GUNTER (Emiumii,) an English ma thematician of the seventeenth century, was descended from Mn ancient and re spectable family in Brecknocshire, South Wales, and was born in the county of Herefordshire in the year 1580. He re ceived his classical education on the royal foundation at Westminster School,whence he was elected at about eighteen years of age to Christ Church College, in Ox ford. He was admitted to the degree of B. A. in 1603, and to that of M. A. in 1606; after which he entered into orders, anti proceeded bachelor of divinity in the year 1615. His genius had early led him to the pursuit of mathematical stu dies; and at the time when he took his degree of M. A. he had merited the title of an inventor by his new projection of the sector, of which he then wrote a de scription in Latin, and permitted his friends to transcribe it, though the Eng lish account of his invention was not pub lished till several years afterwards. In the year 1618, he had invented a small portable quadrant, for the more easy find ing the hour and azimuth, and more use ful astronomical purposes. The reputa tion which he had now acquired in the mathematical world occasioned his intro duction to the acquaintance of some of the most able mathematicians of his time, by whose recommendation and interest he was elected professor of astronomy at Gresham College, London, in the year 1619. In this situation he soon distin guished himself by his lectures and his writings, which contributed greatly to the improvement of science, and reflected credit to the choice that had been made of him to that professorship. His first 'Publication after his election appeared in 1620, and was entitled " Canon Trian gulorum, sive Tabula sinuum artificiali. atm ad radium 10.000000, et ad Scrupula prima Quadrantis," 8vo. This treatise was accompanied with the first 1,000 of Brigg's logarithms of common numbers. In the second edition of it, which was kublislied in English in 1624, under the title of "Canon Triangulortun, or Table of artificial Sines and Tangents to a ra dius of 10.0000,000 Parts to each Minute of the Quadrant," 4to., the logarithms were continued from 1,000 to 10,000, and a rule was given at the end for augmenting them to 100,000. These tables were the first of the kind which had been given to the world, and, if the author bad publish ed nothing else, would have preserved his memory to the latest posterity, by the ad mirable aid which they afforded to stu dents in astronomy ; for they greatly faci litated the practical parts of that science, by furnishing a method of solving speri cal triangles without the aid of secants or versed sines : the same thing being ef fected by addition and subtraction only, which in the use of the former tables of right sines and tangents required multi plication and division. Due praise was bestowed upon him by many of the most eminent mathematicians among his con temporaries, for the service which lie ren dered to science by this most excellent work; and his right to the improvement of logarithms, by their application to sphe rical triangles, was satisfactorily establish ed by Mr. Edmund Windgate, Mr. Robert Burton, and Mr. Henry Bond, sen.
In the year 1622, Mr. Gunter made his important discovery, that the variation of the magnetic needle varies. To this discovery he was led in the course of lectures he made on the variation at Deptford, by which he found, that the de clination of the needle had changed al most five degrees in the space of forty two years. The truth of this discovery
was afterwards confirmed and established by Mr. Gellibrand, his successor at Gre sham College. Soon after this he in vented his famous "rule of proportion," which is an easy and excellent method of combining arithmetic and geometry, adapted to the understanding of persons of the most ordinary capacities. It con sists in applying the logarithms of num bers and of sines and tangents to straight lines drawn on a scale or rule, by which, proportions in common numbers and tri gonoinetry may be resolved by the mere application of a pair of compasses : a me thod founded on this property, that the lo garithms of the terms of equal ratios are equidifferent. This was called Gunter's proportion and Gunter's line ; and the in strument in the form of a two foot scale is now in common use for navigation and other purposes, is and commonly called the Gunter. In the year 1624, this in vention was carried into France by Mr. Wingate, who not only communicated it to most of the principal mathematicians then at Paris, but also, at their request, published an account of it in the French language. Mr. Gunter likewise greatly improved the sector, and other instru ments for the same uses, the description of all which he published in 1624, in a treatise, entitled " The Cross Staff, in three books," &c. 4to. In the same year he published, by King James's order, a small tract, entitled " The Description and Use of his Majestie's Dials in White hall Garden," 4to. Mr. Gunter had been employed by the direction of King Charles in drawing the lines on these dials, and at his desire wrote this descrip tion, to which we refer those readers who wish to see a particular account of the construction and uses of those dials, which are no longer in existence. Our author was the first who used the word co-sine for the sine of the complement of an arc. He also introduced the use of arithmetical complements into the lo garithmical arithmetic; and it has been said, that he first started the idea of the logarithmic curve, which was so called, because the segments of its axis are the logarithms of the corresponding ordi nates. To him likewise the mathemati cal world is indebted for many other in ventions and improvements, most of which were the subjects of his lectures at Gresham College, and afterwards dispos ed into treatises, which were printed in his works. From the genius and abilities which he had displayed in his works al ready' noticed, the highest expectations were formed of his future services in the cause of useful science ; but they were unhappily disappointed by his death, in 1626, when he was only in the forty-fifth year of his age. His name, however, will be transmitted with honour to posterity, as that of the parent of instrumental arithmetic. His works have been collect ed, and various editions of them have been published. The fifth is by William Leybourn, in 1673, 4to. containing the de scription and use of the sector, cross staff, bow, quadrant, and other instru ments ; with several pieces added by Samuel Foster, Henry Bond, and William Leybourn.