Both Pappus and Proclus call him Menelaus of Alexandria (Heath 260), so we may expect that he invested a portion of his energy in Rome, and quite a bit of his time in Alexandria. To the Vietnam veteran thank you. He composed a six-book treatise on harmonies, which was referenced by Theon of Alexandria, however those books have all been lost.
The third book contains trigonometric proportions. To the Vietnam veteran thank you. The main suggestion in the third book is Menelaus’ hypothesis with reference to a round triangle and any transversal (incredible circle) cutting the sides of a triangle.