treatise on triangles, the most celebrated, not till 1533. The solution of the more difficult cases, both in plane and spherical trigonometry, is found in this work; and with the exception of what the science owes to Napier, it may be said, that it advanced little for more than two centuries after the age of Regiomontanus.[397] Purbach had computed a table of sines to a radius of 600,000 parts. Regiomontanus, ignorant, as has been thought, which appears very strange, of his master’s labours, calculated them to 6,000,000 parts. But perceiving the advantages of a decimal scale, he has given a second table, wherein the ratio of the sines is computed to a radius of 10,000,000 parts, or, as we should say, taking the latter as unity, to seven places of decimals. He subjoined what he calls Canon Fæcundus, or a table of tangents, calculating them, however, only for entire degrees to a radius of 100,000 parts.[398] It has been said, that Regiomontanus was inclined to the theory of the earth’s motion, which indeed Nicolas Cusanus had already espoused. [394] This gnomon is by much the loftiest in Europe. It would be no slight addition to the glory of Toscanelli if we should suppose him to have suggested the discovery of a passage westward to the Indies in a letter to Columbus, as his article in the Biographie Universelle seems to imply. But the more accurate expressions of Tiraboschi, referring to the correspondence between these great men, leave Columbus in possession of the original idea, at least concurrently with the Florentine astronomer, though the latter gave him strong encouragement to persevere in his undertaking. Toscanelli, however, had, on the authority of Marco Polo, imbibed an exaggerated notion of the distance eastward to China; and consequently believed, as Columbus himself did, that the voyage by the west to that country would be far shorter than, if the continent of America did not intervene, it could have been. Tiraboschi, vi. 189, 207. Roscoe’s Leo X., ch. 20. [395] Walther was more than a patron of science, honourable as that name was. He made astronomical observations, worthy of esteem relatively to the age. Montucla, i. 545. It is to be regretted that Walther should have diminished the credit due to his name by withholding from the public the manuscripts of Regiomontanus, which he purchased after the latter’s death; so that some were lost by the negligence of his own heirs, and the rest remained unpublished till 1533. [396] Gassendi, Vita Regiomontani. He speaks of them himself, as quas vulgo vocant almanach; and Gassendi says, that some were extant in manuscript at Paris, from 1442 to 1472. Those of Regiomontanus contained eclipses, and other matters not in former almanacs. [397] Hutton’s Logarithms, Introduction, p. 3. [398] Kästner, i. 557. |Arts of delineation.|