Edward Wright and Pedro Nunes

Pedro Nunes (1502 - 1578)

Mathematics, Cosmography and Nautical Science in the 16th century.

Edward Wright's Certaine errors in navigation can be considered as a turning point in the literature about navigation and a crucial step towards its mathematization.

Edward Wright (1561 – 1615) studied at Cambridge University and in 1589, after some years teaching there, he took part on an expedition to the Azores with the goal to explore and pirate the area. In that same year he started working in his book Certaine Errors and, in 1592, he submitted the first copy to the Earl of Cumberland. Between 1594 and 1597 he lived in London where he made essential studies and observations for his work.

Certaine Errors in Navigation¹ was only published in 1599. It’s a work of great importance for the history of navigation and had two more editions in the 17^th century². In that same year, Wright also ordered the publishing of his translation of the important work of Simon Stevin, Havenvinding, with the title The Haven-finding Art[4].

Wright’s Certaine Errors in Navigation is a book with some original characteristics for its time: one can notice the absence of the usual introduction to the Sphere, of chapters on the calculation of Holy days and chapters on tides and winds. The book is divided in 4 main parts :

1) Hydrographicall – deals with the errors associated to the common nautical chart. Mathematical basis of Mercator’s projection.

2) Magneticall – deals with the variation of the magnetical compass. Method for knowing its value.

3) Geometricall – deals with the use of the cross-stafe and ways to avoid errors. 

4) Astronomicall – corrects/updates values of sun’s declination’s and stars tables and of other constants necessary to navigation.

Pedro Nunes’ influence.

To find Pedro Nunes’ name in Wright’s Certaine errors is not a difficult task, alongside with other notable names as Mercator, Frisius, Brahe, Ortelius, Cortés, Ramus, etc. Recently, Henrique Leitão pointed out a preoccupying lack of references to any relation between Nunes’ and Wright’s works in international historiography. This would not be, for sure, Wright’s intention since he keeps “no secret about his intellectual debt. Not only does he cite the Portuguese by name, but he even explains in the Preface that the problems he will treat have been previously addressed by others «especially by Petrus Nonius» out of whom most of the first Chapter of the treatise following is almost word for word translated”[6].

The case of Edward Wright is paradigmatic and exemplary but it is far from being the only one in England. For instance, John Davis wrote about “paradoxical navigation” (that is, the loxodromic navigation studied for the first time by Nunes); Robert Hues published his Tractatus de globis et eorum usu in 1594 and refers to several subjects previously studied by Pedro Nunes; William Barlow published his Navigators supply in 1597 and he mentions the work done by the “learned Nonius”. He even adapted a nonio (nonius scale) to an instrument called pantometra; Thomas Harriot worked on the loxodromic curve. The list could go on. This shows that the scientific work of Pedro Nunes was highly recognized and regarded among English mathematical practitioners.

In 1569, a few years after Nunes published his Opera, Mercator presented his map ad usum navigatium though he didn’t provide a mathematical explanation for it. This would only be accomplished 30 years later by Edward Wright, who would finally show how to avoid the errors of the common sea chart’s and also that Mercator’s cartographic proposal was conformal. In fact, in the common plain sea chart, the North-South distances were maintained, contrasting with the east-west distances that became gradually exaggerated when the latitude was increased, due to the convergence of the meridians in the polar regions.

Before 1590, Wright was already interested in the problems of the sea chart and worked to express mathematically a cartographical projection where the loxodromes were straight lines. In his Certaine errors, Wright would explain the construction of his “nautical planisphere” totally based on mathematical calculus – the Mercator-Wright’s projection.

        Fig. 1 - Wright's “nautical planisphere”.

Wright promoted “his” chart affirming that it would bring advantages when compared to the previous proposals and also called the attention to the fact that the “new” planisphere made the drawing of routes on globes easier, and “By help of this planisphaere (…) the rumbs may much more easily and truly be drawn in the globe then by these mechanical ways which Petrus Nonius taught cap.26 lib.2. de obser. Reg. et Instr. Geom. (…)”[7]. The process imagined by Pedro Nunes was indeed slower. Wright improved it and introduced some variants that made it easier to use.

But Nunes' influence extended to more subjects. In the end of his book, Wright explained the use of solar tables to calculate the latitude of a place - the known Regiment of the Sun - pointing out a technical detail previously analysed by the portuguese and ignored on calculations: the variation and correction of the values of the solar declination with the longitude. He also informed that the sailors should correct the value of the distance of the pole star to the polar region, an issue also addressed by Nunes, stating that these values were calculated for a given and constant latitude and therefore should be corrected for each latitude. This was what Nunes suggested in chapter 7 of his Opera. Wright didn't present a mathematical explanation, excusing himself of the fact that he didn’t linger more on this problem in the present volume.

 ***

To know more: 

David Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, (London: Hollis and Carter, 1958).

David Waters, “English navigational books, charts and globes printed down to 1600”, Revista da Universidade de Coimbra, 33 (1985), 239–257.

Edward Wright, Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected, (London: Valentine Sims, 1599) .

E. G. R. Taylor, The Haven–Finding Art: a History of Navigation From Odysseus to Captain Cook, (London: Hollis & Carter, 1971).

Henrique Leitão, “Maritime discoveries and the discovery of Science: Pedro Nunes and Early Modern Science”, in: Victor Navarro Brotóns e William Eamon (eds.), Más allá de la Leyenda Negra: España y la Revolución Científica. Beyond the Black Legend: Spain and the Scientific Revolution (Valencia: Instituto de Historia de la Ciencia y Documentación López Piñero, Universitat de València, C.S.I.C., 2007), pp. 89–104.

Henrique Leitão, “Ars e ratio: A náutica e a constituição da ciência moderna”, in: La ciencia y el mar, Maria Isabel Vicente Maroto, Mariano Esteban Piñeiro (coords.), (Valladolid: Los autores, 2006), 183–207.

J. S. Parsons, W. F. Morris, “Edward Wright and his work”, Imago Mundi, 3 (1931), p. 61–71.

Pedro Nunes, Obras, vol. I, (Lisboa: Fundação Calouste Gulbenkian, 2002).

Pedro Nunes, Obras, vol. IV, (Lisboa: Fundação Calouste Gulbenkian, 2008).

Raymond D’Hollander, “La théorie de la loxodromie de Pedro Nunes”, in: Luís Trabucho de Campos, Henrique Leitão, João Filipe Queiró (eds.), International Conference Petri Nonii Salaciensis Opera Procedings, Lisbon, Coimbra, 24–25 May 2002 (Lisboa: Departamento de Matemática da Faculdade de Ciências da Universidade de Lisboa, 2003), 63–111.

Stephen Johnston, “The identity of the mathematical practitioner in 16th–century England”, Irmgarde Hantsche (ed.), Der “mathematicus”: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Duisburger Mercator–Studien, vol. 4 (Bochum: Brockmeyer, 1996), 93–120.

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