Anonymous
01/10/25(Fri)23:59:07 No.16542223

File: galileo2.jpg (189 KB, 720x1280)

189 KB JPG

Anonymous 01/10/25(Fri)23:59:07 No.16542223

Hello everyone, it is I, the maker of the last Galileo thread (where I was wrong about Galileo being wrong, kind of only his method was somewhat haphazard).

I have another problem, perhaps this time you could help me with this one.

This is proposition 1 of the Second Day Interlocutors in the Dialogues concerning Two New Sciences. I will post the problem I am having issues with, as I understand the picture is somewhat blurry to see.

"From the preceding, it follows that the magnitude of the force applied at C bears to the magnitude of the resistance, found in the thickness of the prism, i.e. in the attachment of the base BA to its contiguous parts, the same ratio which the length CB bears to half the length BA; if now....'

Now, I seem to think that Galileo has finally made an appreciable error. And I can prove it using the preceding diagram, which he references. Lets take a few things as given, first the force applied at C, is essentially G in the previous paragraph. The force of the resistance of the prism to breaking is the weight of A. Next to length CB is GN, and half of the length BA is X. Now, we know from the preceding, the following ratios
GN:NC :: C:G
NC: X :: FB: BO
A: C :: FB : BO
from this we can derive ourselves that
NC: X : A : C

From compounding the first and that ratio we receive
GN: X :: A : G

But in the sentences just quoted from Galileo, he is stating that G:A:: GN : X.

What happened here? Does anyone else's edition state that these are inversely related? I'm wondering if there is an error in my translation or if maybe Galileo made a mistake. Thank you very much.