Terahertz (THz) communications have naturally promising physical layer security (PLS) performance in the angular domain due to the high directivity feature brought by the ultra-massive multiple-antenna techniques. However, traditional multiple-antenna techniques fail to combat eavesdroppers residing in the THz beam sector, even when the communication distances of legitimate users and eavesdroppers are different. This THz range security challenge motivates us to study new multiple-antenna techniques to provide THz range and angular security. In this paper, we first conduct a theoretical analysis of the secrecy capacity of the multiple antenna channel under the range security scenario. Based on this, the frequency diverse array, as a candidate multiple-antenna technique, is proven ineffective in addressing the range security problem. Then, motivated by the theoretical analysis, a novel widely-spaced array and beamforming design for THz range security are proposed, which realize communications in the near-field regions. A non-constrained optimum approaching (NCOA) algorithm is developed to achieve the optimal secrecy rate. Simulation results illustrate that under the range security scenario where the eavesdropper is inside the beam sector, our proposed widely-spaced antenna communication scheme can ensure a 6 bps/Hz secrecy rate when the transmit power is 10 dBm and the propagation distance is 10 m.