The Collaborative International Dictionary of English v.0.48:

Incompossible \In`com*pos"si*ble\, a. [Pref. in- not +
   compossible: cf. F. incompossible.]
   Not capable of joint existence; incompatible; inconsistent.
   [Obs.]
   [1913 Webster]

         Ambition and faith . . . are . . . incompossible.
                                                  --Jer. Taylor.
   -- In`com*pos`si*bil"i*ty, n. [Obs.]
   [1913 Webster]

The Devil's Dictionary (1881-1906):

INCOMPOSSIBLE, adj.  Unable to exist if something else exists.  Two
things are incompossible when the world of being has scope enough for
one of them, but not enough for both -- as Walt Whitman's poetry and
God's mercy to man.  Incompossibility, it will be seen, is only
incompatibility let loose.  Instead of such low language as "Go heel
yourself -- I mean to kill you on sight," the words, "Sir, we are
incompossible," would convey and equally significant intimation and in
stately courtesy are altogether superior.