Logic and

“Logic is the art of going wrong with confidence.”
Euclid could be said to have gone wrong with confidence. He wrote about geometry and made hundreds of theorems based on a few propositions which most people would believe to be true. If these propositions are considered true the geometry all makes sense and there are no contradictions. It would not be prudent to assume from this that this must be the way the world works. Nicholas Lobachevski, in his Theory of Parallels proved that these propositions don't have to be true for geometry to make sense. He denied the fifth postulate in The Elements and ended up with different but equally valid conclusions about geometry.
This example illustrates that logic can lead someone to conclusions that aren't accurate. To come up with valid conclusions there have to be premises with which to work. Euclid no doubt made his premises based on what he had observed to start his logic of geometry off. But he has no proof for his propositions. You might say that he has based them on what he has observed. But as we have seen in our previous areas of study one cannot trust their senses entirely.
We see from geometry that logic is not the perfect tool for knowledge. The premises on which it is based are not certainly correct. Euclid based all of his knowledge on premises which aren't proven. he was sure that what he learned was absolutely true. But then Lobachevski proved he wasn't certainly correct. Euclid was 'wrong with confidence;' he firmly believed in what wasn't necessarily true. Another example of someone being wrong with confidence is someone who based all their beliefs on what someone else told them. Logic for them could lead to some terrible conclusions if they are being fed incorrect facts the whole time.