It is important not to forget that La Cosa’s chart was a world map, made to be exhibited at the Court, and was neither intended nor suitable for navigation. Gaspar’s planimetric method is consistent with navigation manuals of later decades in the sixteenth century, and may have been successfully used for smaller-scale marine charts, but when cartographers composed world maps they faced different issues and did not necessarily apply the same methods as when drawing marine charts. Nonetheless, use of the planimetric method could be an explanation for the shape of the African coastline drawn by La Cosa, as he is widely assumed to have copied it from some Portuguese source.
    
The following sections of this article will discuss whether a deliberate use by La Cosa of the UP could be consistent with the historical context of Castile in 1500.

—Spirit of Innovation in Cartographic Projections
    
The fifteenth and sixteenth centuries were a period of effervescence in the invention or rediscovery of new cartographic methods and projections. In order to integrate the newly discovered lands with known geography, mapmakers tested new mathematical and empirical solutions. A far-from-exhaustive list would include the trapezoidal projection by Donnus Nicolaus Germanus (1466), the globular projection of the Deutsche Ptolomäus (1490), the cordiform projection invented by Johannes Stabius (possibly before 1502, published in 1514), the stereographic projection by Walther Ludd (1507), the modified equidistant projection by Johannes Ruysch (1508), and the octant projection developed by Leonardo da Vinci (1514).[42]
    
Most of the projections and techniques experimented with at this time were discarded as they were superseded by better or simpler alternatives. The Unnamed Projection could have been one such innovation that was tested and abandoned shortly thereafter.

Spain was not an exception in this period of diversity and innovation in cartography. Two decrees issued by the Crown of Castile, first in 1508 and again in 1512, criticized the fact that there existed at the time many charts of the Indies made by diverse techniques and by diverse mapmakers with substantially different results, and ordered a single, official master chart (“Padrón General” or “Padrón Real”) of the Indies to be drawn and updated regularly. The Padrón General would thenceforth be publicly exhibited in the Casa de la Contratación in Seville, and all pilots would have to carry with them and follow a copy of that master chart. Furthermore, pilots would be prevented from using any other map.[43] The Unnamed Projection may have been one of the projections left aside in the movement towards cartographic standardization initiated by these decrees.

—Determination of Geographical Coordinates

A map can be built in two ways: either from raw numeric data or from graphical information, i.e. previous partial maps. From what has been said up to now, it is safe to assume that La Cosa’s chart is of the second type: it was compiled from a number of partial charts, like a puzzle made of pieces of very different origins. The question is, then, how the cartographer drew each of those separate pieces, and in particular what numeric data were originally used for the fragment that contains the coasts of the Atlantic.

If La Cosa applied the Unnamed Projection in a deliberate way, then logically he must have computed first a table with the longitude and obliquity (calculated from latitude and longitude) of each geographical feature, and must have then plotted these coordinates on the easy-to-draw square grid of the UP. How longitude and obliquity/latitude data may have been obtained is discussed below.

Basic positional data

The navigators of the fifteenth century had developed a number of techniques to collect data on the position of their ships. They could calculate roughly the distance sailed every day and night by estimating the speed of a vessel. Several methods have been described for this, like the “log and line,” but probably the most practiced one was just the pilot’s feel based on his experience.[44] In addition, the magnetic needle, already several centuries old by 1500, provided the heading of the ship, and therefore gave an indication of the rhumb followed along the journey.

Furthermore navigators took advantage of any other information provided by the natural environment that surrounded them: wind direction and force, water color, presence and type of algae, the occasional bird. The firmament brought some information too: the position of the Pole Star indicated the true geographic north, and allowed them to check the deviation of the needle; and the relative duration of days and nights could give the order of magnitude of latitude. The two latter methods were reportedly used by Columbus in his first voyage to the Indies and must have been known to Juan de la Cosa, for he was the owner and master of the ship which Columbus was sailing.

Latitude

Since the mid fifteenth century, the Portuguese had been learning the methods used to determine latitude by astronomic observations. Navigator Diogo Gomes claimed to have used instruments to measure the height of the Pole Star in Guinea in 1460-62,[45] and in the last decades of the century there appeared the first known manual of astronomical navigation, which contains instructions for measuring latitude both from the Pole Star and through the observation of the sun at noon.[46]

There is, however, controversy among historians regarding the extent to which such astronomical methods were actually put into practice, and also regarding the accuracy which they provided. Felipe Fernández-Armesto, for instance, is quite skeptical that astronomic instruments played any important role in fifteenth-century navigation, while at the same time pointing out that “seasoned navigators had skills we have now lost and could make impressive judgment of relative latitude by observing the sun or the Pole Star with the naked eye.”[47] On the contrary, Joaquim Alves Gaspar affirms that “the introduction of astronomical navigation by the Portuguese, in the middle of the fifteenth century, proved to be an adequate and durable solution for the problem [of determining latitude at sea].”[48] W.G.L. Randles provides yet another point of view: astronomical methods may well have been used by the Portuguese, but there is no proof that by 1500 the instruments could provide more accurate readings of latitude than what could be calculated by estimating distances in the traditional way.[49] In an interesting nuance, Douglas T. Peck makes a distinction between navigation, for which he sees no use of astronomic methods at those times, and map making, which could have taken advantage of occasional measurements of latitude performed on land by expert cosmographers so as to better place the new discoveries on general maps of the world.[50]

In any case, all authors agree that the Atlantic coastlines on Portuguese maps became much more accurate in latitude in the period elapsed between the first known charts of 1480s and the Cantino map of 1502. Whatever the methods used—distance estimates, astronomical instruments or naked-eye celestial observations—the knowledge of the methods and the numerical results may have diffused to or been developed simultaneously in the neighboring kingdom of Castile, which would explain the high accuracy of latitudes in La Cosa’s chart.

Longitude

In his review of the different methods used by Iberian navigators to estimate longitude in the sixteenth century, Randles concluded that at sea the only reasonable technique was to estimate distance and rhumb, and then calculate the change in longitude mathematically.[51] On land, knowledgeable astronomers could measure longitude by observing the moon’s position or its eclipses, but all known attempts done in the early exploration of the Americas reportedly gave large errors. Only in the second half of the century did astronomic measurements become reasonably accurate, thanks to the careful observation of eclipses from fixed locations, such as Mexico City.

It may be useful to remember that the famously accurate measurement of longitude performed by al-Biruni (973-1048) between Baghdad and Ghazna was not based on moon’s eclipses, but on the combination of distance estimates, astronomic determination of latitude and the use of spherical trigonometry to take into account the real shape of the Earth.[52] The combined use of astronomic measurements of latitude with distance estimates to better assess the position of a ship on a chart is explained in many manuals of the sixteenth century but, unlike al-Biruni, they assume a flat Earth and therefore use much simpler and less accurate mathematics.[53] A further limitation of this technique is that latitude data cannot improve longitude estimates between points that lie on the same parallel.

For the La Cosa chart, it is most probable that longitudes were estimated from distances and rhumbs, not from lunar observations. However, the fact that on this chart the longitude errors are higher along east-west coastlines (gulf of Guinea, Hispaniola, the Caribbean), hints that astronomic measurements of latitude may have been used to correct longitude estimates in directions other than east-west.