Standing on the Shoulders of Giants

After writing my previous post about tattoos in ancient languages, a former student reminded me that I also helped her track down a Latin text she wanted to have inked.  She wanted to use the phrase found in one of Newton's letters to Hooke, "If I have seen further it is by standing on the shoulders of giants."  This is a funny phrase, one that gets repeated a lot and that has a number of variants. For example, Didacus Stella writes (In Luc. 10 tom. 2) 

Pygmaei Gigantum humeris impositi plusquam ipsi gigantes vident

("Pygmies, placed on the shoulders of Giants, see further than the Giants themselves."  See footnote 20 of Alexandre Koyré's "An Unpublished Letter of Robert Hooke to Isaac Newton," Isis, Vol 43, No. 4 (Dec., 1952), pp312-33, U of Chicago Press.)

It's a funny phrase because it can be used both boastfully and self-deprecatingly.  Newton, in his letter to Hooke, for instance, seems to boast that he sees farther than Hooke, but that he does so as a dwarf.

It also appears in Bernard of Chartres, quoted by John of Salisbury in his Metalogicon.  One source I found has John saying this:

Dicebat Bernardus Carnotensis nos esse quasi nanos, gigantium humeris incidentes, ut possimus plura eis et remotiora videre, non utique proprii visus acumine, aut eminentia corporis, sed quia in altum subvehimur et extollimur magnitudine gigantea. Et his facile acquieverim, quia artis praeparatitia et multos articulos veritatis tradunt artium praeceptores, etiam in introductionibus suis, aeque bene antiquis, et forte commodius. 

("Bernard of Chartres used to say that we are like dwarves, incidentes on the shoulders of giants, so that we might see more than they, and things further off...")

That word incidentes bothered me, though, as did the genitive plural gigantium. Now, I am more of a Hellenist than a Latinist, so if you spot any errors in what I say here, I would be grateful for your corrections.  Gigas is a loan word from Greek, which might explain the two different genitive plurals, Gigantum being correct, but Gigantium appearing to follow the rules.  Incidentes just sounds funny, as though the dwarves had fallen upon the Giants - though it could indicate that the dwarves were fortunate enough to stumble upon the Giants; incido can have that meaning, after all.  But another text I have found has insidentes, which makes more sense to me, meaning "sitting upon" or "standing upon."

As I said in my previous post, I am reluctant to take the responsibility for others' tattoos, but I have tentatively suggested that

NANI GIGANTUM HUMERIS INSIDENTES  

might fit the bill for her, "Dwarves standing upon the shoulders of giants."  If your Latin is better than mine, I welcome your corrections, especially before she makes this a permanent part of her skin.