 | James Hayward - Geometry - 1829 - 218 pages
...distance of the point. We therefore say, — The projection of every point in the surface of a sphere, is at a distance from the centre of the primitive circle, equal to the tangent of half the polar distance of that point. 117. This gives us the radius of the projection of... | |
 | Charles Davies - Geometry, Descriptive - 1840 - 260 pages
...circle which is opposite the eye. THEOREM I. The projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the lemi-tangent of its polar distance. § 192. PL 2. Fig 2. Suppose a plane to be passed through the point... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...stereographically : 1. To project a great circle. The centre of the projection is in the lino of measures at a distance from the centre of the primitive circle equal to the tangent of the inclination of the circle, and the radius of the projection is equal to the secant of... | |
 | Norman Macleod Ferrers - Conic sections - 1861 - 200 pages
...the auxiliary circle inversely proportional to the distance of the line. And conversely, the polar of any point is at a distance from the centre of the auxiliary circle, inversely proportional to the distance of the point itself. 16. If TX, TY be any... | |
 | Albert Ensign Church - Geometry, Descriptive - 1865 - 214 pages
...is one half of NM. That is, the stereographic projection of any point of the surface of the sphere is at a distance from the centre of the primitive circle equal to the tangent of one half its polar distance. In this projection, it should be observed that the polar distance... | |
 | Albert Ensign Church - Geometry, Descriptive - 1865 - 160 pages
...is one half of NM. That is, the stereographic projection of any point of the surface of the sphere is at a distance from the centre of the primitive circle equal to the tangent of one half its polar distance. In this projection, it should be observed that the polar distance... | |
 | Albert Ensign Church - Geometry, Descriptive - 1865 - 164 pages
...is one half of NM. That is, the stereographic projection of any point of the surface of the sphere is at a distance from the centre of the primitive circle equal lo the tangent of one half its polar distance. In this projection, it should be observed that the polar... | |
 | Albert Ensign Church - Geometry, Descriptive - 1867 - 210 pages
...is one half of NM. That is, the stereographic projection of any point of the surface of the sphere is at a distance from the centre of the primitive circle equal to the tangent of one half its polar dig' tance. In this projection, it should be observed that the polar... | |
 | Albert Ensign Church - Mathematics - 1868 - 205 pages
...(194), it follows that either pole of a circle is orthographically projected in its line of measures, at a distance from the centre of the primitive circle equal to the sine of its inclination, Art. (196). 199. PROBLEM 59. To project the sphere upon the plane of any one of its... | |
 | Albert Ensign Church - Mathematics - 1868 - 222 pages
...is one half of NM. That is, the stereographic projection of any point of the surface of the sphere is at a distance from the centre of the primitive circle equal to the tangent of one half its polar distance. In this projection, it should be observed that the polar distance... | |
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... the point of sight. NM is the polar distance and m the stereographic projection of M. Cm is the tangent of the arc Co, computed to the radius CS =CE, and Co is one half of NM. That is, the stereographic projection of any point of the surface of the... 