Edward Wright (mathematician)

For the 20th century mathematician, see Edward Maitland Wright.
Edward Wright

Title page of the first edition of Wright's Certaine Errors in Navigation (1599)
Born Unknown; baptised 8 October 1561
Garveston, Norfolk, East Anglia, England
Died November 1615 (aged at least 54)
London, England
Nationality English
Fields Mathematics; navigation; cartography
Alma mater Gonville and Caius College, Cambridge
Known for Writing Certaine Errors in Navigation (1599) which first explained the mathematical basis for the Mercator projection, producing the Wright–Molyneux map (ca. 1599), and translating John Napier's work on logarithms which was published as A Description of the Admirable Table of Logarithmes (1616)
Influenced Adriaan Metius, Richard Norwood, Willebrord Snellius

Edward Wright (baptised 8 October 1561; died November 1615) was an English mathematician and cartographer noted for his book Certaine Errors in Navigation (1599; 2nd ed., 1610), which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of latitude, calculated for each minute of arc up to a latitude of 75°. This was in fact a table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator charts.

Wright was born at Garveston and educated at Gonville and Caius College, Cambridge, where he became a fellow from 1587 to 1596. In 1589 the College granted him leave after Elizabeth I requested that he carry out navigational studies with a raiding expedition organised by the Earl of Cumberland to the Azores to capture Spanish galleons. The expedition's route was the subject of the first map to be prepared according to Wright's projection, which was published in Certaine Errors in 1599. The same year, Wright created and published the first world map produced in England and the first to use the Mercator projection since Gerardus Mercator's original 1569 map.

Not long after 1600 Wright was appointed as surveyor to the New River project, which successfully directed the course of a new man-made channel to bring clean water from Ware, Hertfordshire, to Islington, London. Around this time, Wright also lectured mathematics to merchant seamen, and from 1608 or 1609 was mathematics tutor to the son of James I, the heir apparent Henry Frederick, Prince of Wales, until the latter's very early death at the age of 18 in 1612. A skilled designer of mathematical instruments, Wright made models of an astrolabe and a pantograph, and a type of armillary sphere for Prince Henry. In the 1610 edition of Certaine Errors he described inventions such as the "sea-ring" that enabled mariners to determine the magnetic variation of the compass, the sun's altitude and the time of day in any place if the latitude was known; and a device for finding latitude when one was not on the meridian using the height of the pole star.

Apart from a number of other books and pamphlets, Wright translated John Napier's pioneering 1614 work which introduced the idea of logarithms from Latin into English. This was published after Wright's death as A Description of the Admirable Table of Logarithmes (1616). Wright's work influenced, among other persons, Dutch astronomer and mathematician Willebrord Snellius; Adriaan Metius, the geometer and astronomer from Holland; and the English mathematician Richard Norwood, who calculated the length of a degree on a great circle of the earth using a method proposed by Wright.

Family and education

The younger son of Henry and Margaret Wright, Edward Wright was born in the village of Garveston in Norfolk,[1] East Anglia, and was baptised there on 8 October 1561. It is possible that he followed in the footsteps of his elder brother Thomas (died 1579) and went to school in Hardingham.[2] The family was of modest means,[3] and he matriculated at Gonville and Caius College, University of Cambridge, on 8 December 1576[2] as a sizar.[4][5] Sizars were students of limited means who were charged lower fees and obtained free food and/or lodging and other assistance during their period of study, often in exchange for performing work at their colleges.

Wright was conferred a Bachelor of Arts (B.A.) in 1580–1581. He remained a scholar at Caius, receiving his Master of Arts (M.A.) there in 1584, and holding a fellowship between 1587 and 1596.[6] At Cambridge, he was a close friend of Robert Devereux, later the Second Earl of Essex, and met him to discuss his studies even in the weeks before Devereux's rebellion against Elizabeth I in 1600–1601. In addition, he came to know the mathematician Henry Briggs; and the soldier and astrologer Christopher Heydon, who was also Devereux's friend.[2][4] Heydon later made astronomical observations with instruments Wright made for him.[7]

Foreign expedition

Further information: Azores Voyage of 1589
Hilliard's portrait of George, Earl of Cumberland (ca. 1590, detail). Wright dedicated his work Certaine Errors in Navigation (1599) to him.

In 1589, two years after being appointed to his fellowship, Wright was requested by Elizabeth I to carry out navigational studies with a raiding expedition organised by the Earl of Cumberland to the Azores to capture Spanish galleons. The Queen effectively ordered Caius to grant him leave of absence for this purpose, although the College expressed this more diplomatically by granting him a sabbatical "by Royal mandate".[8] Wright participated in the confiscation of "lawful" prizes from the French, Portuguese and Spanish – Derek Ingram, a life fellow of Caius, has called him "the only Fellow of Caius ever to be granted sabbatical leave in order to engage in piracy".[8] Wright sailed with Cumberland in the Victory from Plymouth on 8 June 1589; they returned to Falmouth on 27 December of the same year.[2] An account of the expedition is appended to Wright's work Certaine Errors of Navigation (1599), and while it refers to Wright in the third person it is believed to have been written by him.[4]

In Wright's account of the Azores expedition, he listed as one of the expedition's members a "Captaine Edwarde Carelesse, alias Wright, who in S. Frauncis Drakes West-Indian voiage was Captaine of the Hope". In another work, The Haven-finding Art (1599) (see below), Wright stated that "the time of my first employment at sea" was "now more than tenne yeares since".[2] The Oxford Dictionary of National Biography asserts that during the expedition Wright called himself "Captain Edward Carelesse", and that he was also the captain of the Hope in Sir Francis Drake's voyage of 1585–1586 to the West Indies, which evacuated Sir Walter Raleigh's Colony of Virginia. One of the colonists was the mathematician Thomas Harriot, and if the Dictionary is correct it is probable that on the return journey to England Wright and Harriot became acquainted and discussed navigational mathematics.[4] However, in a 1939 article, E.J.S. Parsons and W.F. Morris note that in Capt. Walter Bigges and Lt. Crofts' book A Summarie and True Discourse of Sir Frances Drakes West Indian Voyage (1589),[9] Edward Careless was referred to as the commander of the Hope, but Wright was not mentioned. Further, while Wright spoke several times of his participation in the Azores expedition, he never alluded to any other voyage. Although the reference to his "first employment" in The Haven-finding Art suggests an earlier venture, there is no evidence that he went to the West Indies. Gonville and Caius College holds no records showing that Wright was granted leave before 1589.[2] There is nothing to suggest that Wright ever went to sea again after his expedition with the Earl of Cumberland.[4]

Wright resumed his Cambridge fellowship upon returning from the Azores in 1589,[3] but it appears that he soon moved to London for he was there with Christopher Heydon making observations of the sun between 1594 and 1597, and on 8 August 1595 Wright married Ursula Warren (died 1625) at the parish church of St. Michael, Cornhill, in the City of London.[10] They had a son, Samuel (1596–1616), who was himself admitted as a sizar[4] at Caius on 7 July 1612.[11] The St. Michael parish register also contains references to other children of Wright, all of whom died before 1617.[11] Wright resigned his fellowship in 1596.[4]

Mathematician and cartographer

Certaine Errors in Navigation

Wright explained the Mercator projection with the analogy of a sphere being inflated like a bladder inside a hollow cylinder.[12] The sphere is expanded uniformly, so that the meridians lengthen in the same proportion as the parallels, until each point of the expanding spherical surface comes into contact with the inside of the cylinder. This process preserves the local shape and angles of features on the surface of the original globe, at the expense of parts of the globe with different latitudes becoming expanded by different amounts.[13] The cylinder is then opened out into a two-dimensional rectangle. The projection is a boon to navigators as rhumb lines are depicted as straight lines.

Wright helped the mathematician and globe maker Emery Molyneux to plot coastlines on his terrestrial globe, and translated some of the explanatory legends into Latin.[14] Molyneux's terrestrial and celestial globes, the first to be manufactured in England, were published in late 1592 or early 1593, and Wright explained their use in his 1599 work Certaine Errors in Navigation. He dedicated the book to Cumberland, to whom he had presented a manuscript of the work in 1592,[15][16] stating in the preface it was through Cumberland that he "was first moved, and received maintenance to divert my mathematical studies, from a theorical speculation in the Universitie, to the practical demonstration of the use of Navigation".[17]

The most significant aspect of the book was Wright's method for dividing the meridian; an explanation of how he had constructed a table for the division; and the uses of this information for navigation. Essentially, the problem that occupied Wright was how to depict accurately a globe on a two-dimensional map according to the projection used by Gerardus Mercator in his map of 1569. Mercator's projection was advantageous for nautical purposes as it represented lines of constant true bearing or true course, known as loxodromes or rhumb lines, as straight lines. However, Mercator had not explained his method.[18]

On a globe, circles of latitude (also known as parallels) get smaller as they move away from the Equator towards the North or South Pole. Thus, in the Mercator projection, when a globe is "unwrapped" on to a rectangular map, the parallels need to be stretched to the length of the Equator. In addition, parallels are further apart as they approach the poles. Wright compiled a table with three columns. The first two columns contained the degrees and minutes of latitudes for parallels spaced 10 minutes apart on a sphere, while the third column had the parallel's projected distance from the Equator. Any cartographer or navigator could therefore lay out a Mercator grid for himself by consulting the table.[19] Wright explained:

I first thought of correcting so many gross errors ... in the sea chart, by increasing the distances of the parallels, from the equinoctial towards the poles, in such sort, that at every point of latitude in the chart, a part of the meridian might have the same proportion to the like part of the parallel, that it has in the globe.[20]
Hondius made use of Wright's calculations without acknowledgment in his "Christian Knight Map" of 1597, prompting Wright to publish Certaine Errors in Navigation in 1599.

While the first edition of Certaine Errors contained an abridged table six pages in length, in the second edition which appeared in 1610 Wright published a full table across 23 pages with figures for parallels at one-minute intervals. The table is remarkably accurate – American geography professor Mark Monmonier wrote a computer program to replicate Wright's calculations, and determined that for a Mercator map of the world 3 feet (0.91 m) wide, the greatest discrepancy between Wright's table and the program was only 0.00039 inches (0.0099 mm) on the map.[21] In the second edition Wright also incorporated various improvements, including proposals for determining the magnitude of the Earth and reckoning common linear measurements as a proportion of a degree on the Earth's surface "that they might not depend on the uncertain length of a barley-corn"; a correction of errors arising from the eccentricity of the eye when making observations using the cross-staff; amendments in tables of declinations and the positions of the sun and the stars, which were based on observations he had made together with Christopher Heydon using a 6-foot (1.8 m) quadrant; and a large table of the variation of the compass as observed in different parts of the world, to show that it is not caused by any magnetic pole. He also incorporated a translation of Rodrigo Zamorano's Compendio de la Arte de Navegar (Compendium of the Art of Navigation, Seville, 1581; 2nd ed., 1588).[22]

Edward Wright's map "for sailing to the Isles of Azores" (ca. 1595), the first to be prepared according to his projection
Wright's "Chart of the World on Mercator's Projection" (ca. 1599), otherwise known as the Wright–Molyneux map

Wright was prompted to publish the book after two incidents of his text, which had been prepared some years earlier, being used without attribution. He had allowed his table of meridional parts to be published by Thomas Blundeville in his Exercises (1594)[23] and in William Barlow's The Navigator's Supply (1597),[24] although only Blundeville acknowledged Wright by name. However, an experienced navigator, believed to be Abraham Kendall, borrowed a draft of Wright's manuscript and, unknown to him, made a copy of it which he took on Sir Francis Drake's 1595 expedition to the West Indies. In 1596 Kendall died at sea. The copy of Wright's work in his possession was brought back to London and wrongly believed to be by Kendall, until the Earl of Cumberland passed it to Wright and he recognised it as his work.[25] Also around this time, the Dutch cartographer Jodocus Hondius borrowed Wright's draft manuscript for a short time after promising not to publish its contents without his permission. However, Hondius then employed Wright's calculations without acknowledging him for several regional maps and in his world map published in Amsterdam in 1597. This map is often referred to as the "Christian Knight Map" for its engraving of a Christian knight battling sin, the flesh and the Devil. Although Hondius sent Wright a letter containing a faint apology, Wright condemned Hondius's deceit and greed in the preface to Certaine Errors.[26] He wryly commented: "But the way how this [Mercator projection] should be done, I learned neither of Mercator, nor of any man els. And in that point I wish I had beene as wise as he in keeping it more charily to myself".[27]

The first map to be prepared according to Wright's projection was published in his book, and showed the route of Cumberland's expedition to the Azores. A manuscript version of this map is preserved at Hatfield House; it is believed to have been drawn about 1595.[28] Following this, Wright created a new world map, the first map of the globe to be produced in England and the first to use the Mercator projection since Gerardus Mercator's 1569 original. Based on Molyneux's terrestrial globe, it corrected a number of errors in the earlier work by Mercator. The map, often called the Wright–Molyneux Map, first appeared in the second volume of Richard Hakluyt's The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation (1599).[29] Unlike many contemporary maps and charts which contained fantastic speculations about unexplored lands, Wright's map has a minimum of detail and blank areas wherever information was lacking. The map was one of the earliest to use the name "Virginia".[30] Shakespeare alluded to the map in Twelfth Night (1600–1601),[31] when Maria says of Malvolio: "He does smile his face into more lynes, than is in the new Mappe, with the augmentation of the Indies."[32] Another world map, larger and with updated details, appeared in the second edition of Certaine Errors (1610).[32]

Wright translated into English De Havenvinding (1599) by the Flemish mathematician and engineer Simon Stevin, which appeared in the same year as The Haven-Finding Art, or the Way to Find any Haven or Place at Sea, by the Latitude and Variation. He also wrote the preface to physician and scientist William Gilbert's great work De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (The Magnet, Magnetic Bodies, and the Great Magnet the Earth, 1600),[33] in which Gilbert described his experiments which led to the conclusion that the Earth was magnetic, and introduced the term electricus to describe the phenomenon of static electricity produced by rubbing amber (called ēlectrum in Classical Latin, derived from 'ήλεκτρον (elektron) in Ancient Greek).[34] According to the mathematician and physician Mark Ridley,[35] chapter 12 of book 4 of De Magnete, which explained how astronomical observations could be used to determine the magnetic variation, was actually Wright's work.[4]

Gilbert had invented a dip-compass and compiled a table recording the dip of the needle below the horizon. Wright believed that this device would prove to be extremely useful in determining latitude and, with the help of Blundeville and Briggs, wrote a small pamphlet called The Making, Description and Use of the Two Instruments for Seamen to find out the Latitude ... First Invented by Dr. Gilbert. It was published in 1602 in Blundeville's book The Theoriques of the Seuen Planets.[36] That same year he authored The Description and Use of the Sphære (not published till 1613), and in 1605 published a new edition of the widely used work The Safegarde of Saylers.[37][38]

Surveying

The New River at Enfield Town Park in London – photographed on 3 February 2008

Wright also developed a reputation as a surveyor on land. He prepared "a plat of part of the waye whereby a newe River may be brought from Uxbridge to St. James, Whitehall, Westminster [,] the Strand, St Giles, Holbourne and London",[39] However, according to a 1615 paper in Latin in the annals of Gonville and Caius College, he was prevented from bringing this plan to fruition "by the tricks of others".[22][40] Nonetheless, early in the first decade of the 17th century, he was appointed by Sir Hugh Myddelton as surveyor to the New River project, which successfully directed the course of a new man-made channel to bring clean water from Chadwell Spring at Ware, Hertfordshire,[22] to Islington, London. Although the distance in a straight line from Ware to London is only slightly more than 20 miles (32 km), the project required a high degree of surveying skill on Wright's part as it was necessary for the river to take a route of over 40 miles following the 100-foot (30 m) contour line on the west side of the Lea Valley. As the technology of the time did not extend to large pumps or pipes, the water flow had to depend on gravity through canals or aqueducts over an average fall of 5.5 inches a mile (approximately 8.7 centimetres per kilometre).[8][41]

Work on the New River started in 1608 – the date of a monument at Chadwell Spring – but halted near Wormley, Hertfordshire, in 1610. The stoppage has been attributed to factors such as Myddelton facing difficulties in raising funds, and landowners along the route opposing the acquisition of their lands on the ground that the river would turn their meadows into "bogs and quagmires".[41] Although the landowners petitioned Parliament, they did not succeed in having the legislation authorising the project repealed prior to Parliament being dissolved in 1611; the work resumed later that year. The New River was officially opened on 29 September 1613 by the Lord Mayor of London, Sir John Swinnerton, at the Round Pond, New River Head, in Islington. It still supplies the capital with water today.[41]

Other mathematical work

For some time Wright had urged that a navigation lectureship be instituted for merchant seamen, and he persuaded Admiral Sir William Monson, who had been on Cumberland's Azores expedition of 1589, to encourage a stipend to be paid for this. At the beginning of the 17th century, Wright succeeded Thomas Hood as a mathematics lecturer under the patronage of the wealthy merchants Sir Thomas Smyth and Sir John Wolstenholme; the lectures were held in Smyth's house in Philpot Lane.[42] By 1612 or 1614 the East India Company had taken on sponsorship of these lectures for an annual fee of £50[16][40] (about £6,500 as of 2007).[43] Wright was also mathematics tutor to the son of James I, the heir apparent Henry Frederick, Prince of Wales, from 1608 or 1609[16][38] until the latter's death at the age of 18 on 6 November 1612. Wright was described as "a very poor man" in the Prince's will and left the sum of £30 8s (about £4,300 in 2007).[4] To the Prince, who was greatly interested in the science of navigation,[44] Wright dedicated the second edition of Certaine Errors (1610) and the world map published therein. He also drew various maps for him, including a "sea chart of the N.-W. Passage; a paradoxall sea-chart of the World from 30° Latitude northwards; [and] a plat of the drowned groundes about Elye, Lincolnshire, Cambridgeshire, &c".[38]

Wright was a skilled designer of mathematical instruments. According to the 1615 Caius annals, "[h]e was excellent both in contrivance and execution, nor was he inferior to the most ingenious mechanic in the making of instruments, either of brass or any other matter".[22] For Prince Henry, he made models of an astrolabe and a pantograph,[40] and created or arranged to be created out of wood a form of armillary sphere which replicated the motions of the celestial sphere, the circular motions of the sun and moon, and the places and possibilities of them eclipsing each other. The sphere was designed for a motion of 17,100 years, if the machine should last that long.[22] In 1613 Wright published The Description and Use of the Sphære, which described the use of this device.[4] The sphere was lost during the English Civil War, but found in 1646 in the Tower of London by the mathematician and surveyor Sir Jonas Moore, who was later appointed Surveyor General of the Ordnance Office and became a patron and the principal driving force behind the establishment of the Royal Observatory at Greenwich. Moore asked the King to let him have it, restored the instrument at his own expense and deposited it at his own house "in the Tower".[22][45]

The Caius annals also report that Wright "had formed many other useful designs, but was hindered by death from bringing them to perfection".[22] The 1610 edition of Certaine Errors contained descriptions of the "sea-ring", which consisted of a universal ring dial mounted over a magnetic compass that enabled mariners to determine readily the magnetic variation of the compass, the sun's altitude and the time of day in any place if the latitude was known;[46] the "sea-quadrant", for the taking of altitudes by a forward or backward observation; and a device for finding latitude when one was not on the meridian using the height of the pole star.[22]

The Scotsman John Napier (1550–1617), the inventor of logarithms, depicted in an engraving by Samuel Freeman (1773–1857) based on a 1616 painting at the University of Edinburgh

In 1614 Wright published a small book called A Short Treatise of Dialling: Shewing, the Making of All Sorts of Sun-dials, but he was mainly preoccupied with John Napier's Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Rule of Logarithms),[47] which introduced the idea of logarithms. Wright at once saw the value of logarithms as an aid to navigation, and lost no time in preparing a translation which he submitted to Napier himself. The preface to Wright's edition consists of a translation of the preface to the Descriptio, together with the addition of the following sentences written by Napier himself:

But now some of our countreymen in this Island well affected to these studies, and the more publique good, procured a most learned Mathematician to translate the same into our vulgar English tongue, who after he had finished it, sent the Coppy of it to me, to bee seene and considered on by myselfe. I having most willingly and gladly done the same, finde it to bee most exact and precisely conformable to my minde and the originall. Therefore it may please you who are inclined to these studies, to receive it from me and the Translator, with as much good will as we recommend it unto you.[48]

While working on the translation, Wright died in late November 1615 and was buried on 2 December 1615 at St. Dionis Backchurch in the City of London.[49] The Caius annals noted that although he "was rich in fame, and in the promises of the great, yet he died poor, to the scandal of an ungrateful age".[22] Wright's translation of Napier, which incorporated tables that Wright had supplemented and further information by Henry Briggs, was completed by Wright's son Samuel and arranged to be printed by Briggs.[4] It appeared posthumously as A Description of the Admirable Table of Logarithmes in 1616, and in it Wright was lauded in verse as "[t]hat famous, learned, Errors true Corrector, / England's great Pilot, Mariners Director".[50]

According to Parsons and Morris, the use of Wright's publications by later mathematicians is the "greatest tribute to his life's work".[40] Wright's work was relied on by Dutch astronomer and mathematician Willebrord Snellius, noted for the law of refraction now known as Snell's law, for his navigation treatise Tiphys Batavus (Batavian Tiphys, 1624);[51] and by Adriaan Metius, the geometer and astronomer from Holland, for Primum Mobile (1631).[52] Following Wright's proposals, Richard Norwood measured a degree on a great circle of the earth at 367,196 feet (111,921 m), publishing the information in 1637.[53] Wright was praised by Charles Saltonstall in The Navigator (1642)[54] and by John Collins in Navigation by the Mariners Plain Scale New Plain'd (1659),[55] Collins stating that Mercator's chart ought "more properly to be called Wright's chart".[40] The Caius annals contained the following epitaph: "Of him it may truly be said, that he studied more to serve the public than himself".[22]

Works

Authored

Title page of Wright's Certaine Errors in Navigation (Second edition, 1610)

Edited and translated

Title page of Admirable Table of Logarithmes (2nd ed., 1618)

Notes

  1. ↑ E.J.S. Parsons; W.F. Morris (1939), "Edward Wright and His Work", Imago Mundi 3: 61, doi:10.1080/03085693908591862, JSTOR 1149920.
  2. 1 2 3 4 5 6 Parsons & Morris, p. 61.
  3. 1 2 Paul J. Lewi (11 February 2006), "Mercator, Wright and Mapmaking", Speaking of Graphics: An Essay on Graphicacy in Science, Technology and Business, Turnhout, Belgium: DataScope, p. 24, archived from the original (PDF) on 15 January 2009, Edward Wright was born in 1561 at Garveston, near Norfolk, in a family with modest income (mediocris fortunae).
  4. 1 2 3 4 5 6 7 8 9 10 11 A.J. Apt; B. Harrison (2004), "Wright, Edward (bap. 1561, d. 1615)", Oxford Dictionary of National Biography, Oxford: Oxford University Press, doi:10.1093/ref:odnb/30029.
  5. ↑ "Wright, Edward (WRT576E)". A Cambridge Alumni Database. University of Cambridge..
  6. ↑ John Venn, comp. (1897), Biographical History of Gonville and Caius College, 1349–1897: Containing a List of All Known Members of the College 1, Cambridge: Cambridge University Press, pp. 88–89.
  7. ↑ Bernard Capp (2004), "Heydon, Sir Christopher (1561–1623)", Oxford Dictionary of National Biography, Oxford: Oxford University Press.
  8. 1 2 3 Derek Ingram (2001), "The First Caian Engineer and the First Caian Pirate", The Caius Engineer 13 (1), retrieved 2 May 2008.
  9. ↑ Walter Bigges; Lieutenant Crofts; Thomas Cates, ed. (1589), A Summarie and True Discourse of Sir Francis Drakes VVest Indian Voyage wherein were Taken, the Townes of Saint Iago, Sancto Domingo, Cartagena & Saint Augustine: With Geographicall Mappes exactly Describing each of the Townes with their Scituations, and the Manner of the Armies Approching [sic] to the Winning of them. [Begun by Walter Bigges, continued by Lieutenant Crofts, and edited by Thomas Cates.], London: Imprinted ... [b]y Richard Field, dwelling in the Blacke-Friars by Ludgate.
  10. ↑ Parish register, London, St. Michael Cornhill, 8 August 1595, GL [marriage]: see Apt, "Wright, Edward", Oxford Dictionary of National Biography.
  11. 1 2 Parsons & Morris, p. 71.
  12. ↑ Parsons & Morris, p. 63; see also Marie Boas Hall (1994), "The Uses of Mathematics [ch. 7]", The Scientific Renaissance 1450–1630, New York, N.Y.; London: Dover Publications; Constable, pp. 197–237 at 208, ISBN 0-486-28115-9.
  13. ↑ It is a common misconception that the Mercator projection is mathematically the same as projecting rays of light through the globe onto the cylinder from a source at the centre: Eli Maor (1998), "A Mapmaker's Paradise [ch. 13]", Trigonometric Delights (PDF), Princeton, N.J.; Chichester: Princeton University Press, p. 165 at 176, ISBN 0-691-05754-0.
  14. ↑ Susan M. Maxwell; Harrison, B. (September 2004), "Molyneux, Emery (d. 1598)", Oxford Dictionary of National Biography (Online ed.), Oxford: Oxford University Press, doi:10.1093/ref:odnb/50911.
  15. ↑ Lewi, "Mercator, Wright and Mapmaking", pp. 24–25.
  16. 1 2 3 Richard S. Westfall (1995), "Wright, Edward", The Galileo Project, Rice University, retrieved 3 May 2008.
  17. ↑ Stephen Pumfrey; Frances Dawbarn (2004), "Science and Patronage in England, 1570–1625: A Preliminary Study" (PDF), History of Science 42: 137 at 165.
  18. ↑ Mark Monmonier (2004). "The Wright Approach". Rhumb Lines and Map Wars: A Social History of the Mercator Projection. Chicago, Ill.: University of Chicago Press. pp. 65–67. ISBN 0-226-53431-6..
  19. ↑ Monmonier, Rhumb Lines and Map Wars, pp. 63–64.
  20. ↑ Quoted in Lewi, "Mercator, Wright and Mapmaking", p. 25 (the reference in Lewi to Parsons & Morris, p. 65, is incorrect).
  21. ↑ Monmonier, Rhumb Lines and Map Wars, p. 68.
  22. 1 2 3 4 5 6 7 8 9 10 Charles Hutton (1815), "Wright (Edward)", A Philosophical and Mathematical Dictionary 2, London: Printed for the author by F.C. and J. Rivington [et al.], pp. 619–620.
  23. ↑ Thomas Blundeville (1594), M. Blundevile His Exercises containing Sixe Treatises, the Titles wherof are Set Down in the Next Printed Page: Which Treatises are Verie Necessarie to be Read and Learned of all Yoong Gentlemen that haue not bene Exercised in such Disciplines, and yet are Desirous to haue Knowledge as well in Cosmographie, Astronomie, and Geographie, as also in the Arte of Navigation ... To the Furtherance of which Arte of Navigation, the said M. Blundevile Speciallie Wrote the said Treatises and of Meere Good Will doth Dedicate the same to all the Young Gentlemen of this Realme, London: Printed by Iohn Windet, dwelling at the signe of the crosse Keies, neere Paules wharffe, and are there to be solde.
  24. ↑ William Barlow (1597), The Nauigators Supply. Conteining Many Things of Principall Importance Belonging to Nauigation, with the Description and Vse of Diuerse Instruments Framed Chiefly for that Purpose; but Seruing also for Sundry Other of Cosmography in Generall: the Particular Instruments are Specified on the Next Page, London: Imprinted ... By G. Bishop, R. Newbery, and R. Barker.
  25. ↑ Parsons & Morris, p. 62; Monmonier, Rhumb Lines and Map Wars, p. 70.
  26. ↑ Monmonier, Rhumb Lines and Map Wars, pp. 68–70.
  27. ↑ Lewi, "Mercator, Wright and Mapmaking", p. 29; the quotation is from Parsons & Morris, p. 62.
  28. ↑ Gerard L'Estrange Turner (2000), Elizabethan Instrument Makers: The Origins of the London Trade in Precision Instrument Making, Oxford: Oxford University Press, p. 41, ISBN 0-19-856566-6; citing D.W. Waters (1958), The Art of Navigation in England in Elizabethan and Early Stuart Times, London: Hollis & Carter, pp. 550–551 and xxiv, plate 61.
  29. ↑ Richard Hakluyt (1598–1600), The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation, Made by Sea or Overland ... at Any Time Within the Compasse of these 1500 [1600] Yeeres, &c, London: G. Bishop, R. Newberie & R. Barker, 3 vols: see Parsons & Morris, pp. 67–68; Monmonier, Rhumb Lines and Map Wars, p. 70.
  30. ↑ Novus Orbis: Images of the New World, part 3, Lewis & Clark: The Maps of Exploration 1507–1814, Albert H. and Shirley Small Special Collections Library, University of Virginia, 31 January 2008, retrieved 7 February 2008; "5. Edward Wright. "A Chart of the World on Mercator's Projection." – c. 1599", An Exhibition of Maps and Navigational Instruments, on View in the Tracy W. McGregor Room, Alderman Library, University of Virginia, July 10 to September 26, 1995, University of Virginia, c. 1995, retrieved 4 May 2008.
  31. ↑ Act III, scene ii: see William Shakespeare (July 2000), Twelfth Night; or What You Will [Etext #2247], Champaign, Ill.: Project Gutenberg.
  32. 1 2 Parsons & Morris, p. 68.
  33. ↑ William Gilbert (1600), De Magnete, magneticisque corporibus, et de magno magnete tellure; Physiologia nova, plurimis & argumentis, & experimentis demonstrata [The Magnet, Magnetic Bodies, and the Great Magnet the Earth; New Natural Science, Demonstrated by Many Arguments and Experiments], London: Excudebat Petrus Short (Latin).
  34. ↑ "electrum, n.", OED Online, Oxford: Oxford University Press, March 2008, retrieved 3 May 2008.
  35. ↑ Mark Ridley (1617), Magneticall Animadversions ... upon certaine Magneticall Advertisements lately Published, from Maister W. Barlow, London: [s.n.]: see Stephen Andrew Johnston (1994), "Practitioners and Mechanicians [ch. 4]", Making Mathematical Practice: Gentlemen, Practitioners and Artisans in Elizabethan England, Cambridge: University of Cambridge, p. 182, n. 21.
  36. ↑ Thomas Blundeville; Henry Briggs; Edward Wright (1602), The Theoriques of the Seuen Planets shewing all their Diuerse Motions, and all other Accidents, called Passions, thereunto Belonging. Now more Plainly set forth in our Mother Tongue by M. Blundeuile, than euer they haue been heretofore in any other Tongue whatsoeuer, and that with such Pleasant Demonstratiue Figures, as euery Man that hath any Skill in Arithmeticke, may easily Vnderstand the same. ... VVhereunto is added by the said Master Blundeuile, a Breefe Extract by him made, of Maginus his Theoriques, for the Better Vnderstanding of the Prutenicall Tables, to Calculate thereby the Diuerse Motions of the Seuen Planets. There is also hereto added, the Making, Description, and Vse, of Two Most Ingenious and Necessarie Instruments for Sea-men ... First Inuented by M. Doctor Gilbert ... and now here Plainely set downe in our Mother Tongue by Master Blundeuile, London: Printed by Adam Islip.
  37. ↑ Robert Norman, transl. (1605), Edward Wright, ed., The Safegarde of Saylers, or Great Rutter. Contayning the Courses, Dystances, Deapths, Soundings, Flouds and Ebbes, with the Marks for the Entring of Sundry Harboroughs both of England, Fraunce, Spaine, Ireland. Flaunders, and the Soundes of Denmarke, with other Necessarie Rules of Common Nauigation. Translated out of Dutch ... by Robert Norman ... Newly corrected and augmented by E[dward] W[right], London: By E. Allde for H. Astley.
  38. 1 2 3 Parsons & Morris, p. 69.
  39. ↑ British Museum, Cotton manuscript, Titus book viii, folio 318: see Parsons & Morris, p. 69.
  40. 1 2 3 4 5 Parsons & Morris, p. 70.
  41. 1 2 3 The story of the New River, Thames Water, archived from the original on 11 February 2008, retrieved 1 May 2008.
  42. ↑ Clements R Markham (1903), "Commemoration of the Reign of Queen Elizabeth: Address by the President, Sir Clements R. Markham, K.C.B", Geographical Journal (Blackwell Publishing) 21 (6): 589–602 at 594, doi:10.2307/1775648, JSTOR 1775648: see Parsons & Morris, p. 70 (the citation in n. 24 is incorrect).
  43. ↑ This sum was calculated using the website MeasuringWorth.com based on the retail price index, using a date of 1614: Lawrence H. Officer, Purchasing power of British Pounds from 1264 to 2007, MeasuringWorth.com, retrieved 3 May 2008.
  44. ↑ Alexander Brown (1890), The Genesis of the United States. A Narrative of the Movement in England, 1605–1616, which Resulted in the Plantation of North America ... set forth through a Series of Historical Manuscripts now first Printed, together with a Reissue of Rare Contemporaneous Tracts, accompanied by Bibliographical Memoranda, Notes, and Brief Biographies. Collected ... and Edited by A. Brown .. 2, London; Cambridge, Mass.: William Heinemann, pp. 1025–1026, cited in Note [Prince Henry, eldest son of England's king James I (1594–1612)], She-philosopher.com, January 2007 (revised 7 March 2007), retrieved 19 May 2008 Check date values in: |date= (help).
  45. ↑ John Aubrey's manuscripts, later published as John Aubrey (1898), Andrew Clark, ed., 'Brief Lives,' chiefly of Contemporaries, set down ... between the Years 1669 & 1696. Edited from the Author's Mss. by Andrew Clark.., Oxford: Clarendon Press, 2 vols., cited in Brown, The Genesis of the United States, vol. 2, pp 1025–1026.
  46. ↑ See also William Edward May (1973), A History of Marine Navigation, Henley-on-Thames, Oxfordshire: G.T. Foulis & Co. Ltd., ISBN 0-85429-143-1.
  47. ↑ John Napier (1614), Mirifici Logarithmorum Canonis descriptio; ejusque usus, in utraque trigonometria, ut etiam in omni logistica mathematica, amplissimi, facillimi, & expeditissimi explicatio [Description of the Wonderful Rule of Logarithms: Its use in Trigonometry, as well as in all types of Mathematical Calculations, Explained Broadly, Easily and in an Unemcumbered Manner], Edinburgh: Ex officina Andreæ Hart (Latin).
  48. ↑ J.W.L.G. (1910–1911), "Logarithm", in Hugh Chisholm, The Encyclopædia Britannica (11th ed.), Cambridge: Cambridge University Press.
  49. ↑ Parish register, London, St. Dionis Backchurch, 2 December 1615, GL [burial]: see Apt, "Wright, Edward", Oxford Dictionary of National Biography.
  50. ↑ Lewi, "Mercator, Wright and Mapmaking", p. 31.
  51. ↑ Willebrord Snellius (1624), Willebrordi Snellii à Royen Tiphys Batavus, sive histiodromice, de navium cursibus et re navali. (Tabulæ canonicæ parallelorum Canones loxodromici προχειροι.) Willebrord Snellius van Royen; The Batavian Tiphys; or Navigation, Ships' Courses and Naval Matters. (Canonical Tables of Parallels, Handy Loxodromic Tables.), Leiden: Ex officinâ Elzeviriana [From the office of Elzevir] (Latin). Tiphys was the helmsman of the Argonauts in Greek mythology, while "Batavia" is a name for the Dutch Republic. The main title of Snellius's book therefore means "the Dutch helmsman".
  52. ↑ Adriaan Metius (1631), Adriani Metii Alcmar D.M. et matheseos profess. ordin. Primum mobile: astronomicè, sciographicè, geometricè, et hydrographicè, nova methodo explicatum in ... opus absolutum, IV tomis distinctum [[By Adrianus Metius of Alkmaar, ordained Doctor of Medicine and professor of mathematics.] The Primum Mobile: Astronomically, Sciographically, Geometrically and Hydrographically Explained by a New Method in ... a Complete Work Separated into 4 Tomes], Amsterdam: Apud Ioannem Ianssonium [by Jan Janszoon] (Latin). "Sciography", a variant of "sciagraphy", is the branch of the science of perspective dealing with the projection of shadows, or the art or practice of determining time by observing the shadow of the sun, moon or stars on a dial: "sciagraphy", OED Online (2nd ed.), Oxford: Oxford University Press, 1989, retrieved 26 May 2008.
  53. ↑ Richard Norwood (1637), The Seaman's Practice, contayning a Fundamentall Probleme in Navigation Experimentally Verified; namely Touching the Compasse of the Earth and Sea, and the Quantity of a Degree in our English Measures. Also an Exact Method ... of Keeping a Reckoning at Sea; ... Tables, etc, London: George Hurlock.
  54. ↑ Charles Saltonstall (1636), The Navigator, shewing and explaining all the Chiefe Principles and Parts both Theoricke and Practicke, that are contayned in the Famous Art of Navigation: With a New and Admirable Way of Sayling by the Arch of one of the Greatest Circles: Also contayning Excellent Tables most exactly Calculated, shewing the True Proportion of all Paralels [sic] in respect of the Meridian: With the Proper Phraises used in Working of a Ship according to all Weathers, London: Printed [by B[ernard] Alsop and T[homas] Fawcet] for Geo[rge] Herlock [sic: Hurlock].
  55. ↑ John Collins (1659), Navigation by the Mariners Plain Scale New Plain'd: Or, A Treatise of Geometrical and Arithmetical Navigation; wherein Sayling is Performed in all the Three Kindes by a Right Line, and a Circle Divided into Equal Parts. Containing 1. New Ways of Keeping of a Reckoning, or Platting of a Traverse, both upon the Plain and Mercators Chart ... 2. New Rules for Estimating the Ships Way through Currents, and for Correcting the Dead Reckoning. 3. The Refutation of Divers Errors, and of the Plain Chart, and how to Remove the Error Committed thereby ... as also a Table thereof made to every other Centesm. 4. A New Easie Method of Calculation for Great Circle-sayling, with New Projections, Schemes and Charts ... 5. Arithmetical Navigation, or Navigation Performed by the Pen, if Tables were Wanting .., London: Printed by Tho. Johnson for Francis Cossinet, and are to be sold at the Anchor and Mariner in Tower-street, as also by Henry Sutton mathematical instrument-maker in Thread needle street, behinde the Exchange.
  56. ↑ Erwin Tomash; Michael R. Williams, "N", The Tomash Collection on the History of Computing: An Annotated and Illustrated Catalog (PDF), Calgary, Alta.: [University of Calgary?], p. 913 at 922.

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