Tentative Response--Huygens Method

Huygens is said to present a version of the 'hypothetico-deductive model' of building and understanding nature. What are the elements of such a model, and how does it differ from other possible strategies?

In his preface to the Treatise on Light, Christiaan Huygens provides a brief (but dense) explanation of his model for understanding nature, focusing on light and colors. He writes that “whereas the Geometers prove their Propositions by fixed and incontestable Principles, here the Principles are verified by the conclusions to be drawn from them; the nature of these things not allowing of this being done otherwise.” I found this sentence to be perhaps the most important in the preface. Huygens uses Geometry to illustrate his own method by presenting the two as opposites. Huygens presents the study of Geometry as I commonly think about math; you use mathematical “facts”, or proven theories, to prove your solution to a mathematical problem. Huygens, on the other hand, showcases his own method as the invert of this process. Huygens does not use Principles (the theories) to prove his observations, but instead verifies the Principles themselves by conducting experiments with results that correspond to a hypothesis based off of them. He writes, “It is always possible to attain […] scarcely less than complete proof […] when things which have been demonstrated by the Principles that have been assumed correspond perfectly to the phenomena which experiment has brought under observation; especially when there are a great number of them, and […] when one can imagine […] new phenomena which ought to follow from the hypotheses”. It seems that Huygens employs a method in which the scientist undergoes experiments based on hypotheses that he assumes should follow the Principles in order to prove them. But why does Huygens state that his observations could be “done otherwise”? Is it because theories about the nature of light have not yet been proven, so the “Geometric” method is not possible? Or is it because the Principles he bases his hypotheses off of are not specific enough?