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Edmund Gunter
Edmund Gunter
Edmund Gunter
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Edmund Gunter (1581 – 10 December 1626), was an English clergyman, mathematician, geometer and astronomer[1] of Welsh descent. He is best remembered for his mathematical contributions, which include the invention of the Gunter's chain, the Gunter's quadrant, and the Gunter's scale. In 1620, he invented the first successful analogue device[2] which he developed to calculate logarithmic tangents.[3]

He was mentored in mathematics by Reverend Henry Briggs and eventually became a Gresham Professor of Astronomy, from 1619 until his death.[4]

Biography

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Gunter was born in Hertfordshire in 1581. He was educated at Westminster School, and in 1599 he matriculated at Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity.[5] He became rector of St. George's Church in Southwark.[6]

Mathematics, particularly the relationship between mathematics and the real world, was the one overriding interest throughout his life. In 1619, Sir Henry Savile put up money to fund Oxford University's first two science faculties, the chairs of astronomy and geometry. Gunter applied to become professor of geometry but Savile was famous for distrusting clever people, and Gunter's behaviour annoyed him intensely. As was his habit, Gunter arrived with his sector and quadrant, and began demonstrating how they could be used to calculate the position of stars or the distance of churches, until Savile could stand it no longer. "Doe you call this reading of Geometric?" he burst out. "This is mere showing of tricks, man!" and, according to a contemporary account, "dismissed him with scorne."[7][8]

He was shortly thereafter championed by the far wealthier Earl of Bridgewater, who saw to it that on 6 March 1619 Gunter was appointed professor of astronomy in Gresham College, London. This post he held till his death.[5]

With Gunter's name are associated several useful inventions, descriptions of which are given in his treatises on the sector, cross-staff, bow, quadrant and other instruments. He contrived his sector about the year 1606, and wrote a description of it in Latin, but it was more than sixteen years afterwards before he allowed the book to appear in English. In 1620 he published his Canon triangulorum.[5][a]

In 1624 Gunter published a collection of his mathematical works. It was entitled The description and use of sector, the cross-staffe, and other instruments for such as are studious of mathematical practise. One of the most remarkable things about this book is that it was written, and published, in English not Latin. "I am at the last contented that it should come forth in English," he wrote resignedly, "Not that I think it worthy either of my labour or the publique view, but to satisfy their importunity who not understand the Latin yet were at the charge to buy the instrument."[7] It was a manual not for cloistered university fellows but for sailors and surveyors in real world.

There is reason to believe that Gunter was the first to discover (in 1622 or 1625) that the magnetic needle does not retain the same declination in the same place at all times. By desire of James I he published in 1624 The Description and Use of His Majesties Dials in Whitehall Garden, the only one of his works which has not been reprinted. He coined the terms cosine and cotangent, and he suggested to Henry Briggs, his friend and colleague, the use of the arithmetical complement (see Briggs Arithmetica Logarithmica, cap. xv).[5] His practical inventions are briefly noted below:

Gunter's chain

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Gunter's interest in geometry led him to develop a method of land surveying using triangulation. Linear measurements could be taken between topographical features such as corners of a field, and using triangulation the field or other area could be plotted on a plane, and its area calculated. A chain 66 feet (20 m) long, with intermediate measurements indicated, was chosen for the purpose, and is called Gunter's chain.

The length of the chain chosen, 66 feet (20 m), being called a chain gives a unit easily converted to area.[9] Therefore, a parcel of 10 square chains gives 1 acre. The area of any parcel measured in chains will thereby be easily calculated.

Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter's scale

Gunter's quadrant

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Gunter's quadrant is an instrument made of wood, brass or other substance, containing a kind of stereographic projection of the sphere on the plane of the equinoctial, the eye being supposed to be placed in one of the poles, so that the tropic, ecliptic, and horizon form the arcs of circles, but the hour circles are other curves, drawn by means of several altitudes of the sun for some particular latitude every year. This instrument is used to find the hour of the day, the sun's azimuth, etc., and other common problems of the sphere or globe, and also to take the altitude of an object in degrees.[5]

A rare Gunter quadrant, made by Henry Sutton and dated 1657, can be described as follows: It is a conveniently sized and high-performance instrument that has two pin-hole sights, and the plumb line is inserted at the vertex. The front side is designed as a Gunter quadrant and the rear side as a trigonometric quadrant. The side with the astrolabe has hour lines, a calendar, zodiacs, star positions, astrolabe projections, and a vertical dial. The side with the geometric quadrants features several trigonometric functions, rules, a shadow quadrant, and the chorden line.[10]

Gunter's scale

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Gunter's scale or Gunter's rule, generally called the "Gunter" by seamen, is a large plane scale, usually 2 feet (610 mm) long by about 1½ inches broad (40 mm), engraved with various scales, or lines. On one side are placed the natural lines (as the line of chords, the line of sines, tangents, rhumbs, etc.), and on the other side the corresponding artificial or logarithmic ones. By means of this instrument questions in navigation, trigonometry, etc., are solved with the aid of a pair of compasses.[5] It is a predecessor of the slide rule, a calculating aid used from the 17th century until the 1970s.

Gunter's line, or line of numbers refers to the logarithmically divided scale, like the most common scales used on slide rules for multiplication and division.

Gunter rig

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A sail rig which resembles a gaff rig, with the gaff nearly vertical, is called a Gunter rig, or "sliding gunter" from its resemblance to a Gunter's rule.

See also

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Notes

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Edmund Gunter

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Edmund Gunter (1581–1626) was an English mathematician, astronomer, and Anglican clergyman renowned for his pioneering work in mathematical instrumentation, surveying, and navigation, including the invention of Gunter's chain—a standardized 66-foot measuring tool with 100 links—and Gunter's scale, an early logarithmic device precursor to the slide rule. Born in Hertfordshire, England, Gunter received his early education at Westminster School before attending Christ Church, Oxford, where he earned a B.A. in 1603, an M.A. in 1605, and a B.D. in 1615. Ordained in 1615, he served as rector of St. George's, Southwark, until his death, while simultaneously advancing his scientific career as the third professor of astronomy at Gresham College from 1619 to 1626. Gunter's major contributions included the publication of Canon triangulorum in 1620, the first English table of logarithms for sines and tangents, which facilitated astronomical and navigational calculations, and The Description and Use of the Sector, the Cross-Staff, and Other Instruments in 1623, detailing his inventions such as the sector, cross-staff with logarithmic scales, and Gunter's quadrant for celestial observations. He also introduced the terms "cosine" and "cotangent" into English mathematical terminology and was the first to document the secular variation in magnetic declination in 1622, laying groundwork for geomagnetic studies. His innovations, supported by patrons like Henry Briggs and the future Charles I, transformed practical mathematics: Gunter's chain standardized land measurement in surveying, remaining in use for centuries, while his scale enabled rapid logarithmic computations essential for maritime navigation until the 19th century. Gunter died suddenly in London on 10 December 1626, leaving a legacy that bridged theoretical astronomy with applied sciences.

Biography

Early life and education

Edmund Gunter was born in 1581 in , , to a of Welsh extraction; his hailed from Gunterstown in , . Gunter received his early education at , where he studied as a Queen's Scholar under the royal foundation. In , he was elected to , matriculating on 25 ; he graduated with a Bachelor of Arts degree on 12 December 1603 and proceeded to Master of Arts on 2 July 1606. During his undergraduate years at Oxford, Gunter developed a strong interest in mathematics and astronomy, culminating in the composition of a manuscript titled "New Projection of the Sphere" in his final year, which he circulated among contemporary scholars. This work drew the attention of influential mathematicians, including Henry Briggs, foreshadowing Gunter's later contributions to the field. Following his master's degree, Gunter pursued clerical training and entered holy orders in 1615, obtaining a Bachelor of Divinity from Oxford that year.

Professional career

Gunter was ordained as a priest in 1615 and proceeded to the degree of Bachelor of Divinity at Christ Church, Oxford, on 23 November of the same year. He subsequently assumed clerical duties, serving as rector of St. George's Church in Southwark and St. Mary Magdalen in Oxford from 1615 until his death in 1626; these positions were obtained through the patronage of the Earl of Bridgewater. On 6 1619, Gunter was appointed of Astronomy at in , succeeding Thomas Williams who had resigned two days earlier, largely due to the strong recommendation of his friend Henry Briggs. In this , he delivered astronomical lectures until 1626, often incorporating demonstrations of mathematical instruments and dials to illustrate in , , and celestial . That same year, Gunter applied for the newly established Savilian of at , founded by Henry Savile; during his , Savile him after Gunter demonstrated some instruments, reportedly dismissing the presentation as "showing of tricks" rather than true , and instead selected for the position. Gunter maintained a close with , frequently discussing mathematical topics at .

Death

Edmund Gunter died on 10 1626 in at the age of 45, while serving as of Astronomy at . He was succeeded in the Gresham professorship by Henry Gellibrand, who was appointed to the chair of astronomy in 1627 on the recommendation of Henry . Gunter was buried the next day, 11 1626, in the churchyard of St Peter-le-Poer, Old , ; the church was later rebuilt in 1788 and demolished in 1896. In the years immediately following his death, Gunter earned early tributes within contemporary mathematical circles for his innovations, particularly as his successor Gellibrand verified and extended Gunter's geomagnetic observations, them in A Discourse Mathematical on the Variation of the Magneticall Needle in 1635. Posthumous compilations of his works, edited by Foster, appeared in 1636 and saw multiple subsequent editions through 1680, underscoring his immediate impact.

Scientific contributions

Trigonometry and logarithms

Edmund Gunter published the first English-language in his 1620 work Canon Triangulorum, which included logarithms of and tangents calculated to seven places. These tables featured from 0° to 90° in 1' intervals and tangents up to 45°, providing a structured resource for precise angular computations essential to contemporary . The publication marked a significant advancement by presenting logarithms of trigonometric functions in an accessible format, building directly on John Napier's earlier logarithmic innovations from 1614, which Gunter adapted for enhanced practicality. In this work, Gunter introduced the terms "cosine" and "cotangent" to English mathematical literature, defining them as the sine and tangent of complementary angles to streamline trigonometric notation and usage. These terminological innovations facilitated clearer expression in calculations involving right triangles and angular complements, influencing subsequent texts and standardizing vocabulary in the field. Additionally, Gunter suggested the use of the "arithmetical complement" to his colleague Henry Briggs, a method for handling subtractions in logarithmic arithmetic by using complements to 10, serving as a precursor to modern logarithmic subtraction techniques and improving computational efficiency. Gunter's adaptations of Napier's logarithms emphasized decimal bases, drawing from Henry Briggs's 1617 tables to make them more suitable for everyday applications in navigation and surveying, where rapid trigonometric resolutions were critical for determining positions and distances at sea or on land. By integrating these tables into practical contexts, such as later implementations on his logarithmic scales, Gunter bridged theoretical logarithms with fieldwork demands, enhancing accuracy in maritime voyages and land measurements.

Geomagnetism

Edmund Gunter made pioneering observations of in the early 1620s, becoming the first to document the secular variation of —the angle between magnetic north and —at a fixed . Around 1622–1625, he conducted field measurements in , noting discrepancies with prior that indicated the was not constant over time. These findings marked an early milestone in , shifting attention from static assumptions about to its dynamic . In June 1622, Gunter measured the at as 6° 15' east and at nearby as 5° 56' east, based on multiple observations using a . He compared these to William Borough's 1580 record of 11° 15' east at , recognizing a substantial decrease of approximately 5° over four decades but attributing the difference cautiously to possible errors rather than definitive temporal change. Employing portable instruments crafted by maker Allen, Gunter performed these measurements in outdoor settings to accuracy in real-world conditions. This approach highlighted the practical challenges of magnetic observations and their direct relevance to navigation, where inaccurate declination could lead to significant errors in determining longitude at sea. Gunter's unpublished notes on these variations influenced subsequent researchers, particularly his successor at Gresham College, Henry Gellibrand, who in 1634–1635 measured London's declination at about 4° east and confirmed the ongoing westward drift, solidifying the of secular variation. Gellibrand explicitly referenced Gunter's in his 1635 , A Discourse Mathematical on the Variation of the Magneticall Needle, crediting him for the initial while expanding the observations to demonstrate the phenomenon's . Gunter's work thus laid foundational empirical groundwork for understanding geomagnetic dynamics, bridging early compass-based surveys with later systematic geophysical studies.

Publications

Edmund Gunter's primary publications focused on mathematical tables, instrumental guides, and astronomical applications, reflecting his efforts to make advanced computations accessible to English practitioners. His first major work, Canon Triangulorum, sive Tabulae Sinuum et Tangentium Artificialium (1620), presented logarithmic tables of and tangents to seven decimal places for every minute of the quadrant, comprising 5,400 entries in total. Published in Latin by William Jones in , it was immediately followed by an English , marking the first such available in the vernacular to aid navigators and surveyors without Latin proficiency. The work introduced terms like "cosine" and "cotangent" in print and was dedicated to John Egerton, Earl of Bridgewater. In 1623, Gunter issued De Sectore et Radio: The Description and Use of the Sector, the Crosse-Staffe, and Other Instruments, a practical manual detailing the and application of mathematical tools such as the sector for trigonometric calculations and the cross-staff for angular measurements. This English-language text included engravings of instrument scales and diagrams to illustrate operations like via similar triangles, emphasizing hands-on for astronomers and engineers. It was reissued in 1624 as The Description and Use of the Sector, the Cross-Staff, the Quadrant, and the , expanding coverage to additional devices with further illustrations. That same year, at the request of Prince Charles, Gunter published The Description and Use of His Majesties Dials in White-Hall Garden, describing the multi-faced sundials he designed and installed in the royal gardens at Whitehall . The provided instructions for reading the dials to determine time, dates, and astronomical positions, promoting their use in practical horology. Gunter's writings, characterized by clear, instructional prose in English rather than Latin, aimed to democratize mathematical among non-scholars, influencing subsequent generations through widespread . After his in 1626, his works gained enduring ; Foster compiled The Works of Edmund Gunter in 1653, incorporating the Canon Triangulorum (reprinted that year) and instrumental treatises, with the collection seeing six editions by 1680.

Instruments and inventions

Gunter's chain

, invented by English mathematician in 1620, is a tool consisting of a 66-foot (20.1 m) divided into 100 , with each link measuring 7.92 inches long. This standardized measurements in by providing a precise, repeatable unit for distance in fieldwork. The 's length was specifically chosen to align with traditional English units, making it practical for property delineation and agricultural plotting. The chain's dimensions facilitated efficient area calculations, as 10 square chains equate to 1 acre, or 43,560 square feet. This relation simplified the process of determining land holdings, reducing errors in surveys where boundaries were often irregular. Mathematically, the chain derived from the furlong—a longstanding unit of 660 feet—divided into 10 equal parts, ensuring compatibility with existing systems like the mile (80 chains). Constructed from iron links, the chain offered durability against wear from repeated stretching and terrain challenges in outdoor use, while its coiled form enhanced portability for surveyors carrying it across fields. It became the statutory standard in and its colonies shortly after introduction, enabling consistent legal and commercial land transactions. This tool remained in widespread use for in and former colonies, including the , until the of metric systems and tapes in the 20th century. Its longevity underscores its in shaping imperial division, influencing and rural for nearly three centuries.

Gunter's scale

Edmund Gunter invented the logarithmic known as Gunter's scale around 1620, shortly after John Napier's introduction of logarithms in 1614. This device consisted of a two-foot (610 mm) rule typically made from boxwood or ivory, engraved with multiple parallel scales to facilitate rapid calculations. The scale's design allowed for the practical application of logarithms without relying on extensive tabular lookups, making it a valuable tool for mathematicians and navigators. The scales on Gunter's rule included logarithmic lines for numbers, enabling multiplication and division through proportional distances, as well as dedicated scales for sines and tangents to handle trigonometric functions. Additional markings incorporated stereographic projections, useful for navigational computations involving angular measurements. These engravings were achieved through meticulous division techniques, often using sector instruments for accuracy, resulting in scales precise enough for practical use in resolving proportions and solving right triangles. Gunter calibrated these scales drawing from his own trigonometric tables published in Canon Triangulorum (1620). In operation, users employed a pair of dividers to transfer distances across the fixed scales, effectively "sliding" measurements to find products, quotients, or trigonometric values without logarithmic tables—for instance, multiplying two numbers by setting one at the scale's start and stepping to the second, then reading the result at the end point. This method streamlined computations for navigation reckonings, such as determining distances or bearings at sea. Gunter's scale served as a direct precursor to more advanced analog computing devices, notably influencing William Oughtred's invention of the in 1622, which introduced a movable slide for even greater . Its logarithmic framework laid foundational principles for subsequent instruments used in and through the 19th century.

Gunter's quadrant

Edmund Gunter invented the quadrant around as a versatile astronomical instrument constructed primarily from , featuring a of the onto the plane of the . This allowed for the of altitudes, azimuths, and time by aligning the instrument with celestial bodies. Key features included a pivoted sight for precise alignment with the observed object, a plumb line suspended from one radius to establish the vertical, and multiple engraved scales representing the tropics, ecliptic, horizon, and curved hour lines for determining sun and moon positions. The instrument's portable size, typically with a radius of about 12 inches, made it suitable for field use by practitioners without requiring bulky equipment. In applications, the quadrant enabled surveyors and navigators to determine latitude by measuring the sun's meridian altitude, as well as right ascension and declination of stars, bypassing the need for larger armillary spheres or mural instruments. It could also integrate briefly with magnetic compass observations to aid in deviation corrections during navigation. Detailed usage instructions for these purposes were provided in Gunter's 1624 publication, De Sectore et Radio, which described the quadrant's operation in one dedicated book. Compared to predecessors like Tycho Brahe's large mural quadrants, Gunter's version offered significant advantages in simplicity and portability, while maintaining accuracy to approximately 1 arcminute through fine scale divisions, making it accessible for practical fieldwork rather than use.

Gunter rig

The , also known as the sliding gunter or vertical gaff rig, is a fore-and-aft configuration named after the English and Edmund Gunter (1581–1626) due to the resemblance of its sliding gaff to the mechanism in his Gunter's scale, a navigational computing device popular among seamen. The term "Gunter rig" dates back to the late 17th century, though the configuration itself evolved from earlier lug and gaff rigs in European maritime practice, likely in the 18th century or earlier. This naming ties the rig to Gunter's broader contributions to navigation, where his scale facilitated trigonometric and logarithmic calculations essential for maritime positioning. The rig features a single mast with a triangular mainsail, the lower luff attached directly to the mast and the upper luff bent to a long gaff yard hoisted nearly vertically via parrel beads, rings, or a gunter iron that allows it to slide up and down. The sail's foot extends along a boom secured by an outhaul, creating a high-peaked profile that maximizes sail area on a compact mast without requiring excessive height. This setup, inspired by adaptations of standing lug sails rather than lateen designs, enables efficient wind capture across a wide range of points of sail, particularly close-hauled, while keeping the center of effort low when reefed for stability in gusts. In practical applications, the Gunter rig enhanced maneuverability for smaller vessels, supporting coastal , , and exploratory voyages by allowing quick and easy stowage of within the hull—advantages demonstrated in European workboats like Azorean whaleboats and British dinghies. It complemented Gunter's other navigational tools, such as his quadrant, by facilitating on ships where precise course plotting was critical. The rig's and made it ideal for vessels under 25 feet, reducing the need for tall masts that complicated handling in rough seas or storage. The legacy of the Gunter rig lies in its influence on subsequent fore-and-aft designs, evolving into broader gaff-rigged systems that powered 18th- and 19th-century schooners, yachts, and recreational craft, prized for their balance of power and ease of use before the dominance of Bermuda rigs. Its enduring appeal persists in traditional boatbuilding, where it offers versatility for home constructors using basic materials like wood and canvas, and adaptability for modern small-boat sailing in varied conditions.

References

  1. https://americanhistory.si.edu/collections/nmah_761634
  2. https://www.nps.gov/long/blogs/a-gunter-scale-used-for-navigation-and-mathematics.htm
  3. https://galileo.library.rice.edu/Catalog/NewFiles/gunter.html
  4. https://www.britishmuseum.org/collection/term/BIOG185210
  5. https://mathshistory.st-andrews.ac.uk/Biographies/Gunter/
  6. https://www.encyclopedia.com/people/science-and-technology/mathematics-biographies/edmund-gunter
  7. https://www.gresham.ac.uk/about-us/our-history
  8. https://mathshistory.st-andrews.ac.uk/Biographies/Gellibrand/
  9. https://www.cambridge.org/core/journals/journal-of-navigation/article/edmund-gunter-15811626/842FBA9BED16ABDA5B562A793C8036E7
  10. https://locomat.loria.fr/gunter1620/gunter1620doc.pdf
  11. https://www.sliderulemuseum.com/Papers/EdmundGunterAndTheSector_ByCJSangwin.pdf
  12. https://www.lyellcollection.org/doi/10.1144/M60-2022-19
  13. https://www.sciencedirect.com/topics/physics-and-astronomy/secular-variation
  14. https://inria.hal.science/inria-00543938/document
  15. https://www.usgs.gov/core-science-systems/ngp/tnm-corps/order-surveyors-chain
  16. https://landsurveyorsunited.com/almanac/gunter-s-chain
  17. https://www.eraconsultants.com/our-blog---home-screen/the-gunters-chain
  18. http://www.surveyhistory.org/changing_chains.htm
  19. https://www.lumbermuseum.org/random-artifact-time-gunters-chain/
  20. https://www.sdstate.edu/south-dakota-agricultural-heritage-museum/south-dakota-agricultural-heritage-museumblog/who-gunter
  21. https://www.natickhistoricalsociety.org/surveyors-chain
  22. https://gis.utah.gov/blog/2019-03-11-the-western-grid/
  23. https://www.rushdenheartsandsoles.co.uk/land/gunterchain.html
  24. https://www.legalgenealogist.com/2014/08/13/a-matter-of-measure/
  25. https://osgalleries.org/journal/pdf_files/3.2/V3.2P14.pdf
  26. https://www.whipplemuseum.cam.ac.uk/explore-whipple-collections/calculating-devices/slide-rules
  27. https://www.gutenberg.org/files/42216/42216-h/42216-h.htm
  28. https://www.lostartoflogarithms.com/chapter22/
  29. https://americanhistory.si.edu/collections/object-groups/scale-rules/calculating-rules
  30. https://www.marshallrarebooks.com/all-books/science-astronomy/the-description-and-use-of-a-portable-instrument-vlugarly-sic-known-by-the-name-of-gunters-quadrant-to-which-is-added-the-use-of-nepiars-bones-in-multiplication-division-and-extraction-o/
  31. https://www.whipplemuseum.cam.ac.uk/explore-whipple-collections/astronomy/maps-heavens/gunter-quadrant-and-practical-knowledge
  32. https://americanhistory.si.edu/collections/object/nmah_213182
  33. https://thonyc.wordpress.com/2023/01/18/an-inventor-of-instruments/
  34. https://www.dictionary.com/browse/gunter-rig
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  36. https://www.duckworksmagazine.com/04/s/articles/gunter/index.htm
  37. https://www.hrsms.org/glossary/gunter/
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