Make sure you read the last two chapters as they are the most important and may help explain my reasoning. While I very much appreciate hearing other people's ideas, I would prefer if someone would directly go at some of my reasoning and attack it piece by piece so I can better understand. Your suggested ap items I agree with, however I believe jax scales better as a hybrid. For this, as said in the cons, you need an ap top, an ap jungle, or both. I disagree with dorans shields because the armor is useless. Read countering/laning for this

At first: put your hand on your heart and tell me ONE GOOD REASON, why would you play Jax at mid lane. Jax weakness are AP champs and you put yourself versus one of them. If you go mid, you need AP carry to go top. There can be actualy only few of them: Mordekaiser, Rumble, Kennen, Vladimir, Akali. Rest of AP carries have very few chances to do something at top lane (imagine Brand vs Olaf...). If you would play this at top lane, ok, but mid...? Your build is not bad, however I suggest to get Warmogs sooner, so it can stack up.

No vote here, from my reasons I dont vote on any Jax guide.

I disagree with the Doran's Shields. Why do you need armor against a mid champion? The only problem with mid jax (I play him quite frequently too, and sometimes mid) is that you're not carrying around the AP burst that most mid laners are. So you'll need a Vladimir or Kennen top to counteract this. With that said you could opt for a more AP heavy build such as:
Mercury's Treads
Hextech Gunblade
Guinsoo's Rageblade
Lich Bane
Rylai's Crystal Scepter
Rabadon's Deathcap (can be traded for more health, etc.)

That's how I usually play Jax mid starting with a Hextech Revolver and immediately working towards Lich Bane and finishing my gunblade.

I'll vote it up for now since you max Leap Strike, have some decent advice and you play Jax mid. But there is just wall after wall of text and Jax mid is very situational. This would do better as a mini-section in a guide so you may want to start piling on the coding/images/chapters. Good job though :)

+1

Hey dude,you have good item build,but only one thing I don't like is stacking Doran's Blades,I would rather stack Doran's Shields because has high damage output early game with his spells.

Thank you. I just did it today and am still working on it. I haven't spent the time to figure out how to do it quickly.

Good item build, but you have walls of texts, you need pictures