104 MAPS AND THEIR MAKERS 



profiles of important landmarks persisted for many years. 

 Some of the earliest of the English coasts were drawn in this 

 fashion by Richard Popinjay about 1563. 



The next stage was the adoption of methods based on 

 elementary geometry, the study of which was being developed 

 by the astronomers, using translations of Arabic texts. In the 

 second half of the fifteenth century, the University of Vienna 

 was an important centre of astronomical and mathematical pro- 

 gress. This was in great part due to the work of Georg Peurbach 

 (1423-61) and his pupil, Johannes Regiomontanus (1436-73). 

 These men were interested in geography through astronomy, 

 which led to the consideration of determining positions on the 

 earth's surface. Regiomontanus visited Ferara in the 1460s, 

 where he was captured by the current passion for Ptolemy's 

 'Geography', and projected a world map and new maps of 

 European countries. Later he translated the first book of the 

 'Geography' into Latin. His great work was done at Nurem- 

 berg in the last three years of his life, where he compiled a 

 calendar, his famous 'Ephemerides', or astronomical tables 

 much used by navigators, and a list of geographical positions, 

 largely derived from Ptolemy. He also compiled tables of sines 

 and tangents, in pursuing his aim to make trigonometry useful 

 to astronomers, and wrote the tract, 'De triangulis', dealing 

 with plane and spherical triangles, which introduced a new 

 era in the development of trigonometry. 



A little later another celebrated astronomer and mathemati- 

 cian, Peter Apian, who spent five years as a student at Vienna 

 before he became a professor at Ingoldstadt, was associated 

 with the production of a number of maps, including one of the 

 world on a heart-shaped projection after Waldseemiiller and 

 another of Europe, as well as regional maps. His main work 

 was in astronomy where he improved several instruments, and 

 advocated the determination of longitudes by lunar distances. 

 It is probable that men such as these, specialists in geometry, 

 trained in instrumental observation, and, to some degree, also 

 instrument makers, would have grasped the application of 

 simple geometrical operations to rudimentary survey. In 1503, 

 the encyclopaedic 'Margarita philosophica' of Gregor Reisch 

 contained a description of the 'geometrical square' — a square 



