# Negativus and positivus

When, if ever, did the adjectives negativus and positivus evolve into an antonym pair like the English "negative" and "positive", and how did positivus get this meaning? Deriving negativus from the verb negare produces something that should be close to the English adjective "negative", and this indeed seems to be the case. On the other hand, positivus comes from ponere, and it is not clear how and why it would come to mean "positive". Negare is obviously a "no"-verb, but ponere does not look like a "yes"-verb to me. Is this meaning of positivus (and the pairing with negativus) classical or a later development?

The use of “positive” and “negative” as opposites is surprisingly modern. It seems to have originated (or at least been popularised) in the context of modern (i.e., 17th-century) mathematics with the distinction of positive and negative numbers. “Positive” numbers are numbers that you can posit, put on the table, observe as objective reality. “Negative” numbers negate the corresponding positive numbers (positive 1 plus negative 1 makes zero). A century later we get also "positive" and "negative" electricity.

Here are two early examples from the OED:

1685 J. Hawkins Cocker's Decimal Arithm. iii. 217: The first figure of every logarithme..sheweth the Nature of the number by it signified, viz. whether it be positive, or negative.

1704 J. Harris Lexicon Technicum I: Positive Quantities in Algebra, are such as are of a Real and Affirmative Nature, and either have, or are supposed to have the Affirmative or Positive Sign + before them.

and this from CNRTL:

1761 électricité positive (Euler, Lettres à une Princesse d'Allemagne, éd. Cournot, t.2, p.116)

• +1. Interesting (especially since I'm a mathematician)! Can you cite or quote some mathematical texts for early uses "positive" and "negative"? Aug 29, 2016 at 14:21
• According to L&S, the original opposition was between positivus and naturalis. My suspicion is that the opposition of positive/negative comes from logic: a positive proposition posits something, a negative one negates something. Aug 29, 2016 at 14:33
• @JoonasIlmavirta. I have added some quotations. The one from 1704 is especially interesting, as the author explicitly defines "positive" as "real and affirmative".
– fdb
Aug 29, 2016 at 14:46
• @brianpck. I think that there is actually a direct reversal of meaning: positivus starts off meaning "artificial" and ends up meaning "real".
– fdb
Aug 29, 2016 at 14:50