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362 years before Napier did; but, as is always the case with that remarkable man, without securing the priority by a timely publication. At Uraniborg the method did not make any progress after the departure of Wittich, and it is therefore more likely that it was he, and not Tycho, who was the inventor, as he is known to us (through the repeated testimony of Tycho) as an able mathematician. In 1591 a short treatise on plane and spherical trigonometry was drawn up at Uraniborg, but it does not indicate that Tycho had developed trigonometry in any way, as the rules are similar to those given in other treatises of that day, and are frequently expressed in even clumsier language than usual at that time. The demand for the facilities offered by the Prostaphæresis was, however, so great, that Reymers Bär, Clavius, Joestelius, Magini, and others, with more or less success, continued to work in this direction, until the method was driven from the field by the discovery of Napier.

We have followed Tycho Brahe through his chequered career, and we have reviewed his scientific labours. No doubt his contemporaries were not uninfluenced in their estimation of him by his princely residence, with its tasteful decoration and wonderful observatories, and also by its singular situation on the little island, which contributed to exhibit the noble astronomer in a romantic light. But while these circumstances threw a halo over Tycho even before his works had become known beyond a limited circle, posterity has hardly been influenced by considerations like these when