[58] It may be noticed that the differential method of parallax (chapter VI., [§ 129]), by which such a quantity as 12′ could have been noticed, was put out of court by the general supposition, shared by Coppernicus, that the stars were all at the same distance from us.
[59] There is little doubt that he invented what were substantially logarithms independently of Napier, but, with characteristic inability or unwillingness to proclaim his discoveries, allowed the invention to die with him.
[60] A similar discovery was in fact made twice again, by Galilei (chapter VI., [§ 114]) and by Huygens (chapter VIII., [§ 157]).
[61] He obtained leave of absence to pay a visit to Tycho Brahe and never returned to Cassel. He must have died between 1599 and 1608.
[62] He even did not forget to provide one of the most necessary parts of a mediæval castle, a prison!
[63] It would be interesting to know what use he assigned to the (presumably) still vaster space beyond the stars.
[64] Tycho makes in this connection the delightful remark that Moses must have been a skilled astronomer, because he refers to the moon as “the lesser light,” notwithstanding the fact that the apparent diameters of sun and moon are very nearly equal!
[65] By transversals.
[66] On an instrument which he had invented, called the hydrostatic balance.
[67] A fair idea of mediaeval views on the subject may be derived from one of the most tedious Cantos in Dante’s great poem (Paradiso, II.), in which the poet and Beatrice expound two different “explanations” of the spots on the moon.