"By the help of Microscopes, there is nothing so small, as to escape our inquiry; hence there is a new visable World discovered to the understanding" (Describing the benefit to science of the new instrument)
"We have the opportunity of observing her through these delicate and pellucid teguments of the bodies of Insects acting according to her usual course and way, undisturbed, whereas when we endeavour to pry into her secrets by breaking open the doors upon her, and dissecting and mangling creatures whil'st there is life yet within them, we find her indeed at work, but put into such disorder by the violence offer'd, as it may easily be imagined how differing a thing we should find, if we could, as we can with a Microscope, in these smaller creatures, quietly peep in at the windows, without frighting her out of her usual byas" (This illustrates Hooke's Deist beliefs, that evidence of God can be seen in the natural wonders of the world. He argues that studying living creatures under the microscope is more respectful to Nature, and also a better way of observing life, than dissection. John Toland (1670-1722) later coined the term Pantheism to describe this set of beliefs)
Another famous quote not specifically related to microscopes is:
"The truth is, the Science of Nature has been already too long made only a work of the Brain and the Fancy: It is now high time that it should return to the plainness and soundness of Observations on material and obvious things" (This describes how scientific enquiry can get lost in the esoteric and perhaps limited to the study of scholars and academics only. The interest of amateurs observing the world and of inexperienced scientists also has a place as science is practical and inspired at heart)
Robert Hooke not only invented the microscope but his also famous for his Law regarding the physics of springs. Also, by the use of his microscope, he was the first scientist able to observe what he called 'cells' (from the latin cella meaning 'small room'). As well as mechanics and microscopy, he also studied in detail gravitation, palaentology (fossils), astronomy and memory
"For the Members of the Assembly having before their eyes so many fatal Instances of the errors and falshoods, in which the greatest part of mankind has so long wandred, because they rely'd upon the strength of humane Reason alone, have begun anew to correct all Hypotheses by sense, as Seamen do their dead Reckonings by Clestial Observations; and to this purpose it has been their principal indeavour to enlarge and strengthen the Senses by Medicine, and by such outward Instruments as are proper for their particular works." The microscope was certainly one of the "outward instruments" to which Robert Hooke refers.
As the inventor of the microscope, Hooke had the first opportunity to see what life there was in matter that humans previously had not been able to observe. Hook said, "By this the Earth it self, which lyes so near us, under our feet, shews quite a new thing to us, and in every little particle of its matter, we now behold almost as great a variety of Creatures, as we were able before to reckon up in the Whole Universe it self...."
Nature is rarely predictable, and Hooke knew this. He also understood that a good scientist cannot ignore anomalies to suit existing theories. "The footsteps of Nature are to be traced, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in endeavouring to avoid our discovery."
As mathsworkmusic mentioned, Hooke studied fossils. He defends the validity of such studies when he says, "If the finding of Coines, Medals, Urnes, and other Monuments of famous Persons, or Towns, or Utensils, be admitted for unquestionable Proofs, that such Persons or things have, in former Times, had a being, certainly those Petrifactions may be allowed to be of equal Validity and Evidence, that there have been formerly such Vegetables or Animals. These are truly Authentick Antiquity not to be counterfeited, the Stamps, and Impressions, and Characters of Nature that are beyond the Reach and Power of Humane Wit and Invention, and are true universal Characters legible to all rational Men."