Strength of square, triangular and right-angled screw teeth
Comparing thread-tooth profiles for strength and ease of driving; obliquity of a support
Diagrams at the right show a support (sostentaculo) and screw threads with differently shaped teeth, keyed by many letters. Leonardo compares three tooth profiles — equilateral-triangular, square, and right-angled — concluding that the triangular tooth is weakest, the square strongest but most laborious to drive, and the right-angled tooth as strong as the square yet as easy as the triangle, hence best for a given space. He notes that in the square tooth a b c d the strength lies only in triangle a b c while a d c does nothing when the screw is pushed upward, and adds a marginal note that if the square tooth is loaded at g only o bears the weight and K none.
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A less oblique support carries more of the weight
Leonardo opens with a rule about props: the support whose central line is less oblique with respect to the centre of the weight it sustains will be the more burdened by that weight.
Three screw-tooth profiles compared
Of the three tooth varieties used on screws, the equilateral triangle is the weakest, the square the strongest but most laborious for its driver, and the right-angled tooth is as strong as the square and as easy as the triangle. Where two square teeth go, three triangular or three right-angled ones go, making the latter easier to drive.
The working triangle a b c and the idle triangle a d c
The square tooth a b c d has its strength only in the triangle a b c, while the triangle a d c is of vain operation and does nothing when the screw is driven upward. The opposite tooth n m o has equal value and resistance to the square tooth in the same projection.
Marginal note: loading the square tooth at g
If the square tooth is loaded at g, Leonardo notes that nothing other than o ever bears the weight, and K bears none of it.