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The lords of the seas

The Portuguese sailed to the far reaches of Earth even without the best mathematical knowledge available in the 15th and 16th centuries

Illustration of 12 of the 13 ships in the fleet of Pedro Álvares Cabral, contained in the Book of the Indian armadas (1665)

Book of the Indian armadas (1665) Illustration of 12 of the 13 ships in the fleet of Pedro Álvares Cabral, contained in the Book of the Indian armadas (1665)Book of the Indian armadas (1665)

The voyages of the era of discovery—the 15th and 16th century—were undertaken using just basic astronomical knowledge. This, in turn, was based on mathematics. When the Portuguese and Spanish began their great discoveries, the most advanced mathematics of the time had not yet reached the kingdoms of the Iberian Peninsula. What they used was based on the arithmetic, geometry and astronomy of ancient times.

Mathematics was beginning to blaze new paths, especially in England, home to the philosophical monks Roger Bacon, Thomas Bradwardine, Guilherme de Ockham and others, and the studies carried out at Merton College, the institute that grew to become Oxford University. According to the historiography of the period, this development began in about 1096 due to the contact with Muslim culture during the Crusades, the wars of Christian reconquest against the Moors. The Muslims had preserved and studied the Greek legacy and incorporated elements of Hindu culture.

In the 15th and 16th centuries, the astronomy used by Portuguese navigators was still based on the planetary system developed by Ptolemy, described in Almagest (2nd century), and the astronomy book Tractatus de Sphaera (13th century) by the monk Johannes de Sacrobosco, according to mathematician Ubiratan D’Ambrosio, a researcher in the area of the history of mathematics and now Professor Emeritus at the University of Campinas (Unicamp). The works of both Ptolemy and Sacrobosco had been surpassed by what the English had written about the study of celestial movements.

Tractatus de Sphaera (13th century) by Sacrobosco was an important book for Portuguese navigators

Mario Taddei Ancient Books Collection Tractatus de Sphaera (13th century) by Sacrobosco was an important book for Portuguese navigatorsMario Taddei Ancient Books Collection

Despite this, the Portuguese were very successful, mostly thanks to the actions of Prince Henry in the 15th century. He was the patron of the discoveries due to his establishment of what today we would call a strategy of science and technology development in the Sagres region, in devising navigational techniques and incentives for the maritime industry.

“The development of the caravel, a stable, agile, rapid and deadly ship, was a huge technological project,” says D’Ambrosio. The list of conquests is impressive: Ceuta was conquered in 1415, Gil Eanes took over Cape Bojador in 1434, Bartolomeu Dias rounded the Cape of Good Hope in 1488, Vasco da Gama opened the way to the Indies in 1499, Pedro Álvares Cabral reached Brazil in 1500 and Ferdinand Magellan found the passage to the Pacific Ocean in 1520. And, of course, the Genovese Christopher Columbus reached America, sailing under the flag of Spain, in 1492.

How could so many triumphs have occurred with even less advanced mathematical knowledge than the rest of Europe? “Some navigators knew practical astronomy, others knew how to make proper calculations, and still others had studied cartography,” said D’Ambrosio. “Although rudimentary, this knowledge was amassed and organized in Portugal, and it helped on voyages.”

Replicas of Columbus' ships, the Pinta, Niña and Santa Maria, in a 1893 photo in the United States

History of the USA by Benjamin AndrewsReplicas of Columbus’ ships, the Pinta, Niña and Santa Maria, in a 1893 photo in the United StatesHistory of the USA by Benjamin Andrews

D’Ambrosio stresses the difference between the mathematical knowledge on the Iberian Peninsula and in other regions. In the case of sea voyages, interest was focused on geometry. Arabic numerals were only used in Portugal beginning in the 15th century, although there had already been widespread use of them throughout Europe because they facilitated trade.

Despite its rare interactions with other kingdoms, Portugal attracted individuals who became important. In 1475, Columbus visited his brother—the cartographer Bartholomew Columbus—who lived in Lisbon. The German Martin Behaim of Nuremberg  visited the region in 1480 and introduced trigonometry to Portugal. Upon returning to his hometown in 1492, Behaim presented the Erdapfel, the first known globe of the Earth.

According to D’Ambrosio, Portugal’s relative isolation from the knowledge that circulated in Europe is explained by the fact that the country had closed its doors after expelling the Moorish invaders in the thirteenth century. “The opening to the technical and scientific information available in other regions only occurred with the major reform at the University of Coimbra in 1772,” he says.

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