From Gauss' Disquisitiones Arithmeticae §131:
Sī p est numerus prīmus fōrmae 4n+1, erit +p, sī vērō p fōrmae 4n+3, erit -p residuum vel nōn-residuum cuiusvīs numerī prīmī quī positīvē acceptus ipsīus p est residuum vel nōn-residuum.
(I have taken the liberty to add macrons.)
From what I know about this theorem, that is called quadratic reciprocity nowadays, the translation should roughly be:
If
p
is a prime number of the form4n+1
, letp*
denote+p
; otherwise ifp
is of the form4n+3
, letp*
denote-p
; thenp*
is a [quadratic] residue (resp. non-residue) of whichever prime numberq
that is a [quadratic] residue (resp. non-residue) of this veryp
.
(I have added p*
as an intermediate definition to make the sentence flow better in English.)
The last sentence can also be rephrased as:
p*
is a quadratic residue ofq
iffq
is a quadratic residue ofp
.
However, I do not understand where the phrase positīvē acceptus
fits in this translation.