GREGORY. 



oned his reflecting telescope ; burning 

 "concave mirror; quadrature of the circle 

 and hyperbola, by an infinite converging 

 aeries ; his method for the transformation 

 of curves; a geometrical demonstration 

 of Lord Brounker's series for squaring 

 the hyperbola; his demonstration that 

 the meridian line is analogous to a scale 

 of logarithmic tangents of the half-com- 

 plements of the latitude : he also invent- 

 ed, and demonstrated geometrically, by 

 help of the hyperbola, a very simple con- 

 verging series for makingthe logarithms : 

 he sent to Mr Collins the solution of the 

 famous Keplerian problem by an infinite 

 series ; he discovered a method of draw- 

 ing tangents to curves geometrically, 

 without any previous calculations; a rule 

 for the direct and inverse method of tan- 

 gents, which stands upon the same prin- 

 ciple (of exhaustions) with that of flux- 

 ions, and differs not much from it in the 

 manner and application ; a series for the 

 length of the arc of a circle, from the 

 tangent, and vice versa. Tkese, with 

 others for measuring the length of the 

 elliptic and hyperbolic curves, were sent 

 to Mr. Collins, in return for some receiv- 

 ed from him of Newton's, in which he 

 followed the elegant example of this au- 

 thor, in delivering his series in simple 

 terms, independently of each other. 

 These, and other writings of our author, 

 are mostly contained in the following 

 works, viz. : 1. Optica Promota ; 4to. Lon- 

 don, 1663. 2. Vera Circuli et Hyperbo- 

 lae Quadratura, 4to. Padua, '667 and 

 1668. 3. Geometric Pars Universalis, 

 4to. Padua, 1668. 4. Exercitationes Geo- 

 metricse, 4to. London, 1668. 5. The 

 great and new Art of weighing Vanity, 

 8vo. Glasgow, 1672. The rest of his in- 

 ventions make the subject of several let- 

 ters and papers, printed either in the Phi- 

 los. Trans, vol. iii., the Commerc. Epis- 

 tol. Joh. Collins, et aliorum, 8vo. 1715, in 

 the appendix to the English edition of 

 Dr. David Gregory's Elements of Optics, 

 8vo. 1735, by Dr. Desaguliers, and some 

 series in the Exercitatio Geometrica of 

 the same author, 4to. 1684, Edinburgh ; 

 as well as in his little piece on Practical 

 Geometry. 



GREGORY (DR. DAVID), Savilian profes- 

 sor of astronomy, at Oxford, was nephew 

 of the above-mentioned Mr. James Gre- 

 gory, being the eldest son of his brother, 

 Mr. David Gregory of Kinardie, a gen- 

 tleman who had the singular fortune to 

 see three of his sons all professors of ma- 

 thematics, at the same time, in three of 

 the British universities, viz. our author 



David at Oxford, the second son James at 

 Edinburgh, and the third ?on Charles at 

 St. Andrew's. Our author David, the eld- 

 est 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 himselflikewise as the heir 

 of his genius. In the 23d year of his age 

 he was elected professor of mathematics 

 in the University of Edinburgh : and in 

 the same year he published " Exercitatio 

 Geometrica de Dimensione Figurarunr, 

 sive Specimen Methodi generalis dime- 

 tiendi quasvis Figuras," Edinb. 1684, 4to. 

 He very soon perceived the excellence 

 of the Newtonian philosophy, and had 

 the merit of being the first that intro- 

 duced it into the schools, by his public 

 lectures at Edinburgh " He had (says 

 Mr. Whitson, 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 stu- 

 dying the fictitious hypothesis of the Car- 

 tesian." 



In 1691, on the report of Dr. Bernard's 

 intention of resigning the Savilian pro- 

 fessorship of astronomy at Oxford, our 

 author went to London ; and being pa- 

 tronised by Newton, and warmly be- 

 friended by Mr Flamstead, the astrono- 

 mer royal, he obtained the vacant pro- 

 fessorship, though Dr. Halley was a com- 

 petitor. This rivalship, however, instead 

 of animosity, laid the foundation of friend- 

 ship between these eminent men ; and 

 Halley soon after became the colleague 

 of Gregory, by obtaining the Professor- 

 ship of Geometry in the same university. 

 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 Professor- 

 ship, 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 quadra- 

 bili ; *' and he continued to communicate 

 to the public, from time to time, many in- 

 genious mathematical papers by the same 

 channel. 



1695, he printed at Oxford, Catop- 

 tricae et Dioptrics Sphxricae Elementa," 

 a work, which, we are informed, in the 

 preface, contains the substance of some 

 of his public^lectures read at Edinburgh 



