1. An X-ray positioning apparatus that controls a patient platform by use of an X-ray image so as to position a diseased site of a patient at a radiation irradiation position planned in a treatment plan, the X-ray positioning apparatus comprising: an X-ray video device that obtains first X-ray image data outputted from an X-ray detector for detecting an X-ray radiated by an X-ray tube and generates second X-ray image data in which a respiratory signal related to respiration of the patient and the first X-ray image data are related to each other; a positioning computer that compares a diseased site in the second X-ray image data with a diseased site in a reference image, which is a positioning reference, calculates a postural correction amount in such a way that an actual posture coincides with a posture in the treatment plan, and then generates patient platform control data for controlling the patient platform; and a photographing trigger generation apparatus that outputs a photographing trigger signal for radiating X-rays in accordance with two or more frame rates to the X-ray tube, based on the respiratory signal and a frame rate control signal including photographing conditions for consecutively photographed images in the first X-ray image data, wherein the photographing trigger generation apparatus generates the photographing trigger signal, in accordance with a first frame rate and a second frame rate that is higher than the first frame rate, and wherein the positioning computer generates the patient platform control data, based on the reference image and one X-ray image selected from the consecutively photographed images, in the second X-ray image data, that are photographed at the second frame rate.