For many years I have been arguing that mathematical history cannot be understood without being placed in the proper historical context. Nearly all non-abstract mathematics was created so that people could better deal with changing social and economic conditions. In the 16th century, there was a dramatic expansion in the commercial activity in northern Europe. International commerce was expanding with new goods being developed and many goods being shipped across significant distances.
With money being issued in the form of gold and silver, merchants that needed to travel to buy their goods were at risk for robbery or worse. This led to the development of international banks that could issue a paper draft redeemable in other locations. As business expanded there was a greater need for borrowing, which led to the necessity of computing future value, interest and the introduction of negative numbers. The ruling aristocracy also had a great need to borrow money to fund their military adventures, increasing the size of numbers being used. With more goods traveling on the oceans, accurate navigation when out of sight of land became essential; this required the development of precision instruments and advanced calculations. Once wine was transported in barrels between regions, it was taxed by volume, which required the ability to compute the volume of barrels as well as the amount in barrels that were only partially full.
The development and advancement of these areas of mathematics in the Low Countries in the late 16th century is covered in this book. The historical context is included. Many images of the instruments as well as some of the computations are included. In fact, most of the text covers the contextual history rather than the mathematics. Some of the primary educators of the time and the issues regarding the religious activity of the teachers are also included. These were years of war with religious undertones in Northern Europe, so that was a significant issue.
One question that can be asked in the history of mathematics is, “What came first, the mathematics or the application?” This is not a binary situation, as Meskens clearly demonstrates they are developed in tandem, one driving the other in an interlocking marriage of necessity.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.
3 The Family Coignet
4 Peeter Heyns and the Nymphs of the Laurel Tree
5 The Arithmetic Teacher and his School
6 The Antwerp arithmetic books
9 The Art of Navigation
10 Mapping the World
11 Looking towards the Stars
12 Ballistics and fortifications