Geometry of a screw thread and its pitch
Pen study measuring how the thread b d turns against the circle a o to find its slope c r
In pen, with the notebook inverted, Leonardo analyses the thread ('pan di vite') of a screw. He compares how far the line b d turns against the circle described by a o, takes the intermediate line m n, and measures the slope c r that expresses how far the thread turns and descends. A wedge-shaped segment of screw thread lettered a, p, o, q is drawn at the foot of the page.
On this page
Thread (pan di vite) of a screw
The lowest drawing shows a wedge-like segment of a screw thread lettered a, p, o, q. The turn of the line b d is compared with the turn of the circle a o, and the number found between them is used to make the calculation.
Intermediate line m n between b d and a o
Three horizontal lines b d, m n and a o are ruled across the sheet. The line m n lies between b d and a o and is to be 'straightened out' as the construction directs.
Slope c r of the screw thread
An inclined line c r is joined to a horizontal. It measures how much the line slopes, that is, how much the whole thread of the screw above turns and descends.