Over the past half-century, numerous attempts have been made to derive the centripetal acceleration formula by treating circular motion as a superposition of uniform and accelerated rectilinear motions over short time intervals. Critical examination reveals that these methods are manifestations of the same approach pioneered by Huygens to understand circular motion. Each attempt, however, has pedagogical weaknesses and ambiguities that go unnoticed due to the use of infinitesimals. These weaknesses and ambiguities have likely contributed to the lack of appreciation for this approach among physics educators. This paper offers a unified review of these studies and suggests a refinement using Galileo's superposition principle explicitly, aiming to revitalize interest in the approach among physics educators, particularly those teaching centripetal acceleration in algebra-based undergraduate physics courses.