M U L L E R. 
length procured a great number of manufcripts, and 
being weary of warrdering about, as well as releafed from 
his attendance on Beflarion, who was conltantly employed 
on foreign legations, he returned to Vienna, and for 
fome time delivered mathematical leftures in that city. 
While he was thus occupied, he was perfuaded to re¬ 
move to Buda, on the invitation of Matthias king of 
Hungary, who had a high reputation as a warrior and as 
a lover of letters and the Iciences. This prince accom¬ 
panied his invitation with rich prefents, and a promife of 
an annual penfion of two hundred pieces of gold. But 
what chiefly induced Regiomontanus to accept the king’s 
offer was his defire of having accefs to the rich and noble 
library which Matthias had founded at Buda; in which he 
had placed all the Greek books that he could purchafe 
after the lacking of Conftantinople, as well as at Athens, 
and wherever elle they could be met with throughout the 
Turkilli dominions. Our mathematician was received at 
Buda with great diftinftion ; and was frequently honoured 
with a feat at the king’s table, who exprelfed much fatif- 
faftion at hearing his learned difcourfes. He was alfo 
particularly noticed by the archbifhop of Strigonia, who 
made him many prefents, and at whofe requeft he drew 
up his “ Tables of Direftions for Regiomontanus, 
profoundly as he was verfed in the principles of genuine 
fcience, had not furmounted the prejudices of his age in 
favour of judicial aftrology. See, on this fubjeft, Sibly’s 
Aftrology, p.457-608. 12th edit. 1817. 
In the year 14.71, a war having broken out between the 
king of Hungary and the Bohemians, our author pru¬ 
dently determined to avoid the threatening ftorm; and, 
after obtaining the king’s leave to retire to fome place 
where he might purfue his ftudies in tranquillity, he with¬ 
drew to Nuremberg in Franconia, and fixed his refidence 
in that city. The reafons, as he himfelf tells us, which 
induced him to fettle in this place, were, its vicinity to 
his native country, the peculiar dexterity of the Nurem¬ 
berg artifls in fabricating his aftronomical machines, 
and the facility with which he might maintain a cor- 
refpondence with foreign countries, by means of the mer¬ 
chants in that commercial city. Being now well Ikiiled 
in all the branches of learning, and of the mathematical 
Iciences, he determined to employ himfelf in making 
aftronomical obfervations, and alfo in publifhing the belt 
of the ancient authors, as well as the rel'ults of his own 
labours. With this defign he began to fet up a printing- 
houfe, and formed a nomenclature of the books intended 
by him for publication, which is Hill extant. The fame 
or Regiomontanus had reached Nuremberg long before 
his fettlement there ; and, after he had taken up his abode 
among them, the citizens jultly regarded him as an orna¬ 
ment to their city. Among others, one of the principal 
of that clafs, who was rich, and well-fkilled in the fci- 
ences, particularly aftronomy, cultivated an intimacy w ith 
our mathematician ; and, as foon as he was appriled of 
the laudable defigns which he had in view, he took upon 
himfelf the expenfe of conftrufiting the neceffary aftro¬ 
nomical inftruments, and of erecting a printing-houfe. 
With regard to his printing-houfe, as foon as it was com¬ 
pleted, Muller put to prefs two works of his own, and two 
others. The latter were, the “ New Theories” of his 
mafter Purbach, and the “ Aftronomics” of Manilius. 
His own produdtions were, the “ New Calendar,” and 
his “ Ephemerides.” In the former are given, as he 
fays in the nomenclature above mentioned, “ the true 
oppofitions and conjunctions of the luminaries; delinea¬ 
tions of their eclipfes; the true places of the luminaries 
every day; the difference of the hours, equinoctial and 
temporal, &c.” Of his “ Ephemerides” he fays in the 
fame' nomenclature, that it is “ what is vulgarly called 
an almanac for thirty years; where you may every day 
fee the true motion of all the planets, of the head of the 
lunar dragon, together with the aipeCts of the moon to 
the fun and planets, and the hours of thofe afpeCts noted ; 
hilly, the eclipfes of the luminaries, if any ihould here¬ 
179 
after happen, are defcribed in their places; and in the 
fronts of the pages are marked the latitudes.” So accept¬ 
able was this work at that time, that every copy was fold 
for twelve hundred pieces of gold, and it was eagerly 
purchafed by perfons of all nations. He likewife pub- 
lilhed mod acute “ Commentaries on Ptolemy’s Alma- 
geft:” a work which cardinal Beflarion valued fo highly, 
that he fcrupled not to pronounce it worth a whole pro¬ 
vince. He alfo prepared new verfions of Ptolemy’s Cof- 
mography; and, at his leifure hours, examined and ex¬ 
plained works of another nature. He inquired how high 
the vapours are carried above the earth ; which he fixed 
to be not more than twelve German miles. After mak¬ 
ing obfervations on two comets which appeared in 1471 
and 1472, he publiflied his Treatife “ Concerning the true 
Place and Magnitude of Comets.” 
In the year 1474, pope Sixtus IV. entertained a defign 
of reforming the calendar; and, conceiving Regiomon¬ 
tanus to be the moll proper and able perfon for accom- 
plilhing fuch an undertaking, he lent for him to Rome. 
To induce him the more readily to accept the invitation, 
his holinefs made him magnificent promifes; and, as aa. 
earneft of his future favours, nominated him for the pre- 
fent bilhop of Ratilbon. Regiomontanus was for fome 
time in fufpenfe, before he could prevail with himfelf to 
accept the invitation; but the importunity and authority 
of the pope prevailed, and he confented, though not with¬ 
out great regret, to relinquifh his employments at Nu¬ 
remberg. He repaired to Rome in the year 1475: but 
died in that city about the end of July 1476; not with¬ 
out fufpicions of having been poil'oned by the fons of 
George of Trebifond, out of revenge for the death of 
their father, which was laid to have been haftened by the 
mortification which he felt on account of the criticifms 
made by our author on his tranflation of Ptolemy’s Alma- 
geft. Regiomontanus died at the age of forty years and one 
month; and, as it was the fubjeftof aftonilhment that he 
could undertake fo many and fuch prodigious works in 
fo Ihort a l'pace of time, fo his death w’as attended with 
univerfal lamentation for the lofs of fuch an extraordinary- 
man. He was buried in the Pantheon, and his memory 
was celebrated by the belt poets of the times. 
It may be proper here to obferve, that Purbach was 
the firft mathematician who reduced the trigonometrical 
tables of fines, from the old fexageiimal divifion of the 
radius, to the decimal fcale. The project of Purbach was 
perfected by Regiomontanus, who not only extended the 
fines to every minute, the radius being 600,000, as de- 
figned by Purbach, but afterwards, difliking that fcheme, 
as evidently imperfect, he computed them likewife to the 
radius 1,000,000 for every minute of the quadrant. Re¬ 
giomontanus alfo introduced the tangents into trigo¬ 
nometry, the canon of which he called fcecundus, becaufe 
of the great many advantages arifing from them. Belides 
thefe things, he enriched trigonometry with many theo¬ 
rems and precepts. Indeed, excepting for the ufe of loga¬ 
rithms, the trigonometry of Regiomontanus is but little 
inferior to that of our own time. His Treatife on Plane 
and Spherical Trigonometry, in five books, was written 
about the year 1464, and printed in folio at Nuremberg 
in 1553. In the fifth book are various problems con¬ 
cerning redtilinear triangles, fome of which are refolved 
by means of algebra: a proof that this fcience was not 
wholly unknown in Europe before the treatife of Lucas 
de Burgo. Regiomontanus was author of fome other 
works befides thofe already mentioned: and, of his me¬ 
chanical projects, we are told by Peter Ramus, that in 
his worklhop at Nuremberg there was an automaton in 
perpetual motion: that he made an artificial fly, which, 
taking its flight from his hand, would fly round the 
room, and at laft return to his mailer’s hand; that he 
fabricated an eagle, which, on the emperor’s approach to 
the city, he fent out, high in the air, a conliderable 
diftance to meet him, and that it kept him company to 
the very gates of tli£ city. “ Let us no more wonder,” 
adds 
