墨卡托Gerardus Mercator

墨卡托的父母是胡贝特·克雷默和埃梅伦蒂娅·克雷默。胡贝特·克雷默务农，同时也是一名补鞋匠，也就是鞋匠。胡贝特和埃梅伦蒂娅地位低微，但胡贝特有一个兄弟吉斯贝特，曾在鲁汶大学受教育，是吕佩尔蒙德的牧师。赫拉德就出生在吕佩尔蒙德的圣约翰济贫院，吉斯贝特在那里当牧师。他是胡贝特和埃梅伦蒂娅的第七个孩子，出生几周后，他们回到了家乡甘格尔特。

在他生命的头五年里，杰拉德和他的父母在甘格尔特生活条件艰难。家庭收入不足以提供基本生活所需之外的东西，他们的饮食大部分是面包，因为他们几乎买不起其他食物。1511年，就在杰拉德出生前不久，休伯特在鲁佩尔蒙德租了一所房子，1518年，他们从甘格尔特前往鲁佩尔蒙德开始新生活。全家搬到鲁佩尔蒙德后不久，杰拉德就开始在那里上学。在学校里，他学习拉丁语、宗教和算术。到七岁时，他已经能够流利地说和读拉丁语。

吉斯伯特的影响意味着杰拉德和他的兄弟们自然以教会职业为目标，事实上，他的两个哥哥走的就是这条路。然而，16世纪20年代初，鲁佩尔蒙德的情况开始恶化，税收大幅增加，以资助哈布斯堡家族与法国之间的战争。路德发起的宗教改革在1525年升级为革命。艰难时世和他为养家糊口而付出的辛勤劳动对休伯特造成了损害，他于1526年或1527年去世。他的兄弟吉斯伯特成为杰拉德的监护人。

吉斯伯特希望杰拉德尽可能接受最好的教育，因此大约在1527年，他把他送到荷兰斯海尔托亨博斯的共同生活兄弟会接受教育。杰拉德在那里时，他的母亲去世了，他为自己选择了一个新名字。他的名字“克雷默”在德语中意为“商人”，他有时也被称为“克雷默”，这是荷兰语的对应词。作为新名字，他选择了墨卡托，拉丁语中“商人”的意思，并给自己取了全名墨卡托 de Rupelmonde。

1530年8月29日，墨卡托在鲁汶大学注册入学，修读人文学科和哲学课程。他在城堡学院学习，这是该大学四个教学学院之一，提供两年制文学学位，几乎完全基于亚里士多德的教导。他于1532年从鲁汶大学毕业，获得硕士学位，并选择不继续攻读更高学位。他已经感到自己想要挑战亚里士多德的观点，然而这在当时的鲁汶与挑战天主教会的观点一样被视为异端。

毕业后，墨卡托开始严重担忧如何将《圣经》中给出的宇宙起源记述与亚里士多德所给出的相调和。他后来写道（例如见[12]）：-

但当我看到摩西关于世界起源的叙述在许多方面与亚里士多德及其他哲学家的观点不够吻合时，我开始对所有哲学家的真理性产生怀疑。

这几乎可以肯定地解释了他为何选择离开大学而不是攻读更高学位，因为他已经决定不想成为一名哲学家。在经历这一人生危机期间，他游历了许多地方，包括安特卫普和梅赫伦。他的旅行对他的宗教忧虑帮助不大，却使他对地理学产生了浓厚兴趣，他认为地理学最能解释上帝所创造的世界结构。

墨卡托于1534年回到鲁汶，此时他在海马·弗里修斯指导下学习数学。然而，由于缺乏该学科的基础，墨卡托很快发现数学课程超出了他的能力。意识到墨卡托想学习数学以应用于宇宙志，海马·弗里修斯就学习他所需要掌握的数学的最佳途径给了他建议，并给他书籍在家研读。一旦被海马·弗里修斯引上正轨，墨卡托在理解和享受数学方面迅速进步。他还了解到数学在地理学和天文学中的应用，他觉得这“极其令人愉快”。他后来写道（例如参见10中J Babicz的文章）：-

从青年时代起，地理学就一直是我研究的主要对象。当我从事这一研究时，运用了自然科学和几何学的思考，我逐渐喜欢上的不仅是地球的描述，还有整个世界机器的结构，其众多元素至今尚无人知晓。

墨卡托此时从Gaspard Van der Heyden（又名Gaspar à Myrica）那里学会了雕刻和制作仪器。然而此时墨卡托不仅在学习，也在教学。他通过给鲁汶的学生教授数学获得稳定收入，并获得了大学的许可。他还通过制作质量卓越的数学仪器并出售来赚取额外收入。

1535-1536年，墨卡托在鲁汶与Van der Heyden以及海马·弗里修斯合作，制作了一个地球仪。该地球仪是受皇帝查理五世委托制作的（例如参见11）：-

……使数学更加辉煌……让古老王国与事件的记忆存续下去……并让后世知晓我们的时代与我们的疆域，在其中……许多在前几个世纪不为人知的岛屿和地区已被发现……

为地球仪印刷的纸条是用铜版而非木版印刷的，这是首次使用铜版印刷。地理工作主要归功于海马·弗里修斯，而墨卡托的角色则是雕版师。由于是在铜版而非木版上雕刻地名、区域名称和地理描述，印刷出的地球仪所包含的信息远超此前建造的任何地球仪。

1536年9月，墨卡托与Barbara Schellekens结婚，他们的第一个孩子，儿子弗拉基米尔·阿诺尔德，于1537年8月31日出生。他们共有六个孩子，三个女儿和三个儿子。1537年，墨卡托与Van der Heyden以及海马·弗里修斯合作，制作了一个恒星地球仪。这一次，墨卡托和Van der Heyden作为与海马·弗里修斯更为平等的合作者出现，地球仪上声称它是由以下人士制作的（例如见[11]）：-

海马·弗里修斯，医生和数学家，Gaspard Van der Heyden和Rupelmonde的Gerard Mercator。

墨卡托于1537年制作了他的第一幅地图，那是一幅巴勒斯坦地图[6]：-

墨卡托对巴勒斯坦的了解胜过低地国家以外的任何地方。他伴随着它的奇迹和启示长大。他了解它的历史。巴勒斯坦是他那一代人大多数人所见过的第一幅地图的主题。就像他少年时代的圣经地图一样，他的地图将展示《摩西第四书》中描述的路线。

墨卡托绘制的第一幅世界地图使用了奥文斯·菲内的投影法，于1538年问世。这幅地图之所以引人注目，是因为它首次将美洲表示为从北部地区延伸到南部地区，并给北美洲起了这个名字。

墨卡托于1540年制作的佛兰德地图是出于政治目的委托制作的。必须认识到，地图可以就其覆盖的地区发出重要信号，而该地区现有的地图强调根特而牺牲了安特卫普和其他城镇。它暗示了一个独立的佛兰德，而墨卡托的地图被委托制作以纠正这一印象。事实上，墨卡托使用海马·弗里修斯描述的三角测量方法对佛兰德进行测量所得的数据，制作了一幅高精度的地图。

墨卡托有一个长期计划，通过制作不同地区的单独地图来制作一幅世界地图。作为这个项目的一部分，他在1540年夏天开始着手制作欧洲地图。然而，世界地图存在许多问题，因为来自地球探索的信息迅速增加，意味着地图很快变得过时。此外，不准确的测量常常给出相互矛盾的信息，使地图制作者面临几乎不可能的任务：决定哪些数据是正确的。墨卡托意识到了一些不正确数据的原因；水手们假设沿着特定的罗盘航向会让他们沿直线航行，而这是不正确的。他意识到，一艘朝着同一罗盘点航行的船会沿着一条称为等角航线（也称为恒向线或球面螺旋线）的曲线航行，这是佩德罗·努内斯最近研究的一条曲线，而佩德罗·努内斯是墨卡托非常钦佩的数学家。他于1541年制作的一个新地球仪是第一个在上面显示恒向线的地球仪。

墨卡托于1544年2月被捕，并被指控为异端。这部分是由于他的新教信仰，部分是由于他为了获取地图数据而旅行如此广泛，引起了怀疑。他在Rupelmonde城堡的监狱中度过了七个月。同时被捕的其他人承认，他们不相信基督的身体实际存在于圣餐饼中，也不相信炼狱。他们被烧死在火刑柱上或活埋。即使在他们遭受酷刑之后，也没有发现任何将墨卡托与其他“异端”联系起来的东西。墨卡托的房子被搜查，他的财物被没收，但没有发现任何罪证表明他不是一个好的罗马天主教徒。

他于1544年9月获释，主要得益于鲁汶大学的大力支持。获释后，他回到鲁汶的家中，但此时他们的经济状况已十分窘迫。很可能像当时的许多人一样，他被迫支付了自己被监禁的费用。他努力制作数学仪器，这些是他在被捕前承诺要制作的。约翰·迪伊于1548年抵达鲁汶，很快与墨卡托成为朋友。约翰·迪伊曾与墨卡托共事三年，后来写道：-

我们彼此友谊与亲密关系的习惯是，在整整三年里，我们两人中任何一方都未曾有超过整整三天不见对方。

在此期间，墨卡托制作了一个与1541年地球仪同样大小的天球仪，于1551年完成。恒星的位置根据尼古拉·哥白尼的宇宙模型校正到了1550年的位置。1552年，墨卡托搬到杜伊斯堡，在那里开设了一家制图作坊。该镇计划建立一所新大学，这意味着他预期地图、书籍、地球仪和数学仪器会有现成的需求。

墨卡托于1554年10月完成了制作新欧洲地图的项目。这是一幅大型地图，长1.6米，宽1.3米，使用Johannes Stabius设计的新投影法绘制。这重新确立了墨卡托作为欧洲领先地图制作者的地位，而且这幅地图除了因其学术价值而受到赞誉外，还具有相当大的商业价值。收入有了保障后，墨卡托和他的家人搬进了杜伊斯堡最富裕地区的一所大房子。当时一位朋友这样描述他（见[9]）：-

尽管他吃得很少，喝得也很少，但他保持着极好的餐桌，备有文明生活所需的一切……他总是尽力帮助那些贫穷和不如他幸运的人，并且……他培养和珍视好客之道。每当地方官员邀请他赴宴，或朋友邀请他吃饭，或他自己邀请朋友时，他总是开朗风趣……

1559年至1562年，他在杜伊斯堡的一所新学校教授数学，该校旨在为学生进入拟建的新大学做准备。当该大学的计划于1562年被取消时，墨卡托结束了他在该校的教学工作，将其移交给他的次子。随后又绘制了更多地图；一幅是1564年的洛林地图，另一幅是1564年的不列颠群岛地图。与之前的一些委托一样，这些地图是出于政治目的而需要的，后一幅地图是作为天主教地图而被寻求，用于对抗新教徒女王伊丽莎白。

墨卡托也在1564年被任命为克莱沃公爵威廉的宫廷宇宙志学家。在此期间，他开始完善一种新的地图投影，他最为人所铭记的正是这种投影。以他的名字命名的“墨卡托投影”于1569年首次被他用于一幅世界挂图，该图由18张单独的图幅组成，题为：

适用于航海的地球仪的新颖且更完整的表示。

“墨卡托投影”具有这样的性质：经线、纬线和恒向线在地图上均呈现为直线。他在地图上写道：

……将球面展开到平面上，使得所有地点的位置在各个方面彼此对应，既涉及真实方向和距离，也涉及真实经度和纬度。

他也是第一个使用“地图集”一词来指代地图集的人。他使用地图集一词：

……为了纪念巨人阿特拉斯，毛里塔尼亚国王，一位博学的哲学家、数学家和天文学家。

墨卡托于1578年出版了克劳狄乌斯·托勒密地图的修正和更新版本，作为其“地图集”的第一部分。他的“地图集”在1585年继续收录了法国、德国和荷兰的更多地图系列。尽管该项目从未完成，墨卡托确实在1589年出版了另一系列，包括巴尔干（当时称为斯拉沃尼亚）和希腊的地图。

1590年5月5日，墨卡托中风，导致左侧瘫痪。他因无法再工作而沮丧，慢慢康复，但因无法继续其制图项目而遭受巨大挫折。到1592年，他又能做一些少量工作，但此时他的眼睛几乎失明。1593年末，他第二次中风，使他丧失了说话能力，尽管他勇敢抗争，恢复了一些说话能力，但第三次中风对这位老人来说太过沉重。他去世时一些未完成的地图由他的儿子于1595年完成并出版。

墨卡托与克劳狄乌斯·托勒密方法的决裂对地理学的重要性，正如尼古拉·哥白尼对天文学的重要性一样。

Gerard Mercator's parents were Hubert and Emerentia Kremer. Hubert Kremer worked the land and also was a cobbler, that is a shoemaker. Hubert and Emerentia were people of lowly status but Hubert had an brother Gisbert who had been educated at Louvain University and was a priest in Rupelmonde. It was in the hospice of St Johann in Rupelmonde, where Gisbert was a priest, that Gerard was born. He was the seventh child of Hubert and Emerentia who, a few weeks after the birth, returned to their home town of Gangelt.

For the first five years of his life Gerard and his parents lived in difficult conditions in Gangelt. The family income was insufficient to provide for more than the basic needs of life and most of their diet consisted of bread for they could afford little else. Hubert had leased a house in Rupelmonde in 1511, shortly before Gerard's birth, and in 1518 they journeyed from Gangelt to Rupelmonde to begin a new life. Gerard began attending school in Rupelmonde shortly after the family came to live there. At school he studied Latin, religion and arithmetic. By the time he was seven years old he was able to speak and to read Latin fluently.

Gisbert's influence meant that it was natural for Gerard and his brothers to aim at a career in the Church and indeed that was the route that his two eldest brothers took. Conditions in Rupelmonde began to deteriorate in the early 1520s, however, with huge increases in taxes to fund the war between the Habsburgs and France. The reformation, begun by Luther, escalated into revolution in 1525. The harsh times and the hard work that he put in to try to support his family took their toll on Hubert who died in 1526 or 1527. His brother Gisbert became Gerard's guardian.

Gisbert wanted the very best education possible for Gerard so in about 1527 he sent him to be educated with the Brethren of the Common Life in 'sHertogenbosch in the Netherlands. While Gerard was there his mother died and he chose a new name for himself. His name 'Kremer' means 'merchant' in German and he was sometimes known as 'Cremer' which is the Dutch equivalent. As a new name he chose Mercator, the Latin for 'merchant' and gave himself the full name of Gerardus Mercator de Rupelmonde.

On 29 August 1530 Mercator matriculated at the University of Louvain, taking the course in the humanities and philosophy. He studied at the Castle, one of four teaching houses of the university which offered two year Arts degrees based almost entirely on the teachings of Aristotle. He graduated from Louvain with a Master's Degree in 1532 and chose not to proceed to a higher degree. Already he felt that he wanted to challenge the views of Aristotle, yet this was as heretical at Louvain at that time as challenging the views of the Catholic Church.

After graduating, Mercator began to have serious worries on how to reconcile the account of the origin of the universe given in the Bible with that given by Aristotle. He wrote later (see for example [12]):-

But when I saw that Moses' version of the Genesis of the world did not fit sufficiently in many ways with Aristotle and the rest of philosophers, I began to have doubts about the truth of all philosophers.

This almost certainly explains why he chose to leave the university rather than study for a higher degree, since he had already decided that he did not want to become a philosopher. He travelled to a number of places while going through this personal crisis including Antwerp and Mechelen. His travels did little for his religious worries but gave him a deep interest in geography which he saw at the subject which could best explain the structure of the world which God created.

Mercator returned to Louvain in 1534 where he now studied mathematics under Gemma Frisius. However, not having any background in the subject, Mercator soon found that the mathematics courses beyond him. Realising that Mercator wanted to learn mathematics to apply it to cosmography, Gemma Frisius gave him advice on the best route into learning the mathematics he needed to know, giving him books to study at home. Once put on the right path by Gemma Frisius, Mercator quickly progressed in understanding and enjoyment of mathematics. He also learnt about applications of mathematics to geography and astronomy which he found "extremely agreeable". He later wrote (see for example J Babicz in [10]):-

Since my youth geography has been for me the primary object of study. When I was engaged in it, having applied the considerations of the natural and geometric sciences, I liked, little by little, not only the description of the earth, but also the structure of the whole machinery of the world, whose numerous elements are not known by anyone to date.

Mercator learnt to be an engraver and instrument maker at this time from Gaspard Van der Heyden (also known as Gaspar à Myrica). However at this time Mercator was not only was learning, he was also teaching. He earned a steady income giving mathematics tuition to the students at Louvain, obtaining permission from the university to do this. He also earned extra money by making mathematical instruments of exceptional quality which he sold.

In 1535-1536 Mercator, working in Louvain with Van der Heyden and with Gemma Frisius, constructed a terrestrial globe. The globe had been commissioned by the Emperor Charles V to (see for example [11]):-

... make mathematics more illustrious ... keep alive the memory of old kingdoms and events and ... make known to coming generations our time and our realm in which ... very many islands and areas unknown in earlier centuries have been discovered ...

The paper strips which were printed for the globe were printed using copper rather than wood blocks, the first to be printed using that substance. The geographical work was mainly due to Gemma Frisius while Mercator's role was that of an engraver. With copper rather than wood on which to engrave place names, names of regions and geographical descriptions, the printed globe contained vastly more information than any that had previously been constructed.

In September 1536 Mercator married Barbara Schellekens and their first child, a son Arnold, was born on 31 August 1537. They had six children, thee daughters and three sons. In 1537 Mercator, working with Van der Heyden and with Gemma Frisius, constructed a globe of the stars. This time Mercator and Van der Heyden appeared as more equal collaborators with Gemma Frisius with the globe claiming that is was made by (see for example [11]):-

Gemma Frisius, doctor and mathematician, Gaspard Van der Heyden and Gerard Mercator of Rupelmonde.

Mercator produced his first map, which was one of Palestine, in 1537 [6]:-

Mercator knew Palestine better than any place outside the Low Countries. He had grown up with its miracles and revelations. He knew its history. Palestine had been the subject of the first map that most of his generation had ever seen. And like the Bible maps of his boyhood, his would show the route described in the Fourth book of Moses.

The first map of the world to be produced by Mercator used a projection due to Oronce Fine and appeared in 1538. This map is notable for being the first to represent America as stretching from the northern regions to the southern regions and for giving North America that name.

The map of Flanders which Mercator produced in 1540 was commissioned for political purposes. It must be realised that maps can send important signals about the regions which they cover, and the existing map of the region emphasised Ghent at the expense of Antwerp and other towns. It suggested an independent Flanders and Mercator's map was commissioned to correct this impression. In fact Mercator produced a map of high accuracy using data from a survey of Flanders carried out using the method of triangulation described by Gemma Frisius.

Mercator had a long term plan of producing a world map by producing individual maps of the different regions. As part of this project he set to work on the map of Europe in the summer of 1540. There were many problems with a world map, however, for the rapid increase in information coming from exploration of the Earth meant that maps rapidly became outdated. Also contradictory information was often given from inaccurate surveys leaving the mapmaker with the almost impossible task of deciding which data was correct. Mercator realised the reason for some of the incorrect data; sailors assumed that following a particular compass course would have them travel in a straight line whereas this was untrue. He realised that a ship sailing towards the same point of the compass would follow a curve called a loxodrome (also called a rhumb line or spherical helix), a curve recently studied by Pedro Nunes who was a mathematician greatly admired by Mercator. A new globe which he produced in 1541 was the first to have rhumb lines shown on it.

Mercator was arrested in February 1544 and charged with heresy. This was partly due to his Protestant beliefs, partly due to the fact that he travelled so widely to acquire data for his maps that suspicions were aroused. He spent seven months in prison in Rupelmonde castle. Others that were arrested at the same time admitted that they did not believe that the body of Christ was physically present in the communion host and they did not believe in purgatory. They were burned at the stake or buried alive. Nothing was found to connect Mercator with the others 'heretics' even after they had been tortured. Mercator's house was searched and his belongings confiscated but nothing incriminating was found to show that he was anything other than a good Roman Catholic.

He was released from prison in September 1544, mainly due to strong support from the University of Louvain. After his release he returned to his family in Louvain but their financial position was by now dire. It is likely that he was forced to pay for the cost of his own imprisonment as many were at this time. He worked hard on constructing mathematical instruments that he has promised to construct before his arrest. John Dee arrived in Louvain in 1548 and quickly became friends with Mercator. Dee, who spent three years working with Mercator, later wrote:-

It was the custom of our mutual friendship and intimacy that, during three whole years, neither of us lacked the other's presence for as much as three whole days.

During this time Mercator worked on a celestial globe of the same size as his terrestrial globe of 1541 which he completed in 1551. The positions of the stars were corrected to their positions in 1550 using Copernicus's model of the universe. In 1552 Mercator moved to Duisburg where he opened a cartographic workshop. The fact that a new university was planned for the town meant that he anticipated a ready demand for maps, books, globes and mathematical instruments.

In Duisburg Mercator completed his project to produce a new map of Europe by October 1554. It was a large map, 1.6 metres by 1.3 metres, drawn using a new projection devised by Johannes Stabius. This re-established Mercator as the leading European map maker and, as well as praise for its scholarly value, the map had considerable commercial value. His income secure, Mercator and his family moved into a large house in the wealthiest district of Duisburg. He was described by a friend at this time (see [9]):-

Although he ate and drank very little, he kept an excellent table, well furnished with the necessities of civilised living... He always did his best to help those who were poor and less fortunate than he and ... he cultivated and cherished hospitality. Whenever he was invited by the magistrates to a banquet or by friends to a dinner, or he himself invited friends, he was invariable cheerful and witty ...

He taught mathematics in Duisburg from 1559 to 1562 in a new school designed to prepare students for entry into the proposed new university. When plans for the university were scrapped in 1562, Mercator ended his teaching duties at the school handing them over to his second son. Further maps followed; one of Lorraine in 1564 and one of the British Isles in 1564. Like some previous commissions, these maps were required for political ends, the latter map being sought as a Catholic map to be used against the Protestant Queen Elizabeth.

Mercator was appointed Court Cosmographer to Duke Wilhelm of Cleve, also in 1564. During this period he began to perfect a new map projection for which he is best remembered. The 'Mercator projection' that bears his name was first used by him in 1569 for a wall map of the world on 18 separate sheets entitled:-

New and more complete representation of the terrestrial globe properly adapted for its use in navigation.

The 'Mercator projection' had the property that lines of longitude, latitude and rhomb lines all appeared as straight lines on the map. He had, he wrote on the map:-

... spread on a plane the surface of a sphere in such a way that the positions of all places shall correspond on all sides with each other both in so far as true direction and distance are concerned and as concerns true longitudes and latitudes.

He was also the first to use the term 'atlas' for a collection of maps. He used the word atlas:-

... to honour the Titan, Atlas, King of Mauritania, a learned philosopher, mathematician, and astronomer.

Mercator published corrected and updated versions of Ptolemy's maps in 1578 as the first part of his 'atlas'. His 'atlas' continued with a further series of maps of France, Germany and the Netherlands in 1585. Although the project was never completed Mercator did publish a further series in 1589 including maps to the Balkans (then called Sclavonia) and Greece.

On 5 May 1590 Mercator had a stroke which left his left side paralysed. Frustrated that he could no longer work, he slowly recovered but suffered great frustration at his inability to continue his map making projects. By 1592 he was able to do a small amount of work again but his eyes were by now almost blind. He had a second stroke towards the end of 1593 which took away his power of speech and although he fought bravely, recovering some power of speech, a third stroke was too much for the old man. Some maps which were incomplete at his death were completed and published by his son in 1595.

Mercator's break from the methods of Ptolemy was as important for geography as was Copernicus for astronomy.