HISTORICAL VIEW OF THE

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A comparison of the Alphonsine tables with those ofPtolemy really evinces but a very slight advance in thescience during the eleven centuries intervening. Science,in fact, had not yet begun effectually to awake from thetorpor in which it had so long lain. And it was nottill nearly 200 years later that any very decided resultsof such renovation were perceptible.

The first dawn of improvement may be recognisedin the labours and designs of George Purbach, professor of astronomy at Vienna , about the year 1450. Heundertook to amend the astronomical tables then in use,and felt the necessity for an accurate translation ofPtolemy . Since the very faulty one of Gerard, anotherhad been made from the Greek, by George of Trebi-zond, which appears to have been little better. Pur-bach , however, does not seem to have realised thisdesign. He did effect some improvements in the tablesof the planets ; but the amendments thus introducedwere, perhaps, more than counterbalanced by his ad-herence to the ridiculous notion of trepidation. Themost essential service which he rendered to science wasthe formation of a table of sines upon a decimal divisionof the radius, now for the first time employed.

But these and other similar projects for the improve-ment both of pure mathematics and astronomy, werecarried on with still greater zeal and success by Mullerof Konigsberg (born in 1436), more commonly knownby the latter appellative, latinized, after the fashion ofthe day, into the sonorous title of Regiomontanus . Tohim we owe many translations and commentaries, toge-ther with several original and valuable works. Trigo-nometry, which (as we have remarked) had never beenknown to the Greeks as a separate science, and whichtook that form in Arabia, advanced in the hands ofRegiomontanus to a great degree of perfection, andapproached very nearly to the condition which it hasattained at the present day. He also introduced thatsimple but most valuable modification of the decimalnotation, which consists in fixing the unit’s place at any