Euclid

In the Middle Ages, writers sometimes referred to him as Euclid of Megara, confusing him with a Greek Socratic philosopher who lived approximately one century earlier. In 1998, the observation of the 500th anniversary of da Gama's arrival in India caused controversy, with some in India reluctant to celebrate an event they feel had a substantially negative impact on their history.[3]. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: he was active at the great library in Alexandria and may have studied at Plato's Academe in Greece, but his exact lifespan and place of birth are unknown. The port of Vasco da Gama in Old Goa in India is named for him. Almost nothing is known about Euclid outside of what is presented in Elements and his few other surviving books. Following da Gama's initial voyage, the Portugese crown realized securing outposts on the eastern coast of Africa would prove vital to maintaining their trade routes to the Far East. There are four works credibly attributed to Euclid which have been lost. The Portuguese "national epic", the Lusíadas of Luís Vaz de Camões largely concerns Vasco da Gama's voyages.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions. Besides the first voyage itself, it was his astute mix of politics and war on the other side of the world that placed Portugal in a prominent position in the Indian Ocean trade. In addition to the Elements, four works of Euclid have survived to the present day. As much as anyone after Henry the Navigator, da Gama was responsible for Portugal's success as an early colonizing power. The first correct axiomatic treatment of geometry by modern standards was provided by David Hilbert in 1899, in his Grundlagen der Geometrie. Da Gama and his wife, Caterina de Ataíde, had six sons and one daughter: Francisco da Gama, Conde da Vidigueira; Estevão da Gama; Paulo da Gama; Christovão da Gama; Pedro da Silva da Gama; Alvaro de Athaide; and Isabel de Athaide da Gama. While the Elements was used well into the 20th century as a geometry textbook and has been considered a fine example of the formally precise axiomatic method, Euclid's treatment does not hold up to modern standards of rigor; some logically necessary axioms are missing, and the definitions of primitive terms appeal to spatial intuition.
.

Most of these investigations involved attempts to prove the relatively complex and presumably non-intuitive fifth postulate using the other four (a feat which, if successful, would have shown the postulate to be in fact a theorem). The convent of the Hieronymites in Belém was erected in honor of his voyage to India. These new geometries grew out of more than two millennia of investigation into Euclid's fifth postulate, one of the most-studied axioms in all of mathematics. Francis Church, Fort Kochi, Kochi, India, then later his remains were returned to Portugal in 1539 and re-interred in Vidigueira in a splendid tomb. Today, however, it is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which were discovered in the 19th century. His body was first buried at St. The geometrical system described in Elements was long known simply as "the" geometry. The intention was that he was to replace the incompetent Eduardo de Menezes as viceroy of the Portuguese possessions, but he died not long after arriving in Calicut.

In addition to providing some missing proofs, Euclid's text also includes sections on number theory and three-dimensional geometry. Having acquired a fearsome reputation as a "fixer" of problems that arose in India, he was sent to the subcontinent once more in 1524. Although many of the results in Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single, logically coherent framework. He was also awarded the feudal rights and jurisdiction over Vidigueira and Villa dos Frades. . Returning to Portugal, he was made Count of Vidigueira out of lands that had previously belonged to the future royal Bragança family. Neither the year nor place of his birth have been established, nor the circumstances of his death. In return for peace, he received valuable trade concessions and a vast quantity of plunder that put him in extremely good favor with the Portuguese crown.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. Da Gama assaulted and exacted tribute from the East African Arabian port of Kilwa, which had been one of those involved with frustrating the Portuguese; he played privateer amongst Arab merchant ships; and then finally smashed a Calicut fleet of twenty-nine ships and essentially conquered that port city. Within it, the properties of geometrical objects and integers are deduced from a small set of axioms, thereby anticipating (and partly inspiring) the axiomatic method of modern mathematics. It took four days for the ship to sink, killing all men, women, and children.[2]. Now known as "the father of geometry," his most famous work is Elements, widely considered to be history's most successful textbook. In one instance, da Gama waited for a ship to return from Mecca, and seized all the merchandise; they then locked the 380 passengers in the hold and set the ship on fire. 325 BC–265 BC) was a Greek mathematician who taught at Alexandria in Egypt almost certainly during the reign (323 BC–283 BC) of Ptolemy I. Pedro Álvares Cabral had been sent out two years earlier (on which voyage he incidentally discovered Brazil, though some claim this it was intentional) and found that those at the trading post had been murdered, encountered further resistance and bombarded Calicut.

Euclid of Alexandria (Greek: Εὐκλείδης) (ca. On February 12, 1502 da Gama sailed again with a fleet of twenty warships to enforce Portuguese interests. ISBN 0-19-502754-X. Da Gama's voyage had made it clear that the farther coast of Africa, the Contra Costa, was essential to Portuguese interests: its ports provided fresh water and provisions, timber and harbors for repairs and to wait out unfavorable seasons. Mathematics: The Loss of Certainty. Oxford: Oxford University Press. He also was awarded the title Dom (count) by Manuel I. Kline, Morris (1980). He was given the title "Admiral of the Indian Ocean" and the feudal rights over Sines were confirmed.

ISBN 0-486-24073-8 / ISBN 0-486-24074-6. Paulo da Gama died in the Azores on the homeward voyage, but upon Vasco da Gama's return to Portugal in September 1499 he was richly rewarded as the man who had brought to fruition a plan that had taken eighty years. New York: Dover Publications. Da Gama kept his goods, but left behind a few Portuguese with orders to start a trading post. A History of Greek Mathematics, 2 Vols. Eventually da Gama was able to gain an ambiguous letter of concession for trading rights, but had to sail off without warning after the Zamorin insisted on his leaving behind all his goods as collateral. (1981). Sometimes violent negotiations with the local ruler (the Samoothiri Raja, usually anglicized as Zamorin) ensued in the teeth of resistance from Arab merchants.

Heath, Thomas L. They arrived on May 20, 1498. ISBN 0-486-60088-2. They contracted the services of Ibn Majid, a Gujarati pilot whose knowledge of the monsoon winds allowed him to bring the expedition the rest of the way to Calicut (modern Kozhikode) on the southwest coast of India. New York: Dover Publications. Da Gama continuted north, landing at the more friendly port of Malindi, whose leaders were in conflict with those of Mombasa, and there the expedition first noted evidence of Hindu traders. 1 (2nd ed.). The Portugese became the first known Europeans to visit the port of Mombasa but met with hostility and soon departed.

The Thirteen Books of Euclid's Elements, Vol. In the vicinity of modern Kenya, the expedition resorted to piracy, looting Arab merchant ships, generally unarmed trading vessels that lacked heavy cannon. (1956). Forced to leave Mozambique by a hostile crowd, da Gama departed the harbor, firing his cannon into the city in retaliation.[1]. Heath, Thomas L. With the paltry trade goods he had to offer, da Gama was unable to provide a suitable gift to the ruler, and soon the local populace began to see through the subterfuge of da Gama and his men. "Euclid." Dictionary of Scientific Biography.. Fearing that the local population would be hostile to Christians, da Gama impersonated a Muslim and gained an audience with the Sultan of Mozambique.

Bulmer-Thomas, Ivor (1971). By January they had reached modern-day Mozambique, Arab-controlled territory on the East African coast that was part of the Indian Ocean's network of trade. Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces. With Christmas pending, they gave the coast they were passing the name Natal (Christmas in Portuguese), which it retains to this day. Pseudaria, or Book of Fallacies, an elementary text about errors in reasoning. By December 16 they had passed the White River where Diaz had turned back and continued on into waters unknown to Europeans. Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial. Its ships were:.

Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. On July 8, 1497 the fleet, consisting of four ships, left Lisbon. Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles. Vasco was then given the job by Manuel I on the strength of his record protecting Portuguese trading stations along the Gold Coast from depredations by the French. Phaenomena concerns the application of spherical geometry to problems of astronomy. The task of completing a journey from Portugal to India around the Cape was originally given to Da Gama's father, Estevão da Gama, Alcaide of Sines, but he died before he could begin. It is similar to a third century (AD) work by Heron of Alexandria, except Euclid's work characteristically lacks any numerical calculations. It remained for an explorer to link the findings of Dias with those of da Covilhã and de Paiva, connecting these separate segments of a potentially lucrative trade route into the Indian Ocean.

On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. Concurrent land exploration during the reign of João II of Portugal, who send Pêro da Covilhã and Afonso de Paiva via Barcelona, Naples, and Rhodes, into Alexandria and from there Aden, Hormuz, and to India, supported the theory that India was reachable by sea from the Atlantic Ocean. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. Bartolomeu Dias had returned from rounding the Cape of Good Hope and exploring as far as the Fish River (Rio do Infante) in modern-day South Africa, and verified that the unknown coast stretched away to the northeast. By the time da Gama was 10 years old these long-term plans were coming to fruition. From the 1460s, the goal had become one of rounding that continent's southern extremity and gaining easier access to the riches of India (mainly black pepper and other spices) through a reliable sea route instead of the costly and unsafe overland route.

From the early 15th century, the nautical school of Henry the Navigator had been extending Portuguese knowledge of the coast of Africa. His father died in July 1497 and command of the ship was given to Vasco. Vasco's career began after his father was chosen to lead an expedition to the open sea routes in Asia to outflank Muslims who at the time had a monopoly on the trade with India and other eastern nations. However he would transfer to the Order of Christ in 1507 which was under the governership of King Manuel I.

James along with some of his brothers. By 1488 it is believed that Vasco was admitted into the order of St. Vasco's mother was of English origins, and had links to the household of Dom Diogo, the Duke of Viseu (son of King Edward I) and governor of the military Order of Christ. James.

His father was the governor of Sines and a member of the Household of Prince Dom Fernando, a master of the Order of St. Da Gama was born in 1469 at Sines into a noble family. . Nevertheless, da Gama's initial journey led directly to a several-hundred year era of European domination of sea power and commerce, and 450 years of Portugese colonialism in India, while bringing wealth and power to the Portugese throne.

Da Gama's voyage, while successful in establishing a sea route from Europe to India that would permit trade with the Far East without the use of costly and unsafe Silk Road caravan routes dominated by Muslims in the Middle East and Asia, was hampered by a failure to bring any trade goods of interest to the nations of Asia Minor and India, and was fraught with peril: only fifty-four of his 170 voyagers, and two of four ships, returned to Portugal in 1499. Commissioned by King Manuel I of Portugal to find Christian lands in the East (the King, like many Europeans, being under the impression that India was the legendary Christian Kingdom of Prester John), and to gain Portugese access to the commercial markets of the Orient, da Gama extended the sea route exploration of his predecessor Bartolomeu Dias, who had first rounded Africa's Cape of Good Hope in 1487, culminating a generation of Portugese sea exploration fostered by the nautical school of Henry the Navigator. 1469 at Sines, Alentejo, Portugal - December 24, 1524 in Cochin, India) was a Portuguese explorer, one of the most successful in the European Age of Discovery, and the first person to sail directly from Europe to India. Vasco da Gama (c.

This is a current Biography collaboration of the week!
Please help improve it to featured article standard. da Gama web tutorial with animated maps. English translation of da Gamas Round Africa to India. DuPont.

ISBN 0465037186 — The history of the explosive that changed the world from Vasco da Gama to E.I. Gunpowder: Alchemy, Bombards, & Pyrotechnics. Kelly, Jack (2004). A storage ship of unknown name.

The caravel Berrio, slightly smaller than the former two. The São Rafael, whose commander was his brother Paulo da Gama; similar dimensions to the São Gabriel. The São Gabriel, commanded by Vasco da Gama; a carrack of 178 tons, length 27 meters, width 8.5 meters, draft 2.3 meters, sails of 372 m², 150 crew.