"But where were all the " learned calculators of the 16th and 17th centuries," whom Dr Hutton pictures as evolving the Logarithms by profound reasonings upon the doctrine of progressions? And who were they? Not Kepler, who, when he first heard of Napier's method, could hardly form an accurate idea of its meaning. Not Tycho, nor Longomontanus, nor Galileo, nor any one of Kepler's numerous correspondents, including... nearly all the learned calculators of the period. ...Kepler, who to his dying day never ceased to marvel at the achievement, seems a little excited by discovering that one other person had actually approached the theory without being aware of it. In his Rudolphine Tables... 1627, he remarks,"the accents in calculation led Justus Byrgius on the way to these very Logarithms many years before Napier's system appeared; but being an indolent man, and very uncommunicative, instead of rearing up his child for the public benefit, he deserted it in the birth."This was the result of Kepler's indefatigable inquiries, for nine years... and... it amounts to this, that Byrgius had made some observations upon the adaptation of an arithmetical to a geometrical progression, very naturally occurring to him in trigonometrical calculations. The Apices Logistici ["accents in calculation"], to which Kepler alludes, are those accents which the Greeks used... to change the value or mark the order of a symbol, as we use the cypher; and this is... exemplified in their sexagesimal division of the circle still in use, where the accents ′, ″, ′″, ″″, &c. of minutes, seconds, thirds, fourths, &c. are an arithmetical progression denoting the fractional orders, the values of which descend in a ratio of 60, and form the corresponding geometrical progression."