GREGORY. 
~e ope ; burning 1 concave mirror ; quadrature 
of the circle and hyperbola, by an infinite 
converging series ; his method for the trans- 
formation of curves; a geometrical demon- 
stration of Lord Brounkers’ series for squar- 
ing the hyperbola ; bis demonstration that 
the meridian line is analogous to a scale of 
logarithmic tangents of the half-comple- 
ments of the latitude ; he also invented and 
demonstrated geometrically, by help of the 
hyperbola, a very simple converging series 
for making the logarithms ; he sent to Mr. 
Collins the solution of the famous Keplerian 
problem by an infinite series ; he discover- 
ed a method of drawing tangents to curves 
geometrically, without .any previous calcu- 
lations ; a rale for the direct and inverse 
method of tangents, which stands upon the 
same principle (of exhaustions) with that 
of fluxions, and differs not much from it 
in the manner of application ; a series' for 
the length of the arc of a circle, from the 
tangent, and vice versa. These, with 
others for measuring the length of the el- 
liptic and hyperbolic curves, were sent to 
Mr. Collins, in return for some received 
from him of Newton’s, in which he follow- 
ed the elegant example of this author, in 
delivering his series in simple terms, inde- 
pendently of each other. These and other 
writings of our author are mostly contained 
in the following works, viz. : 1 , Optica 
Promota; 4to. London, 1663. 2. Vera 
Circuli et Hyperbolae Quadrature, 4to. 
Padua, 1667 and 1668. 3. Geometri® 
Pars Universalis, 4to. Padua, 1668. 4. Ex- 
ercitationes Geometric®, 4to. London 1668. 
ft- The great and ne\y Art of weighing Va- 
nity, 8vo. Glasgow, 1672. The rest of his 
inventions make the subject of several let- 
ters and papers, printed either in the Phi- 
los. Trans, vol. iii., the Commerc. Epistol. 
•Toh. Collins, et alibrum, 8vo. 1715, in the 
appendix to the Rnglislj edition of Dr. Da. 
vid Gregory’s Elements of Optics, 8vo. 
1735, by Dr, besagulieus, and some series 
in the Exercitatio Geometries pf the same 
author, 4to. 1684, Edinburgh ; qs well as 
in his little piece on Practical Geometry. 
Gregory (T)r. David,) Savilian pro- 
fessor of astronomy, at Oxford, w^s ne- 
phew of the above-mentioned Mr. James 
Gregory, being the eldest son of his bro- 
ther, Mr. David Gregory, of Kinardie, a 
gentleman who had the singular fortune to 
see three of his sons all professors of mathe- 
matics, at the same time, in three of the 
British universities, viz. our author David 
at Oxford, the second son James, at Edin- 
burgh, and, the third son Charles at St. An- 
drew’s. Our author David, the eldest son, 
was born at Aberdeen, in 1661, where he 
received the early parts of his education, 
but completed his studies at Edinburgh : 
and, being possessed of the mathematical 
papers of his uncle, soon distinguished him- 
self likewise as the heir of his genius. In 
the 23d year of his age, he was elected pro- 
fessor of mathematics in the university of 
Edinburgh ; and, in the same year he pub- 
lished “ Exercitatio Georaetrica de Dimen- 
sione Figurarum, sive Specimen Methodi 
generalis dimetiendi quasvis Figures, Edinb 
1684, 4to. He very soon perceived the 
excellence of the Newtonian philosophy, 
and had the merit of being the first that in- 
troduced it into the schools, by his public 
lectures at Edinburgh. “ He had (says Mr. 
W his ton in the Memoirs of his own life i. 
32.) already caused several of his scholars 
to keep acts, as we call them, upon several 
branches of the Newtonian philosophy ; 
while we, at Cambridge, poor wretches, 
were ignominiously studying the fictitious 
hypothesis of the Cartesian.’! ' 
In 1691, on the report of Dr. Bernard’s 
intention of resigning the Savilian profes'- 
sorship of astronomy, at Oxford, our author 
went to London ; and being patronised by 
Newton, and warmly befriended by Mr, 
Flamstead, the astronomer royal, he ob- 
tained the vacant professorship, thoudi Dr. 
Halley was a competitor. This rirelship", 
however, instead of animosity, laid the foun- 
dation of friendship between these eminent 
men; and Halley soon after became the 
colleague of Gregory, by obtaining the Pro- 
fessorship of Geometry in the same univer- 
sity. Soon after his arrival in London, 
Mr. Gregory had been elected a Fellow of 
the Royal Society; and previously to his 
election into the Savilian Professorship, had 
the degree of Doctor of Physic conferred 
on him by the university of Oxford. 
In 1693, he published in the Philos. 
Trans, a solution of the Florentine pro- 
blem, “ De Testudine veliformi quadrabili ;” 
and he continued to communicate to the 
public, from time to time, many ingenious 
mathematical papers by the same channel. 
1695, he printed at Oxford, “Catoptric® 
et Dioptric® Sphwric® Elemepta,” a work 
which we are informed, in the preface, con- 
tains the substance of some of his public 
lectures read at Edinburgh eleven years 
before. This valuable treatise was repub- 
lished in English, first with additions by 
Dr. William Brown, with the recommends- 
