Dioptrics

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...ous original: "plicium"; completing the word "simplicium" (simple) from the previous page's "varietatum." varieties of simple lenses original: "perspicillorum"; in this context, Kepler refers specifically to convex and concave lenses used in spectacles.; both so that Dioptrics might be in some way complete, and because the principles of the Instrument the telescope are tied to the human eye, and the instrument itself is composed of simple lenses: so that one cannot be explained without the other. Finally, because some judged that I had treated these matters too obscurely in the Optics referring to his 1604 work Ad Vitellionem paralipomena.; so that for many, it was not a dullness of mind, but the fault of the teacher that acted as a barrier, preventing them from perceiving what was written and demonstrated.

Therefore, to look out for them, I have presented some things here more briefly, others more extensively, and conceived some in different words; I have reviewed the definitions of terms, which I use with geometrical freedom original: "geometrica libertate"; the practice of a mathematician defining terms specifically for the scope of their own proofs., in continuous numbering among the propositions at appropriate places; I have added more diagrams (which are the genuine letters of Geometers original: "Geometrarum"; meaning mathematicians who specialize in geometry.). By which effort, if I have not removed every obscurity, I hope that students of Philosophy will grant some indulgence to my weakness and will take this effort in good part.

Furthermore, I devoted myself to this concern at that time above all when my mind, numbed by a certain lamentable cold Kepler may be referring to personal grief or the literal winter of 1610-1611, during which his wife and son fell ill., was warmed by the most generous Sun of Your Most Reverend and Serene Highness's presence, and His most merciful conversations and frequent encouragements, like some Mercury the messenger of the gods, often associated with intellectual stimulation., roused me from sleep. Finally, [I was inspired by] the most delightful and simultaneously most ingenious hand-operated machines original: "machinamenta manuaria"; specialized lathes or tools for grinding glass. of His Noble Mathematician and Chamberlain, Lord Johannes Zuckmesser, and the most skillful polishing of glasses, by which [Your] Reverend Serene Highness...