海马·弗里修斯Gemma Frisius

海马·弗里修斯是弗里斯兰人，这是荷兰北部的一个沿海省份，这解释了他为什么给自己取名为弗里修斯。他出生于弗里修斯 弗里修斯，后来成为学者时才采用了弗里修斯这个名字，因为像他国家的许多学者一样，他采用了拉丁语版本的名字。所以弗里修斯 弗里修斯变成了弗里修斯。他的父母非常贫穷，在他还是个小孩时就都去世了。他成了孤儿和跛子，由继母抚养长大。在一个特别的节日，当弗里修斯六岁时，继母带他去了Dokkum的圣博尼法斯神殿。 certainly after this his legs which could not support his weight became stronger and his family believed that he had been cured by a miracle. Certainly given the difficult start he had in life it was indeed a miracle that he was able to achieve so much but, however, he remained a frail person all his life.

弗里修斯在Gröningen上学，然后于1526年进入鲁汶大学。当然，他的继母没有经济能力支持他上大学，但他在莉莉学院获得了一个贫困学生的名额。他攻读医学学位，但留在鲁汶学习数学和天文学。他后来成为低地国家的领先理论数学家，并成为鲁汶大学的医学和数学教授。他还在鲁汶担任执业医师。

弗里修斯将他的数学专长应用于地理学、天文学和地图制作。在鲁汶，他与雕刻师兼金匠Gaspard Van der Heyden（又名Gaspar à Myrica）合作制作地图、地球仪和天文仪器。他的第一部出版物是在1529年，当时他制作了彼得鲁斯·阿皮亚努斯的Cosmographia的修正版。原版于1524年出版，而弗里修斯的新版本在扉页上说明它是：-

……由弗里修斯精心校正，所有错误都已改正……

这无疑是安特卫普出版商Roeland Bollaert全新印刷的版本。弗里修斯的版本对原文改动极少，但弗里修斯对部分地图作了些改动，尤其是对“美洲”的改动。弗里修斯将“美洲”画成两个不相连的大陆，赤道以南的那个被命名为美洲，而赤道以北的那个则没有名称。

合理的问题是，为什么弗里修斯会在原版出版五年内推出Cosmographia的新版本，且改动相对较少。Cosmographia提供了对天文学、地理学、地图学、测量学、航海学和数学仪器等主题的入门介绍。1524年由彼得鲁斯·阿皮亚努斯自己出版的版本并不太受欢迎，弗里修斯可能看到了将其发展成更受欢迎作品的潜力。他也可能看到了在他的工坊中生产和销售Cosmographia中描述的数学仪器的潜力，这将为他的商品提供出色的广告。这确实是他后来所做的。

弗里修斯着手的下一个项目是制作一个地球与天体合一的双球仪。该球仪由金匠Gaspar Van der Heyden雕刻，到1530年底，该球仪已可在鲁汶的作坊中购得。弗里修斯同年出版了De Principiis Astronomiae Cosmographicae一书，作为该球仪的补充。在该书的献词中，他这样描述自己的地球与天体双球仪（例如参见[7]）：-

……一个地理球仪，上面标有第八天球中最重要的恒星。

这部著作的完整拉丁文标题译为On the Principles of Astronomy and Cosmography, with Instruction for the Use of Globes, and Information on the World and on Islands and Other Places Recently Discovered。这是一部分为三部分的著作，由Johannes Grapheus在安特卫普出版（弗里修斯最初的出版商Roeland Bollaert已经去世）。第一部分描述了地理和天文术语，如纬度、经度、子午线、极、食、黄道十二宫等。第二部分描述了如何使用该球仪，而第三部分则向读者生动描述了遥远国度的人民、植物等。

该著作的第19章首次描述了如何利用时钟确定地方时与绝对时之差来求某地的经度。他说（见[12]）：-

……正是借助这些钟表以及下列方法，经度才得以确定。……准确观测我们出发之地的时刻。……当我们完成一段旅程后……等待我们钟表的指针恰好指向某一时刻的点，与此同时借助星盘……查明我们此刻所在之地的时刻。……这样我就能求出各地的经度，哪怕我在毫无察觉的情况下被带出一千英里之外。

意识到精确计时的困难，他写道：——

……它必须是一只制作极为精良的钟，不会随空气的变化而走时不准。

三年后该著作的第二版中，他增补了一些关于在海上确定经度的注记，这是首次有人着手解决这一问题。值得注意的是，尽管在弗里修斯的工作之后的250年间人们提出了许多确定经度的方法，但最终他所提出的方法成为了在海上确定经度的解决方案。

1533年，弗里修斯出版了Cosmographia的增订版，获得了巨大的商业成功。他将Libellus de locurum附于该著作中，其中描述了三角测量理论，尤其包含首次提出使用三角剖分作为精确定位地点的方法。波兰驻布鲁塞尔大使得知弗里修斯正在进行的杰出工作，邀请他前往布鲁塞尔的帝国宫廷会面。在那里，他试图说服弗里修斯前往波兰与尼古拉·哥白尼合作。这是一个有趣且极具诱惑力的提议，但经过一番犹豫后，弗里修斯决定拒绝这一提议，返回了鲁汶。

1534年，弗里修斯出版了Tractatus de Annulo Astronomicae，书中描述了一种他称为天文学家之环的仪器，该仪器由他设计，Van der Heyden在他的工坊中制作。弗里修斯指出，天文学家之环（例如见[3]）是：——

……并非完全是我的发现。[我]对这个环做了如此大的扩充，以至于它从仅仅显示一天中的时刻和四个方向，如今可与任何数学仪器相媲美。[他人的许多想法被]汇集到这单个环中。

他在将三角学方法应用于天文问题的工作中，正确地注意到彗星相对于背景恒星显示出固有运动。

从1534年起，弗里修斯开始教他的学生墨卡托，并在随后的几年里与Gaspard Van der Heyden和墨卡托合作。他们在1536年制作了一个地球仪，并在次年制作了一个天球仪。这两个地球仪都受到查理五世以帝国特许状形式给予的版权保护，弗里修斯和Van der Heyden在1535年取得了这些特许状，其中阐明了他们的意图[7]：-

……出版一个全世界的地球仪或球体，在上面将添加最近发现的岛屿和陆地，它将得到改进和丰富，比他们早先的地球仪更美丽。[它将]使数学更加辉煌……使古老王国和事件的记忆保持鲜活……并使后代知道我们的时代和我们的王国，在其中……发现了许多在前几个世纪未知的岛屿和地区……[天球仪将]供爱好者普遍使用。

第三位助手被加入团队，其工作是进行雕刻，此人正是墨卡托。当地球仪出现时，它声称其形状是由以下人士赋予的（例如见[7]）：-

弗里修斯，医生和数学家，……根据地理学家所做的各种观测。

完成地球仪后，弗里修斯的兴趣转向了医学。一位医学生Andreas Vesalius加入了他，后者于1536年秋天从巴黎来到鲁汶，他们一起在鲁汶城外发现了一具人的尸体。两人在几个夜晚将其偷偷运入鲁汶，并重建了一具骨架。在几周完全专注于医学事务之后，弗里修斯回到制作他的下一个地球仪的工作。这个天球仪于1537年完成，是由以下人士制作的（例如见[7]）：-

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

此后，弗里修斯继续制作了一幅世界地图，[5]将其描述为“有影响力”，但遗憾的是没有副本留存下来；更多细节见[5]。1542年，一支军队向鲁汶席卷而来，学生们组成了一支防御力量。弗里修斯协助学生，在城墙上花了四天时间监视进攻部队的逼近。在仅持续几天的围攻之后，学生们从鲁汶城墙开火，相当令人惊讶的是，围攻被解除了。

弗里修斯在天文仪器方面的工作在他的几本书中有所描述。例如，在De Radio Astronomico（1545年）中，他描述了他制作一个约1.5米长的十字测角器的工作，其中一个横杆长约3/4米。它有黄铜瞄准叶片和一个滑动叶片。他还发明了一种新的星盘，他在De Astrolabio中描述了它，该书于1556年他去世后出版。

弗瑞兹·约翰 约翰·迪伊于1548年抵达鲁汶，寻找弗里修斯和墨卡托。他带着来自鲁汶的数学仪器作为珍贵财产返回伦敦。这些是：-

... 由弗里修斯设计的第一把黄铜天文尺；墨卡托的两个大地球仪；以及弗里修斯新制作的黄铜天文环。

弗里修斯进行了许多天文观测。特别是他记录了1533年7月、1538年1月和1539年4月30日的彗星。其中一些彗星观测在他儿子Cornelius 弗里修斯的著作中有描述，Cornelius 弗里修斯生于1533年，后来成为鲁汶的医学和天文学教授。弗里修斯在四十七岁时死于“结石”。

Regnier Gemma Frisius was a native of Friesland, a coastal province in northern Netherlands, which explains why he gave himself the name of Frisius. He was born Regnier Gemma and only adopted the name Frisius when he later became a scholar for, like many scholars from his country, he adopted a Latin version of his name. So Regnier Gemma became Gemma Frisius. His parents were very poor people and both died when he was still a young child. Left an orphan and a cripple, he was brought up by his stepmother who on a special feast day, when Gemma was six years old, took him to the shrine of St Boniface in Dokkum. Certainly after this his legs which could not support his weight became stronger and his family believed that he had been cured by a miracle. Certainly given the difficult start he had in life it was indeed a miracle that he was able to achieve so much but, however, he remained a frail person all his life.

Gemma attended school in Gröningen then, in 1526, he entered the University of Louvain. Of course his stepmother did not have the means to support him financially through university but he was given a poor student's place in Lily College. He studied for a medical degree but remained at Louvain to study mathematics and astronomy. He went on to become the leading theoretical mathematician in the Low Countries and also to become professor of medicine and mathematics at the University of Louvain. He was also a practicing physician in Louvain.

Gemma Frisius applied his mathematical expertise to geography, astronomy and map making. In Louvain he cooperated with the engraver and goldsmith Gaspard Van der Heyden (also known as Gaspar à Myrica) in the construction of maps, globes and astronomical instruments. His first publication was in 1529 when he produced a corrected version of Apianus's Cosmographia. The original had been published in 1524 and Gemma's new version, which stated on the title page that it was:-

... carefully corrected and with all errors set to right by Gemma Frisius ...

was certainly a completely new printing by the Antwerp publisher Roeland Bollaert. Gemma's edition contained very few changes to the original text, but Gemma had made some alterations to some of the maps, particularly to 'America'. Gemma showed 'America' as two disconnected continents with the one south of the equator being named America while the one to the north of the equator was left without a name.

It is reasonable to ask why Gemma Frisius would produce a new edition of Cosmographia within five years of the original with relatively few changes. Cosmographia provided a layman's introduction to such subjects as astronomy, geography, cartography, surveying, navigation and mathematical instruments. The 1524 edition published by Apianus himself was not very popular and Gemma Frisius may have seen the potential to develop it into a more popular work. He may also have seen the potential of producing and selling in his workshop the mathematical instruments described in Cosmographia which would then provide an outstanding advertisement for his wares. This was indeed what he went on to do.

The next project undertaken by Gemma was to produce a combined terrestrial and celestial globe. The globe was engraved by the goldsmith Gaspar Van der Heyden and by the end of 1530 the globe could be bought from the workshops in Louvain. Gemma published the book De Principiis Astronomiae Cosmographicae in the same year which was to supplement the globe. In the dedication of this work he described his terrestrial and celestial globe as (see for example [7]):-

... a geographical globe with the most important stars of the eighth celestial sphere.

The full Latin title of this work translates to On the Principles of Astronomy and Cosmography, with Instruction for the Use of Globes, and Information on the World and on Islands and Other Places Recently Discovered. It was a work in three parts published in Antwerp by Johannes Grapheus (Gemma's original published Roeland Bollaert had died). The first part described geographical and astronomical terms such as latitude, longitude, meridian, poles, eclipses, signs of the zodiac etc. The second part described how the globe could be used while the third part vividly described for the reader the peoples, plants etc. in distant lands.

Chapter 19 of this work describes, for the first time, how the longitude of a place may be found using a clock to determine the difference in local and absolute times. He says (see [12]):-

... it is with the help of these clocks and the following methods that longitude is found. ... observe exactly the time at the place from which we are making our journey. ... When we have completed a journey ... wait until the hand of our clock exactly touches the point of an hour and, at the same moment by means of an astrolabe... find out the time of the place we now find ourselves. ... In this way I would be able to find the longitude of places, even if I was dragged off unawares across a thousand miles.

Aware of the difficulties of keeping exact time he writes:-

... it must be a very finely made clock which does not vary with change of air.

In a second edition of the work three years later he added some notes about finding the longitude at sea, the first time anyone had attacked the problem. It is worth noting that although there were many methods of finding longitude proposed in the 250 years following Gemma Frisius's work, ultimately the methods he proposed were to become the solution to finding the longitude at sea.

In 1533 Gemma published an enlarged edition of Cosmographia which became a great commercial success. He included with this work Libellus de locurum which described the theory of trigonometric surveying and in particular contains the first proposal to use triangulation as a method of accurately locating places. The Polish ambassador in Brussels became aware of the outstanding work being undertaken by Gemma Frisius and invited him to come to meet him at the Imperial court in Brussels. There he tried to persuade Gemma Frisius to go to Poland to collaborate with Copernicus. It was an interesting proposition which was very tempting but, after some indecision, Gemma decided to turn the offer down and he returned to Louvain.

In 1534 Gemma Frisius published Tractatus de Annulo Astronomicae in which he described an instrument he called the astronomer's ring which he had designed and Van der Heyden had made in his workshop. Gemma states that the astronomer's ring was (see for example [3]):-

... not entirely a discovery of mine. [I have] augmented the ring so much that from simply showing the hours of the day and the four directions it now rivals whatever mathematical instruments you will. [Many ideas of others are] brought together into this single ring.

His work on applying trigonometric methods to astronomical problems led him to note correctly that comets displayed a proper motion against the background stars.

From 1534 Gemma Frisius began to teach his student Gerardus Mercator and over the following years he cooperated with Gaspard Van der Heyden and Gerardus Mercator. They constructed a terrestrial globe in 1536, and they constructed a celestial globe in the following year. Both globes had been protected by copyright by Charles V with Imperial charters which Gemma and Van der Heyden took out in 1535 which set out their intention [7]:-

... to publish a globe or sphere of the whole world on which the recently discovered islands and lands will be added, which will be improved and enriched and more beautiful than their earlier globe. [It will] 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 celestial globe will be] for the general use of enthusiasts.

A third assistant, whose job it was to do the engraving, was added to the team, this being none other than Gerardus Mercator. When the terrestrial globe appeared it claimed to have been given its form by (see for example [7]):-

Gemma Frisius, doctor and mathematician, ... from various observations made by geographers.

After completing the terrestrial globe, Gemma's interests turned towards medicine. He was joined by a medical student Andreas Vesalius, who came from Paris to Louvain in the autumn of 1536, and together they found a human corpse outside Louvain. The pair, over several nights, smuggled it into Louvain and reconstructed a skeleton. After a few weeks during which he was totally absorbed in medical matters, Gemma returned to working on his next globe. The celestial globe, which was completed in 1537, was made by (see for example [7]):-

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

After this Gemma went on to produce a world map which is described in [5] as 'influential' but sadly no copies have survived; see [5] for further details. In 1542 an army swept towards Louvain and the students formed a defence force. Gemma assisted the students, spending four days on the city walls keeping watch for the approach of the attacking forces. After a siege lasting only a few days the students opened fire from the walls of Louvain and, rather surprisingly, the siege was lifted.

Gemma's work on astronomical instruments was described in several of his books. For example in De Radio Astronomico (1545) he described his work constructing a cross-staff about 1.5 metres long with one cross piece about 3/4 of a metre in length. It had brass sighting vanes and a sliding vane. He also invented a new astrolabe which he described in De Astrolabio which was published in 1556, after his death.

John Dee arrived in Louvain in 1548 and sought out Gemma Frisius and Gerardus Mercator. He returned to London with mathematical instruments from Louvain as prized possessions. These were:-

... the first astronomer's staff in brass that was devised by Gemma Frisius; the two great globes of Gerardus Mercator; and the astronomer's ring of brass as Gemma Frisius had newly framed it.

Gemma Frisius made many astronomical observations. In particular he recorded comets in July 1533, January 1538 and 30 April 1539. Some of these comet observations are described in works by his son, Cornelius Gemma Frisius, who was born in 1533 and went on to become professor of medicine and astronomy at Louvain. Gemma Frisius died of 'stones' at the age of forty-seven.