Motivated by the recent advances in the Internet of Things (IoT) and in Wireless Power Transfer (WPT), we study a network architecture that consists of power beacons (PBs) and passive backscatter nodes (BNs). The PBs transmit a sinusoidal continuous wave (CW) and the BNs reflect back a portion of this signal while harvesting the remaining part. A BN harvests energy from multiple nearby PBs and modulates its information bits on the composite CW through backscatter modulation. The analysis poses real challenges due to the double fading channel, and its dependence on the PPPs of both the BNs and PBs. However, with the help of stochastic geometry, we derive the coverage probability and the capacity of the network in tractable and easily computable expressions, which depend on different system parameters. We observe that the coverage probability decreases with an increase in the density of the BNs, while the capacity of the network improves. We further compare the performance of this network with a regular powered network in which the BNs have a reliable power source and show that for a very high density of the PBs, the coverage probability of the former network approaches that of the regular powered network.