ABSTRACT In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately. The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. Following his idea, this paper shows that not only conformal, but also equal-area and equidistant cylindrical projections can be derived from corresponding conic map projections. KLJUČNE BESEDE kartografska projekcija, konusna projekcija, cilindrična proekcija KEYWORDS map projection, conic projection, cylindrical projection 1 MOTIVATION AND INTRODUCTION In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately, and sometimes it is mentioned that cylindrical and azimuthal projections can be interpreted as limiting cases of conic projections (Lee, 1944; Kavrayskiy, 1958, 1959; Jovanovic, 1983; Vakhrameyeva et al., 1986; Snyder, 1987; Kuntz, 1990; Canters, 2002; Monmonier, 2004; Serapinas, 2005), but it is rarely attempted to prove (Lambert, 1772; Hinks, 1912; Hoschek, 1969; Daners, 2012). The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. Final section presents concluding remarks. 2 LAMBERT'S DERIVATION OF THE MERCATOR PROJECTION AS A SPECIAL CASE OF THE CONFORMAL CONIC PROJECTION The beginnings of the theory of mapping one surface to another belong to Johann Heinrich Lambert (1728-1777), who dealt with the general problem of mapping a sphere and an ellipsoid into a plane in the chapter Anmerkungen und Zusätze zur Entwerfung der Land und Himmelscharten (Notes and additions to the establishment of maps of the Earth and the Sky) printed in to the third part of his Beyträge zum Gebrauche der Mathematik und deren Anwendung (Contributions to the use of mathematics and its application) (Lambert, 1772).