# Origins of the Equals Signs

I asked this over on Math Stackexchange, and someone said it might be good to ask it over here too.

Some authors use different equals signs for different purposes. For the most part, they are "$=$", "$\equiv$", "$:=$", and "$:\equiv$'. I read that "$=$" dates back to 1557, and is of mathematical origin.

What about the others? I have read that "$:=$" appears in some programming languages from the $70$'s. But, does it occur earlier? What about $\equiv$ and $:\equiv$, what are their origins?

See Earliest Uses of Symbols of Relation for the first occurrence of the equality sign $=$, that was first used by Robert Recorde (c.1510-1558) in 1557 in The Whetstone of Witte, with a link to the image of the original print.

For the equivalence sign, see Earliest Uses of Symbols of Set Theory and Logic, with the origin of $\leftrightarrow$, that was apparently first used in 1933 by Albrecht Becker Die Aristotelische Theorie der Möglichkeitsschlüsse, Berlin, 1933.

The double arrow $\Leftrightarrow$ was first used in 1954 by Nicholas Bourbaki, in: Theorie des ensembles, 3rd edition, Paris, 1954 (see page I.30).

The symbol $\equiv$ for the bi-conditional was firstly used by Gottlob Frege (1848–1925) into his 1879 Begriffsschrift and subsequently "popularized" by Alfred North Whitehead and Bertrand Russell's Principia Mathematica (1910-1913).

Principia uses $=$ followed by Df. on the right-end of the formula for definitional identity.(see page 11 and 15).

We can find the usage of $=_{Def}$ already into Cesare Burali-Forti, Logica Matematica (1894), that uses $=$ for (logical) equivalence (see page 26):

$(a=b) =_{Def} (a \supset b) . (b \supset a)$.