Sapping Trenches That Show the Enemy Fewest Angles
Geometry of covered mines driven under fortress walls
Folio 45v, with its notes written upside down, applies the geometry of angles to military mining. The text describes open trenches driven under a fortress wall and argues that a covered underground gallery is better because it presents only a single angle p to the enemy, whereas the alternative exposes four angles n o c q. A faceted, gem-like drawing sits at the upper left, with a lettered angle diagram and a worked multiplication (300 by 200 giving 60000) at the lower left.
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Covered mines that expose only one angle to the enemy
The trench is made to go beneath the walls, with a b equal to a c. A covered underground mine is judged better than the open form because it shows the enemy only one angle, p, whereas the other arrangement exposes the four angles n o c q.
Angles containing equal angles equal the first lines meeting at a point
All the sides of the angles that contain equal angles, joined together, are equal to the first lines when they meet in a point. Thus the lines a n r o f c d q m joined together are equal to the lines a b m.
A worked multiplication
A calculation is set out in columns at the lower left, multiplying to reach 60000 (300 by 200). It sits beside the lettered angle figures.