How Much Maths Must A Napoleonic Artillery Officer Know?

I know that back then, fast and accurate calculation must be done to win an artillery duel.

But anyone knows more precisely about the maths education an officer must undergo before he could competently lead a gun crew? What are the fields he must master? And how good (how fast and accurate) must he be in those fields?

Another way of asking this question would be: if I have an ISOT machine on my hand and I want to be a Napoleonic artillery officers, I much maths must I study before I press the button?
 
Boiler plate arithmetic, a basic understanding of geometry, and a some simple algebra. Most of the math pertains to siege artillery. Field artillery, foot artillery, horse artillery were more tactics than mathmatics.

What I needed to make through the officers basic course at Ft Sill in 1983 was fairly simple. My earlier training in mechanical drawing proved just as valuable. The actual gunnery was so formulated & mechanically aided common shooting required little real math training. It did help if you had a above average feel for geometry when doing basic survey for laying a battery for indirect fire, or locating targets & reference points with precision. Things like safety checks or safety charts for training, required a solid understanding of geometry & skill at arithmetic & a little algebra.

On one occasion I had to create a range safety chart from scratch. We were to shoot on Tinian Island & there was no designated firing range. I spent a interesting three hours using the formulas in the safety order to calculate the size of the safety zones for the ammo and range to targets we would be using.

After the usual few months as a FO, six months as a Fire Direction Officer, and a few more as a supernummary for those jobs I had enough experience to do 'Black Magic' when necessary. That is come up with a elevation & direction for the guns without running through the full calculation or using the various computation devices. Something usefull in a real emergency, or to show off with.
 
Trigonometry, I think. Since a lot of trigonometric concepts came from French mathematicians, IIRC. And this predates Napoleon.
 
Amusing fact of the day: René Descartes was an artillery officer. He did invent cartesian coordinates as a way to locate impacts.
 
One outcome from the First World War was the firing tables developed from all of those artillery rounds fired.
 
Nah - only if you want to be writing the tables on which all the battery officers commanding use.

Which I don't think is where our young ISOT-er wants to go;)

Thats was really on the list of things to learn.

Trigonometry and the like were learnt earlier (You need to know those to be accepted in the Artillery class)

NApoleon got a royal stipend and was first sent to a college in Autun. Later he attended classes at the cadet academy in Brienne where he excelled in MAthematics, but got mixed results in other subjects.

Because of his excellent performance in Brienne he was accepted in the ecole militaire where he comleted artillery class - among the above described mathematics the learned about fortifications and public law (state law). He was allowed to finish early because of his excellent results...
 
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