GREGORY (James)
, professor of mathematics, first in the university of St. Andrews, and afterwards in that of Edinburgh, was one of the most eminent mathematicians of the 17th century. He was a son of the Rev. Mr. John Gregory minister of Drumoak in the county of Aberdeen, and was born at Aberdeen in November 1638. His mother was a daughter of Mr. David Anderson of Finzaugh, or Finshaugh, 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 it seems to have been transmitted to their descendants of the names of Gregory, Reid, &c. Alexander Anderson, cousin-german of the said David, was professor of mathematics at Paris in the beginning of the 17th century, and published there several valuable and ingenious works; as may be seen in the memoirs of his life and writings, under the article Anderson. 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. His education in the languages he received at the grammar school of Aberdeen, and went through the usual course of academical studies in the Marischal college; but he was chiefly delighted with philosophical researches, into which a new door had lately been opened by the key of the mathematics. Galileo, Kepler, Des Cartes, &c, were the great masters of this new method: their works therefore became the principal study of young Gregory, who soon began to make improvements upon their discoveries in Optics. The first of these improvements was the invention of the reflecting telescope; the construction of which instrument he published in his Optica Promota, in 1663, at 24 years of age. This discovery soon attracted the attention of the mathematicians, both of our own and of foreign countries, who immediately perceived its great importance to the sciences of optics and astronomy. But the manner of placing the two specula upon the same axis appearing to 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. It is observable however, that the Newtonian construction of that instrument was long abandoned for the original or Gregorian, which is now always used when the instrument is of a moderate size; though Herschel has preferred the Newtonian form for the construction of those immense telescopes, which he has of late so successfully employed in observing the heavens.
About the year 1664 or 1665, coming to London, he became acquainted with Mr. John Collins, who recommended him to the best optic glass-grinders there, to have his telescope executed. But as this could not be done for want of skill in the artists to grind a plate of metal for the object speculum into a true parabolic concave, which the design required, he was much discouraged with the disappointment; and after a few imperfect trials made with an ill-polished spherical one, which did not succeed to his wish, he dropped the pursuit, and resolved to make the tour of Italy, then the mart of mathematical learning, that he might prosecute his favourite study with greater advantage. And the university of Padua being at that time in high reputation for mathematical studies, Mr. Gregory fixed his residence there for some years. Here it was that he published, in 1667, Vera Circuli et Hyperbola Quadra<*>ura; in which he propounded another discovery of his own, the invention of an infinitely converging series for the areas of the circle and hyperbola. He sent home a copy of this work to his friend Mr. Collins, who communicated it to the Royal Society, where it met with the commendations of lord Brounker and Dr. Wallis. He reprinted it at Venice the year following, to which he added a new work, entitled Geometriæ Pars Universalis, inserviens Quantitatum Curvarum Transmutationi et Mensuræ; in which he is allowed to have shewn, for the first time, a method for the transmutation of curves. These works engaged the notice, and procured the author the correspondence of the greatest mathematicians of the age, Newton, Huygens, Wallis, and others. An account of this piece was also read by Mr. Collins before the Royal Society, of which Mr. Gregory, being returned from his travels, was chosen a member the same year, and communicated to them an account of a controversy in Italy about the motion of the earth, which was denied by Riccioli and his followers.— Through this channel, in particular, he carried on a dispute with Mr. Huygens on the occasion of his treatise on the quadrature of the circle and hyperbola, to which that great man had started some objections; in the course of which our author produced some improvements of his series. But in this dispute it happened, as it generally does on such occafions, that the antagonists, though setting out with temper enough, yet grew too warm in the combat. This was the case here, especially on the side of Gregory, whose defence was, at his own request, inserted in the Philosophical Transactions. It is unnecossary to enter into particulars:| suffice it therefore to say that, in the opinion of Leibnitz, who allows Mr. Gregory the highest merit for his genius and discoveries, M. Huygens has pointed out, though not errors, some considerable deficiencies in the treatise above mentioned, and shewn a much simpler method of attaining the same end.
In 1668, our author published at London another work, entitled, Exercitationes Geometricæ, which contributed still much farther 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 Jameson, 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 1672, he published “The Great and New Art of Weighing Vanity: or a Discovery of the Ignorance and Arrogance of the Great and New Artist, in his Pseudo-philosophical Writings. By M. Patrick Mathers, Arch-bedal to the University of St. Andrews. To which are annexed some Tentamina de Motu Penduli & Projectorum.” Under this asumed name, our author wrote this little piece to expose the ignorance of Mr. Sinclare, professor at Glasgow, in his hydrostatical writings, and in return for some ill usage of that author to a colleague of Mr. Gregory's. The same year, Newton, on his wonderful discoveries in the nature of light, having contrived a new reflecting telescope, and made several objections to Mr. Gregory's, this gave birth to a dispute between those two philosophers, which was carried on during this and the following year, in the most amicable manner on both sides; Mr. Gregory defending his own construction, so far, as to give his antagonist the whole honour of having made the catoptric telescopes preferable to the dioptric; and shewing, that the imperfections in these instruments were not so much owing to a defect in the object speculum, as to the different refrangibility of the rays of light. In the course of this dispute, our author described a burning concave mirror, which was approved by Newton, and is still in good esteem. Several letters that passed in this dispute, are printed by Dr. Desaguliers, in an Appendix to the English edition of Dr. David Gregory's Elements of Catoptrics and Dioptrics.
In 1674, Mr. Gregory was called to Edinburgh, to <*>ill the chair of mathematics in that university. This place he had held but little more than a year, when, in October 1675, being employed in shewing 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, to the great loss of the mathematical world, at only 37 years of age.
As to his character, Mr. James Gregory was a man of a very acute and penetrating genius. His temper seems to have been warm, as appears from his conduct in the dispute with 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. He possessed one of the most amiable characters of a true philosopher, that of being content with his fortune in his situation. But the most brilliant part of his character is that of his mathematical genius as an inventor, which was of the first order; as will appear by the following list of his inventions and discoveries. Among many others may be reckoned, his Reflecting Telescope;— Burning Concave Mirror;—Quadrature of the Circle and Hyperbola, by an insinite converging series;— 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 Complements of the Latitude;— he also invented and demonstrated geometrically, by help of the hyperbola, a very simple converging feries for making the logarithms;—he sent to Mr. Collins the solution of the famous Keplerian problem by an infinite series;—he discovered a method of drawing Tangents to Curves geometrically, without any previous calculations;—a rule 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; as also for the Secant and Logarithmic Tangent and Secant, and vice versa:— These, with others, for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him of Newton's, in which he followed the elegant example of this author, in delivering his series in simple terms, independent 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 Hyperbolæ Quadratura; 4to, Padua 1667 and 1668.
3. Geometriæ Pars Universalis; 4to, Padua 1668.
4. Exercitationes Geometricæ; 4to, London 1668.
5. The Great and New Art of Weighing Vanity, &c. 8vo, Glasgow 1672.
The rest of his inventions make the subject of several letters and papers, printed either in the Philos. Trans. vol. 3; the Commerc. Epistol. Job. 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 professor of astronomy at Oxford, was nephew of the above-mentioned Mr. James Gregory, being the eldest son of his brother Mr. David Gregory of Kinardie, a gentleman who had the singular fortune to see three of his sons all professors of mathematics, 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 son Charles at St. Andrews. 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 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, in the same year, he published Exercitatio Geometrica de Dimensione| Figurarum, sive Specimen Methodi generalis Dimetiendi quasvis Figuras, Edinb. 1684, 4to. He very soon perceived the excellence of the Newtonian philosophy; and had the merit of being the first that introduced it into the schools, by his public lectures at Edinburgh. “He had (says Mr. Wiston, 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 professorship of astronomy at Oxford, our author went to London; and being patronised by Newton; and warmly befriended by Mr. Flamsteed the astronomer royal, he obtained the vacant professorship, though Dr. Halley was a competitor. This rivalship, 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.
In 1693, he published in the Philos. Trans. 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, Catoptricæ et Dioptricæ Sphæricæ Elementa; a work which, we are informed in the preface, contains the substance of some of his public lectures read at Edinburgh, eleven years before. This valuable treatise was republished in English, 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 conclusion of this treatise, there is an observation which shews, that the construction of achromatic telescopes, which Mr. Dollond has carried to such great perfection, had occurred to the mind of David Gregory, from reflecting on the admirable contrivance of nature in combining the different humours of the eye. The passage is as follows: “Perhaps it would 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 power of refracting the rays of light differs very little from that of glass) is by nature, who never does any thing in vain, joined 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 upon the bottom of the eye.”
In 1702 our author published at Oxford, in folio, Astronomiæ Physicæ et Geometricæ Elementa; a work which is accounted his master-piece. It is founded on the Newtonian doctrines, and was esteemed by New- ton 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; being done in prosecution of a design of his predecessor Dr. Bernard, of printing the works of all the ancient mathematicians. In this work, which contains all the treatises that have been 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 geometrician. In prosecution of the same plan, Dr. Gregory engaged soon after, with his colleague Dr. Halley, in the publication of the Conics of Apollonius; but he had proceeded only a little way in this undertaking, when he died at Maidenhead in Berkshire, in 1710, being the 49th year of his age only.
Besides those works published in our author's life time, as mentioned above, he had several papers inserted in the Philos. Trans. vol. 18, 19, 21, 24, and 25, particularly a paper on the catenarian curve, first considered by our author. He left also in manuscript, A Short Treatise of the Nature and Arithmetic of Logarithms, which is printed at the end of 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 the 1st, and died at an advanced age in 1767, after enjoying for many years the dignity of dean of Christchurch in that university.
When David Gregory quitted Edinburgh, he was succeeded in the professorship at that university 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, that furnished the subject of Mallet's well known ballad of William and Margaret.
Another brother, Charles, was created professor of mathematics at St. Andrews 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.
Some farther Particulars of the Family of the Gregorys and Andersons, communicated by Dr. Thomas Reid, Professor of Moral Philosophy in the University of Glasgow, a Nephew of the late Dr. David Gregory Savilian Professor at Oxford.
Some account of the family of the Gregorys at Aberdeen, is given in the Life of the late Dr. John Gregory prefixed to his works, printed at Edinburgh for A. Strahan and T. Cadell, London, and W. Creech, Edinburgh, 1788, in four small 8vo volumes.
Who was the author of that Life, or whence he had his information, I do not know. I have heard it ascribed to Mr. Tytler the younger, whose father was appointed| one of the guardians of Dr. John Gregory's children. Some additions to what is contained in it, and remarks upon it, is all I can furnish upon this subject.
Page 3. I know nothing of the education of David Anderson of Finzaugh. He seems to have been a selftaught Engineer. Every public work which surpassed the skill of common artists, was committed to the management of David. Such a reputation he acquired by his success in works of this kind, that with the vulgar he got the by-name of Davie do a' thing, that is in the Scottish dialect, David who could do every thing. By this appellation he is better known than by his proper name. He raised the great bells into the steeple of the principal church: he cut a passage for ships of burden through a ridge of rock under water, which crossed the entrance into the harbour of Aberdeen. In a long picture gallery at Cullen House, the seat of the earl of Findlater, the wooden ceiling is painted with several of the fables of Ovid's Metamorphosis. The colours are still bright, and the representation lively. The present earl's grandfather told me that this painting was the work of David Anderson my ancestor, whom he acknowledged as a friend and relation of his family.
Such works, while they gave reputation to David, suited ill with his proper business, which was that of a merchant in Aberdeen. In that he succeeded ill; and having given up mercantile business, from a small remainder of his fortune began a trade of making malt; and having instructed his wife in the management of it, left it to her care, and went into England to try his fortune as an engineer; an employment which in his own country he had practised gratuitously. Having in that way made a fortune which satisfied him, he returned to Aberdeen, where his wife had also made money by her malting business.
After making such provision for their children as they thought reasonable, they agreed that the longest liver of the two should enjoy the remainder, and at death should bequeath it to certain purposes in the management of the magistrates of Aberdeen.
The wife happened to live longeft, and fulfilled what had been concerted with her husband. Her legacies, well known in Aberdeen, are called after her name Jane Gu<*>ld's Mortifications, a mortification in Scots law signifying a bequeathment for some charitable purpofe. They consist of sums for different purposes. For orphans, for the education of boys and girls, for unmarried gentlewomen, and for widows; and they still continue to be useful to many in indigent circumstances. She was the daughter of Dr. Guild a minister of Aberdeen. Besides her money, she bequeathed a piece of tapestry, wrought by her own hand, and representing the history of queen Esther, from a drawing made by her husband. The tapestry continues to ornament the wall of the principal church.
In the same page it is said that Alexander Anderson, professor of mathematics at Paris, was the cousingerman of David above-mentioned. I know not the writer's authority for this: I have always heard that they were brothers; but for this I have only family tradition.
P. 4. It is here said that James Gregory was in- structed in the Elements of Euclid by his mother, the daughter of David Anderson.
The account I have heard differs from this. It is, that his brother David, being ten or eleven years older, had the direction of his education after their father's death, and, when James had sinished his course of philosophy, was at a loss to what literary profession he should direct him. After some unsuccessful trials, he put Euclid's Elements into his hand, and finding that he applied to Euclid with great avidity and success, he encouraged and assisted him in his mathematical studies.
This tradition agrees with what James Gregory says in the preface to his Optica Promota; where after mentioning his advance to the 26th proposition, he adds, Ubi diu hæsi omne spe progrediendi orbatus, sed continuis hortatibus et auxiliis sratris mei Davidis Gregorii, in Mathematicis non parum versati (cui si quid in hisce Scientiis præstitero, me illud debere non inficias ibo) animatus, tandem incidi &c. Whether David had been instructed in mathematics by his mother, or had any living instructor, I know not.
P. 5, 6. In these two pages I think the merit of Gregory compared with that of Newton in the invention of the catoptric telescope, is put in a light more unfavourable to Newton than is just. Gregory believing that the imperfection of the dioptric telescope arose solely from the spherical figure of the glasses, invented his telescope to remedy that imperfection. Being less conversant in the practice of mechanics, he did not attempt to make any model. The specula of his telescope required a degree of polish and a figure which the best opticians of that age were unable to execute. Newton demonstrated that the imperfection of the dioptric telescope arose chiefly from the different refrangibility of the rays of light; he demonstrated also that the catopric telescope required a degree of polish far beyond what was necessary for the dioptric. He made a model of his telescope; and finding that the best polish which the opticians could give, was insufficient, he improved the polish with his own hand, so as to make it answer the purpose, and has described most accurately the manner in which he did this. And, had he not given this example of the practicability of making a reflecting telescope, it is probable that it would have passed as an impracticable idea to this day.
P. 11. To what is said of this James Gregory might have been added, that he was led by analogy to the true law of Refraction, not knowing that it was discovered by Des Cartes before (see Preface to Optica Promota); and that in 1670 having received in a letter from Collins, a Series for the Area of the Zone of a Circle, and as Newton had invented an universal method by which he could square all Curves Geometrical and Mechanical by Infinite Series of that kind; Gregory after much thought discovered this universal method, or an equivalent one. Of this he perfectly satisfied Newton and the other mathematicians of that time, by a letter to Collins in Feb. 1671. He was strongly solicited by his brother David to publish his Universal Method of Series without delay, but excused himself upon a point of honour; that as Newton was the first inventor, and as he had| been led to it by an account of Newton's having such a method, he thought himself bound to wait till Newton should publish his method. I have seen the letters that passed between the brothers on this subject.
With regard to the controversy between James Gregory and Huygens, I take the subject of that controversy to have been, not whether J. Gregory's Quadrature of the Circle by a converging series was just, but whether he had demonstrated, as in one of his propositions he pretended to do, That it is impossible to express perfectly the Area of a Circle in any known Algebraical form, besides that of an infinite converging series. Huygens excepted to the demonstration of this proposition, and Gregory defended it; neither of them convinced his antagonist, nor do I know that Leibnitz improved upon what Gregory had done.
P. 12. David Gregory of Kinardie deserved a more particular account than is here given.
It is true that he served an apprenticeship to a mercantile house in Holland, but he followed that profession no longer than he was under authority, having a stronger passion for knowledge than for money. He returned to his own country in 1655, being about 28 years of age, and from that time led the life of a philosopher. Having succeeded to the estate of Kinardie by the death of an elder brother, he lived there to the end of that century. There all his children were born, of whom he had thirty-two by two wives.
Kinardie is above 40 English miles north from Aberdeen, and a few miles from Bamf, upon the river Diveron. He was a jest among the neighbouring gentlemen for his ignorance of what was doing about his own farm, but an oracle in matters of learning and philosophy, and particularly in medicine, which he had studied for his amusement, and begun to practise among his poor neighbours. He acquired such a reputation in that science, that he was employed by the nobility and gentlemen of that county, but took no fees. His hours of study were singular. Being much occupied through the day with those who applied to him as a physician, he went early to bed, rose about two or three in the morning, and, after applying to his studies for some hours, went to bed again and slept an hour or two before breakfast.
He was the first man in that country who had a barometer; and by some old letters which I have seen, it appeared, that he had corresponded with some philosophers on the continent about the changes in the barometer and in the weather, particularly with Mariotte the French philosopher. He was once in danger of being prosecuted as a conjurer by the Presbytery on account of his barometer. A deputation of that body having waited upon him to enquire into the ground of certain reports that had come to their ears, he satisfied them so far as to prevent the profecution of a man known to be so extensively useful by his knowledge of medicine.—About the beginning of this century he removed with his family to Aberdeen, and in the time of queen Anne's war employed his thoughts upon an improvement in artillery, in order to make the shot of great guns more destructive to the enemy, and executed a model of the engine he had conceived. I have conversed with a clock-maker in Aberdeen who was em- ployed in making this model; but having made many different pieces by direction without knowing their intention, or how they were to be put together, he could give no account of the whole. After making some experiments with this model, which satisfied him, the old gentleman was so sanguine in the hope of being useful to the allies in the war against France, that he set about preparing a field equipage with a view to make a campaign in Flanders, and in the mean time sent his model to his son the Savilian professor, that he might have his and Sir Isaac Newton's opinion of it. His son shewed it to Newton, without letting him know that his own father was the inventor. Sir Isaac was much displeased with it, saying, that if it tended as much to the prefervation of mankind as to their destruction, the inventor would have deserved a great reward; but as it was contrived solely for destruction, and would soon be known by the enemy, he rather deserved to be punished, and urged the professor very strongly to destroy it, and if possible to suppress the invention. It is probable the professor followed this advice. He died soon after, and the model was never found.
When the rebellion broke out in 1715, the old gentleman went a second time to Holland, and returned when it was over to Aberdeen, where he died about 1720, aged 93.
He left an historical manuscript of the Transactions of his own Time and Country, which my father told me he had read.
I was well acquainted with two of this gentleman's sons, and with several of his daughters, besides my own mother. The facts abovementioned are taken from what I have occasionally heard from them, and from other persons of his acquaintance.
P. 14. In confirmation of what is said in this page, that the two brothers David and James were the first who taught the Newtonian philosophy in the Scotch Universities; I have by me a Thesis, printed at Edinburgh in 1690, by James Gregory, who was at that time a professor of philosophy at St. Andrews, and succeeded his brother David in the profession of mathematics at Edinburgh. In this Thesis, after a dedication to Viscount Tarbet, follow the names of twenty-one of his scholars who were candidates for the degree of A. M. then twenty-five positions or Theses. The first three relate to logic, and the abuse of it in the Aristotelian and Cartesian philosophy. He desines logic to be the art of making a proper ufe of things granted, in order to find what is sought, and therefore admits only two Categories in logic, viz, Data and Quasita. The remaining twenty-two positions are a compend of Newton's Principia. This Thesis, as was the custom at that time in the Scotch universities, was to be defended in a public disputation, by the candidates, previous to their taking their degree.
The famous Dr. Pitcairn was a fellow student and intimate companion of these two Gregories, and during the vacation of the college was wont to go north with them to Kinardie, their father's house.
David Gregory was appointed a preceptor to the duke of Gloucester, queen Anne's son; but his entering upon that office was prevented by the death of that prince in the eleventh year of his age.
P. 19. D. Gregory's Euclid is said to have been wrote| in prosecution of a design of his predecessor Dr. Bernard, of printing the works of all the antient mathematicians. This design ought to have been ascribed to Savile, who left in charge to the two professors of his foundation, to print the mathematical works of the antients, and I think left a fund for defraying the expence. Wallis did something in consequence of this charge; Gregory and Halley did a great deal; but I think nothing has been done in this design by the Savilian professors since their time.
P. 20. Besides what is mentioned, Dr. Gregory left in manuscript a Commentary on Newton's Principia, which Newton valued, and kept by him for many years after the author's death. It is probable that in what relates to astronomy, this commentary may coincide in a great measure with the author's astronomy, which indeed is an excellent Commentary upon that part of the Principia.
P. 24. This David Gregory published in Latin, a very good compend of arithmetic and algebra, with the title Arithmeticæ et Algebræ Compendium, in Ufum Juventutis Academicæ. Edinb. 1736. He had a design of publishing his uncle's Commentary on the Principia, with extracts from the papers left by James Gregory his grand uncle; but the expence being too great for his fortune, and he too gentle a solicitor of the assistance of others, the design was dropped. His son David, yet alive, was master of an East India ship.
P. 40. To the projectors of the society at Aberdeen, ought to have been added John Stewart professor of mathematics in the Marischal college at Aberdeen. He published an explanation of two treatises of Sir Isaac Newton, viz, his Quadrature of Curves, and his Analysis by Equations of an infinite number of terms. He was an intimate friend of Dr. Reid's.
Another of the first members of that society was Dr. David Skene, who, besides his eminence in the practice of medicine, had applied much to all parts of natural history, particularly to botany, and was a correspondent of the celebrated Linnæus.
Dr. John Gregory and Dr. David Skene were the first who attempted a college of medicine at Aberdeen. The first gave lectures to his pupils in the theory and practice of medicine, and in chemistry; the last, in anatomy, materia medica, and midwifery, in order to prepare them for attending the medical college at Edinburgh. T. R.
Another instance of the prevalence of mathematical genius in the family of Gregory or Anderson, whether produced by an original and inexplicable determinatiòn of the mind, or communicated by the force of example, and the consciousness of an intimate connection with a reputation already acquired in a particular line, is the celebrated Dr. Reid, professor of moral philosophy in the university of Glasgow; a nephew, by his mother, of the late Dr. David Gregory, Savilian professor at Oxford.
This gentleman, well known to the public by his moral and metaphysical writings, and remarkable for that liberality, and that ardent spirit of enquiry, which neither overlooks nor undervalues any branch of science, is peculiarly distinguished by his abilities and proficiency in mathematical learning. The objects of literary pursuit are often directed by accidental occurrences. And apprehension of the bad consequences which might result from the philosophy of the late Mr. Hume, induced Dr. Reid to combat the doctrines of that eminent author; and produced a work, which has excited universal attention, and seems to have given a new turn to speculations upon that subject. But it is well known to Dr. Reid's literary acquaintance, that these exertions have not diminished the original bent of his genius, nor blunted the edge of his inclination for mathematical researches; which, at a very advanced age, he still continues to prosecute with a youthful attachment, and with unremitting assiduity.
It may farther be observed, of the extraordinary family above mentioned, that Dr. James Gregory, the present learned professor of physic and medicine in the university of Edinburgh, is the son of the late Dr. John Gregory, upon the memoirs of whose life the above remarks have been written by Dr. Reid; the said James has lately published a most ingenious work, intitled, Philosophical and Literary Essays, in 2 volumes 8vo, Edinb. 1792; and he seems to be another worthy inheritant of the singular genius of his family.
Gregory (St. Vincent), a very respectable Flemish geometrician, was born at Bruges in 1584, and became a Jesuit at Rome at 20 years of age. He studied mathematics under the learned Jesuit Clavius. He afterward became a reputable professor of those sciences himself, and his instructions were solicited by several princes: he was called to Prague by the emperor Ferdinand the 2d; and Philip the 4th, king of Spain, was desirous of having him to teach mathematics to his son the young prince John of Austria. He was not less estimable for his virtues than his skill in the sciences. His well-meant endeavours were very commendable, when his holy zeal, though for a false religion, led him to follow the army in Flanders one campaign, to confess the wounded and dying soldiers, in which he received several wounds himself. He died of an apoplexy at Ghent, in 1667, at 83 years of age.
As a writer, Gregory St. Vincent was very diffuse and voluminous, but he was an excellent geometrician. He published, in Latin, three mathematical works, the principal of which was his Opus Geometricum Quadraturæ Circuli, et Sectionum Coni, Antwerp, 1647, 2 vol. folio. Although he has not demonstrated, in this work, the Quadrature of the circle, as he pretends to have done, the book nevertheless contains a great number of truths and important discoveries; one of which is this, viz, that if one asymptote of an hyperbola be divided into parts in geometrical progression, and from the points of division ordinates be drawn parallel to the other asymptote, they will divide the space between the asymptote and curve into equal portions; from whence it was shewn by Mersenue, that, by taking the continual sums of those parts, there would be obtained areas in arithmetical progression, adapted to abscisses in geometrical progression, and which therefore were analogous to a system of logarithms.
