埃德蒙·冈特Edmund Gunter

埃德蒙·冈特的父亲是威尔士人，来自南威尔士布雷克诺克郡的Gunterstown。冈特作为女王学者就读于威斯敏斯特学校，然后于1600年1月25日进入牛津大学基督教堂学院。他于1603年12月12日毕业，获得学士学位。冈特在本科阶段就已经对数学和数学仪器产生了浓厚的兴趣。他在本科最后一年写了一篇手稿New Projection of the Sphere，这篇手稿在各种数学熟人之间流传。这使他引起了当时许多领先数学家的注意，包括亨利·布里格斯。

冈特继续在牛津学习，于1606年获得硕士学位，但他留在牛津直到1615年，于11月23日获得神学学士学位。冈特被任命为牧师，并于1615年成为南华克圣乔治教堂和牛津圣玛丽抹大拉教堂的牧师。他在教会中担任这些职位直到去世。

冈特成为了亨利·布里格斯的朋友，并会花很多时间与他一起在格雷沙姆学院讨论数学话题。亨利·布里格斯是格雷沙姆学院的第一位数学教授，自学院成立起就担任该职位。格雷沙姆学院成立于1597年，自学院成立起也设有天文学教授。第一位天文学教授是Edward Brerewood（约1565-1613），曾在牛津大学布雷齐诺斯学院接受教育，他的专业知识广泛，从数学到古物，再到逻辑和语言。他于1613年11月4日去世，亨利·布里格斯支持冈特被任命为格雷沙姆学院的第二位天文学教授。然而，冈特未能获得任命，该职位由Thomas Williams获得。他曾在牛津大学基督堂学院接受教育，并于11月11日被任命为天文学教授，就在Brerewood去世一周后。Thomas Williams于1599年进入基督堂学院，仅比冈特早一年，因此不可能有更多的经验。然而，到1618年，冈特一定在格雷沙姆学院度过了很多时间，以至于威廉·欧垂认为他已经是那里的教授了。威廉·欧垂写道：-

1618年春天，我在伦敦时去格雷沙姆学院拜访我尊敬的朋友亨利·布里格斯硕士：他随后让我结识了最近被选为那里天文学讲师的冈特硕士，当时他在Brooks博士的房间。与他谈起他的象限仪时，我给他看了我的水平仪。他非常仔细地查看：并询问其投影和使用方法，经常说这些话，这是一个非常好的。不久之后，他将我的仪器从黄铜切割中印刷出来交给亨利·布里格斯硕士寄给我：后来我得知他将其赠送给尊贵的布里奇沃特伯爵，并在六年后出版的他的扇形书中，在其他投影中列出了这个。

格雷沙姆学院第二位天文学教授Thomas Williams在1619年3月4日的一封信中辞职。信中写道：-

我，牛津大学的Thomas Williams，文学硕士，伦敦格雷沙姆学院天文学讲座的读者，完全且绝对地辞去我在同一学院天文学讲师职位和职务的所有权利和利益……

我们不知道他为何辞职，但可能是为了结婚。关于Williams似乎没有更多已知信息。冈特于1619年3月6日被任命填补空缺，即Williams辞职两天后，主要是根据亨利·布里格斯的推荐。 certainly Gresham College的任命速度异常迅速。

1619年发生了一件关于任命牛津大学第一位几何学教授的事件，由弗瑞兹·约翰 Aubrey报道。这个牛津大学几何学讲席由亨利·萨维尔爵士创立，他热衷于改善当时被认为极其糟糕的英格兰数学研究状况。亨利·萨维尔要求教授“品行良好”，至少26岁，来自基督教国家，最好是英格兰。教授必须精通亚里士多德和柏拉图，但也必须研究科学的最新发展。亨利·萨维尔面试的第一位教授职位候选人是冈特。Aubrey写道，Seth Ward告诉他冈特来面试：-

... 并带来了他的扇形器和象限仪，开始解决三角形并做了许多精妙的事情。那位严肃的骑士[亨利·萨维尔]说，“你把这叫做阅读几何学？这是在耍把戏，伙计！”，于是轻蔑地打发了他，并派人去请亨利·布里格斯。

我们必须指出，如果这是真的，那么 certainly Seth Ward是从别人那里得知这个故事的，因为当亨利·萨维尔面试冈特时，他只有两岁。

Jon V Pepper在[1]中写道：-

冈特的著作以英语写成，反映了他教学的实用性质，并将他那个时代更学术性的工作与日常需求联系起来；他提供的工具在很久以后都具有巨大价值。

冈特于1620年在Canon Triangulorum sive Tabulae Sinuum et Tangentium ArtificialumⓉ（《三角形准则：或人工正弦与正切表》）中发表了七位数字的正弦和正切对数表（详见[13]）。这是一部拉丁文著作，但同年出版了英文译本，书名为Canon of Triangles: or Tables of Artificial Sines and Tangents。尽管sine和tangent这两个词已经在使用，冈特发明了cosine和cotangent这两个词。这是三角函数对数表的首次出版，冈特对这一创新功不可没。

他制作了一种机械装置，即冈特尺，基于对数用单一刻度和一副圆规来乘数字。海员称之为“gunter”，它是计算尺发展的重要一步。冈特于1623年在Description and Use of the Sector, the Crosse-staffe and other Instruments中发表了他的描述。值得注意的是，在这部著作中，冈特在他绘制的刻度图中使用了缩写sin表示sine、tan表示tangent，尽管书中的正文并未使用这些缩写。Charles Cotter在[11]中写道：-

无论以何种标准衡量，这本书都必须被视为十七世纪出版的关于航海科学的最重要著作。它向每一位有足够兴趣投入时间完善其技艺的航海者，开启了将数学应用于航海和航海天文学的全部主题。

这本书的第二版于1636年出版，艾萨克·牛顿于1667年以5先令购得。艾萨克·牛顿所藏的这一第二版现藏于剑桥大学三一学院图书馆。

C J Sangwin写道[17]：-

扇形尺是一种数学仪器，由两把带铰链的直尺组成，上面刻有刻度。这些刻度利用两个相似（等角）三角形的边长成常比这一性质，可以解决三角学中的各种问题。谁最先发明扇形尺这一问题并非没有争议。……冈特的扇形尺之所以与众不同，在于它是第一件刻有对数刻度以便于解决数值问题的数学仪器。这绝不是任何意义上的计算尺；单一的对数刻度是与一副圆规配合使用的。这样的尺通常被称为冈特线。一把两英尺长、刻有各种刻度的黄杨木尺，直到十九世纪末一直是航海者的标准工具。

冈特是仪器的发明者，但他需要一位仪器制造者来制作它们。Elias Allen（1592-1653）在伦敦河岸街的圣克莱门特丹麦人教堂旁设有工坊，他就是冈特所使用的仪器制造者。Hester Higton写道[14]：-

Allen似乎与冈特有着密切的工作关系。他是他那个时代最受推崇的仪器制造者。他曾是著名制造者Charles Whitwell的学徒，在1611年Whitwell去世前不久自立门户，先是在[靠近]弗利特桥的地方，后来在河岸街的圣克莱门特丹麦人教堂旁，很可能是在他前师父的工坊里。

冈特因让Allen制作他的仪器而获益，而Description and Use of the Sector, the Crosse-staffe and other Instruments中扇形的插图就来自Allen雕刻的版。但两人之间的关系也是反向运作的，因为Allen利用冈特扇形的这幅雕版来为自己的生意做广告。

冈特还发明了“冈特链”，长22码，有100个链节。它用于测量，而称为英亩的面积单位是十个平方链。冈特也研究了磁偏角，并且是第一个观察到长期变化的人。Higton在[2]中写道：-

1622年，冈特在德特福德的莱姆豪斯对罗盘指针的磁偏角进行研究，所得结果与William Borough四十多年前获得的结果不同。他假定Borough的测量有误，但这实际上是对磁偏角随时间变化的首次观测，这一贡献被他的后继者Henry Gellibrand所承认，后者发现了这一现象。

他对数学仪器的迷恋可以一直追溯到他上学的日子，而他的主要数学贡献被正确地认为是在这一领域。事实上，他在1622年制作了一个带有许多刻度盘的新日晷，其中包含大量天文数据，并将其竖立在王室住所白厅的花园中。查尔斯王子，即1625年成为国王的查理一世，说服冈特撰写并出版对这个日晷的描述，他于1624年以The Description and Use of his Majesties Dials in Whitehall Garden为名完成了这件事。

他的贡献在2中被总结如下：-

冈特坚定主张在数学中使用仪器，以减轻各种数学从业者，特别是测量员和航海家的工作。他的仪器设计时就考虑到了这些目标。特别是他对对数的工作、它们在三角学中的应用，以及将它们纳入仪器，极大地简化了数学计算过程。他的书在他去世后多年仍然流行：皮埃尔·萨米埃尔 Foster在1636年出版了他所有作品的版本，之后又有三个版本，最后一个在1680年……

冈特在格雷沙姆学院去世，一天后被安葬在旧宽街的圣彼得勒波尔教堂墓地。圣彼得勒波尔教堂于1788年在其墓地原址上重建，该教堂于1896年被拆除，现已不复存在。

Edmund Gunter's father was Welsh, coming from Gunterstown, Brecknockshire, South Wales. Edmund attended Westminster School as a Queen's Scholar, then entered Christ Church, Oxford on 25 January 1600. He graduated with a B.A. on 12 December 1603. Already as an undergraduate, Gunter had developed a strong interest in mathematics and in mathematical instruments. He wrote a manuscript New Projection of the Sphere in his final year as an undergraduate and this manuscript was circulated around various mathematical acquaintances. This brought him to the attention of a number of leading mathematicians of the time including Henry Briggs.

Continuing his studies at Oxford, Gunter was awarded an M.A. in 1606 but he remained at Oxford until 1615 when he received the divinity degree of B.D. on 23 November. Gunter was ordained and in 1615 became Rector of St George's Church in Southwark and of St Mary Magdalen, Oxford. He held these positions in the Church until his death.

Gunter became a friend of Briggs, and would spend much time with him at Gresham College discussing mathematical topics. Briggs was the first Professor of Mathematics at Gresham College holding the position from the founding of the College. Gresham College had been established in 1597 and there was also a Professor of Astronomy from the founding of the College. The first Professor of Astronomy was Edward Brerewood (about 1565-1613), educated at Brasenose College, Oxford, who had a broad range of expertise from mathematics, to antiquities, to logic and to languages. He died on 4 November 1613 and Briggs supported Gunter to be appointed as the second Professor of Astronomy at Gresham College. However, Gunter failed to gain the appointment which went to Thomas Williams. He had been educated at Christ Church, Oxford, and was appointed as Professor of Astronomy on 11 November, just a week after Brerewood died. Thomas Williams had entered Christ Church in 1599, only one year before Gunter, so could not have had much greater experience. However, by 1618 Gunter must have spent so much time at Gresham College that William Oughtred believed that he was already a professor there. Oughtred wrote:-

In the Spring 1618 I being at London went to see my honoured friend Master Henry Briggs at Gresham College: who then brought me acquainted with Master Gunter lately chosen Astronomical lecturer there, and was at that time in Doctor Brooks his chamber. With whom falling into speech about his quadrant, I showed him my Horizontal Instrument. He viewed it very heedfully: and questioned about the projecture and use thereof, often saying these words, it is a very good one. And not long after he delivered to Master Briggs to be sent to me mine own Instrument printed off from one cut in brass: which afterwards I understood he presented to the right Honourable the Earl of Bridgewater, and in his book of the sector printed six years after, among other projections he setteth down this.

The second Gresham College professor of astronomy Thomas Williams resigned in a letter of 4 March 1619. It reads:-

I Thomas Williams of the University of Oxford, Master of Arts, Reader of the astronomy lecture at Gresham house London, do fully and absolutely resign all the right and interest which I have to the place and office of astronomy lecturer in the same house ...

We do not know why he resigned, but it may have been so that he could marry. Nothing further seems to be known about Williams. Gunter was appointed to fill the vacancy on 6 March 1619, two days after Williams resigned, largely on the recommendation of Briggs. Certainly Gresham College made remarkably rapid appointments.

An episode concerning the appointment of the first professor of geometry at Oxford occurred in 1619 which is reported by John Aubrey. This chair of geometry at Oxford was founded by Sir Henry Savile who was keen to improve the state of mathematical studies in England which, at that time, were considered extremely poor. Savile required the professor to be "of good character", at least 26 years old and from a Christian country, preferably England. The professor had to be thoroughly acquainted with Aristotle and Plato but also have studied the latest developments in science. The first person Savile interviewed for the professorship was Gunter. Aubrey writes that Seth Ward told him that Gunter came to the interview:-

... and brought with him his sector and quadrant, and fell to resolving triangles and doing a great many fine things. Said the grave knight [Savile], "Do you call this reading of geometry? This is showing of tricks, man!", and so dismissed him with scorn, and sent for Henry Briggs.

We must point out that if this is true, then certainly Seth Ward learnt this story from others since he was only two years old when Savile interviewed Gunter.

Jon V Pepper writes in [1]:-

Gunter's works, written in English, reflected the practical nature of his teaching and linked the more scholarly work of his time with everyday needs; the tools he provided were of immense value long afterward.

Gunter published seven figure tables of logarithms of sines and tangents in 1620 in Canon Triangulorum sive Tabulae Sinuum et Tangentium Artificialum Ⓣ (see [13] for details). This was a Latin text but an English translation with title Canon of Triangles: or Tables of Artificial Sines and Tangents was published in the same year. Although the words sine and tangent were already in use, Gunter invented the words cosine and cotangent. This was the first ever publication of logarithms of trigonometric functions and Gunter deserves much credit for this innovation.

He made a mechanical device, Gunter's rule, to multiply numbers based on the logs using a single scale and a pair of dividers. It was called the 'gunter' by seamen and was an important step in the development of the slide rule. Gunter published his description in 1623 in Description and Use of the Sector, the Crosse-staffe and other Instruments. It is worth noting that in this work Gunter uses the contractions sin for sine and tan for tangent in his drawing of his scale although not in the text of the book. Charles Cotter writes in [11]:-

This book must be reckoned, by every standard, to be the most important work on the science of navigation to be published in the seventeenth century. It opened the whole subject of mathematical application to navigation and nautical astronomy to every mariner who was sufficiently interested in devoting time to the perfecting of his art.

A second edition of this book was published in 1636 and purchased by Isaac Newton for 5 shillings in 1667. Newton's copy of this second edition is in the library of Trinity College, Cambridge.

C J Sangwin writes [17]:-

A sector is a mathematical instrument which consists of two hinged rulers on which there are engraved scales. The scales allow various questions in trigonometry to be resolved by using the property that two similar (equiangular) triangles have sides in a constant ratio. The issue of who first invented by the sector is not without controversy. ... What singles out Gunter's sector is that it is the first mathematical instrument to be inscribed with a logarithmic scale to facilitate the resolution of numerical problems. This is not a slide rule in any sense of the term; the single logarithmic scale is used in conjunction with a pair of compasses. Such a rule is frequently referred to as a Gunter line. A two foot long boxwood ruler inscribed with a variety of scales was a standard navigator's tool up until the end of the nineteenth century.

Gunter was the inventor of instruments but he needed an instrument maker to produce them. Elias Allen (1592-1653) who had his workshop beside St Clement Danes Church, the Strand, London, was the instrument maker whom Gunter used. Hester Higton writes [14]:-

Allen appears to have had a close working relationship with Gunter. He was the most highly regarded instrument maker of his day. Having been an apprentice of the famous maker Charles Whitwell, he set himself up in business shortly before Whitwell's death in 1611, first [near] Fleetbridge, then beside St Clement Danes church in the Strand, probably in his former master's workshop.

Gunter gained from having Allen make his instruments and the illustration of the sector in Description and Use of the Sector, the Crosse-staffe and other Instruments is from plates engraved by Allen. But the relationship between the two worked the other way round too, for Allen made use of this engraving of Gunter's sector to advertise his own business.

Gunter also invented 'Gunter's chain' which was 22 yards long with 100 links. It was used for surveying and the unit of area called an acre is ten square chains. Gunter also studied magnetic declination and was the first to observe the secular variation. Higton writes in [2]:-

In 1622 Gunter's investigations at Limehouse, Deptford, of the magnetic variation of the compass needle produced results differing from William Borough's, obtained more than forty years earlier. He assumed an error in Borough's measurements, but this was in fact the first observation of temporal change in magnetic variation, a contribution acknowledged by his successor, Henry Gellibrand, who discovered the phenomenon.

His fascination with mathematical instruments went right back to his days at school and his main mathematical contributions are rightly seen to be in this area. In fact he made a new sundial with many plates containing a considerable amount of astronomical data and erected it in the gardens of Whitehall, a royal residence, in 1622. Prince Charles, who became King Charles I in 1625, persuaded Gunter to write and publish a description of the sundial which he did as The Description and Use of his Majesties Dials in Whitehall Garden (1624).

His contributions are summed up in [2] as follows:-

Gunter was a firm advocate of the use of instruments in mathematics for easing the work of various mathematical practitioners, notably surveyors and navigators. His instruments were designed with these aims in mind. In particular his work on logarithms, their applications to trigonometry, and their inclusion on instruments greatly simplified the processes of mathematical calculation. His books were popular for many years after his death: an edition of all his works was produced by Samuel Foster in 1636 and this had three more editions, the last in 1680 ...

Gunter died at Gresham College and was buried one day later in the churchyard of St Peter-le-Poer, Old Broad Street. St Peter-le-Poer was rebuilt on the site of its churchyard in 1788 and the church no longer exists having been demolished in 1896.