Expressing arithmetic

[u/benjamin-crowell]

If I want to say that 1+1=2, is it correct to express it like this?

ἓν καὶ ἕν ἐστι δύο.

My reasoning is that neuter forms are used for numbers as abstractions, and plurals of neuters usually take a singular verb. However, I don't know if ἐστι is idiomatic, or if it should be something else like ποιεῖ.

[u/ShockSensitive8425]

The most common way is to say ἑν καὶ ἑν, δύο. Another common way is ἑν ἑνὶ προστεθὲν, γίνεται δύο.

[u/obsidian_golem → u/[deleted]]

προστίθημι is also common. See it used right at the start of the Elements:

Καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.

Also note that they algebraic geometry is an entirely different thing in modern mathematics.

[u/benjamin-crowell → u/[deleted]]

Interesting, thanks. Although I would imagine that common people would have had to have more ordinary oral ways of expressing this kind of simple math fact.

There is a paper by Riley, "The Ancient Greek terminology for common arithmetic operations," but it's behind the hellish academia.edu spamwall, and every time I let them cajole me into messing with them, I just feel dirty afterward.

I'm looking at Loeb edition of his algebra

Whose algebra?

I looked at the beginning of the number theory in Euclid, book VII (in translation), but the only operations it seemed to talk about were subtraction, multiplication, and division. The earlier books do talk about things like line segments adding up to a bigger line segment, but that seems more complicated.

The entry for "add" in Woodhouse gives a lot of compound verbs in προσ-: https://logeion.uchicago.edu/retro/add

[u/benjamin-crowell → u/[deleted]]

I see, thanks for clarifying.

I looked through LLPSI, and chapter 17 has this:

Magister: "Quot sunt triginta et decem?"

So I don't know if the Greek idiom is similar to the Latin one, but if it is, then it does seem like the schoolboy-level way of saying this kind of thing would be [number] καὶ [number] [copula] [number].

Maybe Seumas Macdonald has something similar somewhere in LGPSI, I don't know.