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LEYBOURN, WILLIAM (1626–1700?), mathematician, born in 1626, was a teacher of mathematics and professional land surveyor in London. He is said to have begun life as a printer; but as early as 1648 he appears as joint author with Vincent Wing [q. v.] of the first book on astronomy written in English; its title was ‘Urania Practica,’ and it was adapted to the comprehension of beginners. Its authors are styled ‘practitioners in the mathematicks.’ It reached a second edition in 1649, and was criticised by Jeremie Shakerley in ‘The Anatomy of Urania Practica,’ 1649; the authors replied in ‘Ensfictum Shakerlæi, or the Annihilation of Mr. Jeremie Shakerley,’ 1649. In 1650 appeared ‘Planometria, or the Whole Art of Surveying of Land,’ by ‘Oliver Wallinby,’ the pseudonym being a mere transposition of the letters of Leybourn's name. This was republished with additions and acknowledged by its author in 1653, under the title ‘The Compleat Surveyor.’ It passed through four editions in his lifetime; a fifth edition appeared in 1722, edited by Samuel Cunn, who says in the preface: ‘The author of this treatise was frequently employed in surveying, measuring, and mapping gentlemen's estates, as evidently appears from the several draughts by him drawn and to be met with in almost every county in England.’ In 1657 Leybourn published ‘Arithmetick, Vulgar, Decimal, and Instrumental,’ 8vo, in three parts (other editions, 1659 and 1678); and in 1667 ‘The Line of Proportion or [of] Numbers, commonly called Gunter's Line, made easie,’ 12mo, a treatise on the sliding-rule; a second part was published in 1677 (other editions, 1678 and 1684). In 1662 and 1673 he produced the fourth and fifth editions of the ‘Works’ of Edmund Gunter [q. v.], adding some rules of his own for the mensuration of plane and solid figures. An advertisement page gives a list of ‘Arts and Sciences Mathematical professed and taught by William Leybourn,’ viz. arithmetic, geometry, astronomy; and ‘upon these foundations the superstructures’ of the use of geometrical instruments in surveying, &c., trigonometry, navigation, and dialling. In 1667 appeared his ‘Platform Guide Mate for Purchasers, Builders, Measurers,’ 8vo. The first book is on interest, the second and third on building and mensuration; another edition was published in 1685. ‘The Art of Numbering by Speaking Rods, vulgarly termed Nepeirs Bones,’ was published London, 1667, 12mo, 1685; and was enlarged as ‘The Description and Use of Gunters Quadrant … to which is added the Use of Nepiars Bones,’ 2nd edition, London, 1721, 12mo; 3rd edition, 1731. ‘Panorganon, or a Universal Instrument,’ appeared London, 1672, 4to. Other minor works were: ‘Introduction to Astronomy and Geography in VII. Parts,’ London, 1675, 8vo, and ‘The Art of Dyalling,’ which reached a second edition, 1681, 4to; another edition, 1700.

In 1690 Leybourn published his ‘Cursus Mathematicus; Mathematical Sciences in Nine Books.’ This is a folio volume of over nine hundred pages, and includes the substance of his former publications. The first book treats of arithmetic under four headings, natural or vulgar, decimal, logarithmic, and instrumental; the second deals with plane and solid geometry and mensuration; the third with the doctrine of primum mobile and spherical projection in astronomy; the fourth with celestial and terrestrial cosmography; the fifth consists of plane and spherical trigonometry; practical geometry, including surveying and fortification, occupies the sixth; the seventh is devoted to navigation, and the eighth to dialling; the ninth and last deals with theoretical astronomy, principally in connection with the planets; and it is remarkable that the author discusses Kepler's discoveries, but says nothing of Newton's ‘Principia,’ which had appeared three years previously. The work closes with appendices and tables, and a ‘Canon Logarithmus,’ or table of logarithms.

In 1693 Leybourn produced the most enduring of his works, under the title ‘Panarithmologia, being a Mirror Breviate Treasure Mate for Merchants, Bankers, Tradesmen, Mechanicks, and a sure Guide for Purchasers, Sellers, or Mortgagers of Land, Leases, Annuities, Rents, Pensions, &c., in Possession or Reversion, and a constant Concomitant fitted for all men's occasions.’ This supplies, according to De Morgan, the earliest ready reckoner known in English—from one to ten thousand, and a farthing to 1l., calculated, as Leybourn tells us, ‘by another hand … near thirty years since.’ An appendix of 144 pp. is rich in miscellaneous commercial information. This work was long popular; the twenty-third edition appeared in 1808 under the name, ‘The Ready Reckoner, or Traders' sure Guide.’

In 1694 Leybourn published ‘Pleasure with Profit; consisting of Recreations of divers kinds, Numerical, Geometrical, Mechanical, Statical, Astronomical …; to recreate ingenious spirits and to induce them to make farther scrutiny into these Sciences.’ He also added an appendix to Thomas Stirrup's ‘Horometria, or the Compleat Diallist,’ London, 1659, 4to. He edited (London, 1680, 8vo) the second edition of ‘The City and Country Purchaser and Builder,’ by Stephen Primatt. The fourth edition of Scamozzi's ‘Mirror of Architecture’ (London, 1700, 4to) has William Leybourn's name as editor. The year of his death is uncertain.

Leybourn's works all grew out of his teaching, and were deservedly popular. They are clear and attractive in style, and are the work of a man of considerable ingenuity and uncommon industry. His larger works are prefaced with engraved portraits of himself, which preserve a record of his personal appearance from the age of twenty-seven to sixty-four. Gaywood is the engraver of the portrait (æt. 30) before Leybourn's ‘Arithmetick;’ R. White of those placed respectively (æt. 48) before his ‘Compleat Surveyor’ and (æt. 64) before his ‘Cursus Mathematicus.’

[The prefaces, &c., in Leybourn's works, to which the notice in Granger's Biog. Hist., copied by Chalmers, adds nothing of importance. See also De Morgan's Arithmetical Books, Hutton's Mathematical Dict., and Bromley's Cat. of Portraits.]

C. P.