Comparison of profiles

In the seventeenth century, a large number of books on fortification were published. Every self-respecting author had his own system for calculating the dimensions of a fortress. Where one author worked with rectangular triangles only, another showed that he mastered the sine rule or even the tangent rule. Also, each author chose their own starting points with slightly different angles and lengths which made each fortress look slightly different. In GeoGebra an animation has been made to provide an overview of the proposals of a large number of authors, from Simon Stevin and the Van Schooten family to Abraham de Graaf. In this way, the different designs can be compared. More information is available at my website fransvanschooten/Stevin. This page belongs to my GeoGebra book Fortification in the Netherlands in the 16th and 17th century. One of the main differences is the calculation of the bastion angle.
  • always 90° (de Ville)
  • two-thirds of the polygon angle (Metius, Cellarius, Marolois)
  • 15° more than half of the polygon angle (Marolois, Henrion, Frans van Schooten Sr, Goldmann, Pieter van Schooten)
  • 20° more than half of the polygon angle (Freitag)
  • 30° more than one-thirds of the polygon angle (Kinckhuysen, Pieter van Schooten
Note that authors like Marolois proposed many different calculation schemes.