106 MAPS AND THEIR MAKERS 



concludes with confused directions for determining the latitude 

 of the central town, and the book includes a small map of the 

 environs of Heidelberg, given as an example. 



The method of elementary triangulation is for the first time 

 described more or less clearly by Gemma Frisius in his 'Libellus 

 de locorum describendorum ratione', included in his edition of 

 Peter Apian's 'Cosmographia', 1533. Gemma describes the 

 operation in terms very similar to Miinster's, and the instru- 

 ment was probably much the same; he insists strongly on the 

 necessity of placing the compass on the 'planimetrum' to 

 orientate it correctly. But he goes further in fixing the position 

 of places by intersecting rays, and in showing that the measure- 

 ment of one side of a triangle will fix the scale of the map. He 

 illustrates his theories with a diagram of an actual survey by 

 this method between Brussels and Antwerp. 



In the following years this method was practised exten- 

 sively and refinements introduced. If it is referred to as 'tri- 

 angulation', it should not be interpreted in the modern sense, of 

 a base line measured with extreme accuracy and a system of 

 well-conditioned triangles built up on it by careful angular 

 measurements. The sixteenth-century usage was somewhat 

 rough and ready, though it anticipated the use of the plane 

 table for filling in detail. In combination with observations for 

 latitude and calculation of longitude, it was capable of produc- 

 ing a map of considerable accuracy. Perhaps the best-known 

 practitioner of the method was Philip Apian, son of the 

 celebrated astronomer, who surveyed Bavaria between 1555 

 and 1561. Like all cartographers of his day. Apian was at pains 

 to keep his methods secret from his rivals, but there is a good 

 deal of contemporary evidence about them. The calculation of 

 the lengths of sides of a triangle from one known side and the 

 respective angles was clearly set out by Christoph Puehler in a 

 book known to Apian, and one of his pupils, G. Golgemeier, 

 describes in detail the procedure of mapping a small area. In 

 his petition to Duke Albrecht for a privilege to publish his 

 map. Apian complains of the expense to which he had been put. 

 He had traversed Bavaria in the course of six summers, with 

 companions to be supported and three horses to be maintained 

 Moreover, he had been obliged to summon the 'oldest inhabi-- 



