Want to have some fun /sci/?
I am having a problem with this very dense, hard to fathom proposition. Lets work through this, /sci/ please help.
https://www.stmarys-ca.edu/sites/default/files/attachments/files/On_the_Equlibrium_of_Planes.pdf
Proposition nine. Book two. II. fucking 9. This shit is hard. But one of the most complex things I don't understand is perhaps rather simple to explain. Right in the beginning there, I understand everything up until three. (3) makes NO SENSE. At ALL. What the fuck? It almost looks as if someone just added the numerators and denominators of the two equivalences of ((a-c)/(c-d)). But that's not possible. So I'm stuck.
This is famously a very hard proposition, but the translator T.L. Heath has made it a little easier by introducing algebraic variables.
here is the section in particular for those too lazy
>>8562985
whats the problem really? just solve that equation with d in it for d. then use that equation to replace d in (b+c)/d and you get what you are looking for.
>>8562999
From the 2 above: lhs=[b+c]/d = [a+b]/c
lhs*d = b+c
lhs*c = a+b
lhs*d +2lhs*c = b+c + 2(a+b)
lhs*(2c+d) = 2a+3b+c
lhs = [2a+3b+c]/(2c+d)
>>8563002
That's a little vague. What do you mean by 'that equation'?
>>8563002
addendum:
i mean you have:
[math] \frac{2*(a+b)}{2c} = \frac{a-c}{c-d} [/math]
solve for d you get:
[math] \frac{c-d}{a-c} = \frac{2c}{2(a+b)} [/math]
=>
[math] c-d = \frac{2c}{2(a+b)}(a-c) [/math]
=>
[math] c - \frac{2c}{2(a+b)}(a-c) = d [/math]
then use that expression for d to replace it in [math] \frac{b+c}{d} [/math]
>>8563009
But why is it literally just the numerator added on the denominator?
I understand how you got that, it makes sense. It's just, is that something you can do in a situation like this, algebraically? Just add the numerators and denominators??
>>8563024
If r = N/D = n/d
then r = [xN+yn]/[xD+yd]
Usually this is mentioned with proportions, N:D = n:d then N:D = xN+yn : xD+yn
>>8563042
Thanks man, this makes sense now that you put it that way. I love you guys.