The Notebooks of Leonardo Da Vinci. Complete. Leonardo da Vinci

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СКАЧАТЬ pulling, striking, being struck, pressing down and lifting up.

      [As to how a figure should stand with a weight in its hand [Footnote 8: The original text ends here.] Remember].

      369

      A sitting man cannot raise himself if that part of his body which is front of his axis [centre of gravity] does not weigh more than that which is behind that axis [or centre] without using his arms.

      A man who is mounting any slope finds that he must involuntarily throw the most weight forward, on the higher foot, rather than behind—that is in front of the axis and not behind it. Hence a man will always, involuntarily, throw the greater weight towards the point whither he desires to move than in any other direction.

      The faster a man runs, the more he leans forward towards the point he runs to and throws more weight in front of his axis than behind. A man who runs down hill throws the axis onto his heels, and one who runs up hill throws it into the points of his feet; and a man running on level ground throws it first on his heels and then on the points of his feet.

      This man cannot carry his own weight unless, by drawing his body back he balances the weight in front, in such a way as that the foot on which he stands is the centre of gravity.

      [Footnote: See Pl. XXII, No. 4.]

      370

      How a man proceeds to raise himself to his feet, when he is sitting on level ground.

      371

      A man when walking has his head in advance of his feet.

      A man when walking across a long level plain first leans [rather] backwards and then as much forwards.

      [Footnote 3-6: He strides forward with the air of a man going down hill; when weary, on the contrary he walks like a man going up hill.]

      372

      A man when running throws less weight on his legs than when standing still. And in the same way a horse which is running feels less the weight of the man he carries. Hence many persons think it wonderful that, in running, the horse can rest on one single foot. From this it may be stated that when a weight is in progressive motion the more rapid it is the less is the perpendicular weight towards the centre.

      373

      If a man, in taking a jump from firm ground, can leap 3 braccia, and when he was taking his leap it were to recede 1/3 of a braccio, that would be taken off his former leap; and so if it were thrust forward 1/3 of a braccio, by how much would his leap be increased?

      374

      OF DRAWING.

      When a man who is running wants to neutralise the impetus that carries him on he prepares a contrary impetus which is generated by his hanging backwards. This can be proved, since, if the impetus carries a moving body with a momentum equal to 4 and the moving body wants to turn and fall back with a momentum of 4, then one momentum neutralises the other contrary one, and the impetus is neutralised.

      Of walking up and down (375-379)

      375

      When a man wants to stop running and check the impetus he is forced to hang back and take short quick steps. [Footnote: Lines 5-31 refer to the two upper figures, and the lower figure to the right is explained by the last part of the chapter.] The centre of gravity of a man who lifts one of his feet from the ground always rests on the centre of the sole of the foot [he stands on].

      A man, in going up stairs involuntarily throws so much weight forward and on the side of the upper foot as to be a counterpoise to the lower leg, so that the labour of this lower leg is limited to moving itself.

      The first thing a man does in mounting steps is to relieve the leg he is about to lift of the weight of the body which was resting on that leg; and besides this, he gives to the opposite leg all the rest of the bulk of the whole man, including [the weight of] the other leg; he then raises the other leg and sets the foot upon the step to which he wishes to raise himself. Having done this he restores to the upper foot all the weight of the body and of the leg itself, and places his hand on his thigh and throws his head forward and repeats the movement towards the point of the upper foot, quickly lifting the heel of the lower one; and with this impetus he lifts himself up and at the same time extends the arm which rested on his knee; and this extension of the arm carries up the body and the head, and so straightens the spine which was curved.

      [32] The higher the step is which a man has to mount, the farther forward will he place his head in advance of his upper foot, so as to weigh more on a than on b; this man will not be on the step m. As is shown by the line g f.

      [Footnote: See Pl. XXIII, No. 1. The lower sketch to the left belongs to the four first lines.]

      376

      I ask the weight [pressure] of this man at every degree of motion on these steps, what weight he gives to b and to c.

      [Footnote 8: These lines are, in the original, written in ink] Observe the perpendicular line below the centre of gravity of the man.

      [Footnote: See Pl. XXIII, No. 2.]

      377

      In going up stairs if you place your hands on your knees all the labour taken by the arms is removed from the sinews at the back of the knees.

      [Footnote: See Pl. XXIII, No. 3.]

      378

      The sinew which guides the leg, and which is connected with the patella of the knee, feels it a greater labour to carry the man upwards, in proportion as the leg is more bent; and the muscle which acts upon the angle made by the thigh where it joins the body has less difficulty and has a less weight to lift, because it has not the [additional] weight of the thigh itself. And besides this it has stronger muscles, being those which form the buttock.

      379

      A man coming down hill takes little steps, because the weight rests upon the hinder foot, while a man mounting takes wide steps, because his weight rests on the foremost foot.

      [Footnote: See Pl. XXIII, No. 4.]

      On the human body in action (380-388).

      380

      OF THE HUMAN BODY IN ACTION.

      When you want to represent a man as moving some weight consider what the movements are that are to be represented by different lines; that is to say either from below upwards, with a simple movement, as a man does who stoops forward to take up a weight which he will lift as he straightens himself. Or as a man does who wants to squash something backwards, or to force it forwards or to pull it downwards with ropes passed through pullies [Footnote 10: Compare the sketch on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that the weight of a man pulls in proportion as his centre of gravity is distant from his fulcrum, and to this is added the force given by his legs and bent back as he raises himself.

      381

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