The method which was used in a preceding article for the analytical evaluation of Gaussian path-integrals in one euclidean dimension is generalized. As before, the final results are formulae directly applicable to all Gaussian path-integrals, this time in two and in three euclidean dimensions, respectively. The classical action is almost entirely integrated, and the proportionality factor F( t b , t a ) in front of the exponential part is expressed in terms of a number of time-dependent functions which one encounters in the description of the motion along the classical path. The quadratic Lagrange function is kept as general as possible, e.g., involving twenty-eight terms in the three-dimensional case. The well-known time-discretization procedure for path-integrals has been avoided. Instead, one of the main steps in the theoretical development consists in applying the convolution property of quantum-mechanical Green's functions, i.e., in three euclidean dimensions, K( r b,t b; r a,t a)=∫∫ ∫ −∞ +∞ K( r b,t b; r ,t)K( r ,t; r a,t a) d r . This equality leads to a non-linear algebraic relation between F( t b , t a ), F( t b , t) and F( t, t a ). The solution of this equation yields the F-factor which appears in the propagator represented by the Gaussian path-integral. At two locations, the use of some remarkable determinantal identity, previously unknown to the author, has been indispensable in order to attain the desired final result. In the Appendix, the “ n-dimensional” generalization of these identities is formulated.