Difference between revisions of "Mercator"
From ICA Map Projections
(Added modern mathematical development.) |
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{{SUPPORTEDLANGUAGES}} | {{SUPPORTEDLANGUAGES}} | ||
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| − | | Mercator || || || メルカートル || || | + | | Mercator || || || メルカートル ||Поперечно-цилиндрическая проекция Меркатора || || || |
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*{{FORMULATORNAME}} Edward Wright (England). | *{{FORMULATORNAME}} Edward Wright (England). | ||
*{{FORMULATORCITATION}} Wright, Edward. 1610. ''Certaine Errors in Navigation''. London. | *{{FORMULATORCITATION}} Wright, Edward. 1610. ''Certaine Errors in Navigation''. London. | ||
| − | *{{PROJECTIONSYNONYMS}} Wright | + | *{{PROJECTIONSYNONYMS}} |
| − | *{{PROJECTIONPROPERTIES}} [[ | + | **Wright |
| − | *{{PROJECTIONDERIVATIVES}} [[Gauss Kruger|Gauss-Krüger]] | + | *{{PROJECTIONPROPERTIES}} |
| + | **[[conformal]] | ||
| + | **straight [[rhumb|rhumbs]] (in [[equatorial aspect]]) | ||
| + | *{{PROJECTIONDERIVATIVES}} | ||
| + | **[[Gauss Kruger|Gauss-Krüger]] | ||
| + | **[[Hotine]] | ||
| + | **[[Cole]] | ||
| + | **[[Rosenmund]] | ||
| + | **[[Laborde]] | ||
| + | **[[UTM|UTM = Universal Transverse Mercator]] | ||
| + | **[[space oblique Mercator]] | ||
*{{NAIVESPECIALIZATIONS}} | *{{NAIVESPECIALIZATIONS}} | ||
**''transverse cylindrical orthomorphic'' ({{ASPECTTRANSVERSE}}). | **''transverse cylindrical orthomorphic'' ({{ASPECTTRANSVERSE}}). | ||
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*1511: Erhard Etzlaub (Nuremburg) creates maps using an accurate Mercator projection. He records nothing of his method. | *1511: Erhard Etzlaub (Nuremburg) creates maps using an accurate Mercator projection. He records nothing of his method. | ||
*1537: Pedro Nunes (Portugal) describes the [[rhumb]]. | *1537: Pedro Nunes (Portugal) describes the [[rhumb]]. | ||
| − | * | + | *1537: Pedro Nunes suggests the construction of a world chart composed of many large-scale sheets, each of them in the equirectangular projection centred at its middle parallel. Two particular solutions were possible: either use the same principal scale for the whole chart, keeping constant the distance between parallels; or conserve the distance between meridians in order to maintain the graphical continuity between adjacent sheets. The second solution is only a little step from the Mercator projection. However, this development was probably foreign to the ideas of the mathematician, whose main intention was to avoid the inconsistencies of the existing small-scale charts with a system of representation that could be considered, for practical purposes, conformal and with constant scale. |
*1569: Gerardus Mercator (Flanders; probably christened Gerhard Kremer) produces a small-scale map based on the loxodromic principle, and promotes it for the purpose of navigation. His method of construction remains unknown. | *1569: Gerardus Mercator (Flanders; probably christened Gerhard Kremer) produces a small-scale map based on the loxodromic principle, and promotes it for the purpose of navigation. His method of construction remains unknown. | ||
*1599: Edward Wright (London) describes the exact mathematics of the spherical Mercator projection for the first time, although his description amounts to an infinite series rather than the modern, closed form obtained from the calculus. | *1599: Edward Wright (London) describes the exact mathematics of the spherical Mercator projection for the first time, although his description amounts to an infinite series rather than the modern, closed form obtained from the calculus. | ||
| − | *1600 | + | *ca. 1600: Thomas Harriot (London), in unpublished manuscripts, develops the modern logarithmic form of the projection. |
| − | *1610: Wright publishes accurate tables for the construction of the Mercator projection, unaware of Harriot | + | *1610: Wright publishes accurate tables for the construction of the Mercator projection, unaware of Harriot’s unpublished work. |
| − | *1645: Henry Bond (London) publishes the modern logarithmic form of the projection in Norwood | + | *1645: Henry Bond (London) notices that the Wright tables correspond uncannily closely with a table of logarithms, once the latitude is manipulated, and publishes the modern logarithmic form of the projection in Norwood’s ''Epitome of Navigation'' — also unaware of Harriot’s unpublished work. |
| + | *1668: James Gregory proves that Bond's logarithmic form represents the integral of Wright's infinitesimals. | ||
Latest revision as of 09:54, 31 October 2014
Projection name: Mercator
| English | Français | Deutsch | 日本語 | Русский | Español | Polski | Português |
|---|---|---|---|---|---|---|---|
| Mercator | メルカートル | Поперечно-цилиндрическая проекция Меркатора |
- Projection naming principle: Principle of Preponderance of Precedence.
- Year of origin: 1511.
- Name of originator: Erhard Etzlaub (Nuremburg).
- Originator reference:
- Year of formulation: 1599
- Name of formulator: Edward Wright (England).
- Formula citation: Wright, Edward. 1610. Certaine Errors in Navigation. London.
- Projection synonyms:
- Wright
- Projection properties:
- conformal
- straight rhumbs (in equatorial aspect)
- Projection derivatives:
- Naïve specializations:
- transverse cylindrical orthomorphic (transverse aspect).
- oblique cylindrical orthomorphic (oblique aspect).
- Generalizations:
Chronology of projection development
- 1511: Erhard Etzlaub (Nuremburg) creates maps using an accurate Mercator projection. He records nothing of his method.
- 1537: Pedro Nunes (Portugal) describes the rhumb.
- 1537: Pedro Nunes suggests the construction of a world chart composed of many large-scale sheets, each of them in the equirectangular projection centred at its middle parallel. Two particular solutions were possible: either use the same principal scale for the whole chart, keeping constant the distance between parallels; or conserve the distance between meridians in order to maintain the graphical continuity between adjacent sheets. The second solution is only a little step from the Mercator projection. However, this development was probably foreign to the ideas of the mathematician, whose main intention was to avoid the inconsistencies of the existing small-scale charts with a system of representation that could be considered, for practical purposes, conformal and with constant scale.
- 1569: Gerardus Mercator (Flanders; probably christened Gerhard Kremer) produces a small-scale map based on the loxodromic principle, and promotes it for the purpose of navigation. His method of construction remains unknown.
- 1599: Edward Wright (London) describes the exact mathematics of the spherical Mercator projection for the first time, although his description amounts to an infinite series rather than the modern, closed form obtained from the calculus.
- ca. 1600: Thomas Harriot (London), in unpublished manuscripts, develops the modern logarithmic form of the projection.
- 1610: Wright publishes accurate tables for the construction of the Mercator projection, unaware of Harriot’s unpublished work.
- 1645: Henry Bond (London) notices that the Wright tables correspond uncannily closely with a table of logarithms, once the latitude is manipulated, and publishes the modern logarithmic form of the projection in Norwood’s Epitome of Navigation — also unaware of Harriot’s unpublished work.
- 1668: James Gregory proves that Bond's logarithmic form represents the integral of Wright's infinitesimals.
