Fortification in the Netherlands in the 17th century

Henk Hietbrink, May 23, 2020

Fortress building took off in the sixteenth and seventeenth centuries, starting in Italy where Charles V fought his wars against the French king and then in the rebellious Netherlands during the Eighty Years' War. The dimensions of the ideal fortress were first written about in the Dutch language by Simon Stevin in 1594. This GeoGebra book contains the animations developed for my website [url]http://www.fransvanschooten.nl/Stevin.htm[/url].

Table of Contents

  1. Sterctenbovwing Simon Stevin (1594)
    1. Simon Stevin: Grontteyckening
    2. Simon Stevin: Verheven Teyckening
  2. Fortificatie ofte stercken-bouwinghe Adriani Metii Matheseos (1626)
    1. Metius: Fortificatie ofte Sterckten-Bouwinghe
  3. Comparison
    1. Comparison of forms of 17th century fortifications
    2. Comparison of profiles
    3. Design your fortress / Bouw je eigen vesting
    4. Lines of defense
    5. Law of tangents / Tangensregel
    6. Begrippen in de vestingbouw
  4. Answers to the assignments
    1. Nikolaus Goldmann: La nouvelle fortification
    2. Galasso Alghisi da Carpi : Delle fortificationi libri
    3. Adriaan Adriaansz. Metius: Fortificatie ofte stercken-bouwinghe
    4. Pieter van Schooten: handschrift BPL 1013
    5. Andreas Cellarius: Architectura militaris
  5. Examples of calculations
    1. Jean Errard
    2. Samuel Marolois
    3. Pieter van Schooten (Hs 441)

1.

Sterctenbovwing Simon Stevin (1594)

Op mijn website komt een hoofdstuk over fortificatie en de Duytsche Mathematicque, een geschiedenis die begint bij Simon Stevin want hij omschreef het lesprogramma. [url]http://www.fransvanschooten.nl/fvs_fortificatie.htm[/url] Bij leerlingen introduceer ik Simon Stevin met twee posters, een buste en natuurlijk de zeilwagen [url]http://www.fransvanschooten.nl/fvs_stevin_poster.htm[/url] Ad Davidse heeft een transcriptie van "De Sterctenbovwing" op internet gezet. [url]https://adcs.home.xs4all.nl/stevin/index.html[/url] Wikipedia geeft een overzicht van de belangrijkste bijdragen van Simon Stevin op het gebied van taal en wetenschap. [url]https://nl.wikipedia.org/wiki/Simon_Stevin[/url]

  • 1. Simon Stevin: Grontteyckening
  • 2. Simon Stevin: Verheven Teyckening

1.1.

Simon Stevin: Grontteyckening

In the seventeenth century a large number of books on fortification were published. [br]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. [br][br]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.[br][br]Simon Stevin was one of the first authors in the Netherlands in 1594. He described the ideal forms of a regular fortress.[br][br]More informatie is available at my website [url=http://www.fransvanschooten.nl/Stevin.htm]fransvanschooten/Stevin[/url].[br]This page belongs to my GeoGebra book [url=https://www.geogebra.org/m/xeqjdkpj]Fortification in the Netherlands in the 16th and 17th c[/url]entury.[br][br]The animation uses the language of Simon Stevin.[br]A translation in English is available on my website: see Schukking, Principal Works, vol IV, Art of War
Simon Stevin: Grontteyckening
– Henk Hietbrink

1.2.

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2.

Fortificatie ofte stercken-bouwinghe Adriani Metii Matheseos (1626)

Editie van 1626 staat online bij Books.Google [url]https://books.google.nl/books?id=xKLDSKQ0CVgC[/url]

  • 1. Metius: Fortificatie ofte Sterckten-Bouwinghe

2.1.

Metius: Fortificatie ofte Sterckten-Bouwinghe

– Henk Hietbrink

3.

Comparison

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.

  • 1. Comparison of forms of 17th century fortifications
  • 2. Comparison of profiles
  • 3. Design your fortress / Bouw je eigen vesting
  • 4. Lines of defense
  • 5. Law of tangents / Tangensregel
  • 6. Begrippen in de vestingbouw

3.1.

Comparison of forms of 17th century fortifications

[size=100]In the seventeenth century a large number of books on fortification were published. [br]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. [br][br]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.[br][br]More informatie is available at my website [url=https://www.fransvanschooten.nl/Stevin.htm]fransvanschooten/Stevin[/url].[br]This page belongs to my GeoGebra book [url=https://www.geogebra.org/m/xeqjdkpj]Fortification in the Netherlands in the 16th and 17th c[/url]entury.[/size]
– Henk Hietbrink

3.2.

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4.

Answers to the assignments

This chapter contains the answers to the assignments from the handout with exercises for students (in Dutch). The handout is available at my website [url]http://www.fransvanschooten.nl/StevinWorkshop.htm[/url]

  • 1. Nikolaus Goldmann: La nouvelle fortification
  • 2. Galasso Alghisi da Carpi : Delle fortificationi libri
  • 3. Adriaan Adriaansz. Metius: Fortificatie ofte stercken-bouwinghe
  • 4. Pieter van Schooten: handschrift BPL 1013
  • 5. Andreas Cellarius: Architectura militaris

4.1.

Nikolaus Goldmann: La nouvelle fortification

Bij de workshop Vestingbouw is een handout verspreid met een aantal opdrachten, waaronder deze uit het boek [i]La nouvelle fortification[/i] van Nikolaus Goldmann.[br][br]De opdracht staat ook de website [url=http://www.fransvanschooten.nl/Stevin.htm#opdracht1]www.fransvanschooten.nl[/url][br][br]Dit werkblad maakt deel uit van mijn GeoGebra boek [url=https://www.geogebra.org/m/xeqjdkpj]Vestingbouw in de 16de en 17de eeuw[/url].[br]
– Henk Hietbrink

4.2.

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4.5.

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5.

Examples of calculations

  • 1. Jean Errard
  • 2. Samuel Marolois
  • 3. Pieter van Schooten (Hs 441)

5.1.

Jean Errard

Jean Errard wrote a book full of examples how to calculate on the dimensions of a fortification.[br]This worksheet shows an example of his calculations..[br]The source of his book is available online at [url=https://gallica.bnf.fr/ark:/12148/bpt6k1512241w]Gallica.bnf[/url].[br]My source list: [url=http://www.fransvanschooten.nl/Stevin.htm#literatuur]Sterctenbovwing Simon Stevin (www,fransvanschooten.nl)[/url][br]
– Henk Hietbrink

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Information