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While Ptolemy's system is well-founded, the actual data used are of very variable quality, leading to many inaccuracies and distortions. [ 6 ] [ 4 ] : 551–553 [ 7 ] Apart from the difficulties in estimating rectilinear distances and directions, the most important of these is a systematic over-estimation of differences in longitude.
The international standard convention —that east is positive—is consistent with a right-handed Cartesian coordinate system, with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere ) to give a precise position on the Earth's surface.
A Cartesian coordinates graph, using his invented x and y axes. One of Descartes's most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry; the Cartesian coordinate system is named after him. He was first to assign a fundamental place for algebra in the system of knowledge, using it ...
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [1] It is the simplest, oldest and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others.
The armillary sphere was probably invented only later—maybe by Ptolemy 265 years after Hipparchus. The historian of science S. Hoffmann found clues that Hipparchus may have observed the longitudes and latitudes in different coordinate systems and, thus, with different instrumentation. [ 16 ]
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...
Abū Rayhān Bīrūnī (973–1048) later developed ideas which are seen as an anticipation of the polar coordinate system. [74] Around 1025, he describes a polar equi-azimuthal equidistant projection of the celestial sphere.