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" ... at an infinite distance from this circle, the projections of the sphere are orthographic, Art. (2). If E, Fig. 85, be any point, e will be its orthographic projection on the plane of a circle whose axis is CM. But that is, the orthographic projection... "
Elements of Descriptive Geometry: With Their Application to Spherical ... - Page 132
by Charles Davies - 1835 - 174 pages
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

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 every circle...
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Elements of Descriptive Geometry: With Their Application to Spherical ...

Charles Davies - Geometry, Descriptive - 1840 - 260 pages
...THEOREM V. The poles of a circle are projected in its line of measures ; the one farthest from the eye, at a distance from the centre of the primitive circle equal to the semi-tangent of the inclination of the circles ; the one nearest the eye, at a distance from the centre...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...sphere 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 the inclination, the radius of the...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...perpendicular to the primitive plane. The centre of the projection is in the line of measures of the circle, at a distance from the centre of the primitive circle equal to the secant of the circle's polar distance, and the radius of the projection is equal to the tangent of...
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Elements of Descriptive Geometry: With Its Applications to Spherical ...

Albert Ensign Church - Geometry, Descriptive - 1865 - 214 pages
...secant. Hence the centre of the projection of a great circle, is in its line of measures, Art. (207), at a distance from the centre of the primitive circle equal to the tangent of its inclination, and the radius of the projection is the secant of this angle. 213. Let O, Fig. 93,...
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Elements of Descriptive Geometry: With Its Applications to Spherical ...

Albert Ensign Church - Geometry, Descriptive - 1865 - 164 pages
...whose axis is CM. But that is, the orthographic projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the sine of its polar distance. 197. The circumference of a circle, oblique to the primitive plane, is...
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Elements of Descriptive Geometry: With Its Applications to Spherical ...

Albert Ensign Church - Geometry, Descriptive - 1865 - 160 pages
...whose axis is CM. But that is, the orthographic projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the sine of its polar distance. 197. The circumference of a circle, oblique to the primitive plane, is...
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Elements of Descriptive Geometry: With Its Applications to Spherical ...

Albert Ensign Church - Geometry, Descriptive - 1867 - 210 pages
...whose axis is CM. But that is, the orthographic projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the sine of its polar distance. 197. The circumference of a circle, oblique to the primitive plane, is...
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Elements of Descriptive Geometry: With Their Application to Spherical ...

Charles Davies - Geometry, Descriptive - 1868 - 258 pages
...each other equal to that which the circles themselves formed on the surface of the sphere. THEOREM IV. centre of the projection of a great circle is in the...tangent of the inclination of the circles ; and the udius with which the projection is described is equal to the secant of the inclination. § 204. PI....
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Elements of Descriptive Geometry: With Its Applications to Spherical ...

Albert Ensign Church - Mathematics - 1868 - 222 pages
...whose axis is CM. But that is, the orthographic projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the sine of its polar distance. 197. The circumference of a circle, oblique to the primitive plane, is...
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