This paper is about the use of analogical reasoning, models and metaphors in Galileo's discovery of the mountains of the moon, which he describes in the Starry Messenger, a short but groundbreaking treatise published in 1610. On the basis of the observations of the Moon he has made with the newly invented telescope, Galileo shows that the Moon has mountains and that therefore it shares the same solid, opaque and rugged nature of the Earth. I will first reconstruct Galileo's reasoning, and illustrate the counterintuitive and quasi-circular way in which discovery depends on analogy: in order for analogical reasoning to succeed in bridging ontological gaps and thus serve as a discovery tool, a certain similarity between what are considered as radically different domains has to be presupposed. More particularly, in order for analogical reasoning to lead to genuine discoveries, salient features have to be selected in the source domain that will be mapped onto the target domain. There is disagreement as to how this mapping is successfully carried out: the syntactical (Dedre Gentner), pragmatic (Paul Thagard) and ontological-categorical (Rom Harré) approaches, all illuminate some features of this selection in the mapping process. On the basis of an analysis of Galileo's discovery, I will argue that we need a different "bootstrapping" approach which involves the construction of an imaginary temporary model encompassing both the source and the target domains, and which is occasionally strengthened by metaphors which serve as incomplete transitional models.