page_title: Edward Wright (mathematician)
section_title: Certaine Errors in Navigation
hierarchical_section_title: Edward Wright (mathematician) / Mathematician and cartographer / Certaine Errors in Navigation
caption_attribution_description: English: The so-called "Christian Knight map", published by Flemish map-maker Jodocus Hondius in Amsterdam in 1597. To produce the map, Hondius made use of Edward Wright's mathematical methods without acknowledgement.
context_page_description: Edward Wright was an English mathematician and cartographer noted for his book Certaine Errors in Navigation, which for the first time explained the mathematical basis of the Mercator projection by building on the works of Pedro Nunes, 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.
context_section_description: 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. 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, 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".
  The navigation errors addressed by Wright in Certaine Errors in Navigation had been previously treated by Pedro Nunes, whose works had been compiled in Petri Nonii Salaciensis Opera in 1566 (later expanded, corrected and re-edited as De arte adque ratione navigandi in 1573).
  This is pointed out by Wright himself in the Preface:
  Yet it may be, I shall be blamed by some, as being to busie a fault-finder myself. For when they shall, see their Charts and other instruments controlled which so long time have gone for current, some of them perhappes will scarcely with pacience endure it. But they may be pacified, if not by reason of the good that ensueth hereupon, yet towards me at the least because the errors I poynt at in the chart, have beene heretofore poynted out by others, especially by Petrus Nonius, out of whom most part of the first Chapter of the Treatise following is almost worde for worde translated;
  This appeal to the authority of Pedro Nunes and the fact that the first chapter treats the Faults in the common Sea Chart, With Rumbes expressed by right lines and degrees of latitude, everywhere equal, show Nune's influence in Wright's work. In addition, the effect of following a rhumb line course on the surface of a globe was first discussed by Pedro Nunes in 1537 in his Treatise in Defense of the Marine Chart. In this work, Nunes proposes the construction of a nautical atlas composed of several large-scale sheets in the cylindrical equidistant projection as a way to minimize distortion of directions. If these sheets were brought to the same scale and assembled, they would approximate the Mercator projection, later introduced by Gerardus Mercator in 1569. Mercator never explained the method of construction of the projection bearing his name, nor how he arrived at it. Various hypotheses have been tendered over the years, but in any case Mercator's friendship with Pedro Nunes and his access to the loxodromic tables Nunes created likely aided his efforts.  Mercator's projection was advantageous for nautical purposes as it represented lines of constant true bearing or true course (rhumb lines), as straight lines. 
  In Certaine errors of navigation, Wright improved and diversified Nunes' charting method, thus explaining the construction and use of the Mercator projection. As Wright himself puts it in Chapter 2:
  By help of this planisphaere with the meridians, rumbes, and parallels thus described therein, the rumbs may much more easily & truly be drawn in the globe then by these mechanical wayes which Petrus Nonius teacheth cap. 26 lib. 2 de obser. Reg. et Instr. Geom..
  In order to achieve this, Wright introduces the 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. 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 project
caption: 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.
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