In densely populated-cities, the use of private cars for personal transportation is unsustainable, due to high parking and road capacity requirements. The mobility-on-demand systems have been proposed as an alternative to a private car. Such systems consist of a fleet of vehicles that the user of the system can hail for one-way point-to-point trips. These systems employ large-scale vehicle sharing, i.e., one vehicle can be used by several people during one day and consequently, the fleet size and the parking space requirements can be reduced, but, at the cost of a non-negligible increase in vehicles miles driven in the system. The miles driven in the system can be reduced by ridesharing, where several people traveling in a similar direction are matched and travel in one vehicle. We quantify the potential of ridesharing in a hypothetical mobility-on-demand system designed to serve all trips that are currently realized by private car in the city of Prague. Our results show that by employing a ridesharing strategy that guarantees travel time prolongation of no more than 10 minutes, the average occupancy of a vehicle will increase to 2.7 passengers. Consequently, the number of vehicle miles traveled will decrease to 35% of the amount in the MoD system without ridesharing and to 60% of the amount in the present state.