# The description and vse of the sector, crosse-staffe, and other instruments: vvith a canon of artificiall sines and tangents, to a radius of 10000.0000. parts, and the vse thereof in astronomie, navigation, dialling, and fortification, &c. The second edition much augmented. By Edm. Gunter sometime professor of astronomie in Gresham Colledge in London.

London: Printed by William Iones, for Iames Bowler, and are to be sold at the Marigold in Pauls Church-yard, 1636.

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Quarto: 19 x 15.2 cm. Collation: 2 lvs.(engraved t.p., engraved instrument), π2, b4, A-X4, Y2, Aa-Zz4, Aaa-Kkk4, Lll1 (-Ll2 blank); Aaaa-Iiii4, chi1, A-O4. Complete with the volvelle leaf inserted at p. 72 (leaf K4), the woodcut protractor at p. 116 (leaf Q2), the printed scale at p. 120 (leaf R1), and the inserted table at p. 45, second count (leaf Ff3).

FIRST COLLECTED EDITION, EXPANDED WITH NEW MATERIAL (see below).

Bound in contemporary blind-ruled calf, nicely rebacked and re-sewn. Light wear to edges. A clean copy, complete with the inserted slips. Small, light ink spot on engraved title. One leaf dusty. 2 sm. holes in leaf G4. Numerous woodcut diagrams and instruments in the text. The engraved instrument bound after the engraved title has the advertisement: “These and other mathematical instruments are made in brass by Elias Allen dweling (sic) with out Tempel barr a gainst St Clements Church.”.

The DNB describes this as a collected edition of Gunter’s works. It comprises the 2nd English editions of the “Description” -with a chapter on the mathematics of fortification not published before- and the “Canon” (both 1st editions were printed in 1623), and the first edition of the “generall vse of the canon and table of logarithmes”.

The book “must rank with Richard Eden's translation of Martin Cortes's ‘Arte de Navegar’(1561) and Wright's ‘Certaine Errors’(1599) as one of the three most important English books ever published for the improvement of navigation... [Gunter] opened up... an entirely new field, that of arithmetical navigation.” (Waters, Art of Navigation, p. 359)

“This book must be reckoned, by every standard, to be the most important work on the science of navigation to be published in the seventeenth century. It opened the whole subject of mathematical application to navigation and nautical astronomy to every mariner who was sufficiently interested in devoting time to the perfecting of his art.”(Cotter, ‘Edmund Gunter (1581-1626), Journal of Navigation’.)

“Gunter was a firm advocate of the use of instruments in mathematics for easing the work of various mathematical practitioners, notably surveyors and navigators. His instruments were designed with these aims in mind. In particular his work on logarithms, their applications to trigonometry, and their inclusion on instruments greatly simplified the processes of mathematical calculation….

“Easily the most substantial of Gunter's works was The Description and Use of the Sector, the Crosse-Staffe and other such Instruments (1623) which explained instruments which he had designed. Apart from the two mentioned in the title it also included an astronomical quadrant and a 'cross-bow'--an alternative to the backstaff used by sailors for solar altitude measurements.. The Gunter sector was a much more complex instrument than Thomas Hood's. It allowed calculations involving square and cubic proportions, and carried various trigonometrical scales. Moreover it had a scale for use with Mercator's new projection of the sphere, making this projection more manageable for navigators who were only partially mathematically literate. The sector was sold as a navigational instrument throughout the seventeenth century and survived in cases of drawing instruments for nearly three hundred years. The most striking feature of the cross-staff, distancing it from other forms of this instrument, was the inclusion of logarithmic scales. This was the first version of a logarithmic rule, and it was from Gunter's work that logarithmic slide rules were developed, instruments that remained in use until the late twentieth century.”(Higton, DNB)

“What Briggs did for logarithms of numbers, Gunter did for logarithms of trigonometrical functions. In fact, he introduced the terms cosine, cotangent and cosectant for the sine, tangent and secant of complementary angles. Gunter’s most important book was his Description and use of the Sector. .. A sector is a mathematical instrument which consists of two hinged rulers on which there are engraved scales. The scales allow various questions in trigonometry to be resolved by using the property that two similar (equiangular) triangles have sides in a constant ratio. The issue of who first invented by the sector is not without controversy. … What singles out Gunter’s sector is that it is the first mathematical instrument to be inscribed with a logarithmic scale to facilitate the resolution of numerical problems. This is not a slide rule in any sense of the term; the single logarithmic scale is used in conjunction with a pair of compasses. Such a rule is frequently referred to as a Gunter line. A two foot long boxwood ruler inscribed with a variety of scales was a standard navigator’s tool up until the end of the nineteenth century.”(Sangwin, Edmund Gunter and the Sector).

ESTC S103555; STC 12523; Tomash & Williams G102