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Science, technology, history, literature and archaeology, certainty and conjecture on the most ancient and extraordinary astronomical calculating device. With two other scientific studies:
on the Antikythera Planetarium and the Pitcher of Ripacandida

With the appendix:
PYTHAGORAS IN THE CONTEMPORARY WORLD. Influences of Pythagorean scientific philosophy in the modern and contemporary world

Copyright © 2006-2013 - All rights reserved - Reproduction even partial and by any means is prohibited

Original title: IL PLANETARIO DI ARCHIMEDE RITROVATO, Rome 2010, ISBN  9788890471520. The translation of this book was made on the basis of the first Italian edition of 2010. Printed in Rome in May 2013. English translation by the Author.  Revision of the English translation by Caroline Miranda Feetam.

(The book is written in English, ISBN 9788890471544) - The only work of its kind

Presentation of the books (Part Two): Rotondella (Basilicata, Italy) August 2, 2013 - YouTube



The Archimedes Planetarium was one of the most admired technical achievements in antiquity. The best information on this apparatus is given by Cicero, who writes that in the year 212 BC, when Syracuse was sacked by Roman troops, the consul Marcus Claudius Marcellus brought an apparatus constructed by Archimedes to Rome that reproduced the vault of the sky on a sphere, and another that predicted the apparent motions of the Sun, Moon and planets, thus corresponding to a modern planetarium. Cicero, referring to the impressions of Gaius Sulpicius Gallus, who had been able to observe the extraordinary object in person, points out that the genius Archimedes was able to generate the motions of planets, each so different from the next, with a single rotation. Archimedes had described the construction of the Planetarium in the work On Sphere-Making. News of the work, now considered lost, was reported by Pappus of Alexandria.

The discovery of the Antikythera Planetarium in 1902, a gear device that dates back to the first half of the 1st century BC also shows how the ancient people developed mechanisms designed to represent the motion of the stars, which in turn has rekindled interest in the Archimedes Planetarium.

With the discovery in 2006 in Olbia of the fragment of an ancient gear, scientifically and technically more advanced than the gear of Antikythera, and after deep, careful and thorough studies considered part of a planetarium designed by Archimedes, has shed a new and unexpected light on the magnitude of scientific thought of the genius of Syracuse. The scientific and mathematical studies of the find have shown that many inventions that we consider modern had in fact already been developed and designed by Archimedes over two thousand years before. The importance of the find, also, is in the fact that to date only a few written works by Archimedes have ever been retrieved (Codices A, B and C) through transcriptions and translations in Greek, Arabic and Latin. Codex C is the oldest Archimedes Codex, the only one still written in Greek on a parchment paper with laid lines in 975, and which became Palimpsest in Jerusalem in 1229, and it is still the subject of studies in the United States. Of Archimedes’ machines, however, it was thought nothing had survived. The find, although small, is not a simple piece of crockery, but instead a great testimony and thus a new, unique and unexpected contribution to the scientific knowledge of the great Archimedes.

The knowledge of epicyclic motion, also known as planetary motion, necessary for the design of the planetary gear in the Planetarium of Antikythera and in the tooth profile of the gear of Archimedes, allows us to assume that some ancient Greek scientists knew the planetary motion of celestial bodies and had achieved the same results later attributed to modern scientists 2000 years later. I assume that the planetary gear could have been used, given the particular kinematic similarity, as a mathematical model for the calculation of planetary motion in the heavens.

In Part Two of the book both the kinematics of the Antikythera Planetarium, also present in the gear wheel of Olbia and which anticipates the heliocentrism of Copernicus, and the mathematical model and analytical development of planetary motion, in relation to the heavens are widely discussed.

In Part Three of the book, another recent scientific study of mine is exposed on the Pitcher found in Ripacandida, Basilicata, dating from the 5th century BC and of Pythagorean derivation. The picture depicts the real event of a large meteorite impact on the Earth, and the physical laws graphically represented therein prove themselves to be extraordinarily modern and in complete antithesis with the later dogmatic Aristotelian physics.

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In English, an orrery is a mechanical device that illustrates the relative positions and motions of the planets and moons in the solar system in a heliocentric model. Though the Greeks had working planetaria, the first orrery considered to be a planetarium of the modern era was produced in 1704, and such a device was presented to the 4th Earl of Orrery, Charles Boyle, from whence the name came.
A planetarium is a projection device which accurately portrays the position of the stars and planets at any time in the past, present, or future from any point on the Earth or the near region of space; the modern planetarium instrument is a mechanical-electrical analogue of space, as well as the name given to the building and gear associated with this device.
An orrery is used to demonstrate the motion of the planets, while a mechanical device used to predict eclipses and transits is called an astrarium. An orrery should properly include the Sun, Earth and the Moon (plus any other chosen planets). A model that only includes the Earth, its Moon and the Sun is called a tellurion, and one which only includes the Earth and Moon a lunarium. A jovilabe is a model of Jupiter and its moons.
In English, it would in fact be more appropriate to call the "Sphere of Archimedes" an orrery because, from the results of multidisciplinary studies that I have conducted, it is likely to have been made with gears and with a heliocentric system. However, since the book is addressed to international readers, albeit written in English, I decided to call the "Sphere of Archimedes" a planetarium due to the fact that the word has Latin etymology, and because it is the name most widely used in many other languages.
For this English edition, whenever possible, I chose the technical-scientific American terminology, instead of the English version. For decimal numbers, I used the point instead of comma. The numerical calculations were performed using the metric system (International System of Units).
In this English edition, compared to the first Italian edition of 2010, this work was added as an appendix: Pythagoras in the contemporary world. Influences of Pythagorean scientific philosophy in the modern and contemporary world.
The book was originally written in Italian. Considering the intrinsic difficulties of the topics covered, the translation may, in part, be difficult to understand. For this reason, the reference text is the Italian edition of 2010.

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In July 2006, during an emergency excavation in the municipal market square in the city of Olbia, a fragment of a toothed wheel of 43 mm (1.6929 inches) was found. The Superintendence for the Archaeological Heritage of Sardinia, who directed the excavation, gave due importance to a seemingly insignificant and oxidized metal fragment. The find appeared similar to the gears of the Antikythera Mechanism, discovered in Greece, conserved in the National Archaeological Museum of Athens, and much talked about in that period because further modern tomographic analysis was being carried out in Athens. The correct dating of the find of Olbia in the archaeological record of the layer, sealed by the already ancient upper one, was determined by the Superintendence for Archaeological Heritage. The find, and the whole layer of the excavation, was dated from the late 3rd to the mid 2nd century BC due to the presence of other easily datable finds, all pertaining to the same period.
The day after the discovery the Superintendent invited me to scientifically study the mechanical artifact by virtue of my forty years of expertise and experience in the design and construction of modern gears, and especially having long studied and also published works on other ancient gear mechanisms, including Antikythera.
The gear teeth of Olbia, at the time of discovery, seemed to have a triangular profile, such as the Antikythera calculator, which dates back to the 1st century BC, and other similar mechanisms made in later centuries, whose meshing, however, is very coarse.
After restoration a very important surprise emerged: the teeth were not triangular in shape but the flanks had a special curvature. When I examined the high-resolution photographs of the find, with the teeth cleaned of oxide, I saw the extraordinary similitude with curved teeth of modern gears, whose "conjugate profile" is the result of accurate and deep mathematical studies formulated by eminent scientists in the 18th century. Another surprise was the results from of the instrumental analysis by SEM, performed by the Superintendence on the find, which showed that the alloy was not bronze, as would be expected because it was very common in antiquity, but brass, an alloy of copper and zinc much more rare and precious than bronze due to difficulties in manufacturing it, but more appropriate for the construction of the gears thanks to better mechanical and technological properties. The gear is therefore more scientifically advanced, that is in terms of metallurgy and mathematics, even though it was made before all the other mechanisms we have seen so far. This means that those who had created the profile had mathematical knowledge and was also learned in metal technology, at least 20 centuries ahead of his time. This unique profile makes the mathematical meshing technically perfect and this can only be the result of a brilliant mind. The author’s first thought concerning the gear went to Archimedes of Syracuse, both because he was the most esteemed mathematician of his time, and also because we know from classical literary sources (Cicero, Ovid, Lactantius, Claudio) that he had built a Planetarium, presumably with gears. Given the perfect correlation between the evidence and the historical, literary and archaeological data, which I will discuss later, it seems safe to conclude that the fragment of Olbia was an integral part in the Archimedes Planetarium.
As can be noted from the many published articles, the extraordinary findings seen in the mathematical study of the profile of the teeth were immediately released in print, online and in other national and international scientific conferences. The extraordinary and certain incontrovertible scientific evidence that the construction of the piece assumed was made public immediately and exclusively, even if only partially, and that it was obviously scientifically superior to all other gear mechanisms that we are aware of, made in the following twenty centuries. However, despite the fact that the scientific and engineering study of the find conducted by the writer took several years of intense and demanding work, the decision on its attribution was not taken immediately rashly, superficially or even lightly. It was not easy because I was aware of the enormous responsibility that would be derived from the concluding remarks. Precisely because of the unexpected findings that, as I said, have emerged from the first comparative mathematical analysis, further confirmation and insight was needed in order to come to the decision of the attribution to the Planetarium of Archimedes at the end of a long, thoughtful and suffered path of study and research.
The study's findings were published in a few essential lines in the proceedings of the XVIII International Congress of studies on “Roman Africa” held in Olbia on 11th to 14th December 2008. Due to the vast amount of work compared to the space available in the publication referred to above it was not possible to report the whole study and the scientific and engineering aspects were removed. After much thought I felt a special publication was needed in which to present a complete study of the find. This is because I felt a duty to universal culture and the history of science to give a complete view of the gear of the study, especially the scientific and engineering aspects that were fundamental and decisive for the attribution of the gear to the Archimedes Planetarium. In this book all the reasons and scientific texts are listed which led me to attribute the fragment of the gear found in Olbia to the Planetarium of Archimedes.

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Giovanni PastoreL’autore:

The author:
Giovanni Pastore (Rotondella - Basilicata, Italy), received his degree with full marks in Mechanical Engineering at Turin Polytechnic University. Even before graduating he was offered a contract at Fiat Mirafiori in Turin, where for the many years he worked at the automotive design office, dealing with structural calculations.
He was a reserve officer with the
Army Corps of Engineers at the plant of ex-combat vehicles STAVECO at Nola (Naples, Italy), appointed with the task of the revision and testing of tanks (Leopard and M113). Some years later he was recalled to duty, at the same plant, for technical updates and degree advancements.
He has lived and worked in Policoro (Basilicata, Italy), where he works as a freelance engineer and Professor of Mechanical Engineering at the Faculty of Mechanical Engineering at several Italian universities.
He has published numerous scientific articles and books: Gli infortuni domestici. Come prevenirli (ISBN 9788890471506), Antikythera e i regoli calcolatori (ISBN 9788890471513), Il Planetario di Archimede ritrovato (ISBN 9788890471520), Pitagora nel mondo contemporaneo. Influenze della filosofia scientifica pitagorica nel mondo moderno e contemporaneo (ISBN 9788890471537) and The Recovered Archimedes Planetarium (ISBN 9788890471544).
He wrote in Il Sole 24 Ore
, L’Unione Sarda, La Stampa, Corriere della Sera, Davlos (translated into Greek by Yannis Lazaris), Mathesis, Advances in Space Research, Ancient Origins, Il Quotidiano del Sud, La Gazzetta del Mezzogiorno.



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Book by Giovanni Pastore
Science, technology, history, literature and archaeology, certainty and conjecture on the most ancient and extraordinary astronomical calculating device. With two other scientific studies: on the Antikythera Planetarium and the Pitcher of Ripacandida.
With the appendix:
Pythagoras in the contemporary world. Influences of Pythagorean scientific philosophy in the modern and contemporary world.
Summary in: English - Italiano - Ελληνικά - 日本語 - Español - Français - Português - Deutsch - Tiếng Việt
(The book is written in English, ISBN  9788890471544)



Libro di Giovanni Pastore
Scienza, tecnologia, storia, letteratura e archeologia, certezze e congetture sul più antico e straordinario calcolatore astronomico
Con altri due studi scientifici:
sul Planetario di Antikythera e sulla Brocchetta di Ripacandida
Summary in: Italiano - English - Ελληνικά - 日本語 - Español - Français - Português - Deutsch - Tiếng Việt
(Il libro è scritto in Italiano, ISBN  9788890471520)



Documentary film:
Influences of Pythagorean scientific philosophy in the modern and contemporary world
Production and direction by Giovanni Pastore - Copyright © 2013-2014
Color - HD - 16/9 - Duration: 54 min - Languages: English and Italian 



  Italian and English version 



Alla pagina web del libro di Giovanni Pastore
Tecnologia e scienza del calcolatore astronomico dei Greci
Istruzioni per l’uso dei regoli calcolatori logaritmici matematici, cemento armato e speciali, con numerosi esempi di calcolo



Alla pagina web del libro di Giovanni Pastore
Come prevenirli



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(中文版 - to the chinese version)




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