Beams Suspended in Balances: Obliquity and Weight in Air
Non-uniform bodies led by their heavier part; a beam keeps its initial obliquity as it falls
Three small diagrams at the right show a beam hung obliquely in a balance, a second balance figure, and a tall vertical beam, illustrating a study of how beams weigh and fall through the air. Leonardo states that a body of non-uniform figure is led in its descent by its heavier part, while a beam of uniform figure ends its motion at the same obliquity with which it began. He adds that a heavy body weighs less in air the more oblique its motion, and that a straight descent weighs less the less oblique the beam. The final proposition proves that a beam suspended at the extremities of the central line of its thickness gives equal weight to both of its appendages.
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The heavier part guides the descent of non-uniform bodies
For heavy bodies of non-uniform figure, Leonardo states that the heavier part always makes itself the guide of their descent through the air.
A uniform beam keeps its starting obliquity
For beams of uniform figure, the end of the motion finds the beam at the same obliquity as its beginning. This is demonstrated by the beam suspended in the balance n m.
Weight in air varies with the obliquity of the motion
A heavy body weighs less in the air the more oblique its motion; conversely, the straight descent of the beam weighs less in the air the less oblique the beam is.
Beam b f on its central line gives equal weight to a b and n f
A beam suspended at any obliquity by the opposite extremities of the central line of its thickness gives equal weight to its appendages. With b f hung by a b and n f, the line m f of the pole and beam divides it orthogonally into equal parts o b g and h g o, proving the intent by the ninth proposition.