Journal for Geometry and Graphics Volume 10 (2006), No. 1, 63–71. One a Possible Constructive Geometrical Derivation of Mercator’s Conformal Cylindrical Map Projection Based on Some Historical Facts Branislav Popkonstantinovi´ c 1 , Aleksandar Cuˇ cakovi´ c 2 1 Dept. of Machine Theory and Mechanisms, Faculty of Mechanical Engineering Kraljice Marije 16, 11120 Belgrade, Serbia email: bariton@afrodita.rcub.bg.ac.yu 2 Dept. of Descriptive Geometry, Faculty of Civil Engineering Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia email: cucak@grf.bg.ac.yu Abstract. In modern cartography, Mercator’s conformal cylindrical map pro- jection is mathematically described by equations which involve logarithmic and trigonometric functions. It is evident that calculus and differential geometry are necessary for the derivation of these equations. The very fact that Mercator’s map was published in 1569, long before logarithms and calculus were invented, confirms that Mercator created his famous map projection somehow directly — by some simple and plain geometrical constructions. This paper exposes one possible constructive graphical method by which the direct geometrical synthesis of Merca- tor’s conformal cylindrical map projection can be accomplished. We believe that the original inventive process used by Gerhard Kremer Mercator in creation of his famous world map was at least similar or compatible to the method exposed in this paper. Key Words: cartography, Mercator, conformal, loxodrome, map, stereographic MSC 2000: 51N05, 53-03, 01A40 1. Introduction It is well known that Mercator’s map projection belongs to the family of cylindrical, conformal and non perspective cartographic projections (Fig. 1). In modern cartography, its mathematical description represents the formula which trans- forms longitude-latitude (λ, ϕ) of the Earth’s sphere to Cartesian (x, y) in such a way that these Cartesian coordinates are: ISSN 1433-8157/$ 2.50 c  2006 Heldermann Verlag