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I'm reading Galileo's Two New Sciences. But as other Scientific Book it is hard. I am having trouble in First day, where SIMPLICO asks this question(Page 7):

"But how can one make a rope one hundred cubits long out of hempen fibres which are not more than two or three cubits long, and still give it so much strength?"

Then SAGR appeals SALV to answer the question. So SALV goes on to answer it in the following way(Page 8):

[....]How are fibres, each not more than two or three cubits in length, so tightly bound together in the case of a rope one hundred cubits long that great force [violenza] is required to break it? Now tell me, Simplicio, can you not hold a hempen fibre so tightly between your fingers that I, pulling by the other end, would break it before drawing it away from you? Certainly you can. And now when the fibres of hemp are held not only at the ends, but are grasped by the surrounding medium through- throughout their entire length is it not manifestly more difficult to tear them loose from what holds them than to break them ? But in the case of the rope the very act of twisting causes the threads to bind one another in such a way that when the rope is stretched with a great force the fibres break rather than separate from each other. At the point where a rope parts the fibres are, as everyone knows, very short, nothing like a cubit long, as they would be if the parting of the rope occurred, not by the breaking of the filaments, but by their slipping one over the other.

I'm not able to understand what SALV means by example of holding fibers. And how does this answer the question of SIMP?

Thanks.

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  • $\begingroup$ Looks like he's using the fingers&their muscles as an analogy for the frictional force between twisted fibers. $\endgroup$
    – Carl Witthoft
    Commented Jan 10, 2020 at 12:39
  • $\begingroup$ @CarlWitthoft no. Galileo is talking about strength and tensity of materials. $\endgroup$
    – user10963
    Commented Jan 10, 2020 at 13:07
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    $\begingroup$ I think Carl is right. This is not about "materials" but about rope, which is a bundle of multiple fibers tightly wound together. Galileo is analogizing a fiber in the bundle to a fiber held between fingers, and notes that it would sooner break then slip out (because the friction is large when the fingers are pressed hard). Same with the rope, its fibers would sooner break than be pulled apart, and it is hard to break so many of them at once. This is why a long rope manages to hold together despite its fibers being short, and why they give it so much strength. $\endgroup$
    – Conifold
    Commented Jan 10, 2020 at 21:17
  • $\begingroup$ @Conifold I think this comment should be an answer. $\endgroup$
    – user10963
    Commented Jan 11, 2020 at 2:00

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In this passage Galileo is explaining how a bundle of multiple short fibers twisted into a rope functions. He is analogizing a fiber in the bundle to a fiber held between fingers, and notes that it would sooner break then slip out because the friction is large when the fingers are pressed together hard. Same with the rope, its fibers would sooner break than be pulled apart, and it is hard to break so many of them at once. This is why a long rope manages to hold together despite its fibers being short, and why they give it so much strength.

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