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figure, and not necessarily at the right hand, by placingthere a comma, all arithmetical operations going onjust the same ; in a word, the use of decimal fractions.This, indeed, gives the scale its full extent, and conferson numerical computation the utmost degree of simpli-city and enlargement which it seems capable of attaining.The Latin translation of Ptolemy’s Almagest , designedby Purbach , and perhaps commenced by him, was com-pletely executed by Regiomontanus : who added alsoa commentary and a number of problems and illustra-tions. He greatly improved the tables of sines, andadded one of tangents. He appears to have been per-suaded of the reality of the earth’s motion, though hedid not advance to a recognition of the entire solarsystem. He constructed a planetarium, which is de-scribed as exciting great wonder. He also calculatedephemerides of the places of the planets for many yearsin advance. His skill in practical mechanics was suchas to give him in that ignorant age a reputation formiraculous powers; and marvellous things are recordedof the automatons which he constructed. He certainlycontributed much to the improvement of clocks in theimperfect form in which they were then made beforethe application of the pendulum. His high reputationinduced pope Sixtus IV., to request his attendance atRome to assist in a projected reform of the calendar.Arriving at that city, he had not been long engaged inthe preliminaries of the work, when he was carried offby an epidemic disorder in the prime of life [1476],and w'as honoured with a public funeral in the Pan-theon. He died amidst innumerable projects for theadvancement of the sciences, which he had enriched byproductions evincing a genius of the first order, coupledwith the most earnest zeal in the cause, and an inde-fatigable perseverance in pursuing its most laboriousdetails.

The labours of Purbach and Regiomontanus formthe link between the astronomy of the middle ages andi S