Hydraulic Architecture, Volume One, Part One

CHAPTER I. ON MECHANICS.

8. Since there is no relationship—regardless of the nature of its terms—that cannot be expressed by straight lines, we will use them to represent the strength we attribute to Powers; this will suffice for any attentive reader, without it being necessary to characterize these Powers by any other graphical means.

9. When a Power is applied to a machine to produce a specific effect, it is called a motive Power original: "Puissance môtrice"; the force that initiates movement. or acting Power. It is said to act with an absolute force when it employs the full extent of the strength it can exert to overcome the obstacle opposing it; conversely, it is said that this Power acts only with a relative or respective force when it employs only a portion of its absolute force.

10. When a motion results from the combination of two Powers—acting as if they were a single force formed by their combined actions—it is called a compound movement original: "mouvement composé"; modern physics calls this "resultant motion.".

11. Since movements of this kind occur frequently in Machines, and since the most fruitful principle of Mechanics has been deduced from them, we will begin by establishing the properties of the parallelogram of forces, assuming that effects are always proportional to their causes, which is an axiom that cannot be doubted.

For example, the uniform speeds of the same body, or of equal bodies, can only be in the same ratio as the motive forces; the distances traveled by these bodies in equal times will also be in proportion to the motive forces, or the causes that produced them. Furthermore, when the distances traveled in uniform motion by the same body (or by equal bodies) are proportional to their speeds or to the forces that produced them, these distances are traveled in equal times.

12. Regardless of the number of forces or Powers, directed however one wishes, that act simultaneously upon the same body: either this body will not move at all, or it will follow only a single path. This path will be the same line as if, instead of being pushed or pulled by all these Powers at once, the body were moved along that same line and in the same direction by a single force or Power equivalent to the result of the combination of all the others.