Apollonius of Perga
Apollonius of Perga was a Greek geometer and astronomer known for his theories on the topic of conic sections. Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry, his definitions of the terms ellipse and hyperbola are the ones in use today. Apollonius worked including astronomy. Most of the work has not survived except in fragmentary references in other authors, his hypothesis of eccentric orbits to explain the aberrant motion of the planets believed until the Middle Ages, was superseded during the Renaissance. For such an important contributor to the field of mathematics, scant biographical information remains; the 6th century Palestinian commentator, Eutocius of Ascalon, on Apollonius’ major work, states: “Apollonius, the geometrician... came from Perga in Pamphylia in the times of Ptolemy Euergetes, so records Herakleios the biographer of Archimedes....” Perga at the time was a Hellenized city of Pamphylia in Anatolia.
The ruins of the city yet stand. It was a center of Hellenistic culture. Euergetes, “benefactor,” identifies Ptolemy III Euergetes, third Greek dynast of Egypt in the diadochi succession, his “times” are his regnum, 246-222/221 BC. Times are always recorded by ruler or officiating magistrate, so that if Apollonius was born earlier than 246, it would have been the “times” of Euergetes’ father; the identity of Herakleios is uncertain. The approximate times of Apollonius are thus certain; the figure Specific birth and death years stated by the various scholars are only speculative. Eutocius appears to associate Perga with the Ptolemaic dynasty of Egypt. Never under Egypt, Perga in 246 BC belonged to the Seleucid Empire, an independent diadochi state ruled by the Seleucid dynasty. During the last half of the 3rd century BC, Perga changed hands a number of times, being alternatively under the Seleucids and under the Kingdom of Pergamon to the north, ruled by the Attalid dynasty. Someone designated "of Perga" might well be expected to have worked there.
To the contrary, if Apollonius was identified with Perga, it was not on the basis of his residence. The remaining autobiographical material implies that he lived and wrote in Alexandria. A letter by the Greek mathematician and astronomer Hypsicles was part of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements. "Basilides of Tyre, O Protarchus, when he came to Alexandria and met my father, spent the greater part of his sojourn with him on account of the bond between them due to their common interest in mathematics. And on one occasion, when looking into the tract written by Apollonius about the comparison of the dodecahedron and icosahedron inscribed in one and the same sphere, to say, on the question what ratio they bear to one another, they came to the conclusion that Apollonius' treatment of it in this book was not correct, but I myself afterwards came across another book published by Apollonius, containing a demonstration of the matter in question, I was attracted by his investigation of the problem.
Now the book published by Apollonius is accessible to all. "For my part, I determined to dedicate to you what I deem to be necessary by way of commentary because you will be able, by reason of your proficiency in all mathematics and in geometry, to pass an expert judgment upon what I am about to write, because, on account of your intimacy with my father and your friendly feeling towards myself, you will lend a kindly ear to my disquisition. But it is time to have done with the preamble and to begin my treatise itself." Apollonius lived toward the end of a historical period now termed the Hellenistic Period, characterized by the superposition of Hellenic culture over extensive non-Hellenic regions to various depths, radical in some places, hardly at all in others. The change was initiated by Philip II of Macedon and his son, Alexander the Great, subjecting all of Greece is a series of stunning victories, went on to conquer the Persian Empire, which ruled territories from Egypt to Pakistan. Philip was assassinated in 336 BC.
Alexander went on to fulfill his plan by conquering the vast Persian empire. The material is located in the surviving false “Prefaces” of the books of his Conics; these are letters delivered to influential friends of Apollonius asking them to review the book enclosed with the letter. The Preface to Book I, addressed to one Eudemus, reminds him that Conics was requested by a house guest at Alexandria, the geometer, otherwise unknown to history. Naucrates had the first draft of all eight books in his hands by the end of the visit. Apollonius refers to them as being “without a thorough purgation”, he intended releasing each one as it was completed. Hearing of this plan from Apollonius himself on a subsequent visit of the latter to Pergamon, Eudemus had insisted Apollonius send him each book before release; the circumstances imply that at this stage Apollonius was a young geometer seeking the company and advice of established professionals. Pappus states. Euclid was long gone; this stay had been the final stage of Apollonius’ education.
Eudemus was a senior figure in his earlier education at Pergamon.
Ancient Greek astronomy
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Greco-Roman, Late Antiquity eras, it is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt; the development of astronomy by the Greek and Hellenistic astronomers is considered, by historians, to be a major phase in the history of astronomy. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. Most of the constellations of the northern hemisphere derive from Greek astronomy, as are the names of many stars and planets.
It was influenced by Egyptian and Babylonian astronomy. References to identifiable stars and constellations appear in the writings of Homer and Hesiod, the earliest surviving examples of Greek literature. In the oldest European texts, the Iliad and the Odyssey, Homer has several astronomical phenomena including solar eclipses. Eclipses that can permit the dating of these events as the place is known and the calculation of the time is possible if other celestial phenomena are described at the same time. In the Iliad and the Odyssey, Homer refers to the following celestial objects: the constellation Boötes the star cluster Hyades the constellation Orion the star cluster Pleiades Sirius, the Dog Star the constellation Ursa Major Hesiod, who wrote in the early 7th century BC, adds the star Arcturus to this list in his poetic calendar Works and Days. Though neither Homer nor Hesiod set out to write a scientific work, they hint at a rudimentary cosmology of a flat Earth surrounded by an "Ocean River."
Some stars set. At certain times of the year, certain stars will set at sunrise or sunset. Speculation about the cosmos was common in Pre-Socratic philosophy in the 6th and 5th centuries BC. Anaximander described a cyclical earth suspended in the center of the cosmos, surrounded by rings of fire. Philolaus the Pythagorean described a cosmos with the stars, Sun, Earth, a counter-Earth —ten bodies in all—circling an unseen central fire; such reports show that Greeks of the 6th and 5th centuries BC were aware of the planets and speculated about the structure of the cosmos. A more detailed description about the cosmos, Sun and the Earth can be found in the Orphism, which dates back to the end of the 5th century BC, it is even older. Within the lyrics of the Orphic poems we can find remarkable information such as that the Earth is round, it has an axis and it moves around it in one day, it has three climate zones and that the Sun magnetizes the Stars and planets; the name "planet" comes from the Greek term πλανήτης, meaning "wanderer", as ancient astronomers noted how certain lights moved across the sky in relation to the other stars.
Five planets can be seen with the naked eye: Mercury, Mars and Saturn, the Greek names being Hermes, Ares and Cronus. Sometimes the luminaries, the Sun and Moon, are added to the list of naked eye planets to make a total of seven. Since the planets disappear from time to time when they approach the Sun, careful attention is required to identify all five. Observations of Venus are not straightforward. Early Greeks thought that the evening and morning appearances of Venus represented two different objects, calling it Hesperus when it appeared in the western evening sky and Phosphorus when it appeared in the eastern morning sky, they came to recognize that both objects were the same planet. Pythagoras is given credit for this realization. In classical Greece, astronomy was a branch of mathematics; this tradition began with the Pythagoreans. The study of number comprising the four arts was called the Quadrivium. Although he was not a creative mathematician, Plato included the quadrivium as the basis for philosophical education in the Republic.
He encouraged Eudoxus of Cnidus, to develop a system of Greek astronomy. According to a modern historian of science, David Lindberg: "In their work we find a shift from stellar to planetary concerns, the creation of a geometrical model, the "two-sphere model," for the representation of stellar and planetary phenomena, the establishment of criteria governing theories designed to account for planetary observations"; the two-sphere model is a geocentric model that divides the cosmos into two regions, a spherical Earth and motionless and a spherical heavenly realm centered on the Earth, which may contain multiple rotating spheres made of aether. Plato's main books on cosmology are the Republic. In them he described the two-sphere model and said there were eight circles or spheres carrying the seven planets and the fixed stars. According to the "Myth of Er" in the Republic, the cosmos is the Spindle of Nec
Ivor Bulmer-Thomas CBE FSA, born Ivor Thomas, was a British journalist and scientific author who served eight years as a Member of Parliament. His career was much influenced by his conversion to the Church of England in his youth, he became a pious believer on the Anglo-Catholic wing of the Church. A brilliant scholar and champion athlete while at university, Bulmer-Thomas wrote biographies and worked as a sub-editor on The Times during his early life, his experience in wartime Italian propaganda led him to doubt its value. Serving in the Attlee Labour Party government in junior roles made him resent the influence of the Labour left, he was a workaholic and after leaving politics he became a leading layman in the Church of England. Thomas was born in Monmouthshire. E. Thomas, was working class, he went to West Monmouth School in Pontypool, where he abandoned his father's Baptist faith in favour of the Anglo-Catholic wing of the Church of England, a decision, to affect his future career profoundly.
Although a pious believer, his personal piety was described by Robin Denniston in his Guardian obituary as "always gentle and humble". Performing well at school, Thomas won a scholarship to St John's College, Oxford where he studied both Mathematical Mods. and Literae Humaniores, obtaining Firsts in both. He turned to study divinity, but fell into dispute with the President of the college and moved instead to Magdalen College where he became Senior Demy in Theology, he was the Liddon Student in 1928, the Ellerton Essayist in 1929, the Junior Denyer and Johnson Scholar in 1930. Thomas' achievements at Oxford were not confined to academic life, he represented Oxford in varsity matches against Cambridge from 1925 to 1927, in which year he won the three miles race. In 1926 he had represented Wales, in international cross-country running, but for an injury he would have stood a good chance of selection in the Great Britain team for the 1928 Summer Olympics in Amsterdam. On leaving Oxford, Thomas became the Gladstone Research Student at St Deiniol's Library in Hawarden, the residential library founded at William Ewart Gladstone's former house.
The product of his research there was a book on Gladstone's son, published under the title "Gladstone of Hawarden" in 1936. This book was preceded into print by a biography of Lord Birkenhead, published in 1930. Thomas had come to know Birkenhead through his interest in university athletics and the book has been described as witty and entertaining. David Fowler noted the following works Illustrating the History of Greek Mathematics, Loeb Classical Library The Socialist Tragedy, Latimer House Contributed substantial articles to the authoritative Dictionary of Scientific Biography The section on Greek geometry in Geschichte der Algebra Sections in Lehrbücher zur Didaktik der Mathematik Reviewer for Classical Reviews on ancient science and mathematics. Thomas joined the staff of The Times newspaper in 1930, he wrote occasional leader columns and specialist articles on scientific subjects as well as being a sports correspondent for a brief period. He married Dilys Llewelyn Jones in 1932. In 1935, owed some leave from The Times, Thomas took it to coincide with the general election for which he had been chosen as Labour Party candidate for Spen Valley in July.
The sitting Member of Parliament was Sir John Simon, the Home Secretary and the contest was a high-profile one. Thomas moved to the News Chronicle in 1937 as chief leader writer, finding the time to write a biography of Welsh industrialist David Davies, published the following year. However, tragedy struck with the death of his wife in childbirth in the same year. Thomas' reaction was to write "Dilysia", a threnody which combined his increasing love of Italian literature with a Christian philosophical analysis of suffering and bereavement. In life Thomas was to identify it as his favourite piece of writing, it was republished in 1987. Thomas needed only four hours sleep, kept volumes of Dante in the original mediaeval Italian by his bedside to read at night; as the Second World War threatened, Thomas enlisted in 1938 in a Territorial battalion of the Royal Fusiliers as a Fusilier, equivalent in rank to a Private. In 1940 he was commissioned into the Royal Norfolk Regiment. While in the Army, he wrote a two-volume work "Selections Illustrating the History of Greek Mathematics", published by the Loeb Classical Library.
As a fluent Italian speaker, Thomas was drafted into the psychological warfare department of the Foreign Office and Ministry of Information with a brief to develop propaganda for use against Mussolini's Italy. Thomas wrote a 1942 book for Penguin Books called "Warfare by Words" which criticised British propaganda efforts, defined the term as an act of "sabotage leading to revolution". After leaving propaganda work, Thomas was appointed as intelligence officer in the Cambridge area. In January 1942, he was chosen as Labour Party candida
Pappus of Alexandria
Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection, for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than, that he had a son named Hermodorus, was a teacher in Alexandria. Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives, it covers a wide range of topics, including geometry, recreational mathematics, doubling the cube and polyhedra. Pappus was active in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "How far he was above his contemporaries, how little appreciated or understood by them, is shown by the absence of references to him in other Greek writers, by the fact that his work had no effect in arresting the decay of mathematical science," Thomas Little Heath writes. "In this respect the fate of Pappus strikingly resembles that of Diophantus." In his surviving writings, Pappus gives no indication of the date of the authors whose works he makes use of, or of the time at which he himself wrote.
If no other date information were available, all that could be known would be that he was than Ptolemy, whom he quotes, earlier than Proclus, who quotes him. The Suda states that Pappus was of the same age as Theon of Alexandria, who active in the reign of Emperor Theodosius I. A different date is given by a marginal note to a late 10th-century manuscript, which states, next to an entry on Emperor Diocletian, that "at that time wrote Pappus". However, a real date comes from the dating of a solar eclipse mentioned by Pappus himself, when in his commentary on the Almagest he calculates "the place and time of conjunction which gave rise to the eclipse in Tybi in 1068 after Nabonassar"; this works out as October 18, 320, so Pappus must have been writing around 320. The great work of Pappus, in eight books and titled Synagoge or Collection, has not survived in complete form: the first book is lost, the rest have suffered considerably; the Suda enumerates other works of Pappus: Χωρογραφία οἰκουμενική, commentary on the four books of Ptolemy's Almagest, Ποταμοὺς τοὺς ἐν Λιβύῃ, Ὀνειροκριτικά.
Pappus himself mentions another commentary of his own on the Ἀνάλημμα of Diodorus of Alexandria. Pappus wrote commentaries on Euclid's Elements, on Ptolemy's Ἁρμονικά. Federico Commandino translated the Collection of Pappus into Latin in 1588; the German classicist and mathematical historian Friedrich Hultsch published a definitive 3-volume presentation of Commandino's translation with both the Greek and Latin versions. Using Hultsch's work, the Belgian mathematical historian Paul ver Eecke was the first to publish a translation of the Collection into a modern European language. La Collection Mathématique; the characteristics of Pappus's Collection are that it contains an account, systematically arranged, of the most important results obtained by his predecessors, secondly, notes explanatory of, or extending, previous discoveries. These discoveries form, in fact, a text upon. Heath considered the systematic introductions to the various books as valuable, for they set forth an outline of the contents and the general scope of the subjects to be treated.
From these introductions one can judge of the style of Pappus's writing, excellent and elegant the moment he is free from the shackles of mathematical formulae and expressions. Heath found his characteristic exactness made his Collection "a most admirable substitute for the texts of the many valuable treatises of earlier mathematicians of which time has deprived us."The surviving portions of Collection can be summarized as follows. We can only conjecture that the lost Book I, like Book II, was concerned with arithmetic, Book III being introduced as beginning a new subject; the whole of Book II discusses a method of multiplication from an unnamed book by Apollonius of Perga. The final propositions deal with multiplying together the numerical values of Greek letters in two lines of poetry, producing two large numbers equal to 2×1054 and 2×1038. Book III contains geometrical problems and solid, it may be divided into five sections: On the famous problem of finding two mean proportionals between two given lines, which arose from that of duplicating the cube, reduced by Hippocrates of Chios to the former.
Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he failed to appreciate. On the arithmetic and harmonic means between two straight lines, the problem of representing all three in one and the same geometrical figure; this serves as an introduction to a general theory of means, of which Pappus distinguishes ten kinds, gives a table representing examples of each in whole numbers. On a curious problem sugge
Claudius Ptolemy was a Greco-Roman mathematician, astronomer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, held Roman citizenship; the 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou in the Thebaid. This attestation is quite late, and, according to Gerald Toomer, the translator of his Almagest into English, there is no reason to suppose he lived anywhere other than Alexandria, he died there around AD 168. Ptolemy wrote several scientific treatises, three of which were of importance to Byzantine and Western European science; the first is the astronomical treatise now known as the Almagest, although it was entitled the Mathematical Treatise and known as the Great Treatise. The second is the Geography, a thorough discussion of the geographic knowledge of the Greco-Roman world; the third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day.
This is sometimes known as the Apotelesmatika but more known as the Tetrabiblos from the Greek meaning "Four Books" or by the Latin Quadripartitum. Ptolemaeus is a Greek name, it occurs once in Greek mythology, is of Homeric form. It was common among the Macedonian upper class at the time of Alexander the Great, there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter, the first king of the Ptolemaic Kingdom. All male kings of Hellenistic Egypt, until Egypt became a Roman province in 30 BC ending the Macedonian family's rule, were Ptolemies; the name Claudius is a Roman nomen. It would have suited custom if the first of Ptolemy's family to become a citizen took the nomen from a Roman called Claudius, responsible for granting citizenship. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68; the astronomer would have had a praenomen, which remains unknown. The ninth-century Persian astronomer Abu Maʿshar presents Ptolemy as a member of Egypt's royal lineage, stating that the descendants of Alexander's general Ptolemy I, who ruled Egypt, were wise "and included Ptolemy the Wise, who composed the book of the Almagest".
Abu Maʿshar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". We can evidence historical confusion on this point from Abu Maʿshar's subsequent remark "It is sometimes said that the learned man who wrote the book of astrology wrote the book of the Almagest; the correct answer is not known." There is little evidence on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name. Ptolemy can be shown to have utilized Babylonian astronomical data, he was a Roman citizen, but was ethnically either a Greek or a Hellenized Egyptian. He was known in Arabic sources as "the Upper Egyptian", suggesting he may have had origins in southern Egypt. Arabic astronomers and physicists referred to him by his name in Arabic: بَطْلُمْيوس Baṭlumyus. Ptolemy's Almagest is the only surviving comprehensive ancient treatise on astronomy. Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena.
Ptolemy, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets; the Almagest contains a star catalogue, a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky. Across Europe, the Middle East and North Africa in the Medieval period, it was the authoritative text on astronomy, with its author becoming an mythical figure, called Ptolemy, King of Alexandria; the Almagest was preserved, in Arabic manuscripts. Because of its reputation, it was sought and was translated twice into Latin in the 12th century, once in Sicily and again in Spain.
Ptolemy's model, like those of his predecessors, was geocentric and was universally accepted until the appearance of simpler heliocentric models during the scientific revolution. His Planetary Hypotheses went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe, he estimated the Sun was at an average dis
The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, its geocentric model was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, in Western Europe through the Middle Ages and early Renaissance until Copernicus; the Almagest is the critical source of information on ancient Greek astronomy. It has been valuable to students of mathematics because it documents the ancient Greek mathematician Hipparchus's work, lost. Hipparchus wrote about trigonometry, but because his works appear to have been lost, mathematicians use Ptolemy's book as their source for Hipparchus's work and ancient Greek trigonometry in general. Ptolemy set up a public inscription at Canopus, Egypt, in 147 or 148. N. T. Hamilton found that the version of Ptolemy's models set out in the Canopic Inscription was earlier than the version in the Almagest.
Hence it cannot have been completed before about 150, a quarter-century after Ptolemy began observing. The work was titled "Μαθηματικὴ Σύνταξις" in Ancient Greek, called Syntaxis Mathematica or Almagestum in Latin; the treatise was titled Hē Megalē Syntaxis, the superlative form of this lies behind the Arabic name al-majisṭī, from which the English name Almagest derives. The Arabic name is important due to the popularity of a Latin re-translation made in the 12th century from an Arabic translation, which would endure until original Greek copies resurfaced in the 15th century; the Syntaxis Mathematica consists of called books. As with many medieval manuscripts that were handcopied or printed in the early years of printing, there were considerable differences between various editions of the same text, as the process of transcription was personal. An example illustrating how the Syntaxis was organized is given below, it is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein. Book I contains an outline of Aristotle's cosmology: on the spherical form of the heavens, with the spherical Earth lying motionless as the center, with the fixed stars and the various planets revolving around the Earth.
Follows an explanation of chords with table of chords. Book II covers problems associated with the daily motion attributed to the heavens, namely risings and settings of celestial objects, the length of daylight, the determination of latitude, the points at which the Sun is vertical, the shadows of the gnomon at the equinoxes and solstices, other observations that change with the spectator's position. There is a study of the angles made by the ecliptic with the vertical, with tables. Book III covers the length of the year, the motion of the Sun. Ptolemy explains Hipparchus' discovery of the precession of the equinoxes and begins explaining the theory of epicycles. Books IV and V cover the motion of the Moon, lunar parallax, the motion of the lunar apogee, the sizes and distances of the Sun and Moon relative to the Earth. Book VI covers solar and lunar eclipses. Books VII and VIII cover the motions of the fixed stars, including precession of the equinoxes, they contain a star catalogue of 1022 stars, described by their positions in the constellations, together with ecliptic longitude and latitude.
Ptolemy states that the longitudes are for the beginning of the reign of Antoninus Pius, whereas the latitudes do not change with time. The constellations north of the zodiac and the northern zodiac constellations are in the table at the end of Book VII, while the rest are in the table at the beginning of Book VIII; the brightest stars were marked first magnitude, while the faintest visible to the naked eye were sixth magnitude. Each numerical magnitude was considered twice the brightness of the following one, a logarithmic scale; this system is believed to have originated with Hipparchus. The stellar positions too are despite Ptolemy's claim to the contrary. Ptolemy identified 48 constellations: The 12 of the zodiac, 21 to the north of the zodiac, 15 to the south. Book IX addresses general issues associated with creating models for the five naked eye planets, the motion of Mercury. Book X covers the motions of Mars. Book XI covers the motions of Saturn. Book XII covers stations and retrograde motion, which occurs when planets appear to pause briefly reverse their motion against the background of the zodiac.
Ptolemy understood these terms to apply to Venus as well as the outer planets. Book XIII covers motion in latitude; the cosmology of the Syntaxis includes five main points, each of, the subject of a chapter in Book I. What follows is a close paraphrase of Ptolemy's own words from Toomer's translation; the celestial realm is spherical, moves as a sphere. The Earth is a sphere; the Earth is at the center of the cosmos. The Earth, in relation to the distance of the fixed stars, has no appreciable size and must be treated as a mathematical point; the Earth does not move. As mentioned, Ptolemy includes a star catalog containing 1022 stars, he says that he "observed as many stars as it was possible to percei
Francesco Maurolico was a mathematician and astronomer from Sicily. Born to a Greek family and immersed in the study of classical Greek texts, throughout his lifetime he made contributions to the fields of geometry, conics, mechanics and astronomy, he edited the works of classical authors including Archimedes, Autolycus and Serenus. He composed his own unique treatises on mathematics and mathematical science. Born in Messina of a family of Greek descent who originated in Constantinople, they settled in this Sicilian city after the Fall of Constantinople. Recent studies seem indeed to indicate that the family settled in Messina at the end of 15th century. Maurolico received a solid education, his father and his teachers Francesco Faraone and Giacomo Notese-Genovese studied under the Neoplatonic Hellenic scholar Constantine Lascaris. The Maurolico family had a villa outside the city. In 1521, Maurolico took holy orders. In 1550, he entered the Benedictine Order and became a monk at the monastery of Santa Maria del Parto a Castelbuono.
Two years he was consecrated as abbot at the Cattedrale San Nicolò di Messina. In 1535 Maurolico collaborated with the painter Polidoro Caldara da Caravaggio for the realization of the triumphal arches for the entry in Messina of Charles V, Holy Roman Emperor. Like his father, he became head of the Messina mint and for a time was in charge of maintaining the fortifications of the city on behalf of Charles V. Maurolico tutored the two sons of Charles's viceroy in Sicily, Juan de Vega, had the patronage of many rich and powerful men, he corresponded with scholars such as Clavius and Federico Commandino. In 1547 he collaborated with the sculptor Giovanni Angelo Montorsoli for the creation of the famous Orion Fountain in Messina. By Maurolico are the Latin inscriptions on the ground-level basin of the fountain and most of the Neoplatonic program for this monumental civic sculpture. Between 1548 and 1550, he stayed at the castle of Pollina in Sicily as a guest of the marquis Giovanni II Ventimiglia, utilized the castle tower in order to carry out astronomical observations.
Maurolico's astronomical observations include a sighting of the supernova that appeared in Cassiopeia in 1572. Tycho Brahe published details of his observations in 1574. In 1569, he was appointed professor at the University of Messina. Maurolico's Photismi de lumine et umbra and Diaphana concern the refraction of light and attempted to explain the natural phenomenon of the rainbow, he studied the camera obscura. Photismi were completed in 1521, Diaphana first part 1523, the second and third ones in 1552, but all the material was published posthumously only in 1611, his Arithmeticorum libri duo includes the first known proof by mathematical induction. His De momentis aequalibus attempted to calculate the barycenter of various bodies. In his Sicanicarum rerum compendium, he presented the history of Sicily, included some autobiographical details, he had been commissioned to write this work, in 1553 the Senate of Messina granted him a salary of 100 gold pieces per year for two years so that he could finish this work and his works on mathematics.
His De Sphaera Liber Unus contains a fierce attack against Copernicus' heliocentrism, in which Maurolico writes that Copernicus “deserved a whip or a scourge rather than a refutation”. Maurolico published a Cosmographia in which he described a methodology for measuring the earth, employed by Jean Picard in measuring length of meridian arc in 1670. Maurolico published an edition of Aristotle's Mechanics, a work on music, he summarized Ortelius's Theatrum orbis terrarum and wrote Grammatica rudimenta and De lineis horariis. He made a map of Sicily, published in 1575. Maurolico worked on ancient mathematical texts: Theodosius of Bithynia, Menelaus of Alexandria, Autolycus of Pitane, Apollonius of Perga and Archimedes, he did not make new translations, but working on the existing ones, he provided new and sound interpretations of Greek mathematics. He died at Messina; the lunar crater Maurolycus is named after him. There is a school in Messina with his name. In 2009 the Italian Ministry of Cultural Heritage has ordained the establishment of the Edizione nazionale dell'opera matematica di Francesco Maurolico.
List of Roman Catholic scientist-clerics Greek scholars in the Renaissance The Maurolico project - Electronic edition of the scientific works of Francesco Maurolico Francesco Maurolico The Galileo Project: Francesco Maurolico J J O'Connor and E F Robertson, "Maurolico" The Maurolico project - Electronic edition of the scientific works of Francesco Maurolico Works at Open Library