GREGORY, DAVID, Dr, a celebrated astronomer and mathematician, was the nephew of the subject of the pre ceding article, and the eldest son of David Gregory of Kin• nairche. 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, lie was appointed professor of mathematics in the university of Edinburgh, and in the same year he published his work, entitled Exc•citatio Geomctrica de Dimensione Figurarum sive specimen methadi gencralis Dimetiendi guagvis figuras. Mr Gregory having found among his uncle's papers parti cular examples of infinite series, without any of the me thods, 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 in hyperbolas, parabolas, el lipses, spirals, cycloids, conchoids, and cissoids. He also explains several methods of reducing compound quantities into infinite series, so that the method of infinites may be conveniently applied to them.
Dr Gregory seems to have been one of the earliest sup porters of the Newtonian philosophy in Britain; and while the doctrines of Descartes were in the highest esteem at Cambridge, the true system of the universe was publicly taught in the university of Edinburgh.
In consequence of a report that Dr Bernard proposed to resign the. Savilian professorship of astronomy at Ox ford, Gregory went to London in 1691, and, in spite of the brilliant talents of his competitor Dr IIalley, he was ap pointed to succeed Dr Bernard, through the friendship and influence of Sir Isaac Newton and Mr Flamstead. Halley, who lost this appointment in consequence of his attachment to infidelity, became afterwards the colleague of Dr Gregory, when, in 1703, he succeeded to Dr Wallis as Savilian professor of geometry. During Mr Gregory's residence in London, he was elected a fellow of the Royal Society, and before his appointment to the mathematical chair, the university of Oxford had conferred upon him the degree of doctor of physic.
In the year 1692, Viviani, one of the disciples of Galileo, had proposed to mathematicians the Florentine problem of the quadrable dome. Leibnitz and Bernoulli had resolved this problem on the very day on which they had received it, and the Marquis L'Hospital had also given a solution. Dr Wallis and Dr Gregory were equally successful, and the latter published his solution in the Philosophical Tran sactions for 1693, under the title of Solution of the Floren tine Problem, concerning the Testudo veliformis Quadrabilis.
In 1694, he published another paper in the Transactions, containing a vindication of his uncle from a charge pre ferred by the Abbot Galloise,* that James Gregory and Dr Barrow had stolen from Roberval their general proposi tions concerning the transformation of curves. Galloise replied in the Memoirs of the Academy for 1713; and Dr Gregory put an end to the controversy by a very sharp answer, which appeared in the Philosophical Transactions for 1716, and which was the last of his communications to that learned body.
In 1695, Mr Gregory published at Oxford his Catoptri ere et Dioptrica Spherica Elementa, a work which formed the substance of lectures which he delivered in 1684, in the university of Edinburgh, and which require no higher mathematical knowledge than the Elements of Euclid. This work was republished and translated by Dr William Browne, with several important additions; and a third edi tion of it by Dr Desaguliers, appeared in 1735. In this work it is stated, that, in the construction of telescopes, " it would perhaps be of service to make the object lens of a different medium, as we see done in the fabric of the eye, where the crystalline humour (whose powers of re fracting the rays of light differs very little from that of glass) is bynature, who never does any thing in vain, join ed with the aqueous and vitreous humours, (not differing from water as to their power of refraction,) in order that the image may be painted as distinct as possible on the bOltom of the cyc. We cannot agree with the biogra phers of Dr Gregory, in considering this suggestion as any thing like an anticipation of the principle of the achroma tic telescope ; for it was impossible to form an idea of the construction of that instrument, till it was discovered that bodies possess different dispersive powers. This remark able property of light, even the penetrating mind of New ton failed to discover ; and we must not allow ourselves to diminish the well-earned reputation of Dollond, by giving to another any portion of the praise which is so exclusive ly due to himself. In the year 1747, more than 50 years after this conjecture of Dr David Gregory was published, the celebrated Euler suggested the human eye as the mo del of an achromatic telescope, and several ignorant fo reigners have ventured to claim a share of Dollond's merit for this illustrious mathematician. Whatever credit there fore may be given to Euler, must now be claimed for our countryman David Gregory.