GREGORY. 
« Geometric Pars Universalis, ins-erviens 
Quantitatum Curvarum, Transmutatiom et 
Mbiisutsk” ■ in which he is allowed to have 
shown, for the first time, a method for the 
transmutation of curves. These works en- 
gaged the notice, and procured the author 
the correspondence of the greatest mathe- 
maticians of the age, Newton, Huygens, 
Wallis, and others. An account of this 
piece was also read before the Royal Soci- 
ety, of which Mr. Gregory, being returned 
from his travels, was chosen a member the 
same year, and communicated to them an 
account of a controversy in Italy about 
the motion of the earth, which was denied 
by Riccioli, and his followers. Through 
this channel, in particular, he carried on a 
dispute with M. Huygens, on the occasion 
of his treatise on the quadrature of the 
circle and hyperbola, to which that great 
man had started some objections ; in the 
course of which our author produced some 
improvements of his series. But in this 
dispute it happened, as it generally does on 
such occasions, that the antagonists, though 
setting out with temper enough, yet grew 
too warm in the combat. This was the 
case here, especially on the side of Gre- 
gory whose defence was, at his own re- 
quest, inserted in the Philosophical Transac- 
tions. It is unnecessary to enter into parti- 
culars : suffice it therefore to say that, in the 
opinion of Leibnitz, who allows Mr. Gre- 
gory, the highest merit for his genius and 
discoveries, M. Huygens has pointed out, 
though not errors, some considerable defici- 
encies in the treatise above-mentioned, and 
shown a much simpler method of attaining 
the same end. 
In 1688, our author published at London 
another work, entitled “ Exercitationes 
Geometric*, ” which contributed still much 
further to extend his reputation. About 
this time lie was elected Professor of Ma- 
thematics in the University of St. Andrew’s, 
an office which he held for six years. Du- 
ring his residence there he married, in 1669, 
Mary, the daughter qf George Jameson, 
the celebrated painter, whom Mr. Wal- 
•pole has termed the Vandyke of Scotland, 
and who was fellow-disciple with that great 
artist in the school of Rubens, at An- 
twerp. 
In 1672, he published “ The great and 
new Art of weighing Vanity : or a Discovery 
of the Ignorance and Arrogance of the great 
and new Artist, in his pseudo-philosophical 
Writings. By M. Patrick Mathers, Arch- 
bedal to the University of St. Andrews. 
To which are annexed some Tentamina d<* 
Motu Penduli et Projectorum.” Under 
this assumed name, our author wrote this 
little piece to expose the ignorance of Mr. 
Sinclare, professor at Glasgow, in his hy- 
drostatical writings, 'and in return for some 
ill usage of that author to a colleague of 
Mr. Gregory’s. The same year Newton, 
on his wonderful discoveries in the nature 
of light, having contrived a new reflecting 
telescope, and made several objections to 
Mr. Gregory’s, this gave birth to a dispute 
between those two philosophers, which 
was carried on during this and the follow- 
ing year, in the most amicable manner on 
both sides ; Mr. Gregory defending his 
own construction, so far as to give his anta- 
gonist the whole honour of having made the 
catoptric telescopes preferable to the diop- 
tric, and showing that the imperfections in 
these instruments were not so much owing 
to a defect in the object speculum, as to 
the different refrangibility of the rays of 
light. — In the course of this dispute our 
author described a burning concave mirror, 
which was approved by Newton, and is 
still in good esteem. Several letters that 
passed in this dispute, are printed by Dr. 
Desaguliers, in an appendix to the English 
edition of Dr. David Gregory’s “ Elements 
of Catoptrics and Dioptrics.” 
In 1674, Mr. Gregory was called to 
Edinburgh, to fill the chair of mathematics 
in that university. This place he had held 
but little more than a year, when in Octo- 
ber 1675, being employed in shewing the 
satellites of Jupiter through a telescope to 
some of his pupils, he was suddenly struck 
with total blindness, and died a few days 
after, to the great loss of the mathematical 
world, at only 37 years of age. 
As to his character, Mr. James Gregory 
was a man of very acute and penetrating 
genius. His temper seems to have been 
warm, as appears from his conduct in the 
dispute with Huygens : and conscious per- 
haps of his own merits as a discoverer, he 
seems to have been jealous pf losing any 
portion of his reputation by the improve- 
ments of others upon his inventions. He 
possessed one of the most amiable charac- 
ters of a true philosopher, that of being 
content with his fortune in his situation. 
But the most brilliant part of his charac- 
ter is that of his mathematical genius as an 
inventor, which was of the first order ; as 
will appear by the following list of his in- 
ventions and discoveries. Among many 
others may be reckoned his reflecting teles- 
