A mechanical reduction gear for a turbine engine, in particular for an aircraft, this reduction gear comprising: - a sun gear mobile in rotation about an axis and comprising an external toothing comprising two series of adjacent teeth, - a stationary ring gear which extends around the axis and which carries an internal toothing comprising two series of teeth (90d1, 90d2), this stationary ring gear being configured to be secured to a stator of the turbine engine, and - planet gears which are meshed with the sun gear and the stationary ring gear, the planet gears being carried by a planet carrier which is mobile in rotation about the axis and each of the planet gears having a meshing dual-stage and comprising a first external toothing of mean diameter D1 and comprising two series of adjacent teeth (82a, 82b), and a second external toothing of mean diameter D2, different from D1, and comprising two series of teeth (84a, 84b), the two series of teeth (82a, 82b) of the first toothing of each of the planet gears being meshed with the two series of teeth (82a, 82b) of the toothing of the sun gear, characterised in that it further comprises: - a mobile ring gear which extends about the axis and which carries an internal toothing with two series of adjacent teeth (190d1, 190d2), this mobile ring gear being independent of the stationary ring gear and being configured so as to be secured to a rotor of the turbine engine, each of the planet gears being meshed with the sun gear and the stationary and mobile ring gears (90, 190), in that all the series of teeth (82a, 82b, 90d1, 90d2, 190d1, 190d2) are arranged symmetrically with respect to a median plane perpendicular to the axis, and in that the mobile ring gear comprises two half ring gears (190a, 190b) secured to each other and respectively carrying the two series of teeth (190d1, 190d2), these two series of teeth being meshed with the two series of teeth (82a, 82b) of the first toothing of each of the planet gears and the stationary ring gear comprising two rings (90a, 90b) disposed on each side of the mobile ring gear and respectively carrying the two series of teeth (90d1, 90d2), these two series of teeth being meshed with the two series of teeth (84a, 84b) of the second toothing of each of the planet gears. - a sun gear mobile in rotation about an axis and comprising an external toothing comprising two series of adjacent teeth, - a stationary ring gear which extends around the axis and which carries an internal toothing comprising two series of teeth (90d1, 90d2), this stationary ring gear being configured to be secured to a stator of the turbine engine, and - planet gears which are meshed with the sun gear and the stationary ring gear, the planet gears being carried by a planet carrier which is mobile in rotation about the axis and each of the planet gears having a meshing dual-stage and comprising a first external toothing of mean diameter D1 and comprising two series of adjacent teeth (82a, 82b), and a second external toothing of mean diameter D2, different from D1, and comprising two series of teeth (84a, 84b), the two series of teeth (82a, 82b) of the first toothing of each of the planet gears being meshed with the two series of teeth (82a, 82b) of the toothing of the sun gear, - a mobile ring gear which extends about the axis and which carries an internal toothing with two series of adjacent teeth (190d1, 190d2), this mobile ring gear being independent of the stationary ring gear and being configured so as to be secured to a rotor of the turbine engine, each of the planet gears being meshed with the sun gear and the stationary and mobile ring gears (90, 190), in that all the series of teeth (82a, 82b, 90d1, 90d2, 190d1, 190d2) are arranged symmetrically with respect to a median plane perpendicular to the axis, and in that the mobile ring gear comprises two half ring gears (190a, 190b) secured to each other and respectively carrying the two series of teeth (190d1, 190d2), these two series of teeth being meshed with the two series of teeth (82a, 82b) of the first toothing of each of the planet gears and the stationary ring gear comprising two rings (90a, 90b) disposed on each side of the mobile ring gear and respectively carrying the two series of teeth (90d1, 90d2), these two series of teeth being meshed with the two series of teeth (84a, 84b) of the second toothing of each of the planet gears. in that all the series of teeth (82a, 82b, 90d1, 90d2, 190d1, 190d2) are arranged symmetrically with respect to a median plane perpendicular to the axis, and in that the mobile ring gear comprises two half ring gears (190a, 190b) secured to each other and respectively carrying the two series of teeth (190d1, 190d2), these two series of teeth being meshed with the two series of teeth (82a, 82b) of the first toothing of each of the planet gears and the stationary ring gear comprising two rings (90a, 90b) disposed on each side of the mobile ring gear and respectively carrying the two series of teeth (90d1, 90d2), these two series of teeth being meshed with the two series of teeth (84a, 84b) of the second toothing of each of the planet gears.