Is this correct? Does it describe how Europeans do warfare traditionally?

This. The fomality and aesthetics ensured an armies functionality and tactics.

You are essentially correct that they were not mercenaries in the traditional sense but it is still common to call the 18th century armies 'mercenary armies' for the very reason that they consisted of (for a large part very questionable) people from all over Europe commanded by (mostly) aristocratic officers. Arguably this changed to some extent during the Napoleonic period in regards to France and perhaps some of the German resistance, but this particular period is still characterised by the common soldier having no allegiance to his commanders beyond being paid.

>A smoothbore musket with a non-aerodynamic projectile IS an inaccurate weapon. This is a physical fact derived from the very physical properties of the weapon.

The accuracy of the weapon is irrelevant, it was accurate enough it just didn't matter. Line formations came to existence to maximise firepower and minimise vulnerability during long reloading times, it has absolutely nothing to do with accuracy.

>Neither affects what I said. The line maximises fire-power as every man is able to fire his weapon in the direction the formation faces.

Yes and this has nothing to do with aerodynamics of musketball or the accuracy of the weapon itself.

> And it's also the most effective against artillery fire.

Irrelevant, artillery was good against massed formations regardless square formations were still used, especially during Napoleonic wars. Which is what the picture at OP shows.

>What are you talking about? Most armies in Europe employed mercenaries.

They didn't employ mercenaries, they employed paid trainees. You are conflating 16th century, 30 years wars with 18th century and Napoleonic wars.

Mercenary is a different concept than just a soldier who works for wage. A mercenary is a member of an organisation or company that rents his services, a person paid by state to be a soldier is not a mercenary, if it was so then all soldiers paid a wage would be mercenaries. Basically anyone who is not a revolutionary or a rebel.

>Line formations came to existence to maximise firepower and minimise vulnerability during long reloading times
So just what I said? And no, the accuracy of the weapon does matter as it directly affects the effectiveness of the unit. The less accurate your weapon is the more men you need to fire at the target in order to pose a relevant threat. This too is not a matter of debate.

>Yes and this has nothing to do with aerodynamics of musketball or the accuracy of the weapon itself.
Clearly you're not an attentive reader if you interpret any such causality into what I wrote. The formation itself has nothing to do with the accuracy of the weapon. A line maximises firepower, whether you're using a musket or a modern assault rifle. However, you still need a whole lot more muskets than men with assault rifles to pose a comparable threat.

>artillery was good against massed formations regardless square formations were still used
Which has nothing to do with anything I said. I never claimed that other formations were not in use any more. You are debating against claims that were never made. Show me where I said that line formations were exclusively used? You probably can't, because you're not very good at reading attentively. I merely pointed out the advantages of line formations.

>They didn't employ mercenaries, they employed paid trainees. You are conflating 16th century, 30 years wars with 18th century and Napoleonic wars.
No, I'm not. A Hessian in British service is a mercenary of sorts. His allegiance to the flag he fights under ends where he is not being paid any more. Whether you like the term mercenary in this context comes down to personal taste. What you're debating is semantics, nothing else.

This ultimately comes down to semantics. I've already told you that you're essentially right - these people were obviously different from the mercenary companies of the late middle ages and early modern period. However, they are arguably still mercenaries in the sense that they're fighting for the people who pay them and to whom they have otherwise no ties. They're not household troops, they are not levies, etc.

>the common soldier having no allegiance to his commanders beyond being paid.

I'm not sure that's true. I'd frame it as the soldier have no allegiance to the state or the "side" in the war. They follow their commander as long as they trust him to do right by them which generally meant payment or the promise of future booty. Some top commanders would be in their position because of their charisma and leadership encouraging the men to follow them not just who is the wealthiest.

You said this in your initial post.

>First of all, your weaponry is inaccurate. A smoothbore musket with a non-aerodynamic projectile is not the most accurate weapon. If you want to pose a threat you need lots of men firing at the same target.

This has absolutely nothing to do with existence of line formations, if you are no longer claiming this then no point in writing anything further

You might argue that the same was true for mercenaries of earlier periods. If they trusted their leaders and their promises of future wealth and glory they might develop more of a bond, so this cannot be the characteristic.
I'm completely in agreement that the term 'mercenary' is not fully accurate here - but it still fits to some extent. The soldiers in those 18th century armies were quite different from those of WW1 or WW2 whose destinies were intertwined with the nations they fought for.

I said that you're dealing with a relatively inaccurate weapon and thus in order to maximise your threat potential you need to raise your numbers. The line-formation allows you to maximise your fire-power. This is of course something completely independent from the weapon you're using: if that's all you're arguing then we're not in disagreement and we might as well end the debate here. No matter whether you're using muskets, assault rifles, or whatever - a line will always be your primary choice if you want as many men as possible to be able to employ their weapons.

Hes not essentially right. He is 100% correct. Swallow your pride and admit you fucked up next time.

More than any other time (except for modern heavilly medialized conflicts).

Hell, there were battles where two generals flipped a coin who will fire the first volley.

Not entirely, regarding the Napoleonic era the tactics were effective for the weapons that they had and worked well with smoothbore muskets and maximizing their firepower. The uniforms were also reasonable practical, most of the uniforms that you see in illustrations and paintings are just dress/parade uniforms whereas the actual campaign uniforms that were used in battle were much more utilitarian. The bright colours were necessary for identifying troops/units from far distances and through smoke. Riflemen, like the 95th more dark green clothing. A lot of people think that tactics during the Napoleonic era were the same as it was mid 1700's, which is wrong.

kill yourself retard

As I told you: it's a semantic debate.

Are these armies composed in the same fashion as 16th or 17th century armies? No, most certainly not. But they are still not the same as the later national armies of the 20th century. And under that premise it makes sense to characterise the men fighting there as mercenaries, as they had no allegiance to the flag they were fighting under beyond money. And it is not uncommon to refer to these people as mercenaries in literature. This is not a matter of not being willing to swallow pride it is a matter of not wanting false information to be spread for the sake of being all too anal about semantics.
The 18th century soldier had more in common with the mercenary than with the soldier of the national army of the 20th century.

You can't just say "wrong"
you need to provide a valid argument as to why he is incorrect