Pierre Duhem

“ If a force moves a body some time, in some space, it is not necessary that one such power moves a double weight, in a double time, two times this space; because it would be possible that such a force would not be able to move this moving body. Fifth: If a force moves a body so much time, in so much space, it is not necessary that half of this force moves this same moving body in the same time half of one such space, for possibly the force would not be able to move the body. These restrictions express the impossibility of certain motions not to clash with the axiom of Aristotle ”

“ That is to say that if a wheel moves a machine, it is impossible that without employing it one time more times, the wheel moves two of it; therefore the wheel does as much work in an hour as two machines with a second hour; thus the same wheel can make an infinite number of machines turn; but, with a very long time, the machines will not do more work than the first in one hour." A given weight, falling from a given height, produces therefore a mechanical effect of which the magnitude is independent of the circumstances which accompany this fall ”

“ The extremity of a lever which supports itself on a horizontal axis describes a circle's circumference placed in a vertical plane; the path travelled through by this extremity is therefore not directed in the way of the weight of the load to lift, weight which pulls following a vertical right angle. By it, it results that the resistance that it is necessary to surmount to make to turn from a certain angle the lever arm depends on the initial position from this lever arm. It is so much the greater as the lever is closer to the horizontal position. ”

“ I say that the weight of the heavy body a b shares its gravity in two aspects, that is to say according to the line b c and according to the line n m; why and how much the weight is greater for one than for the other aspect and which obliquity is the one which shares the two weights in equal parts, will be said in the book On weights. ”

“ At the extremity of a lever, one can cause to act a force of which the direction is different from the vertical; it will suffice
to employ a cord extended in this direction, passing over a pulley and pulled then by a weight. A rule similar to the preceding will help to evaluate the motive power of a similar engine ”

“ And a force will be more feeble than another by as much as the time between the one from the other." These principles render account very easily of the properties of tackle-blocks; Leonardo da Vinci exposits with the greatest exactitude the properties of these mechanisms. ”

“ If, for example, a weight, hung by a cord at the extremity of a lever arm, oscillates in the manner of a pendulum, it will not weigh at each instant on the lever but by the vertical component of its weight ”

“ Let us suppose that one possesses a cause of motion well-determined: for example, a quantity of water, immobile in a reservoir, expecting that one allows it to fall, from a given height, in a smaller canal. ”

“ If someone descends (17) step by step in making a jump from the one step to the other, and that you add all the powers of the percussions and weights of such jumps, you will find that the powers are equal to the totality of the percussion and of the weight that one such man would give falling, by perpendicular line, from the head to the feet of said steps. ”

“ He recognized that the weight which pulls the moving body towards the center of the earth could be decomposed into two forces, the one normal to the inclined plane upon which the weight slides, the other tangent to this plane ”

“ Of these notebooks, many have been lost; after a good many vicissitudes, many have been saved (2) . An important collection of these writings has found itself at the Library of the Institute of France; diverse leaves, stolen by Libri and sold by him to Lord Ashburnam, have become, thanks to M. Leopold Delisle, the property of the National Library; other manuscripts find themselves in Italy; among those here, a place of choice must be reserved to the registry that the Ambrosian Library of Milan keeps under the name of Codex Atlanticus. ”

“ I Manoscritti di Leonardo da Vinci. Codice sul volo degli uccelli e varie oltre materie. Publicato da Teodoro Sabachnikoff. Transcrizioni e note di Giovanni Piumati. Traduzione in lingua francese di Carlo Ravaisson-Mollien. Parigi, Edoardo Rouveyre, editore, MDCCCXCIII.
(5) "Mechanics is the paradise of the mathematical sciences, for it is by her that these sciences attain the mathematical fruit." (Les Manuscrits de Léonard de Vinci, published by Charles Ravaisson-Mollien; Ms. E from the Library of the Institute, fol. 8, verso. Paris, 1888) . ”