The man a departs from a and comes as far as b, which is 32 [braccia], gaining ground behind him shovel-throw by shovel-throw, each of which is 1/6 of a braccio thick; therefore multiply 32 braccia by the 6 shovel-throws that go to a braccio and you will have the sum of 192/6 of braccia, all of which must be walked forward and then carried back. That is, the first shovel-throw is counted for the one that comes after the 4 braccia by which you have moved back from the embankment, and beyond which you can no longer throw earth so that it reaches the embankment. You will go forward by the least, the thickness of such a shovel-throw, and then, having thrown it, you go back 2/6 of a braccio to take up the next, and then return forward those 2/6 and throw that earth, and then go back those 2/6 and 1 more to reload the shovel anew; and so, in such order, you always go back as far as you went forward and 1/6 more, and so it is done up to the number of the aforesaid 192 sixths. The sum of these, between going and returning, is 18528 sixths only for those of going forward, and as many for those of returning, which in sum would be 37056 sixths, which will be found by the rule of progression. Now you know that an hour is divided into 1080 tempi, and that in such exercises one takes 3 paces, walking, per tempo, which would be, or would contain in themselves, 18/6 of a braccio per tempo. Therefore if you divide 37056 sixths by 18, you will be able to see in how much time this man makes these paces; divide, then, and you will find that such backward and forward movements are made in 2058 tempi and 2/3. Add the 3 tempi that go for each shovel-throw with its throwing, which in 32 braccia, at 6 throws per braccio, were 192 throws. And each throw containing in itself, as I said, 3 tempi, multiply the said 192 throws by the 3 tempi and you will find 576 tempi, which, added to the first, are 2634 tempi and 2/3. Therefore divide these tempi by the 1080 tempi of the hour and you will find it to be 2 hours and 54/180. Now this man carried in this time 192 spadefuls of earth; divide them by the 6 spadefuls that make a barrow, and you will find in that number 32 barrows, which at 20 barrows per case make one case and 3/5. Now, to know what falls to him per hour, do it by the rule of three, saying: if in 2 hours and 54/180 this labourer gives me one case and 3/5, how much will he give in one hour?