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The minor tonic, subdominant, dominant, and their parallels, created by lowering the fifth (German)/root (US) a whole tone. The parallel chord (but not the counter parallel chord) of a major chord will always be the minor chord whose root is a minor third down from the major chord's root, inversely the parallel chord of a minor chord will be ...
Thus, there are no parallel geodesics to a given geodesic, as all geodesics intersect. Equidistant curves on the sphere are called parallels of latitude analogous to the latitude lines on a globe. Parallels of latitude can be generated by the intersection of the sphere with a plane parallel to a plane through the center of the sphere.
Standard parallels at 33°45′N/S; parallels are unequal in spacing and scale; meridians are fourth-order curves. Distortion-free only where the standard parallels intersect the central meridian. 1937 1944 Quartic authalic: Pseudocylindrical Equal-area Karl Siemon Oscar S. Adams. Parallels are unequal in spacing and scale.
This gives the map two standard parallels. In this way, deviation from unit scale can be minimized within a region of interest that lies largely between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels. [2]
The two lines through a given point P and limiting parallel to line R.. In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line through a point not on line ; however, in the plane, two parallels may be closer to than all others (one in each direction of ).
The Clifford parallels through points on the surface all lie in the surface. A Clifford surface is thus a ruled surface since every point is on two lines, each contained in the surface. Given two square roots of minus one in the quaternions , written r and s , the Clifford surface through them is given by [ 1 ] [ 3 ]
If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry.
The angle of parallelism was developed in 1840 in the German publication "Geometrische Untersuchungen zur Theory der Parallellinien" by Nikolai Lobachevsky.. This publication became widely known in English after the Texas professor G. B. Halsted produced a translation in 1891.
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