  1402008481 ) .
  17. ↑ (in) Paul Oskar Kristeller, Italian way: A finding list of uncatalogued or incompletely catalogued humanistic Mss, volume 1 Italy: Agrigento-Novara (a list of Italian manuscripts not – or badly – cataloged), Brill, 1977 (ISBN  900412540 ) , lists, p. 147 , part of the letters of Galileo [ read online (page consulted on September 20, 2010)]] .
  18. ↑ John Ward, The guide to young mathematicians, or watered of mathematics, within everyone’s reach At Ch. An. Jombert, printer-library, 1756, p. 133 [ read online (page consulted on September 20, 2010)]] .
  19. ↑ (in) John J. Roche, The mathematics of measurement: a critical history (Critical history of measure), Springer, 1998, p. 59 and 91 (ISBN  0387915818 ) [ read online (page consulted on September 20, 2010)]] .
  20. ↑ A photograph of the ruins of Pozvizd (1335) is available On Destinacije.com
  21. ↑ . The reconstruction of the Ston fortress was voted in January 1603 and started in March in M. Foretic, The exhibition catalog about the life and work of Marina Ghetaldic , Zagreb, 1968, Institute of History of the Academy of Sciences, ( p. 15 ).
  22. ↑ In 1609, Montucla still gave him for death during her mission to the sublime door, on Mac Tutor ).
  23. ↑ (in) CHIKARA SASAKI, Descartes’s mathematical thought (Descartes’ mathematical thought), Springer, 2003, p. 83 , 72 and 75 (ISBN  1402017464 ) [ read online (page consulted on September 20, 2010)]] .
  24. ↑ This letter from Marino Ghetaldi to Father Christopher Grienberger dates from September 1604 and asserts verbatim, In the corner of the world where no mathematical newspaper can be seen (In a> World Ou Coin if it’s alloy up to Journal Matredumia). Shes est CITTice by Ivica Martin – Aprough by Après R.g. Villoslada: Roman Collegio Dal SOI start (1551) the sipression of Jesus’s compagnes (1773), GREGORIANA, RIM, 1954, pp. 195-199 [ read online (page consulted on September 20, 2010)]] .
  25. ↑ Montaigne, Travel journal published with an introduction, notes, a table of proper names, and the translation of the Italian text of Montaigne , p. 363 , edition commented by Louis Lautrey, edited by Hachette (1906) [ read online (page consulted on September 20, 2010)]] .
  26. ↑ To you, he says, I entitle this book, to you with whom I spent almost the whole of Europe for six years. And to say the right, I don’t know if the field of my intellect recognizes a better lover of you, écrot -il à marino gozzi, d’Aperès (it) G. Barbieri, Illustrious Ragusei gallery , Section XVII, Martecchini, 1841, 208 Pages, Non Paginé [ read online (page consulted on September 20, 2010)]] .
  27. ↑ (hr) A photograph of Betina cave , that is to say of The cave of the beast , work of Ivo Banovac and another, taken by martinav are available on paoramio
  28. ↑ (hr) D’Arès Ivica Martinovic, Marino Ghetaldic , on the site Science in Croats (Sciences in Croatia) [ read online (page consulted on September 20, 2010)]]
  29. ↑ A photograph of this mirror is found here , extract from an article by Ivica Martinovic [ read online (page consulted on September 23, 2010)]] .
  30. ↑ Literally: “I’m here as buried”, in Ž. Dadic, Croats and exact sciences at the dawn of classical age , Zagreb, 1994, pp. 155-192
  31. ↑ According to Richard S. Westfall (from the Department of Philosophy of the University of Indiana), in a short biography of Ghetaldi, published on Galileo.rice.edu [ read online (page consulted on September 20, 2010)]] .
  32. ↑ Marino Ghetaldi Sur Galileo.rice.edu (ibid)
  33. ↑ (it) Francesco Maria Appendini, Historical-critical news on antiquities, history and literature of Ragusei, volume 2 . p. 104 . Apprndini says But the Ghetaldi died, when it was arranged for the departure for Rome (But Ghetaldi dies, while he will go to leave for Rome) [ read online (page consulted on September 20, 2010)]] .
  34. ↑ (it) Šime Ljubić, Biographical dictionary of illustrious men of Dalmatia (Biographical dictionary of illustrious men from Dalmatia), Lechner, 1836, p. 142 [ read online (page consulted on September 20, 2010)]] .
  35. ↑ Rossi Publication, aka Rubeus, South WorldCat [ read online (page consulted on September 20, 2010)]] , or amazon.fr [ read online (page consulted on September 20, 2010)]] . Some of his publications are found in the collections of the decisions of the Roman Rote, [ read online (page consulted on September 20, 2010)]]
  36. ↑ “A Angel Angelo Angelo Angelo A Angel (Devils” Equonious Maceronica » In G. Barbieri, Gallery of Ragusei illustrious] (Portrait of illustrious Ragusans), p. 6 of section XVII [ read online (page consulted on September 20, 2010)]]
  37. ↑ (in) Alasdair A. MacDonald, Michael Lynch, Ian Borthwick Cowan, The Renaissance in Scotland : studies in literature, religion, history, and culture offered to John Durkhan (The Renaissance in Scotland, itery, religious, historical and cultural studies dedicated to John Durkhan), edited by Brill, 1994 (ISBN  9004100970 ) p. 414 [ read online (page consulted on September 20, 2010)]]
  38. ↑ (in) Jenny Wormald, Court, kirk, and community : Scotland, 1470-1625 (The Court, the Scottish Churches and the Community), Edinburgh University Press, 1991 (ISBN  0748602763 ) , p. 185 [ read online (page consulted on September 20, 2010)]]
  39. ↑ Maximilien Marie, History of mathematical and physical sciences (1883) , Gauthier-Villars, Paris [ read online (page consulted on September 20, 2010)]]
  40. ↑ This word which means “I am one of those who would prefer to know rather than be famous, to learn that teaching”, is found in The Works of Francis Bacon (the work of Francis Bacon): “Better to know than being known …” ( p. 192 ), [ read online (page consulted on September 20, 2010)]] . It is also a reminiscence of Saint Augustine: “Better to learn that teaching” according to the Revue des Études Augustiniennes 1999) [ read online (page consulted on September 20, 2010)]] .
  41. ↑ a et b Article by C. Dolbeau, Croatian scholars in Paris on the site of Croatian studies [ read online (page consulted on September 23, 2010)]] .
  42. ↑ To complete the study of this pivotal period, consult (in) J. Ridgeway, The British and foreign review , volume 1, 1835, p. 142-150 [ read online (page consulted on September 23, 2010)]] Et Egidio Festa, Vincent Jullien, Maurizio Torrini, Geometry, atomism and empty in the Galileo school (Ens ed., 1999), p. 82 , (ISBN  2-902126-51-4 ) [ read online (page consulted on September 20, 2010)]] .
  43. ↑ The attraction that the dynamism of Holland of the “golden century” and the financial reasons for this dynamism in Christophe de Voogd, The civilization of the “Golden century” in the Netherlands , article of the former director of the Maison Descartes (French Institute of the Netherlands) on the site Clio [ read online (page consulted on September 23, 2010)]] .
  44. ↑ (in) J.J. o’connor et e.f. Robertson, Article Marino Ghetaldi , in
    MacTutor History of Mathematics archive, 1996 [ read online (page consulted on September 23, 2010)]] .
  45. ↑ Seven letters from Ghetaldi to Clavus, written between 1602 and 1608 have reached until XXI It is Siecle. Eberhard Knobloch, “sur la vie et l’œuvre de Christophora Clavius ​​(1538-1612)» Science History Review , 1988, Volume 41, p. 353 [ read online (page consulted on September 20, 2010)]]
  46. ↑ a et b (it) Antonio-Carlo Garibaldi, The first diffusion of forbidden in Italy , (Department of Mathematics of the University of Genes) published on the occasion of the fourth Congress of the SISM (Italian Society of Mathematics History), in 2004, p. 28 [ read online (page consulted on September 20, 2010)]]
  47. ↑ (it) Francesco Maria Appendini, Historical-critical news about antiquities: history and literature of Ragusei Me fragechini, 1803, p. 47 [ read online (page consulted on September 20, 2010)]] .
  48. ↑ Through the way Ghetaldi writes in his The resolution on the site European Cultural Heritage Online [ read online (page consulted on September 20, 2010)]] .
  49. ↑ (in) Florian Cajori , A History of Mathematical Notations [Detail of editions] , Dover, 1993, p. 238 [ read online ] .
  50. ↑ Father Somasque Antonio Santini (1577-1662), pupil of Galileo and good Algerianist, professor of mathematics at Sapience, teaches in genes, and knows Father Mersenne and the Dupuy. In 1644 he published a Svpplementi Francis Vietae, and the GEOMETRIAE totivs Apud P. Deshayes, 1644 [ read online (page consulted on September 20, 2010)]] , as well as The reflection point to opticen, geometric establishment , 1645; Inclinativm appendix seù to geometry (printing P. Camaccij , 1648 [ read online (page consulted on September 20, 2010)]] ; In the Geometry Male Restaurata by authors A.S.L. RIMA detectae (Toldographia Louis Monteo, 1650) [ read online (page consulted on September 20, 2010)]] .
  51. ↑ Egidio Festa, Vincent Jullien, Maurizio Torrini, Geometry, atomism and empty in the Galileo school , Florence – Fontenay et Saint-cloud: Institute the History Museum of Science – Ens éd., 1999, p. 81 (ISBN  2902126514 ) [ read online (page consulted on September 20, 2010)]]
  52. ↑ A B C D and E (in) Ronald Calinger, mathematica : historical research and integration with teaching (Mathematical life: historical research for teaching), Cambridge University Press, 1996, p. 122 (ISBN  0883850974 ) [ read online (page consulted on September 20, 2010)]]
  53. ↑ Jean Itard, The geometry of Descartes, conference made at the Palais de la Découverte, the or in collaboration with Rushdi Rashed, Mathematical history tests , edited by the scientific and technical bookstore Albert Blanchard, 1984 (ISBN  2853670430 ) .
  54. ↑ Clément Cyriaque de Mangin published by Denis Henrion, publishes against Viete and against Ghetaldi Problems two noble, the analysis of the geometric, seeing you Nuusius John Regiomontanus and Peter Nonius, nor demonstrated enough represented Francis Vieta and Marine Ghetaldus, now finally a Clemente Cyriaco diligently elaborate and new analyzon forms. ; See Calinger, Vita mathematica: historical research and integration with teaching , p. 122 [ read online (page consulted on September 20, 2010)]] ; Ou Charles Knight, The Penny cyclopædia of the Society for the Diffusion of Useful Knowledge , p. 313 [ read online (page consulted on September 20, 2010)]] .
  55. ↑ (in) Zarko Dadić, Some methodological aspects of Getaldić’s mathematical works , Institute for the history of natural, mathematical, and medical sciences , Zagreb, Yougoslavie ( Some methodological aspects of the work of Ghetaldi ).
  56. ↑ This 71 mirror cm of diameter appears in the Barbarini collection under the name of Disposal 884 ; It is listed by Koenraad van Cleempoel and Silke Ackermann in Astrolabes at Greenwich: a catalogue of the astrolabes in the National Maritime Museum, Greenwich , Oxford University Press, 2005, p. twelfth (ISBN  0198530692 ) . [ read online (page consulted on September 23, 2010)]]
  57. ↑ Jean Grisard, Marini Ghetaldi, Opera Omnia, Zagreb [ read online (page consulted on September 23, 2021)]
  58. ↑ A B and C Franz Xaver von Zach, Astronomical, geographic, hydrographic and statistical correspondence , Bonaudo, genes, 1822, p. 130 [ read online (page consulted on September 20, 2010)]] .
  59. ↑ In the correspondence of Father Marin Mersenne: 1617-1627, edited by M me widow Tannery (G. Beauchesne, 1933), p. 247
  60. ↑ Mydorge, Leurechon’s book examination , 1630, p. 260
  61. ↑ (in) John Lawson, The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat’s Treatise on spherical tangencies (“The two books of Apollonius, on the tangents, as they were restored by François Viete and Marino Ghetaldi, with an supplement of Fermat stone extracted from his Treaty on the Tangentes”), Bigg, London, 1771, available on Echo [ read online (page consulted on September 20, 2010)]]
  62. ↑ (of) Samuel Horsley, Wilhelm Adolf Diesterweg, On Bucher des Apollonius Turning out of inclinations (Le Livre d’Apollonios de Perga, inclination ), G. Reimer, Berlin, 1823 [ read online (page consulted on September 20, 2010)]] .
  63. ↑ Reuben Burrow, A restitution of the geometrical treatise of Apollonius Pergæus on inclinations. Also the theory of gunnery; or the doctrine of projectiles in a non-resisting medium At C. Etherington, 1779, in London (a restoration of the geometric treaty of Apolonius de Perge on inclination, as well as the theory of projectiles in a middle -free environment), available via National Library of Australia .
  64. ↑ A restoration of Apollonios by John William Camerer appeared to Gotha in 1795, also containing a story (curious and correct) of the problem, and interesting by the information it provides on the work of mathematicians on this problem, in Hugh James Rose, A new general biographical dictionary, projected and partly arranged by H.J. Rose (a new general biographical dictionary), Volume II, B. Fellowes and Consort, 1848, p. 51 [ read online (page consulted on September 23, 2010)]] .
  65. ↑ Michel Chasles, Historical overview of the origin and development of methods in geometry: particularly those relating to modern geometry, followed by a geometry thesis on two generous principles of science, duality and homography , M. Hayez, 1837, p. 42
  66. ↑ Francesco Maria Appendini draws up a full portrait in his notice on famous Ragusans, (it) Historical-critical news on the ancient history and literature of the Ragusei (1802) , p. 44 and following [ read online (page consulted on September 20, 2010)]]
  67. ↑ (in) Charles Knight, Biography: Third division of the English encyclopedia, Volume 6 , chez Bradbury, Evans & Co., 1868, p. 383 [ read online (page consulted on September 20, 2010)]] .
  68. ↑ (of) Heinrich Wieleitner, Marino Ghetaldi and the beginning of coordinate geometry (Bibliotheca Mathematica) (Ghetaldi and the beginning of the geometry of the location), a report is found in Mathematical education, international review , Gauthier-Villars, Paris, 1914, [ read online (page consulted on September 23, 2010)]] .
  69. ↑ (in) Michael Sean Mahoney, The beginnings of algebraic thought (the origins of algebraic thought), one of the articles of site Who pays tribute to Princeton. [ read online (page consulted on September 23, 2010)]] .
  70. ↑ (in) Michael Sean Mahoney, The mathematical career of Pierre de Fermat, 1601-1665 Posted by Princeton University Press, 1994 (ISBN  0691036667 ) [ read online (page consulted on September 20, 2010)]] .
  71. ↑ ibid p. 47 .
  72. ↑ Marino Ghetaldi, Zarko Dadic, The works (Salt B002G7P0U0 ) (Zagreb, Institute of History of Natural, Mathematical and Medical Sciences JAZU, 1968).
  73. ↑ Andrew Archibald Paton (1811-1874), Researches on the Danube and the Adriatic Elibron 1861, reprinted by Adegi Graphics LLC, 2002 p. 233 (ISBN  1402159927 ) [ read online (page consulted on March 9, 2011)]] .
  74. ↑ (it) Francesco Maria Appendini, What bete is Marino Ghetaldi in Historical-critical news about antiquities , A. BLCChini, 1803, p. forty six [ read online (page consulted on September 23, 2010)]] .

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