Earth-moving: filling boxes and excavator schemes
Diggers, barrow-crews, a mechanical excavating bucket and a crane, with pages of worked sums
A working sheet on the organisation and mechanics of large-scale excavation, with sketches of a spade-blade, a hinged excavating bucket, a crane frame, and several small plans for arranging labourers, surrounded by extensive columns of arithmetic. Leonardo reckons the output of barrow-crews (spadefuls per hoe, barrow-loads per box) and lays out files of diggers, labelled d, b, m and n, who work successively deeper layers. He opens with a mechanical principle — that percussion surpasses every other operation and that a naturally falling heavy body gains degrees of power throughout its descent.
On this page
Spadefuls, barrow-loads and the earth-boxes
Leonardo reckons the rate of filling: at one spadeful per hoe-stroke, twelve men make two barrow-loads at each stroke, so in ten strokes a box of twenty barrow-loads is filled. He debates whether it is better to keep the men still and throw the earth from hand to hand, all being diggers and throwers, or to split them into carriers and throwers, concluding that only the convenience and endurance of the workers should decide.
Two files of diggers working successively deeper
For raising banks of earth on both opposite sides of the river, the diggers d go under one spadeful, always drawing back, while the diggers b make a second spadeful lower down, always going forward; further files would take a third and fourth layer, deeper and deeper. The margin adds that this order m–n should be dug down to three braccia, after which the barrow-loads are carried to the foot of the inner embankment.
The excavating bucket and the falcon-crane
A hinged excavating bucket (benna) is drawn and annotated with the figure 1000: 'this lifts like 1000... as two thousand of weight... natural', with the remark that there is 'great difference in filling'. The boxes are to be filled at the foot of the ditch's inner bank and hauled up with the falcon-crane, since men could not climb the loaded bank without great labour.
Percussion surpasses every operation; falling bodies gain power
Among the natural powers, in equal time percussion surpasses with great excess every other human operation. Among motions made by heavy bodies, the natural one surpasses all the rest, because in every part of its descent it acquires degrees of power. Accidental motion turns to the contrary aspect and is of contrary nature, for the more it proceeds the more it loses, while the other gains velocity and weight.
Columns of worked calculation
Both faces are crowded with columns of multiplication and addition supporting the excavation estimates — products such as 60 × 27 = 1620 and 23 × 27 = 621, and running totals into the thousands. These are Leonardo's ledgers for spadefuls, barrow-loads, boxes and daily output rather than abstract number theory.