28. Purbach, or Peurbach, native of a small Austrian town of that name, has been called the first restorer of mathematical science in Europe. Ignorant of Greek, and possessing only a bad translation of Ptolemy, lately made by George of Trebizond,[342] he yet was able to explain the rules of physical astronomy and the theory of the planetary motions far better than his predecessors. But his chief merit was in the construction of trigonometrical tables. The Greeks had introduced the sexagesimal division, not only of the circle, but of the radius, and calculated chords according to this scale. The Arabians, who, about the ninth century, first substituted the sine, or half chord of the double arch, in their tables, preserved the same graduation. Purbach made one step towards a decimal scale, which the new notation by Arabic numerals rendered highly convenient, by dividing the radius, or sinus totus, as it was then often called, into 600,000 parts, and gave rules for computing the sines of arcs; which he himself also calculated, for every minute of the quadrant, as Delambre and Kästner think, or for every ten minutes, according to Gassendi and Hutton, in parts of this radius. The tables of Albaten the Arabian geometer, the inventor, as far as appears, of sines, had extended only to quarters of a degree.[343] [342] Montucla, Biogr. Univ. It is however certain, and is admitted by Delambre, the author of this article in the Biog. Univ., that Purbach made considerable progress in abridging and explaining the text of this translation, which, if ignorant of the original, he must have done by his mathematical knowledge. Kästner, ii. 521. [343] Montucla, Hist. des Mathématiques, i. 539. Hutton’s Mathematical Dictionary, and his Introduction to Logarithms. Gassendi, Vita Purbachii. Biogr. Univ. Peurbach (by Delambre). Kästner, Geschichte der Mathematik, i. 529-543, 572; ii. 319. Gassendi twice gives 6,000,000 for the parts of Purbach’s radius. None of these writers seem comparable in accuracy to Kästner. |Other mathematicians.|