Edmund Stone

Edmund Stone (c.  1690 – March or April 1768) was an autodidact Scottish mathematician who lived in London and primarily worked as an editor of mathematical and scientific texts and translator from French and Latin into English. He is especially known for his translations of Nicholas Bion's Mathematical Instruments (1723, 1758) and the Marquis de l'Hospital's  Analyse des Infiniment Petits (1730), and for his New Mathematical Dictionary (1726, 1743). Stone was celebrated for having risen from uneducated gardener's son to accomplished scholar.

Biography
The date and place of Edmund Stone's birth are unknown, as are the names of his parents, but he was probably born in Argyllshire, Scotland, at least a few years before 1700. What little is known about his early life comes from a letter by Andrew Michael Ramsay to Louis-Bertrand Castel, excerpted by the Journal de Trévoux. (See below for the letter and a translation.) According to this letter, Stone was the son of the gardener of John Campbell, 2nd Duke of Argyll. He never attended any formal school, but after being taught by a servant to read at age 18, he taught himself arithmetic, geometry, Latin, and French. As the story goes, the Duke found a copy of Isaac Newton's Principia in the grass in his garden, and was astonished to find it belonged to the 28-year-old Stone, and that he understood Latin and advanced mathematics. However, Stone's description of himself having studied mathematical instruments from the age of twelve seems inconsistent with this story. The Duke became his patron.

With the Duke's support, Stone moved to London c. 1720, where he likely worked as a mathematics tutor. He published translations of the Marquis de l'Hospital's posthumous book about conic sections in 1720 and Christopher Clavius's translation of Theodosius's Spherics in 1721. In 1723 he published a translation of Nicholas Bion's Construction and Principal Uses of Mathematical Instruments, to which he added descriptions of the English variants of the French instruments described by Bion; this book became the standard reference about the subject in English throughout the 18th century. In 1725 he was elected a Fellow of the Royal Society, and from 1725 until at least 1736 he was a member of the Board of Green Cloth. His New Mathematical Dictionary appeared in 1726, a cheaper alternative to John Harris's Lexicon Technicum. He also translated Euclid's Elements (1728); l'Hospital's differential calculus book Analyse des Infiniment Petits, to which he adjoined a second part about integral calculus, as The Method of Fluxions (1730); and Isaac Barrow's Geometrical Lectures (1735).

In 1736 Stone submitted a paper to the Philosophical Transactions of the Royal Society (published 1740) about two cubic plane curves not cataloged by Isaac Newton or James Stirling, but unbeknownst to him the two had been previously published in 1731 by François Nicole and 1733 by Nicolaus Bernoulli, respectively. In 1742 Stone submitted a 21-page paper "On Sir Isaac Newton's five diverging Parabolas", which was read to the Society but apparently never published.

In 1742, Stone resigned as a Fellow of the Royal Society, perhaps for inability to pay the small annual membership fee. In October 1743 Stone's patron the Duke of Argyll died. Little is known about Stone's life afterward, though he made another translation of Euclid's Elements in 1752, and he published a second edition of Bion's Mathematical Instruments in 1758, with a long appendix covering advancements of the intervening years. In a 1760 review in The Critical Review, Tobias Smollett wrote of Stone's situation, "His abilities are universally acknowledged, his reputation unblemished, his services to the public uncontested, and yet he lives to an advanced age unrewarded, except by a mean employment that reflects dishonour on the donor". In 1766 Stone published a contrarian polemic contesting the scientific validity of the spherical shape of the Earth and suggesting contemporary evidence was insufficient to discount the possibility Earth is an irregular roundish polyhedron; biographers have suggested this book was the product of cognitive decline. Stone died in March or April 1768.

Works

 * 1720, An Analytick Treatise of Conick Sections, a translation of the Marquis de l'Hospital's posthumous Traité analytique des sections coniques (1707).
 * 1721, The Description, Nature and General Use, of the Sector and Plain-scale. Anonymous, but the preface is signed E.S., and it was later credited to Stone. 2nd edition 1728. 4th edition 1746.
 * 1721, Clavius's Commentary on the Sphericks of Theodosius Tripolitae: or, Spherical Elements, translated from Christopher Clavius's Theodosii Tripolitae Sphaericorum Libri III (1586), a Latin translation of Theodosius of Bithynia's Spherics.
 * 1723, The Construction and Principal Uses of Mathematical Instruments, a translation of Nicolas Bion's Traité de la construction et des principaux usages des instrumens de mathématique (Revised ed. 1723) [1st ed. 1709], expanded with a description of English variants of the French instruments described by Bion, illustrated by the publisher John Senex's handsome engravings. Stone published a 2nd edition in 1758, including "A Supplement: Containing a further Account of some of the most useful Mathematical Instruments as now improved." (pp. 265–325).
 * 1723, Mathesis Enucleata: or, The Elements of the Mathematicks. 2nd ed. of a translation of Johann Sturm's Mathesis Enucleata (2nd ed. 1695). The 1st English ed. (1700) was translated by J. R. A. M. & R. S. S.
 * 1724, An Essay on Perspective translated from Willem 's Gravesande's Essai de perspective (1711).
 * 1726, A New Mathematical Dictionary. 2nd ed. 1743. This dictionary was at least partly compiled from uncredited previous sources such as Joseph Moxon's Mathematicks made Easie (3rd ed. 1701, revised by James Moxon & Thomas Tuttle).
 * 1728, The Elements of Physical and Geometrical Astronomy, 2nd English ed., translated from David Gregory's Astronomiæ Physicæ & Geometricæ Elementa (2nd ed. 1726, Vol. 1 & Vol 2). The 1st English ed. (1715) was translated by Gregory from his 1st Latin ed. (1702).
 * 1728, Euclid's Elements of Geometry, Briefly, yet Plainly Demonstrated, a translation of Isaac Barrow's Euclidis Elementorum libri XV breviter demonstrati (1659), a Latin translation of Euclid's Elements.
 * 1729, A New Treatise of the Construction and Use of the Sector, a posthumous work by Samuel Cunn revised by Stone for publication.
 * 1730, The Method of Fluxions, both Direct and Inverse, the first part translated from l'Hospital's differential calculus book Analyse des infiniment petits (2nd ed., 1715) [1st ed. 1696], and the second part on integral calculus written by Stone. Stone's part was translated into French by Rondet as Analise des infiniment petits, comprenant le calcul integral dans toute son étenduë (1735).
 * 1731, Euclid's Elements, Vol. II. Containing the seventh, eighth, ninth, tenth, thirteenth, and fifteenth Books, with the Data. Translated from David Gregory's Euclidis quæ supersunt omnia (1703). Published by Thomas Woodward as a sequel to John Keill's Euclid's Elements of Geometry (Revised ed. 1723), translated from Federico Commandino's Latin edition, containing books 1–6 and 11–12.
 * 1735, Geometrical Lectures, translated from Isaac Barrow's Lectiones Opticae et Geometricae (1674).
 * 1743, The Theory of the Working of Ships, Applied to Practice, translation of Henri Pitot's Théorie de la manoeuvre des vaisseaux réduite en pratique (1731).
 * 1752, Euclid's Elements of Geometry, The First Six, the Eleventh and Twelfth Books, a translation of the parts of Elements in Gregory's Euclid not previously translated by Stone in 1731. 2nd edition 1765.
 * 1766, Some Reflections on the Uncertainty of Many Astronomical and Geographical Positions

Appendix: Letter from Ramsay
A letter from Andrew Michael Ramsay to Louis-Bertrand Castel was excerpted by the Journal de Trévoux 1732, pp. 109–112, as part of a review of Stone's The Method of Fluxions (1730). Here is the excerpt reproduced, along with an English translation: