But you had the right track; you just overcomplicated it. As noted in post 36, and as you noted, A/P = Q/C, and has some lowest terms form (in the sense of smallest numerator/denominator), which can be taken to be a/b. The rest follows if we know that every fraction is a scaling up of its lowest terms form by a whole number factor (but this fact itself isn’t necessarily obvious to see the reason for!).
By using eyesight maybe and seeing if one divides into the other. It’s really not as difficult as you’re making it sound.
That’ll tell you whether your method works in any single specific case. It doesn’t tell you that your method always works.
Yes; as Chronos notes, you seem to be answering a different question than the one I was asking, Saint Cad. You are simply describing how to carry out the last steps of the AC method in such cases as it is possible to do so; my question was to explain why, in fact, it is always possible to do so.
Oh, I meant to ask about this before; out of curiosity, what are these two examples?
One was his very last theorem, where he demonstrates that there are exactly five regular solids (the Platonic Solids). Except that he didn’t define “regular solid” quite rigorously enough, and so by his definition there are actually seven: The Platonic five, plus the triangular and pentagonal bipyramids.
The other was the proof that the intersection of two planes is a straight line. What he actually proved was that if the intersection of two planes is a line, then that line is straight. But he neglected the possibility of two planes intersecting at a single point, which is the typical case in 4 dimensions.
I used the quadratic formula. I found that x can equal 3 and/or -2.