GREGORY, James, one of the most eminent mathematicians of the 17th century, was a son of the Rev. Mr John Gregory minister of Drumeak in the county of Aberdeen, and was born at Aberdeen in 1638. His mother was a daughter of Mr David Anderson of
VOL. X. Part I.
Finzaugh, a gentleman who possessed a singular turn for mathematical and mechanical knowledge. This mathematical genius was hereditary in the family of the Andersons, and from them seems to have been transmitted to their descendants of the name of Gregory. Alexander Anderson, cousin-german of the above-mentioned David, was professor of mathematics at Paris in the beginning of the 17th century, and published there in 1612, Supplementum, Apollonii redivivi, &c. The mother of James Gregory inherited the genius of her family; and observing in her son, while yet a child, a strong propensity to mathematics, she instructed him herself in the elements of that science. He received his education in the languages at the grammar-school of Aberdeen, and went through the usual course of academical studies in the Marischal college.
At the age of 24 he published his treatise, entitled Optica Promota, seu abditæ radiorum reflexorum et refractorum mysteria, geometrice enucleata; cui subnectitur appendix subtilissimorum astronomiæ problematum resolutionem exhibens, London 1663: a work of great genius, in which he gave the world an invention of his own, and one of the most valuable of the modern discoveries, the construction of the reflecting telescope. This discovery immediately attracted the attention of the mathematicians, both of our own and of foreign countries, who were soon convinced of its great importance to the sciences of optics and astronomy. The manner of placing the two specula upon the same axis appearing to Sir Isaac Newton to be attended with the disadvantage of losing the central rays of the larger speculum, he proposed an improvement on the instrument, by giving an oblique position to the smaller speculum, and placing the eye-glass in the side of the tube. But it is worth remarking, that the Newtonian construction of that instrument was long abandoned for the original or Gregorian, which is at this day universally employed where the instrument is of a moderate size; though Mr Herschel has preferred the Newtonian form for the construction of those immense telescopes, which of late years he has so successfully employed in observing the heavens.
The university of Padua being at that time in high reputation for mathematical studies, James Gregory went thither soon after the publication of his first work; and fixing his residence there for some years, he published, in 1667, Vera Circuli et Hyperboles quadratura; in which he propounded another discovery of his own, the invention of an infinitely converging series for the areas of the circle and hyperbole. To this treatise, when republished in 1668, he added a new work, entitled, Geometria pars universalis, interserviens quantitatum curvarum transmutationi et mensuræ; in which he is allowed to have shown, for the first time, a method for the transmutation of curves. These works engaged the notice, and procured Mr Gregory the correspondence, of the greatest mathematicians of the age, Newton, Huygens, Halley, and Wallis; and their author being soon after chosen a fellow of the royal society of London, contributed to enrich the Philosophical Transactions at that time by many excellent papers. Through this channel, in particular, he carried on a dispute with Mr Huygens, upon the occasion of his treatise on the quadrature of the circle and hyperbole, to
Gregory. which that able mathematician had started some objections. Of this controversy, it is unnecessary to enter into particulars. It is sufficient to say, that, in the opinion of Leibnitz, who allows Mr Gregory the highest merit for his genius and discoveries, Mr Huygens has pointed out, though not errors, some considerable deficiencies in the treatise above mentioned, and shown a much simpler method of attaining the end in view.
In 1668, Mr James Gregory published at London another work, entitled Excitationes Geometricæ, which contributed still to extend his reputation. About this time he was elected professor of mathematics in the university of St Andrew's; an office which he held for six years. During his residence there, he married, in 1669, Mary, the daughter of George Jamefon the celebrated painter, whom Mr Walpole has termed the Vandyke of Scotland, and who was fellow-disciple with that great artist in the school of Rubens at Antwerp.
In 1674, he was called to Edinburgh, to fill the chair of mathematics in that university. This place he had held for little more than a year, when, in October 1675, being employed in showing 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, at the early age of 37.
He was a man of an acute and penetrating genius. His temper seems to have been warm, as appears from the conduct of his dispute with Mr Huygens; and, conscious perhaps of his own merits as a discoverer, he seems to have been jealous of losing any portion of his reputation by the improvements of others upon his inventions.
Gregory, David, Savilian professor of astronomy at Oxford, whom Dr Smith has termed subtilissimi ingenii mathematicus, was the eldest son of Mr Gregory of Kinnaidrie, brother of the above-mentioned Mr James Gregory. He was born at Aberdeen in 1661, and received the earlier part of his education in that city. He completed his studies at Edinburgh; and, being possessed of the mathematical papers of his uncle, soon distinguished himself likewise 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 published, in the same year, Excitatio Geometrica de dimensione figurarum, five specimen methodi generalis dimetendi quasvis figuras, Edinburgh, 1684, 4to. He saw very early the excellence of the Newtonian philosophy; and had the merit of being the first who introduced it into the schools by his public lectures at Edinburgh. "He had (says Mr Whiston*) 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 ignomi-
niously studying the fictitious hypotheses of the Cartesian."
In 1691, on the report of Dr Bernard's intention of resigning the Savilian professorship of astronomy at Oxford, David Gregory went to London; and being patronised by Sir Isaac Newton, and warmly befriended by Mr Flamstead the astronomer royal, he obtained the vacant professorship, for which Dr Halley was a competitor. This rivalry, however, instead of animosity, laid the foundation of friendship between these eminent men; and Halley soon after became the colleague of Gregory, by obtaining the professorship 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 professorship, had the degree of doctor of physic conferred on him by the university of Oxford (A).
In 1693, he published in the Philosophical Transactions a resolution of the Florentine problem de Testudine veliformi quadrabili; and he continued to communicate to the public, from time to time, many ingenious mathematical papers by the same channel. In 1695, he printed at Oxford Catoptrice et Dioptrice Sphericæ Elementa; a work which, as he informs us in his preface, contains the substance of some of his public lectures read, eleven years before, at Edinburgh. This valuable treatise was republished first with additions by Dr William Brown, with the recommendation of Mr Jones and Dr Desaguliers; and afterwards by the latter of these gentlemen, with an appendix containing an account of the Gregorian and Newtonian telescopes, together with Mr Hadley's tables for the construction of both those instruments. It is not unworthy of remark, that, in the end of this treatise, there is an observation which shows, that what is generally believed to be a discovery of a much later date, the construction of achromatic telescopes, which has been carried to great perfection by Mr Dolland and Mr Ramsden, had suggested itself to the mind of David Gregory, from the reflection on the admirable contrivance in nature in combining the different humours of the eye. The passage is as follows: "Quod si ob difficultates physicas in speculis idoneis torno elaborandis et poliendis, etiamnum lentem uti oporteat, fortassis media diversie densitatis ad lentem objectivam componendam adhibere utile foret, ut à natura factum observamus in oculi fabrica, ubi cristallinus humor (tere ejusdem cum vitro virtutis ad radios lucis refringendos) aqueo et vitreo (aqueo quoad refractionem haud absimilibus) conjungitur, ad imaginem quam distincte fieri poterit, à natura nihil frustra moliente, in oculi fundo depingendam." Catopt. et Dioptr. Sphær. Elem. Oxon. 1695, p. 98.
In 1702 our author published at Oxford, Astronomiæ Physicæ
(A) On obtaining the above professorship, he was succeeded in the mathematical chair at Edinburgh by his brother James, likewise an eminent mathematician; who held that office for 33 years, and retiring in 1725 was succeeded by the celebrated Maclaurin. A daughter of this professor James Gregory, a young lady of great beauty and accomplishments, was the victim of an unfortunate attachment, which furnished the subject of Mallet's well-known ballad of William and Margaret.
Another brother, Charles, was created professor of mathematics at St Andrew's by Queen Anne in 1707. This office he held with reputation and ability for 32 years; and, resigning in 1739, was succeeded by his son, who eminently inherited the talents of his family, and died in 1763.
Gregory. Physicæ et Geometricæ Elementa; a work which is accounted his masterpiece. It is founded on the Newtonian doctrines, and was esteemed by Sir Isaac Newton himself as a most excellent explanation and defence of his philosophy. In the following year he gave to the world an edition in folio of the works of Euclid in Greek and Latin; in prosecution of a design of his predecessor Dr Bernard, of printing the works of all the ancient mathematicians. In this work, although it contains all the treatises attributed to Euclid, Dr Gregory has been careful to point out such as he found reason, from internal evidence, to believe to be the productions of some inferior geometer. In prosecution of Dr Bernard's plan, Dr Gregory engaged, soon after, with his colleague Halley, in the publication of the Conics of Apollonius; but he had proceeded but a little way in this undertaking when he died, in the 49th year of his age, at Maidenhead in Berkshire, A. D. 1710. To the genius and abilities of David Gregory, the most celebrated mathematicians of the age, Sir Isaac Newton, Dr Halley, and Dr Keill, have given ample testimonies. Indeed it appears that he enjoyed, in a high degree, the confidence and friendship of Sir Isaac Newton. This philosopher entrusted him with a manuscript copy of his Principia, for the purpose of making observations on that work. Of these observations there is a complete copy preserved in the library of the University of Edinburgh. They contain many valuable commentaries on the Principia, many interesting anecdotes, and various sublime mathematical discussions. Some of the paragraphs are in the hand-writing of Huygens, and they relate to the theory of light of this philosopher. The observations of Dr Gregory had come too late for the first edition of Newton's great work; but he availed himself of them in the second. Besides those works published in his lifetime, he left in manuscript, A Short Treatise of the Nature and Arithmetic of Logarithms, which is printed at the end of Dr Keill's translation of Commandine's Euclid; and a Treatise of Practical Geometry, which was afterwards translated, and published in 1745, by Mr Maclaurin.
Dr David Gregory married in 1695, Elizabeth the daughter of Mr Oliphant of Langtown in Scotland. By this lady he had four sons, of whom, the eldest, David, was appointed regius professor of modern history at Oxford by King George I. and died in 1767, in an advanced age, after enjoying for many years the dignity of dean of Christ-church in that university.