The World of Gerard Mercator: The Mapmaker Who Revolutionised Geography. Andrew Taylor

       Gemma Frisius

      Science Photo Library, London

      Gemma had also found time to tackle the problem of calculating longitude, which had troubled mariners for centuries, and particularly since they had started making long journeys across the Ocean Sea and to the Far East. In theory at least, working out a ship’s latitude was relatively easy – instruments could measure the height of the Sun or other heavenly bodies above the horizon, and sets of tables would give a fairly accurate reading of latitude – but sailors had no accepted way of finding how far east or west they were. Gemma suggested in De principiis astronomiae et cosmographiae that it might be done with a combination of astronomical observations and the use of a reliable clock. Since the Earth was a sphere of 360 degrees that revolved once every twenty-four hours, each fifteen degrees of longitude would make one hour’s difference to the time. First, Gemma advised, the navigator should take an accurate reading of the time and a sighting of the Sun when he set off. If, when he was out at sea, he then marked the time when the Sun was in the same position in the sky, the time difference measured on the clock would tell him how many degrees east or west he had traveled.* “By this art can I find the longitude of regions, although I were a thousand miles out of my attempted course and in an unknown distance,” he declared.⁵ There were no clocks accurate enough for such a technique – it would be more than two centuries before John Harrison’s chronometer solved that problem – but the theory was impeccable. The technique was simply two hundred years ahead of the technology.

      Leuven, from Civitates Orbis Terrarum, 1572

      Historic Cities Research Project http://historic-cities.huji.ac.il, The Jewish National and University Library of the Hebrew University of Jerusalem

      Despite the hard work of his childhood, Mercator found he lacked basic knowledge in his early days at the university. He struggled at first in Gemma’s lectures on astronomy, he admitted later, because he lacked the mathematical knowledge to grasp the arguments, so he went off alone with his geometry textbooks to follow through the logic of the classical mathematicians.

      He started by teaching himself elementary geometry from the books of Gemma’s Friesland countryman Johannes Vögelin, which he said he easily mastered. He then tackled the first six books of Euclid, beginning with the simple, basic definitions – that a line has length but no breadth, for instance, or that a surface has only length and breadth – and gradually building up his understanding of Euclid’s theoretical arguments about lines, points, circles, triangles, and the relationships between them. Mercator’s method was to take a complex geometric proposition and follow it logically, stage by stage, continually referring back to earlier theorems as he went. In Book IV, for instance, he worked painstakingly through Euclid’s seventeen-hundred-year-old instructions for fitting a straight line into a circle, and in Book VI, he followed through the proof that a straight line drawn through a triangle parallel to one side will cut the other two sides in equal proportions. Each proposition built upon the ones before it, so that by the time he had finished, he had mastered the technique of theoretical reasoning to the point where he could follow Gemma’s lectures and understand the principles of triangulation. Mercator shrugged off this minor achievement: “In a few days, I got to the point where there was nothing in the six books that I had not diligently studied and learned,” he wrote later.⁶

      He worked alone but turned to Gemma for help and advice whenever he found himself puzzled by Euclid. In a mark of singular favor, he was invited for private tuition in Gemma’s house as one of the familia of students who sat at his feet. Gemma’s scholarship had won him the regard and friendship of Johann Flaxbinder, the ambassador of the king of Poland to the court of Charles V, and Flaxbinder had tried unsuccessfully to persuade him to leave the lowlands for a post as Polish court cosmographer. The books he published, which supported him during his years at Leuven, were dedicated to such figures as Charles’s advisers Maximilian Transylvain and Jean Obernburger, and to Jean Khreutter, a senior councillor to the queen of Hungary. The emperor himself summoned Gemma to his court in Brussels on occasion for discussions on matters of science and geography. Gemma Frisius was Mercator’s first introduction to the eminent circles on whose support his prosperity would be built.

      His influence over the young student went farther. Euclid was entirely theoretical – the study of logical argument as much as lines, triangles, and circles – but Mercator’s interest, like that of Gemma, was engaged from the start in its practical use. “In geometry, I only pursued those studies that were to do with measuring, the location of places, the laying out of maps, the dimensions of territories, and finding the distances and sizes of celestial bodies,” he reminisced when he was sixty-nine years old in a letter to a Swiss Protestant pastor, offering advice on how a child might be taught geometry. “In mathematics, I directed my studies to cosmography alone.”⁷ His aim throughout was to improve his skills as a geographer, surveyor, cartographer, and astronomer.

      He had other interests as well – interests that went far beyond the apparently innocent theories of geometry and took him into areas on which Aristotle and the Church had laid down unshakable rules. Ever since his boyhood in Rupelmonde, Mercator had been fascinated by the natural world, but at Leuven his interest was piqued by nature in its widest sense – not just in plants and animals but in the shape of the world and the universe. He built on his studies of Euclid to understand the movements of the stars and planets, as he described years later: “The contemplation of Nature delighted me marvellously, because she teaches us the causes of all things, the sources of all knowledge. But I delighted particularly in the study of the creation of the world, which shows us the beautiful order, the harmonious proportion, and the singular beauty which is there to be admired in all created things.”⁸ He saw no clash with his religious belief; to study Creation was a way to understand and appreciate its wonder, not a challenge to divine power.

      The university authorities, though, were not as confident that such contemplations were free of heresy. For them, the Earth was the focus of the universe, the unequivocal center of everything, and arguments about order, proportion, and beauty were at best irrelevant and at worst a direct challenge to Holy Writ.

      Aristotle had also taught that the oikoumene, the habitable world, was limited to the regions of Europe, Asia, and North Africa that lay between the frozen northern zone and the blistering heat of the “torrid zone.” There was, he said, a symmetrical arrangement to the South, although the southern temperate zone remained uninhabited. Since the first centuries of the Christian Church, philosophers and theologians had pointed out that only descendants of the animals in Noah’s Ark – safely in the northern zone – could have survived the Flood. That was a view which the church of Mercator’s day supported, studiously ignoring the fact that sailors over the previous hundred years had encountered both animals and human beings around the equator and farther south.

      For several hundred years, the physical reality of Aristotle had been accepted as fitting most closely with the Christian belief in an all-powerful, eternal Creator; experimentation, measurement, and empirical questioning that might throw Aristotle’s conclusions into doubt were not allowed by the Church. The challenge to Aristotle was as much part of the Reformation as were the attacks on corruption in the Church. Luther’s delight when he declared triumphantly, “Aristotle is going downhill, and perhaps he will go all the way down into hell,”⁹ reflected Aristotle’s position as one of the Catholic Church’s central pillars against reform. Revolution was no less threatening to the authorities because it was in the mind; pull one brick from the towering building of medieval philosophy, faith, and theology, they believed, and the whole structure might come tumbling down.

      FOR TWO YEARS Mercator continued quietly with his studies, avoiding any clash with the authorities, until he was awarded his magisterii gradum. The master’s degree would have allowed him to progress from the Faculty of Arts to further studies in medicine, Church law, civil law, or theology, as Gemma had done. Instead, as he stood on the threshold of the academic