Abstract
35. In order to determine the resistance that a fluid, either in motion or at rest, produces on a body that moves therein, we must first to determine the action that a moving fluid exerts against a body at rest. Because we will show in the next chapter that the whole theory of the resistance of fluids depends upon that, therefore we begin by expounding our research on this subject.
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Notes
- 1.
This will be in §.52-53.
- 2.
“Eadem autem remanet hæc ratio, quando velocitas in M est. gU, in g vero ga” Mss.42.I. “If this same reason is maintained, when the velocity at M is gU, at G it is ga”.
- 3.
“donnent” in the original, but in Mss.42.I is “exurgat”, whose meaning is rather to generate.
- 4.
In this figure B, D and C are not used, however NB = FE and NC = NE.
- 5.
The point N can be seen either as on the body surface, or as belonging in general to a line in any curve FN, whether contiguous to the body or not but described by the fluid particles. The ordinate PN of this curve is generally called z, and when it becomes the ordinate of the body itself, I call it y. In this and the following articles, the FN curve is not regarded as adjacent to the body surface, but away from the body at such distance as liked. It is for not multiplying the figures that we consider it as adjacent to the body in the Fig. 4.5. [Original note].
- 6.
This sentence is unnecessary and confusing. If only to remind us that A = dq/dz and B′ = dp/dz. There is also a misprint dy instead dp. This does not appear in the Mss.47-3rd.
- 7.
There was a major misprint with the next formula. It was written \( \frac{qdA}{dz}+\frac{pdB}{dz}=\frac{qdA^{\prime }}{dx}+\frac{pdB^{\prime }}{dx} \). See Mss.50.
- 8.
In the text says mass.
- 9.
We do not see any sense to call to art. 26, we think that it is a misprint for art. 28.
- 10.
This is deduced from the context and it is mentioned in the Mss. 60.
- 11.
In the original M and N are written instead of q and p [Mss.55].
- 12.
Not clear in the text. We follow Mss.56.
- 13.
In the original the expression for q is missing [Ms.57].
- 14.
In the original A and B are written instead p and q [Ms.58].
- 15.
The original wording “in which the value of m′ in h′, of k′ in n′, of s′ in r′, etc. can be determined” has been changed, because the sense is to apply the relations between each pair of coefficients.
- 16.
We think that this sentence adds clarity to the text. From Mss. 58: “cognita vero p, determinabimur facillime quantitas q” “But once p is known, we will determine the quantity q very easily”.
- 17.
I call identical amounts, those not only equal, but expressed with the same letters: for example \( \frac{a^2-{b}^2}{a+b}=a-b \) or (a 2 − b 2) = (a + b)(a − b) is an identical equation. But I simply call equal the quantities, which although the same, are expressed by different letters. For example y and \( \sqrt{2 ax-{x}^2} \) in the equation \( y=\sqrt{2 ax-{x}^2} \). [Original note].
- 18.
Reference to art. 64 added for clarity.
- 19.
It is obvious that RT should be a straight line; because the parties that are at the right of this line must have (hyp.) a rectilinear motion. [Original note].
- 20.
In the original says AMD y Amd, which corresponds with the quote to Fig. 23 in Mss. 66.
- 21.
Treaty of the Equilibrium and Movement of Fluids, Book 3, Ch. 1. (Original note).
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Simón Calero, J. (2018). On the Pressure That a Fluid Exerts on a Body at Rest and Immersed in It. In: Calero, J. (eds) Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids. Studies in History and Philosophy of Science, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-68000-2_4
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