Galilei, Galileo - Discourse concerning the natation of bodies

Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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mit a Board of Ebony into the Water, you do not put therein a Solid
more grave in ſpecie than the Water, but one lighter, for be ſides the
Ebony, there is in the Water a Maſs of Air, united with the Ebony,
and ſuch, and ſo light, that of both there reſults a Compoſition leſs
grave than the Water: See, therefore, that you remove the Air, and
put the Ebony alone into the Water, for ſo you ſhall immerge a So
lid more grave then the Water, and if this ſhall not go to the Bottom,
you have well Philoſophized, and I ill.

Now, ſince we have found the true Cauſe of the Natation of thoſe
Bodies, which otherwiſe as being graver than the Water, would de
ſcend to the bottom, I think, that for the perfect and diſtinct know
ledge of this buſineſs, it would be good to proceed in a way of diſ
covering demonſtratively thoſe particular Accidents that do attend
theſe effects, and,

PROBL. I.

To finde what proportion ſeverall Figures of different

Matters ought to have, unto the Gravity of the
Water, that ſo they may be able by vertue of the
Contigucus Air to ſtay afloat.

To finde the
proportion Fi
gures ought to
have to the wa
ters Gravity,
that by help of
the contiguous
Air, they may
ſwim.

Let, therefore, for better illuſtration, D F N E be a Veſſell,
wherein the water is contained, and ſuppoſe a Plate or Board,
whoſe thickneſs is comprehended between the Lines I C and
O S, and let it be of Matter exceeding the water in Gravity, ſo that
being put upon the water, it dimergeth and abaſeth below the Levell
of the ſaid water, leaving the little Banks A I and B C, which are at
the greateſt height they can be, ſo that if the Plate I S ſhould but
deſcend any little ſpace farther, the little Banks or Ramparts would
no longer conſiſt, but expulſing the Air A I C B, they would dif
fuſe themſelves over the Superficies I C, and
would ſubmerge the Plate. The height AIBC
is therefore the greateſt profundity that the

[Figure 9]

little Banks of water admit of. Now I ſay,
that from this, and from the proportion in Gra
vity, that the Matter of the Plate hath to the
water, we may eaſily ſinde of what thickneſs, at moſt, we may make
the ſaid Plates, to the end, they may be able to bear up above water:
for if the Matter of the Plate or Board I S were, for Example, as
heavy again as the water, a Board of that Matter ſhall be, at the moſt
of a thickneſs equall to the greateſt height of the Banks, that is, as
thick as A I is high: which we will thus demonſtrate. Lot the So
lid I S be donble in Gravity to the water, and let it be a regular

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