Which prop best supports a loaded beam

Prop a p or prop a q to carry weight n on beam a b

Leonardo wishes to hold the weight n at the extreme point a; knowing that the beam a b lacks the strength to resist such a weight, he proposes to set beneath it either the prop a p or the prop a q, and asks which will be of greater power.

Labour of the mover pulling weight s along n a, a m and f a

Pulling the weight s along the line n a costs as much power as the weight's resistance, since the lever a e equals its counter-lever a e. Pulling along a m the mover gains 1/12 of labour because the lever b e falls short by 1/12; along f a the labour grows by a quarter, the lever line losing 1/4 and the lever d e losing 2/3. Along e a no force could lift it, the lever being divisible to infinity so that at each half the weight is doubled.

Two lines crossing at four right angles meet at points a and r

The intersection of two straight lines made among four right angles is made at a point; it occupies a space larger than a point in proportion as, of the four enclosing angles, the two opposite ones differ more from the other two. The intersection a is made at a point, while r is made in greater contact than that point.

In alto figura con lettere e a lato:

Sotto figura con lettere seguita dal testo:

Nella metà inferiore del foglio, lungo il margine destro dall’alto in basso, sequenza di figure con e senza lettere. A lato:

Above, a figure with letters, and beside it:

Below, a figure with letters followed by the text:

In the lower half of the sheet, along the right margin from top to bottom, a sequence of figures with and without letters. Beside them:

Which prop best supports a loaded beam

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Prop a p or prop a q to carry weight n on beam a b

Labour of the mover pulling weight s along n a, a m and f a

Two lines crossing at four right angles meet at points a and r