The triple-differential dijet cross-section, d^3 sigma_{ep}/dQ2 dE_t2 dxgjets, is measured with the H1 detector at HERA as a function of the photon virtuality Q^2, the fraction of the photon's momentum carried by the parton entering the hard scattering, xgjets, and the square of the mean transverse energy, E_t2, of the two highest E_t jets. Jets are found using a longitudinal boost-invariant k_T clustering algorithm in the gamma* p center of mass frame. The measurements cover the ranges 1.6 < Q^2 < 80 GeV$^2 in virtuality and 0.1 < y < 0.7 in inelasticity y. The results are well described by leading order QCD models which include the effects of a resolved component to the virtual photon. Models which treat the photon as point-like fail to describe the data. An effective leading order parton density for the virtual photon is extracted as a function of the photon virtuality, the probing scale and the parton momentum fraction. The x_gamma and probing scale dependences of the parton density show characteristic features of photon structure, and a suppression of this structure with increasing Q^2 is seen.
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