If you're trying to understand a domain work (such as Euler's) you could probably get a working knowledge in a month of strong study, a year of off-and-on.
I bet you could start this week if you used machine translations as a crutch.
I'd start working with a publication that exists in Latin and a good translation, so you can compare your work.
That's the advantage of it being a particular mathematic domain, you'll learn the terms relatively quickly and be able to catch errors in the math parts; the prose is where you will need the machine.
In fact, you'll find that many philosophers will just use the Latin words directly, and not bother translating them - Latin qua jargon if you will.
Once you've learned the various forms of "is" (sum, very irregular) you can kinda survive reading without conjugations, just like this sentence can be worked out:
Use the book "Lingua Latina per se illustrata" to learn Latin. It's quite magical, you just start reading Latin which is comprehensible due to similarities to English and it stacks on this without using anything but Latin. It's also much faster and more thorough than other textbooks.
I bet you could start this week if you used machine translations as a crutch.
I'd start working with a publication that exists in Latin and a good translation, so you can compare your work.