Elements of mechanics: shared loads and how cords break
A shaft's weight shared between two cords, and where an overloaded cord snaps
Folio 8v treats a shaft suspended by two cords of equal height, whose weight is shared equally between them, and shows how sliding the cord (or a hung weight) from the middle toward one end transfers load in proportion to the distance moved, worked with a shaft of 8 pounds in 8 parts (letters a, e, d, c). Folio 7r is headed 'Machinal elements' and sets out the strength of cords: a cord of uniform power breaks along its whole length when overloaded crosswise, is broken by two equal and opposite powers, and suffers twice the alteration of the weight; a straight cord breaks at the end of its straightness, while an arced cord fixed at its ends breaks at its attachments, the higher-fixed end first (letters d, a, e, b, c). Diagrams of suspended shafts, cords and weights fill both leaves, and further untranscribed calculation is present.
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A shaft's weight shared by two equal cords
The shaft suspended by its ends from two cords at equal height shares its weight equally to each of those cords. This opening principle governs the load-sharing problems that follow on the folio.
Sliding the cord transfers load in proportion
Let a e be the shaft length and d the motion of the cord. When cord d was at e, the shaft of 8 pounds in 8 parts gave each cord 4 parts and 4 pounds; drawn from e to d it leaves 2 parts outside, so a, which held 4, now holds 2, and the 2 taken from a joins d. Thus the load shifted bears the same proportion to the whole as the length d e to the whole shaft.
A mid-shaft weight loads both supports equally
If the shaft is suspended by its ends at equal height and a heavy body is hung at its middle, the gravity of that weight is distributed equally to the shaft's two supports.
Machinal elements: the strength of cords
Folio 7r is headed 'Machinal elements'. A cord of uniform power overcome by excess weight breaks throughout its whole length into minute particles when stretched crosswise; the weight's power penetrates the whole cord; every broken cord is broken by two equal contrary powers; and the cord's length suffers alteration double to that of the weight.
A straight cord breaks at the end of its straightness
The cord attached straight and of uniform power, when its forces are overcome by the weight, will break at the term of its straightness.
An arced cord breaks at its attachments
When a cord d a e is fixed at its ends d, e at equal height and hangs in an arc, it breaks at those attachments, where the whole weight arrives, not at b c which carries only half. Of an arced cord a b c, the end fixed higher breaks more easily, being more burdened at b than at a.