Balance-arm weights, and the opening of a new collection
The 1508 preface to the reader, with rules for counterweights on lever and counter-lever
The right-hand page (f. 1r) opens with Leonardo's programmatic note that he began this collection in Florence, in the house of Piero di Braccio Martelli, on 22 March 1508, gathered without order from many sheets. Below, balance diagrams show heavy bodies hung by doubled cords from the arms of scales, illustrating how a counterweight on the counter-lever resists the descent of a load. Two worked rules explain the multiplication and division by which that counterweight is found, using the labelled points n, m, o, d. Columns of further untranscribed figures fill the lower right, and the facing leaf (f. 14v) is blank.
On this page
Leonardo begins his collection in Florence, 1508
He records that this book was begun in Florence, in the house of Piero di Braccio Martelli, on 22 March 1508. It will be a gathering without order, drawn from many sheets copied here, which he hopes later to arrange by subject. He asks the reader not to blame him if the same thing recurs, since the matters are many and memory cannot hold them all.
A weight suspended by a doubled cord on the balance
The heavy body hung from the arms of the balance by a doubled cord always has its own pendant line (appendiculo). This pendant is wholly or in part a potential one. The remark introduces the four small balance figures drawn with numbers above.
Rule for the counterweight on lever and counter-lever
Multiply the divisions of the lever by the pounds of the attached weight, and divide the sum by the divisions of the counter-lever; the result is the counterweight that resists the load's descent. Thus the 2 of n m times the weight at b makes 8; divided by the 4 of m o it gives 2, and this 2 placed at o s resists the descent of the 4 placed at n d.
The converse check of the balance rule
Conversely: 2 times 4 is 8; divided by the 2 of m n it gives 4. So you have 4 for the weight d, and the rule always comes out right. The two computations verify each other on the same lettered balance.
Untranscribed columns of figures
Beside the lower balance diagrams the sheet carries columns of figures and small numbered sketches that the bundle does not transcribe. They appear to carry the arithmetic of the counterweight rules worked out above. They are noted here only from the image, not read.