Mining a fortress angle; the earth's motion and the moon
Dilating force on convex vs concave angles; the earth's motion; distance to the moon per Pythagoras; sums.
The main note reasons about mining a fortress corner: an explosive 'dilating power' acting between two unequal resistances always breaks toward the weaker side, so a convex angle (a b c) resists while a concave one (e f g) is destroyed, with the mine drawn as ae bf cg. Fortification plans, including a large round bastion, fill the right and lower sheet. Shorter notes ask whether the Adige keeps to its bed, whether the earth's uneven weight gives it circular or straight motion, and record the distance 'from the earth to the moon according to Pythagoras,' beside columns of arithmetic.
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Dilating force breaks toward the weaker resistance
A power of dilation created between two unequal resistances always yields on the side that resists less. Applied to a mine ae bf cg cut in a fortress angle, the convex angle a b c, being more resistant, is preserved while the concave angle e f g is broken. The more a convex angle is pressed the more resistant it grows; the more a concave angle is pushed the sooner it fails.
Why not to mine at a fortress corner
A mine set in the angle of a fortress will only breach the outer half of the thickness while the inner half stays intact, so it is poorly placed. Plans of walls and a large round bastion accompany the reasoning. The argument turns on the differing strength of convex versus concave masonry angles.
Circular or straight motion of the earth
A pair of concentric circles labelled b a and c accompanies the question of whether the inequality of the earth's weight gives that earth a revolving motion or a straight one. It treats the earth's body cosmologically as something that might turn or move.
From the earth to the moon per Pythagoras
A short heading, written with the sheet turned on its left side, notes the distance 'from the earth to the moon according to Pythagoras.' It frames a Pythagorean cosmological measure.
Columns of calculation
Several columns of figures are worked out, including large numbers such as 125000, 15625, 88888 and 77777, together with divisions like 125000 giving 17857 1/7. They appear to be trial calculations rather than a finished result.