Complex sentence: He shows that these curves have an odd number of crossings with the curves generated in the same way for a perpendicular line; therefore, there always exists at least one crossing, which forms the center of a rhombus inscribed in the given curve.
Split into simpler sentences: He shows that, when these curves are intersected with the curves generated in the same way for a perpendicular line, there are an odd number of crossings. Therefore, there always exists at least one crossing, which forms the center of a rhombus inscribed in the given curve.