Euler's Analysis Infinitorum, Bk.1, art.1
I just started reading Euler's Analysis Infinitorum Book 1 and am already stuck on the first article: a definition of "constant quantity." It reads as follows:
- A constant quantity is a determined quantity which always keeps the same value.
For the sake of convenience, call the first phrase in this definition, "a determined quantity," A; and call the second phrase, "which always keeps the same value," B.
My question: Does B include A? In other words, if I tell you that I am talking about a quantity "which always keeps the same value," then is this quantity determined? (I'm assuming that by the word determined, Euler means: known already, or can be known (theoretically or otherwise) from the available data.) I think it is, because a quantity "which always keeps the same value" must:
-Have a value;
-Be something that is unchanging.
In other words, it has a value that is unchanging, and is therefore theoretically well-determined, hence determined.
This would lead me to believe that the definition could be reduced to,
- A constant quantity is a quantity which always keeps the same value,
were this not Euler; the fact that it is Euler makes me slightly hesitant in accepting that he would add a redundant word ("determined") to his definition.
Any clarification would be appreciated!
I would suspect it just has to do with translation.
Euler Archive has the original Latin text:
Quantitas constans est quantitas determinata perpetuo eundum valorem servans.
Google translates the statement as:
A constant quantity is determined by constantly keeping the same value.
I'm not very good with Latin, so I can't verify. I do have friends that know more about it, so I may ask them and update this answer if I learn anything new.
Either way, the particular version you are reading has decided to translate it a bit differently. I wouldn't get too hung up on it as long as you can make out which are the constants in the rest of the book, but I do appreciate your scrutiny.
UPDATE: A trusted friend from classical studies gave me the following translation:
A consistent/constant quantity is defined as a quantity preserving the same value forever.
He said some other things about predicate adjectives and nominatives, but in the end it seems that your idea and Euler's Latin line up.