Rare 1610 second edition (revised and expanded) of the first handbook for ship's pilots in training, with more than 120 illustrations, mostly geometrical and astronomical diagrams but also a fortification plan, navigational instruments and their use, etc. It describes navigational instruments and their use in both the northern and the southern hemisphere, the determination of longitude and the declination of the sun. An appendix on the use of the astrolab largely follows Philippe van Lansberge (18 years before his principal publication on the subject) and illustrates the positions of the sun, moon and earth during eclipses. Brouck also covers the practical mathematics of geometry, trigonometry, surveying, mensuration and calendrical calculations. With the establishment of the VOC (Dutch East India Company) in 1602 and the beginning of the Twelve Years' Truce (1609-1621) between Spain and the Dutch Republic in the 80 Years' War for Dutch independence, the Netherlands saw a great pressing need for well-trained ship's pilots for global exploration and trade. Jan vanden Brouck (1566- 1626), was a schoolmaster teaching applied mathematics at Amsterdam, Rotterdam and Middelburg