Treasure of the ancients
It's ironic that most of the men who participated in the "scientific revolution", whose contributions seem so original and innovative, were themselves convinced that they were merely re- discovering the vast body of pristine knowledge that had been possessed by the ancients, but somehow lost and forgotten during the centuries that came to be called the "dark ages" of western civilization. This was not an entirely unreasonable belief, because the great works, both material and intellectual, of the classical civilizations were very imposing. The intellectual culture of Western Europe really did decline during the fall of Rome, and the institutions for preserving and passing along knowledge, as well as the inclination to do so, were severely diminished. Then, after so long an absence, when the ancient texts were re-discovered, the scholars of the Renaissance and later periods were acutely aware of their intellectual inferiority vis-à-vis "the ancients". Also, the fact that many of the ancient texts were now available only in fragmentary form, often in third- hand translations, and many of the references were to works totally unknown and presumably lost, contributed to the impression that the ancients had known far more, if we could only find it out.
This attitude toward the past is, in some ways, the exact opposite of our usual view today, which is of a totally ordered sequence of eras progressing from less knowledge in the past to more knowledge in the future. It's hard for us to imagine, today, the intellectual climate among people who believed they were scientifically and mathematically inferior to their ancestors in the distant past. Interestingly, this peculiar historical circumstance undoubtedly contributed to the unique flourishing of intellectual affairs in Western civilization that occurred soon after the ancients had been re-discovered. Part of the psychological impetus came from the great appreciation they felt for recorded knowledge, and the esteem they had for the great thinkers of antiquity. Also, the enduring value of the recorded knowledge and the kind of immortality it gave to the authors, surviving a millennium of neglect only to be more wondered at when finally re-discovered, was a source of immense fascination, and inevitably tempted men to participate in the process, even if only (at first) by translating and copying the great works.
The early 16th century discovery of the general solution of cubic polynomials is regarded by some people as a significant turning point in scientific history, because this was the first time a "modern" man made a significant discovery that went beyond the ancient knowledge. Needless to say, there were acrimonious disputes between Cardano, Ferro, Tartaglia about who deserved to be credited with this discovery. The tantalizing prospect of "bettering" the ancients was thus raised, and was an incredibly powerful incentive for making intellectual discoveries. Of course, far more important for convincing Europeans that it was possible to know more than the ancients was the discovery of The New World, beginning with Columbus's voyage in 1492, a world of which the ancients had not even dreamed.
Nevertheless, the belief that the ancients had possessed a vast body of knowledge, of which we have only fragments and scattered hints, persisted. As late as the 1600's men like Fermat were developing their original ideas in the form of speculative "reconstructions" of lost works from antiquity. For example, Fermat completed a re-construction of Appolonius' lost work on "Plane Loci", and Fermat himself said that this effort led directly to his development of what we now call analytic geometry.