ADVERB (2)

1. extremely;
- Example: "it was positively monumental"

2. so as to be positive; in a positive manner;
- Example: "she intended her remarks to be interpreted positively"

The Collaborative International Dictionary of English v.0.48:

Positively \Pos"i*tive*ly\, adv.
   In a positive manner; absolutely; really; expressly; with
   certainty; indubitably; peremptorily; dogmatically; --
   opposed to negatively.
   [1913 Webster]

         Good and evil which is removed may be esteemed good or
         evil comparatively, and positively simply. --Bacon.
   [1913 Webster]

         Give me some breath, some little pause, my lord,
         Before I positively speak herein.        --Shak.
   [1913 Webster]

         I would ask . . . whether . . . the divine law does not
         positively require humility and meekness. --Sprat.
   [1913 Webster]

   Positively charged or Positively electrified (Elec.),
      having a charge of positive electricity; -- opposed to
      negatively charged.
      [1913 Webster]

WordNet (r) 3.0 (2006):

positively
    adv 1: extremely; "it was positively monumental"
    2: so as to be positive; in a positive manner; "she intended her
       remarks to be interpreted positively"

Moby Thesaurus II by Grady Ward, 1.0:

135 Moby Thesaurus words for "positively":
   OK, Roger, absolutely, actually, affirmatively, all right, alright,
   alrighty, amen, and no mistake, as you say, assertively, assuredly,
   at all events, at any rate, aye, beyond question, by all means,
   categorically, certainly, clearly, da, de facto, dead, decidedly,
   decisively, declaratively, definitely, demonstrably, directly,
   distinctly, doubtless, doubtlessly, emphatically, even, exactly,
   expressly, faithfully, fine, for a certainty, for a fact,
   for certain, for real, for sure, forsooth, genuinely, good,
   good enough, hear, in actuality, in all conscience,
   in all respects, in effect, in every respect, in fact, in reality,
   in truth, indeed, indeedy, indisputably, indubitably,
   ipsissimis verbis, ja, just, just so, literally, literatim,
   mais oui, manifestly, most assuredly, most certainly, naturally,
   naturellement, nothing else but, noticeably, observably, obviously,
   of course, okay, oui, patently, plumb, point-blank, precisely,
   predicatively, quite, rather, really, right, righto, rigidly,
   rigorously, sensibly, seriously, square, squarely, straight,
   strictly, sure, sure thing, surely, to a certainty, to be sure,
   to the letter, truly, unambiguously, undeniably, under oath,
   undeviatingly, undoubtedly, unequivocally, unerringly,
   unmistakably, unquestionably, verbally, verbatim,
   verbatim et litteratim, verily, veritably, very well, visibly,
   well and good, why yes, with emphasis, without doubt, word by word,
   word for word, yea, yeah, yep, yes, yes indeed, yes indeedy,
   yes sir, yes sirree