[393] Campbell’s Specimens of British Poets, vol. i.
Mathematics. 71. The progress of mathematical science was regular, though not rapid. We might have mentioned before the gnomon erected by Toscanelli in the cathedral at Florence, which is referred to 1468; a work, it has been said, which, considering the times, has done as much honour to his genius as that so much renowned to Bologna at Cassini.[394] |Regiomontanus.| The greatest mathematician of the fifteenth century, Muller, or Regiomontanus, a native of Königsberg, or Königshoven, a small town in Franconia, whence he derived his latinised appellation, died prematurely, like his master Purbach, in 1476. He had begun at the age of fifteen to assist the latter in astronomical observations; and having, after Purbach’s death, acquired a knowledge of Greek in Italy, and devoted himself to the ancient geometers, after some years spent with distinction in that country, and at the court of Mathias Corvinus, he settled finally at Nuremberg; where a rich citizen, Bernard Walther, both supplied the means of accurate observations, and became the associate of his labours.[395] Regiomontanus died at Rome, whither he had been called to assist in rectifying the calendar. Several of his works were printed in this decade, and among others his ephemerides, or calculations of the places of the sun and moon, for the ensuing thirty years; the best, though not strictly the first, that had been made in Europe.[396] His more extensive productions did not appear till afterwards; and the 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. 72. Though the arts of delineation do not properly come within the scope of this volume, yet, so far as they are directly instrumental to science, they ought not to pass unregarded. Without the tool that presents figures to the eye, not the press itself could have diffused an adequate knowledge either of anatomy or of natural history. As figures cut in wooden blocks gave the first idea of letter-printing, and were for some time associated with it, an obvious invention, when the latter art became improved, was to arrange such blocks together with types in the same page. We find, accordingly, about this time, many books adorned or illustrated in this manner; generally with representations of saints, or other ornamental delineations not of much importance; but in a few instances with figures of plants and animals, or of human anatomy. The Dyalogus creaturarum moralizatus, of which the first edition was published at Gouda, 1480, seems to be nearly, if not altogether, the earliest of these. It contains a series of fables with rude woodcuts, in little more than outline. A second edition, printed at Antwerp in 1486, repeats the same cuts, with the addition of one representing a church, which is really elaborate.[399]
[399] Both these editions are in the British Museum. In the same library is a copy of the exceedingly scarce work, Ortus Sanitatis. Mogunt. 1491. The colophon, which may be read in De Bure (Sciences, No. 1554), takes much credit for the carefulness of the delineations. The wooden cuts of the plants, especially, are as good as we usually find in the sixteenth century; the form of the leaves and character of the plant are generally well preserved. The animals are also tolerably figured, though with many exceptions, and, on the whole, fall short of the plants. The work itself is a compilation from the old naturalists, arranged alphabetically.
Maps. 73. The art of engraving figures on plates of copper was nearly coëval with that of printing, and is due either to Thomas Finiguerra about 1460, or to some German about the same time. |Geography.| It was not a difficult step to apply this invention to the representation of geographical maps; and this we owe to Arnold Buckinck, an associate of the printer Sweynheim. His edition of Ptolemy’s geography appeared at Rome in 1478. These maps are traced from those of Agathodæmon in the fifth century; and it has been thought that Buckinck profited by the hints of Donis, a German monk, who himself gave two editions of Ptolemy not long afterwards at Ulm.[400] The fifteenth century had already witnessed an increasing attention to geographical delineations. The libraries of Italy contain several unpublished maps, of which that by Fra Mauro, a monk of the order of Camaldoli, in the convent of Murano, near Venice, is the most celebrated. It is still preserved there, and is said to attest the cosmographical science of its delineator, such as he could derive from Ptolemy, and from the astronomy of his own age.[401] Two causes, besides the increase of commerce, and the gradual accumulation of knowledge, had principally turned the thoughts of many towards the figure of the earth on which they trod. Two translations, one of them by Emanuel Chrysoloras, had been made early in the century, from the cosmography of Ptolemy; and from his maps the geographers of Italy had learned the use of parallels and meridians, which might a little, though inadequately, restrain their arbitrary admeasurements of different countries.[402] But the real discoveries of the Portuguese on the coast of Africa, under the patronage of Don Henry, were of far greater importance in stimulating and directing enterprise. In the academy founded by that illustrious prince, nautical charts were first delineated in a method more useful to the pilot, by projecting the meridians in parallel right lines,[403] instead of curves on the surface of the sphere. This first step in hydrographical science entitles Don Henry to the name of its founder. And though these early maps and charts of the fifteenth century are to us but a chaos of error and confusion, it was on them that the patient eye of Columbus had rested through long hours of meditation, while strenuous hope and unsubdued doubt were struggling in his soul.