The **Bonne projection** is a pseudoconical equal-area map projection, sometimes called a **dépôt de la guerre**,^{ [1] }^{:104}**modified Flamsteed**,^{ [1] }^{:104} or a **Sylvanus** projection.^{ [1] }^{:92} Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter's usages were approximate, however, and it is not clear they intended to be the same projection.^{ [1] }^{:60}

The Bonne projection maintains accurate shapes of areas along the central meridian and the standard parallel, but progressively distorts away from those regions. Thus, it best maps "t"-shaped regions. It has been used extensively for maps of Europe and Asia.^{ [1] }^{:61}

The projection is defined as:

where

and *φ* is the latitude, *λ* is the longitude, *λ*_{0} is the longitude of the central meridian, and *φ*_{1} is the standard parallel of the projection.^{ [2] }

Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the central meridian and the standard latitude shapes are not distorted.

The inverse projection is given by:

where

taking the sign of *φ*_{1}.

Special cases of the Bonne projection include the sinusoidal projection, when *φ*_{1} is zero (i.e. the Equator), and the Werner projection, when *φ*_{1} is 90° (i.e. the North or South Pole). The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection; an alternative intermediate would be a Bottomley projection.^{ [3] }

The **Mercator projection** is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome, is preferred by navigators because the ship can sail in a constant compass direction to reach its destination, eliminating difficult and error-prone course corrections. Linear scale is constant on the Mercator in every direction around any point, thus preserving the angles and the shapes of small objects and fulfilling the conditions of a conformal map projection. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation starts infinitesimally, but accelerates with latitude to become infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.

In navigation, a **rhumb line**, **rhumb**, or **loxodrome** is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.

In geodesy, **conversion** among different **geographic coordinate** systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.

The **transverse Mercator** map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

The use of **orthographic projection in cartography** dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The *point of perspective* for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges.

The **Mollweide projection** is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the **Babinet projection**, **homalographic projection**, **homolographic projection**, and **elliptical projection**. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.

The **azimuthal equidistant projection** is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.

The **scale** of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.

The **equirectangular projection** is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.

The **sinusoidal projection** is a pseudocylindrical equal-area map projection, sometimes called the **Sanson–Flamsteed** or the **Mercator equal-area projection**. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570.

The **Bottomley map projection** is an equal area map projection defined as:

In cartography, a **Tissot's indicatrix** is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.

A **Lambert conformal conic projection** (**LCC**) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication *Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten*.

The **Albers equal-area conic projection**, or **Albers projection**, is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.

The **Hammer projection** is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.

The **Cassini projection** is a map projection described by César-François Cassini de Thury in 1745. It is the transverse aspect of the equirectangular projection, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Considering the earth as a sphere, the projection is composed of the operations:

In cartography, the **cylindrical equal-area projection** is a family of cylindrical, equal-area map projections.

The **American polyconic** map projection is a map projection used for maps of the United States and regions of the United States beginning early in the 19th century. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Often the American polyconic is simply called the **polyconic projection**.

The **rectangular polyconic** projection is a map projection was first mentioned in 1853 by the U.S. Coast Survey, where it was developed and used for portions of the U.S. exceeding about one square degree. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the **War Office** projection due to its use by the British War Office for topographic maps. It is not used much these days, with practically all military grid systems having moved onto conformal projection systems, typically modeled on the transverse Mercator projection.

The **Eckert-Greifendorff projection** is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.

- 1 2 3 4 5 John Parr Snyder (1993).
*Flattening the Earth: Two Thousand Years of Map Projections*. ISBN 0-226-76747-7. - ↑
*Map Projections - A Working Manual*, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 138–140 - ↑ Between the Sinusoidal projection and the Werner: an alternative to the Bonne, Henry Bottomley 2002

Wikimedia Commons has media related to . Bonne projection |

- Table of examples and properties of all common projections, from radicalcartography.net
- An interactive Java Applet to study the metric deformations of the Bonne Projection
- Bonne Projection (wolfram.com)

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