A Mathematical and Philosphical Dictionary
, an eminent English mathematician, descended from an ancient family in Lincolnshire, was born at Southwick in Sussex, March 1, 1610, where his father was minister. He received his grammar education at the free-school at Stenning in that county. At the age of 13 he was sent to Trinity College in Cambridge, being then as good a scholar as most masters of arts in that university; but though he was eminently skilled in the Greek and Hebrew languages, he never offered himself a candidate at the election of scholars or fellows of his college. His person was handsome; and being of a strong constitution, using little or no recreations, he prosecuted his studies with the more application and intenseness.
In 1629 he drew up the “Description and Use of the Quadrant, written for the Use of a Friend,” in two books; the original manuscript of which is still extant among his papers in the Royal Society. And the same year he held a correspondence with Mr. Briggs on the subject of logarithms.
In 1630 he wrote, Modus supputandi Ephemerides Astronomicas, &c, ad an. 1630 accommodatus; and, A Key to unlock the meaning of Johannes Trithemius, in his Discourse of Steganography: which Key he imparted to Mr. Samuel Hartlib and Mr. Jacob Homedæ. The same year he took the degree of Master of Arts at Cambridge. And the year following he was incorporated in the University of Oxford. June the 7th, he wrote A Letter to Mr. Edmund Wingate on Logarithms; and Oct. 5, 1631, Commentationes in Cosmographiam Alstedii.
In 1632 he married Ithamaria, second daughter of Mr. Henry Reginolles of London, by whom he had four sons and four daughters.—March 6, 1634, he finished his Astronomical History of Observations of Heavenly Motions and Appearances; and April the 10th, his Ecliptica Prognostica, or Foreknower of the Eclipses, &c.—In 1634 he translated The Everlasting Tables of Heavenly Motions, grounded upon the Observations of all Times, and agreeing with them all, by Philip Lansberg, of Ghent in Flanders. And June the 12th, the same year, he committed to writing, The Manner of Deducing his Astronomical Tables out of the Tables and Axioms of Philip Lansberg.—March the 9th, 1635, he wrote A Letter of Remarks on Gellibrand's Mathematical Discourse on the Variation of the Magnetic Needle. And the 3d of June following, another on the same subject.
His eminence in mathematical knowledge was now so great, that be was thought worthy of a professor's chair in that science; and, upon the vacancy of one at Amsterdam in 1639, Sir William Boswell, the English Resident with the States General, used his interest, that he might succeed in that professorship: it was not filled up however till 1643, when Pell was chosen to it; and he read with great applause public lectures upon Diophantus.—In 1644 he printed at Amsterdam, in two pages 4to, A Refutation of Longomontanus's Discourse, De Vera Circuli Mensura.
In 1646, on the invitation of the Prince of Orange, he removed to the new college at Breda, as Professor of Mathematics, with a salary of 1000 guilders a year.— His Idea Matheseos, which he had addressed to Mr. Hartlib, who in 1639 had sent it to Des Cartes and Mersenne, was printed 1650 at London, in 12mo, in English, with the title of An Idea of Mathematies, at the end of Mr. John Durie's Reformed Librarykeeper. It is also printed by Mr. Hook, in his Philosophical Collections, No. 5, p. 127; and is esteemed our author's principal work.
In 1652 Pell returned to England: and in 1654 he was sent by the protector Cromwell agent to the Protestant Cantons in Switzerland; where he continued till June 23, 1658, when he se<*> out for England, where he arrived about the time of Cromwell's death. His negociations abroad gave afterwards a general satisfaction, as it appeared he had done no small service to the interest of king Charles the Second, and of the church of England; so that he was encouraged to enter into holy orders; and in the year 1661 he was instituted to the rectory of Fobbing in Essex, given him by the king. In December that year, he brought into the upper house of convocation the calendar reformed by him, assisted by Sancroft, afterwards archbishop of Canterbury.—In 1673 he was presented by Sheldon, bishop of London, to the rectory of Laingdon in Essex; and, upon the promotion of that bishop to the see of Canterbury soon after, became one of his domestic chaplains. He was then doctor of divinity, and expected to be made a dean; but his improvement in the philosophical and mathematical sciences was so much the bent of his genius, that he did not much pursue his private advantage. The truth is, he was a helpless man, as to worldly affairs, and his tenants and relations imposed upon him, cozened him of the profits of his parsonage, and kept him so indigent, that he wanted necessaries, even ink and paper, to his dying day. He was for some time confined to the King's-bench prison for debt; but, in March 1682, was invited by Dr. Whitler to live in the college of physicians. Here he continued till June following; when he was obliged, by his ill state of health, to remove to the house of a grandchild of his in St. Margaret's Church-yard, Westminster. But he died at the house of Mr. Cothorne, reader of the church of St. Giles's in the Fields, December the 12th, 1685, in the 74th year of his age, and was interred at the expence of Dr. Busby, master of Westminster school, and Mr. Sharp, rector of St. Giles's, in the rector's vault under that church.— Dr. Pell published some other things not yet mentioned, a list of which is as follows: viz,
1. An Exercitation concerning Easter; 1644, in 4to.
2. A Table of 10,000 square numbers, &c; 1672, folio.
3. An Inaugural Oration at his entering upon the Professorship at Breda.
4. He made great alterations and additions to Rhonius's Algebra, printed at London 1668, 4to, under the title of, An Introduction to Algebra; translated out of the High Dutch into English by Thomas Branker, much altered and augmented by D. P. (Dr. Pell). Also a Table of Odd Numbers, less than 100,000, shewing those that are incomposite, &c, supputated by the same Thomas Branker.
5. His Controversy with Longomontanus concerning the Quadrature of the Circle; Amsterdam, 1646, 4to.
He likewise wrote a Demonstration of the 2d and 10th books of Euclid; which piece was in MS. in the library of lord Brereton in Cheshire: as also Archimedes's Arenarius, and the greatest part of Diophantus's 6 books of Arithmetic; of which author he was preparing, Aug. 1644, a new edition, in which he intended to have corrected the translation, and made new illustrations. He designed likewise to publish an edition of Apollonius, but laid it aside, in May, 1645, at the desire of Golius, who was engaged in an edition of that author from an Arabic manuscript given him at Aleppo 18 years before. Letters of Dr. Pell to Sir Charles Cavendish, in the Royal Society.
Some of his manuscripts he left at Brereton in Cheshire, where he resided some years, being the seat of William lord Brereton, who had been his pupil at Breda. A great many others came into the hands of Dr. Busby; which Mr. Hook was desired to use his endeavours to obtain for the Society. But they continued buried under dust, and mixed with the papers and pamphlets of Dr. Busby, in four large boxes, till 1755; when Dr. Birch, secretary to the Royal Society, procured them for that body, from the trustees of Dr. Busby. The collection contains not only Pell's mathematical Papers, letters to him, and copies of those from him, &c, but also several manuscripts of Walter Warner, the mathematician and philosopher, who lived in the reigns of James the First and Charles the First.
Dr. Pell invented the method of ranging the several steps of an algebraical calculus, in a proper order, in so many distinct lines, with the number affixed to each step, and a short description of the operation or process in the line. He also invented the character ÷ for division, <*> for involution, and <*> for evolution.
PENCIL of Rays, in Optics, is a double cone, or pyramid, of rays, joined together at the base; as BGSC: the one cone having its vertex in some point of the object at B, and the crystalline humour, or the glass GLS for its base; and the other having its base on the same glass, or crystalline, but its vertex in the point of convergence, as at C.