We show how, via T duality, intersecting D brane configurations in ten
(six) dimensions can be obtained from the elementary D-brane configur
ations by embedding a type IIB D-brane into a type IIB nine-brane (fiv
e-brane) and give a classification of such configurations. We show tha
t only a very specific subclass of these configurations can be realize
d as (supersymmetric) solutions to the equations of motion of IIA or I
IB supergravity. Whereas the elementary D-brane solutions in d=10 are
characterized by a single harmonic function, those in d=6 contain two
independent harmonic functions and may be viewed as the intersection o
f two d=10 elementary D-branes. Using string-string-string triality in
six dimensions we show that the heterotic version of the elementary d
=6 D-brane solutions correspond in ten dimensions to intersecting Neve
u-Schwarz-Neveu-Schwarz (NS-NS) strings or five-branes and their T dua
ls. We comment on the implications of our results in other than ten an
d six dimensions.