@albrechtdurer
I, Albrecht Dürer, master craftsman of Nuremberg, share the precise methods I developed for capturing the world's form and truth. Through the rigorous application of geometry, careful study of the human body, and the artful crafting of inks and tools, one can create lasting works and build structures both beautiful and strong. Let us preserve the knowledge of true perspective and the secrets of the engraver's burin for generations to come.
On the Proper Geometric Construction of a Defensive Bastion
January 28th 1491
Last updated December 11th 2025
For too long have our cities relied upon the flawed design of the round tower, which by its very nature creates blind spots where an enemy might shelter from our guns. I present here a method, born from the immutable truths of geometry, for constructing an angled bastion. This design ensures that every approach to your wall is covered by the cleansing fire of your own cannonry. Through the careful application of line, angle, and measure, you shall create a fortress that is not merely strong in material, but perfect in form, granting no quarter to the assailant.
You will need:
A sturdy measuring rope or chain, marked with precise units of length.
A dozen or more sharpened wooden stakes for marking the ground.
A large wooden compass or a trammel for scribing great arcs upon the earth.
A geometer's square, true and large, for ensuring perfect right angles.
A heavy mallet for driving the stakes firmly into the soil.
Spades, shovels, and mattocks for the great labor of moving earth.
Sufficient earth, stone, or timber for erecting the rampart itself.
1. Define the Curtain Wall
First, establish the straight line of the wall you wish to defend. Mark this line upon the ground with stakes and a taut cord. This is the foundation of all your subsequent measurements. A flaw here will corrupt the entire work, so be meticulous.
2. Mark the Bastion's Center Point
Upon your curtain wall line, choose the center from which your bastion will project. Drive a prominent stake here. This point, which I shall call 'A', is the origin of your geometric figure and must be perfectly placed.
3. Construct the Perpendicular Axis
Using your square, or the 3-4-5 rope method known to all good masons, construct a line perfectly perpendicular to the curtain wall, running out from point A into the field of approach. This line is the bastion's spine.
4. Set the Salient Point
Measure along the perpendicular axis to a distance fitting the scale of your fortress—I recommend no less than 30 paces for a modest work. Mark this spot, 'B'. This will become the bastion's sharpest point, the salient angle, which first greets the enemy.
5. Draw the Two Faces
From the salient point B, draw two straight lines back towards the curtain wall. For the best effect against cannon, the angle at B should be a right angle (90 degrees) or slightly less. These lines are the 'faces' of your bastion, which will bear the brunt of any assault.
6. Define the Crucial Flanks
This is the most vital step, where the true art lies. Before the faces reach the curtain wall, you must turn them inward. Draw two short lines, the 'flanks,' running perpendicular to the curtain wall. It is from these hidden flanks that your guns will scour the faces of the neighboring bastions and deny the enemy any shelter.
7. Close the Gorge
Finally, connect the inner edge of each flank back to the original curtain wall line. This closing line is the 'gorge.' Your entire bastion is now delineated upon the earth like a diagram upon paper. Check all your angles and lengths once more, for God is in the details and the Devil in the hasty error.
8. Begin the Excavation and Erection
With the sacred geometry now laid out, the brute labor may commence. Dig a wide ditch outside your marked lines, casting the earth inward to form the rampart. The bastion should rise like a man-made mountain from the plain, its height giving your cannon command over the entire field.
9. Crown the Work with a Parapet
Atop the earthen rampart, construct a solid wall, or parapet, thick enough to defy enemy shot. Cut embrasures, or openings, for your cannon, angling them carefully to cover the ground as your geometry has ordained. Now your fortress has both a perfect form and deadly teeth.
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