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Map Projection Reconstruction of the World Map by Leonardno da Vinci

Leonardo da Vinci or one of his collaborators, probably Francesco Melzi, produced a world map about 500 years ago. The map consists of eight parts of equal size, each of which is a projection of one eighth of a globe into a plane. Lines separating those parts are the equator and two arcs of meridian circles. Those parts are equilateral triangles, also known as Reuleaux's triangles after German engineer Franz Reuleaux who lived in the 19th century. Each side of those triangles is an arc of a circle with opposite vertex as the centre of the circle. Diameters of those triangles equal five inches, making the scale of the world map very small. Meridians and parallels are not shown on the map, which is not unusual because the map was produced during a period in which maps were produced to show discoveries rather than help sailors on their voyages. The da Vinci map projection is unique, without predecessors in Antique or Middle Ages. It is unknown which map projection was applied by the map author. The following was demonstrated in a previous research: 1. The angle in the da Vinci-Reuleaux triangle equals 120°. 2. Da Vinci’s projection is not an oblique aspect of azimuthal projection (neither conformal, nor equal-area, nor equidistant). 3. It is possible to derive equations of a pseudoconic map projection with the following properties: parallels of latitude are arcs of concentric circles with the centre in the pole ; meridians of longitude are arcs of circles with the centre on the coordinate axis. Parallels in the projection plane divide the central meridian into equal parts. The research described in this paper investigates an approach by Oronce Finé, who published his method in his De Mundi Sphaera sive Cosmographia libri V 1549, 30 years after da Vinci had died. Furthermore, the first Le Testu projection, which is similar to Finé's projection, is explained in detail. Finally, the paper compares the three possible map projections of da Vinci world map, showing similarities and differences among them.

map projection ; Leonardo da Vinci ; world map ; Reuleaux triangle ; Oronce Finé ; Guillaume Le Testu

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