508 
Gregory, 1668, he was elected a fellow of the Royal Society, and 
James. 
laid before them an account of a dispute in Italy rela- 
tive to the Earth’s motion, which Riccioli and his fol- 
lowers had denied. About this time also he engaged 
in a dispute with the celebrated Huygens through the 
medium of the Philosophical Transactions. oo 
published in the Journal des Sgavans, July 2d 1668, 
some animadversions on Gregory’s quadrature of the cir- 
cle, and particularly objected \to the proposition which 
stated, the impossibility of expressing perfectly the area 
of a circle in any known algebraical form besides that 
ef an infinite converging series. Gregory defended 
himself in the 37th Number of the Philosophical Trans« 
actions, and the dispute was carried on with considers 
able warmth by both parties. The whole, of the con- 
troversy will be found in Huygens’ Opera Varia, vol. ii. 
. 463. 
2? In 1668, Gregory published in London his Exerci- 
tationes Geometric, a small work of twenty-six pages, 
which contains the following subjects: 
Appendicula ad verum Circuli et Hyperbole: Quadra- 
turam. 
N. Mercatoris Quadratura Hyperbole Geometrice 
demonstrata, 
Analogia inter Lineam Meridianam Planispherii Nau- 
tici et Tangentes Artificales Geometrice demonstrata ; 
seu quod secantium. Naturalium additio efficiat Tan- 
gentes Artificiales, 
Item, Quod Tangentium Naturalium additio efficit 
Secantes Artificiales. 
Quadratura Conchoidis. 
Quadratura Cissoidis. 
Methodus Facilis et Accurata componendi Secantes 
et Tangentes Artificiales. 
The preface to this work, and the introduction to the 
Appendicula, &c, are remarkably interesting, in so far as 
they throw considerable light on the dispositions of our 
author. He speaks with'great severity of the jealousy and 
injustice of his contemporaries, and alludes 'to the treat= 
ment which he had received from Huygens. In the in- 
troduction to the Appendicula, he resumes this subject 
with more keenness. He declares, that Huygens had 
accused him of ignorance and plagiarism ; and after ar- 
guing against Huygens’ claim to the discovery, he con- 
cludes with this remarkable passage: * At parum re- 
fert quis sit ejus primus inventor, satis enim constat me 
primum esse publicatorem ; neque: mihi esset» difficile 
affirmare (si modo mentiri vellem) me ante 20 annos 
illam cognovisse: utcunque sit, conabor hic circuli et 
hyperbole quadraturam ad talem perfectionem promo- 
vere, ut Hugenius prolem suam vix cognoscat.’” 
Mr Gregory was about this time elected professor of 
mathematics in the university of St Andrew’s. In 1669, 
he married the daughter of George Jamieson, the cele- 
brated Scottish painter, by whom he had a son, James, 
the father of Dr John Gregory, (the subject of a suc- 
ceeding article,) and two daughters. In August 1672, 
he began a correspondence with his friend Mr Collins, 
relative to the comparative merits of his own telescope, 
and that of Sir Isaac Newton. The sentiments of the 
two philosophers were communicated to each other by 
their respective friends, and the dispute was thus car- 
ried on in the mést amicable manner. The corre- 
spondence has been published by Dr Desaguliers, at the 
end of his edition of Dr Davi 3 . 
and Dioptries. sae es tee heen 
GREGORY. - 
In the year 1669, awotk was published:at Rotter. 
dam, by Mr George Sinclair, professor of i 
the university of Glasgow, entitled Ars nova et Ma 
Gravitatis et Levitatis ; and another work on hydrosta« 
tics, by the same author, appé red at Edinburgh. in 
1672. Mr Sinclair had been dismissed from his pro- 
fessorship soon after the restoration, on account of his 
political principles, and had given offence to the Royal 
Society of London, by charging them with negli 
and. re anne axa ewe mane acted im 
erly tow: one r *s es, and 
serie incurred the displeasure of iat ont ician. 
Inthe year 1672; G ry, under the assumed name of 
Patrick Mathers, archbedal to the university of St 
Andrew’s, attacked Sinclair in a tract, entitled The great 
and new art of weighing Vanity, or a discovery of the 
Ignorance and Arrogance of the great and new Artist, 
in his rea ical writings. .To this work is 
annex ‘entamina de motu t et projectorum.. > 
In 1674, was ‘called to the mathematical 
chair in the university of Edinburgh, a situation which 
he did not live long to enjoy. In the month of Octoe . 
ber 1675, when mtr eee | home from su , he 
was struck suddenly blind, and expired a few days af= . 
terwards, in the 36th year of his age. 13% 
The following is a list of the inventions and disco 
veries of James Gregory, as given by Dr Hutton. The 
reflecting telescope ; burning mirror;* quadrature of 
the circle, ellipse, and hyperbola ; method for the trans- 
mutation of curves ; geometrical demonstration of Lord 
Brouncker’s series for squaring the hyperbola ; demon- 
stration that the-meridian line is analogous toa scale of 
logarithmic ents, of the half complements of the 
latitude ; a simple converging series for making loga- 
rithms; solution of the famous Keplerian problem, by 
an infinite series ; method of drawing tangents to curves 
geometrically, without previous calculation ; a rule for 
the direct and inverse method of tangents, depends 
ing'on the principle of exhaustions; a series for the 
length of the are of a circle fromthe tangent, and vice _ 
versa, and also for the secant and logarithmic 
and secant and vice versa ; and serieses for the length 
of the elliptic and. bolic curves. See Hutton’s 
Mathematical ‘Dictionary, 2d edition, p. 601, &c. and 
the other works quoted in the article. 
GREGORY, Davin, Dr, a celebrated astronomer 
and mathematician, was the nephew of the subject of 
the preceding article, and the eldest son of David Gre- 
ry of Kinnairdie. “He was born at Aberdeen in the 
year 1661, and after receiving his education at the 
grammar ‘school of that town, he went to Edinburgh 
for the purpose of completing his studies. In 1684, 
when he was only 23 years of age, he was appointed 
professor of mathematics in the university of Edinburgh, 
and in the same year he published his work, entitled, 
Exercitatio Geometrica de Dimensione Figurarum sive 
specimen ‘methodi generalis Dimetiendi is figuras. 
Mr Gregory having found among his uncle’s papers par« 
ticular examples of infinite series, without any of the 
methods, proposes in this treatise to explain,a method 
which may suit the examples given by his uncle; and 
he does this by applying the principles of indivisibles, 
and the arithmetic of infinites, to particular cases inhy- 
perbolas, ‘parabolas, ellipses, spirals, cycloids, conchoids, 
and cissoids, He also explains several methods of redu~ 
cing compound quantities into infinite series, so that 
* See our article Burnixe InstRuMENTS, Vol vp. 134 
