On the Development of Map Projections KiG 2007, special issue On the Development of Map Projections Miljenko LAPAINE, Ana KUVEDIÆ University of Zagreb, Faculty of Geodesy, Kaèiæeva 26, 10000 Zagreb, Croatia [email protected], [email protected] Abstract: Many important persons gave their contri- In this paper, dedicated to Professor Nedjeljko Franèu- th bution to development of theory and practice of map la on the occasion of his 70 birthday, a review of the 110 projections through the history. In scripts of professor history of map projections is given. Afterwards, basic in- Franèula on map projections, more than 100 individu- formation about around twenty probably most important als were mentioned by whose credit today we have a persons for the development of map projections over two great number of map projections and possibility of their and a half millennia, were arranged. Finally, the proce- usage. Basic information about around twenty persons dure of creating world maps in different map projections important for the development of map projections over is explained. two and a half millennia were gathered and arranged in this paper. In addition, a historical review of map 2 History of Map Projections projections is given, and procedure of world map cre- ation which served as illustration is explained. Map projections have been developed with the devel- Key words: map projection, history of map projec- opment of map production and cartography in general. tions, cartographers The development of many sciences, technical achieve- ments and needs of everyday life have gradually initiated wider and wider demands for the production of various 1 Introduction topographic and thematic maps in various scales and for various purposes, which requested continuous growth of In the production of maps, first, the points from the map projections and improvement of mathematical basis physical earths surface are transferred onto ellipsoid of maps (Lapaine, 1996). (sphere) surface according to established rules, and af- terwards the ellipsoid (sphere) is projected into the plane. The beginnings of map projections date as far as two Map projections serve this purpose. The goal of studying thousand years ago, originating from the time when old map projections is to create a mathematical basis for the Greek scientists introduced mathematical principles into production of maps and solving theoretical and practical the basis of projecting the earth and starry sky and start- tasks in cartography, geodesy, geography, astronomy, ed to apply the graticule. The works of Anaximander, Era- navigation and other fields. tosthenes, Thales, Apolonious and Hipparchus played an Hence, we can say that map projections are a meth- important role in the development of cartography. od of projecting the ellipsoid surface or sphere in a plane. It is believed that Thales of Miletus made the first map The following topics are usually of particular interest in in a projection 600 years B.C. It was a map of the heav- studying of map projections: enly sphere in gnomonic projection. Stereographic and q Mathematical basis of the map orthographic projections belong to the oldest projections q Constructing a network of meridians and parallels and were used by the Greek astronomer and mathemati- cian Hipparchus for the purpose of making maps of the q Graphic way of construction heavenly sphere about 150 B.C. Hundreds of map pro- q Analytical way of construction (mathematical formu- jections have been invented ever since. lae and calculating) In the 2nd century, Ptolemy wrote the capital work q Basic cartographic equations Geography and included into it the description of map com- q Study of distortions (lengths, surfaces, angles) pilation and determination of the earths dimensions, as q Selection of a projection well as the construction of map projections. The period of KiG 2007, poseban broj O razvoju kartografskih projekcija O razvoju kartografskih projekcija Miljenko LAPAINE, Ana KUVEDIÆ Sveuèilite u Zagrebu, Geodetski fakultet, Kaèiæeva 26, 10000 Zagreb [email protected], [email protected] U ovome radu, posveæenom prof. Nedjeljku Franèuli Saetak: Mnoge znaèajne osobe dale su tijekom povi- u povodu njegova 70. roðendana, najprije je dan pregled jesti svoj prinos razvoju teorije i prakse kartografskih povijesti kartografskih projekcija. Zatim su obraðeni projekcija. U skriptama prof. Franèule o kartografskim 111 osnovni podaci o dvadesetak vjerojatno najznaèajnijih projekcijama navedeno je vie od 100 pojedinaca osoba za razvoj kartografskih projekcija tijekom dva i èijom je zaslugom danas dostupan velik broj karto- pol tisuæljeæa. Na kraju je objanjen postupak izrade grafskih projekcija i moguænost njihove upotrebe. U karata svijeta koje su izraðene posebno za ovu prigodu ovome su radu prikupljeni i obraðeni osnovni podaci u razlièitim kartografskim projekcijama. o dvadesetak osoba znaèajnih za razvoj kartografskih projekcija tijekom dva i pol tisuæljeæa. Osim toga, dan je pregled povijesti kartografskih projekcija i objanjen 2. Povijest kartografskih projekcija postupak izrade karata svijeta koje su posluile kao ilustracije. Razvoj kartografskih projekcija tekao je usporedno s Kljuène rijeèi: kartografska projekcija, povijest razvojem izradbe karata i kartografije opæenito. Razvoj kartografskih projekcija, kartografi mnogih znanosti, tehnièka dostignuæa i potrebe svaki- danjega ivota s vremenom su inicirali sve ire zahtjeve za izradbom raznovrsnih topografskih i tematskih karata 1. Uvod razlièitog mjerila i namjene, to je zahtijevalo neprekidno poveæavanje broja kartografskih projekcija i usavravanje Pri izradi karata najprije se toèke s fizièke Zemljine matematièke osnove karata (Lapaine, 1996). povrine prenose po odreðenim pravilima na plohu elipso- Poèeci kartografskih projekcija stari su oko dvije i pol ida (sfere), a zatim se elipsoid (sfera) preslikava u ravninu. tisuæe godina, otkad su grèki znanstvenici prvi uveli U tu svrhu slue kartografske projekcije. Cilj prouèavanja matematièke principe u temelje preslikavanja Zemlje i kartografskih projekcija ponajprije je stvaranje matemati- zvjezdanoga neba te poèeli primjenjivati mreu meridijana èke osnove za izradu karata, a zatim i rjeavanje teorijskih i paralela. Veliku su ulogu u razvoju kartografije odigrali i praktiènih zadataka u kartografiji, geodeziji, geografiji, radovi Anaksimandara, Eratostena, Talesa, Apolonija i astronomiji, navigaciji i drugim podruèjima. Hiparha. Moemo, dakle, reæi da su kartografske projekcije Smatra se da je prvu kartu u nekoj projekciji izradio naèini preslikavanja plohe elipsoida ili sfere u ravninu. Tales iz Mileta 600. godine pr. Kr. Bila je to karta nebeske Pri prouèavanju kartografskih projekcija obièno su slje- sfere u gnomonskoj projekciji. Meðu najstarije se projek- deæe teme od posebnog interesa: cije ubrajaju stereografska i ortografska, koje je upotrije- q Matematièka osnova neke karte bio poznati grèki astronom i matematièar Hiparh, takoðer q Konstrukcija slike mree meridijana i paralela za izradbu karata nebeske sfere oko 150. godine pr. Kr. Od toga doba do danas izumljeno je nekoliko stotina q Grafièki naèin konstrukcije kartografskih projekcija. q Analitièki naèin konstrukcije (formule i raèunanje) U 2. st. Ptolemej je napisao kapitalno djelo Geografija q Osnovne kartografske jednadbe u koje je ukljuèio opis sastavljanja karata i odreðivanje q Prouèavanje deformacija (duljine, povrine, kutovi) Zemljinih dimenzija te konstrukciju kartografskih projek- q Izbor projekcije. cija. Epohu srednjovjekovlja u Europi obiljeila je pojava On the Development of Map Projections KiG 2007, special issue Middle Ages in Europe was characterised by the so-called ers as e.g. Airy, Clarke, Schwartz and Pierce concentrat- monastery maps reflecting a religious image of the world. ed on more specific, but more complex tasks, and Ger- main, Gretschel and Craig gathered various works by other Special development of cartography started during the scientists into special monographs. New projections by renaissance the period of great geographic discoveries. Mollveide, Albers, Gall and others contain simpler appli- Accurate, reliable maps to be used for state government cation of mathematics, but still deserve the titles accord- and military purposes, for the development of trade and ing to their inventors. Rapid development of the theory of maritime affairs. Such maps could be produced only through map projections in this period is emphasised by a number the application of a mathematical basis and land survey of new projections and a number of published books and results. The first to have appeared were topographic maps. articles (Snyder 1993). At the end of the 16th and beginning of 17th century, According to Frischauf (1905), the beginning of the the compilation and publication of geographic atlases was theory of projecting one surface onto another belongs to a very significant event in further development and popu- J. H. Lambert, who dealt with the general problem of pro- larisation of cartography, which was carried out by the jecting a sphere and spheroid into the plane in his An- famous Dutch cartographers Ortelius and Mercator. Mer- merkungen und Zusätze zur Entwerfung der Land- und cator was the first who ever applied conformal cylindrical Himmelscharten (Remarks and Additions to the Estab- projection which is still being used successfully for mari- lishment of Land and Sky Maps) in the third part of his time navigation charts. Beyträge zum Gebrauch der Mathematik und deren An- In the production