Do Bodies Weigh More in Air Than Under Water?
Center of gravity of a body half- and fully immersed, and how far the water-sphere's surface descends per mile
Leonardo asks whether the earth covered by the sphere of water is heavier or lighter than when uncovered, answering that a heavy body weighs more when surrounded by a lighter medium, so earth under air is heavier than earth under water. A balance sketch pairs a half-immersed weight with a fully immersed one (a b), and a further figure of a pyramid at the centre of the world (a) argues that its centre of gravity shifts once partly covered by the water-sphere, illustrated by two equal columnar weights, one half and one wholly in the water. A final semicircular diagram, labelled 'half-sphere of water', sets a geometric question: taking a straight line equal to the sphere's diameter and touching its surface at the midpoint, how much does the surface descend below that line from one mile to the next.
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A body weighs more when surrounded by a lighter medium
The question is whether earth covered by the sphere of water is heavier or lighter than when uncovered. The answer: that heavy body weighs more which sits in a lighter medium; therefore earth covered by air is heavier than earth covered by water.
Half-immersed weight heavier than the fully immersed one (a b)
By example with two equal, alike columnar weights, one half in the water and the other wholly in it, the one that remains half out of the water is the heavier, as has been proved. A balance labelled a b sets a half-immersed against a fully immersed weight.
A pyramid's center of gravity shifts under the water-sphere (a)
Of the centre of gravity of the pyramid (a) placed at the centre of the world, he says it will change its centre of gravity once it is partly covered by the sphere of water.
How far the water-sphere's surface descends per mile below a chord
Let a straight line equal to the diameter of the sphere of water touch that sphere's surface at the middle of its length. The question is what difference each mile has from another in the descent that the sphere's surface makes below the said line.